■llririiiir'ifn — i i ■' 'ii S 1 Si ■Mi S ■ :^ f LIBRARY OF THE University of California. GIF^T OK Class . OMji^ -E.'^Jy^ ■ft^^'-^iv^* INTO. 9. HYDROGRAPHIC OFFICE. THE AMEKICAS PRACTICAL lAVIGATOR BEING AN epitom:e OF NAVIGATION AND NAUTICAL ASTRONOMY. BY NATHANIEL BOWDITCH, LL. D., Fellow of the Royal Societies of London, Edinburgh, and Dublin; of the Astronomical Society in London; of the American Philosophical Society, held at Philadelphia ; of the American Academy of Arts and Sciences ; of the Connecticut Academy of Arts and Sciences ; of the Literary and Philosophical Society of New York ; Corresponding Member of the Royal Societies of Berlin, Palermo, &c. Revised in 1880, under the direction of the Bureau of Navigation, Navy Department, BY Commander P. H. COOPER, U. s. Navy. Revised in 1903, under the direction of the Bureau of Equipment, Navy Department, BY Lieutenant G. W. LOGAN, U. S. Navy. WASHINGTON: GOVERNMENT PRINTING OFFICE. 1903. OF THE UNIVERSITY n^ A ^^ ^^ ORDERS RELATING TO REVISION. Bureau of Navigation, Navy Departtnent^ January 1\ 1881. In accordance with the purpose contemplated in the purchase of the copyright of the New American Practical Navigator, a thorough and complete revision has been made by Commander P. H. Cooper, U. S. Navy, acting under the direction of the Bureau. The revision consists principally in the substitution of the more concise and convenient methods of the present day for the obsolete methods of the past, and a complete rearrangement under proper chapters and paragraphs for ready reference, keeping in view, however, the character of the work as a Practical Navigator. The revision having been completed, it was submitted to Capt. Ralph Chandler, U. S. Navy, for a final review, and having received a satisfactory report from that officer it has been accepted by the Bureau and will hereafter be substituted for the former editions of the work. WiLLiA^r D. Whiting, Chief of Bureau. Bureau of Equipment, Navy Department, March 18, 1903. A revision of Bowditch's American Practical Navigator having become neces- sar}'-, the work has been completed by Lieut. G. VV. Logan, U. S. Navy, under the supervision of the Hydrographer to the Bureau of Equipment. The revision was approved by a Board consisting of Capt. Colby M. Chester, U. S. Navy, Commander C. J. Badger, U. S. Navy, and Lieut. Commander C. C. Rogers, U. S. Navy. It is directed that this revised edition be substituted for all former editions. R. B. Bradford, Chief (f Bureau. p»ref^ch:. The copyright of the New American Practical Navigator, by the late Dr. Bowditch, became the property of the United States Government under the provision of an act of Congress to establish a Hydrographic Office in the Navy Department, approved June 21, 1866. Under the direction of the Bureau of Navigation, at that time charged with such publications, the work was revised in 1880 by Commander P. H. Cooper, U. S. Navy, certain chapters being contributed by Lieuts. Richard Wainwright and Charles H. Judd, U. S. Navy, and the whole being reviewed by Capt. Ralph Chandler, U. S. Navy. The object of this revision was to improve the general arrangement, and to introduce the more convenient and precise methods of navigation that had come into practice since the book was originally written. The progress that has been made in the science of navigation since 1880 has rendered necessary a second extensive revision, to take cognizance of the changes of methods and instruments that have accompanied the general introduction of high-speed vessels built of iron and steel. This work has been carried out, under the direction of the Bureau of Equipment, by Lieut. G. W. Logan, U. S. Navy, who was aided in the collection of data and preparation for publication b}^ Lieut. T. A. Kearney, U. S. Navy; the chapters on AVinds and Cyclonic Storms were contributed by Mr. James Page, nautical expert, Hydrographic Office. There has been an extensive rewriting of the text, with the object of amplifying those matters that are of the greatest importance in the modern practice of navigation, and of omitting or condensing those of lesser importance; and the revision of the tables has proceeded along similar lines. This has involved, among other things, a much wider treatment of the subject of the compass; an extension of the traverse table for degrees to distances up to 600 miles: an improved table for reducing circum- meridian altitudes; the combination of the tables of maritime positions and tidal data; the omission of certain special methods for finding position by two observations; the addition of a series of annotated forms for the working of all sights, and the intro- duction of a number of new tables of use to the navigator. The explanation of the method of lunar distances, with its accompanying tables, has been retained, in order to be available for use when required; but since this obser- vation is so rarely employed in modern navigation, everything pertaining thereto has been incorporated ih an appendix, that it may be distinct from matter of every-day use to the navigator. For convenience in use the work has been divided into two parts, of which the first comprises the text and its appendices, and the second the tables. W. H. H. SOUTHERLAND, - Commander^ U. S. Navy^ Hydrographer. Hydrographic Office, Bureau of Equipment, Navy Department, Washington^ D. C, March 19^ 1903. 3 1 1 1 140 Digitized by the Internet Archive in 2008 with funding from IVIicrosoft Corporation http://www.archive.org/details/americanpracticaOObowdrich P J^Pt T I. TEXT AND APPENDICES, OOISTTEISTTS O F I> A. R T I. Page. Orders relatipg to revision 2 Preface 3 Abbreviations ' 9 Chapter I. Definitions relating to Navigation 11 II. Instruments and Accessories in Navigation 13 III. The Compass Error 29 IV. Piloting 42 V. The Sailings 50 VI. Dead Reckoning 60 VII. Definitions relating to Nautical Astronomy 63 VIII. Instruments employed in Nautical Astronomy 66 IX. Time and the Nautical Almanac 74 X. Correction of Observed Altitudes 82 XI. The Chronometer Error 87 XII. Latitude 94 XIII. Longitude 103 XIV. Azimuth 109 XV. The Sumner Line 114 XVI. The Practice of Navigation at Sea 1 24 XVII. Marine Surveying 131 XVIIL Winds .' 142 XIX. Cyclonic Storms 147 XX. Tides 153 XXI. Ocean Currents 158 Appendix I. Extracts from the American Ephemerls and Nautical Almanac for the year 1879, which have reference to examples for that year given in this Avork 163 II. A collection of Forms for working Dead Reckoning and various Astronomical Sights, with notes explaining their application under all circumstances 171 III. Explanation of certain Rules and Principles of Mathematics of use in the Solu- tion of Problems in Navigation 178 IV. Maritime Positions and Tidal Data 190 V. Lunar Distances 288 Index 333 7 ABBREVIATIONS USED IN THIS WORK. Alt. {orh) Altitude. A. M Ante meridian. Amp Amplitude. App . Apparent. App. t Apparent time. Ast Astronomical. Ast. t Astronomical time. Aug Augmentation. Az. (or Z) Azimuth. C Course. C. C Chronometer correction. C — 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 DLo ) Difference longitude. Dep Departure. Dev Deviation. Diff Difference. Dist Distance. DL Difference latitude. D. R Dead reckoning. E., Ely East, easterly. Elap. t Elapsed time. Eq. eq. alt Equation equal altitude" Eq. t Equation of time. G. (or Gr. ) Greenwich. G. A. T Greenwich apparent .ne. G. M. T Greenwich mean time. G. S. T : Greenwich sidereal time. h Altitude. H Meridian altitude. H. A. (or /) Hour angle. H. D Hourly difference. H. P. (or Hor. par. ) . . . Horizontal parallax. Hr-s Hour-8. H. W High water. I. 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. m Meridional difference. Merid Meridian or noon. Mag Magnetic. M. D Minute's difference. Mid Middle. Mid. L Middle latitude. M. T Mean time. N. , Nly North, northerly. N. A. (or Naut. Aim. ). Nautical Almanac. Np Neap. Obs Observation. p (or P. D. ) Polar distance. p. c Per compass. P. D. (or «) Polar distance. P. L. (or Prop. Log.) .Proportional logarithm. P. M Post meridian. p. & r Parallax and refraction. Par Parallax. R. A Right ascension. R. A. M. S Right ascension mean sun. Red Reduction. Ref Refraction. S. , Sly South, southerly. S. D Semi-diameter. Sec Secant. Sid Sidereal. Sin Sine. Spg Spring. t Hour angle. T Time. Tab Table. Tan Tangent. Tr. (or Trans. ) Transit. Var V'^ariation. Vert Vertex or vertical. W., Wlv West, westerly. W. T . .' AVatch time 2 Zenith distance. Z Azimuth. The Sun. ° Degrees. c The Moon. ' Minutes of Arc. * A Star or Planet. ^^ Seconds of Arc. (^C Alt. upper limb. " Hours. (•)C Alt. lower limb. "" Minutes of Time (l)0 Azimuthal angle. •^ Seconds of Time. GREEK LETTERS. A a. .Alpha. N v.... .Nu. B(i. .Beta. SI .... .Xi. ry. .Gamma. Oo .... .Omicron. J 6. .Delta. n n.... .Pi. E s . .Epsilon. Pp. ... .Rho. ZC. .Zeta. 26{i). . Sigma. Hr^. .Eta. Tr .... .Tau. t)0 . .Theta. Tv.... .Upsilon. 1 I .. .Iota. $ .Phi. Kk. . Kappa. ^;«:..-- .Chi. AX. .Lambda. Wrl).... .Psi. Mjii. .Mu. £1 00 ... .Omega. DEFINITIONS RELATING TO NAVIGATION. 11 BR ., or THE UNIVERSITY CHAPTER I. DEFINITIONS KELATINQ TO NAVIGATION. 1. That science, generally termed Navigatiou, 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 determination of the position of the ship by reference to the earth, or to objects thereon. It comprises {a) Piloting, in which the position is ascertained from visible objects upon the earth, or from soundings of the depth of the sea, and {h) Dead Reckoning, in which the position at any moment is deduced from the direction and amount of a vessel's progress from a known point of departure. 3. Nautical Astronoim/ is that branch of the science which treats of the determination of the vessel's place by the aid of celestial objects — the sun, moon, planets, or stars. 4. Navigation and Nautical Astronomy have been respectively termed Geo-Naviga^don 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 by 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 Earth 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 shorter axis, around which it rotates, about 7,900 statute miles. The Earth (assumed for purposes of illustration to be a sphere) is represented in figure 1. The ^Lris of Rotation, usually spoken of simply as the Axis, is PP''. The Poles are the points, P and P', in which the axis intersects the surface, and are designated, respectively, as the North Pole and the South Pole. The 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 being 90° from each pole. Meridians are the great c-ircles PQP^ PMP^ PM'P^ formed by the intersection with the earth's surface <4i planes secondary to the equator (that is, passing through its poles and therefore perpendicular to its plane) . Parallels of Latitude are small circles NT/*, N^?/T', formed by the intersection with the earth's surface of planes passed parallel to the eciuator. The Latitude of a place on the surface of the earth is the arc of the meridian intercepted between the equator and •p' that place. Latitude is reckoned JWr//* and »S'Ji<tion of the tallow for arming. Above the lead is a cylindrical case containing the depth- registering mechanism; various devices are in use for this purpose, all depending, however, upon the increasing pressure of the water with increasing depths. 21. In the Lord Keliin machine z. 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 dei)th of the sounding corresponding to this line 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. 17 fathoms from the lead, same as at 7 fathoms. 20 fathoms from the lead, with 2 knots. 25 fathoms from the lead, wi:h 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. INSTRUMENTS AND ACCESSORIES IN NAVIGATION. 15 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 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 sounding. 24. Since the action of the sounding machine, when glass tubes are used, depends upon the com- pression of the air, the barometric pressure of the atmosphere must be taken into account w^hen accurate results are required. The correction consists in increasing the indicated depth bj' a fractional amount according to the following table: Bar. reading. Increase. // 29. 75 m. 00 .so. 50 30. 75 j 1 One-fortieth. : One-thirtieth. ; One-tv.'entieth. One-fifteenth. THE MARINER'S COMPASS. 25. The Mariner^ s Compass i.s an instrument consisting either ot a single magnet, or, more usually, of a series of magnets, which, being attached to a graduated circle i)iv<»ted at the center and allowed to Fig. 2. swing freely in a horizontal plane, has a tendency to lie with its magnetic axis in the plane of the earth's magnetic meridian, thus affording a means of determining the azimuth, or horizontal angular distance from that meridian, of the ship's c-ourse and of all visible objects, terrestrial or celestial. / 16 INSTRUMENTS AND ACCESSORIES IN NAVIGATION. 26. The circular card of the compass (fig. 2) is divided on its periphery into 360°, numbered from 0° at North and South to 90° at East and West; also into thirty-two divisions of 1^° each, called jmnts, the latter being further divided into half-points and quarter-points ; still finer suMivisions, eighth-]>oints, are sometimes used, though not indicated on the card. A system of numbering the degrees from 0° to 360°, always increasing toward the right, is shown in the figure. This system is in use by the mariners of some' nations, and itsgeneral adoption would carry with it certain undoubted advantages. 27. Boxing the (Mmpass is the process of naniing the points in their order, and is one of the first things to be learned by the young mariner. The four principal points are called cardinal points and are named North, South, East, and West; each differs in direction from the adjacent one by 90°, or 8 points. Midway between the cardinal points, at an angular distance of 45°, or 4 points, are the inter-cardinal points, named according to their posititm Northeast, Southeast, etc. Midway between each cardinal and inter-cardinal point, at an angular distance of 22J°, 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 lli°, from each cardinaland inter- cardinal point (and therefore midway between it and the 22J°-division last described), is a point which bears the name of that cardinal or inter-cardinal point joined by the word by to that of the cardi- nal point in the dire<'tion of which it lies: North by East, Northeast by North, Northeast by East, etc. 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. j N. and NNE. J 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 N. i E., N. by E. ^ E., NNE. J E., NE. j N., etc. Some mariners, however, make it a prac- tice to box from each cardinal and inter-cardinal point tmiard a 22i°-point (NNE., ENE., etc.); as N. i E., N. by E. J E., NE. by N. J 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 shows also the degrees, minutes, and seconds from North or South to which each division corresponds: - '•> ^ N. to E. N. to W. S. to E. Pts. Angular measure. North: N. iE N. JE N. |E N.byE N. by E. i E.. N. by E. ^E.. N. by E. |E.. NNE NNE. \E NNE. iE NNE. f E NE. byN NE. J N NE. i N NE. i N NE NE. iE NE. i E NH |E NE. byE NE. by E. i E. NE. by E. i E. NE. by E. I E. ENE ENE. iE ENE. iE ENE. f E E. byN E. IN E. IN v.. iN East North: N. i W N. J W N. f W N.byW N. by W. iW.. N. by W.J W.. N. by W. f W.. NNW NNW. } W.... NNW. iW.... NNW. f W . . . . NW. byN NW. |N NW. IN NW. iN NW NW. i W NW. J W NW. I W NW. by W NW.byW.iW. NW.byW.JW. NW.byW. JW. WNW WNW. J W.... WNW. J W.... WNW. f W.... W.byN W. I N W. JN W. } N West South: S. \E S. JE S. |E S. byE S. by E. i E . S. by E. J E . S. by E. I E . SSE SSE. iE SSE. JE SSE. f E.... SE. by S SE. |S SE. ^S SE. i-S SE SE.iE SE. JE SUf E SE. byE SE. by E. i E SE. by E. i E SE. by E. f E ESE ESE. iE.... ESE. J E . . . . ESE. f E . . . . E.byS E. f S E. JS E. }S East South : S. J W S. iW S. |W S. by W S. by W. i W.. S. by W.J W.. S. by W. I W.. ssw ssw. i w ssw. J w ssw. I w SW. byS SW. f s SW. JS SW. JS SW SW. i w SW. J w SW. f w SW. by W SW. by W. i W SW. by W. J W SW. by W. I W WSW wsw. nv.... WSW. J W.... WSW. iw.... W. byS W. f s W. JS AV. iS West 1 U 1| 2 2\ 2i 2J 3 3i 3J 3i 4 ^ 4i 5 b\ 5J 5J 6 6i 6i 61 7 n n 71 2 5 8 11 14 16 19 22 25 28 30 33 36 39 42 45 47 50 53 56 59 61 64 67 70 73 75 78 81 84 87 90 48 45 37 30 26 15 15 00 03 45 52 30 41 15 30 00 18 45 07 30 56 15 45 00 33 45 22 30 11 15 00 00 48 45 37 30 26 15 15 00 03 45 52 30 41 15 30 00 18 45 07 30 56 15 45 00 33 45 22 30 n 15 00 00 2§. The compass card is mounted in a bowl which is carri^ in gimbals, thus enabling the card to retain a horizontal position while the ship is pitching and rolling. A vertical black line called the bib- ber'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 compass direction of the ship's head. 29. According to the purpose which it is designed to fulfill, a compass is designated as a Standard, Peering, Check, or Boat Compass. INSTEUMENTS AND ACCESSORIES IN NAVIGATION. 17 30. There are two types of compass in use, the v:et or liquid and the dry; in the former the bowl i;j 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 of the motion of the vessel or other cause. On account of its advantages the liquid compass is used in the United States Xavy. 31. The Navy Service 7^-ixch Liquid Compass. — This consists of a skeleton card 7 J inches in diameter, made of tinned brass, resting on a pivot in liquid, with provisions for two pairs of magnets symmetrically placed. The magnet system of the card consists of four cylindrical bundles of steel wires; these wires are laid side by side aiid magnetized as a bundle between the poles of a powerful electromagnet. They are afterwards placed in a cylindrical case, sealed, and secured to the card. Steel wires made up into a bundle were adopted Ijeckuse they are more homogeneous, can be more perfectly tempered, and for the same weiglit give greater magnetic power than a solid 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 they 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 ofthe 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-fourth 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 i-ard. The pivot is fastened to the center of the bottom of the bowl by a flanged plate and screws. Through this plate aiid the bottom of the bowl are two small holes which communicate Avith 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 tills the bowl. This liquid is com- posed of 45 per cent pure alcohol and 55 per cent distilled water, and remains liquid below —10° F. _ The luljber's line is a fine line drawn on an enameled plate on the inside of the bowl, the inner surface of the latter l)eing covered with an insolul)le white paint. Beneath the bowl is a metallic self-adjusting expansion chamber of elastic metal, by means of which the bowl is kept constantly full Avithout 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 Vim 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 Kelrin Compass, which may be regarded as the standard for the nonliquid type, consists of a strong paper card with the central parts cut away and its outer edge stiffened 1)y a thin aluminum ring. The pivot is fitted with an iridium point, upon which. rests a small light aluminum boss fitted with a sapphire Ijearing. 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 parallel silk 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 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 (h) 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. 34. Binnacles. — Compasses are mounted for use in stands known as Binnacles, of which there are two principal types — the Compensating and the Non-Compensating 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. 4 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 edges upon which it is suspended resting in V-shaped bearings; an appropriate method is supplied for centering the compass. A hood is proAided 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. The position of the various binnacles on shipboard and the height at which they carry the compas-^ must be chosen with regard to the purpose which the compass is to serve, having in mind the magnetic conditions of the ship. Compensating binnacles contain the appliances for carrying the various correctors used in the com- pensation of the deviation of the compass. These consist of (a) a system of permanent magnets for 22489—03 2 18 INSTRUMENTS AND ACCESSORIES IN NAVIGATION. semicircular deviation, placed in a magnet chamber lying immediately beneath the compass chamber, so arranged as to permit variation in the height and direction of the magnets employed; (b) a pair of arms projecting horizontally from the compass chamber and supporting masses of soft iron for quad- rantal 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 securinjj a vertical soft iron rod, or "Flinders bar," u^d in certain cases for correction of a part of the semicircular deviation. An explanation of the various terms here used, together with the method of compensating the compass, will be given in Chapter III. THE PELORXJS. 35. This instrument consists of a circular plate, mounted horizontally in gimbals upon a vertical standard, at some point on board ship affording a clear view for taking bearings; radial scores upon a raised flange on the periphery of this plate indicate true directions from its center parallel with the keel line of the vessel and perpendicular thereto — in other words, lines of bearing directly ahead, astern, and abeam. Eevolving about a common center, which is also the center of the plate, are (a) a dumb com- pass card, usually engraved on metal, whose face is level with the raised periphery of the plate on which are marked the scores, and (6) a pivoted horizontal bar carrying at its extremities a pair of sight vanes so arranged that the line of sight always passes through the vertical axis of the instrument, and having an index showing the point at which the line of sight cuts the dumb compass. The dumb compass and the sight-vane bar can each be rigidly clamped. The instrument is used for taking bearings, and may be more convenient than the compass for that purpose because of the better view that it affords, as well as because it may be made to eliminate the compass error from observed bearings. Suppose that the dumb compass be revolved until the degree or division which is coincident with the right-ahead score of the plate is the same as that which is abreast the lubber's line of the ship's compass. Then all directions indicated by the dumb compass will be parallel to the corresponding directions of the live one, and all bearings taken by the pelorus will be. identical with those taken by the compass (leaving out of the question the diffence due to the distance that separates them). Suppose, now, that it is known that the ship's compass has a certain error and that the correct direction that we seek ( which is the one indicated on the charts ) is a certain angular distance to the right or left of that which the compass shows; if, in such a case, instead of setting the pelorus for the direction indicated by compass, we set it for the correct direction in which we know the ship to be heading, all bearings observed by the pelorus will be correct bearings as given by the chart and may be plotted directly thereon without the necessity for the intermediate i)rocess of correction to which the bearings shown by compass are subject. It will at once be evident that the indications of the pelorus will be accurate only when bearings are taken at an instant when the ship is heading exactly in the direction for which it is set, and care must be taken accordingly in its use. The most modern types of pelorus are fitted for illuminating the dumb compass, thus greatly facili- tating night work. THE CHART. 36. A nautical chart is a miniature representation upon a plane surface, in accordance with a defi- nite system of projection or development, of a portion of the navigable waters of the world. It generally incluaes 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 37. There are three principal systems of projection in use: (a) the Mercator, (h) the polyccmic, and (c) the gnomonic; of these, the Mercator is by far the 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. 3§. The Mercator Pro.iection. — 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 l:>een projected upon the cylinder in such manner as they would appear to an observer at the earth's center; this method of projection and development results in a characteristic feature — namely, that the loxodrornic curve or rhumb line (art. 6, Chap. I) apjiears 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 develop- ment; while the series of elements of the cylinder corresponding to the projected terrestrial meridians will appear as equidistant right lines, parallel to each other and perpendicular to the equator of the chart, maintaining the same relative positions and the same distance apart on that equator as the meridians have on the terrestrial spheroid. The series of terrestrial parallels will also appear as a system of right lines parallel to each other and to the equator, and will so intersect the meridians as to form a system of rectangles whose altitudes, for successive intervals of latitude, must be variable, increasing from the equator in such manner that the angles made by the rhumb line with the meridian on the chart may maintain the required equality with the (iorresponding angles on the spheroid. 39. Meridional Parts. — At the equator a degree of longitude is equal to a degree of latitude, but in receding from the equator and approaching the pole, while the degrees of latitude remain always of the same length (save for a slight change due to the fact that the earth is not a perfect sphere), the degrees of longitude become less and less. INSTRUMENTS AND ACCESSORIES IN NAVIGATION. 19 Since, in the Mereator projection, the degrees of longitude are made to appear everywhere of the same length, it becomes necessary, in order to preserve the proportion 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 facilities for constructing charts on the Mereator pro- jection and for solving problems in Mereator sailing. 40. 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 principal parallel, preferably the lowest parallel to be drawn on the chart. The distance of any other parallel of latitude from the "principal parallel is then the difference of the values for the two taken from Table 3. The values so found may either be measured off, without previous numerical conversion, by means of a diagonal scale constructed on the chart, or they may be laid down on the chart by means of any 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 may first be drawn on the sheet on which the transfer is to be made. The distance between these parallels may then be measured, and the number of meridional parts between them ascertained. Dividing the distance by this number will then give the length of one meridional part, or the quantity by which all the meridional parts taken from Table 3 must be multi- plied. This quantity will represent the scale of the chart. If it occurs that the limits of longitude are a governing consideration, the case may be similarly treated. E.K ample: 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 of 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, forjvhich 1' of arc of the_equator is taken as the u nit. On the intended projection, therefore, V of arc of longitude will measure J—-'. = 0.0152 inch, which will be the scale of the chart. 606.6 For the sake of brevity call it 0.015. By this quantity all the values derived from Table 3 will have to be multiplied before laying them down on the projection, if they are to be measured on a diagonal scale of one inch. Draw in the center of the sheet a straight line, and assume it to be the middle meridian of the chart. Construct very carefully on this line a perpendicular near the lower border of the sheet, and assume this perpendicular to be the' parallel of latitude 20° 30'; this will be the southern inner neat line of the chart. From the intersection of the lines lay off on the parallel, on each side of the middle meridian, seven degrees of longitude, or distances each equal to 0.015 X 60 X 7 = 6.3 inches; and through the points thus obtained draw parallel lines to the middle meridian, and these will be the eastern and western neat lines of the chart. In order to construct the parallel of latitude for 21° 00', find, in Table 3, the meridional parts for 21° 00', which are 1280.8. Subtracting from this number the number for 20° 30', and multiplying the difference by 0.015, we obtain 0.478 inch, which is the di.stance on the chart V)etween 20° 30' and 21° 00'. On the meridians lay off distances equal to 0.478 inch, and through the three points thus obtained draw a straight line, which will be the parallel of 21° 00'. Proceed in the same manner to lay down all the parallels answering to full degrees of latitude; the distances will be respectively : 0"'.015X (1344.9—1248.9) = 1.440 inches, 0'".015X (1409.5-1248.9) =2.409 inches, 0'°.015X (1474.5-1248.9) =3.384 inches, etc. Thus will be shown the parallels of latitude 22° 00', 23° 00', 24° 00', etc. Finally, lay down in the same way the parallel of latitude 30° 25', which will be the northern inner neat line of the chart. ' A degree of longitude will measure on this chart 0'".015x60=0'".9. Lay off, therefore, on the low- est 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 subdivide 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 the case of the longitude. The subdivisions between the two eastern as well as those between the two western neat lines will serve for measuring or estimating terrestrial distances. Distances between points bearing North and South of each other may be ascertained by referring them to the subdivisions between the same paral- lels. Distances represented by lines at an angle to the meridians (loxodromic lines) may be measured X 20 INSTRUMENTS AND ACCESSORIES IN NAVIGATION. by taking between the dividers a small number of the subdivisions near the middle latitude of the line to be 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° OC be required, 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. 41. Coast lines an* other positions are plotted on the chart by their latitude and longitude. A chart may be transferred from any other projection to that of Mercator by drawing a system of corre- sponding parallels of latitude and" meridians over 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 j^ole will be represented as being much larger than one of the same size near th6 equator, due to the different scale used to preserve the character of the ])rojection. 42. The Polyco.nic Projection. — This projection is based upon the development of the earth's surface on a series of cones, a different one fi>r each parallel of latitude, each one having the parallel as its base, and its vertex in the pointwhere 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 being closely preserved. A straight line on the polyconic chart represents a great circle, making a slightly different angle with each successive meridian as the meridians converge toward the pole and are theoretically curved lines; but it is only on charts of large extent that this curvature is apparent; the parallels are also curved, this fact being apparent to the eye upon all excepting the largest scale charts. This method of projection is especially adapted to the plotting of surveys; it is also employed for nearly all of the charts of the United States Coast and Geodetic Survey. 43. Gnomonic Peojectiox. — This is based upon a system in which the plane of projection is tangent to the earth at some given point; the eye of the spectator is situated at the center of the sphere, where, being at once in the plane of every great circle, it will see all such circles projected as straight lines where the visual rays passing through them intersect the plane of projection. In a gnomonic chart, a straight line between any two points is projected as an arc of a great circle, and is therefore the shortest line l)etween those points. Excepting in the Polar regions, for which latitudes the Mercator projection can not be constructed, the gnomonic charts are not used for general navigating purposes. Their greatest application is to afford a ready means of finding the course and distance at any time in great circle sailing, the method of doing which will be explained in (^hapter \". 44. Meridiaxs Employed in Chart Construction. — The United States, England, Germany, Italy, Russia, Norway, Sw^eden, Denmark, Holland, Austria, Portugal, and Japan adopt as a prime meridian the meridian of Greemvich. France adopts the meridian of Paris in Long. 2° 20'' 14'". 5 E. of Greenwich. Spain adopts the meridian of Sun Fernando, Cadiz, in Long. 6° 12'' 20" W. of Greenwich. The Pulkowa Observatory of St. Petersburg (sometimes referred to in Russian charts) is in Long. 30° 19' 39''.6 E. of Greenwich. The Royal Observatory of Naples (sometimes referred to in Italian charts) is in Long. 14° 14' 06" V.. of Greenwich. The meridian of Genoa is 8° 55' 21" E. ; of Lisbon, 9° 08' 36" W. ; of Rio de Janeiro, 43° 10' 21".2 W.; of Amsterdam, 4° 53' 03". 8 E.; of Washington, 77° 03' 56". 7 AV. 45. 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 Coral Gravel . . . Mud Rocky C. Co. G. M. Sh. Sf. Clay Coral Gravel . . . Mud Rock Sand Shells ... Stones Weed.... Fine Coarse . . . Stiff Soft Black ... Red Yellow . . cl. ....cri. g- m. ....rk. s. ....sh. St. ...wd. f. c. ....Stf. ....sft. ...blk. ....rd. V Argile Corail Gravier .. Vase Roche Sable Coquille . Pierre.... Herb Fin Gros Dure Molle.... Noire Rouge ... Jaune ....A. ...Cor. ....Gr. ....V. ....R. S. ..Coq. V. .Vh." ...fin. m. n. r. J- Argila CoRlllo Rena orGhiaja Fango Roccia ; . . Arcillo or Barro Coral Cascfljo Fango or Luno . I^iedra or Roca . Arena Conchuela IMedra Alga Fina Gruesa Tenaz Muelle Negro RoJo Amarillo .cl. Co. -F. ..P. .A. .ca. ..P. .A. ..f. ! Lehm Korallen... 1 Grob sand . . ' Schlemm .. Fels Sand Muschel . . . Stein. Gras L. K. ....g. s. ....Sch. F. Sand Shells.... Stone . Sabia or Arena Conc'higlia S. M. Weed Wd. Alga Fino G rosso Tenace G. Fine fne. — crs. stf. sft. bk. rd. yi. gy. f. Coarse . . . Stiff 1 Grob Zahe ; Welch Schwarz... Roth. Gelb. Soft Molle W. Black ..schw. Red Rosse Yellow... Giallo Gray INSTRUMENTS AND ACCESSORIES IN NAVIGATION. 21 46. Measures of Depth. — The following table shows the measures of depth employed in the charts of certain foreign nations, with their equivalents in English measures: 1 English feet. I EngH^h Austrian fathom (klafter) . . Danish and Norwegian fathom (farn) . . Dutch fathom ( vaden ) . . p , /fathom ( brasse) . . ^ ^^"^^ \meter ( metre ) . . . Portuguese . .'. fathom ( braga) . . Prussian fathom (faden) . . Russian fathom (sajen) . . Spanish fathom (braza ) . . Swedish fathom (famn) . . 6.222 6.175 5.575 5.329 3.281 6.004 5.906 6.000 5.492 5.843 fathoms. 1.030 1.029 0.929 0.888 0.547 1.000 0.984 1.000 0.915 0.974 The Dutch elle, the Spanish, Portuguese, and Italian metro, and the French vu'tre are identical. A pied usael=l3A2A inches, or 1.094 feet. A mPtre is 3 pieds; a pied da ro/=12.7896 inches; brasse is used upon old French charts instead of vii'tre. I'^pon some Italian charts soundings are in French pieds. THE BAROMETER. 47. The barometer is an instrument for measuring the pressure of the atmosphere, and is of great service to the mariner in affording a knowledge of existing meteorological con- ditions and of the probable changes therein. There are two cla.sses of barome- ter — mercurial and aneroid. 4§. The Mercurial Barometer. — This instrument, invented by Torricelli in 1643, indicates the pressure of the atmosphere by the height of a column of mercury. If a glass tube of uniform internal diameter somewhat more than 30 inches in length and closed at one end be completely filled with pure mercury, and then placed, open end down, in a cup of mercury (the open end having been temporarily sealed to retain the liquid during the process of inverting), it will be found that the mercurv in the tube will fall until the top of the colunm is about 30 inches above the level of that which is in the cup, leaving in the upper part of the tube a perfect vacuum. Since the weight of the colunm 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 mer- cury falls as the pressure of the atmosphere decreases and rises as that pres- sure 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. 49. In the practical construction of the barometer the glass tube which contains the mercury is encased in a brass tube, the latter terminating at the top in a ring to be used for suspension, and at the bottom in a flange, to which the several i)arts forming 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 measuring 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 mitldle of the brass tube is fixed a thermometer, the bulb of which is covered from the outside but open toward the mercury, and which, being nearly in contact with the glass tube, indicates the temperature of the mercury and not that of the external air; 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 colunm must ])e taken into account in ever}' accurate application of its reading. 50. In the arrangement of further details mercurial barometers are di- vided into two classes, according as they are to be used a« Standards (lig. 4) on shore, or as Sea Bcironicter-'i (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. tThe instruments also differ in the method of obtaining the true height of the mercurial column at varying levels of the liquid in the cistern. It is evi- dent that as the mercury in "the tube rises, upon increase of atmospheric pres- sure, 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 Fig 3 ^^^® ^^ level will occur. As the height of the mercurial colunm is required Yig. 4. above the existing level -in the cistern, some means must be adopted to obtain the true height under varying conditions. In the Standard Barometer the mercury of the cistern is contained in a leather bag, against the bottom of which presses the point of a vertical screw, the milled 22 INSTRUMENTS AND ACCESSORIES IN NAVIGATION. head of the screw projecting from the bottom of the instrument and thus placing it under control of the observer. By this means the surface of the mercury in the cistern (which is visible through a glass casing) may be raised or lowered until it exactly coincides with that level which is chosen as the zero of the scale, and which is indicated by an ivory pointer in plain view. In the Sea Barometer there is no provision for adjusting the level of the cistern to a fixed point, but compensation for tke Aariable level is made in the scale graduations; a division representing an inch on the scale is a certain fraction short of the true inch, proper allowance being thus made for the rise in level which occurs with a fall of the column, and for the reverse condition. Further modification is made in the Sea Barometer to adapt it to the special use for which intended. The tube toward its lower end is much contracted to prevent the oscillation of the mercurial column known as "pumping," which arises from the motion of the ship; and just below this point is a trap to arrest any small bubbles of air from finding their way upward. The instrument aboard ship is sus- pended ill a revolving center-ring, in giml)als, supported on a horizontal brass arm which is screwed to the bulkhead; a vertical position is thus maintained by the tube at all times. 51. The ?'frn(Vr 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 31 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 will correspond with the scale reading indicated. In such a case the top of the vernier will also exactly coincide with a scale division, but none of the intermediate divisions will be evenly abreast of such a division; the division marked "1" will fall short of a scale division by one- tenth of 1 divison of the scale, or by 0.01 inch; that marked "2" by two-tenths of a division, or 0.02 inch, and so on. If the vernier, instead of having the zero coincide with a scale 30 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 length of 1 division of the scale divided by the number of divisions of the vernier; hence, by varying either the scale or the vernier, we may arrive at any subdivision that may be desired. 52. The Sea Barometer is arranged as described for the instrument 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 accunu->' is not attainable in observing the height of a barometer on a vessel at sea, nor is it essential. The Standard Barometer on shore, however, is capa- ble of very exact reading; hence each scale division is made equal to half a tenth, or 0.05 inch, while a vernier covering 24 such divisions is divided into 25 parts; hence the column may be read to 0.002 inch. 53. To adjust the vernier for reading the height of the mercurial column the eye should be brought exactly on a level with the top of the column; that is, the line of sight should be at right angles to the scale. When properly set, the front and rear edges of the vernier and the uppermost point of the mer- cury should all be in the line of sight. A piece of white paper, held at the back of the tube so as to reflect the light, assists in accurately setting the Aeniier 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 inclina- tion will cause the column to rise in the tube. 54. Other things being equal, the mercury will stand higher in the tube when it is warm than when it is cold, owing to expansion. For the purjxjses 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. 56), in order to be enabled to compare the true barometric pressure with the normal that may be expected for any locality. The following table gives the value of this correction for each 2° F., Fig. 5. INSTKUMENTS AND ACCESSORIES IN NAVIGATION. 23 the plus sign showing that tiie correction is to be added to the reading of the ship's barometer and the minus sign that it is to be subtracted: Tempera- ture. Correction. Tempera- ture. Correction. Tempera- ture. Correction. Tempera- ture. Correction. o Inch. o Inch. o Inch. o Inch. 20 +0.02 40 -0.03 60 -0.09 80 -0.14 22 +0.02 42 -0.04 62 -0.09 82 -0.14 24 +0.01 44 -0.04 64 ,-0.09 84 -0.15 26 +0.01 46 -0. 05 66 -0.10 86 -0.15 28 0.00 48 -0.05 68 -0.10 88 -0.16 30 0.00 50 -0.06 70 -0.11 90 -0.16 32 -0. 01 52 -0.06 72 -0.12 92 -0.17 34 - 0. 02 54 -0.07 74 -0.12 94 -0.17 36 -0.02 56 -0.07 76 -0.13 1 96 -0.18 38. -0.03 58 -0.08 78 -0. 13 98 -0.18 As an example, let the ol^served reading of the mercurial Vjarometer be 29.95 inches, and the tem- perature 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 55. 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, tnough not completely, exhausted, the box is hermetically sealed . When the pressure of the atmosphere increases the inclosed air is compressed, the capacity of the box is diminished, and the two flat ends approach each other; when the pressure of the atmosphere decreases, the ends recede from one another in consequence of the expansion of the inclosed air. By means of a combination of levers, this motion of the ends of the box is communicated to an index pointer which travels over a graduated dial plate, the mechanical arrangement being such that the motion of the ends of the box is magnified many times, a very minute movement of the box making 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 correction for temperature can be applied with certainty. Aneroids, as now manufactured, are almost perfectly compensated for temperature by the use of different metals having unequal coefficients of expansion; they 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 transported, can often be usefully employed under circumstances where a mercurial barometer would not be available. It also has an advantage over the mercurial instrument in its greater sensitiveness, and the fact that it gives earlier indications of change of pressure. It can, however, be relied upon only when frequently com- pared with a standard mercurial barometer; moreover, considerable care is required in its handling; while slight shocks will not ordinarily affect it, a severe jar or knock may change its indications by a large amount. When in use the aneroid barometer may be suspended vertically or 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. 56. Comparison of Barometers. — To determine the reliability of the 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 high or too low by a small amount. These errors arise, in a mercurial barometer, from the improper placing of the scale, lack of uniformity of caliber of the 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 published. 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. 54). It is evident that a comparison of the heights by reduced standard and by the ship's barometer will give the correction to be applied to the latter, including the instrumental error, the reduction to sea level, and the personal error of the observer. In the United States, standard barometer readings are made by the Weather Bureau and Branch Hydrographic offices. Aneroid barometers may be adjusted for instrumental error by moving the index hand, but this is usually done only in the case of errors of considerable magnitude. 57. 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 24 INSTRUMENTS AND ACCESSORIES IN NAVIGATION. between them. An approximate rule is to allow 0.0011 inch for each difference in level of one foot, or, more roughly, 0.01 inch for every 9 feet. A very exact method is afforded by Babinet's formula. If B^ and B represent the barometric pres- sure (corrected for all sources of instrumental error) at the lower and at the upper stations respectively, and to and t the corresponding temperatures of the air; then, Diff. in height=Cx B„-B My B„-B' if the temperatures be taken by a Farhenheit thermometer, C ( in feet) = 52,494 (^i+ h+^- if a centigrade thermometer is used, ^ C (in meters)- 10,000(^1-^ V^^. THE THERMOMETER. * 58. The 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 mer- cury 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 Fahrenheit, in which the freezing point of water is placed at 32° and its boiling point (under normal atmospheric pressure) at 212°; the Centifjraxh', in which the freezing point is at 0° and the boiling point at 100°; and the R'aumur, in which these points are at 0° and 80°, respectively. The Fahrenheit thermometer is generally used in the United States and England. Tables will be found in this work for the interconversion of the various scale readings (Table 31). 59. The thermometer is a valuable instrument for the mariner, not only by reason of the aid it affords him in judging meteorological conditions from the temperature of the air and the amount of moisture it contains, but also for the evidences it furnishes at times, through the temperature of the sea water, of the ship's position and the proVjable current that is being encountered. 60. The thermometers employed in determining the temperature of the air (wet and dry bulb) and of the water at the surface, should be mercurial, and of some standard make, with the graduation etched upon the glass stem; they should be compared with accurate standards, and not accepted if their read- ings vary more than 1° from the true at any point of the scale. 61. The dry-bulb thermometer gives the tempera- ture of the free air. The wet-bulb thermometer, an exactly similar instrument the bulb of which is sur- rounded by an envelope of moistened cloth, gives what is known as the temperature of evaporation, whi(;h 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 l)e obliged to precipitate some of its moisture (water vapor) in the form of liquid. With the envelope of the wet \)\\\h removed, the two ther- mometers should read precisely the same; otherwi.se hey 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 ]iractice the two thermometers are generally inclosed within a small lattice case, such as that shown in figure 6; the case should be placed in a j)osition on deck remote from any source of artificial heat, sheltered from the direct rays of the .«un, and from the rain and spray, but freely exposed to the circulation of the air; the door shouUl hi kept closed except during the ])roc- ess of reading. The cloth envelope of the wet bulb should be a single thickness of line 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 coiled in the cistern. The muslin envelope of the wet bulb should V)e 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 bull) in con.sequence soon becomes quite dry, and the thermometer no longer shows the temperature f)f evaporation. At such times the ImP) 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 Fig. 6. INSTRUMENTS AND ACCESSORIES IN NAVIGATION. 25 this process the temperature of the wet bulb is temporarily raised above that of the dry, but only for a brief time, as the water quickly freezes; and inasmuch as evaporation takes place from the surface of the ice thus formed precisely as from the surface of the water, the thermometer will act in the same way 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. 62. 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- ture of the air, dry- r)ifference between dry-bulb and wet-bulb readings. bulb ther- mometer. 1° 2° 3° 40 5° 6° 7° .8° 9° 10° o Perct. Perct. Per ct. Per ct. Per ct. Perct. Per ct. Per ct. Per ct. Per ct. 24 87 75 62 50 38 26 26 88 76 65 63 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 54 94 88 82 76 70 64 59 53 48 42 56 94 88 82 77 71 65 60 55 50 44 58 94 89 83 78 72 67 61 56 51 46 60 94 89 84 78 73 68 63 58 53 48 62 95 89 84 79 74 69 64 59 54 50 64 95 90 85 79 74 70 65 60 56 51 66 95 90 85 80 75 71 66 61 57 53 68 95 90 85 61 76 71 67 63 58 54 70 95 90 86 81 77 72 68 64 60 55 72 95 91 86 82 77 73 69 65 61 57 74 95 91 86 82 78 74 70 66 62 58 76 95 91 87 82 78 74 70 66 63 59 78 96 91 87 83 79 75 71 67 63 60 80 96 92 87 83 79 75 72 68 64 61 82 96 92 88 84 80 76 72 69 65 62 84 96 92 88 84 80 77 73 69 66 63 86 96 92 88 84 81 77 73 70 67 63 88 96 92 88 85 81 77 74 71 67 64 90 96 92 88 85 81 78 74 71 68 65 The table may be readily understood. For example, if the temperature of the air (dry bulb) be 60°, and the temperature of evapoi'ation (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 by 100, and if there occurred any irtcrease of the quantity of vapor beyond this point, the excess would be precipi- tated in the form of liquid. Over the ocean's surface the relative humidity is generally about 90 per cent, or even higher in the doldrums; over the land in dry winter weather it may fall as low as 40 per cent. 63. The sea water of which the temperature is to be taken should be drawn from a depth of 3 feet below the surface, the liucket used being weighted in order to sink it. The bulb of the thermome- ter should remain immersed in the water at least three minutes before reading, and the reading should be made with the bulb immersed. THE LOG BOOK. 64. The Log Book is a record of the ship's cruise, and, as such, an important accessory in the navi- gation. It should afford all the data from which the position of the ship is established by the method of dead reckoning; it should also comprise a record of meteorological oteervations, which should be made not only for the purpose of fortelling the weather during the voyage, luit also for contribution to the general fund of knowledge of marine meteorology. 65. A convenient form for recording the data, which is employed for the log books of United States naval vessels, is shown on page 26; beside the tabulated matter thus arranged, to which one page of the book is devoted, a narrative of the miscellaneous events of the day, written and signed by the proper officers, appears upon the ojipcjsite page. 26 INSTRUMENTS AND ACCESSORIES IN NAVIGATION. •M 10 Ot»vS oo "" « ^- g^s • O . ^ frN s^ig ^saS a5 ^ "^ 3 i £^5 a ■<»^ s (V H ^ S S 0)2 ■2 J3 o-S*s ■£ H3^> a S3 H^l^ "3 0) K 6 o o f^ >> a ■^-o^ '^ a ^ uS III •a Ill » c a III 2>>" 5-^ Sao ^ .5 c . ■C"- 4) !lO g's^ « * m ^ a 1 E-i ft M 2 o c s S -< W o o X GC !1Q DC OG mi I >.0 >-.H ^.'-S >.-° >>'^ t*.'^ g OJ 05 O « O 03 O ,, J J ^ ^ ^ ^ g ■~1 ' ■; c 6C O .S ° Ch OJ C « S != .S 'x o o a o O 03 Q £ 2 o bp 2 OJ -)H S S C C £ tc CO p S 5 6 C 2 *- O o •^ eS t; > W Q OS 5 S -^ 2 « 6C c '^ o c 3 2: 1! p.'-i ?J rt tc c ft'O 'fc fi -c o n fl it: -« o .H Tl 6C C ^ tl 0) ec S3 '^ % ?i ;::- O Q INSTRUMEJSTTS AND ACCESSORIES IN NAVIGATION. 27 66. 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. 67. The Wind. — In recording the force of the wind the scale devised by the late Admiral Sir F. Beaufort is employed. According to this scale the wind varies from 0, a calm, to 12, a hurricane, the greatest velocity it ever attains. In the lower grades of the scale the force of the wind is estimated from the speed imparted to a man-of-war of the early part of the nineteenth centurj^ sailing full and by; in the higher grades, from the amount of sail which the same vessel could carry when closehauled. The scale, with the estimated A-elocity of the wind in both statute and nautical miles per hour, is as follows: Conditions. Velocity. Mean pressure in pounds per square foot. Foree of wind. Statute miles per hour. Nautical miles per hour. 0.— Calm Full-rigged ship, all sails set, no headway. .lust sufficient to give steerage way Speed of 1 or2knots, "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" to 3 8 13 18 23 28 34 40 48 56 65 75 90 and over. to 2. 6 6.9 11.3 15.6 20.0 24.3 29.6 34.7 41.6 48.6 56.4 65.1 78. 1 and over. 03 1.— Light air 2.— Light breeze 3.— Gentle breeze 4.— Moderate breeze . . 0.23 0.62 1.2 1.9 2 9 6.— Strong breeze 7.— Moderate gale — 8.— Fresh gale 9. — Strong gale 10.— Whole gale 11.— Storm Topgallantsails over .single-reefed topsails 4.2 5 9 Treble-reefed topsails (or reefed upper- top.sails 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 11.5 15.5 20.6 12. — Hurricane Under bare poles 29 6 , 68. When steaming or sailing with any considerable speed, the apparent direction and force of the wind, as determined from a vane, flag, (jr pennant 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 that the wind has a velocity of 20 knots an hour (force 4), and take the case of two vessels, each steaming 20 knots, the first with the wind dead aft, the second with the wind dead ahead. The former 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 will prevail and the I^ennant will 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 velocity of 20 knots an hour, the velocity with which the air strikes the ship as a result of the combined motion will be 28 knots an hour, and the direction from which it comes will be NW. If, therefore, the effect of the the speed of the ship is neglected the wind will be recorded as NW., force 6, when in reality it is north, force 4. In order to make a proper allowance for this error and arrive at the true direction and force of the wind. Table 32 may be entered with the ship's speed and the apparent direction and force of the wind as arguments, and the true direction and force wall be found. 69. AVeather. — To designate the weather a series of symbols devised by the late Admiral Beaufort is employed. The system is as follows: b. — Clear blue sky. c. — Clouds. d. — Drizzing, or light rain. /. — Fog, or foggy weather. g. — Cloomy, or dark, stormy-looking weather. ^.— Hail. I. — Lightning. ?». — Misty weather. 0. — Overcast. p. — Passing showers of rain. q. — Squally weather. r. — Eainy weather, or continuous rain s. — Snow, or snowv weather. ^— Thunder. u. r. — Visibility of distant objects. v. — Wet, or heavy dew. z. — Hazv. Ugly appearances, or threatening weather. Visib To indicate great intensity of any feature, its symbol may be underlined; thus: r., heavy rain. 70. ("LorDS. — 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. CiRKUs, (d). ^Detached clouds, delicate and fibrous looking, taking the form of feathers, generally of a white color, sometimes arranged in belts which cross a portion of the sky in great circles, and, by an effect of perspective, converging toward one or two opposite points of the horizon. 2. Cirro-Stratus, [CL-S.). — A thin, whitish sheet, sometimes completely covering the sky and only giving it a whitish appearance, or at others presenting, more or less distinctly, a formation like a tangled web. This sheet often produces 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. 28 INSTRUMENTS AND ACCESSORIES IN NAVIGATION. 5. Alto-Strati's, (^1.-»S'.)- — A thick sheet of a gray or bhiish color, showing a brilliant patch in the neighborhood of the sun or moon, and which, without causing halos, may give rise to corome. This form goes through all the changes like the Cirro-Stratus, but its altitude is only half so great. 6. STRATO-CrMiLrs, {S.-Ch.). — I^rge globular masses or rolls of dark cloud, frequently covering the whole sky, especially in winter, and occasionally giving it a wavy appearance. The layer of Strato- Cumulus is not, as a ^jple, 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-Nimlms (Fr.-N. ), the "scud " of sailors. 8. Cumulus, (Cm.). — 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 protuber- ances. When the light falls aslant, they give deep shadows; when, on the contrary, the clouds are on the same side as the sun, they appear dark, with bright edges. The true Cumulus has clear 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.-(1*«.). 9. CuMULO-NiMBus, ( Cn.-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.). 71. In the scale for the amount of clouds represents a sky which is cloudless and 10 a sky which is completely overcast. 72. State of Sea. — The state of the sea is expressed by the following system of symbols: B. — Broken or irregular sea. M. — Moderate sea or swell. C. — Chopping, short, or cross sea. R. — Rough sea. Cr.^Ground swell. »S'. — Smooth sea. H. — Heavy sea. T. — Tide-rips. L. — Long rolling sea. THE COMPASS EREOR. 29 CHAPTER III THE COMPASS EKEOE. CAUSES OF THE ERROT. 73. When two magnets are near enough together to exert a mutual intiuence, their properties are such as to cause those poles which possess similar magnetism to repel, and those which possess magnet- ism of opposite sorts to attract one another. The earth is an immense natural magnet, having in each hemisphere a pole lying in the neighbor- hood of the geographical pole, though not exactly coincident therewith; consequently, when a magnet, such as that of a compass, is allowed to revolve freely in a horizontal plane, it will so place itself as to be i>arallel to the lines of magnetic force in that plane created 1)y the earth's magnetic poles, the end which we name north pointing to the north, and the south end in the opposite direction. The north end of the compass — north-seeking, as it is sometimes designated for clearness — will be that end Avhich has opposite polarity to the earth's north magnetic pole, this latter possessing the same sort of magnetism as the so-called south pole of the comjiass. 74. By reason of the fact that the magnetic pole differs in position from the geographical pole, the compass needle will not indicate true directions, but each compass point will differ from the correspond- ing true point by an amount dependent upon the angle between the geographical and the magnetic pole at the position of the observer. The amount of this difference, expressed in angular measure, is the Variation of the Compass (sometimes called also the Declination, though this term is seldom employed by navigators). The variation not only changes as one travels from point to point on the earth, being different in different localities, but, as it has Ijeen found that the earth's magnetic poles are in constant motion, it undergoes certain changes from year to year. In taking account of the error it produces, the navigator nmst therefore be sure that the variation used is correct not only for the place, but also for the time under consideration. The variation is subject to a small diurnal fluctuation, but this is not a material consideration with the mariner. 75. Besides the error thus produced in the indications of the compass, a further one, due to Local Attraction, may arise from extraneous influences due to natural magnetic attraction in the vicinity of the vessel. Instances of this are quite common when a ship is in port, as she may be in close jiroximity to vessels, docks, machinery, or other masses of iron or steel. It is also encountered at sea in localities where the mineral substan<'es in the earth itself possess magnetic qualities — as, for example, at certain places in Lake Superior and at others off the coast of Australia. When due to the last-named cause, it may be a source of great danger to the mai'iner, but, fortunately, the number of localities suVjject to local attraction is limited. The amount of this error can seldom, if ever, be determined; if known, it might properly be included with the variation and treated as a part thereof. 76. In addition to the variation, the compass ordinarily has a still further error in its indications, which arises from the effect exerted upon it by masses of magnetic metal within the ship itself. This is known as the 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 undergo modification as a vessel proceeds from one geographical locality to another. APPLYING THE COMPASS ERROR. 77. From what has been explained, it may be seen that there are three methods by which bearings or courses may be expressed: (a) true, when they refer to the angular distance from the earth's geographical meridian; \h) magnetic, when they refer to the angular distance from the earth's magnetic meridian, and must be corrected for variation to be converted into true; and (c) by compass, when they refer to the angular distance from the north indicated ))y 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 circum- stances is one of which the navigator must make himself a thorough master; the various problems of conversion are constantly arising; no course can be set nor liearing plotted without involving the applica- tion of this problem, and a mistake in its solution may produce serious consequences. The student is therefore urged to give it his most careful attention. 30 THE COMPASS ERROR. 7§. 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 rep- resent theobserver's horizon, N and S being the correct north and south points in each case. If N^ and S' repre- sent the corresponding pomts indicated by a compass whose needle is deflected by a com- pass error, then in the first qa.'-e, the north end of the needle being drawn to the right or east, the error will Ije easterly or positive, and in the second case, the north end of the needle being drawn to the left or west, the com- pass error will be westerly or negative. Considering 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 will be found in every case, the corrected bearing being always one point to the right of the compass bearing. Conversely, if we regard figure 8, assuming the same amount of westerly error, a compass bearing of N. by E. is the equivalent of a 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. 79. Having once satisfied himself 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 tlie correct direction is to tite right, the error is east. The words correct-right-east, in such a case, would be the key to all of his solutions. If he had a compass course to change to a corrected one with easterlj^ deviation, he would know that to obtain the result the error must be applied to the right; if it were desired to change a correct course to the one indi- cated by compass, the error being westerly, the converse presents itself — the correct must be to the left — the uncorrected will therefore be to the right; if a correct bearing is to be compared with a com- pass bearing to find the compass error, when the correct is to the right the error is east, or the reverse. §0. 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. §1. 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 deviation to a compass bearing we correct it to magnetic, and by applying to it the combined deviation and variation we correct it to true. Whichever of these operations is undertaken, and whichever of the errors is considered, the process of correction remains the same; the correct direction is always to the right, when the error is east, by the amount of that error. Careful study of the following examples will aid in making the subject clear: Examples: A bearing taken by a compass free from deviation is ,^. 76° H; variation, 5° W. ; required the true bearing. N. 71° E. A bearing taken by a similar compass is NW. bv W. i W. ; variation, \ pt. W. ; requiretl the true bearing. NW. by W. f W. A vessel steers S. 27° ¥j. bv compass; deviation on that heading, 3° W. ; variation in the locality, 12° E. ; required the true course. S. 18° E. A vessel steers S. bv W. § W. ; deviation, \ pt. W. ; variation, 1 pt. E. ; required the true course. SSW. \ W. It is desired to steer the magnetic course N. 38° W.; deviation, 4° E. ; required the course by com- pass. N. 42° W. ' 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, N. 55° E. ; deviation, 7° E.; variation, 14° W.; required the course by compass. N. 62° E. THE COMPASS ERROR. 31 A vessel passing a range whose direction is known to be S. 20° W., magnetic, observes the bearing by compass to be S. 2° E. ; required the deviation. 22° E. The sun's observed bearing l)y compass is S/i89° E. ; it is found by calculation to be N. 84° E. (true) ; variation, 8° W.; required the deviation. 1° E. FINDING THE COMPASS EBBOB. ^ §2. The variation of the compass for any giveiJ^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. 83. The deviation of the compass, varying as it does for every ship, for every heading, and for every geographical locality, must be determined by the navigator, for which purpose various methods are available. Whatever method is used, the ship must be swung in azimuth and an observation made on each of the headings upon which the deviation is required to be known. If a new iron or steel ship is being swung for the first time, observations should be made on each of the thirty-two points. At later swings, especially after correctors have been applied, or in the case of wooden ships, sixteen points will suffice — or, indeed, only eight. In case it is not practicable to make observations on exact compass points, they should be made as near thereto as practicable and platted on the Napier diagram (to be explaine)'! hereafter), whence the deviations on exact points may be found. 84. In swinging ship for deviations the vessel should be on an evei^ keel and all movable masses of iron in the vicinity of the compass secured as for sea. The vessel, upon being placed on any heading, should be steadied there for three to four minutes before the observation is made in order that the compass card may come to rest and the magnetic conditions assume a settled state. To 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 anchor, 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 recjuisite time on each heading), or at anchor, by means of springs and hawsers. 85. The deviation of all compasses on the ship may be obtained from the same swing, it being required to make observations with the standard only. To accomplish this it is necessary to record the ship's head by all compasses at the time of steadying on each even point of the standard; applying the deviation, as ascertained, to the 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 constructeii as explained in article 94. 86. There are four methods for ascertaining the deviations from swinging; namely, by reciprocal hearings, by bearings of the sun, by ranges, and by a distant object. 87. Reciproc.vl 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 repre- sents the deviation of the latter. In determining the deviations of compasses, placed on the fore-and-aft amidship line, when the distribution of magnetic metal to starboard and port is symmetrical, the shore compass may be replaced by a dumb compass, or pelorus, or bv a theodolite in which, for convenience, the zero of the horizontal graduated circle may be termed north; the reading of the shore instrument will, of course, not represent magnetic directions, but by assuming that they do we obtain a series of fictitious deviations, the mean value of which is the error common to all. Upon deducting this error from each of the fictitious devia- tions, we obtain the correct values. If ship and shore observers are provided with watches which have been compared with one another, the times may be noted at each observation, and thus afford a means of locating errors due to misunderstanding of signals. 88. 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 compass 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 iron or steel, may be considered equal to the mean of all the total errors. Other celestial bodies may be observed for this purpose in the same manner as the sun. This method is important as being the only one available for determining the compass error at sea. 89. Ranges. —In many localities there are to be found natural or artificial range marks which are clearly distinguishable, anil which when in line lie on a known magnetic bearing. By steaming about on different headings and noting the compass bearing of the ranges each time of crossing the line that they mark, a series of deviations may be obtained, the deviation of each heading being equal to the difference between the compass and the magnetic bearing. 90. Distant Object. — A conspicuous object is selected which must be at a considerable 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 maybe assumed to be the mean of the compass l)earings. 32 THE COMPASS ERROK. In choosing an oliject for use in this method care must.be taken that it is at such a distance that its bearing from the shii)does not practically differ as the vessel swings in azimuth. If the ship is swung at anchor, the distance should l)e 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'. 91. in all of the inethods 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 aljreast it in successive colunms 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 lieadings and the corresponding deviations. This is known as the Deriation Table of the compass. If compensation is to l)e attempted, this table is the basis of the o])eration; if not, the deviation tables of the standard and steering compass should be posted in such place as to be accessible to all i^ersons concerned with the navigation of the ship. 92. Let it lie assumed that a deviation table has been found and that the values are as follows: Deviation table. Ship's head ht Devia- Ship's head by standard compass. Devia- Ship's head by Devia- Ship's head bv Devia- standard compas.s. tion. tion. standard compass. tion. 1 standard compass. tion. North . . . . o / - 1 00 - 1 50 East E.byS... -19 55 -22 00 South S. by W . . 00 + 10 20 West o / +19 30 N. by E . . . W.byN... +17 00 NNE - 3 00 ESE -23 30 SSW + 17 00 WNW + 13 00 NE. by N . . - 5 15 SE. bv E . -24 00 SW.byS. +21 50 1 NW.byW. +11 10 NE : - 7 10 SE :.... -23 30 SW +24 30 ' NW + 7 40 NE. by E . . -10 15 SE.bvS.. -20 30 SW. bv W T-26 20 NW. by N . + 5 05 ENE -13 05 SSE -16 00 WSW .... +25 00 NNW + 3 00 E.by N ... -17 10 S.byE... - 8 50 1 W.bvS.. +23 30 N.byW... + 1 00 AVe have from the table the amount of deviation on each compass heading; therefore, knowing the ship's head by compass, it is easy to pick out the corresponding deviation and thus to obtain the mag- netic heading. But if we are given the magnetic direction in which it is desired to steer and have to find the 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 they are the same as on the corresponding compass headings. For example, with the deviation ta])le just given, suppose it is required to determine the compass heading corresponding to N. 79° W., magnetic. The deviation corresponding to N. 79° W., per compass, is + 17° 00'. If we apply this to N. 79° W., magnetic, we have S. 84° W. as the compass course. But, consulting the table, it may be seen that the deviation corresponding to S. 84° W., per compass, is + 21 J°, and therefore if Me steer that course the magnetic direction will be N. 74^° AV., and not N. 79° W., 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: Mag. course required Try dev. on X. 79° W., p. c First trial. N. 79° W. 17° E. Trial comp. course S. 84° AV. Dev. on S. 84° W., p. c 2U° E. Mag. course made good N. 74i° A\'. Since this assumption carries the course 4i° too far to the right, assume next a deviation on a course 5° farther to the left than tlie one used here. Mag. course required Try dev. on S. 79° A\'., p. Trial comp. course Dev. onS. 77i° W. p. c /Second trial. N. 79° AA'. ..... 23^° E. 77 i° W 24° E. Mag. course made good X. 782° AV. This is as close to the required course as the ship can be steered. It may occur that further trials will be necessarv in some cases. 93. The Xapier Diagram. — A much more expeditious method for the solution of this problem is afforded by the Xapier Diagram, and as that diagram also facilitates a number of other operations con- nected with compass work it should be clearly understood by the navigator. This device admits of a graphic representation of the table of deviations of the compass by means of a curve; besides furnishing a ready 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 headings it enables one to obtain the most probable value of the deviation on any other course that the ship may head. The last-named feature renders it useful in making a table of deviations of compasses other than the standard when their errors are found as described in article 85. THE COMPASS ERROR. 33 94. The Napier diagram (fig. 9) represents the margin of a compass card cut at the north point and straightened into a vertical line; for convenience, it is usually divided into two sections, representing, respectively, the eastern and western semicircles. The vertical line is of a convenient length and di\ided into thirty-two equal parts corresponding to the points of the compass, beginning at the top with North and continuing around to the right; it is also divided into 360 degrees, which are appropriately marked. DEVIATION WEST DEVIATIOM EAST DEVIATION WEST DEVIATION EAST Fi(4. 9. The vertical line is intersected at each compass point l)y two lines 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 pl(jt a curve on the Napier diagram, if the deviation has been observed with the ship's head ou given coi/(/)a.s-.s' 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 point, 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 points of the standard) , proceed in the same way, excepting that the deviation must be laid down on a plain line or a line parallel thereto. Mark each point thus obtained with a dot or small circle, and draw a free curve passing, as nearly as possible, through all the points. 224X0—0:";- -3 34 THE COMPASS ERROR. To obtain a complete curve, a suflicient number of observations should be taken while the t^hip swings through an entire circle. Generally, observations on every alternate point are enough to estab- lish a good curve, but in cases where the maximum deviation reaches 40° it is preferable to observe on every i)oint. The curve shown in the full line on figure 9 corresponds to the table of deviations given in article 92. From a given compass course to find the corresponding magnetic course, through the point of the vertical line representing the given compass course, draw a line parallel to the dotted lines until the curve is intersected, and from the point of intersection draw another line parallel to the plain lines; the point on the scale where this last line cuts the vertical line is the magnetic course sought. The correctness of this solution will be ap])arent when we consider that the 60° triangles are e(iuilateral, and therefore the distance measured along the vertical side will equal the distance measured along the inclined sides — that is, the deviation; and the direction will be correct, for the construction is such that magnetic directions will be to the right of compass directions when the deviation is easterly and to the left if westerly. From a given magnetic course to find the corresponding compass course, the process is I Ik same, exce])ting that the first line drawn should follow, or be parallel to, the plain lines, and the second, or return line, should be parallel to the dotted; and a proof similar to that previously employed will show the correctness of the result. As an example, the problem given in article 92 may be solved by the diagram, and the result will be found to accord with the solution previously given. THE THEORY OF DEVIATION." ' 95. Features of the Earth's MA(iNETisM. — It has already been stated that the earth is an immense natural magnet, with a pole in each hemisphere which is not coincident with the geographical pole; it has also a magnetic equator which lies close to, but not coincident with, the geographical equator. A magnetic needle freely suspended at a point on the earth's surface, and undisturbed by any other than the earth's magnetic influence, will lie in the plane of the magnetic meridian and at an angle with the horizon depending upon the geographical position. The magnetic elements of the earth which must be considered are shown in figure 10. The earth's total force is represented in direction and intensity by the line AB. Since compass needles are mechan- ically arranged to move only in a horizontal plane, it becomes necessary, when investigating the effect of the earth's mag- netism upon them, to resolve the total force into two com- ponents which in the figure are represented by AC and AD. These are known, respectively, as the horizontal and vertical components oi the earth's total force, and are usually designated as H and Z. The angle CAB, which the line of direction makes with the plane of the horizon, is called the magnetic inclination or dip, and denoted by 0. It is clear that the horizontal comj)onent will reduce to zero at the magnetic poles, where the needle points directly downward, and that it will reach a maximum at the magnetic equator, where the free needle hangs in a horizontal direction. The reverse is true of the vertical component and of the angle of dip. Values representing these different terms may be found from special charts. 96. Induction; Hard and Soft Iron. — When a piece of unmagnetized iron or steel is brought within the influence of a magnet, certain magnetic properties are inunediately imparted to the former, which itself becomes magnetic and continues to remain so as long as it is within the sphere of influence of the permanent magnet; the magnetism that it acquires under these circumstances is said to he induced, and the properties of induc- tion are such that that end or region which is nearest the pole of the influencing magnet will take up a polarity opposite thereto. If the magnet is withdrawn, the induced magnetism is soon dissipated. If the magnet is brought into proximity again, but with its opposite pole nearer, magnetism will again \)e induced, but this time its polarity will be reversed. A further property is that if a piece of iron or steel, while temporarily possessed of magnetic qualities through induction, be subjected to blows, twisting, or mechanical violence of any sort, the magnetism is thus made to acquire a permanent nature. The softer the metal, from a physical point of view, the more quickly and thoroughly will induced magnetism be dissipated when the source of influence is withdrawn; hard metal, on the contrary, is slow to lose the effect of magnetism imparted to it 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 accjuires and parts with its magnetic qualities under the varying influences to which it is subjected. 97. Magnetic Properties Acqutrkd by an Iron or Steel Vessel in Buildinc. — 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 or hammering, bending, and twisting that it undergoes. JforLxonttMl, Forc^ - H Fig. 10. o As it is probable that the Btudent will not have practical need of a knowledge of the theory of deviation and the compensation of the compa.ss 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. THE COMPASS EKKOE. 35 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 inclination to the line of total force; when held at right angles to the line there would be no effect, as each extremity would be equally near the pf)les of the earth and all influence would be neutralized. If, while such a bar is in a magnetic state through inductive action, it should be hammered or twisted, a certain mag- netism of a permanent character is impressed upon it, which is never entirely lost unless the bar i& subjected to causes ecpial and opposite to those that produced the first effect. A sheet of iron is affected by induction in a similar way, the magnetism induced l)y the earth diffusing itself over the entire plate and separating itself into regions of opposite polarity divided by a neutral area at right angles to the earth's line of total force. If the plate is hammered or bent, this magnetism takes up a permanent character. If the magnetic mass has a third dimension, and assumes the form of a ship, a similar condition prevails. The whole takes up a magnetic character; there is a magnetic axis in the direction of the line of total force, with poles at its extremities and a zone of no magnetism perpendicular to it. The distri- bution of magnetism will depend upon the horizontal and vertical components of the earth's force in the locality and upon the direction of the keel in building; its permanency will depend upon_ tho amount of "mechanical violence to which the metal has been subjected by the riveting and other inci- dents of construction, and upon the nature of the metal employed. 98. Causes that Produce Deviation. — There are three influences that operate to produce devia- tion; namely, (o) si(bpernutneni magnetism; (b) transient magnetism induced in reHical soft iron, and (c) transient magnetism induced in horizontal soft iron. Their effect will be explaineil. Suhpernianent magnetism is the name given to that magnetic force which originates in the ship while building, through the process explained in the preceding article; after the vessel is launched and has an opportunity to swing in azimuth, the magnetism thus induced will suffer material diminution until, after the lapse' of a certain time, it will settle down to a condition that continues practically unchanged; the magnetism that remains is denominated subpermanent. The vessel will then approximate to a permanent magnet, in which the north polarity will lie in that region which was north in building, and the south 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 i.-^ transient in nature. Its value or force in any given mass varies with and depends upon the value of the vertical component at the place, and is proportional to the sine of the dip, being a maximum at the magnetic pole and zero at the magnetic equator. Transient magnetism induced in horizontal soft iron is that developed in the soft iron of a vessel through the inductive action of the horizontal component only of the earth's total force, and is transient in nature. 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 poles of these forces d(j not usually lie in the horizontal plane of the compass needle, bTit as this needle is constrained to act in a horizontal plane, its movements will be affected solely by the horizontal component*? of these forces, and its direction will be determined by the resultant of those components. The earth's force operates to retain the compass needle in the plane of the magnetic meridian, but the resultant of the three remaining forces, when without this plane, deflects the needle, and the amount of such deflection constitutes the deviation. 99. Classes of Deviation. — Investigation has developed the fact that the deviation produced as described is made up of three parts, which are known respectively as semicircular, qnadrantal, and con- stant deviation, the latter being the least important. A clear understanding of the nature of each of these classes is essential for a comprehension of the methods of compensation. 100. Semicircular Deviation is that due to the combined influence, exerted in a horizontal plane, of the subpermanent magnetism of a ship and of the magnetism induced in soft iron by the vertical com- ponent of the earth's force. If we regard the effect of these two forces as concentrated in a single resultant pole exerting an attracting influence upon the north end of the compass needle, it may be seen that there will be some heading of the ship whereon that pole will lie due north of the needle and therefore produce no deviation; now consider that, from this position, the ship's head swings in azi- muth to the right; throughout all of the semicircle first described an easterly deviation will be produced, and, after completing 180°, the pole will be in a position diametrically opposite to that from which it started, and will again exert no influence that tends to produce deviation. Continuing the swing, throughout the next semicircle the direction of the deviation produced will be always to the westward, until the circle is completed and the ship returns to her original neutral position. From the fact that this disturbing cause acts in the two semicircles with 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. 101. Returning to the two distinct sources from which the semicircular deviation arises, it may be seen that the force due to subpermanent magnetism remains constant regardless of tlie geographical position of the vessel; but since the horizontal force of the earth, which tends to hold the needle in the magnetic meridian, varies with the magnetic latitude, the deviation due to subpermanent magnetism varies inversely as the horizontal force, or as tt; this may be readily understood if it is considered that the stronger the tendency to cling to the direction of the magnetic meridian, the less will be the deflec- tion due to a given disturbing force. On the other hand, that part of the semicircular force due to magnetism induced in vertical soft iron varies as the earth's vertical force, which is proportional to the 36 THE COMPASS ERROR. sine of the dip; its effect in producing deviation, as in the preceding case, varies inversely as the earth's horizontal force — that is, inversely as the cosine of the dip; hence the ratio representing' the change of deviation arising from this cause on change of latitude is f., or tan 9. If, then, we consider the change in the semicircular deviation due to a change of magnetic latitude, it will be necessary tt> separate the two factors of the deviation and to remember that the portion pro- V duced bv subpermanent magnetism varies as , and that due to vertical induction as tan 0. But for \ ' H any consideration of the effect of this class of deviation in one latitude only, the two parts may be joined together and regarded as having a single resultant. 102. If we now resume our former assumption, that all the forces tending to produce semicircular deviation are concentrated in a single pole exerting an attracting influence upon the north pole of the compass, we maj' consider a line to be drawn joining that theoretical pole with the center of the com- pass, then the angle made by this line with the keel line of the vessel, measured from right ahead, around to the right is called the starboard angle. From this it follows that the disturbing force producing semicircular deviation may be considered to have the same effect as a single magnet whose center is in the vertical axis of the compass, and whose south pole (attracting to the north pule of the compass) is in the direction given by the starboard angle; if, therefore, a magnet be placed with its center in the ver- tical axis of the compass, its north (or repelling) pole in the direction of the starboard angle, and its distance so regulated that it exerts upon the compass a force equal to that of the ship's combined sub- permanent magnetism and vertical induced magnetism, the disturbing effect of these two forces will be counterbalanced, and, so far as they are concerned, the compass deviations will be corrected, provided that the ship does not change her magnetic latitude. 103. It is evident that the force of the single magnet may be resolved into two components — one fore-and-aft, and one athwartship; in this case, instead of being represented by a single magnet with its south pole in the starboard angle, the semicircular forces will be represented by two magnets, one fore- and-aft and the other athwartship, and compensation may be made by two separate magnets lying respec- tively in the directions stated, but with their north or repelling poles in the position occupied by the south or attracting poles of the ship's force. Figure 11 represents the conditions that have been described. If O be the center of the compass, XX'' "* and YY'', respectively, the fore-and-aft and athwart- ship lines of the ship, and OS the direction in which the attracting pole of the disturbing force is exerted, then XOS is the starboard angle, usually designated a. Now, if OP be laid off on the line OS, represent- ing the amount of the disturbing force according to some convenient scale, then Oh and Oc, respectively, represei^t, on the same scale, the resolved directions of that force in the keel line and in the transverse line of the ship. Each of these resolved forces will exert a maximum effect when acting at right angles to the needle, the athwartship one when the ship Yio. 11. heads north or south by compass, and the longitu- dinal one when the heading is east or west. On any other heading than those named the deviation produced by each force will be a fraction of its maximum whose magnitude will depend upon the azimuth of the ship's head. The maximum deviation produced, therefore, forms in each case a basis for reckoning all of the various effects of the disturbing force, and is called a coefficient. The coefficient of semicircular deviation produced by the force in the fore-and-aft line is called B, and is reckoned as positive when it attracts a north pole toward the bow, negative when toward the stern; that produced by the athwartship force is C, and is reckoned as positive to starboard and nega- tive to port. These coefficients are expressed in degrees. « Referring again to figure 11, it will be seen that: Oc. or (what may be shown to be the same thing): tan a-^^^, , sm C. tan a= , -- sin B and when the maximum deviations are small, this becomes: tan '^1'= , X) Since the starboard angle is always measured to the right, it will be seen that, for positive values of B and C, a will Ije between 0° and 90°; for a negative B and a positive C, between 90° and 180°; for a It should be remarked that in a mathematical analysis of the deviations, it would be necessar.v to distinguish between the approximate coefficients, B and C, here described, as also A, D, and E, to be mentioned later, and the exact coefficients denoted by the corresponding capital letters of the German alphabet. In the practical discussion of the subject here given, the question of the diflference need not be entered into. THE COMPASS ERROE. 37 negative values of both B and C, between 180° and 270°; and for a positive B and negative 0, between 270° and 360°. 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. 92), B isequal to -19° 55', or to —19° 80', or to ^ (—19° 55' —19° 30')= -19° 43'. 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 —1° 00' or 0° 00', or i (-1° 00'±0° 00')= -0° 30'. 105. The value of the subpermanent magnetism remaining practically constant under all condi- tions, it will not alter when the ship changes her latitude; but that due to induction in vertical softiron undergoes a change when, by change of geographical position, the vertical component of the earth's force assumes a different value, and in such case the correction by means of one or a pair of permanent magnets will not remain effective. If, however, by series of observations in two magnetic latitudes, the values of the coefficients can be determined under the differing circumstances, it is possible, by solving equations, to determine 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 previ- ously described, and the vertical induction in soft iron can be corrected by a piece of vertical soft iron placed in such a position near the compass as to produce an equal but opposite force to the ship's vertical soft iron. This last corrector is called a Flinders bur. Having thus opposed to each of the component forces a corrector of magnetic character identical with its own, a change of latitude will make no difference in the effectiveness of the compensation, for in every case the modified conditions will produce identical results in the disturbing and in the correcting force. 106. Qiiadrantal, 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 ath wart- ship direction. It may be seen («) 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 athwartship and the fore-and-aft iron having simply exchanged positions) ; and {li) the direction of the deviation produced is opposite in successive quadrants. The action of unsymmetrical soft iron is not (juite 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 opposite name in successive quadrants. From the fact that deviations of this class change sign every 90° throughout the circle, they gain the name of qiiadraidal deviations. One of the curves laid down in the Napier diagram (fig. 11) is that of quadrantal deviations, whence the nature of this disturb- ance of the needle may 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 coeffi- cient due to symmetrical soft iron is designated as D, and is Fui. 12. considered positive when it produces easterly deviations in the quadrant between North and P^ast; 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 inetpiality in the distribution of metal to starboard and to port, as in the case of a compass placed off the midship line. 10§. 1) is approximately equal to the 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 92, D is equal to \ {—1° 10' - 24° 30') = J- 8° 40'; or to h (-i-23° 30' — 7° 40') = -f 7° 55'; or to ^ ( 4- 8° 40' + 7° 55') = — 8° 23'. By reason of the nature of the arrangement of iron in a ship, D is almost invariably positive. E is approximately P(iual to the mean of the deviations on North and South; or to the mean of tho.se on East and West with sign reversed; or to the mean of those means. In the example, E is equal to i (-1° 00'±0° 00') = -0° 30'; or to \ (+ 19° 55'- 19° 30') = + 0° 13'; or to i (-0° 30' J-0° 13') = _ 0° 09'. 109. Quadrantal deviation does not, like semicircular, undergo a change upon change of magnetic latitude; being due to induction in horizontal soft iron, the magnetic force exerted to produce it is propor- tional to the horizontal component of the earth's magnetism ; but the directive force of the needle likewise depends upon that same component; consequently, as the disturbing force exerted upon the needle increases, so does the power that holds it in the magnetic meridian, with the result that on any given heading the deflection due to soft iron is always the same. no. Quadrantal deviation is corrected by placing masses of soft iron (usually two hollow spheres in the athwartship line, at equal distances on each side of the compass), with the center of mass in the horizontal plane of the needle. The distance is made such that the force exerted exactly counteracts that of the ship's iron. As the correcting effect of this iron will, like the directive force and the quad- rantal disturbing force, vary directly with the earth's horizontal component, the compensation once properly made will be effective in all latitudes. In practice, the quadrantal deviation due to unsymmetrical iron is seldom corrected; the correction may be accomplished, however, by placing the soft iron masses on a line which makes an angle to the athwartship line through the center of the card. 38 THE COMPASS EEROR. 111. Constant Deviation is due to induction in horizontal soft iron unsymmetrically placed about the compass. It has already been explained that one effect of such iron is to produce a quadrantal ship, by an auxiliary compas^s or by the pelorus, upon two adjacent magnetic cardinal points (art. l3^). Put the ship on heading North or South (magnetic), and raise or lower the athwartship magnets or alter their number until the deviation disappears; then steady on East or West (magnetic) and similarly adjust the fore-and-aft magnets. Swing ship for a new table of residual deviations. When correctors in the starboard angle are nsed, arrange as before for heading on two adjax-ent cardinal magnetic courses. Steady on one of these, observe amount of compass error, correct half by changing the starboard angle and half by raising or lowering magnets; steady on the adjacent cardinal point and repeat the operation. Continue until adjustment is made on both headings, then swing for residual deviations. 42 PILOTING. CHAPTER IV. PILOTING. 130. Definition'. — Piloting, in the 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 kejit upon the vessel's course and frequent changes to be made therein. 131. Reqiisites. — As requisites to successful piloting, the navigator should be provided with the best available chart of the locality to be traversed, together with the sailing directions and descrip- tions of aids to navigation; and all of these should be corrected for the latest information, published in notices to mariners or otherwise, that bear upon the locality. The vessel should be equipped with the usual instruments employed in navigation. The deep-sea sounding-machine, if i)rovided, should be ready for use when there is a chance that it may be needed. The lead lines should be correctly marked, and as shoal water is entered one or two men should be stationed to sound. The index errors of the sextants should be known, and, above all, there should be at hand a table showing correctly the deviation of the compass on each heading. 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, main- taining the direction of the line, move the ruler until its edge passes through the center of the compass rose and note the direction. If the compass rose indicates true directions, this will be the true course, and must be corrected for variation and deviation ( by applying each in the opposite direction to its name) to obtain the compass course; if it is a magnetic rose, the course need be corrected for deviation only. Before putting the ship on any course a careful look should be taken along the line over which it leads to be assured that it clears all dangers. 1 33. Methods of Fixing Position. — A navigator in sight of objects whose positions are shown ujjon the chart may locate his vessel by either of the following methods: («) cross bearings of two known objects; {h) the bearing and distance of a known object; {(•) 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 fore- going there are two methods by which, without obtaining the precise position, the navigator may assure himself that he is clear of any particular danger. These are: (/) the danger angle; {g) the danger bearing. The choice of the method will be governed by circumstances, depending upon which is best adapted to prevailing conditions. 1 34. Cross Bearings of two Known Objects. — Choose two objects whose i^osition on the chart can ])e unmistakably identified and whose respective bearings from the ship differ, as nearly as possible, bv90°; observe the bearing of each, either by compass or pelorus, taking one as quickly as possible at\er tlie othep; 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 exactlj- on the course for which the i)elorus 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, api)ly deviation and variation to obtain the true bearing, or deviation only to obtain the magnetic; if /" / observed by pelorus, that instrument should be set for the true or mag- n/ti. netic heading, according as one or the other sort of reading is required, y/r\ and no further correction will be necessary. Draw on the chart, by y^ I means of the parallel rulers, lines which shall pass through the respec- y^ \ five objects in the direction that each was observed to bear. As the / \ shi%Ls position on the chart is known to be at some point of each of jT \ the« lines, it must l>e at their intersection, the only point that fulfills ^^/ ) c botn conditions. /\ ^" figure 13, if A and B are the objects and OA and OB the lines X N. ( passing through them in the observed directions, the ship's position / N. I will be at O, their intersection. N. 1 * 135. If it be possible to avoid it, ol)jects should not be selected ' i N. ^ \ for a cross bearing»which subtend an angle at the ship of less than 30° \/ or more than 150°, as, when the lines of bearing approach parallelism, f^B a small error in an observed bearing gives a large error in the result. VTS. For a similar reason objects near the ship should be taken in prefer- ^ N ence to those at a distance. Fig. 13. 1 36. When a third object is available a bearing of that may be taken and ])lotted. 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. PILOTING. 43 V-t;:: Fui. 15. 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 l)ody and noting the time; work out the sight and obtain the Sumner line (as explained in Chapter XV), and the intersection of this with the direction-line from the object will give the observer's position in the same way as from two terrestrial bearings. 13§. Bearing and Distance of a Known Object. — When only one object is available, the ship's position may be found by observing its bearing and distance. Follow the preceding method in the mat- ters of taking, correcting, and plotting the bearing; then, on this line, lay off the distance from the object, which will give the point occupied by the observer. In figure 1-i, if A represents the object and AO the bearing and distance, the position sought will be at O. 139. It is not ordinarily easy to find directly the distance of an object at sea. The most accurate method is when its height is known and it subtends a fair-sized angle from the ship, in which case the angle may be measured by a sextant," and the distance computed or taken from a table. Table 83 of this work gives distances up to 5 miles, corresponding to various heights and angles. Captain Lecky's "Danger Angle and Offshore Dis- tance Tables" carries the computation much further. The use of this method at great distances must not be too closely relied upon, as small 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 employed only when no other is available the best possible approximation has to suflice. 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 inapprecial>le, however, save at very close dis- tances, when it may be sufficiently corrected by getting down as low as possible on board the vessel, so that the eye is near the water-line. One condition exists, however, where the error is material — that shown in figure 16, where the visible shorjp-line is at M^, a considerable distance from M, the point vertically below the summit. In this case there is nothing to mark M in the observer's eye, and it is essential that all angles be measured from a point dose down to the water-line. If a choice of objects can be made, the best results will l)e obtained by observing that one which subtends the greatest angle, as small errors will then have the least effect. There is another method for determining the distance of an o)>ject, Avhich 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 l)osition occupied by the observer the more precise will be the results. 140. In observing small angles, such as those that occur in the methods just described, it is some- times convenient to measure them on and off the limb of the sextant. Firet look at the bottom of the object and reflect the top down into coincidence; then look through the transparent part of the horizon glass at the top and bring the bottom up by its reflected ray. The mean of the two readings will be the true angle, the index correction having been eliminated by the operation. 141. When the methods of finding distance by a vertical or a horizon angle are not available, it must be obtained by such means as exist. Fstimate the distance by the appearance; take a sounding, and note where the depth falls upon the line of bearing; at night, if atmospheric conditions are normal, consider that the distance of a light when sighted is equal to its maximum range of visibility, remem- l^ering that its range is stated for a height of eye of 15 feet; or employ such method as suggests itself under the circumstances, regarding the result, however, as an approximation only. 142. The Bearing of a Known Object and the Ancjle between two Known Objects. — This method is seldom employed, as the conditions always permit of cross bearings being taken, and the latter is generally considered preferable. Take a bearing of a known object by compass or pelorus and observe the sextant angle between some two known objects. The line of bearing is plotted as in former methods. In case one of the objects of the observed angle is that whose bearing is taken, the angle is applied, right or left as the case may be, to the bearing, thus giving the direction of the second object, which is plotted from the compass rose and parallel rulers. If the object whose bearing is taken is not one of the objects of the angle, lay off the angle on a three-armed proti-actor, or piece of tracing paper, and swing it (keeping the legs or lines always over the two objects) until it ])asses over the line of bearing, which defines the position of the ship; there will, except in special cases, be two points of intersection of the line with the circle thus described, and the navigator must know his position with sufficient closeness to judge which is correct. 143. Two Bearin(;s of a Known Object. — This is a most useful method, which is frequently employed, certain special cases arising thereunder being particularly easy of application. The process iThe use of the sextant is explained in Chapter VIII. 44 PILOTING. is to take a careful bearing and at the same moment read the patent log; then, after running a convenient distance, take a second bearing and again read the log, the difference in readings giving the intervening run; when running at a known speed, the time interval will also afford a means for determining the distance run. The problem is as follows: In figure 17, given OA, the direction of a known object, A, at the first observation; PA, the direction at the second observation; and 01*, the distance • traversed between the two; to find AP, the distance at the second observation. Knowing the angle PC) A, the angular distance of the object from right ahead at the first bearing; OPA, the angular distance from right astern at the secontl bearing; and OP, the distance run; we have by Plane Trigonometry: PAO = 180°- (POA + OPA) ; and AP = OP X sin POA sin PAO* If, as is frequently the case, we desire to know the distance of passing abeam^ we have: AQ = AP X sin OPA. Tables 5A and 5B give solutions for this problem, the former for intervals of bearing of quarter points, the latter for intervals of two degrees. The first column of each of these tables gives the value of AP, the distance of the ship from the observed object at the time of taking the last bearing, for values of OP equal to unity; that is, for a run V)etween bearings of 1 mile. The second P 1- column gives AQ, the distance of the object when it bears abeam, likewise for a value of OP of 1 mile. When the run between bearings is other than 1 mile, the number taken from the table must be used as a multiplier of that run to give the required distance. Example: A vessel steering north takes a bearing of a light XW. J W. ; then runs 4.3 miles, when the bearing is found to be WSW. Required the distance of the light at the time of the second bearing. Difference between course and first bearing, 4i pts. Difference between course and second bearing, 10 pts. Multiplier from first column, Table 5A, 0.88. 4.3 miles X 0.88 = 3.8 miles, distance at second bearing. Example: A vessel on a course S. 52° E. takes the first bearing of an object at S. 26° E., and the second at S. 2° W., running in the interval 0.8 mile. Required the distance at which she will pass abeam. Difference between course and first bearing, 26°. Difference between course and second bearing, 54°. Multiplier from second column. Table 5B, 0.79. 0.8 mile X 0.79 = 0.6 mile, distance of passing abeam. 144. 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 equal to unity, and the distance run is therefore equal to the distance from the object. When the angular distance on the bow at the second bearing is twice as great as it was at the first bearing, the distance of the object from the ship at fiecond bearing 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 ol)ject A bears ar°on the bow, and at the second position, P, 2cir°, we have in the triangle APO, observing that APO = 180° — 2ix, and POA = tx: PAO = 180° -(POA -r- APO), = 180°-(cr + 180°-2a), = a. Or, since the angles at O and at A are equal to each other, the sides OP and AP are equal, or the distance at second bearing is equal to the run. This is known as doubling the angle on the buic. 145. A case where this holds good is familiar to every navigator as the botv and beambearing, 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 etiual to the run between bearings. 146. When the first bearing is 26i° from ahead, and the second 45°, the distance at which the object irill be passed abeam will equal the run between bear- ings; this may be proved by computation or by reference to the tables and is a very convenient fact to remember, as it shows the navigator at once, it about to pass a point, how wide a berth he is going to give the offiying dangers. 147. 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), pa^^sing 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 PILOTING. 45 Fig. 19. OP, and therefore O represents the position of the ship at the first bearing and P at the second. For any other positions O^P', O'^P^', the condition is not fulfilled. 14§. Another jiraiihic solution is given by the Dintance Finder, devised by Lieut. J. B. Blish, U. S. Navy. This consists of a semicircle whose circumference is graduated in degrees. Two pieces of thread, made to swing aljout a pin-head at the center, are laid down to represent the lines of bearing, and ease in measuring distances is afforded l)y series of cross lines similar to those on a piece of profile ^ ^ paper. 149. The methoil 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 land- mark in sight. Careful navigators seldom, if ever, miss the opjwr- tunity for a bow and beam bearing in passing a light-house or other well-plotted ol:)ject; 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 whii-h there is a danger — a familiar example of which is when a light-house marks a point off which are rocks or shoals — a good assurance of clearance should l:)e obtained before bringing it abeam, either by doubling the angle on the bow, or by using the 26i°-45° bearing; the latter has the advantage over the former if the object is sighted in time to permit of its use, as it may be assumed that the 45° (bow) bear- ing will always be observed in any event, and this gives the distance al>eam directly, saving the necessity of plotting the position at second Ijearing (as obtained by .doubling the angle) and then carry- ing it forward. 150. It nuist 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 required. Difficulty will occur in estimating the exact course when there is bad steering, a cross current, or when a ship is making leeway; errors in the allowed run will arise when she is being set ahead or back by a current or when the logging is inaccurate. To take a not extreme case, a vessel making 10 knots through the water, running against a 2-knot tide, will overestimate her distance one-fifth of its true amount in taking a bow and beam bear- ing if no allowance is made for the tide, or she will underestimate her distance by one-fifth of its apparent amount if going with the same tide. Therefore, if in a current of any sort, due allowance must be made, and it should be remembered that more 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 ol)ject. 151. Sextant Anules between Three Known Objects. — This method, involving the solution of the three-}ioint 2)rof>len>, will, if the objects be well cho.sen, 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 knowledge of the compass error, improper log- ging, or the effects of current, as are the methods previously described. Three objects represented on the chart are selected and the angles measured with sextants of known index error between the center one and each of the others. Preferably there should be two observers and the two angles be taken sinuiltaneously, but one observer may fii-st 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-jwinter (see art. 432, Chap. XVII). Set the right and left angles on the instrument, and then move it over the chart until the three beveled edges pass respectively and simultaneously through the three objects. The center of the instrument will then mark the ship's position, which may 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 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 l)aper j^ermits the angles being readily laid off, but a plain ])iece of tracing paper may be used and the angles marked by means of a small protractor. The tracing- paper protractor pernnts the laying down, for simultane- ous trial, of a number of angles, where special accuracy is s>ought. 1.52. The three-point problem, by which results are obtained in this method, is: "To find a point such that three lines drawn from this point to three given points shall make given angles with each other. Let A, B, and C, in figure 20, be 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 point will be the center of another circle, on some point of whose circumference the ship must be. Then D, the point of intersection of the circumference of the two circles, will be the position of the ship. Fig. 20. 46 PILOTIKG, The correctness of this sohation may be seen as follows: Take the first circle, DBC; in the triangle EBC, the angle at E, the center, cquah i80°— 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 circumference subtended by that chord, which equals half the angle at the center, eiiuals the observed angle; so the required condition is fulfilled. Should either of the angles exceed 90°, the excess of the angle over 90° must be laid off on the opposite side of the lines joining the stations. 153. It may be seen that the intersection of the 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 fall upon the same circle; the two circles are then identical and there is no intersection; such a case is called a "revolver," because the protractor will revolve around the whole circle, everywhere passing through the observed points. The avoidance of the revolver and the 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 wholly indeterminate), but also all conditions approximating thereto, for in such cases the circles will intersect at a very acute angle, and the inevitable small errors of the observation and plotting will produce large errors in the resulting fix. Without giving an analysis of reasons, which may be found in various works that treat the problem in detail, the following may be enumerated as the general conditions which result in a (/ood fix: (a) When the center object of the three lies between the observer and a line joining the other two, or lies nearer than either of the other two. , (b) When the sum of the right and left angles is equal to or greater than 180°. (c) When two of the objects are in range, or nearly so, and the angle to the third is not less than 30°. (d) When the three objects are in the same straight line. A condition that limits all of these is that angles should be large — at least as large as 30° — excepting in the case where two objects are in range or nearly so, and then the other angle must be of good size. When possible, near objects should be used rather than distant ones. The navigator should not fall into the error of assuming that objects which would give good cuts for a cross bearing are necessarily favorable lor 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 of a dou1)tful 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 running in sight of the land, it is frequently of the greatest importance for the navigator to assure himself that the course leads clear of outlying dangers, and the Danger Angle affords a con- venient means of so doing. There are two sorts of danger angles — the hori- zontal angle taken between two objects, and the vertical angle of a single one. The former will be first described. 155. Suppose, in figure 21, that a vessel standing along the coast on the course indicated nmst pass an offshore danger between two well-marked objects, A and B, and that, allowing a safe margin, it is desired to approach no closer than the point O. Through the points A, B, and O draw a circle, by the usual methods of geometry, and observe that no portion of the danger lies without the circle. Measure the angle AOB with a protractor, and con- sider this the danger angle; as the ship draws near, take frequent observa- tions with a sextant of the angle subtended by the objects A and B. As long as the angle is less than the danger angle the ship is without the circle; but if the angle increases to the amount of the danger angle, she is on the circle, and should at once sheer off to avoid approach- ing closer. The reason will be evident from the con- sideration that all angles AOB, AO'B, AO'^B, AC^B, subtended at points on the circumference of the circle by the chord AB, are equal. 1 56. The vertical danger angle is an application of the same principle where there is in sight only one well-charted object and that is of known height. Draw a circle with that object as a center and of such radius that no neighboring dangei"s lie beyond its circumference; note, from Table 33, the vertical angle which is subtended by the known height at the distance chosen as a radius, and, by frequent observations in i)assing, make sure that this danger angle is not exceeded. By a simple modification, a ship passing inshore of an isolated z rock or shoal could be navigated clear by means of a vertical danger angle which was not allowed to decrease below that corresponding to a safe distance. Considerations governing the taking of vertical angles are given in the description of finding position by one bearing and the distance (arts. 139, 140). Y'' 157. The 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 22, along a coast which must not be approached within a certain distance, the landmark A being a guide. Let the navigator draw through A the line A Fig. 22. PILOTING. 47 XA, clear of the danger at all points, and note its direction bj- the compass rose; then let frequent bearings be taken as the ship proceeds, and so long as the bearings, YA, ZA, are to the right of XA he may be assured that he is on the left or safe side of the lines. If, as in the case given, there is but one object in sight and that nearly ahead, it would be very difficult to get an exact position, but this method would always show whether or not the ship was on a good course, and would, in consequence, be of the greatest value. And even if there were other objects visible by which to get an accurate fix it would be a more simple matter to note, by an occasional glance over the' sight-vane of the pelorus or compass, that the ship was making good a safe course than to be put to the necessity of plotting the position each time. 15§. 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 all such, as they are easier to observe than a compass bearing; but if in a locality with which the navigator has not had previous acquaintance the compass bearing of all ranges should be observed and compared with that indicated on the chart in order to make sure of the identity of the objects. The utility of ranges, either artificial or natural, as guides in navigation is well recognized. 159. SouNDiX(iS. — The practice should be followed of employing one or two leadsmen to take and report soundings continuously while in shoal water or in the vicinity of dangers. The soundings must not be regarded as fixing a position, but they afford a check upon the positions obtained by other methods. An exact agreement with the soundings on the chart need not be expected, as there may be some little inaccuracies in reporting the depth on a shij) moving with speed through the water, or the tide may cause a discrepancy, or the chart itself may lack perfection; but the soundings should agree in a general way, and a marked departure from the characteristic bottom shown on the chart should lead the navigator to verify his position and proceed with caution; especially is this true if the water is more shoal than expected. 160. But if the soundingsinshallow water when landmarks are in sight serve merely as an auxiliary guide, those taken (usually with the patent sounding machine or deep-sea lead) when there exist no other means of locating the ])osition, fulfill a nuich more important purpose. In thick weather, when approaching or running close to the land, and at all times when the vessel is in less than 100 fathoms of water and her pf)sition 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 i)aper over the chart, keeping the various courses parallel to the corresponding directions on the chart, until the observed soundings agree with those laid down, the ship's position will in general be quite well 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 lie off till conditions are more favorable. 161. Lights. — Before coming within range of a light the navigator should ac(iuaint himself with its characteristics, so that when sighted it will be recognized. The charts, sailing directions, and light lists give information as to the color, character, and range of visibility of the various lights. Care should be taken to note all of these and compare them when the light is seen. If the light is of the flashing, revolving, or occulting variety the duration of its periods should be noted to identify it. If a fixed light, a method that may be employed to make sure that it is not a vessel's light is to descend several feet inunediately after sighting it and observe if it disappears from view; a navigation light will usually do so, excepting in misty weather, while a vessel's light will not. The reason for this is that naviga- tion lights are as a rule sufficiently powerful to be seen at the farthest point to which the ray can reach without being interrupted by the earth's curvature. They are therefore seen at the first moment that the ray reaches an observer on a ship's deck, and are cut off if he lowers the eye. A vessel's light, on the other hand, is usually limited by its intensity and does not carry beyond a distance within which it it is visible at all heights. Care nuist be taken to avoid being deceived on first sighting a light, as there are various errors into which the inexperienced may fall. The glare of a powerful light is often seen beyond the distance of visibility of its direct 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 shoVt distances. AVhen a light is picked up at the extreme limit at which the height of the observer will permit, a fixed light may appear flashing, as it is seen when the ship is on the crest of a wave, and lost when in the hollow. Many lights are made to show different colors in different sectors within their range, and by con- sulting his chart or books, the navigator may be guided by the color of the ray in which he finds himself; in such lights one color is generally used on bearings whence the approach is clear, and another covers areas where dangers are to 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 the visibility, and it nmst not he positively assumed, on sighting a light, even in perfectly clear weather, that a vessel's distance is equal to the range of visibility; it may be either greater or less, as the path of a ray of light near the horizon receives extraordinary deflection under certain circumstances; the conditions governing this deflection are discussed in article 301, Chapter X. 162. Buoys. — While buoys are valuable aids, the mariner should always employ a certain amount of caution in being guided by them. In the nature of things 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 imcertain in unfrequented waters, or those of nations that do not keep a good lookout upon their aids to navigation. When, therefore, a buoy marks a place where a ship must be navigated with caution, it is well to have a danger angle or bearing as an additional guide instead of placing too much dependence upon the buoy being in place. Different nations adopt different systems of coloring for their buoys; an important feature of many such systems, including those adopted by the United States and various other great maritime 48 PILOTING. nations (though not all), consists in placing black l)uoyH to be left on the starboard hand of a vessel (johu/ out of a liarbor or fairway, and red biioys (the color of the port side light) on the port hand. ,In these various systems the color and character of the buoy are such as to denote the special purpose for which it is employed. 163. Fogs and Fog Signals. — As with lights, the navigator should, in a fog, acquaint himself with the characteristics of the various sound signals which he is likely to pick up, and when one is heard, its jjeriods shs; W. by S., 16 miles; WNW., 89 miles; S. by E., 40 miles. Required the course and distance made good. Courses. Dist. N. s. E. w. SSE. 15 13.9 5.7 SE. 34 24.0 24.0 W. by S. 16 3.1 15.7 WNW. 39 14.9 36.0 S. by E. 40 39.2 7.8 14.9 80.2 37.5 51.7 S. by W. 66.8 14.9 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 origrnal position. PARALLEL SAILING. 173. Thus far the earth has been regarded as an extended plane, and its spherical figure has not been taken into account; it has thus been impossible to consider one of the important terms involved — namely, difference of longitude. Parallel Sailing is the simplest of the various forms of Spherical Sailing, being the method of interconverting departure and difference of longitude when the ship sails upon an east or west course, and therefore remains always on the same parallel of latitude. In figure 24 T and T' are two places in the same latitude; P, the adjacent pole; TT'', the arc of the parallel of latitude through the two places; MM^, the corre- sponding arc of the equator intercepted between their meridians PM and PM'; and TT', the departure on the parallel whose latitude is TCM = OTC, and whose radius is OT. Let DLo represent the arc of the equator MM^, which is the measure of MPM', the difference of longitude of the meridians PM and PM''; R, the equa- torial radius of the earth, CM = CT; r, the radius OT of the parallel TT''; and L, the latitude of that parallel. Then, since TT' and MM' are similar arcs of two circles, and are therefore -^proportional to the radii of the circles, we have: TT' ^ OT. MM' CM' From the triangle COT, r = R cos L; lience Dep. R cos L or, Dep. _ r DLo ~R' DLo R or, DLo = Dep. sec. L; or, Dep. = DIxi 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. THE SAILINGS. 53 / In working these problems, the computation can be made by logarithms; but the traverse tables may more conveniently be employed. Kemembering that those tables are based upon the formuhe, DL=Dist. cos C, and Uist.=DL sec C, we may substitute for the column marked Lat. the departure, for that marked Dist. the difference of longitude, and for the courses at top and bottom of the page the latitude. The tables then become available for making the required conversions. Example: A ship in the latitude of 49° 30' sails directly east until making good a difference of longitude of 3° 30'. Required the departure. By Computation. By Inspection. L 49° 30' log cos 9.81254 Enter Table 2 with the latitude as C and the difference DLo 210' 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 Dep. 136. 4 log 2.13476 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. Example: A ship in the latitude of 38° sails due west a distance of 215.5 miles. Required the difference of longitude. By Computation. By Inspection. L 38° log sec 0.10347 Entering Table 2 with the latitude, 38°, as a course, Dep. 215. 5 log 2.33345 corresponding with the number 215.5 in column of Lat., is 273.5 in the column of Dist. This is therefore the y^j / 273'. 5 log 2.43692 required difference of longitude, being equal to 4° 33'. 5. JJ1.0 ^ 40 33/ 5 MIDDLE LATITUDE SAILING. 175. When a ship follows a course obliquely across the meridian the latitude is constantly changing, and the method of converting departure and difference of longitude T)y Parallel Sailing, just described, ceases to be applicable. In figure 25, T is the point of departure; T', the point of destination ; P, ? the earth's pole; TT', the rhumb tracrk; r^TT', the course; Tn, «iT', the respective parallels of latitude; and MM', the equator. The difference of longitude between T and T' is MPM', wliich may be measured by the arc of the equator, MM', intercepted between their meridians. This corresponds to a departure Tn in the latitude of T, and to the smaller departure T'rzi in the higher latitude of T'; but since the vessel neither makes all of the departure in the latitude T, nor all of it in the latitude T', the departure actually made in the passage must have some intermediate value between these extremes. Dividing the total difference of longitude into a number of equal parts MPwii, hjjPhIj, etc., of such small extent that, for the purposes of conversion, the change of latitude corresponding to each may be neglected, we have the total departure made up of the sum of a number of small departures, each equal to the same difference of longitude, but each different from the other. These will be c/j r^ in the latitude T, d^ r^ in the latitude ?•,, etc. Hence we have: „ ^_ MM'=d, r-i sec MT-|-f?2 ''21 sec m, rj + da r^, sec 7U2 r^, + etc. *-'• Now, if LL' be a parallel of latitude lying midwav between Tn and T'jij, since there will be as many of the small parts lying above as below it, and since for moderate distances the ratio to be employed in the conversion of departure and difference of longitude may be regarded as varying directly with the latitude, it maybe assumed for such distances that the sum of all of the different small departures equals the single departure between the meridians measured in the latitude LL', and therefore that the departure obtained by the method of plane sailing on any course may be converted into difference of longitude by multiplying by the secant of the Middle Latitude. The niethod 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 Sailing, having found the mean of the latitudes, the solution is identical with that of Parallel Sailing (art. 173), substituting the Middle Latitude for the single latitude therein employed. 177. It niay 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 separatelv. ] 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: Course SE. by S., Dist., 300, we find Lat., 249.4 S. (4° 09'.4), Dep., 166.7 E. Latitude left, 42° 30'.0 N. Latitude left, 42° 30' N. DL, 4 09 .4 S. Latitude arrived at, 38 21 N. Latitude arrived at, 38 20 .6 N. 2)80 51 Mid. latitude, 40 25 N. 54 THE SAILINGS. /^~V Enter Table 2 with the middle latitude, 40°, as a course; the difference of longitude (DLst. ) 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). ^ KjA Longitude left, 58° 51'.0 W. DLo, 3 39 .2 E. * Longitude arrived at, 55 11 .8 W. Example: A ship in I^t. 39° 42' S., Long. 3° 31' E., sails S. 42° W. tude and longitude arrived at. From Table 2: Course, S. 42° Latitude left, DL, 236 miles. Required the lati- ^ W., Dist., 236 miles; we find I^t., 175.4 S. (2° 55'.4), Dep., 157.9 W. 39° 42'.0 S. Latitude left, 39° 42' S. 2 55 .4 S. Latitude arrived at, 42 37 S. I^atitude arrived at, 42 37 .4 S. 2)82 19 Mid. latitude, 41 09 S. From Table 2: Mid. Lat.. (course), 41°, Dep. (Lat.), 157.9; we find DLo (Dist.), 209.3 (3= Longitude left, 3° 31'.0 E. • DLo, 3 29 .3 W. 29'.3). Longitude arrived at, 01 .7 E. Example: A vessel leaves Lat. 49° 57' N., Long. 15° 16' W., and arrives at T^at. 47° 18' N., Long. 20° 10' AV. 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. l^L, {^°159'}S- ^'^' ■ {%S'K 2)97° 15' N. Mid. latitude, 48 38 N. From Table 2: Mid. Lat. (course), 49°, DLo (Dist.), 294; we find Dep. (Lat.), 192.9. From Table 2: DL 159 S., Dep. 192.9 W., we find course S. 51° W., Dist., 251 miles. 17§. The assumption upon which Middle Latitude sailing is based — that the conversion may be made as if the whole distance were sailed upon a parallel midway between the latitudes of departure and destination — while sufficiently accurate for moderate distances, may be materially in error where the distances are large. In such case, either the method of Mercator Sailing (art. 179) must be employed, or else the correction given in the following table should be applied to the mean latitude to obtain what may be termed the latitude of conversion, being that latitude in which the required conditions are accurately fulfilled. The table is computed from the formula: cos Lc=— , ■m where Lc represents the latitude of conversion, and / and m are respectively the differences of latitude and of meridional parts (art. 39, Chap. II) between the latitudes of departure and destination. « Mid. Lat. Difference of latitude. Mid. Lat. 1° 2° 3° 4° 6° 6° 7° 8° 9° 10° 12° 14° 16° 18° 20° o 15 18 21 / -86 -67 -54 -85 -67 -54 / -84 -66 -53 -44 -29 -21 -15 -11 - 7 / -83 -65 -52 -42 -29 -21 -14 -10 - 6 - 3 - 1 - 1 1 2 / -81 -63 -51 / -79 -61 -49 / -76 -59 -47 -38 -24 -17 -73 -56 -44 -.36 -23 -15 / -69 -53 -42 -33 -20 -12 / -65 -50 -39 -56 -43 -32 / -46 -34 -24 / -34 -23 -15 / -21 -12 - 5 1 11 18 ' - 6 1 7 o 15 18 21 24 30 35 24 30 35 -44 1 —44 -31 -30 -23 -22 -41 -28 -19 -13 - 8 - 5 -40 -26 -18 -12 - 7 - 3 2 3 4 5 6 -31 1 -24 -18 -12 -10 - 5 -17 - 6 2 8 14 20 - 8 1 10 T6 22 28 12 21 28 ■ 40 45 50 -17 -12 - 8 - 5 - 4 - 3 -16 -10 - 5 - 1 2 4 5 7 8 9 - 8 - 3 1 - 6 - 1 3 - 4 1 6 10 13 14 17 18 20 2 7 12 25 31 38 34 41 49 40 45 50 55 58 60 - 5 - 3 - 3 - 4 -3 - 2 — 2 1 2 3 4 5 7 8 9 11 12 7 10 11 13 14 16 17 20 22 25 29 32 35 39 43 46 51 55 60 65 71 58 64 69 55 58 60 62 64 66 - 3 - 2 - 1 - 2 - 1 -2-1' 25 27 30 35 38 42 46 50 55 75 81 89 62 64 66 68 70 72 - 1: 0; 1 -1 0: 1 2 2 3 4 5 5 7 8 10 10 12 13 14 16 18 18 20 23 22 25 ?8 33 37 41 46 51 57 61 67 76 78 87 97 98 109 123 68 70 72 a The statement often made, that the latitude of conversion is always greater than the middle latitude, is not correct when the compression of the earth is taken into account, as an inspection of the table will show; that statement is based upon an assumption that the earth is a perfect sphere, and it was iipon 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 - . THE SAILINGS. 55 Example: A vessel sails from Lat. 10° 13' S. to Lut. 20° 2K S., making a departure of 432 miles. 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°, ('orrection, —65' Mid. latitude. Correction, 15 17 S. - 1 05 14° 12' 432 445'. 6 log sec log log Lc, 14''-12 S. L<, Dep. DLo .01348 2.63548 2.64896 MERCATOR SAILING. 1 79. Mercator Sailing is the method by which values of the various elements are determined from <'onsidering them in the relation in which they are .plotted upon a chart constucted according to the Mercator projection. 180. Upon the Mercator chart (art. 38, Chap. II), the meridians being parallel, the arc of a par- allel of latitude is shown as equal to the corresponding arc of the equator; the length of every such arc is, therefore, expanded; and, in order that the rhumb line may appear as a straight line, the merid- ians are also expanded by such amount as is necessary to preserve, in any latitude, the proper propor- tion existing between a unit of latitude and a unit of longitude. The lengths of small portions of the meridian thus increased are called meridional parts (art. 39, Chap. II), and these, computed for every minute of latitude from 0° to 80°, form the Table of Meridional Parts (Table 3), by means of which a INIercator chart may be constructed and all problems of Mercator Sailing may be solved. In the triangle ABC (fig. 26), the angle ACB is the course, C; the side AC, the b distance, Dist. ; the side BC, the difference of latitude, DL; and the side AB, the departure, Dep. Then corresponding to the difference of latitude BC in the lati- tude under consideration, if CE be laid off to represent the meridional difference of latitude, in, completing the right triangle CEF, EF will represent the differ- ence of longitude, DLo. The triangle ABC gives the relations involved in Plane dl Sailing as previously described; the triangle CEF affords the means for the con- version of departure and difference of longitude by Mercator Sailing. 181. To find the arc of the expanded meridian 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 different sides of the equator, the sum of the meridional parts will be the meridional difference of latitude. 1§2. To solve the triangle CEF by the traverse tajbles it is only necessary to substitute merid- ional difference for Lat., and difference of longitude for Dep. Where long distances are involved, <-arrying the computation beyond the limits of the traverse table, as frequently occurs in this method, either of two means may be adopted : the problems may be worked by the trigonometrical formulae, using logarithms, or the given quantities involved may all be reduced b}' 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 various conversions are as follows: tan C=5^; DLo=m tan C; r/i=DLo cot C. Example: A ship in Lat. 42° 3(' N., Long. 58° 51' W., sails SE. by S., 300 miles, latitude and longitude arrived at. From Table 1: Course, SE. by S., Dist, 300; we find Lat. 249.4 S. (4° 09/4). Latitude left, 42° 30'. N. Merid. parts, +2806.4 DL, 4 09 .4 S. Required the Latitude arrived at, 38 20 .6 N. Merid. parts, m, 2480.4 DLo By Computation. 326.0 log 33° 45' ; 217'.8 \3° 37'. 8 2.51322 og tan 9.82489 log 2.33811 326.0 By Inspection. Enter Table 1, course 3 points; since the quantities involved exceed the limits of the table, divide by 2; abreast '|(Lat.), 163.0, find g— (Dep.), 108.9; hence DLo=217'.8 or 3° 37'.8. Longitude left, DLo, 58° 51'.0 W, 3 37 .8 E. Longitude arrived at, 55 13 .2 W. 56 THE SAILINGS. Example: A ship in Lat. 4° 37' S., Ix)ng. 21° 05' W., sails N. 14° W., 450 miles. Required th« latitude and longitude arrived at. From Table 2: Course, (N.) 14° (W.), Dist., 450; we find Lat. 436.6 N. (7° 16'.6). Latitude left, 4° 37'.0 S. i)L, 7 16 .6 N. Merid. parts, -f 275.4 Latitude arrived at, 2 39 .6 N. Merid. parts, -f 159.0 m, 434.4 tation. By Inspection. DLo 434.4 14' log 2.63789 From Table 2: Course, 14°, m (Lat.), 434.4, we tind log tan 9.39677 DLo (Dep. ) 108'. 3 W., or 1° 48'. 3. {v 108'. 3 ' 48'. 3 log 2.03466 Longitude left, DLo, 21° 05'.0 W. 1 48 .3 W. Longitude arrived at, 22 53 .3 W. Example: Required the course and distance by rhumb line from a jwint 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. Lat. destination, 36 59 N. DL Merid. pts., -f 2770.1 Merid. pts., —2377.3 Long, departure, 70° 04' W. Long, destination, 25 10 W. / 5° 04'1 g \ 304'/^- DLo 2694 m 392.8 (E.) m, 392.8 log 3.43040 log 2.59417 DLo C (S.) 81° 42' DL 304' log tan .83623 log sec .84056 log 2.48287 /44° 54'\t \ 2694'/^ Dist. 2106 log 3.32343 The course is therefore S. 81° 42' E., and the distance is 2,106 miles. Since the figures involved are so large, it is best to employ only the method by computation. The formula by which the Dist. is obtained comes from Plane Sailing. GREAT CIRCLE SAILING. 1§3. The shortest distance 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 denominated (ireat 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 navigation or extreme cold which it is expe- dient to avoid; in such a case a certain parallel should be fixed upon as a limit of latitude, and a route laid down such that a great circle is followed as far as the limiting parallel, then the parallel itself, and finally another great circle to the port of destination. Such a modification of the great circle method is called Composite Sailing. 1§5. The rhiuah line (art. 6, Chap. I) also called the loxodromic curve, which cuts all the meridi- ans 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 i)oints, intelligent navigators of the jiresent 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 hue on the Mercator chart the vessel never heads for her port until at the very end of the voyage. 186. The method of great circle sailing is of especial value to steamers, as such vessels need not, in the choice of a route, have regard for the winds to the same extent as must a sailing vessel ; but even in navigating vessels under sail a knowledge of the great circle cour.se may proveof great value. For example, suppose a ship to be bound from Sydney to Valparaiso; the first great circle course is SE. by S., while the Mercator course is almost due east. The distance is 748 miles shorter by the former route (if the THE SAILINGS. 57 p;reat circle is followed throughout, though this would lead to a latitude of 61° S.). With the wind at E. J S. the ship would lie 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 45 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 9i miles out of every 10. Any course between East and SSW. would be better than the Mercator course; and if the wind were anything to the eastward of SE. by S., the ship would gain by taking the port tack in preference to the starboard. 1§7. As the great circle makes a different angle with each meridian that is crossed, it becomes necessary to make frequent changes of the ship's course; in practice, the course is a series of chords joining the various points on the track line. If, while endeavoring to follow a great circle, the ship is driven from it, as by unfavorable weather, it will not serve the purpose to return to the old track at convenience, but it is required that another great circle l)e laid down, joining the actual position in which the ship finds herself with the port of destination. 1§S. The methods of determining the great circle course may be divided generally into four classes; namely, by Great Circle Hailiny Charts, by Computation, by the methods of the Time Azimuth, and by Graphic Approximations. 1 89. Great Circle Sailing Charts. — Of the available methods, that by means 'of charts espe- cially constructed for the purpose is considered greatly superior to all others. A series of great circle .sailing charts covering the navigable waters of the globe is published by the United States Hydrographic Office. Being on the gnoinonic projection (art. 43, Chap. II), all great circles are represented as straight lines, and it is only necessary to join any two points by such a line to represent the great circle track between them. The courses and distance are readily obtainable by a method explained on the charts. The track may be transferred to a chart on the 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 greatest convenience to be pro- vided with these gnomonic charts for the regions which his vessel is to traverse. 190. By CoMPiTATiON. — This method consists in de- termining a series of points on the great circle by their coordinates of latitude and longitude, plotting them upon a Mercator chart, and tracing the curve that joins them. The first point determined is the vertex, or point of highest latitude, even when, as sometimes occurs, it falls without that portion of the great circle which joins the points of departure and destination. Fig. 27. In figure 27, A represents the point of departure; B, the point of destination; AV'B, the great circle joining them, with its vertex at V; and P, the pole of tlie earth. Let Ca = PAB, the initial course; Cb = PBA, the final courser La , Lv, Lb = the latitudesof the respective points A, V, B = (90° — PA), (90° — PV), (90° - PB). Loab, Loav, 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 q> — an auxiliary angle introduced for the computation. We then have: tan cp — cos Loab cot Lb; cot Ca = cot Loab cos (La + f the celestial sphere vertically overhead. The Nadir is the point vertically beneath. 213. The Celestial Horizon is the great circle of the celestial sphere formed by passing a plane through the center of the earth at right angles to the line which joins that point with the zenith of the observer. The celestial horizon differs somewhat from the Visible Horizon, which is that line appearing to an observer at sea to mark the intersection of earth and sky. This difference arises from two causes: first, the eye of the observer is always elevated above the sea level, thus permitting him a range of vision exceeding 90° from the zenith; and second, the observer's position is on the surface, instead of at the center of the earth. These causes give rise, respec- tively, to dip of the horizon and parallax, which will be explained later (Chap. X). 214. In figure 28 the celestial sphere is considered to be projected upon the celestial horizon, represented by NESW. ; the zenith of the observer is projected at Z, and that pole of the earth which is elevated above the horizon, assumed for illustration to be the north pole, appears at P, the Elevated Pole of the celestial sphere. The other pole is not shown in.the figure. 215. The Equinoctial, or Celestial Equator, is the great circle formed by extending the plane of the earth's equator until it intersects the celestial sphere. It is shown in the figure in the line EQW. The equi- noctial intersects the horizon in E and W, its east and west points. 216. Hour Circles, Declination Circles, or Celestial Meridians are great circles of the celestial sphere passing through the poles; they are therefore secondary to the equinoctial, and may be formed by extending the planes of the respective terrestrial meridians until they intersect the celestial sphere. In the figure, PW, PS, PE, are hour circles, and that one, PS, which contains the zenith and is therefore formed by the extension of the terrestrial meridian of the observer, intersects the horizon in N and S, its north and south points. 217. Vertical Circles, or Circles of Altitude, are great circles of the celestial sphere which pass through the zenith and nadir; they are therefore secondary to the horizon. In the figure, ZH, WZE, NZS, are projections of such circles; the vertical circle NZS, which passes through the poles, coincides with the Fig 64 DEFINITIONS RELATING TO NAUTICAL ASTRONOMY. meridian of the observer. The vertical cintle WZE, whose plane is at right angles to that of the merid- ian, intersects the horizon in its eastern and western points, and, iheretV)re, at the points of intersection of the equinoctial; this circle ia distinguished as the Prime Vertk-al. 21 S. The Declination of any point in the celestial sphere is its angular distance from the equinoctial, measiured upon the hour or declination circle which passes through that jxtint; it is designated as North cr South according to the direction of the point from the equinoctial; it is customary to regard north declinations as positive (~r ), and south declinations as negative ( ~ ). In the figure, DM is the declina- tion of the point M. Declination upon the celestial sphere corresponds with latitude upon the earth. 219. The Polar Distance of any point is its angular distance from the jjole (generally, the elevated pole of an observer), measured upon the hour or declination circle passing through the point; it must therefore equal 90° minus the declination, if measured from the pole of the same name as the declina- tion, or 90° pins the declination, if measured from the pole of opposite name. The polar distance of the point M from the elevated. pole, P, is PM. 220. The Altitude of any point in the celestal sphere is its angular distance from the horizon, measured upon the vertical circle passing through the point; it is regarded as positive when the body is on the same side of the horizon as the zenith The altitude of the point ]\I is HM. 5-21. The ZenitJi Distance of any ])oint is its angular distance from the zenith, measured upon the vertical circle passing through the ]>oint; the zenith distance of any point which is above the horizon of an observer must therefore equal 90° )nimis the altitude. The zenith distance of M, in the figure, is ZM. 222. The Hour Angle of any point is the angle at the pole between the 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 tuward 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 C^PD, or the arc QD. 223. The Azimuth of a point in the celestial sphere is the angle at the zenith between the meridian of the observer and the vertical circle passing through the point; it may also be regarded as the arc of the horizon intercepted between those circles. It is measured from either the north or the south point of the horizon (usually that one of the same name as the elevated pole) to the east or west through 180°, and is named accordingly; as, N. 60° W., or S. 120° W. The azimuth of M is the angle NZH, or the arc NH, from the north point, or the angle SZH, or the arc SH, from the south point of the horizon. 224. The Amplitude of a point is the angle at the zenith between the prime vertical and the vertical circle of the point; it is measured from the east or the west jioint 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, by reason of the annual revo- lution of the earth, the sun appears to move in the celestial sphere; the plane of the ecliptic is inclined U) that of the equinoctial at an angle of 23° 21 Y, and this inclination is called the obliquity of the ecliptic. The ecliptic is represented by the great circle CVT. 226. The Equinoxes are those points at which the ecliptic and the equinoctial intersect, and when the sun occupies either of these positions the days and nights are of equal length throughout the earth. The Vernal Equinox is that one at which the sun appears to an observer on the earth when passing from southern to northern declination, and the Aidumnal Equinox that one at which it appears when passing from northern to southern declination. The Vernal Equinox is also designated as the Ftrst Point of Aries, and is used as an origin for reckoning right ascension; it is indicated in the figure 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 attaiiis its highest declination in each hemisphere. They are called respectively the Summer and the Winter Solstice, according to the season in whicn the sun appears to pass these points in its path. 22S. The Right Ascension of a point is the angle at the pole between the hour circle of the point and that of the First Point of Aries; it may also be regarded as the arc of the equinoctial intercepted between those circles. It is measured from the First Point of Aries to the eastward as a positive direction, through twenty-four hours or 360 degrees. The right ascension of the point M is 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 jwint 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 l)lanes by which it is thus referred are called coordinates. 231. In figure 29 is shown a system of rectilinear coordinates for a plane. A fixed line FE U chosen, and in it a definite point C, as the origin. Then the position of a point A is defined by CB = x, the distance from the origin, C, to the foot of a perpendicular let ■ fall from A on FE; and by AB = y, the length of the perpendicular. The distance x is called the abscissa and y the ordinate. Assuming two intersecting right lines FE and HI as standard lines of refer- ence, the location of the point A is defined by regarding the dis- FiG. 29. tances measured to the right hand of HI and above FE af> 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. DEFINITIONS RELATING TO NAUTICA-L ASTEONOMY. 65 332. The great circle is to the sphere wliat tlie straight line is to the i)lane; hence, in order to define the position of a point on the surface of a sphere, some great circle must be selected as the primary, and some particular point of it as the origin. Thus, in figure 30, which represents the case of a sphere, some fixed great circle, CBQ, is selected as the axis and called the primary; and a point C is chosen as the origin. Then to define the pos-ition of any point A, the abscissa x equals the distance from C to the point B, where the secondary great circle through A intersects the primary; the ordinate y equals the distance of A from the primary measured on the secondary — that is, x — C-B and // = AB. 233. In the case of the earth, the primary selected is the equator (its ])lane being j)erpendicular to the earth's axis), and upon this are measured the abscissa', while upon the secondaries to it are measured the ordinates of all points on the earth's surface. The initial point for reference on the equator is determined by the prime meridian chosen, West longitudes and North latitudes being called positive, East longitudes and South latitudes, negativt'. 234. In the case of the celestial si)here, there are four systems of coor- dinates in use for defining the position of any point; these vary according to the circle adopted as the primary and the point used as an origin. They are as follows: 1. Altitude and azimuth. 2. Declination and hour angle. 3. Declination and right ascension. 4. Celestial latitude and longitude. 235. In the system of Altitude and Azimuth, the primary circle is the celestial horizon, the seconda- ries to which are the vertical circles, or circles of altitude. The horizon is intersected by the celestial meridian in its northern and southern points, of which one — usually that adjacent to the elevated pole — is selected as an origin for reckoning coordinates. The azimuth indicates in Avhich vertical circle the point to be defined is found, and the altitude gives the position of the point in that circle. In figure 28 the point M is located, according to this system, by its azimuth NH and altitude HM. 236. In the system of Dedination and Hour Angle, the primary circle is the equinoctial, the seconda- ries to which are the circles of declination, or hour circles. The pcjint of origin is that poiht of inter- section of the equinoctial and celestial meridian which is above the horizon. The hour angle indicates in which declination circle the point to be defined is found, and the declination gives the position of the point in that circle. In figure 28 the point M is located, according to this system, by its hour angle QD and declination DM. 237. Inthe system of Dedination and Right Ascension, the primary and secondaries are the same as in the system just described, but the point of origin differs, being assumed to be at the First Point of Aries, or vernal equinox. The right ascension indicates in which declination circle the point to be defined may be found, and the declination gives the position in that circle. In figure 28 the point M is located by YD, the right ascension, and DM, the declination. 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. 23§. 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 appeaj from the definitions of celestial latitude and longitude already given (art. 229). 22489—03 5 66 INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY. CHAPTER VIII. INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY. THE SEXTANT. 239. The sextant if? an instrument fur measuring the angle between two o))jeets by Itringing into coincidence at the eye of the observer rays of light received directly from the one and by reflection from the other, the measure being afforded by the inclination t)f the reflecting surfaces. By reason of its small dimensions, its accuracy, and, above all, the fact that it does not recjuire a permanent or a stable mounting but is available for u.se 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 31. The frame is of brass or some similar alloy. The graduated arc, AA, generally of silver, is marked in approi)riate divisions; in the finer sextants, each divir sion represents 10^, and the vernier affords a means of reading to 10^'. A wooden handle, H, is provided for holding the instrument. The index mirror, 31, and horizon mirror, 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 through unobstructed. To give greater distinctness to the images, a small telescope, E, is placed in the line of sight; it is supported in a ring, K, which can he moved by a screw in a direction at right angles to the plane of the sex- tant, thus shifting the axis of the telescope, and therefore the plane of reflection; this plane, however, always remains par- allel to that of the instrument, the motion of the telescope being intended merely to regu- late the relative brightness of the direct and reflected images. In the ring K are small screws for the purpose tif adjusting the tele- scope by making its axis parallel with the plane of the sextant. The vernier is carried on the end of an index bar pivotee adjusted. At I' and Q are colored glasses of different shades, which may be used separately or in comlMnation to protect tlie eye from th 3 intense light of the sun. In order to observe with accuracy and make the images come i)recisely in contact, a tanijent-screir, B, is fixed to the index, by means of which the latter may be moved with great;-r ))recision 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 its 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 the colored shades, Pand Q, and elimina- ting any possible errors which might arise from nonparallelism of their surfaces. 341. The rerm«r is an attachment for facilitating the exact reading of the scale of a sextant, by which aliquot parts of the smallest divisions of the graduated scale are measured. The principle of the sextant vernier is identical with that of the barometer vernier, a complete description of which will be found in article 51, Chapter II. The arc of a sextant is usually divided into 120 or more parts, each INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY. 67 division representing 1°; each of these degree divisions is further subdivided to an extent dependent upon the accuracy of reading of which the sextant is capable. In the instruments for 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 ICK'; 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 divi.sion next below, or to the right of, the zero of the vernier, and to add thereto the angle corresponding to that division of the vernier scale which is meet nearly in exact coincidence with a division of the instrument scale. 242. Optical Principle. — When a ray of light is reflected from a plane surface, the angle of inci- dence is equal to the angle of reflection. From this it ^^ may be proved that when a ray of light undergoes two reflections, in the same plane the angle between its first and its last direction is equal to twice the inclina- tion of the i-eflecting surfaces. Upon this fact the con- struction of the sextant is based. In figure 32 let B and C represent respectively the index mirror and horizon mirror of a sextant; draw EF perpendicular to B, and CF perpendicular to C; then the angle CFB represents the inclination of the two mirrors. Suppose a ray to proceed from A and undergo reflection at B and at C, its last direction I leing CD; then ADC is the angle between its first and last directions, and we desire to prove that ADC = 2 CFB. From the eciuality of the angles of incidence and ^m 3'> 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 pro'^ed. 24;?. In the sextant, since the index mirror is immovably attached to L.ie index arm, which also carries the vernier, it follows that no change can occur in the inclination between the index mirror and the horizon mirror, excepting such as is registered l)y the travel of the vernier upon the scale. If, when the index mirror is so placed that it is nearly parallel with the horizon mirror, an observer direct the telescope toward some well-defined object, there will be seen in the field of view two separate images of the object; and if the inclination of the index mirror be slightly changed bv moviug 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 part of the horizon glass, while the movable image is due to rays reflected by the index and horizon mirrors. When the two images coincide these mirrors m^^t be parallel (assuming that the object is sufficiently distant to disregard the space which separates the mir- rors) ; in this position of the index mirror the vernier indicates the true zero of the scale. If, however, instead of observing a single object, the instrument is so placed that the direct ray from one object appears in coin<'idence 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 anple directly. 244. AD.irsTMENTS OF THE Sextaxt. — The theory of the sextant requires that, for accurate indi- cations, the following conditions be fulfilled: (o) The two surfaces of each mirror and shade glass must be parallel plants. {h) The graduated arc or limb must be a plane, and it:; 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 gla.sses 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 perrnaueiit adjvstinenl.^, should be made before the instrument leaves the hands of the maker, and with careful use will never be dranged. 245. The Adjustmi'iit of the Index Mirror consists in making the reflecting surface of tiiis mirror truly perpendicular to the jtlane of the sextant. In onltr to test this, set the index iv ar 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 Adjmtment of the Horizon Mirror consists in making the reflecting surface of this i.iirror gerpendicular to the plane of the sextant. The index mirror having been adjusted, if, in revolving it y means of the index arm, there is found one position in which it is parallel to the horizon glass, then the latter must also be perpendicular to the plane of the sextant. In order to test this, put in the tele- scope and direct it toward a star; move the index until the reflected image appears to pass the direct image; if one ymsses directly over the other the mirrors must be parallel; if one passes on either side of the other the horizon glass needs adjustment, which is accomplished by means of the screws attached. 68 INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY. The sea horizon may also be used for making this adjustment. Hold the sextant vertically and bring the direct and the reflected images of the horizon line into coincidence; then incline the sextant until its plane makes l)ut a small angle with the horizon; if the images still coincide the glasses are parallel; if not, the horizon glass needs adjustment. 247. The Adjustineiit of the Telescope must be so made that, in measuring angular distances, the line of sight, or axis oit th« 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 tele.scope is employed irv which are placed two wires, ])arallel to each other and equidistant from the center of the telescope; by means of these wires the adjuMtment may be made. Screw on the telescope, and turn the tube containing the eyeglass till the wires are parallel to the plane of tlie instrument; then select two dearly-defined objects whose angular distance must be not less than 90°, because an error is more easily discovered when the distance is great; bring the reflected image of one object into exact eoincideuce with the direct image of the other at the inner wire; then, by altering slightly the ])osition of the instru- ment, make the objects appear on the other wire; if the contact still remains perfect, the axis of the telescope is in its right situation; but if the two objects aj)pear 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 adjustinent is to place the sextant upon a tal>le 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 av ^A object above that plane. If, then, SA is a direct ray from the object N. / parallel t~) S'B, an observer at A can measure with the sextant the . \^ / angle 8A8''= S'BS''= 2 S'BM, by bringing the image cf the object N. / reflected by the index mirror into coincidence with the image S'' \^^ / reflected by the mercury and seen through the horizon glass. The \/ instrumental measure, corrected for index error, will be double the /» apparent altitude of the body. / The sun's altitude will be measured by bringing the lower limb / of one image to touch the upper liml) of "the other. Half the cor- / reefed instrumental reading will l)e the apparent altitude of the ^./ sun's loirer or upper limb, according as the lower or upper limb of Pj^, .>.> the reflected image was the one employed in the observation. In observations of the sun with the artificial horizon, the eye is protected by a single dark glass over the eyepiece of the telescope through which direct and reflected rays must pass alike, thereby avoiding the errors that might 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 parallel faces. If they are at all prismatic, the ol)served altitude will l)e erroneous. The error may be removed by observing a second altitude with the roof reversed, and, in general, by taking one halfVjf a set of obser- vations with the roof in one ])osition and the other half with the roof reversed. On the rare occasions when the atmosphere is so calm that the unsheltered mercury Mill remain undisturbed, most satisfac- tory observations may be made by leaving off the roof. 257. In setting up an artificial horizon, care should be taken that the basin is free from dust and other foreign matter, as small particles floating upon the surface of the mercury interfere with a perfect reflection. The basin should be so i)laced 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 lie as free as possible from causes which will produce vibration of the mercury, and precautions should be taken to shelter the horizon from the wind, as the mere placing of the roof will not ordinarily be suf- ficient to accomplish this. Embedding the roof in earth serves to keep out the wind, while setting the whole horizon upon a thick towel or a piece of such material as heavy felt usually affords ample protec- tion from wind, tends to reduce the vibrations from mechanical shoc^ks, and also aids in keeping out the moisture from the ground. In damp climates the roof should lie kept dry by wiping, or the moisture deposited from the inclosed air will form a cloud upon the glass. Molasses, oil, or other viscous fluid may, when necessary, be employed a.s a substitute for mercury. INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY. 71 iiJ.jS. 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 main-spring 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 may not be deranged by the motion of the ship in a seaway, the instrument is carried in gimbals. As the regularity of the chronometer is essential for the correct determination of a ship's position, it is of the greatest importance that every precaution 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 — in order that if an irregularity develop in one, the fact may be revealed V)y the others. 260. Care of Chronometers ox Shipboard. — The box in which the chronometers are kept should have a permanent place as near as practicable to the center of motion of the ship, and where it will be free from excessive shocks and jars, such as thos^e 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 compart- ment for each clironometer, and each compartment should be lined with baize cloth padded with curled hair, for the double purpose of reducing shocks and ecpializing the temperature within. An outer cover of l^aize cloth should be provided for the lx)x, and this should be changed or dried out frequently in damp weather. The chronometers should all be placed with the XII mark in the same position. For transportation for short distances by hand, an instrument should he 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 l)y express, the chronometer should l)e allowed to run down, and should then be dismounted and tlie balance corked. 2611. Since it is not possible to make a perfect in.strument which will be uninfluenced by the dis- turbing causes incident to a sea voyage, it becomes the duty of the navigator to determine the error and to keep watch upon the variable rate of the chronometer. The error of tlte dtronometer .i>i t\w difference l)etween the time indicated and the standard time to which it is referred — usually (ireonwich mean time. The amount the chronometer gai)!.^ or loses daily is the daih/ rate. 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. —Chronometers are ordinarily constructed to run for 56 hours without rew inding, and an indicator on the face always shows how many hours have elapsed since the last winding. To insure a uniiorm rate, they mr.st l)e wound regularly every day, and, in order to avoid the serious conse- quences of their running down, the navigator shoultl take some means to guard against neglecting this duty thnnigh a fault of memory. To wind, turn the clironometer gently on its sicle, enter the key in its hole and ])ush it home, steadying the instrument with the hand, and wind t(j 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 t(^ its natural position. Chronometers should always be wound in the same order tofirevent omissions, and the jn-ecaution taken to insjiect the indicators, as a further assurance of the proper performance of the oj)eralion. After winding each day, the comparisons should Ix; made, and, with the readings of the maximum- and-mininunn thermometer and other necessary data, recorded in a book kept for the purpose. The maximum-and-mininuuu thermometer is one so arranged that its highest and lowest readings are marked by small steel indices that remain in ]>lace imtil 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 tiie 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 designate the Standard as A, and the others as B, C, etc. Chronometers a-e made to beat half-seconds, and any two may be compared by following the beat of one with the ear and of the other with the eye. To make a comparison, say of A and B, open the boxes of these two instruments and close all others. Cret the cadence and, commencing when A has just completed the beat of some even 5-second division of the dial, count "half-one-half-two-half-three-half-four-half-five," glancing at B in time to note the position of its second-hand at the last count; the seconds indicated by A will be five greater than the number 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 from 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. 72 INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY. 364. The following form represents a convenient method of recording comparisons: Stand. A, No. 777. Chro. B, No. 1509. Ghro. C, No. 1802, Date, 1903. Designation of comparisvis. Chro. B Chro. C with Stand. A. 2ddifl. Therm. Bar. Remarks. Stand. A. ! Max. Mln. Air. Jan'uary 1 Stand. A. B and C. Difference. h. m. s. 1 13 40 1 12 21.5 s. h. m. s. 1 14 20 2 04 11 «. 63 o 59 o 60 // 30.07 Fomid errors by t i m e - ball. 1 18^5 11 10 09 2 Stand. A. B and C. Difference. 1 16 30 1 15 10 + 1.5 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. 5 265. The second difference in the form is the difference between the comparisons of the same instruments for two successive days. When a vessel is equipped with only one chronometer there is nothing to indicate any irregularity that it may develop at sea — and even the best instruments may undergo changes from no apparent cause. When there are two chronometers, the second difference, which is equal to the algebraic difference between their daily rates, remains 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 chro- nometers, an irregularity on the part of one is at once located by a comparison of the second differ- ences. Thus, if the predicted rates of the chronometers were such as to give for the second difference of A — B, + 1'.5, and of A — C, —0^.5, suppose on a certain day those differences were -;-4*.5 and — 0'.5, respectively; it would at once be suspected that the irregularity was in B, and that that chronometer had lost 3* on its normal rate during the preceding day. Suppose, however, the second differences were -f 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 all chronometers vary somewhat with the temperature. Where the voyage of a vessel is a long one and marked changes of climate are encoun- tered, the accumulated error from the use of an incorrect rate may be very material, amounting to sev- eral minutes' difference of longitude. Careful navigators will therefore take every means to guard against such an error. By the employment of a temperature curve in connection with the chronometer rate the most satisfactory results are arrived at. 267. There should be furnished with each chronometer a statement showing its daily rate under various conditions of temperature; and this may be supplemented by the observations of the navigator during the time that the chronometer remains on board ship. AVith all available data a temperature curve should be constructed which will indicate graphically the performance of the instrument. It is most convenient to employ for this purpose a piece of "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 tem- perature, numbered at the left edge, from the bottom up; draw a vertical line in red ink to represent the zero rate, and let all rates to the right be plus, or gaining, and those to the left minus, or losing; let the intervals between vertical lines represent intervals of rate (as one-tenth of a second) numbered at the top from the zero rate; then on this scale plot the rate corresponding to each temperature; when there are several observations covering one height of the thermometer, the mean may be used. Through all the plotted points draw a fair curve, and the intersection of this curve with each tempera- ture line gives the mean rate at that temperature. The mean temperature given by the maximum and minimum thermometer shows the rate to be used on any day. 26§. Hack or Comparing Watch. — In order to avoid derangement, the chronometers should never be removed from the permanent box in which they are kept on shipboard. When it is desired to mark a certain instant of time, as for an astronomical observation or for obtaining the chronometer error by signal, the time is marked by a "hack " (an inferior chronometer used for this purpose only), or by a comparing watch. Careful comparisons are taken — preferably both before and afterwards — and the chronometer time at the required instant is thus deduced. The correction represented by the chro- nometer time minus the watch time (twelve hours being added to the former when necessary to make the subtraction possible) is referred to as C — W. Suppose, for example, the chronometer and watch are compared and their indications are as follows: Chro. t., 5''27'"30» W. T., -2 36 45.5 C-W, 2 50 44.5 If then a sight is tak«n when the watch shows 3'' 01"' 27.* 5, we have: W. T., 3" 01" 27^5 C-W, +2 50 44.5 Chrn.t., 5 52 12.0 INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY. 73 It may occur that the values of C — W, as obtained from comparisons before and after marking the desired time, will vary; in that case the value to be used will be the mean of the two, if the time marked is about midway between comparisons, but if much nearer to one comparison than the other, allowance should be made accordingly. Thus suppose, in the case previously given, a second comparison had been taken after the sight as follows: Chro. t, 6M2»'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 only about one-third of the interval had elapsed between the first and second comparisons, it would be assumed that only 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 subtractive; it may sometimes occur that a few figures will thus be saved, but a chance for error arises from the possibilitj' of inadvertently using the wrong sign, which is almost impossible by the other method. Thus, the following example may be taken: rC, 10* 57'" 38' W, U"* 42" 35» Comparison Sight |W, -11 42 35 C, -10 57 38 [C-W, 11 15 03 W-C, 44 57 f\V, 11 50 21 W, 11 50 21 I C-W, +11 15 03 W-C- 44 57 [C, 11 05 24 C, n 05 24 74 TIME AND THE NAUTICAL ALMANAC. CHAPTER IX. TIME AND THE NAUTICAL ALMANAC. 270. The subjects of Tinu aiieration for the astronomical determination of a ship's position. They will be treated in conjunction, as the two are interdependent. METHODS OF RECKONING TIME. 271. The instant at which any point of the celestial sphere is on the meridian of an observer is termed the tramit, cubni)iation, or meridian passaye of that point; when on that half of the me.idian which contains the zenith, it is designated as superior or tipper transit; when on the half containing the nadir, as inferior or lotcer transit. 272. Three different kinds of time are employed in astronomy — (a) apparent or mhn- time, [h] mean time, and (e) sidereal time. These depend ujwn the hour angle from the meridian of the points to which they respectively refer. The point of reference for apparent or solar time is the Center of the >Sun; for mean time, an imaginary point called the Mean Sun; and for sidereal time, the Vernal 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; these into (50 equal parts, called Minutes, and these into 60 equal parts, called Seconds. 273. Apparent or Solar Time. — The hour angle of the center of the sun affords a measure of Apparent or Solar Time. An Apjiarcnt or Sular Jkni is the interval of time between two successive transits over the same meridian of the center of the sun. It is Ajyparent Noou when the suti's hour circle coin- cides 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 the latitude can be most readily determined, and the ordinary method of determining the longitude by the sun involves a calculation to deduce the apparent time first. Since, however, the intervals between the successive leturns 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: fii-st, 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 sinnetimes an arc of hV in a day. At the points where the ecliptic and equinoctial intersect, the direction of the sun's ajyparent motion is inclined at an angle of 23° 27' to the equator, while at the solstices it moves in a direction parallel to the equator. 274. Mean Time. — To avoid the irregularity of time caused by the want of uniformity in the sun's motion, a fictitious sun, called the Mean Sun, is supposed to move in the equinoctial with a imiform 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 Ihuj is the interval between two successive transits of the mean sun over the meridian. Mean Noon is the instant when the mean sun's hour circle coincides with the meridian. Mean time lapses uniformly; at certain times it agrees with apparent time, while sometimes it is behind, and at other times in advance of it. It is this time that is measured by the clocks in ordinary use, and to this the chronometers used by navigators are regulated. 275. The difference between apparent and mean time is called the Equation of Time; l)y 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. 270. Sidereal Ti.me. — Sidereal Time is the hour angle of the First Point of Aries. This point, which is identical with the vernal equinox, is the origin of all coordinates of right ascension. Since the position of the point is fixed in the celestial si)here and does not, like the sun, moon, and planets, have actual or apparent motion therein, it shares in this re.spect the i)roperties of the fixed stars. It may therefore be said that intervals of sidereal time are those which are measured by the stars. A Sideretd Day is the interval between two successive transits of the First Point of Aries across the same meridian. Sidereal Xoon 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 A.^cension of the Mean Sun. 277. Civil and Astronomical Ti.me. — The Civil Day commences at midnight and comprises the twenty-four hours until the following midnight. The hours are counted from to 12, from midnight to noon; then, again, from to 12, from noon to midnight. Thus the civil day is divided into two periods of twelve hours each, the first of which is marked a. m. (ante meridian), while the last is marked p. m. (post meridian) . TIME AND THE NAUTICAL ALMANAC. 75 The Astronomical or Solar Day commences at noon of the civil day of the same date. It comprises twenty-four hours, 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 under- standing of this fact is all that is required for intercon verting 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 hour 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 decli- nation circle and the celestial meridian. In figure 34 let P be the pole of the celestial sphere, of which YMQ 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 v< time; QPS, or QS, the hour angle of the heavenly body; QPV, or QV, the hour angle of the First Point of Aries, or the right ascension of the meridian, both of which are e(]uivalent to the sidereal time; VPS, or YS, the right ascension of the heavenly body; and VPM, or V^I, the right ascension of the mean sun. 279. Time at Different ^Ieridians. — The hour angle of the true sun at any meridian is called the local apparent time; that of the mean sun, the heal vieaii time; that of the First Point of Aries, the local sidereal time. The hour angles of the same body and points from Greenwich are respectively the Green- vrich apparent, mean, and sidereal times. The difference between the local time at any meridian and the Greenwich time is e(]ual to the longitude of that place from Greenwich expressed in time; the conver- sion from time to arc may be effected by a simple mathematical calculation or by the use of Table 7. In comparing corresponding times of different meridians the most easterly meridian may be distin- guished as that at which the time is greatest or latest. In figure 35 P3I and PM^ represent the celestial meridians of two places; PS, the declination circle through the sun, and PG, the Greenwich meridian; let To = the Greenwich time = GPS; Tm = the corresponding local time at all places on the meridian PM = MPS ; 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 lon- gitudes and hour angles as negative, we have: Lo = T«~T„; and Lo' = To — TmS therefore, Lo — Lo' = Tm— Tm. Thus it may be seen that the difference of longitude between two places equals the difference of their local times. This relation may be shown to hold for any two meridians whatsoever. Both local and Greenwich times in the above formula^ must be reckoned westward, always from their respective meridians and from O*" to 24''; in other words, it is the astronomical time which should be used in all astronomical computations. The formula Lo = Tg — Tj, is true for any kind of time, solar or sidereal; or, in general terms, To and T>i are the hour angles of any point of the sphere at the two meridians whose difference of longitude is Lo. S may be the sun (true or mean) or the vernal equinox. 2§0. Fi.vDiNG THE (jREENwicH TiME. — Siuce nearly every computation made by the navigator requires a knowledge of the Greenwich date and time as a preliminary to the use of the Nautical Almanac, the first operation necessary is to deduce from the local time the corresponding (rreenwich date, either exact or approximate, and thence the Greenwich time expressed astronomically. The formula is: To=Tm+Lo, remembering 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 if east; the result is the corresponding Greenwich time. • Example: In longitude 81° 15' \V. the local time is, 1879, April, 15'' 10'' 17'" 30" a. m. Required the Greenwich time. Local Ast. time, April, 14'' 22" 17"' 30" Longitude, + 5 25 00 Fig. 35. Greenwich time, 15 8 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, 5'' 2" 10'" 30' Longitude, - 5 25 00 Greenwich time. 4 20 45 30 76 TIME AND THE NAUTICAL ALMANAC. I Example: In longitude 17° 28' AV. the local time is, May, 1"* S*" 10™ p. m. Required the Greenwich time. ^ Local Agt. time, l"* S** 10™ 00' Longitude, + 1 09 52 _ Greenwich time, 1 4 19 52 Example: In longitude 125° SO' E. the local time ia, May, l"* S*" 10™ 30» a. m. Required the Green- wich time. Local Ast. time, April, SO** 20" 10"' 30' Longitude, — 8 22 00 Greenwich time, 30 11 48 30 2§1. From the preceding article we have: To = Tm + Lo; hence, Tm = Tg — Lo; thus it will be seen that, to find the local time corresponding to any Greenwich time, the above process is simply reversed. Since all observations at sea are referred to chronometers regulated to Greenwich mean time, and as these instruments are usually marked on the dial from 0" to 12", it becomes necessary to distinguish whether it is a.m. or p.m. at Greenwich. Therefore, an approximate knowledge of the longitude and local time is necessary to determine the Greenwich date. Example: In longitude 5" 00™ 00* W., about 3" 30"' p.m. April 15th, the Greenwich chronometer read 8" 25™, and was fast of Gr. time 3™ 15^ Required the local astronomical time. Aprox. local time, 15" 3" 30™ Gr. chro., 8" 25™ 00* Gr. Ast. time \b^, 8" 21™ 45 Longitude, -f 5 00 Corr., — 3 15 Longitude, — 5 00 00 Approx. Gr. time, 15 8 30 Gr. Ast. time 15\ 8 21 45 Local Ast. time 15*, 3 21 45 Example: In longitude 5" 00™ 00* E., about 8 a. m. May 3d, the Gr. chro. read 3" 15™ 20% and was fast of Gr. time 3™ 15*. Required the local astronomical time. Approx. local time. May, 2" 20" Gr. chro., 3" 15™ 20* Gr. Ast. time 2'», 15" 12™ 05 Longitude, — 5 Corr., — 3 15 Longitude, — 5 00 00 Approx. Gr. time, 2 15 Gr. Ast. time 2"», 15 12 05 Local Ast. time 2", 20 12 05 THE NAUTICAL ALMANAC. « 2§2. The American Ephemeris and Nautical Almanac is divided into four parts, a.s follows: Part I, Ephemeris for the meridian of Greenwich, gives the ephemerides of the sun and moon, the geocentric and heliocentric positions of the major planets, the sun's coordinates, and other fundamental astronom- ical data for equidistant intervals of Greenwich mean time; Part II, Ephemeris for the meridian of Washington, gives the ephemerides of the fixed stars, sun, moon, and major planets for transit over the meridian of Washington; Part III, Phenomena, contains predictions of phenomena to be observed, with data ior their computation; and Part IV, Star Numbers and other data, contains matter relating to cer- tain fixed stars. Tables are also appended for the interconversion of mean and sidereal time and for finding the latitude 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 contains the positions of the sun and moon, the distances of the moon from the center of the sun, from the centers of the four most conspicuous planets, and from certain fixed stars, together with the ephemerides of the planets Mercury, Venus, Mars, Jupiter, and Saturn, and the mean places of 150 fixed stars; solar and lunar eclipses are described, and the tables for the interconversion of mean and sidereal time and for finding the latitude by Polaris are included. The elements dependent upon the sun and moon are placed at the beginning of the book, arranged according to the months of the year; eighteen pages are devoted to each month, numbered in Roman notation from I to XVIII. Of these, page I contains the Apparent Right Ascension and Declina- tion of the sun and the Equation of Time for the instant of Greenwich apparent noon; throughout the remaining seventeen pages Greenwich mean time forms the basis of reckoning. Page I is used in com- putations from observations that depend upon the time of the sun's meridian passage, at which instant the local apparent time is 0", and the Greenwich apimrent time is equal to the longitude, if west, or to 24" minus the longitude, if east; this page therefore affords a means for reducing the elements for such observations from a knowledge of the longitude alone. In all other observations the calculation is made for some definite instant of Greenwich mean time (usually as noted by the chronometer) , in which case Pages II to XVIII are employed. 2S3. Rediction' of Elements. — The reduction of elements in the Nautical Almanac is usually accomplished by Interpolation, but in certain cases where extreme preiision is necessary the method of Second Differences must be used. a See extracts from Ephemeris and Nautical Almanac for 1879, Appendix I. TIME AND THE NAUTICAL ALMANAC. 77 The Ephemeris, being computed for the Greenwich meridian, contains the right ascensions, declina- tions, equations of time, and other elements for given equidistant intervals of Greenwich time. Hence, before the value of any of these quantities can be found for a given local time it is necessary to determine the corresponding Greenwich time. Should that time be one for which the Nautical Ahnanac gives the value of the required element, nothing more is necessary than to employ that value. But if the time falls between the Almanac times, the required quantity must be found by interpolation. The Almanac contains the rate of change or difference of each of the principal quantities for some unit of time, and, unless great precision is required, the first differences only need be regarded. In order to use the difference columns to advantage, the Greenwich date should be expressed in the unit of time for which the difference is given. Thus, for using the hourly differences, the Greenwich tin.e should be expressed in hours and decimal parts of an hour; when using the differences for one minute, the time should be in minutes and decimal parts of a minute. Instead of using decimal parts, some may prefer the use of aliquot parts. Since thequan titles in the Almanac are approximate numbers, given to a certain decimal, any inter- polation of a lower order than that decimal is unneces.«ary 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 Ahnanac elements. Simple interpolation assumes that the differences of the quantities are proportional to the differences of the times; in other words, that the differences given in the Almanac are constant; this is seldom the case, but the error arising from the assumption 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 taking from the Almanac the elements relating to the fixed stars the data may be found either in the table which gives the "mean place" of each star for the year or in that which gives the "apparent place " occupied by each one on every tenth day throughout the year. As the annual varia- tion of position of the fixed stars is small, the results will not vary greatly whichever ta])le 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 the abridged " Nautical Almanac; " hence, where the larger book is not at hand, the tiible of mean places nmst be employed. 2§4. To find from the Nautical Almanac a required element for any given time and place, it is first necessary to express the time astronomically and to convert it to Greenwich time and date. Then take from the Almanac, for the nearest given precedivg instant, the required quantity, together with its corresponding "Diff. for l*" " or "Diff. for 1""," noting the name or sign in each cat^e; for the sun use Page I of the proper month in the Almanac when apparent time is to be the I)asi8 for correction, but otherwise use Page II. Multiply the "Diff. for l**" 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 con- siderably 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 application of the correction being reversed. Example: At a place in longitude 81° 15' W., April 17, 1879, find the sun's declination and the equation of time at apj)arent noon. Long. =81° 15' W. G. A. T. = 17'* b^ 25™ = 17'» + 5\42. Eq. t., 17'» 0^ O-" 24\46 Corr., + 3 .18 Dec, 17"'0h, Corr., (-r) + + + + 10° 26' 42". 3 N 4 46 .2 Dec, 17'* 5'> 25™ 10 31 28 .5 N H. D., G. A. T., 52". 80 5\42 Corr., / 286". 18 14'46".18 Eq. t, 17''5h25"', 27.64 H. D., + 0-\587 G. A. T., + 5^.42 Corr., -f 3M82 {Subtract from apparent time.) Example: At a place in Long. 81° 15' E., April 17, 1879, find the sun's declination and the equation of time at apparent noon. Long. =81° 15' E. G. A. T. = 16'» 18" 35™ = 17* — 5h.42. Dec, 17'* 0\ ( + ) 10° 26'42".3N. Eq. t., I71 0^ 0" 24'.46 Corr., - 4 46 .2 Corr., - 3.18 Dec, 16* 18" 35™, 10 21 56 .1 N. Eq. t., 16* 18" 35" H. D., G. A. T., Corr., ', 21 .28 H. D., G. A. T.^ + 52". 80 — 5". 42 -f 0«.587 - 5". 42 Cor.\, ( 286". 18 \4'46".18 — 3M82 78 TIME AND THE NAUTICAL ALMANAC. Example: April 16, 1879, at U** 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, Longitude, Greenwich mean time. IS-i 23'> 55™ 30" 5" 25'" 00" 16* 5" 20"' 30" 16'' 5" 20™.5 16-1 5\34 Dec, 0^ ( + ) 10° 05' 30''. 1 N. Corr., + 4 44 . 3 For the Sun. S. D., 15' 58". (Same as at G. A. Noon.) Dec., H. D., G. M. T., Corr., 10 10 14 . 4 N. 53". 24 5\ 34 Eq. t, Corr., + + 0'" 10' 3 .15 . 22 Eq. t., 13 .37 H. D. G. M. 0\ 5". 604 34 +{ 284". 30 4' 44". 30 Corr., + 3'. 22 {Add to mean time. ] For the Moon. R. A., 5h, Corr., R. A., M. D., No. min., Corr., •J'Jt' 14'" 39'.29 + 38.31 22 15 17 .60 1».869 20^.5 Dec, 5'', Corr., Dec, M. D., No. mln., (-) 7°59'36".l S. + 4 27 .1 7 55 09 .0 S. ]3".03 20'". 5 38'.31 f 267". 12 t 4'27".l Hor. Par-.O!-, Corr., Hor. Par., H. D., G. M. T., Corr., 5,5' 13".6 7 .2 l."34 5i'.34 S-D-.C, •Corr., S. D., H. D., G. M. T., 15' 04".7 1 .8 15 02 .9 - 0".34 7".15 Corr., 1".81 R. A.,0\ 22" 26'" ;^^ 54 Corr., + 9.71 For Jupiter. Dec, 0^ (-) 10° 40' 28". S. Corr., + 53 . 6 R. A., H. D., + G. M. T., + Corr., + 22 26 45 . 25 1". 819 5\ 34 ". 71 Dec, H. D., G. M. T., Corr. , 10 39 34 . 4 S. 10". 03 5". 34 Hor. Par., 16'^, 1". 6 S. D., 16^ 16".{ 53". 6 2§5. Should greater precision be required than that attainable by niraple interpolation, resort must be had to the reduction for second differences. The differences between successive values of the quantities given in the Nautical Almanac are called the first differences; the differences between successive first differences are called the second, differences. Simple interpolation, which satisfies the necessities of sea computations, assumes the first differences to be constant; but if the variation of the first differences be regarded, a further interpolation is required for the second difference. The difference for a unit of time in the American Nautical Almanac abreast any element expresses the rate at which the element in changing at that precise instant of Greenwich time. Now, regarding the second difference as constant, the first difference varies uniformly with the Greenwich time; there- fore it« value may be found for any intermediate time by simple interpolation. Hence the following rule for second differences: Employ the interpolated value of th6 first differ- ence which corresponds to the middle of the interval for which the correction is to be computed. Example: For the Greenwich date 1879, April, 10"* 18'' 25'" 30", find the moon's declination. Dec, 18", (-)26° 19' 41".l S. Corr., + 2 .1 First diff., + 0". 044 Corr., +0 .039 Dec, 26 19 39 .0 S. M. D., 4^0 .083 No. min., +25°'.5 Second diff.. Interval, Corr. , 0".181 f Oh. 213 + 0".039 Corr. , 2". 12 The difference for one minute being 4- 0".044 at 18'', and +0".225 at 19'', the difference for one minute undergoes a change of 4 0".181 during one hour. The time for which it is desired to obtain the difference is at the middle instant between 18*' 0'" and 18'' 25'".5 — that is, at 18'' 12"'. 75, or its equivalent, 18'' 213. With a change of -f 0".181 in one hour, the change in 0''.213 is readily obtainable; correcting the minute's difference at 18''. accordingly, the proces ' of correcting the declination becomes the same as in simple interpolation. TIME AND THE NAUTICAL ALMANAC. 79 CONVERSION OF TIMES. iiS6. Conversion of Time is the process by which any instant of time that if< defined according to one system of reckoning may be defined according to some other system; and also by Avhich any interval of time expressed in units of one system may be con- verted into units of another. 287. Sidereal and Meax Times. — Mean time is the hour angle of the Mean Sun; sidereal time is the hour angle of the First Point of Aries. Since the Right Ascension of the Mean Sun is the angular distance between the hour circles of the Mean Sun and of the First Point of Aries, mean time may be con- verted into sidereal time by adding to it the Right Ascension of the Mean Sun; and similarly, sidereal time may be converted into mean time by subtracting from it the Right Ascension of the ^fean Sun. This is explained in figure 36, vhich represents a projection of the celestial sphere upon the equator. If P be the pole; QPQ', the meridian; V, the First Point of Aries; M, the position of the mean sun (west of the meridian); then QPV, or the arc QV, is the sidereal time; QPM, or the arc QM, is the mean time; and VPM, or the arc VM, is the Right Ascension of the Mean Sun. From tl^s it will appear that: QV=QM+VM, or Sidereal f.me=Mean time-j- Right Ascension of Mean Sun. If the mean sun be on the opposite side of the meridian, at 3F, then the mean time equals 24"— M^Q. In this case: QV = VM'— M'Q, or Sidereal time=Right Ascension of Mean Sun — (24''— Mean time), =Right Ascension of Mean Sun -^ Mean time— 24". Right ascension being measured to the east and hour angle to the west, the sidereal time will therefore always equal the sum of these two; but 24" must be subtracted when the sum exceeds that amount. From the preceding equations, we also have: QM=QV-VM; and M^Q=VM'-QV, or (24"-M'Q) = (24"+QV)-VM^ From this it may be seen that the mean time equals the sidereal time minus the Flight Ascension of the Mean Sun, but the former must be increased by 24" when necessary to make the subtraction possible. 28§. 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 ref>resents 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 api)lication of the ecpiation of time, with its j>roper sign, to the mean time; and the reverse operation by 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 36, we assume that PV is the hour circle of the true sun, PM remaining that of the mean sun; then the arc Q3I will be the mean time; QV, the apparent time; and VM, the equation of time; whence \.e have as before: QV = QM+VM, or Apparent time — ^lean time — Equation of time; the equation of time will be positive or negative according to the relative position-of the two suns. 2§9. 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, ami S the corresponding interval of sidereal time, the relations between the two may be expressed as follows: Therefore, S = 1.0027379 M = M + . 0027379 M; M = 0.9972696 S = S -.0027304 S. If M = 24", S = 24" + 3"' 56^6; or, in a mean solar day, sidereal time gains on mean time 3™ 56'.6, the gain each hour being 9'. 8565. If S = 24", M = 24" — 3"' 55'.9; or, in a sidereal day, mean time loses on sidereal time 3'" 55'.9, the loss each hour being 9^.8296. If 'M and S be expressed in hours and fractional parts thereof, S = M + 9^8565 M; M = S - 9^8296 S. Tables for the conversion of the intervals of mean into those of sidereal time and the reverse are based upon these relations. Tables 8 and 9 of this work give the values for making these conversions, and similar tables are to b^ found in the Nautical Almanac. 80 TIME AND THE NAUTICAL ALMANAC. 390. To Convert Meax Solar ixto Sidereal Time. — Apply to the local mean time the longitude, adding if west and subtracting if east, and thus obtain the Greenwich mean time. Take from tlie Nau- tical Almanac the Right Ascension of the Mean Sun at Greenwich mean noon, and correct it for the Greenwich mean time l)y Table 9 or by the hourly difference of 9". 857. Add to the local mean time this corrected right a.scension, rejecting 24'' if the sum is greater than that amount. The result will be the local sidereal time. Example: April ^2, 1879, 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*' 2" 00"' Oa- R. A. M. S., 22» 0^ 2" 00"' 41^24 L. M. T., 2" 00'" 00^ Long., -t 5 25 00 Red. for 7" 25"" (Tab. 9), -f 1 13.10 R.A.M.S., r 2 01 54.34 G.M.T., 22 7 25 00 R. A. M. S., 7" 25"', 2 01 54.34 L. S. T., 4 01 54.34 Example: April 22, 1879, in Long. 75° E., the local mean time is 4'' 00"' 00" a. m. Ketjuired the local sidereal time. L. M. T., 21'» 16" 00'" 00^ R. A M. S. 21'» 0", 1" 56"" 44^69 L.M.T., 21" 16" 00"' OO'' Long., - 5 00 00 Red. for 11" (Tab. 9), ^ 1 48.42 R.A.M.S.,4 1 58 33.11 G. M. T., 21 11 00 00 R. A. M. S., 11", 1 58 33 .11 L. S. T., 21 17 58 33.11 In these examples the reduction of the R. A. M. S. has formed a separate operation in order to make clear the process. It would be as accurate to add together directly L. M. T., R. A. M. S., and Red., and the work would thus be rendered more brief. 291. To CoxvERT Sidereal ixto Meax Solar Time. — Take from the Nautical Almanac the Right Ascension of the Mean Sun for Greenwich mean noon of the given astronomical day, and apply to it the reduction for longitude, either by Table 9 or by the hourly difference of 9^857, and the result will be the Right Ascension of the Mean Sun at local mean noon, which is equivalent to the local sidereal time at that instant. Subtract this from the given local sidereal time (adding 24" to the latter if necessary), and the result will be the interval from local mean noon, expressed in units of sidereal time. Convert this sidereal time interval into a mean time interval by subtracting the reduction as given by Table 8 or by tlie hourly difference of 9^830; the result will be the local mean time. Example: April 22, 1879, a. m., in Long. 75° E., the local sidereal time is 17" 58"' 33M1. AVhat is the local mean time? Astronomical day, April 21. L. S. T., 17" 58-" 33M1 R. A. M. S., Gr. 21" 0", 1" 56"' 44\69 R. A M.S., — 1 55 55.41 Red. for -5" long. (Tab. 9), — 49.28 Sid. interval from L. M. noon, 16 02 37.70 R. A. M. S., local 0", 1 55 55.41 Red. for sid. interval (Tab. 8), 2 37 .70 L. M. T., 21", 16 00 00 .00 Example: April 22, 1879, p. m., at a place in Long. 81° 15^ W., the sidereal time is 4" 01"' 54».34. What is the corresponding mean time? Astronomical day, April 22. L. S. T., 4" 01"" 54'.34 R. A. M. S , Gr. 22" 0", 2" 00"' 4P.24 R. A. M. S., - 2 01 34 .63 Red. for +5" 25™ long. (Tab. 9), + 53 .39 Sid. interval from L. M. Noon, 2 00 19 .71 R. A. M. S., local 0", 2 01 34 .63 Red. for sid. interval (Tab. 8), — 19 .71 L. M. T., 22", 2 00 00 .00 392. To Covert Mean into Apparent Time and the Reverse. — Find the Greenwich time corre- sponding to the given local time. If apparent time is given, find the Greenwich apparent time and take the equation of time from Page I of the Almanac. It mean time, find the Greenwich mean time and take the equation of time from Page II. Correct the equation of time for the required instant and apply it with its proper sign to the given time. IExample: April 21, 1879, in Long. 81° 15^ W., find the local apparent time corresponding to a local mean time of 3" 05"" 00' p. m. L. M. T., 21"3"05"'00' Long., + 5 25 00 G. M. T., 21 8 30 00 L. M, T., 21" 3" 05"' 00" Eq. t., + 1 22.01 Eq. t., 0", 1'" 17.61 Corr., + 4.40 L. A. T., 21 3 06 22.01 . Eq.t., 1 22.01 H.D., + 0\518 G.M.T.,+ 8".5 Corr., + f.403 {Add to mean time.) TIME AND THE NAUTICAL ALMANAC. 81 Example: April 3, 1879, in Long. 81° 15' E., the local apparent time is 8'' 45™ 00' a. m. Required the mean time. L. A. T., 2^ 20" 45"' 00' L. A. T., 2" 20" 45™ 00' Eq. t., 0", 3™ 42'.46 Long., - 5 25 00 Eq. t., + 3 30.90 Corr., — 11 .56 G. A. T., 2 15 20 00 L. M. T., 2 20 48 30.90 Eq. t., 3 30 .90 H. D., - 0'.754 G. M. T., — 15''.33 Corr., — 11\56 {Add to apparent time.) 293. To Find the Hour Angle of a Body from the Time, and the Eeverse. — In figure 36, if M and M' represent the positions of celestial bodies instead of those of the mean sun as before assumed, then the hour angles of the bodies will be Q M and 24'' - M' Q, respectively, and their right ascen- sions will be V M and V M^ As before, we have: Q V = Q M + V M, , = V M' - M' Q; QM =QV-VM; M' Q = V M' - V Q, or (24" - M' Q) = (24" + Q V) - Y W. Substituting, therefore, hour angle of the body for mean time, and right ascension of the body for Right Ascension of the Mean »S'u«, the rules previously given for the conversion of mean and sidereal times will be applicable for the conversion of hour angle and sidereal time. Thus, the sidereal time is equal to the sum of the right ascension of the body and its hour angle, subtracting 24" when the sum exceeds that amount; and the hour angle equals the sidereal time minus the right ascension of the body, 24" being added to the former when necessary to render the subtraction possible. Example: In Long. 81° 15' W.', on April 25, 1879, at 12" 10'" 30' (astronomical) mean time, find the hour angle of Sirius. L. JVI. T., 12" 10"' 30' L. M. T., 12" 10°' 30" Long., + 5 25 00 R. A. M. S., 0",+ 2 12 30.91 Red. (Tab. 9) , + 2 53.39 G. M. T., 17 35 30 L. S. T., 14 25 54.30 R. A. Sirius, — 6 39 49.83 H. A. Sirius, 7 46 04.47 Example: May 9, 1879, Arcturus being 2" 27"' 42*.52 east of the meridian, find the local sidereal time 24" 00"' 00* H. A., 21" 32'° 17'.48 H. A., 2 27 42.52 E. R. A., ^ 14 10 11 .71 H. A., 21 32 17.48 W. L. S. T., 11 42 29.19 Or thus: H. A., - 2"27"'42'.52 R. A., + 14 10 11 .71 L. S. T., 11 42 29 .19 22489—03 6 82 OOBRECTION OF OBSERVED ALTITUDES. CHAPTER X. OOEEEOTION OF OBSEEVED ALTITUDES. 294. The true altitude of a heavenly body at any place on the earth's surface is the altitnde 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. Tne obsen'ed 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, ParallcLv, and Semidiaynefer. The corrections for parallax and semidiameter are of inappreciable magnitude in observations of the fixed stars, and with planets are so small that they need only be regarded in refined calculations. In observations with the artificial horizon there is no correction for dip. For theoretical accuracy, the corrections should be applied in the order in which they are named, but in ordinary nautical practice the order of application makes no material difference, except in the case of the parallax of the moon as explained in article 306. INDEX CORRECTION. 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 in passing obliquely from one medium into another oi a different density; if the latter be more dense, the ray will be bent toward the perpendicular 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 incident ray ; after it enters the second medium it is called the refracted ray, and the difference of direction of the two is called the refraction. The rays of light from a heavenly body must pass through the atmosphere before reaching the eye of an observer upon the surface of the earth. The earth's atmosphere is not of a uniform density, but is most dense near the earth's surface, gradually decreasing in density toward its upper limit; hence the path of a ray of light, by passing from a rarer medium into one of continually increasing density becomes a curve, which is concave toward the earth. The last direction of the ray is that of a tangent to the curved path at the eye of the observer, and the difftsrence of the direction of the ray before entering the atmosphere and this last direc- tion constitutes the refraction. 297. To illustrate this, consider the earth's atmos- phere as shown in figure 37; let SB be a ray from a star S, entering the atmosphere at B, and bent into the curve BA; then the apparent direction of the star is AS'', the tangent to the curve at the point A, the refraction being the angle between the lines BS and AS'. If CAZ is the vertical line of the observer, by a law of Optics the vertical plane of the observer which contains the tangent AS'' must also contain the whole curve BA and the incident ray BS. Hence refraction increases the apparent altitude of a star without affect- ing its azimuth. At the zenith the refraction is nothing. The less the altitude the more obliquely the rays enter the atmosphere and the greater will be the refraction. At the horizon the refraction is the greatest. 298. The refraction for a mean state of the atmosphere (barometer 30'", Fahr. thermometer 50°) is given in Table 20 A; the combined refraction and sun's parallax in Table 20 B; and the combined refraction and moon's parallax in Table 24. Since the amount of the refraction depends upon the density of the atmosphere, and the density varies with the pressure and the temperature, which are indicated by the barometer and thermometer, the true refra<;tion is found by applying to the mean refraction the corrections to be found in Tables 21 and 22; these are deduced from Be&sel's formuhe, 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 Fig. 37. CORRECTION OE^ OBSERVED ALTITUDES. 83 (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 IHp (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 30'" .67. The mean refraction by Table 20 A is, 9^ 52''' The correction for height of barometer is, + 13 The correction for the temperature, + 42 True refraction, 10 47 299. The correction for refraction should always be subtracted, aa also that for combined refraction and parallax of the sun; the correction for combined refraction and parallax of the moon is invariably additive. DIP. 300. 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 38 suppose A to be the position of an observer whose height above the level of the sea is AB. CAZ is the true vertical at the position of the observer, and AH is the direction of the true hori- \^ z zon, S being an observed heavenly body. Draw ATH' tangent to the earth's surface at T. Disre- garding refraction, T will be the most distant point visible from A. Owing to refraction, however, the most distant visible point of the earth's surface is h- more remote from the observer than the point T, and is to be found at a point T', in figure 39. But to an observer at A the point T'' will appear to lie in the direction of AH''', the tangent at A to the curve AT''. If the vertical plane were revolved about CZ as an axis, the line AH would generate the plane of the true horizon, while the point T' would generate a small circle of the terrestrial sphere called the ViMble 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 in Table 14 for various heights of the observer's eye, and in the calculation of the table allowance has been made for the effect of at- mospheric refraction as it exists under normal con- ditions. Fig. 38. 301. The fact must be emphasized, however, that under certain conditions the deflection of the ray in its path from the horizon to the eye is so irregular as to give a value of the dip widely different from that which is tabulated for the mean state of atmosphere. These irregularities usually occur when there exists a material difference between the temperature of the sea water and that of the air, and they attain a maximum value in calm or nearly calm 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 which 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 tempera- ture of air and water, but none of these afford a satisfactory solution, there being so many elements 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 considerable — reliable observations having frequently placed it above 10', and values as high as 32'' having been recorded — it is necessary for the navigator to be on his guard against the errors thus produced, and to recognize the possible inaccuracy of all i esults derived from observations taken under unfavorable conditions. Without attempting to give any method for the determination of the amount of the extraordinary variation in dip, the following rules may indicate to the navigator the conditions 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 mind in regions such as those of the Red Sea and the Gulf Stream, where the difference frequently exists. Fig. 39. « A sextant attachment devised by Lieutenant-Commander J. B. Blish, U. S. Navy, enables an observer to measure the actual dip at any time. 84 CORRECTION OF OBSERVED ALTITUDES. (6) The error in the tabulated value of the dip will increase with an increase in the difference of temperature, and Mill 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 al^tude is greater than that given by the use of the ordinary dip table. AVhen the water is warmer than the air, the horizon is depressed and the dip is increased. At such times the altitude is really less than that found from the use of the table. The same cause, it may be mentioned here, affects the kindred matter of the visibility of objects. When the air is warmer, terrestrial objects 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 (o be free from all inter- vening land or other objects; but it often happens that an observation is required to be taken from a ship sailing along shore or at anchor in harbor, when the sun is over the land and the shore is nearer the ship than the visible sea-horizon would be if it were unconfined; in this case the dip will be different from that of Table 14, and will be greater the nearer the ship is to that point of the shore to which the sun's image is brought down. In such case Table 15 gives the dip at different heights of the eye and at different distances of the ship from the land. 303. The dip is always to be subtracted from the observed altitude. PARALLAX. 304. The parallax of a heavenly body is, in general terms, the angle between two straight lines drawn to the body from different points. But in Nautical Astronomy geocentric parallax is f.lone considered, this being the differ- ence between the positions of a heavenly body as seen at the same instant from the center of the earth and from a ])oint on its surface. The zenith distance of a body, S (fig. 40), seen from A, on tlie surface of the earth, is ZAS; seen from C it is ZCS; the I) irallax is the difference of these angles, ZAS— ZCS=ASC. Parallax in altUnde is, then, the angle at the heavenly iody subtended by the radius of the earth. If the heavenly body is in the horizon as at H', the ra lius, 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 an the bodies are farther from the earth, as will be evident Yicr. 40. from the figure. 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 If the object is in the horizon at H^, the angle AH^C is the horizontal parallax, and denoting it by H. P. the right triangle AH''C gives: sin H. P. = ^- Substituting this value of r^ i" the above, . sin par. — sin H. P. sin Z. If h = SAH'', the apparent altitude of the heavenly body, then Z = 90° — /;; 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 h. 305. The Nautical Almanac gives the horizontal parallax of the moon, as well as of the planets Mercury, Venus, Mars, Jupiter, Saturn, Uranus, and Neptune. COERECTION OF OBSERVED ALTITUDES. 85 In Table 16 will be found the values of the sun's parallax for altitude intervals of 5° or 10°, while Table 20 B contains the combined values of the sun's parallax and the refraction. In Table 24 is given the parallax of the moon, combined with the refraction, at various altitudes and for various values of the horizontal parallax. 306. Parallax is always additive; combined parallax and refraction additive in the case of the moon, but eubtractive for the sun. Aa the correction for parallax of the moon is so large, it is essential that it be taken from the table with considerable accuracy; the corrections for index correction, semidiameter, and dip should there- fore be applied first, and the "approximate altitude" thus obtained should be used as an argument in entering Table 24 for parallax and refraction. SEMIDIAMETEB. 307. The semidiameter of a heavenly body is half the angle subtended by the diameter of the visible disk at the eye of the observer. For the same body the semidiameter varies with the distance; thus, the difference of the sun's semidiameter at different times of the year is due to the change of the earth's distance from the sun; and similarly for the moon and the planets. In the case of the moon, the earth's radius bears an appreciable and considerable ratio to the moon's distance from the center of the earth; hence the moon is 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 semidiurnal 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. 30§. 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 correc- tion, it being additive for the lower and subtractive for the upper. Example: May 6, 1879, the observed altitude of the sun's upper limb was 62° 10' 40''; I. C, + 3' 10"; height of the eye, 25 feet. Required the true altitude. Obs. alt. 0, 62° 10' 40" I. C, + 3' 10" Corr., - 18 04 S. D. (NautAlm.), - 15' 53" True alt., 61 52 36 dip (Tab. 14), - 4 54 p.&r. (Tab. 20 B), - 27 -21 14 Corr., -18' 04" Example: The altitude of Sirius as observed with an artificial horizon was 50° 59' 30"; I. C, V 30". Required the true altitude. Obs. 2 alt. I.e., 20 A) 50° 59' 30" 1 30 2)50 58 00 Obs. alt., ref. (Tab. 25 29 00 2 02 True alt.. 25 26 58 Example: April 16, 1879, 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" par. (Tab. 17), -r 0' 04" Hor. Par. (Naut. Aim.), 7" Corr., - 2 32 I. C, + 2 30 53 23 38 -r2 34 dip (Tab. 14), - 4' 23" ref. (Tab. 20 A),- 43 - 5 06 Corr., - 2' 32" «6 CORRECTION OF OBSERVED ALTITUDES, Example: May 6, 1879, at 13*" 24™ G. M. T., the observed altitude of the moon's lower limb was 25° 30' 30"; I. C, —1' 30"; height of eye, 20 feet. Required the true altitude. Oba. alt.£, 25° 30' 30" Istcorr., + 10 57 S. D. (Naut. Aim.), Aug. (Tab. 18), dip (Tab. 14), I.e., + 16' 42" 08 Hor. Par. (Naut. Aim.), 61' Approx. alt., « 41 27 p. & r. (Tab. 24), + 53 07 True alt., 26 34 34 + 16 - 4' — 1 50 23" 30 - 5 53 Ist corr.. + 10' 57" Or, the following modification may be adopted: Obs. alt.C, 25° 30' 30" Istcorr., + 8 56 S. D., Aug., dip, ref., I.e., + 16' 42" + 08 A- 16 50 - 4' 23" - 2 01 - 1 30 H. P. App. par.. 3670" alt., 25° 39' / 3308" 155' 08" log 3. 56467 cos 9. 95494 Approx. alt., 25 39 26 par., + 55 08 log 3.51961 True alt., 26 34 34 — 7 54 1st corr., + 8' 56" THE CHRONOMETER ERROR. 87 CHAPTER XI. THE OHRONOMETEE EREOR. 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 dailn 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 sepa- rated 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 was 0"' 48*.0 fast of G. M. T. What was the rate? Error, March IC* 0\ + 0"' 32'. 5 Error, March 20<* 0^ -f-O 48 . Change in 10 days, + 15 . 5 Daily rate, + 1'.55 The chronometer is therefore gaming 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 3'" 27^5 slow of G. M. T. and losing 0^.47 daily. What is the error on December 26? Error Dec. 17,-3'" 27'.5 Daily rate, — 0».47 Correction, — 4.2 No. days, 9 Error Dec. 26, - 3 31 .7 Corr., - 4 .23 The chronometer is therefore f south latitude and declination — . Mark hourly difference of declination when tovmrd north -{-, when toward south — . Enter Table 37 with the elapsed time, and take out log A and log B, prefixing to each its proper sign as given in the table at the head of the page. To log A add the logarithm of the hourly diff. (Table 42) and the log tangent of the latitude (Table 44). Prefix to each logarithm the sign of the quantity it represents, and to their sum the sign which results from the algebraic multiplication of the quantities. This sum is the logarithm (Table 42) of the number of seconds of time in the first part of equation of equal altitudes, to be marked + or — , like its logarithm. To log B add the logarithm of the hourly diff. and the log tangent of the declination, marking the signs as before. The sum is the logarithm of the second part of the equation of equal altitudes, to be marked + or — like its logarithm. Combine the two parts, having regard to signs, to obtain the equation of equal altitudes; apply this, with proper sign, to the Middle Chronometer Time and the result is the Chronometer Time of Local Apparent Noon or Chronometer Time of Local Apparent Midnight, according as observations were taken on opposite sides of the meridian at upper or at lower transit. Apply the equation of time (adding when it is additive to mean time, otherwise subtracting); the result is the Chronometer Time of Local Mean Noon, or Midnight, which, if the chronometer is regulated to local time, will be 12'' 0'" 0* when the chronometer is right, more than 12'' when fast, less than 12*" when slow. If the chronometer is regulated to Greenwich time, apply the longitude (in time) to the chronom- eter time of mean noon (subtracting in west, adding in east longitude) ; the result will be more or less than 12'', according as the chronometer is fast or slow. Example: April 13, 1879, at a place in Lat. 30° 25^ N., Long. 5" 25"' 42' W., observed the following equal altitudes of the sun with a sextant and artificial horizon, noting the times by a watch compared Avith a chronometer regulated to Greenwich mean time. What is the error of the chronometer? A. M. COMPARISONS. Chro., 2'> 22" 30» Watch, C-W, Chro., Watch, C-W, 8 52 02 5 30 28 2'' 56" 9 26 '30« 02 5 30 28 P. M. COMPARISONS. Chro., 8'> 04=' 30" Watch, 2 34 01 C-W, Dec, 9° 00' 54". 1 N. H. D. (13th),+54".40 H. D. (14th), +54 .03 WATCH, A. M. 9h 12m 30s 12 55 13 20 13 46 14 10 Chro., Watch, C-W, ALTS. 91° 00' 10 20 30 40 5 30 29 8" 33" 3 03 '30« 01 5 30 29 H. D. at iioon,+ Long., + 54".32 5''.43 Corr., Dec, (•294".96 t 4'55".0 9° 05' 49" N. Dlfl., 24 hrs.,- .37 Diff., 1 hr., -0".015 Diff., 5''.43, -0 .08 H.D.atnoon,+54".32 WATCH, P. M. 2h 45"' 45" 45 20 44 55 Tab. 37 log A(-)9.4445 logB( + )9.3193 44 30 H. D. +54".32 log ( + )1.7350 log ( + )1.7350 44 05 Lat. +30° 25' tan (+) 9.7687 d + 9°6' tan ( + )9.2045 Mean, W. T., A. M., C-W, A. M. Chro. T., P. M. Chro. T., Mid. Chro. T., Eq. eq. alt., Chro. t. L. A. Noon, Eq. t, Chro. t. L. M. Noon, Long., Chro. fast. 9hl3"- 20" + 5 30 28 2 43 48 + 8 15 24 2)10 69 12 5 29 36 - 7.1 5 29 28.9 - 31.5 5 28 67.4 - 5 25 42.0 Mean, W. T., P. M. C-W. P. M. Chro. T., A. M. Chro. T., Elapsed Time, Eq. t., H. D., Long., 2h 44m 5.5* 1st Part>-8».88 log (_)0.9482 + 5 30 29 2d Part+1 .81 log ( + ) 0.2588 16 24 Eq. eq.l _^ ^ 43 48 alt. / - 2 43 48 alt 5 31 36 0"> 36'.02 0«.65 5h.43 Corr., Eq. t., {Minug to mean time.) 03 16.4 92 THE CHRONOMETER ERROR. 324. A quicker method of solving the same problem « is available when results are not required to be accurate to the fraction of a second. If /i' is the change of altitude in minutes of arc, due to the total change in declination in the time elapsed between sights (the latitude and hour angle remaining the same), and i' the number of seconds it requires for the sun to change its altitude one minute of arc, then: • 1 Equation of equal altitudes =7^h^ X t' . Table 25 gives the change of altitude of an object arising from a change of 100 seconds in declination at various altitudes, declinations, and latitudes. By multiplying the appropriate quantity taken from this table by the total change of declination between sights, dividing by 100, and converting the result from seconds to minutes of arc, // is found. It is marked with the sign indicated in the table. By dividing the number of seconds of time between the first and last sights of one of the series by the number of minutes difference of altitude, we find i' . When the sights are taken on opposite sides of the upper meridian t' is minus; for the lower meridian it is plus. When the artificial horizon is used, if i^ is computed on a basis of the change of the double altitude, its value is only half of the true one and the second term of the equation becomes h^ X t^' instead of as given above. The example given in illustration of the preceding method when worked by this method is as follows: Change in declination between sights = H. D. X elapsed time Change in altitude due to lOO'^ declination (Tab. 25) = + 56'^ 54'''.32 X 5\53 = 300^'. V = 100 X 60 2'»45'"45' — 2''44°K)5" 91° 40^ — 91° 00^ Eq. equal alt. = + 2.80 X - 100^ 40' 2\o = - 2« 7^oo. 325. If equal altitudes of a planet were observed, the correction due to change of declination could be computed as in the case of the sun. It is not ordinarily expedient to use a planet, however, for if night sights are to be taken facility of working would make it preferable to employ a fixed star. On account of its rapid and excessive change of declination the moon would never be observed for equal altitudes. 326. Equal Altitudes op a Fixed Star. — In selecting stars for this observation, it is to be remarked that the nearer to the zenith the star passes the less may the elapsed time be; and when a star passes exactly through the zenith the two altitudes may be taken within a few minutes of each other. But, with the ordinary sextants, altitudes near 90° can not be taken with the artificial horizon, as the double altitude is then nearly 180°. A limit is thus placed upon the extreme altitude that it is practicable to observe. The sextant should be set and the coincidences of the two images of the star awaited, as in the case of the sun's limb, and the times by chronometer or watch noted as usual. 327. Take the mean of the times before the meridian passage as the A. M. Chronometer Time, and the mean of those after the meridian passage as the P. M. Chronometer Time. The mean of these two (adding 12'' to the later one in case the chronometer has passed XII*" in the interval between sights) is the Chronometer Time of Star's Transit. At the instant of transit the local sidereal time will equal the right ascension of the star in case of the upper transit, or it will equal the right ascension plus 12'' in case of the lower transit. By converting local sidereal into Greenwich sidereal and thence into Green- wich mean time in the usual way, the chronometer error is found. Example:— June 8, 1879, at Cape Town, Lat. 33° 56' S., Long. 18° 28' 40" E., using sextant and arti- ficial horizon, observed equal altitudes of star Antares before and after upper transit, as stated below. Required the chronometer error on Greenwich mean time. Chro. A. M. 7" 32'" 10^5 32 32 35.0 59.3 Altitudes. 125° 30^ 40 50 A. M. P. M. Chro. t., 7 Chro. t., 11 32 33 34.9 56.1 2)19 06 31.0 Chro. G. M. t. Transit, 9 T. Transit, 9 33 59 15.5 30.9 Chro. slow, 26 15.4 Chro. P. M. 11" 34"' 20^3 11 33 56.0 11 33 32.0 P. M. Chro. t.. n 33 56.1 L. S. T.(R.A. *), Long., 16" — 1 22"' 14 03%5 54.7 G. S. T., R. A. M. S., 0", 15 — 5 07 05 08.8 59.4 Sid. int. from 0", Red. (Tab. 8), 10 01 1 09.4 38.5 G. M. T., 9 59 30.9 a Suggested by Commander W. E. Sewell, U. S. Navy. THE CHRONOMETER ERROR. 93 32§. Degrek of Dependence. — An error of 5'' in the latitude would not affect the corresponding part of the equation of equal altitudes by more than one-hundredth of its amount in the most unfavorable case, and in general would have no sensible effect. It is one of the advantages of the equal altitude method, therefore, that it does not require an accurate knowledge of the latitude. It is also plain that errors in the longitude affecting the declination and its hourly difference produce but small propor- tionate effects upon the computed equation. The absolute error of the chronometer on Greenwich will be affected by the whole error in the longitude, but the rate v^dll still be correct. Hence, we conclude that by this method the chronometer may be accurately rated at a place whose latitude and longitude are both imperfectly known. The chief source of error is in the observation itself. The best observers with the sextant can not depend on the noted time of a single contact within 0^.5, and hence the intervals between the successive chronometer times (which, if observations could be perfectly taken, would be sensibly equal) may differ 2". But the greatest probable error of the chronometer time of sun's or star's transit, from the mean of six such observations on each side of the meridian, is found to be not more than 0*.2, provided the rate of the chronometer between the observations is uniform. 94 LATITUDE. CHAPTER XII. LATITUDE. BY MERIDIAN ALTITUDE. 329. The latitude of a place on the surface of the earth, being its angular distance from the equator, is measured by an arc of the niieridian between the zenith and the equator; hence, if the zenith distance of any heavenly body when on the meridian be known, together with the declination of the body, the latitude can thence be found. Ivet figure 42 represent a projection of the celestial sphere on the plane of the meridian NZS; C, the center of the sphere; NS, the horizon; P and P', the poles of the sphere; QCQ'', the equator; Z, the zenith of the observer. Then, by the above definition, ZQ will be the latitude of the observer; and NP, the altitude of the elevated pole, will also equal the latitude. Let A be the position of a heavenly body north of the equator, but south of the zenith; QA = (/, its declination; AS = /i, its altitude; and ZA = 2 = 9U°— /i, its zenith distance. From the figure we have: QZ = QA4-AZ, or Fig. 42. • ^y attending to the names of z and d, marking the zenith dis- tance 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 A, A^ A''. In case the body is below the pole, as at A''^^ — 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 = PA^'' + NA^'^ or L=p + h. 330. 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 follow the sun as long as it rises; as soon as the highest altitude is reached, the sun begins to fall and the lower limb will appear to dip. When the sun dips the reading of the limb is taken, and this is regarded as the meridian observation. It will, however, be found more convenient, and frequently more accurate, for the observer to have his watch set for the local apparent time of 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 indi- cates noon. This will save time and try the patience less, for when the sun transits at a low altitude it may remain "on a stand|" without appreciable decrease of altitude for several minutes after noon; more- over, 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 may be very material, and thus have considerable influence on the time of the sun's dipping. This error is large enough to take account of in a fast-moving vessel making a course in which there is a good deal of northing or southing. 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 still another element of inaccuracy. 331. 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 18 slow of the chronometer. For the Sun. For other Bodies. L. A. T. noon. Long. (+ if west), G. A. T., Eq. t., G. M. T., C. C. (sign reversed) Chro. time, C-W, Watch time noon, 0" 00'" OO" L. S. T. transit, Long. (+ if west), G. S. T., R. A. M. S., 0\ Sid int. from O*", Red. (Tab. 8), G. M. T., C. C. (sign reverse*!), Chro. time, C-W, Watch time transit, ( Right ascension. ) LATITUDE. 95 332. From the observed altitude deduce the true altitude, and thence the true zenith distance. Mark the zenith distance North if the zenith is north of the body when on the meridian, South it the zenith is south of the body. Take out the declination of the body frorti the Nautical Almanac for the time of meridian passage, having regard for its proper sign or name. The algebraic sum of tlie 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, 1879, in Long. 60° W., the observed meridian altitude of the sun's lower limb was 40° 4'; sun bearing south ; I. C.j + S'O''; height of the eye, 20 feet; required the latitude. Obs. alt., Corr., 40° + 04^ 13 00'^ 21 S. D., LC, dip, p. <&r. + 15^ + 3 46'^ 00 Dec, H. D., Long., Corr., Dec, 23° 27^ 20^''.5 , + 0'''.32 4". h, 40 17 21 + 18 - ¥ , - 1 46 23'^ 02 2, 49° 23 42^ 27 39'^ N. 22 N. + F''.28 23° 27^ 22^' L, 73 10 01 N. - 5 25 Corr., + 13^ 21'-' Example: At sea, April 14, 1879, in Long. 140° E., the observed meridian altitude of the sun's lower limb was 81° W 30'^; sun bearing north; I. C.,— 2' 30'-'; height of the eye, 20 feet. Obs. alt., 81° 15' 30'^ S. D., + 15' 59'' Dec, 9° 22' 35".4 N. Corr., + 8 59 H. D., + 54^.03 h, 81 24 29 p.'&r., - 07 Long., - 9\33 z, 8° 35' 31" S. p r 504". 1 d, 9 14 II N. - 7 00 *"""•' \8' 24". I L, 38 40 N. Corr., + 8' 59" Dec, 9° 14' 11" N. Example: At sea. May 15, 1879, Long. 0°, the observed meridian altitude of the sun's lower limb was 30° 13' 10"; sun bearing north; I. C, + 1' 30"; height of the eye, 15 feet. Obs. alt., 30° 13' 10" S. D., + 15' 51" Dec, Gr. 0^, 18° 50'48".5 N. Corr., + 12 02 . I. C, + 1 30 h, 30 25 12 + 17 21 z, 59° 34' 48" S. dip, - 3' 48" d, 18 50 49 N. p.&r., - 1 31 L, 40 43 59 S. - 5 19 Corr., + 12' 02" Example: January 1, 1879, the observed meridian altitude of Sirius was 53° 23' 40", bearing south; I. C., + 5' 0"; height of the eye, 17 feet. Dec. *, 16° 33' 04" S. Obs. alt., Corr. , 53° + 23' 40" 15 N. S. N. LC, dip, ref., Corr., + + 5' 00" *, 53 23 55 43 % 36° 16 36' 33 05" 04 4 45 0' 15" L» 20 03 01 Example: June 13, 1879, in Long. 65° W., and in a high northern latitude, the meridian altitude of the sun's lower limb was 8° 16' 10", below the pole; height of the eye, 20 feet; I. C, 0' 00". Greenwich apparent time of lower culmination, June 13, !&" 20'" ( =Long. +12''). S. D., -^r 15' 47" Dec, 23° 13' 03".8 N. dip, - 4 23 p. &T., - 6 12 Obs. alt., Corr., - 8° 16' 10" 5 12 K 8 21 22 z, 180°-(7, 81° 38' 38" S. 156 44 36 N. 75 05 58 N. Alternative method, h, 8° 21' 22" p, 66 44 36 10 35 Corr., -h 5 12 H. D., + G. M. T., 8".58 16" .33 Corr., + -( 2' 140". 5 20". 5 Dec, 23° 15' 24" p, 66° 44' 36" 180°-J, 156° 44' 36" N. L, 75 05 58 N. 96 LATITUDE. Example: June 26, 1879, in Long. 80° W., the observed meridian altitude of the moon's upper limb was 59° 6' 4(y', bearing south; I. C, + 1' ^'\ height of the eye, 19 feet. G. M. T., Gr. trans., 5i> 27'».0 Dec. (llh), 4° 51' 36".5 S. Corr. for Long (Tab. 11),+ 11 .0 h, 59° 18' 00" Obs. alt., I. C, S. D., Aug., dip, 1st Corr., + 59° 06' 40" z, 30° 42' 00" N. d, 4 51 06 S. 2' 00" L, 25 50 54 K. 14 4 16 20 33 18' 33" L. M. T., local trans., 5 38 .0 Long., -*- 5 20 .0 G. M. T., local trans., + 10 58 .0 M. D., No. min., + 15".07 2n'.0 Corr., 30".l Dec, 4° 51' 06" S. Approx. alt., 58° 48' 07" l>. 49'».8 Dec, 10° 44' 20".5 S. CJorr., - 1 41 I.e., +3 00 Corr. for Long., - .9 — .— — H. D., • - 6".58 h, 51 23 43 +3 01 L. M. T., local trans., 10 .50.7 G. M. T., 5'' .84 — ^— — Long., - 5 00 .0 • z, 38° 36' 17" S. dip, -3' 55" Corr., - 38".43 d, 10 44 59 S. ref., - 47 G. M. T. local trans., 5' 50 .7 — — ^— Dec, 10° 44' 53" S. L, 49 21 16 S. -4 42 • H. P., 2".2 Corr.. -1' 41" par. (Tab. 17) , 1" 333. Constant. — In working a meridian altitude, especially the daily noon observation of the sun, it is frequently a convenience to so arrange the terms of the problem 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 has been taken, it benig necessarj^ only to add or subtract the altitude. It is assumed that the noon longitude will be sufficiently accurately known in advance to enable the navigator to correct the declination; also the approximate meridian altitude to correct the parallax and refraction; if the latter is not known, it may readily be found from the declination and approximate latitude. Generally speaking, Lat. = Zenith distance — Dec, = 90° — True alt. + Dec, = 90° - (Obs. alt. + Corr.) + Dec, = (90° -f Dec. - Corr.) - Obs. alt., in which the quantity (90° -f 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 aa the observed altitude is applied. To avoid the confusion that might arise from the necessity of combining the terms algebraically according to their different names, it may be convenient to divide the problem into four cases and lay down rules for the arithmftical 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. -f- 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 illu-strating 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. 2i> Example. 3d Example. 5th Example. Case I. Case II. Case III. Case I V. + 90° 00' 00'^ -90° 00' 00'' +90° 00' 00" -f 90° 00' 0(7' Dec, + 23 27 22 Dec, -f 9 14 11 Dec, -18 50 49 Dec, -23 15 24 Corr., - 13 21 Corr., -f 8 59 Corr., - 12 02 Corr., -f 5 12 Constant, -4-113 14 01 Con8tant,-80 36 50 Constant, + 70 57 09 Constant,+66 49 48 Obs. alt., - 40 04 00 Obs. alt., -f 81 15 30 Obs. alt., -30 13 10 Obs. alt.,-^ 8 16 10 Lat., 73 10 01 (N.) Lat, 38 40 (N.) Lat., 40 43 59 (S.) Lat., 75 05 58 (N.) LATITUDE. 97 BY REDUCTION TO THE MERIDIAN. 334. Should the meridian observation be lost, owing to clouds or for other reason, altitudes may be taken near the meridian and the times noted by a watch compared with the chronometer, from which, knowing the longitude, the hour angle may be deduced. If the observations are within 26'" from the meridian, before or after, the correction to be applied to the observed altitude to reduce it to the meridian altitude may be found by inspection of Tables 26 and 27. Table 26 contains the variation of the altitude for one minute from the meridian, expressed in seconds and tenths of a second. Table 27 contains the product obtained by multiplying the square of the minutes and seconds by the change of altitude in one minute. Let a = change of altitude (in seconds of arc) in one minute from the meridian: H = meridian altitude; h = corrected altitude at observation; and t = interval from meridian passage. The value of the reduction to the meridian altitude of each altitude is found by the formula: H = /* ^ at-, a being found in table 26, and af 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 fi thus found and to the interval, in minutes and seconds, from meridian passage. This quantity will represent the amount necessary to reduce the corrected altitude at the time of observation to the corrected altitude at the meridian pa-ssage; it is always additive when the body is near upper transit, and always to be subtracted when near lower transit. If the mean of a number of sights is to be taken, determine each reduction separately, take the mean of all the reductions, and apjily it U) the mean of the altitud(!s; 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. 335. 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. 331) 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 l;etween watch time of transit and watch time of observation ^ives the watch time — that is, the mean time — elapsing between transit and observation. A fixed star covers in that time an angle corresponding to the sidereal and not to the mean time interval, and a reduction should be made accordingly to give its true hour angle at the instant of observation. A planet's hour angle should be corrected in the same way (for we may disregard its very small change m right ascension). The correction may be entirely neglected in the case of the sun, as the difference between mean and apparent time intervals is immaterial. The reduction of the hour angle in the ca.se 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. 8. T., and finding the difference between the latter and the R. A.; an additional reason for this is that the G. M. T. of observation must be known exactly, with the moon, for the correction of the declination (art. 338). 336. Table 26 includes values of the latitude up to 60°, and those of the declination up to 63°, thus taking in all frequented waters of the globe and all heavenly bodies that the navigator is likely to employ. No values of (i are given when the altitudes are above 86° or below 6°, as the method of reduc- tion to the meridian is not accurate when the body transits very near the zenith, and the altitudes themselves are questionable when very low. In case it is desired to find the change of altitude in one minute from noon for conditions not given in the tables, it may be computed by the formula: l'^9635 cos L cos d sm (L — a) In working sights by this method where great accuracy is required, as in determining latitudes on shore for surveying purposes, it is well to compute the a rather than to take it from the table, as one is thus enabled to employ the value as found to the second decimal jilace. Due regard must be paid to the names of the declination and latitude in working this formula; if thev are of opposite names, the declination is negative, and L and d should be added together to obtain L— '(/. 337. Table 27 contains values of af up to the limits within which the method is con.sidered to apply with a fair degree of accuracy. It nuist not be understood that the plan of reduction to the meridian is not available for wider limits, but it would seem ]ireferable to employ the tp^ cp" 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 sufiiciently so for sea navigation, the limits given are far too wide for the precise determinations required in surveying, where the aim should l)e to observe bodies under such conditions that the total reduction a(^ shall not exceed V. 33§. 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 observation, and to bring it up to noon the run nuist be applied. The declination should properly be corrected for the instant of observation; with the sun or a planet, it is sufiiciently 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 nmst be used in its correction when working with this body. 22489—03—7 98 LATITUDE. Ex.\mplk: In latitude 47° S., having previou.-^ly worked up the constant for meridian altitude; 78° 42^ 10'^ observed altitude of sun near meridian,' 31° 11' 50'';.Dec 11° X.; watch time, 11" 40™ 21% watch fast of L. A. T., 7*. Find the latitude. Watch time, 11" 40°' 21^ AVatch fast, • 07 L. A. T., 11 40 14 t, 19'' I.46S Obs. alt., 31° 11^50'' at\ + 10 24 a (Tab. 26), 1.'''6 Mer. alt., 31 22 14 ConsUnt, 78 42 10 a<2(Tab.27), Lat., 47 19 56 8. l.'''0= 6^30'^ . 6= 3 54 1. 6 = 10 24 Example: At sea, July 12, 1879, in Lat. 50° N., Long. 40° W., observed circum-meridian altitude of the sun's lower limb, 61° 48' 30^', the time bv a chronometer regulated to Greenwich mean time being 2" 41'" 39^; chro. corr., -2"" 30'; I. C, —3' O''; height of the eye, 15 feet. Find the latitude. Chro.t., C.C, 2h 4i« - 2 '39' 30 Q Corr. , h, S. D., dip, p. & r. L C, Corr., h 61° ' 48' 30" 8 31 Dec, H.D., Long., Corr., Dec, 22° 00' 23". 2 N. Eq.t., H. D., Long., Corr., Eq. t, {Suhtrac time. ) [Tab. 26), 2. 2. (Tab. 27), r^- 5'" 17^99 20". 7 2". 7 + 0^32 2". 7 G.M.T., Eq.t., 2 39 — 5 09 19 61 57 01 -T 15' 46" 55". 9 ~ .86 G.A.T., Long., , 2 33 - 2 40 50 00 ) 3 48 27 3 00 21° 59' 27" X. a 1 at' 5"' 18».9 L.A.T., 11 53 50 t, 6 10 - 7 15 61° 57' 1 8 31 01" 35 "5 "0 = 1' 16" 5 = 19 H, 61 58 36 1 35 28 01 24 N. 21 59 27 N. L, 50 00 51 X. Example: May 31, 1879, in Lat. 30° 25' X., Lonsf. 5" 25"' 42' W., about 9 p. m., observed with a sextant and artificial horizon a series of altitudes of Spica; mean observed double altitude 98° 06' 34"; noted times as enumerated below bv a watch compared with a chronometer which was 2"' 33'' fast of G. M. T.; C-W, 5" 29"" 40^ I. C, -3' 00". Find the latitude. R. A. * (L. S. T.transit) , 13" 18'" 52^2 Mean 2 all Long., G. S. T., R. A. M. S. Gr. 0", Sid. int. from 0", Red. (Tab. 8), G. M. T., C. C. (sign reversed), Chro. time transit, C— W, Watch time transit. + 5 25 42 Watch times. 8" 31'" 18^0 33 19.5 36 07.0 38 50.0 41 07.5 43 45.5 45 46.0 47 33.0 51 12.5 18 44 4 34 34.2 26.9 14 10 2 07 .3 re 19.4 ;, 14 07 _U 9 > 1 -^ 47 .9 33 14 10 - 5 29 20.9 40 8 40 41 Intervals from transit. Meantime. — 9'" 23^0 21 .5 34.0 51.0 -r 26.5 3 04.5 5 05.0 6 52.0 31 .5 10 Sid. time. - 9™ 24' 7 23 4 35 1 51 -0 27 3 05 5 06 6 53 10 33 98° 06' 34" 3 00 R. A. *, Dec, a (Tab. 26), 13" 18'" 52^2 10° 32' 04" S. 98 03 34 2".5 49 01 47 50 49 00 57 at^ (Tab. 27). £o 05^ 2!5 ' 2' 56" 0' 44" 3' 40" 1 49 27 2 16 42 10 52 07 01 08 01 00 01 19 04 23 52 13 1 05 1 35 23 1 58 3 42 55 4 37 h, 49° 00' 57" «<*,+ 1 40 H, 49 02 37 40 57 23 N. 10 32 04 S. 30 25 19 N. 9)15 00 1 40 LATITUDE. 99 Example: August 6, 1S79, Lat. 59° S., Long. 175° 27^ E., during evening twilight, observed an altitude of Achernar, near lower transit, 26° 52'; watch time, 4" 31"' 12^; C — W, 0" 18"' 07^; chro. fast of G. M. T., 12"' 42^; I. C, -f V 20^'; height of eye, 24 ft. Find hour angle by both methods; thence the latitude. R. A. JJC -t- 12 1 1 Oh oom 1 Ka A L. S. T. lower trans./ ^'^ ^^^ ^^ '^ Long., - 11 41 48 Watch time, C-W, Chro. t., C. C, G. M. T. 5^ R.A.M.S. Gr.5''0S Red. (Tab. 9), G. S. T., Long., L. S. T., R. A. * + 12h, R. A. *, 1" 33°' 4" 31" + 18 '12^ 07 4 49 — 12 19 42 G. S. T., 1 R. A.M. S. Gr.5'»0^- 8 51 54 27.4 39.8 16 36 + 8 54 + 2 37 39. 43, Sid. int., 16 Red. (Tab. 8), - 56 2 47.6 46.6 ,8 ,7 G. M. T., 16 C. C. (sign reversed ),+ 54 12 01.0 42 1 34 + 11 41 00. 48 .5 Chro. time, 5 C-W, - 06 18 43 07 13 15 13 33 48. 15. ,5 ,4 Watch time transit, 4 Watch time obs., 4 48 31 36 12 17 15^4 27 , fMean time, \Sid. time, Obs. alt: *, 26° 17 17 52' 24 27 00" L C, + 4' 1 20" 48" 55 Dec, 57° 50' ■ 28" S. dip, — ref., - p, 32= ■ 09' 32" a (Tab. 26), at^ (Tab. 27), 0".6 3' 03" - 6 43 Corr. , — y 2.3" /(, 26° at\ - 46' 3 37" 03 H, 26 P, 32 43 09 34 32 L, 58 53 06 S. BY A SINGLE ALTITUDE AT A GIVEN TIME. 339. This observation should be limited to conditions where the body is within three hours of meridian passage and where it is not more than 45° from the meridian in azimuth. On the prime vertical the solution by this method is inexact, and when the hour angle is 6'' it is impracticable. The problem is: Given the hour angle, declination, and altitude, to find the latitude. The solution is accomplished by letting fall, in the usual astronomical triangle, a perpendicular from the body to the meridian, and considering separately the distances on the meridian, from the pole and zenith, respec- tively, to the point of intersection of the perpendicular; the sum or difference of these distances is the co-latitude. Following the usual designation of terms and introducing the auxiliaries ' and - 1 37.5 7 33 32.5 + 4 22 37.3 + 1 14.5 11 57 24.3 -10 22 17 1 35 07 2 01 26 Obs. alt.'C. S. D., Aug., dip, I. C, 75° 33' 00" 15' 51" 16 5 00 3 00 24 07 R. A. C, M. D., No. mill., Corr., R. A., lOh 21" ,. 07» .78 + 28 .06 .54 -{ 1' 69«.09 "09' Dec, M. D., No. mill., Corr., Dec, 6°49'52".4 N. 14".46 33"'.54 486" 05" 6° 41' 47" -I ' I 8' I N. W. \V. Oh 26ni 19* E.. 6° 34' 4.5" Approx. alt., 75° 08' ,53" p. (t-r.(Tab.24), + 14 37 h. 75 23 80 Hor. Par., 58' 03" t d h ^" 9,' Lat. 6° 34' 45" 6 41 47 75 23 30 6 44 26 N. 13 05 40 S. 6 21 14 S. sec tan .00286 9.06973 tan 9.07259 sin sin .93324 9.98573 9.06959 cos 9.98856 Example: August 6, 1879, p. m., in Lat. 52° 47' S. by D. R., Long. 146° 32' E., observed altitude of Achernar, near lower transit, 24° 01' 20" bearing south and west; watch time, 6'' 48"' 22"; C— AV, 9" 46" 27'; chro. corr. on G. M. T., + 1'" 57% height of eve, 18 feet; I. C. + 1' 00". Find the latitude. Watch time, c-w. 6" 48"' + 9 46 '22' 27 Obs. alt. y^, Corr., — I. c, + dip, - ref., — Corr., — 24° 01' 20" 5 19 R.A. *, 1" 33-" 15'. 3 •Dec, 57° 50' 28" S. Chro. t., C.C, 4 + 34 1 49 57 23 56 01 — I'OO" 4' 09" 2 10 G. M. T., 5^ R. A. M. S., Red. (Tab. 9), 16 + 8 36 54 2 46 39.8 43.7 G. S. T., R. A. *, 1 1 34 33 09.5 15.3 6 19 5' 19" H. A. from Gr. Long., ,, 9 00 46 54 W. . 08 E. H. A., 9 47 02 W. t, f 2" I 83° 12"' 58' ' 14' 30" t d 33° 57 23 -'51» >40» 90° 0' 52 a5 89 60 52 30 40 52 55 30 53 20 20 Mean, W. T., P. M., 2h Si-" '30«.0 Mean, W. T. C-W,- ■ +5 31 58 .5 C - W, P. M. Chro. T., 8 24 r A.M. Chro.: V'ATCH , A. M. 8h 59" '00' 58 34 .5 58 09 .5 57 40 .0 57 20 .0 H.D.atMid.,+ .51".10 Long. H-12h, 17'>.43 DiflF. 24^, -0.48 A. M. Chro., T. +12'', 26 30 1 2)10 54 39 .5 Klapsed Time, M., 8h 58" + 5 32 '10" 01 L21', 26 8 30 24 11 .0 28 .5 18 05 42 ,5 1" 04 '.9 + 0'.54 17''.43 + 9».4 Dec, 11° 44' 08" N. f 890".7 Diflf. Ih, _ 0".02 114' .51" — — DiflF. I'^AS, - 0".a5 H. D. at Mid., +.51".10 Mid. Chro. T., 5 27 19 .75 Eq. eq. alt., + 19.35 Eq. t.. 1"04».9 Tab. 37 log A ( + )9.9364 logB(-)9.7912 H.D.+51".101og (+)1.7084 log ( + )1.7084 Chro.t.L.A.Mid., 6 27 39.1 H. D., + 0'.54 Lat. 30° 25' ten ( + )9.7687 ri+ll°44'tan ( + )9.3175 Eq. t., + 1 14 .3 Long. + 12!>, 1st Part 4-25'.911og( + )1.4135 Chro. t.,L.M. Mid., 6 28 53.4 Corr., + 9».4 2d Part - 6 .56 log (-)0.8171 C. C. , - 3 11 .4 Eq.t, lml4.».3 *^%^^- }+19 .35 Lop„ -yy f Sh 25" 42 '.0 {Plus to mean time.) " l81°25' 30" LONGITUDE. 105 348. In the same example the equation of equal altitudes may be found by the less exact method heretofore given (art. 324), as follows: Change in declination between sights = H. D. X Elapsed time = 51'''.10 X IS*".! = 925^''. Change in altitude due to 100'^ declination (Tab. 25) = + 53^^ h' = + V = + 53 X925, 100 X 60 2''53'"20«- = + 8M9. 2 " 51"' 40^ ^ ^ 100' , 90° 00^ - - 89° 20^ ' 40'' Eq. eq. alt. = + 8.19 X 2'.5 = i 20'.5. : + 2'.5. DETERMINATION AT SEA. 349. The Time Sight. — The method of determining longitude at sea which is employed almost to the exclusion of all others is that of the lime sight, sometimes called the chronometer method. The altitude of the body above the sea horizon is measured with a sextant and the chronometer time noted; the hour angle of the body is then found by the process described in article 316, Chapter XI. If the sun is observed, the hour angle is equal to the local apparent time; the Greenwich apparent time may be determined by applying the equation of time to the Greenwich mean time as shown by the chronometer; the longitude is then equal to the difference between the local and the Greenwich appar- ent times, being east when the local time is the later, and west when it is the earlier of the two. If any other celestial body is employed, the hour angle from the local meridian, found from the sight, is compared with the hour angle from the Greenwich meridian to obtain the longitude; the Greenwich hour angle is found by converting the Greenwich mean time into Greenwich sidereal time in the usual manner, and then taking the difference between the latter and the right ascension of the body, the remainder being marked east or west, according as the (xreenwich sidereal time is the lesser or greater of the two quantities; and as the local hour angle may be marked east or west according to the side of the meridian upon which it was observed, the name of the longitude will be indicated in combining the (juantities. 350. As has been stated, the most favorable position of the celestial body for tinding the hour angle from its altitude is when nearest the prime vertical, provided the altitude is not so small as to be seriously affected by refraction. 351. In determining the longitude at sea by this method, it is necessary to employ the latitude by account. This is seldom exactly correct, and a chance of error is therefore introduced in the result- ing hour angle; the magnitude of such an error depends upon the position of the body relatively to the observer. The employment of the Sumner line, which is to be explained in a later chapter, insures the navigator against being misled from this cause, and its importance is to be estimated accordingly. Example: At sea, May 18, 1879, a. m.; Lat. 41° 33' N.; Long. 33° 30' W., by D. K., the following altitudes of the sun's lower limb were observed, and times noted by a watch compared with the Green- wich chronometer. Chro. corr., -f 4'" 59''.2; I. C, — 30^'; height of the eye, 23 feet; C- W, 2" 17'" 06". Required the true longitude. Eq. t., 3"' 47 -.68 VV. T., 7" 20^15' 20 47 21 14 -h A. A. Obs. alt. Mean, Corp., h, .S. D., dip, p. A r., I.e., Corr., 29° 41 70 , 29° 35' 41 46 30" 20 10 Dec, H. D G. M. Corr., Dec, P, 19° 32' 01".S X. + T., - 33".09 2h.3 Mean, C-W, 7 + 2 20 17 4.5.3 06 29 + 41 9 00 05 19° 30' 76". 1 16" 46" N. Ohro. t., C. C, 9 + 37 4 51.3 59.2 29 50 05 + + 50' 33 29 1.5' 51" G. M. T., Eq. t., 17'>, 21 + 42 3 50.5 47.9 70° 29' sec cosec cos sin sin i t 14" 4' 1 42" 34 30 G. A. T., 21 46 38.4 h L P 8 S- G. L. 6 46 9' 05'' 00 14 05" .12588 .02569 2)141 70 41 52 56 06 19 09 04 9.51406 9.81782 T. 21^ T. 19 46™ 32 38' 07 2)19.48345 9.74172 H. D., - 0«.09 G. M.T., - 2';.3 Corr., + 0".21 Eq. t., 3">47».9 {Plun to mean time.) Long. {32: 14; ^i;}w. 106 LONGITUDE. Example: At sea, April 16, 1879, p. m., in T.at. 11° 47' S., Long. 0° 20' E., by D. R., observed au altitude of the star Aldebaran, west of the meridian, 23° 13' 20"; chronometer time, e*" 56'" 32"; chro- nometer fast of G. M. T., 2"' 27"; I. C. —2' 00"; height of eye, 26 feet. What was the longitude? Chro. t., 6" 56'" 32" C. C, - 2 27 « G. M. T., 6 54 05 R. A. M. S., +1 37 01.9 Red. (Tab. 9),+ 1 08.0 G. S. T., 8 32 14.9 R. A. *, 4 28 59. 6 Obs.alt.*, 23° 13' 20" R. A. 5+:, 4" 28°' 59^6 Corr., - 9 16 Dec, 16° 15' 59" IS '', 23 04 04 p, 106° 15' 59" I.e., - 2' 00" dip. - 5 00 ref., - 2 16 H.A.fromGr., 4 03 15 W. Corr., - 9 16 /( 23° 04' 04" L 11 47 00 sec .00925 p 106 15 59 cosec .01774 2)141 07 03 s 70 33 32 cos 9.52223 s—h Al 29 28 sin 9.86757 2)19.41679 Gr.H.A. 4'' 03'" 15^ W. H. A. 4 05 50 W. sin \ t 9. 70839 rO" 02™ 35n, .ong. Iqo 38, 45,/|i Example: At sea, April 17, 1879, 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, 45° 40'; watch time, 5*' 48"" 02'; C — W, 2" 05"" 42'; C. C, +2'» 18^; I. C, +1' 30"; height of eye, 18 feet. Required the longitude. W. T., 5h 48°> 02- Obs. alt. *, C— \V, 2 05 42 Corr., Chro. t., 7 53 44 /(, C.C, + 2 18 G.M.T.,16«, 19 56 02 R. A. M.S., OS +1 37 01.9 Red. (Tab. 9), + 3 16.5 I.e., dip, ref., 45° 40' 3 00" 36 45 36 24 + 1' 30" - 4' 09" 57 _ 5 06 R. A. (17' 10''), 221' 27° >19».0 Dec. (mOk), H.D., G.M.T., Corr.. Dec, P, , 10° 36' 28".l S. H.D., G.M.T., Corr.. + 1».8 4t'.l 7'. 4 + 10".0 4«'.l 41". R.A., 22h 27" ' 11^6 10° 37' ■ 09" S. 79° 22' 51" G.S.T., 21 36 20.4 22 27 11.6 Corr., h L P 8 8— Gr H. h .H A. - 3' 36" 45° 36' 24" 25 12 00 79 22 51 sec cosec cos sin sin J / H.A.fromGr., 50 51 E. . 04343 .00750 2)150 11 15 75 05 38 29 29 14 9.41032 9. 69217 \ . A. 0" 50'"51'E. 2 57 21 E. 2)19.15342 ■ 9. 57671 T^.,„ / 2"06'"30nT^ Long. |3io37,3o//|W. LONGITUDE. 107 Exami'lk: At sea, June 26, 1879, p. m., in Lat. 49° 50' N., Long. 6° 16' W., by account, observed an altitude of the moon's lower limb 21° 18' 10", the body bearing east; chronometer time, 2" 26'" 58»; chronometer slow of G. M. T., 42*; I. C., — 1' 45"; height "of eye, 22 feet. Find the longitude. Chro. t, 2" 26-58 • C. C, + 42 G. M . T., 2 27 40 R. A. M. S., + 6 16 57.5 E< S. (Tab. 9), T., + 24.3 G. 8 45 01.8 R. A. ^C- 11 38 39.3 H. A. from Gr., 2 53 37- E. Ote. alt, •i. , alt rab. 2)" 1 21° 18' 10" R. A., M. D., + No. min., Corr., + R. A., Hor. par., sec cosec cos sin sin i t llh 37'° 41'.96 Dec, M. D., No. min., Corr., Dec. , P. 2° 35' 36".4 S. S. D., Aug., + 15' 59" + 6 2».07 27'". 7 15". 1 27°'. 7 + 16 05 57'.34 _f 419".3 I 6' 59".3 2° 42' 36" S. dip, I.e., - 4' 36" - 1 45 llh 38-" 39^.3 58' 35" .19043 .00049 9.11923 9.93799 - 6 21 92° 42' 36" 1st corr. + 9' 44" Approx, p.&r. (1 21° 27' 54" 24), + 52 06 h L P 22 20 00 22° 20' 00" 49 50 00 92 42 36 8 s—h 164 52 36 82 26 18 60 06 18 Gr. H. . H. A. 2" 53™ 37' E. 3 19 04 E. 2)19.24814 9.62407 Long. 0" 25- 27'-!^ 6° 21' 45"/"^- 352. Equal Altitudes. — The method of finding the longitude at sea by observation of equal alti- tude.'! of a heavenly body is one that may be conveniently employed when applicable, though the limits of apj)licability are narrow. If, on board a vessel which is either stationary in position or moving at a uniform rate of speed in a true east or west direction, equal altitudes of the sun, a planet, or a star be observed before and after transit, and the times noted by chronometer or watch, the interval from meridian being not greater than ten minutes of time and the altitude not less than 75°, the mean of the times will be the time (by the chronometer or watch used) of the meridian passage of the body; from this may be found the Green- wich mean time of transit and thence the longitude. If (the limits of time and altitude remaining as stated) observations be taken when the body bears not less than 80° from the meridian, the time of meridian passage may with accurracy be regarded as equal to the mean of the times of observation, no matter what course may have been steered by tb< vessel in the interval. But if the azimuth of the body is less than 80° from the north or south point of the horizon the method is not available for vessels making a material amount of northing or southing; and if the hour angle is greater than 10™ or the altitude less than 75°, it can not be accurately employed by any vessel, no matter what course is steered. The navigator .«hould not yield to the temptation offered by the simplicity of this method to follow it beyond the limits within which it may properly be considered to apply. 353. To deduce the longitude by this method take the mean of the watch times before and after transit, which will give the watch time of transit; correct this watch time in the usual manner for C— W and chronometer correction, from which is derived the Greenwich mean time of transit. In the case of the sun, apply to the Greenwich mean time the equation of time, giving it its sign of application to mean time; the result is the Greenwich apparent time of transit, which is equal to the longitude if the latter is west, or to 24'' mhiii.^ the longitude if east. For other bodies, convert Greenwich mean time into Greenwich sidereal time by the usual method; the body being on the meridian, the local sidereal time is equal to the body's right ascension; the difference between Greenwich and local sidereal times is the longitude — east if the local time is greater, and west if it is less. 108 LONGITUDE. Example: April 2, 1879, in Lat. 3° 30' X., Long. 86° 00' E., by D. R., observed equal altitudes of Q before and afternoon, using same sextant and same height of eve. Watch: a. m.. 11'' 52°' 37"; p.m., 12" 07"" 22"; C - W, 6" 17" 48'; C. C, + 2™ 32'. Vessel steering west' between sights. Required the longi- tude at noon. W. T., A. M., 11" 52-" 37» Eq. t., 3"' 42\5 W. T., P. M., 12 07 22 « H. D., - 0^.75 G. M.T., - 5".7 W. T.,L. A.,noon, 11 59 59.5 Corr., + 4».3 C-W, Eq. t., 3'" 46^8 Chro. t., L. A.,noon, 6 17 47.5 ( /S'u6- 24°. 1 N. Obsd. amp. E. 18°. 5 N. j ^ v 1 q c xr True amp. E. 24° 08' N. sin 9.61144 Corr. (Tab. 40) 0. 3 left.J ''^'"P* '^'"P- ^^- ^^ ' ^ ^• Comp.amp.E. 18 48 N. Error, 5° 20' W. Error, 5°. 3 W. Example: At sea, in Lat. 40° 27' N., the mean of the observed bearings of the upper and lower limbs of the moon when in contact with the visible horizon at setting was W. 17° S. ; declination, 21° 12' S. What was the error of the compass? By computation. By inspection ( Table 39). L 40° 27' sec .11863 L, "^"^"-^ ^-j True amn W 28° 4 S d 21 12 sin 9.55826 d, 21 . 2 S.j ^™^ '""P- ^^•^^•'if'- Obsd. amp. AV. 17°.0S. ) p ait i^ 7 c True amp. W. 28° 22' S. sin 9.67689 Corr. (Tab. 40) 0.3 right. f <^omp.amp. w. lb ./ b. Comp. amp.W. 16 42 S. Error, 11°. 7 W. Error, 11° 40' W. TIME AZIMUTHS. 359. In this method are given the hour angle at time of observation, t, 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 solution when the altitude is low. 360. Take a bearing of the object, bisecting it if it has an appreciable disk, and note the time with a watch of known error. Record, as usual, the ship's head by compass and the amount of heel. If preferred, a series of bearings may l)e taken with their corresponding times, and the means taken. 361. First prepare the data as follows: (a) Find the Greenwich time corresponding to the local time of observation. {h) Take out the declination of the body from the Nautical Almanac; if the method of computation is employed the polar distance and the co-latitude should be noted. (c) Find the hour angle of the body by rules heretofore given. This having been done, the true azimuth may be determined either by Time Azimuth Tables, by the graphic method of an Azimuth Diagram, or by Solution of the Astronomical Triangle. Owing to the pos- sibility of more expeditious working, either of the first-named two is to be considered preferable to the last, and the navigator is recommended to supply himself with a copy of a book of Azimuth Tables, or with an Azimuth Diagram ; an explanation of the method of use accompanies each of these. 362. To solve the triangle: Let S = ^ sum of polar distance and co-Lat. D = I difference of polar distance and co-Lat. ht = h hour angle. Z = true azimuth. Then, tan X = sin D cosec S cot ^ t; tan Y = cos D sec S cot ^ t; Z = X + Y, or X ~ Y. First Case. — If the half-sum of the polar distance and co-Lat. is less than 90° : take the sum of the angles X and Y if the polar distance is greater than the co-Lat. ; take the difference if the polar distance is less than the co-Lat. Second Ca^e. — 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 prefix N. or S., in order to make it correspond to the compass azimuth when the latter is less than 90°. The cotangent of half the hour angle may be found from Tal)le 44 abreast the whole hour angle in the column headed "Hour P. M." AZIMUTH. Ill Examplk: December 3, 1879, a. m., in Lat. 30° 25' X., Long. 5" 25™ 42^ W., the observed bearing of BUn's center was N. 135° 30' E., and the Greenwich mean time, December 3, 2^ 36'" IP. The corrected decUnation 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), Long., 2h 36m lis 5 25 42 co-Lat., 59° 35' p, 112 07 L.M.T. (Dec.2), 21 10 29 Eq.t, + 10 03 L.A.T., 21 20 32 t, 2" 39"' 28" p+co-L, 171 42 S, 85 51 p-co-L, 52° 32' X+Y 139 03 D, 26 16 True azimuth, N. 139° 03' E. Comp. azimuth, N. 135 30 E. t s D 2" 39"' 85° 51' 26 16 50 44 88 19 28" cot J( .44051 cosec .00114 sin 9.64596 cot it .44051 sec 1.14045 cos 9.95267 X Y tan .08761 tan 1.53363 Compass error, 3 33 E. Example: April 9, 1879, in Lat. 2° 16' N., the observed bearing of the sun's center was N. 85° 15' E; sun's hour angle, 3'' 44" 16% and its declination, 7° 38' N. Required the compass error. co-Lat., 87° p, 82 44' 22 t S D X Y Y-X True a; Comp. Com pa 3" 44"' 16" 85° 03' 2 41 5 03 87 22 cot it .27372 cosec .00162 sin 8. 67039 cot it sec cos tan . 27372 1. 06406 9. 99952 p+co-L, 170 06 tan 8. 94573 82° 19' E. 85 15 E. 8, .85 03 1. 33730 co-L—p, 5° 22' :82 19 zimuth, N. azimuth, N. 88 error, D, 2 41 2 56 W. Example: April 26, 1879, Lat. 16° 32' S., observed bearing of Venus 56° 00' W., its hour angle being 4'' 27"' 31", and its declination 23° 12' N. What was the error of the compass? co-Lat. , P, 73° 28' 113 12 t S D X Y Y- Z -X 4h 27n> 93° 20' 19 52 27 16 87 40 31" cot it . 18022 cosec . 00074 sin 9.53126 cot i I sec cos tan : .18022 1.23549 9. 97335 p+co-L, 186 40 tan 9. 71222 s, 93 20 . 39° 44' 1. 38906 p — co-L, (iO 24 119° 36' D, 19 52 True azimuth, S. 119° 36' W. Comp. azimuth, S. 124 00 W, 4 24 W. ALTITUDE AZIMUTHS. 363. This method is employed when the altitude of the body is observed at the same time as tiie azimuth; in such a case the hour angle 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 ace given the altitude, /(, the polar distance, p, and the latitude, L; to find the azimuth, Z. 364. 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 mean employed. 365. 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 =v/ooH s cos (.s— />) sec L sec h, in which s = i (/i + L -fp)- The resulting azimuth is to be reckoned from the north in north latitude and from the south in south latitude. 112 AZIMUTH. It may occur that the term (s— ; ) will have a negative value, but since the cosine of a negative angle less than 90° is positive, the result will not be affected thereby. Example: December 3, 1879, in Lat. 30° 25' N., the observed l)earing of the sun's center was N. 135° 30' E., and its corrected altitude 24° 59'; the approximate G. M. T. was 2''.6, the declination at that time being 22° 07' S. Required the compass error. h L P •24° 30 112 59' 25 07 sec sec . 04267 . 06431 2)167 31 s 8-p 83 -28 45 22 cos cos 2 9. 03690 9. 94445 ) 19. 08833 z 69 139 30 00 cos 9. 54416 True azimuth, N. 139° 00' E. Comp. azimuth, N. 135 30 E. Compass error, 3 30 E. / 39° 52' (I 22 07 /( 24 59 sin 9. 80686 cos 9. 96681 sec .04267 Z S. 40° 56' E. sin 9. 81634 TIME AND ALTITUDE AZIMUTHS. 366. AVhen, at the time of observing the compass bearing of a celestial body, the altitude is meas- ured and the exact time noted, the true azimuth may be very expeditiously determined, a knowledge of the latitude being unnecessary. In view of the simplicity of the computation this method strongly commends itself to observers not provided with an azimuth table or diagram. SeT. The observation is identical with that of the altitude azimuth (art. 364), with the exception that the times of observation must be exactly instead of approximately noted. 36§. Ascertain the declination of the body at time of sight, and correct the observed altitude; com- I^ute the hour angle. We then have : sin Z=sin t cos d sec h, from which the azimuth may be found. This method has a defect in that there is nothing to indicate whether the resulting azimuth is measured from the north or the south point of the horizon; but as the approximate azimuth is always known, cases are rare when the solution will be in question. Example: December 3, 1879, in Lat. 30° 25' N., Long. 5*' 25™ 42* W., the observed bearing of the sun's center was N. 135° 30' E. ; its altitude at the time was 24° 59'; hour angle, 2" 39™ 28» (39° 52'), and declination 22° 07' S. Find the compass error. (See example under Altitude Azimuths and first example under Time Azimuths. ) True azimuth, N. 139° 04' E. Comp. azimuth, N. 135 30 E. 3 34 E. TRUE BEARING OF A TERRESTRIAL OBJECT. 369. Thus far, sea observations for combined variation and deviation have been discussed, but if it becomes necessary, as in surveying, to ascertain the Tnie Bearing of a Terrestriid Ofijed, 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 Asitronomical Bearing. This consists in finding the true bearing of some well-defined object by taking the angle between it and the sun or other celestial body with a sextant or a theodolite, and simultaneously noting the time by chronometer, or measuring the altitude, or observing both time and altitude. It should always be noted whether the object is right or left of the sun. 370. By Sexiant. — 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 as.sistant, first measure the altitude of the sun; next, the angular distance between the sun and the object; then, a second altitude of the sun, noting the time of each observation. Also measure the altitude of the defined point above the sea or shore horizon. By Tlieodolite. — 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 oljjects. 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 nmst, how- ever, be found by the level attached to the telescope, since it will usually be found to differ from the levels of the horizontal circle. If, in directing the telescope to the sun, there is no colored eye-piece, an image of the sun may be cast on a piece of white paper held at a little distance from the eye-piece, and by adjusting the focus the shadow of the cross-wires will be seen. It should be understood that any celestial body may be used as well as the sun, and there are, in fact, certain advantages in the use of the stars; the sun is chosen for illustration, because it will usually be found most convenient to emi)loy that body. AZIMUTH. 113 371. Find the true azimuth of the celestial body by any one of the methods previously explained in this chapter and applj' to it the azimuth difference, or horizontal angle between the celestial and the terrestrial body, having regard to the direction of one from the other. To find the azimuth difference from sextant observations, change the observed altitudes of the bodies into apparent altitudes by correcting them for index error of the sextant, dip, and semidiameter; change the observed angular distance into apparent angular distance, by correcting for index error and semidiameter. Then if S = J (App. Dist. + App. Alt. Q -f- App. Alt. Object) , we have: cos I Az. Diff. = v/sec App. Alt. sec App. Alt. Object cos S cos (S — App. Dist. ), whence the azimuth difference is deduced. When the theodolite is used, the horizontal angle is given directly. If only one limb of the sun is observed, it will be necessary^ to apply the semidiameter, but it is usual to eliminate this correction by taking the mean of observations of both limbs. Example: Decemlier 10, 1879, a. m., in Lat. 30° 25' 24'' N., Long. 81° 25' 24" W., made observa- tions with a sextant and obtained the following data for finding the true bearing of a station: Watch time, 11" 22-" 36' Obs. Ang. Dist. 0, 117° 07' Left. C-W, 5 21 18 Obs. 2Q, 71° 37' 20" Chro. corr., + 2 16 Obs. 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. 2 0, W. T., C-W, Chro. t., C. C, G.M.T.,Dec. 10, Eq. t., G. A. T., Long., L. A. T., 11" 22"' 36' 5 21 18 4 43 + 2 54 16 4 46 -]-' 7 10 00 4 53 - 5 25 10 42 23 27 28 S. D. 71° 37' 20" 35 48 40 16 17 8° 08' 00" 22 56 27 36 03 37 App. Alt., 36 04 57 ;). &r., — 1 13 ,/ S. 9° 17' E. IN. 170 43 E. sin 9.15069 cos 9.96422 sec .09239 sin 9.20730 36 03 44 t, fO" 32"' 32" \8°08' 00" Obs. Ang. Dist., 117° 07' 00" App. Dist. 117° 23' True bearing 0, N. 170° 43' E. 0'sS. D., + 16 17 App. Alt. 36 05 sec 0.092.50 Az. Diff., 125 00 Left. App. Alt. Object 20 2)153 48 sec 0.00001 Api>. Ang. Dist., 117 23 17 True bearing object, X. 45° 43' E. S 76 54 cos 9.35536 S — App. Dist. -40 29 cos 9.88115 2)19.32902 k Az. Diff. 62° 30' cos 9.6&151 Az. Diflf. 125 00 Example: Same date and place and same objects as in the preceding example; measurement made with a theodolite, angular distance C{), 123° 17'; object left of sun. AVatcli time, ll"" 16"" 34''.5; watch slow of L. A. T., 4"' 53^5. Dec. 0, 22° 56' S. Required the true bearing. W.T., ll''16"'34\5 W. slow, + 4 53.5 L. A. T., 23 21 28 .0 t, 38 32 co-Lat., 59° .35' />, 112 56 p-i - co-L, - co-L, 172 31 S, 86 15 P- 53 21 t S D 0" 38"' 86° 15' 26 41 79° 24' 89 39 32» cot h t 1.07435 cosec .00093 sin 9.65230 cot J< sec cos tan 1.07435 1.18440 9.95110 X tan .72758 Y 2.20985 X + Y169 03 D, 26 41 True bearing 0, Az. Diff., N. 169° 03' E. 123 17 Left. Trtie bearing object, X. 45 46 E. 22489—03- 114 THE SUMNEE LINE. CHAPTER XV. THE SUMNEE LINE. DESCRIPTION OF THE LINE. 372. The method of navigation involving the use of the Sumner Hue 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, the incident which led to its discovery may be related: " Having sailed from Charleston, S. C, 25th November, 1837, bound for Greenock, a series of heavy gales from the westward promised a quick passage; after pansing the Azores the wind prevailed from the southward, with thick weather; after passing .longitude 21° W. no observation was had vmtil 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, ITth 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 oliservation, 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 l)y dead reckoning, and toward the danger, giving a position 27 miles ENPl of the former position; a third latitude was assumed 10' farther north, and still toward the danger, giving a third position ENE. of the second 27 miles. Upon plotting these three positions on the chart, they were seen to be in a straight line, and this line passed through Smalls light. " It then at once appeared that the observed altitude must have happened at all the three i>oints 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 EN?]., and in less than an hour Smalls light was made, bearing ENE. ^ E. and close aboard. The latitude by dead reckoning was found to be 8' in error, and if the ]wsition given by that latitude had been assumed "correct the error Avould have been 8 miles too far S. and 81' 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 ijractical applications of the Sumner line. The properf.es of the line thus found will now be explained. 373. C'iRCLKs OF EQr.\L Altitude. — In figure 43, if EE'E" represent the earth projected upon the horizon of a point A, and if it be assumed that, at some particular instant of time, a celestial body is in the zenith of that point, then the true altitude of the body as observed at A will be 90°. In such a case the great circle EE'E", which forms the hori- zon of A, will divide the earth into two hemi- spheres, and from any point on the surface of one of those 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 botly, is termed the circle of illniiiuuition, and from any point on its circumference the true altitude of the center of the body will be zero. If, now, we con- sider any si'nall circle of the sphere, BB'B", CC'C", DD'D", whose plane is parallel to the plane of the circle of illumination and which lies within the hemisphere throughout which the body is visible, it will be apparent that the true altitude of the body at any point of one of these circles is equal to its true altitude at any otiier point of the same circle; thus, the altitude of the body at B is equal to its altitude at B' or B", and its altitude at 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 wliich a celestial bodv 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 zenith, and whose radius depends upon the zenith distance, or — what is the same thing — upon the altitude. Such circles are termed circles of etjnal altittuk. Fig. 43. THE SUMNER LINE. 115 374. The data for an astronomical s-i^ht comprise merely the time, declination, and altitude. The first two fix the position of the body and may be regarded a^ giving the latitude and longitude of that point on the earth in whose zenith thel)ody is found; the zenith distance (the complement of the altitude) indicates the distance of the observer's zenith from that point; but there is nothing to show at which of the numerous positions fulfilling the required conditions the observation may have been taken. A number of navigators may measure the same altitude of a l)ody at the same instant of time, at places thousands of miles apart;' and each proceeds to work out his position with identical data, so far as this eight is concerned. It is therefore clear that a single observation is not enough, in itself, to locate the point occupied 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 44 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 A() and A^O. 375. The Sumxer Line. — In practice, under the conditions existing at sea, it is never necessary to determine the whole of a circle of equal altitude, as a very small portion of it will suffice for the pur- poses of navigation; the position is always known within a distance which will seldom exceed thirty miles under the most unfavorable conditions, and which is usually very much less; in the narrow linuts thus required, the arc of the circle will practically coincide with the tangent at its middle point, and may be regarded as a straight line. Such a line, pj^. 44 comprising so much of the circle of etjual altitude as covers the probable limits of po.«ition of the ol)Ferver, is called a Sumner line or Lii^e of position. 376. Since the direction of a circle at any point — that is, the direction of the tangent — must be perpendicular to the radius at tliat point, it follows that the Sumner line always lies in a direction at right angles to that in which the body bears from the oliserver. Thus, in figure 44, it may be seen that m n/ an(l n 1/, the extended Sunmer lines corresponding to the Ijodies at A and A^, are respectively perpendiculur to the bearings of the bodies OA and OA''. This fact has a most important application m the employment of the Sumner line. 377. I'sEs OK THE SiMXER 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 lorgitude gives but one of tlie 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 betaken 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, coincid- ing 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 Sunnier line inclined to both meridians and parallels; if the line agrees in direction more nearly with the meridian, latitude should generally be assumed and the longi- tude worked; if it is nearer a parallel, the reverse course is usually preferable. The values of the assumed coordinates may vary from 10' to 1°, according to circumstances. 37S. Tlie greatest l)enelit to be derived from the Sumner method is when two lines are worked and their intersections found. The two lines may be given liy different bodies, which is generally preferable, or two different lines may be obtained from the same IkhIv from observations taken at different times. The position given by the intersection of two lines is more accurate the more nearly the lines are at right angles to each other, as an error in one line thus produces less effect upon the result. When two observations of the same body are taken, the i)osition of the ship at the time of first eight must be brought forward to that at the second in considering the intersection; if, for example, a certain line is determined, and the ship then runs NW. 27 miles, it is evident that her new position is on a line jiarallel with the first and 27 miles to the NW. of it; a second line being obtained, the inter- section of this with the first line, as corrected for the run, gives the ship's position. Besides the employment of two lines for intersections with each other, a single line may be made to serve various useful purposes for the navigator. These are described in article 400, Chapter XVI. METHODS OF DETERMINATION. 379. Any line may be defined in either of two way^ — by two of its points, or by one point and the direction. Tliere are thus two methods by which a Sumner line may be determined: (a) Assume two values of one coordinate and find the corresponding values of the other. Two values of the latitude may be assumed and the longitudes determined, as was done by Captain Sumner on the occasion that led to the discovery of the method; or else two values of the longitude may be assumed and the latitudes determined. Two points are fixed in this way, and the line joining them is the line of position. (6) Assume either one latitude or one longitude and determine the corresponding coordinate. This gives one point of the line. The azimuth of the body is then ascertained, and a line is drawn through 116 THE SUMNER LINE. the determined point at right angles to the direction in which the body bore at the time of sight. This will be the line of position. 3§0. It follows that if the Sumner line be located by the first method and its direction thus defined, the azimuth of the observed body maybe determined by finding the angle made by the line with the meridian and adding or substracting 90°. Example: At sea April 17, 1879, 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, 45° 40'; watch time, 5" 48'° 02'; C — W, 2'> 05'" 42»; C. C, + 2™ 18'; I. C, -t- r 30"; height of eye, 18 feet. Required the Sumner line. From a solution of this same problem'for a single longitude (art. 351, Chap. XIII), the following were found: H. A. from Gr., 0"50'" 51' E.; /*, 45° 36' 24"; ]>, 79° 22' 51". Assume values of Lat. 25° 02' and 25° 22' S. h P 45' 25 36' 24" 02 00 22 51 sec cosec .04278 .00750 Lj 25° 22' 00" sec cosec .04403 .00750 Gr. H H. A 2)150 01 15 cos 9.41282 sin 9.69105 82 75 .tj— 7t 29 10 38 34 14 «! 75 81— /t29 00 24 38 14 cos 9.40794 sin 9.69328 i. A. 0" 2 50" 57 • 51' E. 30 E. 2)19.15415 sin i ^ 9.57708 Gr. H. A. 0" H. A.., 2 50"' 51' 57 12 2)19.15275 sin 1 1, 9.57638 Lony / 2" 06'"39'\ •1 \31° 39' 45"/ ^W. , r 2" 06™21'\„. Lon^-^ \31° 35' 15"r^ It should be observed that s.^ and s-^ — h can be obtained, respectively, from ^-j and s^—h by adding half the difference between Lj and L,^; also that log cosec p is the same for both hour angles. The determination of the second hour angle is thus considerably simplified. A comparison of these results with those obtained by the solution with a single latitude shows that the hour angle, and consequently the longitude, corresponding to the latitude 25° 12' S. are the means of those corresponding to the latitudes here used; and therefore that the assumption that the Sumner line is a straight line is accurate. The line of the same sight might also have been found as follows: Working with the single latitude 25° 12' S., it was found that the corresponding longitude was 31° 37' 30" \V. Now by referring to an azimuth table or azimuth diagram, the azimuth corresponding to Lat., 25°. 2 8., Dec, i0°.6 S., H. A., 2^ 57'". 3 E. is S. 101° 24' E.; therefore the Sumner line extends S. 11° 24' E. The line may therefore be defined in either of two ways, thus: A Or, /25° 02' 00" S. H31 39 45 W. 25° 12' 00" S. 31 37 30 W. ^{: . /25° 22' 00" S. ^^ \31 35 15 W. Line runs S. 11° 24' E. By inspection of the coordinates of Aj and A^ it may l)e seen that — + 20' diff. lat. makes — 4'.5 diff. long.; or, + 20 miles diff. lat. makes — 4.1 miles departure. Therefore by reference to Table 2 it appears that the line runs about S. 11^° E., and the azimuth of the bodv is S.' 101^" E. ; thus the results obtained by the two methods agree. Example: At sea, Mav 18, 1879, A. M., Lat. 41° 33' N., Long. 33° 30' W., by D. R., the mean of a series of observed altitudes of the sun's lower limb was 29° 35' 30"; the mean watch time, 7" 20"" 45'.3; C. C., + 4'" 59'.2; I. C, — 30"; height of the eye, 23 feet; C — AV, 2^ 17'" 06'. Required the Sumner line. From a solution of this same problem for a single longitude (art. 351, Chap. XIII) the following were found: G. A. T., 21" 46'" 38'; h, 29° 50' 05"; p, 70° 29' 14". Assume values of the latitude 41° 03' and 42° 03' X. P 29° 50' 05" 41 03 00 70 29 14 sec cosec . 12255 . 02569 L, 42° 03' 00" sec cosec: 12927 . 02569 2)141 22 19 70 41 09 40 51 04 cos 9. 51950 sin 9. 81564 s-i 71 .*.,—/( 41 11 21 09 04 cos sin sin 9. 50852 9. 81999 21" 46™ 38' 2)19.48338 ■ sin i /i 9. 74169 G. A.T. 21" L. A.T.., 19 46" 32 '38' , 06 2)19.48347 19 32 08 i \.30 A /«° ^^H30 \ h tan 9.07243 sec .00299 tan 9.06973 27' 03" S. 10 00 W. 9\ cos 9.98839 cosec .93324 sin 9.98573 sin 9.06972 Lat., d 1 fi 6° 6 75 6 13 27 43' 41 23 44 01 03 S. 15" 47 30 33 00 h tan 9.07272 16' 27" S. 30 00 W. ¥. cos 9.98869 Lat. J 6 16 27 S. Working by the other method, and finding the azimuth, we have: . / 6° 21' 14" S. T • V- ,.oo Av 130 21 30 W Lnie runs >. . b2° W. It might be shown that the results check with each other, as in previous cases. Example: At sea, July 12, 1879, in Lat. 50° N., Long. 40° W., observed circum-meridian altitude of the sun's lower limb, the time by a chronometer regulated to Greenwich mean time being ^ 41'" 39"; chro. corr., — 2'" 30^; I. C, — 3' 0"; height of the eye, 15 feet. Find the Sumner line. From the solution of the same problem for a single latitude (art. 338, Chap. XII) the following values were obtained: G. A. T., 2" 33'" 50'; /;, 61° 57' 01"; d, 21° 59' 27" N.; a (Tab. 26), 2" .5. Assume longitudes 39° 45' and 40° 15' W. Gr. H. A. Long. 1 2" 33" 50' 2 39 00 k 5 10 h 61° + . 57' 01" 1 06 Hx 61 58 07 2l d 28 21 01 53 N. 59 27 N. Gr. H. Long. . A. 2>'33'"50' i -2 41 00 h 7 10 h at./ 61° 57' 01" + 2 08 H, 61 59 09 22 d 28 00 51 21 59 27 Li 50 01 20 N. The line given by these coordinates is then : . r50° 01' '■^'\39 45 20" N. 00 AV. ■'{ 50 00 18 N. 50° 00' 18" N. 40 15 00 W. 118 THE sumnp:r line. This shows that the Sumner Hne 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 an azimuth table or diagram, it is found that the azimuth of the sun corresponding to Lat. 50° N. Dec. 22° N. and H. A. 6"' 10' E., is N. 177° E. Therefore, using the values given by the earlier solution, the line is defined as follows: 50° OO' 5V' N. T • XT O-O 17 40 00 00 N. LmerunsN. 8/°E. The direction of the line thus given and the one found from the double coordinates mav )>e shown to agree as in examples before given. FINDING THE INTERSECTION OF SUMNER LINES. 3§1. The intersection of Sumner lines may be found either graphically or by computation. 3S2. Graphic Methods. — Each line may be plotted upon the chart of the locality in which the ship is being navigated and the intersection thus found. The details of the plotting will be obvious, whether the line is defined by two of its points, or by one point and its direction. This plan will com- mend itself especially when the vessel is near shore, as the chart in use will then jn-obably be one of conveniently large scale, and it will be an advantage to see where the position falls with reference to soundings and landmarks. 3§3. When clear of the land it is often inconvenient to follow this plan; a large scale chart may not be at hand, it may not be desired to deface the chart with numerous lines, or the necessary space for chart work may not be available. In such a case, the following method « is recommended, as it obviates the disadvantages of the other. To understand the principle of this method, suppose that the lines are defined ])y the latitude and longitude of two points of each, and consider that they are plotted on a chart which is constructed upon a sheet of elastic rubber. It i.s evident that if, while holding it fast in the direction of the meridians, we stretch this rubber along the lines of the parallels in a uniform manner until the length of each minute of longitude is made to equal a minute of latitude, the chart, while losing its accuracy as por- traying actual conditions on the earth's surface, still correctly represents the jiositions of the various points in terms of the new coordinates which have been created, namely, those in which a minute of latitude is equal to a minute of longitude. Thus, if on the true chart a point is m minutes north and n minutes east of another, on the stretched one it will still be vi minutes north and n minutes east, the only difference being that the minutes of longitude will now be of a different length; and if on the orig- inal chart the two Summer lines intersect at a point ?« minutes north and 7i minutes east (on the original scale) of some definite point of one of the lines, the intersection on the stretched chart will lie m minutes north and n minutes (of the new scale) to the east of the same point. A stricter mathematical conception of the stretched chart and its properties may perhaps be obtained by considering the chart of the locality to be projected (with the eye at the zenith) upon a plane Avhich passes through one of the meridians and makes an angle with tbe plane of the horizon which is equal to the latitude; each minute of longitude will then be increased by multiplying it by the secant of the latitude, and thus becomes equal to a minute of latitude. From a consideration of the properties of this hypothetical chart it may be seen that the following rule may be laid down: If two or more Sumner lines be plotted by their latitude and longitude upon any sheet of paper, using a scale whereon latitude and longitude are equal regardless of the latitude of the locality, the intersection of those lines, measured by coordinates on the scale employed, correctly represents the intersection of the lines as it would be measured upon a true chart. It follows from this that we may plot Sumner lines upon any piece of paper, measuring the coordi- nates with an ordinary scale ruler, and assigning any convenient length for the mile; the larger the scale the more accurate will be the determination. Or, what is even more convenient, we may employ "profile paper," whereon lines are ruled at right angles to each other and at equal distances apart, in which case no scale ruler is needed. One caution must be observed in using this method; all longitudes employed on the paper for any purpose must be those of the scale, namely, one minute of longitude equals one minute of latitude. For instance, if the two Sunmer lines be taken at different times, in bringing the first up to the iX)sition of the second by the intermediate run, that run must be laid down to scale; that is, the easting or westing must appear as so many minutes of longitude, not so many miles. To do this enter the traverse table with course and distance run, and pick out latitude and departure; then, by means of the middle latitude, convert departure into minutes of longitude and bring the first line to the second by laying off so many minutes of latitude north or south, and so many of longitude east or west. In the case where the Sumner is defined by one position and its line of direction, it is not correct to lay down the angle to the meridian on the hypothetical chart, for all angles are distorted thereon. The best way is to find another position on the line by assuming a second latitude ten or twenty miles removed from that of the point given, entering the traverse tal)le with the angle that the line makes with the meridian as a course, and abreast the latitude taking out the departure; (convert departure into differ- ence of longitude, and plot the second point by its coordinates from the first. Example: Let it be required to find the intersection, by each of the methods, of the following lines: . /40° 00' N. . f40° 20' N. ^1163 15 W. ^463 07 W. T./40 05 N. „r40 15 N. ^i\63 03 W. ^4^3 12 W. 1 Suggested by Lieut. G. W. Logan, U. 8. Navy. THE SUMNER LINE. 119 Figure 45 shows the intersection, (1) by Mercator chart, (2) by scale, and (3) on profile paper, as follows: 20' f^ / / : A, III'' LrrA 1 1 1 1.| 1 III, y 20' J 40"' >^ 63° L5' 12' 10' err' 03' 63'<'" 1 -prtilft = .06in.cK Fig. 45. Ai, y : .:_ z t : ---JL. -Z-- - - 23:__L \ ': : __ S_ - ;.;_::L.:i : J I " _ ::._ A z :^L-- :_::.::2 __ ...5, :l 5:_- "":::.:::::_;: - -_ Z - --*L ::: :i:: _. .: ' zz-.A ± ^o' 10' 63' iH>* r40° 12' 8 N Intersection :|g3- 09 ig W . Suppose, in the example just given, the first line had been defined as follows: • A|g^° 15^ W ^^"^ '■""^ ^'- ^''° ^• To find a second coordinate bv which to plot it, proceed as follows: In Table 2, for 17°: Lat. 20' X., Dep. 6.1 m. E. For Mid. Lat.: 40°, Dep.'6.1 m., diff. long. 8'.0 E. Hence, as jjreviously given: /40° 00' X. ''iteS 15 W . /40° 20^ N. ^463 07 W. 3§4. Methods by Computation." — The finding of the intersection of two Sumner lines by compu- tation may l)e divided into two cases: Case I. When one line lies in a XP].-S'\V. direction, and the other in a XW.-SE. direction. Case II. When l)oth lie in a XE.-.S\V., or both in a XW.-SE. direction. Suppose, first, that the lines are defined by the latitude and longitude of two points of each, and for the simplification of the problem consider the lines projected on a plane passing through one of the meridians and making an angle with the i^lane of the horizon equal to the latitude, the properties of which were explained under the graphic method, (art. 383); this saves the necessity ot converting minutes of longitude into miles of departure before the solution and converting them back again after- wards; as all points are thus projected in corresponding relative J)08itions, the results are as exact as if the longer method be oUowed of dealing with minutes of latitude and longitude of unequal length. 3§5. Cfw I One line NE.-SW., and the other NW.-SE.— Suppose the two lines, projected as described, are as shown in figure 46, Aj A;^ and Bj Bj; for the present assume that the two Soints, Aj and B,, have a common latitude. Drop the perpen- icular PO from the intersection; then the latitude of the inter- section will be a distance OP above the conmion latitude of Aj and Bi, and its longitude will be a distance XyO to the right of Ai and BjO to the left of Bi. Find the angles Ji. ineretore, /\ the intersection is south of Ai and B3, east of Aj, and west ofBj. (o) By Table 5 B. (90°-a)=48°, (90°4-/i)=109°. Ratio 0.81X9'.9=8'.0 lat.; a=42°, lat.=8'.0, dep.=7'.2. /i=19°; lat. =8'.0, dep.=2'.7. Hence, intersection: (6) By Table 2: 8' S. of 25° 30' S. = 25° 38' S. 7.2 E. of 115 22 E.=115 29.2 E.\ , , 2.7W.ofll5 31.9E.=115 29.2 E.r^^^'^" Assuming lat 6' 8' Dep. for 42° 5.5 7.2 Dep. for 19° 2.1 2.7 Sum 7.G 9.9 122 THE SUMNEE LINE. Intersection: 8^ S. of 25° 30' = 25° 38' 7.2 E. of 115 22 =115 29.2\ , , 2.7 W. of 115 31.9=115 29.2r"^"^- 3§§. The foUow^jpg is a summary of the method when lines are given by coordinates of two points of each: (a) By Tables B. 1. Write down hnes; find a and /?. 2. If there are no points which have a common latitude, reduce one point of one line to latitude of some given point of the other. 3. Write down difference of longitude. 4. Draw rough sketch to illustrate direction of point of intersection. 5. Enter Table 5 B: Case I, angles (90° - a) and (90° + /3) or (90° - fi) and (90° + a). Case II, angles (90° + a) and (90° + ft) or (90° — fi) and (90° -a). Take out ratio from second column, and multiply by difference of longitude; this gives difference of latitude of intersection from the common latitude. 6. Find departure corresponding respectively to cc and ft with latitude; this gives differences, of longitude to the point of intersection from the re- spective points or common latitude. (6) By Table 2. 1. Write down lines; find a and ft. 2. If there are no points which have a common latitude, reduce one point of one line to latitude of some given point of the other. 3. Write down difference of longitude. 4. Draw rough sketch to illustrate direction of point of intersection. 5. Enter Table 2, at pages a and ft; find by trial some latitude at which — Case I, the sum of the corresponding departures equals the total difference of longitude; Case II, the difference of the corresponding de- partures equals the total difference of longitude. These give differences of latitude and longitude to the point of intersection from the respective points of common latitude. 3§9. If the lines, instead of being defined by coordinates of two points, are defined by the coordi- nates of one point of each with its direction as deduced from the azimuth of the body, it will be better not to consider the projection on the fictitious plane through the meridian, as there will then be no advantage in so doing. In this case, consider the angles of the lines with the meridian, as given, a and ft; reduce the difference of longitude Aj Bi to departure, and use this in miles instead of the Ai B, in minutes; and when AjO and BjO are found, being in miles of departure, they must be reduced to min- utes of longitude l)efore being applied to the longitude of A, and Bj. Example: The Sumner lines of the last example being expressed by a single point and the direction, as given below, find the intersection. f 25° 40^ 1115 31 B ill 25 25 S. 115 33.5 E. Line runs (a =) N. 39° W. Line runs {ft =) N. 18° E. First bring second line up to Lat. 25° 40^8. ft = 18°; lat. = + 15'; dep. = — 4.9 m. ; diff. long. = — 5^.4; hence we have: 40' S. 28.1 E. Line runs {ft = ) N. 18° E. Fig. 53. Intersection: AB' = 2'.9 = 2.6 miles. B' Ijeing west of A ( fig. 53) , and the lines through the two points running respectively NE. and NW., the intersection is north of both, east of B', and west of A. (a) By Table 5 B. (90° - a) =51°; (90° +^) = 108°. Ratio 0.88 X 2.6 = 2'.3 lat. a = 39°, lat. = 2'.3, dep. = 1.8 m., diff. long. = 2.0. ft = 18°, lat. = 2'.3, dep. = 0.7 m., diff. long. = 0.8. 2'.3N. of 25° 40' S. = 25° 37'. 7 S. 2 .0 W. of 115 31 E. = 115 29 K-Lheck. .8 E. of 115 28.1 E. = 115 28 (ft) By Table 2: Assuminglat 1-4' 2' 2'.3 Dep. for 39° 3.2 1.6 1.9 = 2'.l Dep.forl8° 1.3 0.7 0.7=0.8 Sum 4.5 2.3 2.6 = 2.9 Intersection: = 25° 37' 7 2 .IW. of 115 31 =115 28:9|^heck. 2'.3 N. of 25° 40 2 .1 W. ol 0.8E. of 115 28.1 = 115 28 THE SUMNEE LINE. 123 The followinjj; Hiimmary gives the various steps when the lines are each given Ity tlie coordinates of one point with the direction: («) By Tables B. 1. Write down lines as given. 2. If the points have not a common latitude, reduce one point to latitude of the other. 3. Write down difference of longitude and con- vert it to departure. 4. Draw rough sketch to illustrate direction of point of intersection. 5. Enter Table 5 B: Case I, angles (90°-a) and (90°! /i) or (90° -/i) and (90°+<:r). Vase IT, angles (90°4-^0 and (90°+/i) or (90°-/i) and (90°— ct). Take out ratio from second column, and multiply by departure between the two points; this gives difference of latitude of intersection from common latitude. 6. Find departure corresponding respectively to a and fi with this difierence of latitude, and con- vert to difference of longitude; this gives differences of longitude to the point of intersection from the respective points of common latitude. {b) By Tabled. 1. Write down lines as given. 2. If the points have not a common latitude, reduce one jjoint to latitude of the other. 3. Write down difference of longitude and con- vert it to departure. 4. Draw rough sketch to illustrate direction of point of intersection. 5. Enter Table 2 at pages cc and fi; find ])y trial some latitude at which — Case I, the sum of the corresponding departures equals the departure between the two points; Case II, the difference of the corresponding departures equals the departure between the two points. This difference of latitude, and these departures (converted into difference of longitude) give dis- tance of point of intersection in latitude and longitude from the respective points of common latitude. 390. The modification of the methods for finding the intersection of two Sumner lines, where there is a run between the observations from which they are deduced, will be readily apparent. It is known that at the time of taking a sight the vessel is at one of the points of the Sumner line, but which of the various points represents her precise position must remain in doubt until further data are acquired. Sujipose, now, that after an observation the ves.«el 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 a second sight is then taken, the position of the vessel may be found from the intersection of two lines — one, the Sumner line given by the second observation, and the other a. line parallel to the first Sumner but removed from it by the amount of the intervening run. Positions may 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 the method given in article 383 be employed, runs in latitude and longitude must each be applied on their own scales, as explained in the description of the method. If one of the methods by computation be adopted, the point or points of the first line are brought forward by the traverse 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. 124 THE PEACTICE OF NAVIGATION AT SEA. • CHAPTER XVI. THE PEACTICE OF NAViaATION AT SEA. 391. Having set forth in previous chapters the methods of working dead reckoning and of solv- ing problems to find the latitude, longitude, chronometer correction, and azinuith from astronomical observations, it will be the aim of the present chapter to describe the conditions which govern the choice and employment of the various problems, together with certain considerations by which the navigator may be guided in his practical work at sea. 392. Departire and Dead Reckoning. — On beginning a voyage, a good departure must be taken while landmarks are still in view and favorably located for the purpose; this becomes the origin of the dead reckoning, which, with frequent new departures from positions by observation, is kept up to the completion of the voyage, thus enabling the mariner to know, with a fair degree of accuracy, the posi- tion of his vessel at any instant. At the moment of taking the departure, the 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 log reading must also be noted. It is likewise well to read the log each hour, for general information as to the speed of the vessel as well as to observe that it is in proper running order and that the rotator has not been fouled by seaweed or by refuse thrown overboard froin the ship. It is a good plan to record the time by ship's clock on each occasion that the log is read, as a supplementary means of arriv- ing at the distance will thus be available in case of doubt. If a vessel does not use the patent log but estimates her speed by the number of revolutions of the engines or the indications of the chip log, the noting of the time becomes essential. A good sight is of no value unless one knows the point in the ship's run at which it was taken, so that the position it gave may be brought forward with accuracy to any later time. 393. Routine Day's Work. — The routine of a day's work at sea, no part of which should ever be neglected unless cloudy weather renders it impossible to follow, consists in working the dead reckoning, an a. m. time sight and azimuth taken when the sun is in its most favorable position for the purpose, a meridian altitude of the sun (or, when clouds interfere at noon, a sight for latitude as near the meridian as possible) , and a p. m. time sight and azimuth. This represents the minimum of work, and it may be antplified as circumstances render expedient. 394. Morning Sights. — The morning time sight and azimuth should be observed, if possible, when the sun is on the prime vertical. As the body bears east at that time, the resulting Sumner line is due north and south, and the longitude will thus be obtained without an accurate knowledge of the latitude. Another reason for so choosing the time is that near this point of the sun's apparent path the body is changing most slowly in azimuth, and an error in noting the time will have the minimum effect in its computed bearing. The time when the sun will be on the prime vertical — that is, when its azimuth is 90° — may be found from the azinmth tables or the azimuth diagram. Speaking generally, during half the year the sun does not rise until after having crossed the prime vertical, and is therefore never visible on a bearing of east. In this case it is best to take the observation as soon as it has risen above the altitude of uncertain atmospheric effects — between 10° and 15°. A series of several altitudes should be taken, partly because the mean is more accurate than a single sight, and partly because an error in the reading of the watch or sextant may easily occur when there is no repetition. If the sextant is set in advance of the altitude on even five or ten minute divisions of the arc, and the time marked at contacts, the method will be found to possess various advantages. As the sight is being taken the patent log should be read and ship's time recorded. It is well, too, to make a practice of noting the index correction of the sextant each time that the sextant is used. The bearing of the sun by compass should immediately afterward be observed, and the heading by compass noted, as also the time (by the same watch as was used for the sight). Before working out the sight, the dead reckoning is brought up to the time of observation, and the latitude thus found used as the approximate latitude at sight. It is strongly recommended that every sight be worked for a Sumner line, either by assuming two latitudes, or by using one latitude and the azi- muth, the advantages derived therefrom being always well worth the small additional labor expended. The compass error is next obtained. From the time sight the navigator learns that his watch is a certain amount fast or slow of L. A. T., and he need only apply this correction to the watch time of azimuth to obtain the L. A. T. at which it was observed; thence he ascertains the sun's true 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 deviation, agrees with that given in his deviation table; but in working the next dead reckoning, if the Ship's course does not change, the total compass error thus found may be used without separating it into its compo- nent parts. It should be increased or decreased, however, as the ship proceeds, by the amount of any change of the variation that the chart may show. 395. If there is any fear of the weather being cloudy at noon, the navigator should take the pre- caution, when the sun has changed about 30° in azimuth, to observe a second altitude and to record the appropriate data for another sight, though this need not actually be worked unless the meridian THE PRACTICE OF NAVIGATION AT SEA. 125 observation is lost. If it is required, it may be worked for either a time sight or cp' cp" sight, according to circumstances, a second Sumner line obtained, and the intersection of the earlier Sumner with it will give the ship's position. 396. Noox SuiHTs. — Between 11 and 11.30 o'clock (allowing for gain or loss of time due to the day's run) the ship's clocks should be set for the L. A. T. of the prospective noon position. The noon longitude may be closely estimated from the morning sight and the probable run. The navigator should also set his own watch for that time, to the nearest minute, and note exactly the number of seconds that it is in error. lie may now compute the constant (art. 333, Chap. XII) for the meridian altitude. The daily winding of the chronometer is a most important feature of the day's routine, and may well be pei'formed at this hour. At a convenient time before noon, the observations for meridian altitude are commenced and continued until the watch shows L. A. noon, at which time the meridian altitude is measured and the latitude deduced. If the weather is cloudy and there is doubt of the sun being visible on the meridian, an altitude may be taken at any time Avithin a few minutes of noon, the time noted, and the interval from L. A. noon found from the known error of the watch. It is then the work of less than a minute to take out the a from Table 26, the of from Table 27, and apply the reduction to the observed altitude to obtain the meridian altitude. Indeed, the method is so simple that it may be practiced every day and several values of the meridian altitude thus obtained, instead of only one. 397. It now becomes necessary to find the longitude at noon. This may be done graphically by a chart, or by computation. The former plan needs no explanation. There are a number of variations in the methods of computation, one of which will l)e given as a type. By the ship's run, work 1)ack the noon latitude to the latitude at a. m. time sight. If the Sumner line was found from two assumed latitudes which differed + '« minutes, while the corresponding longi- tudes differed zfc n minutes, then V difference of latitude causes ± — minutes difference of longitude. If m the true latitude at sight is rf: o- minutes from one of the assumed latitudes, then i .)-• X — is the corre- m sponding difference of longitude. If the Sumner line was found from one assumed latitude and an azimuth, Z, it makes an angle with the meridian equal to 90° — Z. Enter the traverse table with this as a course and with the difference between the true and assumed latitudes as a latitude, and the departure will be found; convert this into difference of longitude at the latitude of observation, and apply the result with its ])roper sign to the longitude corresponding to the assumed latitude. Having thus the longitude at sight, the longitude at noon is worked forward for the run. If the sights show a considerable current it should be allowed for, both in working back the latitude and in bringing uji the longitude for the run between the sight and noon. 39§. CiKRENT AND EuN. — The current may be found by comparing the noon positions as obtained by observation and by dead reckoning; and the day's run is calculated from the difference between the day's noon position by observation and that of the preceding day. To "current" is usually attributed all discrepancies between the dead reckoning and observations; but it is evident that this is not entirely due to motion of the waters, as it includes errors due to faulty steering, improper allowance for the compass error, and inaccurate estimate of the vessel's speed through the water. The noon position by observation becomes the departure for the dead reckoning that follows. 399. Afterxoon SiciHTS. — The p. m. time sight and azimuth is similar to the morning observation. 400. Sumner Lines. — By performing the work that has just been described a good position is obtained at noon each day, which, in a slow-moving vessel with plenty of sea room, may be considered sufficient; but conditions are such at" times as to render it almost imj)eratively necessary that a more frequent determination of the latitude and longituarallel to the coast line, then the Sumner line will point toward shore; the value of a line thafc*!eads to the point that the vessel is trying to pick up is amply demonstrated by the experience of Captain Sumner that led to the discovery of the method (art. 372, Chan. XV). For especially accurate work three Sumner lines may be taken, varying in azimuth about 120°; if they do not intersect in a point, the most probable position of the ship' is at the center of the triangle that they form. If two pairs of lines be determined, each pair based upon observation of two bodies l^earing in nearly opposite directions and at about the same altitude, the mean positi(>n that results from the inter- Bection of the four lines will be as nearly as possible free frf)m those errors of the instrument, of refrac- tion, and of the observer, which can not otherwise be eliminated. This is fullv explained in article 451, Chapter XVII. 401. Use of Staks, Planets, and Moox. — It may be judged that the employment in navigation of other heavenly bodies than the sun is considered of the utmost imi»ortance, ancl mariners are urged to familiarize themselves with the methods by which observations fif star.-;, planets, and the mofni may be utilized to reveal to them the position of their vessels at frequent intervals throughout the twenty- four hours. It should be remembered, however, that in order to be of value these observations must be accu- rate; and to measure an accurate altitude of the body above the horizon it is required not only that the body be visible but also that the horizon be distinctly in view. Care should therefore be taken to make the observations, if possible, at the time when the horizon is plainest — that is, during morning and evening twilight. It may be urgently required to get a position during hours of darkness, and a dim horizon line may sometimes be seen and an observation taken, using the star telescope of the sextant; if the moon is shining, its light will be a material aid; but results ol)tained from such sights should be regarded as questionable and used with caution. Altitudes measured, however, just before sunrise and just after sunset are open to no such criticism; a fairly well-practiced observer who takes a series of sights at such a time, setting the sextant for equal intervals of altitude, will find the regularity of the corre- sponding time intervals" such as to assure him of accuracy. 402. Identification of Unknown Bodies. — On account of the very great value to be derived from the use of stars and planets in navigation, it is stnjngly recommendetl that all navigators familiarize themselves with the names and positions of those fixed stars whose magnitude renders possible their employment for observations, and also with the general characteristics — magnitude and color — of the three planets (Venus, Jupiter, and Mars) which are most frequently used. A study of the different portions of the heavens, with the aid of any of the numerous charts and books which bear upon the subject, W'ill enable the navigator to recognize the more important constellations and single stars by their situation with relation to each other, and to the pole and the equator. It may occur, however, that occa.«ion will arise for observing a body Avhose name is not known, either because it has not been learned, or because the surrounding stars by which it is usually identified are obscured by clouds or rendered invisible by moonlight or daylight. In such a case the observer may estimate the hour angle and declination (the hour angle applied to local sidereal time giving the right ascension), and the star or planet may thus be recognized from a chart or from an inspection of the Nautical Almanac. This rough method will generally suffice when the body is the only one of its magnitude within an extensive region of the heavens; but cases often arise where a much closer approximation is necessary, and more exact data is required for identification. 403. If in doubt as to the name of the body at the time of taking the sight, it should be made an invariable rule to observe its bearing by compass, whence the true azimuth may l)e approximately deduced by applying the compass error. The method « to be descril)ed then affords a convenient n\eans of identification. The quantities given are the corrected altitude of observation, /;, the (approximate) true azimuth of the body, Z, and the latitude by dead reckoning, L; those to be determined are the declination, d, and the hour angle, /. From the astronomical triangle we have: sin Zsin t ~. r; or, sm Z cos /i=.«in t cos (/. sin j) cos ft The value of sin Z cos h (calculated from the given azimuth and altitude) must therefore equal sin t cos (I, whatever the values of t and d mav prove to be. From a given latitude, azimuth and declination, the hour angle may be found either by azimuth tables or an azimuth diagram; or from a given latitude, azimuth and hour angle, the declination may be found by the same means. If, therefore, some probable value of the declination be assumed, using the known'latitude and azimuth, we may ascertain the corresponding hour angle; or, if the hour angle be assumed, the corresponding declination is obtained; then the product of sin t cos d may be calculated, and if it agrees substantially with sin Z cos /(, the trial values of the hour angle and declination are the correct ones; if not, other trials mav be made until the correct ones are found. It may be remembered that absolutely exact results are not sought, and in practice the operation may be made very short; the n Suggested by Lieut. G. W. Logan, U. 8. Navy. THE PRACTICE OF NAVIGATIOlSr AT SEA. 127 values of the quantities may be taken in even degrees and the logarithms need not be carried beyond the third place; the sum of the logarithms will suffice and the corresponding numbers do not have to be taken out. The possibility that the observed body may have been a planet must always be kept in mind in looking it up in the star table or chart. Example: May 16, 1879, in Lat. 5° N., Long. 2'* 53"" W. by I). R., a star is observed whose corrected altitude is 38°, and true azimuth N. 107° E. The Greenwich sidereal time (as computed for use in the regular working of the sight) is 12'' 53'". Let it be required to identify the body. First find the logarithm of sin Z cos //. Z 107° sin 9. 981 h 38° cos 9. 897 sin Z cos h log 9. 878 Now suppose the observer estimates from the position of the body that its declination is 3° S. Look in the azimuth table on the page of latitude 5° (declination contrary name to latitude), and find the hour angle (p. m.) corresponding to Dec. 3° and Az. 107°; this is about 1'' 40"'; then with fZ==3°, ^=1'' 40'", find sin t cos d. (Sin t may be obtained either by converting time into arc and taking from the table in the usual way, or by multiplying by 2 and finding it from the column headed "Hour P. M." Thus in the present case find the sine of 25° 00' or of 3'' 20"'. In using the time column be careful to take the name from the foot of the page when the double angle exceeds 6''. ) t P d 40" 3° sin 9. 626 cos 9. 999 sin t cos d log 9. 625 As this logarithm should equal 9.878, it is seen that the assumj)tion is incorrect. Try a value of the declination 5° farther south — that is, 8° S. The corresponding hour angle is 2'' 50"'. t 2^ 50"' sin 9. 830 d 8° cos 9. 996 sin t cos '/ log 9. 826 The logarithm is not yet (juite large enough; assume rocess of identification.) 2. Correct the observed azimuth for deviation and variation. 3. Find the logarithm of sin Z cos h to the third place. 4. Assume a declination and find the corresponding hour angle that will produce the given azimuth at the given latitude; orassuine an hour angle and find the corresponding declination. ( Use an azimuth table or diagram for the purpose.) 5. Find the logarithm of sin t cos (/ to the third place. 0. Observe whether this agrees with the logarithm of sin Z cos /;, and if it does not, repeat trials until an agreement is found. 7. Having found the hour angle and declination, convert the Greenwich sidereal time into local sidereal time and subtract the hour angle if west, or add it if east; the result is the ri^ht ascension of the observed l)ody, by which, with the declination and magnitude, the identification is accomplished. 405. The exactness with which the comparison of logarithms is carried out will depend upon the possibility of errors of identification in the region of the heavens involved. It will not usually be necessary to find the correspondence as closely as has been done in the examples given, and the cases will be rare when, with a fair estimate of hour angle or declination at beginning, a sufficiently accurate knowleproi)riately marked; then a second station is occupied, and the operation repeateii, and so on, the various intei-sections being marked as the work proceeds. A second method of establishing positions is that of resection; in this the first line is drawn from some known station, as in the preceding method, and the observer next proceeds to the place whose position is required ana occupies it; the plane table is there oriented by means of the line already drawn, placing the edge of the rule along the line, sighting back toward the first station, and swinging the table until that station is in the line of sight of the telescope; then choose some other established station as nearly as possible at right angles to the direction of the first; i:>lace the edge of the rule upon, the plotted position of this station and swing the alidade (the rule always being kept on the plotted point) until the object is bisected by the telescope cross-hairs; draw this line, and its interse(!tion with the first will give the required point, the accuracy of which can be checked from some other plotted station. A third method of locating a point is by means of a single bearing from a known station, with the distance from the occupied station to the required one, the process of plotting being self-evident. A fourth method is given by occupying an luidetermined position from which three established stations are in view; the point occupied by the observer is then plotted by an application of the "three- point problem." 419. It may be seen that where the greatest accuracy is not essential the plane table may be employed for plotting all the points of a survey. In such a case it would only be necessary to begin with the two base stations, plotted on the sheet on any relative bearing whatsoever and at a distance apart eijual to the length of the base line (reduced t ) scale), as measured by the most accurate means available. The work of plotting might even proceed before the base line had been measured, the two stations being laid off at any convenient distance apart; when, later, the base line wa^ measured, the scale of the chart would be determined, being eciual to the distance on the chart between base stations divided by the length of the base line. 420. A plane table could be improvised on shipboard which would greatly facilitate the operation of any, surveying work that a vessel not equipped with instruments might be called upon to perform. A drawing board could be mounted upon a tripod (as, for example, the tripod supplied for compass work on shore) in such manner as to be capable of motion in azimuth; it could be brought nearly to the horizontal, if no better means offered, by moving the tripod legs, and this adjustment could be proved by any small spirit level; sight vanes could be erected upon an ordinary ruler to take the place of the alidade; in case there was difficulty in observing any object with such an alidade, because of its altitude or for other reasons, a horizontal angle might be observed with a sextant and plotted with a pro- tractor. By this means work could be done which, even if it should lack complete accuracy, might be of great value. 421. The Telemeter and Stadia. — Any telescope fitted with a pair of horizontal cross-hairs at the focus may be used as a telemeter, and v/hen accompanied by a graduated staff, called a stadia, affords a means of measuring distance (up to certain limits) with a close degree of accuracy; the method con- sists in observing the number of divisions of the scale subtended by the hairs when the stadia is held up vertically and perpendicular to the line of sight of the teles -ope, it being evident that the closer the distance the fewer divisions will appear between them. The facility with whicli distances can be measured by this method makes it most important that all telescopes of theodolites, transits, and plane tables be fitted as telen^eters, and that stadia rods be provided for all surveying work. Speaking api)roximately, it may be .said that the number of divisions intercepted between the cross- hairs will vary directly as the distance of the stadia rod. This would be exactly true if we looked at the object through an empty tube, directly between the hairs. Since, however, the rays from the stadia are refracted by the object glass before they are intercepted by the wires, the statement, to be absolutely exact, must be slightly modified; but for j^ractical surveying work it may be accepted as given. 422. There are two methods of installing the telemeter cross-hairs — the first, in which they are immovably secured in the telescope and always remain at the same distance apart, and the second, in which the distance of the cross hairs is made variable, being under the control of the observer. The former is generally regarded as the preferable method, and when it is employed it is evident that the subtended height of the stadia bear3 a constant ratio to the distance of the staff from the telescope. It proves mf)st convenient in i)ractice to space the hairs so that this constant ratio is some even multiple of 10, for facility in converting scale readings into distance; it is also advantageous to mark the stadia . in the unit of the chart scale and decimals thereof; for example, if the ratio of stadia height to distance were 100, and the stadia were marked in meters and decimals, a reading of 2.07 would at once be con- verted into a distance of 207 meters. Any units and any ratio may, however, be employed, and for any given setting of cross-hairs it is very easy to graduate a stadia, by experiment, for any desired units; for example, if it is required to mark the stadia in feet, set up and level the telescope, measure off a distance of exactly 100 feet from it, hold up an unmarked staff and mark upon it the points intersected by the cross hairs; the interval between these marks will represent 100 feet of the scale; divide this length into 100 parts, each of which will represent a distance of one foot, and mark the whole staff on the same scale; then if the stadia be held up at any distance, the cross-hairs will intercept a number of divisions corre- sponding to the r. umber of feet of distance. MARINE SUEVEYING. 135 When the cross-hairs are movable the ratio becomes variable, but the principle of measuring remains the same — namely, the distance of the staff from the telescope is equal to the existing ratio multiplied by the distance intercepted on the scale. 4S3. The stadia is made of a light, narrow piece of wood and is usually hinged for convenience in transporting. Ordinarily the background of the scale is painted white, while the main divisions are marked in red, with minor divisions in black, and geometrical figures are employed to facilitate the reading of fractional parts of the scale. Devices are furnished by which the man holding the stadia may know when it is at right angles to the line of sight of the telescope — an essential condition for accuracy of measurements. 424. Tlie use of the telemeter and stadia for measuring distances is limited to the distance at which the scale divisions can be accurately read through the telescope. For fairly close work and with the class of telescope usually supplied with surveying instruments, 400 meters represents about the greatest distance at which it can be employed. With this limitation, the character of the survey determines the nature of its employment. In a careful survey its greatest use would be in connection with the theodolite or plane table in putting in shore lines, contour lines, and topography generally. In a survey where only approximate results are sought it might afford the best means for the measure- ment of the base. 425. If the telemeter be applied to a theodolite, transit, or plane table which is fitted with a graduated vertical arc or circle, it is possible to measure the distance to the stadia not only in a horizontal but also in a vertical direction. In this case the vertical angle must be observed as well as the stadia reading. Tables are computed giving the solution of the triangles involved. 426. In making a survey with the ordinary resources of a ship, the principle of the telemeter and stadia may be profitably employed, using a sextant and improvised staff. In this case it is usual to have the stadia of some convenient flxed length, as, for example, 10 feet, and of slight width and thickness; this is held at right angles to the line of sight from the observer, who notes the angle subtended by the total length; tables are prepared by which the distance corresponding to each angle is given. 427. TiiK Skxtant. — This instrument is of the greatest value in hydrographic surveying. It is fully described elsewhere in this work and its adjustment explained (Chap. VIII). Sextants are manufactured of a form especially adapted to surveying work; they are smaller and lighter than those usually employed in astronomical observations, but have a longer limb, by which angles may be measured up to 135° ; the vernier is marked for quick reading and has no finer graduation than half minutes; the telescope has a large field. This instrument is principally employed in measuring the horizontal angles by means of which soundings are plotted. It may, however, be put to various uses when making an approximate survey, as has already been explained. It should be remembered, in measuring terrestrial angles with a sextant, that rigorous methods require a reduction to the horizontal if either of the objects has material altitude above the horizon. 42S. The Level. — This is an instrument for the accurate measure of differences of elevation. It consists of a telescoi)e, carried in a Y-shaped rest, which is mounted upon a tripod and leveled in a man- ner similar to a theodolite; but it differs from that instrument in that the telescope is not capable of motion about a horizontal axis, and in having no graduated circle for ' measurements of altitude and azimuth. The principle of its use contemplates placing the line of collimation of the telescope in a truly horizontal plane and keeping it so fixed. 429. It is principally employed in marine surveying to determine heights and contour lines — the latter being lines of equal elevation above the sea level — and for locating bench marks for tidal ob.serva- tions (Chap. XX). In connection with it is used a graduated staff called a leveling rod, carrying a con- spicuous mark, adjustable in height, called a target. To ascertain the difference of level between any two points, set up the level with the telescope horizontal at some place between them; let an assistant take the leveling rod to one of the jioints, and, while holding it on the ground in a truly vertical posi- tion, move the target, under the dire(!tion of the observer at the telescope, to a point where it is exactly bisected by the horizontal cross-hair; the height of the target on the staff — that is, the height of the cross- hair above the level of tlie first point — is then accurately read with a vernier; now, without moving the level, shift the rod to the second point and again adjust the target and read it. It is evident that a com- parison of the reading at the first position with that at the second will give the difference of height at the two points. The difference that can be read from one location of the instrument is limited by the length of the rod; but by making a sufficient luimber of shifts any difference may be mea.sured. The work of the level may be performed equally well by a theodolite whose telescope is adjusted to the true horizontal. 430. Heliotrope and HELioGRAPn.-^These are instruments sometimes employed in surveying, by means of which the sun's rays may be reflected in any given direction; the object of their use is to render conspicuous a station which is to be observed at a distance and which would not otherwise jje distinguishable. The instruments vary widely in form of construction and, in the absence of those made for the purpose, substitutes may easily be devised. 4tJl. Astro xoMicAL Transit Ixhtrumexts. — Various instruments are employed for the astronom- ical determinations necessary in a marine survey. Among these are the zenith telescope and portable transit. While differing in detail they consist essentially of a telescope mounted upon a horizontal axis that is placed truly in the prime vertical, thus insuring the revolution of the line of collimation in the meridian; a vertical graduated circle and vernier are supplied, affording a measure of altitude; in the focus are a number of equidistant vertical cross-hairs or lines; a small lamp is so placed that its rays illuminate the cross-hairs and render possible observations at night. Latitude is obtained by observing the meridian altitude of stars; hour angle (and thence longitude) by observing the times of their meridian transit, which is taken from the mean of the times of passing all of the vertical cross-hairs. Excepting in surveys of a most accurate nature, the astronomical determination of position by the sextant and artificial horizon is regarded as satisfactory. 136 MARINE SURVEYING. 432. The Three- Armed Protractor, or Station' Pointer. — This is an instrument whereby posi- tions are plotted on the principle of the "three-point problem," of which an explanation is given in article 152, Chapter IV. It consists (tig. 56) of a graduated circle with three arms pivoted at the center; each arm has one edge that is a true rule, the direction of which always passes through the center of the circle. The middle arm is immov- ably fixed at the zero of the scale; the right and left arms each revolve about the center on their own side^ and are ])ro- vided with verniers giving the angular distance from the middle arm. The pro- tractor being set for the right and left angles, it is so moved that the three arms pass through the respective stations, when the center marks the position of the ob- server. Center pieces of vari-jus forms are provided, being cylindrical plugs made to fit into a socket at the pivot, and by employing one or the other of them the true center may be pricked with a needle, dotted with a pencil, or its position indicated by cross-hairs. Adjustable arms are provided which can be fitted to the ends of the ordinary arms when working with distant signals. The most valuable use of the three- armed protractor is in plotting the posi- tions of soundings taken in boats, where sextant angles between signals are ob- served. It may occur, however, that certain shore stations will be located by its use. 433. In default of a three-armed protractor, a piece of tracing paper may be made to answer its purpose. To use the tracing paper, draw a line, making a dot on it to represent the center station, and with the center of an ordinary pro- tractor on the dot, lay off the two observed angles right and left of the line; then, laying this on the plan, move it about till the three lines pass exactly through the three stations observed. The dot from which thev were laid off will be on the Fu;. 56. position of the observer, and must be pricked lightly through or marked underneath in pencil. 434. The Beam Compass. — This instrument (fig. 57) is employed in chart drafting and performs the functions of compasses and dividers when the dis- tance that must be spanned is beyond the limits of those instruments in their ordinary form. It consists of an angular bar of wood or metal upon which two instruments termed beam heads are fitted in such a manner that the bar may slide easily through them. A clamping screw attached to one side of the beam head will fix it in any jmrt of its course along the beam. Upon each head a socket is constructed to carry a plain point, exchangeable for an ink or a pencil point. For exact purposes the beam head placed at the end of the beam has a fine adjustment, which moves the point a short distance to correct any error in the first rough setting of the instrument. This adjustment generally consists of a milled-head screw, which jjasses through a nut fixed upon the end of the beam head, which it carries with its motion. 435. Proportional Dividers. — These are prin- cipally employed for reducing or enlarging drawings in any given proportion. They consist (fig. 58) of two narrow flat pieces of metal called legs^, which turn upon a pivot whose position is movable in the direction of their length. The ends of both legs are shaped into points like those of ordinary dividers. When the pivot is fixed at the middle of the legs, any distance measured by the points at one end is just equal to that measured by those at the other; for any other location of the pivot, however, the Fig. 57 MARINE SURVEYING. 137 distances thus measured will not be equal, but with a given setting of the pivot any distance measured by one end bears a fixed ratio to that measured by the other. The path of travel of the pivot is gradu- ated so that the ratio may he given any desired value. Being adjusted in this respect, if a distance is taken off a chart with the legs at one end of the instrument, then those at the other end will show the same distance on the scale of a chart enlarged or reduced in the pro- portion represented by the ratio for which the pivot was set. METHODS EMPLOYED IN A HYDROGRAPHIC SURVEY. 436. A geodetic survey has for its object the determination, with the greatest attainable accuracy, of points on the surface of the earth, by the employment of a pro- cess of triangulation, all positions being located either trigonometrically or astronomic- ally, and the curvature of the earth being taken into account. Before commencing a survey a general inspection of the field is made; a base line is located and its extremities marked by Klgnah; certain other positions, known as inahi tricmgvlatlon points, are selected and also marked with signals, being so chosen that, starting with the base and proceeding thence from one to another of these points, a series of well-conditioned triangles or quadrilaterals may cover the field of survey. The base line is measured with the greatest degree of accuracy which the resources of the survey render possible. Each extremity of the base line and each other main tri- angulation point is occupied by an observer with a theodolite, who measures the angles at each station between all the other stations which are in sight. An astronomical determination is made of the latitude and longitude of some point of the survey (fre- quently one of the extremities of the base) and of the true azimuth of some known line (frequently the base line) . Data is now at hand for the location upon the chart of the base line and main triangulation points. If the survey is one of considerable extent it is expedient to measure a check haM' near the end of the triangulatif)n, a comparison between the measured and the computed distance between any two stations showing the accuracy of the work and affording a means of reconciling discrepancies. The position of a second observation spot may be determined for a similar purpose. The primary triangulation gives a skeleton of the field, but the points thus deter- mined are not usually close enough together to afford a basis for all the detail work that must be done. A second system of points is therefore selected and signals erected thereon, and the position of these points is determined by a series of angles from the main triangulation points and from each other. This is known as the secondary tri- angulation. The yjoints thus located are used in the plotting of the topography and hydro- graphy. It is not essential that their determination be as accurate as that of main triangulation points. The topography is put in, and includes the delineation of the features of the land — shore line, light-houses, beacons, contour lines, peaks, buildings, and, in short, every- thing that may be recognized by the navigator and utilized by him in locating the ship's pxG. 58. position. The hydrographic work is taken up and the depth of water and character of bottom determined as accurately as possible for the complete water area, especial care being taken to develop all shoals and dangers to navigation and to locate all aids to navigation, such as buoys, light-ships, and beacons. One or more tidal .'Stations are established where observations are taken, continually and at frequent intervals, of the height of the tide and direction and velocity of the tidal and other currents, whence data is derived for the reduction of all soundings to the plane of reference and for the information aVjout tides and currents which is to appear upon the chart. Observations are made to determine the magnetic A'ariation and dip, and the intensity of the earth's magnetic force. 437. The foregoing represent, in outline, the various steps that must be taken in the accumulation of the data necessary for the construction of a complete hydrograpliic chart. In the following para- graphs the details of the various operations will be more fully set forth. The navigator who is called upon to conduct a marine survey without having available the time, instruments, and general facilities necessary for the most thorough performance of the work must exercise his discretion as to the modifications of method that he will make, and call upon his ingenuity to adapt his means to the particular work in hand, x '838. The Base Line. — As the base line is the foundation for all distances on the chart, the cor- rectness of the results of the survey will depend largely upon the degree of accuracy with which it is measured. The triangulation merely affords a measure of the various distances as compared with the distances between the two initial points from which it began; if that initial distance is 1,000 feet, we have certain values for the sides of the various triangles; if the same base line is 2,000 feet, th^ value of each side becomes twice as great as it was before; with the same triangulation, therefore, distances vary directly with the length of the base line; it may thus be seen that if an error exists in measurement which is only a small fraction of the total length, the error will become much more material as the more distant points of the survey are reached. In a base line 1,000 feet long, if a mistake of 10 feet be made, all distances measured upon the chart will be in error 1 per cent, And a point plotted by trian- gulation 10 miles from the observation spot (the point at which plotting begins), would be out of its correct position one-tenth of a mile. It is important that the base line should be as long as possible, as an error in measurement will thus constitute a smaller percentage of the total length and will not accumulate so rapidly as the work proceeds. The position of the line must be such as to afford favorably conditioned triangles and quadri- 138 MARINE SURVEYING. laterals with adjoining main triangulation points, and its extremities must be visible from those points and from each other. The character of the ground and the facility for measuring will of course form an important consideration in the choice. .439. In measuring a base by tape, chain, or similar means, a number of successive fleets are made with the measure, wliatever its nature, the distance traversed l^eing appropriately marked after each fleet, while an observer, with a theodolite or transit, insures the measurement b?nig made accurately along the line. 440. The most careful measurements are made by a steel tape 100 feet long, stretched along a series of battens which are supported by metal crutches and made exactly horizontal by a level. The tape is stretched to a uniform tens^ion by a spring balance; its exact length at that tension is known from compar- ison with some standard; a correction for temperature is applied. The ends of the fleets are marked by driving into the grouncfa peg carrying in its top a tack; the exact end of the tape is marked by a score filed on the head of the tack at a point marked by a plumb bob from the tape, and this score becomes the origin for the next fleet. An assistant precedes the measuring party before each shift of the battens, and is accurately aligned by the theodolite to mark the true direction of the base line. The result of this method of measurement gives the horizontal distance between the points. It can be depended upon for the greatest degree of accuracy of any method, excepting that with a special hasc-measurmg apparatus, which is seldom employed in marine surveys. 441. A second method of })ase measurement is with the surveyor's chain. This depends for accu- racy upon the surface traversed being plane and level, a condition that is well fulfilled on a sandy beach, where the chain is nearly as accurate as the tape and much more rapid. A surveyor's chain is usiially 100 feet long; the exact value of its length must be obtained by comparison with a standard, and a correction applied for expansion or contraction due to temperature. The ends of the fleets are marked by steel pnis driven into the ground; the alignment is kept by the theodolite. 442. Where neither chain nor ttipe is available substitutes may be improvised from sounding wire taken from the deep-sea sounding machine, or, failing this, from well-stretched cod line. 443. Measurements made by the telemeter and stadia afford a close approximation to the true result, and if these instruments are not at hand the sextant angle of a rod of fixed length can be employed. The masthead height of the vessel may be used in determining the length of base line on this principle, either by making the ship itself mark one of the extremities and observing the masthead angle from the other extremity, or by simultaneously observing the masthead angle from both ends of a shore base, and also the three horizontal angles of the triangle formed by the ship and the two base stations. The latter plan is far preferable where accuracy is sought, as, if the angles are all taken by different observers at the same instant (which can be marked by the hauling down of a flag), the error arising from the motion of the ship about her anchor is eliminated, and, moreover, the data furnished offers a double solution of the triangle and the mean may be taken as giving a closer result. 444. A crude method of measuring a base is by means of the velocity of sound, though this would never be used where close results are expected. Fire a gun at one end of the base and at the other note by the most accurate means available the time between seeing the flash and hearing the report. Eepeat several times in each direction. The mean number of seconds and tenths of a second multiplied by the velocity of sound per second at the temperature of observation (art. 314, Chap. XI) gives the approximate length of base line. 445. When for any reason the existing conditions do not permit of a direct measurement being made along the line between the two base stations, recourse must be had to a broken base, that is, one in which the length of the base is obtained by reduction from the measured length of two or more auxiliary lines. Necessity for resorting to a broken base arises frequently when the two stations are situated on a curving shore line and the straight line between them passes across water, or where wooded or unfavorable country intervenes, or where a stream must be crossed. The most common form of broken base is that in which the auxiliary lines run from each extremity of the base at an acute angle and intersect; in addition to measuring each of these lines, the angles of the triangle formed by them with the base line must be observed and the true length of the base deduced by solution of the triangle. The form that is most frequently used where only a short section of the base is incapable of measure- ment (as is the case where a deep stream flows across) is that of an auxiliary right triangle whose base is the required distance along the base line and altitude a distance measured along a line perpendicular thereto to some convenient point; by this measured distance and the angles which are observed, the triangle is solved and the length of the unmeasured section determined. 446. In a survey of considerable extent, where good means are at hand for the correct determina- tion of latitude and longitude, a base line actually measured upon the earth may be dispensed with, and, instead of that, the jtositions of the two stations which are most widely separated may be deter- mined astronomically and plotted; the triangulation is then plotted upon any assumed scale, and when it has been brought up to connect the two stations the true value of the scale is ascertained. This is called the method of an astronomical base. 447. Signals. — All points in the survey whose positions are to be located from other stations,' or from which other ])ositions are to be located, must be marked by signals of such character as will render them distinguishable at the distance from which they are observed. The methods of constructing signals are of a wi(le variety. " A vessel regularly fitted out for surveying would carry scantlings, lumber, bolts, nuts, nails, white- wash, and sheeting for the erection of signals; however meager the equipment, the whitewash and sheeting (or some substitute for sheeting, preferably half of it white and half dark in color, ) should he provided, if possible, before l)eginning any surveying work. Regular tripod signals, which are quickly erected and are visible, under favorable circumstances, for many miles, are almost invariably employed to mark the main triangulation stations; among other advantages the tripod form permits the occupation with the theodolite of the exact center of the station, and avoids the necessity for the reduction which must otherwise be applied. Signals on secondary stations take an innumerable variety of forms, the require- MARINE SURVEYING. 139 ment being only that they shall be seen throughout the area over which they are to be made use of; a whitewashed spot on a rock, a whitewashed trunk of a tree, a whitewashed cairn of stones, a sheeting flag, a piece of sheeting wrapped about a bush or hung, with stones attached, over a cliff, or a white- washed barrel or box filled with rocks or earth and surmounted by a flag, suggest some of the secondary signals that may be employed; sometimes objects are found that are sufiiciently distinct in themselves to be used as signals without further marking, as a cupola or tower, a hut, a lone tree, or a bowlder; but it is seldom that an object is not rendered more conspicuous by the flutter of a flag above it, or by the dead-white ray reflected from a daub of whitewash. For convenience, each signal is given some short name by which it is designated in the records. 448. The Main Triangulatiox. — ^The points selected as stations for the main triangulation mark in outline the whole area to be surveyed; they are close enough together to afford an accurate means of plotting all intermediate stations of the secondary triangulation; and they are so placed with relation to one another that the triangles or quadrilaterals derived from them are well conditioned. The points are generally so chosen that small angles will be avoided. In order to fulfill the other conditions, it frequently becomes necessary to carry forward the triangulation by means of stations located on points a considerable distance inland, suclii as mountain peaks, which would not otherwise be regarded as properly within the limits of the surv^ey. Great care should be taken in observing all angles upon which the main triangulation is based; the best available instrument should be employed; angles taken with a theodolite or transit should be repeated, and observed with telescope direct and reversed, and the mean result taken; if the sextant is used, a number of separate observations of each angle should be taken and averaged for the most prob- able value. It must be remembered that while, in any other part of the work, an error in an angle affects only the results in its immediate vicinity, a mistake in the main triangulation goes forward through all the plotting that comes after it. It frequently occurs that the purposes of the survey are sufficiently well fulfilled by a graphic plot- ting of the main triangulation, but where more rigorous methods prevail, the results are obtained by calculation. The sum of the angles of each triangle is taken, and if it does not exactly equal 180° the values are adjusted to make them comply with this condition. The lengths of the various sides are then computed, regarding the stations, usually, as forming a series of quadrilaterals, and allowing for the curvature of the earth where the sides are sufficiently long to render it expedient to do so. 449. The Secondary Triangulation. — The points of the secondary triangulation are located, as far as possible, by angles from the main triangulation stations; these angles, having less dependent upon them, need not be repeated. A graphic plotting of these stations, without calculation, will suffice. 450. Astronomical Work. — This comprises the determination of the correct latitude and longitude of some point of the survey, which is the first position plotted, and of the true direction of some other point from the observation spot, which is the first line to be laid down on the chart; it is evident that these determinations form the origin of all positions and of all directions, without which the chart could not be constructed. The methods of finding latitude, longitude, and the true bearing of a terrestrial object are fully set forth in previous chapters. The feature that distinguishes such work in surveying from that of deter- mining the position of a ship at sea lies in the greater care that is taken to eliminate possible errors. At sea, results of absolute exactness are recognized as unattainable and are not required; but in a careful survey no step which will contribute to accuracy should be neglected. Tlie results should therefore be based upon a very large number of observations, employing the best instruments that are available, and the various sights being so taken that probable errors are offset in reckoning the mean. 4.51. By taking a number of sights the observer arrives at the most probable result of which his instruments and his own faculties render him capable; but this result is liable to an error whose amount is indeterminate and which is etiual to the algebraic sum of a number of small errors due, respectively, to his instruments (which must always lack perfection in some details), to an improper allowance for refraction under existing atmospheric conditions, and to his own personal error. Assuming, as we may, that the personal error is approximately constant, these three causes give rise to an error by which all altitudes appear too great or too small by a uniform but unknown amount. Let us assume', for an illustration, that this error has the effect of making all altitudes appear 30'^ too great; if an observer attempted to work his latitude from the meridian altitude of a star bearing south, the result of this unknown error would give a latitude 30''' south of the true latitude; if another star to the southward were observed, this mistake would be repeated; but if a star to the north were taken, the resulting latitude would be 30'^ to the north. It is evident, therefore, that the true latitude will be the mean of the results of observation of the northern and the southern star, or the mean of the average of several northern stars and the average of several southern stars. A similar process of reasoning will show that errors in the determination of hour angle are offset by taking the mean of altitudes of objects respectively east and west of the meridian. 452. It must be remembered that the uniformity of the unknown error only exists where the altitude remains approximately the same, as instrumental and refraction errors may vary with the altitude; another condition of uniformity requires that the instrument and the observer remain the same, and that all observations be taken about the same time, in order that atmospheric conditions remain unchanged; to preserve uniformity, if the artificial horizon is used, the same end of the roof should always be the near one to the observer; in taking the sun, however, as the personal error may not be the same for approaching as for separating limbs, every series of obsers^ations should be made up of an equal number of sights taken under each condition. 453. With all of this in mind, we arrive at the general rule that astronomical determinations shall be based upon the mean of observations, under similar conditions, of l)odies whose respective dis- tances from the zenith are nearly equal, and which bear in opposite directions therefrom. 140 MARINE SURVEYING. 454. This condition eliminates the sun from availability for observations for latitude, though it properly admits the use of that body for longitude where equal altitudes or single a. m. and p. m. sights are taken. Opposite stars of approximately equal zenith distance should always be used for latitude, circum-meridian altitudes being observed during a few minutes before and after transit; excellent results are also obtained from stellar observations for longitude; but very low stars should be avoided, on account of the uncertainty of refraction, and likewise very high ones, as the reflection from the index mirror of the sextant may not be perfectly distinct when tne ray strikes at an acute angle. 455. If there is telegraphic communication, an endeavor should be made to obtain a time signal from a reliable source, instead of depending upon the chronometers. 456. Topography. — The plane-table, with telemeter and stadia, affords the most expeditious means of plotting the topograijhy, and should be employed when available. Points on shore may also be plotted by sextant angled, using the three-point problem, or by any other reliable method. 457. Hydrography. — The correct delineation of the hydrographic features being one of the most important objects of the survey, great care should be devoted to this part of the work. Soundings are run in one or more series of parallel lines, the direction and spacing oi which depend upon the scope of the survey. It is usual for one series of lines to extend in a direction normal to the general trend of the shore line. In most cases a second series runs perpendicular to the first, and in surveys of important bodies of water still other series of lines cross the system diagonally. In developing rocks, shoals, or dangers the direction of the lines is so chosen as will best illustrate the features of the bottom. When lines cross, the agreement of the reduced soundings at their intersection affords a test of the accuracy of the work. As the depth of water increases, if there is no reason to suspect dangers, the interval between lines may be increased. Lines are run by the ship or boat in such manner as to follow as closely as possible the scheme of sounding that has been laid out. The position is located by angles at the beginning of each line, at each change of course, at frequent intervals along the line, and at the point where each line is finished. Soundings taken between positions are plotted by the time interval or patent-log distances. 458. There are a number of methods for determining positions while sounding, which may be described briefly as follows: By tico sextant angles. — Two observers with sextants measure simultaneously the angles between three objects of known position, and the position is located by the three-point problem. This is the method most commonly employed in boat work, and has the great advantage that the results may be plotted at once on the working sheet in the boat and the lines as run thus kept nearly in coincidence with those laid out in the scheme. A study of the three-point problem (art. 153, Chap. IV) will give the considerations that must govern in the selection of objects. By two theodolite angles. — Two stations on shore are occupied by observers with theodolites, and at certain instants, indicated by a signal from the ship or boat, they observe the angular distance thereof from some known point. The intersection of the direction lines thus given is at the required position. This method is expeditious where the signals are small or not numerous. Its disadvantage is that the plotting can not be kept up as the work proceeds. By one sextant and one theodolite angle. — An observer ashore occupies a station with a theodolite and cuts in the ship or boat, while one on board takes a sextant angle between two objects, of which one should preferably be the occupied station. It is plotted by laying off the direction line from the theodo- lite and finding with a three-armed protractor or piece of tracing paper what point of that line subtends the observed angle between the objects. Its advantages and disadvantages are the same as those of the preceding method. In running lines of soundings offshore, where signals are lost sight of, the best method is to get an accurate departure, before dropping the land, by the best means that offers, keeping careful note of the the dead reckoning, and on running in again, to get a position as soon as possible, note the drift and reconcile the plotting of intermediate soundings accordingly. Where circumstances require, the position may be located by astronomical observations as usually taken at sea. 459. A careful record of soundings must be kept, showing the time of each (so that proper tidal correction may be applied), the depth, the character of bottom, and such data as may be required to locate the position. 460. Tidal Observations. — These should begin as early as practicable and continue throughout the survey, it being most important that they shall, if possible, cover the period of a lunar month. In the chapter on Tides (Chap. XX) the nature of the data to be obtained is explained. 461. Magnetic Observations. — The feature of the earth's magnetism with which the navigator is most concerned is the variation, which is set forth on the chart, and upon the determination of which will depend the correctness of all courses and bearings on shipboard. It is usually obtained by noting the compass direction from the observation spot of the object whose true bearing is known by calcula- tion, and comparing the true and compass bearings; or it may be observed by mounting the ship's com- pass in a place on shore free from foreign magnetic influence, and finding the compass error as it is found on board. Observations for dip and intensity are also made when the proper instruments are at hand. 462. Running Survey. — Where time and opportunity permit only a superficial examination of a coast line or water area, or where the interests of navigation require no more, recourse is had to a Run- ning Surrey, in which shore positions are determined and soundings are made while the ship steams along the coast stopping only occasionally to fix her position, and in which the assistance of boat or shore parties may or may not be employed. In this method the ship starts at one end of the field from a known position, fixed either by astro- nomical observations or by angles or bearings of terrestrial objects having a determined location. Care- ful compass bearings or sextant angles are taken from this position to all objects ashore which can be recognized, and a series of direction lines is thus obtained. The ship then steams along the coast, at a convenient distance therefrom, keeping accurate account of her run by compass courses and patent log. MARINE SURVEYING. 141 From time to time other series of bearings or angles are taken upon those objects ashore which are to be located, the direction lines plotted from the estimated position of the ship, and the various objects located by the intersections with their other direction lines. During all the time that the ship is under way, soundings are taken at regular intervals and plotted from the dead reckoning. As frequently as circum- stances permit, the ship is stopped and her position located by the best available means, and the inter- vening dead reckoning reconciled for any current that may be found. If a steam launch can be employed in connection with a running survey, it is usually sent to run a second line inshore of the ship. The boat's position is obtained by bearings of objects ashore which are located by the ship, or by bearings and mast-head angles of the ship, or by such other means as offer. The duty of the boat is to take a series of soundings, and to collect data for shore line and topography. If circumstances allow the landing of a shore party, its most important duty is to mark the various objects on shore by some sort of signals which will render them unmistakable. Beyond this, it can perform such of the duties assigned to shore parties in a regular survey as opportunity permits. 142 WINDS. CHAPTER XVIIL WINDS. 463. Wind is air in approximately horizontal motion. Observations of the wind should include its true direction, and its force or velocity. The direction of the wind is designated by the point of the compass from which it proceeds. The force of the wind is at sea ordinarily expressed in terms of the Beaufort Scale, each degree of this scale corresponding to a certain velocity in miles per hour, as explained in article 67, Chapter II. 464. The Caise of the Wind. — Winds are produced by differences of atmospheric pressure, which are themselves ultimately, and in the main, attributable to differences of temperature. To undei-stand how the air can be set in motion by these differences of pressure it is necessary to have a clear conception of the nature of the air itself. The atmosphere which completely envelops the earth may be considered as a fluid sea at the bottom of which we live, and which extends upward to a considerable height, probably 200 miles, constantly diminishing in density as the altitude increases. The air, or material of which this atmosphere is composed, is a transparent gas, which, like all other gases, is perfectly elastic and highly compressible. Although extremely light, it has a perfectly definite weight, a cubic foot of air at ordinary pressure and temperature weighing 1.22 ouncres, or about one seven hundred and seventieth part of the weight of an equal volume of water. In consequence of this weight it exerts a certain pressure upon the surface of the earth, amounting on the average to 15 pounds for each square inch. To accurately measure this pressure, which is constantly undergoing ■ slight changes, we ordinarily employ a mercurial barometer (art. 48, Chap. II), an instrument in which the weight of a column of air of given cross section is balanced against that of a column of mercury having an equal cross section; and instead of saying that the pressure of the atmosphere is a certain number of pounds on each square inch, we say that it is a certain number of inches of mercury, meaning thereby that it is equivalent to the pressure of a column of mercury that many inches in height, and one square inch in cross section. All gases, air included, are highly sensitive to the action of heat, expanding or increasing in volume as the temperature rises, contracting or diminishing in volume as the temperature falls. Suppose now that the atmosphere over any considerable region of the earth's surface is maintained at a higher temperature than that of its surroundings. The warmed air will expand, and its upper layers will flow off to the surrounding regions, cooling as they go. The atmospheric pressure at sea level throughout the heated areas Mill thus be diminished, while that over the circumjacent cooler areas will be correspondingly increased. As the result of this difference of pressure, there will be movement of the surface air away from the region of high pressure and towards the region of low, somewhat similar to the flow of water which takes place through the connecting bottom sluice as soon as we attempt to fill one compartment of a divided vessel to a slightly higher level than that found in the other. A difference of atmospheric pressure at sea level is thus immediatelj' followed by a movement of the surface air, or by winds; and these differences of pressure have their origin in differences of tempera- ture. If the atmosphere were everywhere of uniform temperature it would lie at rest on the earth's surface — sluggish, torpid and oppressive — and there would be no winds. This, however, is fortunately not the case. The temperature of the atmosphere is continually or periodically higher in one region than in another, and the chief variations in the distribution of temperature are systematically repeated year after year, giving rise to like systematic variations in the distribution of pressure. 465. The Normal Distkibittion of Pressure. — The winds, while thus due primarily to differences of temperature, stand in more direct relation to differences of pressure, and it is from this point of view that they are ordinarily studied. In order to furnish a comprehensive view of the distribution of atmospheric pressure over the earth's surface, charts have been prepared showing the average reading of the barometer for any given period, whether a month, a season, or a year, and covering as far as possible the entire globe. These are known as isobaric charts, from the fact that all points at which the barometer has the same reading are joined by a continuous line or isobar. The isobaric chart for the year (fig. 59) shows in each hemisphere a well-defined belt of high pressure (30.20 inches) completely encircling the globe, that in the northern hemisphere having its middle line about in latitude 35° North, that in the southern hemisphere about in latitude 30° South, these constituting the so-called meteorological tropics. From the summit or ridge of each of these belts the pressure fails off alike toward the equator and toward the pole, although much less rapidly in the former direction than in the latter. The equator itself is encircled by a belt of somewhat diminished pressure (29.90 inches), the middle line of which is ordinarily found in northern latitudes. In the northern hemisphere the diminution of pressure on the poleward slope is much less marked and much less regular than in the southern hemisphere, minima (29.70 inches) occurring in the North Atlantic Ocean near Iceland, and in the North Pacific Ocean near the Aleutian Islands, beyond which the pressure increases. In the southern hemisphere no such minima are apparent, the pressure continuing to diminish uninterruptedly as higher and higher latitudes are attained. Along the sixtieth parallel of south latitude the average barometric reading is 29.30 inches. WIlN'DS. 143 Fig. 59. 144 WINDS. 466. Seasoxal Variatioks of Pressurk. — As might be expected from its close relation to the temperature, the whole system of pressure distribution exhibits a tendency to follow the sun's motion in declination, the barometric equator occupying in July a position slightly to the northward of its position in January. In either hemisphere, moreover, the pressure over the land during the winter season is decidedly above the annual average, during the summer season decidedly below it; the extreme variations occurring in the case of continental Asia, where the mean monthly pressure ranges from 30.50 inches during January to 29.50 inches during July. Over the northern ocean, on the other hand, conditions are reversed, the summer pressures being here somewhat the higher. Thus, in January the Icelandic and the Aleutian minima increase in depth to 29.50 inches, while in July these minima fill up and are well-nigh obliterated, a fact which has much to do with the strength and frequency of the winter gales in high northern latitudes and the absence of these gales during the summer. Over the southern ocean, m keeping with its slight contrast between winter and summer temperatures, similar variations of pressure do not exist. 467. The Prevailing Winds. — As a result of the distribution of pressure just described, there is in either hemisphere a continual motion of the surface air away from the meteorological tropic — on one side towards the equator, on the other side towards the pole, the first constituting in each case the trade winds, the second the prevailing winds of higher latitudes. Upon a stationary earth the direction of this motion would be immediately from the region of high towards the region of low barometer, the moving air steadily following the barometric slope or gradient, increasing in force to a gale where these gradients are steep, decreasing to a light breeze where they are gentle, sinking to a calm where they are absent. The earth, however, is in rapid rotation, and this rotation gives rise to a force which exercises a material influence over all horizontal motions upon its surface, whatever their direction, serving constantly to divert them to the right in the northern hemisphere, to the left in the southern. The air set in motion by the difference of pressure is thus constantly turned aside from its natural course down the barometric gradient or slope, and the direction of the wind at any point, instead of being identical with that of the gradient at that point, is deflected by a certain amount, crossing the latter at an angle which in practice varies between 45° and 90° (4 to 8 compass points), the wind in the latter case blowing parallel to the isobars. As a consequence of this deflection the northerly winds which one would naturally expect to find on the equatorial slope of the belt of high pressure in the northern hemisphere become northeasterly, — the NE. trade; the southerly winds of the polar slope become southwesterly, — the prevailing westerly winds of northern latitudes. So, too, for the southern hemisphere, the southerly winds of the equatorial slope here becoming southeasterly, — the SE. trades; the northerly winds of the polar slope northwesterly, — the prevailing westerly winds ti southern latitudes. 46§. The relation here described as existing between the distribution of atmospheric pressure and the direction of the wind is of the greatest importance. It may be briefly. stated as follows: In the northern hemisphere stand with the back to the wind; in this position the region of high barometer lies on your right hand and somewhat behind you; the region of low barometer on your left hand and somewhat in front of you. In the southern hemisphere stand with the back to the wind; in this position the region of high barometer lies on your left hand and somewhat behind you; the region of low barometer on your right hand and somewhat in front of you. This relation holds absolutely, not only in the case of the general distribution of pressure and cir- culation of the atmosphere, but also in the case of the special conditions of high and low pressure which usually accompany severe gales. 469. The Trade Winds. — The Trade Winds blow from the tropical belts of high pressure towards the equatorial belt of low pressure — in the northern hemisphere from the northeast, in the southern hemisphere from the southeast. Over the eastern half of each of the great oceans they extend consid- erably farther from the line and their original direction inclines more towards the pole than in mid- ocean, where the latter is almost easterly. They are ordinarily looked upon as the most constant of winds, but while they may blow for days or even for weeks with slight variation in direction or strength, their uniformity should not be exaggerated. There are times when the trade winds weaken or shift. There are regions where their steady course is deformed, notably among the island groups of the South Pacific, where the trades during January and February are practically nonexistent. They attain their highest development in the South Atlantic and in the South Indian Ocean, and are every- where fresher during the winter than during the summer season. They are rarely disturbed by cyclonic storms, the occurrence of the latter within the limits of the trade wind region being furthermore con- fined in point of time to the late summer and autumn months of the resijective hemispheres, and in scene of action to the western portion of the several oceans. The South Atlantic Ocean alone, however, enjoys complete immunity from tropical cyclonic storms. 470. The Doldrums. — The equatorial girdle of low pressure occupies a position between the high- pressure belt of the northern and the similar belt of the southern hemisphere. Throughout the extent of this barometric trough the pressure, save for the slight diurnal oscillation, is practically uniform, and decided barometric gradients do not exist. Here, accordingly, the winds sink to stagnation, or rise at most only to the strength of fitful breezes, coming first from one point of the compass, then from another, with cloudy, rainy sky and frequent thunderstorms. The region 'throughout which these conditions prevail consists of a wedge-shaped area, the base of the wedge resting in the case of the Atlantic Ocean on the coast of Africa, and in the case of the Pacific Ocean on the coast of America, the axis extending westward. The position and extent of the belt vary somewhat with the season. Throughout February and March it is found immediately north of the equator and is of inappreciable width, vessels following the usual sailing routes frequently passing from trade to trade without interruption in both the Atlantic and the Pacific Oceans. In July and August it has migrated to the northward, the axis extending east and west along the parallel of 7° north, and the belt itself covering several degrees of latitude, even at its narrowest point. At this season of the year, also, the southeast trades blow with diminished fresh- ness across the equator and well into the northern hemisphere, being here diverted, however, by the effect of the earth's rotation, into southerly and southwesterly winds, the so-called southwest monsoon of the African and Central American coasts. WINDS. 145 471. The Horse jlatitudes. — On the outer margin of the trades, corresponding vaguely with the summit of the tropical ridge of high pressure in either hemisphere, is a second region throughout which the barometric gradients are faint and undecided, and the prevailing winds correspondingly light and variable, the so-called hor^e latitudes, or calms of Cancer and of Capricorn. Unlike the doldrums, how- ever, the weather is here clear and fresh, and the periods of stagnation are intermittent rather than continuous, showing none of the persistency which is so characteristic of the equatorial region. The explanation of this difference will Ijecome obvious as soon as we come to study the nature of the daily barometric changes of pressure in the respective regions, these in the one case being marked by the uniformity of the torrid zone, in the other sharing to a limited extent in the wide and rapid variations of the temperate. 472. The Prevailing Westerly Winds. — On the exterior or polar side of the tropical maxima the pressure again diminishes, the barometric gradients being now directed towards the pole; and the currents of air set in motion along these gradients, diverted to the right and left of their natural course by the earth's rotation, appear in the northern hemisphere as southwesterly winds, in the southern hemisphere as northwesterly — the prevailing westerly winds of the temperate zone. Only in the southern hemisphere do these winds exhibit anything approaching the persistency of the trades, their course in the northern hemisphere being subject to frequent local interruption by periods of winds from the eastern semicircle. Thus the tabulated results show that throughout the portion of the North Atlantic included between the parallels 40°-50° North, and the meridians 10°-50° West, the winds from the western semicircle (South — NNW.) comprise about 74 per cent of the whole number of observations, the relative frequency being somewhat higher in winter, somewhat lower in summer. The average force, on the other hand, decreases from force 6 to force 4 Beaufort scale, with the change of season. Over the sea in the southern hemisphere such variations are not apparent; here the westerlies blow through the entire year with a steadiness little less than that of the trades them- selves, and with a force which, though fitful, is very much greater, their boisterous nature giving the name of the " Roaring Forties" to the latitudes in which they are most frequently observed. The exi)lanation of this striking difference in the extra-tropical winds of the two halves of the globe is found in the distribution of atmospheric pressure, and in the variations which this latter undergoes in different parts of the world. In the landless southern hemisphere the atmospheric pressure after cross- ing the parallel of 30° South diminishes almost uniformly towards the pole, and is rarely disturbed by those large and irregular fluctuations which form so important a factor in the daily weather of the northern hemisphere. Here, accordingly, a system of polar gradients exists quite comparable in stability with the equatorial gradients which give rise to the trades; and the poleward movement of the air in obedience to these gradients, constantly diverted to the left by the effect of the earth's rotation, constitutes the steady westerly winds of the south temperate zone. 473. The Monsoon Winds. — Theairover the land is warmer in summer and colder in winter than that over the adjacent oceans. During the former season the continents thus become the seat of areas of relatively low pressure; during the latter of relatively high. Pressure gradients, directed outward during the winter, inward during the summer, are thus established between the land and the sea, which exercise the greatest influence over the winds prevailing in the region adjacent to the coast. Thus, off the Atlantic seaboard of the United States southwesterly winds are most frequent in summer, north- westerly winds in winter; while on the Pacific coast the reverse is true, the wind here changing from northwest to southwest with the advance of the colder season. The most striking illustration of winds of this class is presented by the monsoons {Mausum, season) of the China Sea and of the Indian Ocean. In January abnormally low temperatures and high pressure obtain over the Asiatic plateau, high temperatures and low pressure over Australia and the nearby portion of the Indian Ocean. As a result of the baric gradients thus established, the southern and eastern coast of the vast Asiatic continent and the seas adjacent thereto are swept by an outflowing current of air, which, diverted to the right of the gradient by the earth's rotation, appears as a north- east Avind, covering the China Sea and the northern Indian Ocean. Upon entering the southern hemisphere, however, the same force which hitherto deflected the moving air to the right of the gradient now serves to deflect it to the left; and here, accordingly, we have the monsoon appearing as a northwest wind, covering the Indian Ocean as far south as 10°, the Arafura Sea, and the northern coast of Australia. In July these conditions are precisely reversed. Asia is now the seat of high temperature and correspondingly low pressure, Australia of low temperature and high pressure, although the departure from the annual average is by no means so pronounced in the case of the latter as in that of the former. The baric gradients thus lead across the equator and are addressed toward the interior of the greater continent, giving rise to a system of winds whose direction is southeast in the southern hemisphere, southwest in the northern. The mtrtheast (winter) monsoon blows in the China Sea from October to April, the southwest (summer) monsoon from May to September. The former is marked by all the steadiness of the trades, often attaining the force of a moderate gale; the latter appears as a light breeze, unsteady in direction, and often sinking to a calm. Its prevalence is frequently interrupted by tropical cyclonic storms, locally known as t;/phoons, although the occurrence of these latter may extend well into the season of the winter monsoon. 474. Land and Sea Breezes. — Corresponding with the seasonal contrast of temperature and pressure overland and water, there is likewise a diurnal contrast which exercises a similar though more local effect. In summer particularly, the land over its whole area is warmer than the sea by day, colder than the sea by night, the variations of pressure thus established, although insignificant, sufficing to evoke a system of littoral breezes directed landward during the daytime, seaward during the night, which, in general, do not penetrate to a distance greater than 30 miles on and off shore, and extend but a few hundred feet into the depths of the atmosphere. The sea breeze begins in the morning hours — from 9 to 11 o'clock — as the land warms. In the late afternoon it dies away. In the evening the land breeze springs up, and blows gently out to sea until 22489—03 10 1 46 WINDS. morning. In the tropics this process is repeated day after day with great regularity. In our own latitudes, the land and sea breezes are often masked by winds of cyclonic origin. 475. A single important effect of the seasonal variation of temperature and pressure over the land remains to be described. If there were no land areas to break the even water surface of the globe, the trades and westerlies of the terrestrial circulation would be developed in the fullest simplicity, with linear divisions along latitude circles between the several members — a condition nearly approached in the land-barren southern hemisphere during the entire year, and in the northern hemisphere during the winter season. In the summer season, however, the tropical belt of high pressure is broken where it crosses the warm land, and the air shouldered off from the continents accumulates over the adjacent oceans, particularly in the northern or land hemisphere. This tends to create over each of the oceans a circular or elliptical area St high pressure, from the center of which the baric gradients radiate in all directions, giving rise to an outflowing system of winds, which by the effect of the earth's rotation is converted into an outflowing spiral eddy or aniicydonic whirl. The sharp lines of demarcation which would otherwise exist between the several members of the general circulation are thus obliterated, the southwesterly winds of the middle northern latitudes becoming successively northwesterly, northerly, and northeasterly, as we approach the equator and round the area of high pressure by the east; the northeast trade becoming successively southeasterly, southerly, and southwesterly, as we recede from the equator and round this area by the west; similarly for the other hemisphere. 147 chaptp:r XIX. OYCLONIO STOEMS. 476. Variations of the Atmospheric Pressure. — The distribution of the atmospheric pressure previously described (Chap. XV^III) and the attendant circulation of the winds are those which become evident after the effects of many disturbing causes have been eliminated by the process of averaging, or embracing in the summation observations covering an extended period of time. The distribution of pressure and the system of winds which actually exist at a given instant will in general agree with these in its main features, but may differ from them materially in detail. Confining our attention for the time being to the subject of atmospheric pressure, it may be said that this, at any given point on the earth's surface, is in a constant state of change, the mercury rarely becoming stationarv, and then only for a few hours in succession. The variations which the pressure undergoes may be divided into two classes; viz, periodic, or those which are continuously in operation, repeating themselves within fixed intervals of time, long or short; and non-periodic or accidental, which occur irregularly, and are of varying duration and extent. 477. Periodic Variations. — Of the former class of changes the most important are the seasonal, which have been already to some extent described, and the diurnal. The latter consists of the daily occurrence of two barometric maxima, or points of highest pressure, with two intervening minima. Under ordinary circumstances, with the atmosphere free from disturbances, the barometer each day attains its first minimum about 4 a. ra. As the day advances the pressure increases, and a maximum, or point of greatest pressure, is reached about 10 a. m. From this time the pressure diminishes, and a second minimum is reached about 4 p. m., after which the mercury again rises, reaching its second maximum about 10 p. m. The range of this diurnal oscillation is greatest at the equator, where it amounts to ten hundredths (0.10) of an inch. It diminishes with increased latitude, and near the poles it seems to vanish entirely. In middle latitudes it is much more apparent in summer than in winter. 478. Non-periodic Variations. — The equatorial slope of the tropical belt of high pressure which encircles the globe in either hemisphere is characterized by the marked uniformity of its meteorological conditions, the temperature, wind, and weather changes proper to any given season repeating them- selves as day succeeds day with almost monotonous regularity. Here the diurnal oscillation of the barometer constitutes the main variation to which the atmospheric pressure is subjected. On the polar slope of these belts conditions the reverse of these obtain, the elements which go to make up the daily weather here passing from phase to phase without regularity, with the result that no two days are pre- cisely alike; and as regards atmospheric pressure, it may be said that in marked contrast with the uniformity of the torrid zone, the barometer in the temperate zone is constantly subjected to non-periodic or accidental fluctuations of such extent that the periodic diurnal variation is scarcely apparent, the mercury at a given station frequently rising or falling several tenths of an inch in twenty-four hours. 479. Progressive Areas of High and Low Pressure. — The explanation of this rapid change of conditions is found in the approach and passage of extensive areas of alternately high and low pressure, which affect alike, although to a different degree, all the barometers coming within their scope. The general direction of motion of these areas is that of the prevailing winds; eastward, therefore, in the latitudes which are under consideration. Taken in conjunction, these areas of high and low pressure exercise a controlling influence over the weather changes of the temperate zones. As the low area draws near, the sky becomes overclouded, the prevailing westerly wind falls away, and is succeeded by a wind from some easterly direction, faint at first, but increasing as the pressure continues to diminish; the lowest pressure having been reached, the wind again goes to the westward, the glass starts to rise, and the weather clears; all marking the eastward recession of the low area and the approach of the subsequent high. The first stage in the development of the low is a slight diminution of the atmospheric pressure, amounting in general to not more than one or two hundredths of an inch, throughout an area covering a more or less extensive portion of the earth's surface, either land or water, but far more frequently over the former than over the latter. Shortly after the advent of this initiatory fall the decrease of pres- sure throughout some small region within the larger area assumes a more decided character, the mercury here standing at a lower level than elsewhere and reading successively higher as we go outward, the region thus becoming, as it were, the center of the whole barometric depression. A system of baro- metric gradients is by this means established, all directed radially inward, and in obedience to these gradients there is a movement of the surface air towards the center or point of lowest barometer. The air once in motion, however, the effect of the earth's rotation is brought into play precisely as in the case of the larger movements of the atmosphere, with the result that the several currents, instead of following the natural course along these gradients, are deflected from them, in the northern hemisphere to the right hand, in the southern hemisphere to the left, the extent of the deflection being from 4 to 8 compass points. 4§0. Cyclones and Cyclonic Circulations. — A central area of low barometer will thus be sur- rounded by a system of winds which constantly draw in towards the center but at the same time circulate about it, the whole forming an inflowing spiral; the direction of this circulation being in the southern hemisphere with the motion of the hands of a watch, in the northern hemisphere opposed to this 1.48 CYCLONIC STORMS. motion. Where the barometric gradients are steep, these winds are apt to be strong; where they are gentle, the winds are apt to be weak; where they are absent, as is the case at the center or bottom of the depression, cahns are apt to prevail. Around the center of the area of high pressure a similar system of wind will be found, but l)lowmg in a contrary direction. Here the barometric gradients are directed radially outward, with the result that in place of the inflowing, we have an outflowing spiral, the circulatory motion being right handed or with the hands of a watch in the northern hemisphere, left handed or against the hands of a watch in the southern. All of these features are shown in the accompanying diagrams (fig. 60), which exhibit the general character of cyclonic (around the low) and anticy clonic (around the high) circulations in the northern An'icyclonic. northern hemisphekk. Otielnnir. Aiiticyclonic. Cyclonic. SOl'THERN HEMISPHERE. Fig. 60. The light arrows .show the direction of the gradients; the heavy arrows the direction of the winds. and the southern hemisphere, respectively. The closed curves represent the isobars, or lines along Avhich the barometric pressure is the same; the short arrows show the direction of the gradients, which are everywhere at right angles to the isobars; the long arrows give the direction of the winds, deflected by the earth's rotation to the right of the gradients in the northern hemisphere, to the left in the southern. 4§1. Features op Cyclonic and Anticyclonic Regions. — Certain features of the two areas may here be contrasted. In the anticyclonic, the successive isobars are as a rule far apart, showing weak gradients and consequently light winds; the areas themselves are of relatively great extent, and their rate of progression is sIoav. During the summer they originate as extensions into higher latitudes of the margins of the tropical belts of high pressure; during the winter, as offshoots of the strong anticy- clone which covers the land throughout that season. Their approach and presence is accompanied by polar or westerly winds, temperature below the seasonal average, fair weather, and clear skies. In the cyclonic area the successive isobars are crowded together, showing steep gradients and strong winds; they may appear either as trough-like extensions into the temperate zone of the polar belt of low pres- sure, in which case the easterly winds proper to their polar side are nonexistent, or (in lower latitudes) as independent areas, sometimes, indeed, as detached portions of the equatorial low-pressure belt, which move eastward and poleward across the temperate zone, and are ultimately merged into the great cyclonic area surrounding the pole. The progress of these independent areas is invariably attended by the strong and steadily shifting winds, foul weather, and other features which make up the ordinary storm at sea. In the trough-like depressions of higher latitudes these features may or may not be observed, their presence depending upon the depths of the barometric trough and the steepness of its slopes. In these, moreover, the cyclonic circulation is never completely developed, the storm winds having rather the character of right line gales, blowing from an equatorial or easterly direction until the axis of the trough is at hand, and as this passes shifting by the west at one bound to a polar direction. 482. Cyclonic Storms. — Strong winds are the result of steep barometric gradients. These may occur with cyclonic or with anticyclonic areas, the latter being exemplified in the case of the northers in the Gulf of Mexico and the northwesterly winter gales along the Atlantic coast of the United States, which are almost invariably accompanied by barometers above the average. They are, however, so much more frequent in the case of areas of low pressure and consequent cyclonic circulations, wnth their attendant foul weather characteristics, that the latter are generally known as cyclonic storms, i. e., storms in which the wind circulation is cyclonic. Cyclonic storms may with convenience be divided into two classes; viz, tropical, or those which originate near but not on the equator; and extra-tropical, or those which first appear in higher latitudes. 4§3. Tropical Cyclonic Storms. — The occurrence of tropical cyclonic storms is confined to the summer and autumn months of the respective hemispheres, and to the w^estern part of the several oceans, the North Atlantic, the North Pacific, the South Pacific, and the Indian Ocean. They are unknown in the South Atlantic Ocean. The Arabian Sea and the Bay of Bengal are also visited by cyclonic storms, the season of their occurrence extending from May to October. 4§4. Motion of the Storm Center. — In the case of tropical cyclonic storms there is always a tendency for the barometric depression, impelled by the general motion of the atmosphere in the CYCLONIC STORMS. 149 trade wind region, to follow a path which tends at once westward and away from the equator. This motion conthmes until the limits of the trades are reached, where the path ordinarily recurves, and the subsequent motion of the depression is eastward and towards the pole, the disturbance at the same time assuming the features of the extra-tropical cyclonic storm. 4§5. Rate of Progress op the Stor.^i Center. — Within the tropics (in the northern hemisphere) the average velocity of the storm center along the track is about 17 miles per hour; in the latitudes of recurvature this drops to 8 miles per hour, the center at the time frequently becoming stationary; in higher latitudes it again increases, rising to 20 or even to 30 miles per hour. In the southern hemisphere the average velocity of progress as far as determined is somewhat less than in the northern, but shows about the same relation in different parts of the track. The general path of the tropical cj-clonic storm in either hemisphere and the cyclonic circulation of the wind about the storm center are given in figures 61 and 62; that for the northern hemisphere applying to the West India hurricane; that for ^ the southern hemisphere to the hurricanes of ,„ ,, ^P° ^ .,.,.■. . ,'i i— i >""^ h i/iiT the South Pacific Ocean. ■' ' ' '^ '^^ ^ . . , . . . i ^^^ 486. Character of Tropical Cycloxic Storms. — Within the tropics the storm area is small, the region covered by violent winds ex- tending in general not more than 150 miles from the center. The barometric gradients are, how- ever, exceedingly steep, instances having been recorded in which the difference of pressure for this distance amounted to 2 inches. In the typhoons of the North Pacific Ocean gradients of one inch in 60 miles are not infrequent. The successive isobars are almost circular. As a consequence of this distribution of pressure the winds on the slopes of the depression are fre- quently of great violence, and in the matter of direction they are more symmetrically disposed about the center than is the case with the larger and less regularly shaped depressions of higher latitudes. In these low latitudes the average values of the deflection of the wind from the barometric gradient is in the neighborhood of six compass points, — to the right in the northern hemisphere, to the left in the southern. 4§7. To Fix the Bearing of the Storm Center from the Vessel. — On this assumption, the following rules will enable an observer to fix the bearing of the storm center from his vessel : — In the northern hemisphere, stand with the back to the wind; the storm center will bear six points to the observer's left. In the southern hemisphere, stand with the back to the wind; the storm center will bear six points to the observer's right. On the basis of these rules the tables here- after given (art. 492) show the bearing of the center corresponding to a wind of any direction. 488. To Fix the Distance of the Storm Center from the Vessel. — The following table, taken from Piddington's "Sailor's Horn Book," may prove of some assistance in estimating the distance of the storm center from the vessel: Fig. 61. Average fall of the barometer per hour. From 0.02 to 0.06 in. From 0.06 to 0.08 in. From 0.08 to 0.12 in. From 0.12 to 0.15 in. Distance from the storm center. From 250 to 150 miles. From 150 to 100 miles. From 100 to 80 miles. From 80 to 50 miles. The table assumes that the vessel is hove-to in front of the storm, and that the latter is advancing directly toward it. 489. To Avoid the Center of the Storm. — In the immediate neighborhood of the center itself the winds attain full hurricane force, the sea is exceedingly turbulent, and there is danger of being struck aback. Every effort should therefore be made to avoid this region,' either by running or by heaving-to; and if recourse is had to the latter maneuver, much depends upon the selection of the proper tack; this being in every case the tack which will cause the wind to draw aft with each successive shift. A vessel hovo-to in advance of a tropical cyclonic storm will experience a long heavj' swell, a falling barometer with torrents of rain, and winds of steadily increasing force. The shifts of wind will depend upon the position of the vessel with respect to the path followed by the storm center. Immediately upon the path, the wind will hold steady in direction until the passage of the central calm, the ''eye of the storm," after which the gale will renew itself, but from a direction opposite to that which it previ- 150 CYCLONIC STOEMS. ously had. To the right of the path, or in the right-hand semicircle of the stomi (the observer being supposed to face along the track ), the wind, as the center advances and i)asses the vessel, will constantly shift to the right, the rate at which the successive shifts follow each other increasing with the prox- imity to the center; in this semicircle, then, in order that the wind shall draw aft with each shift, the vessel must be hove-to on the starboard tack; similarly, in the left-hand semicircle, the wind will con- stantly shift to the left, and here the vessel must l)e hove-to on the port tack. These rules hold alike for both hemispheres and for cyclonic sti)rms in all latitudes. The above shifts of the wind are based upon the supposition that the vessel is lying-to. A vessel in rapid westerly motion may, in low latitudes, readily overtake the storm center, in which case the observed shifts will be just the reverse of those here described. 490. Dangerois and Navigable Semicircles. — Prior to recurving, the winds in that semicircle of the storm which is more remote from the equator (the right-hand semicircle in the northern hemi- sphere, the left-hand semicircle in the 180° 170° southern ) are liable to be more severe than those of the opposite semicircle. A vessel hove-to in the semicircle adjacent to the equator has also the advantage of immu- nity from bec(jming involved in the actual center itself, inasmuch as there is a distinct tendency on tiie part of the latter to move away from the equator. For these reasons the more remote semicircle has been called the dangerouK; the less remote, ihenavigable. 491. Maneuvering. — A vessel sus- l^ecting the dangerous proximity of a trop- ical cyclonic storm should lie-to for a time on the starboard tack to locate the center by observing shifts of the wind and the behavior of the barometer. If the former holds steady and increases in force, while the latter falls rapidly, say at a greater rate than 0.03 of an inch per liour, the vessel is probably on the track of the storm and in advance of the center. In this position the proper step (providing, of course, that sea room permits) is to run, keeping the wind, in the northern hemisphere, at all times well on the starboard quarter; in the 1^ southern hemisphere, well on the port; and thus constantly increasing the distance to the storm center. The same rule holds good if the observation places the vessel at but a scant distance within the forward quad- rant of the dangerous semicircle. Here, too, the natural course will be to seek the navigable semicircle of the storm, even though such a course involves crossing the track in advance of the center, always ex- ercising due caution to keep the wind frotn drawing too far aft. The critical case is that of a vessel — which finds herself in the forward quad- rant of the dangerous semicircle and at a considerable distance from the track, for here the shifts of the wind are sluggish and the indications of the barometer are unde- cided, both causes conspiring to render the bearing of the center doubtful. If, upon heaving-to, the barometer becomes station- ary, the position should be maintained until indications of a rise are apparent, upon which the course may be resumed with safety and held as long as the rise continues. If, however, the barometer falls, a steamer should make a run to the NNE. or NE. (southern hemisphere, SSE. orSE. ), keeping the wind and sea a little on the.port (southern hemisphere, starboard) bow, and using such speed as will at least keep the mercury stationary. Such a step will in general be attended with the assurance that the present weather conditions will in any case grow no worse. For a sailing vessel, unable to stand closer to the wind than six points, the last maneuver will be impossible, and driven to leeward bj'^ wind, sea, and current, she may be compelled to cross the track immediately in advance of the center, or may even become involved in the center itself. In this extremity the path of the storm center during the past twenty-four hours should be laid down on a diagram as accurately as the observations permit, and the line prolonged for some distance beyond the present position of the center. Having assumed an average rate of progress for the center, its probable position on the line should be frequently and carefully plotted, and the handling of the vessel should be in accordance with the diagram. 492. Summary of Rules. — The following summary comprises the rules for maneuvering in the Northern Hemisphere, so far as they may be made general: — Fig. 62. CYCLONIC STORMS. 151 In the Right Semicircle: Haul by the wind on the starboard tack and carry sail as long as possible; if obliged to heave-to, do so on starboard tack. In the Left Semicircle: Bring the wind on the starboard quarter, note course and keep it; if obliged to heave-to, do so on port tack. In Front of Center: Bring wind two points on starboard quarter, note course and keep it; if obliged to heave-to, do so on port tack. In Rear of Center: Run out with wind on starboard quarter; if obliged to heave-to, do so on star- board tack. The application of these rules for the various directions of the wind is shown in the following table: — Storm Table, Northern Hemisphere. If wind 1 Direcyon Direction shifts to- If wind shifts towards the If wind steady with falling If wind steady with rising of wind. of center. wards the left. barometer. barometer. right. North. ESE. a Run SSW. K ■ Run SSW. K Run SSW. a NNE. NE. ENE. SE. SSE. South. aul b> and cs ble; il on sta Run SW. Run WSW. Run West. old CO if obli port ti Run SW. Run AVSW. Run West. old course obliged to port tack. Run SW. RunAVSW. Run West. old coi if obli starbo East. ESE. SSW. SW. ' wind irry sa oblige rboard RunWNW. Run NW. arse ged ick. RunWNW. Run NW. RunWNW. Run NW. P5 ||I^ ^ "1 ^ 7i SE. WSW. Run NNW. f-i- a Run NNW. fo _^ao Run NNW. 1^: SSE. West. on SI il as 1 dtoh tack. Run North. Run North. ffi O Run North. r ET ^ South. WNW. Run NNE. 2 o Run NNE. ^1 Run NNE. ^o- ssw. NW. Run NE. < D Run NE. Run NE. < D SW. NNW. 1%^ Run ENE. Run ENE. Run ENE. WSW. North. t^ g Run East. p m Run East. t3 ClO Run East. P § West. NNE. ?^S S Run ESE. S'o Run ESE. ogg Run ESE. Cu^c WNW. NE. d ta pos ), do Run SE. Run SE. g E Run SE. CD 00 NW. ENE. Run SSE. ° 5-' Run SSE. ° a Run SSE. o :f NNW. East. 00 ^^ rt Run South. 2Jf Run South. o Run South. Dif a Courses given are for wind two points on starboard quarter, but it is preferable to take wind broad on quarter if possible. Similarly, the following rules and table apply for the Southern Hemisphere: — In the Right Semicircle: Bring the wind on the port quarter, note course and keep it; if obliged to heave-to, do so on starboard tack. In the Left Semicircle: Haul by the wind on the port tack and carry sail as long as possible; if obliged to heave-to, do so on port tack. In Front of Center: Bring wind two points on port quarter, note course and keep it; if obliged to heave-to, do so on starboard tack. In Rear of Center: Run out with wind on port quarter; if obliged to heave-to, do so on port tack. Storm Table, Southern Hemisphere. If wind 1 Direction Direction If wind shifts towards the shifts to- If wind steady with falling If wind steady with rising of wind. of center. right. wards the left. barometer. barometer. North. WSW. Run SSE. a a Run SSE. W Run SSE. a NNE. NE. West. WNW. Run South. Run SSW. old CO if obli starbo aul carr obli port Run South. Run SSW. old obli star Run South. Run SSW. old cour if oblige port tacl ENE. NW. Run SW. te 2 -». "^ Run SW. o rti o Run SW. East. NNW. Run WSW. S5 aq — 5 2?^ O 03 D- Run WSW. iirse d to ard Run WSAV. ESE. North. Run West. CLP.^ Run West. Run West. Kl p^ CO SE. SSE. NNE. NE. Run WNW. Run NW. fS o o Run WNW. Run NW. 1^^ Run WNW. RunNW. o a p-i South. ENE. Run NNW. S o . ,' ^ N I / ,' V f\ /I / ■** / v / / \ \ ,' ' - -.^ ^ / / \'l /' '\ / ^' ''\ \ ^ ^^^ / / 1 ,- ''' \ " / ^ / / L'l \ / K --j- 7 / / r*' \ / 4-' \^ V - V ^ r i7 "Vrr /I — V L U'1 ■ Semi-diurnal. diurnal. Fig. 64. • mixed. TIDES. 155 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 bights. Examples of the latter class will be found in narrow bays and long channels. TIMES OF HIGH AND LOW WATER. 506. Tide Tablks. — 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 himself with such a publication. The United States Coast and Geodetic Survey pubUshes annually, in advance, tables giving, for every day in the year, the predicted time and height of the tides at certain principal porta of the world, and from these, by a simple reduc- tion, the times and heights at a multitude of other ports may readily be obtained; data for ascertaining the tidal currents in certain important regions are also provided. General tide tables are also published by the governments of other maritime nations, and special tables are to be had for many particular localities. 507. Where no tide tables are available, the method of calculation by applying the lunitidal inter- val to the time of the moon's meridian passage must be resorted to. To do this, find first the time of the moon's meridian passage, upper or lower, as may be required. The Greenwich mean time of upper transit at Greenwich is given in 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 longitude 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. Example: Find the times of the high and low waters at the New York navy yard, occurring next after noon on April 22, 1879. G. M. T. of Gr. transit, 22'» 0" 32™. 2 Corr. for + 74° Long. (Tab. 11) , + 10 L. M. T. of local transit, 22 42 Transit, 22'i O"- 42'" Transit, 22^ O** 42'" H.W.Lun. Int. (App. IV), 8 44 L. W. Lun. Int. (App. IV), 2 49 L.M.T.,H.W., {iyi22!9.26p.m. L. M. T., L. W., • {'^J,2f,3.Sl^. rn. Example: Find the time of high water at the Presidio, San Francisco, Cal., on the afternoon of May 7, 1879. G. M. T. of Gr. transit, 6'' 12" Se^.G Corr. for + 122° Long. (Tab. 11), -f- 22 L. M. T. of local transit, 6 12 59 H. W. Lun. Int. (App. IV), + 11 43 L. M. T., H. W., I L ^T ^-Fo Ao ' ' \ May 7, 12.42 p. m. Example: Find the time of low water at Singapore on the night of May 28, 1879. G. M. T. of Gr. transit, 28^ 5'> 55™. 3 Corr. for —104° Long. (Tab. 11), — 13 G. M. T. of local transit, 28 5 42 L. W. Lxm. Int. (App. IV), -f 4 02 L. M. T., L. W., j?J ^oQ"^n^. ' ' \ May 28, 9.44 p. m. 156 TIDES. Example: Find the time of morning high water and afternoon low water at GibraUar on June 26, 1879. G. INI. T. of Gr. upper transit, 25'' 4" 40'».l G. M. T. of Gr. upper transit, 26 5 27 .0 2)51 10 07 .1 G. M. T. of Gr. lower transit, 25 ] 7 04 Corr. for -f 5° Long. (Tab. 11 ), -[- 01 L. M. T. of local lower trans., 25 17 05 Transit, 25'M7''05"" Transit, 25'^! 7** 05™ H.W.Lun.Int. (App. TV), 185 L. W. Lun. Int. (App. IV), 7 55 L AI T H W P^ ^^ ^^ I M T T W f 26 1 00 L. 31. i., n. W., I j^^^ 26, 6.40 a. m. ^- ^^- ^^ ^- ^^ - { June 26, 1 p. m. TIDAL OBSERVATIONS. 508. Since navigators will frequently have opportunity to observe tidal conditions, either in con- nection with a hydrographic survey or otherwise, at places where existing knowledge of the tides is incomplete, an understanding of the methods employed in tidal observations may be important. _509. Tides. — For the proper study of tides, frequent and continuous observations are necessary; it will not suffice to observe the heights of the high and low waters only, even if they present them- selves as distinct phases, but the whole tidal curve for each day should be develoi^ed by recording the height of water at intervals, which, preferably, should not exceed thirty minutes. Observations, to be complete, must cover a whole lunar month ; or, if it be impracticable to observe the tides at night, the day tides of two lunar months may be substituted. 510. When made for the purposes of a hydrographic survey the tidal observations are used to correct the soundings, and care must be taken to make sure that the gauge is placed in a situation visited by the same form of tide as that which occurs at the place where soundings are being made. It will not answer, for instance, to correct the soundings upon an inlet-bar liy tidal observations made within the lagoon with which this inlet communicates, because the range of the tide within the lagoon is less than upon the outside coast. A partial obstruction, like a bridge, or a natural contraction of the channel section, while it may not reduce the total range of the tide or materially affect the time of high or low tides, will alter the relative heights above and below at intermediate stages, so that the hydrographer must be careful to see that no such obstruction intervenes between his field of work and the gauge. 511. Tidal Currents. — Observations for tidal currents should be made with the same regularity as for tides; the intervals need not ordinarily be more frequent than once in every half hour. They should always be made at the same point or points, which should be far enough from shore to be repre- sentative of the conditions prevailing in the navigable waters. The ordinary log may be employed for measuring the current, but it is better to replace the chip by a pole weighted to float upright at a depth of about fifteen feet; the line should be a very light one, and buoyed at intervals by cork floats to keep it from sinking; the set of the current should be noted by a compass bearing of the direction of the pole at the end of the observation. 512. Record. — The record of observations should be kept clearly and in complete form. It should include a description of the locality of observation, the nature of gauge and of instruments used for measuring currents, and the exact position of both tidal and current stations, together with situation and height of bench mark. The time of making each observation should be shown, and data given for reduction to some standard time. In extended tidal observations the meteorological conditions should be carefully recorded, the instruments used for the observations being properly compared with standards. 51 3. There are freciuently remarkable facts in reference to tides and currents to be obtained from persons having local knowledge; these should be examined and recorded. The date and circumstances of the highest and lowest tides ever known form important items of information. 514. Planes of Keference. — The plane of reference is the plane to which soundings and tidal data are referred. One of the principal objects of observing tides when making a survey is to furnish the means for reducing the soundings to this plane. Four planes of reference are used; namely, mean low water, mean low water springs, mean lower low waters, and the harmonic or Indian tide plane. Mean low water is a plane whose depression below mean sea level corresponds with half the mean semi-diurnal range, while the depression of mean low-water springs corresponds with half tlie mean range of spring tide; mean lower loiv water depends upon the diurnal inequality in high and low water; the harmonic or Indian tide plane was adopted as a convenient means of expressing something of an approxi- mation to the level of low water of ordinary spring tides, but where there is a large diurnal inequality in low waters it falls considerably below the true mean of such tides. As these planes may differ considerably, it is important to ascertain which plane of reference is adopted before making use of any chart or considering data concerning the tides. 515. The tides are subject to so many variations dependent upon the movements of the sun and moon, and to so many irregularities due to the action of winds and river outflows, that a very long series of observations would be necessary to fix any natural plane. In consideration of this, and keeping in view the possibilities of repetitions of the surveys or subsequent discoveries within the field of work, it is necessary to define the position of the plane of reference which has resulted from any series of obser- vations. This is done by leveling from the tide gauge to a permanent bench, precisely as if the adopted plane were arbitrary. 516. Bench ]\!ark. — The plinth of a light-house, the water table of a substantial building, the base of a monument, and the like, are proper l^enches; and when these are not within reach, a mark TIDES. 157 may be made on a rock not likely to be moved or started by the frost, or, if no rock naturally exists in the neighborhood, a block of stone buried l)elow the reach of frost and plowshare should be the resort. When a bench is made on shore, it should be marked by a circle of 2 or 3 inches diameter with a cross in the center, iudicating the reference point. The levelings between this point and the gauge should be be run over twice and the details recorded. A bench made upon a wharf or other perishable structure is of little value, but in the absence of- permanent objects it is better than nothing. The marks should be cut in, if on stone, and if on wood, copper nails should be used. The bench must be sketched and carefully described, and its location marked on the hydrographic sheet, with a statement of the relative position of the plane of reference. 517. The leveling from the bench mark to the tide gauge may be done, when a leveling instrument is not available, by measuring the difference of height of a number of intermediate points' by means of a long straight-edged board, held horizontal by the aid of a carpenter's spirit level, or even a plummet square, taking care to repeat each step with the level inverted end for end. A line of sight to the sea horizon, when it can be seen from the bench acrot^s the tide staff, will afford a level line of sufficient accuracy, especially when observed with the telescope. It may often be convenient to combine these methods. 518. Tide Gauges. — The Staff Gauge is the simplest device for measuring the heights of tides, and in perfectly sheltered localities it is the best. It consists of a vertical staff graduated upward in feet and tenths, and so placed that its zero shall lie below the lowest tides. The same gauge may also be used where the surface is rough, if a glass tube with a float inside is secured alongside of the staff, care being taken to practically close the lower end of the tube so as to exclude undulations; readings may also be made by noting the point midway between the crest and trough of the waves. A staff gauge should always be erected for careful tidal observations, even where other classes of gauge are to be employed, as it furnishes a standard for comparison of absolute heights, and also serves to detect any defects in the mechanical details upon which all other gauges are to a greater or less extent dependent. 519. Where there is considerable swell, and where, from the situation of the gauge or the great range of the tide (makiBg it inconvenient for the observer to see the figures in certain positions) the staff gauge can not be used, recourse must be had to the Box Gauge. This gauge consists of a vertical box, closed at the bottom, with a few small holes in the lower part which admit sufficient water to keep the level within equal to the mean level without, but which do not permit the admission of water with sufficient rapidity to be affected by the waves. Within the box is a copper float; in some cases this float carries a graduated vertical rod whose position with reference to a fixed point,of the box affords a measure for the height of the water; in other gauges of this class the float is attaclied to a wire or cord which passes over ])ulleys and terminates in a counterpoise whose position on a vertical graduated scale shows the height of tide. 520. An Automatic Gauge requires a box and float such as has just been described. The motion of the float in rising and falling with the tide is communicated to a pencil which rests upon a moving sheet of paper; uniform motion is imparted to the paper by the revolution of a cylinder driven by clock- work; the motion of the pencil due to the tide is in a direction perpendicular to the direction of motion of the paper, and a curve is thus traced, of which one coordinate is time, and the other height. The paper, which is usually of sufficient length to contain a month's record, is paid out from one cylinder, passes over a second whereon it receives the record, and is rolled upon a third cylinder, which thus contains the completed tidal sheet. This gauge, besides giving a perfectly continuous record, has the further merit of requiring but little of the observer's time. But its indications, both of time and heights, should be checked by occasional comparisons with the standard clock and tlie staff gauge, the readings of which should be noted by hand at api^ropriate jioints of the graphic record. 158 OCEAN CURRENTS. CHAPTER XXL OCEAN OUKRENTS. 521. An ocenn current is a progressive horizontal motion of the water occurring throughout a region of the ocean, as a result of which all bodies floating therein are carried with the stream. The set of a current is the direction toward which it flows, and its drift, the velocity of the flow. 522. Cause. — The principal cause of ocean currents is the wind. Every breeze sets in motion, by its friction, the surface particles of the water over which it blows; this motion of the upper stratum is imparted to the stratum next beneath, and thus the general movement is communicated, each layer of particles acting upon the one below it, until a current is established. The direction, depth, strength, and permanence of such a current will depend upon the direction, steadiness, and force of the wind; all, however, subject to modification on account of extraneous causes, such as the intervention of land or shoals and the meeting of conflicting currents. A minor cause in the generation of ocean currents is the difference in density of the sea water in different regions, as a result of which a set is produced from the more dense toward the less dense, in the effort to establish equilibrium of pressure; the difference of density may be due to temperature, the warmer water near the equator being less dense than the colder water of higher latitudes; or it may be created by a difference in the amount of contained saline matter, resulting from evaporation, freezing, or other causes. Another minor factor that may have influence upon ocean currents is the difference of pressure exerted by the atmosphere upon the water in different regions. But neither of the last- mentioned causes may be regarded as of great importance when compared with the influence, direct and indirect, of the wind. 523. Drift and Stream Currents. — Ocean currents may be divided into two classes: Ihnfl and Stream Currents. A Drift Current is one which arises from the effect of wind upon the surface water, impelling the particles to leeward. Such currents reach only to shallow depths, except in regions where caused by winds whose prevalence is almost unbroken, and where, in consequence, motion is communicated stratum by stratum, during a long series of years, until the influence is felt at great depths. A Stream Current is one which arises when the water carried forward by a drift current encounters an obstacle which prevents a further flow in the direction which it has been following, and the particles are forced to acquire a new motion which takes such direction as may be imposed by the conditions existing in the locality. Some currents are compounded of both drift and stream ; for a stream already formed may pass through the region of a prevalent wind in such direction that it will receive an accelerating effect due to the wmd. 524. Submarine Currents. — In any scientific investigation of the circulation of ocean waters it is necessary to take account of the submarine currents as well as those encountered upon the surface; but for the practical purposes of the navigator the surface currents alone are of interest. 525. Methods of Determination. — The methods of determining the existence of a current, with its set and drift, may be divided into three classes; namely, (a) by observations from a vessel occupying a stationary position not affected by the current; (6) by comparison of the position of avessel under way as given by observation with that given by dead reckoning; and (c) by the drift of objects abandoned to the current in one locality and reappearing in another. 526. Of these methods, the first named, by observations from a vessel at anchor, is by far the most accurate and reliable, but being possible only under special circumstances is not often available. The most valuable information about ocean currents being that which pertains to conditions in the open sea, the great depths there existing usually preclude the possibility of anchoring a vessel; ships especially fitted for the purpose have at times, however, carried out current observations with excellent results; the most notable achievements in this direction are those of the survey of the Gulf Stream, made by United States naval officers acting under the Coast and Geodetic Survey, during which the vessel was anchored and observations were made in positions where the depth reached to upward of 2,000 fathoms. 527. The method of determining current from a comparison of positions obtained, respectively, by observation and by dead reckoning is the one upon which our knowledge must largely depend. This method is, however, always subject to some inaccuracy, and the results are frequently quite erroneous, for the so-called current is thus made to embrace not only the real set and drift, but also the errors of observation and dead reckoning. In the case of a modern steamer accurately steered and equipped with good instruments for determining the speed through the water as well as the position by astronomical observations, the current may be arrived at by this method with a fairly close degree of accuracy. It is not always possible, however, to keep an exact reckoning, and this is especially true in sailing vessels, where the conditions render it difficult to determine correctly the position by account; this source of error may be combined with faulty instrumental determinations, giving apparent currents differing widely from those that really exist. 528. Much useful knowledge regarding ocean currents has been derived from the observed drift of objects from one to another locality. This is true not only of the bottles thrown overboard from vessels with the particular object of determining the currents, but also of derelicts, drifting buoys, and pieces OCEAN CURRENTS. 159 of wreckage, which fulfill a similar mission. The deductions to be drawn from such drift are of a general nature only. The point of departure, point of arrival, and elapsed time are all that are posi- tively known. The route followed and the set and drift of current at different points are not indicated, and in the case of objects floating otherwise than in a completely submerged condition account must be taken of the fact that the drift is influenced l)y the wind. But even this general information is of great value in researches as to ocean currents, and navigators who desire to aid in the work of investi- gation may do so by throwing overboard, from time to time, sealed bottles containing a statement of date and position at which they are launched. 529. Currents of the Atlantic Ocean. — A consideration of the currents of the Atlantic most conveniently begins with a description of the Equatorial Currents. The effect of the northeast and southeast trade winds is to form two great drift currents, setting in a westerly direction across the Atlantic from Africa toward the American continent, whose combined width covers at times upward of fifty degrees of latitude. These are distinguished as the Northern or Southern Equatorial Currents, according as they arise from the trade winds of the northern or southern hemisphere. Of the two, the Southern Equatorial Current is the more extensive. It has its origin off the conti- nent of Africa south of the Guinea coast, and begins its flow with a daily velocity that averages about 15 miles; it maintains a general set of west, the portion near the equator acquiring later, however, a northerly component, while the drift steadily increases until, on arriving off the South American coast, a rate of 60 miles is not uncommon. AttCape San Roque the current bifurcates, the main or equatorial branch flowing along the Guiana coast, while the other branch is deflected to the southward. The Northern Equatorial Current originates to the northward of the Cape Verde Islands and sets across the ocean in a direction that averages due west; though parallel to the corresponding southern drift, its velocity is not so high. 330. Between the Northern and Southern Equatorial Currents is found the Equatorial Counter Current, which sets to the eastward, being apparently a flowing back, in the region of equatorial calms, of water carried westward by the trade drifts. The extent and strength of this current varies with the season, a maximum being attained in July or August, when its effect is apparent to ths westward of the flftieth meridian of west longitude, while at its minimum, in November or December, its influence is but slight and prevails over a limited area only. 531. To the westward of the region of the Equatorial Counter Current the North and the South Equatorial Currents unite. A large part of the combmed stream flows into the Caribbean Sea through the various passages between the Windward Islands, takes up a course first to the westward and then to the northward and westward, finally arriving off the extremity of the peninsula of Yucatan; from here some of the water follows the shore line of the Gulf of Mexico, while another portion passes directly toward the north Cuban coast; by the reuniting of these two branches in the Sti-aitsof Florida there is formed the most remarkable of all ocean currents — the Gulf Stream. From that portion of the combined equatorial currents which fails to find entrance to the Caribbean Sea a current of moderate strength and volume takes its course along the north coasts of Porto Rico, Haiti, and Cuba, flows between the last-named island and the Bahamas, and enters the Gulf Stream off the Florida coast, thus adding its waters to those of the main branch of the equatorial current which have arrived at the same point by way of the Caribbean, the Yucatan Passage, and the Gulf. 532. The Gulf Stream, which has its origin, as has been described, in the Straits of Florida, and receives an accession from a branch of the Equatorial Current off the Bahamas, flows in a direction that averages true north as far as the parallel of 31°, then curves sharply to ENE. until reaching the latitude of 32°, when a direction a little to the north of NE. is assumed and maintained as far as Cape Hatteras; at this point its axis is about 40 miles, while its inner edge is in the neighborhood of 20 miles off the shore. Thus far in its flow the average position of the maximum current is from 11 to 20 miles outside the 100-fathom curve, disregarding the irregularities of the latter, and the width of the stream — about 40 miles — is nearly uniform. From off Hatteras the stream broadens rapidly and curves more to the eastw^ard, seeking deeper water; its northern limit may be stated to be 60 to 80 miles off Nantucket Shoals and 120 to 150 miles to the southward of Nova Scotia, in which latter place it has expanded to a width of about 250 miles. Further on, its identity as the Gulf Stream is lost, but its general direction is preserved in a current to be described later. The water of the Gulf Stream is of a deep indigo-blue color, and its junction with ordinary sea water may be plainly recognized; in moderate weather the edges of the stream are marked by ripples; in cool regions the evaporation from its surface, due to difference of temperature between air and water, is apparent to the eye; the stream carries with it a quantity of weed known as "gulf weed," which is familiar to all who have navigated its waters. In its progress from the tropics to higher latitudes the transit is so rapid that time is not given for more than a partial cooling of the water, and it is therefore found that the Gulf Stream is very much warmer than the neighboring waters of the seas through which it flows. This warm water is, however, divided by bands of markedly cooler water which extend in a direction parallel to the axis and are usually found near the edges of the stream of warm water. The most abrupt change from warm to cold water occurs on the inshore side, where the name of the Cold Wall has been given to that band which has appeared to some oceanographers to form the northern and western boundary of the stream. The investigations of Pillsbury tend to prove that the thermometer is only an approximate guide to the direction and velocity of the current. Though it indicates the limits of the stream in a general way, it must not be assumed that the greatest velocity of flow coincides with the highest temperature, nor that the northeasterly set will be lost when the thermometer shows a region of cold sea water. The same authority has also demonstrated that in the vicinity of the land there is a marked varia- tion in the velocity of current at different hours of the day, which may amount to upward of 2 knots, and which is due to the elevation and depression of the sea as a result of tidal influences, the maximum current being encountered at a period which averages about three hours after the moon's transit. Another effect noted is that at those times when the moon is near the equator the current presents a narrow front with very hi^h vel >city in the axis of maximum strength, while at periods of great northerly or 160 OCEAN CUREENTS. southerly declination the front broadens, the current decreasing at the axis and increasing at the edges. These tidal effects are not, however, obi-erved in the open sea. The velocity of the Gulf Stream varits with the seasons, following the variation in the intensity of the trade winds, to which it largely owes its origin. The drift of the current under average conditions may be stated as follows: ' Between Key West and Habana: Mean surface velocity in axis of maximum current, 2\ knots; allowance to be made by a vessel crossing the entire width of the stream, 1.1 knots per hour. Off Fowey Rocks: Mean surface velocity in axis, 3.5 knots; allowance in crossing, 2} knots per hour. Off Cape Hatteras: Mean surface velocity in axis, upward of 2 knots; allowance in crossing the stream, IJ knot,s jser hour between the lOC-fathora curve and a point 40 miles outside that curve. 533. After passin|: beyond the longitude of the easternmost portions of North America, it is gen- erally regarded that the Gulf Stream, as such, ceases to exist; but by reason of the prevalence of westerly winds the direction of the set toward Europe is continued until the continental shores are approached, when the current divides, one branch going to the northeastward and entering the Arctic regions and the other running off toward the south and east in the direction of the African coa.st. These currents have received, respectively, the designations of the Easterly, Nortiwasf, and Southeast Drift Currents. 534. The effect of the currents thus far described is to create a general circulation of the surface waters of the North Atlantic, in a direction coinciding with that of the hands of a Avatch, about the periphery of a huge ellipse, whose limits of latitude maybe considered as 10° N. and 45° N., and which IS bounded in longitude by the P^astern and Western continents. The central space thus inclosed, in which no av ell-marked currents are observed, and in the waters of which great quantities of the Sargasso or gulf weed are encountered, is known as the Sargasso Sea. 535. The Southeast Drift Current carries its waters to the northwest coast of Africa, whence they follow the general trend of the land from Cape Spartel to Cape ^"erde. From this point a large part of the current is deflected to the eastward close along the upper Guinea coast. The steam thus formed, greatly augmented at certain seasons by the prevailing monsoon and by the waters carried eastward with the Equatorial Counter Current, is called the Guinea Current. A remarkable characteristic of this current is the fact that its southern limit is only slightly removed from the northern edge of the west- moving Equatorial Current, the effect being that the two currents flow side by side in close proximity, but in diametrically opposite directions. 536. The Arctic or Labrador Current sets out of Davis Strait, flows southward down the coasts of Labrador and Newfoundland, and thence south westward past Nova Scotia and the coast of the United States, being found inshore of the Gulf Stream. It brings with it the ice so frequently met at certain seasons off Newfoundland. 537. RennelVs Current is a temporary but extensive stream, which sets at times from the Bay of Biscay toward the west and northwest, across the entrance to the English Channel and to the westward of Cape Clear. 538. Of the two branches of the Southern Equatorial Current which are formed by its bifurcation off Cape San Roque, the northern one, setting along the coasts of northeastern Brazil and of Guiana and contributing to the formation of the Gulf Stream, has already been described; the other, known as the Brazil Current, flows to south and west, along the southeastern coast of Brazil, as far as the neighborhood of the island of Trinidad; here it divides, one part continuing down the coast and having some slight influence as far as the latitude of 45° S., and the other curving around toward east. 539. The last-mentioned branch of the Brazil Current is called the Soutlieryi Connecting Cm-rent and flows toward the African coast in about the latitude of Tristan d'Acunha. It then joins its waters with these of the general northerly current that sets out of the Antarctic region, forming a current which flows to the northward along the southwest African coast and eventually connects with the Southern Equatorial Current, thus completing the surface circulation of the South Atlantic. 540. There are two other currents whose effects are felt in the Atlantic, one originating in the Indian Ocean and flowing around the Cape of Good Hope, the other originating in the Pacific and flow- ing around Cape Horn. They will be described under the currents of the oceans in which they first appear. 541. Currents of the Pacific Ocean. — As in the Atlantic, the waters of the Pacific Ocean, in the region between the tropics, have a general drift toward the westward, due to the effect of the trade Avinds, the currents produced in the two hemispheres being denominated, respectively, the Nortltern and the Southern Equatorial Currents. These are separated, as also in the case of the Atlantic, by an ea.st- setting stream, about 300 miles wide, whose mean position is a few degrees north of the equator, and which receives the name of the Equatorial Counter Current. 542. The major portion of the Northern Equatorial Current, after having passed the Mariana Islands, flows toward the eastern coast of Formosa in a WNW. direction, whence it is deflected north- ward, forming a current which is sometimes called the Jajmn Stream, but which more frequently receives its Japanese name of A'ttro >S'm'o, or "black stream." This current, the waters of which are dark in color and contain a variety of seaweed similar to "gulf Aveed," carries the Avarm tropical water at a rapid rate to the northward and eastward along the coasts of Asia and its offlying islands, presenting many analogies to the Gulf Stream of the Atlantic. The limits and volume of the Kuro Siwo A'ary according to the monsoon, being augmented during the season of southwesterly Avinds and diminished during the prevalence of those from northeast. The current sets to the north along the east coast of Formosa, and in about latitude 26° N. changes its course to northeast, arriving at the extreme south Avestern point of Japan by a route to westward of the Meiaco- sima and Loo-choo islands. A branch makes off from the main stream to follow northAvard along the west coast of Japan, entering the Sea of Japan by the Korea Channel; but the principal current bends toward the east, floAvs through Van Diemen Strait and the passages betAveen the Linschoten Isles, and runs parallel to the general trend of the south shores of the Japanese islands of Kiushu, Sikok, and Nipon, attaining its greatest velocity l>etween Bungo and Kii channels, where its average drift is between 2 and 3 knots per hour. Continuing beyond the southeastern extremity of Nipon, the direction ^ . I OCEAN CURRENTS. 161 of the stream ))ecomes somewhat more northerlj-, and its width increases, with consequent loss of velocity. In the Knro Siwo, as in the Gulf Stream, the temperature of the sea water is an approximate, though not an exact, guide as to the existence of the current. 543. Near 146° or 147° E. and north of the fortieth parallel the Kuro Siwo divides into two parts. One of these, called the Kamchatka Current, flows to the northeast in the direction of the Aleutian Islands, and its influence is felt to a high latitude. The second branch continues as the main stream, and maintains a general easterly direction to the 180th meridian, where it is merged into the north and northeast drift currents which are generally encountered in this region. 544. A cold counter current to the Kamchatka Current sets out of Bering Sea and flows to the south and west close to the shores of the Kuril Islands, Yezo and Nipon, sometimes, like the Labrador Current in the Atlantic, bringing with it quantities of Arctic ice. This is often called by its Japanese name of 0//a Sivo. 545. On the Pacific coast of North America, from about 50° N. to the mouth of the Gulf of California, 23° N., a cold current, 200 or 300 miles wide, flows with a mean speed of three-quarters of a knot, being generally stronger near the land than at sea. It follows the trend of the land (nearly SSE. ) as far as Point Concepcion (south of Monterey), Avhen it begins to bend toward SSW., and then to WSW,, off Capes San Bias and San Lucas, ultimately joining the great northern equatorial drift. On the coast of Mexico, from Cape Corrientes (20° N.) to Cape Blanco (Gulf of Nicoya), there are alternate currents extending over a space of more than 300 miles in width, whicli appear to be produced by the prevailing winds. During the dry season — January, February, and ^larch — the currents generally set toward southeast; during the rainy season — from ]\Iay to October — especially in July, August, and September, the currents set to northwest, particularly from Cosas Island and the Gulf of Nicova to the parallel of 15°. 546. The Southern Equatorial Current prevails between limits of latitude that may be approxi- mately given as 4° N. and 10° S., in a broad region extending from the American continent almost to the one hundred and eightieth meridian, setting always to the west and with slowly increasing velocity. In the neighborhood of the Fiji Islands this current divides; one part, known as the Ronsel Cwn-enf, con- tinues to the westward, following a route marked by the various passages between the islands, and later acquiring a northerly component and setting through Torres Strait and along the north coast of New Guinea; the other part, called the Australia Cui-revt, sets toward south and west, arriving off the east coast of Australia, along Avhich it flows southward to about latitude 35° S., whence it bends toward southeast and east and is soon after lost in the currents due to the prevailing wind. 547. The general drift current that sets to the north out of the Antarctic regions is deflected until, upon gaining the regions to the southwest of Patagonia, it has acquired a nearly easterly set; in striking the shores of the South American continent it is divided into two branches. The first, known as the Cape Horn Cnrrcnt, maintains the general easterly direction, and its influence is felt, where not modified by winds and tidal currents, throughout the vicinity of Cape Horn, and, in the Atlantic Ocean, off the Falkland Islands and eastern Patagonia. The second branch flows northeast in the direction of Valdivia and Valparaiso, follows generailj' the direction of the coast lines of Chile and Peru (though at times setting directly toward the shore iia such manner as to constitute a great danger to the navigator), and forms the important current which has been called variously the Peruvian, Chilean, or Humboldt Current, the last name having been given for the distinguished scientist who first noted its existence. The principal characteristic of the Peru- vian Current is its relatively low temperature. The direction of the waters between Pisco and Payta is between north and northwest; near Cape Blanco the current leaves the coast of America and bears toward the Galapagos Islands, passing them on both the northern and southern sides; here it sets toward AVNW. and west; beyond the meridian of the Galapagos it widens rapidly, and thecuiTent is lost in the equatorial current, near 108° W. As often happens in similar cases, the existence of a counter-current has been proved on different occasions; this sets toward the south, is very irregular, and extends only a little distance from shore. 54§. CiRRENTs OF THE IxDiAN OcEAN. — In this occau the currents to the north of the equator are-very irregular; the periodical winds, the alternating breezes, and the changes of monsoon produce currents of a variable nature, their direction depending upon that of the wind which produces them, upon the form of neighboring coasts, or, at times, upon causes which can not be satisfactorily explained. 549. There is, in the Indian Ocean south of the equator, a regular Equatorial Current which, by reason of owing its source to the southeast trade winds, corresponds with the Southern Equatorial Currents of the Atlantic and Pacific. The limits of this west-moving current vary with the longitude as well as with the season. Ui)on reaching about the meridian of Rodriguez Island, a l)ranch makes off toward the south and west, flowing past Mauritius, then to the south of Madagascar (on the meridian of which it is 480 miles broad) , and thereafter, rapidly diminishing its breadth, forming jiart of the Agulhas Cur- rent a little to the south of Port Natal. The main equatorial current continues westward until passing the north end of Madagascar, where, encountering the obstruction presented by the African continent, it divides, one branch following the coast in a northerly, the other in a southerly, direction. The former, in the season of the south-nest monsoon, is merged into the general easterly and northeasterly drift that prevails throughout the ocean from the northern limit of the Equatorial Current on the .'■'outh, as far as India and the adjacent Asiatic shores on the north; but during the northeast monsoon, when there exists in the northern regions of the Indian Ocean a westerly drift current analogous to the Northern Equatorial Currents produced in the Atlantic and Pacific by' the northeast trades, there is formed an east-setting Equatorial Counter Current, which occupies a narrow area near the equator and is made up of the waters accumu- lated at the Avestern continental boundary of the ocean by the drift currents of both hemispheres. 550. The southern branch of the Equatorial Current flows to the south and west down the Mozambique channel, and, being joined in the neighborhood of Port Natal by the stream which arrives from the open ocean, there is formed the warm Agulhas Current, which possesses many of the characteristics of the Gulf and Japan streams. This current skirts the east coast of South Africa and 22489—03 11 162 OCEAN CUERENTS. attains considerable velocity over that part between Port Xatal and Algoa Bay. During the summer months its effects are felt farther to the westward; during the winter it diminishes in force and extent. The meeting of the Agulhas Current with the cold water of higher latitudes is frequently denoted by a broken and confused sea. Upon arriving at the southern side of the Agulhas Bank, the major part of the current is deflected to the south, and then curves toward east, flowing back into the Indian Ocean with diminished strength and temperature, on about the fortieth parallel of south latitude, where its influence is felt as far as the eightieth meridian. A small part of the stream which reaches Agulhas Bank continues across the southern edge of that bank, then turns to the northwest along the west coast of the continent until it is united with the waters of the Southern Connecting Current of the Atlantic. 551. Along the fortieth parallel of south latitude, between Africa and Australia, there is a general easterly set, due to the branch of the Agulhas current already described, to the continuation of the drift current from the Atlantic which passes to southward of the Cape of Good Hope, and to the westerly winds which largely prevail in this region. At Cape Leeuwin, the southwestern extremity of Australia, this east-setting current is divided into two branches; one, going north along the west coast of Australia, blends with the Equatorial current nearly in the latitude of the Tropic of Capricorn; the other preserves the direction of the original current and has the effect of producing an easterly set along the south coast of Australia. 552. As in the other oceans, a general northerly current is observed to set into the Indian Ocean from the Antarctic regions. EXTRACTS FROM NAUTICAL ALMANAC. 163 APPENDIX I. EXTEAOTS FEOM THE AMEKIOAN EPHEMEEIS AND NAUTICAL ALMA- NAC, FOE THE YEAE 1879, WHICH HAVE EEFEEENCE TO THE EXAMPLES FOE THAT YEAE GIVEN IN THIS WOEK. [Extracts: Page I.] AT GREENWICH APPARENT NOON. THE sun's Apparent Right Ascension. Diff. for 1 hour. Apparent Dewination. Diff. for 1 hour. Semi- diameter. Sidereal Time of the Semi- diameter passing the Meridian Equation of Time, to be added to suhtraxied from Appar- ent Time. Diff. for 1 hour. JANUARY. Sun. 19 Mon. 20 Tues. 21 20 4 60. 17 10. 626 20 9 14.84 10.595 20 13 28. 75 10.564 20 21 9. +31.54 20 8 20.4 32.49 19 55 9. 1 -1-33.43 16 17.58 16 17.48 16 17.38 69.72 69.61 69. 51 10 56. 68 11 14. 74 11 32.05 0.769 0.738 0.706 APRIL. Tues. 1 Wed. 2 Thur. 3 Sun. 13 Mon. 14 Tues. 15 Wed. 16 Thur. 17 Frid. 18 Sat. 19 Sun. 20 Mon. 21 41 45 49 1 25 1 29 1 33 54.87 9.096 33.24 9.100 11.70 9.106 47.34 9.206 28.45 9.219 9.91 9.234 51.74 9.250 33.95 9.268 16.56 9.285 59.58 9.302 43.01 9.320 26.87 9.337 N. N. 4 30 43. 2 +57.85 ' 4 53 49. 1 57.64 t 5 16 49. 8 .57.41 9 54. 1 .54.40 9 22 35.4 M.03 ; 9 44 7.5 53.64 10 5 29.9 53.23 10 26 42. 3 52.80 10 47 44. 7 62.37 11 8 36.4 61.92 11 29 17.1 .51. 46 11 49 46.4 +50.97 16 2.16 64.51 16 1. 89 64.53 16 1.61 64.55 15 58. 86 64.89 15 58. 59 64.94 15 58. 31 64.99 65.04 15 58. 04 15 57. 77 65.09 15 57. 50 65.15 15 57. 24 65.21 15 56. 98 65. 27 15 56. 72 65. 33 4 0. 3 42. 3 24. 35. 19. 4. 10. 24. 38. 51. 1 4. 1 17. 0.758 0.754 0.748 0.649 0.635 0.620 0.604 0.587 0.570 0.553 0.536 0.518 MAY. Mon. 5 Tues. 6 Sat. 10 Sun. 11 Thur. 15 Frid. 16 Sat. 17 Sun. 18 48 30. 72 9.626 52 22. 03 9.650 7 53. 03 9.747 11 47.27 9.771 27 30. 07 9.871 31 27. 26 9.895 35 25. 03 9.919 39 23. 37 9.942 N. 16 13 40. 4 16 30 40. 4 17 35 53. 8 17 51 29. 1 18 50 48. 5 19 4 51.6 19 18 35.5 N. 19 31 59. 8 +42.86 42.17 39.33 38.59 35.52 34.72 33.91 +33.06 15 53. 36 66.37 15 53. 14 66.45 15 52. 25 66.78 15 52. 03 66.86 15 51. 20 67.19 15 51.00 67.27 15 50. 80 67.35 15 50.61 67. 43 3 25. 18 3 30. 40 3 45.58 3 47.90 3 51.32 3 50.68 3 49. 47 3 47.69 0.229 0.206 0.109 0.084 0.014 0.039 0.062 0.086 Note.— Mean Time of the Semidiameter i)assing may be found by substracting 0".18 from the Sidereal Time. + prefixed to the hourly change of declination indicates that north declinations are increasing and south declinations are decreasing; — indicates that north declinations are decreasing and south declinations increasing. 164 EXTRACTS FROM NAUTICAL ALMANAC. [Extracts: Page I.] AT GREENWICH APPARENT NOON— Continued. THE SUN'S Apparent Right Ascension. Diff. for 1 hour. Apparent Declination. DifE. for 1 hour. Semi- diameter. Sidereal Time of the Semi- dinmeter passing ^he Meridian. Erjuation of Time, to be \ subtracted from atlfled to Apparent Time. Diff. for 1 hour. JUNE. Sat. 7 Tues. 10 Wed. 11 Frid. 13 Sat. 14 Frid. 20 Sat. 21 Wed. 25 Thur. 26 Frid. 27 12 17 25 29 54 58 15 6 19 6 23 33.74 10. 312 57.61 10. 348 6.09 10. 3.^8 23.73 10. 376 32. 85 10.383 30. 05 10. 402 39.75 10. 402 18.00 10. 389 27.29 10.383 36.42 10.376 22 45 9.5 + 14.64 23 55. 9 11.63 23 5 22.9 10.62 23 13 3.8 8.58 23 16 17.4 7.55 23 27 0. 3 1.36 23 27 20.5 -f 0.32 23 24 33. 1 - 3.78 23 22 49. 5 4.81 23 20 41. 3 - 5.84 15 15 15 15 15 15 15 15 15 15 47.63 47.30 47.20 47.00 46.91 46.48 46.43 46.27 46.24 46.22 68. 70 68. 81 68.84 68.90 68.92 68.98 68.98 68.94 68.93 68.91 1 28.86 54. 76 42. 87 18.42 5.89 1 11.75 1 24.86 2 16.72 2 29.42 2 41.97 0. 4-V) 0.490 0.500 0. 518 0. 525 0. .546 0.546 0.532 0.526 0. 519 JULY. Frid. 11 Sat. 12 Tues. 22 Wed. 23 Thur. 24 7 21 16.72 10.197 7 25 21. 24 10. 179 8 ^ 39. 82 9.%4 8 9 38. 68 9.939 8 13 36. 94 9.914 N. 22 8 29. 2 22 23. 2 20 19 8.9 20 7 5.2 X. 19 54 41.3 -19. 76 20.71 29. 72 30.57 -31.41 15 46. 30 68.30 15 46.33 68.24 15 46. 94 67.51 15 47. 03 67.43 15 47. 13 67.35 5 10.04 5 17.99 6 10. 85 6 13. 15 6 14.84 0. 339 0.321 0.108 0.083 0.059 SEPTEMBER. Tobesubtract- edfrom A])- 2Mrent Time. Wed. Thur. 11 13 33.93 11 17 9.68 8.993 8.988 4 59 24.2 -56.90 15 55. 81 4 36 36. 2 -57.10 15 56.06 64.12 64.10 3 1.29 3 22.03 0.862 0.867 DECEMBER. Mon. Tues. 18 18 1 24. 12 5 50. 72 11. 108 11.107 S. 23 27 17. 3 S. 23 26 54. 3 + 0.37 16 18. 13 71. 30 + 1.55 16 18. 18 71.30 1 16.61 46. 64 1.248 1.246 Note. — Mean Time of the Semidiameter pas.sing may be found by subtracting 0'.18 from the Sidereal Time. -(- prefixed to the hourly change of declination indicates that north declinations are increasing and south declinations are decreasing ; — indicates that north declinations are decreasing and south declinations increasing. EXTRACTS FROM KAUTICAL ALMANAC. 165 [Extracts: Page II.J AT GREEN^A^ICH MEAN NOON. Day of the Week. Day of the Month. THE sun's Apparent Right Ascension. h. m. s. Diff. for 1 hour. Apparc7it Declination. Diff. for 1 hour. E(^uation of Time, to be sitbtractal from Diff. for .. ,, '■- 1 hour. added to Mean Time. JANUARY. Sidereal Time or Right As- cension of Mean Sun. //. m. Frid. 10 Rat. 11 Mon. 20 Tues. 21 19 26 16.08 10.866 19 30 36.59 10.842 20 9 12.84 10.593 20 13 26. 71 10.562 S.21 58 32.0 21 49 22. 7 20 8 26. 6 S. 19 55 15. 6 + 22. 35 23.41 32. 48 + 33.42 7 43. 42 1.010 [ 8 7.37 0. 986 1 11 14.60 0.738 1 11 31.91 0. 706 1 19 18 32. 66 19 22 29. 22 19 57 58. 24 20 1 54.80 APRIL. Tues. 1 Wed. 9 Tues. 8 Wed. 9 Tues. 15 Wed. 16 Thur. 17 Sun. 20 Mon. 21 Tues. 22 Wed. 23 Thur. 24 Frid. 25 Tues. 29 Wed. 30 41 45 1 7 11 33 36 40 51 55 59 2 2 2 6 2 10 2 25 2 29 54.27 9.098 32.68 9.102 26.22 9.146 5.87 9. 1.57 9.91 9.236 51.77 9.252 34.02 9.269 43.19 9.321 27.08 9.338 11.41 9.356 56.19 9.375 41.42 9.394 27.11 9.414 34.67 9.494 22.79 9.515 . 4 30 4 53 7 10 7 32 9 44 10 5 10 26 11 29 11 49 12 10 12 30 12 50 13 9 14 26 14 44 39.4 + 57.86 45.6 57.65 20.3 66.08 42.8 55.77 7.4 53.65 63.24 30.1 42.8 62.81 18.1 61.46 47.6 50.98 5.4 50.48 11.2 49.97 4.7 49.46 45.4 48.92 14.5 46.65 46.7 + 46.04 4 0.65 0.758 3 42. 50 0.754 1 56. 74 0.709 1 39.83 0.698 4.54 0.620 0.604 10. 15 24. 46 0.587 1 4.94 0.536 1 17.61 0.518 1 29.83 0.600 1 41. 61 0.481 1 52.93 0.462 2 3.80 0.442 2 42. 46 0.361 2 50. 89 0.340 37 41 2 32 53.62 50.16 29.48 26.04 5. 37 1.92 58.48 48.13 44.69 41.24 37. 80 34. 35 30.91 17.13 13.68 MAY. Frid. 9 Sat. 10 Sun. 11 Mon. 12 Frid. 16 Sat. 17 Sun. 18 Wed. 28 Thur. 29 Frid. 30 Sat. 31 Sat. 7 Sun. 8 Wed. 11 Sat. 14 Sun. 15 Wed. 25 Thur. 26 Frid. 27 0.01 9. 723 53.65 9.747 47.89 9.771 42.71 9.7% 27.90 9.895 25.67 9.919 24.01 9.942 36.81 10.155 40.75 10. 173 45.12 10.190 49.91 10.207 17 17 17 18 19 N.17 20 3.5 35 56. 3 51 31.6 6 48.9 4 53.8 19 18 37.6 19 32 1. 8 21 27 5.9 21 36 37. 4 21 45 46. 5 N. 21 54 33. JUNE. 5 34. GO 10. 311 5 4 41. 64 10. 324 5 17 6.22 10.357 5 29 32. 87 10.382 5 33 42. 11 10.388 6 15 17.60 10.888 6 19 26. 86 10.382 6 23 35. 96 10. 375 N. 22 45 9. 9 22 50 49. 3 23 5 23.0 23 16 17.4 23 19 6.4 23 24 33. 2 23 22 49. 7 N.23 20 41.6 + 40.06 39.33 38.69 37.84 34. 72 33.91 33.09 24.28 23.34 22.40 + 21. 45 + 14. 64 13.64 10.62 7. 55 + 6.52 -3.78 4.81 -5.84 3 42. 68 3 45. 59 3 47. 91 3 49.64 3 50. 68 3 49. 47 3 47. 68 3 0.46 2 53.08 2 4,5.26 2 37.03 To be added to wbtrarted from Mean Time. 1 28.85 1 17.77 42. 86 5.89 6.80 2 16. 70 2 29. 40 2 41. 95 0.134 0.109 0.084 0. 060 0.U39 0.062 0.086 0.297 0.315 0.334 0.3.51 3 7 42.69 3 11 39.24 3 15 35. 80 3 19 32. 35 3 35 18.58 3 39 15. 14 3 43 11.69 4 22 37. 27 4 26 33. 83 4 30 30. 38 4 34 26.94 0.456 0. 467 0.500 0. .525 0.532 0.532 0. 526 0.519 Note. — The Semidiameter for Mean Noon may be assumed the same as that for Apparent Noon. + prefixed to the hourly change of declination indicates that north declinations are increasing and south declinations are decreasing; — indicates that noMh declinations are decreasing and south declinations increasing. 5 2 2. 85 5 5 59. 41 5 17 49. 08 5 29 38. 76 5 33 35. 31 6 13 0.90 6 16 57. 46 6 20 54. 01 Diff. for 1 hour. -^9».8565. 166 EXTRACTS FROM NAUTICAL ALMANAC. [Extracts: I'age II.] AT GREENWICH MEAN NOON— Continued. Day of the Week. Dav of the Month. THE sun's Apparent Right Ascension. h. m. Difif. for 1 hour. Appareiit Declination. Diff. for 1 hour. Equation of Time, to be subtracted frovi Mean Time. Diff. for 1 hour. Sidereal Time or Ri^ht As- cension of Mean Sun. AUGUST. Tiies. Wed. 27.45 4 17.82 9.610 9.586 N. 17 1 29. 2 N. 16 45 8. 6 -40.62 -41.20 SEPTEMBER. Wed. 10 Thur. 11 11 13 3-1. 39 8. 995 11 17 10. 19 8.990 N. 4 59 21.3 -56.91 N. 4 36 32.9 i -57.12 5 47. 69 5 41.51 To be added to Mean Time. 3 1.33 3 22.07 0.246 0.270 0. 862 0.867 8 54 39. 76 8 58 36. 31 11 16 35.72 11 20 32. 26 OCTOBER. Wed. 15 Thur. 16 Frid. 17 Tues. 28 Wed. 29 13 20 28.07 9.309 13 24 11. 75 9.333 13 27 56. 01 9.357 14 9 44.78 9.662 14 13 37.03 9.693 S. 8 29 16. 2 8 51 28. 1 9 13 32.4 13 6 2.6 S. 13 26 4. 6 55.65 55.34 55.02 50.34 49. 82 14 7. 02 0.548 14 19.89 0. 524 14 32. 18 0..T00 16 5.51 0.195 16 9.82 0. 164 13 34 35.08 13 38 31. 64 13 42 28. 19 14 25 50. 29 14 29 46. 84 NOVEMBER. Wed. Thur. 12 13 15 9 14.01 15 13 18. 76 10.180 10.216 s. i; s.i; 41 18.4 57 27.6 - 40. 77 -39.99 15 44. 60 15 36.41 0.323 0. 359 15 24 58. 61 15 28 55. 17 DECEMBER. Wed. 3 Thur. 4 Mon. 8 Tues. 9 Wed. 10 Thur. 11 Mon. 22 Tues. 23 Wed. 24 16 37 40. 65 10.844 16 42 1. 22 10. 869 16 59 29. 19 10. 960 17 3 52.48 10. 979 17 8 16.23 10.998 17 12 40. 41 11.015 18 1 24.34 11.104 18 5 50. 85 11. 103 18 10 17.33 11. 101 S. 22 6 24. 6 22 14 43. 22 43 35. 6 22 49 42. 3 22 55 21.9 23 34. 3 23 27 17. 3 23 26 54. 3 S. 23 26 2. 9 - 21. 30 20. 23 15.83 14.71 13.58 - 12.45 0.37 1.55 2.73 + + 5.66 41.65 59.91 33.18 5.99 6 38. 37 1 16.58 46. 63 16. 71 10 9 7 7 7 0.987 1.013 1.104 1.123 1.142 1.159 1.248 1.246 1.244 16 47 46, 31 16 51 42. 87 17 7 29. 10 17 11 25.66 17 15 22.22 17 19 18. 78 18 2 40. 92 18 6 37. 48 18 10 34.03 Note. — The Semidiameter for Mean Noon may be a.<«umed the same a.s that for Apparent Noon. + prefixed to the hourly change of declination indicates that north declinations are increasing and south declinations are decreasing: — indicates that north declinations are decreasing and south declinations increasing. Difl. for 1 hour. + 9».a565 EXTRACTS FROM NAUTICAL ALMANAC. 167 [Extracts: Page III.] AT GREENWICH MEAN NOON. Day of the Month. Day of the Year. THE SUN'S Logarithm of the Radius Vector of the Earth. Diff. for 1 hour. Mean time of Sidereal Oh. Tvue LONGITUDE. Diff. for 1 hour. LATITUDE. A. A' ' II 1 II " II h. m. s. APRIL. 21 22 Ill 112 30 60 16. 5 31 58 46. 1 59 47. 4 58 16.9 146.27 146. 19 +0.52 +0.52 0. 0023923 0. 0025087 +48.8 +48.3 21 59 38.53 21 55 42.62 [Extracts: Page IV.] GREEN\VICH MEAN TIME, THE MOON SEMIDIAMETER. Noon. Midnight. HORIZONTAL PARALLAX. Noon. Diff. for 1 hour. Midnight. Diff.J- MERIDIAN PASSAGE. Diff. for 1 hour. Noon. APRIL. 16 17 18 19 20 21 22 23 24 25 26 15 4.7 14 57.0 14 51.1 14 47.0 14 44. 5 14 43. 4 14 43. 8 14 45. 7 14 49.2 14 54.5 15 1. 6 15 0.6 14 53. 8 14 48. 9 1 14 45. 6 14 43. t 14 43. 4 14 44. 6 14 47. 2 14 51. 6 14 57. 8 15 5. 9 55 13.6 -1.34 54 45.1 1.04 54 23.5 0.76 54 8.4 0.50 53 59. 1 0.27 53 55.3 -0.06 53 56. 7 +0.17 54 3.6 0.41 54 16.5 0.67 54 35. 8 0.94 55 2.1 +L24 54 58.5 -1.19 54 33. 5 0.90 54 15.2 0.63 54 3.1 0.38 53 56. 5 -0.16 53 55. 3 +0.06 53 59. 4 0.29 54 9.3 0.54 54 25. 3 0.80 54 48. 1.09 55 17.9 +1.39 21 3.8 1.71 21 44.3 1.67 22 24. 6 1.68 23 5.4 1.73 23 47. 7 1.81 6 32.2 1.90 1 19.0 2.01 2 8.2 2.10 2 59,3 2.15 3 51. 2 2.16 24.6 25.6 26.6 27.6 28.6 29.6 0.9 1.9 2,9 3,9 4.9 MAY. 28 29 16 44. 6 16 38.5 15 47.0 15 59.4 16 42. 1 16 33. 7 15 53. 2 16 5.6 61 20,1 -0..53 60 57. 8 -1.29 57 48, 8 +1.86 58 34,3 +1.90 61 11.3 -0.93 60 40. 2 -1.62 58 11.4 + 1.90 58 57. 1 +L88 12 36, 6 2.66 13 41,2 2.69 5 55.3 1.95 6 42.5 1.98 14.9 15.9 7.3 8.3 25 26 27 15 49. 8 15 58. 7 16 7.2 JUNE. 15 54.3 16 3.0 16 11.1 57 59.1 1 37 58 31.7 1 34 59 3.0 1 25 58 15.5 1.36 58 47. 6 1.30 59 17.5 1.17 4 40.1 5 27.0 6 15.6 1.94 1.98 2.08 5.7 6.7 7. 7 168 EXTRACTS FROM NAUTICAL ALMANAC. [Extracts: Pages V-XII.] GREENWICH MEAN TIME. THE MOOX'S RIGHT ASCENSION AND DECLINATION. Hour. Right Ascension. ' j^^^^^ 1 Declination. j^^iff^ Hour. Right Ascension. f»\«^ Declination. Diff. for 1 m. ■ I-* h. m. #. s. 1 O 1 H II h. m. s. s. o < "1 "1 THURSDAY, APRIL 10. WEDNESDAY, MAY 28. 17 18 19 17 18 38.57 1 2.6448 17 21 17.16 i 2.6414 17 23 55.54 2.6379 S. 26 19 38. 3 26 19 41. 1 S. 26 19 33. - 0.138 + 0.044 + 0.225 6 7 8 10 19 4.23 10 21 7. 78 10 23 11. 34 2.0.591 2.0592 2.0593 N. 7 4 18.5 6 49 52.4 N. 6 35 23. 4 -14.411 14. 459 -14.507 WEDNESDAY, APRIL 16. THURSDAY, JUNE 26. t 6 22 12 47. 08 22 14 39. 29 22 16 31. 30 1.8718 1.8685 1.86.53 S. 8 12 37.4 7 59 36. 1 S. 7 46 33.5 +13.010 13.032 + 13.054 2 3 11 11 37 41.96 11 39 46.49 11 56 28. 42 2. 0743 i S. 2 35 36. 4 2.0767 i 2 50 44.4 2.0989 S. 4 51 36.5 -15.135 15. l;?3 -1.5.069 FRIDAY, APRIL 25. :\rONDAY, DECEMBER 8. 16 17 18 5 41 33. 19 5 43 48. 55 5 46 3. 93 . 2. 2558 2.2562 2.2566 N. 26 5 43. 8 26 4 23. 5 N. 26 2 55. 2 - 1.272 1. 405 - 1.5.37 2 3 4 12 23 13.52 2.1615 S. 8 9 24.4 12 25 23.37 2.1668 8 23 44.9 12 27 3.'].54 ! 2.172-2 S. 8 38 3.8 14. 354 14.328 14.302 TUESDAY, APRIL 29. 11 12 13 9 2 56. 23 2. 1384 9 5 4.49 2.1369 9 7 12.66 2.13.56 X. 15 27 3. 6 15 14 52. 7 N. 15 2 36.3 -IJ.lSo 12. 227 -12.318 EXTRACTS FROM NAUTICAL ALMANAC. [Extracts: Pages relating to Planets.] GREENWICH MEAN TIME. 169 JXJPITKR. VEJiTXJS. April. April. Apparent Right Ascension. Noon. 22 25 51.70 22 26 35.54 22 27 19.02 22 28 2.14 Var. of R. A. fori Hour. Noon. Apparent Declination. Noon. +1.834 —10 44 29.6 1.819 10 40 28.0 1-804! 10 36 28.1 +1.789, _io 32 30.0 Var. of Pec. fori Hour. Noon. +10.10 10.03 9.9d Meridian Passage. Apparent Right Ascension. Var. of R. A. fori Hour. Noon. Noon. h. m. 20 50.0 20 46.8 20 43.6 +9.89 20 40.3 h. III. n. s. 4 19 14.43+12.686 4 24 19.28' 12.718 4 29 24.88+12.748 Day of the Month. Polar Semidiameter Horizontal Parallax 1st. 11th. 16.4 1.5 16.7 1.6 17.1 Day of the month. 17.5 1.6 1.6 Semidiameter Hor. Parallax 1st. 6.0 Apparent Declination. Noon. +22 40 33.2 22 55 4.9 4-23 8 59.5 Var. of Dec. fori Hour. Noon. Meridian Passage. +37.08 35.55 +34.00 h. m. 2 10.7 2 11.9 2i3.0 6th. 6.2: 6.3 6.2 6.4 16th. 6.3 6.5 6.4 26th. 6.6 6.7 6.8 September. M^RS. Apparent Right Ascension. Var. of R. A. fori Hour. Noon. Noon. h. m. s. 22 32 5.11 22 31 38.03 Apparent Decimation. Noon. -1.134 -1.120 -10 44 20.5 -10 46 57.2 Var. of Dec. for 1 Hour. -6.58 -6.47 March. Meridian h. m. 10 49.8 10 45.5 Day of Month. Polar Semidiameter Horizontal Parallax 23.6 2.2 nth. 21st. II II 23.5 23.2 2.2 2.2 Apparent Right Ascension. h. ni. s. 20 5 56.83 20 9 1.27 20 12 5.45 Noon. s. +7.690 7.680 +7.669 Apparent Declination. Noon. -21 13 58.1 21 5 40.4 -20 57 10.7 Var. of Dec. fori Hour. Noon. +20.48 20.98 +21.48 Meridian Passage: h. m. 20 26.4 20 25.6 20 24.7 22.8 2.2 Note. — North declinations are marked +, south declinations — . + prefixed to the hourly change of declination, indicates that north declinations are increasing and south declinations are decreasing; — indicates that north declinations are decreasing and south declinations increasing. 170 EXTKACTS FROM NAUTICAL ALMANAC. [Extracts: Pages relating to Fixed Stars.] FIXED STARS. MEAN PLACES FOR 1879.0. (J.\n. O+0.OI6, Washington.) Star'»Name. Magni- tude. Right Ascension. An. Variation. Declination. An. Varia- tion. • (x Ursse Min. (Polanfi) *.. 2 //. Vi. 8. 1 14 24.861 1 33 12.133 4 28 58.716 6 15 38.457 6 39 48.935 13 18 49.216 14 10 8.551 16 21 59.432 +21.485 + 2.233 + 3.437 + 3.633 + 2.645 + 3.154 + 2.735 + 3.670 / ff +88 39 49.92 —57 51 5.79 +16 15 53.35 +22 34 26.94 -16 33 4.30 -10 31 44.21 +19 48 48.59 -26 9 41.94 n +19.00 +18.40 + 7.59 - 1.48 - 4.68 —18.90 —18.87 - 8.34 orEridani {Acheriiar) a Tauri {Aldebaran) 1 1 3 1 1 1 1.2 Jit Geminorum a Canis Maj. {Sirius) a Virginis { Spica ) cc Bootis {Arctui'ua) a Seorpii (Antares) * Circnmpolar Star. APPARENT PLACES FOR THE UPPER TRANSIT AT WASHINGTON. oUrsae Minorls. {Polaris.) a Erldani. ( Achertiar. ) a Tauri. ( Aldebaran. ) Mean Solar Right Declination Mean Solar Right Declination Mean Solar Right Declination Date. Ascension. North. Date. Ascension. South. Date. Ascension. North. h. m. 1 h. m. 1 h. m. 1 1 13 +88 39 1 33 -57 50 4 28 +16 15 June 10.8 63.54 n 47.1 July 27. 7 14.91 +.47 II 28.6 +0.5 Apr. 9.1 59.66 -.10 58.7 -0.2 11.8 64.35 47.0 Aug. 6.7 15.37 +•« 28.3 0.0 19.1 59.57 .07 58.6 -0.1 12.8 65.21 46.9 29.1 59.52 -.02 58.5 0.0 aCani s Majoris. (Si rius.) a Virginis. (Spica.) a Bootis. ( Arcturus. ) Mean Solar Right Declination Mean Solar Right Declination Mean Solar Right Declination 1 Date. Ascension. Soidh. Date. Ascension. South. Date. Ascension. North. h. m. , h. TO. I ■ h. TO. 1 6 39 -16 32 13 18 -10 31 14 10 +19 48 (Dec. 30.5) 51'. 06 +.10 63.7 -2.5 Apr. 29.5 52^28 +.02 ! 64.6 -o.i May 9.4 8. " 11.71 +.02 II 32 A +1-6 Jan. 9.5 51.14 +.05 66.1 -2.3 May 9.4 52.29 .00 ! 64.7 0.0 19.4 11.71 -.01 33.7 +1.6 1 Apr. 9.2 50.09 -18 76.2 +0.3 19.4 52.28 -.03 64.6 +0.1 1 19.2 49.92 -16 75.8 0.6 29.4 52.24 .04 64.4 0.3 29.2 49.77 -13 75.0 0.9 June 8.3 52.19 -.60 64.1 +0.4 May 9.2 49.65 -10 74.0 +1-1 • aSC( )rpli. (Antare 8.) Mean Solar Right Declination Date. Ascension. South. h. m. 16 21 1 -26 9 May 9.5 63;il +19 II 53.8 -0.5 19.5 63.28 16 54.3 0.4 29.5 63.43 12 54.7 0.4 June 8.5 63.53 09 55.0 0.3 18.4 63.60 +-05 55.3 -0.3 1 July 28.3 63.49 -10 56.0 0.0 Aug. 7.3 63.38 -13 55.9 +0.1 17.3 63.24 -i-i 55.8 +0.2 FORMS FOR WORK. 171 APPENDIX II. A COLLECTION OF FOEMS FOE WOEKING DEAD EECKONINa AND YAEI- OUS ASTEONOMICAL SIGHTS, WITH NOTES EXPLAINING THEIE APPLICATION UNDEE ALL CIECUMSTANCES. (The figures in parenthesis refer to the Notes following these forms.) FOKM FOK DAY'S WORK, DEAD BEUKOMNG. Time. Compass Course. Var. Dey. Lee- way. Total error. True Course. Patent log. Dist. N. S. E. W. Diflf.(i) Long. ' Laliti de. Longiixidf. Left at departure (or noon) . (S) N. or S. . (2) E. or W Run to N. or S. N. or S. E. orW ByD. R.at E. or W Run to N. or S. E. or W. By D. R.at N. or S. E. or W. FURM FOK TLVE SIGHT OF SUN'S LOWER LIMB (SIMNER LIKE). h. m. s. W. T. C-W Chro. C.C. (11) G. M. T (T)Eq.t. G. A. T. Obs. alt. Q . Corr. ± (3) S. D. i.*) L C. dip p. & r. (MDec. H.D. G.M.T. N.orS. Corr. ± . Dec. («)!> N.orS. (5) Eq. t. H. D. G. M. T. Corr. Eq. t. Corr. 2). h. m. s. G.A.T. .. L.A.T.I.. (h. m. S.I (8) Long.Ji----,----„4E.orW. sec cosec cos sin sin i ti 2). DLo (10) So-ll h. m. s. G.A.T L.A.T., Jll. 7)1. S.' i"'T"„-\E.orW. sec cosec cos sin sin i ti 2). 172 FORMS FOR WORK, W. T, C-W Chro, , t. C. C. (!•) G.M. T. R. A. M.S. Red. (Tab. 9) G. S. T. R. A. * FORM FOK TIME SIGHT OF A STAR (SUMKEB LIXE). h. m. s. o , „ ^ ^ g_ Obs. alt. * R. A , + Corr. ± Dec N.orS. + .....«L. + (*).I.C. + («)p dip xef. (IS) H. A. from Gr E. or VV. Corr. ± h ° ' " Li sec (9) La sec p cosec cosec «1 si-h. cos sin Gr. H. A. (18) H. A.i h. m. f:. 2 .. E.orW. . E.orW. 8ini?i h. m. f. (14) Long.i o , II •'Ie.oj-W. (1") «■> cos sin *)-/t Gr. H. A. li. m. s. H. A.» h. m. 8. Long.o o ' II sin i U >¥.. or W. FORM FOB TIME SIGHT OF A PLANET (SUMNER LINE). W. T. C-W S. .b.9 h. m. s. + Chro. t. C. C. ^..".\.. (11) G. M. T. R. A. M. Red. (Ta + ) + G. S. T. R. A.* (i2)H.A.fromGr E.orW. Obs. alt. * R. A. Corr. 4- h H. D. ' II G. M. T (15) par. + (4) I. C. + Corr. + ' // R. A. dip - ref. - ' II Corr. i h. m. .V. o ' " Dec. N.orS. h. TO. «. H. D. G. M. T. Corr. Dec. N.orS. («)p 7i. / // o ' II O ; ' II 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)." W. T. C-W S. b.9 h. m. 8. + Chro. t. C. C. ± (")G. M. T. R. A. M. Red. (Ta + ')+ G. S. T. R. A. C FORMS FOR WORK. 173 FORM FOR TIME SIGHT OF MOON'S LOWER LIMB (SUMXER LINE). ° ' " !i. m. 8. o I II Obs.alt. C (i-)R. A. (i-)Dec. N.orS. (i«)S. D. + M.I). + M. D. Aug. + m. (*)I. C. + No. mill. ± No. mill. ±. ^— — Corr. ± Corr. dip — h. m. 8, — — R. A. Dee. / // (i2)H.A.fromGr E.orW. 1st corr. ± (6)p O / fl Approx. alt p.ct-r.(Tab.24)+ For the remainder f)f the Wf)rk, by which the hour angles and thence the longitude.s are found, employ the method given under " Form for Time Sight of a Star (Sumner Line)." FORM FOR MERIIUAX ALTITIDE OF SIN'S L(MVER LIMB. O I II I II O I II Obs.alt.Q (3)S.D. + (") Dec N.orS. Corr. ± (*)I. C. + (18) c N.orS. dip — rf N. or S. p.ii-r. — Lat. N.orS. H. D. 4- Long. ± h. Corr. 4- O 1 II Dec N.orS. Corr. ± FORM FOR MERIDIAN ALTITUDE OF A STAR. O I II I II O I II Obs.alt.* (<) I. C. + Dec N.orS. dip - ref. - h (18) Z d N.orS. N.orS. Lat. N.orS. Corr. ± • FORM FOR MERIDIAN ALTITUDE OF A PLANET. O I II I II ii^ „j o / // Obs.alt. =)< (15) par. + G. M. T., Gr. trans Dec N.orS. Corr. 4: (4)1. C. + Corr. for Long. + — ^— L. M. T., local trans H. D. + Long. ± h. G.M.T (18); N.orS. dip- G. M. T., local trans. d N.orS. ref. - Lat. N.orS. — Corr. ± Dec N.orS. 174 FORMS FOR WORK. (IS); FORM FOR MERIDIAN ALTITUDE 0¥ MOON'S LOWER LIMB. ° ' " h. VI. O I II Obs. alt. ^ N.orS. (W}S.D. X.orS. Aujr. (<)I.C. Lat N.orS. dip G. M. T., Gr. trans. ■^-^— Corr. for Long.(Tab. 11) ± + L. M. T., local trans. + Long. + . + + .. G. M. T., local trans. ('■) Dec II M. D. ±... m. Xo. min. ± . . . I II Corr. + . . . t II Dec. N.orS. N.orS. Ist corr. Approx. Alt. jj.' " Method. (s*)9>i" N.orS. a> 1 ' N. or 8. Lat. 1 N. or S. h «>j" . + ... «. No. min. -4- .. «). Corr. -1- *•• R. A. /(. m. i<. (•■) Dec ^ ^__ II i\r D. 4- ... m. No .ram ■ dt- ■ Coi rr. 1 II _ De( B. 1 II N.orS. N.orS. Long.o //. m. i. h. m. s. E.orW For the remainder of the work, by which the latitudes are found from either the 9' q>" formula or the reduction to the meridian, employ the method.s given under " Forms for Latitude Sights of Sun's Lower Limb (Sumner Line)." FORM FOR CHRONOMETER CORRECTION BY EQUAL ALTITUDES OF SUN. W. T., A. M. h. m. s. h. m. s. W. T.,P. M (28) Dec. H. D. a merid. Long. Corr. Dec. (31) Tab. 37 H. D. L 1st pt. 2dpt. Eq.eq.l ± . ±. .. ± . .. ±... ± - -. 1 II N.orS. H. D. ( noon; H. D. noon) Diff. 24" Diff. li> Diff. for H. D. at .. d ±... P'-e^-} ± Wll.Ji i 4- n + C-W + C-W h. A. M. Chro. t. P. M. Chro. t P. M. Chro. t. + A.M.Chro.t.- 2) 4- , ■" — Mid. Chro. t. " 1 II -1-.. Eq. eq. alt. long. 4- " II s. N.orS. ]ogA(±)... log (±)... tan ( + )... log (±)... } Chro. t. L. Ai noon C) Eq. t. merid. ± II TO. S. — (2'*)Eq. t. logB( + ). log (±)., ... tan (±).. log (±).. Chro. t. L. M. noon (29) Long. } S. H. D. -4- — /j ]- G. M. T. Corr. ± m. 8. Eq. t. \~.. ~ FORM FOR FINDING THE TIME OF HIGH (OR LOW) WATER. d. h. m. G. M. T. of Greenwich transit (32) Corr. for Long. (Tab. 11) L. M. T. of local transit ' Lunitidal int. (App. IV) L. M. T. of high (or low) water FORMS FOR WORK. 177 NOTES KELATIXG TO THE FORMS. 1. It Is not necessary to convert departure into difference of longitude for eacli course; it will suffice 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 worli Lat. and Long, in minutes and tenths, rather than in minutes and seconds. 3. If upper limb is observed, the correction for S. D. should be negative, instead of positive. 4. A positive I. C. has been assumed for illustration throughout the forms; if negative, it should be included with the minvs terms of the correction. 6. For time sights and 9' q>" sights, take Dee. and Eq. t. from Naut. Aim., p. II (G. M. noon). 0. To obtain p, subtract Dec. from 90° if of same name as Lat.: add to 90° if of opposite name. 7. Sign of Eq. t. that of application to mean time. 8. If G. A. T. is later than L. A. T., Long, is west; otherwise it is east. P. If Lat. is exactly known, a second latitude need not be employed. 10. So and So— /( may be obtained by applying half the difference between Lj and L.^, with proper sign, to Sj andsj— ^, respectively. 11. The G. M. T. must represent the proper number of hoiirs from noon, the beginning of the astronomical daj'; to obtain this it may be necessary to add V2^ to the Chro. t. 12. H. A. from Greenwich is the difference between G. S. T. and R. A., and should be marked W. if the former is greater; otherwise, E. 1;^. Local H. A. is marked E. or W., according as the body is east or west of the meridian at time of observation. 11. Subtract local hour angle from Greenwich hour angle to obtain longitude; that is, change name of local hour angle and combine algebraically. 15. The forms include a correction for the parallax of a planet, but in most cases this is small, and may be omitted. When used, take hor. par. from Kaut. Aim. and reduce to observed altitude by Table 17. The semidiameter of a planet may be disregarded in sextant work if the center of the body is brought to the horizon line. 16. If upper limb is observed, the corrections for S. D. and Aug. should be negative, instead of positive. 17. R. A. and Dec. are to be picked out of Naut. Aim. for nearest hour of G. M. T., and to be corrected for the number of minutes and tenths. IS. Mark zenith di.stance N. or S. according as zenith is north or south of the body observed: mark Dec. according to its name, subtracting it from 180° for cases of lower transit; then, in combining the two for Lat., have regard to their names. 19. For meridian altitudes, take Dec. from Naut. Aim., p. I (G. A. noon). 20. This form enables "Constant" to be worked up before sight is taken, and gives latitude directly on completion of meridian observation. Longitude and altitude at transit must be known in advance with sufficient accuracy for correcting terms. 21. The details of obtaining Dec. at transit and correction for altitude are shown in the meridian altitude forms for each of the various bodies. 22. In an a. m. sight subtract L. A. T. from 24'' to obtain t; in a p. m. sight L. A. T. is equal to t. 23. If Long, is exactly known, a second longitude need not be employed. 24. Mark ' N. or S. according as zenith is north or south of the body; then combine for Lat. having regard to the names. 25. Take a from Table 26 and at- from Table 27. 26. Add for upper, subtract for lower transits. 27. Subtract longitude from Greenwich hour angle to obtain local hour angle; that is, change name of longitude and combine algebraically. 28. For equal altitude sights, take Dec. and Eq. t. from Naut. Aim., p. I (G. A. noon). 29. Add longitude if east; subtract if west. 80. If error is +, the chronometer is fast, and the correction is subtractive; and the reverse. 31. Mark log A and log B as indicated in Table 37; mark N. Lat., N. Dec, an consisting of a whole number and a fractional one, is written 3. 14. In setting down a decimal fraction the numerator must consist of as many places as there are ciphers in the denominator; and if it has not so many figures the defect must be supplied by placing ciphers before it; thus, yVV = -16, y^f (y = .016, xjyVVff = -0016, etc. And as ciphers on the right-hand side of integers increase their value in a tenfold proportion, as 2, 20, 200, etc., so when set on the left hand of decimal fractions they decrease their value in a tenfold proportion, .as .2, .02, .002, etc.; but ciphers set on the right hand of these fractions make no alteration in their value; thus, .2 is the same as .20 or .200. -" The common arithmetical operations are performed the same way in decimals as they are in inte- gers, regard being had only to the particular notation, to distinguish the integral from the fractional part of a sum. Addition of Decimals. — Addition of decimals is performed exactly like that of whole numbers, placing the numbers of the same denomination under each other, in which case the separating decimal points will range straight in one column. Ex.\MPLES. Add: Sum: Miles. 26.7 32.15 143.206 .003 202.059 Feet. 1.26 2.31 1.785 2.0 7.355 Inches. 272.3267 .0134 2.1576 31.4 305.8977 Subtraction of Decimals. — Subtraction of decimals is performed in the same manner as in whole numbers, observing to set the figures of the same denomination and the separating points directly under each other. Examples. From : Take: 31.267 2.63 36.75 .026 1.254 .316 1364.2 25.163 Difference: 28.637 36.724 .938 1339.037 Multiplication of Decimals. — Multiply the numbers together as if they were whole numbers, and point off as many decimals from the right hand as there are decimals in both factors together; and when it happens that there are not so many figures in the product as there must be decimals, then prefix such number of ciphers to the left hand as will supply the defect. Example I. Multiply 3.25 by 4.5. 3.25 4.5 1.625 13.00 Answer: 14.625 In one of the factors is one decimal, and in the other two; their sum, 3, is the number of decimals of the product. Example II. Multiply .17 by .06. .17 .06 Answer: .0102 In each of the factors are two decimals; the pro- duct ought therefore to contain 4; and, there being only three figures in the product, a cipher umst be prefixed. RULES AND PRINCIPLES OF MATHEMATICS. 179 Example III. Multiply 0.5 by 0.7. Answer: 0.5 0.7 0.35 Example IV. Multiply .18 by 24. .18 24 Answer: 72 36 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 divisor. Examplk I. Divide 14.625 by 3.25. 3.25 ) 14.625 ( 4.5 1300 1625 1625 In this 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 divishm affix three ciphers to the right hand of 3.1, to make the numl)er of deci- mals in the dividend equal the number in the divisor. .0062) 3.1000(500 310 Example III. Divide 17.256 by 1.16. 1.16 ) 17.25600 ( 14.875 116 565 464 1016 928 880 812 680 580 100 000 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 earlier instants of time. In multiplying by this method, omit writing down that part of the operation which involves decimal places below the required order, but 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 7^43 17454 23272 40726 1.74 23.27 407.26 432^^2774, ^. 432.^^27 In the contracted method, for the multiplier .03 it is not necessary to record the product of any figures in the multiplicand below units; for the multiplier .4, none below tenths; but in each case observe the product of the left-hand one of the rejected figures and carry forward the number of tens. 180 RULES AND PRINCIPLES OF MATHEMATICS. REDrcTioN OF 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 uj) the number. Example I. Reduce ^V to a decimal. 50)^.00 .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 = 1 foot this fraction is xi- 12)3.00 Example IV. Reduce 15 minutes to the decimal of an hour. Since 60"' = 1\ this fraction is f§. 60)15.00 .25 Answer. Example V. Reduce 1 7m 22' to the decimal of an hour 22» 22"' = — =0'".37. 60 IT^.S? iT'-.s: = =0\289 Answer. 60 .25 Answer. Any decimal may be reduced to lower denominations of the same quantity by multiplying it by the number representing the relation Vjetween the respective denominations. Example VI: Reduce 7.231 days to days, hours, minutes, and seconds. 01.231 24 924 462 5\544 0\544 60 32". 640 0™.640 60 38\400 Answer: 7* 5'' 32'» 38'. 4. GEOMETRY. Geometry is the science which treats of the description, properties, and relations of magnitudes, of which there are three kinds; viz, a line, which has only length without either breadth or tnickness; a surface, comprehended by length and breadth; and a solid, which has length, breadth, and thickness. A point, 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 curve line of which every point is equally distant from a point within called the center. The bounding curve of the circle is called the circumference. The radius of a circle, or semi-diameter, is a right line drawn from the center to the circumference, as AC (fig. 65) ; 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 segmivti, 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. RULES AND PRINCIPLES OF MATHEMATICS. 181 Anypart of a circle contained between two radii and an arc is called a sector, as GCH. A quadnmt is half a semicircle, or one-fourth part of a whole circle, as CAG. All circles are supposed to have their circumferences divided into 360 equal parts, called degrees; each degree is divided into 60 equal parts, called minutes; and each minute into 60 equal parts, called seconds; an arc is measured by the number of degrees, minutes, and seconds that it contains. A aphere 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 intersecting lines, and is measured by the arc of a circle inter- cepted between the two lines that form the angle, the center of the circle being the point of intersection. A i-ig}tt angle is one that is measured by a quadrant, or 90°. An acute angle is one which is less than a right angle. An obtuse angle is one which is greater than a right angle. A plane triangle is a figure contained by three straight lines in the same plane. When the three sides are equal, the triangle is called equilateral; when two of them are equal, it is called isosceles. When one of the angles is 90°, the triangle is said to be right-angled. When each angle is less than 90°, it is said to be acute-angled. When'one is greater than 90°, it is said to be obtuse-angled. Triangles that are not right-angled are generally called oblique-angled. A quadrilateral figure is one bounded by four sides. If the opposite sides are parallel, it is called a parallelogram. A parallelogram having all its sides equal and its angles right angles is called a square. When the angles are right angles and only the opposite sides equal, it is called a rectangle. In a right-angled triangle the side opposite the right angle is called the hi/potenuse, one of the other sides is called the base, and the third side is called the }>erjiendicular. 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, is the j)erpendicular. In a parallelo- gram, one of the sides having been assumed as the base, the distance from its opposite side, measured at right angles to its direction, is the perpendicular. The term altitude is sometimes substituted for perpendicular in this sense. 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 small circle is a section by a plane which intersects the sphere without j)assing through the center. A great circle may be drawn through any two points on the surface of a sphere, and the arc of that circle lying between those points is shorter than any other distance between them that can be measured upon the surface. All great circles of a sphere have equal radii, and all bisect each other. The extremities of that diameter of the sphere which is perpendicular to the plane of a circle are called the poles of that circle. In the case of a small circle the poles are named the adjacent pole and the remote pole. All circles of a sphere that are parallel have the same poles. All points in the circum- ference of a circle are equidistant from the poles. In the case of a great circle, the poles are 90° distant from every point of the circle. Assuming any great circle as a primary, all great circles which pass through its poles are called its secondaries. All secondaries cut the primary at right angles. Useful Formll.e Derived from Geometry. — In these formulae the following abbreviations are adopted: h, base of triangle or parallelogram. r, radius of sphere or circle. h, perpendicular of triangle or parallelogram. d, diameter of sphere or circle. /, height of cylinder or cone. A, major axis of ellipse. 7t, ratio of diameter to circumference a, minor axis of ellipse. ( = 3.141593). s, side of a cube. Area of parallelogram = bxh. Area of triangle = ^ b X h. Area of any right-lined figure = sum of the areas of the triangles into which it is divided. Sum of three angles of any triangle = 180°. Circumference of circle = 27tr, or Ttd. Area of circle = TCr', or —j-- Angle subtended by arc equal to radius = 57°. 29578. Volume of sphere = -^ • Surface of sphere = 7td\ or 47rr*. Area of ellipse = — r — Volume of cube = s*. Volume of cylinder = Area of base X I- Volume of pyramid or cone = Area of base X "3 • 182 EULES 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 ABC (lig. 66) 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 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: perpendicular . „ , ^, . , , . , , hypotenuse ' ^^ called the sine of angle A, abbreviated sin A; hvpotenuse' ^^ called the cosine of angle A, abbreviated cos A; ])erpendicular . ,, , , is called the tangent of the angle A, abbreviated tan A; base base is called the cotangent of the angle A, abbreviated cot A; a c' b a v b a' c F c^ a' 1- 1 — sine A, is called the co-versed sine of A, abbreviated covers A. The following relations may be seen to exist between the various functions: c . = - = cosec A; > is called the secant of the angle A, abbreviated sec A; perpendicular' hypotenuse base hvpotenuse . ,, , , , , , . , , . , or rtprnendicular ' ^^ called the cosecant of the angle A, abbreviated cosec A; cosine A, is called the versed sine of A, abbreviated vers A. = 1 cosA = l-^7=ft=^^«^' !HLA^£_ii = «=tanA. cos A c ' c h 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: 8inB= — = cosA; tan B = = cot A ; sec B = — = cosec A. RULES AND PRINCIPLES OF MATHEMATICS. 183 Fig. 67. 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 complement, a and the secant of an angle is the cosecant of its com- plement. The functions of angles vary in sign according to the quadrant in which the angles are located. Let AA^ and BB^ (fig. 67) be two lines at right angles intersecting at the point O, and let that point be the center about Avhich a radius revolves from an initial position OB, successively passing the points A, B', A'. In considering the angle made bv this radius at any position, P^ P^^ V'^', V'^, with the line , OB, its position of origin, the functions will depend * upon the ratios existing between the sides of a right triangle whose base, h, will always lie within BB,^ and whose perpendicular, a, will always be parallel to AA/', while its hypotenuse, c (of a constant length equal to that of the radius), will depend upon tlie position occupied by the radius. Now, if OB and OA be regarded as the positive directions of the base and perpendicular, respectively, and OB^ and OA^ as their negative directions, the sign of the hypotenuse being always positive, the sign of any function may be deter- mine'd by 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 h is measurent, recant, 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 { =- J and cos A f =7 J are both negative, because both d and h have negative values; tan A f =r ) is positive for the same reason. In the fourth quadrant, between 270° and 360°, sin A f =^ ) is negative, cos A f =- J is positive, and tan A f =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° +A) = — sin (360° -A). cos A = — cos (180°— A) = -co8 (180° + A) = co8 (360°— A). tan A = - tan (180° -A) = tan (180° + A) = — tan (360° -A). sin A = cos (90° — A) = - cos (90°+A) = -cos (270° -A) = cos (270°+ A). Any similar relation may be deduced from the figure. It is of great importance to have careful regard for the signs of the functions in all trigonometrical solutions. 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 index, with a period or dot to separate it from the other part, as in decimal fractions; 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 184 RULES AND PRINCIPLES OF MATHEMATICS. 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) l)etween 10 and 100 is 1; from 100 to 1000 it is 2; from 1000 to 10000 it is 3, etc. ; the method of finding the logarithms from this table will be evident from the rules that follow: To find the logarithm of amj 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 willjae 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 toj) (or bottom) is found 17319, pre- fixing to which the index 2, we have the logarithm of 149, 2.17319. To find the logarithtn 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 four places of figures. Thus, if the logarithm of 1495 was required, opposite to 149, and in the column marked 5 at the top (or bottom) is 17464, to which prefix the index 3, and we have the logarithm, 3.17464. To find the logarithm of any number above 10000, find the first three figures of the given number in the left-hand column of the table, and the fourth figure at the top or bottom, and takeout the corresponding logarithm as in the preceding rule; take also the difference between this logarithm and the next greater, and multiply it by the remaining figure or figures of the number whose logarithm is sought, pointing off as many decimal places in the product as there are figures in the multiplier. To facilitate the calcula- tion of the proportional parts several small tables are placed in the margin, which give the correction corresponding to the difference, and to the fifth figure of the proposed number. Thus, if the logarithm of 14957 was required, opposite to 149, and under 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 y 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 as above, by means of the marginal table marked at the top 29, taking at the side 7.38 (or 7^ nearly), to which corresponds 21, as before. To find the logarithm of any mixed decimal number, find the logarithm of the number, as if it Avere 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. lb 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 quantities, 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 + 8; and so on. In this way we may find the logarithm of any decimal fraction by the followmg rule: Find the logarithm of a fraction as if it were a whole number; see how many ciphers precede the first figure of the decimal fraction, subtract that number from 9, and the remainder will be the index of the given fraction. Thus the logarithm of 0.0391 is 8.59218 — 10; the logarithm of 0.25 is 9.39794 — 10; the logarithm of 0.0000025 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; carry the eye along the line until the next smallest logarithm to the given one is found, and the fourth figure of the required number will be at the top and bottom of the column in which this stands; take the difference between this next smallest logarithm and the next larger one in the table, and also the difference between the next smallest logarithm and the given one; entering the small marginal table 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, proper 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. EULES AND PRINCIPLES OF MATHEMATICS. 185 If the number corresponding to the logarithm 2.57345 were required, look in the column and find in it, against the number 374, the logarithm 57287, and, guiding the eye along that line, find the given logarithm, 57345, in the column marked 5; therefore the mixed number 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 numljer Avill 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 878 and under 5, the logarithm 57807, the difference between this and the next greater logarithm, 57818, being 11, and the difference between 57807 and the given number, 57811, being 4: in the marginal table headed 11, find in the right hand column the 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 immediateh' 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 beyond the fifth figure. To show, at one view, the indices corresponding to mixed and decimal numbers, the following examples are given: Mired number. Logarithms. 40943.0 Log. 4.61218 4094. 3 Log. 3. 61 21 8 409. 43 Log. 2. 61218 40.943 Log. 1.61218 4. 0943 Log. 0. 61218 Decimal nnmher. Logarithms. 0. 40943 Log. 9. 61218 — 10 0. 040943 Log. 8. 6121 8 — 1 0. 0040943 Log. 7. 61218 - 10 0. 00040943 Log. 6. 61218 — 10 0. 000040943 Log. 5. 61218 — 10 To perform multiplicaiitm hi/ logarithms, add the logarithms (jf 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. 1.54407 Product, 875 Log. 2. 94201 Example II. Multiply 22.4 by 1.8. 22.4 Log. 1.35025 1.8 Log. 0. 25527 Product, 40.32 Log. 1.60552 Example III. Multiply 3.26 by 0.0025. 3. 26 Log. 0. 51322 0. 0025 Log. 7. 39794 Product, 0. 00815 Log. 7. 91 116 Example IV. Multiply 0.25 by 0.(X)3. 0. 25 Log. 9. 39794 0. 003 Log. 7. 47712 Product, 0. 00075 Log. 6. 87506 In the last example, the sum of the two logarithms is really 16.87506 — 20; this is the same as 6.87506— 10, or, remembering that the quantity is less than unity, simply 6.87506. To perform divivon hg logarithms, from the logarithm of the dividend subtract the logarithm of tlie divisor; the remainder will be the logarithm of the quotient. Example I. Divide 875 by 25. 875 Log. 2. 94201 25 Log. 1 . 39794 Quotient, 35 Log. 1. 54407 Example II. Divide 40.32 by 22.4. 40.32 Log. 1.60552 22.4 Log. 1.35025 Quotient, 1.8 Log. 0. 25527 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 Lop:. 8. 39794 Quotient, 0.03 Log. 8.47712 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; forxthis 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. 186 RULES AND PRINCIPLES OB' MATHEMATICS. The arithmetical complement of a l>gan.thm is the difference between that logarithm and the loga- rithm of unity (10.00000— 10, of 0.00000). It is therefore the logarithm of unity divided by that num]>er which is 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 bv logarithms, we may either subtract the logarithm of the divisor or add the arithmetical complement of that logarithm. As the addition Of a number of quantities can be performed in a single operation, while in subtraction the difference between only two quantities can lie taken at a time, it is frequently a convenience to deai with the arithmetical complements rather than with the logarithms themselves. Example I. Divide 875 by 25. 875 Log. 2. 94201 25 Log. 1.39794.... Colog. 8.60206 Quotient, 85 Log. 1.54407 Ex.\MPI.E II. Divide 0.00075 by 0.025. 0.00075 Log. 6. 87506 0.025 Log. 8.39794 Colog. 1.60206 Ex.\MPLE III. Simplifv the expression, 40.32 X .00815 * ■ ^ ' 22.4 X. 0025 40.32 Log. 1. 60552 .00815 Log. 7.91116 22.4 Log. 1.35025 Colog. 8.64975 .0025 Log. 7.39794 Colog. 2.60206 Result, 5.868 Log. 0.76849 Quotient, 0.03 Log. 8.47712 To perform involution by logarithms, maltiply the logarithm of the given number by the index of the power to which the quantity is to be raised; the product will be the logarithm of the power sought. Example I. Required the square of 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 Answer, 40.96 Log. 1. 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, Avhich 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 Ije 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. 1,25527 Example II. Required the cube root of 2197. 2197 Log.3)3.34183 Answer, 13 Log. 1.11394 Example III. Required the square root of 40.96. 40.96 Log.2) 1.61236 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— 30i which, divided by 3, gives 9.39794—10. To find the loganthm of any function of an angle, Table 44 must be employed. This table is so arrangeJl that on every page there appear the logarithms of all the functions of a certain angle A, together with those of the angles 90°— A, 90° + A, and 180°— A; thus on each page may be found the logarithms of the functions of four different angles. The number of degrees in the respective angles are printed in bold-faced type, one in each corner of the page; the number of minutes corresponding appear in one column at the left of the i)age and another at the right; the names of the functions RULES AND PRINCIPLES OF MATHEMATICS. 187 to which the various logarithms correspond are printed at the top and bottom of the columns. The invarial)le rule must be to take the name of the function from the top or the bottom of the page, according as the number of degrees of the given angle is found at the top or bottom; and to take the minutes from the right or left hand column, according as the 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 right-hand, 59° at the lower right-hand, and 120° at the lower left-hand corner. Suppose that it is desired to find the log. sine of 30° 10'; following the rule given, we find 10' in the left-hand column and Sine at the top of the page, and abreast one and below the other is the required logarithm, 9.70115. But if the log. sine of 59° 10' were sought, as 59° appears below and at the right of the page, the logarithm 9.93382 would be taken from the column marked Sine at the bottom and abreast 10' on the right. It may also be seen that log. sin 30° 10'=log. cos 59° 50'=log. cos 120° 10'=log. sinl49° 50'=9.70115,theequality of the functions agreeingwith trigonometrical deductions; (in this statement numerical values only are regarded, and not signs; the latter must, of course, be taken into account in all operations). Example I. 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 Log. tan 9. 73687 Log. cos 9. 94342 E.XAMPLE II. Required the log. sine, cosecant, tangent, cotan- gent, secant, and cosine of 75° 42'. Log. sin 9. 98633 Log. cot 9. 40636 Log. cosec 10. 01367 Log. sec 10. 60730 Log. tan 10. 59364 Log. cos 9. 39270 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 interpolate by computation, let n represent the number of seconds, D the difference between the logarithms of the next less and next greater even minute, and d the difference between the logarithm of the next less even minute and that of the required angle. Then, It should be noted when the number of seconds is 30, 20, 15, or some similar nimiber, permitting the reduction of the fraction w^ to a simple value, such as i, J, J, as the interpolation by this method may thus be made with greater facility. Having obtained the difference of the logarithm from that of the next lower even minute, it must be applied in the proper direction — that is, if the function is such that its logarithm increases as the angle increases, the logarithmic difference must be added; but if it decreases, then that difference must be subtracted. For example, let it be required to find the log. sin and log. cosec of 30° 10' 19". The log. sin of 30° 10' is 9.70115; the difference between this logarithm and that of the sine of 30° 11' (9.70137) is + 22, which is D. Hence, d = ^X( + 22) = -|-7; and the required logarithm is 9.70122. The log. cosec of 30° 10' is 10.29885; the difference, D, between that and log. sin 30° 11' (10.29863) is — 22. In this case rf = Wx(-22) = --; therefore, log. cosec 30° 11' 19" = 10.29878. The method of interpolating by inspection consists in entering that column marked "Diff." which ia adjacent to the one from which the logarithmic function for the next lower minute is taken, and finding, abreast the number in the left-hand minute column which corresponds to the seconds, the required logarithmic difference; and the latter is to be added or subtracted according as the logarithms increase or decrease with an increa.sed angle. Thus, if it be required to find log. sin 30° 10' 19", find as before log. sin 30° 10' = 9.70115; then, in the adjacent column headed "Diff." and abreast the number of seconds, 19, in the left-hand minute column will be found 7, the logarithmic difference; add this, as the function is increasing, and we have the required logarithm 9.70122. If log. cosec 30° 10' 19" be sought, find log. cosec 30° 10' = 10.29885; then in the adjacent difference column, which is the same as was used for the sines, find as before the logarithmic difference, 7; and since this function decreases as the angle increases, this must be subtracted; therefore, log. cosec 30° 10' 19" = 10.29878. This method of interpolation by inspection is not available in that portion of the table where the logarithmic differences vary so rapidly that no values will apply alike to all the angles on the same page; on such pages the difference for one minute is given in a column headed "Diff. 1'," instead of the usual difference for each second; in this case, the interpolation must be made by computation, the given difference for one minute being D. In other parts of the table the interpolation by inspection may be liable to slight error because of the variation in logarithmic difference for different angles on the same page; but the tabulated values are sufficiently accurate for the usual calculations in navigation. It will be evident that while the methods explained have contemplated entering the tables with a smaller angle and interpolating ahead, it would be equally correct to enter with a greater angle and interjwlate hack for the proper number of minutes, making the requisite change in the sign of the correction. 188 RULES AND PRINCIPLES OF MATHEMATICS. Example I. Required the log. sine, cosine, and tangent of 42° 57' 06'''. For 42° 57 For 42° 57' 06". Log. sin Log. cos Log. tan 9.83338 I 9.86448 9.96890 9. 83339 9. 86447 9. 96893 EXAMIM.H II. Required the log. secant, cosecant, and cotangent of 175° 32' 36". For 175° 32' For 175° 32' 36" Log. sec Log. cosec Log. cot 10. 00132 11. 10858 11. 10726 - 1 +97 4^8 10. 00131 11. 10955 11. 10824 It should be observed that, for uniformity and convenience, all logarithms given in Table 44 have been increased by 10 in the index, and it is understood that —10 ought properly to be written after each; thus all logarithms under 10.00000 represent functions whose value is less than unity, and all over 10.00000 those greater than unity; for example, 11.10726 is the logarithm of a number in which the decimal point should be placed after the second figure from the left. To find the angle corresponding to anij logarithmic function, the process is the reverse of the one just described. Find, in the column marked with the name of the function, either at top or bottom, the two logarithms between which the given one falls; write down the degrees and minutes of the lesser of the two corresponding angles, which will be the degrees and minutes of the angle required. Call the difference between the two tabulated logarithms D, and the difference between the given logarithm and that which corresponds to the lesser angle, d; then if n represent the number of seconds, we have: n = p X 60. Or, the same may be obtained by inspection (except where, as before explained, the differences for seconds are not tabulated) byfinding, in the "Diff." column adjacent to that from which the logarithm was taken, the logarithmic difference, d, and noting the number of seconds abreast which it stands in the left-hand minute column. Interpolation may be also made in the reverse direction from the next greater even minute. Thus, if it be required to find the angle corresponding to log. sin 9.61400, we find log. sin 24° 16', 9.61382, and log. sin 24° 17', 9.61411; hence D = 29, and d = 18; 18 ,^ n = 29 X 60 37; and the angle is 24° 16' 37". Or, in adjacent column headed "Diff.," 18 would be found abreast 38, 39, or 40 (seconds) in the left-hand minute column — a correspondence sufficiently close for navigation work. If the angle were known to be in the second quadrant, we find log. sin 155° 43', 9.61411, and log. sin 155° 44', 9.61382; here, D = 29, and d = 11 ; n = 29 X 60 = 23; therefore, the angle is 155° 43' 23". Or, in adjacent "Diff." column find, abreast 11, 23 or 24 seconds. Example I. Example II. Find angles less than 90° corresponding to log. cot 10..3.3621, log. sec 10.11579, and log. cos 8.70542. Log. cot 10. 33621 24 45 Log. sec 10. 11579 40 00 Log. cos 8. 70542 87 05 4 116 15 22 28 Find angles in second quadrant corresponding to log. tan 10.15593, log. sin 8.87926, and log. cosec 10.04944. Log. tan 10. 15593 Log. sin 8. 87926 Log. cosec 10. 04944 ' d II 124 55 19 42 175 39 69 25 116 49 3 27 The Hour Columns in Table 44 give the measure in time corresponding to twice the angular distance given in arc. Thus, abreast the angle 13° 00' stands in the P. M. column l"" 44" 00", corresponding in time to 2 X 13° 00', and in the A. M. column lO*" 16™ 00% which is the same subtracted from 12\ These columns are of use in working the various formula? which involve functions of half the hour angle. Interpolation for values intermediate to those given in the tables is made on the same principle as for the angular measure; this operation may be performed by inspection by the use of the small tables at the bottom of each page, where n, the number of seconds of time, is given in bold-faced type, and (/, the logarithmic difference for the respective columns, appears below. Example I. Given t=V' 48'" 44% find log. cot J t. For 1" 48'° 40", log. cot. i t 10. 61687 Diff. for 4% Col. B, - 28 For 1" 48'» 44', log. cot J t 10. 61659 Example II. Given log. sin § t 9.91394, find the Hour A. M. corresponding. For 9.91389, 4''39'°12» Diff. for 5, Col. C, - 5 For 9.91394, 4 39 07 RULES AND PRINCIPLES OF MATHEMATICS. 189 jytlSCELLANEOUS TJSEFTJL DATA. Earth's Polar radius =6, 356, 583. 8 meters. Earth's Equatorial radius=6,378,206.4 meters. Earth's Compression = ^qq An h- Earth's Eccentricity =^0.0824846 Number of feet in one statute mile=5280 Number of feet in one nautical mile=6080.27 Sine of 1^^=0.00000485 Sine of 1^=0.00029089 The Napierian base £=2.7182818 The modulus of common logarithms=0. 4342945 French meter in Enplish feet, 3.28087 French meter in En-^lish statute miles, 0.00062138 French meter in nautical miles, 0.00053959 1 pound Avoirdupois=7,000 grains Troy. French gramme=0.00220606 Imperial pound Troy. French kilogramme=0.0196969 English cwts. Cubic inch of distilled water, in grains =252. 458. Cubic foot of water, in ounces Troy =908. 8488. Cubic foot of water, in pounds Troy=75.7374. Cubic foot of water, in ounces Avoirdupois=997. 1366691. Cubic foot of water, in pounds Avoirdupois =62. 3210606. J Length of pendulum which vibrates second at Greenwich, 39.1393 inches. log 8. 9163666. log 3. 7226339. log 3. 7839232. log 4. 6855749. log 6. 4637261. log 0. 4342945. log 9. 6377843. log 0. 5159890. log 6. 7933560. log 6. 7320620. Bar. 30.00 in. ; ther. 62° F. APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. The following table contains the latitude and longitude of a large number of places, together with lunitidal intervals and tidal ranges at the more important ones. It is arranged geographically and followed by an alphabetical index. The geographical position generally relates to some specified exact location, and is based upon the best available authority. The tidal data relate to the waters adjacent to the point whose latitude and longitude are given, being abstracted from the Tide Tables published by the United States Coast and Geodetic Survey for the year 1903. The high water and low water lunitidal intervals represent the mean intervals between the moon's transit and the time of next succeeding high and low waters throughout a lunar month. The spring and neap ranges are the differences in height between high water and low water at spring and at neap tides. For those places where the tide is chiefly of a diurnal type, and where there is usually but one high and one low water during a lunar day, the tidal values are bracketed; in such cases the lunitidal intervals are for the semi-diurnal part of the tide ( which, however, is only appreciable for a few days when the moon is near the equator), and the range given in the column headed "Spg." does not, as in other cases, apply to the spring tide, but to the greatest periodic daily range, which usually occurs a day or two after the moon attains its extreme of declination, and is therefore near one of the tropics. As those places where the diurnal type predominates seldom experience large tidal effects, the general data furnished regarding such tides will suffice for the ordinary purpose of the navigator. The method of finding the time of high or low water from this table is illustrated in article 507, Chapter XX. 190 APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. EAST COAST OF NORTH AMERICA. [Page 191 Place. Salisbury Island: E. pt Nottingham Island : S. ] )t Digges Island : W. extreme Cape AVostenholme Charles Island: E. pt w. pt :.... Cape Weggs Prince of Wales Sound : Center of ent Cape of Hopes Advance Akpatok Island: E. pt Green Island : NE. pt Button Islands: N. pt Cape Chidleigh Resolution Island: S. pt., Hutton h'dl'd E. pt., C. Resolution Black Head Eclipse Harbor: E. side Nachvack Bay: Islands off entrance Saddle Island Port Man vers : Entrance Nain: Church Hopedale Harbor: Hill to E'd Aillick Harbor: Cape Mokkivik Cape Harrison : N. extreme Indian Harbor: Obs Outer Gannet Island: Summit Gready Harbor Cartwright Harbor: Caribou Castle Indian Tickle : Summit Roundhill Island : Summit Occasional Harbor: E. summit of Twin I. Cape St. Lewis: SE. pt Battle Islands: NE. extreme, SE. I Table Head Belle Isle; Light-house Cape Bauld : Light-house Bell Island : S. end Cape St. John: Gull Island light Tilt Cove, L^nion Copper Mine Funk Island: Summit Offer Wadham : Light-house Toulinguet Islands: Light-house Seldom-come-by Harbor: Shiphill Cape Freels : Gull I Greenspond Island Cape Bonavista: Light-house Catalina Harbor: Green I. light-house .. Bonaventure Head Hearts Content: Light-house Baccalieu Island : Light-house Harbor Grace: Light-house on beach Cape St. Francis: Light-house St. Johns Harbor: Chain Rock Battery.. Cape Race: Light-house Cape Pine: Light-house Trepassey Harbor: Shingle Neck Cape St. Mary : Light- house Little Placentia Harbor: W. side Coopers Cove Burin Island : Light-house Laun : Gr. Laun R. C. Church St. Pierre: U. S. Coast Survey Station .. . Brunet Island: Mercers Hd. light-house. Boar Islands: Burgeo I. lijiht-house Lat. N. Long. W. Liin. Int. Range. H.W. L. W. Spg. Neap. o / // 63 27 00 O / II 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 56 10 36 55 51 40 57 36 52 h. m. h. m. ft. ft. 63 06 00 62 37 00 8 58 2 46 13.5 6.1 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 ' i 8 00 7 00 1 48 48 5.0 5.2 2.0 2.1 57 00 00 1 ; 56 32 45 55 27 04 55 13 33 7.00 5 30 48 11 43 6.5 6.9 3.0 3.2 54 55 50 t 1 54 26 55 54 00 05 6 10 12 23 7.0 3.2 53 oO 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 6 27 15 6.0 2.8 6 38 6 30 26 18 5.0 3.5 2.3 L6 1 ' i 1 ' 49 45 29 1 49 35 40 1 49 41 20 ; 1 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 46 46 51 47 15 30 47 35 13 i 1 1 1 ; 7 23 1 11 4.1 1.9 7 15 1 03 3.3 r.5 7 12 6 50 1 01 38 3.3 6.5 1.5 3.0 6 50 8 20 38 2 08 6.6 7.2 3.1 3.3 8 05 8 23 1 8 53 8 22 1 53 2 11 2 41 2 10 7.0 6.6 6.5 6.2 3.2 3.1 3.0 2.9 Page 192] APPENDIX IV. MAKITIME POSITIONS AND TIDAL DATA. EAST COAST OF NORTH AMERICA— Continued. al Place. Lat. N. LaPoileBay: (ir. Espic Church Cape Ray : Light-house Codrov island: S. side Boat Harbor ' Cape St. George: Red I., SE. pt Cow Head : N W. extreme ' Port Saunders: NE. point of entry Rich Point: Light-house j Ferolle Point: Cove Point, NE. extreme J Flower Cove: Capstan Pt ' Green Island: 150 fms. from NE. end . . .| Cape Norman : Light-house I Chateau Bay: S. pt. Castle I Amour Point : Light-house | Wood Island: S. pt ; Greenly Island : Light-house Bradore Bav : Obs. Spot, Jones Pt i Old Fort Island : Center Great Mecatina Island : SE pt Mecatina Harbor: S. point of Dead Cove. Little Mecatina I. : S. pt. C. McKinnon. . St. INIary Reefs South Makers Ledge Cape Whittle , Natashquan Point : S. edge , Clearwater Point: SW. extreme. Carousel Island: Light-house Point de Monts: Light-house Quebec: Mann's Bastion, Citadel. Montreal : Cathedral Father Point : Light-house Cape Chatte: Extreme Cape iVIagdalen : Light- house Cape Rosier: Light-house Cape Gaspe : Light-house Anticosti Island: Heath Pt. light-house SW. pt. light-house . . E. pt Bonaventure Island: Leander Shoal Macquereau Point Chaleur Bay : Carlisle Dalhousie I Miscou Island: NE. pt., Point Birch Miramichi Bay: Portage I., N. pt... Point Escumenac: Light-house North Point: Light-house Richmond Harbor: Royalty Pt.. East Point: Light-house Charlottetown : Flag-staff on fort 47 39 50 47 37 00 47 52 30 48 33 48 49 55 20 50 38 30 50 41 39 51 02 10 51 17 25 51 24 10 51 38 00 51 58 00 51 27 35 51 22 45 51 22 35 51 27 30 51 21 40 50 47 30 50 46 44 50 31 40 50 14 00 50 09 30 50 11 00 50 06 00 50 12 27 50 05 40 49 19 35 46 48 17 45 30 24 48 31 25 49 06 00 49 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 00 47 14 00 47 05 00 47 03 46 46 34 00 46 27 15 46 13 55 Gt. Bird Rock : Light-house East Island : E. extreme Entry Island : Light-house Amherst Hbr. : N. side of entrance Deadman Rock: W. pt St. Paul Island: Light-house, NE. end.. Light-house, SW. end.. Cape North : Light-house St. Anns Harbor: K. pt. entrance 50 40 37 40 16 30 14 23 16 03 47 13 50 47 11 20 47 01 45 46 21 00 Sydney Harbor: Light-house 46 12 25 Long. \V. 58 24 10 59 18 00 59 23 40 69 13 10 57 50 00 57 17 07 57 24 20 57 02 40 56 44 45 56 33 40 55 53 52 55 50 20 56 51 05 57 08 00 57 10 50 57 14 12 57 46 00 58 51 00 58 59 20 59 20 00 59 45 00 59 57 00 60 08 00 61 44 00 63 27 03 66 22 44 67 21 55 71 12 19 73 33 04 68 27 40 66 46 00 65 19 30 64 12 00 64 09 35 61 42 30 63 35 46 64 08 00 64 18 00 64 46 30 65 19 00 66 22 10 64 29 00 65 02 00 64 47 33 63 59 19 63 43 00 61 58 05 63 07 23 61 08 32 61 24 30 61 41 20 61 49 38 62 12 25 60 08 32 60 09 50 60 23 27 60 27 00 60 12 50 Lun. Int. Range. H.W. /*. m. 8 50 8 50 "9'46' 1 25 1 43 1 48 6 07 1 52 1 46 1 33 1 25 1 55 2 20 3 10 2 00 4 16 L. \v. Spg. h. VI. 2 38 6.0 2 32 "3*13' 4.3 'I'd 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 Neap. 4 20 5 15 8 17 11 07 8 30 8 35 8 25 8 10 11 00 11 55 2 20 4 23 2.4 1.8 1.4 6.4 2 12 2.7 2 17 2 13 2 05 3.1 6.0 5.0 ft. 2.8 2.1 "2."5 2.0 6.0 8.0 10.8 8.9 7.8 4.7 4.1 1.8 2.5 2.3 2.4 4.1 2.0 1.2 1.2 0.9 0.7 3.2 1.4 1.6 3.7 3.1 BSfl APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. EAST COAST OF NORTH AMERICA— Continued. [Page 193 Place. Lat. N. Scatary Island: Light-house, NE. pt Louisburg: Light-house, NE. pt Madame Island : S. pt Port Hood : Just-au-corps I Sable Island: Light- house, E. end Pictou: Custom-house Cape St. George North Canso: Light-house, NW. entrance. Arichat Harbor: R. C. Church steeple . . Cape Canso: Cranberry I., light-house .. White Head Island: Light- house Green Island : Light-house Wedge Island : Light-house Halifax : Dock-yard ob.«ervatory Sambro Island: Light-house Margaret Bay : Shut-in I Tancook Island Lunenburg: Battery Pt. light Cape Le Havre: Black Rock Coffin Island : Light-house Little Hope Island : Light-house Shelburne Hbr.: Two lights, McNutts I Cape Sable: Light-house Seal Island : Light-house Yarmouth : Cape Fourchu light Cape St. Mary.. Bryer Island : Light-house Annapolis Harbor: Prim Pt. light Haute Island : Light-house Cape Chignecto Burntcoat Head : Light-house Cape Enrag^: Light-house Cape Quaco: Light-house St. Johns: Partridge I. light Cape Lepreau : Light- house L'Etang Harbor: S. pt. tower St. Andrew: S. pt. light Campo Bello Island: Light-house, N. pt. Grand Manan Island: Light-house, NE. pt. GannetRock: Light-house, NE. pt Machias Island: Light-house 46 02 15 45 54 34 45 28 00 46 00 00 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 Long. W. Calais: Astronomical station 45 11 Eastport: Cong. Church 44 54 Quoddy Head: Light-house [ 44 48 Machias: Town Hall 44 43 Petit Manan Island : Light-house 44 22 Bakers Island : Light-house Mount Desert Rock : Light-house Bangor: Thomas Hill Belfast: Methodist Church Rockland : Episcopal Church Matinicus Rock : Light-house Monhegan Island : Light-house Seguin Island : Light-house Bath: Winter St. Church Brunswick: College spire Augusta: Baptist Churcli Portland: Custom-house Portland Head light-house . . . Cape Elizabeth: Li^ht-house (west) Wood Island : Light-house Boon Island : Light-house 44 14 43 58 44 48 44 25 44 06 43 47 43 45 43 42 43 54 43 54 44 18 43 39 43 37 43 33 43 27 43 07 59 40 25 59 59 26 61 03 00 61 36 00 59 46 08 62 42 61 52 61 29 61 01 60 55 61 08 61 32 61 52 63 35 63 33 63 54 64 06 64 17 64 18 64 37 64 47 65 15 65 37 66 00 66 09 66 12 66 23 65 47 65 00 64 57 63 48 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 66 59 66 57 67 27 67 51 68 11 68 07 68 46 69 00 69 06 68 51 69 18 69 45 69 49 69 57 69 46 70 15 70 12 70 12 70 19 70 28 Lun. Int. H. W. h. TO. 7 45 7 55 9 05 9 34 9 20 9 26 7 55 7 43 7 45 7 34 '7'32 39 8 17 9 35 10 00 10 29 10 49 11 07 27 11 21 11 07 11 04 11 09 11 00 11 02 "io'si' 11 36 11 09 11 02 23 11 35 11 09 10 45 12 13 2 54 11 06 11 12 L. W. h. m. 1 35 1 47 2 47 Range. Spg. Neap. ft. 5.0 5.0 3.5 3.9 2.8 3.1 5.0 6.5 1 46 1 30 'i"36' 2 05 3 23 3 41 4 36 4 41 5 27 7 27 5 21 'I'm 5 40 5 05 5.2 7.1 '7."6' 8.5 12.8 16.0 20.8 27.5 33.0 50.5 30.0 23.9 24.5 23.3 24.9 22.5 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 6 16 10 18 4 51 4.9 10.1 4 51 10.2 ft- 3.1 3.1 1.8 2.0 1.4 1.6 3.1 4.0 4.1 3.2 "4.' 4 "4.' 3 5.2 9.5 11.8 15. 4 20.4 24.4 37.4 22.2 17.7 18.2 17.1 18.2 16.7 13.2 17.1 15.2 11.3 11.0 8.6 8.1 7.5 5.8 3.6 7.3 22489—03- -13 Page 194] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. EAST COAST OF NORTH AMERICA— Continued. Place. Whale Back: Light-house Portsmouth : Ntfvy-y ard flagstaff Fort Constitution Hampton: Baptist Church Isles of Shoals: White I. light-house Newburyport: Academy Plum I. light-house Ipswich : Light-house ( rear) Annisquam Harbor: Light-house Cape Ann: Thatchers I. light-house (N.) . Gloucester: Universalist Church Ten-pound I. light-house Beverly : Hospital Pt. light-house Salem : Derbys Wharf light-house Marblehead : Light-house Cambridge: Harvard Observatory Boston : Navy-yard flagstaff State house Little Brewster I. light-house. . . Minots Ledge: Light-house Plymouth : Pier head Gurnet light-house Barnstable: Light-house Cape Cod : Highlands light- house Chatham : Light-house (south ) Monomoy Point: Light-house Nantucket: South Church Nantucket South shoal: Light ship Sankaty Head : Light-house Tarpaulin Cove: Light-house Vineyard Haven: W. Chop light-house.. Gay Head: Light-house Cuttyhunk: Light-house New Bedford : Baptist Church Sakonnet Point: Light-house Beaver Tail: Light-house Newport: Flagstaff, torpedo station Bristol Ferry: Light-house Providence: Unitarian Church Point Judith : Light-house Block Island: Light-house (SE) Watch Hill Point: Light-house Lat. N. 43 03 32 43 04 56 43 04 16 42 56 15 42 58 02 48 30 48 55 41 07 39 43 38 21 36 46 36 07 32 48 31 00 30 20 22 48 22 22 21 28 19 41 16 11 58 44 00 12 43 20 02 23 40 15 33 34 16 55 37 05 17 01 28 08 28 51 20 55 24 52 38 10 41 26 30 41 26 58 41 29 07 41 38 34 41 49 26 41 21 40 41 09 10 41 18 14 Montauk Point: Light-house 41 Stonington: Light-house 41 New London : (proton Monument 41 Little Gull Island : Light-house 41 Gardners Island: Light-house, N. pt 41 Plum Island: Light-house, W. pt 41 Say brook: Light-house, Lynde Pt 41 New Haven: Yale College spire (middle). 41 Bridgeport Harbor: Light-house ; 41 Norwalk Island: Light-house | 41 Shinnecock Bay : Light-house . . Fire Island : Light-house Albany: Dudley Observatory. .. New York: Navy-vard flagstaff. City Hall 40 40 42 40 40 Fort Wadsworth : Light-house ■ 40 04 16 19 31 21 16 12 23 08 29 10 25 16 17 18 28 09 24 02 56 51 03 37 57 39 50 42 02 42 44 36 20 Long. W. 70 41 49 70 44 22 70 42 34 70 50 12 70 37 25 70 52 28 70 49 10 70 46 00 70 40 55 70 34 31 70 39 59 70 39 58 70 51 23 70 53 03 70 50 03 71 07 43 71 03 05 71 03 50 70 53 26 70 45 35 70 39 12 70 36 04 70 16 52 70 03 40 60 57 01 60 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 24 19 71 28 55 71 33 08 71 51 32 71 51 27 71 54 49 72 04 47 72 06 26 72 08 44 72 12 43 72 20 37 72 55 45 73 10 49 73 25 11 72 30 16 73 13 08 73 44 56 73 58 51 74 00 24 74 03 15 Lun. Int. H. W. h. m. "ii"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 86 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 11 09 11 03 7 48 7 19 5 13 8 44 7 41 L. W. Range. Spg. h. m. ft. '5"69 Tio.'s' 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 11 54 04 56 38 20 46 2 49 1 38 10.0 9.1 10.1 10.1 10.2 10.6 10.6 11.0 i6.*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 8.4 8.2 3.0 2.2 2.8 5.3 5.4 APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. EAST COAST OF NORTH AMERICA— Continued. [Page 195 Place. Lat. N. Sandy Hook: Light-house (rear) Light-ship Navesink Highlands: N. Hght-house Barnegat Inlet: Light-house Tuckers Beach : Light-house Absecon Inlet: Light-house Five Fathom Bank: Light-ship Cape May : Light-house Philadelphia, Pa. : Statehouse Navy-yard flagstaff, League I v . Wilmington, Del. : Town hall Cape Henlopen : Light-house Assateague Island: Light-house Hog Island: Light-house Cape Charles: Light-house Baltimore: Washington Monument Annapolis: Naval Academy observatory. Point Lookout: Light-house Washington, D. C. : Navy-yard flagstaff . Naval Observatory . Capitol dome Old Point Comfort: Light-house Norfolk : Navy-yard flagstaff Richmond, Va. : Capitol Cape Henry : Light-house Elizabeth City : Court-house . . . Eden ton : Court-house Currituck Beach : Light-house . Bodie Island : Light-house Cape Hatteras: Light-house Ocracoke: Light-house Newbern, Episcopal spire Cape Lookout: Light-house ... Beaufort, N. C. : Court-house . . Frying- Pan Shoals: Light-ship Georgetown : Episcopal Church Light-house, North I Cape Romain : Light-house Charleston: Light-house, Morris I St. Michael's Church Beaufort, S. C. : Episcopal Church Port Royal: Martins Industry light-ship. Tybee Island : Light-house Savannah : Exchange spire Sapelo Island: Light-house Darien : Winnowing House St. Simon : Light-house Brunswick: Academy Amelia Island : Light-house Fernandina: Astronomical station .. St. Johns River: Light-house Jacksonville: Methodist Church St. Augustine: Presbyterian Church Light-house Cape Canaveral : Light-house Jupiter Inlet: Light-house Fowey Rocks: Light-house Carysfort Reef: Light-house 40 27 42 40 28 15 40 23 48 39 45 52 39 30 22 39 21 59 38 47 20 38 65 59 39 56 53 39 53 14 39 44 27 38 46 42 37 54 40 37 23 46 37 07 22 39 17 48 38 58 53 38 02 19 38 52 30 38 53 39 38 53 20 37 00 06 36 49 33 37 32 16 36 55 35 36 17 58 36 03 24 36 22 36 35 49 07 35 15 17 35 06 32 35 06 21 34 37 22 34 43 05 33 34 26 33 22 08 33 13 21 33 01 06 32 41 43 32 46 34 32 26 02 32 05 33 32 01 20 32 04 52 31 23 28 31 21 54 31 08 02 31 08 51 30 40 23 30 40 18 30 23 36 30 19 43 29 53 20 29 53 07 28 27 37 26 56 54 25 35 25 25 13 17 Long. W. 74 00 09 73 50 09 73 59 10 74 06 24 74 17 08 74 24 52 74 34 36 74 57 39 75 09 03 75 10 32 75 33 03 75 05 03 75 21 23 75 41 59 75 54 24 76 36 59 76 29 08 76 19 20 76 59 45 77 03 06 77 00 36 76 18 24 76 17 46 77 26 04 76 00 27 76 13 23 76 36 31 75 49 51 75 33 49 75 31 16 75 59 11 77 02 24 76 31 29 76 39 48 77 49 12 79 16 49 79 10 55 79 22 19 79 52 54 79 55 49 80 40 27 80 33 15 80 50 37 81 05 26 81 17 01 81 25 39 81 23 30 81 29 26 81 26 26 81 27 47 81 25 27 81 39 14 81 18 41 81 17 12 80 32 30 80 04 48 80 05 41 80 12 40 Lun. Int. Range. H.W. h. m. 7 30 7 50 7 48 9 59 8 16 1 28 53 12 00 8 17 8 03 6 34 4 39 31 7 42 8 44 9 05 4 30 7 53 7 37 7 00 6 29 7 21 8 39 "6"59' 7 20 8 10 8 00 7 39 7 36 8 12 8 00 8 00 8 20 8 21 L.W. Spg. h. TO. 1 23 1 43 1 42 3 57 1 47 8 58 8 02 6 40 1 50 2 19 44 10 53 6 52 1 56 2 17 2 47 11 55 1 43 1 26 45 20 1 08 3 38 "o'So' 1 10 2 06 1 31 1 33 ft. 5.6 2.7 4.2 4.7 5.6 6.2 7.0 6.7 5.4 3.0 1.4 1.0 1.7 3.5 3.0 3.2 4.3 3.2 3.4 2.2 4,4 3.3 4.3 '5.'9' 6.0 8.5 7.9 7.6 8.4 7.5 7.5 7.8 5.4 5.3 5.9 1.8 2.6 2.7 Neap. ft. 3.6 1.7 2.7 3.0 3.6 4.4 5.2 4.9 3.5 2.0 1.0 0.8 1.1 2.5 2.0 2.1 2.8 2.1 2.2 1.5 3.0 2.3 2.9 "4.'i 4.2 5.9 5.5 5.3 5.8 5.2 5.3 5.4 4.8 3.7 3.6 4.0 1.2 1.3 1.4 Page 196] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. EAST COAST OF NORTH AMERICA— Continued. Place. Alligator Reef: Light-house Sombrero Key: ^ight-house Sand Key : Light-house Key West: Light-house Loggerhead Key : Light-house Sanibel Island: Light-house Gasparilla Island: Light-house Tampa Bay : Egmont Key light Cedar Keys: Ast. station, Depot Key Seahorse Key light St. Marks: Fort St. Marks Apalachicola: Flag-staff Cape St. George: Light-house Cape San Bias: Light-house Pensacola: Light-house Navy-yard chimney Sand Island: Light-house (front) Mobile Point: Light-house Mobile: Episcopal Church Horn Island : Light-house East Pascagoula: Coast-Survey station. . . Mississippi City: Coast-Survey station... Ship Island : Light-house Cat Island: Light-house Chandeleur: Light-house Mouth Mississippi River: Pass a 1' Outre light S. Pass light (East Jetty) SW. Pass light New Orleans: United States Mint Barataria Bay : Light-house Timbalier Island : Light-house Ship Shoal: Light-house Southwest Reef: Light-house Calcasieu Pass: Light-house Sabine Pass: Light-house Galveston: Cathedral, N. spire Light-house, Bolivar Pt Matagorda: Coast-Survey station Light-house Indianola: Coast-Survey station Lavaca: Coast-Survey station Aransas Pass: Light-house Brazos Santiago: Light, S. end Padre I .. Point Isabel : Light-house Rio Grande del Norte: Obs. N. side of entrance San Fernando River: Entrance Santander River: Entrance Mount Mecate: Summit Tampico: Light-house Cape Roxo Lobos Cay : Light-house Tuspan Reefs: Middle islet Mexico: National Observatory Bernal Chico: Middle of islet Zempoala Point: Extreme Vera Cruz: San Juan d'Ulloa light Sacrificios Island Orizaba Mountain : 1 7, 400 feet Cofre de Perote Mount: 14,000 feet Al varado : E. side of entrance Roca Partida: Summit Tuxtla, volcano: Summit Montepio: Landing place Lat. N. 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 25 23 40 23 46 20 22 38 40 22 15 50 21 35 00 21 28 12 21 03 00 19 26 01 19 39 50 19 27 26 19 12 29 19 10 10 19 04 00 19 29 30 18 49 00 18 44 00 18 29 00 18 40 00 Long. W. 80 37 08 81 06 40 81 52 40 81 48 04 82 55 42 82 00 43 82 15 34 82 45 40 83 01 57 83 03 58 84 12 42 84 59 12 85 02 54 85 21 30 87 18 32 87 16 06 88 03 02 88 01 26 88 02 28 88 31 39 88 32 45 89 01 57 88 57 56 89 09 41 88 52 19 89 02 28 89 08 08 89 23 30 90 03 28 89 56 43 90 21 25 91 04 15 91 30 14 93 20 43 93 51 00 94 47 26 94 46 00 95 57 26 96 25 28 96 31 01 96 37 21 97 03 23 97 10 00 97 12 28 97 08 57 97 21 25 97 46 55 98 04 55 97 49 55 97 22 00 97 13 00 97 13 35 99 06 39 96 24 39 96 20 22 96 07 57 9() 05 30 97 15 55 97 07 30 95 44 48 95 11 14 95 08 00 95 05 12 Lun. Int. H. W. h. m. 8 22 8 24 8 40 9 20 9 44 12 17 42 11 32 42 2 00 [12 10] [11 10] iii'28i [11 25] [1 35] [12 00] [0 20] [0 23] [11 53] [11 15] [10 55] [10 54] [11 00] [11 50" [0 18 [0 40 2 17 3 17 [4 18] [4 07] L.W. 00 05 20 36 21 6 10 6 19 5 07 7 13 Range. Spg. Neap. ■ft 2.6 1.9 1.5 1.6 1.4 2.3 1.4 1.8 3.1 8 30 2. 6 [5 35] i [2.5] [4 55] [4 20] [3 09] [6 50] [5 40] [5 45] [6 35] [5 33] [5 00] [4 42] [4 41] [4 35] [4 25] [155] 4 47] '5 38] 6 33] 6 56] 8 41 9 36 [10 33] [10 23] [10 47] [10 35] [8 03] [1 06] [7 19] [2 49] [8 38] [2.1]; [1.7] J. 5] [2.1] 2.0] 2.3] [2.1] [1.8] [1.6] [1.7] [1.9] 2.1] 2.0] 2.2] 2.0] 1.7 0.9 [1.4] [1.6] [1.6] [1.6] [1.4] [1.3] [2.4] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA, EAST COAST OF NORTH AMERICA— Continued. [Page 197 Place. Zapotitlan Point: Light-house San Juan Point: Light-house Coatzacoalcos: Light-house Santa Ana Lagoon: Entrance Tupilco River: Entrance Tabasco River: Light-house Carmen Island : N E. pt Laguna de Terminos: Vigia tower, W. end Carmen I Paypoton Mount: Summit Lerma: Church Campeche: Light-house Fort San Jo^6 Point Palmas Sisal : Fort light Madagascar Reef: Center Progreso: Light-house Silan: Village Lagartos: Milage Cape Catoche: Light-house Areas Cays: Light-house Obispo Shoal : 16-foot spot New Bank : Center Triangles, E. reef: Beacon Triangles, W. reef: Cay at SW. end Bajo Nuevo Reef: Center Arenas Cays: N W. Cay Alacran Reef: Perez Cay Con toy Island : Light-house Mugeres Island : Light-house Cancun Island: Nisuc Pt Cozumel Island: N. pt. light-house S. pt. light-house Ascension Bay : Allen Pt Chinchorro Bank: Cayo Lobos light Half-Moon Cay: Light-house Mauger Cav, NW. end: Light-house Glover Ree'f : SW. Cay English C^y : Light-house St. Georges Cay : Center Sand-Fly Cays": II ut, S. end South Water Cay : Center Belize: Fort George light 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 River: Entrance, W. side Dulce Gulf: Fort St. Philip Isabel Hospital Bight: Hut, N. pt. of entrance. Cape Three Points: NAV. extreme Seal Cays: S. Cay Omoa: Entrance Cape Triunfo: Bluff pt Congrehoy Peak: Summit, 8,040 feet Truxillo: Fort Utilla Island: S. Cay Hog Islands: Highest hill on W. islet. . . Roatan: Center of Coxen Cay Port Royal, NW.pt. of GeorgeCay Bonacca Island: Summit, 1,200 feet Misteriosa Bank: S. Point Swan Islands: NW. pt. of W. I Lat. N. Long. W. Lun. Int. Range. H. W. L. W. Spg. Neap. O 1 II 18 34 00 O 1 II 94 50 00 94 38 57 94 24 46 93 51 53 93 25 25 92 42 00 91 30 50 91 50 17 90 43 27 90 36 11 90 32 20 90 30 51 90 22 00 90 02 37 90 18 27 89 39 30 88 54 27 88 10 27 87 04 10 91 57 45 92 13 27 91 52 27 92 12 47 92 18 57 92 04 26 91 24 21 89 41 45 86 48 00 86 43 39 86 46 45 86 43 55 86 59 04 87 28 27 87 23 40 87 32 30 87 46 30 87 50 50 88 03 20 88 04 45 88 06 05 88 05 36 88 11 20 88 13 48 88 15 15 88 37 40 88 22 13 88 35 51 88 56 20 88 46 22 89 01 36 89 09 44 88 33 22 88 38 50 88 20 15 88 04 31 87 27 46 86 55 00 85 59 18 86 59 15 86 32 09 86 34 27 86 18 41 85 55 00 84 02 00 83 56 27 h. m. h. m. ft. ft. 18 19 45 18 08 56 18 18 49 18 26 44 18 39 30 18 47 08 18 38 44 19 38 00 [12 16] [6 00] [1.6] 19 48 24 1 19 50 20 19 51 36 2 59 9 28 2.1 1.3 21 02 00 1 21 10 06 21 26 30 10 20 4 10 1.8 0.9 21 17 00 21 23 00 1 21 36 30 21 35 50 20 12 45 20 29 00 9 30 [12 06] 3 19 [5 50] 1.5 [1.6] 0.8 20 32 00 20 54 54 20 58 00 [12 00] [5 45] [1.6] 21 50 00 22 07 10 22 23 36 .... 21 33 00 21 12 00 21 03 00 9 20 3 08 1.6 0.9 20 35 50 20 16 20 8 20 2 08 1.5 0.8 19 46 55 18 23 20 17 12 15 17 36 15 16 42 20 17 19 30 17 33 15 16 57 50 16 48 50 17 29 20 16 57 40 8 00 1 50 1.5 0.8 16 47 45 16 48 10 16 30 54 16 14 15 15 54 00 15 49 45 15 38 00 9 00 2 50 2.0 1.1 15 24 20 15 52 20 15 57 45 16 08 00 15 47 11 I 15 48 45 15 38 00 15 55 45 16 03 40 15 58 00 16 18 00 16 24 20 7 35 1 23 3.5 1.8 16 28 00 18 44 00 8 50 2 38 1.5 0.8 17 24 30 Page 198] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. EAST COAST OF NORTH AMERICA— Continued. o s « j §2 8 • s « ■M i a 1 c PS !fi S 5 Place. L*t. N. Long. W. Lun. Int. Range. 1 H. W. L. W. Spg. Neap. • Great Rock Head : Bluff extreme Cape Camaron o / « 15 53 00 16 00 00 15 51 50 15 48 50 15 23 40 15 00 00 16 03 30 o / // 85 27 10 85 03 00 84 38 33 84 17 10 83 42 36 83 10 00 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 81 43 06 81 27 53" 81 49 54 83 21 27 83 23 10 83 37 12 83 45 57 83 41 57 82 58 35 83 03 35 83 42 15 83 47 27 83 02 00 82 39 06 82 21 47 82 20 31 83 03 27 82 20 33 82 07 51 81 55 02 81 33 57 h. m. h. m. ft. ft. Brewers Lagoon: E. side of entrance Patook River: E. side of entrance Carataska Lagoon: E. side of entrance . . Cape Gracias-d-Dios: Light-house Caxones Reef: Great Hobby Islet 10 20 4 07 2.0 1.1 GordaBank: Gorda Cay ' 15 52 00 Farrall Rock: Center 15 51 00 Half-Moon Cay: Center 15 08 50 15 07 00 14 21 12 16 54 00 15 47 45 14 21 33 14 08 00 14 30 00 13 34 30 13 22 54 12 31 40 12 24 00 12 10 00 14 03 00 12 22 35 12 20 39 12 15 30 11 59 00 12 17 30 12 09 17 10 56 15 10 01 30 10 00 05 9 38 30 9 25 45 9 24 47 9 16 30 9 14 22 9 14 30 9 10 30 9 06 30 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 j Old Providence: Isabel House 4 00 io 13 i.6 0.5 St. Andrews Island : SW. cove, Entrance I . Courtown Cays: Middle Cay 1 Albuquerque Bank: Smith Cay ' Brangmans Bluff: Extreme Pearl Cays: Colombilla Cay 1 50 8 03 2.0 1.1 Pearl Cays Lagoon: Mosquito Pt Cookra Hill : Summit Bluefields: Schooner Pt 1 40 7 52 2.0 1.1 Little Corn Island : Gun Pt Great Corn Island: Wells N. of Quin Bluff. Greytown : Light-house 1 35 1 00 7 47 7 13 2.0 1.5 1.1 0.8 Mount Cartago: Peak, 11,100 feet Port Limon: Grape Cay light 1 00 7 13 1.6 0.9 Carreta Point: Extreme Tirby Point: Extreme Columbus Island : Lime Pt Blanco Peak: Summit, 11,740 feet Shepherd Island: Hut on summit Cobbler Rock: Center Valiente Peak: Summit, 722 feet Escudo de Veragua: W. pt. of island 1 ........I ..... 1 WEST COAST OF NORTH AMERICA. • 1 Point Barrow: Highest lat. of U. S 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 65 00 00 64 26 00 63 26 00 63 34 30 61 40 00 63 16 00 63 50 00 60 18 00 60 13 00 60 25 22 58 48 31 156 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 30 168 02 00 165 05 00 162 02 30 162 42 30 166 15 00 168 41 00 171 31 00 172 02 00 172 36 00 166 08 30 160 50 00 11 41 5 33 0.6 0.2 Cape Lisburne: 849 feet Cape Krusenstern : Extreme Chamisso Island : Summit 7 45 1 50 2.0 0.6 Cape Espenberg: Extreme Diomede Island: Fairway Rock Cape Prince of Wales: W. pt 1 . Port Clarence: Point Spencer 6 10 1 10 1.1 0.9 King Island: N. pt Cape Nome: Extreme [2 05] ;8 05] rs 25] r2.ni St. Michael: Fort [1 20]' [4.5]i 1 Stuart Island: W. pt Cape Romanzof : Extreme St. Lawrence Island : E. pt NW.pt 1 St. Matthew Island: SE.pt 4 40 11 3. 1 1.6 Pinnacle Islet: Summit, 930 feet Nunivak Island : Cape Etolin Hagenmeister Islant ! 1 ":r: r i APPENDIX IV. MAKITIME POSITIONS AND TIDAL DATA. WEST COAST OF NORTH AMERICA— Continued. [Page 199 Place. Cape Menchikof : Extreme Port Moller St. George Island: S. side Lat. N. Attu Island: Chichagof Harbor Kiska Island : Kiska Harbor, Ast. sta . . . Amchitka Island : Constantine Harbor . . Adakh Island : Bay of Islands Atka Island: Nazan Bay (church) Pribilof Island: St. Paul I., village Unalaska Island: C. S. station, Iliuliuk . Sannakh Reefs: S. edge Sannakh Island : NE. end Unga Island Popof Island : Humboldt I Nagai Island : Sanborn Harbor Koniushi Island: NW. harbor NE. harbor Simeonof Island : Simeonof Harbor Cape Strogonof : Extreme Chignik Bay : Anchorage Anowik Island : S. end Chiachi Islands Light-House Rocks Chirikof Island Kodiak Island, St. Paul Harbor: Cove N W. 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: J^xtreine Massett Harbor: Uttewas village Cape Edenshaw : Extreme Hecate Bay: Observatory Islet Stamp Harbor: Observatory Islet... Island Harbor: Observatory Islet... Cape Beale: Light-house Refuge Cove: Village on W. side . . . Hesquiat Harbor: Boat Cove Estevan Point: S. extreme Nootka Sound : Friendly Cove Port Langford: Colwood Islet Esperanza Inlet: Observatory Rock. Kyuquot Sound : Shingle Pomt Nasparti Inlet: Head Beach Cook Cape: Solander I North Harbor: Observatory Rock. . . 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 56 48 00 56 19 20 56 05 13 55 51 58 55 45 24 55 48 22 57 47 57 60 20 43 59 27 22 60 20 45 59 33 42 58 36 57 57 02 52 58 18 00 56 27 00 54 15 00 54 10 30 52 56 31 52 09 07 51 54 00 53 02 00 53 22 20 54 13 00 54 01 40 54 04 30 49 15 22 49 13 46 48 54 41 48 47 23 49 20 50 49 27 31 49 22 07 49 35 31 49 47 20 49 52 45 49 59 55 50 11 21 50 06 31 50 29 25 Long. W. 157 58 30 160 34 54 169 39 50 Long. E. J 73 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 03 158 46 00 158 24 24 156 39 19 159 05 24 157 27 04 155 42 51 152 21 21 146 37 38 146 18 45 141 00 12 139 46 16 137 40 06 135 19 31 134 24 00 132 23 00 132 56 20 132 57 50 132 09 06 131 03 20 131 01 26 131 31 00 131 51 00 131 34 00 132 10 00 132 20 56 125 55 43 124 50 07 125 16 54 125 13 14 126 16 06 126 24 53 126 31 58 126 36 58 126 56 31 126 59 21 127 08 56 127 37 24 127 56 46 128 03 05 Lun. Int. H.W. h. m. 3 35 3 30 3 25 4 17 3 50 12 13 2 40 2 20 1 45 16 50 34 06 45 30 00 07 12 15 45 12 20 12*65' 12 05 11 55 11 50 11 47 L. W. h. m. 9 48 9 43 9 38 10 29 9 58 6 10 8 55 8 33 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 Range. Spg. ft. 5.7 5.2 5.0 2.7 2.9 5.7 8.2 7.5 8.1 9.0 10.1 9.5 9.9 18.6 17.7 11.5 12.8 10.0 12.4 9.9 io.'s' 9.7 9.3 9.3 Neap. 2.9 2.7 2.6 1.4 1.5 2.8 4.1 3.8 4.0 4.5 5.1 5.0 5.2 9.7 9.2 5.7 5.8 7.1 5.7 5.9 5.6 5.5 5.3 5.3 Page 200] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. WEST COAST OF NORTH AMERICA— Continued. Place. Lat. N. Lun. Int. Long. W. H.W. L.W. Range. Spg. Neap. Koprino Harbor: Observatory Rock Hecate Cove : Kitten Islet Triangle Island : *NV. side Cape Scott: Summit Bull Harbor, Hope Island : N. pt. Indian I . Port Alexander: Islet in center Beaver Harbor: Shell Islet Cormorant I.: Yellow Bluff in Alert Bay. Baynes Sound : Beak Pt Nanoose Harbor: Entrance Rock Nanaimo: Light-house Benson's House Victoria: Light-house Esquimalt: Fisgard I. light Race Island : Light-house Sooke Inlet : Secretary I Port Sail Juan : Pinnacle Rock 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 Atkinson Point: Light-house Vancouver, Burrard Inlet: Govt. Re- serve, English Bay Eraser River: Garry Pt New Westminster: Military barracks Point Roberts: Parallel station Semiamoo Bay : Parallel station Admiralty Head : Light-house , Steilacoom: Methodist Church Seattle: C. S. ast. station Port Townsend : C. S. ast. station Smith Island : Light-house New Dungeness: Light-house Port Angeles: Ediz Hook light-house Cape Flattery : Light-house Cape Shoalwater: Light-house Cape Disappointment: Light-house .. Kalama : Methodist Church Bremerton : Navy-yard flagstaff Tacoma: St. Luke Church Astoria: Flagstaff Yaquina Head : Light-house Cape Arago, or Gregory: Light-house .. Cape Blanco : Light-house Crescent City: Light-house Trinidad Head : Light-house Eureka: Methodist Church Humboldt: Light-house Cape Mendocino: Light-house Point Arena: Light-house Point Reyes: Light-house San Francisco: Coast Survey ast. station . Presidio station . Mare Island: Stone block, obs. station. . Benicia: Church Farallon Islet: Light-house Santa Clara: Catholic Church Mount Hamilton: Obs. peak San Jos^: Spire Pigeon Point: Light-house 50 30 00 50 32 26 50 51 53 50 46 41 50 54 47 50 50 49 50 42 36 50 35 02 49 36 29 49 15 43 49 12 50 49 10 1ft 48 25 26 48 25 50 48 17 53 48 19 .35 48 33 30 50 33 58 50 31 09 50 24 15 50 02 42 49 24 39 49 19 42 49 16 18 49 07 04 49 13 01 49 00 00 49 00 00 48 09 19 47 10 20 47 35 54 48 06 56 48 19 07 48 10 52 48 08 24 48 23 30 46 43 00 46 16 29 46 00 26 47 33 24 47 15 32 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 55 37 47 30 38 05 53 38 03 05 37 41 51 37 20 49 37 21 03 37 19 58 37 10 49 127 51 42 127 35 44 129 05 58 128 26 11 127 55 29 127 39 23 127 24 33 126 56 56 124 50 44 124 07 32 123 48 11 123 56 02 123 23 28 123 26 46 123 31 47 123 42 40 124 27 37 126 16 06 126 03 47 125 38 26 125 14 34 123 28 46 123 15 54 123 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 50 39 122 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 24 32 122 27 49 122 16 16 122 09 23 123 00 07 121 56 26 121 36 40 121 53 39 122 23 39 ft. 10 32 30 55 4 45 4 52 4 40 [2 17] [2 00] 4 59 08 12 22 3 39 4 27 4 32 15 11 50 11 55 11 33 11 27 11 57 11 33 11 00 10 36 11 23 12 07 11 43 1 05 1 35 10 40 6 22 6 44 6 42 7 08 11 00 11 18 10.7 11.6 11.5 12.8 10.6 10.2 11 05 [8 31] [8 14] [5.7] [5.8] 8 10 8 47 10 00 10 15 11 58 11 35 12 01 11 23 14.1 16.0 15.7 7.2 9.0 7.8 8.2 7.0 11 10 7.1 11 04 10 33 9 32 9 28 8 34 8 23 6 16 11.0 9.2 7.1 6 19 11 25 10 35 10 45 6 42 5 37 5 49 5 15 5 11 5 45 5 19 4 50 4 21 5 08 5 34 5 07 7 15 7 48 4 25 7.7 3.2 9.4 9.8 7.8 7.3 6.0 4.1 5.1 5.1 4.6 5.6 5.6 4.5 appp:ndix IV. MARITIME POSITIONS AND TIDAL DATA. * WEST COAST OF NORTH AMERICA— Continued. [Page 201 1 Place. Lat. N. Long. W. Lun. Int. Range. H. W. L. W. Spg. Neap. • £ u. © i s .0 u Santa C niz : Warehouse flagstaff Monterey: C. S. azimuth station Point Pinos: Light-house o / // 36 57 31 36 35 21 36 37 55 35 39 50 34 26 49 34 26 10 34 15 46 33 42 14 34 03 05 32 39 48 32 43 06 32 31 58 34 04 19 33 56 30 34 03 12 34 00 25 33 28 16 33 14 55 33 23 09 31 51 10 31 33 04 30 57 39 30 28 58 30 22 16 29 47 20 29 25 29 29 10 50 28 56 06 28 40 16 28 14 26 28 03 52 28 18 08 27 39 35 27 06 10 26 45 45 26 42 49 26 18 56 26 03 18 24 58 00 24 47 31 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 O / " 122 01 29 121 52 59 121 56 02 121 17 06 120 28 18 119 42 42 119 15 56 118 17 41 118 14 32 117 14 37 117 09 41 117 07 32 120 21 55 119 58 29 119 33 51 119 23 04 119 02 29 119 31 19 118 24 05 116 38 05 116 40 51 116 17 28 116 06 46 115 59 07 115 48 12 115 12 14 118 18 30 114 31 06 114 14 15 114 06 21 115 11 32 115 36 10 114 54 27 114 17 25 113 16 25 113 35 04 112 41 44 112 17 52 115 51 54 112 18 25 112 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 no 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 h. m. 10 54 10 43 h. m. 4 27 4 24 ft. 5.2 4.8 ft. 3.3 3.1 Piedras Blancas: Light-house Point Conception : Light-house Santa Barbara: N. tower, Mission Church San Buenaventura: C. S. ast. station Pt. Fermin, San Pedro Bay: Light-house. Los Angeles: Court-house 9 37 9 53 9 36 3 15 3 21 3 13 4.8 4.9 5.5 2.2 2.2 2.5 Point Lonia: Light-house 9 29 9 32 3 07 3 20 5.2 5.1 2.3 2.3 San Diego: C. S. ast. station Mexican Boundary : Obelisk San Miguel Island": Seal Pt 9 23 3 02 4.9 2.2 Santa Rosa Island : P-. pt Santa Cruz Island : NE. pt 9 29 3 06 4.9 2.2 Anacapa Island : E. pt Santa Barl)ara Island : Summit : :::::::: i San Nicolas Island: Summit 9 20 9 28 9 28 3 04 3 08 3 06 4.9 5.1 6.0 2.2 2.3 2.2 Santa Catalina Island: Catalina Peak . . . Ensenada Harbor: Head of bay, close to beach San Tomas: NW. shore of cove Colnett Bay: Head of bav 9 27 3 05 5.8 2.6 San Martin Island: Hassler Cove Port San Quentin: Sextant Pt 9 23 3 00 4.9 2.2 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 9 15 2 53 7.6 3.4 9 05 2 42 7.8 3.5 San Benito Island: Summit of W. island. San Bartolom6: N. side of entrance Asuncion Island: Summit of island San Ignacio Point: J* xtreme 9 00 2 37 8.2 2.8 Abreojos Point: Extreme of rocky ledge. Sau Domingo Point: Edge of clifi San Juanico f*oint: Knoll Alijos Rocks : South Rock 9 00 2 48 6.7 2.3 8 29 2 17 5.7 1.6 Cape San Lazaro: Extreme Magdalena Bay: Obs. spot (post) N^ of Port Magdalena 8 25 2 12 5.5 1.5 Cape Tosco: Extreme El Conejo Point: Extreme Todos Santos: Foot of hill, Lobos Pt San Lucas: Steep sand beach, NW. pt. of bay San Jose del Cabo: NE. side of entrance. Arena Point : Extreme l... Arena de la Ventana: Extreme 8 36 2 20 4.5 1.2 Pichilinque Bay: SE. pt. of San Juan, Nepomezeino I ! La Paz: Obs. spot, El Mogote Lupona Point: P^xtreme 9 40 3 34 5.4 1.3 San f^varisto: 3 m. S. of S. Evaristo Hd. San Marcial Point : E.xtreme Salinas Bay: Beach, NE. pt. of bay. Loreto: Cathedral Pulpito Point: Summit Muleje: Equipalito Pt San Marcos Is'and: S. sand spit Santa Maria Cove: Beach on NW. shore. San Carlos Point: Extreme Santa Teresa Bay: Beach on N. side 11 50 5 47 11.2 2.6 Page 202] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. "WEST COAST or NORTH AMERICA— Continued. Place. Las Animas: Lo^ pt Raza Island: Landing place, S. side. Angeles Bay: Bight on NW. shore.. Remedios Bay: Beach on W. shore . Mejia Island: S. side San Luis Island: SE. side San Firinin: Beach, N. of bight San Felipe Point: Peak, 1,000 feet 28 47 40 28 49 11 28 56 39 29 13 52 29 33 08 29 57 27 30 25 16 31 02 57 Philips Point: Beacon ! 31 46 10 Lat. N. Long. W. Georges Island : NE. shore Cape Tepoca: Hill, 300 feet Libertad Anchorage: Beach Patos Island : SE. end Tiburon Island: SE. end Kino Point: 0.2 mile N. 88° W. of mound. San Pedro: N. side of bay Guaymas: Light-house Claris Island : NW. part Santa Barbara: N W. side of bay Agiabampo: SE. side of entrance Topolobampo : SE. end of Santa Maria I . . Navachista: W. side of creek Playa Colorado: N. side of entrance Altata: N. side of entrance Mazatlan : Light-house Palenita Village: Boca Tecapan San Bias: Custom-house Maria 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... ManzanillaBay: 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: Light-house Maldonado: El Recordo Pt Port Angeles: Light-house Sacrificios Point: Highest pt. of cape Port Guatulco: Cross Morro Ayuca: SummitofN. edge of cape. Salina Cruz: Light-house Champerico: Inshore end of iron wharf. . San Jos6 de Guatemala: Light-house Acajutla: Light-house Libertad: Light-house La Union : Light-house Chicarene Point: Extreme Corinto: Light-house San Juan del Sur: Signal station Salinas Bay : Salinas Islet Port Culebra: Extremity of Mala Pt Ballena Bay: N. Estero Toussa .' Parida Anchorage: S. pt. of Deer Id Port Nuevo: Entrada Pt Bahia Honda: W. end of Centinela I Coiba (Quibo) Island: Observation pt. . , 31 00 54 30 16 05 29 54 12 29 16 12 28 45 55 28 45 28 28 03 22 27 50 28 26 58 59 26 41 09 26 16 35 25 33 56 25 23 06 25 11 42 24 38 52 23 10 40 22 30 26 21 32 30 21 30 45 20 45 50 20 36 26 20 25 00 19 34 48 19 17 15 18 42 57 18 59 41 18 20 55 10 17 00 19 13 25 19 03 15 17 58- 21 17 40 15 17 37 50 17 31 28 17 16 13 16 49 10 16 19 37 15 39 09 15 40 41 15 44 58 15 52 17 16 09 49 14 17 44 13 55 15 13 34 20 13 28 49 13 20 00 13 17 09 12 27 54 11 14 45 11 03 10 10 36 46 9 43 45 8 10 13 8 04 30 7 43 32 7 24 20 113 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 28 109 57 17 109 40 48 109 17 30 109 10 23 108 49 00 108 23 37 107 59 37 106 26 47 105 44 25 105 18 40 106 33 14 105 33 37 105 16 00 105 39 21 105 08 54 110 49 22 110 56 53 112 04 07 114 44 17 109 13 00 104 43 26 104 19 50 102 07 06 101 40 25 101 33 23 101 27 14 101 04 32 99 55 50 98 35 05 96 30 43 96 15 04 96 08 10 95 46 43 95 12 31 91 55 36 90 49 45 89 50 26 89 19 25 87 51 00 87 47 06 87 12 31 85 52 59 85 43 38 85 42 46 85 00 46 82 14 32 81 43 30 81 31 58 81 41 51 Lun. Int. Range. H.W. h. m. 11 30 10 07 9 08 08 9 07 9 07 50 L.W. h. m. 2 50 2 50 2 55 3 05 3 15 2 55 3 00 2 50 2 45 3 15 3 10 3 59 2 51 5.8 3.8 2 52 3. 2 2 53 2.5 2 54 I 1.9 '2'38T'2.'6* 9 02 9 02 9 08 9 18 9 28 9 08 9 12 9 02 8 58 9 28 9 22 8.5 9.0 9.5 10.0 10.5 10.5 10.0 9.5 9.0 Neap. 5 26 i 5.0 1.2 1.4 0.9 1.0 1.1 1.3 0.9 4.6 4.9 5.1 5.4 5.7 5.7 5.4 5.1 4.9 10. 5 5. 7 11.0 5.9 APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. WEST COAST OF NORTH AMERICA— Continued. [Page 203 o Place. Lat. N. Long. W. Lun Int. Range. H. W. L. W. Spg. Neap. ii s Cocos Island : Head of Chatham Bay Panama: NE. bastion, ast. station Taboga Island : Church O 1 II 5 32 57 8 57 12 8 47 45 7 27 40 4 03 00 O 1 II 86 59 17 79 32 05 79 33 16 79 59 25 81 36 00 h. m. h. m. ft. ft. 3 00 3 00 3 10 9 14 9 13 9 22 16.0 15.4 13.0 8.7 8.3 7.0 Cape Mala : Extreme Malpelo Island: Summit i 1 1 WEST INDIA ISLANDS. i K M & P s Memory Rock : Center Bahama Island : W. pt 26 56 53 26 41 18 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 09 41 74 29 34 74 53 44 75 .33 18 75 36 59 75 47 18 75 47 40 75 52 18 76 07 48 7 40 1 28 3.2 L7 Abaco Island : Light-house 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 10 20 21 40 20 41 41 20 47 14 21 04 24 21 09 00 21 07 00 21 07 30 21 07 05 1 Little Guana Cav : Light-house Walker Cay: Highest part Great Isaac Cay: Light-house Gun Cay : Light-house 8 20 2 08 ...... 3.0 1.5 Ginger Cay: Center Cay Lobos: Light-house St. Domingo Cav : Center Cay Verde: Hill at S. end Ragged Island : Gun Pt Nairn Cay : E. pt Nurse Channel Cay : Beacon Long Island: S. pt Great Emma Island : Beacon 1 Clarence Harbor: Light-house 8 20 7 00 2 08 48 4.1 4.0 2.1 2.1 Eleuthera Island : Light-house Royal Island : Eastern Pass Nassau: Light-house 7 20 7 40 1 08 1 28 4.0 3.0 2.1 L5 Andros Island : Light-house Great Stirrup Cav : Light-house Little Stirrup Cay : W. end San Salvador ( Cat I. ) : Light-house Concepcion Island : AY. bay 7 00 48 4.0 2.1 AVatlings IslarSd: Hunchinbroke Rock .. Rum Cay : Harbor Pt 1 1 Castle Island : Light-house Fortune Island : S. end 1 Crooked Island: Moss flagstaff " Bird Island: Light-house Samana Cay: W. pt 1 Plana Cay: NW. pt. j Mariguana Island : SE. pt 7 20 1 08 3.0 1.5 Hogsty Reef: NW. Cay Inagua Island: Light-house 7 50 1 38 3.5 1.8 Little Inagua Island: N W. pt W. CaicosCay: Hill, SE. end French Cay: W^. pt I Fort George Cay: Old magazine Caicos Island: Parsons Pt., S. islet Turk Island : Light-house 7 30 1 18 3.0 1.5 Square Handkerchief Bank: NE. breaker Silver Bank : E. extreme f Navidad Bank : Center of E. side Cape Maysi : Light-house 5 40 11 53 2.8 1.6 Port Baracoa: Light-house Port Cavo Moa: Carenero Pt Port Nipe: Roma Pt Lucrecia Point: Light-house Port Sama: E. side of entrance Peak of Sama: Summit, 885 feet Port Naranjo: E. side of entrance Jibara: Fort San Fernando 6 20 08 2.4 1.4 Port Padre: Guinchos Pt 21 18 30 76 35 34 21 37 30 77 04 ,34 Port Nuevitas: Light-house 7 00 48 2.2 1:2 1 Page 204] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. WEST INDIA ISLANDS— Continued. Place. Maternillos Point: Light-house Cay Verde: NW. «nd Cay Contites: S. pt Paredon Grande Cay : Light-house Cay Sal : Light-house Bahia de Cadiz Cay: Light-house Piedras Cay : Light-house Matanzas: Summit of peak Habana: Morro Hght- house Transit pier, arsenal yard Cape San Antonio : Light-house San Felipe Cays: SW. pt Isle of Pines: Port Frances Piedras Cay : Light-house Cienfuegos: Colorados Pt. light Cape Cruz: Light-house Santiago de Cuba: Light-house Port Guantanamo : Fisherman Pt Cayman Brae: E. pt Little Cayman : W. pt Grand Cayman: Fort George, W. end Morant Point : Light-house Port Antdnio : Folly Pt. Light Port Maria: NW. wharf St. Ann Bay: Long wharf Falmouth : Fort Montego Bay : Fort St. Lucia: Fort Savanna-la-Mar : Fort Kingston : Plum Pt. light Port Royal: Fort Charles, flagstaff Morant "Cays: NE. Cay Pedro Bank: Portland Rock, E. end Baxo Nuevo: Sandy Cay Samana Town : Fort Cape Cabron : Extreme Port Plata: Light-house Grange Point: W. end Manzanilla Point: Presidente Pt Cape Haitien : Town fountain Port Paix: Wharf Nicolas Mole: Fort George, flagstaff Gonaives: Verreur Pt Gonave Island : W. pt Arcadius Islands: Light-house Port au Prince: Fort Islet light Petite Riviere Village: Sand beach in front of huts Jeremie: Fort Navassa Island: N. extreme Formigas Bank: Shoal spot Vache Island: Sand beach, near NW. pt. Jacmel : Wharf .•. Beata Island : NW.pt Frayle Rock: Center Alta Vela: Summit Avarena Point: Extreme Salinas Point ( Caldera) : Extreme St. Domingo City : Light-house Point Espada: Extreme Lat. N. 21 40 02 22 08 45 22 11 14 22 29 10 23 56 30 23 12 34 23 14 10 23 01 54 23 09 21 23 08 03 21 51 44 21 55 00 21 35 30 21 57 45 22 01 58 19 50 13 19 57 31 19 54 39 19 45 15 19 39 10 19 17 45 17 55 05 18 11 31 18 23 00 18 26 24 18 30 34 18 29 25 18 27 45 18 12 20 17 55 32 17 55 56 17 26 30 17 06 20 15 53 00 19 12 29 19 21 17 19 49 15 19 54 45 19 45 34 19 46 20 19 57 40 19 49 15 19 25 42 18 55 26 18 48 13 18 33 54 18 37 15 18 38 15 18 25 10 18 33 00 18 06 00 18 13 30 17 36 45 17 37 00 17 28 50 18 07 00 18 12 00 18 27 54 18 19 43 Long. W. 77 08 77 37 77 39 78 09 80 27 80 29 81 07 81 43 82 21 82 21 84 57 83 31 83 09 81 07 80 26 77 43 75 52 75 09 79 46 07 80 07 17 81 23 17 76 11 08 76 26 31 76 54 22 77 12 52 77 39 52 77 56 16 78 10 52 78 08 54 76 46 45 76 50 38 75 58 20 77 26 28 78 39 04 19 23 16 00 41 23 39 03 47 20 11 42 49 45 23 07 42 52 18 34 39 05 22 01 74 23 55 74 05 54 75 02 03 75 44 24 73 43 40 72 34 30 71 33 44 71 41 00 71 39 11 70 59 18 70 35 18 69 52 00 68 27 34 Lun. Int. Range. H. W, h. TO. 7 20 30 18 30 4 47 8 20 7 50 9 00 6 50 L. W. h. TO. Spg. I Neap. 1 08 2 18 1 56 2 18 11 00 2 30 2 00 2 48 39 [1.3]!. I [1.1]. [1.2] [LI] 3.0 5.5 [1.2] [2.5] [2.2] ft. I ft. 2.8 t 1.6 2.2 1.2 1.3 I 0.7 1.5 I 0. 2.0 i 1.1 2.2 I 1.1 2.6 I 1.3 1.5 2.9 APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. WEST INDIA ISLANDS— Continued. [Page 205 Place Mona Island : Light-house Mayaguez : Mouth of Mayaguez R Aguadilla Bay : Village San Juan de Porto Rico: Morro light- house Cape San Juan : Light-house Guanica: Meseta Pt Culebrita Island : Light-house Vieques (Crab) Island: Port Ferro light. St. Thomas: Fort Christian, SW. bastion. St. John Island : Ram Head Tortola: Fort Burt Virgin Gorda: Vixen Pt Anegada: W. pt E. extreme of reefs Christiansted, Santa Cruz: SW. bastion of fort Sombrero : Light-house Dog Island : Center Anguilla: Custom-house St. Martin : Fort Marigot light St. Bartholomew : Fort Oscar Saba : Diamond Rock St. Eustatius: Fort flagstaff St. Christopher: Basseterre Church Booby Island : Center Nevis: Fort Charles Barbuda: Flagstaff, Martello Tower Antigua, English Harbor: Flagstaff, dockyard Sandy Island : Light-house . . Redonda Islet: Center Montserrat: Plymouth Wharf Guadeloupe, Basseterre: Light on mast. Port Louis: Light on mast Gozier Islet: Light-house. Manroux Id. : Light-house Point h Pitre: Jarry Mill. . Desirade: E. pt Petite Terre : Light-house Marie Galante: Light-house Saintes Islands: Tower on Chameauhill Dominica, Prince Ruperts Bay: Sand beach W. of church Roseau: Flagstaff, Fort Young Aves Island : Center Martinique, Fort de France: Fort St. Louis light St. Pierre: Ste. Marthe Bat- tery CaravellePen.: Light-house Cabrit Islet: Summit St. Lucia, Port Castries: Light-house... Barbados, Bridgetown: Flagstaff, Rick- ett's Battery S. Point: Light-house Ragged Point: Light-house . St. Vincent, Kingstown: Light-house.. Bequia Island, Admiralty Bay: Church Grenada: St. George light-house Tobago, Rocky Bay: Light-house Lat. N. Long. W. Lun. Int. Range. H. W. L. W. Spg. Neap. ' n 18 02 43 o / r/ 67 50 30 67 09 04 67 16 08 66 07 28 65 36 31 66 54 11 65 13 34 65 25 26 64 55 52 64 42 03 64 36 47 64 21 48 64 24 58 64 10 45 64 42 16 63 28 13 63 16 00 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 61 28 14 61 23 52 63 37 46 61 04 30 61 11 12 60 53 20 60 52 33 61 00 48 59 37 19 59 31 50 59 26 04 61 14 34 61 14 09 61 45 06 60 42 38 h. m. h. TO. ft. ft- 18 11 56 18 25 09 7 04 2 00 2.0 1.0 18 28 56 18 23 05 8 21 2 20 1.3 0.9 17 57 10 [1.0] 1.0] ;i-i] [1.2] 18 18 44 18 05 20 18 20 23 18 18 08 [7 31] [7 35] [7 11] [1 30] [1 40] [0 58] 18 25 04 18 30 39 18 45 11 18 36 30 17 45 09 18 35 37 18 16 42 18 13 06 18 04 07 17 53 58 [1.5] 17 39 10 17 29 10 17 18 12 17 13 38 17 07 52 17 35 50 17 00 00 [2.0] 17 06 54 16 55 18 16 42 12 15 59 50 16 25 09 16 11 57 [1.3] 16 13 14 16 13 56 16 19 56 16 10 17 15 52 59 15 51 32 15 34 34 15 17 27 4 00 10 12 1.5 0.8 15 42 00 14 35 44 14 43 54 14 46 13 14 23 23 3 50 10 02 1.1 0.6 14 01 54 13 05 42 13 02 45 2 50 9 02 3.0 1.5 13 09 40 1 13 09 19 13 00 25 2 50 9 05 1.6 0.8 12 03 02 11 10 08 2 30 3 50 8 42 10 02 1.5 2.1 0.8 1.1 Page 206] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. WEST INDIA ISLANDS— Continued. Place. Lat. N. Long. w. Lun. Int. Range. 1 H. W. L. W. Spg. Neap. Testigos Islets: Center of Testigo Grande. Sola Island : Center O t II 11 25 02 11 19 00 10 59 43 10 57 45 11 47 57 11 56 16 12 02 06 11 59 30 12 06 45 12 06 36 12 31 05 O 1 II 63 05 48 63 36 00 h. m. h. m. ft. ft. Pampatar, Margafttal. : San Carlos Castle . •Tortugas Island: S. end of W. Tortugillo Islet 63 48 00 65 26 38 66 12 31 66 39 10 68 14 10 68 39 19 68 56 44 68 56 36 70 02 34 Orchila Island : S. side Roques Islands: Pirate Cay . Bonaive Island: Light-house Little Curasao Island : Light-house Curasao Island: Time-ball station Light-house Oruba Island: Light-house ' NORTH AND EAST COASTS OF SOUTH AMERICA. i s 9 W i a > •9 « 1 Chagres: San Lorenzo Castle 9 19 27 9 22 39 9 22 09 9 32 30 8 54 52 8 47 00 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 12 23 09 12 04 00 10 57 30 11 48 56 12 11 00 12 29 15 11 27 56 10 47 00 11 10 00 10 29 53 10 36 57 10 35 00 10 34 06 10 49 30 10 13 30 10 27 20 10 40 00 10 42 00 10 40 00 10 40 15 10 42 00 10 43 27 10 45 00 10 44 19 10 43 48 10 38 15 8 39 25 10 38 37 10 40 03 10 50 02 10 03 29 10 16 59 80 00 22 79 57 16 79 54 45 79 39 40 77 42 25 77 38 00 76 52 55 76 10 45 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 63 50 25 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 38 61 45 54 60 54 10 61 55 41 61 28 12 Toro Point: Light-house Colon: Light-house 06 6 18 1.1 0.6 Porto Bello : Ft. St. Geronimo Caledonia Harbor: Scorpion Cay Carreto Port: Peak 11 30 5 17 L5 0.8 Caribana Point: Extreme Fuerte Island: N. extreme Cispata Port: Zapote Pt Cartagena: Light-house Sa vanilla: Light-house Magdalena River: NW. pt. of Gomez I.. Santa Marta: Light-house Rio de la Hacha: Light on church Cape La Vela: Sand beach inside cape . . Baiia Honda: E. pt., S. side Espada Point: Extreme 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 Vela de Coro: Light-house Tucacas Island : Ore house St. Juan Bay: Cay Puerto Cabello: Light-house La Guaira: Light-house 6 00 12 12 ,2.8 L7 Cape Codera: Morro. Corsarios Bay: W. pt Centinela Islet: Center Barcelona: Morro Cumana: Light-house Escarseo Point: Extreme Chacopata: Morro Esmeralda Islet: Center Carupano : Light-house Pt. Herman Vasquez Puerto Santo Bay: Sand spit S. of Morro. Tres Puntas Cape : Extreme UnareBay: Obs. spot, 200yds. 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, light-house. Icacos Point: Light-house 4 20 10 30 3.2 1.9 San Fernando : Pierhead APPENDIX IV. [Page 207 MARITIME POSITIONS AND TIDAL DATA. NORTH AND EAST COASTS OF SOUTH AMERICA— Continued. 1 Place. Lat. N. Long. W. Lun. Int. Range. 1 H. W. L. W. Spg. Neap. S a g Demerara: Georgetown light-house Nickerie River: Light-house 1 II 6 49 20 5 58 30 5 49 30 5 44 50 5 16 50 5 02 40 4 56 20 4 49 30 4 23 20 4 20 45 2 46 30 1 40 17 Lat. S. 17 00 1 26 59 35 03 2 10 11 2 31 48 2 16 22 2 41 55 2 53 20 3 42 05 4 25 35 5 03 15 5 29 15 5 45 05 5 46 41 6 56 30 7 06 35 8 00 50 8 03 22 8 20 45 8 43 40 9 39 35 10 30 30 10 58 20 11 09 45 11 27 40 12 12 05 12 33 40 13 00 37 12 52 48 13 22 37 13 56 42 14 17 40 14 47 40 14 56 40 15 13 27 15 21 00 16 17 20 16 25 38 17 21 40 17 31 45 17 43 30 17 57 31 18 06 15 20 19 23 20 38 25 20 49 00 20 57 35 21 38 40 22 02 00 22 23 45 O 1 II 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 00 37 45 46 38 02 16 38 32 06 38 41 28 38 54 38 39 07 05 39 00 45 39 03 25 39 01 45 39 01 15 39 16 45 39 02 05 39 04 15 39 13 15 39 12 00 39 14 36 38 41 46 39 31 16 40 16 36 40 23 46 40 40 45 40 46 35 41 02 21 40 59 00 41 47 35 h. m. ' 4 18 h. m. 9 50 St. 8.6 ft. 3.9 Parainaribo : Stone steps 5 50 12 00 9.5 4.3 Maroni River: W. light-house Salut Islands: Light-house Enfant Perdu Islet: Light-house. Cayenne: Light-house 4 27 10 30 6.0 2.7 Connetable Islet: Center Cariniare Mount: Summit Orange Cape : Extreme Maye Mountain : Summit i North Cape: Extreme i Cape Magoari : Extreme Para: Custom-house ii 50 5 37 11.0 5.2 Atalaia Point: Light-house Itacolomi Point: Light-house Maranhao Island: Landing place Santa Anna Island : Light-house Tutoya: Entrance Paranahiba River: Amargao Village Ceara: Light-house 6 50 5 35 5 05 38 11 47 11 17 16.5 13.1 11.7 7.9 6.2 5.6 5 25 5 50 11 37 12 00 8.2 8.0 3.9 3.8 Jaguaribe River: Pilot station Cai^ara: Village Cape St. Roque : Extreme Rio Grande do Norte: Light-house Natal : Cathedral 4 05 10 17 8.8 4.2 Parahiba River: Light-house at entrance. Parahiba: Cathedral Olinda: Light-house Pernambuco: Picao light-house 4 33 10 50 7.0 3.3 Cape St. Augustine: Light-house Tamandare: Village Maceio: Light-house 4 20 4 17 10 32 10 29 8.5 7.8 4.1 3.7 San Francisco River: Light-house at en- trance • Cotinguiba River: Light-house at en- trance Vaza Barris River: Semaphore at en- trance Real River: Light-house Conde: Village Garcia d' Avila: Tower ' Bahia: Santo Antonio light-house Itaparica : Fort on N. pt 4 10 10 22 7.6 3.6 Morro de Sao Paulo: Light-house Camamu : Village 3 50 3 50 10 00 10 00 6.0 6.3 2.9 3.0 Contas: Church Ilheoa: Church Oliven^a: Center of village 3 35 9 47 6.4 3.1 Una: Center of village Comandatuba: Center of village Santa Cruz: Church 3 25 9 37 6.0 2.9 Porto Seguro: INIatriz Church Prado : River entrance Alcobaga: Center of village Caravellas: Center of village j 3 10 3 15 9 23 9 27 6.4 7.5 3.1 3.6 Abrolhos Island: Light-house Porto Alegre: Center of village Espiritu Santo Bay : Light-house Guarapiri Islets : E. islet 2 50 9 00 4.0 L9 Benevente: Village 2 40 8 52 5.0 2.4 Itapemirim: Moscas Islet Sao Joao da Barra: Light-house Cape St. Tl .ome : Extreme Macahe : Fort at entrance 1 2 20 8 30 9.2 4.4 Page 208] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. NORTH AND EAST COASTS OF SOUTH AMERICA— Continued. riace. Santa Anna Island : Summit Barra Sao Joao: Village Busies: Church Cape Frio: Light-house Port Frio: Village Maricas Islands: S. islet Rio de Janeiro: Fort Villegagnon Light. Imperial Observatory. . . Raza Island : Light-house Petropolis: Center of town Cape Guaratiba: Summit Marambaya Island: Summit of SW. end. Mangaratiba: Village Palmas Bay : Beach at head of bay Angra dos Reis: Landing-place Ilha Grande: Light-house Parati : Fort Ubatuba: Cathedral Porcos Grande Islet: Summit Busios Islets: Summit St. Sebastian Island: Boi Pt. light Villa Nova da Princessa: Center Santos:^ Moela I. light-house Quay Alcatrasses Island: Summit, 880 ft Conceigao: Church i Quemada Grande Island: Summit, 628ft. Iguape: Quay Bom Abrigo Islet: Light-house Ilha do Mel : Light-house : Paranagua: Quay Antonina: Quay Coral Islet: Center Itacolomi Islet: Center Sao Francisco: Center of town Itapacaroya: Church Cambria: Church Arvoredo Island : Light-house Anhatomirim: Light-house St. Catharine Island: Rapa Pt Naufragados light Nostra Senhora do Deserto : Quay Coral Island: Summit, 230 feet Cape St. Martha: Light-house Torres Point: Extreme Rio Grande do Sul: Light-house Lat. s. Castillos: Beuna Vista Hill, 184 feet. Cape Santa Maria: Light-house Lobos Island : Center Maldonado : Light-house Flores Island : Light-house Montevideo: Cathedral, SE. tower.. Colonia: Light-house Martin Garcia Island : Light-house Buenos Ayres: Cupola of custom-house. La Plata Indio Point : Light-house Piedras Point: Extreme Cape San Antonio: Light-house Madanas Point: Light-house Cape Corrientes: E. summit Port Belgraoo: Anchor.-Stock Hill Argentina: Fort 22 26 00 22 37 00 22 46 00 23 00 42 22 53 15 23 01 43 22 54 46 22 54 15 23 03 40 22 32 00 23 03 40 23 04 20 22 57 20 23 09 20 23 00 30 23 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 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 Long. W. 43 15 59 45 54 05 00 00 01 15 54 05 09 24 10 16 08 45 11 01 33 24 59 26 02 29 08 24 19 04 05 45 42 04 04 04 03 50 00 39 15 20 21 04 15 57 19 09 40 49 47 44 41 04 32 54 51 50 19 53 31 03 43 14 23 14 25 51 39 29 36 59 36 44 22 20 34 25 26 09 35 16 34 14 33 44 49 45 43 39 07 44 Lun. Int. 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 H. W. h. m. 2 30 2 50 1 35 2 50 2 55 2 35 4 00 8 20 2 00 6 30 6 43 9 50 6 00 L. W. h. m. Range. Spg. Neap. ft. 8 42 4. 9 9 00 4. 2 7 47 9 05 8 47 10 12 2 08 8 12 00 12 15 3 35 '6'66' 2.0 3.5 4.0 5.3 15.8 2.3 2.0 5. 3 2. 5 9 00 5. 2. 6:4 3.1 5.9 I 2. 1.8 0.9 0.9 2.3 2.7 2.1 I 1.4 3.5 8.2 APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. NORTH AND EAST COASTS OF SOUTH AMERICA— Continued [Page 209 Place. 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 Bermeja Head : E. summit Port San Antonio: Point Villarino San Antonio Sierra: Summit Port San Jos6: San Quiroga Pt Delgado Point: SE. cliff Cracker Bay: Anchorage Port Madryn: Anchorage off cave bluff Chupat River: Entrance Port St. Elena: St. Elena pen Leones Island: SE. summit Melo Port: W. pt Port Malaspina : S. pt Cape Three Points: NE. pitch Port Desire: Largest ruin Sea Bear Bay : Wells Pt Port San Julian: Sholl Pt Port Santa Cruz : Mount at entrance Coy Inlet: Height S. side of entrance. . . Gallegos River: Observation mound Cape Virgins: SE. extreme Cape San Diego: Extreme Staten Island, Cape St. John: Light- house, W. pt Port Cork: Observation mark, summit Cape St. Bartholomew: Middle pt Good Success Bay: S. end of beach Lennox Cove: Bluff, N. end of beach . . . Goree Road: Guanaco Pt Wollaston Island : Middle Cove Barneveldt Islands: Center Cape Horn: South summit, 500 ft Hermite Island: St. Martin Cove Lat. S. 39 26 30 39 57 30 40 32 52 40 36 10 41 02 00 41 11 00 40 49 00 41 41 10 42 14 15 42 46 15 42 57 00 42 45 40 43 20 45 44 30 40 45 04 00 45 03 00 45 10 10 47 06 20 47 45 05 47 57 15 49 15 20 50 08 30 50 58 27 51 33 21 52 18 35 54 40 35 54 43 24 54 45 16 54 53 45 54 48 02 55 17 00 55 19 00 55 35 30 55 48 54 55 58 41 55 51 20 Long. W. 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 Lun. Int. H.W. L.W. h. m. h. m. 10 50 10 35 7 05 00 10 35 9 20 9 00 8 40 8 18 4 20 4 19 3 50 4 07 4 38 4 23 52 3 50 I 10 03 6 12 10 33 10 32 10 03 10 02 Range. 14.7 23.5 13.2 16.8 18.3 29.5 39.6 40.0 45.6 38.7 9.9 6.7 4.8 Neap. St. 7.7 12.3 6.9 9.6 15.4 20.7 20.9 23.9 20.2 5.2 6.0 5.2 3.8 WEST COAST OF SOUTH AMERICA. False Cape Horn: S. extreme 55 43 15 Ildefonso Island: Highest summit 55 52 30 Diego Ramirez Island : Highest summit . 56 28 50 York Minster Rock: Summit, 800 ft \ 55 24 50 Cape Desolation : S. summit 54 45 40 Mount Skyring: Summit, 3,000 ft 54 24 48 Noir Island: SE. extreme 54 30' 00 Landfall Island: Summit of Cape Inman J 53 18 30 Cape Deseado: Peaked summit 52 55 30 Apostle Rocks: W. rocks 52 46 15 Cape Pillar: N. cliff 52 42 50 Dungeness Point: Light-house 52 23 55 Cape Espiritu Santo: NE. cliff 52 39 00 Catharine Point: NE. extreme ! 52 32 00 Cape Possession : Light-house 52 17 54 Cape Orange: N. extreme 52 28 40 Delgada Point: Light-house 52 28 00 Cape Gregory : Light-house 52 38 18 Cape San Vicente: W. extreme 52 46 20 04 40 17 30 41 30 01 30 36 10 10 20 00 00 18 15 36 30 46 50 42 20 25 45 34 00 45 20 57 10 24 00 33 00 14 16 25 25 3 50 2 20 1 50 32 8 19 8 20 8 24 8 35 8 47 9 23 10 03 8 33 8 03 6 45 2 07 2 08 2 12 2 25 6.0 4.8 4.7 2 40 3 20 4.0 39.4 39.0 30.0 39.0 39.0 21.0 3.9 3.7 3.7 3.1 20.6 20.4 15.7 20.4 20.4 11.0 '22489—03- -14 Page 210J APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. WEST COAST OF SOUTH AMEBICA— Continued. 1 Place. ■ Lat. S. Long. W. Lun Int. Range. 1 H. W. L. W. Spg. Neap. 6 Elizal)eth Islanc^ NE. ])luff O t II 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 52 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 45 53 20 44 55 50 44 09 00 43 48 30 43 41 50 43 19 35 43 17 10 43 11 20 42 48 00 42 27 45 O f II 70 37 51 70 54 24 70 34 27 70 58 31 70 55 03 71 17 15 71 55 30 71 59 41 72 04 45 72 10 42 72 19 30 72 27 10 72 34 15 72 32 25 72 38 00 72 47 30 72 47 55 73 00 30 73 12 05 73 21 30 73 15 30 73 17 45 73 16 15 73 44 28 73 59 33 74 17 45 74 13 30 74 38 14 74 04 00 74 17 39 74 23 27 74 25 10 74 20 55 74 23 10 75 06 00 74 55 00 75 13 20 75 27 45 74 51 30 75 22 00 75 13 20 75 31 00 75 40 30 75 28 20 75 10 00 75 18 20 75 25 30 75 37 55 75 31 30 75 12 00 ?5 06 00 75 08 45 74 07 45 73 59 35 74 42 00 73 41 50 74 22 00 72 44 40 72 30 30 73 45 20 //. m. 10 24 11 03 h. in. 4 24 5 03 ft. 8.0 5.0 ft. 4.2 2.6 Sandy Point: Light-house Cape St. Valentine: Sununit, at extreme. Port Famine: Observatory 11 58 12 21 28 5 58 6 21 6 53 6.0 8.0 7.0 3.1 4.2 3.7 Cape San Isidro: Extreme Cape Fro ward : Summit of bluff Mount Pond: Summit Port Gallant: Wigwam Pt 1 20 7 40 8.0 4.2 Charles Island: White rock near NW. end Rupert Island : Summit Mussel Bay : Entrance Tillv Bav: Sarah I Borja Bay : Bluff on W. shore 1 54 8 11 5.5 2.9 Cape Quad : P^xtreme Barcelo Bay : J^ntrance 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 1 53 8 08 5.0 3.9 1 31 7 44 4.5 3.5 1 09 7 21 4.0 3.1 55 7 07 6.0 4.6 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 Bav : Observation islet Westminster Hall Islet: E. summit Evangelistas Island: Light-house Cape Victory: Extreme 55 7 08 4.4 3.4 Cape Isabel: W. extreme Cape Santiago: Summit. Molyneux Sound : Romalo I Cape Tres Puntas: Summit, 2,000 ft Port Henry : Observation spot 30 6 45 4.5 3.5 Mount Corso: SW. summit Rock of Dundee: Summit Santa Barbara Port: N. extreme obs. pt. Guaineco Islands: Speedwell Bay, hill, np:. pt 15 6 30 5.3 4.1 Port Otwav : Observation spot 10 6 25 5.3 4.1 Cape Tres Montes: Extreme Cape Raper: Rock close to cape Christmas Cove: SK. extreme Hellyer Rocks: Middle Cape Taytao: W. extreme Socorro Island: S. extreme Mayne Mountain: Summit, 2,080 ft Port Low : Observation islet 00 6 13 4.4. 3.4 12 20 12 10 6 10 6 00 6.2 6.1 4.8 3.1 Huafo Island : S. extreme Port San Pedro: Cove on S. shore Cape Quilan: SW. extreme Corcovado Volcano: Summit, 7,510 ft... Minchinmadiva Volcano: S. summit, 8,000 feet Castro: E. end of town 01 6 21 18.0 9.1 APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. WEST COAST OF SOUTH AMERICA— Continued. [Page 211 Place. Dalcahue: Chapel Oscuro head : Observation pt Coman Inlet: Olvidada I Port Calbuco: Lg, Picuta San Carlos de ARcud: Light-house Condor Cove: Landing Eanu Cove: Anchorage Muilcalpue Cove: Landing place Milagro Cove: Landing place Laruehuapi Cove: Landing place Valdivia : Niebla Fort light Queule Bay : Choros Pt Mocha Island : Light-house Lebu River: Tucapel Head Yanez Port: Anchorage Lota: Light-house Santa Maria Island : Light-house Talcahuano : Fort Galvez Light on Quinquina I Llico: Village Port San Antonio: Village Aconcagua Mountain: Summit Santiago : Observatory Valparaiso: Playa Ancha Pt. light Site of Fort San Antonio Quintero Point: Summit Pichidanque: SP]. pt. of island Tablas Point: SW. extreme Chuapa River: S. entrance pt Maitencillo Cove: N. head Talinay Mount: Summit Lengua de Vaca: Light-house Port Tongoi: Obs. spot. W. of village Coquimbo : Tortuga Pt. light Smelting works, N. of town. N. islet Pajaros Islets : Light-house Choros Islands: SW. pt. of largest id Chaiiaral Island: Light-house Huasco: Light on mole Herradura de Carrizal: Landing place. . . Port Carrizal": Middle Point Matamoras Cove: Outer pt. S. side Salado Bay: Summit of Cachos Pt Copiapo: Landing place Caldera: Light-house Light on mole head Cabeza de Vaca Point: Extreme Flamenco: SE. corner of bay Chanaral Bay : Observation pt St. Felix I. : Peterborough Cathedral Rock Pan de Azucar Island : Summit Lavata: Cove near SW. pt San Pedro Point: Summit Port Taltal : Light-house Grande Point: Outer summit Paposo Road : Huanillo Pt Reyes Head : Extreme pitch Cobre Bay: Pt. W. of village Jara Head : Summit Antofagasta: Light-house Chimba Bay: E. pt. of large island Lat. S. O / l> 42 23 00 42 04 00 42 03 00 41 46 08 41 46 40 40 46 19 40 43 18 40 35 52 40 21 04 40 11 47 39 51 37 39 23 00 38 21 22 37 35 20 37 22 30 37 05 20 36 59 07 36 42 00 36 36 45 34 46 02 33 34 13 33 38 30 33 26 42 33 01 08 33 01 52 32 46 00 32 07 55 31 51 45 31 39 30 31 17 05 30 50 45 30 14 00 30 15 14 29 56 15 29 56 24 29 55 10 29 34 40 29 15 45 29 00 50 28 27 20 28 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 25 39 30 25 31 00 25 25 20 25 07 00 25 05 25 24 34 30 24 15 00 23 53 00 23 38 50 23 33 05 Long. W. 36 00 25 00 45 00 07 15 52 54 51 00 49 50 45 00 45 20 41 50 26 25 14 00 58 06 39 55 40 00 11 13 32 30 07 27 02 49 06 12 38 00 56 30 41 32 38 52 38 42 32 56 33 22 34 51 35 20 39 21 39 00 39 00 31 09 21 00 21 53 22 21 33 20 34 38 36 40 15 45 12 48 11 32 09 38 03 26 58 45 52 54 53 45 51 55 44 25 37 25 11 43 43 57 44 03 41 18 34 10 30 16 29 50 36 29 33 00 32 28 25 18 26 55 Lun. Int. H. W. 1 10 04 00 10 25 10 18 10 20 10 15 10 10 10 05 10 10 10 04 10 05 9 57 9 44 9 37 9 35 9 30 9 26 9 15 8 58 8 23 8 50 8 21 8 50 9 00 9 05 9 10 9 20 9 35 9 30 9 05 L. W. Range. 7 35 6 20 14.8 5.9 6 13 3 25 3 20 3 16 3 05 2 48 2 10 2 38 2 08 2 37 2 47 2 52 2 57 5. 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 26 3.9 4.1 3.9 4.2 4.1 4.9 4.9 4.9 5.0 4.9 5.0 4.9 3 07 : 4. 9 3 22 I 5. 3 17 i 4.9 2 52 I 4. 7 Neap. 7.5 3.0 3.7 2.8 2.5 1.7 2.5 2.7 2.5 3.0 2.7 2.5 2.1 2.0 2.0 2.1 2.0 2.1 2.1 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.4 Page 212] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. WEST COAST OF SOUTH AMERICA— Continued. ■g Place. Lat. s. Long. W. Lun .Int. Range. 1 H. W. L. W. Spg. Neap. Moreno Mountain! Summit o / ;/ 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 n 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 6 55 50 6 46 00 6 46 45 6 26 45 5 55 30 5 12 00 5 05 00 4 40 50 4 1^ 40 3 30 42 O 1 II 70 34 56 70 37 11 70 31 39 70 17 42 70 13 40 70 11 17 70 02 45 70 12 12 70 10 26 70 14 40 70 11 20 70 10 30 70 15 21 70 17 50 70 21 50 70 20 00 70 52 31 71 22 31 71 20 01 72 02 53 72 07 16 72 27 16 73 16 41 73 41 31 74 27 16 74 51 01 75 09 36 75 30 46 75 49 56 76 16 36 76 27 31 76 18 31 76 10 00 76 24 15 76 31 06 76 38 11 76 48 56 77 02 31 77 15 44 77 14 45 77 16 11 77 50 04 77 43 42 78 10 02 78 21 33 78 30 03 78 35 57 78 45 16 78 56 53 79 06 46 79 26 00 79 33 15 79 51 30 79 57 55 80 42 54 80 51 56 81 09 19 81 05 36 81 07 03 81 17 01 81 12 01 80 28 12 h. TO. h. m. ft. A 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 i Lobos Point : Outward pitch 9 00 2 47 4.9 2.5 Pabellon de Pica: Summit 6 Patache Point: Extreme , Iquique: Light-house 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 church 7 49 1 37 5.6 2.8 Schama Mount: Highest summit Coles Point: Extreme « ft* Ho: Mouth of rivulet 7 55 1 43 5.3 2.7 Port Mollendo : Light-house Islay: Custom-house 7 39 1 27 6.2 3.1 Quilca: W. head of cove Pescadores Point: SW. extreme Atico: E. cove Chala Point: Extreme Lomas: Flagstaff on pt San Juan Port: Needle Hummock Nasca Point: Summit 6 47 35 3.9 2.0 Mesa de Dofia Maria: Central summit. . . Carreta Mount: Summit San Gullan Island: N. summit Paraca Bay: N. extreme of W. pt Pisco: Light-house 6 16 04 3.8 1.9 Chincha Islands: Boat slip, E. side N. id. Frayles Point: Extreme " Asia Rock: Summit Chilca Point: SW. pitch Morro Solar: Summit San Lorenzo Island: Light-house Callao: Palominos Rock Light 5 47 12 00 3.5 1.8 Pescadores Islands: Summit of largest. . . Pelado Island : Summit Sup^ : W. end of village Huarmey : W. end of sandy beach Colina Redonda: Summit 5 08 11 21 2.1 1.1 Saraanco Bay : Cross Pt Chimbote : Village, N. part 4 50 11 03 2.0 LO Chao Islet: Center Guanape Islands: Summit of highest Huanchaco Point: SW. extreme Malabrigo Bay : Rocks 4 19 10 32 2.1 1.1 Pacasmayo : Light-house Eten Head : Light-house 4 04 10 17 2.5 1.3 Lambayeque: Beach opposite Lobos de Afuera Island: Cove on E. side. Lobos de Tierra Island: Central summit. Aguja Point: W. cliff summit Paita, Saddle: S. summit Paita: Light-house 3 20 9 33 3.5 1.8 Parinas Point: Extreme Cape Blanco: Under middle of high cliff. Tumbez: Malpelo Pt APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. WEST COAST OF SOUTH AMERICA— Continued. [Page 213 Place. Guayaquil River: Lighten Santa Clara I. Guayaquil, Concejo: S. pt. of city Puna: Mandinga Pt. light Point Santa Elena: Veintemilla light Plata Isle: E. pt Cape San Lorenzo: Marlingspike Rock.. Manta Bay: Light-house Caraques Bay: Punta Playa Cape Pasado: Extreme Point Galera: N. extreme Cape San Francisco: S\V. extreme Lat. S. 10 40 12 24 44 30 12 00 16 55 03 30 56 50 35 25 21 30 Lat. N. 50 10 40 00 Esmeralda River : Light-house Mangles Point: S. pt. of creek entrance. Tumaco: S. pt. of El Morro I Guascama Point: Extreme Gorgona Island: Watering Bay Buenaventura: Basan Pt Chirambiri Point: N. extreme Cape Corrientes: SW. extreme Cupica Bay: Entrance to Cupica River. Cape Marzo: SE. extreme Isla del Rey: Extreme of Cocos Pt Darien Harbor: Graham Pt Flamenco Island : N. Pt Chepillo Island: Center Point Cham^: Extreme 03 30 36 00 49 36 37 10 58 10 49 27 17 06 28 46 41 19 6 49 45 8 12 30 8 28 50 8 54 30 8 56 32 8 39 00 Long. W. 80 25 29 79 52 19 79 53 45 80 59 00 81 03 55 80 55 55 80 42 50 80 25 24 80 30 37 80 05 40 80 07 55 79 42 00 79 03 30 78 45 29 78 24 24 78 11 16 77 11 45 77 29 44 77 33 28 77 30 31 77 40 55 78 54 40 78 05 35 79 31 15 79 07 55 79 41 45 Lun. Int. Range. H. W. h. m 4 00 7 00 3 00 3 10 3 15 3 35 6 00 3 40 3 30 3 00 3 05 3 30 L. W. 10 13 1 00 Spg. ft. 10.0 11.0 9 13 9 23 7.5 9 28 9 48 13.2 12 13 13.2 9 53 9 43 13.1 13.3 9 13 15.7 9 18 9 42 16.0 15.0 Neap. ft. 5.1 5.6 4.0 3.8 5.0 7.1 7.1 7.0 7.2 8.5 8.7 8.1 ISLAITDS nr THE ATLANTIC OCEAN. Faeroe Islands, Strom Islet: Thorshaven Fort flagstaff Halderoig Islet: Halde- roig Church Numken 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 : Summit St. George Island : Light-house Graciosa Island: Santo Fort light Terceira Island: Monte del Brazil, near Angra St. Michael Island : Custom-house, Ponta Delgada Pt. Arnel light Santa Maria Island: Villa do Porto light Formigas Islands : Highest rock Porto Santo Island : Light-house Desertas: Chao I., Sail Rock Madeira Island : Funchal light Fora I. light-house Pico Ruivo, summit 6,056 ft Pargo (W.) Pt 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 38 05 24 38 38 20 37 44 16 37 49 20 36 56 00 37 16 44 33 03 15 32 35 45 32 37 42 32 43 14 32 45 00 32 48 07 6 43 08 7 GO 36 6 45 30 13 42 21 31 08 00 31 08 49 28 34 00 28 37 39 28 44 00 28 28 12 28 13 00 28 00 45 27 13 45 25 40 40 25 08 21 25 10 00 24 47 06 16 16 20 16 33 30 16 55 16 16 39 31 16 57 30 17 16 05 11 30 20 15 40 35 5 18 3.9 6 32 4.4 6 27 5.7 6 52 6 47 6.6 1.8 2.0 2.6 3.0 "3."6 Page 214] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ISLANDS IN THE ATLANTIC OCEAN— Continued. 1 Place. Lat. N. Long. W. Lun. Int. Range. 1 H. W. L. W. Spg. Neap. i s m g 7 M - 9 t s N u |2 Salvage Islands: Cight-house, Gran Sal- vage I -\. O 1 II 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 54 36 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 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 O / II 15 54 00 13 29 31 13 33 07 13 52 05 13 49 13 14 31 35 15 25 11 15 24 56 16 08 11 16 15 09 16 38 02 17 05 55 17 54 22 17 47 01 24 59 15 25 17 00 25 01 12 24 47 08 24 38 08 24 16 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 60 04 52 58 30 56 58 08 04 57 51 30 57 41 48 38 15 00 43 25 00 27 45 00 26 33 00 h. m. h. m. ft. ft. Alegranza Island: Delgada Pt. light Lanzarote Island: Port Naos light Pechinguera Pt. light. Lobos Island : Martino Pt. light Fuerta Ventura Island: Jandia Pt. light. Gran Canada: Isleta Pt. light Palmas light 50 7 00 8.5 3.9 40 6 50 9.3 4.3 Teneriffe Island: Anga Pt. light Santa Cruz, Br. con- sulate 1 15 7 27 7.8 3.6 Summitof peak, 12,180 ft Gomera Island : Port Gomera Ferro Island : Port Hierro Palma Island : Light, NE. pt 20 6 30 8.6 4.0 San Antonio Island: Bull Pt. light Summit, 7,400ft... St. Vincent Island: Porto Grande light . St. Lucia Island: N. pt 5 50 12 00 3.3 1.5 Raza Island : E. pt St. Nicholas Island : Light-house Sal Island: N. pt. light s. pt:.... Boavista Island : N W. pt NE. pt Light-house Mayo Island : English Jload 7 30 1 20 4.4 2.0 St. Jago Island: Reta Pt. light Porto Praya, S. light Fogo Island : N. S. da Luz,'village Brava Island: Light-house 5 50 12 00 4.8 2.2 Ireland Island: Dock yard clock tower. . Bastion C 7 04 52 4.0 2.6 Hamilton Island: Gibbs Hill light St. Davids Island : Light-house St. Paul Rocks: Summit, 64 ft Rocas Reef: NW. sandy islet 5 05 5 00 5 20 3 00 3 35 3 40 11 18 11 13 11 30 9 10 9 48 9 53 10.0 6.0 2.0 2.8 3.5 4.0 4.6 2.7 0.9 1.3 1.6 1.8 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: Center Tristan d' Acunha Islands: NW. pt Gough Island : Penguin Islet 12 50 5 40 5. .2 2.4 Port Egmont: Observation spot 7 20 1 08 10.7 5.6 Mare Harbor: Observation spot Port Louis: Flagstaff, govt, house Port Stanley: Governor's house Cape Pembroke: Light-house 5 31 11 27 4.3 2.2 South Georgia Island: N. cape Shag Rocks: Center Sandwich Islands: S. Thul6 Traverse I. volcano . . i 1 APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ISLANDS IN THE ATLANTIC OCEAN— Continued. [Page 216 Place. New S. Orkney Is. : E. pt. Laurie I E. summit Corona- tion I., 5,397 ft... New S. Shetland Islands, Deception Island: Port Foster Bouvets Island (Circumcision): Center.. Lat. s. 60 54 00 60 46 00 62 55 36 54 16 00 Long W. 44 25 00 45 53 00 60 35 00 Long. E. 6 14 00 Lun. Int. H. W. h. m. L. W. h. TO. Range. Spg. ft. Neap. ft. ATLANTIC COAST OF EUROPE. Greenwich : Observatory Oxford : University Observatory ... Cambridge : Observatory North Foreland: Light-house South Foreland: Light-house Dungeness: Light-house Beachy Head : Light-house Southsea Castle : Light-house Portsmouth : Observatory Southampton : Royal Pier light Hurst Castle: W. light Needles Rocks: Old light-house St. Catharine: New light-house Portland : Notch Bill light Start Point: Light-house Plymouth: Breakwater light Eddystone: Light-house Falmouth: St. Anthony Pt. light Lizard Point: W. light-house Porthcurnow: SE. cor. telegraph co.'ssta Lands End: Longships lignt-house Scilly Hands: St. Agnes light-house Trevose Head : Light-house Bideford : High light-house Lundy Island : Light-house, N. pt Bristol: Cathedral Cardiff: Light-house, W. pier Swansea: Light-house, W. pier Caldy Island : Light-house St. Anns: Upper light-house Smalls Rocks: Light-house Aberystwith : Light-house Bardsey Island : Light-house South Stack: Light-house on rocks Holyhead: Light-house on old pier Skerries Rocks : Light-house, highest I . Bidstone: Light-house on hill Liverpool : Rock light Observatory Morecambe Bay: Fleetwood highlight. Calf of Man: Upper light-house Isle of Man : Ayre Pt. light-house St. Bees: Light-house White Haven: W. pier-head light Mull of Galloway: Light-house Ayr, Firth of Clyde: Light-house, N. side harbor Troon: Light-house, inner pier Lat. N. 51 28 38 51 45 34 52 12 52 51 22 28 51 08 23 50 54 47 1 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 1 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 1 53 18 30 53 18 54 53 25 15 53 24 02 53 26 38 53 24 04 1 53 55 03 54 03 14 I 54 24 56 54 30 50 54 33 00 54 38 10 55 28 10 55 32 55 Long. W. 00 00 1 15 04 05 40 Long. E. 1 26 48 1 22 22 58 18 13 00 Long. W. 05 15 05 58 24 00 33 04 35 25 17 47 27 30 38 28 09 27 15 53 01 00 12 06 39 18 44 45 6 20 38 5 01 55 12 30 40 35 35 55 09 42 56 00 40 59 5 10 30 5 40 15 05 40 47 50 42 00 37 01 36 20 10 42 02 27 04 16 00 20 49 37 22 01 37 50 36 00 51 20 4 38 10 4 41 00 1 10 11 24 11 09 10 35 11 10 11 31 35 11 05 6 29 5 25 5 20 4 45 4 15 5 45 5 00 7 00 6 45 5 45 5 40 5 41 5 40 7 25 7 24 10 00 11 08 11 00 10 55 11 00 11 05 11 40 7 46 18.8 5 53 5 43 4 23 4 58 16.8 19.8 21.5 19.8 4 19 6 48 4 53 1.3.2 12.8 12.2 09 11 38 11 33 6.7 14.9 15.3 10 58 14.2 10 28 15.9 11 58 11 13 48 33 11 58 11 53 11 54 11 53 1 13 1 12 22.7 26.9 31.3 36.2 27.1 25.3 24.0 20.9 14.2 14.9 3 48 i 15. 8 5 27 4 48 27.6 27.4 4 43 19.7 4 48 4 53 5 28 25.9 14.8 12.6 8.4 10.0 11.0 10.1 6.7 6.5 6.2 1.0 6.8 7.0 6.5 7.3 11.4 13.5 15.7 18.1 13.6 12.7 12.0 10.5 7.1 7.5 7.9 14.0 13.9 10.0 13.1 8.9 5.2 Page 216] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ATLANTIC COAST OF EUROPE— Continued. Place. Ardrossan : S. breakwater light Pladda Island : *Light-hou8e Glasgow: Observatory Cantyre: Light-house Rhynns of Islay : Light-house Oban: Light-house on N. pier Skerry vore Rocks: Light-house Barra Head: Light-house Glas Island: Light-house, Scalpay I Stornoway : Arnish Pt. light Butt of Lewis: Light-house Cape Wrath : Light-house Dunnet Head : Light-house Kirkwall (Orkneys): New pier-head light Startpoint (Orkneys): Light-house North Ronaldeay: Light-house Fair Isle Skroo: Light-house Sumburgh Head: Light-house Blackness (Shetland Is.): Light-house pier Lerwick (Shetland Is. ) : Fort Hillswickness (Shetland Is. ) : S. extreme. Balta I. (Shetland Is.): Cairn on E. side. Pentland Skerries: Upper light-house... Tarbertness: Light-house Buchanness: Light-house Aberdeen (Girdleness) : Light-house Buddonness: Upper light-house Bell Rock: Light-house May Island: Light-house Inch Keith Rock: Light-house Edinburgh : Observatory Berwick: Light-house Farn Island: NW. light-house Coquet Island: Light-house Tynemouth: Souter Point light-house. . . North Shields: Light-house Sunderland: N. pier light Hartlepool : Light-house Flam borough : New light-house Humber River: Kilhngholme middle light Lat. X. Spurn Head: Upper light-house Lowestoft: Light-house Orfordness: N. light-house Harwich: Landguard Pt. light.. Cape Clear: Old light -house Fastnet Rock : Light-house Mount Gabriel : Ordnance survey station . Castlehaven : Light-house Mizen Hill: Ordnance survey station Ban try Bay : Roancarrig light Bull Rock : Light-house Skelligs Rocks: Light-house Valentia: Light-house Port Magee Dingle Bay: Light at entrance Blasket Islands: Westernmost rock Smerwick : Signal tower Tralee Bay: Light-house Beeves Rocks : Light-house Limerick : Cathedral Shannon River: Loop Head light 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 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 Long. W. 4 49 28 5 07 09 4 17 39 5 48 00 6 30 46 5 28 20 7 06 32 7 39 09 6 38 28 6 22 10 6 16 01 4 59 41 3 22 25 2 57 33 2 22 25 2 22 45 1 36 30 1 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 54 59 00 39 00 32 00 21 30 26 00 21 30 10 19 3 1 2 2 2 2 3 3 1 1 1 1 1 1 1 05 00 12 00 Long. E. 07 10 1 45 24 1 34 30 1 19 10 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 Lun. Int. H. W. h. m. 11 35 55 10 20 5 10 "5*35' 9 57 10 50 9 35 10 20 9 30 10 00 24 50 1 56 1 58 2 08 3 11 3 12 3 21 4 20 5 16 9 47 11 05 11 56 3 50 4 10 3 30 3 40 3 40 3 50 6 00 L. W. h. VI. 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 10 03 10 23 Range. Spg. ft. 8.8 11.2 4.0 12.8 ii.'i' 13.' 4" 5.0 5.2 6.0 '6.4" 11.2 11.7 15.5 16.5 15.0 14.8 14.5 14.2 15.8 18.5 6.2 7.8 11.2 10.6 9 43 10.8 9 53 10.7 9 53 10 03 10.7 12.3 13 18.7 APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ATLANTIC COAST OF EUROPE— Continued. [Page 217 Place. Eeragh Island : Light-house Arran Island: Light-house Gal way : Mutton I. light Golam Head: Tower Slyne Head : N. light-house Clifden Bay: Gortrumnagh Hill TuUy Mountain: Ordnance survey station Inishboffin : Lyon Head light Inishturk Island : Tower Clew Bay: Inishgort light Newport: Church Clare Island: Light-house Blacksod Point: Light-house Eagle Island: W. light-house 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 Killvbegs (Donegal Bay): St. Johns Pt. light.- .....: Rathlin O'Birne Islet: Li^ht-house Aran Island : Rinrawros light Bloody Foreland: Ordnance survey sta- tion Tory Island: Light-house Horn Head: Ordnance survey station . . . Melmore Head : Tower Fanad Point: Light-house Glashedy Island: Ordnance survey station Malin Head : Tower Inishtrahull : Light-house Inishowen Head : E. light-house Moville: New Pier Londonderry: Cathedral Scalp Mountain : Ordnance survey station Benbane Head : Summit Rathlin Island: Altacarry light-house... Maiden Rocks: W. light-house Lough Larne: Farres Pt. light-house Belfast Bay : Light, east side Mew Islands: Light-house Donaghadee: Light-house South Rock : Light vessel Dundrum Bay: St. John Pt. light Carlingford Lough: Haulbowline Rk. It. . Drofiheda: Light-house Rockabill : Light-house Howth Peninsula: Bailey light Dublin : Observatory N. wall light., Poolbeg: Light-house Kingstown : IC. pier light Killiney Hill: Mapas obelisk Bray Head: 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 : Light-house Great Saltee: S. end Waterford : Hoop Pt. light 53 08 55 53 07 38 53 15 13 53 13 46 53 23 58 53 29 47 53 35 00 53 36 40 53 42 27 53 49 34 53 53 06 53 49 30 54 05 45 54 17 00 54 16 00 54 19 36 54 16 33 54 15 30 54 18 00 54 20 50 54 34 08 54 39 47 55 00 52 55 08 13 55 16 26 55 12 31 55 15 14 55 16 33 55 19 07 55 22 50 55 25 55 55 13 38 55 10 20 54 59 40 55 05 23 55 15 03 55 18 05 54 55 47 54 51 07 54 40 20 54 41 50 54 38 45 54 24 04 54 13 30 54 01 10 53 43 00 53 35 47 53 21 40 53 23 13 53 20 47 53 20 30 53 18 10 53 15 52 53 10 39 52 57 54 52 41 55 52 32 55 52 20 53 52 20 04 52 18 57 52 12 09 52 06 41 52 07 25 Long. W. 9 51 30 9 42 06 9 03 10 9 46 03 10 14 01 10 03 54 10 00 15 10 09 40 10 06 41 9 40 12 9 32 56 9 59 00 10 03 34 10 05 31 9 53 00 9 20 41 8 46 02 8 34 25 8 37 00 8 40 14 8 27 33 8 49 52 8 33 48 8 15 38 8 15 00 7 57 15 47 12 37 53 23 51 22 22 13 37 55 38 7 02 20 7 19 25 7 21 51 6 28 45 6 10 45 44 18 47 21 49 30 31 30 32 01 22 20 39 30 6 04 45 6 15 00 6 00 20 6 03 06 6 20 30 6 13 33 6 09 00 6 07 30 6 06 37 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 Lun. Int. Range. H. W. h. m. 4 15 4 19 4 16 4 20 4 50 5 03 5 28 6 65 7 48 10 30 10 42 "ii"66' 10 45 10 45 10 55 11 00 10 52 10 30 10 10 7 05 5 30 Spg. h. m. 10 28 10 19 13.4 15.1 10 29 13.2 10 33 12.1 11 03 10.4 5 10 ! 11 23 11.4 11 16 11.2 11 41 11.6 43 1 35 7.5 8.0 4 18 4 06 "4'48' 9.3 ii.'i' 4 33 4 33 15.8 11.6 4 43 12.7 4 48 4 27 13.0 10.9 4 18 3 58 11.8 8.7 53 4.9 11 43 'ii'is' 12.3 Neap. ft. 5.7 6.4 5.2 4.5 5.3 4.8 5.3 3.4 3.6 4.5 "6."3 "7.'4 9.2 6.8 "7.' 5 7.6 6.4 6.9 5.1 2.9 5.1 6.' 2 Page 218] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ATLANTIC COAST OF EUROPE— Continued. Place. Waterford: Cath^ral Great Newton Head: Metal Man Tower. Dungarvan: Ballinacourty light Knockmealdown Mount: Ordnance sur- vey station Helvick Head: Ordnance survey station. Mine Head : Light-house Youghal: Light-liouse Capel Island : Tower Ballycottin : Light-house Cork Harbor: Haulbowline Coal Wharf. Queenstown : Roches Pt. light Kinsale: Light-house, S. pt Seven Heads: Tower Galley Head : Light on summit Stag Rocks : Largest Alderney Harbor: Old pier light St. Heliers: Light on Victoria Pier Lat. N. 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 Vardo: Fortress 70 Vadso : Light-house 70 North Cape : Extreme ; 71 Fruholm : Light-house 71 Hammerfest : Light-house 70 Tromso: Observatory ] 69 Hekkingen: Light-house 69 Andenes: Light-house 69 Lodingen (Hjertholm): Light-house 68 Lofoten Island: Skraaven I. light 68 Glopen light 67 Grvto : Light-house 67 Stot: Light-house 66 Tra?nen: Soe Islet light 66 Bronnosnnd: Light-house 65 Villa: Light-house 64 Halten Island : Light-house 64 Koppem '63 Agdenes: Light-house 63 Trondheini: Mumkholmen flagstaff ■. 63 Grip: Church :.' 63 Christiansund : Storvaden 63 Freikallen • 63 Hestskjaer: Light-house 63 Steinshesten 62 62 62 62 ^ratenen : Light-house Svinoen Islet Hjcerringa Mountain : Summit Hornelen Mountain: Summit 61 Batalden Island : Store 61 Kinnsund : Light-house 61 Alden 61 Helliso: Light-house 60 Bergen : Cathedral 60 Lorstakken Mountain : Summit 60 Marstenen Islet: Light-house 60 Furen Islet 59 Ulsire: Light-house 59 Hvidingso : Light-house I 59 Port Stavanger : Light-house ' 58 Obristadbrci'kke: Light-house .58 Synesvarde Mountain : Summit j 58 Kompas Mountain: Summit. Lister: Light-house Lindesnes : Light-house Ryvingen Island: Light-house.. Christianssand: Odderoen light. 22 00 04 00 11 00 06 00 40 15 39 12 36 05 19 30 24 40 09 20 53 15 23 15 56 35 25 50 28 40 32 55 10 25 48 25 38 45 27 04 13 11 07 01 03 04 05 00 58 49 48 20 19 38 11 12 51 21 38 40 33 35 19 16 45 05 23 37 21 39 07 50 57 44 18 20 03 10 58 30 39 25 36 56 25 51 06 25 58 55 58 00 07 50 Long. W. 7 06 24 7 10 15 7 33 05 7 54 54 7 32 39 7 35 08 7 50 34 7 51 10 7 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. 31 07 29 45 25 40 23 59 23 40 18 57 17 50 16 08 16 02 14 40 13 04 13 52 13 28 11 59 12 13 10 42 9 24 9 44 9 45 10 23 7 36 7 43 7 46 7 29 7 12 6 36 5 16 5 07 5 20 5 19 5 01 5 03 4 52 5 24 5 45 5 33 5 49 5 58 6 34 7 03 7 29 8 00 Lun. Int. Range. H.W. h. m. 5 00 5 02 4 40 4 33 4 30 4 20 6 21 6 09 5 40 2 20 1 35 42 11 35 11 18 11 00 lO 15 9 43 4 16 L.W. Spg. Keap. h. m. 11 13 12.4 11 15 12.6 10 53 11.8 10 59 10 43 10 33 11.6 11.4 10.7 16 00 11 57 17.2 3L2 9.0 8 40 7 48 8.3 7.8 6 55 7.0 5 23 6.9 5 04 8.4 4 48 5.0 3 55 4.1 3 40 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 2.1 0.8 10 15 1.1 0.5 APPENDIX IV. [Page 219 MARITIME POSITIONS AND TIDAL DATA. ATLANTIC COAST OF ETJK.OPE— Continued. o Place. Lat. N. Long. E. Lun. Int. Range. 1 H. W. L. W. Spg. Neap. i 9 1 Okso: Light-house O 1 II 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 36 47 55 23 00 55 22 00 55 25 42 55 22 58 56 00 54 56 10 04 56 09 45 56 11 50 56 55 18 57 26 29 57 57 24 57 45 38 58 08 52 58 17 55 58 44 26 59 20 35 59 51 31 59 45 24 59 45 15 60 10 35- 60 15 19 60 20 26 60 22 15 60 22 26 60 31 41 60 40 29 60 43 48 60 55 57 61 18 22 61 32 54 o / // 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 35 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 12 59 49 12 49 02 h. in. h. m. /'. St. Hamberg: Mill Arendal Inlet: Inner Torungerne light.. Jomf ruland : Light-house Langotangen : Light-house 4 17 10 10 LO 0.7 Langesund: Church Frederiksvsern : Lookout tower 4,34 10 00 1.3 1.0 Svenor: Light-house Foerder Islet: Light-house. Fulehuk : Light-house Basto : Light-house ' Horten : Church Holmestrand : Church Drobak : Church Oscarsberg: Fort flagstaff . . Christiania: Observatory 5 22 10 37 1.2 0.9 Strom tangen (Torgauten): Light-house. Fredriksten : Fort clock tower Torbjornskjter: Light-house Koster; Light-house Stromstad : Steeple Nord Koster Islands : Light-house Wadero Island: Light-house . Hollo Island: Light-house Paternoster Rocks: Light-house Gottenburg: Signal station Nidingen Islet: Light-house Warberg: Castle tower Falkenberg: Church Halmstad : Palace Engelholm : Church Kullen Point; Light-house Helsingborg: Light-house Landskrona : Light-house Malmo: Light-house Falsterbo: Light-house Trelleborg: Light-house 13 09 20 13 49 38 14 n 10 14 50 57 14 52 02 15 36 05 16 24 04 Ystad : Light-house Sandhammaren : Light-house ^.. Hano Island : Light-house ;.. Karlshamn : Light-house Karlskrona: Stum holm Tower Oland Island : Light on S. pt Gottland Island: Hoburg light, S. pt Ostergarns light Faro Island: Holmadden light Sparo Vestervik : Granso light 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 39 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 Haradsskar Islet: Light-house Norrkopings Inlopp : Light-house Landsort: Light-house Stockholm : Observatory Upsala: Observatory Norrtelge: Inn Soderarm : Light-house Svartklubben : Light-house Osthammar : Church Oregrund : Clock tower Djursten : Light-house Forsmark: Church Orskar Rock : Light-house Gefle: Church Eggegrund Islet: Light-house Hamrange: Church Soderhamm : Court-house Enanger: Church ::::::;::::: i 1 Page 220] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ATLANTIC COAST OF ETTROPE— Continued. Place. Hudiksvalls : Coyrt-house Gnarp: Church Sundsvall: Church Lungo: Light-house Skags Head : Light-house Holmogadd : Light-house Umea: Bredekar Light Bjuroklubb: Light-house Pitea Rodkallen : Light-house Maloren : Light-house Tomea: Light-house Uleaborg: Karlo I. light Ulko Kalla Rock: Light-house Norrsher Islet: Kvarken light Kaske: Shelgrund I. light Bierheborg: Sebsher light Nuistad: Ensher light Abo: Observatory Aland Island; Shelsher light Ekkere light Logsher light Bogsher: Beacon Ute Islet: Light-house Gauge: Gange I. light Rensher: Light-house Helsingfors: Observatory 8oder Skars: Light-house Kalboden Island: Light vessel Rodsher Island: Light-house Hogland Island: Lower light Upper light Sommer Island : Light-house ,. Vieborg Bay: Nelva I. light Stirsudden : Light-house Kronstadt: Light on Frederikstadt t tion Cathedral St. Petersburg: Observatory Pulkowa : Observatory Peterhof : Pier-head light Oranienbaum: Light-house Seskar Islet: Light-house Narva: Light S. pt. of entrance Stensher Rock: Light-house Ekholm Islet: Light-house Koksher: Light-house Revel: Light N. end of W. mole . . . Cathedral Nargen Island : Light-house Surop: W. light Baltic Port: Light-house Odenskholm Island: Light-house Takhkona Point: Light-house Dago Island : Dagerort light Filzand Island: Light-house Svalferort Tzerel : Light-house Kuino: Light-house Pernau: Light at S. entrance Riga: Light on Fort Kametskoi dike Cathedral Runo Island: Light-house Domesnes : Light-house Windau : Light on S. jetty Libau: Light at entrance of port Lat. N. 61 43 57 62 02 51 62 23 30 62 38 35 63 11 55 63 35 34 63 39 33 64 28 50 65 19 10 65 18 53 65 31 30 65 65 64 63 62 61 60 60 60 60 59 59 59 59 59 60 60 59 59 60 60 60 60 60 59 59 59 59 59 59 60 59 59 59 59 59 59 59 59 59 59 59 58 58 57 58 58 57 56 57 57 57 56 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 12 31 14 43 11 05 58 14 59 44 56 30 46 19 53 26 55 40 02 08 28 04 49 10 41 06 42 00 27 05 26 28 36 22 27 55 21 30 18 06 05 25 55 02 23 02 54 37 05 50 23 10 03 28 56 36 48 02 48 10 24 00 31 01 Long. E. 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 57 17 25 25 51 25 37 30 26 41 05 27 01 40 26 58 44 27 33 46 27 58 36 29 03 01 29 47 12 29 46 07 30 19 22 30 19 40 29 54 54 29 46 38 28 23 01 28 03 31 26 23 00 25 48 58 25 02 37 24 46 10 24 44 45 24 31 57 24 24 05 24 04 30 23 23 15 22 36 15 22 11 36 21 49 56 22 04 15 23 59 34 24 49 25 24 00 59 24 08 25 23 15 00 22 39 15 21 34 00 20 59 40 Lun. Int. Range. L. W. h. m. Spg. Neap. ft. APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ATIiANTIC COAST OF EUROPE— Continued. [Page 221 Memel: Light-house Heiligen Creutz: Church tower Brusterort : Light-house Pillau : Light-house Fischausen: City-hall tower Konigsberg: Observatory Tolkemit: Church tower Elbing: Church tower Tiegenort : Church tower Danzig: Observatory Neufahrwasser light Weichselmunde: Fortress tower Putziger Heisternest: Church tower Oxhoft: Light-house Hela: Light-house Rixhoft: Light-house Leba: Church tower Stopelmunde: Church Jershoft: Light-house Rugenwalde: St. Mary's Church Coslin: St. Mary's Church Funkenhagen : Light-house Colberg: St. Marv's Church Gross-Horst : Light-house Cammin: Cathedral tower Wollin: Church tower Stettin; N. Castle tower Swinemunde : Light-house Streckelsberg: Survey station near beacon Usedom: Church tower Lassau: Church tower Wolgast: Church tower Grieiswald: St. Nicholas Church Griefswalder Oie : Light-house Granitz: Castle tower Bergen : Church tower Arkona: Light-house Stralsund: St. Mary's Church Darsserort: Light-house Wustrow : Church Ribnitz: Church tower Wamemunde: Church Rostock : St. Jacob' s Church Diedrichshagen : Survey station Basdorf : Survey station Wismar: St. Nicholas Church Hohenschonberg: Survey station Travemunde: Light-house Burg: Church tower Manenleuchte: Light-house Petersdorf : Church tower Hessenstein : Flagstaff of lookout tower . Schonberg: Church Bulk : Light-house Kiel : Observatory Eckemforde : Church Schleswig: Cathedral Kappeln: Church Flensberg: Church Duppel: Survey station Schleimunde: Light-house Augustenburg: Church Hugeberg : Survey station Apenrade: Church Skoorgaarde : Survey station Ballum : Church List: E. light-house Lat. N. 55 43 45 54 53 47 54 57 40 54 38 25 54 43 49 54 42 51 54 19 19 54 09 44 54 16 30 54 21 18 54 24 28 54 23 51 54 12 16 54 33 09 54 36 06 54 49 55 54 45 29 54 35 16 54 32 29 54 25 27 54 11 28 54 14 40 51 10 40 54 05 47 53 58 29 53 50 41 53 25 41 53 55 03 54 03 08 53 52 17 53 56 59 54 03 18 54 05 49 54 15 02 54 22 56 54 25 08 54 40 53 54 18 42 54 28 28 54 20 47 54 14 42 54 10 42 54 05 27 54 06 32 54 08 00 53 53 50 53 58 54 53 57 44 54 26 16 54 29 43 54 28 54 54 19 47 54 23 52 54 27 25 54 20 30 54 28 25 54 80 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 Long. E. Lun. Int. Range. H. W. 21 06 20 01 19 59 19 53 20 00 20 29 19 31 19 23 19 08 18 39 18 39 18 41 18 40 18 33 18 49 18 20 17 33 16 51 16 32 16 24 16 11 15 52 15 34 15 04 14 46 14 37 14 33 14 17 14 01 13 55 13 51 13 46 13 22 13 55 13 37 13 26 13 26 13 05 12 30 12 24 12 26 12 05 12 08 11 46 11 41 11 28 11 05 10 52 11 11 11 14 11 04 10 32 10 22 10 12 10 08 9 50 9 34 9 56 9 26 9 45 10 02 9 52 9 58 9 25 9 23 8 39 8 26 h. m. 20 L. W. Spg. h. m. 6 33 5.2 Page 222] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ATLANTIC COAST OF EUROPE— Continued. Place. Keitum: Church Fohr: St. Nicholaf Church Ualgenberg: Survey station Husum : Church '... Tonning: Church Busuin: Church Helgoland : Ijight-house Scharhorn : Beacon Neuwerk : Li^ht-house Cux haven : Light-house Stade: Church steeple Steinkirchen : Church Altona : Observatory Hamburg: Observatory Berlin: Observatory Harburg: Light-house Hohe Weg: Light-house Langwarden : Church Bremerhaven: New harbor light. Minsener Sand: Light vessel Schillighorn: Light-house Wilhelmshaven: Observatory Wangeroog: Light-house Spikeroog: Church Langeoog: Belvedere Balstrum : Church Norderney: Light-house Juist: Church Emden: City Hall tower Lat. N. Falster: Gjedser light Moen Island : Stege Church spire Moen light, SE.pt Prceste : Church spire Kjorge: Church tower Amager Island: Holloenderby Ch. spire. . Nordse Rase light Copenhagen: New observatory Bornholm: Ronne light Christianso Island: Great tower Kronberg: High spire Nakkehooed : Upper light Hesselo Island : Light-house Anholt Island : Light-house Spodsbjerg: Light-house Roeskilde: Cathedral Nykjobing: Church tower Oddensby : Church tower Sejro Island : Sejro Point light Kallundborg: Church Omo Island: Church Vordingborg: Waldeniar's tower Veiro Island: Light-house Langeland Island: Fakkebjerg light JEto Island : Church spire Lyo Island: Church tower Assens: Church tower Baago Island : Light-house 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 Church spire 54 54 13 54 41 51 54 41 21 54 28 43 54 19 08 54 07 52 54 10 57 53 57 15 53 55 01 53 52 25 53 36 12 53 33 43 53 32 45 53 33 07 52 30 17 53 28 30 53 42 50 53 36 20 53 32 52 53 46 57 53 42 21 53 31 52 53 47 25 53 46 19 53 45 06 53 43 46 53 42 39 53 40 45 53 22 06 54 33 50 54 59 03 54 56 46 55 07 24 55 29 44 55 35 45 55 38 10 55 41 14 55 05 40 55 19 19 56 02 20 56 07 10 56 11 50 56 44 16 55 58 36 55 38 34 55 55 30 55 57 52 55 55 09 55 40 50 55 09 48 55 00 26 55 02 19 54 44 23 54 51 14 55 02 34 55 16 09 55 17 44 55 29 31 55 34 03 55 18 41 55 03 00 55 03 37 55 45 32 55 48 02 55 51 44 Long. E. 8 22 03 8 33 13 8 33 58 9 03 21 8 56 38 8 51 53 7 53 11 8 24 35 8 29 58 8 42 43 9 28 48 9 36 40 9 56 35 9 58 25 13 23 44 9 59 37 8 14 48 8 18 30 8 34 25 8 04 47 8 01 43 •8 08 48 54 09 41 45 35 41 22 03 13 58 6 59 53 7 12 25 n 58 03 12 17 16 12 32 40 12 03 07 12 07 36 12 38 24 12 41 26 12 34 47 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 Lun. Int. Range. H. W. h. m. 1 35 2 10 1 45 1 11 11 29 39 4 00 '5"66' L. W. Spg. h. m. 7 47 8 23 7 57 7 24 5 17 10.8 11.0 11.7 8.1 6 51 10.1 10 13 "ii'i2' 8.5 'e.'i' 25 6 38 10.1 54 i 7 07 10 ! 6 23 10.4 9.5 04 11 27 11 05 "'6"24" 6 17 5 15 13.2 8.0 4 53 7.3 6 36 9 33 3 21 0.6 Neap. ft. 4.5 6.2 6.4 6.8 4.7 5.8 4.9 3.5 5.7 5.8 5.3 7.4 4.5 4.1 5.0 0.3 APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ATLANTIC COAST OF ETJROPE— Continued. [Page 223 Lat. N. Tuno Island : Light-house Samsoe Island: Nordby Church tower . Aarhns: Cathedral spire Hjelm Islet: Light-house Fornpes : Light-Jiouse Hals: Church tower Aalborg: St. Rudolph's Church Cape Skaw, or Skagen: Old light-house Hirtshals: Light-house .' Haustholm : Light-house Boobjerg : Light-house Ringkjobing: Church spire Loune: Church tower Blaabjerg: Summit, 100 ft Guldager: Church Fano Island : Nordby Church Mano Island: Church spire Niewe Diep: Time-ball station Amsterdam : W. church tower Utrecht: Observatory Leyden : Observatory The Hague: Church tower Scheveningen : Light-house Brielle: Light-house Rotterdam : Time-ball station Hellevoetsluis: Time- ball station , Willemstadt: Light-house Goedereede: Light on church tower Flushing: Time-ball station Light, Westhaven bastion . '. Brussels: Observatory , Antwerp: Observatory Notre Dame Cathedral . Blankenberghe: Fort light-house . Ostend : Light- house Church tower Nieuport: Templars tower Paris: Observatory Dunkerque : Tower Gravelines: Light on N. breakwater . . . Calais: Light on old fort Cape Gris Nez : Light-house Boulogne, C. Alprech: Light-house Abbeville: Tower Cay eux : Light-house Dieppe: W. jetty light Ailly Point: Light-house 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 Corseulles: W. jetty light Point De Ver: Light-house Cape La Hougue: Light-house Cape Bartieur: Light-house Cherbourg: Light, W. head of break- water Naval Observatory Cape La Hague: Light-house Casquets Rocks: Light on NW. rock . . . 55 56 58 55 57 06 56 09 26 56 08 00 56 26 36 56 59 54 57 02 54 57 43 46 57 35 06 57 06 50 56 30 48 56 05 27 55 47 17 55 44 50 55 31 52 55 26 26 55 16 11 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 51 11 51 12 28 51 13 17 51 18 47 51 14 13 51 13 50 51 07 53 48 50 11 51 02 09 51 00 18 50 57 45 50 52 10 50 41 57 50 07 05 50 11 42 49 56 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 Long. E. 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 46 36 53 04 07 50 29 03 18 30 15 10 10 45 28 50 07 40 26 26 58 35 35 48 34 32 4 22 18 4 24 44 4 24 12 3 06 54 2 55 51 2 55 22 2 45 34 2 20 14 2 22 31 2 06 34 1 51 07 1 35 02 1 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 1 16 21 1 15 56 1 43 44 1 38 08 1 57 15 2 22 41 Lun. Int. Range. H. W. 5 46 4 18 2 35 2 35 2 34 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 Spg. I Neap. h. m. ft- 11 58 10 30 1.0 1.2 8 47 2. 1 47 ! 4.5 46 i 4.7 1 05 I 3. 9 9 02 9 47 8 32 9 32 6 56 10 27 6 17 6 32 6 22 5 58 6 16 6 13 5 51 5 52 5 48 5 33 5 02 4 14 2 45 2 37 1 44 15 4.8 6.7 5.2 14.7 14.8 12.5 16.1 15.7 16.8 19.0 21.0 21.5 25.2 27.3 26.8 23.3 22.5 18.5 17.0 17.6 15.5 ft. 0.5 0.7 1.2 2.6 2.7 2.0 2.5 3.5 2.8 5.2 5.7 i.i 8.4 8.5 9.6 10.7 11.0 12.8 13.3 13.1 11.4 11.0 8.2 7.5 6.9 Page 224J APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ATLANTIC COAST OF EUROPE— Continued. Place. Port St. Peter, Guernsey: Light on Cas- tle Coonet Breakwater Douvres Rocks: Light-house Cape Carteret: Light-house Coutances: Cathedral tower Granville : Light-house Chausey Is. : Light on SE. end of large id St. Malo: Roehebourne light Cape Frehel: Light-house Heau de Brehat: Light-house Morlaix, He Noire: Light-house De Bas Islet: Light-house Abervrach : Light on Vrach Islet Usiiant: Stiff Point light Brest: Observatory Brest (approach ) : Quelern light De Sein Islet: Light-house Bee du Raz: Light-house Audierne: Pier-head light Penmarch Rocks: Light-house Glenan Islands: Light, Penfret I De Groix Island: Light-house Lorient: Church-tower light Belle Isle: Light-house Port Haliguen : Light on N. jetty Haedic Island : Light-house Port Navalo: Light-house Vannes: St. Pierre Church Le Four Rock : Light-house Croisic: End of breakwater Guerande: Steeple Port St. Nazaire: Light-house Paimbffiuf : Steeple Nantes : Cathedral Noir Moutier Island: Light-house Le Pilier Island : Light-house D'Yeu Island: Light-house La Chaume: Light-house Point de Grouin du Cou: Light-house.. R6 Island: Light, NW.pt Rochelle: E. Quay light Aix Island : Light-house Rochefort: Hospital Oleron Island: Light NW. pt Point de la Coubre: Light-house Point Cordouan: Light-house Point de Grave: Light-house Bordeaux: St. Andr6 Bayonne: Cathedral Biarritz : Light-house St. Jean de Luz; St. Barbe Point light . Fuenterrabia: Light on Cape Higuera.. Port Pasages : Light at entrance San Sebastian: Monte Igueldo light Bilbao: Light on Galea Castle Castro Urdiales: Santa Ana Castle light Santofia: Pescador Point light Santander: Cape Mayor light San Martin de la Arena: Light-house. . . San Vincent de la Barquera: End of new mole Rivadesella: Mount Somos light Gijon: Santa Catalina light Aviles: Light-house Rivadeo: Light-house Estaca Point: Light-house Lat. N. 49 27 13 49 06 28 49 22 27 49 02 54 48 50 07 48 52 13 48 40 18 48 41 05 48 54 33 48 40 23 48 44 45 48 36 57 48 28 31 48 23 32 48 19 10 48 02 40 48 02 28 48 00 47 47 47 52 47 43 17 47 38 51 47 44 53 47 18 42 47 29 10 47 19 18 47 32 53 47 39 30 47 17 53 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 19 43 29 29 43 29 38 43 23 58 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 Long. W. 2 31 31 2 48 49 1 48 25 1 26 39 1 36 46 1 49 20 58 41 19 08 05 11 52 33 01 38 34 34 03 26 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 1 08 57 1 10 40 57 50 1 24 37 1 15 16 1 10 24 1 04 27 34 42 1 28 43 1 33 16 1 39 53 Lun. Int. Range. 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 H. w. h. m. 6 12 6 07 5 50 5 55 5 43 5 35 5 00 4 35 4 00 3 35 3 23 3 25 3 04 3 05 3 00 3 09 3 25 3 35 3 20 3 45 5 47 3 25 3 35 4 18 5 50 ■3 05 3 18 3 20 3 27 3 27 3 45 3 35 6 30 3 07 3 00 2 50 2 45 2 45 L. W. h. TO. 07 ft. 26.0 15 30.8 09 04 04 36.7 34.7 36.0 12 00 11 25 11 00 10 25 10 00 9 45 30.4 23.1 22.0 20.6 18.9 19.5 9 53 17.2 9 31 9 34 9 27 11.1 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 15.3 9 14 12.3 9 05 9 03 9 03 9 07 9 18 9 14 9 14 11.7 12.7 11.8 12.3 14.8 1L7 10.4 9 03 8 58 8 58 13.5 12.0 14.4 Neap. ft. 11.5 13.5 16.0 15.2 15.7 13.3 10.6 10.1 9.5 8.7 9.0 5.1 6.1 6.0 6.3 7.7 7.9 7.7 7.7 7.4 7.7 7.7 7.9 7.7 7.7 6.8 5.9 7.7 7.7 7.7 7.8 7.1 5.8 5.5 5.9 5.5 5.7 6.9 5.5 4.9 6.3 4.9 3.9 APPENDIX IV. [Page 225 MARITIME POSITIONS AND TIDAL DATA. ATLANTIC COAST OF EUKOPE— Continued. 1 Place. Lun. Int. Range. 1 H. W. 1 L. W. spg. Neap. 1 © s u d i s Kandeliupa Island : Light-house StampaU Island, Maltezana Port: Agios loanes o / // 36 29 40 36 34 25 36 15 20 36 40 27 36 59 12 37 06 32 37 00 01 37 08 38 37 26 12 37 07 36 37 25 55 37 38 00 37 39 28 37 44 00 37 57 30 36 47 05 37 18 42 37 31 45 37 44 30 37 56 14 37 58 20 37 38 45 37 52 48 38 01 28 38 28 15 o r II 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 h. m. h. m. fl. ft. Christiana Islands: N. pt .. .. Milo Island: Summit, Mt. St. Elias Siphano Island : Light-house Naxos Island, Naxia: Gate on Bacchus I. Paros Island, Port Trio: Trio Pt Port Naussa: St. Yanni Church ! Syra: Mole light Sermo Island : Aniyno Pt 24 32 23 24 23 35 24 44 32 24 19 44 24 04 12 24 42 30 23 05 40 23 08 53 23 25 45 23 25 30 23 38 10 23 43 55 24 02 15 24 03 00 24 16 42 Therm ia Island: Ruins of Cythnus Jura Island: North pt .. ... .. 1 1 Port St. Nikolo: Light-house •-(■--■■■ St. Nikalao Island: Port Mandri Andros Island, Cape Fasse: Light-house, leraka : Acropolis i i Port K heli : Light-house Poros Island: Light-house 1 1 JEgina: Light-house Pirajus: Light-house \ Athens: Observatory < Cape Colonna: Extreme 1 Port Raphti: Statue I Petali Island : Trago I. peak Euripo Strait: Light-house 1 23 36 45 Skiathos Island: Mount Stavros Salonika: S. bastion Port Baklar: Cape Xeros 39 10 48 23 27 07 40 37 28 40 32 40 39 52 10 39 50 52 39 31 58 39 12 35 39 06 10 39 03 20 38 32 00 38 19 55 37 41 24 37 16 33 22 58 00 26 45 00 25 03 20 25 14 14 24 59 13 25 50 00 26 34 54 26 31 39 25 35 00 26 17 45 26 58 42 27 36 55 Lemnos Island : Kastro Castle Port Moudros: Sangrada Pt Strati Island : St. Strati Church 1 Mityleni Island, PortSigri: Light-house. Mitvleni: LightonMity- leni Pt ! Port lero: Sidero Islet . Psara Island: Fort Tchesm6: C. K^zil light Samos Island : Fonia Pt. light Port Isene: Tower Kos: Light-house 36 55 00 ! 27 18 25 36 48 00 ; 28 18 00 36 39 33 ' 29 06 13 36 26 00 28 16 24 Marmorice Harbor: Adassi Pt. light Makrv Harbor: Kasil I Rhodies Port: Arab's Tower light Port Lindo: Tower 36 05 53 40 02 30 40 24 27 41 01 20 41 01 02 41 00 35 41 00 16 41 21 15 41 52 04 28 08 10 26 10 54 26 41 24 29 01 00 29 00 29 29 01 14 28 58 59 28 42 14 27 58 45 Dardanelles: Hellas Pt. light (jallipoli : Light-house :::::::;::: i Bosphorus: Tofana Pt. light Scutari: Leander Tower light Constantinople: Seraglio Pt. light St. Sophia Mosque Cape Kara Burnu: Light-house Yuiada Road : Fort Tersana Burghaz : Light-house 42 27 52 27 35 54 43 10 00 27 58 35 44 10 20 28 39 14 45 09 47 29 41 14 Varna Bav : Light-house Kusterjeh: Cape Kusterjeh light Danube River: Salina light Fidonisi Island: Light-house Odessa : Observatory 45 16 00 46 28 36 46 34 27 44 36 55 44 29 50 45 21 03 46 45 00 42 58 00 41 39 30 30 14 14 30 45 34 31 33 36 33 36 26 33 36 25 36 28 30 36 46 40 40 55 10 41 38 15 Dnieper Bay: Fort Nikolaeo light Sebastopol: E. light-house Balaklava Bav : Hospital Kertch: Light-house Berdiansk: Breakwater light Saukhoum : Light-house Batoum: Light-house Page 230] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. COASTS OF THE MEDITERBAXEAN, ADRIATIC, AND BLACK SEAS— Continued. Plac'o. Trebizond : Light>4iouse Sinope : Light-house Bender ErekH : Light-house Marmora Island : Light off E. pt Artaki Bay: Zeitijn Adasi Islet Tenedos Island: Ponente Pt. light Port Ajano: Nikolo Rock Port Ali-Agha: W. pt. of entrance Smyrna: English consulate flag-staff . . . Vourlah : Custom-house Sighajik Harbor: Beacon on islet Budrum : Light-house Adalia: Light-house Alexandretta: Light-house Latakiyah: Light-house Tripoli Roadstead: Bluff Islet light Ruad Island : Light-house Beirut: Light-house Saida ( ancient Sidon ) : Light-house SAr (ancient Tyre) : Light-house Acre: Li^ht-house Haifa: Light-house Famagusta: Light-house C. Gata: Light Lamaka: Light-house Port Said : High light-house River Nile: Damietta Mouth Rosetta Mouth light Aboukir Bay: Nelson I. peak Alexandria: Eunostos Pt. light Ben Ghazi : Castle Tripoli Harbor: Light-house Sfax: Ras Tina light Mehediah : Sidi Jubber Monastir: Burj el Kelb battery Hammamet Bay: Castle flag-staff Kalibia Road : Light-house Cape Bon : Light-house Tunis: Goletta light Cape Farina: Extreme Benzert: N. Jetty light Galita Island: Monte Guardia Bona: Fort Genois light Stora: Singe I. light Cape Bougaroni : Light-house Cape Carbon : Light-house Algier : Light-house near Admiralty Cape Tenez : Light-house Oran: Mers el Kebir light Habibas Island : Light-house Zafarin Islands: Light Isabel Segunda I Alboran Island : Light-house Ceuta: Light-house Tangier: Casbah tower Cape Spartel : Light-house 41 01 00 42 01 20 41 18 03 40 38 10 40 23 30 39 50 00 39 01 21 38 50 10 38 25 40 38 21 48 38 12 21 37 02 00 36 52 00 36 35 30 35 30 30 34 29 25 34 52 00 33 54 10 33 34 20 33 16 30 32 54 35 32 47 40 35 07 10 34 33 45 34 54 00 31 15 41 31 31 40 31 29 30 31 21 23 31 11 43 32 06 51 32 54 03 34 39 01 35 30 24 35 45 24 36 23 20 36 50 12 37 04 45 36 48 19 37 10 42 37 16 38 37 31 16 36 57 15 36 54 29 37 05 17 36 46 41 36 47 16 36 33 07 35 44 21 35 43 22 35 11 05 35 58 00 35 53 44 35 47 00 35 47 14 Long. E. 39 46 25 35 13 20 31 25 49 27 46 09 27 47 30 25 58 34 26 47 57 26 57 20 27 09 10 26 47 00 26 47 32 27 27 05 30 45 34 36 10 20 35 46 30 35 44 24 35 51 00 35 28 25 35 21 30 35 14 40 35 08 00 35 05 00 33 57 22 33 01 30 33 38 59 32 18 45 31 51 00 30 19 10 30 06.00 29 51 40 20 02 40 13 10 50 10 41 17 11 05 15 10 50 42 10 37 10 11 07 00 11 03 15 10 18 31 10 17 30 9 53 21 8 56 12 7 46 40 6 53 11 6 28 37 5 06 22 3 04 13 1 20 36 Long. W. 41 38 1 07 57 2 25 45 3 03 29 5 16 46 5 48 31 5 55 41 Lun. Int. H. W. i L. W. h. m. h. m. 9 15 9 45 9 40 9 40 9 45 9 55 10 00 3 35 3 33 2 46 1 55 1 30 Range. 3 15 i 2.5 3 35 3 30 3 30 3 15 3 45 3 50 9 57 9 55 8 58 8 07 7 40 1.2 1.4 LO 1.1 1.2 1.9 4.2 3.0 2.6 3.3 8.0 Neap. 0.7 0.3 0.4 0.3 0.3 0.3 0.5 1.1 0.8 L3 1.5 3.7 WEST COAST OF AFRICA. El Araish: S. pt. of entrance ... Sali: Fort Cape Dar el Beida: Light-house 35 12 50 34 04 10 33 36 00 6 09 13 6 48 00 7 33 00 1 35 7 45 10.4 4.8 APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. WEST COAST OF AFRICA— Continued. [Page 231 Place. Cape Blanco, North : Extreme Mogador Harbor: English consulate Cape Ghir: Extreme Cape Noun : Extreme Cape Juby : Extreme Cape Bojador: Extreme Penha Grande Ouro River entrance: Dumford Pt Pedra de Galha Cape Blanco, South : Extreme Portendik: Village St. Louis: Light-house Almadie Point: Light-house Cape Verde: Light-house Port Dakar: Light-house Cape Manoel : Light-house Goree Island: Fort Bird Island : Flagstaff Bathurst: Flagstaff Carabane: Light-house Nunez River: Sand I Ponga River entrance: Observation pt . . Isles de Los: Light-house Matacong Island: House Scarcies River: W. end of Yellaboi I Sierra Leone: Light on cape N. battery Sherbro Island: N. island Sherbro River: Manna Pt Gallinas River: AV. elbow of Kamaaounl. Cape Mount: W. peak Cape Mesurado : Light-house Monrovia: Light-house Marshall: Agent's house Grand Bassa: Agent's house Cestos: Factory Sangwin River: Sangwin Pt Sinon : Bloobarra Pt Cape Palnias: Light-house Tabou River: Tabou Pt Axim Bay: Ft. St. Anthony Cape Three Points: Light-house Dix Cove: Fort Tacorady Bay: Tacorady Pt Chama Bay: Dutch Fort El Mina Bay: Ft. St. George Cape Coast Castle: Light-house Accra: Light-house Lat. N. Volta River entrance: Dolbens Pt Lagos River: Light-house Benin River entrance: N. pt Brass River: Entrance (approx. ) Calebar River (New) : Rough Corner . . . Opobo River: W. pt. beacon (approx. ) . . Quaebo River: Bluff Pt Calebar River (Old) : Townsend flagstaff ( Dunketown) Fernando Po Island: Light-house San Bento River: Joho Pt. (approx.) ... Princes Island: Diamond Rocks, center of largest St. Thomas Island: Ft. San Sebastian light Anno Bon Island: Turtle Islet. Cape Lopez: Light-house Mayumba Bay: Light- house . . . 33 08 00 31 30 30 30 38 00 28 45 00 27 56 00 26 07 57 25 07 06 23 36 03 22 12 37 20 46 27 18 18 45 16 01 31 14 44 45 14 43 20 14 40 30 14 38 55 14 39 55 13 39 45 13 28 00 12 35 00 10 36 37 10 03 15 9 30 30 9 16 10 8 57 05 8 30 00 8 29 57 7 40 36 7 22 45 7 00 08 6 44 30 6 19 10 6 19 00 6 08 06 5 54 08 5 26 25 5 12 42 59 15 22 10 24 47 52 18 45 00 47 45 53 00 5 01 00 5 04 48 5 06 20 5 31 50 5 46 00 6 25 15 5 46 01 4 16 40 4 23 07 4 27 00 4 30 40 4 56 24 3 46 10 1 35 00 1 40 42 20 30 Lat. S. 1 24 18 36 25 3 23 00 Long. W. 8 35 05 9 43 30 9 50 00 11 02 00 12 56 00 14 29 00 14 50 44 15 58 00 16 48 11 17 05 40 16 02 00 16 30 22 17 32 25 17 30 55 17 25 28 17 26 47 17 24 30 16 40 30 16 35 00 16 44 00 14 42 00 14 04 30 13 44 00 13 26 20 13 18 25 13 18 30 13 14 30 13 04 30 12 31 55 11 38 45 11 22 51 10 49 25 10 50 00 10 22 45 10 04 05 9 34 45 9 20 16 9 02 05 7 44 15 7 21 30 2 14 45 2 05 45 1 56 40 45 00 38 00 21 05 13 50 11 30 Long. E. 41 00 3 25 15 5 03 05 6 15 00 7 07 00 7 40 00 7 59 00 8 20 46 8 47 05 9 39 00 7 27 56 6 42 45 5 38 12 8 43 10 10 38 00 Lun. Int. Range. H.W. L.W. Spg. Neap 1 05 11 55 11 50 11 35 h. m. "r'ii 5 43 5 38 ft. 'i6."9' 8.5 7.3 5 23 9 00 7 30 7 40 5 50 5 40 4 50 4 30 4 00 2 50 1 20 1 30 12 00 11 54 11 05 10 43 10 13 4 20 10 32 4 20 10 33 4 50 11 05. 4 25 10 38 5.5 5.9 11.4 11.6 10.4 6.0 4.8 4.3 4.7 6.0 4.2 3.3 7.0 ft. 5.0 3.9 3.4 2.5 2.7 5.2 5.3 4.8 2.5 2.0 1.8 1.9 2.5 1.8 1.3 2.9 1 Page 232] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. WEST COAST OF ATRICA— Continued. 1 Place. Lat. S. Long. £. Lun. Int. Range. 1 H. W. L. W. Spg. 1 Neap. 1 Loango Bav : Indian Pt. light o / // 4 40 00 4 49 00 5 18 30 5 32 30 6 04 36 6 31 50 8 48 24 12 20 00 12 34 43 13 12 30 13 26 05 15 09 00 15 47 30 16 30 00 18 23 00 22 57 00 26 17 00 26 37 52 26 58 30 29 15 12 30 18 33 30 33 07 33 07 51 33 48 52 33 56 04 34 21 12 O 1 If 11 46 30 11 45 00 12 08 00 12 11 00 12 15 00 12 25 25 13 13 20 13 32 00 13 23 45 12 48 55 12 36 00 12 12 00 11 52 40 11 42 00 11 57 12 14 30 00 14 57 20 15 07 02 15 12 22 16 52 02 17 16 20 17 27 30 18 01 21 18 22 33 18 28 40 18 29 26 *. 7?!. 4 13 /(. m. 10 26 ft. 6.5 St. 2.7 Black Point Bay : Sandy Pt Malemba Bay : Landing Cove Kabenda Bay: Kabenda Pt. light Congo River entrance: Shark Pt Margate Head: Summit 4 10 10 25 6.0 2.5 St. Paul de Loando: Flag staff, Ft. San Miguel 3 40 9 53 4.8 2.0 Lobito Point : Extreme Benguela: Telegraph office 3 30 9 43 5.5 2.3 Elephant Bay : Friar Rocks St. Marv Bay: Bav I Little Fish Bay : Light-house Port Alexander: Bateman Pt Great Fish Bay: Tiger Pt 3 00 9 12 5.7 2.4 Cape Frio: Extreme Walfisch Bay : Light-house Ichabo Island Angra Pequena: Diaz Pt Elizabeth Bay: S. pt. of Possession I Port Nolloth: Magistrate's house Hondeklip Bay 2 35 2 25 8 47 8 38 5.5 5.3 2.3 2.2 Roodewal Bay Saldanha Bav : Constable Hill 2 20 8 33 5.1 2.1 Table Bay: Robben I. light Cape Town : Observatory 1 36 7 47 4.6 2.0 Cape of Good Hope: Light-house EAST COAST OF AFRICA AND THE RED SEA. 34 10 45 34 23 48 34 46 45 34 49 45 34 23 47 34 11 10 34 04 35 34 06 15 34 12 30 34 01 41 33 57 43 33 50 27 33 36 09 33 28 00 33 23 10 33 05 10 18 27 30 18 50 20 19 38 17 20 00 37 20 48 40 22 09 31 23 03 38 23 24 23 24 50 20 25 42 12 25 37 21 26 17 13 26 54 10 27 03 00 27 20 48 27 49 12 27 55 02 28 22 36 29 06 40 29 21 15 29 33 16 29 48 40 31 03 50 31 51 39 32 27 39 32 38 10 32 35 52 35 29 45 35 31 41 35 29 00 35 29 30 34 53 30 34 46 00 36 11 47 36 58 30 37 01 09 2 35 8 48 5.2 2.2 Cape Hangklip: Extreme Quoin Point: Extreme Cape Agulhas : Light-house 2 40 8 53 5.2 2.2 Port Beaufort: Flag-staff St. Blaize: Light-house 3 18 9 31 5.6 2.0 Knysna Harbor: Fountain beacon Plettenberg Bay: Summit of Seal Pt St. Francis: Light-house Cape Recife: Light-house . Port Elizabeth : Light-house 3 21 9 33 5.4 1.9 Bird Islands: Light-house Port Alfred: Signal staff ■ Waterloo Bay: Maitland Signal Hill Madagascar Reef' Center Cove Rock: Center East London: Light-house 33 01 45 32 42 00 32 02 30 ^^ 4« 1."^ 3 37 9 50 5.0 1.8 Cape Morgan: Extreme Hole-in-the-Wall Rame Head* Extreme Cape Hermes: Extreme 31 38 06 Waterfall Bluff ! 31 26 15 Port Natal (Durban): Light-house I 29 52 40 Dumford Point: Extreme | 29 00 12 Cape St. Lucia: Extreme ' 28 32 30 CapeVidal- Extreme ^s f^f ^(^ 3 58 10 11 5.6 1.6 Delagoa Bay: Reut^en Pt. light Cape Corrientes: Small rock 25 58 49 24 05 30 5 10 11 22 n.9 3.4 Innamban Bay: Barrow Hill light Cape St. Sebastian: Extreme 23 45 30 22 05 00 21 31 00 20 38 10 20 10 42 18 52 50 18 01 24 17 51 50 4 30 10 42 n.o 3.2 Bazaruto Island: N pt light Chuluwan Island* Light-house Sofala: Fort on N. side of entrance Zambesi River: Kangoni Mouth Quillimane River: Light-house 4 15 10 27 13.5 3.9 Quillimane: Town Mazemba River: Entrance 17 15 00 M8 04 00 APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. EAST COAST OF AFRICA AND THE RED SEA— Continued [Page 233 1 Place. Lat. S. Long. E. Lun Int. Range. H. W. L. W. Spg. Neap. Premeira Islands: Center of Casuarina I. Angoxa Islands: Center of Hurd I Mafamale Island : Center O / II 17 06 30 16 33 24 16 20 30 15 08 00 15 02 12 15 00 45 14 58 20 14 53 00 13 23 40 12 55 45 12 19 30 11 09 18 10 41 20 10 19 22 10 16 31 10 06 43 9 59 30 9 44 22 9 25 36 8 57 15 7 38 10 6 49 41 6 26 10 6 09 43 5 00 35 4 04 30 3 12 48 2 15 42 2 13 35 1 13 00 22 35 Lat. N. 1 06 48 1 42 06 2 01 48 2 30 00 10 26 30 11 50 30 12 26 00 12 11 15 12 39 00 11 27 30 11 13 00 10 25 00 11 22 00 12 39 00 14 44 00 15 28 10 15 37 12 18 15 12 19 07 00 20 44 00 23 36 20 24 56 30 26 06 24 O 1 II 39 06 27 39 49 57 40 03 57 40 36 12 40 48 45 40 45 06 40 45 10 40 40 00 40 46 00 40 31 15 40 40 09 40 43 21 40 38 35 40 26 34 40 10 33 40 02 14 39 46 41 39 47 07 39 39 31 39 30 42 39 54 42 39 17 05 38 54 27 39 11 08 39 10 20 39 41 13 40 11 21 40 56 21 40 59 40 41 54 15 42 33 57 44 03 27 44 53 49 45 24 39 46 07 00 51 22 55 51 16 45 52 09 35 52 25 35 53 59 31 49 35 40 47 17 00 44 59 35 43 29 35 43 25 35 40 52 00 39 45 30 39 27 23 38 19 30 37 19 09 37 15 30 36 10 15 35 51 00 .34 17 03 h. m. h. m. Jt. ft. ::::::::::::::: i Port Mokamba: Mokambo Pt i Port Mozambique: St. George I. light... San Sebastian light. . Cape Cabeceira: Light-house 1 4 00 10 12 11.8 3.4 Port Conducia: Bar Pt i Lurio Bay : Pando Pt 1 Peniba Bav : N. pt. light ::::::::::::::::: i Querimba Islands: Ibo I. light Numba Island : K. pt \ Cape Delgado : Light-house 3 59 10 11 11.3 3.3 Msimbati : Ran Matunda Mikindini Harbor: Kinizi Mgan Mwania: Madjori Rock Lindi River: Fort flagstaff 3 55 10 08 10.9 4.5 Mchinga Bay : Observation spot Kiswere Harbor: Rustmigi Kilwa Kisiwani: Fort Mafia Island: Moresby Pt Dar-Es-Salaam : Flagstaff 1 Bagauioyo; French Mission Zanzibar: English consulate 4 05 10 17 14.5 6.0 Tanga Bay: Light-house Mombasa: Light-house :::::;:::: i Port Melinda: Vasco de Gama's Pillar . . Lamo Bay : Lamo Castle 4 00 10 13 12.1 5.0 Manda Roads: E. side of Manda Toto I . Port Durnford: Foot Pt 4 30 10 42 n.7 4.9 Kisimayu Bay: S. pt. of Kisimayu I Brava: Well 4 15 10 27 7.5 3.1 Meurka Anchorage: S. pt. of town Magadoxa: Tower Murat Hill: Peak Ras Hafun: E. extreme of Africa Cape Guardafui : E. pt 6 00 12 12 6.1 2.5 Kal Farun Islet: Center Abd-al-Kuri Island : NE. pt 1 Socotra Island: Tamarida, mosque Ras Antareh: Extreme of rocky pt Miiit Island : Center 7 05 1 17 7.5 3.1 1 Port Berbera: Light-house 1 Zeyla: Mosque 7 30 7 50 1 18 1 38 8.5 7.2 3.5 3.0 Perim Island: Light- house Hanfelah Bay: Hanfelah Pt Disei Island : Village Baj' Massaua Harbor: N. pt. of entrance Khor Nowarat: Shatireh Islet 45 6 57 4.0 1.7 Suakin : Light-house 2 10 8 22 L7 0.7 Makaua Island : S. pt St. Johns Island : Peak Daedalus Shoal : Light-house [ Kosair Anchorage: SW. angle of fort Brothers Island : Light- house .1 _ ._ ..1 26 18 50 1 34 50 45 26 45 48 ' 33 59 43 6 40 28 2.0 0.8 Safajah Island: N. summit Ashrafi Island: Light-house 27 47 21 28 20 52 29 06 29 29 53 05 28 13 47 27 35 45 27 33 00 26 13 00 24 38 35 24 05 15 33 42 28 33 06 31 32 39 43 32 32 50 33 36 56 35 30 30 35 32 30 36 27 00 37 17 45 38 02 45 1 Ras Gharib: Light-house 10 35 10 40 10 45 4 23 4 28 4 32 1.5 5.5 6.8 0.6 2.3 2.8 Zafarana: Light-house Suez : Newport Rock Tor: Ruined fort Sherm Yahar: Entrance i Sherm Joobbah : Entrance t Sherm Wej : Light-house Sherm Hassejy : Anchorage 1 Yembo: Anchorage :::::: i « Page 234] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. PIAST COAST OF AFRICA AND THE RED SEA— Continued. o Place. Lat. N. Long. E. Lun. Int. Range. 1 H.W. L.W. Spg. Neap. 1 i Sherm Rabigh : ^ichorage Jiddah: Jezirah el Mifsaka I / // 22 43 50 O 1 II 39 00 30 39 10 38 40 12 00 40 30 00 41 03 20 41 27 30 41 58 15 42 29 00 42 38 45 42 34 00 42 56 00 42 45 28 43 13 36 h. m. h. VI. ft. ft. 21 28 00 20 09 00 3 30 9 42 2. 0. 8 Lith: Agha Islet Jelalil: Anchorage 19 55 30 Kunfidah: Islet ' 19 07 40 j Khor Nohud: Entrance 18 15 50 Farisan I. Anchorage: Jebel Mandhakh . Gizau : Fort .. 16 50 15 16 53 00 15 42 00 15 20 30 14 47 00 14 03 53 13 19 43 Loheiya: Hill Fort 1 15 7 27 2.9 1.2 Kauiardn Bay : Harbor. .... Hodeida Road Jebel Zukur Island: N. pt Mokha: N. Fort 11 45 5 33 4.5 L9 ISLANDS OF THE INDIAN OCEAN. i d > • fl e g ss Chitlac Islet: S. end 11 40 45 11 35 00 11 27 30 11 13 00 11 06 00 10 47 00 10 32 00 10 06 00 10 03 00 8 16 00 6 55 00 6 59 00 6 25 00 5 26 30 5 01 30 4 25 45 4 44 00 4 10 15 3 41 00 2 57 00 3 16 00 2 10 30 2 07 00 14 30 Lat. S. 41 30 5 40 56 4 52 26 5 53 00 4 37 15 3 43 06 5 15 00 7 13 37 16 25 12 19 40 22 19 52 36 19 59 45 20 08 46 20 24 20 72 42 54 72 09 54 72 59 00 72 44 00 72 41 00 73 40 00 72 37 40 72 15 10 73 35 54 73 01 15 72 55 54 73 12 54 72 41 54 73 20 00 72 53 00 72 57 24 73 28 00 73 30 24 73 24 54 73 34 24 72 48 00 73 03 00 73 35 54 73 13 00 73 06 54 53 41 03 53 23 38 55 27 10 55 27 23 55 12 19 71 43 47 72 23 50 59 46 40 63 25 38 57 39 14 57 32 35 57 29 26 57 47 14 Betrapar Islet: N. Island Kittau Islet : S. end 10 20 4 00 6.3 3.0 Cardamum Islet: Center Ameni Islet: N. end Underut Islet: Center Cabrut Islet: E. end Seuheli Par: N. islet Kalpeni Islet: S. end Minikoi Island : Light-house 11 27 5 15 2.5 1.2 Heawandu Island : S. end Kee-lah Island : N. end . Mah Kundu Island: NE, extreme Nar Foree Island Hee-tah-doo Island To-du Island : Center .. Gafor Island : Center Male, or Kings Island: Flagstaff Pha-li-du Island : Northern end 20 6 25 2.9 1.4 Moluk Island: Center Himniittee Island Kimbeedso Island : S. end Esdu Island : NE. pt Wahdu Island : E. end Addu Atoll: Gung I Amirante Islands: Iledes Roches, N. beach African Islands Seychelle Is., Platte I. : S. end Port Victoria: End of Ho- doul Jettv 4 22 10 35 4.3 1.2 Bird Island: Tree Chagos Archipelago, Peros Banhos: Dia- mond Islet Diego Garcia : N. end of Middle I Cargados Carajos: Establishment I., flag- staff 1 30 1 50 20 7 43 8 03 6 32 5.8 4.0 5.5 L7 1.2 1.6 Rodriguez Island: Mathurina Bay, Point Venus Flat Island : Light-house Cannonier Point: Light-house Port Louis: Martello tower. Ft. George.. Grand Port: Fouquet I. light 48 7 00 1.6 0.3 APPENDIX IV. [Page 235 MARITIME POSITIONS AND TIDAL DATA. ISLANDS OF THE INDIAN OCEAN— Continued. 1 Place. Lat. s. Long. E. Lun. Int. Range. 1 H.W. L. W. Spg. Neap. it -0 Reunion Island: St. Denis light Bel- Air light O 1 II 20 51 38 20 53 11 20 59 45 21 19 47 15 51 .37 10 21 30 10 06 45 7 00 30 7 06 00 25 39 10 25 12 30 25 03 00 23 38 25 22 05 18 21 54 24 20 18 18 19 49 30 17 53 00 17 29 00 16 12 10 16 07 00 15 46 30 15 43 45 15 11 42 14 40 18 13 59 00 13 55 40 13 27 15 13 23 38 12 49 30 12 27 20 12 03 18 11 57 30 12 23 20 12 44 02 12 49 00 12 56 48 13 21 15 15 15 48 15 54 50 15 27 55 16 14 00 17 00 05 16 42 30 17 23 16 18 09 47 19 55 00 21 58 10 24 46 25 24 59 42 24 58 50 25 01 30 22 22 30 21 29 00 12 26 30 12 47 02 12 16 20 L2 25 00 LI 34 48 LI 40 44 9 46 20 9 22 35 9 41 20 O / II 55 26 59 55 36 18 55 16 18 55 28 58 54 28 46 56 32 00 51 10 21 52 44 57 56 22 00 45 06 50 44 17 57 44 07 20 43 38 20 43 15 20 43 20 21 44 19 21 44 31 30 44 02 20 43 45 18 44 29 05 45 17 09 45 43 09 46 18 45 46 57 29 47 24 36 47 58 21 47 48 05 47 59 30 48 17 34 48 38 57 48 45 45 49 11 21 49 17 25 49 35 56 49 45 06 49 54 00 49 56 25 50 01 59 50 31 21 50 16 05 49 49 11 49 50 59 49 50 59 49 56 15 49 32 04 49 25 31 48 52 10 48 14 50 47 10 34 47 07 20 47 04 24 46 59 11 40 24 10 39 40 39 46 32 35 45 16 27 44 24 54 43 47 00 47 24 09 43 19 15 46 31 07 46 14 52 47 32 25 h. m. h. m. ft- ft. St. Paul light St. Pierre light Tromelin Island : N. end Agalegas Island: NW. pt 11 50 5 38 3.5 0.6 FarQuhar Islands" Hall's house Alphonse Island: SE. part (Trees) Coetivv Island : N. en( Cape St. Mary : S. extreme Lev en Island : Center Port Machikora : Barracouta I . St. Augustine Bay : Nosi Vei I 5 40 11 52 9.8 2.9 Murderers Bay: Center of Murder I Cape St. Vincent' Extreme .... Mourondava : Village Tsniano: Village Kovra Rythi Point: Extreme Coffin Island : Nosi Vao Cape St. Andrew : Extreme Boyanna Bay : Barabata Pt ........ Cape Tauzon : Extreme Majunga (Mojanga): Light-house Majamba Bay : W. pt 4 15 11 28 10.9 3.2 Narendri Bay : Modrmora Pt Port Radama: Pt. Blair ... Radama Islands: N. pt. Nossuvee I Baratoube Bay : Ambubuka Pt. Nosi Be : Hellville jetty Minow Islands: N. pt. Great I Cape San Sebastian : Extreme Port Liverpool: N. pt. of entrance Cape Amber: NE. extreme Port Lady Frances: Sunson Pt Port Looke: Pt. Bathurst PortLeven: S. pt. Nosi Haul . Andrava Bav : Berry Head Vohemar : Flagstaff Cape East: Ugoncy I Venangue Be Bay : Entrance Port Choiseul: Maran Seelzy Village Cape Bellone : Extreme 3 45 9 57 5.1 1.5 St. Marys Island: Light on Madame I .. Port Tantang: Flagstaff ::::::::.::: i 1 Fenerive Point: Flagstaff Tamatave: Pt. Hastie Mahanuru : Town 4 00 10 12 7.3 2.1 Matatane: Village Santa Lucia: N. end of town, Obs. Rock. Point Ytapere : Extreme Ytapere Ba v : N. pt ! Fort Dauphin : Flagstaff 4 15 10 27 4.7 1.3 Europa Island : Center Bassas da India: E. pt j Geyser Reef: SE. extreme Mayotta Island : Zaoudzi 4 00 10 13 1L9 2.0 Johanna Island: Landing place, Pomoni Harbor Mohilla Island: Numa Choa Harbor Glorioso Islands: W. islet Comoro Island: Islet in Mauroni Bay... Assumption Island : Hummock 4 45 10 58 10.0 L7 Aldabra Island: Westl., E. sideentrance. Cosmoledo Islands: Observation islet 1 Page 236J APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ISLANDS OF THE INDIAN OCEAN— Continued. 1 Place. Lat. S. Long. E. Lun. iHt. Range. 1 H. W. L. W. Spg. Neap. M N 2 •s M e « s « Prince Edwards Islands: Marion I., Obs. spot, NE. side.? o / // 46 49 30 46 36 00 46 22 00 46 01 00 46 28 18 46 10 40 46 26 00 48 40 00 48 26 45 49 42 00 49 21 22 o r II 37 49 15 50 41 30 51 30 15 50 40 00 51 50 00 50 35 00 52 13 00 69 04 00 68 48 20 68 54 00 70 04 31 70 15 00 70 29 50 73 15 30 73 52 00 72 31 45 77 31 53 77 29 15 96 53 02 105 45 57 A. TO. h. m. ft. ft. Penguin Islands: Center of SW. islet ... Possession Island : N W. pt Twelve Islands: Summit NE. I Navire Bav Hog Island: Summit East Island: Center Christmas Harbor Blighs Cape Cape Bourbon :::::: i Mollov, Port Roval Sound: U. S. Tr. of Venus Obs., 18*74 14 6 36 4.6 L3 Cape Challenger 49 41 00 Balfour Rock 49 29 00 53 02 45 53 13 00 53 02 50 38 42 51 37 50 00 12 06 22 10 25 19 ::::::::::: i Heard Island: Cape Laurens, NW. end.. Sealing station . McDonald Island, Summit St. Pauls Island : Ninepin Rock 10 40 10 50 5 20 7 10 4 28 4 38 11 32 1 00 3.0 3.3 5.1 4.5 0.9 1.0 1.5 L3 Amsterdam Island: Summit, 2,750 feet.. Keeling or Cocos Islands: Direction I Christmas Island: Flying Fish Cove SOUTH COAST OF ASIA. 1 i £ Aden : Telegraph station Lat. N. 12 47 16 13 22 00 13 24 50 13 28 45 14 20 10 14 31 15 14 43 50 14 49 00 14 54 40 15 12 00 15 38 00 16 30 00 16 59 00 17 32 45 17 53 15 19 00 25 20 10 00 20 31 30 22 32 40 23 38 00 23 52 00 23 51 30 24 21 50 25 21 00 26 24 13 26 30 00 25 21 34 24 29 02 25 17 24 26 10 55 26 13 56 30 32 00 29 22 56 29 15 25 28 59 07 26 47 40 26 33 37 Long. E. 44 59 07 45 40 50 46 26 35 46 39 00 48 56 45 49 07 35 49 35 05 49 57 05 50 16 35 51 10 30 52 14 20 52 48 00 54 43 29 56 03 05 56 20 35 57 51 35 58 38 35 58 58 35 59 48 35 58 30 50 58 08 00 57 26 00 56 46 12 56 22 56 56 32 22 56 31 29 55 24 12 54 22 14 51 33 32 51 13 46 50 32 17 47 51 23 48 00 55 50 21 11 50 50 35 53 23 36 54 02 21 7 49 1 41 4.9 2.0 Sughra: Sheik's house Mokatein : Black ruin Howaivuh: Sheik's house Banderburum : SE. house of town Makalleh Bay: Flagstaff 8 20 2 07 6.8 2.8 Shahah Roads: Custom-house Sharmoh : Single house Kosair: High house Sihut : Center of town . Ras Fartak: Extreme pt Damghot: Town Merbat: Town 8 50 2 38 7.0 2.9 Kuria Maria Is., Hullaniyeh I. : NE. bluff Ras Sherbedat : Point Cape Isolette: Islet Masirah Island : Point Abu-Rasas Point Ras Ye 9 45 9 15 9 30 3 32 3 03 3 20 9.6 8.9 6.0 4.4 4.1 2.8 Ras-al-Hed : Extreme pt Maskat ( Muscat ) : Maskat Pt Deimaniveh Islands: E. islet Sueik : Fort Sohar' SE tower of town hall Khaur Fakan Bay: W. end of village... Ras INIusendom : N. end of island Great Quoin Islet: Center Sharjah: High tower with flagstaff Abu-Thabi: Fort flagstaff Al Beda'a Harbor: Nes8ahPt.,N. extreme Ras Rakkin: NW. pt Bahrain Harbor: Portuguese fort Basrah: Custom-house flagstaff 6 15 11 30 6.4 3.7 Kuweit Harbor: N. end of town Khdrig Islet: Fort fla^taff 06 6 17 8.3 4.8 Abu Shahr: Residencv flagstaff 7 12 1 13 2.6 1.5 Shaikh Shu'aib Islet: E. end. Kais Islet: NE. pt 30 6 40 6.6 3.8 APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. SOUTH COAST OF ASIA— Continued. [Page 237 Place. Lat. N. Basidiih: Chapel 26 39 12 Haujam Islet: Ruined mosque ' 26 40 49 Kasm: Fort ' 26 57 27 Jashak Bay: Telegraph office 25 38 19 KubKalat: High peak, 1,680 feet 25 29 45 ChahbarBay: Telegraph office 25 16 43 GwatarBay: Islet 25 03 17 ! Gwadar Bay : Telegraph office | 25 07 19 Pasni: Telegraph office 25 15 52 Onnarah: Telegraph office Sunmiyani: Jam's house.. Cape Monze: Peak Karachi : Manora light Observatory Mandavi : Light-house Bey t ( Bet ) : Light-house Dwarka: Light-house Temple spire Porebander: Light-house Mangarol: Light-house Diu Head : Light-house Kutpur: Light-house Bhaunagar: Light-house Perim Island : Light-house Cambay : Flagstaff Surat River: Tapti light Surat: Minaret Adrusah Bassein : Center of town Bombay : Observatory Kenery Island light Bankot: Fort Victoria Ratnagherry : Fort Viziadrug: Fort flagstaff Cape Ramas: W. bastion of fort ... Goa: St. Denis Church Agaada light Vingorla: Signal-station light Vingorla Rocks: Light-house Sedashigar Bay: Oyster Rock light. Kumpta: Light-house Hindwar: Monument Kundapur: Light-house Mangalore: Light-house Kannanur: Light-house Tellicherri : Flagstaff Mahe : Light-house Calicut: Light-house Cochin : Light-house Alipee : Light-house Quilon: Tongacherri Point light Trevandrum : Observatory Cape Comorin : Light-house Trichendore : Pagoda on pt Tuticorin : Light-house Paumben Pass : Light-house Manaar: Center of town Colombo : Light-house , Dondra Head : Light-house , Point de Galle: Light-house Great Bassas Rocks: Light-house Little Bassas Rocks: Light-house , Batticaloa: Light-house Trincomali : Dock-yard flagstaff. . Calimere Point: Light-house Negapatam : Light-house Pondicherri: Light-house ... 25 11 55 25 25 19 24 50 03 47 37 49 50 50 00 29 20 14 00 14 00 38 00 06 00 41 20 02 21 47 00 35 54 17 00 05 20 12 19 20 10 53 45 42 08 58 00 59 30 33 26 05 12 21 24 29 25 51 10 53 20 49 00 25 00 17 28 38 15 52 17 5i 10 45 00 42 00 15 10 58 00 30 00 53 20 30 47 04 00 29 55 47 10 17 20 8 59 00 6 55 40 5 55 30 6 01 25 6 10 10 6 25 00 7 45 00 8 33 30 10 18 00 10 45 28 11 55 40 Long. E. 55 16 47 55 54 25 56 17 37 57 46 14 59 40 32 60 37 40 61 26 24 62 19 42 63 28 37 64 37 02 66 35 39 66 39 58 60 58 06 67 01 33 69 20 15 69 04 40 68 57 06 68 58 54 69 36 00 70 06 32 70 50 45 71 49 35 72 14 00 72 21 08 72 35 10 72 38 40 72 49 27 72 48 44 72 48 56 72 48 49 73 02 40 73 15 56 73 19 39 73 54 50 73 54 00 73 46 10 73 37 00 73 27 15 74 03 40 74 22 30 74 26 40 74 39 50 74 50 40 75 21 51 75 29 40 75 31 10 75 46 40 76 14 40 76 20 40 76 34 00 76 56 45 77 32 35 78 07 47 78 11 26 79 12 50 79 53 52 79 50 40 80 34 12 80 13 04 81 28 15 81 44 00 81 41 00 81 13 42 79 51 30 79 50 47 79 50 10 Lun. Int. h. m. 10 50 9 20 9 20 8 50 10 15 "i2'65' 4 27 11 26 'Ai 10 34 10 50 11 21 11 33 18 1 55 2 02 8 10 8 37 L. W. h. m. 4 35 3 05 3 05 2 35 4 00 '5*39' 11 18 5 08 4 10 4 11 4 28 4 59 5 06 6 16 1 52 7 51 1 37 7 36 7 49 8 07 1 44 2 37 Range. Spg. 11.6 7.8 ^.1 7.3 10.8 12.0 5.2 5.0 6.5 2.7 2.1 2.5 3.0 2.0 2.0 2.0 2.1 Neap. 5.3 3.6 3.7 3.8 3.4 5.2 29. 8 15. 1 4.9 2.5 2.4 3.4 1.4 1.0 1.3 0.8 0.5 0.4 0.4 0.5 0.9 Page 238] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. SOUTH COAST OP ASIA— Continued. Place. Madras: Observatory Light-house Pulicat: Light-house Armeghon : Light-house Kistna: Light-house Masulipatam : Flagstaff Coconada: Light-house Vizagapatam: Fort flagstaff Kalingapatam : Light-house Gopalpur: Light-house Gaujam: Fort Juggernath : Great temple False Point : Light-house Balasor River: Chandipur light .. Saugor Island: Light-house Diamond Harbor: Flagstaff Calcutta: Ft. William semaphore. Chittagong River: Light-house Akyab: Oyster Reef light Old temple Ramree Island: S. pt Chedubah Island: N W. peak Cape Negrais: Extreme Bassein River: Alguada Reef light Bassein: Port Dalhousie Andaman Is.: Table Id., Light-house . Port Cornwallis, Rock in entrance Port Blair, Light- house. Little Andaman Island, SE.pt Krishna Shoal: Light vessel Rangoon River: Grove Pt. light Rangoon : Great Dagon pagoda Moulmein : Docks Moulmein River: Amherst Pt. light. . . Double Island : Light-house Tavoy River: Light-house Mergui: Court-house Tenasserim St. Matthew Island: Hastings Harbor.. Pak Chan River: Light-house Tongka Harbor, Junkseylon Island: Light-house Pulo Penang: Fort Cornwallis Dinding Channel : Hospital Rock One Fathom Bank : Light-house Cape Rachado : Light-house Malacca; Stat. St. Pauls Hill Singapore Strait: Coney Island light... Singapore: Fullerton Battery Singapore Strait: Pedra Branca light . . . Summit Bintang great hill, 1,253 feet Rhio Straits, Pulo Sauh: Light-house .. Terkolei : Light-house Little Garras: Light-house Rhio, Bintang Island: Residency flag- staff Pitong Island : Peak Abang Besar Island : N. pt Linga Island : Flagstaff Singkep Island: Mountain summit. Menali Island: N. pt Nicobar Islands, Car Nicobar: N. pt . . . l^t. N. 13 04 06 13 05 15 13 25 15 13 53 08 15 47 00 16 09 45 16 56 21 17 41 34 18 19 00 19 13 00 19 22 30 19 48 17 20 20 20 21 27 15 21 38 40 22 11 10 22 33 25 22 11 00 20 05 00 20 08 53 18 51 00 18 50 30 16 01 30 15 42 14 16 01 30 14 12 30 13 18 40 11 40 40 10 27 00 15 37 26 16 30 01 16 46 00 16 26 00 16 04 45 15 52 00 13 36 40 12 26 15 12 06 00 10 05 05 9 58 00 50 00 24 45 13 05 52 10 24 08 11 30 1 09 57 1 17 11 1 19 57 1 04 20 1 03 13 57 10 44 30 55 50 36 52 36 30 Lat. S. 12 34 26 13 57 51 Lat. N. 9 15 40 Lun. Int. Long. E. H.W. 80 14 51 80 17 00 80 19 12 80 12 30 80 59 00 81 11 00 82 15 05 83 17 42 84 07 30 84 52 06 85 03 29 85 49 09 86 44 00 87 02 20 88 02 00 88 11 07 88 20 12 91 49 00 92 39 00 92 52 40 93 56 30 93 31 00 94 13 16 94 12 00 94 23 00 93 22 30 92 57 10 92 45 15 92 31 10 95 37 32 96 23 00 96 07 30 97 38 00 97 33 05 97 35 00 98 13 00 98 35 59 99 03 00 98 10 15 97 35 00 98 25 30 100 21 44 100 34 15 100 59 12 101 51 02 102 15 00 103 44 47 103 51 15 104 24 08 104 27 21 104 10 30 104 19 52 104 21 19 104 25 43 104 04 42 104 11 31 104 36 14 104 30 15 105 38 20 92 48 00 h. m. 8 41 8 42 8 48 9 21 1 25 1 02 9 40 3 05 9 50 9 40 4 26 3 07 2 12 10 50 10 40 11 50 5 50 7 20 10 18 9 40 L. W. h, tn. Range. Spg. Neap. ft. 2 26 3. 1 2 36 2 34 4.5 4.4 3 00 I 6. 8 9 06 11.2 7 56 3 28 9 55 3 37 3 27 11 15 10 49 8 49 4 20 4 10 5 40 12 00 "I'os "'4'62 3 14 6 00 1 12 13 13.1 18.7 6.3 16.9 11.7 19.2 15.6 18.0 14.4 10.5 "7.*6" 7.1 11.6 ft. '{'.2 1.9 1.8 2.6 4.4 5.6 "3.'6' 2.9 2.1 7.0 5.0 7.4 3.8 6.2 "4.' 5 "3.'2 3.1 APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. SOUTH COAST OF ASIA— Continued. [Page 239 Place. Nicobar Islands, Nancowrv Harbor: Naval Pt Great Nicobar: AV. pt. Galathea Bay . . Acheen (Acheh) Head: Pulo Bras light N. extreme Diamond Point: Light-house Point Baru or Datu: Extreme Point Bon or Djabon : Extreme Moeara-Kompehi : Fort Djambi: Flagstaff of fort Palembang: Residency flagstaff Lam pong Bay: Telok Betong light Blimbing Bay Kroe: V'^illage Engano Island: Barioe anchorage Bintoean: River mouth Mega Island : N. pt Benkulen : Light-house Bantal : Village Indrapura Point: Extreme Pisang: Light-house Padang: Light-house Siberaet Island : Sigeb Pt Katiagam : Village Batoe Islands: N. point of Simoe Islet. Summit of Tello Lat. N. 8 02 10 6 46 20 5 45 00 5 34 40 5 15 58 Lat. S. 00 32 Ayer Bangis: Fort flagstaff Natal: Fort flagstaff. Nias Island : Lagoendi Bay Sitoli Lapan Siboga: Flagstaff Singkel : Post-office Bangkaru Islands: Bay Simaloe Island: NW. pt Tampat Toewon; Flagstaff Analaboe Batve Toetong: Landing place. 00 55 23 13 35 33 59 26 27 00 55 02 11 24 18 50 48 35 59 25 47 22 44 54 10 35 59 56 57 53 53 58 07 41 03 13 02 56 Lat. N. 11 41 33 11 34 47 17 36 24 16 44 24 16 47 02 32 51 30 14 59 08 14 38 21 Long. E. 93 29 42 93 49 20 95 04 33 95 19 00 97 30 11 103 47 58 104 21 30 103 59 14 103 36 41 104 45 34 105 15 58 104 32 36 103 55 42 102 07 28 103 20 18 101 00 58 102 14 50 101 17 25 100 50 06 100 19 28 100 20 19 98 53 58 99 45 20 98 05 55 98 16 43 99 22 09 99 06 33 97 43 43 97 36 46 97 12 28 98 46 08 97 45 06 97 06 53 95 56 02 97 10 13 96 07 23 95 34 29 Lun. Int. Range. H. W. h. m. 9 05 10 00 11 50 5 50 5 35 5 29 L. W. Spg. Neap. h. TO. 2 52 ft- 8.3 ft. 2.8 3 44 5 34 5.2 8.7 2.3 3.7 5 40 11 52 2.6 0.7 12 03 4.0 1.1 11 48 5.5 1.4 11 42 2.8 0.7 EAST COAST OF ASIA. Java Head : First Pt. light Sunda Strait: Krakatoa I. peak North Watcher Island: Light-house. . . Lucipara I. : Beacon Banka Island: Tobol Ali Fort . . . . Berikat, summit Nanka I. : Light-house Banka Island: Mintok light Blinyu Crassok Pt Shoal water Island : Light-house Pulo Lepar: Light-house Pulo Jelaka: Light-house Billiton Island: Tandjong Pandanflag staff Langkuas I. light ' Caspar Island: Peak Lat. S. 6 44 30 6 08 46 5 12 17 3 13 05 3 00 48 2 34 18 •2 23 20 2 04 03 1 38 26 1 29 00 3 19 10 2 56 52 2 52 05 2 44 40 2 32 12 2 24 30 105 11 48 105 26 58 106 27 33 106 13 02 106 27 22 106 50 36 105 44 30 105 09 45 105 46 28 106 57 30 107 12 42 106 54 38 107 00 43 107 38 46 107 37 15 107 03 33 5 30 6 50 [9 05] [6 50] [2 08] [3 17] 11 42 37 2.5 3.8 [2 52] [10. 1] [0 38] [9.3] [8 21] [5. 6] [9 29] [6. 6] 0.7 1.1 Page 240] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. EAST COAST OF ASIA— Continued. Place. Carimata Island : Sharp peak Pulo Eu: Center? Pulo Aor: S. peak, 1,805 feet St. Barbe Island: Center of W. side Direction Island: S. pt Dato Island: Summit St. Julian Island: Summit Tambelan Island: S. pt Tamban I. obs. station Victory Island : S. pt Anamba Islands: White rock Pulo Repon Pulo Domar St. Pierre Rock: S. pt. Natuna Islands: Pyramidal rocks Semione I Pulo Varella: Center Pulo Brala: Center Tringano River: N. pt Great Redang Harbor: Bukit Maria I . . Kalantan: Entrance small river Cape Patani: NE. pt Singora: SW. pt. of Ticos I Koh Krah Islet: SE.pt Bangkok: Old British factory Cape Liant: NW. rock of Koh Mesan . . Chentabun River: Entrance, Bar I Koh Chang: Small island on W. side .. Koh Kong: S. pt. of river entrance Kusrovie Rock: Center Koh Tang Rocks: SW. rock of group . . Panjang Island : NW. corner of SW. bay. Obi Islands: Light-house Saigon : Observatory Mitho: S. gate of citadel Cape St. James : Light-house Cape Padaran: Extreme Cape Varella: Extreme Quin Hon : Battery flagstaff Condore Islands: Light-house Safatu Island : Summit Ceicer de Mer Island : SW. hill Natuna Islands: Murundum I., SE. pt. . Low I Canton Pulo: Light-house Cham-Callao Islet: Watering place Tourane Bay: Light-house Hon-Me: Sunmiit Nam-Dinh : Citadel tower Hon Dau Island: Light-house Hai-Fong: Observation pagoda Hai-Duong: Citadel tower Ha-Noi: Citadel tower Pak-Hoi : Custom-house flagstaff Hainan Island : Cape Bastion, extreme . Gaalong Bay, E. Brother Lat. S. 1 33 24 2 07 00 2 26 30 Lat. N. 07 26 14 19 06 37 55 00 56 52 00 27 34 41 18 10 25 00 44 31 51 42 03 00 31 00 3 17 00 4 53 00 5 21 40 5 44 21 6 11 53 6 58 01 7 13 54 8 24 47 13 44 20 12 35 08 12 27 43 12 01 20 11 33 00 11 06 25 10 21 20 9 18 14 8 25 20 10 46 47 10 21 16 10 19 51 11 21 00 12 53 40 13 45 23 8 40 06 9 58 23 10 32 36 2 02 55 3 00 00 15 23 34 15 57 10 16 07 00 19 22 14 20 25 30 20 40 03 20 51 44 20 56 29 21 01 57 21 29 00 18 09 00 18 11 30 Long. K. Lun. Int. Range. H. W. L. W. Spg. Neap. 1 II 108 55 13 h. m. h. m. ft. ft. 104 17 00 104 34 06 1 107 13 00 108 01 47 108 37 05 106 45 00 107 32 57 106 24 10 106 18 27 105 35 58 105 52 00 105 22 57 108 38 55 107 21 40 107 42 30 103 40 00 103 38 00 103 08 00 103 01 37 8 00 1 48 5.8 2.5 102 20 47 101 18 39 100 36 12 100 45 27 8 20 2 08 2.8 L2 100 28 42 100 56 47 8 00 2 00 7.3 3.1 102 04 19 102 15 47 10 00 3 50 4.5 2.1 102 57 14 102 47 49 102 56 34 103 29 14 104 48 30 106 42 10 106 20 38 5 00 11 20 9.8 4.2 107 04 55 108 58 00 109 23 42 109 14 52 106 41 42 109 06 00 108 56 27 109 06 10 107 48 00 109 05 35 108 32 47 108 11 30 105 55 22 106 08 41 106 47 10 106 41 08 9 00 2 48 4.3 2.1 106 17 56 105 48 40 109 06 00 109 35 00 5 00 11 12 14.0 6.6 109 41 30 APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. EAST COAST OF ASIA— Continued, [Page 241 Place. Hainan Island : Light-house Paracel Islands : Triton I Observation bank . . . Lincoln I Woody I Pratas Island : NE. part Ty-f ung-kyoh Island : Center Tien-pak Harbor: Pauk Pyah Islet ... Song-yui Point: Extreme Hui-lang-san Harbor: Mamechow Islet Mandarins Cap: Summit, 200 ft Macao ; Fort Guia light Fort San Francisco Canton : Dutch Folly light Raleigh Rock : Center Gap Rock: Light-house Hongkong: Cathedral Wellington Battery Lema Island : Lema Head Nine-pin Rock : Center Tuni-ang Island : Summit Single Island : E. summit Mendoza Island : Summit Pank Piah Rock: Summit Pedra Blanca Rock: Summit, 130 ft... Chino Bav: Obs. spot Cupchi Point: Hill Breaker Point: Light-house Cape of Good Hope: Light-house Swatau : British consulate Lamock Island : Light-house Brothers Islets: SE. Islet Tong-sang Harbor: Fall Peak Chapel Island : Light-house Amov : Taitan I. light Dodd Island : Light-house Chinchin Harbor: Pisai Islet Pyramid Point: Extreme Ockseu Island : Light-house Sorrel Rock: Summit Lamyit Island : High Cone Peak Hungwha Channel : Sentry I Turnabout Island : Light-house East Dog Island : Light-house Min River: Pagoda, Losing I TemplePt Alligator Island : Summit Tung-yung Islands: Peak, N. end Coney Island: Summit Double Peak Island : Highest peak . . . Pih-seang Island : Town I Dangerous Rock: Summit Tae Islands: Summit Nam-.. Capa Bojeador: Light- house Mairaira Pt. : Semaphore Aparri : Plaza 5 43 -0 02 3.2 1.9 , Port San Vicente: San Vicente Islet CapeEngano: Rona Islet Camiguin I. : Summit Fuga Island: W. summit. Dalupiri Island : Peak . . . Calayan Island : NE. pt 6 00 -0 12 5.0 2.7 Babayan Claro Island : W. pt Page 246] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. EAST COAST OF ASIA— Continued. Place. Lat. N. Balingtang Islands Batan Island : Morfnt Irada Ibayat Island : Mount Santa Rosa Yami Island: Islet off SW. part Luzon Island, Port Dimasalasan: En- f 1*3.11 OP Polillo I.V PoVt'PoliYlo' '. Tabaco: Church belfry . Cautanduanco Islands: N. islet Cautanduanco Islands: S. extreme Point Calaan : S. extreme' Port Sorsogon, Tinacos Islet Masbate Island, Palanog: Pier Bugui Pt. light-house.. Camasusu I.: Summit . Tintolo Point: Extreme Burias Island : Busainga Marinduque I. : Summitof MountCatala. Maestro de Campo Island, Port Con- cepcion: Point Fernandez Ban ton Island : Ban ton Mountain Tablas Island : Tablas Head Sanguilan Pt Carabao Island: W. pt Romblon Island: Sabang Pt. light Summit over port Sibuyan Island : Summit Samar Island, Guiuan : Pier Catbalogan : Fort Maripipi Island: Summit ^ . . Leyte, Tacloban Ormoc: Ast. station Palompon : Church Maasin Bohol I., Lapiniu I. : Mount Basiao Cebu Island, Cebu : Plaza Siquiquor Island, Port Canoan: S. pt. of entrance Negros Island, Port Bunbonon: E. pt. of entrance Dumaguete : Town Volcano of Malaspina, 8,192 ft Bacalod: Town Guimaras I., Inampulugan I., SW. pt .. Panay Island, Iloilo: Fort San Jos^ Pan de Azucar Batbatan Island: Summit Pucio Point: Extreme... Port Batan: Village Capiz: Town Siargao Island, Port Sapao: Semaphore. Gibdo Island : Semaphore Bucas Island: E. pt. of Port Sibanga . . . Mindanao Island: Surigao Cape St. Augustin . . . Mindanao Island, Davao: Mole Saranguni Islets: W. islet Basianang Bay: N. pt. of Donauang I. Polloc: Small hill back of town 19 58 30 20 28 30 20 48 00 21 04 56 17 20 17 14 51 00 13 21 33 14 09 00 13 28 30 12 31 20 12 52 20 12 22 10 12 36 00 12 10 03 11 56 09 13 07 40 13 18 10 12 54 03 12 56 56 12 38 42 12 33 44 12 03 15 12 36 00 12 35 33 12 24 55 11 01 30 11 46 44 11 47 30 11 15 08 11 00 17 11 02 37 10 07 39 10 03 22 10 17 30 9 15 17 9 03 37 9 18 25 10 24 35 10 40 21 10 26 38 10 41 27 10 44 08 11 16 47 11 28 20 11 45 30 11 35 40 11 35 06 10 11 26 9 53 00 9 41 34 9 47 53 6 14 30 7 01 22 5 22 30 6 28 50 7 21 15 Long. £. 122 14 00 122 01 20 121 52 30 121 58 24 122 19 20 121 54 48 123 43 53 124 06 48 124 04 48 124 04 18 123 49 22 123 35 58 123 14 36 123 12 47 123 07 34 123 02 45 121 54 33 121 43 08 122 04 48 122 08 38 121 58 32 121 53 53 122 17 08 122 16 26 122 33 23 126 43 14 124 51 37 124 18 15 124 59 56 124 36 20 124 22 07 124 50 15 124 32 35 123 54 18 123 34 26 123 06 09 123 18 43 123 07 05 122 55 42 122 40 20 122 34 26 121 54 27 122 09 09 121 52 36 121 58 59 122 28 50 122 45 03 126 02 53 125 31 17 125 58 22 125 28 30 125 47 48 125 34 35 125 13 48 123 57 37 124 11 42 Lun. Int. Range. H. W. L. W. Spg. Neap. h. m. h. TO. ft- ft- 6 08 00 5.2 2.8 [4 30] [10 20] [5.5] 6 53 1 25 1.5 1.1 11 47 4 50 2.8 2.0 11 06 5 22 4.2 1.9 [11 40] [6 15] [6.5] 6 00 -0 13 6.9 5.1 APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. EAST COAST OF A RIA— Continued. [Page 247 o i g • » e a. a. a i 2 i £ e Place. Lat. N. Long. E. Lun. Int. Range. 1 H. W. L. W. Spg. Neap. Mindanao Island, Santa Cruz Islands: SE islet o / // 6 52 15 6 54 03 7 18 05 7 45 41 8 40 15 8 08 29 9 10 19 10 43 00 10 27 00 9 35 30 7 43 00 7 00 38 4 54 10 4 49 30 4 55 30 5 50 00 5 00 30 5 13 00 5 25 15 5 27 10 5 32 40 5 41 30 5 44 30 5 54 45 6 02 30 6 03 40 5 52 30 6 15 15 6 42 43 35 39 00 36 02 50 36 45 29 37 24 00 37 27 41 37 34 10 37 36 00 38 23 37 38 58 16 39 09 00 38 56 00 40 35 00 39 30 46 39 16 00 38 43 17 38 47 50 38 52 38 38 40 00 39 04 00 38 27 00 37 58 00 37 27 40 36 26 45 36 24 30 36 07 00 O 1 II 122 04 00 122 04 52 122 03 18 122 04 58 123 23 13 123 50 44 124 42 50 121 33 00 121 03 00 121 23 30 118 27 00 118 26 06 119 22 45 119 48 00 119 46 45 118 11 00 119 44 15 120 40 45 120 35 00 120 11 30 120 48 25 120 49 45 120 55 00 121 00 40 121 18 20 120 58 40 119 55 55 120 29 30 121 56 50 119 51 30 120 17 30 122 16 48 122 42 00 122 15 05 121 31 09 121 26 21 120 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 34 124 34 40 124 34 30 126 36 27 126 28 00 126 24 00 126 01 09 h. m. h. TO. ft. /t. Zamboanga: Fort... Sibuco Bay: Hill S. of beach 6 50 42 3.8 2.8 Port Sta. Maria: Fort Dapitan: Village Misamis: Fort Camiguin Island: Mount Camiguin Sombrero Rock : Center 1 [10 48] [4 50]! [5.1] 1 Piedra Blanca : Center .... Cagayanes Islands: Rocky islet be- tween two larger islands . . San Miguel Isles: E. pt. of Manuk Ma- nukan Cagayan Jolo Island: Middle of W. coast .... Omapui Island: NW. extreme Sibutu Island: Hill on E. coast Simonor Island: NW. pt 1 Bahaltolis Island: Sandakan Harbor... Bongao Island : S. pt 1 Keenapoussan Island : Center . Bubuan Island : Lagoon entrance Cuad Basang Island: SW. pt 1 i Siassi: Town 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 i Dalrymple Harbor, Tul- yan Islet Jolo light-house [9 38] [3 10] [5.0] Doc Can Islet: W. extreme . . Pangituran Island: SW. pt. .. .... j _ Basilan Island : La Isabela W^ang-kia-tia Bay: Langwang temple .. Kyauchau Bay : Yunuisan light Staunton Island: Landing place, N. side. Shantung Promontory: Light-house Weihaiwei: Light, S. side harbor Chifu: Light-house 4 50 11 03 11.4 6.0 4 00 9 20 10 25 10 12 3 08 4 13 6.8 9.0 8.1 5.0 6.6 6.0 Fort Miautao Island: Peak of N. Island Pei-ho: S. Taku Fort, S. Cavalier Tientsin: Shore opp. NE. angle of wall. . Shaluitien Island: Light-house Niuchwang: Lightship 6 50 1 00 4.5 3.3 4 30 10 50 11.7 8.7 Hulu-shan Bav: N. side 1 Liao-ti-shan Promontory: SW. pt. light Port Arthur: Obs. spot 1 10 05 3 53 7.5 5.5 Ta-lien-wan Bay: Isthmus on S. San- shan I Round Island : Summit Thornton Haven, Hai-yun-tan Island: Beach opposite Temple Point Choda Island: S. pt Sir James Hall Islands: N. island Chemulpo : So W^olmi 4 19 10 31 28.8 11.6 Marjoribanks Harbor: Manzoc Islet Tas de foin Islet: Center Guerin Island: Summit, 969 ft.. .. 1 Page 248] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. EAST COAST OF ASIA— Continued. Place. Lat. N. Kokoun-tan Islands: Camp Islet Barren Island : Center, 600 ft Sea Rock: Center, 160 ft Modeste Island: N. peak, 1,228 ft Ross Island: Peak, 1,920 ft Kuper Harbor: NE. extreme of Josling I . Port Hamilton: W. pt. of Obs. Island.. Bate Islands: Summit Thornton Islet Montravel Island: Center, 1,041 feet Quelpart Island: Beaufort I., middle of W. side Observation Island: Point of W. arm... Sentinel Island: Summit, 400 feet Broughton Head : Extreme Tsau-liang-hai Harbor: Light-house Tsu Sima : Observation rock Iki Sima: Summit, S. end of island Oro No Sima: Summit, 277 ft Kosime No Osima: Summit Wilson I. . . Yeboshi Sima: Light-house Yobuko Harbor: Bluff opposite Nicoya. Hirado No Seto: Taske light Goto Island : Ose Saki light Pallas Rocks: S. rock Meiaco Sima: Ears Peak Nagasaki : Transit Venus Station Kuchinotsu : Light-house Kagoshima: Breakwater light .Tsukarase Rocks: Summit, 96 ft Uji Shima: High peak, 1,097 ft Yamagawa Harbor: Spit N. of town Satano Misaki : Light-house Kusakaki Jima: Ingersoll Rocks, 530 ft. Kuro Sima: 2, 160 ft Iwo Shima: Peak, 2,469 ft Yakuno Shima: Mount Matomi,6,252 ft. Firase Rocks: Highest, 92 ft Kuchino Shima: Summit, 2,230 ft Guaja Shima: Summit, 1,687 ft Naka no Shima: Peak, 3,400 ft Suwanose Jima: Volcano, 2,706 ft Tokara Jima: Summit, 860 ft Yoko Shima: Summit, 1,700 ft Shimonoseki Strait: Meji Zaki, extreme. Rokuren Island : Light-house Shirasu Reef: Light-house Susaki: SW. battery Tomo Roads: Tamatsu Sima Port Okayama: Take Sima temple Wusimado Pt. : Wusimado Peak, 548 ft. Akashi-no-seto: Maico Fort Hiogo: Wada Misaki light Kobe: Light-house Osaka: Fort Temposan light Sakai: Pier-head light Osaki Bay : Tree Islet, S. pt Yura No Uchi: Pier Tanabe Bay:- Fossil pt Oo-sima Hbr. : Kashinosaki light, E. pt. Uragami Harbor: Village pt 0\va.shi Bay: Hikimoto Mura Harbor: Osima Islet 35 48 08 35 21 00 34 42 00 34 42 30 34 06 00 34 17 20 34 01 23 33 57 00 33 59 00 33 29 40 34 39 00 34 33 00 34 48 00 35 07 15 34 18 55 33 44 30 33 52 10 33 53 50 33 41 30 33 32 30 33 23 31 32 36 45 32 13 12 32 03 00 32 43 21 32 36 05 31 35 39 31 20 00 31 12 00 31 12 43 30 59 30 30 51 00 30 50 00 30 47 00 30 17 00 30 05 00 29 59 00 29 54 00 29 52 00 29 38 00 29 08 00 28 47 30 33 57 46 33 58 53 33 59 11 33 23 19 34 22 37 34 35 58 34 37 27 34 38 05 .34 39 20 34 41 18 34 39 45 34 35 12 34 07 42 33 57 34 33 41 14 33 28 15 33 33 37 34 06 10 34 13 ^ Lun. Int. Long. E. Range. H.W. 126 31 00 125 58 00 126 19 45 125 16 00 125 07 00 126 35 28 127 18 34 126 18 00 126 55 00 126 58 25 128 14 00 128 40 00 128 44 00 129 02 10 129 13 06 129 42 30 130 02 00 130 25 20 129 58 50 129 52 43 129 33 21 128 36 10 128 04 39 128 25 00 129 52 25 130 13 40 130 33 49 129 46 20 129 29 00 130 37 00 130 39 30 129 28 00 129 55 30 130 18 00 130 32 00 130 03 00 129 56 00 129 33 00 129 52 30 129 42 00 129 13 30 129 01 30 130 57 50 130 52 07 130 47 36 133 17 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 61 9 06 7 36 8 56 L. W. 9 23 7 54 6 40 7 20 30 5 55 11 16 h. 111. 2 52 10.5 1 23 2 44 7.0 3 10 6.4 1 41 1 00 8.4 ib'.h' 1 08 9.5 2 20 6.7 12 08 5 04 6.0 10.2 7 30 6 23 1 26 4.7 10 4.7 Neap. ft. 4.2 3.0 2.4 2.5 3.5 *4."4 3.9 2.4 2.0 4.5 2.0 2.0 APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. EAST COAST OF ASIA— Continued. [Page 249 Place. Matoya Harbor: Anori-saki light Oinoi Saki: Light-house Shimizu Bay : Mound on pt Mikomoto Island : Light-house Simoda Harbor: Center I Yokosuka Harbor: Eyi Yama pt Yokohama: P^nglish Hatoba light Tokio: Naval Observatory No Sima Saki: Light- house Vries Island (O Sima) Volcano: Sum- mit, 2,512 ft Kozu Shima V^olcano: 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 : Light-house Kinkwosan Island: Light-house Kamaishi Harbor: SE. end of village . . Yamada Harbor: Ko Sima, 90 ft Siriya Saki: Light-house Toriwi Saki: Center of Low Islet off . . . Awomori: Light-house Tatsupi Saki: N. side Bittern Rocks: SW. rock Tobi Shima: Takamori Yama Awa Sima: NE. extreme Sado Island: Ya Saki Fushiki Harbor: Light-house Cape Roigen : Extreme Niigata: Buddhist temple Mana Sima: Summit, 200 ft Manao Harbor: Sorenjo Pt Tsuruga: Town 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: Light-ship Endermo Harbor: Bluff on E. side Okishi Bay: Light-house Noshiaf Saki : Light-house Nemuro: Benten Sima light Notsuke Anchorage: Village Noshiaf Misaki : Light-house Risiri Islet: Peak, 5,713 ft Lat. N. Kunashir Island: St. Anthonys Peak . Iturup Island : NE. pt Urup Island: Cape Vanderlind Broughton Island : Summit. . . y. 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 Poro musir Island: Fool's Peak Soumshu Island : Center Lun. Int. 34 21 57 34 35 52 35 00 51 34 34 25 34 39 49 35 17 30 35 26 52 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 I 38 16 57 1 39 16 30 I 39 27 17 41 25 58 41 33 34 40 50 00 41 16 17 40 31 00 39 12 02 I 38 29 23 ' 38 19 55 I 36 47 47 I 37 28 00 37 55 14 37 35 00 37 02 37 35 40 24 36 30 00 34 40 00 34 32 00 34 48 00 34 21 12 41 47 36 42 19 54 42 56 52 43 22 56 43 20 22 43 33 11 45 26 30 45 11 00 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 Long. E. Range. H. W. 136 54 09 138 13 49 138 31 19 138 56 30 138 57 30 139 39 43 139 38 41 139 44 30 139 53 24 139 23 139 08 139 31 138 48 139 34 139 17 139 50 139 43 140 00 140 02 140 14 140 19 140 52 141 35 141 52 141 59 141 27 140 56 140 44 140 22 139 31 139 32 139 15 138 27 137 03 137 22 139 03 136 54 136 58 136 01 133 23 131 36 131 18 131 09 130 50 140 41 140 59 144 52 145 49 145 34 145 18 141 38 141 19 146 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 5 52 5 52 5 25 5 04 L. w. Spg. Neap. 4 30 2 30 11 41 3 40 3 32 3 41 3 48 3 33 4 50 12 04 12 04 11 30 11 17 10 45 8 42 5 28 10 00 9 45 9 53 10 00 9 46 11 05 4.3 3.9 4.9 3.7 3.4 0.6 1.1 3.0 3.5 3.0 3.1 2.1 3.7 ft. 1.7 1.6 1.9 1.4 1.3 0.4 0.5 1.8 ^'' Or- the' l^NIVERSITY ^^' Page 250] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. EAST COAST OF ASIA— Continued. *s Place. Lat. N. Long. E. Lun. Int. Range. 1 H. W. L. W. Spg. Neap. t i t 9 P Cape Clonard : E^reme O > t> O 1 II 36 05 45 ! 129 33 30 36 36 00 1 129 20 00 37 09 30 1 131 55 00 37 30 00 ' 130 53 00 39 19 12 127 32 48 42 14 30 ! 137 17 00 42 38 05 1 130 48 45 42 33 40 1 131 10 00 43 05 13 131 53 56 42 41 00 133 02 00 43 22 00 135 15 00 43 53 40 j 135 27 19 44 30 00 136 02 00 44 43 45 136 22 30 44 46 15 ! 136 27 15 45 05 00 136 44 00 h. m. h. m. ft. ft. Ping-hai Harbor Liancourt Rocks: Summit, 410 ft Matu Sima: Peak, 4,000 ft i ■ 1 1 Port Lazaref: S. IJ miles from the S. end of Bontenef I i Wawoda Rock : Summit, 12 ft Expedition Bay : Light-house Port Novogorod : Light-house Vladivostok : Cape Galdobin light Caj>e Povorotnyi : Light-house 2 45 9 00 1.9 0.8 Port Olga: Light-house St. Vladimir Bay: Orekhera Pt Shelter Bay Sybillo Bay Pique Bay Bullock Bav Luk^ Point: Extreme 45 19 30 45 41 30 47 20 00 48 59 30 51 28 00 45 53 10 46 01 20 i4 24 30 53 08 05 55 11 00 56 25 28 56 22 30 59 19 45 51 02 00 52 52 37 53 04 30 54 56 00 54 32 24 56 10 00 58 26 00 59 55 00 62 14 30 60 18 00 63 12 00 64 16 00 64 25 55 64 24 30 64 46 00 137 10 15 137 38 15 138 58 00 140 23 40 140 48 00 142 04 51 143 26 30 142 46 30 140 42 58 137 40 00 138 25 50 143 15 45 143 07 14 156 46 00 158 46 42 160 04 00 166 43 00 168 09 00 163 24 00 163 34 00 170 22 00 179 04 30 Long. W. 172 04 00 159 50 00 173 10 00 173 07 15 172 12 30 172 07 00 Cape Disappointment: Extreme Cape Suff ren : Extreme Cape St. Nikolaia: Light-house De Kastri : Light-house * 9 50 10 45 3 40 4 40 2.7 6.3 1.1 2.6 Sakhalin I., Cape Notoro: Light-house. Cape Siretoku: Extreme .. Cape Elizabeth: N. pt Nikolaevsk: Cathedral 11 20 5 08 4.2 1.7 Great Shantar Island :N. pt Port Aian: Cape Vneshni 10 7 30 8.4 3.4 St. Jona Island: Summit, 1,200 ft Okhotsk: Battery ::: i : Cape Lopatka: Extreme 3 55 3 30 10 08 ! 4. 6 1.9 2.1 Petropavlovsk : Rakof light 9 45 5.1 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 St. Matthew Island: Cape Upright, SE. pt St Lawrence Island: N pt 6 00 12 15 4.5 1.8 1 Cape Tchoukotskoi' Extreme Port Providence: Emma Harbor Cape Indian : Extreme Arakam Island : Cape Kiguinin Anadir River* Mouth 1 Long. E. 64 50 00 178 40 00 Long. W. 65 00 30 [ 175 54 00 66 02 00 169 32 30 1 Cape Bering' Extreme ' East Cape : Extreme ... .... ... 1 1 ISLANDS OF THE PACIFIC. m Si i 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 81 36 00 86 69 17 9l' 03 00 89 58 43 90 30 08 90 44 9.^ Towel's Island: W. cliff Bindloe Island: S. summit Abingdon Island : Summit, 1,950 ft AVenman Island: Summit, 550 ft d 1 22 55 91 49 4.3 :::;:::::::: i tf 1 APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ISLANDS OF THE PACIFIC— Continued. [Page 261 Place. Albemarle Island : Iguana Cove Marlborough Island: Cape Hammond.. James Island: Sugarloaf, 1,200 ft Jervis Island : Summit Duncan Island : Center hill Indefatigable Island : N\V. bay Barrington Island: W. summit, 900 ft.. Charles Island: Summit, 1 ,780 ft Fatu Huku 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 Washington Island Palmyra Island Baker Islet: Center Howland Islands: Center island Arorai or Hurds Island: S. pt Tamana Island : Center Onoatoa Island : Center Taputeuea or Drummond Island: SE. pt. Nukunau or Byron Island: SH pt Peru or Francis Island: NW. pt Nonuti or Sydenham Island Aranuka or Henderville Island: W. pt. of W. island Apamama or Hoppers Island: Entrance islet Maiana Island: S. pt Tarawa Island : NE. pt Apaiang Island: S. pt Maraki Island: N. pt Taritari Island: S. pt Ebon Atoll: Rul:)e Pt Jaluit or Bonham Islands: Jarbor Pier. Burrh Island: Port Rhin, N. pt. of en- trance Majuro or Arrowsmith Islands: An- chorage Djarrit I Arno 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: Capenmr Islet Bigar Islet : Center Kongelab or Pescadores Islands: Center of group Rongerik or Radakala Islands: Obser- vation spot Ailinginae Island: Easternmost Islet... Bikini or Eschholtz Islands: W. ex- treme Wottho or Schanz Island : Center Eniwetok Islands: North or Engibil.. Ujelang or Providence Island: Center of atoll Lat. S. Long. W. Lun. Int. Range. H. W. L. W. Spg. Neap. O / tl 59 00 31 00 15 20 25 00 36 30 33 25 50 30 1 19 00 1 25 00 44 15 Lat. N. 1 57 17 3 51 26 4 41 10 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 LonR. 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 40 168 41 31 169 39 31 171 46 00 171 24 30 171 55 51 168 46 00 168 03 00 168 26 00 171 09 00 170 49 00 170 16 05 169 01 57 169 59 20 170 07 00 167 24 57 167 35 00 166 35 00 166 24 25 166 04 00 162 15 00 161 08 30 h. m. 2 00 h. m. 8 13 ft. 6.2 ft. 3.1 2 45 8 58 5.2 2.6 :::::::::::::::: 2 00 8 13 6.2 3.1 2 10 8 23 6.0 3.0 2 20 4 25 6 00 8 33 10 38 12 15 6.5 2.4 2.4 3.3 1.4 1.4 5 52 15 13 30 5 25 11 40 1.5 0.9 49 00 Lat. S. 2 40 54 7 10 1 00 6.2 3.6 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 i 1 ' 4 30 10 45 4.7 2.7 1 44 15 2 03 00 4 45 11 00 4.7 2.7 3 01 30 4 35 25 5 55 07 6 14 00 7 05 30 7 09 17 7 15 00 8 14 00' 8 27 00 8 19 00 8 54 21 9 28 09 10 03 40 10 17 25 11 48 00 11 19 21 4 45 11 00 4.7 2.7 5 00 11 15 5.0 2.8 4 50 11 00 6.2 3.6 1 11 24 00 [ 11 07 00 11 40 00 10 05 00 11 40 00 9 39 00 i j i Page252J APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ISLANDS OF THE PACIFIC— Continued. *j Place. Lat. X. Long. E. Liin. Int. 1 Range. 1 H.W.I L. W. Spg. Neap. • a * m m « d 2 3 i •9 n « * « ■ « M 1 h 0_ 4> fl 2 ■d « Greenwich Island: Northern islet • Matelotas group: Easternmost of the S. islands / If 1 04 00 8 18 30 9 29 00 9 52 30 / n 154 47 55 137 33 30 138 04 00 139 42 00 h. m. h. m. ft. ft. Yap Island: Light in Tomil Bay Eau Island : Center 7 15 1 00 3.4 1.9 Uluthi or Mackenzie Islands: Mogmog Islet ; 10 06 00 139 46 00 Feys or Tromelin Island: E. extreme .. 9 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 Sorol or Philip Island : Center 1 8 06 00 Eauripik or Kama Islands: E. islet ' 6 40 00 Oleai group: Raur Islet, N. pt Ifalik or Wilson Islets: N. end Faraulep Island : S. end 7 21 45 7 15 00 8 35 00 8 03 00 7 43 30 W. Faiu Islet: Center Oliniarao Islet: Center Toass Island: Center 7 29 30 146 24 30 7 22 00 147 06 48 8 09 00 147 42 00 Satawal Island : Center Coquille or Pikelot Island: Center Suk or Polusuk Island : S. end 6 40 00 7 38 00 8 59 45 8 25 30 7 18 30 5 55 00 5 29 18 3 51 00 7 39 00 5 48 00 7 00 35 6 41 45 6 14 00 5 20 06 6 53 55 7 02 00 7 08 00 7 19 00 7 40 30 8 08 00 4 20 00 3 02 00 5 20 00 13 25 48 14 07 30 14 59 22 15 08 30 15 17 10 16 20 00 16 41 00 17 17 00 17 36 00 18 04 00 18 46 20 19 45 00 20 00 00 20 32 54 149 21 00 Los Martires: Ollap Islet, N. pt Namonuito Islands: Magur Islet Hall Island: Namuine Islet 149 27 30 150 14 30 151 49 15 151 56 30 153 13 30 153 58 00 155 00 54 155 05 00 157 31 30 158 12 21 159 50 00 160 38 43 163 00 45 134 05 24 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. MokilorDuperrey Islands: Aoura, NE.pt Pingelasp or MacAskill Islands: E. end of island 4 00 10 15 4.3 2.4 Ualan or Strong Island: Chabrol Harbor. Angaur Island: SW. pt 6 00 12 15 3.5 2.0 Pililu Island: S. pt 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 30 145 13 04 Earakong or Akamokan Island: Center. Korror Islands: Korror Harbor, Mal- akal pier . Baubeltaub Island : Cape Artingal Kyangle Islets: Center of largest Warren Hastings Island: Center Nevil or Lord North Island: Center Sonserol Island : Approx Guam Island: Fort Sta. Cruz, San Luis d' Apra. 7 20 1 20 2.6 1.5 Rota Island' Summit Tinian Island : Sunharon village Saipan Island: Magicienne Bay, land- ine 145 36 20 145 43 55 145 42 50 145 39 00 Tanapag Hbr. , Garapag . Anataxan Island: Center 7 00 50 2.0 1.1 Sariguan Island: Center 145 47 00 145 57 00 145 55 00 145 52 00 145 41 45 145 30 00 145 21 00 144 54 00 Guguan Island: Center Alamaguan Island ■ Center . . . Pagan Island: SW. pt Agrigan Island : SE. pt Asuncion Island : Crater, 2,600 ft Urracas Islands ■ Lai^est islet Farralon de Pajaro.«: S. end APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ISLANDS OF THE PACIFIC— Continued. [Page 253 Place. Lat. N. Lun. Int. Long. E. H. W. L. W. Range. Spg. Neap. Wake Island: Center ; 19 10 54 Gaspar Rico Reef: N. clump of rocks. .. 14 41 00 Johnston or Comwallis Islands: staff on W. island Clipperton Island : Center Flag- Hawaii Island: Hilo, Kanaha Pt. light. Kawaihae light Kealakeakua Bay light. Kailua, stone church... Kahoolawe Island: Summit Maui Island: Kanahena Pt. light Lahaina light Molokai Island: Light-house Oahu Island: E. pt. Makapuu station .. Diamond Head Honolulu, Tr. of V. Obs . Honolulu, Reef light Kauai Island: Hanalei, Black Head Waimea, stone church . . I Bird Island: Center Necker Island : Center French Frigate Shoal: Islet (120 ft.) ... Gardiner Island : Center Maro Reef: NW. pt Laysan Island : Light-house Lisiansky Island: Light- house Pearl and Hermes Reef: NE. extreme.. i Midway Islands: N. end Sand Islet Ocean Island: Sand Islet ' Marcus Island: Center Bonin Is. , Parrys Group: N. rock Kater Island: N, rock Peel Island: Port Lloyd, ob- servatory Volcano Is., San Alessandro or North Island: Center Sulphur Island San Augustine Island: Center , Rosario Island : Center, 148 ft Douglass Rocks: Center Borodino Islands: Center of N. island.. Center of S. island . . Rasa Island : Center Fatu Hiva Island : S. pt Motane Island: SSE. pt Tahuata Island: Port Resolution, wa- tering place Hiva-Oa Island : C. Balguerie Fatu Huku Island: Center Roa Poua Island : Obelisk Islet Nuka-Hiva Island : Port Tai-o-hae light. Hiaou Island: S. pt Motu-ili Island : Summit, 130 ft Ua-Huka or Ua-L^na Island: N. pt Fetouhouhou Island : NE. pt Caroline Islands: Solar Eclipse Transit Pier Vostok Island : Center Flint Island : S. extremity 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 27 45 00 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 23 166 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. 153 58 00 142 06 53 142 11 53 142 11 23 141 11 00 141 13 00 141 20 00 140 50 28 136 10 00 131 19 30 131 12 17 131 01 50 Long. 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 h. m. h. m. ft- 3 09 9 06 2.3 1.3 2 20 8 10 0,9 3 32 2 38 9 58 8 56 2.2 2.1 1.2 1.1 3 46 j 9 59 '4"66' "i6"26 1.5 0.8 2.0 1.1 3 30 6 10 9 45 1.1 0.6 00 2.4 1.4 2 30 8 45 3.1 1.9 3 50 10 05 4 00 3.5 2.1 10 14 I 1. 1 0.7 Page 254] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ISLANDS OF THE PACIFIC— Continued. Place. Maiden Island: Flagstaff, W. side Starbuck Island: l^lagstaff, W. side Penrhyn 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 , Pho'nix Island, N. pt Birneys Island : S. pt Gardners Island : Center McKean Island: Center Hulls Island: W. pt Mukulaelae or Mitchells Island: S. pt. . , Funafuti or 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 Ocean or Paanopa Island : Center (appx ) Pleasant Island : Center Indispensable Reefs: S. pt. of S. reef.. Rennel Island: SE. extreme AV.end San Christoval Island: Point Wanga- laha Guadalcanar 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 en- trance Traisury Islands: Observation Islet Bougainville Island: Hiisker Pt., Ga- zelle Harbor Buka Island : Cape North Lord Howe Group: Center, small SW. islet Center, small NE. islet NW. pt. of Ham- mond I New Britain, Blanche Bay: Matupi I. N. pt Duke of York Island: Makada Har- bor, Spit Pt Lat. S. 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 2 44 25 3 08 30 3 42 28 3 34 15 , 4 37 42 3 35 10 4 30 95 9 18 00 8 25 19 8 04 02 7 32 00 7 15 45 6 12 00 6 06 00 5 39 00 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 00 4 14 12 4 06 25 Long. W. 155 01 00 155 56 00 158 07 00 159 54 11 161 05 30 161 01 12 171 14 46 171 44 40 172 28 10 171 45 29 171 10 00 170 42 37 171 32 07 174 40 18 174 17 26 172 13 28 Long. E. 179 50 00 179 07 25 178 28 51 178 41 01 177 16 50 176 16 30 177 20 01 176 06 15 169 35 00 167 05 00 160 26 00 160 40 15 159 55 00 161 33 30 159 39 30 160 27 20 161 27 40 162 58 15 159 38 20 156 50 15 156 23 16 155 34 00 155 05 00 154 35 00 159 21 00 159 34 00 159 17 00 152 11 35 152 06 15 Lun. Int. Range. H, W. L. W. Spg. Neap. ft. m. ft. ft. 6 00 12 15 1.5 0.9 6 00 12 13 2.4 1.4 5 00 11 15 4.6 2.7 6 45 33 3.3 2.0 5 00 11 15 3. 5 2. 1 12 00 5 47 I 2. 7 1.6 9 00 2 45 i 2. 1 1.3 APPENDIX IV. [Page 265 MARITIME POSITIONS AND TIDAL DATA. ISLANDS OF THE PACIFIC— Continued. u Place. Lat. S. Long. E. Lun. Int. Range. 1 H. W. L.W. Spg. Neap. i g s ■0 m « S e a a M © i « 2 a » m N B b » New Ireland: Carteret Harbor, Cocoa- nut I / // 4 41 26 3 11 00 2 47 30 2 33 43 2 26 30 1 35 00 1 55 10 2 25 40 2 22 00 45 00 53 15 1 28 00 2 51 00 1 25 40 2 44 00 3 47 00 8 22 00 8 41 00 9 25 30 10 14 30 10 43 35 10 37 00 6 43 00 8 24 00 9 03 30 9 38 00 9 41 00 9 43 53 10 42 00 10 52 40 11 23 25 11 29 10 16 50 00 16 55 50 17 43 00 17 07 20 17 24 39 19 08 00 19 14 00 22 10 30 23 15 02 9 48 00 10 21 00 10 23 30 10 40 00 11 17 30 11 40 24 o / // 152 42 25 151 35 30 150 57 35 150 04 33 149 55 36 149 37 00 146 40 56 147 28 .35 147 55 00 145 17 00 145 33 04 145 08 00 146 15 00 135 28 12 132 04 00 134 06 00 137 40 00 143 36 04 147 07 04 148 30 30 150 14 20 150 40 34 147 53 20 151 01 24 152 47 00 150 30 00 150 58 00 150 44 43 152 42 04 152 47 12 154 08 00 154 25 14 149 58 00 149 11 54 150 42 04 152 06 20 155 52 24 158 40 00 159 00 00 155 28 24 155 33 04 166 53 15 166 17 15 165 47 30 166 00 30 166 32 14 166 57 45 h. m. ft. m. ft. ft. Katharine Haven Holz Haven, E. side New Hanover Island: Water Haven, creek mouth. North Haven anchorage St. Matthias Island: SW. extreme Admiralty Island: Nares Harbor, obs. islet 2 50 9 03 2.4 1.4 2 30 8 43 2.4 1.4 St. Andrew Island: Violet Islet, 60 ft .. Jesus Maria Island : SE. pt Commerson Island: Center of largest islet Anchorite Island : N. pt Hermit or Loaf Island: Pem6 Islet Purdy Island: Mole Islet Point d' Urville : extreme Drei Cap Peninsula: Wass Islet Triton Bay: Fort Dubus, Dubus Haven. Cape Walsche: Extreme 6 55 7 08 7.3 4.3 Fly River: Free Islet, S. pt Port Moresby: N. end of Jane I Cape Rodney : Extreme 8 50 2 38 8.0 4.8 South Cape: S. pt. Su Au I 9 15 8 25 3 00 2 12 8.1 5.8 4.8 3.4 Hayter Island : VV^. end Cape Cretin : Cretin Islets Trobriand Islands: NE. pt. Cape Denis. Woodlark Islands: N. pt 4 45 7 05 10 58 53 .... 3.0 4.2 1.8 2.5 D'Entrecasteaux Is. : Ferguson I., SW. extreme Well Island, E. pt. Normanbyl., obs. islet St. Aignan Island : Summit 1 Rossel Island : E. pt Adele Island : S. extreme Coringa Islands: Chilcott Islet Herald Cays: NE. Cay j Tregosse Islands; S. islet i Lhou Reef: Observation Cay 1 . Bampton Island 1 Renard Island : Center 1 Wreck Reef: Bird Islet 1 Cato Island : Center 1 Duff or Wilson Group: N. island Matema or Swallow Group: Nimanu Islet Tinakula Island: Summit, 2,200 ft Nitendi Island: NE. pt.. Cape Byron .. Tapua Island: Basilisk Harbor, S. pt. of entrance Vanikoro: Ocili village 4 50 11 05 3.8 2.3 Page 256] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ISLANDS OF THE PACIFIC— Continued. i •9 5 a M a V t 9 8 « •9 S « Place. Lat. 8. Long. E. Lun. Int. Range. 1 H. W. L. W. Spg. Neap. Torres or Ababa Island: Hayter Bay, Middle I..... O ' II 13 15 00 13 48 00 14 11 00 14 58 00 16 26 00 17 44 58 18 47 30 / II 166 33 00 .167 30 31 167 30 00 168 02 00 167 47 15 168 18 50 168 58 00 169 27 30 170 11 15 169 44 45 171 20 30 172 05 15 168 56 45 170 10 00 177 07 15 178 32 15 177 57 09 178 10 24 177 38 00 178 49 00 177 09 00 178 24 40 178 06 53 179 44 27 179 56 25 179 14 08 178 59 29 178 57 46 179 20 44 178 54 15 178 48 32 179 16 08 Long. W. 179 58 46 179 51 00 179 54 26 179 17 00 179 32 17 179 10 00 179 05 45 179 10 33 179 19 49 178 50 27 179 04 00 178 52 00 178 27 04 178 30 54 178 44 00 h. m. h. m. ft. ft. Vanua Lava Island: Port Patterson, Nusa Pt 6 40 30 3.8 2.3 Santa Maria Island: Lasolara Anchor- ase Aurora Island : Laka-rere MallicoUo Island: Port Sandwich, pt. on E. side 4 38 5 15 10 50 11 27 3.8 3.0 1.9 1.8 Vate or Sandwich Island: Havannah Harbor, Matapou Bay flagstaff Erromango Island: Dillon Bay, Pt. Williams Tanna Island: Port Resolution, Mission. 19 31 17 Erronan or Futuna Island: NW. pt 19 31 20 Aneitvum Island: Port Anatom, Sand Islet • 20 15 17 5 10 11 23 3.1 1.9 Matthew Island: Peak, 465 feet Hunter Island: Peak, 974 feet 22 20 12 22 24 02 22 38 07 Walpole Island: S. pt Mitre Island: Center 11 55 00 Rotumah Island: Epipigi Peak 12 30 10 Kandavu Island: N. rock Astrolabe Reef i light ! 18 38 15 Mt. Washington, N. peak 19 07 09 . 6 15 00 4.2 2.5 N'galoa Harbor, outer beacon 19 05 30 6 40 25 4.0 2.4 Vatu Lele Island : S. pt 18 36 00 17 40 45 Ovalau Island : Levuka light-house Yiti Levu Island; Summit of Malolo Islet 17 44 45 Suva Harbor, low light 18 06 50 6 30 15 3. 6 2. 2 1 Mbega or Mbengha Island: Swan Har- bor, Leaven Pt 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 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 V^anua Levu Island : Mount Dana Nandi, observation islet :::::;::::: i Savu Savu Pt. ; ex- treme 6 00 12 13 4.3 2.6 NE. Pt Taoiuni Island: Somu-Somu town Thikombia Island: E. hummock \ 15 44 45 Naitamba Island : Center 17 03 00 Vatu Vara Island: N. end, summit i 17 25 33 Kanathea Island: S. pt | 17 17 20 Vanua Mbalavu Island: NW. pt 17 10 00 Mango Island: Pier end 1 17 25 26 Thithia Island: Highest peak 17 44 12 Tuvutha Island: Peak 17 39 33 Naian Island: Summit, 580 ft i 17 59 00 Lakemba Island: Kendi Pt i 18 14 10 6 10 00 3.1 1.9 Oneata Island : Summit of Loa I Mothe Island: Summit 18 25 46 18 38 56 18 46 00 Mamuka Island : Center, 260 feet 1 APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ISLANDS OF THE PACIFIC— Continued. [Page 257 Place. Kambara Island : Highest peak Totoya Island : Black Rock Bay, W. side Fulanga Island: W. bluff Ongea Leva Island : Center Vatoa or Turtle Island: Hummock Ono Islands: Peak 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. extreme Keppel Island : Center Boscawen Island: Center Savaii Island : Paluale village Upulo Is. : Apia Harbor, obs. spot Tutuila Island : Pago-Pago, obs. pt Manua Island: Village, NW. side Rose Island: Center Iniue or Sarage Island : S. pt Danger, or Bernardo, Is. : Middle rock . Suwarrow or Souwaroff Island: Cocoa- nut Islet Palmerston Islands: W. islet Scilly Islands: E. islet Bellingshausen Island : Center Mopelia (Lord Howe) Island: Center.. Maitea Island: Summit Tahiti Island : Light-house Tubuai-Manu or Maia-iti I. : NW. pass. . Eimeo Island : Talu H br. , Vincennes Pt . Huaheine Island : Light-house Ulietea Island : Regent Pt Tahoa Island: Center Bola-Bola Island: Otea-Vanua village. . Tubai or Motu-iti Island: N. pt. of reef. . Marua or Maupili Island: Center Ducie Island: NE. entrance Pitcairn Island: Village Henderson or Elizabeth Island: Center. Oeno Island : N. pt Mangareva or Gambler Island : Flagstaff Maruteaor Lord Hood Island: Center.. Maria or Moerenhout Island: Center Vahanga Island : W. pt Morane or Cadmus Island : Center Tureia or Carysf ort Island : E. pt Mururoa or Osnabrug Island: Obs. spot. Tematangi or Bligh Island: N. pt Nukutipipi : SW.pt Hereheretue or St. Paul Island: Center. Vanavana or Barrow Island: Center Nukutavake or Queen Charlotte I. : N. pt Reao or Clermont Tonnere Island: NW. point Puka-ruha or Series Island: NW. pt Vahitahi Island : W. pt Ahunui or Byam Martin Island : NW. pt. Pinaki or Whitsunday Island: E. pt Tatakoto or Gierke Island: Flagstaff on western coast Lat. S. 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 17 53 00 17 29 10 17 36 39 17 29 23 16 42 30 16 50 00 16 35 00 16 31 35 16 11 00 16 26 00 24 40 20 25 03 50 24 21 20 24 01 20 23 07 36 21 31 30 22 01 00 21 20 00 23 07 50 20 46 20 21 50 00 21 38 00 20 43 00 19 53 17 20 46 07 19 16 30 18 29 00 18 16 00 18 43 30 19 37 00 19 25 00 17 19 30 Long. W. 178 59 05 179 52 58 178 47 25 178 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 00 00 148 05 00 149 29 00 150 36 56 149 50 30 151 01 28 151 27 21 151 35 00 151 46 00 151 48 00 152 12 00 124 48 00 130 08 30 128 19 00 130 41 00 134 57 54 135 33 05 136 10 15 136 38 53 137 06 15 138 27 45 138 56 30 140 38 45 143 03 15 144 57 00 139 08 45 138 48 30 136 26 30 137 03 30 138 53 15 140 15 45 138 40 45 138 26 26 Lun. Int. Range. H. W. L. W. Spg. Neap. h. m. 1 h. m. ft. ft. 6 35 [ 20 "6"i6T"6"66' 3.5 2.1 3.1 1.9 6 40 28 4.4 2.7 25 13 7 00 6 00 45 12 13 3.1 2.7 4.6 1.9 1.6 2.7 3 10 i 9 23 2.4 1.4 12 00 5 48 LO 0.6 12 10 6 00 1.4 0.8 1 50 03 2.4 1.4 22489—03- 1 Page 268] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ISLANDS OF THE PACIFIC— Continued. 1 Place. Lat.S. Long. W. Lun. Int. Range. 1 H.W. L.W. Spg. Neap. e I s 9 s s m ■0 1 « M e a a. r Hao or La Harpe Island: NW. pass Paraoa or Gloceater Island: Center Ravahere Island: S. pt O f 11 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 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 28 55 00 29 15 30 30 15 00 30 35 00 21 44 45 O 1 II 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 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 h. m. 2 40 h. TO. 8 55 ft- 2.4 Jt- 1.4 Reitoru or Bird Island: N. beach Hikueru or Melville Island, E. pt Tauere Island: NW. pt 1 Puka-puka Island : E. pt Napuka Island : W. pt Angatau or Araktcheff Island: W. pt .. Tukume or Wolkonsky Island: NW . pt. Tuanske Island: N W. pt i 1 , Nihiru Island (Tuanake): SAV. pt Anaa Island: Islet in N. pass Tepoto Island: N. pt ! Haraiki or Crocker Island: SW. pt Makemo or Phillips Island: AV. pass... Fakarana or Wittgenstein Island: SE. . pass Taiaro or Kings I. : Middle of W. shore . Aratika Island: E. pt Toau or Elizabeth Island: Amyot Bay. Takapoto Island: S. pt Aheu Island : Lagoon Entrance Rangiroa Island: E. pt 4 30 10 43 2.1 1.3 Makatea Island: W. pt Matahiva Island: W. pt 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: NW. pt 4 00 40 10 10 15 6 53 6 25 3.3 2.8 2.4 2.0 1.7 1.4 Easter Island : Cooks Bay, mission Rapa or Oparo Island: Tauna Islet Bass Islets (Morotiri): SE. islet, 344 ft . Tubuaior Austral Is., Vavitoa I. : Center. Tubuai I.: Flag staff, N. side Rurutu I. : N. pt . . Rimitara I. : Cen- ter Hull Island: NW. pt 3 00 9 13 2.4 1.4 Mangara Island: Center Rarotonga Island : N W. pt 6 00 12 15 2.7 1.7 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 6 20 10 3.8 2.3 Tofua Island : Summit, 2,800 ft Tongatabu Island: Light-house Minerva Reefs, N. Minerva: NE. side.. S. Minerva: S. side of entrance 6 20 7 50 10 1 35 3.8 5.5 2.3 3.3 Kermadec Is. , Raoul or Sunday I. : Den- ham B. flag staff Macauley I. : Center Curtis I. : Center Conwav Reef: Center 6 00 12 13 3.3 2.7 APPENDIX IV. [Page 269 MAKITIME POSITIONS AND TIDAL DATA. ISLANDS OF THT3 PACIFIC— Continued. 1 o o Place. Lat. S. Long. E. Lun. Int. Range. 1 H. W. L. W. Spg. Neap. Loyalty Is., Uvea or Halgan I.: Uvea Church. o / // 20 27 06 20 46 00 21 42 00 21 29 12 22 00 10 22 16 22 O / II 166 36 25 1 h. m. h. m. ! ft. fl. LifuL: Wreck Bay, NW. shore 167 02 30 168 00 00 165 58 50 166 05 00 6 30 ! 18 1 4.2 2.5 Mare or Britannia I. : S. pt. Port Kanala: Observatory 1 Port St. Vincent: ^larceau I 5 40 11 52 3.3 3.1 2.0 1.9 Noumea : Light-house .. 166 25 52 8 25 2 13 Balari Pass' Amedee I Ught 22 28 44 166 28 51 22 42 30 167 27 55 Port Alcmene : Alcmene I 7 55 7 30 1 45 I 17 3.6 4.7 2.2 3.9 Norfolk Island: Inner end of jetty Elizabeth Reef : Center 29 03 45 29 56 00 31 31 38 167 58 06 159 04 30 159 05 58 159 16 10 Lord Howe Island: S. end of middle beach 8 20 2 08 5.4 .3.3 Balls Pyramid- Summit, 1,816 ft . ... 31 45 10 Macquarie Island : N. pt 54 19 00 158 56 00 166 13 20 169 08 41 178 43 05 179 00 27 Long. W. 176 32 15 1 Auckland Is. : Port Ross, Terror Cove. . Campbell Island: S. harbor. Shoal Pt.. Antipodes Island: Summit, 600 ft Bounty Islands : Anchorage N. I. , West Group .. 50 32 15 52 33 26 49 42 00 47 43 00 43 57 24 43 49 03 11 50 11 45 3 20 5 38 5 33 9 30 3. 2 2. 6 3. 5 2. 9 5. 3 4. 3 Chatham Island, Whare-Kauri Island: Port Waitangi, Pt. Hanson , Chatham Island, Whare-Kauri Island: Port Hutt, Gordon Pt 176 42 00 5 22 23 2.5 2.1 AUSTRALIA. i 1 s e i £ « B s ■ Groate Eylandt: SE. pt 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 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 :6 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 Bickerton Island : Summit Cape Arnheim : Extreme Cape Wilberforce: E. extreme 8 00 1 48 9.8 5.8 Cape W^essel: Extreme Dale Point: Extreme Cape Stewart: Extreme Liverpool River: W. pt. entrance Cape Croker: Extreme 6 17 05' 12.0 7.1 Port Essington: Government house Melville Island: Cape Van Diemen Bathurst Island : Cape Fourcroy Adelaide River: E. entrance pt' Port Darwin : Charles Pt. light 5 15 4 57 3 50 5 45 6 45 11 27 11 18 10 00 11 58 27 16.8 17.0 16.7 21.9 23.0 9.9 10.0 9.9 12.9 13.6 Port Patterson : Quail Islet Port Keats: Tree Pt Pearce Point: Extreme Victoria River: Water Vallev Cape Dussejour : Rock off cape Cape Londonderry : Extreme Cape Bougainville: Extreme Cassini 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 Page 260] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. AUSTRALIA— Continued. Place. MacLeay Islets: Rock off N. end PortUsbome: S*pt Fitz Roy River: Escape Pt Cape L' Ev^que: Extreme Lacepede Island : N W . islet Cape Baskerville: Extreme Cape Latouche Tr^ville : Extreme Turtle Isles: Center of N. isle Cape Lambert: Extreme Legendre Island: NW. extreme Rosemary Island : W. summit Enderby Island: Rocky Head Montebello Island: N. extreme of reef. Barrow Island: N. pt Northwest Cape: Extreme Cape Cuvier: Extreme Cape Inscription : Extreme Houtman Rocks: N. islet Port Gregory Cape Leschenault: Extreme Rottnest Island: Light-house Perth (Fremantle) : Arthur Head light Peel : Robert Pt Cape Naturaliste: Extreme Cape Leeuwin : Light-house D' Entrecasteaux Point: Extreme Nuyts Point: Extreme West Cajie Howe: Extreme , Eclipse Islets: Summit of largest King George Sound: Commissariat house near Albany jetty 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: Light-house Port Adelaide: Wonga Shoal light Cape Jervis : Light-house Cape Borda: Light-house Cape Willoughby: Light-house Port Victor: Flagstaff. Cape Jaffa : Margaret Brock light-house Cape Northumberland: Light-house ... Cape Nelson : S. extreme Portland Bay : Lawrence Rock Port Fairy: Griffith Island summit Cape Otway : Light-house King Island: Cape Wickham light Port Phillip: Point Lonsdale light Geelong: Custom-house Mell)ourne : Observatorv Lat. S. Long. E. Lun Int. ki inge. H. W. L. W. Spg. Neap. O / It 15 52 00 O / n 123 45 00 123 36 27 123 39 47 122 55 45 122 05 30 122 15 00 121 54 00 118 48 00 117 11 00 116 45 00 116 30 00 116 23 00 115 22 00 115 27 45 114 10 08 113 21 00 112 57 09 113 35 33 114 14 30 115 30 00 115 30 12 115 44 23 115 44 00 115 00 15 115 08 00 116 01 00 116 38 00 117 40 00 117 53 45 117 54 04 118 27 00 119 34 00 121 58 00 124 39 00 125 30 00 132 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 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 h. in. h. m. ft. ft. 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 11 30 5 10 17.6 10.4 20 27 00 20 35 00 20 16 45 20 40 40 21 46 41 24 00 00 25 29 19 28 18 05 28 12 00 31 18 00 32 00 20 32 03 12 32 27 00 [10 16] [3 43] [2.1] 33 31 45 34 21 55 34 52 00 35 05 00 35 09 00 35 11 54 35 02 20 34 55 00 [10 53] [4 40] [2.6] 34 24 00 34 30 00 32 57 00 32 34 00 32 01 30 32 48 00 11 50 9 35 5.1 0.3 34 29 29 35 00 15 35 6 55 5.5 0.3 35 20 15 34 43 22 33 44 08 32 29 42 34 28 25 8 20 2 15 11.4 0.7 35 18 21 35 07 31 34 12 00 34 50 25 35 36 45 4 31 4 04 10 45 10 22 10.2 6.3 0.6 0.9 35 45 30 35 51 00 35 34 06 4 00 10 15 5.8 0.3 36 57 00 38 04 18 38 26 00 11 52 5 40 4.2 0.2 38 24 39 38 23 47 20 6 35 2.7 2.1 38 51 45 39 35 38 143 57 03 144 37 00 144 21 47 144 58 35 38 18 00 38 08 52 37 49 53 10 43 2 02 2 19 4 30 8 20 8 41 2.5 3.0 1.9 1.9 2.3 1.5 APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. AUSTRALIA— Continued. [Page 261 Place. Cape Schanck : Light-house Port Western : Extreme of W. head Wilson PromontoiV: Light, SE. pt Kent Island: Deal Island light Flinders Is. : Strzelecki Peaks, SE. peak Goose Island: Light on S. end Banks Strait: Swan Island light Port Albert: Light-house Gabo Island : Light-house Cape Howe (east): Extreme Cape Green : SE. pt Twofold Bay: Lookout Pt. light Dromedary Mountain: Summit Montagu Island : Light-house Bateman Bay : Observation head Ulladulla: Inner end of pier Jervis Bay : Light-house Kiama Harbor : Outer extreme of S. head WoUongong: Summit of head Sydney : Observatory Port Jackson: Outer S. head light ... Broken Bay: Baranjo Head light Newcastle: Nobby Head light Port Stephens: Light-house Sugar Loaf Point: Light-house Port Macquarie : Entrance Solitary Islands: S. Isle light Clarence River: S. Headlight Lat. S. Richmond River: N. Head light Brisbane : Signal station Lookout Point: Extreme Cape Moreton : Light-house Double Island Point: Light-house Indian Head : Extreme Sandy Cape: Light-house Burnett River: S. Head light Lady Elliot Islet: Light-house Bustard Head : Light-house Rodd Bay : Spit end Port Curtis: Gatcombe Head light Cape Capricorn : Light-house Port Bowen: Observation rock Percy Isles: Pine I. light Northumberland Isles : Summit of Prud- hoe I Cape Palmerston : N. extreme Cape Conway: SE. pt Port Molle: S. side of entrance Cumberland Island: Whitsunday I., summit on W. side Port Denison: Obs. pt., W. side of Stone Isle Gloucester Island: Summit near N. end. Holborne Islet: Center Cape Bowling Green: Light-house Cape Cleveland : Light-house Palm Islands: SE. point of SE. island.. Rockingham Bay: Peak of Goold Isle.. Barnard Island: Light-house Frank land Island: High islet Cape Tribulation : Extreme Hope Island: S. islet Cook Mountain: Summit Cape Bedford : SE. extreme 38 29 42 38 29 15 39 08 00 39 29 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 28 51 30 27 27 32 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 16 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 Long. E. 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 10 153 35 55 153 01 48 153 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 Lnn. Int. H.W. L.W. Range. Spg. Neap. 10 38 8 40 8 05 20 "26' 8 40 8 35 8 15 9 00 10 45 10 05 8 55 h. m. \ ft. i ft. 4 25 "2'27' 1 52 "2"67' '2"67' 2 27 2 23 2 00 2 46 "2"66' 2 43 4.5 5.2 5.3 4.2 4.7 5.8 4.1 "4.'6' 4 30 6. 4 6.2 3.4 3.1 3.2 '3." 3 2.5 2.8 3.6 2.4 "2." 4 3.9 3 53 9. 5. 4 7.5 I 4.5 Page 262] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. AUSTRALIA— Continued. Place. Lat. s. Long. E. Lun. Int. 1 Range. 1 H.W. L.W. Spg. Neap. e i c (3 « s 9 Murdock Point ^Extreme , O / II 14 37 15 14 10 00 O ' II 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 II. TO. h. TO. ft. ft. Cape Melville: NE. extreme 1 Flinders Island: N. extreme of N. island. 14 07 45 Claremont Point: Extreme 14 00 30 Cape Sidmouth: Extreme 13 24 45 Cape Direction: NE. extreme i 12 51 00 Cape Grenville: Extreme 11 58 15 Sir Charles Hardv Island: N. extreme , of SE. isle ' ' 11 55 00 Bird Island: NW. isle 11 46 30 9 00 2 47 1 9. 6 5.8 Hannibal Isles: E. isle 11 36 30 10 41 30 10 37 45 10 22 00 10 46 00 10 36 05 17 36 40 17 35 10 17 06 50 Cape York : Sextant Rock 142 32 24 142 39 20 142 21 19 142 10 50 141 53 49 140 37 06 139 45 56 139 38 36 1 00 7 10 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 TASMANIA. Cape Portland: NW. pt 40 44 15 41 03 25 41 07 05 41 10 00 41 08 30 41 02 50 40 23 40 40 40 10 40 22 00 41 04 00 41 41 00 42 11 37 42 11 00 43 19 00 43 33 30 43 44 30 43 29 40 43 21 00 42 53 25 43 14 00 42 52 00 42 13 00 41 34 00 40 59 40 147 56 09 146 47 54 146 33 30 146 24 30 146 12 00 145 56 39 144 47 45 144 39 44 144 39 19 144 44 00 144 57 00 145 12 34 145 10 30 145 53 00 146 01 04 146 22 04 147 08 49 147 23 40 147 20 07 148 02 00 148 00 00 148 18 04 148 19 30 148 20 50 Port Dalrymple: Low Head light Port Sorrell: NW. entrance head Port Frederick : Entrance Leven River: W. entrance head Emu Bay : Blackman Pt . 11 10 5 00 9.0 6.9 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 : Light-house . 7 20 1 07 2.7 2.1 Port Davey : Pollard Head Southwest Cape: Extreme pt. Mewstone Rock: Center Cape Bninj'^: Light-house . Bruny Island : Penguin Islet Hobart Town: Transit of Venus station. Cape Pillar* Tasman Islet ... 8 05 1 52 4.2 3.2 Cape Frederik Hendrik: Extreme Freycinet Peninsula: Summit . St. Patrick Head: N. pt.... Eddystone Point : Extreme NEW ZEAIiAND. If. Three Kings Islands: NE. extreme of NE. island 34 m 20 34 25 07 34 31 00 35 00 20 35 01 44 35 17 00 172 08 49 173 03 34 173 00 54 173 32 39 173 45 48 174 06 06 North Cape : Cape Islet Parenga-renga Harbor: Kohan Pt Maunganui Harbor: White Pt Wangaroa Harbor: Peach Islet Bay of Islands: Motu Mea Islet 7 40 7 26 1 30 1 55 6.4 5.9 4.5 4.2 APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. NEW ZEAIiAND— Continued. [Page 263 Place. Wangaruru Harbor: Grove Pt Wangari Harbor: Loot Pt Great Barrier Island: Needles Pt Auckland Harbor: Light-house Coromandel Harbor: Tuhnia I Cape Colville: N. pt Cuvier Island: Light-house Tauranga Harbor: Mount Maunganui, 860 ft AVhite 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: Light-house Kidnappers Cape: Extreme Cape Palliser: Light-house Port Nicholson: Pencarrow light Wellington: Queen's Wharf light Mana-watu River: Light-house Wanganui River: N. head Egmont Mountain: Summit, 8,270 ft... New Plymouth: Flag-staff Kawhia Harbor: S. head Aotea Harbor: S. head Whaingaroa Harbor: S. entrance pt Manukau Harbor: Paratutai flag-staff.. Kaipara Harbor : Light-house Hokianga River: Flag-staff at entrance. Cape Campbell : Light-house Port Cooper: Lyttleton custom-house .. Akaroa Island: Light-house Ashburton River: N. entrance pt Waitangi River: N. entrance head Otago Harbor: Taivoa Head light Molyneux Bay : Landing place , Nugget Point: Light-house Bluff Harbor: Light-house Tewaewae Bay: Pahia Pt Solander Islands: Summit, 1,100 ft Preservation Inlet: Light-house West Cape : Extreme Queenstown: U. S, Tr. of Venus station Milford Sound: Freshwater Basin Cascade Point: N. extreme Grey River: Entrance Hokitika: Entrance light , Cape Foul wind : Light-house Cape Farewell : Extreme Nelson: Bowlder Bank light D' Urville Island : Port Hardy Port Gore: Head of Melville Cove Port Underwood; Flag Pt Port William: Howell's House Paterson Inlet: Glory Cove Port Adventure: White Beach, S. end.. Port Pegasus: Cove abreast Anchor- age I Codfish Island : N W. extreme Snares Islands: SW. islet. Lat. s. 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 40 27 10 39 57 00 39 18 00 39 03 35 38 04 50 37 59 35 37 46 22 37 03 00 36 23 00 35 32 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 Long. E. 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 25 175 14 40 174 59 44 174 03 59 174 04 35 174 48 04 174 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 Lun. Int. H. W. 166 44 h. m. 7 15 7 05 7 20 7 05 L. W. h. m. 1 05 55 1 10 55 7 05 55 8 10 8 00 2 00 1 50 05 ! 12 15 4 40 '4'52' 9 40 10 50 "i6'54 3 30 Range. Spg. Neap. ft. 6.5 6.7 10.8 10.7 6.6 6.8 3.5 5.7 3.6 6.3 9 15 9 10 3 05 3 00 11.6 11.9 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 3 31 1 05 ii'io' 9 39 5.6 7 15 "s'oo' 7.8 '7."5' 10 10 10 20 4 00 4 10 9.8 9.5 9 55 9 45 6 00 1 00 11 45 3 45 3 35 12.0 11.6 12 15 I 7.6 9 15 7.8 5 40 7.9 4.6 4.8 7.7 7.6 4.4 4.7 5.8 3.0 4.9 3.1 5.4 8.2 8.5 8.7 9.0 7.1 6.5 6.5 5.8 4.4 "6.'2 "5.'9 7.7 7.5 9.4 9.2 6.6 6.2 Page 264] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. THE ARCTIC REGIONS. Place. Cape Waleingham^ Extreme Mile Island: N. p* Marble Island : E. end Cape Kendall: Extreme Iglooik Island: E. pt Victoria Harbor: N. shore Elizabeth Harbor: Entrance Magnetic Pole, 1831 Port Neill: N. pt. of entrance Port Bowen: N. cove 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 Liakhov Islands: E. pt. of New Siberia Cape Tscheljuskin : E. pt Nova Zembla: Vaigats I. , N. pt Cape Costin (Kostina) . NE. pt., Cape Desire... Franz Josef Land : Wilczek I Mezen: Epiphany Church Morjovetz Island : Light-house Archangel : Trinity Church Jighinsk Island : Light-house Onega: St. Michael's Church Salovetski : Light-house Cape Sviatoi Nos: Light-house Bear Island Spitzbergen Island : S. cape Cloven Cliff Danes I., Robbe Bay Thank God Harbor Cape York : Extreme Upernivik: 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 Fiskernaes: 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 Lat.N. 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 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 38 00 55 00 47 48 20 42 40 00 14 04 13 12 07 30 49 06 42 30 58 30 55 54 48 42 24 30 10 36 29 12 05 12 50 00 42 36 59 36 28 20 10 24 09 42 12 12 47 30 48 36 Long. W. 28 00 50 00 06 00 15 00 31 00 30 33 10 56 47 00 00 54 54 48 08 00 12 00 10 00 45 00 18 00 38 00 45 00 20 00 48 15 57 00 91 87 81 91 92 96 89 88 91 90 73 64 61 63 64 70 110 179 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. 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 63 40 18 53 23 00 52 54 00 51 45 48 51 10 48 50 43 36 48 57 00 50 20 48 49 44 00 48 51 00 48 26 00 48 30 42 48 10 30 47 52 00 47 46 48 Lun. Int. Range. H.W. 4 00 6 50 11 38 10 35 1 20 10 00 7 18 5 05 9 02 L.W. h. m. ft. 10 15 "'olo' 12.0 "8."6' 5 29 4 20 7 40 3.8 3 50 7.0 2 00 11'30 3 10 2.2 3.8 9.1 9 05 2 55 14 12 14 "i6"56' 8 05 6 20 13.9 6 25 5 58 5.3 5.4 4 38 8.0 1 52 07 7.5 10.0 6 40 27 12.5 6 12 j 00 '6"i5 6 03' 9.0 'i2.'6" Neap. ft. 5.1 "4." 2 5. 5 2. 9 2.6 I 1.0 4.0 1.3 2.1 5.2 3.0 2.0 3.0 3.6 4.8 6.0 3.6 "4." 8 APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. THE ARCTIC REGIONS— Continued. [Page 265 Julianshaab: Village Neunortalik: Village Frederiksthal : Village Cape Farewell : Staten Huk Aleuk Islands : Center Cape Tortlenskjold: Extreme Cape Bille: Extreme Cape Juul: Extreme Cape Lo wenorn : Extreme Dannesbrog Island : Beacon Ingolsfjeld Rigny Mount : Summit Pendulum Islands Cape Philipp Broke Cape Bismark: Extreme Jan Maven Island: Mt. Beerenberg, 6,870ft Youngs Fore- land, or Cape Northeast Mary Muss Bay.. Langanaes Point. Rissnaes Point Grimsey Norddranger: Tr. Station Skagataaa Point North Cape: Kalfatindr Straumness Point Fugle or Staabierg Huk: Point Snaefells Yokul : Tr. Station Reykiavik : Observatory Cape Skagi : Light-house Reykianaes : Light-house Ingolfshofde: Tr. Station Papev Island: Tr. Station Reytnur Fjeld: Tr. Station Balatangi : Light-house Dia Fjeld: Tr. Station Lat. N. 60 43 07 60 08 12 60 00 00 59 49 00 60 09 00 61 25 00 62 01 00 63 14 00 64 30 00 65 18 00 66 19 02 69 00 12 74 40 00 74 55 00 76 47 00 71 04 00 71 08 00 71 00 00 22 45 32 40 33 42 07 30 27 29 26 30 30 15 48 04 08 40 04 09 48 06 48 19 35 42 55 27 16 14 45 00 Long. W. 46 01 00 45 16 00 44 40 00 44 01 42 42 55 00 42 15 00 42 00 00 40 50 00 39 30 00 38 30 00 35 11 00 26 10 24 18 17 00 17 33 00 18 40 00 7 36 00 7 26 00 8 28 00 14 30 46 16 10 24 17 57 36 20 05 26 22 23 04 23 08 00 24 31 26 23 45 08 21 55 00 22 39 04 22 39 00 16 36 13 14 08 31 13 41 10 13 32 22 14 23 35 Lun. Int. Range. H. W. h. m. 4 56 5 33 2 55 4 00 11 05 11 10 L. W. Spg. Neap. h. m. 11 09 11 46 9 10 10 13 4 53 4 58 11 21 5 06 ft. 7.0 8.6 9.4 7.5 ft. 2.8 3.4 3.8 3.0 6.7 3.7 3.9 2.1 3.8 2.2 5 10 11 25 14.5 Page 266J INDEX TO APPENDIX IV. Page. Admiralty Islands 255 Adriatic Sea 226-228 Africa, east coast 232, 233 north coast 230 west coa.«t 230-232 Alabama 196 Alaska 198,199 Aleutian Islands 199 Algeria 230 Arabia 236 Arctic regions 264, 265 Argentina 208, 209 Asia, east coast 239-250 islands . 243, 244 south coast 236-239 Atlantic Ocean, islands. 213-215 Australia 259-262 Austria 227,228 Azores Islands 213 Bahama Islands 203 Balearic Islands 226 Baluchistan 237 Banka Strait 239 Belgium 223 Belize 197 Bermuda Islands 214 Black Sea 229,230 Borneo 242 Brazil 207,208 British Columbia 200 Burma 238 California 200, 201 Canary Islands . . 214 Cape Breton Island 192, 193 Verde Islands 214 Caroline Islands 252 Celebes Island 242 Central America, east coast . . . 197, 198 west coast . . . 202, 203 Cevlon 237 Chile 209-212 China 240-242, 247 Sea 240 I^ntrance 240 Cochin China 240 Colombia, north coast . 198, 206 west coast 213 Connecticut 194 Cook Islands 258 Coral Sea Archipelago 255 Corsica 226 Costa Rica 198 Crozet Islands 236 Cuba 203,204 Cyprus 230 Delaware 195 Denmark 222,223 REGIONS AND COASTS. Page. Ecuador 213 Egypt 230 Ellice Islands 254 Europe, Atlantic coast. 215-225 Falkland Islands 214 Fiji Islands 256,257 Florida 195,196 Formosa Island 242 France, north and west coasts 223,224 France, south coast 225, 226 Galapagos Islands 250, 251 Gaspar Strait 239 Georgia 195 Germany 221,222 Gilbert Islands 251 Great Britain 215-218 Greece 228,229 Greenland 264, 265 Guatemala 197 Guiana 207 Haiti 204 Hawaiian Islands 253 Holland 223 Honduras 197,198 Iceland 265 India 237,238 Indian Ocean, islands. . 234-236 Italy 226,227 Jamaica 204 Japan 248,249 Java 243 Kerguelen Islands 236 Korea..... 247,248,250 Kuril Islands 249 Labrador 191,192 Laccadive Islands 234 Ladrone Islands 252 Linschoten Islands 248 Louisiade Archipelago 255 Louisiana 196 Lower California 201, 202 Madagascar 235 Madeira Islands 213 Magdalen Islands 192 Mame 193 Malaysia 238,239 Maldive Islands 234 Mariana Islands 252 Marquesas Islands 253 Marshall Islands 251 Maryland 195 Page. Massachusetts 194 Mauritius Island 234 Mediterranean Sea 225-230 Mexico, east coast 196, 197 west coast 202 Mississippi 196 Morocco 230 Mosquito Coast 198 New Brunswick 192, 193 Caledonia 259 Newfoundland 191,192 New Guinea Island 255 Hampshire 194 Hebrides Islands 256 Jersey 195 South Wales 261 York 194 Zealand 262,263 Nicaragua 198 North America, east coast . . . 191-198 west coast . . . 198-203 Australia 259 Carolina 195 Island, New Zea- land 262,263 Norway 218-219 Nova Scotia 193 Oregon 200 Pacific Ocean, islands -- 250-259 Pelew Islands 252 Persia 236, 237 Peru 212 Philippine Islands 245-247 Phoenix Islands 254 Porto Rico 205 Portugal 224,225 Prince Edward Island 192 Queen Charlotte Islands . . . 199 Queensland 261,262 Red Sea 233-234 Rhode Island 194 Russia, south coast 229 west coast 220 St. Lawrence, River and Gulf 192 Samoan Islands 257 Santa Cruz Islands 255 Sardinia 226 Siam, Gulf 240 Siberia 250 Society Islands 257 Solomon Islands 254 South America, north and east coasts 206-209 INDEX TO APPENDIX IV. [Page 267 Page. South America, W. coast 209-213 Australia 260 Carolina 195 Island, New Zealand.. 263 Spain, north and west coasts 224,225 south and east coasts. . 225 Stewart Island 263 Sumatra 239 Sweden 219,220 Uruguay REGIONS AND COASTS — Continued. Page. Tasmania 262 Texas 196 Tonga Islands 258 Trinidad 206 Tuamotu Archipelago. . 257, 258 Tunis 230 Turkey 228,229,230 208 Aalborg 223 Aarhus 223 Ababa Island 256 Abaco Island 203 Abang Besar Island 238 Abbeville 223 Abd-al-Kuri Island 233 Aberdeen 216 Abervrach 224 Aberystwith 215 Abingdon Island 250 Abo... 220 AboukirBay 230 Abreojos Point 201 Abrolhos Island 207 Ab.secon Inlet 195 Acajutla 202 Acapulco 202 Accra 231 Acheen Head 239 Aconcagua Mountain 21 1 Acre 230 Adakh Island 199 Adalla 230 Adams, Port 247 Addu Atoll 234 Adelaide, Port 260 River 259 Adele Island 255 Aden 236 Adenara Island 243 Admiralty Head 200 Islands 255 Adolphus Mountain 262 Adventure, Port 263 ^gina 229 Aero Island 222 Ji^rstenen 218 Africa Rock 226 Agalegas Island 235 Agdenes .•. 218 Agiabampo 202 Agrigan Island 252 Aguadilla Bay 205 Aguja Point 212 Agulhas.Cape 232 Agutava Islet 245 Aheu Island 258 Ahunui Island 257 Ahuriri 263 AiSima 249 Aian 250 Aignan, St., Island 255 Aigues Mortes 226 Ailinginae Islands 251 Aillick Harbor 191 Ailly Point 223 Ailuk Islands 251 Aitutaki Island 258 Aix Island 224 Ajaccio 226 Ajano 230 Akamokan Island 252 Akaroa Island 263 Akashi-no-seto 248 Akpatok Island 191 Akyab 238 Alacran Reef 197 Alamaguan Island 252 Aland Island 220 AlargateReef 198 Albany 194 Albatross Islet 262 Albemarle Island 251 Albert, Port 261 River 262 Alboran Island 230 Albuquerque Bank 198 Alcatrasses Island 208 Alcmene 259 Alcoba^a 207 Aldabra Island 235 Aldeu 218 Alderney Harbor 218 Alegranza Island 214 Alegre, Porto 207 Alert's Winter Quarters ... 264 Alessandro, San, Island 253 Aleuk Islands 265 Alexander, Port 232 Vancouver 200 Alexandretta 230 Alexandria 230 Alfaciues, Port 225 Alfred, Port 232 Algeciraa 225 Algier 230 Ali-Agha, Port 230 Alicante 225 Alij OS Rocks 201 Alipee 237 Alligator Island 241 Reef 196 Alraadie Point 231 Almeria 225 Alphonse Island 235 Alta Vela 204 Altata 202 Altea 225 Altona 222 Alvarado 196 Amager Island 222 Amber, Cape 235 Amboina Island 244 Ambrose, St. , Island 258 Amchitka Island 199 Page. Vancouver Island 199, 200 Venezuela 206 Victoria .». . 260, 261 Virginia 195 Washington 200 Western Australia 259, 260 West India Islands 203-206 Yucatan 197 Amelia Island 195 Ameni Islet 234 Amherst Harbor 192 Amirante Islands 234 Amour Point 192 Amoy 241 Amsterdam 223 Island 236 Ana, Sta., Lagoon 197 Anaa Island 258 Anacapa Island 201 Anadir River 250 Analaboe 239 Anamba Islands 240 Anataxan Island 252 Anchorite Island 255 Ancona 227 Andaman Islands 238 Andenes 218 Andrava Bay 235 Andrea, St. , Rock 228 Andrew, St 193 Cape 235 Island 255 Andrews, St. , Island 198 Andros Island, Bahamas... 203 Grecian Arch 229 Anegada 205 Aneityum Island 256 Angatau 258 Angaur Island 252 Angeles Bay 202 Los 201 Port, Mexico 202 , Washington 200 Anghris Head 217 Angosto, Port 210 Angoxa Island 233 AngradosReis 208 Pequena 232 Anguilla 205 Anhatomirim 208 Anholt Island 222 Animas, Las 202 Anjer 243 Anjoe, Cape 243 Ann, Cape 194 St., Bay 204 Anna, Sta., Island, N.Brazil. 207 S. Brazil .... 208 Annapolis, Maryland 195 Nova Scotia 193 Anne, St., Island 210 Annisquam 194 Anno Bon Island 231 Anns, St., C. Breton 1 192 England 215 Anowik Island 199 Page 268J INDEX TO APPENDIX IV. Page. Antareh, Ras 233 Antibes 226 Anticosti fcland 192 Antigua 205 Antipodes Island 259 Antivari 228 Antofagasta .*... 211 Antonina 208 Antonio, Port 204 San, Cape, Argentina . 208 Cuba 204 Mt. and Island... 214 Port, Argentina. . 209 Chile 211 Sierra 209 Antwerp 223 AogaShinia 249 Aor, Pulo 240 Aotea 263 Apaiang Island 251 Apalaehicola 196 Apamama 251 Aparri 245 Apenrade 221 Apo Islet 245 Apostle Rocks 209 AragoCape 200 Araish, El 230 Arakam Island 250 Araktcheff Island 258 Aran Island 217 Aransas Pass 196 Aranuka Island 251 Aratika Island 258 Arcadius Islands 204 Areas Cays 197 Archangel 264 Ardassier Islands 243 Ardrossan 216 Arena de la Ventana 201 Point, California 200 L. C^alif ornia .... 201 Arenas Cay 197 Arendal Inlet 219 Arentes Island 243 Argentina 208 Argostoli, Port 228 Arica 212 Arichat Harbor 193 Arkona 221 Armeghon 238 Amheiin, Cape 259 Arno Atoll 251 Arorai Island 251 Arran Island 217 Arrowsmith Islands 251 Arru Islands 244 Arsuk 264 Artaki Bay 230 Arthur River 262 Port 247 Arvoredo Island 208 Ascension Bay 197 Island 214 Ashburton River 263 Ashrafi Island 233 Asia Rock 212 Assateague Island 195 Assens 222 Assumption Island 235 Astoria 200 PLACES — continued. Page. Asuncion Island, Ladrones. 252 L.Calif 201 Atalaia Point 207 Athene 229 Atico 212 Atiu Island 258 Atka Island 199 Atkinson Point 200 Attu Island 199 Auckland 263 Islands 259 Audierne 224 Augusta 193 Port, Australia 260 Sicily 227 Augustenberg 221 Augustin, St., Cape, Brazil. 207 Philippines. 246 Augustine, San, Island 253 St., Bay 235 Harbor 195 Aurh Island 251 Aurora Harbor 264 Island 256 Austral Islands 258 Avarena Point 204 Aves Island 205 Aviles 224 Avlona 228 Axim Bay 231 Awa Sima 249 Awomori 249 Ayamonte 225 Ayer Bangis 239 Ayr 215 Baago Island 222 Babayan Claro Island 245 Baccalieu Island 191 Baganiovo 233 Bahal tolls Island 247 Bahama Island 203 Bahia,Brazil 207 Colombia 206 de Cadiz Cay 204 Honda, C. America 202 Bahrain Harbor 236 Bajo Nuevo 197 Bajuren Island 242 Baker Islet 251 Bakers Island 193 Baklar 229 Balabac Island 245 Balaklava Bay 229 Balari Pass 259 Balasor River 238 Balatangi 265 Balayan 245 Bald Isle 260 Balfour Rock 236 Bali Island 243 Balingtang Islands 246 Ballena Bay 202 Balls Pyramid 259 Ballum 22i Ballycottin 218 Balstrum 222 Balta Island 216 Baltic Port 220 Baltimore 195 Bampton Island 255 Page. Banda Island 244 Banderburum 236 Band jerinasin 242 Bangkaru Islands 239 Bangkok 240 Bangor 193 Bangs Havn 264 Banjuwangi 243 Banka Island 239 Strait 239 Bankot 237 Banks Strait 261 Bantal 239 Bantam 243 Bantenan 243 Banton Island 246 Bantry Bay 216 Baracoa 203 Barataria Bay 196 Baratoube Bay 235 Barbados Island 205 Barbara, Santa, California . 201 Island 201 Mexico 202 Port 210 Barbe, St. , Island 240 Barbuda 205 Barcelo Bay 210 Barcelona, Spain . . 225 Venezuela 206 Bardsey Island 215 Barfleur, Cape 223 Bari 227 Barker Islets 259 Barnard Island 261 Barnegat Inlet 195 Barneveldt Islands 209 Barnstable 194 Barra Head 216 Sao Joao 208 da 207 Barren Island 248 West 242 Barrier, Great, Island 263 Barrington Island 251 Barrow Island, Australia . . 260 Tuamotu Arch . . . 257 Point 198 Bartholomew, St 205 Cape 209 Bartolom^, San 201 Barton, Port 245 Baru,.Point 239 Barung Island 243 Bas, De, Island 224 Basdorf 221 Basianang Bay 246 Bilsiduh 237 Basilan Island 247 Baskerville, Cape 260 Basrah 236 Bass Islets 258 Bassa, Grand 231 Bassas Rocks 237 da India 235 Bassein, Burma 238 India 237 River 238 Basseterre 205 Bastia 226 Bastion, Cape 240 INDEX TO APPENDIX IV. [Page 269 Page. Basto 219 Batalden Island 218 Batan Island 246 Port 246 Batangas 245 Batavia 243 Batbatan Island 246 Bate Islands 248 Bateman Bay 261 Bath 193 Bathurst 231 Island 259 Batian Island 244 Batoe Islands 239 Batoura 229 Batticaloa 237 Battle Islands 191 Batty Bay 264 Batve Toetong 239 Baubeltaub Island 252 Bauld Cape 191 Baxo Nuevo 204 Bay of Islands 262 Baynes Sound 200 Bayonnaise Island 249 Bayonne 224 Bazaruto Island 232 BeachyHead 215 BealeCape 199 Bear Island 264 Cape 225 Beata Island 204 Beaufort, N. Carolina. ..... 195 S.Carolina 195 Port 232 Beaver Harbor 200 Beaver-tail Light 194 Bee du Raz 224 Beda'a,Al 236 Bedford, Ca]ie 261 Bees, St 215 Beeves Eocks 216 Beirut 230 Bel Air 235 Belfast 193 Bay 217 Belgrano 208 Belize 197 Bell Island 191 Rock, Scotland 216 Bellavista Cape 226 Belle Isle, France 224 Labrador 191 Bellingshausen Island 257 Bellone, Cape 235 BenGhazi 230 Benbane Head 217 Bender Erekli 230 Benedicto, San, Island 202 Benevente 207 Benguela 232 Benicia 200 Benidonne 225 Benin River 231 Benito, San, Island 201 Benkulen 239 Bento, San, River 231 Benzert 230 Bequia Island 205 Berbera 233 Berdiansk 229 PLACES — continued. Page. Bergen, Germany 221 Norwav 218 Berikat '. 239 Bering, Cape 250 Island 250 Berlanga Island 225 Berlin 222 Benneja Head 209 Bermudas 214 Bernal Chico 196 Bernardo Islands 257 Berwick 216 Besuki 243 Betrapar Islet 234 Beverly 194 Beyt 237 Bhaunagar 237 Blanche Point 227 Biarritz 224 Bickerton I.«land 259 Bideford 215 Bidstone 215 Bierneborg 220 Bigar Islet.. 251 Bikini Islands 251 Bilbao 224 Bille, Cape 265 Billiton Island 239 Bindloe Island 250 Bintang Hill 238 Bintoean 239 Bird Island, Australia 262 Bahamas 203 BandaSea 244 N. Pacific 253 Seychelle Islands. 234 Tuamotu Arch. . . 258 W. Africa 231 Islands, Magdalen Is. . 232 Birneys Island 254 Bismark, Cape 265 Bittern Rocks 249 Bjuroklubb 220 Blaabjerg 223 Black Head 191 Point Bay 232 Stairs Mountain 217 Blackness 216 Blacksod Point 217 Blair, Port 238 Blaize, St 232 Blanco Cape, N., Africa 231 Oregon 200 Peru 212 S. , Africa 231 Peak 198 Blankenberghe 223 Bias, San, Argentina 209 Cape, Florida 196 Mexico 202 Blasket Islands 216 Bligh Island 257 Blighs Cape 236 Blimbing Bav 239 Blinyu ' 239 Block Island 194 Bloody Foreland 217 Blueflelds 198 BluffHarbor 263 Boar Islands 191 Boavista Island 214 Page. BobaraRock 228 Bodie Island 195 Bogense 222 Bogsher 220 Bohol Island 246 Bojador, Cape 231 Bojeador, Cape 245 Bola-Bola Island 257 Bom Abrigo Islet 208 Bombay 237 Bon, Cape 230 Point 239 Bona 230 Bonacca Island 197 Bonaive Island 206 Bona venture Head 191 Island 192 Bonavista Cape 191 Bongao Island 247 Bonham Islands 251 Bonifacio 226 Bonin Islands i . 253 Boobjerg 223 Booby Island, Leeward Is. . 205 Queensland 262 Boompjeo Island 243 Boon Island 193 Borda, Cape 260 Bordeaux 224 Bordelaise Island 252 Borja Bay 210 Bornholm 222 Borodino Islands 253 Boscawen Island 257 Bosphorus 229 Boston 194 .Botel Tobago Sima 242 Bougainville, Cape 259 Island 254 Bougaroni, Cape 230 Boulogne 223 Bounty Islands 259 Bourbon, Cape 236 Bouro Island 244 Bouton Island 242 Bouvets Island 215 Bovlilu van, Cape 245 Bowditch Islet 254 Bowen, Port, Australia 261 BaffinsBay 264 Bowling Green, Cape 261 Boyanna Bay 235 Bradore Bay 192 Brala, Pulo 240 Brangmans Bluff 198 Bras, Pulo 239 Brass River 231 Brava Island, C.Verde Is.. 214 E. Africa 233 Brazos Santiago 196 Bray Head 217 Breaker Point 241 Bremerhaven 222 Bremerton 200 Brest 224 Brewers Lagoon 198 Bridgeport 194 Brielle 223 Brill Reef 243 Brindisi 227 Brisbane 261 Page 270j INDEX TO APPENDIX IV. Page. Bristol, England 215 Rhode Island 194 Britannia Island 259 Broadhaven 217 Broken Bay 261 Bronnosnnd 218 Brothers Island, Red Sea . . 233 Islets, China 241 Broughton Bay 244 Head 248 Island 249 Rock 249 Brunet Island 191 Bruni River 242 Brunswick, Georgia 1 95 Maine 193 Bruny, Cape 262 Island 262 Brussels 223 Brusterort 221 Bryer Island 193 Bubn^n Island 247 Bucas Island 246 Buchanness 216 Buddonness 216 Budrum 230 Budua 228 Buenaventura 213 San 201 Buenos Avres 208 Bugui Point 246 Buitenzorg 243 Buka Island 254 Bulipongpong Island 247 Biilk 221 Bull Harbor 200 Rock 216 Bullock Bay 250 Burg 221 Burghaz 229 Burias Island 246 Burin Harbor 191 Burnett River 261 Burntcoat Head 193 Burrh Island 251 Busios 208 Islets 208 Bustard Head 261 Busuanga Island 245 Busum 222 Butt of Lewis 216 Button Islands 191 Byam Martin Island 257 Byron Island 251 Caballo Island 245 Cabeceira, Cape 233 Cabeza de Vaca 211 Cabrera Island 226 Cabron Cape 204 Cabrut Islet 234 Cadaques 225 Cadiz 225 C'admus Island 257 Caen "... 223 Cagayan Jolo Island 247 Cagayanes Islands 247 Cagliari 226 Caigara 207 Caicos Island 203 West, Cay 203 PLACES — continued. Pivge. Calaan, Point 246 Calais, France 223 Maine 193 Calavite, Monte 245 Calavan Island 245 Calbuco 211 Calcasieu Pass 196 Calcutta • 238 Caldera 211 Caldy Island 215 Calebar River, New 231 Old 231 Caledonia 206 Calf of Man 215 Calicut - 237 Calimere Point 237 Callao 212 Calpe 225 Caluya Island 245 Calvi 226 Caniamu 207 Camaron Cape 198 Camasusu Island 246 Cam bay 237 Cambria 208 Cambridge, England 215 United States 194 Camiguin Island, Luzon . . . 245 Mindanao 247 Cammin 221 Campbell, Cape 263 Island 259 Campeche 197 Campobello Island 193 Canaria, Gran, Island 214 Canaveral Cape 195 Cancun Island 197 Candia Island 228 Candon 245 Cannes 226 Cannonier Point 234 Canoas Point 201 Canso, Cape 193 North 193 Canton 241 Island 254 Pulo 240 Cantyre 216 Cape Town 232 Cape Verde Islands 214 Capel Island 218 Cape d'Istria 246 Capones Islet 245 Capraia Island 226 Caprera Island 226 Capri Island 226 Capricorn, Cape 261 CarNicobar 238 Carabane 231 Carabao Island 246 Caraques Bay 213 Carataska Lagoon 198 Caravellas., 207 Carbon, Cape 230 Carbonera Cape 226 Cardamum Islet 234 Cardiff 215 Careys Islands 264 Cargados Carajos 234' Caribana Point 206 Carimare Mountain 207 Page. Carimata Island 240 Carl ingford Lough 217 Carlobago 227 Carlos, San, deAncud 211 Point 201 Carmen Island 197 Caroline Islands, N. Pacific. 252 S.Pacific 253 Carousel Island 192 Carreta Mountain 212 Point 198 Carreto, Port 206 '^^arrizal. Port 211 Cartagena, Colombia 206 Spain 225 Cartago Mountain 198 Carteret Cape 224 Harbor 255 Cartwright Harbor 191 Carupano 206 Carysfort Island 257 Reef 195 Cascade Point 263 Casquets Rocks 223 Cassini Island 259 Castillos 208 Castle Island 203 Caatlehaven 216 Castro 210 Urdiales 224 Catlsland 196 Catalina Harbor 191 Sta., Island 201 Catania 227 Catastrophe, Cape 260 Catbalogan 246 Catharine Point 209 St 215 Island 208 Cato Island 255 Catoche Cape 197 Cattaro 228 Cautanduanco Islands 246 Cavite 245 Caxones 198 Cayenne 207 Cayeux 223 Caymans 204 Cazza Island 228 Ceara 207 Cebu Island 246 Cedar Keys 196 Cedeira 225 Ceicer de Mer Island 240 Celebes 242 Centinela Islet 206 Ceram Island 244 Cerros Island 201 Cestos 231 Cette 226 Ceuta 230 Ceylon 237 Chacachacare Island 206 Chacopata 206 Chagos Arch 234 Chagres 206 ChahbarBav 237 Chala Point.".... 212 ChaleurBay 192 Challenger, Cape 2.36 Chama Bav 231 INDEX TO APPENDIX IV. [Page 271 Page. Cham-Callao Island 240 Chame, Point 213 Chamisso Island 198 Champerico 202 Chanaral Bay 211 Island 211 Chandeleur Islands 196 Chao Islet 212 Chapel Island 241 Chapu 242 Charles Cape 195 Island, Chile 210 Galapagos Group. 251 Hudson Strait 191 Charleston 195 Charlottetown 192 ChateauBay 192 Chatham Harbor 194 Island, Galapagos Group 251 S. Pacific 259 ChatteCape 192 Chaume,La 224 Chausey Islands 224 Chedubah Island 238 Chemulpo 247 Chentabun River 240 Chepillo Island 213 Cherbourg 223 Cheribon 243 Cherso 227 Chiachi Islands 199 Chicarene Point 202 Chidleigh Cape 191 Chifu 247 Chignecto Cape 193 ChignikBay 199 Chilca Point 212 ChimbaBay 211 Chimbote 212 Chincha Islands 212 Chinchin Harbor 241 Chinchorro Bank 197 Chin-hai 241 ChinoBay 241 Chirambiri Point 213 Chirikof Island 199 Chitlaclslet 234 Chittagong River 238 Choda Island 247 Choiseul Island 254 Port... 235 Choros Islands 211 Christiana Islands 229 Christiania 219 Christianshaab 264 Christianso Island 222 Christianssand 218 Christiansted 205 Christiansund 218 Christmas Cove 210 Harbor 236 I., Indian Ocean 236 N. Pacific 251 Christopher, St 205 Christoval, San, Island 254 Chuapa River 211 Chuluwan Island 232 Chupat River 209 Churriica, Port 210 Chusan Islands 241 PLACES — continued . Page. Claris Island 202 Cica. Mount 228 Cienfuegos 204 Ciotat 226 Cispata, Port 206 CittaNuova 227 Civitavecchia 226 Clara, Sta 200 Clare Island 217 Claremont Point 262 Clarence Harbor, Bahamas. 203 Port, Alaska 198 River 261 Clarion Island 202 Claushavn 264 Clear Cape 216 Clearwater Point 192 Gierke Island 257 Clermont Tonnere Island 257 Cleveland, Cape 261 Clew Bay 217 ClifdenBay 217 Clipperton Island, Mexico . 202 N.Pacific 253 Clonard, Cape 250 Coast Castle, Cape 231 Coatzacoalcos 197 Cobbler Rock 198 Cobija 212 CobreBay 211 Cochin 237 Cockell Islet 259 Cockscomb Mountain 197 Coconada 238 Cocos Island, C. America . . 203 N.Pacific 250 Cod, Cape 194 CoderaCape 206 Codfish Island 263 Codroy Island 192 Coetivy Island 235 Coffin Bay 260 Island, Madagascar 235 Nova Scotia 193 Cofre de Perote Mt 196 Coiba Island 202 Colberg 221 Colbert Islet 259 Coles Point 212 Colina Redonda 212 ColnettBay 201 Colombo 237 Colon 206 Colonia 208 Colonna, Cape, Greece 229 Italy 227 Columbia, Cape 264 Columbretes Islands 225 Columbus Island 198 Colville, Cape 263 Coman Inlet 211 Comandatuba 207 Commerson Island 255 Comorin, Cape 237 Comoro Island 235 Concei^ao 208 Conception Island 203 Point 201 Conde 207 CondorCove 211 Condore Islands 240 Page. Conducia 233 Conejo, El, Point 201 Coney Island 241 ConfitesCay 204 Congo River 232 Congrehoy Peak 197 Conn^table Islet 207 Constantinople 229 Constitution Cove 212 Contas 207 Conte, Port 226 Contoy Island 197 Conway, Cape 261 Reef 258 Cook Cape 199 Mountain 261 CookraHill 198 Cooper, Port 263 Copenhagen 222 Copiapo 211 Copper Island 250 Coquet Island 216 Coquille Island 252 Coquimbo 211 Coral Island 208 Islet 208 Corcovado Volcano 210 Cordouan, Point 224 Corfu 228 Coringa Islands 255 Corinto 202 Cork, Ireland 218 Port, Staten Island ... 209 Cormorant Island 200 Corn Islands 198 Corn wal lis Islands 253 Port 238 Coro, Vela de 206 Coromandel Harbor 263 Coronation Island 215 Corregidor Island 245 Cotrientes, Cape, Argentina . 208 Colombia 213 Mexico 202 S. Africa 232 Corsarios Bay 206 Corseulles, Port 223 Corso, Cape 226 Mountain 210 Corti 226 Coruna 225 Corvolsland 213 Coslin 221 Cosmoledo Island 235 Cotinguiba 207 Cotrone 227 Coubre, Point de la 224 Courtown Cays 198 Coutances 224 Cove Rock 232 Cow Head 192 Coy Inlet 209 Cozumel Island 197 Cracker Bav 209 Crassok Point 239 Crescent City 200 Cretin, Cape 255 Creux, Cape 225 Crocker Island 258 Croisic 224 Croker, Cape 259 Page 272] INDEX TO APPENDIX IV. Page. Crooked Island 203 Crozet Islands 236 Cruz Cape 204 Sta., Brazil 207 California 201 Island 201 Islands, Philijv pines 247 S. Pacific ... 255 Leeward Islands . 205 Luzon 245 Port 209 Cuad Basang Island 247 Cuba 203,204 Culebra 202 Culebrita Island 205 Culion Island 245 Cullera, Cape 225 Culver Point 260 Cumana 206 Cumberland Island 261 Cumshewa Harbor 199 Cupchi Point 241 Cupica Bay 213 Cura^-ao Island 206 Little 206 Currimao 245 Currituck Beach 195 Curtis Island 258 Port 261 Curzola Island 228 Cuttyhunk Light 194 Cuvier, Cape 260 Island 263 Cuxhaven 222 Cuyo Island 245 Cyprus 230 Dfedalus Shoal 233 Dago Island 220 Dakar, Port 231 Dalcahue 211 Dale Point 259 Dalrymple Harbor 247 Port 262 Dalupiri Island 245 Damghot 236 Dam ma Island 244 Danger Islands 257 Dangerous Rock 241 Dannesbrog Island 265 Danube River 229 Danzig 221 Dapitan 247 Dardanelles 229 Dar el Beida, Cape 230 Dar-es-Salaam 233 Darien, Colombia 213 Georgia, U.S 195 Darsserort 221 Darwin, Port 259 Dato Island 240 Datu, Point 239 Dauphin, Fort 235 Davao 246 Davey, Port 262 Davids, 8t. , Island 214 De Kastri 250 De Pevsters Island 254 Deadman Rock 192 PLACHS — continued . Page. Deception Island 215 Deimaniveh 236 Delagoa Bay 232 Delgada Point 209 Delgado, Cape 233 Point 209 Demerara 207 Denia 225 Denis,St 235 Denison, Port 261 D'Entrecasteaux Islands 255 Point 260 Deseado Cape 209 Desert, Mt., Rock 193 Desertas 213 Desirade 205 Desire, Port 209 Desolation Cape 209 DiaFjeld 265 Diamond Harbor 238 Point 239 Diedrichshagen 221 Diego Garcia 234 • Ramirez Island 209 San 201 Cape 209 Dieppe 223 Digges Islands 191 Dimasalasan, Port 246 Dinding Channel 238 Dingle Bay 216 Diomede Island 198 Direction, Cape 262 Island 240 Disappointment, Cape, Sib. 250 Washington 200 Discovery Harbor 264 Disei Island 233 DiuHead 237 DixCove 231 Djabon, Point 239 Djambi 239 Djursten 219 Dnieper Bay 229 Doc Can Islet 247 Dodd Island 241 Dog Island 205 Domar, Pulo 240 Domesnes 220 Domingo, San, Point 201 St., Cay 203 City 204 Dominica ^ 205 Donaghadee 217 Dondra Head 237 Donegal Bay 217 Double Island 238 Point 261 Peak Island 241 Douglass Rocks 253 Dounpatrick Head 217 Douvres Rocks 224 Dover Point 260 Drei Cap Peninsula 255 Drepano, Port 228 Drobak 219 Drogheda 217 Dromedary Mountain 261 Dnimmond Island 251 Dublin 217 Ducie Island 257 Page. Duff Islands 255 Duke of Clarence Island . . . 254 York I., N.Britain. 254 S. Pac... 254 Dulce Gulf 197 River 197 Dulcigno 228 Dumaguete 246 Dumaly Point 245 Dumf ord Point 232 Duncan Island 251 Dundee, Rock of 210 Dundrum Bay 217 Dungarvan 218 Dungeness 215 New 200 Point 209 Dunkerque 223 Dunnet Head 216 Duperrey Islands 252 Duppel .' 221 Durazzo 228 Durnford, Port 233 D' Urville Island 263 Point 255 Dussejour, Cape 259 Dwarka 237 Eagle Island 217 Earakong Island 252 East Cape, Madagascar 235 New Zealand 263 Siberia 250 Dog Island 241 Island, Crozet Is 236 Magdalen Is 192 Easter Island 258 Eastport 193 Eau Island 252 Eauripik Islands 252 Ebon Atoll 251 Eckemforde 221 Eclipse Harbor 191 Islands 260 Eddvstone 215 'Point 262 Eden Harbor 210 Edenshaw Cajje 199 Edenton 195 Edinburgh 216 Eeragh Island 217 Egedesmunde 264 Eggegrund Islet 219 Egmont Mountain 263 Port 214 Eimeo Island 257 Ekholm Islet 220 Elba Island 226 p]lbing 221 Elena, St., Port 209 Sta., Point 213 Elephant Bav- 232 Eleuthera Island 203 Elias, St. , Mount 199 Elizabeth Bav 232 Cape ..." 193 City 195 Harbor 264 Island, Chile 210 Tuamotu Arch 257, 258 Port 232 INDEX TO APPENDIX IV. [Page 273 I "age. Elizabeth Eeef 259 Ellice Islands 254 Emden 222 Emma, Great, Island 203 Emu Bay 262 Enanger 219 Endelave Island 222 Enderbury Island 254 Enderby Island 260 Endermo 249 Enfant Perdu Islanerg 222 Galiola Rock 227 Galita Island .♦ 230 Gallant, Port 210 Galle, Point de 237 Gallegos River 209 Galley Head 218 Gallinas River 231 Gallipoli, Italy 227 Turkey , 229 Galloway, iVliill of 215 Galveston 196 Galway 217 Gambler Island 257 Gange 220 Gannet, Outer, Island 191 Rock 193 Gap Rock 241 Garcia d' Avila 207 Gardiner Island 253 Gardners I., I^ong Island . . 194 S. Pacific 254 Garra^, Little 238 Gaspar, Island and Strait . . 239 Rico Reef 253 Gasparilla Island 196 Gaspe Cape 192 Gata, Cape, Cyprus 230 de, Spain 225 Gaujam 238 Gay Head 194 Gebey Islands 244 Geelong 260 Gefle 219 Genoa 226 Geoi^e, Fort, Cay 203 St., Cape, Florida 196 Newfdl'd . . 192 Nova Scotia. 193 Island, Alaska . .-. 199 Azores 213 Georges Island 202 St., Cay 197 Georgetown 195 Georgia, South, Island 214 Geronimo, San, Island 201 Geyser Reef 235 Gharib, Has 233 Ghir,Cape 231 Gilxlo Island 246 Gibraltar 225 Giglio Island 226 Gijon 224 Gilbert Islands 251 Gillolo Island 244 Ginger Cay 203 Girgenti 227 Gizau 234 Gizo Island 254 Glas Island 216 Glasgow 216 Glashedy Island ^21 7 Glenan Islands 224 Glocester Island 258 Glorioso Islands 235 Gloucester Island, Aus 261 Massachusetts 194 PLACES — continued. Page. Glover Reef 197 Gnarp 220 Goa 237 Godhavn 264 Godthaab 264 Goedereede 223 Golam Head 217 Gomenitza 228 Gomera Island 214 Gonaives 204 Gonave Island 204 Good Hope, Cape, Africa.. 232 China 241 >• Island 257 Success Bay 209 Goose Island 261 Gopalpur 238 Goram Islands 244 GordaCay 198 Point 212 Gore, Port 263 Goree Island 231 Road 209 Gorgona Island 213 Goro Island 256 Goroiitalo 242 Goto Island 248 Gottenburg 219 Gottland Island 219 Gough Island 214 Gozier Islet 205 Gozo Island 227 Gracias a Dios Cape 198 Graciosa Island 213 Grado 227 Grand Manan Island 193 Port 234 Riband Island 226 Grande Point 211 Grange Point 204 Granitz 221 Granville 224 Grappler, Port 210 Grave, Point de 224 Gravelines 223 Gready Harbor 191 GreatBirdRock 192 Rock Head 198 Green, Cape 261 Island, Labrador 191 Newfoundland. . . 192 Nova Scotia 193 Greenly Island 192 Greenspond Island 191 Greenwich 215 Island 252 Gregory, Cape 209 Port 260 Grenada 205 Grenville, Cape 262 Grey River 263 Greytown 198 Griefswald 221 Grief swalder Die 221 Grim, Cape 262 Grimsey Nordd ranger 265 Grip 218 GrisNezCape 223 Groate Eylandt 259 Groix, Island de 224 Gross-Horst 221 Page. Grouin du Cou, Point de 224 Gruizza Rock 227 Gryto 218 Guadalcanar Island , 254 Guadeloupe, L. California. . 201 West Indies 205 Guaineco Islands 210 Guaira, La 206 Guaja Shima 248 Guam Island 252 Guana, Little, Cay 203 Guanape Islands 212 Guanica 205 Guantanamo 204 Guarapiri Islets 207 Gnaratiba Cape 208 Guardafui, Cape 233 Guascama Point 213 Guatulco, Port 202 Guayaquil 213 Guaymas 202 Guerande 224 Guerin Island 247 Guguan Island 252 Guimaras Island 246 Guiuan 246 Guldager 223 Gull Island, Little 194 Gullan, San, Island 212 Gun Cay 203 Gunong Api Island 243 Gutzlaff Island 242 Gwadar Bay 237 Gwatar Bay 237 Habana 204 Habibas Island 230 Hacha, Rio de la 206 Haddington, Port 244 Haedic Island 224 Hafun, Ras 233 Hagenmeister Island 198 Hague, Cape la 223 The 223 Hai-Duong 240 Hai-Fong 240 Haifa 230 Hainan Island 240, 241 Haitien, Cape » 204 Hai-vun-tan Island 247 Hakodate 249 Half Port Bay 210 Half-Moon Cay, Belize 197 Nicaragua 198 Halgan Island 259 Halifax 193 Haliguen, Port 224 Hall Island 252 Islands, Sir James 247 Halmstad 219 Hals 223 Halt Bay 210 Halten Island 218 Hamberg 219 Hamilton Island 214 Mountain 200 Port 248 Hammamet Bay 230 Hammerfest 218 Hampton.. 194 Hamrange 219 INDEX TO APPENDIX IV. [Page 275 Page. Hanalei 253 Hanfelah Bay 233 Hangklip, Cape 232 Hannibal Isles 262 Hano Island 219 Ha-Noi 240 Hao Island 258 Haradsskar Islet 219 Haraiki Island 258 Harbor Grace 191 Harburg 222 Hardy, Sir C, Island 262 Harpe, La, Island 258 Harrison Cape 191 Hartlepool 216 Harvey, Port 200 Harwich 216 Hatteras Cape 195 Haujani Islet 237 Haustholni 223 Haute Island 193 Havre 223 Cape le 193 Hawaii 253 Hayter Island 255 Heard Island 236 Hearts Content 191 HeaudeBrehat 224 Heawandu Island 234 Hecate Bay 199 Cove 200 Hecla, Cape 264 Hed, Rasal 236 Hee-tah-doo Island 234 Hegadis Island 243 Heiligen Creutz 221 Hekkingen 218 Hela 221 Helena, St., Island 214 Helgoland 222 Heliers, St 218 Hellevoetsluis 223 Helliso 218 Hellyer Rocks -... 210 Helsinborg 219 Helsingfors 220 Helvick Head 218 Henderson Island 257 Henderville Island 251 Henlopen Cape 195 Henrv Cape 195 Port 210 Heongsan, Port 242 Herald Cays 255 Hereheretue Island 257 Hermes, Cape 232 Hermit Island 255 Hermite Island 209 Herradura de Carrizal 211 Hervey Islets 258 Hesquiat Harbor 199 Hesselu Island 222 Hessenstein 221 Hestskjaer 218 Heve, Cape la 223 Hiaou Island 253 Hikueru Island 258 Hillswickness 216 Hilo 253 Himmittee Island 234 Hiniiwar 237 PLACES — continued. Page. Hiogo 248 Hirado No Seto 248 Hirtshals 223 Hi va-Oa Island 253 Hjelm Islet 223 Hjertholm 218 Hjoerringa Mountain 218 Hoa-pin-su Island 244 Hobart Town 262 Hodeidah Road 234 Hog Island, Indian Ocean. . 235 Virginia.. 195 Islands 197 Hogland Island 220 Hogolu Islands 252 Hogsty Reef 203 Hogulu Islands 252 HoheWeg 222 Hohenschonberg 221 Hokianga River 263 Hokitika 263 Holborne Islet 261 Hole-in-the-Wall 232 Hollo Island 219 Holmestrand 219 Holmogadd 220 Holsteinberg 264 Holvhead 215 HoiiDau Island 240 Hondeklip Bav 232 Honfleur .....' 223 Hongkong 241 Hon-M6 240 Honolulu 253 Hood Island 251 Lord, Island 257 Point, Australia 260 Port, Cape Breton Id . . 193 Hope Island 261 Hopedale Harbor 191 Hopes Advance, Cape 191 Hoppers Island 251 Horn, Cape 209 Head 217 Island 196 Home Island 257 Hornelen Mountain 218 Horsens 222 Horten 219 Hospital Bight 197 Hougue, Cape La 223 Houtman Rocks 260 Howaivuh 236 Howe, Cape, East 261 West 260 Lord, Island 257, 259 Islands 254 Sound 200 Howland Islands 251 Howth Peninsula 217 Huafo Island 210 Huaheine Island 257 Huanchaco Point 212 Huarmey 212 Huasco 211 Hudiksvalls 220 Huelva 225 Hiigeberg 221 Hui-lang-san 241 Hull Island..... 258 Hulls Island 254 Page. Hulu-shanBay.. 247 Humber River 216 Humboldt 200 Humphrey Island 254 Hungwha Channel 241 Hunter Island, N. Hebrides. 256 Tasmania 262 Hurds Island 251 Hurst Castle 215 Husum 222 Hvidingso 218 Iba 245 Ibayat Island 246 Ibbetson Island 251 Ibiza, Port 226 Icacos Point, Belize 197 Trinidad 206 Ichabo Island 232 Icy Cape 198 leraka 229 Ifalik Islands 252 Iglooik Island 264 Ignacio, San, Point 201 Iguape 208 IkiSima 248 Ildefonso Islands 209 Ilha Grande 208 Ilheos 207 Ho 212 Iloilo 246 Inaboye Saki 249 Inaccessible Island 214 Inagua Islands 203 Inch Keith Rocks 216 Indefatigable Island 251 Indian, Cape 250 Harbor : 191 Head 261 Tickle 191 Indianola 196 Indio Point 208 Indispensable Reefs 254 Indrapura Point 239 Ingolfshofde 265 Ingolsfjeld 265 Inishboffin 217 Inishowen Head 217 Inishrahull 217 Inishturk Island 217 Iniue Island 257 Innamban Bay 232 Inscription, Cape 260 Investigator Strait 260 Ipswich 194 Iquique 212 Ireland Island 214 Isaac, Great, Cay 203 Isabel Cape 210 Island 254 Point 196 Isene 229 Isidro, San, Cape 210 Isla Grande 202 Island Harbor 199 Islav 212 Isle'of Man 215 Isola 227 Isolette, Cape 236 Istria, Caped' 227 Page 276] INDEX TO APPENDIX IV Page. Itacolomi Islet 208 Point 207 Itapacaroya Point 208 Itaparica 207 Itapemirim 207 Itnrup Island 249 Ivigtuk f 2()4 IwoShima 248 Iwo-sima 244 Jabwat Island 251 Jackson, Port 261 Jacksonville 1 95 Jacinel 204 Jacobshavn 264 Jaffa, Cape 260 Jago, St., Island 214 Jaguaribe River 207 Jaluit Island 251 Jamaica 204 James Island 251 St., Cape, C. China... 240 Vancouver 1 . 199 Jan May en Island 265 Jara Head 211 Jarea... 225 Jarvis Island 254 Jashak Bay 237 Java 243 Head 239 Jean, St. , de Luz 224 Jebel Zukur Island 234 Jelaka, Pulo 239 Jelalil 234 Jensen Nunatak 264 Jeremie 204 Jershoft 221 Jervis Bav 261 Cape 260 Island 251 J esus Maria Island 255 Jibara 203 Jiddah 234 Jighinsk Island 264 Joao, San, da Barra 207 Johanna Island 235 John, St., Cape, Newfdl'd. 191 Staten Island 209 Island ^205 Johns, St., Island, Red Sea. 233 N. Brunswick . . . 193 Newfoundland. . . 191 River 195 Johnston Islands 253 Jolo Islands 247 Jomf ruland 219 Jona, St. , Island 250 Jos6, San, California 200 de Guatemala 202 del Cabo 201 Port 209 Joseph Henry, Cape 264 Juan Fernandez Island 258 San 205 Cape 205 delSur 202 Point 197 Port, Peru 212 Vancouver 1 . 200 St., Bay...- 206 Juanico, San, Point 201 PLACES — continued . Page. Jubv, Cape 231 Judith Point 194 Juggernath 238 Juist 222 Julian, San, Port 209 St., Island 240 Julianshaab 265 Juneau 199 Jupiter Inlet 195 Jura Island 229 Juul, Cape 265 Kabenda Bay 232 Kabuli Island 245 Kado Sima 249 Kagoshima 248 Kahoolawe Island 253 Kaipara Harbor 263 Kais Islet 236 Kajartalik Island 264 Kakirouma 244 Kal Farun Islet 233 Kalama 200 Kalantan 240 Kalboden Island 220 Kalibia 230 Kalingapatam 238 Kallundborg 222 Kalpeni Islet 234 Kama Islands 252 Kamaishi 249 Kamardn Bay 234 Kambangan Island 243 Kambara Island 257 Kamchatka, Cape 250 Kanala, Port 259 Kanathea Island 256 Kandavu 256 Kandeliusa Island 229 Kangamint 264 Kangarssuk Havn 264 Kaniongan Point 242 Kannanur 237 Kao Island 258 Kappeln 221 Kara Burnu, Cape 229 Karachi 237 Karajinski Island 250 Karimon Djawa Island 243 Karlshamn 219 Karlskrona 219 Ka^ke 220 Kasm 237 KatakoloBay 228 Kater Island 253 Katiagam 239 Katie Rock 228 Kauai Island 253 Kawhia Harbor 263 Keats, Port 259 Kee-lah Island 234 Keeling Islands 236 Keenapoussan Island 247 Keitum 222 Kelung 242 Kendall, Cape 264 Kent Island 261 Keppel Island 257 Kermadec Islands 258 Kertch 229 Ketoy Island 249 Page. Key West 196 Khurig Islet 236 Kharim-Kotan Island 249 Khaur Fakan Bav 236 Kheli '. 229 Khor Nohud 234 Xowarat 233 Ki Islands 244 Kiama Harbor 261 Kidnappers Cape 263 Kiefali, Cape 228 Kiel 221 Kikai-jima 244 Killiney Hill 217 Killybegs 217 Kilwa Kisiwani 233 Kimbeedso Island 234 King George Sound 260 Island, Alaska 198 Australia 260 Kings Island 258 Kingston 204 Kingstown 217 Kink wosan Island 249 Kinnsund 218 Kino Point 202 Kinsale 218 Kirkwall 216 Kisimayu Bay 233 Kiska Island '. 199 Kistna 238 Kiswere 233 Kittan Islet 234 Kjorge 222 Knocklane 217 Knockmealdown Mountain. 218 Knocknarea 217 Knox Bay 2OO Cape 199 Knysna 232 Kobe 248 Kodiak Island 199 Koh Chang 240 Kong 240 Krah Islet 240 Tang Rocks 240 Kokoun-tan Islands . . . 248 Koksher : 220 Kolding 222 Komba Island 243 Kompas Mountain 218 Kongelab Islands 251 Konigsberg 221 Koniushi Island 199 Koppem 21 8 Koprino Harbor 200 Koroni Anchorage 228 Korror Islands 252 Kos 229 Kosair, Arabia 236 Red Sea 233 Kosime No Osima . . : 248 Koster 219 Kottaringin Bay 242 Kovra Rythi Point 235 Kozu Shima Mountain 249 Krakatoa Island 239 Krishna Shoal 238 Kroe 239 Kronberg 222 Kronstadt 220 INDEX TO APPENDIX IV. [Page 277 Page. Krusenstern Cape 198 Kub Kalat 237 Kuchino Shima 248 Kuchinotsu 248 Kuino 220 Kullen Point 219 Kumi Island 244 Kunipta 237 Kunashir Island 249 Kundapur 237 Kuntidah 234 Kuper Harbor 248 Port 199 Kiiria Maria Islands 236 KuroSima 248 Kusakaki Jima 248 Kusrovie Rock 240 Kusterjeh 229 Kutpur 237 Kuweit 236 Kweshan Islands 241 Kyangle Islets 252 Kyauchau Bay . . 247 Kyuquot Sound 1^'9 Labuan Island 242 Labyrinth Head 209 Laccadive Islands 234 Lacepede Island 260 Lady Elliot Island 261 Frances, Port 235 Lagartos 197 Laghi, Cape 228 Lagoon Head 201 Lagos 225 River 231 Lagosta Island 228 Lagostini Island 228 Lakemba Island 256 Laniaka 230 Lambayeque 212 Lambert, Cape 260 Lamo Bay 233 Lamock Island 241 Lampedusa Island 227 Lam pong Bay 239 Lamyit Island 241 Landfall Island 209 Lands End 215 Landskrona 219 Landsort 219 Langanaes Point 265 Langeland Island 222 Langeoog 222 Langesund 219 Langford, Port 199 Langkuas Island 239 Langotangen 219 Langwarden 222 Lanzarote Island 214 Laruehuapi Cove 211 Lassa, Cape 242 Lassau 221 Latakivah 230 Latouche Treville, Cape ... 260 Laun 191 Laurie Island 215 Laut, Pulo 242 Lavaca 196 Lavata 211 PLACES — continued. Page. Lawrence, St. , Island , Alaska 198 Siberia 250 Laykan, Port 242 Laysan Island 253 Lazaref , Port 250 Lazaro, San, Cape 201 Leander Shoal 192 Leba 221 Lebu River 211 Leeuwin, Cape 260 Legendre Island 260 Leghorn 226 Lema Island 241 Lemnos Island 229 Lengua de Vaca Point 211 Lennox Cove 209 Leones Island 209 Leopold, Port 264 Lepar, Pulo 239 I^epreau Cape 193 Lernia 197 Lerwick 216 Leschenault, Cape 260 Lesina Island 228 L' Etang Harbor 193 Leven Island 235 Port 235 River 262 L' Eveque, Cape 260 Lewis, St., Cape 191 Leyden 223 Levte Island 246 Lhou Reef 255 Liakhov Islands 264 Liancourt Rocks 250 Liant, Cape 240 Liao-ti-shan 247 Libau 220 Libertad, C. America 202 Mexico 202 Lifu Island 259 Lighthouse Rocks 199 Limerick 216 Limon, Port 198 Lincoln Island 241 -^— Port 260 Lindesnes 218 Lindi River 233 Lindo, Port 229 Linga Island 238 Linguelta, Cape 228 Linosa Island 227 Lipari Island 226 Lisbon 225 Lisburne Cape 198 Lisian.sk y Island 253 Lissa Island 228 List 221 Lister 218 Lith 234 Litkieh Island 251 Little Hope Island 193 Lituya Bay 199 Liverpool 215 Port 235 River. : 259 Livorno 226 Lizard Point 215 Llico 211 Loa River 212 Page. Loango Bay 232 Lobito Point 232 Loboa Cay, Bahamas 203 Mexico 196 de Afuera Island 212 Tierra 212 Island, Canaries 214 T Jruguaj^ 208 Point, N. Chile 212 S. Chile 212 Lodingen 218 Lofoten Island 218 Loggerhead Key 196 Loheiyah 234 Loma Point 201 Lonias Point 212 Lombata Island 243 Lombok Island 243 London, East 232 Londonderry 21 7 Cape 259 Long Island, Bahamas 203 United States 194 Loo Choo Islands 244 Looke, Port 235 Lookout Cape, N. Carolina. 195 1 Point, Australia 261 Maryland 195 Lopatka, Cape 250 Lopez, Cape 231 Lorenzo, San, Cape 213 Island 212 Loreto 201 Lorient 224 Loro, Mount 245 Lorstakken Mountain 218 Los, Isles de 231 Lota 211 Lots Wife Rock 249 Lough Larne 217 Louis, Port, Falkland Is . . . 214 Guadeloupe 205 Mauritius Island. 234 St 231 Louisburg 193 Louisiade Archipelago 255 Loune 223 Low Island 240 Port 210 Lowenorn, Cape 265 Lowestoft 216 Loyalty Islands 259 Lubang Island 245 Lucar, San 225 Lucas, San 201 Lucia, Santa 235 St 204 Cape 232 Id., C. Verde Is. . 214 Windward Is 205 Lucipara Is\Jind 239 Lucipari Islantk 243 Lucrecia Point 203 Lucrietta Island 227 Liiis, San, Island 202 Luke Point 250 Lundy Island 215 Lunenburg 193 Lungo 220 Lupona Point 201 Page 278] INDEX TO APPENDIX IV Page. LiirioBay 233 Lussin Piccolo 227 Luzon Island 245, 246 Lyo Island 222 Maasin a. 246 Macah6 207 IVlflORo 241 MacAskiil" Islands! ........ 252 Macassar 242 Macauley Island 258 Maceio 207 Machias 193 Island 193 Machikora 235 Mackenzie Islands 252 MacLeay Islets 260 Macquarie Harbor 262 Island 259 Port 261 Macquereau Point 192 Madagascar 235 Reef, Africa 232 Yucatan 197 Madame Island 193 Madanas Point 208 Madeira Island 213 Madras 238 Madryn, Port 209 Madura Island 243 Maestro de Campo Island. . 246 Mafamale Island 233 Mafia Island 233 Magadoxa 233 Magdalen Cape 192 Islands 192 Magdalena Bay 201 River 206 Magnetic Pole 264 Magoari Cape 207 Mah Kundu Island 234 Mahanuru 235 Mah6 237 Mahia Peninsula 263 Mahon, Port 226 Maiana Island 251 Maiden Rocks 217 Mairaira Point 245 Mill t Island 233 Maitea Island 257 Maitencillo Cove 211 Majamba Bay 235 Majorca 226 Majunga 235 Majuro Islands 261 Makalleh Bay 236 Makarska 228 Makatea Island 258 Makaua Island 233 Makemo Island 258 Makers Ledge, South 192 Makkian Island 244 Makongai Island 256 Makry 229 Mala Point 203 Malabrigo Bay 212 Malacca 238 Malaga 225 Malaita Island 254 Malamocco 227 Malaspina, Port 209 PLACBS — continued . Page. Maiden Island 254 Maldonado, Mexico 202 Uruguay 208 Male Island " 234 MalembaBay 232 Malin Head ". 217 Mallicollo Island 256 Malmi) 219 Malo, St 224 Maloclab Islands 251 Maloren 220 Malpelo Island, Galapagos. 250 Panama 203 Malta 227 Marauka Island 256 Manaar 237 Mana Sima 249 Manado Bay 242 Manao 249 Mana-watu River 263 Manda Roads 233 Mandarins Cap 241 Mandavi 237 Manfredonia 227 Mangalore , 237 Mangara Island 258 Mangaratiba 208 Mangareva Island 257 Mangarin Point 245 Mangarol 237 Mangles Point 213 Mango Island 256 Manila 245 Mano Island, Asia 244 Denmark 223 Manoel, Cape 231 Manta Bay 213 Manua Island 257 Manukau Harbor 263 Manvers, Port 191 Manzanilla Bav 202 Point ' 204 Maracaibo 206 Maraki Island 251 Marambaya Island 208 Maranhao Island 207 Marble Island 264 Marblehead 194 Marcial, San, Point 201 Marcos, San, Island 201 Marcus Island 253 Mare Harbor 214 Island, California. .... 200 S. Pacific 259 Maret Islets 259 Margaret Bay 193 Margate Head 232 Maria Island 257 INIadre Island 202 Port 204 Sta., Cape, Portugal. . . 225 Uruguay . . . 208 Cove 201 di Leuca, Cape 227 Island, Azores 213 Chile 211 S. Pacific . . . 256 Port 247 Mariana Islands 252 Maricas Islands 208 Marie Galante 205 Page. Marienleuchte 221 Mariguana Island 203 Marinduque Island 246 Marion Island 236 Maripipi Island 246 Maritimo Island 227 Marjes Islets 206 Marjoribanks 247 Marks, St 196 Marlborough Island 251 Marmora Island 230 Marmorice 229 Maro Reef 253 , Maroni River 207 Marsala 227 Marseille 226 Marshall 231 Islands 251 Marstenen Islet 218 Marta, Sta 206 Martha, St. , Cape 208 Martin de la Arena, San 224 Garcia Island 208 San, Island, L. Calif . . 201 St. , I. , Leeward Is 205 Vaz Rocks 214 Martinique 205 Martires, Los 252 Marua Island 257 Marutea Island 257 Mary Island 254 St., Bay 232 Cape, Madagascar . 235 Newfound- land 191 Nova Scotia. 193 Reefs 192 Marys, St. , Island 235 MarzoCape 213 Mas-af uera Island 258 Maabate Island 246 Masinloc 245 Masirah Island 236 Maskat 236 Massaua Harbor 233 Masset Harbor 199 Masulipatam 238 Matabella Islands 244 Matacong Island 231 Matagorda 196 Matahiva Island 258 Matamoras Cove 211 Matana Island 249 Matanzas Peak 204 Matatane 235 Matelotas Islands 252 Matema Islands 265 Maternillos Point 204 Matinicus Rock 1 93 Matoya 249 Matthew Island 256 St., Island, Alaska 198 Burma 238 — Siberia 250 Matthias, St. , Island 256 Matu Sima 250 Matuku Island 256 Mauger Cay 197 Maui Island 253 Mauki Island 258 Maunganui Harbor 262 INDEX TO APPENDIX IV [Page 279 Maupili Island 257 Mauritius 234 May, Cape , 195 Island 216 Mayaguez 205 Maye Mountain 207 Mayne Harbor 210 Mountain 210 Mayo Island 214 Mayotta Island 235 Maysi Cape 203 Mayumba Bay 231 Mazarron 225 Mazatlan 202 Mazeraba River 232 Mbega Island 256 Mchinga Bay 233 McKean Island 254 Mecate Mountain 196 Mecatina Islands 192 Mednoi Island 250 Mega Island 239 Megalo Kastron 228 Mehediah 230 Meiaco Sima 248 Meiaco-sima Islands 244 Mejia Island 202 Mel, Ilhado 208 Melbourne 260 Meleda Island 228 Melinda 233 Melle, Cape 226 Mellish Reef 255 Melmore Head 217 Melo, Port 209 Melville, Cape, Baliibac I.. 245 Queensland 262 Island, Australia 259 Barrows Strait. . . 264 Tuamotu Arch 258 Memel 221 Memory Rock 203 Menali Island 238 Menchikof C'ape 199 Mendocino Cape 200 Mendoza Island 241 Merbat 236 Mercy Harbor 210 Mergui 238 Mesa de Dona Maria 212 Messina 227 Mesurado, Cape 231 Meurka 233 Mew Islands 217 Mewstone Rock 262 Mexican Boundary 201 Mexico, City of .'. 196 Mexillon Bay 212 Mexillones Mountain 212 Mezen 264 Mugan Mwania 233 Miautao Island 247 Michael, St. , Fort 198 Island 213 Michaeloff Island 257 Middleton Island 199 Midway Islands 253 Miguel, San, Island 201 Islands 247 Mikake Jima 249 Mikindini 233 PLACES — continued . Page. Mikomoto Island 249 Mikura Jima 249 Milagro Cove 211 Milazzo 226 Mile Island 264 Milford Sound 263 Milo Island 229 Min River 241 MinaBay, El 231 Minchinmadiva Mountain . 210 Mindanao Island 246, 247 Mindo»o Island 245 Mine Head 218 Minerva Reefs 258 Minikoi Island 234 MinoSima 249 Minorca 226 Minots Ledge 194 Minow 235 Minsener Sand 222 Mintok 239 MiramichiBay 192 Misamis 247 Miscou Island 192 Mississippi River, mouth . . 196 City 196 Misteriosa Bank 197 Mita Point 202 Mitchells Island 254 Mitho 240 Mitiero Island 258 Mitre Island 256 Mityleni Island 229 MizenHill 216 Moa Cayo, Port 203 Island 244 Moala Island 256 Mobile 196 Mocha Island 211 Mocomoco Point 206 Modeste Island 248 Moeara Kompehi 239 Moen Island 222 Moerenhout Island 257 Mogador 231 Mohilla Island 235 Mojanga 235 Mokamba, Port 233 Mokatein 236 Mokha 234 Mokil Islands 252 Molle, Port 261 Mollendo, Port 21 2 MollerPort 199 Molloy 236 Molokai Island 253 Molonta Peninsula 228 Molucca Islands 244 Moluk Island 234 Molyneux Bay 263 Sound 210 Mombasa 233 Mona Island 205 Monastir 230 Mondego, Cape 225 Monfalcone 227 Monhegan Island 193 Monomoy Point 194 Monrovia 231 Montagu Island 261 Montalivet Islands 259 Page. Montauk Point 194 Monte Christo Islet 226 Montebel lo Island 260 Montego Bay 204 Montepio 196 Monterey 201 Monteverde Islands 252 Montevideo 208 Montravel Island 248 Montreal 192 Monts, Point de 192 Montserrat 205 Monze, Cape 237 Mopelia Island 257 Morane Island 257 MorantCays 204 Point 204 Moray va 225 Morecambe Bay 215 Moreno Mountain 212 Moresby, Port 255 Moreton, Cape 261 Morgan, Cape 232 Morjovetz Island 264 Morlaix 224 Morotiri Islands 258 Morro Avuca 202 de Sao Paulo 207 Petatlan 202 Solar 212 Mortlock Islands 252 Mosquito Cays 198 Motane Island 253 Mothe Island 256 Mothoni 228 Motu-ili Island 253 Motu-iti Island . . . ; 257 Moudros 229 Moukon rushi Island 249 Moulmein 238 River 238 Mount, Cape 231 Mourondava 235 Moville 217 Mozambior 193 Shelter Bay 250 Shepherd Island 198 Sherbedat, Ras 236 Sherbro Island 231 River 231 Sherm Hassejy 233 Joobbah 233 Rabigh 234 Wej 233 Yahar . 233 Shetland Islands' '. 216 PLACES — continued. Page. Shiash-Kotan Island 249 Shields, North 216 Shimizu Ba.v 249 Shimonoseki Strait 248 Shinnecock Buy 194 Ship Island 196 Shoal 196 Shipunski, Cape 250 Shirasu Reef 248 Shoals, Isles of 194 Shoal water Cape 200 Island 239 Siargao Island 246 Siassi 247 Siberaet Island 239 Siboga 239 Sibuco Bay 247 Sibutu Island 247 Sibuyan Island 246 Sidtnouth, Cape 262 Sierra Leone 231 Sighajik 230 Sigri, Port 229 Sihuatanejo Point 202 Sihut 236 Silan 197 Silaqui Islet 245 Silver Bank 203 Simaloe Island 239 Simeonof Island 199 Simoda 249 Simon, St. , Island 195 Simonoff Island 257 Simonor Island 247 Simons Bay 232 Simusir Island 249 Singapore 238 Singkel Island 239 Singkep Island 238 Single Island 241 Singora 240 Sinon 231 Sinope 230 Siphano Island 229 Siquiquor Island 246 Sirik, Cape 242 SiriyaSaki 249 Sisal 197 Sitka 199 Sittee Point 197 Skagataas Point 265 Skagi, Cape 265 SkagsHead 220 Skaw, Cape 223 Skelligs Rocks 216 Skerries Rocks 215 Skerry vo re Rocks 216 Skiathos Island 229 Skidegate Bay 199 Skoorgaarde 221 Skumbi River 228 Skyring Mountain 209 SligoBay 217 Slyne Head 217 Smalls Rocks 215 Smerwick 216 Smith Island, Japan 249 Washington 200 Sni vrna 230 Snaefells Yokul 265 Snares Islands 2()3 Page. Socorro Island, Chile 210 Mexico 202 Socotra Island 233 SoderSkars 220 Soderarm 219 Soderhamm 219 Sofala 232 Sohar 236 Sola Island 206 Solander Islands 263 Solitary Islands 261 Solombo, Great, Island 243 Solomon Islands 254 Solta Island 228 Sombrero 205 Key 196 Rock 247 Sommer Island 220 Song-yui Point 241 Sonserol Island 252 SooBay 242 Sooke Inlet 200 Sorelle Rocks 228 Sorol Island 252 Sorrel Rock 241 Sorrell, Cape 262 Port 262 Sorsogon, Port 246 Soumshu Island 249 South Cape, Formosa 242 N. Guinea 255 Rock 217 Water Cay 197 Southampton 215 Southsea Castle 215 Southwest Cape 262 Reef 196 Spalato Passage 228 Port 228 Sparo Vestervik 219 Spartel, Cape 230 Spartivento Cape, Italy 227 Sardinia 226 Spencer, Cape 260 Spezzia 226 Spikeroog 222 Spiridione, St. , Port 228 Spitz bergen 264 Spodsbjerg 222 Spurn Head 216 Square Handkerchief Bank . 203 Staabierg Huk 265 Stack, South 215 Stade 222 Stag Rocks 218 Stamp Harbor 199 Stampali Island 229 Stanley, Port 214 Starbuck Island 254 Start Point 215 Startpoint 216 Staten Island 209 Staunton Island 247 Stavanger 218 Steilacoom 200 Steinkirchen 222 Stemshesten 218 Stensher Rock 220 Stephens, Port 261 Stettin 221 Stewart, Cape 259 INDEX TO APPENDIX IV. [Page 285 Stewart Islands 254 Stirrup Cavs 203 Stirsudden 220 Stockholm 219 Stonington 19-1 Stopelmiinde 221 Stora 230 Storiiowav 216 Stot '. 218 Stralsimd 1:21 Strati If^land : 229 StraumneHS Point 265 Streaker Bav 260 Streckelsberg 221 Stro>ionof Cape 199 Stroinytad 219 Stromtaiigen 219 Strong Island 252 Strovathi Island 228 Stuart Island 198 Suakin 233 Sual 245 Subig 245 Sucoadana 242 Suda,Port 228 Sueik 236 Suez 233 Suff ren, Cape 250 Sugar Loaf Point 261 Sughrah 236 Suk Island 252 Suli)hur Island 253 Sunibawa Island 243 Sum burgh Head 216 Sunda Strait 239 Sunday Island 258 Sunderland 216 Sundsvall 220 Sunraivani 237 Sup6/- 212 Sur 230 Surabava 243 Surat.: 237 River 237 Surigao 246 Surop 220 Susaki 248 Suvvanose Jima 248 Suwarrow Island 257 Svalferort Tzerel 220 Svartklubben 219 Svendborg 222 Svenor 219 Sviatoi Nos 264 Svinoen 218 Swallow Bay 210 Islands 255 Swan Islands 197 Swansea : 215 Swatau 241 Sweers Island 262 Swinemunde 221 SybilloBay 250 Sydenham Island 251 Sydney, Australia 261 Harbor, C. Breton I . . 192 Synesvarde Mountain 218 Syra 229 Syracuse 227 Tabaco 246 Taljasco River 197 PLACES — continued. Page. Tablas Island 246 Point 211 Table Bav 232 Head 191 Island 238 Taboga Island 203 Tabou River 231 Tacloban 246 Tacoma 200 TacoradyBay 231 Tae Islands 241 Tagulanda Island 242 Tahiti 257 Tahoa Islanc I 257 Tahuata Island 253 Taiaro Island 258 Tai-pin-san 244 Tajer, Port 227 Taka Yama 249 Takapoto Island '. . 258 Takau 242 Takhkona Point 220 Talabo, Cape 242 Talcahuano 211 Ta-lien-wan Bay 247 Talinay Mountain 211 Taltal, Port 211 Taluat Island 242 Tamana Island 251 Tamandar^ 207 TamarPort 210 Tamatave 235 Tambelan Island 240 Tampa Bay 196 Tampat Toe won Point 239 Tampico 196 Tam-sui Harbor 242 Tanabe Bay 248 Tancook Island 193 Tandjong Pandan 239 Tanga Bay 233 Tangier 230 Tanjong Barram 242 Datu 242 Tanna Island 256 Tantang, Port 235 Taoiunu 256 Taormi na Cape 227 Tapua Island 255 Tapul Island 247 Taputeuea 251 TaraHill 217 Taranto 227 Tarawa Island 251 Tarbertness 216 Tarifa 225 Taritari Island 251 Tarpaulin Cove 194 Tarragona 225 Taa de Foin Islet 247 Tatakoto 257 Tatsupi Saki 249 Tauere Island 258 Tauranga Harbor 263 Tauzon, Cape 235 Tavolara Cape 226 Tavov River 238 Taytao Cape 210 Taytay Fort 245 Tchesme 229 Tchoukotskoi, Cape 250 Tegal 243 Page. Tehor Island 244 Tellicherri 237 Tel lo Islands 244 Tematangi Island 257 Tenasserim 238 Tenedos Island 230 Teneriffe Island 214 Tenez, Cape 230 Tepoca Cape 202 Tepoto Island 258 Tequepa 202 Terceira Island 213 Teresa, Sta. , Bav 201 Terkolei ' ■ 238 Terminos Lagoon 197 Ternate Island 244 Terstenik Rock 227 Testa, Cape 226 Testigos Islets.. _ 206 Tewaewae Bav 263 Thabi, Abu. .'. 236 Thank God Harbor 264 Thermia Island 229 Thikombia Island 256 Thithia Island 256 Thomas, St.,Id.,B.ofBiafra 231 West Indies. 205 Thome, St. , Cape 207 Three Kings Islands 262 Points Cape, Africa . . . 231 Argentina . . 209 Honduras .. 197 Ti-ao-usu Island 244 Tiburon Island 202 Tiegenort 221 Tien-pak 241 Tientsin 247 Tilly Bay 210 Timbalier Island 196 Timor Island 243 Laut Island 244 Tinakula Island 255 Tinian Island 252 Tintolo Point 246 Tirby Point 198 Toass Island 252 Toau 258 Tobago 205 Tobi Shima 249 Tobol Ali 239 Tocopilla 212 Todos Santos 201 To-du Island 234 Tofua Island 258 Tokara Jima 248 Tokelau Islands 254 Token Bessi Island 243 Tokio 249 Tolaga Bav 263 Tolkemit.' 221 Tomas, San 201 Tomo Roads 248 Tongarewa Island 254 Tongatabu Island 258 Tongka Harbor 238 Tongoi 211 Tong-sang Harbor 241 Tong-ting Islet 241 Tonning 222 Topolobampo 202 Tor 233 Torbjornskjaer 219 Page 286j INDEX TO APPENDIX IV. Page. Tordenskjokl, Cape 265 Torgauten 219 ToriwiSaki 249 Tornea 220 Toro Point 206 Torres Island 256 Point * 208 Port 226 Tortola 205 Tortosa, Cape 225 Tortugas Island 206 Tory Hill 217 Island 217 Tosco Cape 201 Totoya Island 257 Toulinguet Islands 191 Toulon 226 Tourane Bay 240 Towers Island 250 Townsend, Port 200 Trsenen 218 Trafalgar, Cape 225 Tralee Bay 216 Trani 227 Trapani 226 Travemunde 221 Travers Islands 262 Treasury Islands 254 Trebizond 230 Tregosse Islands 254 Trelleborg 219 Tremiti Islands 227 Trepassey Harbor 191 Tres Montes Cape 210 Puntas Cape, Chile ... 210 Venezuela . . 206 Trevandrum 237 Trevose Head 215 Triangle Island 200 Triangles 197 Tribulation, Cape 261 Trichendore 237 Trieste 227 Trincomali 237 Tringano River 240 Trinidad Head 200 Island 214 Tripoli, Africa 230 Turkey 230 Tristan d' Acunha 214 Triton Bay 255 Island 241 TriunfoCape 197 Trobriand Islands 255 Tromelin Island, Carolinels. 252 Indian Ocean 235 Troniso 218 Trondheim 218 Troon 215 Truxillo 197 Tsau-liang-hai 248 Tscheljuskin, Cape 264 Tsmano 235 TsuSima 248 Tsukarase Rocks 248 Tsuruga 249 Tuanske Island 258 Tubal Island 257 Tubuai Islands 258 Tubuai-Manu Island 257 Tucacas Island 206 Tuckers Beach 195 PLACES — continued. Page. Tukume Island 258 Tully Mountain 21 7 Tumaco 213 Tuinbez 212 Tung-chuh Island 241 Tung-yung Islands 241 Tuni-ang Island 241 Tunis 230 Tuni) Island 223 Tupilco River 197 Tureia Island 257 Turk Island 203 Turnabout Island 241 Turo Island 222 Turtle Island 257 Isles 260 TuskarRock 217 Tuspan Reefs 196 Tuticorin 237 Tutova 207 Tutuila Island 257 Tuvutha Island 256 Tuxtla Volcano 196 Twelve Islands 236 Twofold Bay 261 Tybee Island 195 Ty-fung-kyoh Island 241 Tynemouth 216 Ua-Huka Island 253 Ualan Island 252 Ubatuba 208 Uea Island 257 Ujelang Island 251 Uji Shima 248 Uleaborg 220 Ulietea Island 257 Ulko Kalla Rock 220 Ulladulla 261 Ulsire 218 Uluthi Islands 252 Umea 220 Una 207 Unalaska Island 199 UnareBav 206 Underut Islet 234 Underwood, Port 263 Unga Island 199 Unie Island 227 Union Bay 209 Islands 254 Port de la 202 Unsang 242 Upernivik 264 Upright Port 210 Upsala 219 Upulo Islands 257 Uragami 248 Urracas Islands 252 Urup Island 249 Usborne, Port 260 Usedom 221 Ushant 224 Ustica Island 226 Ute Islet 220 Utilla Island 197 Utrecht 223 Uvea Island 259 Vache Island 204 Vadso 218 Vahanga Island 257 Page. Vahitahi Island 257 Vaitupu Island 254 Valdes Island 200 Valdivia 211 Valencia 225 Valentia 216 Valentine Harbor 210 St., Cape 210 Valery en Caux, St 223 Valiente Peak 198 Valientes Islands 252 Valparaiso 211 Vanavana Island 257 Vancouver 200 Vanikoro 255 Vannes 224 Vanua Lava Island 256 Levu Island 256 Mbalavu Island 256 Vardo 218 Varella Cape 240 Pulo -. 240 Varna Bay 229 Vate Island 256 Vathi, Port 228 Vatiu Island 258 Vatoa Island 257 Vatu Lele Island 256 - — Vara Island 256 Vavau Island 258 Vavitoa Island 258 Vaza Barris River 207 VegUa 227 Veiro Island 222 Vela,La,Cape 206 Venangue Be Bay 235 Vendres, Port 225 Venice 227 Ver, Point de 223 Vera Cruz 196 Verde Cape 231 Cay, Bahamas 203 Cuba 204 Vicente, San, Cape 209 Port 245 Victor, Port 260 Victoria 200 Harbor 264 Port, Australia 260 Seychelle Islands. 234 River 259 Victory Cape 210 Lsland 240 Vidal, Cape .• 232 Video Island 242 VieborgBay 220 Vieques Island 205 Vieste 227 Vigan 245 Vigo 225 Villa 218 Nova da Princessa 208 Villajoyose 225 Ville Tranche 226 Vinaroz 225 Vincent, San, de la Barquera 224 St., Cape, Madagascar. 235 Portugal 225 Id., C. Verde Is.. 214 Windward Is. 205 Port, S. Pacific... 259 ^"ineyard Haven 194 INDEX TO APPENDIX IV. [Page 287 Page. Vingorla 23" Rocks 237 Virgin Gorda 205 Virgins, Cape 209 Viti Levu 256 Vizagapatam 238 Viziadrug 23" Vladimir, St., Bav 250 Vladivostok 250 Vliko, Port 228 Vohemar 235 Vojazza River 228 Volcano Island, West 242 Islands 253 Volta River 231 Voltaire, Cape 259 Vordate Island 244 Vordingborg 222 Vostok Island 253 Vourlah 230 Vriea Island 249 Wadero Island 219 Wadsworth, Fort 194 Wahdu Island 234 Waimea 253 Waitangi River 263 Wakaya Island 256 Wake Island 253 Wakefield, Port 260 Walfisch Bay 232 Walker Cav 203 Wallis Island 257 Walpole Island 256 Walsche, Cape 255 Walsingham, Cape 264 Wanganui River 263 Wangari Harbor 263 Wangaroa Harbor 262 Wangaruru , 263 Wangeroog 222 Wang-kia-tia Bay 217 Warberg 219 Warnemunde 221 Warren Hastings Island . . . 252 Washington 195 Island 251 Watch Hill Point 194 Watcher, North, Island 239 Waterfall Bluff 232 Waterford 217, 218 PLACES — continued. Page. Waterloo Bav 232 Watlings Island 203 WawodaRock 250 Wedge Island 193 Weggs Cape 191 Weichselmunde 221 Weihai wei 247 Wellington 263 Wenman Island 250 Wessel, Cape 259 AVest Cape 263 Western, Port 261 Westminster Hall Islet 210 Wetta Island 243 Wexford 217 Whaingaroa Harbor 263 Whale Back 194 Whalefish Island 264 AVhite Haven 215 Head Island 193 Island 263 Rock 240 Whitsunday Island 257 Whittle Cape 192 Wicklow 217 Wilberforce, Cape 259 Wilhelmshaven 222 Willemstadt 223 William, Port 263 Willoughby, Cape 260 Wilmington 195 Wilson Islands 255 Islets 252 Promontory 261 Windau 220 Winter Harbor 264 Wismar 221 Wittgenstein Island 258 Wolgast 221 Wolkonsky Island 258 Wollaston Island , . 209 Wollin 221 Wollongong 261 Wood Island, Labrador 192 Maine 193 Woodlark Islands 255 Woody Island 241 Wostenholme Cape 191 Wotje Islands 251 Wottho Island 251 Wowoni Island 242 Page. Wrangell 199 Wrath, Cape 216 Wreck Reef 255 AVusimado Point 248 Wustrow 221 Wusung 242 Xulla Islands 244 Yakuno Shima 248 YakutatBav 199 Yamada . . /. 249 Yamagawa 248 Yami Island 246 Yanez 211 Yap Island 252 Yaquina Head 200 Yarmouth 193 Yeboshi Sima 248 Yembo 233 Yerabu-sima.. 244 Yen, Island de 224 Ylin Island 245 Yobuko 248 Yoke Shima 248 Yokohama 249 Yoko-shima 244 Yokosuka 249 York, Cape, Greenland 264 Queensland 262 Minster Rock 209 Youghal 218 Ystad 219 YtapereBav 235 Point .". 235 YuiadaRoad 229 YuraNoUchi 248 Zafarana 233 Zafarin Islands 230 Zambesi River 232 Zamboanga 247 Zante 228 Zanzibar 233 Zapotitlan Point 197 Zara 227 Vecchia 227 Zempoala Point 196 Zengg 227 Zeyla 233 Zirona Grande Island 227 288 LUNAB DISTANCES. APPENDIX V. LUNAE DISTANCES. By reason of the comparative rapidity of motion of the moon relatively to the earth, it occurs that the angular distance, measured from the earth, between the moon and a body that occupies a fixed, or nearly fixed, position in the celestial sphere, is constantly changing. If, therefore, an observer accu- rately measures with a sextant the angle between the moon and one of the various celestial bodies for which the lunar distance is tabulated in the Nautical Almanac, this observed distance, reduced to true distance, affords a means for determining the absolute instant of time at which the observation was taken; and from this may be deduced the longitude and the chronometer error. If it were practicable to obtain results with a close degree of accuracy l)y this method, it would be an invaluable aid to the navigator, eliminating all anxiety as to change of rate of the chronometer, and even rendering it possible to navigate a vessel without such an instrument. It is unfortunately the case, however, that the method does not afford results that may be regarded as reliable within small limits, since a very small error in the observed angle, which it may not be possible to avoid even though every care be taken, causes a large error in the deduced time. Navigators of the present day do not, there- fore, employ the method of lunar distances except under extraordinary circumstances, such as when an accident to the chronometer occurs, or, on a very long voyage, when there is reason to suspect the cor- rectness of the chronometer error as brought forward by the rate. In order to facilitate the method of determining the longitude from lunar distances, there is pub- lished in the Nautical Almanac, for every third hour of Greenwich mean time, the angular distances of the center of .the moon from the center of the sun, from the brightest planets and from certain blight fitted stars selected in tlie path of the moon. All the distances that can be observed on the same day are grouped together under that date, and the columns are read from left to right across both pages of the same opening. The letter W. or E. is affixed to the name of the sun, jilanet, or star to indicate that it is on the west or east side of the moon. An observer on the surface of the earth having meas- ured a lunar distance, corrected it for instrumental errors and for the semidiameters of the objects, and cleared it from the effects of refraction and parallax, finds the true or geocentric distance. With this distance and the distances in the Nautical Almanac of the same bodies on the same day, the Greenwich mean time of the observation can be found, as will hereafter be described. The unavoidable errors to which the observation of lunar distance is subject are diminished by making a number of measurements. Errors of the instrument may be diminished by measuring distances on opposite sides of the moon, when possible, ana combining the results. Before taking the observation, the Nautical Almanac must be examined to see from what objects the •distances are computed. If the star or planet selected for observation is not recognized from its position relatively to other bodies in the heavens, it can easily be identified from the distance given in the Almanac; for the observer may set the sextant to the distance, computed roughly for the estimated time at the meridian of Greenwich, and direct his sight to the east or west of the moon, according as the object is marked E. or W. in the Nautical Almanac, and, having found the reflected image of the moon upon the horizon glass, sweep the instrument to the right or left, and the image will pass over the star or planet sought, if above the horizon and the weather clear; the star or planet is always one of the brightest, and is situated nearly in the arc passing through the moon's center, perpendicular to the line connecting the two horns. Although all the instruments used in these observations ought to be well adjusted, yet particular care should be taken of the sextant used in measuring the angular distance of the moon from the sun or star, since an error of V in this distance will cause an error of nearly 30'' in the longitude deduced therefrom. When a great angular distance is to be measured it is absolutely necessary to use a telescope, and its parallelism with respect to the plane of the instrument must be carefully' examinel<:'s Red. P. and i2." If a star is observed, its reduced refraction is at once the required " -X-'s Red. P. and R." Computation of the True Distanx-e. — Take from Tables II, III, IV, and V respectively the four logarithms A, B, C, 'D,f> and place these logarithms each at the head of a colunni, marking the columns A, B, C, and D; then put the— log of (t s Red. P. and R. (Table IX) in columns A and B. log of O's or jfc's Red. P. and R. (Table IX) in columns C and D. log sin a 's App. Alt. (Table 44) in columns A and D. log sin O's or sjc's App. Alt. (Table 44) in columns B and C. log cot App. Dist. (Table 44) in columns A and C. log cosec App. Dist. (Table 44) in columns B and D. The sum of the four logs in Col. A is the log (Table IX) of the First Part of (i's Correction, which is to be marked + when the app. dist. is less than 90°, but — when the app. dist. is greater than 90°. The sum of the four logs in Col. B is the log (Table IX) of the Second Part of C's Correction, which is always to be marked — . The sum of the four logs in Col. C is the log (Table IX) of the First Part of the Q's or >\i:'s Correction, which is to be marked — when the app. dist. is less than 90°, but + when the ajjp. dist. is greater than 90°. The sum of the four logs in Col. D is the log (Table IX) of the Second part of the Q' s or ■}ii' s Correc- tion, which is always to be marked —• Combine the first and second parts of the (J 's correction according to the signs prefixed; that is, take their sum if they have the same sign, but their difference if they have different signs, and prefix the sign of the greater to the result, which call " C's ivJiole correction." In the same manner form the "O's or >|<:'s vjhole correction." Firiit Correction of Distance. — Combine the (i's whole corr. and the O'* or >|<'s whole corr., according to their signs; the result is the First Correction of Distance, which is to be added to or subtracted from the apparent distance, according as its sign is -p or — . Second Correction of Distance. — Enter Table VI with the Apparent Distance and the First Correction of Distance, and take out the Second Correction of Distance, which is to be applied to the distance according to the directions in the side columns of the Table. Correction for the Elliptical Figure of the Moon's Dish, or Contraction of the Ifoon's Semi-diameter. — Enter Table VII A .with the C's App. Alt. and C's Red. P. and R., and take out the number. With this number and the (L's whole correction enter Table VII B and take out the required contraction, which is to be added to the app. dist. when the farther limb is observed, but subtracted when the nearer limb is observed. Correction for the Elliptical Figure of the Sun's Disk, or Contraction of the Sun's Semi-diameter. — Enter Table VIII A with the O's App. Alt. and O's Red. P. and R., and take out the number. With this number and the O's whole corr. enter Table VIII B and take out the required contraction, which is always to be sxibtracted from the distance (the nearer limb of the sun being always observed). Correction for Compression, or for the Spheroidal Figure of the Earth. — Take from the Nautical Alma- nac for the Greenwich date the declinations of the bodies to the nearest whole degree. With the moon's declination and apparent distance, take from Table XI A the first part of N, and mark it with the sign , in the table if the declination is North; but if the declination is SoutJi, change the sign from + to — or from — to -p. With the sun's or star's declination and the apparent distance, take from Table XI B the second part of N, giving it the same sign as the declination. Take the sum, or difference, of the two parts, according as their signs are the same or different, and to the resulting number prefix the sign of the greater. The logarithm of this number of seconds, taken from Table IX, with its sign prefixed, is the required log N. To log N add the log sine of the latitude of the place of observation; the sum is the log (Table IX) of the required correction for compression. In north latitude add this correction if log N is +, or subtract it if log N is — ; in south latitude subtract the correction when log N is +> and add it when log N is — . All these corrections being applied to the Apparent Distance, the result is the True Distance. To FixD THE Greenwich Time. — Find in the Nautical Almanac the two distances between which the true distance falls. Take out the first of these, together with the Prop. Log following it, and the hours of Greenwich time over it. Find the difference tetween the distance taken from the Almanac and the true distance, and to the log of this difference (Table IX) add the Prop. Log from the Almanac; the sum is the log (Table IX) of an interval of time to be added to the hours of Greenwich time taken from the Almanac. The result is the approximate Greenwich time. To correct this Greenwich time, take the difference between the two Prop. Logs in the Almanac which stand against the two distances between which the true distance falls. With this difference and the interval of time just found enter Table X and take out the seconds, which are to be added to the approximate Greenwich time when the Prop. Logs are decreasing, but subtracted when the Prop. Logs are increasing. The result is the true Greenwich time. By comparing with this the local mean time the longitude will be found; or, if testing the time shown by chronometer, the difference between the true Greenwich time and the time shown by the chronometer is the error of the chronometer as determined bv the lunar observation. a The parallax of a star being zero, its "reduced parallax and refraction " become, of course, merely its " reduced refrac- tion; " but as no mistake can arise from marking it as " 3|c'8 Red. P. r nd R.," this designation has been retained in order to give simplicity and uniformity at once to the rules and the tables. b No interpolation is necessary in taking out these logarithms. LUXAR DISTANCES. 291 Degree of Dependenxe. — If the error thus determined agrees with that deduced by means of the rate and original error, it may be accepted as a confirmation of the rate of the chronometer; if otherwise, more or less doubt is thrown upon the chronometer, according to the degree of accuracy of the lunar observation itself. An error of 10^^ in the measurement of the distance produces about 20' error in the Greenwich time; and since, even with the best observers, a single set of distances is subject to a possible error of 10'^, it may be well to consider the chronometer as still to be trusted so long as it does not differ from the lunar by more than 20^ Since, however, so much depends upon skill in measuring the distance, the observer can only form a correct judgment of the degree of dependence to be placed upon his own observations by repeated trials and a careful comparison of his several results. Example: In Lat. 35° 30^ N., Long. 30° W., by account, at the local mean time, 1855, September 6, IS*" 8'" 0% the observed distance of Q'a andC 's nearer limbs was 43° 52^ 10^^; observed alt. C, 49° 32^ 50^^ observed alt. 0, 5° 27^ 10^^; barometer, 29'". 1; thermometer, 75°; height of the eye above the sea, 20" I. C, 0^ 00'''; required the longitude. L. M. T., Sept. 6, Long., D. R., G. 31. T., approx., Obs. Alt. C, Dip, Table 14, C's Aug. S. D., (T'sApp. Alt., C'sRed. R., Table! Bar. 29'". 1, Table 21 Ther. 75°, Table 22, C'sRed. R., C'sRed. P., C'sRed. P. andR., Preparation of the Data. 18" OS-" + 2 00 20 08 49' + 32^ 50^' 4 23 15 01 49 43 28 V 16^^ 3 4 1 54 09 23 53 14 C'sS. D., Aug. Table 18, C's Aug. S. D, Obs. Alt. 0, Dip, O'sS. D., O's App. Alt, O'sRedR., Table I, Bar., Table 21, Ther., Table 22, 0's Red. R., O's Par., O's Red. P. aiid R., 14^ 50^^0|C'aPar., N. A., 11 .2 Aug., Table 19, C'sRed. P., 54^ 15 01 .2 5° 27^ 10^^ — 4 23 + 15 55 5 38 42 8^ 57'^ 16 — 28 8 13 8 + 19''^ 4 3 .6 54 23 .0 Obs. Dist. 01 IC, 43° 52^ 10^^ 8 05 C's Aug. S. D., O'sS. D., App. Dist., C'sDec, N. A., O's Dec, N. A., + 15 01 15 55 44 23 06 25° N. 6°N. log A, Table II, 0. 0021 log ([ 's Red. P. and R., 3. 5043 log sin C 's App. Alt. , 9. 8825 log cot App. Dist. , 0. 0093 flog. Table IX, 3. 3982 \lst Part C 's corr., +41' 4^' B. log B, Table III, 9. 9951 log (L 's Red. P. and R., 3. 5043 log sin O's App. Alt., 8. 9929 log cosec App. Dist. , 0. 1552 /log. Table IX, 2. 6475 \2d Part C's corr., - 7' 24'^ C 's whole corr., +34' 18'' log N, Tabs. XIandIX, ( - ) 0. 845 log sin Lat, + 35° 30', ( + ) 9. 764 riog. Table IX, (-) 0.609 \Corr. for Compression, — 4" Computation of the True Distance. C. log C, Table IV, 9. 9949 log O's Red. P. and R., 2. 6857 log sin O's App. Alt, 8. 9929 log cot App. Dist. , 0. 0093 flog. Table IX, list I Part O's corr.. 1. 6828 -0' 48" D. log D, Table V, 9. 9992 log O's Red. P. and R., 2. 6857 log sin C ' s App. Alt , 9. 8825 log cosec App. Dist., 0. 1552 /log. Table IX, 2. 7226 t2d Part O ' s corr. , +8' 48" O ' s whole corr. , +8' 00" App. Dist, Ist Corr., 2d Corr., Table VI, — Contraction of d's S.D., Table VII, Contraction of O's S.D., Table VIII, Corr. for Comp. True Distance, 44° 23' 06" + 42 18 16 20 45 04 44 292 LUNAR DISTANCES. Extract from Nautical Almanac, September, 1855. GREENWICH MEAN TIME: LUNAR DISTANCES. to 1 1 ' i PL Star's name and i Midnitrht of ' position. 1 Midnight. ^o^ xv. p. L. Of Diff. XVIIIh. p. L. Of Diff. XXI"". P. L. of Diff. 6 Si-N E. '48° 46' 55'' 3422 47° 25' 3" 3427 46° 3' 17" 3433 44° 41' 38" 3438 Computation of Greemcich Mean Time. True Distance, Distance, N. A., at XVIIl", Difference, Approximate interA'al, Add— Approx. G. M. T., Corr., Table X, True G. M. T., L. M. T., Longitude, 45° 04' 44" 46 03 17 58 33 2'' 18 09" 04^ 20 09 04 2 20 18 09 08 02 00 P. L., 0.3433 log, Table IX, 3.5457 log, Table IX, 3.8890 2 01 02 = 30° 15' 30" W. Diff. P. logs + 5 Example: In Lat. 55° 20' S., Long. 120° 25' W., by account, on August 29, 1855, at 9'> 40" 00' p. m., local mean time, the following distance and altitudes were found, being the mean of six observations corrected for index error. Observed distance of Fomalhaut and moon's farther limb, 46° 30' 23"; observed alt. C, 6° 26' 10"; observed alt. Fomalhaut, 52° 34' 40"; barometer, 31'°; thermometer, 20°; height of the eye above the sea, 18". L. M. T. , August 29, 9" 40"' 00^ Long, by D. K., +8 01 40 Approx. G. M. T., Obs, alt. C Dip, - C'saug. S. D., + C's A pp. Alt., C 's Red R., Table I, Bar., Table 21, + Ther., Table 22, + (C'sRedR., C'sRetl. P., C'sRed. P. andR., 17 41 40 6° 26' 4 16 10" 09 28 6 38 29 7' 48" 16 32 8 60 36 20 51 44 Preparation of the Data. C'sS.D.,Naut.Al., Aug., Table 18, + \ C's aug S. D., Obs. alt. >)«, Dip, :!|!:'s Ai>p. Alt., *'sRed.R.,TableI, Bar., Table 21, -f Ther., Table 22, -j >|<'s Red. R., *'s Red P., *'s Red. P. and R. 16' 26". 3 2 .0 16 28 .3 52° 34' 4 40" 09 52 30 31 1' 13" 2 5 1 20 > 1 20 C'sPar., N. A., Aug., Table 19, C Red P., Obs. Dist. -X- IC, C's aug., S. D., App. Dist., C's Dec, N. A., >l<:'s Dec, N. A., + 60' 11". 8 8 .3 60 20 .1 46° 30' 16 23" 28 46 13 55 4°N. 30° S. LUNAR DISTANCES. 293 log A, Table II, 0.0274 log C 's Red. P. and R., 3.4919 log sin C ' s App. Alt. , 9. 0632 log cot App. Dist., 9.9813 I log, Table IX, 2.5638 tlst Part C's com, + 6^ 06^^ B. log B, Table III, 0.0001 log C 's Red. P. and R., 3.4919 log sin sjc's App. Alt., 9.8995 log cosec App. Dist. , 0.1414 flog, Table IX, 3.5329 \2d Part (T's corr., - 56^ 51'^ C's whole corr., — 50 45 log N, Tabs. XI and (-) 1.2.30 IX, logsinLat., -55°, ( — ) 9.913 flog Table IX, \Corr. for Comp., ;+; 1.143 14'' Computation of the True Distance. C. log C, Table IV, 9.9999 log )f:'s Red. P. and R., 1.9031 log sin *'s App. Alt., 9.8995 log cot App. Dist., 9.9813 flog. Table IX, \lst Part >)i:'s corr. D. 1.7838 log D, Table V, 0.0267 log *'s Red. P. and R., 1.9031 log sin (L 's App. Alt, 9.0632 log cosec App. Dist., 0.1414 flog. Table IX, 1.1344 [2d Part >|c's corr., + 0' 14'' >|<'s whole corr., — 47 App. Dist., 46= 13' 55" 1st corr., — 51 32 2dcorr., Table VI, — 22 Contraction of d 's \ , S.D., Table VII,i + 17 Corr. for Comp., + 14 True Distance, 45 22 32 Extract from Nautical Almanac, August, 1855. GREENWICH MEAN TIME: LUNAR DISTANCES. j3 Star's name and position. Midnight. P. L. P. L. of XV h. 1 of Diff. ' Diff. i 1 XVIII >>. P. L. of Diff. XXI ^ P. L. of Diff. 29 Fomalhaut W. 42° 11' 34" 2.535 ; 43° 51' 59" .2527 i 1 45° 32' 35" 2521 47° 13' 19" 2516 Computation of Greenwich Mean Time. True Distance, Dist., N. A., at XV^ Difference, Approx. interval. Add— Approx. G. M. T., Corr., Table X, True G. M. T., L. M. T., Long., 45° 22' 32" 43 51 59 1 30 33 2'' 15 42"' 01' 17 + 42 01 01 17 9 42 02 40 00 P. L., 0.2527 log, Table IX, 3.7350 Diff. P. logs — 6 loe, Table IX, 3.9877 + 8 02 02 = 120° 30' 30" W. Method op Taking a Lunar Observation by One Observer. — Three observers are required to make the necesssary observations for determining the longitude — one to measure the distance of the bodies, and the others to take the altitudes. In case of not having a sufficient number of instruments or observers to take the altitudes, the latter may be calculated, there being given the latitude of the place, the time, the right ascensions, and the declinations of the objects. These calculations are long, however, especially in the case of the moon, and a considerable degree of accuracy is required in finding from the Nautical Almanac the moon's right ascension and declination, which must be liable to some error on account of the uncertainty of the ship's longitude. The following method of obtaining those altitudes is far more simple, and sufficiently accurate. This method depends on the supposition that the altitudes increase or decrease uniformly. 294 LUNAR DISTANCES. Before measuring the distance of the bodies, take their altitudes, and note the times by a chro- nometer; then measure the distance and note the time (or measure a number of distances, and note the corresponding times, and take the means); after having measured the distances, again measure the altitudes, and note the times; then, from the two observed altitudes of either of the objects, the required altitude of that object may be found from the following formula, which is based upon simple proportion: dXe where x = change of altitude, in minutes, between first altitude and time of measuring the lunar distance, being positive or negative according as body is rising or falling; d = difference between first and second altitudes, in minutes; e = time, in seconds, between first altitude and lunar observations; and / = time in seconds, between first and second altitudes. The change of altitude thus deduced, applied w-ith proper sign to the first altitude, gives the altitude at time of observing the lunar distance. Example: Suppose the dista,nces and altitudes of the sun and moon were observed, as in the following table; it is required to find the altitudes at the time of measuring the mean distance. Times by chro- nometer. 2" 03™ 20' 2 04 20 2 05 50 Mean, 2 04 30 Lunar dis- tance. 40° 00' 00'' 40 00 30 40 01 30 40 00 40 Times hy chro- nometer. 2^ 02 2 06 "00^ 10 '.{ Obs. alt. d's L. L. 20° 46' 21 20 (/, 34 For C- Time of lunar obs., Time of 1st alt.. 2" 04" 2 02 30^ 00 , 34 X 150 "^ 250~ First altitude, X, / 2 30 \ ISO" = + 20'.4 = + 20' 24" 20° 46' 00" + 20 24 10 250^ For Q. Time of lunar obs., Time of 1st alt., Times by chro- nometer. 2^ 02™ 30" 2 07 00 / 4 30 1 270' 2'> 04" 2 02 Ob><. alt. Q's L. L. 40° 20' 39 12 <' 08 30^ 30 «, X 120 270 First altitude, = -30'.2 Required altitude. J 2 00 \ 120' = — 30' 12" 40° 20' 00" 30 12 39 49 48 Required altitude, 21 06 24 To obtain the altitudes by calculation the following formulae may be employed: tan A = tan d sec t; smh= ^•OB(A-L)sind sm A in which d is the declination; t, the hour angle; L, the latitude; /;, the true altitude of the center of the object; A, an arc Avhich has the same name or sign as the declination and is numerically in the same quadrant as t. In the solution, strict regard must be had for the signs. Example: Required the apparent altitude of the sun's center on December 22, 1879, in Lat. 48° 23' N., Long. 60° W., at 10" 01™ 14' a. m., app. time. L. A. T., December 21, 22" 01™ 14» Long., + 4 00 00 t, O's Dec. 1" 58™ 46' 23° 27' 16" S. G. A. T., December 22, 2 01 14 t d A L 29° 41' 30" — 23 27 16 -26 32 20 + 48 23 00 sec 0.06113 tan (-) 9.63735 tan (-) 9.69848 74 55 20 h 13 23 58 ref.— par. + 3 50 sin (-) 9.59991 cosec(— ) 0.34989 cos ( + ) 9.41520 sin (+) 9.36500 App. alt. 13 27 48 Page 296] APPENDIX V: TABLE II. Log. A, for computing the First Correction of the Lunar Distance. App alt. of moon. Redticed parallax and refraction of moon. 1 41' 42' 48' 44' 45' 46' 4i' 48' 40' 50' 51' 52' 58' 54' 55' 5° 0^ 2 4 6 8 .0288 .0286 .0284 .0282 .0281 0295 0293 0291 0289 0287 0301 0299 0297 0294 0308 0306 0304 0302 0300 0298 0296 0295 0293 0291 0289 0288 0286 0284 0282 0281" 0279 0277 0276 0274 0315 0313 0311 0309 0307 0305 0303 0301 0299 0297 0296 0294 0292 0290 0289 0321 0319 0317 0315 0313 0311 0309 0307 0306 0304 0302 0300 0298 0296 0295 0328 0326 0324 0322 0320 0318 0316 0314 0312 0310 0335 0333 0330 0328 0326 0324 0322 0320 0318 0316 0341 0339 0337 0335 0333 0331 0329 0327 0325 0323 0321 0319 0317 0315 0313 0348 0346 0344 0341 0339 0337 0335 0333 0331 0329 0327 0325 0323 0321 0319 0355 0352 0350 0348 0346 0344 0341 0339 0337 0335 0361 0359 0357 0354 0352 0368 0366 0363 0361 0359 5 10 12 14 16 18 5 20 22 24 26 28 .0279 .0277 .0275 .0274 .0272 0285 0284 0282 0280 0278 0292 0290 0288 0286 0285 0350 0348 0346 0344 0341 0339 0337 0335 0333 0331 0329 0327 0326 0324 0322 0320 0318 0316 0315 0313 0356 0354 0352 0350 0348 0346' 0344 0341 0339 0337 0335 0334 0332 0330 0328 0326" 0324 0322 0320 0319 .0270 .0269 .0267 .0265 .0264 0277 0275 0273 0272 0270 0283 028r 0280 0278 0276 0308 0306 0304 0303 0301 0314 0313 0311 0309 0307 0333 0331 0329 0327 0325 0346 0344 5 30 32 34 36 38 .0262 .0261 .0259 .0258 0268 0267 0265 0264 0262 0261 0259 0258 0256 0255 0253 0252 0251 0249 0248 0275 0273 0271 0270 0268 0267 0265 0264 0262 0261 0287 0285 0283 0282 0280 0279 0277 0275 0274 0272 0293 0291 0290 0288 0286 0285 0283 0281 0280 0278 0299 0297 0296 0294 0292 0290 0289 0287 0286 0284 0305 0303 0302 0300 0298 0296 0295 0293 0291 0290 0288 0287 0285 0283 0282 0311 0309 0308 0306 0304 0317 0315 0314 0312 0310 0323 0321 0320 0318 0316 0314 0312 0311 0309 0307 0342 0340 0338 0336 0334 0332 0330 0328 0326 0324 5 40 42 44 46 48 5 50 52 54 56 58 0273 0271 0270 0268 0267 0302 0301 0299 0297 0296 0308 0306 0305 0303 0301 0259 0258 0256 0255 0254 0265 0264 0262 0261 0259 0271 0269 0268 0266 0265 0277 0275 0274 0272 0271 0282 0281 0279 0278 0276 0294 0292 0291 0289 0287 0300 0298 0296 0295 0293 0305 0304 0302 0300 0299 0311 0309 0308 0306 0304 0303" 0.301 0299 0298 0296 0317 0315 0313 0312 0310 0308 0307 0305 0303 0302 0323 0321 0319 0317 0316 6 2 4 6 8 0247 0245 0244 0243 0241 0252 0251 0249 0248 0247 0246 0244 0243 0242 0240 0258 0256 0255 0254 0252 0263 0262 0261 0259 0258 0269 0268 0266 0265 0263 0275 0273 0272 0270 0269 0267 0266 0265 0263 0262 0280 0279 0277 0276 0274 0273 0271 0270 0269 0267 "0266 0264 0263 0262 0260 0286 0284 0283 0281 0280 0278 0277 0275 0274 0273 0291 0290 0288 0287 0285 0284 0282 0281 0279 0278 0297 0295 0294 0292 0291 0289 0288 0286 0285 0283 0314 0312 0310 0309 0307 6 10 12 14 16 18 0240 0239 0237 0236 0235 0234 0233 0231 0251 0250 0248 0247 0246 0256 0255 0254 0252 0251 0262 0261 0259 0258 0257 0295 0293 0292 0290 0289 0287 0286 0284 0283 0281 0300 0299 0297 0295 0294 0306 0304 0302 0301 0299 6 20 22 24 26 28 0239 0238 0237 0236 0234 0233 0232 0231 0230 0229 0245 0243 0242 0241 0240 0238 0237 0236 0235 0234 0250 0249 0247 0246 0245 0255 0254 0253 0251 0250 0261 0259 0258 0257 0255 0271 0270 0268 0267 0266 0276 0275 0274 0272 0271 0282 0280 0279 0277 0276 0292 0291 0289 0288 0286 0298 0296 0295 0293 0292 0297 0295 0294 0292 0291 0290 6 30 32 34 36 38 0244 0242 0241 0240 0239 0249 0248 0246 0245 0244 0254 0253 0251 0250 0249 0248 0246 0245 0244 0243 0259 0258 0257 0255 0254 0253 0252 0250 0249 0248 0264 0263 0262 0260 0259 0270 0268 0267 0266 0264 0275 0273 0272 0271 0269 0268 0267 0265 0264 0263 "0262 0260 0259 0258 0257 0280 0278 0277 0276 0274 0285 0284 0282 0281 0279 0290 0289 0287 0286 0284 6 40 42 44 46 48 0227 0226 0225 0224 0223 0232 0231 0230 0229 0228 0238 0236 0235 0234 0233 0232 0231 0230 0229 0227 0243 0241 0240 0239 0238 0258 0257 0255 0254 0253 0252 0250 0249 0248 0247 0263 0262 0260 0259 0258 0257 0255 0254 0253 0252 0273 0272 0270 0269 0268 "0266' 0265 0264 0263 0261 0278 0277 0275 0274 0273 0271 0270 0269 0267 0266 0283 0288 0282 ! 0287 0280 0285 0279 '■ 0284 0278 0283 6 50 52 54 56 58 0222 0221 0220 0219 0218 0227 0226 0225 0224 0223 0237 0236 0235 0233 0232 0242 0241 0239 0238 0237 0247 0246 0244 0243 0242 0276 0275 0274 0272 0271 0281 0280 0279 0277 0276 7 0217 0222 0226 0231 0236 0241 0246 0251 0255 0260 0265 0270 0275 APPENDIX V: TABLE II. [Page 297 Log. A, for computing the Mrst Correction of the Lnnar Distance. App alt. of moon. Reduced parallax and refraction of moon. 1 44' 45' 46' 47' 48' 1 49' 50' 51' 62' 68' 54' 55' 66' j 67' 7° 0^ 3 6 9 12 .0222 .0220 .0218 .0217 .0215 0226 0225 0223 0222 0220 0231 0230 0228 0226 0225 0236 0234 0233 0231 0230 0241 0239 0238 0236 0234 0246 0251 0244 0249 0242 i 0247 0241 0245 0239 0244 0255 0254 0252 0250 0248 0260 0258 0257 0255 0253 0265 0263 0261 0260 0258 0270 0268 0266 0264 0262 0275 0273 0271 0269 0267 7 15 18 21 24 27 .0214 .0213 .0211 .0210 .0208 .0207 .0206 .0204 .0203 .0202 0219 0217 0216 0214 0213 0211 0210 0209 0207 0206 0205 0203 0202 0201 0200 0198 0197 0196 0195 0193 0223 0222 0220 0219 0217 0228 0226 0225 0223 0222 0220 0219 0218 0216 0215 0233 0231 0230 0228 0227 0225^ 0224 0222 0221 0219 0237 0236 0234 0233 0231 0230 0228 0227 0225 0224 0222 0221 0219 0218 0217 0215 0214 0213 0211 0210 0242 0240 0239 0237 0236 0247 0245 0243 0242 0240 0251 0250 0248 0246 0245 0256 0254 0253 0251 0249 0261 0259 0257 0255 0254 0252 0250 0249 0247 0246 0265 0263 0262 0260 0258 7 30 33 36 39 42 0216 0215 0213 0212 0210 0209 0208 0206 0205 0204 0203 0201 0200 0199 0198 0234 0232 0231 0229 0228 0227' 0225 0224 0222 0221 0239 0237 0235 0234 0232 0231 0229 0228 0227 0225 0243 0248 0241 0246 0240 0244 0238 ! 0243 0237 0241 0257 0255 0253 0252 0250 ! 7 45 48 51 54 57 8 3 6 9 12 .0200 .0199 .0198 .0196 .0195 .0194 .0193 .0192 0213 0218 0212 0216 0211 0215 0209 0214 0208 0212 0207 0211 0206 1 0210 0204 0208 0203 i 0207 0202 ' 0206 02a5 0234 0232 0231 0229 0240 0238 0237 0235 0234 0232 0231 0229 0228 0227 0244 0242 0241 0239 0238 0236' 0235 0233 0232 0231 0229 0228 0226 0225 0224 0248 0247 0245 0244 0242 0241 0239 0238 0236 0235 0233 0232 0231 0229 0228 0226 0225 0224 0223 0221 0249 0248 0246 8245 0243 0242 0240 0239 0219 0218 0217 0215 0214 0224 0222 0221 0220 0218 0217 0217 0214 0213 0212 0211 0209 0208 0207 0206 0228 0227 0225 0224 0222 8 15 18 21 24 27 8 30 33 36 39 42 8 45 48 51 54 57 0192 0191 0190 0189 0188 0196 0195 0194 0193 0192 0191 0190 0188 0187 0186 0201 0199 0198 0197 0196 0205 0203 0202 0201 0200 0209 0207 0206 0205 0204 0213 0212 0210 0209 0208 0221 0225 0220 0224 0218 0222 0217 0221 0216 0220 0237 0236 0235 0233 0232 0187 0186 0184 0183 0182 0195 0193 0192 0191 0190 0199 0197 0196 0195 0194 0203 0201 0200 0199 0198 0207 0205 0204 0203 0202 0215 0213 0212 0211 0210 0219 0217 0216 0215 0214 0223 0221 0220 0219 0217 0216 0215 0214 0212 9211 0230 0229 022S 0226 0225 0181 0180 0179 0178 0177 0185 0189 0184 0188 0183 ' 0187 0182 1 0186 0181 0185 0193 0192 0191 0190 0189 0197 0196 0195 0193 0192 0201 0200 0198 0197 0196 0205 0203 0202 0201 0200 0208 0207 0206 0205 0204 0212 0211 0210 0209 0208 0220 0224 0219 0223 0218 0221 0216 0220 0215 1 0219 9 3 6 9 12 0176 0175 0174 0173 0172 0180 0184 0179 0183 0178 0182 0177 0181 0176 ! 0180 0188 0186 0185 0184 0183 0191 0190 0189 0188 0187 0195 0194 0193 0192 0191 0199 0198 0197 0196 0194 0203 0201 0200 0199 0198 0206 0205 0204 0203 0202 0210 0209 0208 0207 0206 0214 0218 0213 0216 0211 0215 0210 1 0214 0209 1 0213 • 9 15 18 21 24 27 0171 0170 0170 0175 0174 0173 0172 0171 0179 0178 0177 0176 0175 0182 0181 0180 0179 0179 0186 0185 0184 0183 0182 0190 0189 0188 0187 0186 0193 0192 0191 0190 0189 0197 0196 0195 0194 0193 0201 0200 0199 0198 0196 0204 0203 0202 0201 0200 0208 j 0212 0207 1 0211 0206 ! 0209 0205 0208 0204 0207 9 30 33 36 39 42 9 45 48 51 54 57 0170 0170 0169 0168 0167 0174 0173 0172 0171 0170 0178 0177 0176 0175 0174 0173 0172 0171 0170 0169 0181 0180 0179 0178 0177 0185 0184 0183 0182 0181 0180 0179 0178 0177 0176 0188 0192 0187 0191 0186 0190 0185 0189 0184 0188 0195 0194 0193 0192 0191 0190 0189 0188 0187 0186 0199 0198 0197 0196 0195 0194 0193 0192 0191 0190 0203 0206 0201 ! 0205 0200 i 0204 0199 0203 0198 1 0202 1 0166 0165 0164 0163 0163 0169 0169 0168 0167 0166 0176 0176 0175 0174 0173 0183 0182 0182 0181 0180 0187 0186 0185 0184 0183 0197 0196 0195 0194 0193 0201 0200 0199 0198 0197 0203 0202 0201 0200 10 0162 0165 0169 0172 0175 0179 0182 0186 0189 0192 0196 0199 Page 298] APPENDIX V: TABLE II. Log. A, for computing the First Correction of the Lunar Distance. App. alt. of moon. Reduced parallax and refraction of moon. 1 46' 47' 48' 49' 50' 61' oS' o8' 54' 55' 56' 0196 57' 68' 10° 0' .0162 0165 0169 0172 0175 0179 0182 0186 0189 ' 0192 0199 5 .0160 0164 0167 0171 0174 0177 0181 0184 ; 0187 0191 0194 0197 10 .0159 0162 0166 0169 0172 0176 0179 0182 1 0186 0189 0192 0196 15 .0158 0161 0164 0168 0171 0174 0178 0181 ; 0184 i 0187 0191 i 0194 I 20 .0156 0160 ^163 0166 0170 0173 0176 0179 0183 i 0186 0189 0192 25 .0155 0158 0162 0160 0165 0168 0171 0175 0178 0181 0180 0184 0188 0191 10 30 .0154 0157 0164 0167 0170 0173 0177 0183 0186 0189 35 .0153 0156 0159 0162 0166 0169 0172 0175 0178 0181 0185 j 0188 40 .0151 0155 0158 0161 0164 0167 0171 0174 0177 0180 0183 i 0186 45 .0150 0153 0157 0160 0163 0166 0169 0172 0175 0179 0182 0185 • 50 .0149 0152 0155 0158 0162 0165 0168 0171 i 0174 i 0177 0180 0183 55 .0148 i 0151 0154 0157 0160 0163 0167 0170 1 0173 i 0176 0179 0177 0182 11 .0147 1 0150 0153 0156 0159 0162 0165 0168 ! 0171 0174 0181 5 .0146 0149 0152 0155 0158 0161 0164 0167 1 0170 0173 0176 0179 10 0148 0151 0154 0157 0160 0163 0166 0169 0172 0175 0178 15 0146 0149 0152 0155 0158 0161 0164 0167 0170 0173 1 0176 20 0145 0148 0151 0154 0157 0160 0163 0166 0169 0172 0175 25 11 30 0144 0147 0150 0153 0156 0159 0162 1 0165 0168 i 0171 1 0174 0143 0146 0149 0152 0155 0158 0161 0164 0167 0170 1 0172 35 0142 0145 0148 0151 0154 0157 0160 1 0162 0165 0168 0171 40 0141 0144 0147 0150 0153 0156 0158 0161 0164 0167 0170 45 0140 0143 0146 0149 0151 0154 0157 ! 0160 0163 0166 0169 50 0139 0142 0145 0148 0150 0153 0156 : 0159 0162 0165 0167 55 12 0138 0141 0144 0146 0145 0149 0148 0152 0155 0158 0161 0163 0162' 0166 0137 0140 0143 0151 0154 ! 0157 0159 0165 5 0136 0139 0142 0144 0147 0150 0153 0156 0158 0161 0164 10 0135 0138 0141 0143 0146 0149 0152 0154 0157 0160 0163 15 0134 0137 0140 0142 0145 0148 0151 0153 0156 0159 0162 20 0133 0136 0139 0141 0144 0147 0150 0152 0155 0158 1 0160 25 0132 0135 0138 0140 0143 0146 0148 0151 0154 0157 0159 12 30 0131 0134 0137 0139 0142 0145 0147 ! 0150 0153 0155 0158 35 0130 0133 0136 0138 0141 0144 0146 0149 0152 0154 ; 0157 40 0129 0132 0135 0137 0140 0143 0145 ! 0148 0151 1 0153 0156 45 0129 0131 0134 0136 0139 0142 0144 \ 0147 0150 0152 0155 0158 50 0128 0130 0133 0136 0138 0141 0143 0146 0149 0151 ' 0154 0156 1 55 0127 0129 0129 0132 0131 0135 0137 0136 0140 0142 0145 0148 0150 0153 0155 13 0126 0134 0139 0141 0144 0147 0149 0152 0154 5 0125 0128 0130 0133 0135 0138 0141 0143 0146 0148 0151 0153 10 0124 0127 0129 0132 0135 0137 0140 0142 0145 0147 0150 0152 15 0123 0126 0129 0131 0134 0136 0139 0141 0144 0146 0149 0151 1 20 0123 0125 0128 0130 0133 0135 0138 0140 0143 0145 0148 0150 25 0122 0124 0127 0129 0132 0131 0134 0133 0137 0136 0139 0142 0144 1 0147 0143 1 0146 0149 1 13 30 0121 0124 0126 0129 0138 0141 0148 35 0120 0123 0125 0128 0130 0133 0135 0138 0140 0142 0145 0147 40 0120 0122 0124 0127 0129 0132 0134 i 0137 0139 0142 0144 0146 45 0121 0124 0126 0128 0131 0133 0136 0138 0141 1 0143 0145 50 0120 0123 0125 0128 0130 0132 0135 0137 0140 ; 0142 0145 55 0120 0122 0124 0127 0129 0132 0131 0134 0133 0136 0136 0139 ! 0141 0144 0143 14 0119 0121 0124 0126 0128 0138 0140 ! 5 0118 0121 0123 0125 0128 0130 0132 0135 0137 i 0139 0142 10 0117 0120 0122 0124 0127 0129 0132 0134 0136 i 0139 0141 15 0117 0119 0121 0124 0126 0128 0131 0133 0135 0138 0140 20 0116 0118 0121 0123 0125 0128 0130 0132 0135 0137 0139 25 0115 0118 0120 0122 0124 0127 0129 0131 0134 0136 0138 ! 14 30 0114 0117 0119 0121 0124 0126 0128 0131 0133 0136 i 0137 i 35 0114 0116 0118 0121 0123 0125 0128 0130 0132 0134 0137 40 0113 0115 0118 0120 0122 0124 0127 0129 0131 0134 0136 \ 45 0112 0115 0117 0119 0121 0124 0126 0128 0130 0133 0135 1 50 0112 0114 0116 0118 0121 0123 0125 0127 0130 0132 0134 1 55 0111 0113 0116 0118 0120 0122 0124 0127 0129 0131 0133 15 0110 0113 0115 0117 0119 0121 0124 0126 0128 0130 ; 0133 ! APPENDIX V: TABLE 11. [Page 298 Log. A, for computing the First Correction of the Lunar Distance. App alt. of moon. Reduced parallax and refraction of moon. 1 43' 49' 50' 51' 52' 58' 54' 56' 56' 57' 58' 59' 15° 0' 10 20 30 40 50 16 10 20 30 .0110 .0109 .0108 .0107 .0105 0113 0111 0110 0109 0107 dlO'6 0105 0104 0103 0102 0115 0113 0112 0111 0110 0117 0116 0114 0113 0112 0119 0121 0118 1 0120 0116 0119 0115 ' 0117 0114 ' 0116 0124 0122 0121 0119 0118 0126 0124 0123 0121 0120 0128 0127 0125 0124 0122 0130 0129 0127 0126 0124 0133 0131 0129 0128 0126 .0104 .0103 .0102 .0101 .0100 0108 0107 0106 0105 0103 0110 0109 0108 0107 0105 0112 0111 0110 0109 0107 0115 0113 0112 0111 0109 0117 0115 0114 0113 0111 0119 0117 0116 0115 0113 0121 0119 0118 0117 0115 0123 0121 0120 0119 0117 0125 0124 0122 0121 0119 40 50 17 10 20 .0098 .0097 .0096 .0095 .0094 0100 0099 0098 0097 0096 0102 0101 0100 0099 0098 0104 0103 0102 0101 0100 0106 0105 0104 0103 0102 0108 0107 0106 0105 0104 0110 0109 0108 0107 0106 0112 0111 0110 0109 0107 0114 0113 0112 0110 0109 0116 0115 0114 0112 0111 0118 0117 0116 0114 0113 30 40 50 18 10 0095 0094 0093 0092 0091 0097 0096 0095 0094 0093 0099 0098 0097 0096 0095 0101 0100 0099 0098 0097 0103 0101 0100 0099 0098 0104 0103 0102 0101 0100 0106 0105 0104 0103 0102 0108 0107 0106 0105 0104 0110 0109 0108 0107 0105 0112 0111 0109 0108 0107 0109 0108 0107 0106 0105 0104 20 30 40 50 19 10 20 30 40 50 0090 0089 0088 0088 0087 0092 0091 0090 0089 .0088 0094 0093 0092 0091 0090 0096 0095 0094 0093 0092 0097 0096 0095 0094 0093 0099 0098 0097 0096 0095 0101 0100 0099 0098 0097 0103 0102 0101 0099 0098 0104 0103 0102 0101 0100 0106 0105 0104 0103 0102 0086 0087 0085 0087 0084 0086 0083 1 0085 0082 j 0084 0089 0088 0087 0087 0086 0085 0084 0083 0082 0082 0091 0090 0089 0088 0087 0092 0092 0091 0090 0089 0088 0087 0086 0086 0085 0084 0083 0082 0082 0081 0094 0096 0093 0095 0092 : 0094 0091 0093 0090 1 0092 0098 0097 0096 0095 0094 0093 0092 0091 0090 0089 0088 0088 0087 0086 0085 0099 0098 0097 0096 0095 0101 0100 0099 0098 0097 0103 0102 0101 0100 0099 0098 0097 0096 0095 0094 0093 0092 0091 0090 0090 20 10 20 30 • 40 50 21 10 20 30 0082 0081 0080 0079 0079 0078 0077 0076 0076 0075 0083 0082 0082 0081 0080 0086 0086 0085 0084 0083 0090 0089 0088 0087 0086 0091 0090 0089 0089 0088 0094 i 0096 0093 1 0095 0093 0094 0092 ' 0093 0091 0092 ■ 0079 0079 0078 0077 0076 0081 0080 0079 0079 0078 0082 0082 0081 0080 0079 0085 1 0087 0085 ' 0086 0084 1 0085 0083 ! 0085 0082 0084 0090 0091 0089 0091 0088 i 0090 0087 0089 0087 i 0088 40 50 22 10 20 0074 0074 0073 0072 0072 0076 0075 0074 0074 0073 0077 0076 0076 0075 0074 0079 0078 0077 0076 0076 0075 0074 0074 0073 0072 0080 0079 0079 0078 0077 0076 0076 0075 0074 0074 0082 0081 0080 0079 0079 0078 0077 0076 0076 0075 0083 0082 0081 0081 0080 0084 0084 0083 0082 0081 0086 0085 0084 0083 0083 0087 0086 0086 0085 0084 0089 0088 0087 0086 0086 30 40 50 23 10 0071 0070 0070 0069 0068 0072 0072 0071 0070 0070 0074 0073 0072 0072 0071 0079 0079 0078 0077 0076 0081 0080 0079 0078 0078 0082 0081 0081 0080 0079 0083 0083 0082 0081 0080 0085 0084 0083 0082 0082 1 20 30 40 50 24 0068 0067 0067 0066 0069 0069 0068 0067 0067 0070 0070 0069 0069 0068 0072 0071 0071 0070 0069 0073 0072 0072 0071 0071 0074 0074 0073 0073 0072 0076 0075 0074 0074 0073 0077 0076 0076 0075 0074 0078 0078 0077 0076 0076 0080 0079 0078 0078 0077 0081 0080 0080 0079 0078 10 20 30 40 50 0066 0066 0065 0065 0064 0067 0067 0066 0066 0065 0069 0068 0068 0067 0066 0070 0069 0069 0068 0068 0071 0071 0070 0069 0069 0073 0072 0071 0071 0070 0074 0073 0072 0072 0071 0075 0074 0074 0073 0072 0076 0076 0075 0074 0074 0078 0077 0076 0076 0075 25 0063 0065 0066 0067 j 0068 0069 1 0071 0072 1 0073 0074; Page 300] APPENDIX V: TABLE 11. Log. A, for computing the First Correction of the Lunar Distance. App. alt. of moon. Reduced parallax and refraction of moon. 1 50' 51' 52' 58' j 54' 1 56' 56' 57' i 58' 59' 80' 1 25° 0' .0063 0065 0066 ' 0067 0068 0069 0071 0072 0073 0074 1 1 20 .0062 0064 0065 0066 I 0067 0068 0069 0071 0072 0073 40 .0061 0062 0064 1 0065 0066 i 0067 0068 ' 0069 0071 i 0072 26 .0060 006f 0063 0064 0065 0066 0067 0068 0069 : 0071 1 20 .0059 0060 0062 1 0063 ' 0064 0065 0066 1 0067 0065 ; 0066 0068 0069 1 40 .0058 0059 0061 0062 0063 0064 0067 0068 1 27 .0057 0058 0060 0061 ' 0062 0063 0064 0065 0066 0067 20 .0056 0057 0059 0060 0061 0062 0063 0064 0065 0066 40 .0055 0057 0058 0059 i 0060 0061 0062 0063 0064 ■ 0065 28 .0055 0056 0057 0058 0059 0060 0061 0062 j 0063 0064 20 .0054 0055 0056 0057 0058 0059 0060 i 0061 0062 0063 40 .0053 0054 0055 0056 0057 ■ 0058 0059 i 0060 0061 0062 j 29 .0052 0053 0054 0055 0056 0057 0058 0059 0060 0061 1 20 .0051 0052 0053 i 0054 0055 0056 0057 0058 1 0059 0060 40 .0050 0051 0052 1 0053 0054 0055 0056 0057 0058 0059 30 .0050 0051 0051 0052 j 0053 0054 ; 0055 0056 0057 i 0058 1 20 .0049 0050 0051 1 0052 1 0052 0053 0054 0055 0056 0057 40 .0048 0049 0050 i 0051 0052 0053 0053 0054 0055 0056 31 .0047 0048 0049 0050 0051 0052 0053 0053 0054 0055 20 .0047 0047 0048 0049 0050 0051 0052 0053 0054 0054 0055 40 .0046 0047 0048 ^ 0048 0049 0050 0051 : 0052 0053 i 0054 0054 32 .0045 0046 0047 1 0048 1 0048 0049 0050 ! 0051 0052 0053 0054 20 .0044 0045 0046 ' 0047 0048 0049 0049 0050 I 0051 0052 0053 1 40 .0044 0045 0045 ; 0046 0047 0048 0049 0049 | 0050 0051 0052 1 33 .0043 0044 0045 1 0045 0046 0047 ! 0048 0049 0044 i 0045 0046 0046 , 0047 ! 0048 0049 0050 0051 20 .0042 0043 0049 i 0050 0050 1 1 40 .0042 0043 0043 0044 0045 i 0045 ' 0046 ' 0047 i 0048 ! 0049 0050 34 .0041 0042 0043 0043 1 0044 0045 0046 | 0046 ! 0047 - 0048 0049 20 .0040 0041 0042 0043 i 0043 0044 0045 i 0046 0047 0047 0048 40 .0040 .0039 0041 0040 0041 j 0042 0043 0044 \ 0044 | 0045 0041 1 0041 0042 0043 1 0044 j 0044 0046 0047 0047 35 0045 0046 0047 20 .0039 0039 0040 0041 0042 0042 j 0043 0044 0044 0045 0046 40 .0038 0039 0039 i 0040 0041 0042 0042 0043 i 0044 0044 0045 36 .0037 0038 0039 0040 . 0040 0041 0042 0042 \ 0043 0044 0044 20 .0037 0038 0038 0039 0040 0040 0040 0041 0042 0042 | 0043 0044 0043 40 .0036 0037 0038 1 0038 0039 0040 0041 i 0042 0042 1 1 37 .0036 0036 0037 ' 0038 0038 0039 | 0040 0040 0041 0042 ! 0042 20 .0035 0036 0037 0037 0038 0039 0039 0040 ! 0040 0041 0042 40 .0035 0035 0036 0037 0037 0038 0039 0039 0040 0040 0041 38 .0034 0035 0035 i 0036 i 0037 0037 0038 0039 0039 0040 0040 20 .0034 0034 0035 0036 1 0036 0037 1 0037 0038 0039 1 0039 0040 40 .0033 0034 0034 0035 0036 0036 0037 0037 0038 0039 0039 39 0033 0034 0034 0035 0036 \ 0036 0037 ! 0037 0038 ' 0039 20 0033 0033 0034 i 0035 i 0035 0036 0036 0037 0037 1 0038 40 40 0032 0033 0033 ' 0034 0035 0035 0036 0036 1 0037 ' 0037 0032 0032 0033 0033 0034 i 0035 0035 0036 0036 0037 20 0031 0032 0032 0033 0034 0034 0035 0035 0036 0036 40 0031 0031 0032 ; 0032 0033 i 0034 0034 0035 0035 0036 41 0030 0031 0031 1 0032 ; 0033 1 0033 0034 1 0034 1 0035 0035 20 0030 0030 0031 0031 0032 0033 0033 0034 I 0034 i 0033 1 0034 ; 0035 40 0029 0030 0030 0031 0032 0032 0033 0034 42 1 0029 1 0029 0030 0031 0031 0032 0032 0033 1 0033 j 0034 20 0029 0029 0030 0030 0031 0031 0032 0032 ! 0033 0033 40 0028 0029 0029 0030 0030 1 0031 0031 0032 0032 0033 43 1 0028 0027 0028 0028 0029 0028 0029 0029 0030 0029 0030 0031 0031 0032 ! 0032 20 0030 0030 0031 0031 0032 40 0027 0027 0028 0028 0029 0029 0030 0030 0031 0031 44 0026 0027 0027. 0028 0028 0029 0029 0030 0030 0031 20 1 0026 0026 0027 0027 0028 0028 0029 0029 0030 ' 0030 40 0026 ; 0026 0026 0027 0027 0027 0028 0028 0029 0029 j 0030 45 1 0025 j 0026 0026 0027 0027 0028 0028 0029 , 0029 APPENDIX V: TABLP] II. [Page 301. Log. A, for computing the First Correction of the Lunar Distance. App alt. of moon. Reduced parallax and refraction of moon. 1 51' 52' 53' 54' 55' 56' 57' 58' 69' 60' 45° 0^ 30 40, 30 47 30 48 30 49 30 .0025 . 0025 .0024 .0023 .0023 .0022 .0022 .0021 .0021 .0020 0026 0025 0024 0024 0023 0026 0025 0025 0024 0024 0027 0026 0025 0025 0024 0024 0023 0022 0022 0021 0027 0026 0026 0025 0025 0024 0023 0023 0022 0022 0027 0027 0026 0026 0025 0028 0027 0027 0026 0025 0028 0028 0027 0026 0026 0029 0028 0027 0027 0026 0025' 0025 0024 0024 0023 0029 0028 0028 0027 0026 0023 0022 0022 0021 0021 0023 0023 0022 0022 0021 0024 0024 0023 0023 0022 0025 0024 0024 0023 0022 0022 0021 0021 0020 0020 0025 0024 0024 0023 0023 0022 0022 0021 0021 0020 0020 0019 0019 0018 0018 0017" 0017 0016 0016 0015 0026 0025 0025 0024 0023 50 30 51 30 52 30 53 30 54 30 .0020 .0019 .0019 .0018 .0018 0020 0020 0019 0019 0018 0018 0017 0017 0016 0016 "0016 0015 0015 0014 0014 0020 0020 0020 0019 0019 0018 0018 0017 0017 0016 0016 0015 0015 0015 0014 0021 0020 0020 0019 0019 0018 0018 0017 0017 0017 0021 0021 0020 0020 0019 0022 0021 0020 0020 0019 0023 0022 0021 0021 0020 0020 0019 0019 0018 0018 0017 0017 0017 0016 0016 0023 0022 0022 0021 0021 0020 0020 0019 0019 0018 .0018 .0017 .0017 .0016 .0016 0019 0018 0018 0017 0017 0019 0018 0018 0018 0017 0019 0019 0018 0018 0017 0017 0016 0016 0016 0015 1 55 30 56 30 57 .0015 . 0015 . 0015 .0014 .0014 0016 0016 0015 0015 0015 0016 0016 0016 0015 0015 0017 0016 0016 0015 0015 0018 0017 0017 0016 0016 1 i 30 58 30 59 30 .0014 . 0013 .0013 .0012 .0012 0014 0013 0013 0013 0012 0014 0014 0013 0013 0012 0014 0014 0013 0013 0013 0014 0014 0014 0013 0013 0015 0014 0014 0013 0013 0015 0014 0014 0014 0013 0015 0015 0014 0014 0013 0015 0015 0014 0014 0014 0015 0015 0015 0014 0014 60 61 62 63 64 .0012 .0011 .0011 .0010 .0009 .0009 .0008 .0008 . 0007 .0007 0012 0011 0011 0010 0010 0009 0008 0008 0007 0007 0007 0006 0006 0005 0005 000b 0005 0004 0004 0004 0012 0011 0011 0010 0010 0009 0009 0008 0008 0007 0012 0012 0011 0010 0010 0009 0009 0008 0008 0007 0013 0012 0011 0011 0010 0009 0009 0008 0008 0007 0007 0006 0006 0006 0005 0005 0005 0004 0004 0004 0013 0012 0011 0011 0010 0013 0012 0011 0011 0010 0013 0012 0012 0011 0010 0010 0009 0009 0008 0008 0013 0012 0012 0011 0010 0010 0009 0009 0008 0008 0007 0007 0006 0006 0005 0005 0005 0004 0004 0004 0004 0003 0003 0003 0003 0013 0013 0012 0011 0011 0010' 0009 0009 0008 0008 65 66 67 6S 69 0009 0009 0008 0008 0007 0007 0006 0006 0006 0005 0005 0005 0004 0004 0004 0010 0009 0008 0008 0007 0007 0007 0006 0006 0005 0005 0005 0004 0004 0004 0004 0003 0003 0003 0003 0003 0003 0003 0003 0003 i 70 71 72 73 74 .0007 .0006 . 0006 .0005 . 0005 ^ 0007 0006 0006 0006 0005 0005 0005 0004 0004 0004 0007 0006 0006 0006 0005 0005 0005 0004 0004 0004 0004 0003 0003 0003 0003 0003 0003 0003 0003 0003 0003" 0007 0007 0006 0006 0005 0005 0005 0004 0004 0004 0004 0003 0003 0003 0003 0007 0007 0006 0006 0006 75 76 77 78 79 . 0005 .0004 .0004 .0004 .0004 .0004 . 0003 .0003 . 0003 .0003 .0003 .0003 .0003 . 0003 .0003 0005 0005 0004 0004 0004 80 81 82 83 84 0004 0003 0003 0003 0003 0004 0003 0003 0003 0003 0004 0003 0003 0003 0003 0003 0003 0003 0003 0003 0004 0003 0003 0003 0003 0003 0003 0003 0003 0003 0004 0003 '0003 0003 0003 85 86 87 88 89 0003 0003 0003 0003 0003 0003 0003 0003 0003 0003 0003 0003 0003 0003 0003 0003 0003 0003 0003 0003 0003 0003 0003 0003 0003 90 . 0003 0003 0003 0003 0003 0003 0003 0003 0003 Page 302J APPENDIX V: TABLE III. Log. B, for computing the First Correction of the Lunar Distance. App. alt. of sun or star. Reduced refraction and parallax of sun or star. 0' 0" 0' 80" V 0" 1' 30" 2' 0" 2' 80" 1 8' 0" 1 8' 80" 4' 0" 4' 80" 5' 0" 5' 80" 5° 0' 10 20 30 40 • 50 6 20 40 7 9. 9976 9. 9977' 9. 9978 9. 9979 9. 9980 9. 9981 '9. 9982 9. 9983 9. 9983 9. 9984 9. 9986 9. 9987 9. 9989 9. 9990 9. 9991 9. 9970 9. 9972 9. 9974 9. 9975 9. 9976 9. 9977 9. 9978 9. 9979 9.99M 9. 9981 9. 9982 9. 9982 9. 9984 "9. 9986 9. 9987 20 40 8 20 40 9. 9981 9. 9982 9. 9982 9. 9983 9.9984 9. 9985 9. 9985 9. 9986 9. 9987 9. 9989 9. 9990 9. 9991 9. 9992 9. 9993 9 20 40 10 11 9. 9992 9. 9993 9. 9994 9. 9994 9. 9995 9. 9995 9. 9996 9. 9997 9. 9998 9. 9999 9. 9989 9. 9991 9. 9986 9. 9986 9. 9987 9. 9988 9. 9989 12 13 14 15 16 9. 9997 9. 9997 9. 9995 9. 9995 9. 9996 9. 9996 9. 9992 9. 9992 9. 9993 9. 9994 9. 9994 9. 9995 9. 9996 9. 9998 9. 9990 9. 9991 9. 9992 9. 9993 9. 9993 18 20 25 30 50 0.0001 0.0001 0.0001 0.0000 0. 0000 0. 0001 0. 0001 9. 9999 9. 9999 0. 0000 0. 0000 0. 0001 9.9998 9. 9998 9. 9999 0. 0000 0. 0001 9. 9997 9. 9998 9. 9999 0. 0000 0.0001 9. 9995 9. 9996 90 0.0001 0.0002 0. 0002 1 0. 0002 1 App. alt. of sun or star. Reduced refraction and parallax of sun or star. 1 6' 0" 6' 80" 7' 0" 1 7' 30" 8' 0" 8' 30" 0' 0" 0' 80" 10' 0" 10' 80" i 11' 0" 11' 80" 1 5° 0' 10 20 30 40 50 6 20 40 7 9. 9959 9. 9960 9. 9962 9. 9963 9. 9965 9. 9967 9. 9968 9. 9970 9. 9971 9. 9973 9. 9974 9. 9975 9. 9976 9. 9977 9. 9978 9. 9979 9. 9981 9. 9951 9. 9953 9. 9954 9. 9956 9. 9957 9. 9947 9. 9949 9. 9951 9. 9952 9. 9954 9. 9944 9. 9946 9. 9948 9. 9949 9. 9951 9. 9952 9. 9954 9. 9956 9. 9959 9. 9961 9. 9963 9. 9965 9. 9966 9. 9968 9. 9940 9. 9942 9. 9944. 9. 9946 9. 9948 9. 9949 9. 9951 9. 9954 9. 9956 9. 9958 9. 9960 9. 9962 9. 9964 9. 9937 9. 9939 9. 9941 9. 9943 9. 9944 '9. 9946 9. 9948 9. 9951 9. 9953 9. 9956 9. 9933 9. 9935 9. 9937 9. 9939 9. 9941 9.9943 9. 9945 9. 9948 9. 9951 9. 9953 9. 9929 9. 9932 9. 9934 9. 9936 9. 9938 9. 9926 9. 9928 9. 9931 9. 9933 9. 9935 9. 9922 9. 9925 9. 9927 9. 9929 9. 9932 9. 9919 9. 9921 9. 9924 9. 9965 9. 9966 9. 9968 9. 9969 9. 9971 9. 9958 9. 9960 9. 9962 9. 9964 9. 9966 9.9968 9. 9969 9. 9971 9. 9972 9. 9973 9. 9974 9. 9975 9. 9976 9. 9977 9. 9955 9. 9957 9. 9959 9. 9961 9. 9963 9. 9940 9. 9942 9. 9945 9. 9948 9. 9937 9. 9939 20 40 8 20 40 9. 9972 9. 9974 9. 9975 9. 9976 9. 9977 9. 9965 9. 9967 9. 9968 9. 9970 9. 9971 9.9972 9. 9958 9 20 40 10 11 9. 9978 9. 9979 9. 9980 9. 9981 9. 9983 12 13 14 15 16 9. 9985 18 20 25 30 50 -^ 90 APPENDIX V: TABLE IV. [Page 303 Log. C, for computing the First Correction of the Lunar Distance. App. alt. of sun or star. Reduced refraction and parallax of sun or star. 1 O'O" 0'30" I'O" i 1'30" 1 2'0" 2' 30" 3' 0" 3' 80" 4' 0" 4' 80" 5'0" 5' 30" 5° 0' 20 40 6 20 9. 9969 40 7 8 9 10 9. 9988 9. 9984 9. 9986 9. 9980 9. 9982 9. 9984 9. 9986 9. 9987 9. 9988 9. 9989 9. 9990 9. 9990 9. 9991 9. 9974 9. 9978 9. 9980 9. 9982 9. 9984 9. 9985 9. 9987 9. 9988 9. 9989 9. 9970 9. 9972 9. 9975 9. 9978 9. 9981 11 12 13 14 15 9. 9995 9. 9993 9. 9994 9. 9994 9. 9990 9. 9991 9. 9992 9. 9993 9. 9993 9. 9994 9. 9994 9. 9994 9. 9995 9. 9996 9. 9989 9. 9990 9. 9991 9. 9991 9. 9992 9. 9987 9. 9988 9. 9989 9. 9990 9. 9991 9. 9982 9. 9984 9. 9985 16 17 18 20 25 9. 9998 9. 9999 9. 9999 9. 9999 0. 0000 0. 0000 9. 9997 9. 9998 9. 9998 '9. 9999 9. 9999 9. 9999 0. 0000 9. 9996 9. 9996 9. 9996 9. 9997 9. 9998 9. 9998 9. 9999 9. 9999 9. 9995 9. 9995 9. 9995 9. 9996 9. 9997 9. 9993 i 9. 9992 9. 9993 9. 9992 9. 9994 9. 9993 9.9994 9.9993 9. 9996 30 40 50 90 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 0. 0000 9. 9998 9. 9999 9. 9997 \ ' App. alt. of sun or star. Reduced refraction and parallax of sun or star. 1 6'0" 6' 30" 7'0" 7' 30" 8'0" 8' 80" O'O" 9' 80" 10' 0" 10' 80" 11' 0" 11' 30" 5° 0^ 20 40 6 20 . 40 7 8 9 10 9. 9962 9. 9964 9. 9966 "9. 9968 9. 9969 9.9973 9. 9976 9. 9979 9. 9956 9. 9959 9. 9961 9. 9963 9. 9949 9. 9953 9. 9955 9. 9958 9. 9960 9. 9962 9. 9964 9. 9969 9. 9972 9. 9975 9. 9946 9. 9949 9. 9952 9. 9955 9. 9957 9. 9960 9. 9962 9. 9966 9. 9970 9. 9942 9. 9946 9. 9949 9. 9952 9. 9955 9. 9957 9. 9959 9. 9964 9. 9968 9. 9938 9. 9942 9. 9946 9. 9949 9. 9952 9. 9954" 9. 9956 9. 9962 9. 9935 ' 9. 9931 9. 9939 9. 9936 9. 9943 9. 9939 9. 9946 9. 9943 9. 9949 i 9. 9946 9. 9927 9. 9932 9. 9936 9. 9940 9. 9943 9. 9946 9. 9924 9. 9929 9. 9933 9. 9937 9. 9920 9. 9925 9. 9930 9. 9916 9. 9922 9. 9965 9. 9967 9. 9971 9. 9974 9. 9977 9. 9951 9. 9954 9. 9960 9. 9949 9. 9951 11 12 13 14 15 9. 9981 9. 9983 9. 9979 16 17 18 20 25 30 40 50 90 APPENDIX V: TABLE V. [Page 305 Log. D, for computing tlie First Correction of the Lunar Distance. A pp. alt. ot moon. Reduced parallax and refraction of moon. 1 45' 46' 47' 48' 49' 60' ! 51' 52' i 68' 54' 55' 56' 67' 58' 8° 0' .0192 0196 0200 0204 0208 0212 ! 0217 0221 0225 0229 0233 0237 5 .0190 0194 0198 0202 0206 0210 0214 0218 0222 0227 ' 0231 0235 10 .0188 0192 0196 0200 0204 0208 ' 0212 0216 0220 0224 ! 0228 0232 15 .0186 0190 0194 0198 0202 0206 : 0210 0214 0218 0222 0226 0230 20 .0184 . 0182' 0188 0186 0192 0190 0196 0194 0200 0197 0204 0207 020r 0205' 0211 0215 0209 0213 0219 1 0223 0227 25 0217 ; 0221 0225 8 30 .0180 0184 0188 0192 0195 0199 0203 0207 0211 0215 1 0219 0223 35 .0178 0182 0186 0190 0193 0197 0201 1 0205 i 0209 0213 0216 0220 40 .0176 0180 0184 0188 0191 0195 0199 ! 0203 { 0207 0210 0214 0218 45 50 .0174 .0173 0178 0176 0182 0180 0186 0184 0189 0193 0197 I 0201 ! 0205 0195 1 0199' 0202 0208 ' 0212 0206 0210 0216 0214 0188 0191 55 .0171 0175 0178 0182 0186 0189 1 0193 1 0197 0200 0204 0208 0212 9 . 0169 0173 0177 0180 0184 0188 0191 0195 0198 0202 0206 0209 5 .0167 0171 0175 0178 0182 0186 0189 I 0193 0197 0200 1 0204 0207 10 15 .0166 0169 0168 0173 0171 0177 0180 0184 0187 1 0191 0195 1 0198 0186 0189 0193 0196 0202 0205 . 0164 0175 0179 0182 0200 0203 20 . 0163 0166 0170 0173 0177 OIHO 0184 0187 0191 ' 0194 0198 0201 25 .0161 0165 0168 0172 0175 0179 0182 0186 0189 0193 0196 0199 9 30 0163 0166 0170 0173 0177 , 0180 0184 , 0187 0191 0194 0198 35 0161 0160 0165 0168 0167 0172 0170 0175 1 0179 ' 0182 0185 0189 0192 0196 40 0174 1 0177 j 0180 t 0184 0187 0191 ' 0194 45 0158 0162 0165 0169 0172 i 0175 0179 • 0182 0185 i 0189 0192 0195 50 0157 0160 0164 0167 0170 ; 0174 ' 0177 0180 0184 ! 0187 0190 0194 55 0156 0159 0162 0165 0169 ; 0172 j 0175 0179 0182 1 0185 0189 0192 10 5 0154 0153 0157 0156 0161 0159 0164 0162 0167 i 0171 1 0174 i 0177 0166 j 0169 1 0172 0175 0180 i 0184 0187 0179 0182' 0185 0190 0188 1 10 0151 0155 0158 0161 0164 ' 0167 0171 0174 0177 ' 0180 ' 0183 0187 15 0150 0153 0156 0160 0163 0166 0169 1 0172 0175 0179 0182 0185 20 0149 0152 0155 0158 0161 i 0164 0168 0171 0174 0177 ! 0180 0183 25 10 30 0147 0146 0150 0149 0154 0152 0157 0155 0160 1 0163 0166 0169 0172 0175 1 0179 0182 0J58 0162 1 0165 0168 0171 1 0174 0177 0180 35 0145 0148 0151 0154 0157 0160 0163 0166 0169 i 0172 1 0175 0179 40 0143 0147 0150 0153 0156 0159 0162 0165 0168 0171 1 0174 0177 . -l-^ 0142 0145 0148 0151 0154 0157 ; 0160 0163 0166 0169 0172 0175 50 55 0141 0144 0147 0150 0149 0153 0156 ! 0159 0162 0161 0166 0168 0171 0174 0172 0140 0143 0146 0152 0155 0158 0164 1 0167 i 0170 11 0139 0142 0145 0147 0150 0153 0156 0159 0162 ■ 0165 1 0168 0171 0137 0140 0143 0146 0149 1 0152 0155 0158 0161 ! 0164 1 0167 0170 10 0139 0142 0145 0148 0151 0154 0157 0159 i 0162 0165 0168 15 0138 0137 0141 0140 0144 0143 0147 0150 0152 i 0155 0158 i 0161 0164 0167 20 0145 1 0148 0151 0154 0157 0160 0163 0165 25 0136 0139 0141 0144 ' 0147 0150 0153 0156 0158 ! 0161 0164 11 30 0135 0137 0140 0143 0146 0149 0151 0154 0157 : 0160 0163 35 0133 0136 0139 0142 0145 0147 0150 0153 0156 1 0159 0161 40 45 0132 0135 0138 0137 0141 0143 0146 0140 0142 0145 0149 0152 0154 1 0157 0160 0159 "- 0131 0134 0148 0150 0153 i 0156 50 0130 0133 0136 0138 0141 0144 0147 0149 0152 i 0155 0157 55 0129 0132 0135 0137 0140 0143 0145 0148 0151 ! 0153 0156 12 0128 0131 0134 0136 0139 0142 0144 0147 0150 ' 0152 0155 5 10 0127 0126 0130 0132 0135 0138 0140 0137 0139 0143 0146 0142 0145 0148 0151 0154 0129 0131 0134 0147 0150 0152 15 0125 0128 0130 0133 0136 0138 0141 0143 0146 0149 0151 20 0124 0127 0129 0132 0135 0137 0140 0142 0145 0147 0150 25 0123 0126 0128 0131 0133 i 0136 0139 1 0141 0144 0146 0149 12 30 35 0122 0125 0127 0130 0132 ! 0135 0131 1 0134 0138 i 0140 1 0143 0145 0144 0148 0147 0121 0124 0126 0129 0136 i 0139 0141 40 0120 0123 0125 0128 0130 0133 0135 0138 0140 0143 0145 45 0119 0122 0124 0127 0129 0132 0134 0137 0139 0142 0144 0147 50 0118 0121 0123 0126 0128 0131 0133 0136 0138 0141 0143 0146 55 0118 0120 0123 0125 0127 0130 0132 0135 0137 0140 0142 0145 13 0117 0119 0122 0124 0126 0129 0131 0134 0136 0139 0141 0143 22489—03- -20 Page 306] APPENDIX V: TABLE V. Log. D, for computing the First Correction of the Lunar Distance. App. alt. of moon. Reduced parallax and refraction of moon. 47' 48' 40' 60' 51' 62' 68' 84' 66' 66' 67' 58' 59' 13° 0' 10 20 30 40 .0117 .0115 .0113 .0112 0119 0117 0116 0114 0112 0122 0124 ': 0120 0122 0118 0120 0116 0119 0114 ! 0117 0126 0125 0123 0121 0119 0129 0127 0125 0123 0121 0131 0129 0127 0125 0124 0134 0132 0130 0128 0126 0136 0134 0132 0130 0128 0139 0137 0134 0132 0131 0141 0139 0137 0135 0133 0143 0141 0139 0137 0135 0133 0131 0129 0127 0126 50 14 10 20 30 0111 0109 0107 0106 0104 0113 0111 0110 0108 0106 0115 0113 0112 OHO 0109 0117 0116 0114 0112 0111 0120 0118 0116 0114 0113 0122 0120 0118 0117 0115 0124 0122 0121 0119 0117 0115 0114 0112 0111 0109 0126 0125 0123 0121 0119 0118 0116 0114 0113 0111 0110 0108 0107 0105 0104 0102 0101 0100 0098 0097 0129 0131 0127 0129 0125 0127 0123 ! 0125 0121 1 0123 40 50 15 10 20 0103 0101 0100 0099 0097 0105 0103 0102 0101 0099 0098 0096 0095 0094 0093 0107 0106 0104 0103 0101 0109 0108 0106 0105 0103 0111 0110 0108 0107 0105 0113 0112 0110 0109 0107 0120 0118 0116 0115 0113 0112' 0110 0108 0107 0106 0122 ! 0124 0120 i 0122 0118 0120 0117 0119 0115 0117 "0113 "0115" 0112 0114 0110 0112 0109 0111 0107 0109 30 40 50 16 10 0096 0094 0093 0092 0091 0100 0098 0097 0096 0094 0102 0100 0099 0098 0096 0104 0102 0101 0099 0098 0106 0108 0104 0106 0103 0105 0101 0103 0100 0102 20 30 40 50 17 0089 0088 0087 0086 0085 0091 0090 0089 0088 0087 0093 i 0095 0092 1 0094 0091 0092 0089 0091 0088 0090 0097 0096 0094 0093 0092 0099 0097 0096 0095 0093 0100 0099 0098 0096 0095 0104 0103 0101 0100 0099 0097 0096 0095 0094 0092 0106 0108 0105 0106 0103 0105 0102 ! 0104 0100 i 0102 10 20 30 40 50 0084 0083 0085 0084 0083 0082 0081 0087 0086 0085 0084 0083 0089 0088 0086 0085 0084 0091 0089 0088 0087 0086 0092 0091 0090 0089 0087 0094 0093 0091 0090 0089 0096 0094 0093 0092 0091 0090 0087 0085 0083 0081 0079 0077 0075 0073 0071 0099 0098 0096 0095 0094 0101 0099 0098 0097 0096 18 20 40 19 20 0080 0078 0076 0074 0072 0082 0083 0079 0081 0077 0079 0075 0077 0073 ; 0075 0085 0083 0080 0078 0076 0086 0088 0084 0086 0082 0083 0080 0081 0078 0079 0091 0089 0087 0084 0082 0093 0090 0088 0086 0084 0094 0092 0090 0087 0085 0083 0081 0079 0077 0075 0093 0091 0089 0086 40 20 20 40 21 0070 0068 0067 0065 0063 0072 0070 0068 0066 0065 0073 0071 0069 0068 0066 0074 0073 0071 0069 0067 0076 0077 0074 0075 0072 0073 0070 0072 0068 0070 0080 0078 0076 0074 0072 0081 0079 0077 0075 0074 0084 0082 0080 0078 0076 0074 0072 0070 0069 0067 0065 0064 0062 0060 0059 20 40 22 20 40 0062 0063 0060 0061 0059 0060 0057 0058 0056 0057 0064 0063 0061 0059 0058 0065 0064 0062 0061 0059 0067 0065 0063 0062 0060 0068 0066 0065 0063 0061 0060 0058 0057 0055 0054 0069 0067 0066 0064 0062 0061 0059 0058 0056 0055 0070 0069 0067 0065 0064 "0062 0060 0059 0057 0056 0072 0070 0068 0066 0065 0073 0071 0069 0068 0066 0064 0063 0061 0059 0058 23 20 40 24 20 0054 0053 0052 0050 0055 0054 0053 0051 0050 0057 0055 0054 0052 0051 0058 0056 0055 0053 0052 0059 0057 0056 0054 0053 0063 0061 0060 0058 0057 40 25 20 40 26 0049 0047 0046 0045 0044 0050 0048 0047 0046 0045 0051 0049 0048 0047 0046 0044 0043 0042 0041 0040 0039 0052 0050 0049 0048 0046 0045 0044 0043 0042 0040 . 0039 0053 0051 0050 0049 0047 0046 0045 0044 0042 0041 0040 0053 0052 0051 0049 0048 0054 0053 0052 0050 0049 0055 0054 0053 0051 0050 0048 0047 0046 0045 0043 0042; 0056 0055 0053 0052 0051 0049 0048 0047 0045 0044 0043' 0057 0056 0054 0053 0052 0"05"0 0049 0047 0046 0045 0044 20 40 27 20 40 0043 0041 0040 0039 0038 0043 0042 0041 0040 0039 0047 0046 0044 0043 0042 0048 0046 0045 0044 0043 0042' 28 0037 0038 0041 APPENDIX V: TABLE V. [Page 307 Log. D, for computing tiie First Correction of the Lunar Distance. App alt. of moon. Reduced parallax and refraction of moon. 1 50' 51' 1 52' 58' 54' 55' 1 56' 67' I 58' 59' 60' 28° 0^ 0. 0037 0. 0038 0. 0039 0. 0039 0. 0040 0. 0041 0. 0042 0. 0042 0. 0043 0.0044 30 0. 0036 0. 0036 0. 0037 0. 0038 0. 0038 0. 0039 0. 0040 0. 0040 1 0. 0041 0. 0042 29 0. 0034 0. 0035 0. 0035 0. 0036 0. 0037 0.0037 0.0038 0. 0039 1 0. 0039 0. 0040 30 0. 0033 0. 0033 0.0034 0. 0035 0. 0035 0. 0036 0. 0036 0. 0837 0. 0038 0. 0038 30 30 0. 0031 0. 0030 0. 0032 0. 0030 0. 0032 0. 0031 0. 0033 0. 0031 0. 0034 0. 0032 0. 0034 0. 0035 0. 0033 1 0. 0033 0.0035 0.0036 a 6034 0.0034 0. 0037 "0.0035 31 0. 0028 0. 0029 0. 0029 0. 0030 0. 0031 0. 0031 0. 0032 0. 0032 0. 0033 0. 0033 30 0. 0027 0. 0028 0. 0028 0. 0029 0. 0029 0. 0030 0. 0030 0. 0031 0. 0031 0. 0032 0. 0032 32 0. 0026 0. 0026 0. 0027 0. 0027 1 0. 0028 0. 0028 i 0. 0029 0. 0029 1 0. 0030 0. 0030 0. 0031 30 0. 0024 0. 0025 0. 0024 0. 0025 0. 0026 0. 002(i 0. 0027 0. 0027 0. 0025 0. 0026 0. 0028 1 0. 0028 0. 0026 ! 0. 0027 0. 0029 0. 0029 0.0027 0.0028 33 0. 0023 0. 0024 0. 0025 0. 0025 30 0. 0022 0. 0022 0. 0023 0. 0023 0. 0024 0. 0024 0. 0025 0. 0025 ! 0. 0025 0.0026 0.0026 34 0. 0021 0. 0021 0. 0022 0. 0022 0. 0022 0. 0023 0. 0023 0. 0024 0. 0024 0.0024 0.0025 30 0. 0020 0. 0020 0. 0020 0. 0021 0. 0021 0. 0022 0. 0022 0. 0022 0. 0023 0.0023 0.0023 35 0.0018 0. 0019 0. 0019 0. 0020 0.0018 0. 0020 0. 0019 0. 0020 0. 0019 0. 0021 0.0019 0.0021 "0. 0020 0. 0021 0. 0020 0.0022 0.0022 0.0020 0.0021 30 0. 0017 0. 0018 0. 0018 3(5 0. 0016 0.0017 0.0017 0.0017 0. 0018 0. 0018 0. 0018 0.0019 0. 0019 0.0019 0.0019 30 0.0015 0.0016 0.0016 0.0016 0. 0016 0. 0017 0. 0017 0. 0017 0.0018 0.0018 0.0018 37 0. 0014 0.0014 0.0015 0. 0015 0. 0015 0. 0016 0. 0016 0. 0016 0. 0016 0.0017 0.0017 30 0. 0013 0. 0013 0.0012 0.0014 0. 0013 0.0014 0. 0014 0.0013 0. 0014 0. 0013 0.0015 0. 0014 0. 0015 6. 0014 0. 0015 0. 0014 0.0015 0.0016 0.0014 0.0014 38 0. 0012 0. 0013 30 0.0011 0.0011 0. 0012 0.0012 0.0012 0. 0012 0. 0012 0. 0013 0. 0013 0. 0013 0. 0013 39 0. 0010 0. 0010 0. 0011 0. 0011 0. 0011 0. 0011 0.0011 0.0012 0.0012 0.0012 0.0012 30 0.0009 0. 0010 0.0010 0. 0010 0. 0010 0. 0010 0.0010 0.0011 0.0011 0.0011 40 0.0008 0.0009 0. 0009 0. 0009 0. 0007 0. 0009 0. 0007 0. 0009 0. 0007 0. 0009 0. 0010 070607 0. 0010 0. 0008 0. 0010 41 0.0007 0.0007 0. 0007 0. 0007 0. 0008 1 1 42 0. 0005 0. 0005 0. 0005 0. 0005 0. 0005 0. 0005 0. 0005 0. 0005 0. 0005 ' 0. 0006 43 0. 0003 0. 0003 0. 0003 0. 0003 0. 0003 0. 0003 0. 0003 0. 0003 0.0003 0.0004 44 0.0001 0.0001 0.0001 0. 0001 0. 0001 0. 0001 0. 0002 0. 0002 0.0002 0.0002 45 0.0000 9. 9998 0.0000 0. 0000 0. 0000 9. 9998 0. 0000 9. 9998 0.0000 9. 9998 0. 0000 9. 9998 0.0000 0. 0000 0. 0000 46 9. 9998 9. 9998 9. 9998 9. 9998 I 9. 9998 47 9. 9997 9. 9997 9. 9997 9. 9997 9. 9996 9. 9996 9. 9996 9. 9996 i 9. 9996 9. 9996 48 9. 9995 9. 9995 9. 9995 9. 9995 9. 9995 9. 9995 9. 9995 9. 9995 9. 9994 . 9. 9994 49. 9. 9994 9. 9994 9. 9994 9. 9993 9. 9993 9. 9993 9. 9993 9. 9993 I 9. 9993 1 9. 9993 50 9. 9992 9. 9992 9. 9992 9. 9991 9. 9992 979991 9. 9992 9. 9992 9. 9992 9. 9990 9. 9991 i 9. 9991 9. 9991 9. 9990 9. 9990 i 9. 9990 1 51 9. 9991 9. 9991 9. 9990 9. 9990 52 9. 9990 9. 9990 9. 9990 9. 9989 9.9989 9.9989 9. 9989 9. 9989 9. 9988 i 9. 9988 53 9. 9989 9. 9988 9. 9988 9. 9988 9.9988 9.9988 9. 9987 9. 9987 9. 9987 9. 9987 54 9. 9988 9. 9987 9. 9987 9. 9987 9. 9987 9. 9986 9. 9986 9. 9986 9. 9986 9. 9985 55 9. 9986 9. 9986 9. 9986 9. 9986 9. 9984" 9. 9985 9. 9984 9. 9985 9. 9984 9. 9985 9. 9984 9. 9984 9. 9984 9. 9983 9. 9983 9. 9984 9. 9983 1 56 9. 9985 9. 9985 9. 9985 57 9. 9984 9. 9984 9. 9984 9. 9983 9. 9983 9. 9983 9. 9982 9. 9982 9. 9982 9. 9981 ' 58 9. 9983 9. 9983 9. 9983 9. 9982 9. 9982 9. 9982 9. 9981 9. 9981 9. 9981 9. 9980 59 9. 9982 9. 9982 9.9981 9.9981 9. 9981 9. 9980 9. 9980 9. 9980 9. 9979 9. 9979 60 9. 9981 9. 9981 9. 9980 9. 9980 9.9979 9. 9980 9. 9979 9. 9979 9. 9979 9.9978 9. 9979 9. 9978 9. 9978 9. 9977 9. 9978 1 9. 9977 61 9. 9980 9. 9980 9. 9980 9. 9978 62 9. 9979 9. 9979 9. 9979 9. 9978 9. 9978 9. 9977 9. 9977 9. 9977 9. 9976 9. 9976 63 9.9979 9. 9978 9. 9978 9. 9977 9. 9977 9. 9976 9. 9976 9. 9976 9. 9975 9. 9975 64 9. 9978 9. 9977 9. 9977 9. 9976 9: 9976 9. 9976 9. 9975 9. 9975 9. 9974 9. 9974 65 9. 9977 9. 9976 9. 9977 9.9976 9. 9976 9. 9975 9. 9976 9. 9975 9. 9975 9. 9974 9. 9975 9.9974 9. 9974 9.9974 9.9973 9. 9972 66 9. 9973 9. 9973 9. 9973 9. 9972 67 9. 9976 9. 9975 9. 9975 9. 9974 9. 9974 9. 9973 9. 9973 9. 9972 9. 9972 9. 9971 68 9. 9975 9. 9974 9. 9974 9. 9973 9.9973 9.9972 9. 9972 9. 9971 9. 9971 9. 9970 1 69 9. 9974 9. 9974 9. 9973 9. 9973 9. 9972 9. 9972 9. 9971 9. 9971 9. 9970 9. 9970 70 72 9. 9974 9. 9973 9. 9972 9. 9973 9. 9971 9. 9972 9. 9971' 9. 9972 9. 9970 9. 9971 9. 9970 9. 9970 9. 9969 9. 9970 9. 9969 9. 9969 9. 9968 9. 9972 9. 9969 9. 9968 74 9. 9971 9. 9971 9. 9970 9. 9970 9. 9969 9. 9969 9. 9968 9. 9968 ' 9. 9967 9. 9966 76 9. 9971 9. 9970 9. 9969 9. 9969 9. 9968 9. 9968 9. 9967 9. 9966 ; 9. 9966 9. 9965 78 9. 9970 9. 9969 9. 9969 9. 9968 9. 9967 9. 9967 9. 9966 9. 9966 9. 9965 9. 9964 80 9. 9969 9. 9969 9. 9968 9. 9967 9. 9967 { 9. 9966 9. 9965 9. 9964 9. 9965 9. 9964 9. 9964 9. 9962 90 9. 9968 9. 9967 9.9966 9.9966 9. 9965 9. 9964 9. 9963 9. 9963 Page 308J APPENDIX V: lABLE VI. Second Correction of the Lunar Distance. Appar- ent dis- tance. First correction of distance. Appar- 3' V 10 12' 14' 16' 18' 20' 21' 22' 28' 24' 26' 26' 27' 28' ent dis- tance. Sub. II II II II // II // II II It II // II II II II Add. 15° (y 2 3 5 6 8 11 13 14 16 i 17 19 20 22 24 26 30 2 3 6 8 10 13 14 15 1 17 18 20 21 23 25 16 3 \ 6 8 10 i 12 13 15 16 18 19 21 22 24 30 3 6 8 10 12 13 14 16 17 18 20 21 23 17 3 3 4 4 6 5 7 9 11 13 14 15 16 18 19 21 22 30 7 9 11 12 13 15 16 17 19 20 22 18 3 4 5 7 9 11 12 13 14 15 17 18 20 21 30 3 4 5 7 8 , 10 12 13 14 15 16 18 19 20 19 3 4 5 6 8 10 11 12 13 15 16 17 18 20 30 2 4 5 5 6 6 8 10 11 12 13 14 15 17 18 17- 19 19 20 2 3 8 10 11 12 13 14 15 16 21 2 3 4 6 7 9 10 11 12 13 14 15 17 18 22 0. 2 3 4 6 7 9 10 10 11 12 14 15 16 17 23 2 3 4 5 7 8 9 10 11 12 13 14 15 16 24 2 2 3 3 4 4 5 5 6 8 9 9 10 U 12 13 14 15 15 25 6 7 8 9 10 11 12 13 14 26 2 3 4 5 6 1 7 8 9 9 10 11 12 13 14 27 2 2 3 4 6 7 8 8 9 10 11 12 12 13 28 2 2 3 4 5 7 < 8 9 9 10 11 12 13 29 " 2 2 2 2 3 3 4 5 6 7 8 8 9 10 11 11 12 30 4 5 6 1 7 8 9 9 10 11 12 31 2 3 4 5 6 6 7 8 8 9 10 11 11 32 2 3 4 5 6 6 7 7 8 9 9 10 11 33 2 3 3 4 5 6 7 7 8 8 9 10 11 34 — j- 2 2 3 3 4 5 6 6 7 "■ 8 9 9 10 35 2 3 4 ; 5 5 6 7 7 8 8 9 10 36 2 2 3 4 5 5 6 6 ( 8 8 9 9 37 2 2 3 4 5 5 6 6 / 7 8 8 9 38 2 2 3 4 4 5 5 6 6 / 8 8 9 39 Oj 1 2 2 2 2 3 3 4 5 5 6 6 6 7 7 7 7 8 8 8 "140°" 40 1 2 3 3 4 5 5 6 8 42 2 2 3 4 4 5 5 6 6 7 / 8 138 44 1 2 2 3 4 4 4 5 5 6 6 7 7 136 46 2 2 3 3 4 4 4 5 5 6 6 7 134 48 50 6 ~1 2 2 3 3 3 4 4 5 5 5 6 6 132 "130 2 2 3 3 4 4 4 5 5 5 6 52 2 2 3 3 3 4 4 4 5 5 5 128 54 1 2 2 3 3 3 3 4 4 4 5 5 126 56 2 2 2 3 3 3 3 4 4 4 5 124 58 2 2 2 3 3 3 3 4 4 4 122 120 60 2 2 2 2 3 3 3 3 4 4 62 2 2 2 2 2 3 3 3 3 4 118 64 2 i . 2 2 2 2 3 3 3 3 116 66 2 1 2 2 2 2 2 3 3 3 114 68 — j- 1 i 2 2 2 2 2 2 2 3 3 112 70 1 1 i 1 2 2 2 2 2 2 110 74 1 1 1 1 1 1 2 2 2 2 106 78 1 1 1 1 1 1 1 1 1 102 82 ! 1 1 1 1 1 1 1 1 98 86 7' 10' 12' 94 90 '0 90 Appar- ent dis- tance. 3' 14' 16' 18' 20' 21' 22' 28' 24' 25' 26' 27' 28' Appar- ent dis- tan<'c. First correction ol distance. APPENDIX V: TABLE VI. [Page 309 Second Correction of the Lxinar Distance. Appar- ent dis- tance. First correction of distance. Appar- ent dis- tance. 29' 80' 81' II 31 30 29 28 27 27" 26 25 24 24 23 22 21 20 19 18 17 16 16 15 14 14 13 13 12 82' II 33 32 31 30 29 28 28 27 26 25 25 23 22 21 20 19 18 18 17 16 15 15 14 14 13 88' 84' 85' 86' 37' 88' 89' 40' 41' 42' 48' 44' Sub. 15° 0' 30 16 30 17 27 26 26 25 24 '23 23 22 21 21 20 19 18 17 16 16 15 14 14 13 13 12 12 11 11 29 28 27 27 26 25' 24 23 23 22 22 20 19 19 18 17' 16 15 15 14 14 13 13 12 12 II 35 34 33 32 31 30 29 28 28 27 II 38 36 35 34 33 32 31 30 29 28 II 40 39 37 36 35 34 33 32 31 30 II 42 41 39 38 37 II 45 43 42 40 39 II 47 45 44 43 41 II 50 48 46 45 43 II 52 50 49 47 46 II 55 53 51 50 48 II 57 56 54 52 50 II 60 58 56 54 53 63 61 59 57 55 Add. 30 18 30 19 30 36 35 34 33 32 38 37 36 35 34 40 39 38 37 36 42 41 40 39 37 36 35 33 31 30 44 43 42 41 39 38' 36 35 33 31 47 45 44 43 41 49 47 46 45 43 51 50 48 47 46 54 52 50 49 48 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 26 25 24 22 21 20 19 19 18 17 16 16 15 15 14 28 26 25 24 23 29 28 26 25 24 31 29 28 27 25 24 23 22 21 20 33 31 30 28 27 35 33 31 30 28 40 38 36 35 33 42 40 38 36 35 44 42 40 38 36 46 44 42 40 38 22 21 20 19 18 23 22 21 20 19 26 25 23 22 22 27 26 25 24 23 28 27 26 25 24 30 29 27 26 25 24 23 22 22 21 31 30 29 28 26 33 32 30 29 28 35 33 32 30 29 36 35 33 32 30 17 17 16 16 15 19 18 17 16 16 20 19 18 17 17 21 20 19 18 18 22 21 20 19 19 23 22 21 20 20 25 24 23 23 22 27 26 25 24 23 28 27 26 25 24 29 28 27 26 25 35 36 37 38 39 10 10 10 9 9 9 8 8 7 7 6 6 5 5 5 4 4 4 3 3 3 2 2 i 1 11 11 10 10 10 9 9 8 8 7 7 6 6 5 5 5 4 4 4 3 3 2 2 1 1 12 12 11 11 10 10 9 9 8 8 7 7 6 6 5 13 12 12 11 11 11 10 9 9 8 8 7 6 6 6 14 13 13 12 12 14 14 13 13 12 15 15 14 14 13 16 16 15 14 14 17 16 ■ 16 15 15 18 17 17 16 16 19 18 18 17 16 20 19 19 18 17 21 20 19 19 18 22 21 20 20 19 23 22 21 .21 20 24 23 22 22 21 140° 138 136 134 , 132 40 42 4-f 46 48 11 11 10 9 9 8 7 7 6 6 12 11 10 10 9 13 12 11 10 10 13 13 12 11 10 14 13 12 12 11 15 14 13 12 11 16 15 14 13 12 17 16 14 13 13 17 16 15 14 13 18 17 16 15 14 19 18 17 16 15 -20 19 17 16 15 50 52 54 56 58 60 62 64 66 68 70 74 78 82 86 8 8 7. 7 6 9 8 8 7 7 9 9 8 8 7 10 9 9 8 7 11 10 9 9 8 11 10 10 9 8 10 9 9 12 11 11 10 9 13 12 11 10 10 14 1 14 13 13 12 12 11 11 10 11 130 128 126 124 122 5 4 4 4 3 5 5 4 4 4 5 5 5 \ 6 6 5 4 4 6 6 5 5 4 7 6 6 5 5 6 6 5 5 7 7 6 6 5 8 i 8 7 1 7 6 7 6 6 5 6 8 8 7 7 6 9 8 8 7 6 9 9 8 7 7 10 9 8 8 7 120 118 116 114 112 3 2 2 1 1 3 3 2 1 1 3 3 2 1 1 4 3 2 1 1 4 3 2 2 1 4 3 2 2 1 4 3 3 9 5 4 3 2 1 5 4 3 2 1 5 4 3 2 1 5 4 3 2 1 6 4 3 2 1 6 5 3 2 1 6 5 4 2 1 110 106 102 98 94 90° 90° Appar- ent dis- tance. 29' 30 81' 82' 33' 84' 86' 86' 87' 38' 89' 40' 41' 42' 48' 44' Appar- ent dis- tance. First correction of distance. Page 310] APPENDIX V: TABLP: YI. Second Correction of the Lunar Distance Appar- ent dis- tance. First correction of distance. Appar- ent dis- tance. 45' 46' 47' 1 48' 49' 50' 51' 52' 68' 64' 55' 56' 57' 68' 69' 60' Sub. 15° 0' 66 II 69 // 72 II 75 78 II 81 II 85 II 88 91 II 95 99 II 102 II 106 110 113 II 117 Add. 30 64 67 70 72 76 79 82 85 88 92 95 99 102 106 110 113 16 62 64 67 L 70 65 '68 73 76 79 82 85 89 92 95 99 102 106 110 30 60 62 71 74 77 80 83 86 89 92 96 99 103 106 17 58 ! 60 56 59 63 61 66 69 71 69 74 77 80 83 86 90 93 96 99 103 100 30 64 66 72 75 78 81 84 87 90 93 96 18 54 57 59 1 62 64 67 70 73 75 78 81 84 87 90 94 97 30 53 55 58 ; 60 63 65 68 71 73 76 79 82 85 88 91 94 19 51 54 56 1 58 61 63 66 69 71 74 77 79 82 85 88 91 30 50 , 52 49 51 54 57 53 55 59 62 64 62 67 65 69 72 75 77 80 83 86 83 89 86 20 58 60 67 70 73 75 78 81 21 46 48 50 52 55 57 59 61 64 66 69 71 74 76 79 82 22 44 ; 46 48 j 50 52 54 56 58 61 63 65 68 70 73 75 78 23 42 44 45 47 49 51 53 56 58 60 62 64 67 69 72 74 24 40 41 38 40 43 41 45 43 47 45^ 49 47 51 49 53 55 57 59 61 59 64 61 66 63 68 65 71 67 25 51 53 55 57 26 36 38 40 41 43 45 47 48 50 52 54 56 58 60 62 64 27 35 36 38 39 41 43 45 46 48 50 52 54 56 58 60 62 28 33 35 36 j 38 39 41 43 44 46 48 50 51 53 55 57 59 29 32 33 31 32 35 36 33 i 35 38 39 41 43 44 1 46 48 49 51 53 55 53 57 30 36 38 39 41 42 44 46 47 49 51 54 31 29 31 32 ' 33 35 36 38 39 41 42 44 46 47 49 51 52 32 28 30 31 1 32 34 35 36 38 39 1 41 42 44 45 47 49 50 33 27 28 30 31 32 34 35 36 38 39 41 42 44 45 47 48 34 26 27 26 29 1 30 28 29 31 30 32 34 35 36 38 39 41 42 44 45 43 47 45 35 25 31 32 34 35 36 38 39 40 42 36 24 25 27 28 29 30 31 32 34 35 36 38 39 40 42 43 37 23 25 26 27 28 29 30 31 33 34 35 36 38 39 40 42 38 23 24 25 26 27 28 29 30 31 33 34 35 36 38 39 40 39 22 1 23 24 25 26 27 26 28 29 30 31 33 34 35 36 38 39 37 40 21 22 23 24 25 27 28 29 30 31 33 34 35 36 140° 42 20 21 21 22 23 24 25 26 27 28 29 30 31 33 34 35 138 44 18 19 20 21 22 23 24 24 25 26 27 28 29 30 31 33 136 46 17 18 19 19 20 21 22 23 24 25 26 26 27 28 29 30 134 48 16 15 17 16 17 16 18 17 19 20 20 21 22 23 24 25 26 26 27 28 132 50 ' 18 18 19 20 21 21 22 23 24 25 25 26 130 52 14 14 15 16 16 17 18 18 19 20 21 21 22 23 24 25 128 54 13 13 14 15 15 16 16 17 18 18 19 20 21 21 22 23 126 56 12 12 13 14 14 15 15 16 17 17 18 18 19 20 20 21 124 58 11 10 12 11 12 11 13 12 13 14 14 15 15 16 16 17 18 18 19 20 122 60 12 13 13 14 14 15 15 16 16 17 18 18 120 62 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 118 64 9 9 9 10 10 11 11 12 12 12 13 13 14 14 15 15 116 66 8 8 9 9 9 10 10 11 11 11 12 12 13 13 14 14 114 68 7 . 6 7 7 8 8 8 9 9 10 10 10 9 11 11 11 12 12 13 112 70 7 7 8 8 8 9 9 10 10 10 11 11 11 110 74 5 5 6 6 6 6 7 7 7 • 7 8 8 8 8 9 9 106 78 4 4 4 4 4 5 5 5 5 5 6 6 6 6 6 7 102 82 2 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 98 86 1 45' 1 46' 1 1 1 2 2 2 2 2 2 2 2 2 2 2 94 90° 90° Appar- ent dis- tance. 47' 48' 49' 50' 61' 62' 68' 64' 65' 56' 57' 68' 59' 60' Appar- ent dis- tance. First correc tion of distan ce. APPENDIX V: TABLE VII. [Page 311 For finding the Correction of the Lunar Distance for the Contraction of the Moon '9 Semidiameter. 1 TABLE VII A.— GIVING THE ARGUMENT FOR TABLE VII B. Red. P. and R. of moon. Apparent altitude of moon. 6° 5i° 6° 64° 7° 7i° 8= 8i' 9° |9ic ic ' 11<: 12 ' 18' » 14°| 15<= 10° 17° 18° 20° 25° 80° 40° 60° iV 65 56 [ 42 63 54 47 41 43 62 53 46 40 35 44 60 51 45 39 34 30 27 45 58 50 43 42 38 37 33 33 30 29 26 26 24 23 21 21 20 19 17 l5 1 1 46 57 149 47 56 48 41 36 32 28 25 23 20 19 17 14 12 10 48 54 46 40 35 31 28 25 22 20 ;i8 17 14 12 10 9 8 7 6 49 53 45 39 35 30 27 24 22 19 18 16 14 12 10 9 8 7 6 6 5 3 50 52 44138 34 30 26 24 21 19 il7 16 13 11 10 9 8 7 6 5 5 3 3 2 51 50 43 38 33 29 26 23 21 19 17 15 13 11 10 8 7 7 6 5 5 3 2 2 2 52 49 42 37 32 28 25 23 20 18 17 15 13 11 9 8! 7 7 6 5 4 3 2 2 2 53 48 41:36 32 28 25 22 20 18 16 15 12 11 9 8- 7 6 6 5 4 3 2 2 2 54 47 41135 31 27 24 22 19 18 16 15 12 10 9 8; 7 6 6 5 4 3 2 2 2 55 35 30 27 26 24 23 21 21 19 19 17 17 16 15 14 12 10 10 9 9 81 7 6 6i 6 5 5 5 4 4 3 3 2 2 2 2 2 2 56 1 14 12 8 7 57 18 17 15 14 12 10 9 7 7 6 5 5 4 3 2 2 2 58 13111 10 8 7 7 6 5 5 4 3 2 2 2 59 8 7 6 6 5 5 4 3 2 2 2 60 1 \ 4 3 2 2 2 1 AB LE VII B.— CONTRACTION OF MOON'S SEMI-DIAMETER. 01 2; 2 3! 2 4 4 • ff ] It Oi 0: 2! 1 2 2 3; 3 1 2 3 n 1 2 3 4 5 6 7 8 9 11 12 13 15 1 2 3 4 5 ? 8 9 10 12 13 14 It 1 2 3 4 5 6 7 8 9 10 11 12 14 // 1 2 3 4 5 6 7 8 9 10 11 12 13 1 2 3 4 5 5 6 7 8 9 10 12 13 1 2 3 3 5 5 6 7 8 9 10 11 13 II 1 2 2 3 4 5 6 7 8 9 10 11 12 1 2 2 3 4 5 6 7 8 9 10 11 12 II 1 2 2 3 4 5 6 6 7 8 9 10 11 30 4 20 40 5 — — — — 5 7 5 6 7 9 10 5 ; 4 6 6 7 7 8 8 9( 9 4 6 7 8 9 20 40 6 20 40 1 ! 11 12 10 10 ]2lll 13 12 14 14 16 15 7 20 40 8 20 1 1 1 18 17 19 16 18 20 21 16 17 19 21 15 17 18 20 22 15 16 18 19 21 14 16 17 19 20 22^ 24 14 15 17 18 20 21 23 25 13 15 16 17 19 20 22 24 25 13 14 16 17 18 20 21 23 25 26 13 14 15 16 18 19 21 22 24 26 28 12 13 15 16 17 19 20 22 23 25 27 28 40 9 20 40 10 j ! 23 23 20 40 11 20 1 Subtract this correction from the distance. APPENDIX V: TABLE IX. [Page 313 Lo garithms of Smal Arcs in Space or Time. Arc. 0" 1" 2" 3" 4" 5" 6" 7" i 8" 1 9" O t II 0" 0™ 0' 0.0000 0. 3010 0. 4771 0. 6021 0.6990 0. 7782 0. 8451 0. 9031 0. 0542 10 1.0000 1.0414 1.0792 1.1139 1. 1461 1. 1761 1. 2041 1.2304 1.2553 1. 2788 20 1. 3010 1. 3222 1. 3424 1.3617 1. 3802 1. 3979 1.4150 1. 4314 1 1. 4472 1.4624 30 1.4771 1. 4914 1.5051 1.5185 1.5315 1. 5441 1. 5563 1.5682 1.5798 1.5911 40 1. 6021 1.6128 1.6232 1. 6335 1.6435 1.6532 1. 6628 1.6721 1.6812 1.6902 50 10 1.6990 1. 7782 1. 7076 1. 7853 1. 7160 1. 7243 1. 7324 1. 7404 1. 7482 1.8195 1. 7559 1. 8261 1. 7634 1.8325 1. 7709 1. 7924 1. 7993 1.8062 1 1.8129 1. 8388 1 10 1. 8451 1.8513 1. 8573 1. 8633 1.8692 1.8751 1.8808 1. 8865 1. 8921 1. 8976 1 20 1. 9031 1.9085 1.9138 1.9191 1.9243 1 1.9294 1. 9345 1. 9395 1. 9445 1.9494 1 30 1. 9542 1.9589 1.9638 1. 9685 1.9731 1.9777 1. 9823 1.9868 1 1.9912 1. 9956 1 40 2. 0000 2. 0043 2. 0086 2. 0128 2.0170 2.0212 2. 0253 2. 0294 ! 2. 0334 2. 0374 1 50 2. 0414 2. 0453 2. 0492 2. 0531 2. 0569 2. 0607 2.0645 2. 0682 2. 0719 2. 1072 2. 0755 2 2.0792 ! 2.0828 2. 0864 2. 0899 2.0934 2.0969 2.1004 2. 1038 2. 1106 2 10 2.1139 2.1173 2. 1206 2. 1239 2. 1271 2. 1303 2. 1,335 2. 1367 2. 1399 2. 1430 2 20 2. 1461 2. 1492 2. 1523 2. 1553 2.1584 2.1614 2. 1644 2. 1673 2. 1703 2. 1732 2 30 2.1761 2.1790 2. 1818 2. 1847 2. 1875 1 2. 1903 2. 1931 2. 1959 2. 1987 2. 2014 2 40 2.2041 2.2068 2. 2095 2.2122 2. 2148 2. 2175 2. 2201 2. 2227 2. 2253 2. 2279 2 50 2. 2304 2. 2330 2. 2.355 2. 2380 2. 2405 2. 2430 2. 2455 2. 2480 2. 2504 2. 2529 3 2. 2553 2. 2577 2. 2601 2. 2625 2. 2648 1 2. 2672 2. 2695 2. 2718 2. 2742 2. 2765 3 10 2. 2788 2. 2810 2. 2833 2. 2856 2. 2878 2. 2900 2. 2923 2. 2945 2. 2967 2. 2989 3 20 2. 3010 2. 3032 2. 3054 2. 3075 2. 3096 2. 3118 2. 3139 2.3160 2.3181 2. 3201 3 30 2. 3222 2. 3243 2. 3263 2. 3284 2.3304 2.3324 2. 3345 2. 3365 : 2. 3385 2. 3404 3 40 2. 3424 2. .3444 2. 3464 2. 3483 2.3502 ! 2.3522 2. 3541 2. 3560 5 2. 3579 2. 3598 3 50 4 2. 3617 2. 3636 2. 3655 2. 3674 2. 3692 2. 3874 2.3711 2. 3729 2. 3747 2. 3766 2. 3945 2. 3784 2. 3962 2. 3802 2. 3820 2. 3838 2. 3856 2. 3892 2. 3909 2. 3927 4 10 2. 3979 2. 3997 2. 4014 2. 4031 2. ':048 1 2.4065 2. 4082 2. 4099 2. 4116 2. 4a 33 4 20 2. 4150 2. 4166 2.4183 2. 4200 2.4216 ' 2.4232 2. 4249 2. 4265 2. 4281 2. 4298 4 30 2. 4314 2. 43.30 2. 4.346 2. 4362 2.4378 2.4393 2. 4409 2. 4425 2. 4440 2. 4456 4 40 2. 4472 2. 4487 2.4502 ' 2.4518 2.4533 2.4548 2. 4564 2. 4579 2. 4594 2. 4609 4 50 5 2. 4624 2. 4639 2.4654 i 2.4669 2.4683 2.4698 2.4713 2. 4728 2. 4742 2. 4886 2. 4757 2. 4900 2. 4771 2. 4786 2. 4800 2. 4814 2.4829 2.4843 2. 4857 2. 4871 5 10 2. 4914 2. 4928 2. 4942 2. 4955 2.4969 \ 2.4983 ' 2.4997 2.5011 2. 5024 2. 5038 5 20 2. 5051 2. 5065 2. 5079 2.5092 2.5105 2.5119 i 2.5132 2. 5145 2.5159 2.5172 5 30 2.5185 2.5198 2.5211 2. 5224 2. 5237 2. 5250 2. 5263 2. 5276 2. 5289 2. 5302 § 40 2.5315 2.5328 2. 5340 2. 5353 2. 5366 2. 5378 2. 5391 2. 5403 2. 5416 2. 5428 5 50 2. 5441 2. 5453 2. 5575 2. 5465 2. 5587 2. 5478 2. 5599 2. 5490 2.5611 2. 5502 2. 5514 2. 5527 2. 5539 2.5551 6 2. 5563 2.5623 2.5635 2. 5(547 2. 5658 2. 5670 6 10 2.5682 1 2.5694 2. 5705 2.5717 2.5729 2.5740 2.5752 2. 5763 2. 5775 2. 5786 6 20 2.5798 ! 2.5809 2. 5821 2. 5832 2.5843 2.5855 i 2.5866 2. 5877 2. 5888 2. 5899 6 30 2.5911 2.5922 2. 5933 2. 5944 2. 5955 2. 5966 2. 5977 2. 5988 ! 2. 5999 2. 6010 6 40 2.6021 i 2.6031 2. 6042 2. 6053 2. 6064 2. 6075 2. 6085 2.6096 2.6107 2.6117 6 50 7 2. 6128 2. 6138 2. 6149 2.6160 2. 6170 2. 6180 2.6191 2.6201 2.6212 2. 6222 2. 6232 2. 6243 2. 6253 2. 6263 2. 6274 2.6284 1 2.6294 2. 6304 2. 6314 2. 6325 7 10 2.6335 I 2.6345 2. 6355 2. 6365 2. 6375 2.6385 2.6395 2. 6405 1 2. 6415 2. 6425 7 20 2.6435 i 2.6444 2. 6454 2. 6464 2. 6474 2.6484 2.6493 2. 6.503 1 2. 6513 2. 6522 7 30 2. 6532 2. 6542 2. 6551 2. 6561 2. a571 2.6580 2.6590 2. 6599 2. 6609 2. 6618 7 40 2. 6628 2. 6637 2.6646 2. 6656 2. 6665 2.6675 2.6684 2. 6693 2. 6702 2. 6712 7 50 8 2. 6721 2. 6812 2. 6730 2. 6821 2. 6739 2. 6830 2. 6749 2. 6758 2.6767 2.6776 2.6857 1 2.6866 2. 6785 1 2. 6794 2. 6803 2. 6839 2. 6848 2. 6875 2. 6884 2. 6893 8 10 2. 6902 2. 6911 2. 6920 2. 6928 2. 6937 2.6946 ! 2.6955 2. 6964 2. 6972 2. 6981 8 20 2. 6990 2. 6998 2. 7007 2. 7016 2. 7024 2. 7033 ! 2. 7042 2. 7050 2. 7059 2. 7067 8 30 2. 7076 2. 7084 2. 7093 2. 7101 2.7110 2.7118 1 2.7126 2. 7135 2. 7143 2. 7152 8 40 2.7160 1 2.7168 2.7177 2. 7185 2. 7193 2.7202 1 2.7210 2. 7218 2. 7226 2. 7235 8 50 2. 7243 2. 7251 2. 7259 2. 7267 2. 7275 2.7284 2.7292 2. 7300 2. 7308 2. 7316 9 2. 7324 2. 7332 2. 7340 2. 7348 2. 7356 2. 7364 2. 7372 2. 7380 2. 7388 2.7396 9 10 2. 7404 2. 7412 2. 7419 2. 7427 2. 7435 2.7443 2.7451 2. 7459 2. 7466 2. 7474 9 20 2. 7482 2. 7490 2. 7497 2. 7505 2. 7513 2.7520 2.7528 2. 7536 2. 7543 2. 7551 9 30 2. 7559 2. 7566 2. 7574 2. 7582 2. 7589 2.7597 2.7604 2. 7612 2. 7619 2. 7627 9 40 2.7634 1 2.7642 2. 7649 2. 7657 2. 7664 2. 7672 ! 2. 7679 2. 7686 2. 7694 2. 7701 9 50 2.7709 2.7716 2. 7723 2. 7731 2. 7738 2. 7745 1 2. 7752 2. 7760 2. 7767 2. 7774 Page 314] APPENDIX V: TABLE IX. \ Logarithms of Small Arcs in Space or Time. Arc. 0" 1" 2" 8" 4" 6" 6" 7" 8" 9" O ' 0" 10° n ' 0" 2. 7782 2. 7789 2. 7796 2.7803 2. 7810 2. 7818 2. 7825 2. 7832 2. 7839 2. 7846 10 10 2.7853 2. 7860 2. 7868 2.7875. 2. 7882 2. 7889 2. 7896 2. 7903 2. 7910 2. 7917 10 20 2. 7924 2. 7931 2. 7938 2. 7945 2. 7952 2. 7959 2. 7966 2. 7973 2. 7980 2. 7987 10 30 2. 7993 2.8000 2. 8007 2. 8014 2. 8021 2. 8028 2.8035 2. 8041 2.8048 2. 8055 10 40 2.80Q2 2. 8069 2. 8075 2. 8082 2. 8089 2.8096 2. 8102 2.8109 2. 8116 2. 8122 10 50 2. 8129 2. 8136 2. 8142 2. 8149 2. 8156 2. 8162 2. 8169 2. 8176 2.8241" 2. 8182 2. 8189 11 2. 8195 2. 8202 2. 8209 2. 8215 2. 8222 2. 8228 2. 8235 2. 8248 2. 8254 11 10 2. 8261 2. 8267 2. 8274 2. 8280 2. 8287 2. 8293 2.8299 2. 8306 2. 8312 2. 8319 11 20 2. 8325 2. 8331 2. 8338 2. 8344 2. 8351 2. 8357 2. 8363 2. 8370 2. 8376 2. 8382 11 30 2. 8388 2. 8395 2. 8401 2. 8407 2. 8414 2. 8420 2.8426 2. 8432 2. 8439 2.8445 11 40 2. 8451 2. 8457 2. 8463 2. 8470 2.8476 2. 8482 2. 8488 2. 8494 2.8500 2. 8506 11 50 2. 8513 2.8519 2. 8525 2. 8531 2. 8537 2. 8543 2. 8549 2. 8555 2. 8561 2. 8567 12 2. 8573 2. 8579 2.8585 2. 8591 2. 8597 2. 8603 2. 8609 2. 8615 ! 2. 8621 2. 8627 12 10 2. 8633 2. 8639 2.8645 2. 8651 2. 8657 2. 8663 2. 8669 2. 8675 2. 8681 2. 8686 12 20 2. 8692 2. 8698 2.8704 2.8710 2. 8716 2. 8722 2. 8727 2. 8733 2. 8739 2. 8745 12 30 2. 8751 2. 8756 2. 8762 2. 8768 2. 8774 2. 8779 2. 8785 2. 8791 2. 8797 2. 8802 12 40 2. 8808 2. 8814 2. 8820 2. 8825 2. 8831 2. 8837 2. 8842 2.8848 2. 8854 2. 8859 12 50 2.8865 2. 8871 2.8876 1 2.8882 2. 8887 2. 8893 2.8899 2.8904 2. 8910 2. 8915 13 2. 8921 2. 8927 2. 8932 2. 8938 2. 8943 2. 8949 2. 8954 2. 8960 2. 8965 2. 8971 13 10 2. 8976 2. 8982 2. 8987 2. 8993 2. 8998 2.9004 2. 9009 2. 9015 2. 9020 2. 9025 13 20 2. 9031 2. 9036 2.9042 2. 9047 2. 9053 2. 9058 2.9063 2. 9069 2. 9074 2. 9079 13 30 2. 9085 2. 9090 2. 9096 2. 9101 2. 9106 2.9112 2.9117 2.9122 2. 9128 2. 9133 13 40 2. 9138 2. 9143 2. 9149 2. 9154 2. 9159 2. 9165 2. 9170 2. 9175 2. 9180 2. 9186 13 50 2. 9191 2. 9196 2.9201 2.9206 i 2.9212 2.9217 2. 9222 2. 9227 2. 9232 ! 2. 9238 | 14 2. 9243 2. 9248 2.9253 2.9258 ; 2.9263 2. 9269 2. 9274 2. 9279 2. 9284 2. 9289 14 10 2. 9294 2. 9299 2.9304 : 2.9309 2.9315 2. 9320 2. 9325 2. 9330 2. 9335 2. 9340 14 20 2. 9345 2. 9350 2. 9355 2.9360 ' 2.9365 2. 9370 2. 9375 2. 9380 2. 9385 2. 9390 14 30 2. 9.395 2. 9400 2. 9405 2.9410 2.9415 2. 9420 2. 9425 2. 9430 2.9435 2. 9440 14 40 2. 9445 2. 9450 2. 9455 2.9460 2.9465 2. 9469 2. 9474 2. 9479 2. 9484 2. 9489 14 50 2. 9494 2. 9499 2. 9504 2.9509 2.9513 2. 9518 2. 9523 2. 9528 2. 9533 ! 2. 9538 15 2. 9542 2. 9547 2. 9552 2.9557 j 2.9562 2. 9566 2. 9571 2. 9576 2. 9581 2. 9586 15 10 2. 9590 2. 9595 2.9600 1 2.9605 i 2.9609 2. 9614 2. 9619 2. 9624 2. 9628 2. 9633 15 20 2. 9638 2. 9643 2.9647 2.9652 1 2.9657 2. 9661 2. 9666 2. 9671 2. 9675 2. 9680 15 30 2. 9685 2. 9689 2.9694 2.9699 2.9703 2. 9708 2.9713 2.9717 2. 9722 2. 9727 15 40 2. 9731 2. 9736 2. 9741 2. 9745 2. 9750 2. 9754 2. 9759 2. 9763 2. 9768 2. 9773 15 50 2. 9777 2. 9823 2. 9782 2. 9786 2.9791 2.9795 2. 9800 2. 9805 2. 9809 2. 9814 2.9818 16 2. 9827 2. 9832 2.9836 2.9841 2. 9845 2. 9850 2. 9854 2. 9859 2. 9863 16 10 2. 9868 2. 9872 2. 9877 2.9881 2.9886 2. 9890 2. 9894 2. 9899 2. 9903 2. 9908 16 20 2. 9912 2. 9917 2. 9921 2.9926 2.9930 2. 9934 2. 9939 2. 9943 2. 9948 2. 9952 16 30 2. 9956 2. 9961 2. 9965 2.9969 2.9974 2. 9978 2. 9983 2. 9987 2. 9991 2. 9996 16 40 3. 0000 3.0004 3. 0009 3. 0013 3. 0017 3. 0022 3. 0026 3.0030 3. 0035 3.0039 16 50 3.0043 3.0048 3. 0052 3. 0056 3. 0060 3. 0065 3. 0069 3. 0073 3. 0077 3. 0082 17 3. 0086 3. 0090 3.0095 3. 0099 3. 0103 3. 0107 3.0111 3.0116 3.0120 3. 0124 17 10 3. 0128 3. 0133 3. 0137 3.0141 , 3.0145 3. 0149 3. 0154 3.0158 3. 0162 3. 0166 17 20 3. 0170 3. 0175 3. 0179 3.0183 1 3.0187 3. 0191 3. 0195 3. 0199 3. 0204 3. 0208 17 30 3. 0212 3. 0216 3. 0220 3. 0224 3. 0228 3. 0233 3. 0237 3. 0241 3. 0245 3. 0249 17 40 3. 0253 3. 0257 3. 0261 3.0265 i 3.0269 3. 0273 3. 0278 3. 0282 3. 0286 3. 0290 17 50 3. 0294 3. 0298 3. 0302 3. 0342 3. 0306 3. 0346 3. 0310 3. 0314 3. 0318 3. 0322 3. 0326 3. 0366 3. 0330 18 3. 0334 3. 0338 3. 0350 3. 0354 3. 0358 3. 0362 3. 0370 18 10 3. 0374 3. 0378 3. 0382 3.0386 i 3.0390 3. 0394 3. 0398 3. 0402 3. 0406 3.0410 18 20 3. 0414 3. 0418 3. 0422 3. 0426 3. 0430 3. 0434 3. 0438 3. 0441 3. 0445 3.0449 18 30 3. 0453 3. 0457 3. 0461 3. 0465 3. 0469 3. 0473 3. 0477 3. 0481 3. 0484 3. 0488 18 40 3. 0492 3. 0496 3. 0500 3.0504 3.0508 3. 0512 3. 0515 3. 0519 3. 0523 3. 0527 18 50 3. 0531 3. 0535 3. 0538 3. 0542 3. 0546 3. 0550 3. 0554 3. 0558 3. 0561 3. 0565 19 3. 0569 3. 0573 3. 0577 3. 0580 3. 0584 3. 0588 3. 0592 3.0596 3.0599 3. 0603 19 10 3. 0607 3. 0611 3. 0615 3. 0618 3. 0622 3. 0626 3. 0630 3. 0633 3. 0637 3. 0641 19 20 3. 0645 3. 0648 3. 0652 3. 0656 3. 0660 3. 0663 3. 0667 3. 0671 3.0674 3. 0678 19 30 3. 0682 3. 0686 3. 0689 3. 0693 3. 0697 3.0700 3. 0704 3. 0708 3. 0711 3. 0715 19 40 3.0719 3. 0722 3. 0726 3. 0730 3. 0734 3. 0737 3. 0741 3. 0745 3. 0748 3. 0752 19 50 3. 0755 3. 0759 3. 0763 3. 0766 3. 0770 3. 0774 3. 0777 3. 0781 3. 0785 3. 0788 APPENDIX V: TA.BLE IX. [Page 315 Logarithms of Small Arcs in Space or Time. Arc. 0" 1" 2" 8" 4" 5" 6" 7" 8" 9" O ' 0" 20" 0' 3. 0792 3. 0795 3.0799 3.0803 3.0806 3. 0810 3. 0813 3. 0817 3. 0821 3. 0824 20 10 3. 0828 3. 0831 3.0835 3.0839 3.0842 3. 0846 3. 0849 3. 0853 3. 0856 3. 0860 20 20 3. 0864 3. 0867 3.0871 3.0874 3. 0878 3. 0881 3. 0885 3. 0888 3. 0892 3. 0896 20 30 3. 0899 3. 0903 3.0906 3.0910 3.0913 i 3.0917 3. 0920 3. 0924 3. 0927 3. 0931 20 40 3. 0934 3. 0938 3.0941 3.0945 3.0948 j 3.0952 3. 0955 3. 0959 3. 0962 3. 0966 20 50 3. 0969 3. 0973 3.0976 3.0980 3.0983 1 3.0986 3. 0990 3. 0993 3. 0997 3. 1000 21 3. 1004 3. 1007 3.1011 : 3.1014 3. 1017 3. 1021 3. 1024 3. 1028 3. 1031 3. 1035 21 10 3. 1038 3. 1041 3.1045 ' 3.1048 3. 1052 3. 1055 3. 1059 3. 1062 3. 1065 3. 1069 21 20 3. 1072 3. 1075 3. 1079 ■ 3. 1082 3. 1086 3. 1089 3. 1092 3. 1096 3. 1099 3. 1103 21 30 3. 1106 3.1109 3. 1113 3.1116 3. 1119 3. 1123 3. 1126 3. 1129 3. 1133 3. 1136 21 40 3. 1139 3. 1143 3. 1146 3. 1149 3. 1153 3. 1156 3.1159 3. 1163 3. 1166 3. 1169 21 50 3. 1173 3. 1176 3. 1179 3.1183 3. 1186 1 3. 1189 3. 1193 . 3.1196 3. 1199 3. 1202 22 3. 1206 3. 1209 3.1212 3. 1216 3. 1219 3. 1222 3. 1225 3. 1229 3. 1232 3. 1235 22 10 3. 1239 3.1242 3. 1245 3. 1248 3.1252 3.1255 3. 1258 3. 1261 3. 1265 3. 1268 22 20 3. 1271 3. 1274 3. 1278 3. 1281 3. 1284 3. 1287 3.1290 3. 1294 3. 1297 3.1300 22 30 3. 1303 3. 1307 3. 1310 3. 1313 3. 1316 3. 1319 3. 1323 3. 1326 3. 1329 3. 1332 22 40 3. 1335 3. 1339 3. 1342 3. 1345 3. 1348 3. 1351 3. 1355 3.1358 3. 1361 3. 1364 22 50 3. 1367 3. 1370 3. 1374 3. 1377 3.1380 3. 1383 3. 1.386 3. 1389 3. 1392 3. 1396 23 3. 1399 3. 1402 3. 1405 3. 1408 3. 1411 3.1414 3. 1418 3. 1421 3. 1424 3. 1427 23 10 3. 1430 3. 1433 3. 1436 3.1440 3. 1443 3. 1446 3. 1449 3. 1452 3. 1455 3. 1458 23 20 3. 1461 3.1464 3. 1467 3. 1471 3. 1474 3. 1477 3. 1480 3. 1483 3. 1486 3. 1489 23 30 3. 1492 3. 1495 3. 1498 3. 1501 3. 1504 3. 1508 3. 1511 3.1M4 3. 1517 3. 1520 23 40 3. 1523 3. 1526 3. 1529 3. 1532 3. 1535 3. 1538 3. 1541 3. 1544 3. 1547 3. 1550 2a 50 3. 1553 3. 1556 3. 1559 3. 1562 3. 1565 3. 1569 3. 1572 3. 1575 3.1578 3.1581 24 3. 1584 3. 1587 3. 1590 3.1593 3.1596 3. 1599 3. 1602 3. 1605 3. 1608 1 3. 1611 24 10 3. 1614 3.1617 3. 1620 3.1623 3.1626 3. 1629 3. 1632 3. 1635 3. 1638 3. 1641 24 20 3. 1644 3. 1647 i 3. 1649 3.1652 1 3.1655 3. 1658 3. 1661 3. 1664 3. 1667 ! 3. 1670 24 30 3. 1673 3.1676 3.1679 3. 1682 : 3. 1685 3. 1688 3. 1691 3. 1694 3. 1697 ! 3. 1700 24 40 3. 1703 3. 1706 i 3. 1708 3.1711 i 3.1714 3. 1717 3. 1720 3. 1723 3. 1726 ! 3. 1729 24 50 3. 1732 3.1735 3.1738 3. 1741 3. 1744 3. 1746 3. 1749 3. 1752 3. 17.55 3. 1758 25 3.1761 3. 1764 [ 3. 1767 3. 1770 3. 1772 3. 1775 3. 1778 3. 1781 3. 1784 3. 1787 25 10 3. 1790 3. 1793 I 3. 1796 3. 1798 3. 1801 3. 1804 3. 1807 3. 1810 3. 1813 3.1816 25 20 3. 1818 3.1821 i 3.1824 3. 1827 3. 1830 3. 1833 3. 1836 3. 1838 .3. 1841 3.1844 25 30 3. 1847 3. 1850 1 3. 1853 3. 1855 3. 1858 3. 1861 3.1864 3. 1867 3. 1870 1 3. 1872 25 40 3. 1875 3. 1878 3. 1881 3. 1884 3. 1886 3. 1889 3. 1892 3. 1895 3. 1898 i 3. 1901 25 50 3. 1903 3.1906 3. 1909 3. 1912 3. 1915 3.1917 3. 1920 3. 1923 3. 1926 ! 3. 1928 26 3. 1931 3. 1934 3. 1937 3.1940 3.1942 3.1945 3. 1948 3. 1951 3. 19.53 3. 1956 26 10 3. 1959 3. 1962 3. 1965 3.1967 3.1970 3. 1973 3. 1976 3. 1978 3. 1981 3. 1984 26 20 3. 1987 3. 1989 3. 1992 3.1995 3.1998 3. 2000 3. 2003 3. 2006 3. 2009 3. 2011 26 30 3. 2014 3. 2017 3. 2019 3.2022 3.2025 3. 2028 3. 2030 3. 2033 3. 2036 3. 2038 26 40 3. 2041 3.2044 1 3.2047 3.2049 3.2052 3. 2055 3. 2057 3. 2060 3. 2063 3. 2066 26 50 3. 2068 3.2071 3.2074 3.2076 ! 3.2079 3. 2082 3. 2084 3. 2087 3. 2090 3. 2092 27 3. 2095 3.2098 3.2101 3.2103 j 3.2106 3. 2109 3.2111 3. 2114 3.2117 3.2119 27 10 3. 2122 3.2125 ; 3.2127 3.2130 1 3.2133 3. 2135 3. 2138 3. 2140 3. 2143 3. 2146 27 20 3. 2148 3.2151 i 3.2154 3.2156 3.2159 3. 2162 3.2164 3. 2167 .3. 2170 3. 2172 27 30 3. 2175 3.2177 1 3.2180 3.2183 3. 2185 3. 2188 .3. 2191 3. 2193 3. 2196 3. 2198 . 27 40 3. 2201 3.2204 1 3.2206 3. 2209 3. 2212 3. 2214 3.2217 3. 2219 3. 2222 3. 2225 27 50 3. 2227 3. 2230 3. 2232 3. 2235 3. 2238 3.2240 3. 2243 3. 2269 3. 2245 3. 2248 3. 2250 28 3. 2253 3. 2256 3. 2258 3. 2261 3. 2263 3. 2266 3. 2271 3. 2274 3. 2276 28 10 3. 2279 3. 2281 3. 2284 3. 2287 3. 2289 3. 2292 3. 2294 3. 2297 3. 2299 3. 2302 28 20 3.2304 3. 2307 3. 2310 3. 2312 3. 2315 3.2317 3. 2320 3. 2322 3. 2325 3. 2327 28 30 3. 2330 3. 2333 3. 2335 3. 2338 3.2340 3. 2343 3. 2345 3. 2348 3. 23.50 3. 2353 28 40 3. 2355 3. 2358 3. 2360 3. 2363 3. 2365 3. 2368 3. 2370 3. 2373 3. 2375 3. 2378 28 50 3. 2380 3. 2383 3. 2385 3. 2388 3.2390 I .3.2393 3. 2395 3. 2398 3. 2400 3.2425 3. 2403 29 3. 2405 3. 2408 3. 2410 3. 2413 3.2415 1 3.2418 3. 2420 3. 2423 3. 2428 29 10 3. 2430 3. 2433 3.2435 3. 2438 3. 2440 3.2443 3. 2445 3. 2448 3. 2450 3. 2453 29 20 3. 2455 3. 2458 3.2460 3. 2463 3. 2465 3. 2467 3. 2470 3. 2472 3. 2475 3. 2477 29 30 3. 2480 3. 2482 3. 2485 3. 2487 3. 2490 3. 2492 3. 2494 3. 2497 3. 2499 3. 2502 29 40 3.2504 3. 2507 3. 2509 3. 2512 3. 2514 3. 2516 3. 2519 3. 2521 3. 2524 3. 2526 29 50 3. 2529 3. 2531 3. 2533 3. 2536 3. 2538 3. 2.541 3. 2.543 3. 2545 3.2548 3. 2550 Page 316J APPENDIX V: TABLE IX. Logarithms of Small Arcs in Space or Time. Arc. «" 1" 2" 8" 4" 5" 6" 7" 8" 1 a" o / 0" 30™ II 0» 3.2553 3.2555 3.2558 3.2560 3. 2562 .3.2565 ' 3.2567 3. 2570 3. 2572 3. 2574 30 10 20 3. 2577 3. 2579 3. 2582 3. 2584 3. 2586 .3.2589 3.2591 3. 2594 3. 2,596 ' 3. 2598 30 3. 2601 3. 2603 3.2605 3. 2608 3. 2610 3.2613 1 3.2615 3.2617 3. 2620 3. 2622 30 30 3. 2625 3. 2627 3. 2629 3. 2632 3. 2634 3.2636 : 3.2639 3. 2641 3. 2643 3. 2646 30 40 3. 2648 < 3. 2651 3. 2653 3. 2655 3. 2658 3.2660 ; 3.2662 3. 2665 3. 2667 3. 2669 30 50 3. 2672 3. 2674 3. 2676 3. 2679 3. 2681 3.2683 ; 3.2686 3. 2688 3. 2690 1 3. 2693 31 3. 2695 3. 2697 3.2700 3.2702 3. 2704 j 3. 2707 3. 2709 3.2711 3.2714; 3.2716 31 10 3.2718 3. 2721 3. 2723 3. 2725 3. 2728 3. 27.30 3. 27.32 3. 2735 3. 2737 : 3. 2739 31 20 3. 2742 3. 2744 3. 2746 3. 2749 3.2751 3.2753 3. 2755 3. 2758 3. 2760 3. 2762 31 30 3. 2765 3. 2767 3. 2769 3. 2772 3.2774 3.2776 3. 2778 3. 2781 3. 2783 3. 2785 31 40 3. 2788 3. 2790 3. 2792 3. 2794 3.2797 i 3.2799 3. 2801 3. 2804 3. 2806 3. 2808 31 50 3. 2810 3. 2813 3.2835 3.2815 \ 3.2817 3.2838 ; 3.2840 3. 2819 1 3. 2822 3. 2824 3. 2826 3.2828 3.2831 | 32 3. 2833 3.2842 ' 3.2844 3. 2847 .3:2849 3. 2851 3. 2853 32 10 3. 2856 3. 2858 .3.2860 1 3.2862 3.2865 .3.2867 3.2869 3. 2871 3. 2874 3. 2876 32 20 3. 2878 3. 2880 3. 2882 3. 2885 3.2887 1 3.2889 3. 2891 3. 2894 3. 2896 3. 2898 32 30 3.2900 3. 2903 3. 2905 3. 2907 .3.2909 3.2911 3. 2914 3. 2916 3. 2918 3. 2920 32 40 3. 2923 3. 2925 3. 2927 3. 2929 3. 2931 3. 2934 3. 2936 3. 2938 3. 2940 3. 2942 32 50 3. 2945 3. 2947 3. 2949 3. 2951 3. 2953 3. 2956 3. 2958 3. 2960 3. 2982 3. 2962 \ 3. 2964 | 33 3. 2967" 3. 2969 3.2971 ! 3.2973 3.2975 i 3.2978 3. 2980 3.2984 3. 2986 33 10 3. 2989 3. 2991 3.2993 j 3.2995 3. 2997 3.2999 3.3002 3. 3004 3. 3006 3. 3008 33 20 3. 3010 3. 3012 3.3015 3.3017 3. 3019 3.3021 1 .3.3023 3. 3025 3. 3028 3. 30,30 33 30 3.3032 3. 3034 3.3036 ' 3.3038 3. 3041 3.3043 ' 3.3045 3. 3047 3. 3049 3. 3051 33 40 3. 3054 3. 3056 3.3058 3.3060 3. 3062 3.3064 3. .3066 3. 3069 3. 3071 3. 3073 33 50 3. 3075 3. 3077 3.3079 ' .3.3081 3. 3084 3.3086 3.3088 3. 3090 3.3092 3,3094 | 34 3. 3096 3. 3098 3.3101 3.3103 3. 3105 3.3107 3.3109 3.3111 3. 3113 3.3115 34 10 3. 3118 3. 3120 .3.3122 ! 3.3124 3.3126 3.3128 3.3130 3. 3132 3. 3134 3.3137 34 20 3. 3139 3. 3141 3.3143 1 3.3145 3. 3147 .3.3149 3.3151 .3.31,53 3. 3156 3. 31.58 34 30 3. 3160 3. 3162 .3.3164 j 3.3166 .3. 3168 • 3.3170 3.3172 3.3174 .3.3176 ,3.3179 34 40 3.3181 3.3183 3.3185 ! 3.3187 3. 3189 3. .3191 ' 3.3193 3. 3195 3. 3197 ! .3. 3199 34 50 3. 3201 3. 3204 3.3206 i 3.3208 3. 3210 3. 3230 3. 3212 3. 3233 3. 3214 3. 3216 3. 3218 ! 3. 3220 35 3". 3222 3. 3224 3. 3226 3. 3228 3. 3235 3. 3237 3. .3239 ! 3. 3241 35 10 3. 3243 3. 3245 3. 3247 3. 3249 3. 3251 .3.3253 ' 3.3255 3. 3257 3. 32,59 3. 3261 35 20 3. 3263 3. 3265 3. 3267 3. 3269 3. 3272 3.3274 i 3.3276 3. 3278 3. 3280 3. 3282 35 30 3. 3284 3. 3286 ■ 3. 3288 3. 3290 3. 3292 3.3294 3.3296 3. 3298 3. 3300 ! 3. 3302 35 40 3. 3304 3. 3306 3. 3308 3. 3310 3.3,312 3.3314 \ 3. .331 6 3. .3318 3. 3320 1 3. 3322 35 50 3. 3324 3. 3326 3. 3328 3. 3330 3. 3332 3.3334 : 3.3336 3.3355 3.3357' 3. 3339 3. 33,59 3.3.341 3. .3343 3. 3361 3. 3363 36 3. 3345 3. 3347 "3: 3349 3. 3351 3.3353' 36 10 3. 3365 3. 3367 3. 3.369 3. 3371 3. 3373 3. 3375 3. 3377 3. 3379 3. 3381 j 3. 3383 36 20 3. 3385 3. 3387 3. 3389 3. 3391 3. 3393 3.3.395 ! 3. .3397 3. .3398 3. 3400 : 3. 3402 36 30 3. 3404 3. 3406 3. 3408 3. 3410 3.3412 1 .3.3414 | 3.3416 3. 3418 3. 3420 I 3. 3422 36 40 3. 3424 3. 3426 3. 3428 3. 34.30 3.3432 3. .3434 .3.34.36 3. 3438 3. 3440 3. 3442 36 50 3. 3444 3. 3446 3.3448 3.3450 3.3452 ' 3.3454 ! 3.3456 3. 3458 3. 3460 ' 3. 3462 37 3. 3464 3. 3465 3.3467 3. 3469 3. .3471 ! 3.3473 3. .3475 3. 3477 3. 3479 3. 3481 37 10 3. 3483 3. 3485 3. 3487 3. 3489 3. 3491 3. 3493 3. 3495 3. M97 3. 3499 : 3. 3.501 37 20 3. 3502 3. 3504 3. 3506 3. 3508 3. 3510 3. ,3512 3. 3514 3. 3516 3. ,3518 1 3. 3.520 37 30 3. 3522 3. 3524 3. 3526 3. 3528 3. 35.30 .3.35.31 3.3.533 3. 3535 3. 3.537 1 3. 3.5.39 37 40 3. 3541 3. 3543 3. 3545 3. 3547 3. 3549 3. 3.551 3. 3553 3. ,3555 3. 3556 3. 3,558 37 50 3. 3560 3. 3562 3. 3564 3.3566 3. 3568 3. 3570 3. 3572 3. 3574 3. 3576 3. 3577 38 3. 3579 3.3581 3. 3583 3. 3585 3. 3587 3. .3589 3. 3591 3. 3593 3. 3595 3. 3596 38 10 3. 3598 3. 3600 3. 3602 3.3604 3. 3606 3. 3608 3. .3610 3. 3612 3. .3614 3. .3615 38 20 3. 3617 3.3619 3. 3621 3. 3623 3. .3625 3. ,3627 3. 3629 3. 3630 3. 3632 3. 3634 38 30 3. 3636 3. 3638 3. 3640 3. 3642 3. 3644 3. 3646 3. 3647 3. 3649 3. 3651 3. 3653 38 40 3. 3655 3. 3657 3. 3659 3. 3660 3. 3662 3. 3664 3. .3666 3. ,3668 3. .3670 3. 3672 38 50 3. 3674 3. 3675 3. 3677 3. 3679 3. 3681 3. 3683 3. ,3685 3. .3687 "3.:3705 3. 3688 3. 3690 39 3. 3692 3. 3694 3. 3696 3. 3698 3. 3700 3. 3701 3. 3703 3. 3707 3. 3709 39 10 3.3711 3. 3713 3. 3714 3. 3716 3. 3718 3. 3720 3. 3722 3. 3724 3. 3725 3. 3727 39 20 3. 3729 3. 3731 3. 3733 3. 37.35 3. 3736 3. 3738 3. 3740 3. 3742 3.3744 3. 3746 39 30 3. 3747 3.3749 3. 3751 3. 3753 3. 3755 3. 3757 3. 37.58 3. 3760 3. 3762 3. 3764 39 40 3. 3766 3. 3768 3. 3769 3. 3771 3. 3773 3. 3775 3. 3777 3. 3779 3. 3780 3. 3782 39 50 3. 3784 3. 3786 3. 3788 3. 3789 3. 3791 3. 3793 3. 3795 3. 3797 3. 3798 ■ 3. 3800 1 APPENDIX V: TABLE IX. [Page 317 Logarithms of Small Arcs in Space or Time. Arc. 0" 1" 2" 8" 4" 5" ' 6" 7" 8" S" c / Qh 40.T II 0» 3. 3802 3. 3804 3. 3806 3. 3808 3. 3809 3. 3811 3. 3813 3. 3815 j 3.3817^ 3.3818 40 10 3. 3820 3. 3822 3. 3824 3. 3826 3. 3827 3. 3829 3. 3831 3. 3833 3. 3835 1 3. 3836 40 20 3. 3838 3. 3840 3. 3842 3. 3844 3. 3845 3. 3847 3. 3849 3. 3851 3.3852 3.3854 40 30 3. 3856 3. 3858 3. 3860 3. 3861 3. .3863 3. 3865 3. 3867 3. 3869 3.3870 3.3872 40 40 3. 3874 3. 3876 3. 3877 3. 3879 3. 3881 3. 3883 3. 3885 3. 3886 3. 3888 1 3. 3890 40 50 3. 3892 3. 3893 3. 3895 3. 3897 3. 3899 3. 3901 3. 3902 3. 3904 3. 3906 3. 3908 41 3. 3909 3.3911 3. 3913 3. 3915 3. 3916 3.3918 3.3920 3. 3922 3. 3923 3. 3925 41 10 3. 3927 3. 3929 3. 3930 3. 3932 3. 3934 3.3936 3.3938 3. 3939 3. 3941 3. 3943 41 20 3. 3945 3. 3946 3. 3948 3. 3950 3. 3952 3.3953 3.3955 3. 3957 3. 3959 3. 3960 41 30 3. 3962 3. 3964 3. 3965 3. 3967 3. 3969 3. 3971 3. 3972 3. 3974 3. 3976 3. 3978 41 40 3. 3979 3. 3981 3. 3983 3. 3985 3. 3986 3. 3988 3. 3990 3. 3992 3. 3993 3. 3995 41 50 3. 3997 3. 4014 3. 3998 3. 4016 3.4000 3. 4017 3.4002 3. 4019 3. 4004 3. 4021 3. 4005 3. 4023 3. 4007 3. 4024 3. 4009 3.4011 3. 4028 3.4012 42 3. 4026 3. 4029 42 10 3. 4031 3. 4033 3. 4035 3.4036 3.4038 3. 4040 3. 4041 3. 4043 3. 4045 1 3. 4047 42 20 3. 4048 3. 4050 3. 4052 3. 4053 3. 4055 3. 4057 3. 4059 3. 4060 3. 4062 1 3. 4064 42 30 3. 4065 3. 4067 3. 4069 3. 4071 3. 4072 3. 4074 3. 4076 3. 4077 3. 4079 i 3. 4081 42 40 3. 4082 3. 4084 3. 4086 3. 4087 3. 4089 3. 4091 3. 4093 3. 4094 3. 4096 3. 4098 42 50 3. 4099 3.4101 3. 4103 3. 4104 3. 4106 3. 4108 3. 4109 "3. 4126 3.4111 3.4113 3.4115 43 3.4116 3.4118 3. 4120 3.4121 3.4123 ! 3.4125 3. 4128 3. 4130 3. 4131 43 10 3. 4133 3. 4135 3.4136 3. 4138 3. 4140 3. 4141 3. 4143 3. 4145 3. 4146 3. 4148 43 20 3. 4150 3. 4151 3. 4153 3. 4155 3. 4156 3. 4158 3. 4160 3. 4161 3. 4163 3. 4165 43 30 3. 4166 3. 4168 3. 4170 3.4171 3.4173 3.4175 3.4176 3.4178 3. 4180 3.4181 43 40 3. 4183 3. 4185 3. 4186 3. 4188 3.4190 3.4191 3. 4193 3. 4195 3. 4196 3. 4198 43 50 3. 4200 3. 4201 3. 4203 3. 4205 3. 4206 3. 4208 3. 4224 3. 4209 3.4226 3. 4211 3. 4228 3. 4213 3. 4214 44 3. 4216 3.4218 3.4219 3. 4221 3. 4223 3. 4229 3. 4231 44 10 3. 4232 3. 4234 3. 4236 3. 4237 3.4239 1 3.4241 3. 4242 3. 4244 3. 4246 3. 4247 44 20 3. 4249 3. 4250 3. 4252 3. 4254 3. 4255 3. 4257 3. 4259 3. 4260 3. 4262 3. 4263 44 30 3. 4265 3. 4267 3. 4268 3. 4270 3. 4272 3. 4273 3. 4275 3. 4276 3. 4278 3. 4280 44 40 3. 4281 3. 4283 3. 4285 3. 4286 3. 4288 3. 4289 3. 4291 3. 4293 3. 4294 3. 4296 44 45 50 3. 4298 3. 4314 3. 4299 3. 4315 3. 4301 3. 4302 3. 4318 3. 4304 3. 4320 3. 4306 3.4322 3. 4307 3. 4309 3. 4310 3. 4326" 3.4312 3. 4328 3.4317 3. 4323 3. 4325 45 10 3. 4330 3. 4331 3. 4333 3. 4334 3. 4336 3. 4338 3. 4339 3. 4341 3. 4342 3. 4344 45 20 3. 4346 3. 4347 3. 4349 3. 4350 3. 4352 3. 4354 3. 4355 3. 4357 3. 4358 3. 4360 45 30 3. 4362 3. 4363 3. 4365 3. 4366 3. 4368 3. 4370 3. 4371 3. 4373 3. 4374 3. 4376 45 .40 3. 4378 3. 4379 3. 4381 3. 4382 3. 4384 3. 4385 3. 4387 3. 4389 3. 4390 i .3. 4392 | 45 46 50 3. 4393 3. 4395 3.4411 3. 4396 3. 4412' 3. 4398 3.4414 3.4400 3. 4415 3. 4401 3. 4403 3.4417 1 3.4419 3. 4404 3. 4406 3. 4408 3. 4409 3. 4420 3. 4422 3. 4423 46 10 3. 4425 3. 442(> 3.4428 3. 4429 3. 4431 3.4433 1 3.4434 3.4436 3. 4437 3. 4439 46 20 3. 4440 3. 4442 3.4444 3. 4445 3. 4447 3.4448 i 3.4450 3. 4451 3. 4453 3. 4454 46 30 3. 4456 3. 4458 3. 4459 3. 4461 3. 4462 3.4464 .3.4465 3.4467 3. 4468 3. 4470 46 40 3. 4472 3. 4473 3. 4475 3. 4476 3. 4478 3.4479 3.4481 3. 4482 3. 4484 3. 4486 46 50 3. 4487 3. 4489 3. 4490 3. 4492 3. 4493 3.4495 3.4496 3. 4498 3. 4499 3. 4501 47 3. 4502 3. 4504 3. 4506 3. 4507 3. 4509 3.4510 3. 4512 3.4513 3. 4515 3. 4516 47 10 3. 4518 3. 4519 3. 4521 3. 4522 3. 4524 3. 4526 3. 4527 3. 4529 3. 4530 3. 45.32 47 20 3. 4533 3. 4535 3. 4536 3. 4538 3. 4539 3. 4541 3. 4542 3. 4544 3.4545 3. 4547 47 30 3. 4548 3. 4550 3. 4551 3. 4553 3. 4555 3. 4556 3. 4558 3.4559 3. 4561 3. 4562 47 40 3. 4564 3. 4565 3. 4567 3. 4568 3. 4570 3. 4571 3. 4573 3. 4574 3.4576 3. 4577 47 50 3. 4579 3. 4580 3. 4582 3. 4583 3.4585 1 3.4586 3. 4588 3. 4589 3. 4591 3. 4592 48 3. 4594 3. 4595 3. 4597 3. 4598 3. 4600 3. 4601 3. 4603 3. 4604 3. 4606 i 3. 4607 | 48 10 3. 4609 3. 4610 3. 4612 3. 4613 3. 4615 3.4616 3. 4618 3. 4619 3. 4621 3. 4622 48 20 3. 4624 3. 4625 3. 4627 3. 4628 3. 4630 3. 4631 3. 4633 3. 4634 3. 4636 3. 4637 48 30 3. 4639 3. 4640 3. 4642 3. 4643 3. 4645 3. 464(5 3. 4648 3.4649 3. 4651 3. 4652 48 40 3. 4654 3. 4655 3. 4657 3. 4658 3. 4660 3. 4661 3. 4663 3.4664 3. 4666 3. 4667 48 50 3. 4669 3. 4670 3. 4672 3. 4673 3. 4675 3.4676 1 3.4678 3. 4679 3. 4681 3. 4682 49 3. 4683 3. 4685 3. 4686 3. 4688 3. 4689 3. 4691 3. 4692 3. 4694 3.4695 3. 4697 49 10 3. 4698 3. 4700 3. 4701 3.4703 3. 4704 3. 4706 3. 4707 3.4709 3. 4710 3.4711 49 20 3. 4713 3. 4714 3. 4716 3.4717 3. 4719 3. 4720 3. 4722 3. 4723 3. 4725 3. 4726 49 30 3. 4728 3. 4729 3. 4730 3. 4732 3. 4733 3. 4735 3. 4736 3. 4738 3. 4739 3. 4741 49 40 3. 4742 3. 4744 3. 4745 3. 4747 3. 4748 3. 4749 3. 4751 3. 4752 3. 4754 3. 4755 49 50 3. 4757 3. 4758 3. 4760 3. 4761 3. 4763 3. 4764 3. 4765 3. 4767 3. 4768 3. 4770 Page 318] APPENDIX V: TABLE IX. Logarithms of Small Arcs in Space or Time. 7" Arc. 0" 1" 2" 8" *" 5" 6" 8" 9" O 1 0" 50" 0» 3. 4771 3. 4773 3. 4774 3. 4776 3. 4777 3. 4778 3. 4780 1 3. 4781 ' 3. 4783 3. 4784 50 10 3. 4786 3. 4787 3. 4789 3. 4790 3. 4791 3. 4793 3. 4794 3. 4796 i 3. 4797 3. 4799 50 20 3. 4800 3. 4802 3. 4803 3.4804 3. 4806 3. 4807 3. 4809 3. 4810 3. 4812 3. 4813 50 30 3. 4814 3. 4816 3.4817 3. 4819 3. 4820 3. 4822 3. 4823 3. 4824 8. 4826 3. 4827 50 40 3. 4829 ► 3. 4830 3. 4832 3. 4833 3. 4834 3. 4836 3. 4837 3. 4839 8. 4840 3. 4842 50 50 3. 4843 3. 4844 3. 4846 3. 4847 3.4849 3. 4850 3. 4852 3. 4858 3. 4854 3. 4856 51 3.4857 3. 4859 3.4860 3. 4861 3. 4863 3. 4864 3. 4866 3. 4667 3. 4869 8. 4870 51 10 3. 4871 3. 4873 3. 4874 3. 4876 3. 4877 3. 4878 3. 4880 8. 4881 3. 4883 8. 4884 51 20 3. 4886 3. 4887 3. 4888 3.4890 3. 4891 3. 4893 3. 4894 8. 4895 3. 4897 8. 4898 51 30 3. 4900 3. 4901 3. 4902 3. 4904 3. 4905 3. 4907 3. 4908 8. 4909 3. 4911 8. 4912 51 40 3. 4914 3. 4915 3. 4916 3. 4918 3.4919 3. 4921 3. 4922 3. 4923 3. 4925 3. 4926 51 50 3. 4928 3. 4929 3. 4930 3. 4932 3. 4933 3. 4935 3. 4936 3. 4987 3. 4939 3. 4940 52 3. 4942 3. 4943 3. 4944 3. 4946 3. 4947 3. 4949 3. 4950 8. 4951 3. 4953 8. 4954 52 10 3. 4955 3. 4957 3. 4958 3. 4960 3. 4961 3. 4962 3. 4964 3. 4965 3. 4967 8.4968 .52 20 3. 4969 3. 4971 3. 4972 3. 4973 3. 4975 3. 4976 3. 4978 3. 4979 3. 4980 8. 4982 52 30 3. 4983 3. 4984 3. 4986 3.4987 1 3.4989 3. 4990 3. 4991 3. 4998 3. 4994 8. 4995 52 40 3.4997 3. 4998 3. 5000 3.5001 ! 3.5002 3. 5004 3. 5005 3. 5006 3. 5008 8. 5009 52 50 3.5011 3. 5012 3. 5013 3. 5015 3. 5016 3. 5030 3. 5017 3.5031 3. 5019 3.5032 3. 5020 3.5034 3. 5022 3.5035 8. 5023 53 3. 5024 3. 5026 3. 5027 3. 5028 8. 5037 53 10 3. 5038 3. 5039 3.5041 3. 5042 3. 5043 3. 5045 3. 5046 3. 5047 3. 5049 8. 5050 53 20 3. 5051 3. 5053 3. 5054 3. 5056 3. 5057 3. 5058 3. 5060 3.5061 13.5062 3. 5064 53 30 3. 5065 3. 5066 3. 5068 3. 5069 3. 5070 3. 5072 3. 5073 3. 5075 3. 5076 8. 5077 53 40 3. 5079 3. 5080 3.5081 3. 5083 3. 5084 3. 5085 3. 5087 3. 5088 8. 5089 8. 5091 53 50 3. 5092 3. 5093 3. 5095 3. 5096 3. 5097 3. 5099 3. 5100 3. 5101 3.5103 8. 5104 54 3. 5105 3. 5107 3. 5108 3. 5109 3.5111 3.5112 3.5113 3.5115 5.5116 8.5117 54 10 3.5119 3.5120 3.5122 3.5123 3. 5124 3. 5126 3. 5127 3.5128 8.5180 8. 5131 54 20 3. 5132 3. 5134 3.5135 3. 5136 3. 5138 3. 5139 3. 5140 3.5141 8.5143 3. 5144 54 30 3. 5145 3. 5147 3.5148 3. 5149 3. 5151 3. 5152 3. 5153 3. 5155 3.5156 8.5157 54 40 3. 5159 3. 5160 3. 5161 3.5163 3. 5164 3. 5165 3. 5167 3. 5168 3. 5169 3.5171 54 50 3.5172 3. 5173 3. 5175 3.5176 3.5177 3. 5179 3. 5180 3.5181 3. 5183 3.5184 55 3. 5185 3. 5186 3. 5188 3. 5189 3. 5190 3. 5192 3. 5193 3. 5194 3. 5196 3. 5197 55 10 3. 5198 3. 5200 3. 5201 3. 5202 3. 5204 3. 5205 3. 5206 3. 5207 3. 5209 3. 5210 55 20 3. 5211 3.5213 3.5214 3. 5215 3. 5217 3. 5218 3. 5219 8. 5221 8. 5222 3. 5228 55 30 3. 5224 3. 5226 3. 5227 3. 5228 3. 5230 3. 5231 3. 5232 3. 5234 3. 5235 3. 5286 55 40 3. 5237 3. 5239 3. 5240 3. 5241 3. 5243 3. 5244 3. 5245 3. 5247 3. 5248 3. 5249 55 50 3. 5250 3. 5252 3. 5253 3.5254 3.5256 3. 5257 3. 5258 3. 5271 3. 5260 3. 5272 8. 5261 3. 5274 3. 5262 56 3. 5263 3. 5265 3. 5266 3.5267 1 3.5269 3. 5270 3. 5275 56 10 3. 5276 3. 5278 3. 5279 3. 5280 3. 5281 3. 5283 3. 5284 3. 5285 3. 5287 3. 5288 56 20 3. 5289 3. 5290 3. 5292 3. 5293 3. 5294 3. 5296 3. 5297 8. 5298 3. 5299 8. 5801 56 30 3. 5302 3. 5303 3. 5305 3. 5306 3. 5307 3. 5308 3. 5310 3. 5311 3. 5312 3. 5314 56 40 3. 5315 3. 5316 3. 5317 3. 5319 3. 5320 3. 5321 3. 5322 3. 5324 3. 5325 3. 5326 56 50 3. 5328 3. 5329 3. 5330 3. 5331 3. 5333 3. 5334 3. 5835 3. 5336 3. 5388 3. 5339 57 3. 5340 3. 5342 3.5343 1 3.5344 3.5345 3. 5347 3. 5348 3. 5849 3. 5850 8. 5352 57 10 3. 5353 3. 5854 3. 5355 3. 5357 3. 5358 3. 5359 3. 5361 3. 5862 3. 5363 3. 5364 57 20 3. 5366 3. 5367 3. 5368 3. 5369 3. 5371 3. 5372 3. 5373 3. 5374 3. 5376 3. 5377 57 30 3. 5378 3. 5379 3. 5381 3. 5382 3. 5383 3. 5384 3. 5386 3. 5387 3. 5388 8. 5390 57 40 3. 5391 3. 5392 3. 5393 3. 5395 3. 5396 3. 5397 3. 5398 3. 5400 3. 5401 3. 5402 57 50 3. 5403 3. 5405 3.5406 3. 5407 3. 5408 3. 5421 3.5410 3. 5422 3. 5411 3.5428 3. 5412 8. 5425 3. 5413 375426 3. 5415 58 3. 5416 3. 5417 3.5'418 ; 3.5420 3. 5427 58 10 3. 5428 3. 5429 3.5431 1 3.5432 3. 5433 3. 5434 3. 5436 3. 5437 3. 5438 8. 5489 58 20 3. 5441 3. 5442 3.5443 j 3.5444 3.5446 3. 5447 3. 5448 3. 5449 3. 5451 3. 5452 58 30 3. 5453 3. 5454 .3.5456 i 3.5457 3. 5458 3. 5459 3. 5460 3. 5462 3. 5463 3. 5464 58 40 3. 5465 3. 5467 3.5468 i 3.5469 3.5470 3. 5472 3. 5473 3. 5474 8. 5475 3.5477 58 50 3. 5478 3. 5479 3.5480 1 3.5481 3.5483 3. 5484 3. 5485 3. 5486 8. 5488 3. 5489 59 3. 5490 3. 5491 3.5492 j 3.5494 3.5495 3. 5496 3. 5497 3. 5499 8. 5500 3. 5501 59 10 3. 5502 3. 5504 3.5505 i 3.5506 3.5507 3. 5508 3. 5510 3.5511 3. 5512 3.5518 59 20 3.5514 3. 5516 3. 5517 3. 5518 3. 5519 3. 5521 3. 5522 8. 5528 3. 5524 3. 5525 59 30 3. 5527 3. 5528 3. 5529 3. 5530 3. 5532 3. 5533 3. 5534 3. 5535 8. 5536 3. 5538 59 40 3. 5539 3. 5540 3.5541 3.5542 1 3.5544 3. 5545 3. 5546 3. 5547 8. 5549 3. 5550 59 50 3. 5551 3. 5552 3. 5553 3.5555 1 3.5556 3. 5557 3. 5558 3. 5559 3. 5561 3. 5562 APPENDIX Y: TABl^E IX. [Page 319 Logarithms of Small Arcs in Space or Time. Are. 0" 1" 2" 3" 4" 5" 6" 7" 8" j 9" / Ih 0" 0^ 3. 5563 3. 5564 3. 5565 3. 5567 3. 5568 3. 5569 3. 5570 3. 5571 3. 55^3 3. 5574 10 3. 5575 3. 5576 3. 5577 3. 5579 3. 5580 ' 3. 5581 3. 5582 3. 5583 3. 5585 3. 5586 20 3. 5587 3. 5588 3. 5589 3. 5591 3. 5592 3. 5593 3. 5594 3. 5595 3. 5597 3. 5598 30 3. 5599 3. 5600 3. 5601 3. 5603 3. 5604 3. 5605 3. 5606 3. 5607 3. 5609 3. 5610 40 3. 5611 3. 5612 3. 5613 3. 5615 3.5616 3.5617 3. 5618 3. 5619 3. 5621 3. 5622 50 3. 5623 3. 5624 3. 5625 3. 5626 3. 5628 3. 5629 3. 5630 3. 5631 3. 5632 3. 5634 . 1 1 3. 5635 3. 5636 3. 5637 3. 5638 3. 5640 3. 5641 3. 5642 3. 5643 3. 5644 3. 5645 10 3. 5647 3. 5648 3. 5649 3. 5650 3. 5651 3. 5653 3. 5654 3. 5655 3. 5656 3. 5657 20 3. 5658 3. 5660 3. 5661 3. 5662 3. 5663 3. 5664 3. 5666 3. 5667 3. 5668 3. 5669 30 3. 5670 3. 5671 3. 5673 3. 5674 3. 5675 3. 5676 3. 5677 3. 5678 3. 5680 3. 5681 40 3. 5682 3. 5683 3. 5684 3. 5686 3. 5687 3. 5688 3. 5689 3. 5690 3. 5691 3. 5693 50 3. 5694 3. 5695 3. 5696 3. 5697 3. 5698 3. 5700 3. 5701 3. 5702 3. 5703 i 3. 5704 1 2 3. 5705 3. 5707 3. 5708 3. 5709 3.5710 3.5711 3.5712 3. 5714 3.5715 3.5716 2 10 3.5717 3.5718 3. 5719 3. 5721 3. 5722 3. 5723 3. 5724 3. 5725 3. 5726 ] 3. 5728 2 20 3. 5729 3. 5730 3. 5731 3. 5732 3. 5733 3. 5735 3. 5736 3. 5737 3. 5738 ! 3. 5739 2 30 3. 5740 3. 5741 3. 5742 3. 5744 3. 5745 3. 5746 3. 5747 3. 5748 3. 5750 1 3. 5751 2 40 3. 5752 3. 5753 3. 5754 3. 5755 3. 5756 3. 5758 3. 5759 3. 5760 3. 5761 3. 5762 2 50 3. 5763 3. 5765 3. 5766 3. 5767 3. 5768 3. 5769 3. 5770 3. 5771 3.5773 3.5774 1 3 3. 5775 3. 5776 3.5777 3. 5778 3. 5780 3. 5781 3. 5782 3. 5783 3. 5784 i 3. 5785 3 10 3. 5786 3. 5788 3. 5789 3. 5790 3. 5791 3. 5792 3. 5793 3. 5794 3. 5796 3. 5797 3 20 3. 5798 3. 5799 3. 5800 3. 5801 3. 5802 3. 5804 3. 5805 3.5806 3. 5807 3. 5808 3 30 3. 5809 3. 5810 3. 5812 3. 5813 3. 5814 3.5815 3. 5816 3. 5817 3. 5818 3. 5819 3 40 3. 5821 3. 5822 3. 5823 3. 5824 3. 5825 3. 5826 3. 5827 3.5829 3. 5830 3. 5831 3 50 3. 5832 3. 5833 3. 5834 3. 5835 3. 5837 3. 5838 3. 5839 3. 5840 3. 5841 3. 5842 1 4 3. 5843 3. 5844 3. 5846 3. 5847 3. 5848 3. 5849 3. 5850 3. 5851 3. 5852 1 ;i 5853 4 10 3. 5855 3. 5856 3. 5857 3. 5858 3. 5859 3. 5860 3. 5861 3. 5862 3. 5864 1 3. 5865 4 20 3. 5866 3. 5867 3. 5868 3. 5869 3. 5870 3. 5871 3. 5873 3. 5874 3. 5875 3. 5876 4 30 3. 5877 3. 5878 3. 5879 3. 5880 3. 5882 3. 5883 3. 5884 3. 5885 3.5886 3.5887 4 40 3. 5888 3. 5889 3. 5891 3. 5892 3. 5893 3. 5894 3. 5895 3. 5896 3. 5897 1 3. 5898 4 50 3. 5899 3. 5901 3. 5902 3^. 5903 3.5904 3. 5905 3. 5906 3. 5907 3. 5908 3. 5910 1 5 3.5911 3. 5912 3. 5913 3. 5914 3. 5915 3. 5916 3.5917 3. 5918 3. 5920 3. 5921 5 10 3. 5922 3. 5923 3. 5924 3. 5925 3. 5926 3. 5927 3. 5928 3. 5930 3. 5931 3. 5932 5 20 3. 5933 3.5934 3. 5935 3. 5936 3. 5937 3. 5938 3. 5940 3. 5941 3. 5942 3. 5943 5 30 3. 5944 3. 5945 3. 5946 3. 5947 3. 5948 3. 5949 3. 5951 3. 6952 3. 5953 3. 5954 5 .40 3. 5955 3. 5956 3. 5957 3. 5958 3. 5959 3. 5960 3. 5962 3. 5963 3.5964 3. 5965 5 50 3. 5966 3. 5967 3. 5968 3. 5969 3. 5970 3. 5971 3. 5973 3. 5974 3. 5975 3. 5976 1 6 3. 5977 3. 5978 3. 5979 3. 5980 3. 5981 3. 5982 3. 5984 3. 5985 3. 5986 3. 5987 6 10 3. 5988 3. 5989 3. 5990 3. 5991 3. 5992 3. 5993 3. 5994 3. 5996 3. 5997 3. 5998 6 20 3. 5999 3. 6000 3. 6001 3. 6002 3. 6003 3.6004 3. 6005 3. 6006 3. 6008 3. 6009 6 30 3. 6010 3. 6011 3. 6012 3. 6013 3. 6014 3. 6015 3. 6016 3. 6017 3. 6018 3. 6020 6 40 3. 6021 3. 6022 3. 6023 3. 6024 3. 6025 3. 6026 3. 6027 3. 6028 3. 6029 3. 6030 6 50 3. 6031 3. 6033 3. 6034 3. 6035 3. 6036 3. 6037 3. 6038 3. 6039 3. 6040 3. 6041 1 7 3.6042 3. 6043 3. 6044 3. 6046 3. 6047 3.6048 3. 6049 3. 6050 3. 6051 3. 6052 7 10 3. 6053 3. 6054 3. 6055 3. 6056 3. 6057 3. 6058 3. 6060 3. 6061 3. 6062 3. 6063 7 20 3. 6064 3. 60a5 3. 6066 3. 6067 3. 6068 3. 6069 3. 6070 3. 6071 3. 6072 3. 6073 7 30 3. 6075 3. 6076 3. 6077 3. 6078 3. 6079 3. 6080 3. 6081 3. 6082 3. 6083 3. 6084 7 40 3. 6085 3. 6086 3. 6087 3. 6088 3. 6090 3. 6091 3. 6092 3. 6093 3. 6094 3. 6095 7 50 3. 6096 3. 6097 3. 6098 3. 6099 3.6100 3. 6101 3. 6102 3. 6103 3. 6104 j 3. 6106 1 8 3. 6107 3. 6108 3.6109 ; 3.6110 3.6111 3.6112 3.6113 3.6114 3.6115 i 3.6116 8 10 3. 6117 3.6118 3.6119 i 3.6120 3. 6121 3. 6123 3. 6124 3.6125 3.6126 3.6127 8 20 3. 6128 3.6129 3.6130 1 3.6131 3. 6132 3. 6133 3. 6134 3. 6135 3. 6136 3. 6137 8 30 3. 6138 3. 6139 3.6141 i 3.6142 3. 6143 3. 6144 3. 6145 3. 6146 3. 6147 3. 6148 8 40 3. 6149 3. 6150 3.6151 i 3.6152 3. 6153 3. 6154 3. 6155 3. 6156 3. 6157 3. 6158 8 50 3. 6160 3. 6161 3.6162 i 3.6163 3. 6164 3. 6165 3. 6166 3. 6167 3. 6168 3. 6169 3. 6179 1 9 3.6170 3.6171 3. 6172 3. 6173 3. 6174 3. 6175 3. 6176 3. 6177 3. 6178 9 10 3. 6180 3. 6182 3. 6183 3. 6184 3. 6ia5 3. 6186 3. 6187 3. 6188 3. 6189 3. 6190 9 20 3. 6191 3.6192 3. 6193 3. 6194 3. 6195 3. 6196 3. 6197 3.6198 3. 6199 3. 6200 9 30 3. 6201 3. 6202 3. 6203 3. 6204 3.6206 3. 6207 3. 6208 3. 6209 3.6210 3.6211 9 40 3. 6212 3. 6213 3. 6214 3. 6215 3. 6216 3. 6217 3. 6218 3. 6219 3. 6220 3. 6221 9 50 3. 6222 3. 6223 3.6224 1 3.6225 3. 6226 3. 6227 3. 6228 3. 6229 3. 6230 3. 6231 Page 320J APPENDIX V: TABLE IX. Logarithm ;! of Small Arcs in Space or Time. Are. 0" 1" 3. 6235 8" 4" 5" 6" «" 8" 1 9" O ' 1" 10" 0* 3. 6232 3. 6234 3. 6236 3. 6237 3. 6238 i 3. 6239 3. 6240 3. 6241 1 3. 6242 10 10 3. «)243 3. 6244 3. 6245 3. 6246 3. 6247 3. 6248 3. 6249 3. 6250 3. 6251 3. 6252 10 20 3. (5253 3. 6254 3. 6255 3. 6256 3. 6257 3. 6258 3. 6259 3. 6260 3. 6261 1 3. 6262 10 30 3. 6263 3.6264 3. 6265 3. 6266 3. 6268 3. 6269 3. 6270 3. 6271 3. 6272 ! 3. 6273 10 40 3. 6274 »3. 6275 3. 6276 3. 6277 3.6278 3. 6279 3. 6280 3. 6281 3. 6282 3. 6283 10 50 3. 6284 3. 6285 3. 6286 3. 6287 3. 6297 3. 6288 3. 6298 3. 6289 3. 6299 3.6290 376300 3. 6291 3. 6301 3. 6292 3. 6293 3.6302 1 3.6303 1 11 3. 6294 3. 6295 3.6296 11 10 3. 6304 3. 6305 3. 630() 3. 6307 3. 6308 3. 6309 3. 6310 3.6311 3. 6312 3. 6313 11 20 3. 6314 3. 6315 3.6316 3. 6317 3. 6318 3. 6320 3. 6321 3. 6322 3. 6323 3. 6324 11 30 3. 6325 3. 6326 3. 6327 3. 6328 3. 6329 3. 6330 3. 6331 3. 6332 3. 6333 3. 6334 11 40 3. 6335 3. 6336 3. 6337 3. 6338 3. 6339 3. 6340 3. 6341 3. 6342 3. 6343 i 3. 6344 11 50 3. 6345 3. 6346 3. 6347 3. 6348 3. 6349 3. 6350 3. 6351 3. 6352 3. 6353 ! 3. 6354 1 12 3. 6355 "3.6356 3. 6357 3. 6358 3. 6359 3. 6360 3. 6361 3.6362 3. 6363 1 3. 6364 12 10 3. 6365 3. 6366 3. 6367 3. 6368 3. 6369 3. 6370 3. 6371 3. 6372 3. 6373 i 3. 6374 12 20 3. 6375 3. 6376 3. 6377 3. 6378 3. 6379 3. 6380 3. 6381 3. 6382 3. 6383 3. 6384 12 30 3. 6385 3. 6386 3. 6387 3. 6388 3. 6389 3. 6390 3. 6391 3. 6392 3. 6393 3. 6394 12 40 3. 6395 3. 6396 3. 6397 3. 6398 3. 6399 3. 6400 3. 6401 3. 6402 3. 6403 3. 6404 12 50 3.6405 3. 6406 3. 6407 3. 6408 3. 6418 3. 6409 3.6419 3.6410 3.6411 3. 6412 3. 6422 3. 6413 3. 6423 3. 6414 3.6424 " 1 13 3. 6415 3. 6416 3. 6417' 3. 6420 3. 6421 13 10 3. 6425 3. 6426 3. 6427 3. 6428 3. 6429 3. 6430 3. 6431 3. 6432 3. 6433 3. 6434 13 20 3. 6435 3. 6436 3. 6437 3. 6437 3. 6438 3. 6439 3. 6440 3. 6441 3. 6442 3. 6443 18 30 3. 6444 3. 6445 3. 644(5 3.64-17 3.6448 3. 6449 3.6450 1 3.6451 3. 6452 i 3. 6453 13 40 3. 6454 3. 6455 3. 6456 3. 6457 3. 6458 3. 6459 3. 6460 3. 6461 3.6462 3.6463 13 50 3. 6464 3. 6465 3. 6466 3. 6467 3. 6468 3.6469 3. 6470 3.6471 3. 6472 3. 6473 1 14 . 3. 6474 3. 6475 3. 6476 3. 6477 3. 6478 3. 6479 3. 6480 3. 6481 3. 6482 1 3. 6483 14 10 3. 6484 3. 6485 3. 6486 3. 6487 3. 6488 3. 6488 3. 6489 3. 6490 3. 6491 I 3. 6492 14 20 3. 6493 3. ^494 3. 6495 3. 6496 3. 6497 3. 6498 3.6499 3. 6500 3. 6501 ! 3. 6502 14 30 3. 6503 3. 6504 3. 6505 3. 6506 3. 6507 3. 6508 3. 6509 3. 6510 3.6511 1 3.6512 14 40 3. 6513 3. 6514 3. 6515 3. 6516 3. 6517 3. 6518 3.6519 3. 6520 3. 6521 i 3. 6521 14 50 3. 6522 3. 6523 3. 6524 3. 6525 3. 6.526 3. 6527 3. 6528 3. 6538 3. 6529 3. 6539 3. 6530 "3. 6540 3. 6531 1 15 3. 6532 " 3. 6533 3. 6534 3. 6535 3. 6536 3. 6537^ 3. 6541 15 10 3. 6542 3. 6543 3. 6544 3. 6545 3. 6546 3. 6547 3. 6548 3. 6549 3.6549 3.6550 1 15 20 3. 6551 3. 6552 3. 6553 3. 6554 3.6555 i 3.6556 3. 6557 3. 6558 3.6559 3.6560 | 15 30 3. 6561 3. 6562 3. 6563 3. 6564 3. 6565 3. 6566 3. 6567 3. 6568 3. 6569 3. 6570 15 40 3. 6571 3. 6572 3. 6572 3. 6573 3. 6574 3. 6575 3. 6576 3. 6577 3. 6578 3. 6579 15 50 3. 6580 3. 6581 3. 6591 3. 6582 3. 6592 3. 6583 3. 6584 3. 6585 3. 6586 3. 6587 3. 6588 3. 6589 1 16 3. 6590 3. 6593 3. 6593" 3. 6594 3. 6595 3. 6596 3.6597 3. 6598 16 10 3. 6599 3. 6600 3. 6601 3. 6602 3. 6603 3. 6604 3. 6605 3. 6606 3. 6607 ! 3. 6608 | 16 20 3. 6609 3. 6610 3.6611 3.6611 3. 6612 3. 6613 3. 6614 3. 6615 3. 6616 3. 6617 16 30 3. 6618 3. 6619 3. 6620 3. 6621 3. 6622 3. 6623 3. 6624 3. 6625 3. 6626 3. 6627 16 40 3. 6628 3. 6629 3. 6629 3. 6630 3. 6631 3. 6632 3. 6633 3. 6634 3. 6635 3. 6636 16 50 3. 6637 3. 6638 3. 6639 3. 6640 3. 6641 3. 6642 3. 6643 3. 6644 3. 6645 3. 6645 1 17 3. 6646^ 3. 6647 3.6648 3. 6649 3. 6650 3. 6651 3. 6652 3. 6653 3. 6654 3. 6655 17 10 3. 6656 3. 6657 3. 6658 3. 6659 3. 6660 3. 6660 3. 6661 3. 6662 3. 6663 3. 6664 17 20 3. 6665 3. 6666 3. 6667 3. 6668 3.6669 j 3.6670 3. 6671 3. 6672 3. 6673 3. 6674 17 30 3. 6675 3. 6675 3. 6676 3. 6677 3.6678 ' 3.6679 3. 6680 3. 6681 3. 6682 3. 6683 17 40 3. 6684 3. 6685 3. 6686 3. 6687 3. 6688 3. 6689 3. 6689 3. 6690 3. 6691 3. 6692 17 50 3. 6693 3. 6694 "3.6703 3. 6695 3. 6704 3. 6696 3. 6697 3. 6698 "3. 6707" 3. 6699 3. 6700 3. 6701 3. 6710 3. 6702 3.6711 1 18 3. 6702 3. 6705 3. 6706 3. 6708 3. 6709 18 10 3. 6712 3. 6713 3. 6714 3. 6715 3.6715 3.6716 3.6717 3. 6718 3. 6719 3. 6720 18 20 3. 6721 3. 6722 3. 6723 3. 6724 3. 6725 3. 6726 3. 6727 3. 6727 3. 6728 3. 6729 18 30 3. 6730 3. 6731 3. 6732 3. 6733 3. 6734 3. 6735 3. 6736 3. 6737 3. 6738 3. 6738 18 40 3. 6739 3. 6740 3. 6741 3. 6742 3. 6743 3. 6744 3. 6745 3. 6746 3. 6747 3. 6748 18 50 3. 6749 3. 6750 3.6759 3. 6750 3. 6760 3. 6751 3. 6761 3. 6752 3. 6753 3. 6754 3. 6755 3. 6756 3. 6757 1 19 3. 6758 3. 6761 3. 6762 3. 6763 3. 6764" 3. 6765 3.6766 19 10 3. 6767 3. 6768 3. 6769 3. 6770 3. 6771 3. 6772 3. 6772 3. 6773 3. 6774 3. 6775 19 20 3. 6776 3. 6777 3. 6778 3. 6779 3. 6780 3. 6781 3. 6782 3. 6782 3. 6783 3. 6784 19 30 3. 6785 3. 6786 3. 6787 3. 6788 3. 6789 3. 6790 3. 6791 3. 6792 3. 6792 3. 6793 19 40 3. 6794 3. 6795 3. 6796 3. 6797 3. 6798 3. 6799 3. 6800 3. 6801 3. 6802 3. 6802 19 50 3. 6803 3. 6804 3. 6805 3. 6806 3. 6807 3. 6808 3. 6809 3. 6810 3. 6811 3. 6812 APPENDIX V: TABLE IX. [Page 321 | Logarithms of Small Arcs in Space or Time. Arc. 0" 1" 2" 3" 4" 5" 6" 7" 8" 9" o / 1» 20'" 0« 3. 6812 3. 6813 3. 6814 3. 6815 3. 6816 3. 6817 3. 6818 3. 6819 3. 6820 3. 6821 20 10 3. 6821 3. 6822 3. 6823 3. 6824 3. 6825 3. 6826 3. 6827 3. 6828 3. 6829 3. 6830 20 20 3. 6830 3. 6831 3. 6832 3. 6833 3. 6834 3. 6835 3. 6836 3. 6837 3. 6838 3. 6839 20 30 3. 6839 3. 6840 3. 6841 3. 6842 3. 6843 3. 6844 3. 6845 3. 6846 3. 6847 3. 6848 20 40 3. 6848 3. 6849 3. 6850 3. 6851 3. 6852 3. 6853 3. 6854 3. 6855 3. 6856 3. 6857 20 50 3. 6857 3. 6858 3. 6859 3. 6860 3. 6861 3. 6862 3. 6863 3. 6864 3. 6865 3.6865 1 21 3. 6866 3. 6867 3. 6868 3. 6869 3. 6870 3. 6871 3. 6872 3. 6873 3. 6874 3. 6874 21 10 3. 6875 3. 6876 3. 6877 3. 6878 3. 6879 3. 6880 3. 6881 3. 6882 3. 6882 3. 6883 21 20 3. 6884 3. 6885 3. 6886 3. 6887 3. 6888 3. 6889 3. 6890 3. 6890 3. 6891 3. 6892 21 30 3. 6893 3. 6894 3. 6895 3. 6896 3. 6897 3. 6898 3. 6898 3. 6899 3. 6900 3. 6901 21 40 3. 6902 3. 6903 3. 6904 3. 6905 3. 6906 3. 6906 3. 6907 3. 6908 3.6909 3. 6910 21 50 3.6911 3. 6912 3. 6913 3. 6913 3.6914 3. 6923 3. 6915 3. 6916 3.6917 3. 6918 3. 6927 3. 6919 1 22 3. 6920 3. 6921 3. 6921 3. 6922 3. 6924 3. 6925 3. 6926 3. 6928 22 10 3. 6928 3. 6929 3. 6930 3. 6931 3. 6932 3. 6933 3. 6934 3. 6935 3. 6936 3. 6936 22 20 3. 6937 3. 6938 3. 6939 3. 6940 3. 6941 3. 6942 3. 6943 3. 6943 3. 6944 3. 6945 22 30 3. 6946 3. 6947 3. 6948 3. 6949 3. 6950 3. 6950 3. 6951 3. 6952 3. 6953 3. 6954 22 40 3. 6955 3. 6956 3. 6957 3. 6957 3. 6958 3. 6959 3. 6960 3. 6961 3. 6962 3. 6963 22 50 3.6964 3.6964 3. 6965 3. 6966 3. 6967 3. 6968 3. 6969 3. 6970 3. 6971 3. 6971 1 23 3. 6972 3. 6973 3. 6974 3. 6975 3. 6976 3. 6977 3. 6978 3. 6978 3. 6979 3. 6980 23 10 3. 6981 3. 6982 3. 6983 3. 6984 3. 6984 3. 6985 3. 6986 3. 6987 3. 6988 3. 6989 23 20 3. 6990 3. 6991 3. 6991 3. 6992 3. 6993 3. 6994 3. 6995 3. 6996 3. 6997 3. 6998 23 30 3. 6998 3. 6999 3.7000 3.7001 3.7002 3. 7003 3. 7004 3. 7004 3.7005 3. 7006 23 40 3. 7007 3. 7008 3.7009 3. 7010 3. 7010 3. 7011 3. 7012 3. 7013 3. 7014 3. 7015 23 50 3. 7016 3. 7017 3, 7017 3. 7026 3. 7018 3. 7019 3. 7020 3. 7021 3. 7022 3. 7023 3. 7023 1 24 3. 7024 3. 7025 3. 7027 3. 7028 3. 7029 3.7029 3. 7030 3. 7031 3. 7032 24 10 3. 7033 3. 7034 3. 7035 3. 7035 3. 7036 3. 7037 3. 7038 3. 7039 3. 7040 3. 7041 24 20 3. 7042 3. 7042 3. 7043 3. 7044 3.7045 3. 7046 3. 7047 3. 7048 3. 7048 3. 7049 24 30 3. 7050 3. 7051 3. 7052 3. 7053 3. 7054 3. 7054 3. 7055 3. 7056 3. 7057 3. 7058 24 40 3. 7059 3.7060 3. 7060 3. 7061 3. 7062 3. 7063 3. 7064 3. 7065 3. 7065 3. 7066 24 50 3. 7067 3. 7068 3. 7069 3. 7070 3. 7071 3. 7071 3. 7072 3. 7073 3. 7074 3. 7075 1 25 3. 7076 3. 7077 3. 7077 3. 7078 3. 7079 3. 7080 3. 7081 3. 7082 3. 7083 3. 7083 25 10 3. 7084 3. 7085 3. 7086 3. 7087 3. 7088 3. 7088 3. 7089 3. 7090 3.7091 3. 7092 25 20 3. 7093 3. 7094 3. 7094 3.7095 3. 7096 3. 7097 3. 7098 3.7099 3.7099 3.7100 25 30 3. 7101 3. 7102 3. 7103 3. 7104 3. 7105 3. 7105 3. 7106 3. 7107 3. 7108 3. 7109 25 .40 3. 7110 3. 7110 3.7111 3. 7112 3. 7113 3. 7114 3. 7115 3.7116 3. 7116 3.7117 25 50 3.7118 3. 7119 3. 7120 3. 7121 3. 7121 3. 7122 3. 7123 3. 7124 3. 7125 3. 7126 1 26 3. 7126 3. 7127 3. 7128 3. 7129 3. 7130 3. 7131 3. 7132 3. 7132 3. 7133 3. 7134 26 10 3. 7135 3. 7136 3. 7137 3. 7137 3. 7138 3. 7139 3.7140 3. 7141 3. 7142 3. 7142 26 20 3. 7143 3. 7144 3. 7145 3. 7146 3. 7147 3. 7147 3. 7148 3. 7149 3. 7150 3. 7151 26 30 3. 7152 3. 7153 3. 7153 3. 7154 3. 7155 3. 7156 3. 7157 3. 7158 3. 7159 3. 7159 26 40 3. 7160 3. 7161 3. 7162 3. 7163 3. 7163 3. 7164 3. 7165 3. 7166 3. 7167 3. 7168 26 50 3. 7168 3. 7169 3. 7170 3.7171 3. 7172 3. 7173 3. 7173 3. 7182 3. 7174 3. 7175 3. 7176 1 27 3.7177 3. 7178 3. 7178 3. 7179 1 3. 7180 3. 7181 3. 7183 3. 7183 3. 7184 27 10 3.7185 3. 7186 3. 7187 3.7188 1 3.7188 3. 7189 3. 7190 3. 7191 3. 7192 3. 7192 27 20 3. 7193 3. 7194 3. 7195 3. 7196 I 3. 7197 3.7197 3. 7198 3. 7199 3. 7200 3. 7201 27 30 3. 7202 3. 7202 3. 7203 3. 7204 3. 7205 3.7206 3. 7207 3. 7207 3. 7208 3. 7209 27 40 3. 7210 3. 7211 3. 7212 3.7212 3. 7213 3. 7214 3. 7215 3. 7216 3. 7216 3. 7217 27 50 3. 7218 3. 7219 3. 7220 3. 7221 3. 7221 3. 7222 3. 7223 3. 7224 3. 7225 3. 7226 1 28 3. 7226 3. 7227 3. 7228 3.7229 3. 7230 3. 7230 3. 7231 3. 7232 3. 7233 3. 7234 28 10 3. 7235 3. 7235 3. 7236 3. 7237 3. 7238 3. 7239 3. 7239 3. 7240 3. 7241 3. 7242 28 20 3. 7243 3. 7244 3. 7244 3. 7245 3. 7246 3. 7247 3. 7248 3. 7248 3. 7249 3. 7250 28 30 3. 7251 3. 7252 3. 7253 3. 7253 3. 7254 3. 7255 3. 7256 3. 7257 3. 7257 3. 7258 28 40 3. 7259 3. 7260 3. 7261 3. 7262 3. 7262 3. 7263 3. 7264 3. 7265 3. 7266 3. 7266 28 50 3. 7267 3. 7268 3. 7269 3. 7270 3. 7278 3. 7271 3. 7279 3. 7271 3. 7272 3. 7273 3. 7274 3. 7275 1 29 3. 7275 3. 7276 3. 7277 3. 7279 3. 7280 3. 7281 3. 7282 3. 7283 29 10 3. 7284 3. 7284 3. 7285 3. 7286 3. 7287 3. 7288 3. 7288 3. 7289 3. 7290 3. 7291 29 20 3. 7292 3. 7292 3. 7293 3. 7294 3. 7295 3.7296 3. 7297 3. 7297 3. 7298 3. 7299 29 30 3. 7300 3. 7301 3. 7301 3. 7302 3. 7303 3. 7304 3. 7305 3. 7305 3. 7306 3. 7307 29 40 3. 7308 3. 7309 3. 7309 3. 7310 3. 7311 3. 7312 3. 7313 3. 7313 3. 7314 3. 7315 29 50 3.7316 3. 7317 3. 7317 3. 7318 3. 7319 3. 7320 3. 7321 3. 7322 3. 7322 3. 7323 22489—03- -21 Page 322] APPENDIX V: TABLE [X. Logarithms of Small Arcs in Space or Time. Arc. 0" i X" 2" 8" 4" 5" 6" 7" 8" 9" 1 O I II 1" 30"' 0" 3. 7324 3. 7325 3. 7326 3. 7326 3. 7327 3. 7328 3.7329 3. 7330 3. 7330 3.7331 30 10 3. 7332 3. 7333 3. 7334 3. 7334 3. 7335 3. 7336 3. 7337 3. 7338 3. 7338 3. 7339 30 20 3. 7340 3. 7341 3. 7342 3. 7342 3. 7343 3.7344 3. 7345 3. 7346 3.7346 3. 7347 30 30 3. 7348 3. 7349 3. 7350 3. 7350 3. 7351 3. 7352 3. 7353 3. 7354 3. 7354 3. 7355 30 40 3.7356 ►3. 7357 3.7358 3, 7358 3. 7359 3.7360 3. 7361 3. 7362 3. 7362 3. 7363 30 50 3. 7364 3.7365 3. 7366 3. 7366 3. 7367 3. 7368 3. 7369 3. 7370 3. 7370 3. 7371 1 31 3. 7372 3. 7373 3. 7374 3. 7374 3. 7375 3. 7376 3. 7377 3. 7377 3. 7378 3. 7379 31 10 3. 7380 3. 7381 3. 7381 3. 7382 3. 7383 3. 7384 3.7385 3. 7385 3. 7386 3. 7387 31 20 3. 7388 3. 7389 3. 7389 3. 7390 3. 7391 3. 7392 3. 7393 3. 7393 3. 7394 3. 7395 31 30 3. 7396 3. 7397 3. 7397 3. 7398 3. 7399 3.7400 3.7400 3. 7401 3. 7402 3. 7403 31 40 3. 7404 3. 7404 3. 7405 3. 7406 3.7407 3. 7408 3. 7408 3. 7409 3. 7410 3. 7411 31 50 3. 7412 3. 7412 3. 7413 3. 7414 3. 7415 3. 7415 3. 7416 3. 7417 3. 7418 3. 7419 1 32 3. 7419 3. 7420 3. 7421 3. 7422 3. 7423 3. 7423 3. 7424 3. 7425 3. 7426 3. 7426 32 10 3. 7427 3. 7428 3. 7429 3. 7430 3. 7430 3. 7431 3. 7432 3. 7433 3. 7434 3. 7434 32 20 3.7435 3. 7436 3. 7437 3. 7437 3. 7438 3. 7439 3. 7440 3. 7441 3. 7441 3. 7442 32 30 3. 7443 3.7444 3.7444 3. 7445 3. 7446 3. 7447 3.7448 3. 7448 3. 7449 3. 7450 32 40 3. 7451 3. 7452 3.7452 3. 7453 3. 7454 3. 7455 3. 7455 3. 7456 3. 7457 3.7468 32 50 3. 7459 3. 7459 3.7460 3. 7461 3. 7462 3. 7462 3. 7463 3.7464 3.7465 3. 7466 1 33 3. 7466 3. 7467 3. 7468 3. 7469 3. 7469 3. 7470 3. 7471 3. 7472 3. 7473 3. 7473 33 10 3. 7474 3. 7475 3. 7476 3. 7476 3. 7477 3. 7478 3. 7479 3. 7480 3. 7480 3. 7481 33 20 3. 7482 3. 7483 3. 7483 3. 7484 3. 7485 3. 7486 3. 7487 3. 7487 3. 7488 3. 7489 33 30 3. 7490 3. 7490 3. 7491 3. 7492 3. 7493 3. 7493 3. 7494 3. 7495 3. 7496 3. 7497 33 40 3. 7497 3. 7498 3. 7499 3.7500 3.7500 3. 7501 3. 7502 3. 7503 3. 7504 3. 7504 33 50 3. 7505 3. 7506 3. 7507 3. 7507 3. 7508 3. 7509 3. 7510 3. 7510 3. 7511 3. 7512 1 34 3. 7513 3. 7514 3. 7514 3. 7515 3. 7516 3. 7517 3. 7517 3. 7518 3. 7519 3. 7520 34 10 3. 7520 3. 7521 3. 7522 3. 7523 3. 7524 3. 7524 3. 7525 3. 7526 3. 7527 3. 7527 34 20 3. 7528 3. 7529 3. 7530 3. 7530 3. 7531 3. 7532 3. 7533 3. 7534 3. 7534 3. 7535 34 30 3. 7536 3. 7537 3. 7537 3. 7538 3. 7539 3. 7540 3. 7540 3. 7541 3. 7542 3. 7543 34 40 3. 7543 3. 7544 3. 7545 3. 7546 3. 7547 3. 7547 3. 7548 3. 7549 3. 7550 3. 7550 34 50 3. 7551 3. 7552 3. 7553 3. 7553 3. 7554 3. 7555 3. 7556 3. 7556 3. 7557 3. 7558 1 35 3. 7559 3. 7560 3.7560 3. 7561 3. 7562 3. 7563 3. 7563 3. 7564 3. 7565 3. 7566 35 10 3. 7566 3. 7567 3. 7568 3. 7569 3. 7569 3. 7570 3. 7571 3. 7572 3. 7572 3. 7573 35 20 3. 7574 3. 7575 3. 7575 3. 7576 3. 7577 3. 7578 3. 7579 3. 7579 3. 7580 3. 7581 35 30 3. 7582 3. 7582 3. 7583 3. 7584 3. 7585 3. 7585 3. 7586 3. 7587 3. 7588 3. 7588 35 40 3. 7589 3. 7590 3. 7591 3. 7591 3. 7592 3. 7593 3. 7594 3. 7594 3. 7595 3. 7596 35 50 3. 7597 3. 7597 3. 7598 3. 7599 3. 7600 3. 7600 3. 7601 3. 7602 3. 7603 3. 7603 1 36 3. 7604 3. 7605 3. 7606 3. 7606 3. 7607 3. 7608 3. 7609 3. 7609 3. 7610 3. 7611 36 10 3. 7612 3. 7613 3. 7613 3. 7614 3. 7615 3. 7616 3. 7616 3. 7617 3. 7618 3. 7619 36 20 3. 7619 3. 7620 3. 7621 3. 7622 3. 7622 3. 7623 3. 7624 3. 7625 3. 7625 3. 7626 36 30 3. 7627 3. 7628 3. 7628 3. 7629 3. 7630 3. 7631 3. 7631 3. 7632 3. 7633 3. 7634 36 40 3. 7634 3. 7635 3. 7636 3. 7637 3. 7637 3. 7638 3. 7639 3. 7640 3. 7640 3. 7641 36 50 3. 7642 3. 7643 3. 7643 3.7644 3. 7645 3. 7645 3. 7646 3. 7647 3. 7648 3.7648 1 37 3. 7649 3. 7650 3. 7651 3.7651 3. 7652 3. 7653 3. 7654 3. 7654 3.7655 3. 7666 37 10 3. 7657 3.7667 3. 7658 3. 7659 3. 7660 3. 7660 3. 7661 3. 7662 3. 7663 3. 7663 37 20 3. 7664 3. 7665 3. 7666 3. 7666 3. 7667 3. 7668 3. 7669 3. 7669 3. 7670 3. 7671 37 30 3. 7672 3. 7672 3. 7673 3. 7674 3. 7675 3. 7675 3. 7676 3. 7677 3. 7677 3. 7678 37 40 3. 7679 3. 7680 3. 7681 3. 7681 3. 7682 3. 7683 3. 7683 3. 7684 3. 7685 3. 7686 37 50 3. 7686 3. 7687 3. 7688 3. 7689 3. 7689 3. 7690 3. 7691 3. 7692 3. 7692 3. 7693 1 38 3. 7694 3. 7695 3. 7695 3. 7696 3. 7697 3. 7697 3. 7698 3. 7699 3. 7700 3. 7700 38 10 3. 7701 3. 7702 3. 7703 3. 7703 3. 7704 3. 7705 3. 7706 3. 7706 3. 7707 3. 7708 38 20 3. 7709 3. 7709 3. 7710 3. 7711 3. 7711 3. 7712 3. 7713 3. 7714 3. 7714 3.7715 38 30 3. 7716 3. 7717 3. 7717 3. 7718 3. 7719 3. 7720 3. 7720 3. 7721 3. 7722 3. 7722 38 40 3. 7723 3. 7724 3. 7725 3. 7725 3. 7726 3. 7727 3. 7728 3. 7728 3. 7729 3. 7730 38 50 3. 7731 3. 7731 3. 7732 3. 7733 3. 7733 3. 7734 3. 7735 3. 7736 3. 7736 3. 7737 1 39 3. 7738 3. 7739 3. 7739 3. 7740 3. 7741 3. 7742 3. 7742 3. 7743 3. 7744 3. 7744 39 10 3. 7745 3. 7746 3. 7747 3. 7747 3. 7748 3. 7749 3. 7750 3. 7750 3. 7751 3. 7752 39 20 3. 7752 3. 7753 3. 7754 3. 7755 3. 7755 3. 7756 3. 7757 3. 7758 3. 7758 3. 7759 39 30 3. 7760 3. 7760 3. 7761 3. 7762 3. 7763 3. 7763 3. 7764 3. 7765 3. 7766 3. 7766 39 40 3. 7767 3. 7768 3. 7768 3. 7769 3. 7770 3. 7771 3. 7771 3. 7772 3. 7773 3. 7774 39 50 3. 7774 3. 7775 3. 7776 3. 7776 3. 7777 3. 7778 3. 7779 3. 7779 3. 7780 3. 7781 APPENDIX V: TABLE IX. [Page 323 Logarithms of Small Arcs in I Space or Time. Arc. 1 0" 1" 2" 8" 4" 5" 6" 7" 8" 9" / Ih 40.n II 0^ 3. 7782 3. 7782 3. 7783 3. 7784 3. 7784 3. 7785 3. 7786 3. 7787 3. 7787 3. 7788 40 10 3. 7789 3. 7789 3. 7790 3. 7791 3. 7792 3. 7792 3. 7793 3. 7794 3. 7795 3. 7795 40 20 3. 7796 3. 7797 3. 7797 3. 7798 3. 7799 3. 7800 3. 7800 3. 7801 3. 7802 3. 7802 40 30 3. 7803 3. 7804 3. 7805 3. 7805 3. 7806 3. 7807 3. 7807 3. 7808 3. 7809 3. 7810 40 40 3.7810 3. 7811 3. 7812 3. 7813 3. 7813 3. 7814 3. 7815 3. 7815 3. 7816 3. 7817 40 50 3. 7818 3. 7818 3. 7819 3. 7826 3. 7820 3. 7820 3. 7828 3. 7821 3. 7822 3. 7823 3. 7823 3. 7824 1 41 3. 7825 3. 7825 3. 7827 3. 7828 3. 7829 3. 7830 3. 7830 3. 7831 41 10 3. 7832 3. 7833 3. 7833 3. 7834 3. 7835 3. 7835 3. 7836 3. 7837 3. 7838 3. 7838 41 20 3. 7839 3. 7840 3. 7840 3. 7841 3.7842 3. 7843 3. 7843 3. 7844 3. 7845 3. 7845 41 30 3. 7846 3. 7847 3. 7848 3. 7848 3. 7849 3. 7850 3. 7850 3. 7851 3. 7852 3. 7853 41 40 3. 7853 3. 7854 3. 7855 3. 7855 3. 7856 3. 7857 3. 7858 3.7858 3. 7859 3. 7860 41 50 3. 7860 3. 7861 3. 7862 3. 7863 3. 7863 3. 7864 3. 7865 3. 7865 3. 7866 3. 7867 1 42 3. 7868 3. 7868 3. 7869 3. 7870 3. 7870 3. 7871 3. 7872 3. 7872 3. 7873 3. 7874 42 10 3. 7875 3. 7875 3. 7876 3. 7877 3. 7877 3. 7878 3. 7879 3. 7880 3. 7880 3. 7881 42 20 3. 7882 3. 7882 3. 7883 3. 7884 3. 7885 3. 7885 3. 7886 3. 7887 3. 7887 3. 7888 42 30 3. 7889 3. 7889 3. 7890 3. 7891 3. 7892 3. 7892 3. 7893 3. 7894 3. 7894 3. 7895 42 40 3. 7896 3. 7897 3. 7897 3. 7898 3. 7899 3. 7899 3. 7900 3. 7901 3. 7901 3. 7902 42 50 3. 7903 3. 7904 3. 7904 3. 7905 3. 7906 3. 7906 3. 7907 3. 7908 3. 7908 3. 7909 1 43 3. 7910 3. 7911 3. 7911 . 3. 7912 3. 7913 3.7913 3. 7914 3. 7915 3. 7916 3. 7916 43 10 3. 7917 3. 7918 3. 7918 3. 7919 3. 7920 3. 7920 3. 7921 3. 7922 3. 7923 3. 7923 43 20 3. 7924 3. 7925 3. 7925 3. 7926 3. 7927 3. 7927 3. 7928 3. 7929 3. 7930 3. 7930 43 30 3. 7931 3. 7932 3. 7932 3. 7933 3. 7934 3. 7934 3. 7935 3. 7936 3. 7937 3. 7937 43 40 3. 7938 3. 7939 3. 7939 3. 7940 3. 7941 3. 7941 3. 7942 3. 7943 3. 7943 3. 7944 43 50 3. 7945 3. 7946 3. 7946 3. 7947 3. 7948 3. 7948 3. 7949 3. 7950 3. 7950 3. 7951 1 44 3. 7952 3. 7953 3. 7953 3. 7954 3. 7955 3. 7955 3. 7956 3. 7957 3. 7957 3. 7958 44 10 3. 7959 3. 7959 3. 7960 3. 7961 3. 7962 3. 7962 3. 7963 3. 7964 3. 7964 3. 7965 44 20 3. 7966 3. 7966 3. 7967 3. 7968 3. 7969 3. 7969 3. 7970 3. 7971 3. 7971 3. 7972 44 30 3. 7973 3. 7973 3. 7974 3. 7975 3. 7975 3. 7976 3. 7977 3. 7978 3. 7978 3. 7979 44 40 3. 7980 3. 7980 3. 7981 3. 7982 3. 7982 3. 7983 3. 7984 3. 7984 3. 7985 3. 7986 44 50 3. 7987 3. 7987 3. 7988 3. 7989 3. 7989 3. 7990 3. 7991 3. 7991 3. 7992 3. 7993 1 45 3. 7993 3. 7994 3. 7995 3. 7995 3. 7996 3. 7997 3. 7998 3. 7998 3. 7999 3.8000 45 10 3. 8000 3. 8001 3. 8002 3. 8002 3. 8003 3. 8004 3. 8004 3.8005 3. 8006 3.8006 45 20 3. 8007 3. 8008 3. 8009 3. 8009 3. 8010 3.8011 3. 8011 3. 8012 3. 8013 3. 8013 45 30 3. 8014 3. 8015 3. 8015 3. 8016 3. 8017 3. 8017 3.8018 3. 8019 3. 8020 3. 8020 45 •40 3. 8021 3. 8022 3. 8022 3. 8023 3. 8024 3. 8024 3. 8025 3. 8026 3. 8026 3. 8027 45 50 3. 8028 3. 8028 3. 8029 3. 8030 3. 8030 3. 8031 3. 8032 3. 8033 3. 8033 3. 8034 1 46 3. 8035 3. 8035 3. 8036 3. 8036 3. 8037 3. 8038 3. 8039 3. 8039 3. 8040 3. 8041 46 10 3. 8041 3. 8042 3. 8043 3. 8043 3. 8044 3. 8045 3. 8045 3. 8046 3. 8047 3. 8048 46 20 3. 8048 3. 8049 3. 8050 3. 8050 3. 8051 3. 8052 3. 8052 3. 8053 3. 8054 3. 8054 46 30 3. 8055 3. 8056 3. 8056 3. 8057 3. 8058 3. 8058 3. 8059 3. 8060 3. 8060 3. 8061 46 40 3. 8062 3. 8062 3. 8063 3. 8064 3. 8065 3. 8065 3. 8066 3.8067 3. 8067 3. 8068 46 50 3. 8069 3. 8069 3. 8070 3. 8071 3. 8071 3. 8078 3. 8072 3. 8073 3. 8073 3. 8074 3. 8075 1 47 3. 8075 3. 8076 3. 8077 3. 8077 3. 8079 3. 8079 3. 8080 3. 8081 3. 8081 47 10 3. 8082 3. 8083 3. 8083 3. 8084 3. 8085 3. 8085 3. 8086 3. 8087 3. 8088 3. 8088 47 20 3. 8089 3. 8090 3. 8090 3. 8091 3. 8092 3. 8092 3. 8093 3. 8094 3. 8094 3. 8095 47 30 3. 8096 3. 8096 3. 8097 3.8098 3. 8098 3.8099 3. 8099 3. 8100 3. 8101 3. 8102 47 40 3. 8102 3. 8103 3. 8104 3. 8104 3. 8105 3. 8106 3. 8106 3. 8107 3. 8108 3. 8108 47 50 3. 8109 3.8110 3. 8110 3.8111 3. 8112 3.8112 3. 8113 3. 8114 3.8114 3.8115 1 48 3.8116 3. 8116 3.8117 3.8118 3.8118 3.8119 3. 8120 3. 8120 3.8121 3. 8122 48 10 3. 8122 3. 8123 3. 8124 3. 8124 3. 8125 3. 8126 3. 8126 3. 8127 3. 8128 3. 8128 48 20 3. 8129 3.8130 3. 8130 3. 8131 3. 8132 3.8132 3. 8133 3. 8134 3. 8134 3. 8135 48 30 3. 8136 3.8136 3. 8137 3. 8138 3. 8138 3. 8139 3. 8140 3. 8140 3. 8141 3. 8142 48 40 3. 8142 3. 8143 3.8144 3. 8144 3. 8145 3. 8146 3. 8146 3. 8147 3. 8148 3. 8148 48 50 3. 8149 3. 8150 3. 8150 3. 8151 3. 8152 3. 8152 3. 8153 3. 8154 3. 8154 3. 8155 1 49 3.8156 3. 8156 3. 8157 3. 8158 3. 8158 3. 8159 3. 8160 3. 8160 3. 8161 3. 8162 49 10 3. 8162 3. 8163 3. 8164 3. 8164 3. 8165 3. 8166 3. 8166 3. 8167 3. 8168 3. 8168 49 20 3. 8169 3. 8170 3. 8170 3. 8171 3. 8172 3. 8172 3.8173 3. 8174 3. 8174 3. 8175 49 30 3. 8176 3.8176 3. 8177 3.8178 3. 8178 3.8179 3. 8180 3. 8180 3. 8181 3. 8182 49 40 3. 8182 3. 8183 3. 8184 3. 8184 3. 8185 3. 8185 3. 8186 3. 8187 3. 8188 3. 8188 49 50 3. 8189 3. 8190 3. 8190 3. 8191 3. 8191 3. 8192 3. 8193 3. 8193 3. 8194 3. 8195 Page 324] APPENDIX V: TABLE IX. Logarithms of Small Arcs in Space or Time. Arc. 0" 1" 2" 8" 4" 6" 6" 7" 8" 9" O 1 1" 50™ II 0» 3. 8195 3. 8196 3. 8197 3. 8197 3. 8198 3. 8199 3. 8199 3.8200 3. 8201 3. 8201 50 10 3. 8202 3. 8203 3. 8203 3. 8204 3. 8205 3. 8205 3. 8206 3. 8207 3. 8207 3. 8208 50 20 3.8209 3. 8209 3.8210 3.8211 3. 8211 3. 8212 3. 8213 3. 8213 3. 8214 3. 8214 50 30 3. 8215 3. 8216 3. 8216 3. 8217 3. 8218 3. 8218 3. 8219 3. 8220 3. 8220 3. 8221 50 40 3. 8222 •3. 8222 3. 8223 3. 8224 3. 8224 3. 8225 3. 8226 3. 8226 3. 8227 3. 8228 50 50 3. 8228 3. 8229 3. 8230 3. 8236 3. 8230 3. 8231 3. 8231 3. 8232 3. 8233 3. 8239 3. 8233 3. 8240 3. 8234 3. 8241 1 51 3. 8235 3. 8235 3. 8237 3. 8237 3. 8238 3. 8239 51 10 3. 8241 3. 8242 3. 8243 3. 8243 3. 8244 3. 8245 3. 8245 3. 8246 3. 8246 3. 8247 51 20 3. 8248 3. 8248 3. 8249 3. 8250 3. 8250 3. 8251 3. 8252 3. 8252 3. 8253 3. 8254 51 30 3. 8254 3. 8255 3. 8256 3. 8256 3. 8257 3. 8258 3. 8258 3. 8259 3. 8259 3. 8260 51 40 3. 8261 3. 8261 3. 8262 3. 8263 3. 8263 3.8264 3.8265 3. 8265 3. 8266 3, 8267 51 50 3. 8267 3. 8268 3. 8269 3. 8269 3. 8270 3. 8270 3. 8271 3. 8272 3. 8272 3. 8273 1 52 3. 8274 3. 8274 3. 8275 3. 8276 3. 8276 3. 8277 3. 8278 3. 8278 3. 8279 3. 8280 52 10 3. 8280 3. 8281 3. 8281 3. 8282 3. 8283 3. 8283 3. 8284 3. 8285 3. 8285 3. 8286 52 20 3. 8287 3. 8287 3. 8288 3. 8289 3. 8289 3. 8290 3. 8290 3. 8291 3. 8292 3. 8292 52 30 3.8293 3. 8294 3. 8294 3. 8295 3. 8296 3. 8296 3. 8297 3. 8298 3. 8298 3. 8299 52 40 3. 8299 3.8300 3. 8301 3. 8301 3. 8302 3. 8303 3. 8303 3. 8304 3. 8305 3. 8305 52 50 3. 8306 3. 8307 3. 8307 3. 8308 3. 8308 3. 8309 3. 8310 3. 8310 3. 8311 3. 8312 1 53 3. 8312 3. 8313 3. 8314 3. 8314 3. 8315 3. 8315 3. 8316 3. 8317 3. 8317 3. 8318 53 10 3. 8319 3. 8319 3. 8320 3. 8321 3. 8321 3. 8322 3. 8323 3. 8323 3. 8324 3. 8324 53 20 3. 8325 3. 8326 3. 8326 3. 8327 3. 8328 3. 8328 3. 8329 3. 8330 3. 8330 3. 8331 53 30 3. 8331 3. 8332 3. 8333 3. 8333 3. 8334 3. 8335 3. 8335 3. 8336 3. 8337 3. 8337 53 40 3. 8338 3. 8338 3. 8339 3. 8340 3. 8340 3. 8341 3. 8342 3. 8342 3. 8343 3. 8344 53 1 54 50 3. 8344 3. 8345 3. 8345 3. 8346 3. 8347 3. 8347 3. 8348 3. 8349 3. 8349 3. 8350 3. 8351 3. 8351 3. 8352 3. 8352 3. 8353 3. 8354 3. 8354 3. 8355 3. 8356 3. 8356 54 10 3. 8357 3. 8358 3. 8358 3. 8359 3. 8359 3. 8360 3. 8361 3. 8361 3. 8362 3. 8363 54 20 3. 8363 3. 8364 3. 8365 3. 8365 3. 8366 3. 8366 3.8367 3. 8368 3. 8368 3. 8369 54 30 3. 8370 3. 8370 3. 8371 3. 8371 3. 8372 3. 8373 3. 8373 3. 8374 3. 8375 3. 8375 54 40 3. 8376 3. 8377 3. 8377 3. 8378 3. 8378 3. 8379 3. 8380 3. 8380 3. 8381 3. 8382 54 50 3. 8382 3. 8383 3. 8383 3. 8384 3. 8385 3. 8391 3. 8385 3. 8392 3. 8386 3. 8387 3. 8393 3. 8387 3. 8388 1 55 3. 8388 3. 8389 3. 8390 3. 8390 3. 8392 3. 8394 3. 8394 55 10 3. 8395 3. 8395 3. 8396 3. 8397 3. 8397 3. 8398 3. 8399 3. 8399 3. 8400 3. 8400 55 20 3. 8401 3. 8402 3. 8402 3. 8403 3. 8404 3. 8404 3. 8405 3. 8405 3. 8406 3. 8407 55 30 3. 8407 3. 8408 3. 8409 3. 8409 3. 8410 3. 8410 3. 8411 3. 8412 3. 8412 3.8413 55 40 3. 8414 3. 8414 3. 8415 3. 8415 3. 8416 3. 841/ 3. 8417 3. 8418 3. 8419 3. 8419 55 50 3. 8420 3. 8420 3. 8421 3. 8422 3. 8422 3. 842S 3. 8424 3. 8424 3. 8425 3. 8425 1 56 3. 8426 3. 8427 3. 8427 3. 8428 3. 8429 3. 8429 3. 8430 3. 8430 3. 8431 3. 8432 56 10 3. 8432 3. 8433 3. 8434 3. 8434 3.8435 3. 8435 3. 8436 3. 8437 3. 8437 3. 8438 56 20 3. 8439 3. 8439 3. 8440 3. 8440 3. 8441 3. 8442 3.8442 3. 8443 3. 8444 3. 8444 56 30 3. 8445 3.8445 3. 8446 3. 8447 3. 8447 3.8448 3. 8448 3. 8449 3. 8450 3. 8450 56 40 3. 8451 3. 8452 3. 8452 3. 8453 3. 8453 3. 8454 3. 8455 3. 8455 3. 8456 3. 8457 56 50 3. 8457 3. 8458 3. 8458 3. 8459 3. 8460 3. 8460 3. 8461 3. 8462 3. 8462 3. 8463 1 57 3. 8463 3. 8464 3.8465 3. 8465 3. 8466 3. 8466 3. 8467 3. 8468 3. 8468 3. 8469 57 10 3. 8470 3. 8470 3. 8471 3. 8471 3. 8472 3. 8473 3. 8473 3. 8474 3. 8474 3. 8475 57 20 3. 8"476 3. 8476 3. 8477 3. 8478 3. 8478 3. 8479 3. 8479 3. 8480 3. 8481 3. 8481 57 30 3. 8482 3. 8483 3. 8483 3. 8484 3. 8484 3. 8485 3. 8486 3. 8486 3. 8487 3. 8487 57 40 3. 8488 3. 8489 3. 8489 3. 8490 3. 8491 3. 8491 3. 8492 3. 8492 3. 8493 3. 8494 57 50 3. 8494 3. 8495 3. 8495 3. 8496 3. 8497 3.8503' 3. 8497 3. 8498 3. 8499 3. 8499 3. 8500 1 58 3. 8500 3. 8501 3. 8502 3. 8502 3. 8503 3. 8504 3. 8505 3. 8505 3. 8506 58 10 3. 8506 3. 8507 3; 8508 3. 8508 3. 8509 3. 8510 3. 8510 3. 8511 3. 8511 3. 8512 58 20 3. 8513 3. 8513 3. 8514 3. 8514 3. 8515 3. 8516 3. 8516 3.8517 3. 8517 3. 8518 58 30 3. 8519 3. 8519 3. 8520 3. 8521 3. 8521 3. 8522 3. 8522 3. 8523 3. 8524 3. 8524 58 40 3. 8525 3. 8525 3. 8526 3. 8527 3. 8527 3. 8528 3. 8528 3. 8529 3. 8530 3. 8530 58 50 3. 8531 3. 8532 3. 8532 3. 8533 3. 8533 3. 8534 3. 8535 3. 8535 3. 8536 3.8536 1 59 3. 8537 3. 8538 3. 8538 3. 8539 3. 8539 3. 8540 3. 8541 3.8541 3. 8542 3. 8542 59 10 3. 8543 3. 8544 3. 8544 3. 8545 3. 8545 3. 8546 3. 8547 3. 8547 3. 8548 3. 8549 59 20 3. 8549 3. 8550 3. 8550 3. 8551 3. 8552 3. 8552 3. 8553 3. 8553 3. 8554 3. 8555 59 30 3. 8555 3. 8556 3. 8556 3. 8557 3. 8558 3. 8558 3. 8559 3. 8559 3. 8560 3. 8561 59 40 3. 8561 3. 8562 3. 8562 3. 8563 3. 8564 3. 8564 3. 8565 3. 8565 3. 8566 3. 8567 59 50 3. 8567 3. 8568 3. 8568 3. 8569 3. 8570 3.8570 3. 8571 3. 8572 3. 8572 3. 8573 APPENDIX V: TABLE IX. [Page 325 Logarithms of Small Arcs in Space or Time. Arc. 0" 1" 2" 3" 4" 6" 6" 7" 8" 9" o / 2" 0™ 0« 3. 8573 3. 8574 3. 8575 3.8575 3. 8576 3. 8576 3. 8577 3. 8578 3. 8578 3. 8579 10 3. 8579 3. 8580 3. 8581 3. 8581 3. 8582 3. 8582 3. 8583 3. 8584 3. 8584 3. 8585 20 3. 8585 3. 8586 3. 8587 3. 8587 3. 8588 3. 8588 3. 8589 3. 8590 3. 8590 3. 8591 80 3. 8591 3. 8592 3. 8593 3. 8593 3. 8594 3. 8594 3. 8595 3. 8596 3. 8596 3. 8597 40 3. 8597 3. 8598 3. 8599 3. 8599 3. 8600 3. 8600 3. 8601 3. 8602 3. 8602 3. 8603 50 3. 8603 3. 8604 3. 8605 3. 8605 3. 8606 3. 8606 3. 8607 3. 8608 3. 8608 3. 8609 2 1 3. 8609 3. 8610 3. 8611 3. 8611 3. 8612 3. 8612 3. 8613 3. 8614 3. 8614 3. 8615 10 3. 8615 3. 8616 3. 8617 3. 8617 3. 8618 3. 8618 3. 8619 3. 8620 3. 8620 3. 8621 20 3. 8621 3. 8622 3. 8623 3. 8623 3. 8624 3. 8624 3. 8625 3. 8625 3. 8626 3. 8627 30 3. 8627 3. 8628 3. 8628 3. 8629 3. 8630 3. 8630 3. 8631 3. 8631 3. 8632 3. 8633 40 3. 8633 3. 8634 3. 8634 3. 8635 3. 8636 3. 8636 3. 8637 3. 8637 3. 8638 3. 8639 50 3. 8639 3. 8640 3. 8640 3. 8641 3.8642 3. 8642 3. 8643 3. 8643 3. 8644 3. 8645 2 2 3. 8645 3. 8646 3. 8646 3. 8647 3.8647 3. 8648 3. 8649 3. 8649 3. 8650 3. 8650 2 10 3. 8651 3. 8652 3. 8652 3. 8653 3. 8653 3. 8654 3. 8655 3. 8655 3. 8656 3. 8656 2 20 3. 8657 3. 8658 3. 8658 3. 8659 3. 8659 3. 8660 3. 8661 3. 8661 3. 8662 3. 8662 2 30 3. 8663 3. 8663 3. 8664 3. 8665 3. 8665 3. 8666 3. 8666 3. 8667 3. 8668 3. 8668 2 40 3. 8669 3. 8669 3. 8670 3. 8671 3. 8671 3. 8672 3. 8672 3. 8673 3. 8673 3. 8674 2 50 3. 8675 3. 8675 3. 8676 3. 8676 3. 8677 3. 8678 3. 8678 3. 8679 3. 8679 3. 8680 3. 8686 2 3 3. 8681 3. 8681 3. 8682 3. 8682 3. 8683 3. 8684 3. 8684 3. 8685 3. 8685 3 10 3. 8686 3. 8687 3. 8688 3. 8688 3. 8689 3. 8689 3. 8690 3. 8691 3. 8691 3. 8692 3 20 3. 8692 3. 8693 3. 8693 3. 8694 3. 8695 3. 8695 3. 8696 3. 8696 3. 8697 3. 8698 3 30 3. 8698 3. 8699 3. 8699 3. 8700 3. 8701 3. 8701 3. 8702 3. 8702 3. 8703 3. 8703 3 40 3. 8704 3. 8705 3. 8705 3. 8706 3. 8706 3. 8707 3. 8708 3. 8708 3. 8709 3. 8709 3 50 3. 8710 3. 8710 3. 8711 3.8712 3. 8712 3.8713 3. 8713 3. 8714 3. 8715 3. 8715 2 4 3. 8716 3. 8716 3.8717 3.8717 3. 8718 3. 8719 3. 8719 3. 8720 3. 8720 3. 8721 4 10 3. 8722 3. 8722 3. 8723 3. 8723 3. 8724 3. 8724 3. 8725 3. 8726 3. 8726 3. 8727 4 20 3. 8727 3. 8728 3. 8729 3. 8729 3. 8730 3. 8730 3. 8731 3. 8731 3. 8732 3. 8733 4 30 3. 8733 3. 8734 3. 8734 3. 8735 3. 8736 3. 8736 3. 8737 3. 8737 3. 8738 3. 8738 4 40 3. 8739 3. 8740 3. 8740 3. 8741 3. 8741 3. 8742 3. 8742 3. 8743 3. 8744 3. 8744 4 50 3. 8745 3. 8745 3. 8746 3. 8747 3. 8747 3. 8748 3. 8748 3. 8749 3. 8749 3. 8750 2 5 3. 8751 3. 8751 3. 8752 3. 8752 3. 8753 3. 8754 3. 8754 3. 8755 3. 8755 3. 8756 5 10 3. 8756 3. 8757 3. 8758 3. 8758 3. 8759 3. 8759 3. 8760 3. 8760 3. 8761 3. 8762 5 20 3. 8762 3. 8763 3. 8763 3. 8764 3. 8764 3. 8765 3. 8766 3. 8766 3. 8767 3. 8767 5 30 3. 8768 3. 8769 3. 8769 3. 8770 3. 8770 3. 8771 3. 8771 3. 8772 3. 8773 3. 8773 5 .40 3. 8774 3. 8774 3. 8775 3. 8775 3. 8776 3. 8777 3. 8777 3. 8778 3. 8778 3. 8779 5 50 3. 8779 3. 8780 3. 8781 3. 8781 3. 8782 3. 8782 3. 8783 3. 8783 3. 8784 3. 8790 3. 8785 2 6 3. 8785 3. 8786 3. 8786 3. 8787 3. 8788 3.8788 i 3.8789 3. 8789 3. 8790 6 10 3. 8791 3. 8792 3. 8792 3. 8793 3. 8793 3. 8794 3. 8794 3. 8795 3. 8796 3. 8796 6 20 3. 8797 3. 8797 3. 8798 3. 8798 3. 8799 3. 8800 3. 8805 3.8800 3. 8801 3. 8801 3. 8802 6 30 3. 8802 3. 8803 3. 8804 3. 8804 3. 8805 3. 8806 3. 8806 3. 8807 3. 8808 6 40 3. 8808 3. 8809 3. 8809 3. 8810 3. 8810 3. 8811 3.8812 3. 8812 3. 8813 3. 8813 6 50 3. 8814 3. 8814 3. 8820 3.8815 i 3.8816 3. 8816 3. 8822 3. 8817 3. 8822 3. 8817 3. 8818 3. 8824 3. 8818 3. 8824 3. 8819 3. 8825 2 7 3. 8820 3. 8821 3. 8821 3. 8823 ( 10 3. 8825 3. 8826 3. 8826 3. 8827 3. 8828 3. 8828 3. 8829 3. 8829 3. 8830 3. 8830 7 20 3. 8831 3. 8832 3. 8832 3. 8833 3. 8833 3. 8834 3. 8834 3. 8835 3. 8835 3. 8836 7 30 3. 8837 3. 8837 3. 8838 3. 8838 3. 8839 3. 8839 3. 8840 3. 8841 3.8841 3. 8842 7 40 3. 8842 3. 8843 3. 8843 3. 8844 3. 8845 3. 8845 3. 8846 3. 8846 3. 8847 3. 8847 7 50 3. 8848 3. 8849 3. 8849 3. 8850 3. 8850 3. 8851 3. 8851 3. 8852 3. 8852 3. 8853 2 8 3. 8854 3. 8854 3. 8855 3. 8855 3. 8856 3. 8856 3. 8857 3. 8858 3.8858 3. 8859 8 10 3. 8859 3. 8860 3. 8860 3. 8861 3. 8862 3. 8862 3. 8863 3. 8863 3. 8864 3. 8864 8 20 3. 8865 3. 8865 3. 8866 3. 8867 3. 8867 3. 8868 3. 8868 3. 8869 3. 8869 3. 8870 8 30 3. 8871 3. 8871 3. 8872 3. 8872 3. 8873 3. 8873 3. 8874 3. 8874 3. 8875 3. 8876 8 40 3. 8876 3. 8877 3. 8877 3. 8878 3. 8878 3.8879 3. 8880 3. 8880 3. 8881 3. 8881 8 50 3. 8882 3. 8882 3. 8883 3. 8883 3. 8884 3. 8885 3. 8885 3. 8886 3. 8886 3. 8887 2 9 3. 8887 3. 8888 3. 8889 3. 8889 3. 8890 3.8890 3. 8891 3. 8891 3. 8892 3. 8892 9 10 3. 8893 3. 8894 3. 8894 3. 8895 3. 8895 3. 8896 3. 8896 3. 8897 3. 8897 3. 8898 9 20 3. 8899 3. 8899 3. 8900 3. 8900 3. 8901 3. 8901 3. 8902 3. 8903 3. 8903 3. 8904 9 30 3. 8904 3. 8905 3. 8905 3. 8906 3. 8906 3. 8907 3. 8908 3. 8908 3. 8909 3. 8909 9 40 3. 8910 3. 8910 3. 8911 3. 8911 3. 8912 3. 8912 3. 8913 3. 8914 3. 8914 3. 8915 9 50 3. 8915 3. 8916 3. 8916 3. 8917 3. 8918 3. 8918 3. 8919 3. 8919 3. 8920 3. 8920 Page 326J APPENDIX V: TABLE IX. 1 Logarithms of Small Arcs in Space or Time. Arc. 1 0" 1" 2" 8" 4" 5" 6" V 8" 9" o / 2h 10"' 0' 3. 8921 3. 8922 3. 8922 3. 8923 3. 8923 3. 8924 3. 8924 3. 8925 3. 8925 3. 8926 10 10 5. 8927 3. 8927 3. 8928 3. 8928 3. 8929 3.8929 3. 8930 3. 8930 3. 8931 3. 8932 10 20 3. 8932 3. 8933 3. 8933 3. 8934 3. 8934 3. 8935 3. 8935 3. 8936 3. 8937 3. 8937 10 30 3. 8938 3. 8938 3. 8939 3. 8939 3. 8940 3. 8940 3. 8941 3. 8941 3. 8942 3. 8943 10 40 3. 8943 3. 8944 3. 8944 3. 8945 3. 8945 3. 8946 3. 8946 3. 8947 3. 8948 3. 8948 10 50 3. 8949 * > 3. 8949 3. 8950 3. 8950 3. 8951 3. 8951 3. 8952 3. 8953 3. 8953 3. 8954 2 11 3. 8954 3. 8955 3. 8955 3. 8956 3. 8956 3. 8957 3. 8958 3. 8958 3. 8959 3. 8959 11 10 3. 8960 3. 8960 3. 8961 3. 8961 3. 8962 3. 8963 3. 8963 3.8964 3.8964 3. 8965 11 20 3. 8965 3. 8966 3. 8966 3. 8967 3. 8967 3. 8968 3. 8969 3. 8969 3. 8970 3. 8970 11 30 3. 8971 3. 8971 3. 8972 3. 8972 3. 8973 3. 8974 3. 8974 3. 8975 3. 8975 3. 8976 11 40 3. 8976 3. 8977 3. 8977 3. 8978 3. 8978 3. 8979 3. 8980 3. 8980 3. 8981 3. 8981 11 50 3. 8982 3. 8982 3. 8983 3. 8983 3. 8989 3. 8984 3. 8989 3.8985 3. 8985 3. 8991 3. 8986 3. 8991 3. 8986 3."8992 3. 8987 3. 8992 2 12 3. 8987 3. 8988 3. 8988 3. 8990 12 10 3. 8993 3. 8993 3. 8994 3. 8994 3. 8995 3. 8995 3. 8996 3. 8997 3. 8997 3. 8998 12 20 3. 8998 3. 8999 3. 8999 3.9000 3. 9000 3. 9001 3.9001 3. 9002 3. 9003 3. 9003 12 30 3. 9004 3. 9004 3. 9005 3. 9005 3.9006 3. 9006 3. 9007 3. 9007 3. 9008 3. 9009 12 40 3. 9009 3. 9010 3. 9010 3. 9011 3.9011 3. 9012 3. 9012 3. 9013 3. 9013 3. 9014 12 50 3. 9015 3. 9015 3. 9016 3. 9016 3.9017 3. 9017 3. 9018 3. 9018 3.9019 3. 9019 2 13 3. 9020 3. 9021 3. 9021 3. 9022 3. 9022 3. 9023 3. 9023 3. 9024 3. 9024 3. 9025 13 10 3. 9025 3. 9026 3. 9027 3. 9027 3. 9028 3. 9028 3. 9029 3. 9029 3. 9030 3. 9030 13 20 3. 9031 3. 9031 3. 9032 3. 9033 3. 9033 3. 9034 3. 9034 3. 9035 3. 9035 3. 9036 13 30 3. 9036 3. 9037 3. 9037 3. 9038 3. 9038 3. 9039 3. 9040 3. 9040 3. 9041 3. 9041 13 40 3. 9042 3. 9042 3.9043 3. 9043 3. 9044 3. 9044 3. 9045 3. 9046 3. 9046 3. 9047 13 50 3. 9047 3. 9048 3. 9048 3. 9049 3. 9049 3. 9050 3. 9050 3. 9051 3. 9051 3. 9052 2 14 3. 9053 3. 9053 3. 9054 3. 9054 3. 9055 3. 9055 3. 9056 3. 9056 3. 9057 3. 9057 14 10 3. 9058 3. 9058 3. 9059 3. 9060 3. 9060 3. 9061 3. 9061 3. 9062 3. 9062 3. 9063 14 20 3. 9063 3. 9064 3. 9064 3. 9065 3. 9066 3. 9066 3. 9067 3. 9067 3. 9068 3. 9068 14 30 3. 9069 3. 9069 3. 9070 3. 9070 3. 9071 3. 9071 3. 9072 3. 9073 3. 9073 3. 9074 14 40 3. 9074 3. 9075 3. 9075 3. 9076 3. 9076 3. 9077 3. 9077 3. 9078 3. 9078 3. 9079 14 50 3. 9079 3. 9080 3. 9081 3. 9081 3. 9082 3. 9087 3. 9082 3. 9088 3. 9083 3. 9088 3. 9083 3. 9089 3. 9084 "3. 9089 3. 9084 3. 9090 2 15 3. 9085 3. 9085 3. 9086 3. 9086 15 10 3. 9090 3. 9091 3. 9091 3. 9092 3. 9092 3. 9093 3. 9093 3. 9094 3. 9094 3. 9095 15 20 3. 9096 3. 9096 3. 9097 3. 9097 3. 9098 3. 9098 3. 9099 3. 9099 3. 9100 3. 9100 15 30 3. 9101 3. 9101 3. 9102 3. 9103 3. 9103 3. 9104 3.9104 3. 9105 3. 9105 3. 9106 15 40 3. 9106 3. 9107 3. 9107 3. 9108 3. 9108 3. 9109 3. 9109 3. 9110 3. 9111 3.9111 15 50 3.9112 3. 9112 3. 9113 3. 9113 3.9114 3.9114 3.9115 3. 9115 3. 9116 3. 9116 2 16 3.9117 3.9117 3.9118 3.9118 3.9119 3. 9120 3.9120 3. 9121 3.9121 3. 9122 16 10 3. 9122 3.9123 3. 9123 3. 9124 3. 9124 3. 9125 3. 9125 3. 9126 3. 9126 3.9127 16 20 3. 9128 3. 9128 3. 9129 3. 9129 3. 9130 3. 9130 3. 9131 3. 9131 3. 9132 3. 9132 16 30 3. 9133 3. 9133 3. 9134 3. 9134 3. 9135 3. 9135 3. 9136 3. 9137 3.9137 3. 9138 16 40 3. 9138 3. 9139 3. 9139 3. 9140 3. 9140 3. 9141 3. 9141 3. 9142 3. 9142 3. 9143 16 50 3. 9143 3. 9144 3. 9144 3. 9145 3. 9146 3.9146 3. 9147 3. 9147 3. 9148 8. 9148 2 17 3. 9149 3. 9149 3. 9150 3. 9150 3. 9151 3. 9151 3. 9152 3. 9152 3. 9153 3.9153 17 10 3. 9154 3.9155 3. 9155 3. 9156 3. 9156 3.9157 3. 9157 3. 9158 3. 9158 3.9159 17 20 3. 9159 3. 9160 3. 9160 3. 9161 3. 9161 3. 9162 3. 9162 3. 9163 3. 9163 3. 9164 17 30 3. 9165 3. 9165 3. 9166 3. 9166 3. 9167 3.9167 3. 9168 3.9168 3. 9169 3. 9169 17 40 3. 9170 3. 9170 3. 9171 3.9171 3. 9172 3. 9172 3. 9173 3.9173 3. 9174 3. 9175 17 50 3. 9175 3. 9176 3. 9176 3.9177 3.9177 3. 9178 3. 9178 3. 9179 3. 9179 3. 9180 2 18 3. 9180 3. 9181 3. 9181 3. 9182 3. 9182 3. 9183 3. 9183 3. 9184 3. 9184 3. 9185 18 10 3. 9186 3. 9186 3. 9187 3. 9187 3. 9188 3. 9188 3. 9189 3. 9189 3. 9190 3. 9190 18 20 3. 9191 3. 9191 3. 9192 3. 9192 3. 9193 3. 9193 3. 9194 3. 9194 3. 9195 3. 9195 18 30 3. 9196 3. 9197 3. 9197 3. 9198 3. 9198 3. 9199 3. 9199 3. 9200 3. 9200 3. 9201 18 40 3. 9201 3. 9202 3. 9202 3. 9203 3. 9203 3. 9204 3.9204 3. 9205 3. 9205 3.9206 18 50 3. 9206 3. 9207 3. 9207 3. 9208 3. 9209 3. 9214 3. 9209 3. 9210 3. 9210 3. 9215 3. 9211 3. 9216 3. 9211 2 19 3. 9212 3. 9212 3. 9213 3. 9213 3. 9214 3. 9215 3. 9216 19 10 3. 9217 3. 9217 3. 9218 3. 9218 3. 9219 3. 9219 3. 9220 3. 9221 3. 9221 3. 9222 19 20 3. 9222 3. 9223 3. 9223 3. 9224 3. 9224 3. 9225 3. 9225 3. 9226 3. 9226 3. 9227 19 30 3. 9227 3. 9228 3. 9228 3. 9229 3.9229 3. 9230 3. 9230 3. 9231 3. 9231 3. 9232 19 40 3. 9232 3. 9233 3. 9233 3. 9234 3. 9235 3. 9235 3. 9236 3. 9236 3. 9237 3. 9237 19 50 3. 9238 3. 9238 3. 9239 3. 9239 3. 9240 3. 9240 3. 9241 3. 9241 3. 9242 3. 9242 1 APPENDIX V: TABLE IX. [Page 327 Logarithms of Small Arcs in Space or Time. Arc. 0" 1" 2" 8" 4" 5" 6" 7" 8" 9" / 2*^ 20™ 0' 3. 9243 3. 9243 3. 9244 3. 9244 3. 9245 3. 9245 3. 9246 3.9246 3. 9247 3, 9247 20 10 3. 9248 3. 9248 3. 9249 3. 9250 3. 9250 3. 9251 3. 9251 3. 9252 3. 9252 3. 9253 20 20 3. 9253 3. 9254 3. 9254 3. 9255 3. 9255 3. 9256 3. 9256 3. 9257 3. 9257 3. 9258 20 30 3. 9258 3. 9259 3. 9259 3. 9260 3. 9260 3. 9261 3. 9261 3. 9262 3. 9262 3. 9263 20 40 3. 9263 3. 9264 3. 9264 3. 9265 3. 9265 3. 9266 3. 9267 3. 9267 3. 9268 3. 9268 20 50 3. 9269 3. 9269 3. 9270 3. 9270 3. 9271 3. 9271 3. 9272 3. 9272 3. 9273 3. 9273 2 21 3. 9274 3. 9274 3. 9275 3. 9275 3.9276 i 3.9276 3. 9277 3. 9277 3. 9278 3. 9278 21 10 3. 9279 3. 9279 3. 9280 3. 9280 3.9281 1 3.9281 3. 9282 3. 9282 3. 9283 3. 9283 21 20 3. 9284 3. 9284 . 3. 9285 3. 9285 3.9286 1 3.9287 3. 9287 3. 9288 3. 9288 3. 9289 21 30 3. 9289 3. 9290 3. 9290 3. 9291 3. 9291 3. 9292 3. 9292 3.9293 3.9293 3. 9294 21 40 3. 9294 3. 9295 3. 9295 3. 9296 3. 9296 3. 9297 3. 9297 3.9298 3.9298 3. 9299 21 50 3. 9299 3.9300 3. 9300 3. 9301 3. 9301 3. 9302 3. 9302 3. 9303 3. 9303 3. 9304 2 22 3. 9304 3. 9305 3. 9305 3. 9306 3. 9306 3. 9307 3. 9307 3. 9308 3. 9308 1 3. 9309 | 22 10 3. 9309 3. 9310 3. 9311 3.9311 3. 9312 3. 9312 3. 9313 3. 9313 3. 9314 3. 9314 22 20 3. 9315 3. 9315 3. 9316 3. 9316 3.9317 3.9317 3. 9318 3. 9318 3. 9319 3. 9319 22 30 3. 9320 3. 9320 3. 9321 3. 9321 3.9322 1 3.9322 3. 9323 3. 9323 3. 9324 3. 9324 22 40 3. 9325 3. 9325 3. 9326 3. 9326 3.9327 3.9.327 3. 9328 3. 9328 3. 9329 3. 9329 22 50 3. 9330 3. 9330 3. 9331 3. 9331 379336" 3.9332 3.9332 3. 9333 3. 9333 3. 9334 3. 9334 2 23 3. 9335 3. 9335 3. 9336 3.9337 ; 3.9337 3. 9338 3.9338 3.9339 3. 9339 23 10 3. 9340 3. 9340 3. 9341 3. 9341 3. 9342 3.' 9342 3. 9343 3. 9343 3. 9344 3. 9344 23 20 3. 9345 3. 9345 3. 9346 3. 9346 3. 9347 3. 9348 3. 9348 3. 9349 3. 9349 3. 9350 23 30 3. 9350 3. 9351 3. 9351 3. 9352 3.9352 ! 3.9353 3. 9353 3.9354 3. 9354 3. 9355 23 40 3. 9355 3. 9356 3. 9356 3. 9357 3.9357 1 3.9358 3. 9358 3. 9359 3. 9359 3. 9360 23 50 3. 9360 3. 9361 3. 9361 3. 9362 3.9362 1 3.9363 3. 9363 3. 9364 3. 9364 3. 9365 2 24 3. 9365 3. 9366 3. 9366 3. 9367 3. 9367 3. 9368 3. 9368 3. 9369 3. 9369 i 3. 9370 24 10 3. 9370 3. 9371 3. 9371 3. 9372 3. 9372 3. 9373 3. 9373 3. 9374 3.9374 3.9375 24 20 3. 9375 3. 9376 3. 9376 3. 9377 3. 9377 3. 9378 3. 9378 3. 9379 3. 9379 3. 9380 24 30 3. 9380 3. 9381 3. 9381 3. 9382 3. 9382 3. 9383 3. 9383 3. 9384 3. 9384 i 3. 9385 24 40 3. 9385 3. 9386 3. 9386 3. 9387 3. 9387 3. 9388 3. 9388 3. 9389 3. 9389 i 3. 9390 24 50 3. 9390 3. 9391 3. 9391 3. 9392 3. 9392 3. 9397 3. 9393 3. 9398 3. 9393 3. 9394 3. 9394 3. 9399 3. 9395 2 25 3. 9395 3. 9396 3. 9396 3. 9397 3. 9398 3. 9399 3.9400 25 10 3. 9400 3. 9401 3. 9401 3. 9402 3. 9402 3. 9403 3. 9403 3. 9404 3. 9404 3. 9405 25 20 3. 9405 3. 9406 3. 9406 3. 9407 3. 9407 3. 9408 3. 9408 3. 9409 3. 9409 3. 9410 25 30 3. 9410 3.9411 3. 9411 3. 9412 3. 9412 3. 9413 3. 9413 3. 9414 3. 9414 3. 9415 25 40 3. 9415 3. 9416 3. 9416 3. 9417 3. 9417 3. 9418 3. 9418 3. 9419 3. 9419 3. 9420 25 50 3. 9420 3. 9421 3. 9421 3. 9422 3. 9422 3. 9423 3. 9423 3. 9424 3. 9424 3. 9425 2 26 3. 9425 3. 9426 3. 9426 3. 9427 3. 9427 3. 9428 3. 9428 3. 9429 3. 9429 3. 9430 26 10 3. 9430 3. 9430 3. 9431 3. 9431 3. 9432 3. 9432 3. 9433 3. 9433 3. 9434 3. 9434 26 20 3. 9435 3. 9435 3. 9436 3. 9436 3. 9437 3. 9437 3. 9438 3. 9438 3. 9439 3. 9439 26 30 3. 9440 3.9440 3. 9441 3. 9441 3. 9442 3. 9442 3. 9443 3. 9443 3. 9444 3. 9444 26 40 3. 9445 3.9445 3. 9446 3. 9446 3. 9447 3. 9447 3. 9448 3. 9448 3.9449 3. 9449 26 50 3. 9450 3. 9450 3. 9451 3. 9451 3. 9452 3. 9452 3. 9453 3. 9453 3. 9454 3. 9454 2 27 3. 9455 3. 9455 3. 9456 3. 9456 3. 9457 3. 9457 3. 9458 3. 9458 3. 9459 3. 9459 27 10 3. 9460 3. 9460 3. 9461 3. 9461 3. 9462 3. 9462 3. 9463 3. 9463 3.9464 3. 9464 27 20 3. 9465 3. 9465 3. 9466 3. 9466 3. 9466 3. 9467 3. 9467 3. 9468 3. 9468 3. 9469 2-' 30 3. 9469 3. 9470 3. 9470 3. 9471 3. 9471 3. 9472 3. 9472 3. 9473 3. 9473 3. 9474 27 40 3. 9474 3. 9475 3. 9475 3. 9476 3. 9476 3. 9477 3. 9477 3. 9478 3. 9478 3. 9479 27 50 3. 9479 3. 9480 3. 9480 3. 9481 3. 9481 3. 9482 3. 9482 3. 9483 3. 9483 3. 9484 2 28 3. 9484 3. 9485 3. 9485 3. 9486 3. 9486 3. 9487 3. 9487 3. 9488 3. 9488 3. 9489 28 10 3. 9489 3. 9490 3. 9490 3. 9490 3. 9491 3. 9491 3. 9492 3. 9492 3. 9493 3. 9493 28 20 3. 9494 3. 9494 3. 9495 3. 9495 3. 9496 3. 9496 3. 9497 3. 9497 3. 9498 3. 9498 28 30 3. 9499 3. 9499 3. 9500 3. 9500 3. 9501 3. 9501 3. 9502 3. 9502 3. 9503 3. 9503 28 40 3. 9504 3. 9504 3. 9505 3. 9505 3. 9506 3. 9506 3. 9507 3. 9507 3. 9508 3. 9508 28 50 3. 9509 3. 9509 3.9509 3. 9510 3. 9510 3. 9511 3. 9511 3. 9512 3. 9512 3. 9513 2 29 3. 9513 3. 9514 3. 9514 3. 9515 3. 9515 3. 9516 3. 9516 3. 9517 3. 9517 3. 9518 29 10 3. 9518 3. 9519 3. 9519 3. 9520 3. 9520 3. 9521 3. 9521 3. 9522 3. 9522 3. 9523 29 20 3. 9523 3. 9524 3. 9524 3. 9525 3. 9525 3. 9526 3. 9526 3. 9526 3. 9527 3. 9527 29 30 3. 9528 3. 9528 3. 9529 3. 9529 3. 9530 3. 9530 3. 9531 3. 9531 3. 9532 3. 9532 29 40 3. 9533 3. 9533 3. 9534 3. 9534 3. 9535 3. 9435 3. 9536 3. 9536 3. 9537 3. 9537 29 50 3. 9538 3. 9538 3. 9539 3. 9539 3. 9540 3. 9540 3. 9540 3. 9541 3. 9541 3.9542 Page 328] APPENDIX V: TABLE IX. Logarithms of Small Arcs in Space or Time. Arc. 0" 1" 2" 8" 4" 5" 6" 7" 1 8" 1 9" 1 o / 2^ 30" 0' 3.9542 1 3.9543 3.9543 3.9544 3.9544 3. 9545 3. 9545 3. 9546 3.9546 3. 9547 30 10 3.9547 1 3.9548 3. 9548 3. 9549 3. 9549 3.9550 3. 9550 3. 9551 3. 9551 3. 9552 30 20 3. 9552 3. 9553 -3.9553 3. 9554 3. 9554 3. 9554 3. 9555 3. 9555 3. 9556 3. 9556 30 30 3. 9557 3. 9557 3. 9558 3. 9558 3. 9559 3. 9559 3. 9560 3. 9560 3. 9561 3. 9561 30 40 3. 9562 1 ^. 9562 3.9566 ! 3.9567 3. 9563 3. 9563 3. 9564 3. 9564 3. 9565 3. 9565 3. 9566 3. 9566 30 50 3. 9567 3. 9568 3. 9573 3. 9568 3. 9573 3. 9569 3.9574 3. 9569 3. 9570 3. 9570 3:9575' 3. 9571 3. 9576 2 31 3.9571 3.9572 3. 9572 3. 9574 3. 9575 31 10 3.9576 3.9577 3. 9577 3. 9578 3. 9578 3. 9578 3. 9579 3. 9579 3. 9580 3. 9580 31 20 3.9581 t 3.9581 3. 9582 3. 9582 3. 9583 3. 9583 3. 9584 3. 9584 3. 9585 3. 9585 31 30 3.9586 3.9586 3. 9587 3. 9587 3. 9588 3. 9588 3. 9589 3.9589 3.9589 3. 9590 31 40 3.9590 3.9591 3. 9591 3. 9592 3. 9592 3. 9593 3. 9593 3. 9594 3. 9594 3. 9595 31 50 3.9595 ! 3.9596 3. 9596 3. 9597 3. 9597 3. 9598 3. 9598 3. 9599 ! 3. 9599 3. 9599 2 32 3.9600 1 3.9600 3. 9601 3. 9601 3. 9602 3. 9602 3. 9603 3. 9603 3. 9604 3. 9604 32 10 3. 9605 3. 9605 3. 9606 3. 9606 3. 9607 3. 9607 3. 9608 3. 9608 3. 9609 3. 9609 32 20 3. 9609 3. 9610 3. 9610 3. 9611 3.9611 3. 9612 3. 9612 3. 9613 3. 9613 3. 9614 32 30 3. 9614 3. 9615 3. 9615 3. 9616 3. 9616 3. 9617 3. 9617 3. 9618 3. 9618 3. 9618 32 40 3. 9619 3. 9619 3. 9620 3. 9620 3. 9621 3. 9621 3. 9622 3. 9622 3. 9623 3. 9623 32 50 3. 9624 3. 9624 3. 9625 3. 9625 3. 9626 3. 9626 3. 9627 3. 9627 3. 9627 3. 9632 3. 9628 3. 9633 2 33 3. 9628 3. 9629 3. 9629 3. 9630 3. 9630 3. 9631 3. 9631 3. 9632 33 10 3. 9633 3. 9634 3. 9634 3. 9634 3. 9635 3. 9635 3. 9636 3. 9636 3. 9637 3. 9637 33 20 3. 9638 3. 96.38 3. 9639 3. 9639 3. 9640 3. 9640 3.9641 3.9641 3. 9642 3. 9642 33 30 3. 9642 3. 9643 3. 9643 3. 9644 3.9644 3.9645 3. 9645 3. 9646 3.9646 3. 9647 33 40 3. 9647 3. 9648 3. 9648 3. 9649 3. 9649 3. 9650 3. 9650 3. 9651 3. 9651 3. 9652 33 50 3. 9652 3. 9653 3. 9653 3. 9653 3. 9654 3. 9654 3. 9655 3. 9655 3. 9656 3. 9656 2 34 3.9657 3. 9657 3. 9658 3. 9658 3. 9658 3. 9659 3. 9659 3. 9660 3. 9660 3. 9661 34 10 3. 9661 3. 9662 3. 9662 3. 9663 3. 9663 3. 9664 3. 9664 3. 9665 3. 9665 3. 9665 34 20 3. 9666 3. 9666 3. 9667 3. 9667 3. 9668 3. 9668 3. 9669 3. 9669 3. 9670 3. 9670 34 30 3. 9671 3. 9671 3. 9672 3. 9672 3. 9672 3. 9673 3.9673 3. 9674 3. 9674 3. 9675 34 40 3. 9675 3. 9676 3. 9676 3. 9677 3. 9677 3.9678 I 3.9678 3. 9679 3. 9679 3. 9680 34 50 3. 9680 3. 9681 3. 9681 3. 9682 3. 9682 3. 9682 3. 9683 3. 9683 3. 9684 3. 9684 2 35 3. 9685 3. 9685 3. 9686 3. 9686 3. 9687 3. 9687 3. 9688 3. 9688 3. 9689 i 3. 9689 35 10 3. 9689 3. 9690 3. 9690 3. 9691 3. 9691 3. 9692 3. 9692 3. 9693 3. 9693 3. 9694 35 20 3. 9694 3. 9695 3. 9695 3. 9696 3. 9696 3. 9696 3. 9697 3. 9697 3. 9698 3. 9698 35 30 3. 9699 3. 9699 3. 9700 3. 9700 3. 9701 3. 9701 3. 9702 3. 9702 3. 9703 3. 9703 35 40 3. 9703 3. 9704 3. 9704 3. 9705 3. 9705 3. 9706 3. 9706 3. 9707 3. 9707 i 3. 9708 | 35 50 3. 9708 3.9713 3. 9709 3. 9709 3. 9710 3. 9710 3. 9710 3.9711 3.9711 3. 9712 3. 9712 2 36 3.9713 3. 9714 3. 9714 3. 9715 3. 9715 3. 9716 3. 9716 3. 9716 3. 9717 36 10 3. 9717 3.9718 3. 9718 3. 9719 3. 9719 3. 9720 3. 9720 3. 9721 3. 9721 3. 9722 36 20 3. 9722 3. 9722 3. 9723 3. 9723 3. 9724 3. 9724 3. 9725 3. 9725 3. 9726 3. 9726 36 30 3. 9727 3. 9727 3. 9728 3. 9728 3. 9729 3. 9729 3. 9729 3. 9730 3.9730 3.9731 36 40 3. 9731 3. 9732 3. 9732 3. 9733 3. 9733 3. 9734 3. 9734 3. 9735 3. 9735 1 3. 9735 36 50 3. 9736 3. 9736 3. 9737 3. 9737 3. 9738 3. 9738 3. 9739 3. 9739 3. 9740 : 3. 9740 2 37 3. 9741 3. 9741 3. 9741 3. 9742 3. 9742 3. 9743 3. 9743 3. 9744 3. 9744 i 3. 9745 37 10 3. 9745 3. 9746 3. 9746 3. 9746 3. 9747 3. 9747 3. 9748 3. 9748 3. 9749 i 3. 9749 37 20 3. 9750 3. 9750 3. 9751 3. 9751 3. 9752 3. 9752 3. 9752 3. 9753 3. 9753 3. 9754 37 30 3. 9754 3. 9755 3. 9755 3. 9756 3. 9756 3. 9757 3. 9757 3. 9758 3. 9758 3. 9758 37 40 3. 9759 3. 9759 3. 9760 3. 9760 3. 9761 3. 9761 3. 9762 3. 9762 3. 9763 3. 9763 37 50 3. 9763 3. 9764 3.9764 3. 9765 3. 9765 3. 9766 3. 9766 3. 9767 3. 9767 3. 9768 2 38 3. 9768 3. 9769 3. 9769 3. 9769 3. 9770 3. 9770 3. 9771 3. 9771 3. 9772 3. 9772 38 10 3. 9773 3. 9773 3. 9774 3. 9774 3. 9774 3. 9775 3. 9775 3. 9776 3. 9776 3. 9777 38 20 3. 9777 3. 9778 3. 9778 3. 9779 3. 9779 3. 9779 3. 9780 3. 9780 3. 9781 3. 9781 38 30 3. 9782 3. 9782 3. 9783 3. 9783 3. 9784 3. 9784 3. 9785 3. 9785 3. 9785 3. 9786 38 40 3. 9786 3. 9787 3. 9787 3. 9788 3. 9788 3. 9789 3. 9789 3. 9790 3. 9790 3. 9790 38 50 3. 9791 3. 9791 3. 9792 3. 9792 3. 9793 3. 9793 3. 9794 3. 9794 3. 9795 3. 9795 2 39 3. 9795 3. 9796 3. 9796 3. 9797 3. 9797 3. 9798 3. 9798 3. 9799 3. 9799 3. 9800 39 10 3. 9800 3. 9800 3. 9801 3. 9801 3. 9802 3. 9802 3. 9803 3. 9803 3. 9804 3. 9804 39 20 3. 9805 3. 9805 3. 9805 3. 9806 3. 9806 3. 9807 3. 9807 3. 9808 3. 9808 3. 9809 39 30 3. 9809 3.9810 3. 9810 3. 9810 3.9811 3. 9811 3. 9812 3. 9812 3. 9813 3. 9813 39 40 3. 9814 3.9814 3. 9815 3. 9815 3. 9815 3. 9816 3. 9816 3.9817 3.9817 3.9818 39 50 3. 9818 3.9819 .3. 9819 3.9819 3. 9820 3. 9820 3. 9821 3. 9821 3. 9822 3. 9822 APPENDIX V: TABLE IX. [Page 329 Logarithms of Small Arcs in Space or Time. Arc. 0" 1" 2" 8" 4" 5" 6" 7" 1 8" 9" o / // 2h 40m 0* 3. 9823 3. 9823 3. 9824 3. 9824 3. 9825 3. 9825 3. 9825 3. 9826 3. 9826 3. 9827 40 10 3. 9827 3. 9828 3. 9828 3. 9829 3. 9829 3. 9829 3. 9830 3. 9830 3. 9831 3. 9831 40 20 3. 9832 3. 9832 3. 9833 3. 9833 3. 9834 3. 9834 3. 9834 3. 9835 3. 9835 3. 9836 40 30 3. 9836 3. 9837 3. 9837 3. 9838 3. 9838 3. 9839 3. 9839 3. 9839 3. 9840 3. 9840 40 40 3. 9841 3. 9841 3. 9842 3. 9842 3. 9843 3. 9843 3. 9843 3. 9844 3. 9844 3. 9845 40 50 3. 9845 3. 9846 3. 9846 3. 9847 3. 9847 3. 9848 3. 9848 3. 9848 3. 9849 3. 9849 2 41 3. 9850 3.9850 3. 9851 3. 9851 3. 9852 3. 9852 3. 9852 3. 9853 3. 9853 3. 9854 41 10 3. 9854 3. 9855 3. 9855 3. 9856 3. 9856 3. 9857 3. 9857 3. 9857 3. 9858 3. 9858 41 20 3. 9859 3. 9859 3. 9860 3. 9860 3. 9861 3. 9861 3. 9861 3. 9862 3. 9862 3. 9863 41 30 3. 9863 3. 9864 3. 9864 3. 9865 3. 9865 3. 9865 3. 9866 3.9866 3. 9867 3. 9867 41 40 3. 9868 3. 9868 3. 9869 3. 9869 3. 9870 3.9870 3. 9870 3. 9871 3. 9871 3. 9872 41 50 3. 9872 3. 9873 3. 9873 3. 9874 3. 9874 3. 9874 3. 9875 3. 9875 3. 9876 3. 9876 2 42 3. 9877 3. 9877 3. 9878 3. 9878 3. 9878 3. 9879 3. 9879 3. 9880 3. 9880 3. 9881 42 10 3. 9881 3. 9882 3. 9882 3. 9882 3. 9883 3. 9883 3. 9884 3. 9884 3. 9885 3. 9885 42 20 3. 9886 3. 9886 3. 9886 3. 9887 3. 9887 3. 9888 3. 9888 3. 9889 i 3. 9889 3. 9890 42 30 3. 9890 3. 9890 3. 9891 3. 9891 3. 9892 3. 9892 3. 9893 3. 9893 i 3. 9894 3. 9894 42 40 3. 9894 3. 9895 3. 9895 3.9896 i 3.9896 3. 9897 3. 9897 3. 9898 i 3. 9898 3. 9898 42 50 3. 9899 3. 9899 3.9900 3.9900 ! 3.9901 3. 9901 3. 9902 3. 9902 3. 9903 3. 9903 2 43 3. 9903 3. 9904 3. 9904 3. 9905 3. 9905 3.9906 3. 9906 3. 9906 3. 9907 1 3. 9907 43 10 3. 9908 3. 9908 3. 9909 3. 9909 3. 9910 3. 9910 3. 9910 3.9911 3.9911 1 3.9912 43 20 3. 9912 3. 9913 3. 9913 3.9914 : 3.9914 3. 9914 3. 9915 3. 9915 3.9916! 3.9916 43 30 3. 9917 3. 9917 3. 9918 3.9918 I 3.9918 3. 9919 3. 9919 3. 9920 3. 9920 1 3. 9921 43 40 3. 9921 3. 9922 3. 9922 3. 9922 3. 9923 3. 9923 3. 9924 3. 9924 3. 9925 ! 3. 9925 43 50 3. 9926 3. 9926 3. 9926 3. 9927 3. 9927 3. 9928 3. 9928 3. 9929 3. 9929 3. 9930 2 44 3. 9930 3. 9930 3. 9931 3. 9931 3. 9932 3. 9932 3. 9933 3. 9933 1 3. 9933 3. 9934 44 10 3. 9934 3. 9935 3. 9935 3. 9936 3. 9936 3. 9937 3. 9937 3. 9937 1 3. 9938 [ 3. 9938 44 20 3. 9939 3. 9939 3. 9940 1 3. 9940 3. 9941 3. 9941 3. 9941 3. 9942 3. 9942 3. 9943 44 30 3. 9943 3. 9944 3. 9944 3. 9944 3. 9945 3. 9945 3. 9946 3. 9946 I 3. 9947 ; 3. 9947 44 40 3. 9948 3. 9948 3. 9948 3. 9949 3. 9949 3. 9950 3. 9950 3. 9951 3. 9951 i 3. 9952 | 44 50 3. 9952 3. 9952 3. 9953 3. 9953 3. 9954 3.9954 i 3.9955 3. 9955 3. 9955 3. 9956 2 45 3. 9956 3. 9957 3. 9957 3. 9958 3. 9958 3. 9959 3. 9959 3. 9959 3. 9960 3. 9960 45 10 3. 9961 3. 9961 3. 9962 3. 9962 3. 9962 3. 9963 3. 9963 3. 9964 3. 9964 3. 9965 45 20 3. 9965 3. 9966 3. 9966 3. 9966 3. 9967 3. 9967 3. 9968 3. 9968 3. 9969 3. 9969 45 30 3. 9969 3. 9970 3. 9970 3. 9971 3. 9971 3. 9972 3.9972 3. 9973 3. 9973 3. 9973 45. 40 3. 9974 3. 9974 3. 9975 3. 9975 3. 9976 3. 9976 3. 9976 3. 9977 3.9977 3. 9978 45 50 3. 9978 3. 9979 3. 9979 3. 9980 3. 9980 3. 9980 3. 9981 3. 9981 3. 9982 3. 9982 2 46 3. 9983 3. 9983 3.9983 1 3.9984 3. 9984 3. 9985 3. 9985 3. 9986 3. 9986 3. 9987 46 10 3. 9987 3. 9987 3. 9988 3. 9988 3. 9989 3. 9989 3. 9990 3. 9990 3. 9990 3. 9991 46 20 3. 9991 3. 9992 3. 9992 3. 9993 3. 9993 3. 9993 3. 9994 3. 9994 3. 9995 3. 9995 46 30 3. 9996 3. 9996 3. 9997 3. 9997 3. 9997 3. 9998 3. 9998 3.9999 3. 9999 4. 0000 46 40 4. 0000 4. 0000 4. 0001 4.0001 4. 0002 4. 0002 4. 0003 4.0003 4. 0003 4.0004 46 50 4. 0004 4. 0005 4. 0005 4.0006 4. 0006 4.0007 4. 0007 4.0007 4. 0008 4. 0008 2 47 4. 0009 4.0009 4. 0010 4. 0010 4. 0010 4.0011 4.0011 4. 0012 4.0012! 4.0013 1 47 10 4. 0013 4. 0013 4. 0014 4.0014 4. 0015 4. 0015 4. 0016 4. 0016 4. 0016 4.0017 47 20 4. 0017 4.0018 4. 0018 4. 0019 4. 0019 4. 0019 4. 0020 4. 0020 4. 0021 4.0021 47 30 4. 0022 4.0022 4.0023 4. 0023 4. 0023 4. 0024 4. 0024 4. 0025 4. 0025 4. 0026 47 40 4. 0026 4. 0026 4. 0027 4. 0027 4. 0028 4.0028 4. 0029 4.0029 4. 0029 4. 0030 47 50 4. 0030 4. 0031 4.0031 4. 0032 4. 0032 4. 0032 4. 0033 4. 0037 4. 0033 4. 0038 4. 0034 4.0038 4. 0034 4. 0038 2 48 4. 0035 4.0035 4. 0035 4. 0036 4. 0036 4. 0037 48 10 4. 0039 4.0039 4.0040 4. 0040 4. 0041 4. 0041 4. 0041 4.0042 4. 0042 4. 0043 48 20 4. 0043 4. 0044 4. 0044 4. 0045 4. 0045 4. 0045 4. 0046 4. 0046 4.0047 4. 0047 48 30 4. 0048 4. 0048 4. 0048 4. 0049 4. 0049 4. 0050 4. 0050 4. 0051 4. 0051 4.0051 48 40 4. 0052 4.0052 4. 0053 4. 0053 4. 0054 4.0054 4. 0054 4. 0055 4.0055 4. 0056 48 50 4. 0056 4. 0057 4. 0057 4.0057 4. 0058 4. 0058 4.0059 4. 0059 4.0060 4. 0060 2 49 4. 0060 4. 0061 4. 0061 4. 0062 4. 0062 4. 0063 4. 0063 4. 0063 4.0064 4. 0064 49 10 4. 0065 4. 0065 4. 0066 4.0066 4. 0066 4. 0067 4. 0067 4. 0068 4. 0068 4. 0069 49 20 4. 0069 4. 0069 4. 0070 4. 0070 4. 0071 4. 0071 4. 0072 4. 0072 4. 0072 4.0073 49 30 4. 0073 4.0074 4.0074 4. 0074 4. 0075 4. 0075 4. 0076 4. 0076 4. 0077 4. 0077 49 40 4.0077 4. 0078 4. 0078 4.0079 4. 0079 4. 0080 4. 0080 4. 0080 4. 0081 4. 0081 49 50 4. 0082 4.0082 4. 0083 4. 0083 4. 0083 4. 0084 4. 0084 4. 0085 4. 0085 4.0086 Page 330] APPENDIX V: TABLE IX. Logarithms of Small Arcs in Space or Time. Arc. 0" 1" 2" 8" 4" 6" 6" 7" 8" 9" O ' II 2" 50™ 0' 50 10 50 20 50 30 50 40 50 50 4.0086 4. 0090 4.0095 4. 0099 4. 0103 4. 0107 4.0086 4. 0091 4.0095 4. 0099 4. 0103 '4. 0108 4.0087 4.0091 4.0095 4. 0100 4. 0104 4. 0108 4.0087 4.0092 4.0096 4. 0100 4. 0104 4.0109 4.0088 4.0092 4.0096 4. 0100 4. 0105 4. 0109 4.0088 4. 0092 4.0097 4. 0101 4. 0105 4. 0109 4.0089 4. 0093 4. 0097 4. 0101 4. 0106 4.0110 4.0089 4.0093 4.0097 4. 0102 4. 0106 4.0110 4.0089 4. 0094 4. 0098 4. 0102 4. 0106 4.0111 4.0090 4. 0094 4.0098 4. 0103 4. 0107 4.0111 2 51 51 10 51 20 51 30 51 40 51 50 4. 0111 4.0116 4. 0120 4. 0124 4. 0128 4. 0133 4.0112 4.0116 4. 0120 4. 0125 4. 0129 4. 0133 4.0112 4.0117 4. 0121 4. 0125 4. 0129 4. 0133 4. 0113 4.0117 4. 0121 4. 0125 4. 0130 4. 0134 4.0113 4.0117 4. 0122 4.0126 4. 0130 4. 0134 4. 0114 4.0118 4.0122 4. 0126 4. 0130 4. 0135 4.0114 4.0118 4. 0122 4. 0127 4. 0131 4. 0135 4. 0114 4.0119 4. 0123 4. 0127 4. 0131 4. 0136 4.0115 4. 0119 4. 0123 4. 0128 4. 0132 4. 0136 4.0115 4. 0120 4. 0124 4. 0128 4. 0132 4. 0136 2 52 52 10 52 20 52 30 52 40 52 50 4. 0137 4. 0141 4. 0145 4. 0149 4. 0154 4. 0158 4. 0137 4. 0141 4. 0146 4. 0150 4. 0154 4. 0158 4. 0138 4. 0142 4. 0146 4. 0150 4. 0154 4. 0159 4. 0138 4. 0142 4. 0146 4. 0151 4. 0155 4. 0159 4. 0138 4. 0143 4. 0147 4. 0151 4. 0155 4. 0159 4. 0139 4. 0143 4. 0147 4. 0152 4. 0156 4. 0160 4. 0139 4.0144 4. 0148 4. 0152 4. 0156 4. 0160 4. 0140 4.0144 4. 0148 4. 0153 4. 0157 4. 0161 4. 0140 4. 0144 4. 0149 4. 0153 4. 0157 4. 0161 4. 0141 4. 0145 4. 0149 4. 0153 4. 0157 4. 0162 2 53 53 10 53 20 53 30 53 40 53 50 4. 0162 4. 0166 4.0170 4. 0175 4. 0179 4. 0183 4. 0162 4. 0167 4. 0171 4. 0175 4. 0179 4. 0183 4. 0163 4. 0167 4. 0171 4. 0175 4. 0180 4. 0184 4. 0163 4. 0167 4. 0172 4. 0176 4. 0180 4. 0184 4. 0164 4. 0168 4. 0172 4. 0176 4. 0180 4. 0185 4. 0164 4. 0168 4. 0172 4.0177 4.0181 4. 0185 4. 0164 4. 0169 4. 0173 4. 0177 4.0181 4. 0185 4. 0165 4. 0169 4. 0173 4.0177 4. 0182 4. 0186 4. 0165 4. 0169 4. 0174 4. 0178 4. 0182 4. 0186 4. 0166 4. 0170 4. 0174 4. 0178 4. 0182 4. 0187 2 54 54 10 54 20 54 30 54 40 54 50 4. 0187 4. 0191 4. 0195 4. 0199 4.0204 4. 0208 4. 0187 4. 0192 4. 0196 4. 0200 4. 0204 4. 0208 4. 0188 4. 0192 4. 0196 4. 0200 4. 0204 4. 0209 4.0188 4. 0192 4. 0197 4. 0201 4. 0205 4. 0209 4. 0189 4. 0193 4. 0197 4. 0201 4. 0205 4. 0209 4. 0189 4. 0193 4. 0197 4. 0202 4. 0206 4. 0210 4. 0190 4. 0194 4:0198 4. 0202 4. 0206 4. 0210 4. 0190 4. 0194 4. 0198 4. 0202 4. 0207 4.0211 4. 0190 4. 0194 4. 0199 4. 0203 4. 0207 4. 0211 4. 0191 4. 0195 4. 0199 4. 0203 4. 0207 4. 0211 2 55 55 10 55 20 55 30 55 40 55 50 4. 0212 4. 0216 4. 0220 4. 0224 4. 0228 4. 0233 4. 0212 4. 0216 4. 0221 4. 0225 4. 0229 4. 0233 4. 0213 4. 0217 4. 0221 4. 0225 4. 0229 4. 0233 4. 0213 4. 0217 4. 0221 4. 0225 4. 0230 4. 0234 4. 0214 4. 0218 4. 0222 4. 0226 4. 0230 4. 0234 4. 0214 4. 0218 4. 0222 4. 0226 4. 0230 4. 0235 4. 0214 4. 0219 4. 0223 4. 0227 4. 0231 4. 0235 4. 0239 4. 0243 4. 0247 4. 0251 4. 0256 4. 0260 4. 0215 4.0219 4. 0223 4. 0227 4. 0231 4. 0235 4. 0240 4. 0244 4. 0248 4. 0252 4. 0256 4. 0260 4. 0215 4. 0219 4. 0223 4. 0228 4. 0232 4. 0236 4. 0240 4. 0244 4. 0248 4. 0252 4. 0256 4. 0260 4. 0216 4. 0220 4. 0224 4. 0228 4. 0232 4. 0236 2 56 56 10 56 20 56 30 56 40 56 50 4. 0237 4. 0241 4.0245 4. 0249 4. 0253 4. 0257 4. 0237 4. 0241 4. 0245 4. 0249 4. 0253 4. 0258 4. 0237 4. 0242 4. 0246 4. 0250 4.0254 4. 0258 4. 0238 4. 0242 4. 0246 4. 0250 4. 0254 4. 0258 4. 0238 4. 0242 4. 0246 4. 0251 4. 0255 4. 0259 4. 0239 4. 0243 4. 0247 4. 0251 4. 0255 4. 0259 4. 0240 4. 0244 4. 0249 4. 0253 4. 0257 4. 0261 4. 0265 4. 0269 4. 0273 4. 0277 4. 0281 4. 0285 4. 0289 4. 0293 4. 0297 4. 0302 4. 0306 4. 0310 2 57 67 10 57 20 57 30 57 40 57 50 4. 0261 4. 0265 4. 0269 4. 0273 4. 0278 4. 0282 4. 0262 4. 0266 4. 0270 4. 0274 4. 0278 4. 0282 4. 0262 4. 0266 4. 0270 4. 0274 4. 0278 4. 0282 4. 0262 4. 0267 4. 0271 4. 0275 4. 0279 4. 0283 4. 0263 4. 0267 4. 0271 4. 0275 4. 0279 4. 0283 4. 0263 4. 0267 4. 0271 4. 0276 4. 0280 4. 0284 4. 0264 4. 0268 4. 0272 4. 0276 4. 0280 4. 0284 4. 0264 4. 0268 4. 0272 4. 0276 4. 0280 4. 0284 4. 0265 4. 0269 4. 0273 4. 0277 4. 0281 4. 0285 2 58 58 10 58 20 58 30 58 40 58 50 4. 0286 4. 0290 4. 0294 4. 0298 4. 0302 4. 0306 4. 0286 4.0290 4. 0294 4. 0298 4. 0302 4. 0306 4. 0287 4. 0291 4. 0295 4. 0299 4. 0303 4. 0307 4. 0287 4. 0291 4. 0295 4. 0299 4. 0303 4. 0307 4. 0287 4. 0291 4. 0295 4. 0300 4. 0304 4. 0308 4. 0288 4. 0292 4. 0296 4. 0300 4. 0304 4. 0308 4. 0288 4. 0292 4. 0296 4.0300 4. 0304 4. 0308 4. 0289 4. 0293 4. 0297 4. 0301 4. 0305 4. 0309 4. 0289 4. 0293 4. 0297 4. 0301 4. 0305 4. 0309 2 59 59 10 59 20 59 30 59 40 59 50 4. 0310 4. 0314 4. 0318 4. 0322 4. 0326 4. 0330 4. 0310 4. 0314 4. 0319 4. 0323 4. 0327 4. 0331 4.0311 4. 0315 4. 0319 4. 0323 4. 0327 4. 0331 4. 0311 4. 0315 4. 0319 4. 0323 4. 0327 4. 0331 4. 0312 4. 0316 4. 0320 4. 0324 4. 0328 4. 0332 4. 0312 4. 0316 4. 0320 4. 0324 4. 0328 4. 0332 4. 0312 4. 0317 4. 0321 4. 0325 4. 0329 4. 0333 4. 0313 4. 0317 4. 0321 4. 0325 4. 0329 4. 0333 4. 0313 4. 0317 4. 0321 4. 0325 4. 0329 4. 0333 4. 0314 4. 0318 4. 0322 4. 0326 4. 0330 4. 0334 APPENDIX V: TABLE X. [Page 331 Table showing the correction required, on account of Second Differences of the Moon's Motion, in Finding the Greenwich Time corresponding to a Corrected Lunar Distance. Approximate interval. Difference of the proportional logarithms in the Ephemeris. 1 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 82 34 36 h. m. 10 20 h. m. 3 2 50 2 40 8. s. 8. 1 1 1 2 2 2 2 2 8. 1 1 2 2 2 2 2 3 3 8. 1 1 2 2 3 3 3 3 3 8. 1 2 2 3 3 3 4 4 4 8. 1 2 2 3 4 4 4 4 4 8. 1 2 ■ 3 3 4 4 5 5 5 8. 1 2 3 4 5 5 5 6 6 8. 1 2 3 4 5 6 6 6 6 8. 1 3 4 5 5 6 6 7 7 8. 2 3 4 5 6 7 7 7 8 8. 2 3 8. 2 3 8. 2 4 8. 2 4 8. 2 4 8. 2 4 30 40 50 2 30 2 20 2 10 1 5 6 6 7 8 8 8 5 6 7 5 6 7 6 7 8 6 7 8 6 8 9 1 1 10 1 20 1 30 h. TO. 10 20 2 1 50 1 40 1 30 h. m. 3 2 50 2 40 1 1 1 1 8 8 9 9 8 9 9 9 9 9 10 10 9 10 10 11 10 11 11 11 Difference of the proportional logarithms in the Ephemeris. 38 ». 2 5 40 8. 3 5 7 9 10 11 12 12 12 42 8. 3 5 7 9 10 12 12 13 13 44 8. 3 5 8 10 11 12 13 14 14 46 8. 3 6 8 10 12 13 14 14 14 48 8. 3 6 8 10 12 13 14 15 15 50 8. 3 6 9 11 13 62 54 56 58 60 62 64 66 68 70 8. 3 6 8. 4 7 8. 4 7 8. 4 7 8. 4 7 8. 4 8 8. 4 8 8. 8. 4 i 4 8 8 8. 5 9 30 40 50 2 30 2 20 2 10 7 8 9 10 11 12 12 9 11 13 9 12 14 10 10 12 13 14 15 10 13 15 11 13 16 11 14 16 12 ] 12 14 1 15 16 1 17 12 15 17 1 1 10 1 20 1 30 h. TO. 10 20 30 40 50 2 1 50 1 40 1 30 h. m. 3 •2 50 2 40 2 30 2 20 2 10 14 15 15 16 14 15 16 16 15 16 17 17 16 17 17 18 16 17 18 18 17 18 19 19 17 18 19 19 18 19 20 20 18 19 19 , 20 20 \ 21 21 ; 21 19 21 21 22 Difference of the proportional logarithms in the Ephemeris. 72 74 76 78 80 82 84 86 88 90 92 94 06 98 100 102 104 8. 5 9 13 16 18 20 21 22 23 8. 5 9 13 16 19 21 22 23 23 8. 5 9 13 16 19 21 22 23 24 8. 5 10 14 17 20 22 23 24 24 8. 5 10 14 17 20 22 24 25 25 8. 5 10 14 18 21 23 24 25 25 8. 6 10 14 18 21 23 25 26 26 8. 6 11 8. 6 11 8. 6 11 8. 6 11 8. 6 12 8. 6 12 8. 6 12 8. 7 12 8. i 13 8. 7 13 15 19 22 15 19 22 16 19 22 16 20 23 16 20 23 17 21 24 17 21 24 17 22 25 18 22 26 18 22 26 1 1 10 1 20 1 30 h. m. 10 20 2 1 50 1 40 1 30 /(. m. 3 2 50 2 40 24 25 26 27 24 26 27 27 25 27 28 28 25 27 28 29 26 28 29 29 27 28 29 30 27 29 30 31 38 30 31 31 28 30 31 32 29 31 32 32 Difference of the proportional logarithms in the Ephemeris. . 1 106 108 110 112 114 116 118 120 122 124 126 128 180 132 134 136 138 s. 7 13 8. 7 13 8. 7 14 19 24 27 30 32 34 34 8. 7 14 19 24 28 31 33 34 35 8. 7 14 20 25 29 31 34 35 35 8. 8 14 20 25 29 8. 8 15 8. 8 15 8. 8 15 8. 8 15 8. 8 15 8. 8 16 8. 8 16 8. 9 16 8. 9 16 8. 9 17 8. 9 17 30 40 50 2 30 2 20 2 10 18 23 26 19 23 27 30 32 33 34 20 25 29 21 26 30 21 26 30 21 27 31 22 27 22 28 32 22 28 32 23 28 33 23 29 33 37 40 41 42 24 29 34 38 40 42 42 24 30 34 38 41 42 43 1 1 10 1 20 1 30 2 1 50 1 40 1 30 29 31 33 33 32 34 35 36 33 35 36 36 33 35 37 37 34 36 38 38 34 37 38 39 J5 J7 J9 J9 35 38 39 40 36 38 40 40 37 39 41 41 The correction is to be added to the approximate Greenwich time when the proportional logarithms in the Ephemeris are decreasing, and subtracted when they are increasing. Page 332] APPENDIX V: TABLE XI. 1 For finding the value of N for Correcting Lunar Distances for the Compres sion of the Earth. Table XI A, giving 1st part of N. Table XI B, giving 2d part of N. 1 Moon's declination. Other body' 3 declination. App. dist. App. dist. 1 0° 3° 6° 9° 12° 15° 18° 21° 24° 27° 80° 0° 8° 6° 9° 12° 16° 18° 21° 24° 27° 80° II „ „ „ „ „ „ „ It „ /' rt It // // „ It II 20 -0 3 6 10 13 16 19 22 25 28 31 20 +0 3 7 10 14 17 20 24 27 30 33 22 3 6 9 12, . 14 17 20 23 25 28 22 3 6 9 13 16 19 22 25 27 30 24 3 5 8 11 13 16 18 21 23 25 24 3 6 9 12 14 17 20 23 25 28 26 2 5 7 10 12 14 17 19 21 23 26 3 5 8 11 13 16 18 21 23 26 28 2 4 7 9 11 13 15 17 19 21 28 3 5 8 10 12 15 17 20 22 24 30 -0 2 4 6 8 10 12 14 16 18 20 30 +0 2 5 7 9 12 14 16 18 21 23 32 2 4 6 8 9 11 13 15 16 18 32 2 4 7 9 11 13 15 17 19 21 34 2 4 5 7 9 10 12 14 15 17 34 2 4 6 8 11 13 15 16 18 20 36 2 3 5 7 8 10 11 13 14 16 36 2 4 6 8 10 12 14 16 17 19 38 2 3 5 6 8 9 8 10 10 12 11 13 12 14 38 2 2 4 4 6 6 8 7 10 9 11 11 13 13 15 14 17 16 18 18 40 -0 3 4 6 7 13 40 +0 42 3 4 5 7 8 9 10 11 13 42 2 4 5 7 9 10 12 14 15 17 44 2 4 5 6 7 8 10 11 12 44 2 3 5 7 8 10 12 13 15 16 46 \ 2 3 5 6 7 8 9 10 11 46 2 3 5 6 8 10 11 13 14 16 48 2 3 4 5 6 7 8 9 10 48 2 3 5 6 8 9 11 12 14 15 50 -0 2 3 4 5 6 7 8 9 10 50 +0 2 3 5 6 8 9 11 12 13 15 52 3 4 5 5 6 7 8 9 52 2 3 4 6 7 9 10 12 13 14 54 3 3 4 5 6 7 7 8 54 3 4 6 7 9 10 11 13 14 56 2 3 4 5 5 6 7 8 56 3 4 6 7 8 10 11 12 14 58 J y 2 2 3 3 4 3 4 4 5 5 6 5 6 6 7 7 58 Y 3 3 4 4 6 5 7 7 8 8 10 9 11 11 12 12 13 13 60 -0 60 +0 m 2 3 3 4 4 5 5 6 62 3 4 5 7 8 9 10 12 13 64 2 2 3 3 4 4 5 6 64 3 4 5 7 8 9 10 11 13 66 2 2 3 3 4 4 5 5 66 3 4 5 6 8 9 10 11 12 68 Y -Y 2 2 2 2 3 3 3 3 4 3 4 4 5 4 68 70 +0 Y 3 3 4 4 5 5 6 6 8 7 9 9 10 10 11 11 12 12 70 -0 72 2 2 2 3 3 3 4 72 2 4 5 6 7 9 10 11 12 74 2 2 2 3 3 3 74 2 4 5 6 7 8 10 11 12 76 2 2 2 3 3 76 2 4 5 6 7 8 9 11 12 78 "Y "Y 1 1 2 1 2 2 2 2 2 78 Y 2 2 4 4 5 5 6 6 7 7 8 8 9 9 11 10 12 11 80 -0 2 80 +0 82 1 1 1 1 2 82 2 4 5 6 7 8 9 10 11 84 1 1 1 1 1 84 2 4 5 6 7 8 9 10 11 86 1 1 1 1 86 2 4 5 6 7 8 9 10 11 88 88 Y 2 2 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 90 -0 90 +0 92 +0 92 2 4 5 6 7 8 9 10 11 94 1 1 1 1 94 2 4 5 6 7 8 9 10 11 96 1 1 1 1 1 96 2 4 5 6 7 8 9 10 11 98 _o "Y 1 1 1 1 1 2 1 2 2 2r 98 Y 2 2 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 100 +0 100 +0 102 1 2 2 2 2 102 2 4 5 6 7 8 9 11 12 104 2 2 2 3 3 104 2 4 5 6 7 8 9 11 12 106 2 2 2 3 3 3 106 2 4 5 6 7 8 10 11 12 108 110 +0 Y -^ 2 2 2 2 2 3 3 3 4 108 2 3 4 4 5 5 6 6 7 7 9 9 10 10 11 11 12 12 3 3 3 4 4 110 +0 112 2 2 3 3 4 4 5 112 3 4 5 6 8 9 10 11 12 114 2 2 3 3 4 4 5 5 114 3 4 5 6 8 9 10 11 12 116 2 2 3 3 4 4 5 6 116 3 4 5 7 8 9 10 11 13 118 Y 1 2 2 3 3 3 3 4 4 4 5 5 5 5 6 6 7 118 Y 3 3 4 4 5 5 7 7 8 8 9 9 10 11 12 12 13 13 120 +0 120 +0 122 2 3 4 4 5 6 6 7 122 3 4 6 7 8 10 11 12 13 124 2 2 3 4 5 5 6 7 8 124 3 4 6 7 8 10 11 12 14 126 2 3 3 4 5 6 7 7 8 126 3 4 6 7 9 10 11 13 14 128 2 3 4 5 5 6 7 8 9 128 2 3 4 6 7 9 10 12 13 14 130 +0 \ 2 3 4 5 6 7 8 9 10 130 +0 2 3 5 6 8 9 11 12 13 15 The signs in the 0° column apply to all the numbers in the same line, and are to be used when the declination is North. When the declination is South change the sign + to — and — to +. INDEX TO PART I. Subject. Abbreviations Account. (»S'ee Dead reckoning. ) Adjustments, horizon mirror index mirror plane table sextant permanent theodolite or transit Afternoon sights Agulhas current Airy's method for great circle sailing.. Alidade, plane table Almanac, Nautical. {See Nautical Al- manac. ) Altitude and azimuth time azimuth azimuth circle, definition . . .' circum-meridian forms for . . . definition ex-meridian forma for meridian, constant form for . . forms for latitude by observation of reduction to forms. observed, how corrected of Polaris for latitude single, for chronometer error. latitude longitude ashore .. at sea... true, definition Altitudes, equal, forchro. error form longitude ashore . . at sea... Amplitude, definition determination of Anchorage, position to be plotted Angle, danger. {See 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. 26J°-45° on bow Anticyclonic regions, features of Apparent day, definition variation in length noon, definition time, conversion to mean definition Art. 246 245 417 244 248 414 399 550 194 416 235 366 363 217 334 220 334 333 329 330 334 294 340 316 339 346 349 294 321 347 352 224 357 166 415 151 139 415 458 139 146 481 273 273 273 292 273 Page. 67 133 67 68 132 125 161 58 133 65 112 111 63 97 174 64 97 174 96 174 173 94 94 97 174 82 101 88 99 104 105 82 90 176 104 107 64 109 49 132 45 43 132 140 43 44 148 74 74 74 80 74 Subject. Art. Page. Apparent time, inequality of relation to mean Arctic current Aries, first point of, definition Arming of lead Artificial horizon, description method of use should be tested 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 determined named of body determines use terrestrial object time and altitude determination diagram for compass errors in great circle sailing . . tables Barometer, aneroid comparisons definition effect of, on tides mercurial 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 273 288 536 226 19 256 257 258 446 369 277 431 450 529 494 75 546 6 363 235 33 223 380 355 354 407 369 366 359 361 88 191 361 55 56 47 501 48 50 50 54 57 51 446 438 434 142 138 157 134 369 145 134 143 67 333 334 INDEX TO PART 1. Subject. Bench mark, definition Binnacles, description Bottom, quality of, on chart Boxing the compass Brazil current Buoys C — W, definition • Cape Horn current Celestial coordinates equator, definition horizon, definition latitude and longitude definition longitude and latitude 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 equal alts form, single altitude . time sight signals . . . transits definition differs from corr . from rate hack, use of max. and min. ther- mometer minus watch, definition. second difference sight. ( »S'ee Time sight. ) temperature curve transportation of winding Circle, declination, definition hour, definition of altitude, definition equal altitude illumination vertical, definition Circum-meridian altitude forms Civil time Clouds, description and symbols Coefficients, constant quadrantal ^ . . . semicircular value and relation Collimation, line of, definition Art. 516 34 45 27 538 162 268 547 234 215 213 238 229 238 229 216 210 4 166 165 36 189 197 465 46 40 45 44 547 265 268 260 263 264 259 321 316 316 314 315 261 312 311 268 262 268 265 266 260 262 216 216 217 373 373 217 334 Page. 277 70 112 107 103 114 414 156 17 20 16 160 47 72 161 66 63 63 65 64 65 64 63 63 11 49 48 18 57 59 143 21 19 20 20 161 72 72 71 71 72 71 90 176 88 88 87 88 71 87 87 72 71 72 72 72 71 71 63 63 63 114 114 63 97 174 74 27 38 37 36 38 132 Subject. Page. Comparing watch, use of Comparison, barometer chronometer, method ... record Compass, beam, description boxing compensation. {See Devia- tion. ) declination definition deviation. (.S'fe Deviation.) divisions on card dry error. (*See Error, compass.) local attraction Lord Kelvin Navy service, 7 J-inch variation wet Compasses (drawing) Compensation, compass. {See Devia- tion. ) Composite sailing, computation definition graphic approxima- tion shortest course for. . terrestrial globe 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, sextant 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 Kuro Si wo Labrador ocean, Atlantic cause of definition determination of drift, definition of Atlantic Indian Pacific 268 56 263 264 434 27 74 25 26 30 75 32 31 74 30 198 184 199 196 200 210 333 292 286 292 290 291 234 230 250 294 6 132 271 550 206 536 546 538 547 547 398 164 529 549 541 535 532 547 542 543 542 536 529 522 521 525 523 533 548 541 72 23 71 72 136 16 29 15 16 17 29 17 17 29 17 13 59 66 59 59 59 63 96 174 80 79 80 80 80 65 64 69 82 12 42 74 161 61 160 161 160 161 161 126 48 169 161 160 160 159 161 160 161 160 160 169 168 158 158 158 160 160 161 INDEX TO PART I. 335 Subject. Current, ocean, stream, definition submarine ! Oya Si wo Peruvian Rennell's Rossel Southern connecting tidal, definitions description of observation of to find Curve, temperature, chronometer Cyclones and cyclonic circulations . Cyclonic regions, features of storms, description maneuvering in summary of rules tropical 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 voyage 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 I^apier 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. Distance and bearing by horizon angle Art. 523 524 544 547 537 546 539 495 505 511 207 266 480 481 482 491 492 483 486 155 156 157 393 392 202 236 237 216 218 74 416 209 1 6 392 204 46 23 98 99 119 112 111 76 126 116 93 107 106 129 103 100 91 95 77 83 361 300 303 294 301 302 138 139 Page. 158 158 161 161 160 161 160 153 154 156 62 72 147 148 148 150 150 148 149 46 46 46 189 124 124 60 171 60 60 178 65 65 63 64 29 133 63 11 11 124 60 21 15 35 35 38 38 38 29 40 38 32 37 37 41 36 35 32 34 29 31 110 83 84 82 83 84 43 43 Subject. Art. Page. Distance, definition 6 139 219 90 503 503 7 435. 470 144 523 533 6 248 225 214 321 12 lunar. {See Lunar distance. ) of objects of known height. . polar, definition 43 64 zenith. (»S'i?^ Zenith distance. ) Distant object for compass error Diurnal inequality of tide 31 154 type of tide 154 Dividers, description 13 proportional, description Doldrums 136 144 Doubling angle on bow 44 Drift current, definition 158 currents, Atlantic 160 Earth, definitions relating to 11 Eccentricitv, sextant 68 Ecliptic, definition 64 Elevated pole 63 Ephemens. (>See Nautical Almanac.) Equal altitudes for chro. error form 90 176 longitude ashore . . at sea . . . Equation of time, definition 347 352 275 288 215 6 6 215 226 73 77 82 249 410 497 334 104 107 74 in conversion of time . Equator, celestial, definition 79 63 earth's 11 Equatorial currents. {See Current. ) Equiangular spiral 12 Equinoctial, definition 63 Equinox, definition 64 vernal. {See First point of Aries. ) Error, chro. (»S'ee Chronometer. ) compass, causes 29 to applv 29 find 31 heeling. ((See Deviation.) index, sextant, description probable, of position, how shown sextant. ( See Sextant. ) Establishment, tidal, definitions Ex-meridian altitudes 68 130 153 97 forms 174 Extraordinary refraction near horizon. Extra-tropical cyclonic storms First point of Aries, definition hour angle is si- i dereal time Flinders bar, definition 301 493 226 276 105 127 163 83 152 64 74 37 to place 40 Fogs and fog signals 48 Forms for sights, etc 171 notes on 177 use recommended . Fractions, decimal 411 130 178 Gauges, tide, description 518 412 157 } Geodesy, definition 131 i Geometry 180 ! formulae derived from 181 ' Geo-Navigation, definition 4 28 259 200 193 248 189 197 6 186 11 Gimbals, compass 16 chronometer 71 i Glasses, shade. (»9('e Shade glasses.) Globe, terrestrial, for comp. sailing. . . gt. circle sailing. Graduation, sextant, error - Great circle charts 59 58 68 57 for comp. sailing. . . course 59 12 sailing, advantages 56 336 INDEX TO PART I. Subject. Great circle sailing, Airy's method ... computation definition graphic approx methods terrestrial globe., time azimuth rifethods Greenwich adopted as prime meridian. time, to find Guinea current Gulf Stream, description extraordinary dip in Hack chronometer, use of Heading, magnetic, determination of.. Heeling error. {See Deviation.) Height, determination by barometer. . Heliograph, use in surveymg 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, conversion definition how measured circle, definition Humboldt current Hydrographic survey, method of surveying, definition Hydrography in survey, description . . to plot Identification of unknown bodies Index correction, sextant, to find error, sextant, description mirror, adjustment description prismatic Induction, magnetic 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 Kamchatka current Knot, length of Kuro Si wo current Labrador current Lagging of tide „ Land and sea breezes Art. 194 Page. 58 190 57 183 56 192 58 188 57 193 58 191 58 342 103 280 75 535 160 532 159 301 83 268 72 122 39 57 23 430 135 430 135 139 43 256 70 257 70 294 82 258 71 213 63 300 83 303 84 294 82 i 301 83 1 302 84 246 67 240 66 248 68 213 63 471 145 236 65 293 81 222 64 278 75 216 63 547 161 436 137 412 131 457 140 458 140 402 126 250 69 249 68 245 67 240 66 248 68 '• 96 34 431 135 239 66 7 13 413 131 283 76 497 153 190 79 289 96 34 465 143 542 160 543 160 6 12 542 160 536 160 502 154 474 145 Subject. Latitude, by meridian altitude forms .. Polaris reduction to meridian reduction to meridian, forms single altitude forms 9/ cp'^ 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 collimation, definition position. ( iSt'^ 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 equal altitudes ashore . . at sea... single altitude ashore . . at sea . . . time sights, forms transit observations celestial, definition definition difference of of secondary meridians tertiary meridians Loxodromic Curve Lubber's line Lunar distance, explanation of tables observations, value of Lunitidal intervals, definitions list of Magnetic observations in survey Magnetism, acquired in building vessel. features of earth's subpermanent transient Main triangulation Maneuvering, cyclonic storms summary of rules Marine surveying Mean day, definition directive force noon, definition sun, definition time, conversion to apparent sidereal definition intervals, relation to side- real Art. 329 340 334 339 339" "229" 471 19 18 18 517 429 428 161 438 414 414 75 281 64 10 12 13 15 17 347 352 346 349 '344' 229 6 6 343 345 6 28 406 497 461 97 95 98 98 448 491 492 412 274 115 274 274 292 290 274 289 INDEX TO PART I. 337 Subject. Mean time, relation to apparent sidereal Mercator projection, description to construct sailing Meridian altitude, constant forms 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 Middle latitude sailing correction Mile, nautical or sea, length of Mirror, horizon. (See Horizon mirror. ) index. (*See Index mirror.) sextant, resilvering Monsoon winds Moon, correction of observed altitude . form for latitude sights meridian altitude time sight planets, and stars, use of value of observations of Morning sights Nadir, definition Napier diagram Nautical Almanac, description for 1879, extracts . . gives horizontal parallax interpolation reduction of ele- ments second differences . Astronomy, definitions instruments mile, length of Navigation, definitions instruments and accessories Neap tides Noon sights Notes on forms for sights, etc Occupying a station Ocean current. {See Current, ocean.) Octant, description Optical principle of sextant Orient, to, a i)lane table Oya Siwo current Parallax, definition horizontal, in Nautical Al- manac how applied of planet or star Parallel of latitude, definition rulers, description sailing, description Passage, meriaian, definition Pelorus, description Peruvian current Piloting, definition requisites '.. Art. 288 287 38 40 179 333 329 330 334 216 6 271 342 342 343 44 342 345 39 175 178 6 254 473 294 401 406 394 212 93 282 305 283 283 285 209 239 6 1 7 499 396 415 255 242 418 544 304 305 306 294 173 271 35 547 130 131 Page. 79 79 18 19 55 96 173 94 94 97 63 11 74 103 103 103 20 103 103 18 53 54 12 69 145 82 176 174 173 126 128 124 63 32 76 163 84 76 76 78 63 66 12 11 13 153 125 177 132 70 67 1.33 161 84 84 85 82 11 13 52 74 18 161 42 42 Subject. Art. Plane of reference, tidal 514 sailing 169 417 416 420 418 294 table, adjustments description to improvise use of Planet, correction of observed altitude form for latitude sights meridian altitude . . . time sight identification of unknown 402 401 219 340 214 340 6 431 151 146 142 138 145 134 144 143 133 166 407 458 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°onbow-.. bearing and angle distance bow and beam bearings . . cross bearings doubling angle on bow . . . two bearings and run methods of fixing of anchorage to be plotted. . . body determines its use... soundings in survey probable error of by Sumner lines, how shown Pressure, effect in wind progressive areas of seasonal variations in variation of atmospheric Prime meridian, Greenwich adopted .. vertical, .definition Priming of tide Projection, gnomonic Mercator polyconic systems in use Proportional dividers, description Prosection method, plane table Protractor, ordinary three armed, description . . substitute use of Quadrantal deviation. {See Deviation.) Quintant, description Range of tide at various places definitions Ranges for finding compass error in piloting Rate, chronometer. (jSee 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 410 465 479 466 476 342 217 502 43 38 42 37 435 418 9 432 433 151 255 498 89 158 411 264 166 512 301 334 Page. 514 298 296 300 156 50 133 132 134 133 82 175 173 172 126 126 64 101 63 101 11 135 45 44 43 43 44 42 44 43 42 49 128 140 130 142 147 144 147 103 64 154 20 18 20 18 136 134 13 136 136 45 70 190 153 31 47 31 130 72 49 156 83 97 174 156 82 82 83 22489—03- 338 INDEX TO PART I. Subjet't. Refraction, extraordinary,near horizon how applied Relative humidity Rennell's current Repeat, to, an angle Resection method, plane table Residual deviation ---^ Rhumb line, definition not shortest course Right ascension and declination definition Roaring forties Rossel ctirrent Round of angles Run, calculation of determined at noon Running survey, description Sailing, composite. (See Composite. ) great circle. {See Great circle. ) Mercator middle latitude correction parallel plane spherical traverse Sailings, definition kinds of Sargasso sea Sea and land breezes mile, length of symbols for state of water temperature Second difference, chronometer Nautical Almanac. Secondary meridian, definition determination of. triangulation Seconds, employment in naut. sights.. Semicircles, storm Semicirculardeviation. (*SeeDeviation. ) Semidiameter, definition how applied measured of planet or star Semidiurnal type of tide Sextant adjustments permanent angles for plotting soundings . choice of definition description eccentricity graduation errors index correction, to find error, description method of use optical principle prismatic mirrors shade glasses resilvering mirrors surveying vernier Shade glasses, for artificial horizon sextant, description prismatic Sidereal day, definition noon, definition time, conversion to mean definition intervals, relation to mean Art. 1 Page. 301 83 299 83 62 25 537 160 415 132 418 134 124 40 6 12 185 56 237 65 228 64 472 145 546 161 415 132 208 ,62 398 125 462 140 179 55 175 53 178 54 173 52 169 50 168 50 172 52 167 50 168 50 534 160 474 145 6 12 72 28 63 25 265 72 285 78 342 103 343 103 449 139 409 129 490 150 307 85 308 85 251 69 294 82 503 154 244 67 248 68 458 140 253 69 239 66 240 66 248 68 248 68 250 69 249 68 252 69 242 67 248 68 248 68 254 69 427 135 241 66 256 70 240 66 248 68 276 74 276 74 291 80 276 74 289 Subject. Sidereal time, relation to mean Sight, chronometer. ( See Time sight. ) equal alts. {See Equal altitudes. ) latitude. (♦See Latitude. ) line of, definition longitude. {See Longitude.) time. ( Sec 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, 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 equal altitudes for chro. error form for latitude sights meridian altitude time sight identification observations in surveying Starboard angle, definition Stars, planets, and moon, use of Station pointer. {See Protractor, three armed. ) Storm center, motion of rate of progress to avoid fix bearing distance semicircles tables Storms, along transatlantic routes cyclonic. (»%cCyclonicstorms. ) Stream current, definition Submarine ocean currents Sumner line, always recommended applications of choice of bodies description ' determination 287 414 399 408 394 396 447 314 254 227 314 24 i 23 ! 20 I 21 458 159 539 210 168 499 294 326 79 uses lines, intersection,computation graphically . when run in- tervenes.. Sun, correction of observed altitude . . . equal altitudes for chro. error long, ashore . . form for equal altitudes latitude sights meridian altitude time sight mean, definition observations in surveying Survey, astronomical work of hydrographic, method of running, description 402 454 102 401 484 485 489 487 488 490 492 494 523 524 394 400 400 372 379 377 384 382 390 294 322 347 274 454 450 436 462 INDEX TO PART I. 339 Subject. Survey, to plot soundinga in Surveying, hydrograpliic, definition instruments marine, definition topographic, definition transit, description Symbols for clouds sea , weather Ta))le, plane, (See Plane table.) tide time azimuth Telemeter, descrii)tion 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, definition cause of definitions relating to diurnal inequality type-,- effect of, in piloting wind and barometer on gauges, description observation of planes of reference of priming and lagging of range of, at various places definitions semidiurnal type spring and neap tables time of high and low form for tropic types of Time and altitude azimuth hour angle, conversion of apparent. {See Apparent time.) astronomical at different meridians azimuth. (/Sf'e Azimuth, time.) civil conversion of. (/See Conversion.) equation of. {See Equation of time. ) 458 412 413 412 412 413 70 72 69 506 361 421 426 424 415 247 240 431 266 369 342 345 414 458 413 415 58 58 61 262 153 152 502 497 460 508 512 516 496 495 503 503 164 501 518 509 514 502 498 503 499 506 506 503 503 366 293 277 279 277 Page. 140 131 131 131 131 131 27 28 27 155 110 134 135 135 132 68 66 135 72 112 103 103 132 140 131 1.32 24 24 24 71 46 45 154 153 140 156 156 156 153 153 154 154 48 154 157 156 156 154 190 153 154 153 155 155 176 154 154 112 81 74 75 74 Subject. Time, Greenwich, to find local, to find mean. {See Mean time. ) of high and low water form for . . transit, how found sidereal. (/SVe Sidereal time.) signals for chrenometer error sight for chronometer error longitude ashore at sea forms for solar. {See Apparent time.) Topographic surveying, definition Topography in hydrographic survey . . Tracing paper to plot soundings 3 -point problem . Trade wind Transit, astronomical definition observations for chronometer error longitude portable surveying. (*S'ce 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 non-periodic . . periodic Vernier, barometer sextant theodolite Vertical angles, terrestrial, to measure . circle, definition prime Visible horizon, definition Watch, comparing, use of Weather symbols Wind, Beaufort's scale causes of definition doldrums effect of, on tides land and sea breezes monsoon normal i)ressure prevailing westerly ' * Roaring forties " storms. {See Cyclonic storms. ) Trade true direction and force Zenith, definition distance, definition how named telescope Page. 280 281 506 331 314 316 346 349 412 456 160 433 469 431 271 315 344 431 331 172 170 448 449 603 483 486 21 402 74 77 82 476 478 477 51 241 413 139 217 217 213 268 69 67 464 463 470 501 474 473 465 467 472 472 469 68 212 221 329 431 P^BT II. TABLES 341 CONTENTS OF I>A.IIT II. Page. Explanation of the Tables 345 Table 1. Traverse Table, Quarter Points 352 2. Traverse Table, Degrees 368 3. Meridional Parts 458 4. Length of Degrees of Latitude and Longitude 466 5A. Distance of an Object by Two Bearings, Quarter Points 468 5B. Distance of an Object by Two Bearings, Degrees 471 6. Distance of Visibility of Objects of different Heights 477 7. Conversion of Arc and Time 478 8. Conversion of Sidereal into Mean Solar Time 479 9. Conversion of Mean Solar into Sidereal Time 482 10. Local mean time of Sun's visible Rising and Setting 485 11. Reduction of Moon's Meridian Passage for Longitude 509 12. Reduction of Quantities from Nautical Almanac 510 13. Change of Sun's Right Ascension 520 14. Dip of Sea Horizon 522 15. Dip at Distances short of Horizon 522 16. Parallax of Sun 522 17. Parallax of Planet 523 18. Augmentation of Moon's Semidiameter 524 19. Augmentation of Moon's Horizontal Parallax 524 20A. Mean Refraction 525 20B. Mean Refraction and Parallax of Sun 526 21. Correction of Refraction for Barometer 527 22. Correction of Refraction for Thermometer 528 23. Mean Refraction and Mean Parallax of Moon 530 24. Mean Refraction and Parallax of Moon 530 25. Variation of Altitude due to change of Declination 539 26. Variation of Altitude in one minute from Meridian 541 27. Variation of Altitude in given time from Meridian 551 28A. First Correction of Polaris •. 554 28B. Second Correction of Polaris 555 28C. Third Correction of Polaris 555 28D. Fourth Correction of Polaris 560 29. Nautical and Statute Miles 562 30. Conversion of Metric and English Linear Measure. .., 563 31. Fahrenheit, Centigrade, and Reaumur Temperatures 564 32. True Force and Direction of Wind 565 33. Distance by Vertical Angle 566 34. Distance by Horizon Angle 568 35. Speed Table for Measured Mile , 569 36. Local Mean and Standard Meridian Times 570 37. Logarithms for Equation of Equal Altitudes 571 38. Error in Longitude produced by Error in Latitude 575 39. Amplitudes 576 40. Correction for Amplitude observed in Apparent Horizon 581 41. Natural Sines and Cosines 582 42. Logarithms of Numbers 591 43. Logarithms of Trigonometric Functions, Quarter Points 607 .44. Logarithms of Trigonometric Functions, Degrees 608 343 EXPLANATION OF THE TABLES. TABLES 1, 2: TRAVERSE TABLES. Tables 1 and 2 were originally calculated by the natural sines taken from the fourth edition of Sherwin's Logarithms, which were previously examined, by differences; when the proof sheets of the first edition were examined the numbers were again calculated by the natural sines in the second edition of Hutton's Logarithms; and if any difference was found, the numbers were calculated a third time by Taylor's Logarithms. The first table contains the difference of latitude and departure corresponding to distances not exceeding 300 miles, and for courses to every quarter point of the compass. Table 2 is of the same nature, but for courses consisting of whole degrees; it was 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 imder the different problems of Plane, Middle Latitude, and Mercator Sailing in Chapter V. The tables may be employed in the solution of any right triangle. TABLE 3: MERIDIONAL PARTS. This table contains the meridional parts, or increased latitudes, for every degree and minute to 80°, calculated by the following formula: in which ~ivr ^^^ ^^ \ '*'^° '^ 2 y ~ " (^^ *^^" I-" + 4 ^* sin' T-i + 5 <^ sin* L + . . . . ), 10800'' the Equatorial radius a = — ~ — = 3437^74677 (log 3.5362739); M, the modulus of common logarithms = 0.4342945; ^= 2.3025^51 ( log 0.3622157) ; C, the comprenKion or meridional eccentricity of the earth according to Clarke ( 1880) = 293 465 = 0.003407562 (log 7.5324437) ; ^ =v/ 27 -V^ = 0.0824846 (log 8.9163666) ; from which ^ =7915^ 7044558 ( log 3. 8984895) ; ae^ = 23^38871 (log 1.3690072); ^ae* = 0^05.3042 (log 8. 7246192 ) ; !« ' E. i E. s. by w. i \y. 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 ^ 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 9.7 2.4 70 67.9 17.0 17.3 30 126.1 31.6 90 191 184. 3 185.3 46.2 46.4 50 242.5 60.7 11 10.7 2.7 71 68.9 131 127.1 31.8 251 , 243.5 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 i 245.4 61.5 14 13.6 3.4 74 71.8 18.0 34 130. 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. 16 15.5 3.9 76 73.7 18.5 36 131. 9 33. 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 78.6 19.4 40 135.8 34.0 200 194.0 48.6 60 252.2 261 253.2 63.2 21 20.4 5.1 81 19.7 141 136.8 34.3 201 195. 48.8 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 i 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. 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 51. 3 70 1 261.9 271 ' 262.9 65.6 31 30.1 7.5 91 88.3 22.1 151 146.5 36.7 211 204.7 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 35 34.0 8.5 95 92.2 23.1 55 150.4 37.7 15 208.6 52.2 75 i 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 i 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 i 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 60 161 155.2 156.2 38.9 39.] 20 213.4 53.5 53. 7' 80 i 271.6 281 i 272.6 68.0 68.3 41 39.8 10.0 101 98.0 24.5 221 214.4 42 40.7 10.2 02 98.9 24.8 62 157.1 39.4 22 215.3 53.9 82 273.5 68.5 43 41.7 10.4 03 99.9 25.0 63 158.1 39.6 23 216.3 54.2 83 274. 5 68.8 44 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 j 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 i 278.4 69.7 48 46.6 11.7 08 104.8 26.2 68 163. 40.8 28 221.2 55.4 88 279.4 70.0 49 47.5 11.9 09 105.7 26.5 69 163.9 41.1 29 222. 1 55.6 89 280.3 70.2 50 48.5 12.1 12.4 10 111 106.7 107. 7" 26.7 70 164.9 41.3 41.5 30 231 223.1 224.1 55. 9 56.1 90 281.3 70.5 51 49.5 27.0 171 165.9 291 282.3 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 11-4.5 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 Diat. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. E] J?E. f E Ef ?E. 1 E. WNW. 1 V V. WSW. 1 VV. [For 6| P aints. TABLE 1. [Page 357 Difference of Latitud e and Departure for 1 i Points. N . byE. ^E. N. by W. ^ 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 0.3 61 58.4 17.7 121 115.8 35.1 181 173.2 52.5 241 230.6 70.0 2 1.9 0.6 62 59.3 18.0 22 116.7 35.4 82 174.2 52.8 42 231.6 70.2 3 2.9 0.9 63 60.3 18.3 23 117.7 35.7 83 175.1 53.1 43 232.5 70.5 4 3.8 1.2 64 61.2 18.6 24 118.7 36.0 84 176.1 53.4 44 233.5 70.8 5 4.8 1.5 65 62.2 18.9 25 119.6 36.3 85 177.0 53.7 45 234.5 71.1 6 5.7 1.7 66 63.2 19.2 26 120.6 36.6 86 178.0 54.0 46 235.4 71.4 7 6.7 2.0 67 64.1 19.4 27 121.5 36.9 87 178.9 54.3 47 236.4 71.7 8 7.7 2.3 68 65.1 19.7 28 122.5 37.2 88 179.9 54.6 48 237.3 72.0 9 8.6 2.6 69 66.0 i 20.0 29 123.4 37.4 89 180.9 54.9 49 238.3 \ 72.3 10 9.6 2.9 70 67. 20. 3 30 124.4 37.7 90 181.8 55.2 50 239.2 i 72.6 11 10.5 3.2 71 67.9 20.6 131 125.4 38.0 191 182.8 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 i 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 j 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 I 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 1 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 1 57.8 59 247.8 1 75.2 20 19.1 5.8 80 76.6 23.2 40 134.0 40.6 200 191.4 1 58.1 60 248.8 1 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 i 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 i 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 i 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 85.2 25.8 49 142.6 43.3 09 200.0 60.7 69 257.4 ; 78.1 30 28.7 8.7 90 86.1 26.1 50 143.5 43.5 10 201.0 201.9 61.0 70 271 258.4 1 78.4 31 29.7 9.0 91 87.1 26.4 151 144.5 43.8 211 61.3 259. 3 i 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 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. 1 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 11.9 100 101 95.7 96.7 29.0 60 153.1 46.4 20 210.5 63.9 80 267.9 268.9 81.3 41 39.2 29.3 161 154.1 46.7 221 i 211.5 64.2 281 81.6 42 40.2 12.2 02 97.6 29.6 62 155.0 47.0 22 212.4 64.4 82 269.9 81.9 43 41.1 12.5 03 98.6 29.9 63 156.0 47.3 23 1 213.4 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 1 215.3 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 1 217.2 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 i 220. 1 66.8 90 277.5 278.5 84.2 84.5 51 48.8 14.8 111 106.2 32.2 171 163.6 49.6 231 221. 1 67.1 291 52 49.8 15.1 12 107.2 32.5 72 164.6 49.9 32 222. 67.3 92 279.4 84.8 53 50.7 15.4 13 108.1 ! 32.^ 73 165.6 50.2 33 ! 223.0 67.6 93 280.4 85.1 54 51.7 15.7 14 109.1 i 33.1 74 166.5 50.5 34 I 223.9 67.9 94 281.3 85.3 55 52.6 16.0 15 110.0 33.4 75 167.5 50.8 35 i 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 i 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 Dlst. Dep. Lat. Dist. 1 Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. EJ TE. h E. ES E. i E. WN \V. * W WSW. i W. [For 6J Point?. Page 358J TABLE - 1. Difference of Latitude and Departure for 1| Points. N. by E. 1 E. N. by W. 1 AV. S. by E. % 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 6% 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 1 6.6 2.4 67 63.1 22.6 27 119.6 42.8 87 176.1 63.0 47 232.6 83.2 8 7.5 2.7 68 64.0 22.9 28 120.5 43.1 88 177.0 63.3 48 233.5 83.5 9 8.5 3.0 69 65.0 23.2 29 121.5 43.5 89 178.0 63.7 49 234.4 83.9 10 11 9.4 10.4 3.4 3.7 70 65.9 23.6 30 122.4 123.3 43.8 44.1 90 178.9 64.0 50 235.4 236.3 84.2 71 66.8 23.9 131 191 179.8 64.3 251 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 7.1 80 75.3 27.0 40 141 131.8 132.8 47.2 47.5 200 2or 188.3 189.3 67.4 67.7 60 261 244.8 245. 7 87.6 21 19.8 81 76.3 27.3 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 69 253.3 90.6 30 28.2 10.1 90 84.7 85.7 30.3 50 141.2 142.2 50.5 10 197.7 198.7 70.7 70 271 254.2 255.2 91.0 91.3 31 29.2 10.4 91 30.7 151 50.9 211 71.1 32 30.1 10.8 92 86.6 31.0 52 143. 1 51.2 12 199.6 71.4 72 256.1 91.6 33 31.1 11.1 93 87.6 31.3 53 144.1 51.5 13 200.5 71.8 73 257.0 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 18 205.3 73.4 78 261.7 93.7 39 36.7 13.1 99 ; 93.2 33.4 59 149.7 53.6 19 206.2 73.8 79 262.7 94.0 40 37.7 13.5 100 1 94.2 33.7 60 150.6 53.9 54.2 20 207.1 74.1 80 263.6 94.3 41 38.6 13.8 101 95.1 34.0 161 151.6 221 208.1 74.5 281 264.6 94.7 42 39.5 14.1 02 96.0 34.4 62 152.5 54.6 22 I 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 i 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 i 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 i 215.6 77.1 89 272.1 97.4 50 51 47.1 48.0 16.8 17. 2" 10 103.6 104. 5 37.1 70 171" 160.1 161.0 57.3 57.6 30 216.6 77.5 77.8 90 291 273.0 274.0 97.7 98.0 111 37.4 231 217.5 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. ESE. \ } "^ A^ 'NW. \ w. wsw. \ W. [F or 61 To ints. TABLE 1. [Page 359 Di£ferenc3 of Latitude and Departure for 2 Points. NNE. NNW. SSE. ssw. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 0.9 0.4 61 56.4 23.3 121 111.8 46.3 181 167.2 69.3 241 222.7 92.2 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 10.2 3.8 4.2 70 64.7 26.8 27.2 30 120.1 49.7 50.1 90 175.5 72.7 50 231.0 231.9 95.7 11 71 65.6 131 121.0 191 176.5 73.1 251 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 18.5 19.4 7. 7 8.0 80 73.9 30.6 40 129.3 53.6 200 184.8 185.7 76.5 60 240.2 99.5 21 81 74.8 31.0 141 130.3 54.0 201 76.9 261 241.1 99.9 22 20.3 8.4 82 75.8 31.4 42 131.2 54.3 02 186.6 77.3 62 242.1 100.3 23 21.2 8.8 83 76.7 31.8 43 132.1 54.7 03 187.5 77.7 63 243.0 100.6 24 22.2 9.2 84 77.6 32.1 44 133.0 55.1 04 188.5 78.1 64 243.9 101.0 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 31 27.7 11.5 90 91 83.1 84.1 34.4 50 138.6 139.5 57.4 10 194.0 80.4 70 249.4 103.3 28.6 11.9 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. 105.6 37 34.2 14.2 97 89.6 37.1 57 145.0 60.1 17 200.5 83.0 77 255.9 106.0 38 35.1 14.5 98 90.5 37.5 58 146.0 60.5 18 201.4 83.4 78 256.8 106.4 39 36.0 14.9 99 91.5 37.9 59 146.9 60.8 19 202.3 83.8 79 257.8 106.8 40 37.0 15.3 100 92.4 38.3 60 147.8 148.7 61.2 20 203.3 84.2 80 258.7 259.6 107.2 41 37.9 15.7 101 93.3 38.7 161 61.6 221 204.2 84.6 281 107.5 42 38.8 16.1 02 94.2 39.0 62 149.7 62.0 22 205.1 85.0 82 260. 5 107.9 43 39.7 16.5 03 95.2 39.4 63 150.6 62.4 23 206.0 85.3 83 261.5 108.3 44 40.7 16.8 04 96.1 39.8 64 151.5 62.8 24 206.9 85.7 84 262.4 108.7 45 41.6 17.2 05 97.0 40.2 65 152.4 63.1 25 207.9 86.1 85 263.3 109.1 46 42.5 17.6 06 97.9 40.6 66 153.4 63.5 26 208.8 86.5 86 264.2 109.4 47 43.4 18.0 07 98.9 40.9 67 154.3 63.9 27 209.7 86.9 87 265. 2 109.8 48 44.3 18.4 08 99.8 41.3 68 155.2 64.3 28 210.6 87.3 88 266.1 110.2 49 45.3 18.8 09 100.7 41.7 69 156.1 64.7 29 211.6 87.6 89 267.0 110.6 50 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 53 49.0 20.3 13 104.4 43.2 73 159. 8 66.2 33 215.3 89.2 93 270.7 112.1 54 49.9 20.7 14 105. 3 43.6 74 160.8 66.6 34 216.2 89.5 94 271.6 112.5 55 50.8 21.0 15 106.2 44.0 75 161.7 67.0 35 217.1 89.9 95 272.5 112.9 56 51.7 21.4 16 107.2 44.4 76 162.6 67.4 36 218.0 90.3 96 273.5 113.3 57 52.7 21.8 17 108.1 44.8 77 163.5 67.7 37 219.0 90.7 97 274.4 113.7 58 53.6 22.2 18 109.0 45.2 78 164.5 68.1 38 219.9 91.1 98 275.3 114.0 59 54.5 22.6 19 109.9 45.5 79 165.4 68.5 39 220.8 91.5 99 276.2 114.4 60 55.4 23.0 20 110.9 45.9 80 166.3 68.9 40 221.7 91.8 300 277.2 114.8 Dist. Dep. Lat. Dist. Dep. Lat, Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. ENE. ESE. WNW wsw [F or 6 Poi nts. Page 360 TABLE 1. 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 42 218.8 103.5 3 2.7 1.3 63 57.0 26.9 23 111.2 52.6 83 165.4 78.2 43 219.7 103.9 4 3.6 1.7 64 57.9 27.4 24 112.1 53.0 84 166.3 78.7 44 220.6 104.3 5 4.5 2.1 65 58.8 27.8 25 113.0 53.4 85 167.2 79.1 45 221.5 104.8 6 5.4 2.6 6» 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 49 225.1 106.5 10 9.0 4.3 70 63.3 29.9 30.4 30 117.5 118.4 55.6 56.0 90 171.8 172.7 81.2 81.7 50 251 226.0 226.9 106.9 11 9.9 4.7 71 64.2 131 191 107.3 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 82.5 53 228.7 108.2 14 12.7 6.0 74 66.9 31.6 34 121.1 57.3 94 175.4 82.9 54 229.6 108.6 15 13.6 6.4 75 67.8 32.1 35 122.0 57.7 95 176.3 83.4 55 230.5 109.0 16 14.5 6.8 76 68.7 32.5 36 122.9 58.1 96 177.2 83.8 56 231.4 109.5 17 15.4 7.3 77 69.6 32.9 37 123.8 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 72. 3 34. 2 40 126.6 59.9 60.3 200 180.8 85.5 60 235.0 235.9 111.2 21 19.0 9.0 81 73.2 34.6 141 127.5 201 181.7 85.9 261 111.6 22 19.9 9.4 82 74.1 35.1 42 128.4 60.7 02 182. 6 86.4 62 236.8 112.0 23 20.8 9.8 83 75.0 35.5 43 i 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. 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 187a 88.5 67 241.4 114.2 28 25.3 12.0 88 79.6 37.6 48 133. 8 63.3 08 188.0 88.9 68 242.3 114.6 29 26.2 12.4 89 80.5 38.1 49 134. 7 63.7 09 188.9 89.4 69 243.2 115.0 30 31 27.1 28.0 12.8 90 81.4 38.5 38.9 50 135.6 151 136. 5 64.1 10 189.8 89.8 70 244.1 245.0 115.4 13.3 91 82.3 64.6 211 190.7 90.2 271 115.9 32 28.9 13.7 92 83.2 39.3 52 137.4 i 65.0 12 191.6 90.6 72 245.9 116.3 33 29.8 14.1 93 84.1 39.8 53 i 138.3 1 65.4 13 192.5 91.1 73 246.8 116.7 34 30.7 14.5 94 85.0 40.2 54 i 139.2 1 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 15 194.4 91.9 to 248.6 117.6 36 32.5 15.4 96 86.8 41.0 56 i 141. i 66. 7 16 195.3 92.4 76 249.5 118.0 37 33.4 15.8 97 87.7 41.5 57 i 141.9 67.1 17 196.2 92.8 / 1 250.4 118.4 38 34.4 16.2 98 88.6 41.9 58 142.8 67.6 18 197.1 93.2 78 251.3 118.9 39 35.3 16.7 99 89.5 42.3 59 143.7 68.0 19 198.0 93.6 79 252.2 119.3 40 36.2 17.1 100 90.4 42.8 60 144.6 68.4 20 198.9 94.1 80 253.1 119.7 41 37.1 17.5 'lOl 91.3 43.2 161 145.5 68.8 221 199.8 94.5 281 254.0 120.1 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 95.3 83 255. 8 121.0 44 39.8 18.8 04 94.0 44.5 64 148.3 70.1 24 202.5 95.8 84 256.7 121.4 45 40.7 19.2 05 94.9 44.9 65 149.2 70.5 25 203.4 96.2 85 257.6 121.9 46 41.6 19.7 06 95.8 45.3 66 150.1 71.0 26 204.3 96.6 86 258.5 122.3 47 42.5 20.1 07 96.7 45.7 67 151.0 71.4 27 205.2 97.1 87 259.4 122.7 48 43.4 20.5 08 97.6 46.2 68 151.9 71.8 28 206.1 97.5 88 260.3 123.1 49 44.3 21.0 09 98.5 46.6 69 152.8 72.3 29 207.0 97.9 89 261.3 123.6 50 45.2 21.4 10 99.4 100.3 47.0 70 153.7 72.7 30 207.9 98.3 90 262.2 124.0 51 46.1 21.8 111 47.5 171 154.6 73.1 231 208.8 98.8 291 263.1 124.4 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 93 264.9 125.3 54 48.8 23.1 14 103.1 48.7 74 157.3 74.4 34 211.5 100.0 94 265.8 125.7 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. NI :. by E. IE. SI :. by E. i E. NW. by W. 1 W. SW. by W. |W. [J For 5| P oints. TABLE 1. [Page 361 Difference of Latitude and Departure for 2J Points. NNE ^E. NNW . i W. SSE iE. SSW. JW. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 0.9 0.5 61 53.8 28.8 121 106.7 57.0 181 159. 6 85.3 241 212.5 113.6 2 1.8 0.9 62 54.7 29.2 22 107.6 57.5 82 160. 5 85.8 42 213.4 114.1 3 2.6 1.4 63 55.6 29.7 23 108.5 58.0 83 161.4 86.3 43 214.3 114.5 4 3.5 1.9 64 56.4 30.2 24 109.4 58.5 84 162.3 86.7 44 215.2 115.0 5 4.4 2.4 65 57.3 30.6 25 110.2 58.9 85 163.2 87.2 45 216.1 115. 5 6 5.3 2.8 66 58.2 31.1 26 111.1 59.4 86 164.0 87.7 46 217.0 116.0 7 6.2 3.3 67 59.1 31.6 27 112.0 59.9 87 164.9 88.2 47 217.8 116.4 8 7.1 3.8 68 60.0 32.1 28 112.9 60.3 88 165.8 88.6 48 218.7 116.9 9 7.9 4.2 69 60.9 32.5 29 113.8 60.8 89 166.7 89.1 49 219.6 117.4 10 8.8 4.7 70 61.7 62. 6" 33.0 30 114. 6 61.3 90 167.6 89.6 50 220.5 117.8 11 9.7 5.2 71 33.5 131 115.5 61.8 191 168.4 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 90.5 52 222.2 118.8 13 11.5 6.1 73 64.4 34.4 33 ! 117.3 62.7 93 170.2 91.0 53 223.1 119.3 14 12.3 6.6 74 65.3 34.9 34 { 118.2 63.2 94 171.1 91.5 54 224.0 119.7 15 13.2 7.1 75 66.1 35.4 35 ! 119.1 63.6 95 172.0 91.9 55 224.9 120.2 16 14.1 7.5 76 67.0 35.8 36 119.9 64.1 96 172.9 92.4 56 225.8 120.7 17 15.0 8.0 77 67.9 36.3 37 120.8 64.6 97 173.7 92.9 57 226.7 121.1 18 15.9 8.5 78 68.8 36.8 38 121.7 65.1 98 174.6 93.3 58 227.5 121. 6 19 16.8 9.0 79 69.7 37.2 39 122.6 65.5 99 175.5 93.8 59 228.4 122.1 20 17.6 9.4 80 70.6 37.7 40 123.5 66.0 200 201 176.4 177.3 94.3 60 229. 3 122.6 21 18.5 9.9 81 71.4 38.2 141 124.4 66.5 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 05 180.8 96.6 65 233.7 124.9 26 22.9 12.3 86 75.8 40.5 46 128.8 68.8 06 181.7 97.1 66 234.6 125. 4 27 23.8 12.7 87 76.7 41.0 47 129.6 69.3 07 182.6 97.6 67 235.5 125.9 28 24.7 13.2 88 77.6 41.5 48 130.5 69.8 08 183.4 98.1 68 236.4 126.3 29 25.6 13.7 89 78.5 42.0 49 131.4 70.2 09 184.3 98.5 69 237. 2 126.8 30 31 26.5 27.3 14.1 90 91 79.4 42.4 50 132.3 133.2 70.7 10 185.2 99.0 70 238.1 127.3 14.6 80.3 42.9 151 71.2 211 186.1 99.5 271 239.0 127.7 32 28.2 15.1 92 81.1 43.4 52 134.1 71.7 12 187.0 99.9 72 239.9 128.2 33 29.1 15.6 93 82.0 43.8 53 134.9 72.1 13 187.8 100.4 73 240.8 128.7 34 30.0 16.0 94 82.9 1 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 55 136.7 73.1 15 189.6 101.4 75 242.5 129.6 36 31.7 17.0 96 84.7 45.3 56 137.6 73.5 16 190.5 101.8 76 243.4 130.1 37 32.6 17.4 97 85.5 45.7 57 138.5 74.0 17 191.4 102.3 77 244.3 130.6 38 33.5 17.9 98 86.4 46.2 58 139.3 74.5 18 192.3 102.8 78 245.2 131.0 39 34.4 18.4 99 87.3 46.7 59 140.2 75.0 19 193.1 103.2 79 246.1 131.5 40 35.3 18.9 100 101 88.2 47.1 60 141.1 142.0 75.4 75.9 20 194.0 103.7 80 246.9 247.8 132.0 41 36.2 19.3 89.1 47.6 161 221 194.9 104.2 281 132.5 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 84 250.5 133.9 45 39.7 21.2 05 92.6 49.5 65 145. 5 77.8 25 198.4 106.1 85 251.3 134.3 46 40.6 21.7 06 93.5 50.0 66 146.4 78.3 26 199.3 106.5 86 252.2 134.8 47 41.5 22.2 07 94.4 50.4 67 147.3 78.7 27 200.2 107.0 87 253.1 135. 3 48 42.3 22.6 08 95.2 50.9 68 148.2 79.2 28 201.1 107.5 88 254.0 135.8 49 43.2 23.1 09 96.1 51.4 69 149.0 79.7 29 202.0 107.9 89 254.9 136.2 50 44.1 23.6 10 97.0 51.9 70 149.9 80.1 30 202. 8 108.4 90 255.8 136.7 51 45.0 24.0 111 97.9 52.3 171 150.8 80.6 231 203.7 108.9 291 256.6 137.2 52 45.9 24.5 12 98.8 52.8 72 151.7 81.1 32 204.6 109.4 92 257.5 137.6 53 46.7 25.0 13 99.7 53.3 73 152.6 81.6 33 205. 5 109.8 93 258.4 138.1 54 47.6 25.5 14 100.5 53.7 74 153.5 82.0 34 206.4 110.3 94 259.3 138.6 55 48.5 25.9 15 101.4 54.2 75 154.3 82.5 35 207.3 110.8 95 260.2 139.1 56 49.4 26.4 16 102.3 54.7 76 155.2 83.0 36 208.1 111.2 96 261.0 139.5 57 50.3 26.9 17 103.2 55.2 77 156.1 83.4 37 209.0 111.7 97 261.9 140.0 58 51.2 27.3 18 104.1 55.6 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 80 158.7 84.9 40 211.7 113.1 300 264.6 141.4 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. NE .. by E. ^E. SE . by E. J E. NW. by W. J W. SW. by W. * w. [I ^or 5^ P oints. Page 362; TABLE 1. Difference of Latitude and Departure for 2| Points. NNE. 1 E. NNW. JW. SSE. 1 E SSW. 1 W. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. : Lat. Dep. 1 0.9 0.5 61 52.3 31.4 121 103.8 62.2 181 155. 2 93. 1 241 ' 206.7 123.9 2 1.7 1.0 62 53.2 31.9 22 104.6 62.7 82 156. 1 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 Of 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 5.7 70 71 60.0 36.0 30 111.5 66.8 90 163.0 163.8 97.7 50 214.4 128.5 11 9.4 60.9 36.5 131 112.4 67.3 191 98.2 251 215.3 129.0 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 ; 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 81 68.6 69.5 41.1 40 120.1 120. 9 72.0 200 171. 5 102.8 60 223.0 133.7 134.2 21 18.0 10.8 41.6 141 72.5 201 172.4 103.3 261 223.9 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. g 83 71.2 42.7 43 122.7 73.5 03 174.1 104.4 63 225.6 135.2 24 20.6 12.3 84 72.0 43.2 44 123.5 74.0 04 175.0 104.9 64 226.4 135.7 25 21.4 12.9 85 72.9 43.7 45 124.4 74.5 05 175.8 105.4 65 227.3 136.2 26 22.3 13.4 86 73.8 44.2 46 125.2 75.1 06 176.7 105.9 66 228.2 136.8 27 23.2 13.9 87 74.6 44.7 47 126.1 75.6 07 177.5 106.4 67 229.0 137.3 28 24.0 14.4 88 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 25.7 15.4 90 77.2 46.3 50 128.7 77.1 10 180.1 108.0 108. 5 70 231.6 138.8 139.3 31 26.6 15.9 91 78.1 46.8 151 129.5 77.6 211 181.0 271 232.4 32 27.4 16.5 92 78.9 47.3 52 130.4 78.1 12 181.8 109.0 72 233.3 139.8 33 28.3 17.0 93 79.8 47.8 53 131. 2 78.7 13 182.7 109.5 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 16 185.3 111.0 76 236.7 141.9 37 31.7 19.0 97 83.2 49.9 57 ! 134.7 80.7 17 186.1 111.6 77 237.6 142.4 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 82.8 20 221 188.7 113.1 80 240.2 143.9 41 35.2 21.1 101 86.6 51.9 161 138.1 189.6 113.6 281 241.0 144.5 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 43.7 25.7 10 111 94.4 95.2 56.6 70 145.8 146. 7" 87.4 30 197.3 198.1 118.2 118.8 90 291 248.7 149.1 149.6 51 26.2 57.1 171 87.9 231 249.6 52 44.6 26.7 12 96.1 57.6 72 147.5 88.4 32 199.0 119.3 92 250. 5 150.1 53 45.5 27.2 13 96.9 58.1 73 148.4 88.9 33 199.9 119.8 93 251.3 150.6 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 Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. N. E. by E iE. SI <:. by E. 1 E. NW. by \^' JW. SW . by W. \ W. [For 5i Poi nt«. TABLE 1. [Page 363 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 67.2 181 150.5 100.6 241 200.4 133.9 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 52.4 35.0 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 85 153.8 102.8 45 203. 7 136.1 6 5.0 3.3 66 54.9 36.7 26 104.8 70.0 86 154. 7 103.3 46 204. 5 136.7 7 5.8 3.9 67 55.7 37.2 27 105. 6 70.6 87 155. 5 103. 9 47 205. 4 137.2 . 8 6.7 4.4 68 56.5 37.8 28 106.4 71.1 88 156.3 104.4 48 206.2 137.8 9 7.5 5.0 69 57.4 38.3 29 107.3 71.7 89 157. 1 105.0 49 207.0 138.3 10 8.3 5.6 70 58.2 38.9 30 108.1 72.2 90 158.0 105.6 50 207.9 138.9 11 9.1 6.1 71 59.0 39.4 131 108.9 72.8 191 158.8 106.1 251 "208. 7 139.4 12 10.0 6.7 72 59.9 40.0 32 109.8 73.3 92 159.6 106. 7 52 209.5 140.0 13 10.8 7.2 73 60.7 40.6 33 110.6 73.9 93 160. 5 107.2 53 210.4 140.6 14 11.6 7.8 74 61.5 41.1 34 111.4 74.4 94 161. 3 107.8 54 211.2 141.1 15 12.5 8.3 75 62.4 41.7 35 112.2 75.0 95 162. 1 108.3 55 212.0 141.7 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 99 165. 5 110.6 59 215. 4 143.9 20 16.6 11.1 80 66.5 67.3 44.4 45. 40 116.4 77.8 200 201 166. 3 167.1 111.1 60 216.2 217.0 144.4 21 17.5 11.7 81 141 117.2 78.3 111.7 261 145.0 22 18.3 12.2 82 68.2 45.6 42 118.1 78.9 02 168.0 112.2 62 217.8 145.6 23 19.1 12.8 83 69.0 46.1 43 118.9 79.4 03 168.8 112.8 63 218.7 146.1 24 20.0 13.3 84 69.8 46.7 44 119.7 80.0 04 169.6 113.3 64 219.5 146.7 25 20.8 13.9 85 70.7 47.2 45 120.6 80.6 05 170.5 113.9 65 220.3 147.2 26 21.6 14.4 86 71.5 47.8 46 121.4 81.1 06 171.3 114.4 66 221.2 147.8 27 22.4 15.0 87 72.3 48.3 47 122.2 81.7 07 172.1 115. 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 91 74.8 75.7 50.0 50 124.7 125.6 83.3 83.9 10 174.6 116.7 70 224.5 225. 3 150.0 150.6 31 25.8 17.2 50.6 151 211 175.4 117.2 271 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 73 227.0 151.7 34 28.3 18.9 94 78.2 52.2 54 128. • 85.6 14 177.9 118.9 74 227.8 152.2 35 "29.1 19.4 95 79.0 52". 8 55 128.9 86.1 15 178.8 119.4 75 228.7 152. 8 36 29.9 20.0 96 79.8 53.3 56 129.7 86.7 16 179. 6 120.0 76 229. 5 153.3 37 30.8 20.6 97 80.7 53.9 57 130. 5 87.2 17 180.4 120.6 77 230.3 153.9 38 31.6 21.1 98 81.5 54.4 58 131.4 87.8 18 181.3 121.1 78 231.1 154.4 39 32.4 21.7 99 82.3 55.0 59 132.2 88.3 19 182.1 121.7 79 232.0 155.0 40 41 33.3 34.1 22.2 100 83.1 55. 6 60 133.0 133.9 88.9 20 182.9 122.2 80 232.8 23.3.6 155.6 22.8 101 84.0 56.1 161 89.4 221 183. 8 1 122. 8 281 156.1 42 34.9 23.3 02 84.8 56.7 62 134.7 90.0 22 184.6 123.3 82 234. 5 156.7 43 35.8 23.9 03 85.6 57.2 63 135. 5 90.6 23 185.4 123.9 83 235.3 157.2 44 36.6 24.4 04 86.5 57.8 64 136. 4 91.1 24 186.2. 124.4 84 236.1 157. 8 45 37.4 25.0 05 87.3 58.3 65 137.2 91.7 25 187.1 125.0 85 237. 158.3 46 38.2 25.6 06 88.1 58.9 66 138.0 92.2 26 187. 9 125.6 86 237. 8 158. 9 47 39.1 26.1 07 89.0 59.4 67 138.9 92.8 27 188.7 126. 1| 87 238. 6 159.4 48 39.9 26.7 08 89.8 60.0 68 139.7 93.3 28 189.6 126.7 88 239. 5 160.0 49 40.7 27.2 09 90.6 60.6 69 140.5 93.9 29 190.4 127.2 89 240.3 160.6 50 41.6 42.4 27.8 10 91.5 61.1 70 141.3 94.4 30 191.2 192.1 127.8 90 291 241.1 161.1 51 28.3 111 92.3 61.7 171 142.2 95.0 231 128.3 242.0 161.7 52 43.2 28.9 12 93.1 62.2 72 143.0 95.6 32 192.9 128.9 92 242.8 162.2 53 44.1 29.4 13 94.0 62.8 73 143.8 96.1 33 193.7 129.4 93 243.6 162.8 54 44.9 30.0 14 94.8 63.3 74 144.7 96.7 34 194.6 130.0 94 244. 5 163.3 55 45.7 30.6 15 95.6 63.9 75 145. 5 97.2 35 195. 4 130. 6 95 245.3 163.9 56 46.6 31.1 16 96.5 64.4 76 146.3 97.8 36 196.2 131.1 96 246.1 164.4 57 47.4 31.7 17 97.3 65.0 77 147.2 98.3 37 197.1 131.7 97 246.9 165. 58 48.2 32.2 18 98.1 65.6 78 148.0 98.9 38 197.9 132.2 98 247.8 165. 6 59 49.1 32.8 19 98.9 66.1 79 148.8 99.4 39 198.7 132.8 99 248.6 166.1 60 1 49.9 33.3 20 99.8 66.7 80 149.7 100.0 40 199.6 1.33. 3 300 249.4 166.7 Dist. j Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. NE. by E. (; E. by I :. N^ V. by W. SW. by W. [For 5 Points. 1 Page 364 1 TABLE 1. Difference of Latitude and Departure for S^ Points. NE. i N. NW. IN. SE. 1 S. SW. IS. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 0.8 0.6 61 49.0 36.3 121 97.2 72.1 181 145.4 107.8 241 193.6 143. 6 2 1.6 1.2 62 49.8 36.9 22 98.0 72.7 82 146.2 108.4 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 m 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 1 147.1 8 6.4 4.8 68 54.6 40.5 28 102.8 76.2 88 151.0 112.0 48 199.2 i 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 30 104.4 105.2 77.4 90 152.6 113.2 50 200.8 201.6 148.9 149.5 11 8.8 6.6 71 57.0 42.3 131 78.0 191 153. 4 113. 8 251 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 65 212.8 157.9 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 10 168.7 169.5 125. 1 70 216.9 160.8 31 24.9 18.5 91 73.1 54.2 151 121.3 90.0 211 125.7 271 217.7 161.4 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 41 32.1 32.9 23.8 100 80.3 81.1 59.6 60.2 60 128.5 95.3 20 176.7 131.1 80 281 224.9 166.8 24.4 101 161 129.3 95.9 221 177.5 131.6 225.7 167.4 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 63 130.9 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 10 111 88.4 89.2 65.5 70 136.5 101. 3 30 184.7 185. 5 137.0 90 232.9 233. 7 172.8 51 41.0 30.4 66.1 171 137.3 101. 9 231 137.6 291 173.3 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 58 46.6 34.6 18 94.8 70.3 78 143.0 106.0 38 191.2 141.8 98 239.4 177.5 59 47.4 35.1 19 95.6 70.9 79 143.8 106.6 39 192.0 142.4 99 240.2 178.1 60 48.2 35.7 20 96.4 71.5 80 144.6 107.2 40 192. 8 143.0 300 241.0 178.7 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. j Lat. NE. 1 E. SE. 1 E X^ V. f w. sw. i w. [F or 4J Points. OF THE UNIVERSITY X^cyi/ °L. :l\i- ..y / TABLE 1. [Page 365 Difference of Latitude and Departure for 3i Points. NE. i N. NW . JN. SE . ^S. SW. i s 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 93.5 76.8 181 139.9 114.8 241 186.3 152.9 2 1.5 1.3 62 47.9 39.3 22 94.3 77.4 82 140.7 115.5 42 187.1 153. 5 3 2.3 1.9 63 48.7 40.0 23 95.1 78.0 83 141.5 116.1 43 187.8 154.2 4 3.1 2.5 64 49.5 40.6 24 95.9 78.7 84 142.2 116.7 44 188.6 154.8 5 3.9 3.2 65 50.2 41.2 25 96.6 79.3 85 143. 117.4 45 189.4 155.4 6 4.6 3.8 66 51.0 41.9 26 97.4 79.9 86 143.8 118.0 46 190.2 156.1 7 5.4 4.4 67 51.8 42.5 27 98.2 80.6 87 144.6 118.6 47 190.9 156.7 8 6.2 5.1 68 52.6 43.1 28 98.9 81.2 88 145. 3 119.3 48 191.7 157.3 9 7.0 5.7 69 53.3 43.8 29 99.7 81.8 89 146.1 119.9 49 192.5 158.0 10 11 7.7 8.5 6.3 70 71 54.1 44.4 30 100.5 82.5 90 146.9 147.6 120. 5 121. 2 50 193.3 158.6 7.0 54.9 45.0 131 101.3 83.1 191 251 194.0 159.2 12 9.3 7.6 72 55.7 45.7 32 102.0 83.7 92 148.4 121.8 52 194.8 159.9 13 10.0 8.2 73 56.4 46.3 33 102.8 84.4 93 149.2 122.4 53 195. 6 160.5 14 10.8 8.9 74 57.2 46.9 34 103.6 85.0 94 150. 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 55 197.1 161.8 16 12.4 10.2- 76 58.7 48.2 36 105.1 86.3 96 151.5 124. 3 56 197.9 162.4 17 13.1 10.8 77 59.5 48.8 37 105.9 86.9 97 152.3 125.0 57 198.7 163.0 18 13.9 11.4 78 60.3 49.5 38 106.7 87.5 98 153.1 125.6 58 199.4 163.7 19 14.7 12.1 79 61.1 50.1 39 107.4 88.2 99 153. 8 126.2 59 200.2 164.3 20 15.5 12.7 80 61.8 50.8 40 108.2 88.8 200 201 154.6 155.4 126.9 60 201.0 201.8 164.9 21 16.2 13.3 81 62.6 51.4 141 109.0 89.4 127.5 261 165.6 22 17.0 14.0 82 63.4 52.0 42 109.8 90.1 02 156.1 128.1 62 202.5 166.2 23 17.8 14.6 83 64.2 52.7 43 110. 5 90.7 03 156.9 128.8 63 203.3 166.8 24 18.6 15.2 84 64.9 53.3 44 111.3 91.4 04 157.7 129.4 64 204.1 167.5 25 19.3 15.9 85 65.7 53.9 45 112.1 92.0 05 158.5 130.1 65 204.8 168.1 26 20.1 16.5 86 66.5 54.6 46 112.9 92.6 06 159.2 130.7 66 205.6 168.7 27 20.9 17.1 87 67.3 55.2 47 113.6 93.3 07 160.0 131.3 67 206.4 169.4 28 21.6 17.8 88 68.0 55.8 48 114.4 93.9 08 160.8 132.0 68 207.2 170.0 29 22.4 18.4 89 68.8 56.5 49 115. 2 94.5 09 161.6 132.6 69 207.9 170.7 30 31 23.2 24.0 19.0 90 69.6 70.3 57.1 57."7 50 151 116.0 95.2 10 211 162.3 163.1 133.2 133.9 70 208.7 171.3 19.7 91 116.7 95.8 271 209.5 171.9 32 24.7 20.3 92 71.1 58.4 52 117.5 96.4 12 163.9 134.5 72 210.3 172.6 33 25.5 20.9 93 71.9 59.0 53 118.3 97.1 13 164.7 135.1 73 211.0 173.2 34 26.3 21.6 94 72.7 59.6 54 119.0 97.7 14 165.4 135.8 74 211.8 173.8 35 .27. 1 22.2 95 73.4 60.3 55 119.8 98.3 15 166.2 136.4 75 212.6 174.5 36 27.8 22.8 96 74.2 60.9 56 120.6 99.0 16 167.0 137.0 76 213.4 175. 1 37 28.6 23.5 97 75.0 61.5 57 121.4 99.6 17 167.7 137.7 77 214.1 175.7 38 29.4 24.1 98 75.8 62.2 58 122.1 100.2 18 168.5 138.3 78 214.9 176.4 39 30.1 24.7 99 76.5 62.8 59 122.9 100.9 19 169.3 138.9 79 215. 7 177.0 40 30.9 25.4 100 101 77.3 78.1 6.3.4 60 123.7 101.5 102. 1" 20 221 170.1 170.8 139.6 140. 2 80 216.4 177.6 41 31.7 26.0 64.1 161 124.5 281 217.2 178.3 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 65.3 63 126.0 103.4 23 172.4 141. 5 83 218.8 179.5 44 34.0 27.9 04 80.4 66.0 64 126.8 104.0 24 173.2 142.1 84 219.5 180.2 45 34.8 28.5 05 81.2 66.6 65 127.5 104.7 25 173.9 142.7 85 220.3 180.8 46 35.6 29.2 06 81.9 67.2 66 128.3 105. 3 26 174.7 143.4 86 221.1 181.4 47 36.3 29.8 07 82.7 67.9 67 ' 129. 1 105. 9 27 175.5 144.0 87 221.9 182.1 48 37.1 30.5 08 83.5 68.5 68 129.9 106.6 28 176.2 144.6 88 222.6 182.7 49 37.9 31.1 09 84.3 69.1 69 130.6 107.2 29 177.0 145. 3 89 223.4 183.3 50 38.7 31.7 10 85.0 69.8 70 131.4 107.8 30 177.8 145.9 90 224.2 184. 51 39.4 32.4 111 85.8 70.4 171 132.2 108.5 231 178.6 146.5 291 224.9 184.6 52 40.2 33.0 12 86.6 71.1 72 133.0 109.1 32 179.3 147.2 92 225.7 185.2 53 41.0 33.6 13 87.4 71.7 73 133.7 109.8 33 180.1 147.8 93 226.5 185.9 54 41.7 34.3 14 88.1 72.3 74 134.5 110.4 34 180.9 148.4 94 227.3 186.5 55 42.5 34.9 15 88.9 73.0 75 135.3 111.0 35 181.7 149.1 95 228.0 187.1 56 43.3 35.5 16 89.7 73.6 76 136. 111.7 36 182.4 149.7 96 228.8 187.8 57 44.1 36.2 17 90.4 74.2 77 136.8 112.3 37 183.2 150.4 97 229.6 188.4 58 44.8 36.8 18 91.2 74.9 78 137.6 112.9 38 184.0 151.0 98 230.4 189.0 59 45.6 37.4 19 92.0 75.5 79 138.4 113.6 39 184.7 151.6 99 231.1 189.7 60 Dist. 46.4 38.1 20 92.8 76.1 80 139.1 114.2 40 185.5 152.3 300 231.9 190.3 Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. NE. i ] E. SE. JE N \V. J ^\ sw. i -^ V. [F or 4J Points. 1 Page 366] TABLE 1. Difference of Latitude and Departure for 3| Points. NE. i N. NW. }N. 3E. J s. SW. J 8. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. 241 Lat. Dep. 1 0.7 0.7 61 46.2 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 ^ 48.2 43.7 25 92.6 83.9 85 137.1 124.2 45 181.5 164.5 6 4.4 4.0 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 52.6 47.0 47.7 30 96.3 97.1 87.3 88.0 90 191 140.8 141.5 127.6 128. 3 50 185.2 167.9 11 8.2 7.4 71 131 251 186.0 168.6 12 8.9 8.1 72 53.3 48.4 32 97.8 88.6 92 142.8 128.9 52 186.7 169.2 13 9.6 8.7 73 54.1 49.0 33 98.5 89.3 93 143.0 129.6 53 187.5 169.9 14 10.4 9.4 74 54.8 49.7 34 99.3 90.0 94 143.7 130.3 54 188.2 170.6 15 11.1 10.1 75 55.6 50.4 35 100.0 90.7 95 144.5 131.0 55 188.9 171.2 16 11.9 10.7 76 56.3 51.0 36 100.8 91.3 96 145.2 131.6 56 189.7 171.9 17 12.6 11.4 77 57.1 51.7 37 101.5 92.0 97 146.0 132.3 57 190.4 172.6 18 13.3 12.1 78 57.8 52.4 38 102.3 92.7 98 146.7 133.0 58 191.2 173.3 19 14.1 12.8 79 58.5 53.1 39 103.0 93.3 99 147.4 133.6 59 191.9 173.9 20 21 14.8 13.4 80 81 59.3 60.0 53.7 40 103.7 104.5 94.0 200 148.2 134.3 60 192.6 174.6 15.6 14.1 54.4 141 94.7 201 148.9 135.0 261 193.4 175.3 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 50 111.1 111.9 100.7 10 155.6 156.3 141. 70 200.1 200.8 181.3 31 23.0 20.8 91 67.4 61.1 151 101.4 211 141.7 271 182.0 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. 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 41 29.6 30.4 26.9 100 101 74.1 67.2 60 118.6 107.4 108.1 20 221 163.0 163.8 147.7 80 207.5 188.0 27.5 74.8 67.8 161 119.3 148.4 281 208.2 188.7 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 34.2 10 111 81.5 82.2 73.9 70 126.0 126.7 114.2 30 231 170.4 171.2 154.5 90 214.9 194.8 51 37.8 74.5 171 114.8 155.1 291 215.6 195. 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 40 177.8 161.2 300 222.3 201.5 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. NE. i E. <; E. JE. N) V. i W. S^ w. \ w. [For 4J Points. 1 TABLE 1. [Page 367 Difference of Latitude and Depart ure for 4 Points. NE NW. SE. sw. 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 99.0 200 201 141.4 142.1 141.4 60 183.8 183.8 184.6 21 14.8 14.8 81 57.3 57.3 141 99.7 99.7 142.1 261 184.6 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 31 21.2 21.2 90 63.6 63.6 50 151 106.1 106.1 10 211 148.5 149.2 148.5 149.2 70 190.9 191.6 190.9 21.9 21.9 91 64.3 64.3 106.8 106.8 271 191.6 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 60 161 113.1 113.1 20 155. 6 155.6 156.3' 80 198.0 198.0 41 29.0 29.0 101 71.4 71.4 113.8 113.8 221 156.3 281 198.7 198.7 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 il7.4 117.4 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 70 120.2 126.9 120.2 120.9 30 162.6 163.3 162.6 90 205.1 205.1 51 36.1 36.1 111 78.5 78.5 171 231 163.3 291 205.8 205.8 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. ?E. SW [1 ^'or 4 Po ints. Page 368 TABLE i 2. Difference of Latitude and Departure for 1° (179", 181' ', 359°] . Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 1.0 0.0 61 61.0 1.1 121 121.0 2.1 181 181.0 3.2 241 241.0 4.2 2 2.0 0.0 62 62.0 1.1 22 122.0 2.1 82 182.0 3.2 42 242. 4.2 3 3.0 0.1 63 63.0 1.1 23 123.0 2.1 83 183.0 3.2 43 243.0 4.2 4 4.0 0.1 64 64.0 1.1 24 124.0 2.2 84 184.0 3.2 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 ^6 •67 66.0 1.2 26 126.0 2.2 86 186.0 3.2 46 246.0 4.3 7 7.0 0.1 67.0 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 2.3 90 191 190.0 191.0 3.3 3.3 50 251 250.0 4.4 11 11.0 0.2 71 71.0 1.2 131 131. 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 55 255.0 4.5 16 16.0 0.3 76, 76.0 1.3 36 136.0 2.4 96 196.0 8.4 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 0.3 78 78.0 1.4 38 138.0 2.4 98 198.0 3.5 58 258.0 4.5 19 19.0 0.3 79 79.0 1.4 39 139.0 2.4 99 199.0 3.5 59 259.0 4.5 20 20.0 21.0 0.3 80 80.0 81.0 1.4 40 140.0 141.0 2.4 200 201 200.0 3.5 60 261 260.0 261.0 4.5 4.6 21 0.4 81 1.4 141 2.5 201.0 3.5 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 91 90.0 1.6 50 150.0 2.6 10 210.0 3.7 70 270.0 4.7 4.7 31.0 0.5 91.0 1.6 151 151.0 2.6 211 211.0 3.7 271 271.0 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. 2.7 15 215.0 3.8 75 275.0 4.8 36 36.0 0.6 96 96.0 1.7 56 156.0 2.7 16 216.0 3.8 76 276.0 4.8 37 37.0 0.6 97 97.0 1.7 57 157.0 2.7 17 217.0 3.8 / 1 277.0 4.8 38 38.0 0.7 98 98.0 1.7 58 158.0 2.8 18 218.0 3.8 78 278.0 4.9 39 39.0 0.7 99 99.0 1.7 59 159.0 2.8 19 219.0 3.8 79 279.0 4.9 40 40.0 0.7 0.7 100 100.0 1.7 1.8 60 160.0 161.0 2.8 2.8 20 221 220.0 3.8 80 280.0 4.9 41 41.0 101 101.0 161 221.0 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. 3.9 86 286.0 5.0 47 47.0 0.8 07 107.0 1.9 67 167.0 2.9 27 227.0 4.0 87 287.0 5.0 48 48.0 0.8 08 108.0 1.9 68 168.0 2.9 28 228.0 4.0 88 288.0 5.0 49 49.0 0.9 09 109.0 1.9 69 169.0 2.9 29 229.0 4.0 89 289.0 5.0 50 50.0 0.9 10 110.0 1.9 70 170.0 3.0 30 230.0 231. 4.0 90 290.0 5.1 51 51.0 0.9 111 111.0 1.9 171 171.0 3.0 231 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. 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. 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. 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 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° n°, 269 ^ 271° . TABLE 2. [Page 369 Difference of Latitude and Departure for 1° (179°, 181 =, 359°). Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 301.0 5.3 361 ' 360.9 6.3 421 420.9 7.3 481 480.9 8.4 541 540.9 • 9. 5 02 302.0 5.3 62 361.9 6.3 22 421.9 7.4 82 481.9 8.4 42 541.9 9.5 03 303. 5.3 63 1 362.9 6.3 23 422.9 7.4 83 482.9 8.5 43 542.9 9.5 04 304.0 5.3 64 363.9 6.4 24 423.9 7.4 84 483.9 8.5 44 543.9 9.5 05 305.0 5.3 65 1 364.9 6.4 25 424.9 7.4 85 484.9 8.5 45 544.9 9.5 06 306.0 5.3 66 365.9 6.4 26 425.9 7.4 86 485.9 8.5 46 545.9 9.5 07 307.0 5.4 67 366.9 6.4 27 426.9 7.4 87 486.9 8.5 47 546. 9 9.6 08 308.0 5.4 68 367.9 6.4 28 427.9 7.5 88 487.9 8.6 48 547. 9 9.6 09 309.0 5.4 69 368. 9 6.4 29 428.9 7. 5 89 488.9 8.6 49 548.9 9.6 10 311 310.0 311.6 5.4 70 369.9 370.'9^ 6.5 6.5 30 431 429.9 430.9 7.5 7.5 90 491 489.9 490.9 8.6 876 50 549. 9 9.6 5.4 371 551 550.9 9.6 12 312.0 5.4 72 371.9 6.5 32 -431. 9 7.5 92 491.9 8.6 52 551.9 9.6 13 313.0 5.5 73 372.9 6.5 33 432.9 7. 5 93 492.9 8.7 53 552.9 9.7 14 314.0 5.5 74 373.9 6.5 34 433.9 7.6 94 493.9 8.7 54 553.9 9.7 15 315.0 5.5 75 374.9 6.5 35 434.9 7.6 95 494.9 8.7 55 554.9 9.7 16 316.0 5.5 76- 375.9 6.6 36 435.9 7.6 96 495.9 8.7 56 555. 9 9.7 17 317.0 5.5 77 376.9 6.6 37 436.9 7.6 97 496.9 8.7 57 556.9 9.7 18 318.0 5.5 78 377.9 6.6 38 437.9 7.6 98 497.9 8.7 58 557. 9 9.7 19 319.0 5.6 79 378.9 6.6 39 438.9 7. 7 99 498.9 8.8 59 558.9 9.8 20 321 320.0 5.6 80 381 379.9 380.9 6.6 6.7 40 439.9 7. 7 500 499.9 500.9 8.8 60 559.9 "560.9 9.8 321.0 5.6 441 440.9 7. 7 501 8.8 561 9.8 22 322.0 5.6 82 381.9 6.7 42 441.9 7. 7 02 501.9 8.8 62' 561.9 9.8 23 323.0 5.6 83 382.9 6.7 43 442.9 7. 7 03 502. 9 8.8 63 562.9 9.8 24 324.0 5.6 84 383.9 6.7 44 443.9 7. 7 04 503.9 8.8 64 563.9 9.8 25 325.0 5.7 85 384.9 6.7 45 444.9 7.8 05 504.9 8.8 65 564. 9 9.9 26 326.0 5.7 86 385. 9 6.7 46 445.9 7.8 06 505.9 8.9 66 565.9 9.9 27 327.0 5.7 87 386.9 6.8 47 446.9 7.8 07 506.9 8.9 67 566.9 9.9 28 328.0 5.7 88 387.9 6.8 48 447.9 7.8 08 507.9 8.9 68 567.9 9.9 29 329.0 5.7 89 388.9 6.8 49 448.9 7.8 09 508.9 8.9 69 568.9 9.9 30 330.0 5.8 90 389. 9 390. 9 6.8 50 449. 9 7.8 10 509.9 8.9 70 571 569. 9 9.9 10.6 331 331.0 5.8 391 6.8 451 450.9 7.9 511 510.9 9.0 570. 9 32 332. 5.8 92 391. 9 6.8 52 451.9 7.9 12 511.9 9.0 72 571.9 10.0 33 333.0 5.8 93 392. 9 6.9 53 452.9 7.9 13 512.9 9.0 73 572. 9 10.0 34 333.9 5.8 94 393.9 6.9 54 453.9 7.9 14 513.9 9.0 74 573.9 10.0 35 334. 9 5.8 95 394.9 6.9 55 454. 9 7.9 15 514.9 9.0 75 574.9 10.0 36 335.9 5.9 96 395.9 6.9 56 455. 9 8.0 16 515.9 9.0 76 575.9 10.0 37 336.9 5.9 97 396.9 6.9 57 456. 9 8.0 17 516.9 9.1 77 576. 9 10.1 38 337.9 5.9 98 397.9 6.9 58 457.9 8.0 18 517.9 9.1 78 577. 9 10.1 39 338.9 5.9 99 398.9 7.0 59 458.9 8.0 19 518.9 9.1 79 578.9 10.1 40 341 339. 9 340.9 5.9 6.0 400 401 399.9 400.9 7.0 60 459.9 8.0 20 519.9 520.9 9.1 80 579.9 10.1 7.0 461 460.9 8.0 521 9.1 581 580.9 10.1 42 341.9 6.0 02 401.9 7.0 62 461.9 8.1 22 521.9 9.1 82 581.9 10.1 43 342.9 6.0 03 402.9 7.0 63 462. 9 8.1 23 522. 9 9.2 83 582.9 10.2 44 343.9 6.0 04 403. 9 7. 1' 64 463. 9 8.1 24 523. 9 9.2' 84 583.9 10.2 45 344.9 6.0 05 404.9 7. 1 65 464.9 8.1 25 524. 9 9.2 85 584.9 10.2 46 345.9 6.0 06 405.9 ■7. 1 66 465.9 8.1 26 525. 9 9.2 86 585.9 10.2 47 346.9 6.1 07 406.9 7. 1 67 466.9 8.1 27 526.9 9.2 87 586.9 10.2 48 347.9 6.1 08 407.9 7. 1 68 467.9 8.2 28 527.9 9.2 88 587.9 10.2 49 348.9 6.1 09 408.9 7. 1 69 468.9 8.2 29 528. 9 9.3 89 588. 9 10.3 50 351 349.9 6.1 10 409.9 7.2 70 471 469.9 470.9 8.2 8.2 30 531 529.9 9.3 90 589.9 590.9 10.3 350.9 6.1 411 410.9 7.2 530.9 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 1 7.2 73 472.9 8.2 33 532.9 9.3 93 592. 9 10.3 54 353.9 6.2 14 413.9 7.2 74 473.9 8.3 34 533.9 9.3 94 593.9 10.3 55 354. 9 6.2 15 414.9 7.2 75 474.9 8.3 35 534.9 9.4 95 594. 9 10.4 56 355.9 6.2 16 415. 9 7.3 76 475.9 8.3 36 535. 9 9.4 96 595.9 10.4 57 356. 9 6.2 17 416.9 7.3 77 476. 9 8.3 37 536.9 9.4 97 596. 9 10.4 58 357.9 6.2 18 417.9 7.3 78 477.9 8.3 38 537.9 9.4 98 597. 9 10.4 59 358.9 6.3 19 418.9 7.3 79 478.9 8.4 39 538.9 9.4 99 598.9 10.4 60 359.9 6.3 20 419.9 7.3 80 479.9 8.4 40 539.9 9.4 600 599.9 10.5 Bist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 39° (91°, 269° , 271°) 22489—03- -24 Page 370] 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 «7 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 31 30.0 31.0 1.0 90 89.9 90.9 3.1 50 149.9 5.2 10 211 209.9 7.3 70 269.8 9.4 1.1 91 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 80 279.8 280.8 9.8 9.8 41 41.0 1.4 101 100.9 3.5 161 160.9 5.6 221 220.9 7.7 281 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 i 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. Jj&t. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 88° (9 2°, 268° , 272°) TABLE 2. [Page 371 | Difference of Latitude and Depart are for 2° (178°, 182 ', 358° ). Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 300.8 10.5 361 360.8 12.6 421 420.8 14.7 481 480.7 16.8 541 540.7 18.9 02 301.8 10.5 62 361.8 12.6 22 421.8 14.7 82 481.7 16.8 42 541.7 18.9 03 302.8 10.6 63 362.8 12.7 23 422.8 14.7 83 482.7 16.8 43 542.7 18.9 04 303.8 10.6 64 363.8 12.7 24 423.8 14.8 84 483.7 16.9 44 543.7 19.0 05 304.8 10.6 65 364.8 12.7 25 424.8 14.8 85 484.7 16.9 45 544.7 19.0 06 305.8 10.7 66 365.8 12.8 26 425. 7 14.9 86 485.7 16.9 46 545.7 19.0 07 306.8 10.7 67 366.8 12.8 27 426.7 14.9 87 486.7 17.0 47 546.7 19.1 08 307.8 10.7 68 367. 8 12.8 28 427.7 14.9 88 487.7 17.0 48 547.7 19.1 09 308.8 10.8 69 368.8 12.9 29 428.7 15.0 89 488.7 17.0 49 548.7 19.1 10 309.8 10.8 70 369.8 370.8 12.9 12.9 30 429.7 15.0 90 489.7 17.1 50 549.7 19.2 311 310.8 10.8 371 431 430.7 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 20 319.8 11.2 80 379.8 13.2 13.3 40 441 439.7 15.3 500 499.7 17.4 60 559.7 19.5 19.5 321 320.8 11.2 381 380.8 440.7 15.4 501 500.7 17.5 561 560.7 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 1.3.3 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 n.4 88 387.8 1 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 90 389.8 390.8 13.6 50 449.7 450.7 15.7 10 509.7 17.8 70 569.7 19.9 331 330.8 11.5 391 13.6 451 15.7 511 510.7 17.8 571 570.7 19.9 32 331.8 11.6 92 391. 8 1 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 j 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 I 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 i 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 1 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 1 519.7 18.1 80 579.6 20.2 341 340.8 11.9 401 400.8 1 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 i 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 1 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 -165.7 16.2 26 j 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 1 526.7 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 50 349.8 12.2 10 409. 8 14.3 70 469.7 16.4 30 ! 529. 7 18.5 90 589.6 20.5 351 350.8 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 •/5 474.7 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 1 419.8 1 14.6 80 479.7 16.7 40 539. 7 18.8 600 599.6 20.9 Dist. Dep. Lat. Dist. 1 Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 88° {{ )2°, 268' > 979° ^ ) -' - . Page 372] '1 ABLP I '2. Difference of Latitude and Departure for 3° (177°, 183 °, 357° ). Dist. Lat. Dep. Dist. Lat. ' Dep. Dist. Lat. Dep. Dist. i Lat. Dep. Dist. Lat. Dep. 1 1.0 0.1 61 60.9 3.2 121 120.8 6.3 181 180.8 9.5 241 240.7 12.6 2 2.0 0.1 62 61.9 3.2 22 121.8 6.4 82 181.8 9.5 42 241.7 12.7 3 3.0 0.2 63 62.9 3.3 23 122.8 6.4 83 182.7 9.6 43 242.7 12.7 4 4.0 0.2 64 63.9 3.3 24 123.8 6.5 84 183.7 9.6 44 243.7 12.8 5 5.0 0.3 65 64.9 3.4 25 124.8 6.5 85 184.7 9.7 45 244.7 12.8 6 6.0 0.3 ^ 65.9 3.5 26. 125.8 6.6 86 185.7 9.7 46 245.7 12.9 7 7.0 0.4 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 50 249.7 13.1 11 11.0 0.6 71 70.9 3.7 131 130.8 6.9 191 190.7 10.0 251 250.7 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 53 252. 7 13.2 14 14.0 0.7 74 73.9 3.9 34 133.8 7.0 94 193.7 10.2 54 253.7 13.3 15 15.0 0.8 75 74.9 3.9 35 134.8 7.1 95 194.7 10.2 55 254.7 13.3 16 16.0 0.8 76 75.9 4.0 36 135.8 7.1 96 195.7 10.3 56 255. 6 13.4 17 17.0 0.9 77 76.9 4.0 37 136. 8 7.2 97 196.7 10.3 57 256.6 13.5 18 18.0 0.9 78 77.9 4.1 38 137.8 7.2 98 197.7 10.4 58 257.6 13.5 19 19.0 1.0 79 78.9 4.1 39 138.8 7.3 99 198.7 10.4 59 258.6 13.6 20 20.0 1.0 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 25.0 1.3 85 84.9 4.4 45 144.8 7.6 05 204.7 10.7 65 264.6 13.9 26 26.0 1.4 86 85.9 4.5 46 145.8 7.6 06 205. 7 10.8 66 265. 6 13.9 27 27.0 1.4 87 86.9 4.6 47 146.8 7.7 07 206.7 10.8 67 266.6 14.0 28 28.0 1.5 88 87.9 4.6 48 147.8 7.7 08 207.7 10.9 68 267.6 14.0 29 29.0 1.5 89 88.9 4.7 49 148.8 7.8 09 208.7 10.9 69 268.6 14.1 30 30.0 1.6 90 89.9 90.9 4.7 4.8 50 149.8 7.9 10 209.7 11.0 70 269.6 270.6 14.1 31 31.0 1.6 91 151 150.8 7.9 211 210.7 11.0 271 14.2 32 32.0 1.7 92 91.9 4.8 52 151.8 8.0 12 211.7 11.1 72 271.6 14.2 33 33.0 1.7 93 92.9 4.9 53 152.8 8.0 13 212.7 11.1 73 272.6 14.3 34 34.0 1.8 94 93.9 4.9 54 153.8 8.1 14 213.7 11.2 74 273.6 14.3 35 35.0 1.8 95 94.9 5.0 55 154.8 8.1 15 214.7 11.3 75 274.6 14.4 36 36.0 1.9 96 95.9 5.0 56 155.8 8.2 16 215.7 11.3 76 275.6 14.4 37 36.9 1.9 97 96.9 5.1 57 156.8 8.2 17 216.7 11.4 77 276.6 14.5 38 37.9 2.0 98 97.9 5.1 58 157.8 8.3 18 217.7 11.4 78 277.6 14.5 39 38.9 2.0 99 98.9 5.2 59 158. 8 8.3 19 218.7 11.5 79 278.6 14.6 40 39.9 2.1 100 99.9 100.9 5.2 60 159.8 8.4 20 219.7 11.5 11.6 80 281 279.6 280. 6 14.7 41 40.9 2.1 101 5.3 161 160.8 8.4 221 220.7 14.7 42 41.9 2.2 02 101.9 5.3 62 161.8 8.5 22 221.7 11.6 82 281.6 14.8 43 42.9 2.3 03 102.9 5.4 63 162.8 8.5 23 222.7 11.7 83 282.6 14.8 44 43.9 2.3 04 103.9 5.4 64 163.8 8.6 24 223.7 11.7 84 283.6 14.9 45 44.9 2.4 05 104.9 5.5 65 164.8 8.6 25 224.7 11.8 85 284.6 14.9 46 45.9 2.4 06 105.9 5.5 66 165.8 8.7 26 225.7 11.8 86 285. 6 15.0 47 46.9 2.5 07 106.9 5.6 67 166.8 8.7 27 226.7 11.9 87 286.6 15.0 48 47.9 2.5 08 107.9 5.7 68 167.8 8.8 28 227.7 11.9 88 287.6 15.1 49 48.9 2.6 09 108.9 5.7 69 168.8 8.8 29 228.7 12.0 89 288.6 15.1 50 49.9 2.6 10 109.8 5.8 70 169.8 170.8 8.9 30 229.7 230.7 12.0 90 291 289.6 290.6 15.2 51 50.9 2.7 111 110.8 5.8 171 8.9 231 12.1 15.2 52 51.9 2.7 12 111.8 5.9 72 171.8 9.0 32 231.7 12.1 92 291.6 15.3 53 52.9 2.8 13 112.8 5.9 73 172.8 9.1 33 232.7 12.2 93 292.6 15.3 54 53.9 2.8 14 113.8 6.0 74 173.8 9.1 34 233. 7 12.2 94 293.6 15.4 55 54.9 2.9 15 114.8 6.0 75 174.8 9.2 35 234.7 12.3 95 294.6 15.4 56 55.9 2.9 16 115.8 6-i 76 175.8 9.2 36 235. 7 12.4 96 295. 6 15.5 57 • 56.9 3.0 17 116.8 6.i 77 176. 8 9.3 37 236.7 12.4 97 296.6 15.5 58 57.9 3.0 18 117.8 6.2 78 177.8 9.3 38 237.7 12.5 98 297.6 15.6 59 58.9 3.1 19 118.8 6.2 79 178.8 9.4 39 238.7 12.5 99 298.6 15.6 60 59.9 3.1 20 119.8 6.3 80 179.8 9.4 40 239.7 12.6 300 299.6 15.7 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 87° {i )3°, 267' ', 273°] . TABLE 2. [Page 373 | Difference of Latitude and Departure for 3° (177°, 183°, 357° ). Dist. Lat. Dep. Dist. Lat. 360. 5 Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 300.6 15.7 361 18.9 421 420.4 22.0 481 480.3 ! 25.2 541 540.2 28.3 02 301.6 15.8 62 361.5 19.0 22 421.4 22.1 82 481.3 25.2 42 541.2 28.4 03 302.6 15.9 63 362.5 19.0 23 422. 4, 22.2 83 482.3 25.3 43 542.2 28.4 04 303.5 15.9 64 363.5 19.1 24 423.4 22.2 84 483.3 25.3 44 543.2 28.5 05 304.5 16.0 65 364.5 19.1 25 424.4 22.3 85 484.3 ; 25.4 45 544.2 28.5 06 305.5 16.0 66 365. 5 19.2 26 425.4 22.3 86 485.3 25.4 46 545.2 28.6 07 306.5 16.1 67 366.5 19.2 27 426.4 22.4 87 486. 3 25. 5 47 546.2 28.6 08 307.5 16.1 68 367.5 19.3 28 427.4 22.4 88 487. 3 25. 5 48 547.2 28.7 09 308.5 16.2 69 368.5 19.3 29 ' 428.4 22.5 89 488. 3 25. 6 49 548.2 28.7 10 311 309.5 310. 5 16.2 16.3 70 369.5 19.4 19.4 30 429. 4 431 430. 4 22.5 90 489.3 490.3 25.6 50 549. 2 28.8 371 370.5 22.6 491 25.7 551 550.2 28.8 12 311.5 16.3 72 371.5 19.5 32 431. 4 22.6 92 491.3 1 25.7 52 551.2 28.9 13 312.5 16.4 73 372.5 19.5 33 432.4 22. 7 93 492.3 1 25.8 53 552.2 28.9 14 313. 5 16.4 74 373.5 19.6 34 433. 4 22.7 94 493.3 25.9 54 553. 2 29.0 15 314.5 16.5 75 374.5 19.6 35 434.4 22.8 95 494.3 25.9 55 554.2 29.1 16 315.5 16.6 76 375.5 19.7 36 435.4 22.8 96 495.3 26.0 56 555.2 29.1 17 316.5 16.6 77 376.5 19.8 37 436.4 22.9 97 496.3 ' 26.0 57 556.2 29.2 18 317.5 16.7 78 377.4 19.8 38 437.4 22.9 98 497. 3 i 26. 1 58 557.2 29.2 19 318.5 16.7 79 378.4 19.9 39 438.4 23.0 99 498.3 26.1 59 558.2 29.3 20 319.5 16.8 16.8 80 379. 4 380.4 19.9 40 439.4 23.0 500 501 499.3 1 26.2 500.3 26.2 60 561 559.2 560.2 29.3 29.4 321 320.5 381 20.0 441 440.4 23.1 22 321.5 16.9 82 381.4 20.0 42 441.4 23.1 02 501.3 26.3 62 561.2 29.4 23 322.5 16.9 83 382.4 20.1 43 442.4 23.2 03 502.3 26.3 63 562.2 29.5 24 323.5 17.0 84 383.4 20.1 44 443.4 23. 3 04 503.3 26.4 64 563.2 29.5 25 324.5 17.0 85 384. 4 20.2 45 444.4 23.3 05 504.3 26.4 65 564.2 29.6 26 325.5 17.1 86 385.4 20.2 46 445. 4 23.4 06 505.3 1 26.5 66 565.2 29.6 27 326.5 17.1 87 386.4 20.3 47 446.4 23.4 07 506.3 26.5 67 566.2 29.7 28 327.5 17.2 88 387.4 20.3 48 447.4 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 50 449.3 450.3 23.6 10 509.3 26.7 70 569.2 29.8 29.9" 331 330.5 17.3 391 390. 4 20.5 451 23.6 511 j 510. 3 i 26. 7 571 570.2 32 331.5 17.4 92 391.4 20.5 52 451.3 23. 7 12 1 511.3 ' 26.8 72 571.2 29.9 33 332.5 17.5 93 392.4 20.6 53 452.3 23.7 13 512.3 26.8 73 572.2 30.0 34 333. 5 17.5 94 393.4 20.6 54 453. 3 23.8 14 513.3 26.9 74 573.2 30.0 35 334.5 17.6 95 394.4 20.7 55 454.3 23.8 15 514.3 27.0 75 574.2 30.1 36. 335.5 17.6 96 395.4 20.7 56 455. 3 23.9 16 515.3 27.0 76 575.2 30.1 37 336. 5 17.7 97 396.4 20.8 57 456.3 23.9 17 516.3 27.1 77 576.2 30.2 38 337. 5 17.7 98 397.4 20.8 58 457. 3 24.0 18 517.3 27.1 78 577.2 30.2 39 338.5 17.8 99 398.4 20.9 59 458.3 24.0 19 518.3 27.2 79 578.2 30.3 40 339.5 17.8 400 399. 4 400.4 20.9 21.0 60 459. 3 24.1 20 521 519.3 520.3 27.2 80 579.2 30.3 341 340. 5 17.9 401 461 460. 3 24.1 27.3 581 580.2 30.4 42 341.5 17.9 02 401.4 21.1 62 461.3 24.2 22 1 521. 3 27.3 82 581.2 30.4 43 342.5 18.0 03 402.4 21.1 63 462. 3 24.2 23 522.3 27.4 83 582.2 30.5 44 343.5 18.0 04 403.4 21.2 64 463. 3 24.3 24 i 523.3 27.4 84 583.2 30.5 45 344.5 18.1 05 404.4 21.2 65 564. 3 24.4 25 i 524.3 27.5 85 584.2 30.6 46 345.5 18.1 06 405.4 21.3 66 465. 3 24.4 26 1 525.3 27.5 86 585. 2 30.6 47 346.5 18.2 07 406.4 21.3 67 466. 3 24.5 27 526.3 27.6 87 586.2 30.7 48 347.5 18.2 08 407.4 21.4 68 467.3 24.5 28 527.3 27.6 88 587.2 30.7 49 348.5 18.3 09 408.4 21.4 69 468.3 24.6 29 528.3 27.7 89 588.2 30.8 50 349.5 '350.5 18.3 18. 4 10 409.4 21.5 21.5 70 469.3 24.6 24.7 30 531 529.3 530.3 27.7 27.8 90 591 589.2 590.2 30.9 351 411 410.4 471 470.3 30.9 52 351.5 18.4 12 411.4 21.6 72 471.3 24.7 32 531.3 27.8 92 591.2 31.0 53 352.5 18.5 13 412.4 21.6 73 472.3 24.8 33 532.3 27.9 93 592.2 31.0 54 353.5 18.5 14 413.4 21.7 74 473. 3 24.8 34 533.3 27.9 94 593.2 31.1 55 354.5 18.6 15 414.4 21.7 75 474.3 24.9 35 534.3 28.0 95 594.2 31.1 56 355.5 18.6 16 415.4 21.8 76 475. 3 24.9 36 535. 3 28.1 96 595.2 31.2 57 356.5 18.7 17 416.4 21.8 77 476. 3 25.0 37 536.3 28.1 97 596.2 31.2 58 357.5 18.8 18 417.4 21.9 78 477.3 25.0 38 537.3 28.2 98 597.2 31.3 59 358. 5 18.8 19 418.4 21.9 79 478. 3 25.1 39 538.3 28.2 99 598.2 31.3 60 359.5 18.9 20 419.4 22.0 80 479.3 25.1 40 ,539.3 28.3 600 599.2 31.4 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 87° (93°, 267= , 273°) Page 374J r rABLE 2. Difference of Latitude and Depart! cirefor4° (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 42 241.4 16.9 3 3.0 0.2 63 62.8 4.4 23 122.7 8.6 83 182.6 12.8 43 242.4 17.0 4 4.0 0.3 64 63.8 4.5 24 123.7 8.6 84 183.6 12.8 44 243.4 17.0 5 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 ^ 65.8 4.6 26 125.7 8.8 86 185.5 13.0 46 245.4 17.2 7 7.0 0.5 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 i 188.5 13.2 49 248.4 17.4 10 10.0 0.7 70 69.8 70.8 4.9 30 129.7 9.1 90 189.5 190. 5" 13.3 13.3 50 249.4 17.4 11 11.0 0.8 71 5.0 131 130.7 9.1 191 251 2.50. 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 9.8 200 199.5 200.5 14.0 60 259. 4 18.1 18.2 21 20.9 1.5 81 80.8 5.7 141 140.7 9.8 201 14.0 261 260.4 22 21.9 1.5 82 81.8 5.7 42 141.7 9.9 02 201.5 14.1 62 261.4 18.3 23 22.9 1.6 83 82.8 5.8 43 142.7 10.0 03 202. 5 14.2 63 262.4 18.3 24 23.9 1.7 84 83.8 5.9 44 143.6 10.0 04 203.5 14.2 64 263.4 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 i 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 6.3 6.3 50 151 149.6 10.5 10 209.5 14.6 70 271 269.3 270.3 18.8 18.9 30.9 2.2 91 90.8 150.6 10.5 211 210.5 14.7 82 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 1.52. 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 lb. 4: 80 281 279.3 19.5 41 40.9 2.9 101 100.8 7.0 161 11.2 221 220.5 280.3 19.6 42 41.9 2.9 02 101.8 7.1 62 161.6 11.3 22 221.5 1.5.5 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 1.5.7 85 284. 3 19.9 46 45.9 3.2 06 105.7 7.4 66 165.6 11.6 26 225.4 15.8 86 285. 3 20.0 47 46.9 3.3 07 106.7 7.5 67 166.6 11.6 27 226.4 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 7.7 70 171 169.6 11.9 30 229.4 230.4 16.0 90 291 289. 3 20.2 51 50.9 3.6 111 110.7 170.6 11.9 231 16.1 290.3 20.3 52 51.9 3.6 12 111.7 7.8 72 171.6 12.0 32 231.4 16.2 92 291. 3 20.4 53 52.9 3.7 13 112.7 7.9 73 172.6 12.1 33 232.4 16.3 93 292.3 20.4 54 53.9 3.8 14 113.7 8.0 74 173.6 12.1 34 233.4 16.3 94- 293.3 20.5 55 54.9 3.8 15 114.7 8.0 75 174.6 12.2 35 234.4 16.4 95 294.3 20.6 56 55.9 3.9 16 115.7 8.1 76 175.6 12.3 36 235. 4 16.5 96 295. 3 20.6 57 56.9 4.0 17 116.7 8.2 77 176.6 12.3 37 236.4 16.5 97 296.3 20.7 58 57.9 4.0 18 117.7 8.2 78 177.6 12.4 38 237.4 16.6 98 297.3 20.8 59 58.9 4.1 19 118.7 8.3 79 178.6 12.5 39 238.4 16.7 99 298.3 20.9 60 59.9 4.2 20 119.7 8.4 80 179.6 12.6 40 239.4 16.7 300 299.3 20.9 Dlst. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 86°; ( M°, 266 °, 274°). tablp: 2. [Page 375 Difference of Latitude and Departure for 4° (176°, 184 °, 356° ). Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 300.3 21.0 361 360.1 25.2 421 420.0 29.4 481 479.8 33.5 541 539.7 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. 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 10 309.2 310. 2 21.6 70 369. 1 370.1 25.8 30 428.9 30.0 90 488.8 489.8 34.2 34.2 50 551 548.7 549.7 38.3 311 21.7 371 25.9 431 429.9 30.1 491 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 39 437.9 30.6 99 497.8 34.8 59 557.6 38.9 20 319.2 320. 2 22.3 80 379. 1 380.1 26.5 40 438.9 439. 9 30.7 30.8 500 501 498.8 499.8 34.8 60 558.6 559. 6 39.0 321 22.4 381 26.6 441 34.9 561 39.1 22 321.2 22.5 82 381.1 26.6 42 440.9 30.8 02 500.8 35.0 62 560.6 39.2 23 322.2 22.5 83 382.1 26.7 43 441.9 30.9 03 501. 8 35. 63 561.6 39.2 24 323. 2 22.6 84 383.1 26.8 44 442.9 31.0 04 502.8 35.1 64 562.6 39.3 25 324.2 22.7 85 384. 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. 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 30 331 329.2 23.0 90 389.0 27.2 27.3 50 451 448.9 31.4 31.5 10 511 508.8 35.6 35.6 70 568.6 39.8 330.2 23.1 391 390. 449.9 509.8 571 569.6 39.8 32 331.2 23.2 92 391.0 27.3 52 450.9 31.5 12 510.8 35.7 72 570.6 39.9 33 332.2 23.2 93 392.0 27.4 53 451.9 31.6 13 511.8 35.8 73 571.6 40.0 34 333. 2 23.3 94 393.0 27.5 54 452.9 31.7 14 512.7 35.8 74 572.6 40.0 35 334.2 23.4 95 394.0 27.6 55 453.9 31.7 15 513.7 35.9 75 573.6 40.1 36 • 335. 2 23.4 96 395.0 27.6 56 454.9 31.8 16 514.7 36.0 76 574.6 40.2 37 336.2 23. 5 97 396.0 27.7 57 455.9 31.9 17 515.7 36.0 II 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 2.3.6 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 36.3 80 578.6 40.5 341 ;wo.2 23.8 401 400.0 28.0 461 459. 9 32.2 521 519.7 581 579.6 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 24.5 10 409.0 28.6 70 468.8 32.8 30 531 528.7 529.7 37.0 37.0 90 591 588.6 41.2 41.3 .351 350. 1 411 410.0 28.7 471 469.8 32.9 589.6 52 351.1 24.6 12 411.0 28.7 72 470.8 32.9 32 530.7 .37.1 92 590.6 41.3 53 352. 1 24.6 13 412.0 28.8 73 471.8 33.0 33 531.7 37.2 93 591.6 41.4 54 353.1 24.7 14 413.0 28.9 74 472.8 33. 1 34 532.7 37.2 94 592.6 41.5 55 354. 1 24.8 15 414.0 28.9 75 473.8 33.1 35 533. 7 37.3 95 593.6 41.5 56 355. 1 24.8 16 415. 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 1 475. 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 37.7 600 698.6 41.9 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat i 36°; (94°, 266°, 274°). 1 Page 376 1 TABLE 2. Difference of Latitude and Departure for 5° (1 75°, 185 °, 355° ). DLst. 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 4 4.0 0.3 64 63.8 5.6 24 123.5 10.8 84 183.3 16.0 44 243.1 21.3 5 5.0 0.4 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 f 65.7 5.8 26 125.5 11.0 86 185. 3 16.2 46 245.1 21.4 7 7.0 0.6 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 21.8 11 11.0 1.0 71 70.7 6.2 131 130.5 11.4 191 190.3 16.6 251 250.0 21.9 12 12.0 1.0 72 71.7 6.3 32 131.5 11.5 92 191.3 16.7 52 251.0 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 1.8 80 79.7 7.0 40 139.5 140.5 12.2 12.3 200 201 199.2 17.4 60 259.0 22.7 21 20.9 81 80.7 7.1 141 200.2 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. 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 50 149.4 150. 4 13.1 10 209.2 18.3 70 269.0 23.5 31 30.9 2.7 91 90.7 7.9 151 13.2 211 210.2 18.4 271 270.0 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 20 221 219.2 19.2 80 278.9 24.4 41 40.8 3.6 101 100.6 8.8 161 160.4 14.0 220.2 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 43 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 4.4 10 109.6 9.6 70 169.4 14.8 30 229.1 230. 1 20.0 90 288.9 25.3 51 50.8 4.4 111 110.6 9.7 171 170.3 14.9 231 20.1 291 289.9 25.4 52 51.8 4.5 12 111.6 9.8 72 171. 3 15.0 32 231.1 20.2 92 290.9 25.4 53 52.8 4.6 13 112.6 9.8 73 172. 3 15.1 33 232. 1 20.3 93 291.9 25.5 54 53.8 4.7 14 113.6 9.9 74 173.3 15.2 34 233.1 20.4 94 292.9 25.6 55 54.8 4.8 15 114.6 10.0 75 174.3 15.3 35 234. 1 20.5 95 293.9 25.7 56 55.8 4.9 16 115.6 10.1 76 175.3 15.3 36 235. 1 20.6 96 294.9 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° (S 5°, 265°, 275°). TABLE 2. [Page 377 Difference of Latitude and Departure for 5° (175°, 185 °, 355° )• Dist. Lat. Dep. Dist. 1 Lat. Dep. Dist. Lat. 1 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 41.9 541 538.9 47.2 02 300.8 26.3 62 360.6 31.6 22 420. 4 36. 8 82 480.2 42.0 42 539. 9 47.3 03 301.8 26.4 63 361.6 i 31.6 23 421.4 36.9 83 481.2 42.1 43 540.9 47.4 04 302.8 26.5 64 i 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 1 31.8 25 423. 4 1 37. 1 85 483.2 42.3 45 542.9 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 i 37.3 88 486. 1 42.5 48 545. 9 47.8 09 307.8 26.9 69 367. 6 32.2 29 427.4 ' 37.4 89 487.1 42.6 49 546.9 47.9 10 308.8 309.8 27.0 70 368.6 1 32.3 369.6 i 32.3 30 428.4 37.5 90 488.1 "489.1 42.7 42,8 50 551 547.9 48.0 311 27.1 371 431 429.4 37.6 491 548.9 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 1 37. 7 93 491.1 43.0 53 550. 9 48. 3 14 312.8 27.4 74 1 372.6 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 i 32.7 35 433. 3 37.9 95 493.1 43.1 55 552.9 , 48.4 16 314.8 27.5 76 374.6 32.8 36 434.3 38.0 96 494.1 43.2 56 553. 9 ! 48. 5 17 315.8 27.6 77 375.6 32.9 37 435.3 38.1 97 495.1 43.3 57 554.9 : 48.6 18 316.8 27.7 78 376.6 33.0 38 436.3 38.2 98 496.1 43.4 58 555. 9 48. 7 19 317.8 27.8 79 377.6 33. 39 437.3 38.3 99 497.1 43.5 59 556.9 48.8 20 318.8 27.9 80 378.6 i 33.1 40 438.3 38.4 500 498.1 499.1 43.6 60 557.9 48.8 321 "319. 8 28.0 381 379.5 I 33.2 441 439.3 1 38.4 501 43.7 561 558.8 ; 48.9 22 320.8 28.1 82 380.5 33.3 42 440.3 ; 38.5 02 : 500. 1 43.8 62 559.8 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 i 49. 1 24 322. 8 28.2 84 382.5 33.5 44 442. 3 I 38. 7 04 502.1 43.9 64 561. 8 1 49. 2 25 323.8 28.3 85 383.5 33.6 45 443.3 1 38.8 05 503.1 44.0 65 562. 8 j 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 07 505.1 44.2 67 564. 8 i 49. 5 28 326. 7 28.6 88 386.5 33.8 48 446. 3 39. 1 08 506.1 44.3 68 565.8 1 49.6 29 327. 7 28.7 89 387.5 33. 9 49 447. 3 : 39. 1 09 507.1 44.4 69 566. 8 1 49. 7 30 328.7 28.8 90 388. 5 34.0 50 448.3 1 39.2 10 508.1 44.5 70 567. 8 [ 49. 7 331 329. 7 28.9 391 389.5 34.1 451 449.3 i 39.3 511 509.0 44.5 571 568.8 1 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 1 49.9 33 331. 7 29.0 93 391.5 34.3 53 451.3 [ 39.5 13 511.0 44.7 73 570. 8 i 50. 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 15 513.0 44.9 75 572.8 50.2 36 .334.7 29.3 96 394.5 34.5 56 454. 3 39. 8 16 514.0 45.0 76 573.8 50.3 37 335.7 29.4- 97 395. 5 34.6 57 455. 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 i 40.0 19 517.0 45.2 79 576.8 i 50.5 40 341 338.7 339.7 29.6 400 398.5 34.9 60 458.2 40.1 40.2 20 521 518.0 519.0 45.3 80 577.8 1 50.6 578.8 1 50.7 29.7 401 399.5 35.0 461 459.2 45.4 581 42 340.7 29.8 02 400.5 35.0 62 460.2 1 40.3 22 520.0 45.5 82 579.8 ! 50.8 43 341.7 29.9 03 401.5 35.1 63 46i.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 24 522.0 45.7 84 581.8 50.9 45 343.7 30.1 05 403.5 35.3 65 463.2 40.5 25 523.0 45.8 85 582.8 51.0 46 344.7 30.2 06 404.5 35.4 66 464.2 40.6 26 524.0 45.9 86 583. 8 51.1 47 345. 7 30.3 07 405.4 35.5 67 465.2 40.7 27 525. 45.9 87 584.8 51.2 48 346.7 30.3 08 406.4 35.6 68 466. 2 40.8 28 526.0 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 30.5 10 408.4 35.7 70 468.2 469.2 41.0 30 528.0 529. 46.2 90 587.8 51.5 351 349.7 30.6 411 409.4 j 35.8 471 41.1 531 46.3 591 588.7 51.6 52 350.7 30.7 12 410.4 1 35.9 72 470. 2 41.1 32 530. 46.4 92 589.7 51.6 53 351. 7 30.8 13 411.4 ' 36.0 73 471. 2 41.2 33 531.0 46.5 93 590.7 51.7 54 352.6 30.9 14 412.4 i 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. 46.6 95 592.7 51.9 56 354.6 31.0 16 414.4 36.3 76 474.2 41.5 36 533.9 46.7 96 593.7 52.0 57 355.6 31.1 17 415.4 1 36.4 77 475.2 41.6 37 534. 9 46.8 97 594.7 52.1 58 356.6 31.2 18 416.4 [ 36.4 78 476.2 41.7 38 535. 9 46.9 98 595. 7 52.2 59 357.6 31.3 19 417.4 [ 36.5 79 477.2 41.8 39 536.9 47.0 99 596.7 52.3 60 358.6 31.4 20 418.4 36.6 1 80 478.2 41.8 40 537.9 47.1 600 597.7 52.3 Dist. Dep. Lat. Dist. Dep. 1 Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 85° (95°, 265°, 275°) 1 Page 378] TABLE 2. Difference of Latitude and Departure for 6° (174°, 186 °, 354° )• Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 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 25.4 4 4.0 0.4 64 63.6 6.7 24 123.3 13.0 84 183.0 19.2 44 242.7 25.5 5 5.0 0.5 65 64.6 6.8 25 124.3 13.1 85 184.0 19.3 45 243.7 25.6 6 6.0 0.6 1? 65.6 6.9 26 125. 3 13.2 86 185. 19.4 46 244.7 25.7 7 7.0 0.7 66.6 7.0 27 126.3 13.3 87 186.0 19.5 47 245. 6 25.8 8 8.0 0.8 68 67.6 7.1 28 127.3 13.4 88 187.0 19.7 48 246.6 25.9 9 9.0 0.9 69 68.6 7.2 29 128.3 13.5 89 188.0 19.8 49 247.6 26.0 10 9.9 1.0 70 69.6 7.3 30 131 129.3 130.3 13.6 90 189.0 190.0 19.9 50 251 248.6 249.6 26.1 11 10.9 1.1 71 70.6 7.4 13.7 191 20.0 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 i 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 14.6 200 201 198.9 20.9 60 258. 6 259.6 27.2 21 20.9 2.2 81 80.6 8.5 141 140.2 14.7 199.9 21.0 261 27.3 22 21.9 2.3 82 81.6 8.6 42 141.2 14.8 02 200.9 21.1 62 260.6 27.4 23 22.9 2.4 83 82.5 8.7 43 142.2 14.9 03 201.9 21.2 63 261.6 27.5 24 23.9 2.5 84 83.5 8.8 44 143.2 15.1 04 202.9 21.3 64 262.6 27.6 25 24.9 2.6 85 84.5 8.9 45 144.2 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 08 206.9 21.7 68 266.5 28.0 29 28.8 3.0 89 88.5 9.3 49 148.2 15.6 09 207.9 21.8 69 267.5 28.1 30 29.8 3.1 3.2 90 89.5 9.4 50 151 149.2 15.7 10 208.8 22.0 70 268.5 269.5 28.2 31 30.8 91 90.5 9.5 150.2 15.8 211 209.8 22.1 271 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 28.5 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 41 39.8 4.2 100 99.5 10.5 60 159.1 160. 1 16.7 20 218.8 219.8 23.0 23.1 80 281 278.5 279.5 29.3 29.4 40.8 4.3 101 100.4 10.6 161 16.8 221 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 2.3.9 89 287.4 30.2 50 49.7 5.2 10 109.4 11.5 70 169.1 17.8 30 228.7 24.0 24.1 90 291 288.4 30.3 51 50.7 5.3 111 110.4 11.6 171 170.1 17.9 231 229.7 289.4 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 2.35. 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 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 84° (£ ►6°, 264= , 276°) TABLE 2. [Page 379 | Difference of Latitude and Departure fpr 6° (174°, 186° , 354°) Dlst. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 299.3 31.5 361 359.0 37.7 421 418.7 44.0 481 478.4 50.3 541 538.0 56. 5 02 300.3 31.6 62 360.0 37.8 22 419.7 44.1 82 479.4 50.4 42 539. 56.6 03 301.3 31.7 63 361.0 37.9 23 420.7 44.2 83 480. 4 50.5 43 540.0 56.7 04 302.3 31.8 64 362.0 38.0 24 421.7 44.3 84 481.3 50.6 44 541.0 56.8 05 303.3 31.9 65 363. 38.1 25 422.7 44.4 85 482.3 50.7 45 542. 56.9 06 304.3 32.0 66 364. 38.3 26 423.7 44.5 86 483. 3 50.8 46 543.0 57.0 07 305.3 32.1 67 365. 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 70 368.0 369.0 38.7 38.8 30 431 427.6 428.6 44.9 45.0 90 491 487.3 51.2 50 551 547.0 548.0 57.4 57. 5 311 309.3 32.5 371 488. 3 51.3 12 310. 3 32.6 72 370. 38.9 32 429.6 45.2 92 489.3 51.4 52 549.0 57.6 13 311.3 32.7 73 371.0 39.0 33 430.6 45.3 93 490. 3 51.5 53 550. 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 i 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. 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. 58.3 19 317.3 33.3 79 376.9 39.6 39 436. 6 45.9 99 496.3 52.1 59 556. 58.4 20 318.2 33.4 80 377.9 39.7 40 437.6 46.0 46.1 500 497.3 52.3 60 556.9 58.5 58.6 321 319.2 33.6 381 378.9 39.8 441 438.6 501 1 498.3 52.4 561 557.9 22 320.2 33.7 82 379. 9 39.9 42 439.6 46.2 02 499.3 52.5 62 558.9 58.7 23 321.2 33.8 83 380.9 40.0 43 440.6 46.3 03 500.2 52.6 63 559.9 58.8 24 322.2 33.9 84 381. 9 40.1 44 441.6 46.4 04 501.2 52.7 64 560.9 59.0 25 323.2 34.0 85 382.9 40.2 45 442.6 46.5 05 502.2 52.8 65 561.9 59.1 26 324.2 34.1 86 383.9 40.3 46 443.6 46.6 06 503.2 52.9 66 562.9 59.2 27 325.2 34.2 87 384. 9 40.5 47 444.5 46.7 07 504.2 53.0 67 563.9 59.3 28 326.2 34.3 88 385.9 40.6 48 445. 5 46.8 08 505. 2 53.1 68 564.9 59.4 29 327.2 34.4 89 386.9 40.7 49 446.5 46.9 09 506.2 53.2 69 565.9 59.5 30 328.2 34.5 90 391 387.9 40.8 50 447.5 47.0 10 507.2 53.3 70 571 566.9 59.6 331 329.2 34.6 388.9 40.9 451 448.5 47.1 511 508.2 53.4 567.9 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 57 454.6 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 40 338.1 339.1 35. 5 35.6 400 401 397.8 398.8 41.8 41.9 60 457.5 48.1 20 517.2 518.1 54.3 80 576.8 60.6 341 461 458. 5 48.2 521 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 50 351 348.1 349.1 36.6 36.7 10 407.8 42.9 43. 70 467.4 49.1 30 531 527.1 55.4 90 586.8 61.7 411 408.7 471 468.4 49.2 528.1 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. 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 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dlst. Dep. Lat. 84° ( 96°, 264 °, 276° ). Page 380] TABLE 2. Difference of Latitude and Departure for 7° (17 •3°, 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 1 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 ft4 63.5 7.8 24 123.1 15.1 84 182.6 22.4 44 242.2 29.7 5 5.0 0.6 65 64.5 7.9 25 124.1 15.2 85 183.6 22.5 45 243. 2 29.9 6 6.0 0.7 66 65.5 8.0 26 125.1 15.4 86 184.6 22.7 46 244.2 30.0 7 6.9 0.9 *7 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 10.9 1.2 70 69.5 8.5 8.7 30 129.0 15.8 90 188.6 23.2 23.3 50 248.1 30.5 30.6 11 1.3 71 70.5 131 130.0 16.0 191 189.6 251 249.1 12 11.9 1.5 72 71.5 8.8 32 131. 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. 16.3 94 192.6 23.6 54 252.1 31.0 15 14.9 1.8 75 74.4 9.1 35 134. 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 58 256.1 31.4 19 18.9 2.3 79 78.4 9.6 39 138.0 16.9 99 197.5 24.3 59 257.1 31.6 20 21 19.9 20.8 2.4 2.6 80 79.4 9.7 40 139.0 17.1 200 201 198.5 24.4 60 258.1 259.1 31.7 81 80.4 9.9 141 139.9 17.2 199. 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 3.8 90 89.3 11.0 50 148.9 18.3 10 208.4 25.6 70 268.0 32.9 31 30.8 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 3.3.4 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 4.9 100 99.3 12.2 60 158.8 19.5 20 218.4 26.8 80 277.9 34.1 40.7 5.0 101 100.2 12.3 161 159.8 19.6 221 219.4 26.9 281 278.9 34.2 42 41.7 5.1 02 101.2 12.4 62 160.8 19.7 22 220. 3 27.1 82 279.9 34.4 43 42.7 5.2 03 102.2 12.6 63 161.8 19.9 23 221.3 27.2 83 280.9 34.5 44 43.7 5.4 04 103.2 12.7 64 162.8 20.0 24 222.3 27.3 84 281.9 34.6 45 44.7 5.5 05 104.2 12.8 65 163.8 20.1 25 223.3 27.4 85 282.9 34.7 46 45.7 5.6 06 105.2 12.9 66 164.8 20.2 26 224 3 27.5 86 283.9 34.9 47 46.6 5.7 07 106.2 13.0 67 165. 8 20.4 27 225.3 27.7 87 284.9 35.0 48 47.6 5.8 08 107.2 13.2 68 166.7 20.5 28 226.3 27.8 88 285. 9 35.1 49 48.6 6.0 09 108.2 13.3 69 167.7 20.6 29 227.3 27.9 89 286.8 35.2 50 49.6 6.1 10 109.2 13.4 70 168.7 20.7 30 228.3 28.0 90 287.8 35.3 51 50.6 6.2 111 110.2 13.5 171 169.7 20.8 231 229.3 28.2 291 288.8 35.5 52 51.6 6.3 12 111.2 13.6 72 170.7 21.0 32 230. 3 28.3 92 289.8 35.6 53 52.6 6.5 13 112.2 13.8 73 171.7 21.1 33 231.3 28.4 93 290.8 35.7 54 53.6 6.6 14 113.2 13.9 74 172.7 21.2 34 232. 3 28.5 94 291.8 35.8 55 54.6 6.7 15 114.1 14.0 75 173. 7 21.3 35 233.2 28.6 95 292.8 36.0 56 55.6 6.8 16 115. 1 14.1 76 174.7 21.4 36 234. 2 28.8 96 293.8 36.1 57 56.6 6.9 17 116.1 14.3 77 175. 7 21.6 37 235. 2 28.9 97 294.8 36.2 58 57.6 7.1 18 117.1 14.4 78 176.7 21.7 38 236.2 29.0 98 295.8 36.3 59 58.6 7.2 19 IS.l 14.5 79 177.7 21.8 39 237. 2 29.1 99 296.8 36.4 60 59.6 7.3 20 ip..l 14. 6 80 178.7 21.9 40 238.2 29.2 300 297.8 36.6 Dist. Dep. Lat. JDist. 1 ^ep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. / 83° ( 97°, 263°, 277° ). TABLE 2. [Page 381 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. 801 298.7 36.7 361 858. 3 44.0 421 417.9 51.3 481 477.4 58.6 541 537. 65.9 02 299.7 36.8 62 859. 3 44.1 22 418.8 51.4 82 478.4 58.7 42 537.9 • 66.0 08 300.7 36.9 63 360. 8 44.2 28 419.8 51.5 83 479.4 58.8 48 588.9 66.2 04 301.7 37.0 64 861.3 44.4 24 420.8 51.7 84 480.4 59.0 44 589. 9 66.3 05 302.7 87.2 65 862.8 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 27 428. 8 52.0 87 488.4 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 10 811 307.7 308.7 37.8 70 367.2 45.1 45.2 80 426.8 52.4 90 486.3 487.8 59.7 59.8 50 545. 9 67.0 37.9 371 368.2 431 427.8 52.5 491 551 546. 9 67.1 12 309.7 88.0 72 369.2 45.3 82 428.8 52.6 92 488.3 59.9 52 547.9 67.2 18 810.7 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 38.8 74 371.2 45.6 34 430.8 52.9 94 490.3 60.2 54 549.9 67.5 15 312.6 88.4 75 372.2 45.7 35 431.7 58.0 95 491.3 60.3 55 550. 8 67.6 16 313.6 88.5 76 373.2 45.8 36 432.7 58.1 96 492.3 60.5 56 551. 8 67.8 17 314.6 88.6 77 374.2 45.9 37 433.7 53.3 97 493.3 60.6 57 552.8 67.9 18 315.6 88.7 78 375.2 46.1 38 434.7 58.4 98 494.3 60.7 58 558.8 68.0 19 316.6 38.9 79 876.2 46.2 39 ! 435. 7 58.5 99 495.3 60.8 59 554.8 68.1 20 821 317.6 39.0 39.1 80 877.2 46.8 40 486.7 437.7 5.3.6 58.7 500 501 496.8 497.2 61.0 61.1 60 555. 8 68.3 318.6 881 878.1 46.4 441 561 556. 8 68.4 22 319.6 89.2 82 879.1 46.5 42 ! 438. 7 58.9 02 498.2 61.2 62 557. 8 68.5 28 320.6 89.4 83 880.1 46.7 43 439.7 54.0 08 499.2 61.3 63 558. 8 68.6 24 321.6 89.5 84 881.1 46.8 44 440.7 54.1 04 500. 2 61.4 64 559. 8 68.7 25 322.6 39.6 85 882.1 46.9 45 441.7 54.2 05 501.2 61. 5 65 560.8 68.9 26 823. 6 39.7 86 383.1 47.0 46 442.7 54.3 06 502.2 61.0 66 561. 8 69.0 27 324.6 89.8 87 384.1 47.2 47 44.3.7 54.5 07 503.2 61.8 67 562.8 69.1 28 325. 5 40.0 88 385. 1 47.8 48 444.7 54.6 08 504.2 61.9 68 563.8 69.2 29 326. 5 40.1 89 886.1 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 50 446.6 447.6 54.8 10 511 506.2 507.2 62.1 62.8" 70 571 565.8 566.7 69.4 381 828. 5 40.8 391 888.1 47.6 451 55.0 69.6 32 329. 5 40.5 92 889.1 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 18 509.2 62.5 73 568.7 69.8 34 881.5 40.7 94 891.1 48.0 54 450. 6 55.3 14 510.2 62.6 74 569.7 69.9 35 882.5 40.8 95 892.0 48.1 55 451.6 55.4 15 511.1 62.7 75 570. 7 70.1 36 ^33.5 40.9 96 393. 48.3 56 452.6 55.6 16 512.1 62.9 76 571.7 70.2 37 334.5 41.1 97 894.0 48.4 57 453.6 55.7 17 518.1 68.0 77 572. 7 70.8 38 335.5 41.2 98 895.0 48.5 58 454.6 55.8 18 514.1 63.1 78 573.7 70.4 39 886. 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 41.4 400 397.0 398.0 48.7 48.9 60 456.6 457.6 56.1 56.2 20 516.1 63.4 63.5 80 581 575. 7 70.7 341 838. 4 41.6 401 461 521 517.1 576.7 70.8 42 839.4 41.7 02 399.0 49.0 62 458^5 56.3 22 518.1 63. 6 82 577.6 70.9 43 840.4 41.8 03 400.0 49.1 68 459. 5 56.4 23 519.1 68.7 88 578.6 71.0 44 841.4 41.9 04 401.0 49.2 64 460. 5 56.5 24 520. 1 63.8 84 579.6 71.2 45 842.4 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 42.8 07 404.0 49.6 67 463. 5 56.9 27 523. 1 64.2 87 582. 6 71.5 48 845.4 42.4 08 405.0 49.7 68 464.5 57.0 28 524.1 64.3 88 583.6 71.6 49 846.4 42.5 09 405.9 49.8 69 465. 5 57.2 29 525.0 64. 5 89 584. 6 71.8 50 847.4 42.6 10 411 406.9 407.9 50.0 70 466. 5 467.5 57.3 57. 4 30 581 526.0 '527. 64.6 64.7 90 591 585. 6 71.9 351 348.4 42.8 50.1 471 586. 6 72.0 52 349.4 42.9 12 408.9 50.2 72 468. 5 57.5 32 528. 64.8 92 587. 6 72.1 53 850.4 48.0 13 409.9 50.3 78 469.5 57.6 38 529. 64.9 93 588. 6 72.2 54 851.4 43.1 14 410.9 50.4 74 470.5 57.8 84 580. 65.1 94 589.6 72.4 55 852. 3 48.8 15 411.9 50.6 75 471.5 57.9 85 581.0 65.2 95 590.6 72.5 56 858.3 43.4 16 412.9 50.7 76 472.4 58.0 36 582. 65.8 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. 65.6 98 598.5 72.9 59 356.3 43.7 19 415.9 51.1 79 475.4 58.4 39 585.0 65.7 99 594. 5 7.3.0 60 357.3 43.9 20 416.9 51.2 80 476.4 58.5 40 536. d" 65.8 600 595. 5 73. 1 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. " Lat. Dist. Dep. Lat. 88° (97°, 263^ , 277°) . Page 382] 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 «7 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 30 128.7 18.1 90 188.2 26.4 50 247.6 34.8 11 10.9 1.5 71 70.3 9.9 131 129.7 18.2 191 189.1 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 40 141 138.6 139.6 19.5 200 198.1 27.8 60 257.5 36.2 21 20.8 2.9 81 80.2 11.3 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 25 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. 29.1 69 266.4 37.4 30 31 29.7 4.2 4.3 90 89.1 12.5 50 148.5 20.9 10 211 208.0 29.2 70 271 267.4 268.4 37.6 37.7 30.7 91 90.1 12.7 151 149.5 21.0 208.9 29.4 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 5.7 100 99.0 13.9 14.1 60 158.4 159.4 22.3 20 217.9 30.6 80 281 277. 3 278.3 39.0 41 40.6 101 100.0 161 22.4 221 218.8 30.8 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 51 49.5 7.0 7.1 10 108.9 15.3 70 168.3 23.7 30 227.8 32.0 90 287.2 40.4 50.5 111 109.9 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. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 82° ({ )8°, 262< ', 278° . TABLE 2. [Page 383 | Difference of Latitude and Departure for 8° (172°, 188°, 352' )• Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. 1 Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 298.0 41.9 361 357.5 50.2 421 416.9 58.6 481 476.3 66.9 541 535.7 75.2 U2 299.0 42.0 62 358.5 50.4 22 417.9 58.7 82 477.3 67.1 42 536.7 75.4 03 300.0 42.2 63 359. 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 59.2 85 480.3 67.5 45 539.7 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 75.9 07 304.0 42.7 67 363. 4 51.1 27 422.8 59.4 87 482.2 67.8 47 541.6 76.1 08 305. 42.9 68 364.4 51.2 28 423.8 59.6 88 483.2 67.9 48 542.6 76.2 09 306. 43.0 69 365. 4 51.4 29 424.8 59.7 89 484.2 68.1 49 543.6 76.4 10 307.0 43.1 70 366.4 51.5 51.6 30 425.8 426.8 59.8 90 485.2 68.2 50 544.6 545.6 76.5 311 307.9 43.3 371 367.4 431 60.0 491 486.2 68.3 551 76.6 12 308.9 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 74 369.3 51.9 33 428.8 60.3 93 488.2 68.6 53 547.6 76.9 14 310.9 43.7 370.3 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 55 549.6 77.2 16 312.9 44.0 76 372.3 52.3 36 431.7 60.7 96 491.2 69.0 56 550.6 77.4 17 313.9 44.1 77 373.3 52.5 37 432.7 60.8 97 492.1 69.2 57 551.5 77.5 18 314.9 44.3 78 374.3 52.6 38 433.7 61.0 98 493. 1 69.3 58 552.5 77.6 19 315.9 44.4 79 375.3 52.7 39 434.7 61.1 99 494.1 69.5 59 553.5 77.8 20 321 316.9 44.5 80 376.3 52.9 53.0 40 441 435.7 61.2 500 501 495.1 496.1 ■69.6 60 554.5 77.9 317.9 44.7 381 377.3 436.7 61.4 69.7 561 555.5 78.1 22 318.8 44.8 82 378.3 53.2 42 437.7 61.5 02 497.1 69.9 62 556.5 78.2 23 319.8 45.0 83 379.2 53.3 43 438. 7 61.7 03 498.1 70.0 63 557.5 78.3 24 320.8 45.1 84 380.2 53.4 44 439.7 61.8 04 499.1 70.2 64 558. 5 78.5 25 321.8 45.2 85 .381. 2 53.6 45 440.6 61.9 05 500.1 70.3 65 559.5 78.6 26 322.8 45.4 86 382.2 53.7 46 441.6 62.1 06 501.0 70.4 66 560.5 78.8 27 323.8 45.5 87 383.2 53.9 47 442.6 62.2 07 502.0 70.6 67 561.5 78.9 28 324.8 45.7 88 384.2 54.0 48 443.6 62.4 08 503.0 70.7 68 562.5 79.0 29 325.8 45.8 89 385.2 54.1 49 444.6 62.5 09 504.0 70.8 69 563.5 79.1 30 331 326.8 327.8 45.9 90 386.2 387.2 54.3 50 445.6 446.6 62.6 62.8 10 505.0 70.9 70 571 564.5 79.3 46.1 391 54.4 451 511 506.0 71.1 565.4 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 73 567.4 79.7 34 330.7 46.5 94 390.1 54.8 54 449.6 63.2 14 509.0 71.5 74 568.4 79.8 35 331.7 46.6 95 391.1 55.0 55 450. 5 63.3 15 510.0 71.6 75 569.4 80.0 36 332.7 46.8 96 392.1 55.1 56 451.5 63.5 16 510.9 71.8 76 570.4 80.1 37 *333. 7 46.9 97 393.1 55.3 57 452.5 63.6 17 511.9 71.9 77 571.4 80.2 38 334.7 47.0 9$ 394.1 55.4 58 453. 5 63.7 18 512.9 72.0 78 572.4 80.4 39 335.7 47.2 99 395.1 55.5 59 454.5 63.9 19 513.9 72.2 79 573.4 80.5 40 341 336. 7 47.3 400 396.1 55.7 55.8 60 455.5 456.5 64.0 20 514.9 72.3 80 574.4 80.6 337.7 47.5 401 397.1 461 64.2 521 515.9 72.4 581 575.4 80.8 42 338.6 47.6 02 398.1 56.0 62 457.5 64.3 22 516.9 72.6 82 576.4 80.9 43 339.6 47.7 03 399.1 56.1 63 45S. 5 64.4 23 517.9 72.8 83 577.4 81.1 44 340.6 47.9 04 400.0 56.2 64 459.5 64.6 24 518.9 73.0 84 578.4 81.3 45 341.6 48.0 05 401.0 56.4 65 460.4 64.7 25 519.9 73.1 85 579.4 81.4 46 342.6 48.2 06 402.0 56.5 66 461.4 64.9 26 520.9 73.2 86 580.3 81.6 47 343.6 48.3 07 403.0 56.6 67 462.4 65.0 27 521.8 73.4 87 581.3 81.7 48 344.6 48.4 08 404.0 56.8 68 463.4 65.1 28 522.8 73.5 88 582.3 81.8 49 345.6 48.6 09 405.0 56.9 69 464.4 65.3 29 523.8 73.7 89 583.3 82.0 50 351 346.6 48.7 48.9 10 411 406. 407. 57.1 70 465.4 466.4 65.4 65.6 30 531 524.8 525. 8 73.8 90 584.3 82.1 347.6 57.2 471 73.9 591 585.3 82.2 52 348.5 49.0 12 408.0 57.3 72 467.4 65.7 32 526.8 74.1 92 586.3 82.4 53 349.5 49.1 13 409.0 57.5 73 468.4 65.8 33 527.8 74.2 93 587.3 82.5 54 350. 5 49.3 14 409.9 57.6 74 469.4 66.0 34 528.8 74.3 94 588.3 82.6 55 351.5 49.4 15 410.9 57.8 75 470.4 66.1 35 529.8 74.5 95 589.3 82.8 56 352.5 49.5 16 411.9 57.9 76 471.3 66.2 36 530.8 74.6 96 590.3 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 66.5 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 75.1 600 594.2 83.5 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 82° (98°, 262°, 278°). 1 Page 384] TABLE 2. Difference of Latitude and Departure for 9° (171°, 189°, 351° • Dist. 1 Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1.0 0.2 61 60.2 9.5 121 119.5 18.9 181 178.8 28.3 241 238. 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 «7 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 69.1 11.0 11.1 30 131 128.4 129.4 20.3 20. 5 90 187.7 29.7 50 246.9 247. 9 39.1 1.7 71 70.1 191 188.6 29.9 251 39.3 12 11.9 1.9 72 71.1 11.3 32 130.4 20.6 92 189.6 30.0 52 248.9 .39.4 13 12.8 2.0 73 72.1 11.4 33 131.4 20.8 93 190.6 30.2 53 249.9 39.6 14 13.8 2.2 74 73.1 11.6 34 132. 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 21 19.8 20.7 3.1 80 • 79.0 12.5 12.7 40 138.3 21.9 200 197.5 31.3 60 256.8 40.7 3.3 81 80.0 141 139.3 22.1 201 198.5 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 89.9 14.1 14.2 50 151 148.2 23.5 23.6 10 207.4 32.9 70 271 266.7 42.2 42.4 31 30.6 4.8 91 149. 1 211 203. 4 33.0 267.7 32 31.6 5.0 92 90.9 14.4 52 150.1 2.3.8 12 209.4 33.2 72 268.7 42.6 33 32.6 5.2 93 91.9 14.5 53 151.1 23.9 13 210.4 33.3 73 269.6 42.7 34 33.6 5.3 94 92.8 14.7 54 •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 15+. 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 41 39.5 40.5 6.3 6.4 100 101 98.8 99.8 15.6 15. 8^ 60 161 158.0 159.0" 25.0 20 217.3 34.4 80 276.6 277. 5 43.8 44.0 25.2 221 218.3 34.6 281 42 41.5 6.6 02 100.7 16.0 62 160.0 25.3 22 219.3 34.7 82 278.5 44.1 43 42.5 6.7 03 101.7 16.1 63 161.0 25.5 23 220. 3 34.9 83 279.5 44.3 44 43.5 6.9 04 102.7 16.3 64 162.0 25.7 24 221.2 35.0 84 280.5 44.4 45 44.4 7.0 05 103.7 16.4 65 163.0 25.8 25 222.2 35.2 85 281.5 44.6 46 45.4 7.2 06 104.7 16.6 66 164.0 26.0 26 223. 2 35.4 86 282. 5 44.7 47 46.4 7.4 07 105.7 16.7 67 164.9 26.1 27 224.2 35.5 87 283.5 44.9 48 47.4 7.5 08 106.7 16.9 68 165.9 26.3 28 225.2 35.7 88 284.5 45.1 49 48.4 7.7 09 107.7 17.1 69 166.9 26.4 29 226.2 35.8 89 285.4 45.2 '•50 49.4 7.8 10 108.6 109.6 17.2 17.4 70 171 167.9 168.9 26.6 26.8 30 231 227.2 228.2 36.0 90 286.4 45.4 51 50.4 8.0 111 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 j 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 1 175.8 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 Lat. 300 296.3 46.9 Dist. Dep. Lat. Dist. Dep. Lat. Dist. 1 Dep. Lat. Dist. Dep. Dist. Dep. Lat. 81° (99°, 261°, 279° ). TABLE S [Page 385 | 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.l 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 10 306.2 48.5 48.7 70 365.4 57.9 58.1 30 431 424.7 67.3 90 491 484.0 485.0 76.5 76.7 50 551 543. 3 544.3 86.0 311 307.2 371 366.4 425.7 67.4 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 96 589.9 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 80 381 375.3 59.5 40 434.6 68.8 500 501 493.8 4914.8 78.2 78.4" 60 561 553.1 554. 1 87.6 87.7 321 317.0 50.2 376. 3 59.6 441 435.6 69.0 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. 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 30 331 325. 9 51.7 90 391 385.2 386.2 61.0 50 444.5 445. 4 70.4 10 503.7 504.7 79.7 79.8 70 571 563.0 564.0 89.1 326.9 51.8 61.2 451 70.6 511 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. 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 S32.8 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 40 341 335.8 53.2 400 395. 1 62.6 60 454. 3 72.0 20 513. 6 81.3 80 572.9 90.7 336. 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 (59 463.2 73.4 29 522.5 82.7 89 581.8 92.1 50 351 345. 7 346.7 54.8 10 405.0 64.1 70 464.2 73.5 30 523.5 82.9 90 582.8 92.2 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 Dep. 75.0 40 533.4 84.4 600 592.6 93.8 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 81° {{ )9°, 261' ', 279° . 22489—03- -25 Page 386 TABLE 2. Difftreiue of Latitude and Departure for 10° (170°, 190°, 350° ). Dist. Lat. Dep. Dist. Lat. Dep. Dist. 1 Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 1.0 0.2 61 60.1 10.6 121 119.2 21.0 181 178. 3 31.4 241 237.3 41.8 2 2.0 0.3 62 61.1 10.8 22 120.1 21.2 82 179.2 31.6 42 238.3 42.0 3 3.0 0.5 63 62.0 10.9 23 121.1 21.4 83 180.2 31.8 43 239.3 42.2 4 3.9 0.7 64 63.0 11.1 24 122.1 21.5 84 181.2 32.0 44 240.3 42.4 5 4.9 0.9 65 64.0 11.3 25 123.1 21.7 85 182.2 32.1 45 241.3 42.5 6 5.9 1.0 .66 65.0 11.5 26 124.1 21.9 86 183. 2 32.3 46 242.3 42.7 7 6.9 1.2 •67 66.0 11.6 27 125.1 22.1 87 184.2 32.5 47 243.2 42.9 8 7.9 1.4 68 67.0 11.8 28 126.1 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 fe9 186.1 32.8 49 245.2 43.2 10 11 9.8 1.7 70 71 68.9 12.2 12.3 30 131 128.0 129.0 22.6 22.7 90 191 187.1 18'8. 1 33.0 50 251 246.2 247.2 43.4 43.6 10.8 1.9 69.9 33.2 12 11 8 2.1 72 70.9 12.5 32 130.0 22.9 92 189.1 33.3 52 248.2 43.8 13 12.8 2.3 73 71.9 12.7 33 131.0 23.1 93 190.1 33.5 53 249.2 43.9 14 13.8 2.4 74 72.9 12.8 34 132.0 23.3 94 191.1 33.7 54 250.1 44.1 15 14.8 2.6 75 73.9 1.3.0 35 132.9 23.4 95 192.0 33. 9 55 251.1 44.3 16 15.8 2.8 76 74.8 1.3.2 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 21 19.7 20.7 3.5 80 78.8 13.9 40 137. 9 24.3 200 197.0 197.9 34.7 34.9 60 261 256.1 257.0 45.1 45.3 3.6 81 79. 8 14.1 141 138.9 24.5 201 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 31 29.5 30.5 5.2 90 88.6 15.6 15.8 50 147.7 148.7 26.0 26.2 10 211 206.8 36.5 70 265.9 46.9 6.4 91 89.6 151 207.8 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 7.1 100 101 98.5 17.4 17.5 60 157.6 158.6 27.8 20 216.7 38.2 80 275.7 48.6 41 40.4 99.5 161 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 10 108.3 109. 3~ 19.1 70 167.4 29.5 30 226.5 227.5 39.9 90 . 285.6 50.4 50.5 51 50.2 8.9 ni 19.3 171 168.4 29.7 231 40.1 291 286.6 52 51.2 9.0 12 110.3 19.4 72 169.4 29.9 32 228.5 40.3 92 287.6 50.7 53 52.2 9.2 13 111.3 19.6 73 170.4 30.0 33 229.5 40.5 93 288.5 50.9 54 53.2 9.4 14 112. 3 19.8 74 171.4 30.2 34 230.4 40.6 94 289. 5 51.1 55 54.2 9.6 15 113.3 20.0 75 172.3 30.4 35 231.4 40.8 95 290. 5 51.2 56 55.1 9.7 16 114.2 20.1 76 173.3 30.6 36 232.4 41.0 96 291.5 51.4 57 56.1 9.9 17 115. 2 20.3 77 174. S 30.7 37 233. 4 41.2 97 292.5 51.6 58 57.1 10.1 18 116.2 20.5 78 175.3 30.9 38 234.4 41.3 98 293.5 51.7 59 58. 1 10.2 19 117.2 20.7 79 176.3 31.1 39 235. 4 41.5 99 294.5 51.9 60 59.1 1 10.4 20 118.2 20.8 80 177.3 31.3 40 236.4 41.7 300 295.4 52.1 Dist. Dep. Lat. DLst. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 80° (100°, 260°, 280°). TABLE 27 [Page 387 Difference of Latitude and Departure for 10° (170°, 190°, 350' ') Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 296. 4 52.3 361 .355. 5 62.7 421 414.6 73.1 481 473.7 83.5 541 532.8 93.9 02 297.4 52.5 62- 356. 5 62.9 22 415.6 73.3 82 474.7 83.7 42 533.8 94.1 03 298.4 52.6 63 357. 5 63.0 23 416.6 1 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. 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. 3 306. 3 53.8 70 364. 4 . 64.3 64.4 30 431 423.5 424. 5 74.7 90 482.6 483. 5 85.1 50 541. 6 542.6 95.5 311 54.0 371 365.4 74.9 491 85.2 551 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 3S 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 1 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.* 17 312.2 55.1 77 371.3 65.5 3t 430.4 i 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 55.8 80 381 374.2 375. 2 66.0 40 433.3 76.4 76.6 500 501 492.4 493.4 86.8 87.0 60 551.5 97.2 97.4 316. 1 66.2 441 434. 3 561 552. 5 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 i 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 1 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 i 381.1 67.2 47 440.2 77.6 07 499.3 88.0 67 558.4 98.4 28 323.0 57.0 88 382. 1 67.4 48 441.2 77.8 08 500.3 88.2 68 559.4 98.6 29 324.0 57.1 89 383.1 67.6 49 442.2 78.0 09 501.3 88.4 69 560.3 98.8 30 325. 326.0 57.3 90 384. 1 67.7 50 443.2 78.2 10 502.2 88.6 70 561.3 99.0 331 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 36 530.9 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 59.2 400 401 393. 9 69.5 69.6 60 461 453.0 79.9 20 512.1 513. 1 90.3 90.5 80 581 571.2 572. 2" 100.7 100.9 341 335. 8 394.9 454.0 80.1 ^521" 42 336.8 59.4 02 395.9 69.8 62 455. 80.2 22 514.1 90.6 82 573.2 101.0 43 837.8 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. 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 50 351 344 7 60.8 10 403.8 71.2 70 471 462.9 463.8 81.6 81.8 30 521.9 92.0 90 591 581.0 102.4 345.7 61.0 411 404.8 71.4 531 522. 9 92.2 582.0 102.6 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 Dep. 62.5 20 413.6 72.9 80 472.7 83.4 40 531. 8 93.8 600 590.9 104.2 Dist. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. j Dep. Lat. Dist. Dep. Lat.' 1 ^0° (100°, 260°, 280° )• Page 388] TABLE '2. Difference of Latitude and Depart ure for 11° (169°, 191°, 349 '). Dist. Lat. 1 Dep. Dist. Lat. Dep. Dist. Lat. ; Dep. Dist. Lat. Dep. Dist. 1 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 1 122.7 23.9 85 181.6 35. 3 45 240.5 46.7 6 5.9 1.1 M 64.8 12.6 26 123. 7 24.0 86 182.6 35.5 46 241.5 46.9 7 6.9 1.3 65.8 12.8 27 1 124. 7 24.2 87 183.6 3.5.7 47 242.5 47.1 8 7.9 1.5 68 66,8 13.0 28 125.6 24.4 88 184.5 35.9 48 243.4 47.3 9 8.8 1.7 69 67.7 13.2 29 126.6 24.6 89 185.5 36.1 49 244.4 47.5 10 9.8 1.9 70 68.7 13.4 30 127.6 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 1 247.4 48.1 13 12.8 2.5 73 71.7 13.9 33 130.6 25.4 93 189.5 36.8 53 i 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 *6 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 20a 196.3 38.2 60 2.55. 2 49.6 21 20.6 4.0 81 79.5 15.5 141 138.4 26.9 201 1«7.3 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.S 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 40. 3 70 265.0 51.5 51.7 31 30.4 5.9 91 89.3 17.4 151 148.2 28.8 211 207. 1 271 266.0 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 1 211.0 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 18.6 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 1 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 1 42.0 80 274.9 53. 4 41 40.2 7.8 101 99.1 19.3 161 158. 30.7 221 216.9 42.2 281 275.8 53.6 42 41.2 8.0 02 100.1 19.5 62 159.0 30.9 22 217.9 ; 42.4 82 276.8 53.8 43 42.2 8.2 03 101. 1 19.7 63 160.0 31.1 23 218.9 : 42.6 83 277.8 64.0 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 1 4.3.1 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. X)' 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 66.1 50 49.1 9.5 10 108.0 21.0 70 166.9 32.4 30 225.8 43.9 90 291 284.7 56.3 51 50.1 9.7 111 109.0 21.2 171 167.9 32.6 231 226.8 44.1 285.7 65.5 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 56.9 54 53.0 10.3 14 111.9 21.8 74 170.8 33.2 34 229. 7 1 44. 6 94 288.6 66.1 55 54.0 10.5 15 112.9 21.9 75 171.8 33.4 35 230.7 44.8 95 . 289. 6 66.3 56 55.0 10.7 16 113.9 22.1 76 172.8 33.6 36 231. 7 1 45. 96 290.6 56.5 57 56.0 10.9 17 114.9 22.3 77 173.7 33.8 37 232.6 i 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 i 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 67.2 Dlst. Dep, Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. 1 Lat. Dist. Dep. Lat. 7 9° (101°, 259' ',■281°). TABLE 2. [Page 389 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. 104.0 06 300.3 58.4 66 359. 2 69.8 26 418.1 j 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 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 i 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 1 81.9 89 480.0 93.3 49 538. 9 104.8 10 311 304.3 305.3 59.2 70 363. 2 364.1 70.6 30 422.1 1 82.1 90 491 481.0 93.5 50 539.9 540.8 105.0 59.3 371 70.8 431 423.0 1 82.2 481.9 93.6 551 105. 1 12 306.2 59.5 72 365.1 71.0 32 424.0 82.4 92 482.9 93.8 52 541.8 105.3 13 307.2 59.7 73 366. 1 71.2 33 425. 82.6 93 483.9 94.0 53 542.8 105.5 14 308.2 59.9 74 367.1 71.4 34 426.0 82.8 94 484.9 94.2 54 543.8 105.7 15 309.2 ,60.1 75 368.1 71.6 35 427.0 83.0 95 485.9 94.4 55 544.8 105. 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 20 321 314.1 315.1 61.1 80 381 373.0 72.5 40 431.9 432.9 84.0 84.1 500 501 490.8 491.8 95.4 60 549.7 550. T 106.9 107.1 61.3 374.0 72.7 441 95.6 561 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 73.7 46 437.8 85.1 06 496.7 96.6 66 555.6 108.0 27 321.0 62.4 87 379.9 73.8 47 438.8 85.3 07 497.7 96.8 67 556.6 108.2 28 321.9 62.6 88 380.8 74.0 48 439.7 85.5 08 498.6 97.0 68 557.6 108.4 29 322.9 62.8 89 381.8 74.2 49 440.7 85.7 09 499.6 97.2 69 558.6 108.6 30 323.9 63.0 90 382. 8 74.4 50 441.7 85.9 10 500.6 97.3 70 571 559.5 560.5 108.8 331 324.9 63.2 391 383.8 74.6 451 442.7 86.1 511 501.6 97.5 109.0 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 77 566.4 110.1 38 331.8 64.5 98 390.7 75.9 58 449.6 87.4 18 508.5 98.8 78 567.4 110.3 39 332.7 64.7 99 391.6 76.1 59 450.5 87.6 19 509.4 99.0 79 568.3 110.5 40 333.7 64.9 400 401 392. 6 393.6 76.3 60 451.5 87.8 20 510.4 511.4 99.2 80 569.3 570.3 110.7 341 334.7 65.1 76.5 46] 452.5 88.0 521 99.4 581 110.9 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 50 351 343.5 66.8 10 402.4 403.4 78.2 78.4 70 471 461. 3 462.3 89.7 30 520.2 101.2 90 579.1 112.6 344.5 67.0 411 89.9 531 521.2 101.4 591 580. 1 112.8 52 345.5 67.2 12 404.4 78.6 72 463.3 90.1 32 522.2 101.6 92 581.1 113.0 53 346.5 67.4 13 405.4 78.8 73 464.3 90.3 33 523.2 101.7 93 582.1 113.2 54 347. 5 67.5 14 406.4 79.0 74 465.3 90.4 34 524.2 101.8 94 583.1 113.3 55 348.4 67.7 15 407.3 79.2 75 466.2 90.6 35 525.1 102.0 95 584.0 113.5 56 349.4 67.9 16 408.3 79.4 76 467.2 90.8 36 526.1 102.2 96 585.0 113.7 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 99 588.0 114.3 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. 1 Dep. Lat. D:st. Dep. Lat. 79° (101°, 259°, 281°). Page 390] 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 5.9 1.2 6/ 64.6 13.7 26 123.2 26.2 86 181.9 38.7 46 240.6 51.1 7 6.8 1.5 65.5 13.9 27 124.2 26.4 87 182.9 38.9 47 24L6 51.4 8 7.8 1.7 68 66.5 14.1 28 125. 2 26.6 88 183.9 39.1 48 242.6 51.6 9 8.8 1.9 69 67.5 14.3 29 126.2 26.8 89 184.9 39.3 49 243.6 51.8 10 11 9.8 10.8 2.1 2.3 70 68.5 1 14.6 30 131 127.2 27.0 27.2 90 191 185.8 186.8 39.5 50 244. 5 245.5 52.0 52.2 71 69.4 14.8 128.1 39.7 251 12 11.7 2.5 72 70.4 15.0 32 129.1 27.4 92 187.8 39.9 52 246.5 52.4 13 12.7 2.7 73 71.4 15.2 33 130.1 27.7 93 188.8 40.1 53 247.5 52.6 14 13.7 2.9 74 72.4 15.4 34 131.1 27.9 94 189.8 40.3 54 248.4 52.8 15 14.7 3.1 75 73.4 15.6 35 132.0 28.1 95 190.7 40.5 55 249.4 53.0 16 15.7 3.3 76 74.3 15.8 36 133.0 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 21 19.6 4.2 80 78.3 16.6 40 136.9 29.1 29.3 200 201" 195.6 196.6 41.6 41.8 60 261 254.3 54.1 20.5 4.4 81 79.2 16.8 141 137.9 255. 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 10 205.4 206.4 43.7 43.9 70 264.1 56.1 31 30.3 6.4 91 89.0 18.9 151 147.7 31.4 211 271 265.1 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 20 215.2 216.2 45.7 45.9 80 281 273.9 274. 9 58.2 58.4 41 40.1 8.5 101 98.8 21.0 161 157.5 33.5 221 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 i9.1 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 oS 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 35.6 30 231 225.0 226.0 47.8 48.0 90 291 283.7 60.3 51 49.9 10.6 111 108.6 23.1 171 167.3 284.6 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. Lit. Dist. Dep. Lat. 1 '8° (1 32°, 258 =,.282°). TABLE 2. [Page 391 Difference of Latitude and Departure for 12° ( 168°, 192°, 348 °)- Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. j 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. 75.9 25 415. 7 88.3 85 474.4 100.8 45 533.1 113.3 0(5 299. 3 63.6 66 358. 76.1 26 416.7 88.6 86 475.4 101.0 46 534. 1 113.5 07 300. 3 63.8 67 359. 76.3 1 27 417.7 88.8 87 476.4 101. 2 47 535.1 113.7 08 301.3 64.0 68 360. 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 10 311 303. 2 304. 2 64.4 70 371 361.9 76.9 77.1 30 420.6 421.6 89.4 89.6 90 491 479.3 101.9 50 538. 538.9 114.4 114.6 64.6 362.9 1 431 480.3 102.1 551 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 33 423.5 ; 90.0 93 482.2 102.5 53 540.9 115.0 14 307. 1 65.3 74 365.8 77.7 34 424.5 i 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. 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 i 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. 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 ! 9.3.1 08 496.9 105. 6 68 555.6 118.0 29 321.8 68.4 89 380. 5 80.9 49 439.2 i 93.3 09 497.9 105. 8 69 556.6 118.2 30 331 322. 8 323.8 68.6 90 381.5 382.5 81.1 81.3 50 440.2 93.5 93.7 10 498.9 106.0 106. 2 70 571 557.5 118.5 118.7 68.8 391 451 441.1 511 499.8 558.5 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 9'4.4 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 1 448.0 95.2 18 506. 7 107.6 78 565.4 120.1 39 331.6 70.5 99 390.3 82.9 59 j 449.0 95.4 19 507.7 107.8 79 566,4 120.3 40 332.6 333. 5 70.7 400 391.3 392.2 83.1 60 450. 450. 9 95.6 95. 8 20 521 508.7 509. 6 108.1 80 567.4 120.6 120. 8 341 70.9 401 83.4 461 108.3 581 568.3 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 44 386.5 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 i 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 1 458.8 97.5 29 517.5- 110.0 89 576.2 122.4 50 342.4 72.7 10 411 401.0 402.0 85.2 85. 4" 70 i 459. 7 97.7 30 518. 4 519.4 110.2 90 591 577.1 122. 6 122.8 351 343. 3 73.0 471 460. 7 97.9 531 110.4 578.1 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. Di.st. Dep. Lat. 7 8° (102°, 258°, 282° )• Page 392] 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 1? 64.3 14.8 26 122.8 28.3 86 181.2 41.8 46 239.7 55.3 7 6.8 1.6 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 10.7 2.2 70 68.2 15.7 30 126.7 29.2 29.5 90 185.1 42.7 50 243.6 244.6 56. 2 11 2.5 71 69.2 16.0 131 127.6 191 186.1 43.0 251 56.5 12 11.7 2.7 72 70.2 16.2 32 128.6 29.7 92 187.1 43.2 52 245.5 56.7 13 12.7 2.9 73 71.1 16.4 33 129.6 29.9 93 188.1 43.4 53 246.5 56.9 14 13.6 3.1 74 72.1 16.6 34 130.6 30.1 94 189.0 43.6 54 247.5 57.1 15 14.6 3.4 75 73.1 16.9 35 131.5 30.4 95 190.0 43.9 55 248.5 57.4 16 15.6 3.6 76 74.1 17.1 36 132.5 30.6 96 191.0 44.1 56 249.4 57.6 17 16.6 3.8 77 75.0 17.3 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 45.0 60 261 253. 3 254.3 58.5 58.7 21 20.5 4.7 81 78.9 18.2 141 137.4 31.7 201 195.8 45.2 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 3.3.3 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 91 87.7 20.2 50 151 146.2 33.7 10 204.6 205.6 47.2 47.5 70 263.1 264.1 60.7 61.0 31 30.2 7.0 88.7 20.5 147.1 34.0 211 271 32 31.2 7.2 92 89.6 20.7 52 148.1 34.2 12 206.6 47.7 72 265.0 61.2 33 32.2 7.4 93 90.6 20.9 53 149.1 34.4 13 207.5 47.9 73 266.0 61.4 34 33.1 7.6 94 91.6 21.1 54 150.1 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 20 221 214. 4 49.5 80 272.8 63.0 41 39.9 9.2 101 98.4 22.7 161 156.9 36.2 215.3 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 11.2 10 107.2 24.7 70 165. 6 166.6 38.2 38.5 30 231 224.1 51.7 90 282.6 65.2 51 49.7 11.5 111 108.2 25.0 171 225.1 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 67.5 Dlst. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dlst. Dep. Lat. Dist. Dep. Lat. 11° (103°, 257 °, 283° )• TABLE 2. [Page 393 ] 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 1 471.6 108.8 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 i 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 70 360.5 361.5 83.2 30 419.0 96.7 90 1 477.5 1110.1 50 535.9 123.7 311 303.0 69.9 371 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 1 482. 3 i 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 1 112. 58 543.7 125.5 19 310.8 71.7 79 369.3 85.2 39 427.8 98.7 99 486. 2 ! 112. 2 59 544.7 125.8 20 321 311. 8 72.0 72.2 80 381 370.3 85.5 40 428.7 98.9 500 487.2 488.2 112.4 60 545.7 126.0 312.8 371.2 85.7 441 429.7 99.2 501 112.6 561 546.7 126.2 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 1 494.0 114.0 67 552.5 127.6 28 319.6 73.8 88 378.1 87.3 48 436.5 100.7 08 495.0 114.2 68 553. 5 127.8 29 320.6 74.0 89 379.0 87.5 49 437.5 101.0 09 496.0 114.5 69 554.5 128.0 30 321.5 322.5 74.2 74.4 90 391 380. 87.7 50 438.5 101.2 10 496.9 497. 9 114.7 70 555.4 556.4 128.3 128.5 331 381.0 87.9 451 439.4 101.4 511 114.9 571 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 i 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 i 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 40 331.3 332.3 76.5 400 389.8 390. 7 90.0 60 448.2 449. 2 103.4 103. 7 20 506.7 116.9 80 565.2 566.2 130.4 341 76.7 401 90.2 461 521 507.7 :117.2 581 130.7 42 333.2 76.9 02 391. 7 90.4 62 450.2 103.9 22 508.6 1117.5 82 567.1 131.0 43 334.2 77.1 03 392.7 90.6 63 451.1 104.1 23 509. 6 i 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 87 572.0 132.0 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 i 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. 1 Lat. Dist. Dep. Lat. 77° (1 03°, 257 °, 283° )• Page 394] TABLE 2. Difference of Latitude and Departure for 14° (166°, 194 °, 346° )• Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 1 0.2 61 59.2 14.8 121 117.4 29.3 181 175.6 43.8 241 233.8 58.3 2 1.9 0.5 62 60.2 15.0 22 118.4 29.5 82 176.6 44.0 42 234.8 58.5 3 2.9 0.7 63 61.1 15.2 23 119.3 29.8 83 177.6 44.3 43 235.8 58.8 4 3.9 1.0 64 62.1 15.5 24 120.3 30.0 84 178.5 44.5 44 236.8 59.0 5 4.9 1.2 65 63.1 15.7 25 121.3 30.2 85 179.5 44.8 45 237.7 59.3 6 5.8 1.5 66 (54.0 16.0 26 122.3 30.5 86 180.5 45.0 46 238.7 59.5 7 6.8 1.7 t7 65.0 1 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. ! 16. 7 29 125.2 31.2 89 183.4 45.7 49 241.6 60.2 10 11 9.7 10.7 2.4 70 67.9 1 16.9 30 126.1 31.4 31.7 90 191 184.4 46.0 46.2 50 251 242. 6 243.5 60.5 2.7 71 68.9 17.2 131 127.1 185. 3 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. 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 10 203.8 204.7 50.8 70 262.0 65.3 31 30.1 7.5 91 88.3 22.0 151 146.5 36.5 211 51.0 271 '263. 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 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 i 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 68.0 41 39.8 9.9 101 98.0 j 24.4 161 156. 2 38.9 221 214.4 53.5 281 272.7 42 40.8 10.2 02 99. ' 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 1 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 1 26.6 70 165.0 165.9 41.1 30 223.2 55.6 90 281.4 282.4 70.2 70. 4 51 49.5 12.3 111 107. 7 26. 9 171 41.4 231 224.1 55. 9 291 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 1 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. 57.3 97 288.2 71.9 58 56.3 14.0 18 114. 5 28.5 78 172.7 43.1 38 230. 9 57.6 98 289.1 72.1 59 57.2 14.3 19 115.5 28.8 79 173.7 43.3 39 231.9 57.8 99 290.1 72.3 60 58.2 14.5 20 116.4 29.0 80 174.7 43.5 40 232.9 58.1 300 291.1 72.6 Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. ■6° (1 04°, 256°,. 284° ). TABLE J 2. [Page 395 Difference of Latitude and Departure for 14° (166°, 194 °, 346° )• Dist. 301 Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 292.0 72.8 361 350. 2 87.3 421 408.5 101.8 481 466.7 116.3 541 525. 130.9 02 293.0 73.0 62 351. 2 87.6 22 409.4 102.1 82 467.7 116.6 42 525. 9 131.2 03 294.0 73.3 63 352. 2 87.8 23 410.4 102.3 83 468.6 116.8 43 526. 9 131.4 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 26 413.3 103.0 86 471.5 117.6 46 52a. 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 10 311 300.8 75.0 70 359.0 359.9 89.5 30 431 417.2 104.0 90 475.4 118.5 50 551 533. 7 534.6 133.0 133.3 301. 7 75.2 371 89.7 418.2 104.2 491 476.4 118.8 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 7S.9 74 362.9 90.5 34 421.1 105.0 94 479.3 119.5 54 537.5 134.0 15 305.6 76.2 75 363.8 90.7 35 422.0 105. 2 95 480.3 119.7 55 538.5 134. 3 16 306.6 76.4 76 364.8 90.9 36 423.0 105.5 96 481.3 120.0 56 539.5 134. 5 17 307.6 76.7 77 365.8 91.2 37 424.0 105.7 97 482.2 120.2 57 540. 5 134.8 18 308.5 76.9 78 366.7 91.4 38 425.0 105. 9 98 483.2 120.4 58 541.4 135. 19 309.5 77.2 79 367. 7 * 91.7 39 425. 9 106.2 99 484.2 120.7 59 542.4 135. 2 20 321 310.5 77.4 80 368.7 91.9 40 426.9 106.4 500 501 485.1 486.1 121.0 60 543.4 544. 3 135. 5 135. 7 311.4 77.6 381 369. 6 92.2 441 427.9 106.7 121.2 561 22 312.4 77.9 82 370.6 92.4 42 428.8 106.9 02 487.1 121.4 62 545. 3 135.9 23 313. 4 78.1 83 371.6 92.6 43 429.8 107.1 03 488.0 121.7 63 546.3 136.2 24 314.3 78.4 84 372. 6 92.9 44 430.8 107.4 04 489.0 122.0 64 547.2 136. 5 25 315. 3 78.6 85 373.5 93.1 45 431.7 107.6 05 490.0 122.1 65 548.2 136.6 26 316. 3 78.8 86 374. 5 93.4 46 432. 7 107.9 06 491.0 122.4 66 549.2 136.9 27 317. 3 79.1 87 375. 5 93.6 47 433. 7 108.1 07 491.9 122.6 67 550.1 137.1 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 30 331 320.2 79.8 90 378.4 94.3 94.6 50 451 436.6 437.6 108.8 109.1 10 511 494. 9 495. 8 123. 4 70 553.1 554.0 137.9 138.1 321.1 80.1 391 379.4 123.6 571 32 322. 1 80.3 92 380.3 94.8 52 ! 438.5 109.3 12 496.8 123. 8 72 555. 138. 3 33 323. 1 80.5 93 381. 3 95.1 53 1 439.5 109.6 13 497.8 124.1 73 556.0 138.6 34 324. 80.8 94 382. 3 95. 3 54 440.5 109.8 14 498.7 124.3 74 557.0 138. 8 35 325. 81.0 95 383. 2 95. 5 55 441.5 110.1 15 499. 7 124.6 75 557.9 139.1 36 ■ 326. 81.3 96 384. 2 95.8 56 442.4 110.3 16 500.7 124.8 76 558.9 139.3 37 327. 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 I 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 97.0 60 1 446. 3 461 i 447. 3 111.3 20 521 504. 6 505.5 12.5. 8 126. 80 581 562.8 i 140.3 330.8 82.5 401 389.1 111.5 563.8 140.5 42 331.8 82.7 02 390. 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. 113.4 29 513.3 128.0 89 571. 5 142.5 50 351 339.6 340.5 84.7 84.9 10 411 397. 8 99.2 70 456.0 457.0 113.7 113.9 30 531 514.3 515.3 128.2 128.5 90 591 572.5 142.8 398.8 99.4 471 573.5 1 143.0 52 341.5 85.1 12 399.7 99.7 72 457.9 114.2 32 516.2 128.8 92 574.4 1 143.3 53 342.5 85.4 13 400. 7 99.9 73 458. 9 114.4 33 517.2 129.0 93 575.4 j 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 i 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 i 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. 130. 4 99 581.2 144.9 60 349.3 87.1 20 407. 5 101.6 80 465.7 116.1 40 524. 130.6 600 582.2 145.1 Dist. Dep. Lat. Dist. Dep. Lat. Dist. 1 Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 76° (104°, 256 °, 284° )• 1 Page 396] 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 2.8 70 71 67.6 18.1 30 125.6 33.6 90 191 183.5 184.5 49.2 50 241.5 242.4 64.7 65.0 11 10.6 68.6 18.4 131 126.5 33.9 49.4 251 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 T92.2 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 60 251.1 252.1 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 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 50 144.9 38.8 10 202.8 54.4 70 260.8 69.9 31 29.9 8.0 91 87.9 23.6 151 145.9 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 57.2 271.4 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 )J^ 216.4 58.0 84 274.3 73.5 45 43.5 11.6 05 101.4 27.2 65 159.4 42.7 '-^5 217.3 58.2 85 275. 3 73.8 46 44.4 11.9 06 102.4 27.4 66 160.3 43.0 26 218.3 58.5 86 276.3 74.0 47 45.4 12.2 07 103.4 27.7 67 161.3 43.2 27 219.3 58.8 87 277.2 74.3 48 46.4 12.4. 08 104.3 28.0 68 162.3 43.5 28 220.2 59.0 88 278.2 74.5 49 47.3 12.7 09 105.3 28.2 69 163.2 43.7 29 221.2 59.3 89 279.2 74.8 50 51 48.3 12.9 10 106.3 28.5 70 171 164.2 44.0 30 222.2 59.5 90 280.1 75.1 49.3 13.2 111 107.2 28.7 165.2 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 397 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. 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 10 311 299.4 300.4 80.2 70 357. 4 358.3 95.8 96.0 30 431 415.3 416.3 111.3 90 473.3 126.9 50 551 531. 3 532. 2 142.4 80.5 371 111.6 491 474. 3 127.1 142.6 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 i 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. 144.2 18 307. 1 82.3 78 1 365. 1 97.8 38 423.1 113.4 98 481.0 128.9 58 539. 144.4 19 308.1 82.6 79 i 366. 1 98.1 39 424.0 113.6 99 482.0 129.1 59 540. 144.7 20 309. 1 82.8 80 367.0 98.4 40 425.0 113.9 500 483.0 483.9 129.4 129.7 60 540. 9 144.9 321 310. 83.1 381 368.0 98.6 441 426.0 114.1 501 561 541.9 145.2 22 311.0 83.3 82 369.0 98.9 42 426.9 114.4 02 484.9 129.9 62 542.9 145.4 23 312.0 83.6 83 369. 9 99.1 43 427.9 114.7 03 485.9 130. 2 63 .543.8 145.7 24 312.9 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 1 372. 8 99.9 46 4.30. 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 30 318.7 85.4 90 376.7 100.9 50 434.6 116. 5 10 492.6 493.6 132. 70 550.6 147.5 331 319.7 85.7 391 377.7 101.2 451 435. 6 116. 7 511 132.3 571 551.6 147.8 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. 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 T03.8 60 444.3 119.1 20 502. 3 134.6 80 560.2 150.1 341 329. 4 88.3 401 387.3 461 445.3 119.3 521 503.2 134.8 581 561.2 150.3 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. 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. 121.1 28 510.0 136. 6 88 568.0 152.2 49 337.1 t)0.3 09 395. 105.9 69 453.0 121. 4 29 511.0 136.9 89 568.9 152.4 50 351 338.1 90.6 10 396.0 106.1 70 454.0 121.7 30 511.9 137.2 137.4 90 569.9 152.7 339. 90.9 411 397. 106.4 471 454. 9 121.9 531 512.9 591 570.9 153. 52 340.0 91.1 12 397.9 106.6 72 455. 9 122.2 32 513. 9 137. 7 92 571.8 153.2 53 340.9 91.4 13 398.9 106.9 73 456.9 122.4 33 514.8 137. 9 93 572.8 153.5 54 341. 9 91.6 14 399.9 107.2 74 457.8 122.7 34 515. 8 138.2 94 573.8 153.7 55 342.9 91.9 15 400.8 107.4 75 458.8 122.9 35 516. 8 138.4 95 574.7 154.0 56 343.8 92.1 16 401.8 107.7 76 459. 8 123.2 36 517. 7 138. 7 96 575. 7 154. 2 57 344.8 92.4 17 402. 8 107.9 77 460.7 123.5 37 518. 7 139.0 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. "i '5° (1 [)5°, 255°, 285°; . Page 398] TABLE 2. difference of Latitude and Departure for 16° ( L64°, 196°, 344= )• Dist. Lat. Dep. Dist. Lat. Dep. Dist. 1 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 1 117.3 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 6 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 ^6 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 11 9.6 2.8 70 67.3 19.3 30 125.0 125.9 35.8 90 182.6 52.4 50 251 240. 3 241.3 68.9 69. 2 10.6 3.0 71 68.2 19.6 131 36.1 191 183.6 52.6 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 1 .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 1 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 1 38.3 99 191.3 54.9 59 249.0 71.4 20 19.2 5.5 80 81 76.9 22.1 40 134.6 38.6 200 201 192.3 193.2 55.1 55.4 60 261 249.9 250.9 71.7 21 20.2 5.8 77.9 22.3 141 135.5 38.9 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 87.5 24.8 50 144.2 145. 2 41.3 41.6 10 201.9 57.9 70 259.5 260.5 74.4 31 29.8 8.5 91 25.1 151 211 202.8 58.2 271 74.7 32 30.8 8.8 92 88.4 25.4 52 146.1 41.9 12 203.8 58.4 72 261.5 75.0 33 31.7 9.1 93 89.4 25.6 53 147.1 42.2 13 204.7 58.7 73 262.4 75.2 34 32.7 9.4 94 90.4 25.9 54 148. 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. 8 154.8 44.1 44.4' 20 221 211.5 60.6 80 269.2 77.2 41 39.4 11.3 101 97.1 27.8 161 212.4 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 1 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 1 159.6 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 14.1 10 111 105. 7 1 30. 3 1 70 163.4 164.4 46.9 30 221.1 222.1 63.4 63.7 90 291 278.8 279.7 79.9 80. 2 51 49.0 106.7 30.6 171 47-1 231 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 Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. ri° (106°, 254°, 286° ). TABLE 2. [Page 399 Difference of Latitude and Departure for 16° (164°, 196°, 344' )■ Dist. Lat. Dep. Dist. 1 Lat. Dep. Dist. 1 Lat. Dep. 116.0 1 Dist. 481 Lat. Dep. 132.5 Dist. Lat. Dep. 301 289.3 82.9 361 347.0 99.5 421 404.7 462.4 541 520.1 149.1 02 290.3 83.2 62 348.0 99.7 22 405.6 116.3 82 1 463.3 132.8 42 521.0 149.4 03 291.2 83.5 68 348. 9 100.0 23 406.6 116. 6 83 1 464.3 133.1 43 522.0 149.7 04 292.2 83.8 64 349.9 100. 3 24 407.6 116.8 84 i 465.2 133.4 44 523.0 150. 05 293.2 84.0 65 350.8 100.6 25 408.5 117.1 85 i 466.2 133. 6 45 523.9 150.2 06 294.1 84.3 66 351.8 100.8 26 409.5 117.4 86 ( 467.2 133. 9 46 524.9 150.4 07 295. 1 84.6 67 352.8 101.1 27 410.4 117.7 87 1 468. 1 134.2 47 525.9 150.7 08 296.0 84.9 68 353.7 101.4 28 411.4 117.9 88 469.1 134.5 48 526. 8 151.0 09 297.0 85.1 69 354.7 101.7 29 412.4 118.2 89 j 470. 1 134. 8 49 527.8 151.3 10 298.0 85.4 70 355. 6 356. 6 101. 9 102.2 30 431 413. 3 414.3 118. 5 90 1 471.0 135.0 135.3 50 551 528.7 529.7 151.6 151.9 311 298.9 85.7 371 118.8 491 472.0 12 299.9 86.0 72 357.6 102.5 32 415.2 119. 92 472.9 135. 6 52 530.6 152.2 13 300.9 86.2 73 358.5 102.8 33 1 416.2 119. 3 93 473. 9 135. 9 53 531.6 152. 5 14 301.8 86.5 74 359.5 103. 1 34 417.2 119.6 94 474.9 136. 2 54 532.6 152.8 15 302.8 86.8 75 360.4 103.3 35 i 418. 1 119.9 95 475. 8 136.4 55 533. 5 153.0 16 303.7 87.1 76 361.4 103.6 36 419. 1 120.1 96 476.8 136. 7 56 534.5 153.2 17 304.7 87.3 77 362.4 103.9 37 1 420.0 120.4 97 477.7 137.0 57 535. 4 153. 5 18 305.7 87.6 78 363.3 104.2 38 1 421.0 120.7 98 478.7 137.3 58 536.4 153.8 19 306. 6 87.9 79 364.3 104.4 39 i 422.0 121.0 99 479.7 137. 5 59 537.4 154. 1 20 321 307.6 308.5 88.2 88.4 80 381 365.3 366.2 104.7 105. 40 441 422.9 121.2 121. 5 500 501 480. 6 ' 137. 8 481.6 138.1 60 538.3 154.4 154. 7 423. 9 561 539.3 22 309.5 88.7 82 367.2 105.3 42 i 424.9 121.8 02 482. 6 138. 3 62 540.3 154.9 23 310.5 89.0 83 368.1 105. 5 43 425.8 122.1 03 483. 5 138. 6 63 541.2 155.2 24 311.4 89.3 84 369.1 105.8 44 426.8 122.3 04 , 484.5 138.9 64 542.2 155.4 25 312. 4 89.5 85 370.1 106.1 45 427.7 122.6 05 [ 485. 4 139. 2 65 543.1 155.7 26 313.3 89.8 86 371.0 106.4 46 428.7 122.9 06 4^6. 4 139. 4 66 544.1 156.0 27 314.3 90.1 87 372.0 106.6 47 429.7 123. 2 07 487. 3 i 139. 7 67 545.1 156.3 28 315. 3 90.4 88 372.9 106.9 48 430.6 123.4 08 488. 3 140. 68 546.0 156.6 29 316.2 90.6 89 373.9 107.2 49 431.6 123. 7 09 489.3 !l40.3 69 547.0 156.9 30 331 317.2 318.2 90.9 91.2 90 391 374. 9 375.8 107.5 107.7 50 451 432.6 433.5 124.0 124.3 10 511 490.2 140.6 70 547.9 548. 9" 157.1 491.2 140.8 571 157.3 32 319.1 91.5 92 376.8 108.0 52 434.5 124.6 12 492.1 141.1 72 549.8 157.6 33 320.1 91.8 93 377.8 108.3 53 435.4 124.8 13 493.1 141.4 73 550.8 157.9 34 321.0 92.0 94 378. 7 1 108. 6 54 436. 4 125. 1 14 494.1 jl41.7 74 551.8 158.2 35 322.0 92.3 95 379.7 108.8 55 437. 4 125.4 15 495.0 !l41.9 75 552.7 158.4 36 323.0 92.6 96 380.6 109.1 56 438.3 125.7 16 496.0 142.2 76 553.7 158.7 37 323.9 92.9 97 381.6 109.4 57 439. 3 125. 9 17 496.9 142.5 77 554.6 159.0 38 324.9 93.1 98 382.6 109.7 58 440.2 126.2 18 497.9 142.8 78 555.6 159.3 39 325. 8 93.4 99 383.5 109.9 59 441.2 126.5 19 498.9 143.0 79 556.5 159.5 40 341 326. 8 93.7 400 384.5 110.2 60 442.2 443.1 126.8 127.0 20 521" 499.8 143.3 80 557.5 159. 8 327.8 94.0 401 385.4 110.5 461 500.8 143.6 581 558.4 160.1 42 328.7 94.2 02 386. 4 110.8 62 444.1 127. 3 22 501.7 143.9 82 559.4 160.4 43 329.7 94.5 03 387.4 111.0 63 445.0 127.6 23 502.7 144.1 83 560.4 160.6 44 330.7 94.8 04 388.3 111.3 64 446. 127.9 24 503.7 144.4 84 561.3 161.0 45 331.6 95.1 05 389.3 111.6 65 447.0 128.1 25 504.6 144.7 85 562.3 161.3 46 332. 6 95.3 06 390.2 1111.9 66 447.9 128.4 26 505.6 145. 86 563.2 161.6 47 333. 5 95.6 07 391.2 112.1 67 448.9 128.7 27 506. 6 145.3 87 564.2 161.8 48 334.5 95.9 08 392.2 112.4 68 449.8 129.0 28 507.5 145.6 88 565.2 162.1 49 335. 5 96.2 09 393.1 112.7 69 450. 8 129.2 29 508. 5 145. 8 89 566.1 162.4 50 351 336.4 96.4 96.7 10 411 394.1 395.1" 113.0 70 471" 451.8 452.7 129.5 129.8 30 531 509.4 146.1 146.4 90 591 567.1 568.1 162.7 337. 4 113.3 510.4 162.9 52 338.3 97.0 12 396.0 113.5 72 453. 7 130. 1 32 511.4 146.7 92 569.0 163. 2 53 339. 3 97.3 13 397.0 113. 8 73 454. 7 130.3 33 512. 3 146.9 93 570.0 163. 5 54 340. 3 97.5 14 397. 9 114.1 74 455.6 130.6 34 513. 3 147.2 94 571.0 163.8 55 341.2 97.8 15 398.9 114.4 75 456.6 130.9 35 514.3 147.5 95 571.9 164.0 56 342. 2 98.1 16 399. 9 114.6 76 457.5 131.2 36 515. 2 147.8 96 572.9 164.3 57 343. 1 98.4 17 400.8 114.9 77 458.5 131.4 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 99 575.8 165.1 60 346.0 99.2 20 403.7 115.8 80 461.4 132.3 40 519.1 148.8 600 576.8 165.4 Dist. Dep. Lat. Dist. Dep. Lat. Di.st. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. •4° (106°, 254 =, 286° ). Page 400 TABLE 2. Difference of Latitude and Departure for 1 7° (163°, 197 =, 343° )• Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 1.0 0.3 61 58.3 17.8 121 115.7 35.4 181 173.1 52.9 241 230.5 70.5 2 1.9 0.6 62 59.3 18.1 22 116.7 35.7 82 174.0 53.2 42 231.4 70.8 3 2.9 0.9 63 60.2 18.4 23 117.6 36.0 83 175.0 53.5 43 232.4 71.0 4 3.8 1.2 64 61.2 18.7 24 118.6 36.3 84 176.0 53.8 44 2.33. 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 ^6 63.1 19.3 26 120.5 36.8 86 177.9 54.4 46 235.3 71.9 7 6.7 2.0 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 11 9.6 10.5 2.9 70 66.9 20.5 30 124.3 38.0 38.3 90 181.7 55.6 55. 8 50 251 239.1 240.0 73.1 3.2 71 67.9 20.8 131 125.3 191 182.7 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 i 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 6.0 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 76.3 21 20.1 81 77.5 23.7 141 ]34.8 41.2 201 192.2 58.8 261 249.6 22 21.0 6,4 82 78.4 24.0 42 135.8 41.5 02 193.2 59.1 62 250.6 76.6 23 22.0 6.7 83 79.4 24.3 43 136.8 41.8 03 194.1 59.4 63 251.5 76.9 24 23.0 7.0 84 80.3 24.6 44 137. 7 42.1 04 195.1 59.6 64 252. 5 77.2 25 23.9 7.3 85 81.3 24.9 45 138.7 42.4 05 196.0 59.9 65 253.4 77.5 26 24.9 7.6 86 82.2 25.1 46 139.6 42.7 06 197.0 60.2 66 254.4 77.8 27 25.8 7.9 87 83.2 25.4 47 140.6 43.0 07 198.0 60.5 67 255. 3 78.1 28 26.8 8.2 88 84.2 25.7 48 141.5 43.3 08 198.9 60.8 68 256.3 78.4 29 27.7 8.5 89 85.1 26.0 49 142.5 43.6 09 199.9 61.1 69 257. 2 78.6 30 28.7 8.8 90 86.1 26.3 50 143.4 144.4 43.9 10 200.8 61.4 61. 7' 70 271 258.2 78.9 31 29.6 9.1 91 87.0 26.6 151 44.1 211 201.8 259.2 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 .4a 38.3 11.7 100 101 95.6 96.6 29.2 29.5 60 161 153.0 154.0 46.8 20 210.4 211.3 64.3 80 267.8 81.9. 41 39.2 12.0 47.1 221 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 90 277.3 278.3 84.8 85.1 51 48.8 14.9 111 106.1 32.5 171 163.5 50.0 231 220.9 67.5 291 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°, 253°, 287° )• TABLE 2. [Page 401 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 1 461.9 141.2 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. 106.7 25 406.4 124.3 85 463.8 141.8 45 521.2 159. 3 06 292.6 89.5 66 350. 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 1 525.0 160.5 10 311 296.4 297.4 90.6 70 353. 8 108.2 30 411.2 412.1 125.7 90 468.6 143. 2 50 1 526.0 160.8 161.1 90.9 371 i 354.8 108.5 431 126.0 491 469.5 143. 5 551 526. 9 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 i 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 i 529.8 162.0 ]5 301.2 92.1 75 358.6 109.6 35 416.0 127.2 95 473.4 144.7 55 530.8 162.3 16 302.2 92.4 76 359. 5 109.9 36 416.9 127.5 96 474.3 145. 56 531.7 162.6 17 303. 1 92.7 77 360. 5 110.2 37 i 417.9 1127.8 97 475. 3 145.3 57 532.7 162.9 18 304.1 93.0 78 361.4 110.5 .38 ; 418.8 1128.1 98 476.2 145. 6 58 533.6 163.2 19 305.0 93.3 79 362.4 110.8 39 419. 8 128. 4 99 477.2 145. 9 59 i 534.6 163. 5 20 306. 306.9 93.6 80 381 363.4 111.1 40 1 420. 7 128. 6 500 478.1 479. 1 146.2 60 1 535.5 561 536.5 163.8 321 93.9 364.3 111.4 441 i 421. 7 : 128. 9 501 146.5 164.1 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 1 129. 5 03 481.0 147.1 63 i 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 : 5,39.4 164.8 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. 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. 5 316. 5 96.5 90 372.9 373.9 114.0 50 430.3 431. 3 131.6 10 487.7 149.1 70 545. 1 546.1 166.7 331 96.8 391 114.3 451 131.9 511 488.7 149.4 571 167.0 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 55 435.1 133. 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 4.38. 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. 1 326.1 99.4 99. 7 400 382. 5 383.4 117.0 117. 2 60 i 439.9 461 440. 8 f34.5 134.8 20 521 497.2 152.0 80 554.6 169.6 341 401 498.2 152.3 581 555.6 169.9 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 i 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 i 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 1 388. 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 1 446.6 136.5 27 503. 9 154.1 87 561.3 171.6 48 332.8 101.8 08 390. 1 119.3 68 i 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 50 351 334.7 335. 6 102. 3 10 ! 392.0 393.0 119.9 70 449.4 450.4 137.4 30 531 506. 8 155. 90 591 564.2 172.5 172.8 102. 6 411 i 120.2 471 137. 7 507.8 155. 3 565. 1 52 336.6 102.9 12 1 394. 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. 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. 19 400.7 1 122.5 79 458. 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. ^3° (107°, 253°, 287° )• 22489—03- -26 Page 402] TABLE 2. Difference of Latitude and Departure for 18° (162°, 198 °, 342° )• Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 1.0 0.3 61 58.0 18.9 121 115.1 37.4 181 172.1 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. 56.9 44 232.1 75.4 5 4.8 1.5 «5 61.8 20.1 25 118.9 38.6 85 175.9 57.2 45 233.0 75.7 6 5.7 1.9 66 62.8 20.4 26 119.8 38.9 86 176.9 57.5 46 234. 76.0 7 6.7 2.2 67 63.7 20.7 27 120.8 39.2 87 177.8 57.8 47 234.9 76.3 8 7.6 2.5 68 64.7 21.0 28 i 121.7 .39.6 88 178.8 58.1 48 2.35. 9 76.6 9 8.6 2.8 69 65.6 21.3 29 1 122. 7 39.9 89 179.7 58.4 49 236.8 76.9 10 11 9.5 10.5 3.1 3.4 70 71 66.6 21.6 21.9 30 123.6 124.6 40.2 40.5 90 191 180.7 181.7 58.7 50 237. 8 238. 7 77.3 67.5 131 59.0 251 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 20.0 6.2 6. 5 80 81 76.1 24.7 40 133.1 43.3 200 190.2 61.8 60 247. 3 248.2 80.3 80.7 21 77.0 25.0 141 134.1 43: 6 201 191.2 62.1 261 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. 63.0 64 251.1 81.6 25 23.8 7.7 85 80.8 26.3 45 137.9 44.8 05 195. 63.3 65 252.0 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 91 85.6 27.8 50 142.7 46.4 10 199.7 ^200.7 64.9 70 256.8 83.4 83.7 31 29.5 9.6 86.5 28.1 151 143.6 46.7 211 65.2 271 257. 7 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 59 551.2 49.1 19 208. 3 67.7 79 265.3 86.2 40 38.0 12.4 12.7 100 95.1 30.9 31.2 60 152.2 153. 1 49.4 20 209.2 210.2 68.0 80 266.3 86.5 41 39.0 101 96.1 161 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. 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. 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 51 47.6 15.5 10 104.6 34.0 70 161. 7 52.5 52.8 30 231 218.7 71.1 90 275.8 89.6 48.5 15.8 111 105.6 34.3 171 162.6 219.7 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 Dist. Dep.' Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. ^2° (1 }8°, 252°, 288° )• TABLE 2. Difference of Latitude and Departure for 18° (162°, 198°, 342°). [Page 403 341 42 43 44 45 46 Lat. 286.3 287.2 288.2 289.1 290.1 291.0 292. 292.9 293.9 294.8 295.8 296.7 297.7 298.6 299.6 300.5 301. 5 302. 4 303. 4 304.3 305. 3 306. 2 307. 2 308.2 309.1 310. 1 311.0 312. 312.9 313.9 Dep. 314. 8 315. 8 316.7 317.7 318.6 319.6 320.5 321.5 322.4 323.4 324.3 325. 3 326.2 327.2 328. 1 329.1 93.0 93.3 93.7 94.0 94.3 94.6 94.9 95.2 95.5 96.1 96.4 96.7 97.0 97.4 97.7 98.0 98. 3 98.6 98^ 99.2 99.5 99.8 100.1 100.4 100.7 101. 1 101.4 101.7 102.0 102.3 102.6 102.9 103.2 103.5 103.8 104.1 104.5 104.8 105.1 Dist. 361 62 63 64 65 66 67 68 69 70 47 330.0 48 331.0 49 331.9 50 332.9 351 333.8 52 334.8 53 335.7 54 336.7 55 337.6 56 338.6 57 339.5 58 340.5 59 341.4 60 342.4 Dist. Dep. 105.4 105. 7 106.0 106. 3 106.6 106.9 107.2 107.5 107.9 1 08.2 108. 5 108.8 109.1 109.4 109.7 110.0 110. 3 110.6 110.9 111.3 Lat. Dist. 371 72 73 74 75 76 77 78 79 80 381 82 83 84 85 86 87 88 89 90 391 92 93 94 95 96 97 98 99 400 401 02 03 04 05 06 07 08 09 10 411 12 13 14 15 16 17 18 19 20 Lat. 343. 3 344.3 345. 2 346.2 347.1 348.1 349. 350. 350. 9 ^1.9 352. 9' 353. 8 354. 8 355.7 356.7 357.6 358.6 359.5 360.5 361.4 362.4 363. 3 364.3 365.2 366.2 367. 1 368.1 369.0 370.0 370.9 371.9 372.8 373. 8 374.7 375. 7 376.6 377.6 378. 5 379. 5 380.4 Dep. 111.6 111.9 112.2 112.5 112.8 113.1 113.4 113.7 114.0 114.3 114.7 115.0 115.3 115.6 115.9 116.2 116.5 116.8 117.1 117.Jl^ 117.7 118.1 118.4 118.7 119.0 119. 3 119.6 119.9 120.2 120.5 Dist. 381.4 382.3 383. 3 384.2 385.2 386.1 387. 1 388.0 389.0 389.9 390. 9 391.8 392.8 393. 7 394.7 395. 6 396.6 397.5 398. 5 399.5 Dep. 120.8 121.1 121.5 121.8 122.1 122.4 122.7 123.0 123. 3 123. 6 123.9 124.2 124.5 124.9 125.2 125. 5 125. 8 126.1 126.4 126^ 127.0 127.3 127.6 127.9 128. 3 128.6 128.9 129.2 129.5 129.8 Lat. Dist 421 22 23 24 25 26 27 28 29 30 431 32 33 34 35 36 37 38 39 40 441 42 43 44 45 46 47 48 49 50 451 52 53 54 55 56 57 58 59 60^ 461 62 63 64 65 66 67 68 69 JO 471 72 73 74 75 76 77 78 79 80 lAt. 400.4 401.4 402.3 403. 3 404.2 405.2 406.1 407.1 408.0 409^0 "409. 9 410.9 411.8 412.8 413.7 414.7 415.6 416.6 417.5 418.5 Dep. 130.1 130.4 130. 7 131.0 131.3 131.7 132.0 132.3 132.6 132.9 133.2 133.5 133.8 134.1 134.4 134.7 135.1 135.4 135.7 136.0 419.4 420.4 421.3 422.3 423.2 424.2 425. 1 426. 1 427.0 4 28.0 428. 9 429.9 430.8 431.8 432.7 433.7 434.6 435.6 436. 5 437. 5 448.0 448.9 449. 9 450. 8 451.8 452.7 453.7 454.6 455. 6 456.5 Dep. 136.3 136.6 136.9 137.2 137. 5 137. 8 138.1 138.4 138.8 139. 1 139.4 139.7 140.0 140. 3 140.6 140.9 141.2 141.5 141.8 142.2 142.5 142.8 143.1 143. 4 143.7 144.0 144. 3 144.6 144.9 145. 2 145.6 145. 9 146.2 146.5 146.8 147.1 147.4 147.7 148.0 148.3 Lat. Dist, Dist. 481 82 83 84 85 86 87 88 89 90 491 92 93 94 95 96 97 98 99 500 501 02 03 04 05 06 07 08 09 10 Lat. 457.5 458.5 459.4 460.4 461. 3 462.3 463.2 464.2 465. 1 466.1 Dep. Dist 467.0 468.0 468.9 469.8 470.8 471.7 472.7 473. 6 474.6 475.5 476 477, 478, 479 480, 481, 482.2 483.2 484.1 485.1 511 12 13 14 15 16 17 18 19 20 521 22 23 24 25 26 27 28 29 30 486.0 487.0 487.9 488.9 489.8 490.8 491.7 492.7 493.6 494.6 531 32 33 34 35 36 37 38 39 40 495.5 496. 5 4^^7.4 498.4 499. 3 500.3 501.2 502.2 503. 1 504 .1 505. 0' 506. 506. 9 507. 9 508. 8 509.8 510.7 511.7 512. 6 513. 6 Dep. 148.6 148.9 149. 3 149.6 149.9 150.2 150. 5 150.8 151. 1 15L4 151. 7 152.0 152.3 152. 6 153. 153.3 153. 6 153.9 154.2 154.5 154.8 155.1 155. 4 155. 7 156.1 156. 4 156. 7 157. 157. 3 157^ 157. 9 158. 2 158. 5 158. 8 159. 1 159. 4 159.7 160.0 160.3 160.^ 161. 161.3 161.6 161.9 162.2 162.5 162.9 163.2 163.5 163. 8 164.1 164.4 164.7 165. 165.3 165. 6 165. 9 166.2 166.5 166.9 541 42 43 44 45 46 47 48 49 50 551 52 53 54 55 56 57 58 59 60 561 62 63 64 65 66 67 68 69 70 571 72 73 74 75 76 77 78 79 80 581 82 83 84 85 86 87 88 89 90 591 92 93 94 95 96 97 98 99 600 Lat. Dist. Lat. 514.5 515. 5 516. 4 517.4 518. 3 519. 3 520.2 521.2 522.1 523. 1 524. 525. 525. 9 526.9 527.8 528.8 529.7 530.7 531. 6 ^2^6_ 533.5 534.5 535. 4 536.4 537. 3 538.3 539. 2 540. 2 541.1 542.1 543.0 544. 544. 9 545. 9 546. 8 .547.8 548. 7 549. 7 550. 6 551.6 552. 5 553. 5 554. 4 555.4 556.3 557. 3 558. 2 559.2 560.1 561.1 562. 563. 563. 9 564.9 565. 8 566.8 567. 7 568. 7 569. 6 570.6 Dep. Dep. 167.2 167. 5 167.9 168.2 168. 5 168.8 169.1 169.4 169.7 170^0^ 170. 3 170.6 170.9 171.2 171.5 171.8 172.1 172.4 172.7 173.0 173.3 173. 6 173.9 174.2 174.6 174.9 175.2 175.5 175.8 176.1 176. 4" 176.7 177.0 177.3 177.6 178.0 178.3 178.6 178.9 179^ 179. 5 179.8 180.1 180.4 180.7 181.1 181.4 181.7 182.0 182.^ 182. 7 183.0 183.3 183. 6 183.9 184.2 184.5 184.8 185. 1 185. 4 Lat. 72° (108, 252°, 288°). Page 404] TABLE 2. Difference of Latitude and Departure for 19° (161°, 199 °, 341°). Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 0.9 0.3 61 57.7 19.9 121 114.4 39.4 181 171.1 58.9 241 227.9 78.5 2 1.9 0.7 62 58.6 20.2 22 115.4 39.7 82 172.1 59.3 42 228.8 78.8 3 2.8 1.0 63 59.6 20.5 23 116. 3 40.0 83 173.0 59.6 43 229.8 79.1 4 3.8 1.3 64 60.5 20.8 24 117.2 40.4 84 174.0 59.9 44 230. 7 79.4 5 4.7 1.6 65 61.5 21.2 25 118.2 40.7 85 174.9 60.2 45 231. 7 79.8 6 5.7 2.0 «6 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 30 122.9 123.9 42.3 90 179.6 61.9 50 251 236.4 237.3 81.4 81.7 11 10.4 3.6 71 67.1 23.1 131 42.6 191 180.6 62.2 12 11.3 3.9 72 68.1 23.4 32 124.8 43.0 92 181.5 62.5 52 238.3 8gi0 13 12.3 4,2 73 69.0 23.8 33 125.8 43.3 93 182.5 62.8 53 239.2 8^.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 2.5.4 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 45.9 200 189.1 190.0 65.1 60 245.8 246.8 84.6 21 19.9 6.8 81 76.6 26.4 141 133. 3 201 65.4 261 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 10 211 198.6 199. 5 68.4 68. 7 70 271 255.3 256.2 87.9 31 29.3 10.1 91 86.0 29.6 151 142.8 49.2 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 71.6 72.0 80 264.7 91.2 41 38.8 13.3 101 95.5 32.9 161 152.2 52.4 221 209.0 281 265.7 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. 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 30 217.5 218.4 74.9 75.2 90 291 274.2 275.1 94.4 94.7 51 48.2 16.6 111 105. 36.1 171 161.7 55.7 231 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. 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 Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. ■1° (1 09°, 251 °, 289° )• TABLE '2. [Page 405 Difference of Latitude and Departure for 19° (161°, 199 °, 341° )• Dlst. Lat. Dep. Dlst. Lat. Dep. Dist. Lat. Dep. 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 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. 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 10 311 293.1 294. 1 100.9 101.2 70 371 349.8 120.4 30 431 406.6 407.5 140.0 90 491 463.3 464.3 159.5 50 551 520.0 521.0 179.0 179.4 350.8 120.8 140.3 159.8 12 295. 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. 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 20 321 302.6 303. 5 104.2 104. 5" 80 359.3 123.7 124. 0' 40 441 416.0 143.2 143. 6' 500 472.8 473.7 162.8 60 529. 5 530. 4" 182.3 182.6 381 360. 2 417.0 501 163.1 561 22 304.5 104.8 82 361.2 124.4 42 417.9 143.9 02 474.7 163.4 62 531.4 182.9 23 305.4 105.1 83 362. 1 124.7 43 418.9 144.2 03 475. 6 163.7 63 532.3 183.3 24 306.3 105.5 84 363.1 125.0 44 41§.8 144.5 04 476. 5 164.1 64 533.2 183. 6 25 307.3 105.8 85 364. 125. 3 45 420.8 144.9 05 477. 5 164.4 65 534.2 183. 9 26 308.2 106.1 86 365. 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. 184. 9 29 311.1 107.1 89 367.8 126.6 49 424. 5 146.2 09 481.2 165.7 69 538. 185.2 30 331 312.0 107.4 90 368.8 369. 7 127.0 50 425. 5 426.4 146.5 10 482.2 483.1 166.1 70 538.9 185. 6 185. 9 313.0 107.7 391 127.3 451 146.8 511 166.4 571 539.9 32 313.9 108.1 .92 370.6 127.6 52 427.4 147.1 12 484.1 166.7 72 540.8 186.2 33 314.9 108.4 93 371.6 127.9 53 428. 3 147.5 13 485. 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. 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. 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. 79 547.4 188. 5 40 341 321. 5 110.7 400 378.2 130.2 60 434.9 149.7 150.1 20 521 491.6 492.6 169. 3 169. 6 80 581 548.4 549. 3 188.8 189.1 322.4 111.0 401 379.2 130.5 461 435.9 42 323.4 111.3 02 380. 1 130.9 62 436.8 150.4 22 493.5 170.0 82 550. 3 189. 5 43 324.3 111.7 03 381.0 131.2 63 437.8 150.7 23 494.5 170. 3 83 551. 2 189.8 44 325.3 112.0 04 382.0 131.5 64 438.7 151.0 24 495.4 170.6 84 552.2 190.1 45 326. 2 112.3 05 382.9 131.8 65 439.7 151.4 25 496.4 170.9 85 553.1 190.4 46 327.1 112. 6 06 383.9 132. 2 66 440.6 151.7 26 497.3 171.2 86 554. 1 190. 8 47 328.1 113.0 07 384.8 132.5 67 441.6 152.0 27 498. 3 171.6 87 555. 191.1 48 329.0 113.3 08 385. 8 132.8 68 442.5 152.4 28 499.2 171.9 88 555. 9 191.4 49 330. 113.6 09 386. 7 133.1 69 443.4 152.7 29 500.1 172.2 89 556. 9 191.7 50 330.9 331.9 113.9 114. 3 10 411 387.7 388.6 133.5 70 444.4 445.3 153. 30 531 501.1 502. 172.5 90 557.8 558.8 192.1 192. 4 351 133.8 471 153.3 172.9 591 52 332.8 114.6 12 389.6 134.1 72 446.3 153.7 32 503. 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. 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 76 450.1 155.0 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. 60 340.4 117.2 20 397.1 136.7 80 Dist. 453. 8 156.3 40 510.6 175. 8 600 567.3 195. 3 Dist. Dep. Lat'. Dist. Dep. Lat. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 71° (1 09°, 251 °, 289°). Page 406] TABLE 2. Difference of Latitude and Departure for 20° (160°, 20C °, 340° ). DIst. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 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 j 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 1 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 i 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. 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 11 9.4 10.3 3.4 70 65.8 23.9 30 131 122.2 123.1 44.5 90 178. 5 65.0 50 251 234.9 1 85.5 235.9 j 85.8 3.8 71 66.7 24.3 44.8 191 179.5 65.3 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. 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 19.7 6.8 7.2 80 75.2 76.1 27.4 27.7 40 141 131.6 132. 5 47.9 48.2 200 187.9 188. 9 68.4 60 244.3 88.9 21 81 201 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. 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 85.5 30.8 31.1 50 140.9 51.3 10 197.3 198.3 71.8 72.2 70 271 253.7 254.7 92.3 92.7 31 29.1 10.6 91 151 141.9 51.6 211 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 58 148.6 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 60 161 150.4 151.3 54.7 20 221 206.7 207.7 75.2 75.6 80 28 r 263.1 264.1 95.8 41 38.5 14.0 101 94.9 34.5 55.1 96.1 42 39.5 14.4 02 95.8 34.9 62 152.2 55.4 22 208.6 75.9 82 265. 96.4 43 40.4 14.7 03 96.8 35.2 63 153.2 55.7 23 209.6 76.3 83 265. 9 96. 8 1 44 41.3 15.0 04 97.7 35.6 64 154. 1 56.1 24 210. 5 76.6 84 266.9 97.1 45 42.3 15.4 05 98.7 35.9 65 155. 56.4 25 211.4 77.0 85 267.8 97.5 46 43.2 15.7 06 99.6 36.3 66 156.0 56.8 26 212.4 77.3 86 268.8 97.8 47 44.2 16.1 07 100.5 36.6 67 156.9 57.1 27 213. 3 77.6 87 269.7 98.2 48 45.1 16.4 08 101.5 36.9 68 157.9 57.5 28 214.2 78.0 88 270.6 98.5 49 46.0 16.8 09 102.4 37.3 69 158.8 57.8 29 215.2 78.3 89 271.6 98.8 50 47.0 17.1 10 103.4 37.6 38.0 70 159.7 58.1 30 216.1 217.1 78.7 90 272.5 99.2 99.5 51 47.9 17.4 111 104.3 171 160.7 58.5 231 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 Dlst. Dep. Lat. Dlst. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 70° (110°, 250 % 290° )■ 1 TABLE 2. [Page 407 Difference of Latitude and Departure for 20° (160°, 20C )°, 340= )• Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. 481 Lat. i j Dep. Dist. Lat. j Dep. 301 282,9 103. 361 339.2 123.5 421 395. 6 144.0 452.0 164.5 541 508.4 185.0 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. 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. 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 10 291.3 106.0 106.4 70 371 347.7 348.6 126.6 126.9 30 431 404.1 405.0 147.1 147.4 90 191^ 460.5 167.7 50 516.8 188.2 311 292.3 461.4 168.0 551 517.8 188.5 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 14 395.1 107.4 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 i 128. 6 36 409.7 149.1 96 466.1 169.6 56 522.5 190.2 17 297.9 108.4 77 354. 3 129.0 37 410.7 149.5 97 467.0 170.0 57 523. 4 190. 5 18 298.8 108.8 78 355. 2 129.3 38 411.6 149.8 98 468.0 170. 3 58 524. 4 190.8 19 299.8 109.1 79 356. 2 129.6 39 412.5 150.2 99 468.9 170.7 59 525.3 191.2 20 300. 7 301.6 109. 5 80 357. 1 130.0 130. 3 40 441 413.5 414.4 150.5 500 501 469.9 470.8 171.0 60 561 526.2 191.6 321 109.8 381 358. 150.8 171.3 527.2 191.9 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. 5 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 50 451 422.9 153.9 10 511 479.2 174.4 70 535. 6 195.0 331 i 311.0 113. 2 391 367.4 133.7 423.8 154. 3 480.2 174.8 571 536. 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. 175.8 74 539.4 196.3 35 314.8 114.6 95 371.2 135. 1 55 427. 6 i 155. 6 15 484.0 176.1 75 540. 3 196.6 36 t 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 40 319.5 116.3 400 401 375.9 136.8 60 432.3 433.2 157.4 20 488.7 489. 6 177.9 80 545.0 198.4 341 320.4 116.6 376.8 137.2 461 157.7 521 178.2 581 546.0 198.7 42 ! 321.4 117.0 02 377.8 137.5 62 434. 1 158. 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. 119.0 08 383.4 139.6 68 439.8 160.1 28 496.2 180.6 88 552. 6 201.2 49 328.0 119.4 09 384.3 139.9 69 440.7 160.4 29 497.1 181.0 89 553. 5 201.5 50 328.9 329.8 119.7 120.1 10 411 385.3 386.2 140.2 70 471 441.7 442.6 160.8 161.1 30 531 498.1 181.3 90 554. 4 201.8 351 140.6 499.0 181.6 591 555.4 202.1 52 330.8 120.4 12 387.2 1 40. 9 72 443.5 161.4 32 499.9 181.9 92 556.3 202.4 53 331.7 120.7 13 388.1 141.3 73 444.5 161.8 33 500.9 182.3 93 557.3 202.8 54 332.7 121.1 14 389.0 141.6 74 445.4 162.1 34 501.8 182.6 94 558. 2 203.2 55 333.6 121.4 15 390.0 141.9 75 1 446.4 162.5 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. 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. Di.st. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 70° (110°, 250°, 290°). Page 408] TABLE 2. Difference of Latitude and Departure for 21° (159°, 201 °, 339° ). Dist 1 Lat. Dep. Dist. Lat. Dep. iDlst. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 0.9 0.4 61 56.9 21.9 1 121 1 113.0 43.4 181 169.0 64.9 241 225.0 86.4 2 1.9 0.7 62 57.9 22.2 22 1 113.9 j 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 1 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 1 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 j 44.8 85 172. 7 66.3 45 228.7 87.8 6 5.6 2.2 i? 61.6 23.7 26 117.6 45.2 86 173.6 66.7 46 229.7 88.2 7 6.5 2.5 62.5 24.0 27 118.6 i 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 1 45.9 88 475.5 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 i 121.4 1 46.6 90 177.4 178. 3 68.1 68.4 50 251 233.4 234.3 89.6 90.0 11 10.3 3.9 71 66.3 25.4 131 122.3 1 46.9 191 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 1 124.2 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 I 48. 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 1 128.8 49.5 98 184.8 71.0 58 240.9 92.5 19 17.7 6.8 79 73.8 28.3 39 1 129.8 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 60 242.7 243.7 93.2 93.5 21 19.6 7.5 81 75.6 29.0 141 131.6 1 50.5 201 187.6 72.0 261 22 20.5 . 7.9 82 76.6 29.4 42 132.6 i 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 1 52.0 05 191.4 73.5 65 247.4 95.0 26 24.3 9.3 86 80.3 30.8 46 136.3 \ 52.3 06 192. 3 73.8 66 248.3 95.3 27 25.2 9.7 87 81.2 31.2 47 137.2 i 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 90 84.0 85.0 32.3 32.6 50 151 140.0 ! 53.8 10 196.1 197.0 75.3 75.6 70 252.1 253.0 96.8 97.1 31 28.9 11.1 91 141.0 54.1 211 271 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 i 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 1 148.4 57.0 19 204.5 78.5 79 260.5 100.0 40 37.3 14.3 100 93.4 35.8 36.2 60 149.4 57.3 20 221 205.4 78.8 80 281 261.4 262. 3 100.3 41 38.3 14.7 101 94.3 161 150.3 57.7 206.3 79.2 100.7 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 86.9 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 I 153.1 58.8 24 209.1 80.3 84 265. 1 101.8 45 42.0 16.1 05 98.0 37.6 65 154. 59. 1 25 210.1 80.6 85 266. 1 102.1 46 42.9 16.5 06 99.0 38.0 66 155. 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 51 46.7 17.9 18.3 10 111 102.7 103. 6~ 39.4 39.8 70 171 158.7 60.9 30 231 214.7 215.7 82.4 90 270.7 103.9 104. 3 47.6 159.6 61.3 82.8 291 271.7 52 48.5 18.6 12 104.6 40.1 72 1 160.6 61.6 32 216.6 83.1 92 272.6 104.6 53 49.5 19.0 13 105.5 40.5 73 ; 161.5, 62.0 33 217.5 83.5 93 273. 5 105. 54 50.4 19.4 14 106.4 40.9 74 j 162.4 62.4 34 318.5 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 1 167. 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 j 64.5 40 224.1 86.0 300 280.1 107.5 Dist. Dep. Lat. Di.st. Dep. Lat. Dist. 1 Dep. j Lat. Dist. Dep. Lat. Dist. Dep. Lat. 69° (111°, 249°., 291°). TABLE 2. [Page 409 Difference of Latitude and Departure for 21° (159°, 201°, 339 ")■ Dist. Lat. 1 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 08 282. 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 1 108. 9 64 339. 8 130.4 24 1 395.8 152.0 84 451.8 173.5 44 507. 9 195.0 05 284. 7 109. 3 65 340.7 130. 8 25 1 396.8 152.3 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. 87 454. 6 174.5 47 510.7 196.0 08 287.5 110. 4 68 343. 5 131.9 28 399. 6 153. 4 88 455.6 174.9 48 511.6 196.4 09 288.5 110.7 79 344.5 132.2 29 400.5 153.7 89 456. 5 175.2 49 512.6 196.8 10 289.4 111.1 Til. 5 70 371 345.4 346.3 132.6 30 401.4 154.1 90 457.4 175.6 176.0 50 551 513.5 514.4 197.1 197.5 311 290.3 133. 431 402.4 154.5 491 458. 4 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 1112.5 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. 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. 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. 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 20 298.7 114.7 115.0 80 354. 7 136.2 40 410.8 157. 7 158. 500 566.8 179.2 60 522. 8 523.8 200.7 201. 321 299.7 381 355. 7 136. 5 441 411.7 501 467.7 179.5 561 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 1 115. 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 1 117. 5 88 362.2 139. 1 48 418.2 160. 5 08 474.3 182.0 68 530. 3 203.5 29 307.1 '117.9 89 363.1 139.4 49 419.2 160. 9 09 475.2 182.4 69 531.2 203.9 30 308.1 1118.3 90 364.1 365. 139. 8 140. 1 50 420.1 161.3 10 476.1 477.1 182.8 70 532.2 533.1 204.3 204.6 331 309.0 118.6 391 451 421.0 161.6 511 183.1 571 32 309.9 119.0 92 365.9 140.5 52 422.0 162.0 12 478.0 183.5 72 534. 205.0 33 310.9 119.3 93 366.9 140.8 53 422. 9 162. 3 13 478.9 183. 8 73 535. 205. 4 34 311.8 119.7 94 367.8 141.2 54- 423. 8 162. 7 14 479.9 184.2 74 535. 9 205. 7 35 312. 7 120.1 95 368.7 141.6 55 424. 8 163. 1 15 480.8 184.6 to 536.8 206.1 36 313.7 120.4 96 369.7 141.9 56 425. 7 163. 4 16 481.7 184.9 76 537.8 206.4 37 314.6 120.8 • 97 370. 6 142.3 57 426. 6 163. 8 17 482.7 185.3 77 538.7 206. 8 38 315.5 121.1 98 371.5 142.6 58 427.6 164.1 18 483.6 185. 6 78 539. 6 207.1 39 316.5 121.5 99 372.5 143.0 59 428.5 164.5 19 484.5 186.0 79 540. 6 207.5 40 341 317.4 121.8 400 373. 4 143.4 143. 7 60 429.4 164.9 20 485. 5 486.4 186.4 186.7 80 581 541.5 '542. 4 207.9 318.3 122: 2 401 374.3 461 430. 4 , 165. 2 521 208.2 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 U 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. 145. 5 66 435. 167. 26 491.1 188.5 86 547. 1 210.0 47 323. 9 124. 4 07 379.9 145.9 67 436. ; 167. 4 27 492.0 188.9 87 548. 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 i 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 1 125. 4 10 382. 7 146.9 70 438. 8 1 168. 4 30 494.8 189.9 90 550.8 551.8 211.4 351 327.7 125.8 411 383.7 147.3 471 439. 7 ! 168. 8 531 495. 7 190.3 591 211.8 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. 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 1170.2 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 1 447.2 171.7 39 503. 2 193. 2 99 559. 2 214.7 60 336.1 129.0 20 392.1 150.5 80 448. 1 t 172.0 40 504.1 193.5 600 560.1 215. Dist. Dep. Lat. Dist. Dep. Lat. Dist. j Dep. 1 Lat. Dist. Dep. Lat. Dist. Dep. Lat. 6 )9° (111°, 249°, 291° )• Page 410] TABLE 2. Difference of Latitude and Departure for 22° (158°, 202, 338°) . Dist. Lat. Dep. Dist. Lat. Dep. 22.9 Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 0.9 0.4 61 56.6 121 112.2 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 / 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 90 191 176.2 71.2 50 231.8 232.7 93.7 11 10.2 4.1 71 65.8 26.6 131 121.5 49.1 177.1 71.5 251 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 54 235.5 95.2 15 13.9 5.6 75 69.5 28.1 35 125.2 50.6 95 180.8 73.0 55 236.4 95.5 16 14.8 6.0 76 70.5 28.5 36 126.1 50.9 96 181.7 73.4 56 237.4 95.9 17 15.8 6.4 77 71.4 28.8 37 127.0 51.3 97 182.7 73.8 57 238.3 96.3 18 16.7 6.7 78 72.3 29.2 38 128.0 51.7 98 183.6 74.2 58 239.2 96.6 19 17.6 7.1 79 73.2 29.6 39 128.9 52.1 99 184. 5 74.5 59 240.1 97.0 20 18.5 7.5 80 74.2 30.0 40 129.8 52.4 200 185.4 74.9 60 241.1 242.0 97.4 21 19.5 7.9 81 75.1 30.3 141 130.7 52.8 201 186. 4 75.3 261 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 28.7 11.2 90 83.4 84.4 33.7 34.1 50 151 139. 1 1 56. 2 10 194.7 78.7 70 250.3 101.1 31 11.6 91 140. 56.6 211 195.6 79.0 271 251.3 101.5 32 29.7 12.0 92 85.3 34.5 52 140.9 56.9 12 196.6 79.4 72 252.2 101. 9' 33 30.6 12.4 93 86.2 34.8 53 141.9 57.3 13 197.5 79.8 73 253.1 102.3 34 31.5 12.7 94 87.2 35.2 54 142. 8 57.7 14 198.4 80.2 74 254.0 102.6 35 32.5 13.1 95 88.1 35.6 55 143.7 58.1 15 199.3 80.5 75 255.0 103.0 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 38.0 15.0 100 92.7 93.6 37.5 37.8 60 148.3 59.9 60.3 20 204.0 82.4 82.8 80 281 259.6 260.5 104.9 15.4 101 161 149.3 221 204.9 105.3 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 2or.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 41.2 70 157.6 63.7 30 213.3 86.2 90 268.9 108.6 19.1 111 102.9 41.6 271 158.5 64.1 231 214.2 86.5 291 269.8 109.0 52 48.2 19.5 12 103.8 42.0 72 159.5 64.4 32 215.1 86.9 92 270.7 109.4 53 49.1 19.9 13 104.8 42.3 73 160.4 64.8 33 216.0 87.3 93 271.7 109.8 54 50.1 20.2 14 105.7 42.7 74 161.3 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 1 163.2 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° (112°, 248°, 292°). TABLE 2. [Page 411 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. 301 279.1 112.7 361 334.7 135.2 421 390.3 157.7 481 446.0 180.2 541 501.6 202.7 02 280. 113.1 62 335. 6 135. 6 22 391.3 158.1 82 446.9 180.6 42 502.5 203.1 03 280.9 113.5 63 336.6 136.0 23 392.2 158.4 83 447.8 180.9 43 503.4 203.5 04 281.9 113.9 64 337.5 136. 3 24 393.1 158.8 84 448.8 181.3 44 504.4 203.8 05 282.8 114.2 65 338. 4 136.7 25 394.1 159. 2 85 449.7 181.7 45 505.3 204.2 06 283. 7 114.6 66 339.3 1.37. 1 26 395. 159.6 86 450.6 182.1 46 506. 2 204.6 07 284.6 115.0 67 340. 3 137.5 27 395.9 159. 9 87 451.6 182.4 47 507.2 205. 08 285.6 115. 4 68 341.2 137.8 28 396.8 160.3 88 452. 5 182.8 48 508. 1 205.3 09 286. 5 115.7 69 342.1 138.2 29 397.8 160.7 89 ! 453.4 183. 2 49 509.0 205. 7 10 287.4 116.1 70 343.1 138.6 30 398.7 161.1 90 454.3 183.6 50 551 510.0 206.1 206.5 311 288.4 116. 5 371 344.0 139.0 431 399.6 161.4 491 \ 455.3 184. 0' 510.9 12 289.3 116.8 72 344.9 139.3 32 400.5 161.8 92 456.2 184.3 52 511.8 206.8 13 290.2 117.2 73 345.8 139.7 33 401.5 162.2 93 457.1 184.7 53 512.7 207.2 14 291.1 117.6 74 346.8 140.1 34 402.4 162.6 94 458.0 185.1 54 513.6 207.6 15 292.1 118.0 75 347.7 140.5 35 403. 3 162.9 95 459.0 185.4 55 514.6 208.0 16 293.0 118.3 76 348.6 140.8 36 404.3 163. 3 96 459.9 185.8 56 515.5 208.3 17 293.9 118.7 77 349.5 141.2 37 405.2 163.7 97 460.8 186.2 57 516.4 208.7 18 294.8 119.1 78 350.5 141.6 38 406.1 164.1 98 461.8 186.6 58 517.4 209.1 19 295. 8 119.5 79 351. 4 141.9 39 407.0 164.4 99 462.7 186.9 59 518.3 209.4 20 296.7 119.8 80 352. 3 142.3 40 408.0 164.8 500 463.6 187.3 60 519.2 209.8 321 297.6 120.2 381 353.3 142.7 441 408.9 165.2 501 464.5 187.7 561 520.1 210.2 22 298.6 120.6 82 354.2 143.1 42 409.8 165.5 02 4a5.4 188.0 62 521.0 210.5 23 299.5 121.0 83 355. 1 143.4 43 410.7 165.9 03 466.4 188.4 63 522.0 210.9 24 300.4 121.3 84 356.0 143.8 44 411.7 166. 3 04 467.3 188.8 64 522.9 211.3 25 301.3 121.7 85 357.0 144.2 45 412.6 166.7 05 468.2 189.2 65 523.8 211.7 26 302.3 122.1 86 357. 9 144.6 46 413.6 167.0 06 469.2 189. 5 66 524.8 212.0 27 303.2 122.5 87 358.8 144.9 47 414. 5 167.4 07 470.1 189.9 67 525.7 212.4 28 304.1 122.8 88 359.7 145.3 48 415. 4 167.8 08 471.0 190. 3 68 526.6 212.8 29 305. 123.2 89 360.7 145. 7 49 ■ 416. 3 168.2 09 471.9 190.7 69 527.5 213.2 30 306. 123. 6 90 361.6 146.1 50 417.2 418.2 168.5 10 472.9 191.1 191. 4 70 571 528.5 213.5 331 306.9 124.0 391 362.5 146.4 451 168.9 511 473.8 529.4 213.9 32 307.8 124.3 92 363.5 146.8 52 419.1 169.3 12 474.7 191.8 72 530.3 214.3 33 308.8 124.7 93 364.4 147.2 53 420.0 169.7 . 13 475.6 192.2 73 531.2 214.7 34 309.7 125. 1 94 365. 3 147.6 54 420.9 170.0 14 476.6 192.5 74 532.2 215. 35 310.6 125.5 95 366.2 147.9 55 421.9 170.4 15 477.5 192.9 75 533.1 215. 4 36 311.5 125.8 96 367.2 148.3 56 422.8 170.8 16 478.4 193. 3 76 534.0 215.8 37 312. 5 126.2 97 368.1 148.7 57 423.7 171.2 17 479.3 193. 7 77 534. 9 216.2 38 313.4 126.6 98 369.0 149.1 58 424.6 171.5 18 480.3 194.0 78 535. 9 216. 5 39 314.3 127.0 99 369.9 149.4 59 425. 6 171.9 19 481.2 194.4 79 536. 8 216.9 40 341 315. 2 127.3 400 370.9 149.8 60 426.5 427.4 172.3 20 482.1 194.8 195.2 80 581 537. 7 538.6 217.3 316.2 127.7 401 371.8 150.2 461 172.7 521 483.0 217.7 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 83 540.5 218.4 44 319.0 128.8 04 374.6 151.3 64 430.2 173.8 24 485.8 196.3 84 541.4 218.8 45 319.9 129.2 05 375.5 151.7 65 431.1 174.2 25 486.7 196.7 85 542.4 219.2 46 320. 8 129.6 06 376. 4 152.1 66- 432.1 174. 5 26 487.7 197.0 86 543.3 219. 5 47 321. 7 130.0 07 377.4 152. 4 67 433.0 174.9 27 488.6 197.4 87 544. 2 219.9 48 322.7 130.3 08 378. 3 152.8 68 433. 9 175. 3 28 489.5 197.8 88 545.1 220. 3 49 323.6 130.7 09 379.2 153.2 69 434.8 175.7 29 490.4 198.2 89 546.1 220.7 50 324.5 131. 1 10 380.1 381. i 153.6 153.9 70 471 435.8 436.7 176.0 176. 4 30 531 491.4 492.3 198.5 90 547.0 221.0 351 325. 4 131.5 411 198.9 591 547.9 221.4 52 326.4 131.8 12 382.0 154.3 72 437.6 176.8 32 493.2 199.3 92 548. 9 221.8 53 327.3 132.2 13 382.9 154.7 73 438.6 177.2 33 494.2 199.7 93 549.8 222.2 54 328.2 132.6 14 383. 9 155. 1 74 439.5 177.5 34 495.1 200.0 94 550.7 222. 5 55 329.2 133.0 15 384.8 155.4 75 440.4 177.9 35 496.0 200.4 95 551. 7 222.9 56 330.1 133.3 16 385.7 155.8 76 441.3 178.3 36 496.9 200.8 96 552.6 223.3 57 331.0 133.7 17 386.6 156.2 77 442.3 178.7 37 497.9 201.2 97 553.5 223.7 58 332.0 134.1 18 387. 6 156.6 78 443.2 179. 38 498.8 201.5 98 554.4 224.0 59 332.9 134.5 19 388.5 156.9 79 444.1 179.4 39 499.7 201.9 99 555. 4 224.4 60 333.8 134.8 20 389.4 157.3 80 445.0 179.8 40 500.7 202. 3 600 556.3 224.8 Dlst. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. € 8° (112°, 248°, 292° ). Page 412] TABLE L>. Difference of I-atitude 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 2S.8 121 111.4 47.3 181 166.6 70.7 241 221.8 94.2 2 1.8 0.8 62 57.1 24.2 22 112.3 47.7 82 167. 5 71.1 42 222.8 94.6 3 2.8 1.2 63 58.0 24.6 23 113. 2 48.1 83 168.5 71.5 43 223.7 94.9 4 3.7 1.6 64 58.9 25.0 24 114.1 48.5 84 169.4 71.9 44 224.6 95.3 5 4.6 2.0 65 59. 8 25. 4 25 115.1 48.8 85 170.3 72.3 45 225.5 95.7 6 5.5 2.3 1? 60. 8 25. 8 26 116.0 49.2 86 171.2 72.7 46 226.4 96.1 7 6.4 2.7 61. 7 26. 2 27 116.9 49.6 •87 172.1 73.1 47 227.4 96.5 8 7.4 3.1 68 62.6 : 26.6 28 ! 117.8 50.0 88 173.1 73.5 48 228.3 96.9 9 8.3 3.5 69 63.5 27.0 29 118. 7 50.4 89 174.0 73.8 49 229.2 97.3 10 11 9.2 3.9 70 64.4 65.4 27.4 27.7 30 119. 7 50.8 51.2 90 191 174.9 175.8 74.2 50 251 230.1 231.0 97.7 98.1 10.1 4.3 71 131 120.6 74.6 12 11.0 4.7 72 66. 3 i 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 1 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 i 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 i 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 1 77.8 59 238.4 101.2 20 21 18.4 7.8 80 81 73.6 31.3 31.6 40 141 128.9 129.8 54.7 55.1 200 201 184.1 78.1 60 239.3 240.3 101.6 19.3 8.2 74.6 185.0 78.5 261 102.0 22 20.3 8.6 ■ 82 75.5 1 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 1 32.8 44 132.6 56.3 04 187. 8 1 79.7 64 243.0 103. 2 25 23.0 9.8 85 78.2 1 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. 47 135.3 57.4 07 190.5 80.9 67 245. 8 104.3 28 25.8 10.9 88 81.0 i 34.4 48 136.2 57.8 08 191.5 81.3 68 246.7 104.7 29 26.7 11.3 89 81.9 ; 34.8 49 137. 2 58.2 09 192.4 81.7 69 247.6 105. 1 30 31 27.6 28.5 11.7 90 82.8 1 35.2 50 138.1 139.0 58.6 59.0 10 211 193.3 194.2 82.1 82.4 70 271 248.0 249. 5 105. 5 f05. 9 12.1 91 83.8 ' 35.6 151 32 29.5 12.5 92 84. 7 1 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 i 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 1 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 j 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 1 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. 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 93.0 39.5 60 147.3 62.5 20 221 202.5 86.0 80 257.7 258.7 109.4 41 37.7 16.0 101 161 j 148.2 62.9 203.4 86.4 281 109.8 42 38.7 16.4 02 93.9 1 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. 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 &4.9 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 2a5. 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 51 46.0 I 46.9 1 19.5 19.9 10 111 101. 3 43. 70 156.5 66.4 30 211.7 212.6 89.9 90.3 90 291 266. 9 267. 9 113.3 113. 7 102.2 43.4 171 157. 4 66.8 231 52 47.9 1 :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 4o.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 1 162.9 69.2 37 218.2 92.6 97 273.4 116.0 58 53.4 22.7 18 108.6 46.1 78 i 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°, 247^, 293°). TABLE 2. [Page 413 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 65 336.0 142.6 25 391.2 166.1 85 446.4 189.5 45 501.7 213.0 06 281.7 119. 6 66 336. 9 143.0 26 392.1 166.5 86 447.3 189.9 46 502. 6 213. 4 07 282.6 120.0 67 337.8 143.4 27 393.1 166.8 87 448. 3 190.2 47 503. 5 213. 8 08 283. 5 120.4 68 338.7 143.8 28 394.0 167.2 88 449. 2 : 190. 6 48 504.4 214.2 09 284.4 120.8 69 339. 7 144.2 29 .394. 9 167.6 89 450. 1 191. 49 505. 3 214.6 10 311 285. 4 121.2 70 371 340.6 341. 5 144.6 14.5. 30 431 395.8 396.7 168.0 90 451.0 191.4 191.8 50 506.3 507.2 215.0 215.3 286.3 121.6 168.4 491 451. 9 551 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. 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 15 290.0 123.1 75 345.2 146.5 35 400.4 170.0 95 455. 6 193.4 55 510. 9 216. S 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. 147.3 37 402.3 170.8 ■ 97 457. 5 194.2 Oi 512. 7 217.6 18 292.7 124.3 78 348.0 147.7 38 403. 2 171.1 98 458.4 194.6 58 513. 6 218.0 19 293.6 124.6 79 348. 9 148.1 39 404.1 171. 5 99 459. 3 195. 59 514. 5 218.4 20 294.6 295.5 125. 80 349. 8 148. 5 40 405. 171.9 500 460.2 461.2 195.4 60 515. 5 516.4 218. 8 219.2" 321 125.4 381 350.7 148.9 441 405.9 172.3 501 195.8 561 22 296.4 125.8 82 351.6 149.3 42 406.9 172.7 02 462.1 196.2 62 517.3 219.6 23 297.3 126.2 83 352.6 149.7 43 407.8 173.1 03 463.0 196.6 63 518. 2 220.0 24 298.2 126.6 84 353.5 150.0 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 1 356.2 151.2 47 411.5 174.7 07 466.7 198.1 67 521.9 221.6 28 301.9 128.2 88 1 357.2 151.6 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 1.52. 4 50 414.2 415.2 175.8 10 469.5 199.3 70 524. 7 222.7 223. 1 331 304.7 129.3 391 359. 9 152.8 451 176.2 511 1 470.4 199.7 571 525. 6 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. 37 310.2 131.7 97 365.4 155. 1 57 420.7 178.6 17 i 475.9 202. 77 531.1 225. 4 38 311.1 132.1 98 366.4 155. 5 58 421.6 179.0 18 476.8 202.4 78 532.0 225. 8 39 312.1 132.5 99 367.3 155. 9 59 422. 5 179.4 19 477. 7 202.8 79 533. 226.2 40 341 313.0 132.9 400 j 368.2 156. 3 60 423.4 424.4 179.7 20 ' 478.6 521 , 479.6 203.2 203.6 80 533.9 226.6 313.9 133.2 401 369.1 156. 7 461 180.1 581 534.8 227.0 42 314.8 133.6 02 370.0 157. 1 62 425. 3 180.5 22 1 480. 5 204.0 82 535. 7 227.4 43 315. 7 134.0 03 371.0 157.5 63 426.2 180.9 23 i 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 1 482.3 204.8 84 537.6 228.2 45 317.6 134.8 05 372.8 158. 3 65 428.0 181.7 25 1 483.2 205. 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. 67 429. 9 182.5 27 i 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 50 322.2 136.8 137.2 10 377.4 378.3 160. 2 160.6 70 471 432.6 433. 6 183.7 184.0 30 531 487.8 488.8 207.1 207. 4 90 591 543. 1 .544. 230. 6 231.0 351 323.1 411 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. 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 4.39. 1 186.4 37 494.3 209.8 97 549. 5 233.2 58 329.5 139.9 18 384.8 163. 3 78 440.0 186.8 38 495. 2 210.2 98 550. 4 233. 6 59 330.5 140.3 19 385.7 163. 7 79 440. 9 187.2 39 496.1 210.6 99 .551.3 234. 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. ( )7°(11 3°, 247°, 293°). Page 414] TABLE 2. Difference of Latitude and Departure for 24' (156 =,204°, 336°). Dlst. 1 Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 49.2 Dist. Lat. Dep. Dist. Lat. Dep. 0.9 0.4 61 55.7 24.8 121 110.5 181 165.4 73.6 241 220.2 98.0 2 1.8 0.8 62 56.6 25.2 22 111.5 49.6 82 166. 3 74.0 42 221. 1 98.4 3 2.7 1.2 63 57.6 25.6 23 112.4 50.0 83 167.2 74.4 43 222.0 98.8 4 3.7 1.6 64 58.5 26.0 24 113.3 50.4 84 168.1 74.8 44 222.9 99.2 5 4.6 2.0 65 59.4 26.4 25 114.2 50.8 85 169.0 76.2 45 223.8 99.7 6 5.5 2.4 i6 60.3 26.8 26 115.1 51.2 86 169.9 76.7 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 47 226. 6 100.5 8 7.3 3.3 68 62.1 27.7 28 116.9 52.1 88 171.7 76.6 48 226. 6 1(X).9 9 8.2 3.7 69 63.0 28.1 29 117.8 52.5 89 172.7 76.9 49 227. 6 101.3 10 11 9.1 4.1 4.5' 70 71 63.9 64.9 28.5 28. 9 30 131 118.8 119.7 52.9 53.3 90 173.6 174.5 77.3 "77.7 60 228.4 101.7 102.1 10.0 191 251 229. 3 12 11.0 4.9 72 65.8 29.3 32 120.6 53.7 92 175.4 78.1 62 230.2 102.6 13 11.9 5.3 73 66.7 29.7 33 121.5 54.1 93 176.3 78.5 63 231.1 102.9 14 12.8 5.7 74 67.6 30.1 34 122.4 54.5 94 177.2 78.9 64 232.0 103. 3 15 13.7 6.1 75 68.5 30.5 35 123.3 54.9 95 178.1 79.3 56 233. 103. 7 16 14.6 6.5 76 69.4 30.9 36 124.2 55.3 96 179.1 79.7 66 233.9 104.1 17 15.5 6.9 77 70.3 31.3 37 125.2 55. 7 97 180.0 80.1 67 234.8 104.5 . 18 16.4 7.3 78 71.3 31.7 38 126.1 56.1 98 180.9 80.5 68 235. 7 104. 9 19 17.4 7.7 79 72.2 32.1 39 127.0 56.5 99 181.8 80.9 69 236. 6 105. 3 20 21 18.3 19.2 8.1 8.5' 80 81 73.1 74.0 32.5 32.9 40 141 127.9 56.9 57.3 200 201 182.7 183.6 81.3 60 261 237.6 105.8 106. 2 128.8 81.8 238.4 22 20.1 8.9 82 74.9 33.4 42 129.7 57.8 02 184.5 82.2 62 239.3 106.6 23 21.0 9.4 83 75.8 33.8 43 130.6 58.2 03 185.4 82.6 63 240.3 107.0 24 21.9 9.8 84 76.7 34.2 44 131.6 58.6 04 186.4 83.0 64 241.2 107.4 25 22.8 10.2 85 77.7 34.6 45 132.5 69.0 05 187.3 83.4 66 212.1 107.8 26 23.8 10.6 86 78.6 35.0 46 133.4 59.4 06 188.2 83.8 66 243.0 108.2 27 24.7 11.0 87 79.5 35.4 47 134.3 59.8 07 189.1 84.2 67 243.9 108. 6 28 25.6 11.4 88 80.4 35.8 48 135. 2 60.2 08 190.0 84.6 68 244.8 109.0 29 26.5 11.8 89 81.3 36.2 49 136.1 60.6 09 190. 9 85.0 69 246.7 109.4 30 27.4 28.3 12.2 12.6 90 82.2 36.6 37.0 50 137.0 61.0 10 191.8 192.8 86.4 85.8 70 246.7 109.8 110.2 31 91 83.1 151 137.9 61.4 211 271 247.6 32 29.2 13.0 92 84.0 37.4 52 138.9 1 61.8 12 193.7 86.2 72 248.5 110.6 33 30.1 13.4 93 85.0 37.8 53 139.8 ! 62.2 13 194.6 86.6 73 249.4 111.0 34 31.1 13.8 94 85.9 38.2 54 140.7 i 62.6 14 195.6 87.0 74 260.3 111.4 35 32.0 14.2 95 86.8 38.6 55 141.6 , 63.0 15 196.4 87.4 76 261.2 111.9 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 78 264.0 113.1 39 35.6 15.9 99 90.4 40.3 59 145. 3 I 64. 7 19 200.1 89.1 79 254.9 113.6 40 36.5 37.5 16.3 100 91.4 92.3 40.7 60 146.2 147.1 65.1 20 201.0 201.9 89.5 80 281 265.8 256.7 113.9 "114. 3 41 16.7 101 41.1 161 65.5 221 89.9 42 38.4 17.1 02 93.2 41.5 62 148.0 ! 65.9 22 202.8 90.3 82 267.6 114.7 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 25 206.5 91.5 85 260.4 116.9 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 10 111 100. 5 101.4 44.7 45. 1' 70 155.3 69.1 69. 6 30 210.1 211.0 93.6 90 291 264.9 118.0 51 46.6 20.7 171 156.2 231 94.0 265.8 118.4 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 64 49.3 22.0 14 104.1 46.4 74 159.0 70.8 34 213.8 96.2 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 96 269.6 120.0 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 37 216.6 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 415 | Difference of Latitude and Departure for 24° (156°, 204 °, 336° )• Dlst. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 275.0 122.4 361 329.8 146.8 421 384. 6 171.2 481 439.4 195.6 541 494.2 220.0 02 275.9 122.8 62 330. 7 I 147. 2 22 385.5 171.6 82 440.3 196.0 42 495.1 220.4 03 276.8 123.2 63 331.6 147.6 23 386.4 172.1 83 441.2 196.5 43 496.0 220.9 04 277.7 123.7 64 332.5 148.1 24 387.3 172.5 84 442.1 196.9 44 496.9 . 221.3 05 278.6 124.1 65 333.4 148.5 25 388.2 172.9 85 443.0 197.3 45 497.8 221.7 06 279.5 124.5 66 334.3 148.9 26 389. 2 173.3 86 444.0 197.7 46 498.8 222.1 07 280.4 124.9 67 335. 3 149.3 27 390.1 173.7 87 444.9 198.1 47 499.7 222.5 08 281.4 125.3 68 336.2 149.7 28 391.0 174.1 88 445.8 198.5 48 500.6 222.9 09 282.3 125.7 69 337.1 150.1 29 391.9 174.5 89 446.7 198.9 49 501.5 223.3 10 283.2 126.1 70 338.0 150.5 30 392.8 174.9 90 447.6 199.3 50 502.4 223.7 311 284.1 126.5 371 338.9 m).9 431 393.7 175.3 491 448.6 199.7 551 503. 4 224.1 12 285.0 126.9 72 339.8 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. 59 510.6 227.4 20 292.3 293.2 130.2 130.6 80 381 347.1 348. i 154.6 155.0 40 441 402.0 179.0 500 456.8 203.4 60 511.6 512. 5 227.8 321 402.9 179.4 501 457.7 203.8 561 228.2 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 83 349. 9 155.8 43 404.7 180.2 03 459.5 204.6 63 514.3 229.0 24 296.0 131.8 84 350. 8 156. 2 44 405.6 180.6 04 460.4 205.0 64 515.2 229.4 25 296.9 132. 2 85 351.7 156:6 45 406.5 181.0 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. 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 30 301.5 302.4 134.2 90 356. 3 158.6 50 411.1 183.0 10 465.9 207.4 70 "571 520.7 521.6 231.8 232.2 331 134.6 391 357.2 159.0 451 412.0 183. 4 511 466.8 207.8 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. 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 40 341 310.6 138.3 400 365.4 366.3 162.7 60 420.2 187.1 20 475.0 475.9 211.5 80 529.8 235.9 236.3 311.5 138.7 401 163.1 461 421.1 187.5 521 211.9 581 530.8 42 312.4 139.1 02 367.2 163.5 62 422.0 187.9 22 476.8 212.3 82 531.7 236.7 43 313.3 139.5 03 i 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 1 369. 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 i 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 i 373.6 166.4 69 428.4 190.8 29 483.2 215. 2 89 538.0 239.6 50 319.7 142.4 10 ! 374. 5 166.8 167.2 70 429.4 191.2 30 484.2 485. 1 215. 6 90 539.0 539. 9 240.0 351 320.6 142.8 411 ! 375.5 471 430. 3 191.6 531 216.0 591 240.4 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. 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. 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. Dlst. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. ( 56° (114°, 246 °, 294° ). Page 416] TABLE 2. Difference of Latitude and Departure for 25° (155°, 205 °, 335° ). Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 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 «6 59.8 27.9 26 114.2 53.2 86 168.6 78.6 46 223. 104.0 7 6.3 3.0 67 60.7 28.3 27 115.1 53.7 87 169. 5 79.0 47 223.9 104.4 8 7.3 3.4 68 61.6 28.7 28 116.0 54.1 88 170.4 79.5 48 224.8 104.8 9 8.2 3.8 69 62.5 29.2 29 116.9 54.5 89 171.3 79.9 49 225.7 105.2 10 9.1 10.0 4.2 70 63.4 29.6 30.0 30 131 117.8 54.9 90 172.2 80.3 50 226.6 105.7 106.1 11 4.6 71 64.3 118.7 55.4 191 173.1 80.7 251 227.5 12 10.9 5.1 72 65.3 30.4 32 119.6 55.8 92 ^74.0 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 17^.8 82.0 54 230.2 107. 3 15 13.6 6.3 75 68.0 31.7 35 122.4 57.1 95 176.7 82.4 55 231.1 107.8 16 14.5 6.8 76 68.9 32.1 36 123.3 57.5 96 177.6 82.8 56 232.0 108.2 17 15.4 7.2 77 69.8 32.5 37 124.2 57.9 97 178.5 83.3 57 232.9 108.6 18 16.3 7.6 78 70.7 33.0 38 125.1 58.3 98 179.4 83.7 58 233.8 109.0 19 17.2 8.0 79 71.6 33.4 39 126.0 58.7 99 180.4 84.1 59 234.7 109.5 20 18.1 19.0 8.5 80 72.5 73.4 33.8 34.2 40 126.9 59.2 59.6 200 201 181.3 182. 2" 84.5 84.9 60 261 235.6 236.5 109.9 110.3 21 8.9 81 141 127.8 22 19.9 9.3 82 74.3 34.7 42 128.7 60.0 02 183.1 85.4 62 237.5 110.7 23 20.8 9.7 83 75.2 35.1 43 129.6 60.4 03 184.0 85.8 63 238.4 111.1 24 21.8 10.1 84 76.1 35.5 44 130.5 60.9 04 184.9 86.2 64 239.3 111.6 25 22.7 10.6 85 77.0 35.9 45 131.4 61.3 05 185.8 86.6 65 240.2 112.0 26- 23.6 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 ^38. 5 50 135.9 136.9 63.4 10 190. 3 88.7 70 271 244.7 114.1 31 28.1 13.1 91 82.5 151 63.8 211 191.2 89.2 245.6 114.5 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 35 31.7 14.8 95 86.1 40.1 55 140.5 65.5 15 194.9 90.9 75 249.2 116.2 36 32.6 15.2 96 87.0 40.6 56 141.4 65.9 16 195.8 91.3 76 250.1 116.6 37 33.5 15.6 97 87.9 41.0 57 142. 3 66.4 17 196.7 91.7 77 251.0 117.1 38 34.4 16.1 98 88.8 41.4 58 143.2 66.8 18 197.6 92.1 78 252.0 117.5 39 35.3 16.5 99 89.7 41.8 59 144.1 67.2 19 198.5 92.6 79 252.9 117.9 40 36.3 16.9 17.3 100 101 90.6 91.5 42.3 42.7 60 161 145.0 67.6 20 221 199.4 200.3^ 93.0 80 253.8 118.3 118.8 41 37.2 145.9 6870 93.4 281 254.7 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 i 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 1 205.7 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 10 111 99.7 100.6 46.5 46. 9 70 171 154.1 155.0 71.8 30 208.5 209.4 97.2 97.6" 90 262.8 263.7 122.6 123.0 51 46.2 21.6 72.3 231 291 52 47.1 22.0 12 101.5 47.3 72 155.9 72.7 32 210.3 98.0 92 264. 6 123.4 53 48.0 22.4 13 102.4 47.8 73 156. 8 73.1 33 211.2 98.5 93 265.5 123. 8 54 48.9 22.8 14 103.3 48.2 74 157. 7 73.5 34 212.1 98.9 94 266.5 124.2 55 49.8 23.2 15 104.2 48.6 75 158.6 74.0 35 213.0 99.3 95 267.4 124.7 56 50.8 23. 7 16 105.1 49.0 76 159.5 74.4 36 213.9 99.7 96 268.3 125.1 57 51.7 24.1 17 106.0 49.4 77 160.4 74.8 37 214. 8 100. 2 97 269.2 125. 5 58 52.6 24.5 18 106.9 49.9 78 161.3 75.2 38 215. 7 100.6 98 270.1 125. 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 Dlst. Dep. Lat. Dist. Dep. Lat. Dlst. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 65° (1 15°, 245°, 295°). TABLE 2. [Page 417 Difference of Latitude and Departure for 25° (155°, 205 ^ 335° )• Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 272.8 127.2 361 327. 1 152.5 421 381.5 177.9 481 435.9 203.3 541 490.3 228.6 02 273.7 127.6 62 328.0 153. 22 382.4 178.3 82 436.8 203.7 42 491.2 229.0 03 274.6 128.0 63 329. 153. 4 23 383. 3 178.7 83 437.7 204.1 43 492.1 229.4 04 275. 5 128.4 64 329. 9 153. 8 24 384.2 179.2 84 438.6 204. 5 44 493.0 229.9 05 276. 4 128.9 65 330. 8 1.54.2 25 385. 1 179.6 85 439. 5 204.9 45 493.9 230.3 06 277.3 129. 3 66 331. 7 154.6 26 386.0 180.0 86 440.4 205. 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 10 280.9 131.0 131.4 70 335. 3 156.3 30 389.7 181.7 90 491 444.0 207.1 50 551 498.4 232.4 311 281.8 371 336. 2 156. 8 431 390.6 182.1 444.9 207. 5 499.3 232.8 12 282.7 131.8 72 337. 1 157.2 32 391.5 182.5 92 445.9 207.9 52 500.2 233. 2 13 283.6 132. 2 73 338. 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 55 503.0 234.5 16 286.4 133. 5 76 340. 7 158.9 36 395.1 184.2 96 449.5 209.6 56 503. 9 235.0 17 287.3 133.9 77 341. 6 159. 3 37 396.0 184.7 97 450.4 210.0 57 504.8 235.4 18 288.2 134.4 78 342. 5 159.7 38 396. 9 185. 1 98 451.3 210.4 58 505.7 235.8 19 289.1 134.8 79 343. 5 160. 1 39 397. 8 185.5 99 452.2 210.9 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 60 507. 5 236.6 321 290.9 135. 6 381 34573 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 02 454.9 212.1 62 509.3 237. 5 23 292.7 136.5 83 347.1 161.8 43 401.5 187.2 03 455.8 212.5 63 510.2 237.9 24 293.6 136.9 84 348. 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 05 457.7 213.4 65 512.0 238.7 26 295.4 137.7 86 349. 8 163. 1 46 404. 2 i 188. 5 06 458.6 213.8 66 512.9 239.2 27 296.3 138.2 87 350. 7 163.5 47 405.1 '188.9 07 459.5 214.2 67 513.8 239.6 28 297.2 138.6 88 351.6 163.9 48 406. i 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 i 189. 7 09 461.3 215.1 69 515. 7 > 240.5 30 331 299.0 300. 139.4 139. 9 90 391 353.4 354. 3 164.8 50 407.8 190.1 10 462.2 215.5 215. 9 70 571 516.6 517.5 240.9 165.2 451^ 408.7 190.6 511 463.1 241.3 32 300.9 140. 3 92 355. 2 165. 6 52 409.6 191.0 12 464.0 216.4 72 518.4 241.7 33 301.8 140.7 93 356.1 166.1 53 410.5 191.4 13 464.9 216.8 73 519.3 242.1 34 302.7 141.1 94 357. 166.5 54 411.4 191.8 14 465.8 217.2 74 520. 2 242.6 35 303.6 141.5 95 358.0 166.9 55 412.3 192.3 15 466.7 217.7 75 521. 1 243.0 36 304.5 142. 96 358.9 167.3 56 413. 2 192.7 16 467.6 218.1 76 522.0 243.4 37 305.4 142.4 97 359. 8 167.7 57 414.1 193.1 17 468.5 218.5 77 522. 9 243. 8 38 306. 3 142.8 98 360.7 168.2 58 415.1 193.5 18 469.4 218.9 78 523. 8 244.3 39 307. 2 143.2 99 361.6 168.6 59 416.0 194.0 19 470.3 219.3 79 524.7 244.7 40 341 308.1 309.0 143.7 144. 1 400 362.5 169.0 169.4 60 I 416.9 194.4 20 471.2 219.8 220.2 80 581 525. 6 526. 5 245.1 245. 5 401 363.4 461 417.8 194.8 521 472.2 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. 171.1 65 421.4 196.5 25 475. 8 221.9 85 530. 2 247.2 46 313.5 146.2 06 367.9 171.6 66 422. 3 196.9 26 476.7 222.3 86 531.1 247.7 47 314.5 146.6 07 368.8 172.0 67 423.2 197.3 27 477.6 222.7 87 532.0 248.1 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 5.33. 8 248.9 50 317.2 318.1 147.9 148.3 10 411 371.5 372.5 173.2 173.7 70 471 425.9 426.8 198.6 199.0 30 531 480.3 481.2 224.0 224. 4 90 534.7 249.4 249.8 351 591 535. 6 52 319.0 148.7 12 373. 4 174.1 72 427.7 199.4 32 482.1 224.8 92 536. 5 250. 2 53 319.9 149.2 13 374.3 174.5 73 428.6 199.9 33 483.0 225. 3 93 537. 4 250. 6 54 320.8 149.6 14 375.2 174.9 74 429.6 200. 3 34 483.9 225.7 94 538.3 251. 1 55 321.7 150.0 15 376.1 175.4 75 430.5 200.7 35 484.8 226.1 95 539.2 251. 5 56 322.6 150.4 16 .377. 175.8 76 431.4 201.1 36 485.7 226.5 96 540.1 251. 9 57 323.5 150.8 17 377.9 176.2 77 432.3 201.6 37 486.7 226.9 97 541.0 252.3 58 324.4 151.3 18 378. 8 176. 6 78 433.2 202.0 38 487. 6 227.4 98 541.9 252.7 59 1 325.3 151. 7 19 379. 7 177.0 79 434. 1 202.4 39 488. 5 227.8 99 542.8 253. 1 60 326.2 152.1 20 380.6 177.5 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° (115°, 245°, 295° )• 22489—03- -2V Page 418] TABLE 2. Difference of Latitude and Departure for 26° (154°, 206°, 334 '). Dist. Lat. Dep. Di.st. Lat. Dep. Dist. Lat. Dep. Dist. 181 Lat. Dep. Dist. 241 Lat. Dep. 1 0.9 0.4 61 54.8 26.7 121 108.8 53.0 162.7 79.3 216.6 105.6 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 %5 58.4 28.5 25 112.3 54.8 85 166.3 81.1 45 220.2 107.4 6 5.4 2.6 66 59. 3 28.9 26 113.2 55.2 86 167.2 81.5 46 221.1 107.8 7 6.3 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 4.4 70 62.9 30.7 30 116.8 57.0 90 170.8 83.3 50 224.7 109. 6 9.9 4.8 71 63.8 31.1 131 , 117.7 57.4 191 171.7' 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 57 231.0 112.7 18 16.2 7.9 78 70.1 34.2 38 124.0 60.5 98 178.0 86.8 58 231.9 113.1 19 17.1 8.3 79 71.0 34.6 39 124.9 60.9 99 178.9 87.2 59 232.8 113.5 20 21 18.0 18.y~ 8.8 9.2 _80 81 71.9 35.1 40 125.8 126. 7 61.4 200 179.8 87.7 60 233.7 114.0 72.8 35.5 141 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 i 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 i 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 I 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 2p.2 12.3 88 79.1 38.6 48 133.0 64.9 08 186. 9 91.2 68 i 240.9 117.5 29 26.1 12.7 89 80.0 39.0 49 133.9 65.3 09 i 187.8 91.6 69 241.8 117.9 30 27.0 27.9 13.2 90 80.9 39.5 50 134.8 65.8 10 1 188.7 92.1 70 242.7 243.6 118.4 118.8 31 13.6 91 81.8 39.9 151 135.7 66.2 211 189.6 92.5 271 32 28.8 14.0 92 82.7 40.3 52 136.6 66.6 12 190.5 92.9 72 244.5 119.2 33 29.7 14.5 93 83.6 40.8 53 137.5 67.1 13 191.4 93.4 73 245.4 119.7 34 30.6 14.9 94 84.5 41.2 54 138.4 67.5 14 192.3 93.8 74 246.3 120. 1 35 31.5 15.3 95 85.4 41.6 55 139.3 67.9 15 193.2 94.2 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 41 36.0 36.9 17.5 100 101 89.9 90.8^ 43.8 60 143.8 144. 7 70.1 20 197.7 96.4 80 251.7 252. 6 122.7 123.2 18.0 44.3 161 70.6 221 198.6 96.9 281 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. 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 45.8 21.9 22.4' 10 98.9 48.2 70 152.8 74.5 30 206. 7 100.8 90 260.7 127.1 111 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 1 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. 1 Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. ( 34° (116°, 244°, 296° )• TABLE ± [Page 419 | Difference of Latitude and Departure for 26° (154°, 206°, 334). Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 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. 238. 04 273.2 133. 3 64 327. 2 1.59. 6 24 381.1 185. 9 84 435. 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 2li!6 45 489.8 238. 9 ^06 275. 1.34. 1 66 329. 160.4 26 382. 9 186.7 86 436.8 213. 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 4.39. 5 214.4 49 493.4 240. 7 10 278.6 135. 9 136. 3 70 -37r 332. 6 162.2 30 431 386. 5 387.4 188. 5 188.9 90 491 440.4 441. 3 214.8 215.2 50 494.3 241.1 311 279.5 333.5 162.6 551 495.2 241. 5 12 280.4 136.8 72 334.4 163.1 32 388.3 189.4 92 442.2 215.7 52 496.1 242.0 13 281. 3 137.2 73 335.3 163.5 33 389.2 189.8 93 443. 1 216.1 53 497. 242.4 14 282.2 137. 7 74 336.2 164.0 34 390.1 190.3 94 444.0 216.6 54 497.9 242.9 15 283.1 138.1 75 337.1 164.4 35 391.0 190.7 95 444.9 217.0 55 498. 8 243. 3 16 284.0 138.5 76 338.0 164.8 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 20 321 287.6 288. 5 140.3 80 341.5 166.6 40 441 395.5 396.4 192.9 500 449.4 219.2 60 503.3 504.2 245.5 245.9 140.7 381 342.4 167. 193. 3 501 450. 3 219. 6 561 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 65 507. 8 247.7 26 293.0 142.9 86 346.9 169.2 46 400.9 195.5 06 454.8 221.8 • 66 508. 7 248. 1 27 293. 9 143. 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 30 331 296.6 297. 5 144.7 145. 1 90 391 350. 5 171.0 50 451 404.5 405.4 197.3 197.7 10 458.4 223.6 70 512.3 249.9 351.4 171.4 511 459.3 224.0 571 513.2 250.3 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. 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 40 305.6 306.5 149.0 149. 5 400 401 359.5 175.4 60 413.5 201.7 202.1 20 521 467.4 468.3 228.0 228.4 80 521.3 254. 3 341 360. 4 175.8 461 414.4 581 522.2 254.7 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. 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 70 422.4 206.0 206.5 30 476.4 232. 3 90 530.3 258.6 259. 1 351 153.9 411 369.4 180.2 471 423.3 531 477.3 232. 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 I 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 1 426.9 208.2 35 480.9 234.5 95 534.8 260.8 56 320. 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. Dlst. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 64° (116°, 244°, 296°). Page 420 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 i 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 %S 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 5.0 70 62.4 31.8 30 115.8 116. 7 59.0 59.5 90 169.3 170. 2 86.3 86.7 50 251 222.8 223.6 113.5 11 9.8 71 63.3 32.2 131 191 114.0 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. 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 1^2.1 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 1%.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 j 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 i 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 1«5.3 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 10 187.1 188.0 95.3 70 240.6 241. 5 122.6 31 27.6 14.1 91 81.1 41.3 151 134.5 68.6 211 95.8' 271 123.0 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 16.3 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 60 142.6 143.5 72.6 20 196.0 196.9 99.9 80 249.5 250.4 127.1 127.6 41 36.5 18.6 101 90.0 45.9 161 73. 1 221 100.3 281 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 10 111 98.0 49.9 70 151.5 152. 4 77.2 77.6 30 204.9 104.4 90 258.4 131.7 51 45.4 23.2 98.9 50.4 171 231 205.8 104.9 291 259.3 132.1 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. 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 i 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 421 Difference of Latitude and Departure for 27° (153°, 207°, 333°). Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 268.2 136.7 361 321.7 163.9 421 375. 1 191.1 481 428.6 218.3 541 482.0 245.6 02 269.1 137.1 62 322.5 164.4 22 376.0 191.6 82 429.4 218.8 42 482.9 246.1 03 270.0 137. 6 63 323.4 164.8 23 376.9 192.0 83 430.3 219.2 43 483.8 246.5 04 270.9 138. 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 10 311 276.2 277. 1 140.7 141.2 70 329.7 330.6 168.0 30 431 383.1 384.0 195.2 90 436.6 222.4 222. 9 50 551 490.0 249.7 371 168.4 195.7 491 437.5 490.9 250.1 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 j 197.0 94 440.1 224.2 54 493.6 251.5 15 280.7 143. 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 20 321 285.1 286.0 145.3 80 338.6 172.5 173.0^ 40 441 392.0 199.8 392.9 200.2 500 501 445.5 446. 4 227.0 227.5 60 561 499.0 499.8 254.2 145. 7 381 339. 5 254.7 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 30 294.0 294.9 149.8 150. 3 90 391 347. 5 348.4 177.1 177.5 50 451 401.0 401.8 204.3 204.7 10 511 454.4 455.3 231.5 70 507.9 258.8 259.2 331 231.9 571 508.7 32 295. 8 150.7 92 349. 3 178.0 52 402.7 205. 2 12 456.2 232.4 72 509.6 259.7 33 296.7 151.2 93 350.2 178.4 53 403.6 205. 7 13 457.1 232.9 73 510.5 260.1 34 297.6 151.6 94 351.1 178.9 54 404.5 206.1 14 458.0 233.3 74 511.4 260.6 35 298.5 152.1 95 352. 179.3 55 405.4 206.6 15 458.8 233.8 75 512.3 261.1 36 299.4 152. 5 96 352.8 179.8 56 406.3 207.0 16 459.7 234.2 76 513.2 261.5 37 300.3 153.0 97 353. 7 180.2 57 407.2 207.5 17 460.6 234.7 77 514.1 262.0 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 40 341 302.9 154.4 154. 8 400 401 356.4 357.3 181.6 182.1 60 461 409.9 410.8 208.8 209.3 20 521 463.3 464.2 236.1 80 581 516.8 517.7 263.4 303.8 236.6 263.8 42 304.7 155.3 02 358.2 182.5 62 411.6 209. 8 22 465.1 237. 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. 183. 4 64 413.4 210.7 24 466.9 237.9 84 520.3 265.2 45 307.4 156.6 05 360.9 183.9 65 414.3 211.1 25 467.8 238. 4 85 521. 2 265.6 46 308.3 157.1 06 361. 8 ' 184. 3 66 415.2 211.6 26 468.7 238.8 86 522.1 266.0 47 309.2 157. 5 07 362. 6 : 184. 8 67 416.1 212.0 27 469.5 239.3 87 523.0 266.5 48 310.1 158.0 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 50 311.9 158.9 159.4 10 365. 3 ! 186. 1 70 418.8 213.4 30 531 472.2 473.1 240.6 90 525.7 267.9 268.3 351 312.7 411 366. 2 j 186. 6 471 419.7 213.8 241.1 591 526.6 52 313.6 159.8 12 367.1 Il87. 1 72 420.6 214. 3 32 474.0 241.5 92 527.5 268.8 53 314.5 160.3 13 368. i 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. 1 Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. ( J3° (1 17°, 243°, 297°, . 1 Page 422] 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. i)ep. 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 57.4 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 m 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. 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 71 61.8 62.7 32.9 33.3 30 114.8 61.0 61.5 90 167.8 89.2 50 220.7 117.4 117.8 11 9.7 5.2 131 115.7 191 168.6 89. 7 251 221.6 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 38.0 40 141 123. 6 - 124.5 65.7 200 176.6 93.9 60 229.6 230.4 122.1 21 18.5 9.9 81 71.5 66.2 201 177.5 94.4 261 122.5 22 19.4 10.3 82 72.4 38.5 42 125. 4 66.7 02 178.4 94.8 62 231.3 123.0 23 20.3 10.8 83 73.3 39.0 43 126.3 67.1 03 179.2 95.3 63 232.2 123.5 24 21.2 11.3 84 74.2 39.4 44 127.1 67.6 04 180.1 95.8 64 233.1 123.9 25 22.1 11.7 85 75.1 39.9 45 128.0 68.1 05 181.0 96.2 ()5 234.0 124.4 26 23.0 12.2 86 75.9 40.4 46 128.9 68.5 06 181.9 96.7 66 234.9 124.9 27 23.8 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 14.6 90 79.5 42.3 42.7 50 151 132.4 70.4 10 185.4 98.6 99.1 70 271 238.4 239.3 126.8 127.2 31 27.4 91 80.3 133.3 70.9 211 186.3 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 4.5.1 56 137.7 73.2 16 190.7 101.4 76 243.7 129.6 37 32.7 17.4 97 85.6 4.5.5 57 138.6 73.7 17 191.6 101.9 77 244.6 130.0 38 33.6 17.8 98 86.5 46.0 58 139.5 74.2 18 192.5 102.3 78 245.5 130.5 39 34.4 18.3 99 87.4 46.5 59 140.4 74.6 19 193.4 102.8 79 246.3 131.0 40 35.3 36. 2 18.8 19. 2 100 88.3 46.9 60 141.3 142.2 75.1 75.6 20 221 194.2 195.1 103.3 103.8 80 281 247.2 248. i 131.5 41 101 89.2 47.4 161 131.9 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 70 150.1 151.0 79.8 80.3 30 231 203.1 204.0 108.0 108.4 90 256.1 256. 9" 136. 1 51 45.0 23.9 111 98.0 52.1 171 291 136. 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. 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 9f) 261.4 139. 57 50. 3 26.8 17 103.3 54.9 77 156. 3 83.1 37 209.3 111.3 97 262. 2 139. 4 58 51. 2 27.2 18 104.2 55.4 78 157.2 83.6 38 210.1 111.7 98 263.1 139.9 59 52.1 27.7 19 105.1 55.9 79 158.0 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. Dep. Lat. Dist. Dep. l^t. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 62° (118°, 242°, 298° )• TABLE 2. [Page 423 | Dist. Difference of Latitude and Departure for 28° (152°, 208°, 332= ). Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. ; Lat. Dep. Di.st. 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. 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 70 326.7 173.7 30 379.6 201.9 90 432.6 230.0 230.5 50 551 485.6 258.2 258. 7 311 146.0 371 327.5 174.2 431 380. 5 202.3 491 433.5 486.5 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 59 493.5 262.5 20 321 282.5 150.2 80 335. 5 336.4 178.4 40 388.5 206.6 500 441.5 234.7 235. 2 60 494.4 262.9 283.4 150. 7 381 178.9 441 389.4 207. 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 23 285.2 151.6 83 338.1 179.8 43 391.1 208.0 03 444.1 236.1 63 497.1 264.3 24 286.0 152. 1 84 339. 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 30 291.3 154.9 155.4 90 391 344.3 183.1 50 397.3 398. 2" 211.3 10 450.3 239.4 239. 9 70 571 503.3 267.6 268.0 331 292.2 345.2 183.6 451 211. 7 511 451.2 504.2 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 40 341 300.2 301.0 159.6 400 401 353. 1 187.8 60 406. 1 407.0 216.0 20 521 459.1 460.0 244.1 80 512.1 513.0 272.3 272. 7 160.1 354 . 188.3 461 216.4 244.6 581 42 301.9 160.6 02 354.9 188.7 62 407.9 216.9 22 460.9 245. 82 513. 9 273.2 43 302.8 161.0 03 355.8 189.2 63 408.8 217.4 23 461.8 245.5 83 514.8 273.7 44 303.7 161.5 04 356. 7 189.7 64 409.7 217.8 24 462.7 246.0 84 515.7 274.2 45 304.6 162.0 05 357. 6 190.1 65 410.5 218.3 25 463.5 246.5 85 516.5 274.7 46 305.5 162.4 06 358.4 190. 6 66 411.4 218.8 26 464.4 246.9 86 517.4 275.1 47 306.4 162.9 07 359.3 191.1 67 412.3 219.2 27 465.3 247.4 87 518.3 275.5 48 307.2 163.4 08 360.2 191.5 68 413.2 219.7 28 466.2 247.9 88 519.2 276.0 49 308.1 163.8 09 361. 1 192.0 69 414.1 220.2 29 467.1 248.3 89 520.1 276.5 50 309.0 164.3 10 411 362.0 362.9 192.5 193. 70 471 415.0 415.8 220.7 30 531 468.0 248.8 90 521. 521.8 277.0 351 309.9 164.8 221.1 468.9 249.3 591 277.4 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 53 311.7 165.7 13 364. 6 193. 9 73 417.6 222.1 33 470.7 250. 2 93 523.5 278.4 54 312.5 166.2 14 365. 5 194.4 .74 418.5 222.5 34 471.5 250. 7 94 524.4 278.8 55 313. 4 166.7 15 366. 4 194.8 75 419.4 223.0 35 472.4 251.1 95 525. 3 279.3 56 314. 3 167.1 16 367.3 195. 3 76 420.3 223.5 36 473.3 251.6 96 526.2 279.8 57 315.2 167.6 17 368. 2 195.8 77 421. 1 223.9 37 474.2 252. 1 97 527.1 280.3 58 316.1 168.1 18 369.0 196.2 78 422.0 224.4 38 475.1 252.6 98 528.0 280.8 59 316.9 168.5 19 369.9 196.7 79 422.9 224.9 39 476.0 253.1 99 528.9 281.3 60 317.8 169.0 20 370.8 197.2 80 423.8 225.3 40 476.8 253.6 600 529.8 281.7 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. ( 52° (118°, 242°, 298° ). Page 424] TABLE 2. Difference of Latitude and Departure for 29° (151°, 209°, 331°). Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 0.9 0.5 61 53.4 29.6 121 105.8 58.7 181 158.3 87.8 241 210.8 116.8 2 1.7 1.0 62 54.2 30.1 22 106.7 59.1 82 159.2 88.2 42 211.7 117.3 3 2.6 1.5 63 55.1 30.5 23 107.6 59.6 83 160.1 88.7 43 212.5 117.8 4 3.5 1.9 64 56.0 31.0 24 108.5 60.1 84 160.9 89.2 44 213.4 118.3 5 4.4 2.4 65 56.9 31.5 25 109.3 60.6 85 161.8 89.7 45 214.3 118.8 6 5.2 2.9 66 57.7 32.0 26 110.2 61.1 86 162.7 90.2 46 215.2 119.3 7 6.1 3.4 ^7 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 57 224.8 124.6 18 15.7 8.7 78 68.2 37.8 38 120.7 66.9 98 173.2 96.0 58 225.7 125.1 19 16.6 9.2 79 69.1 38.3 39 121.6 67.4 99 174.0 96.5 59 226.5 125.6 20 17.5 9.7 80 70.0 38.8 40 122.4 67.9 200 201 174.9 97.0 60 227.4 126. 1 126.5 21 18.4 10.2 81 70.8 39.3 141 123.3 68.4 175.8 97.4 261 228.3 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 65 331.8 128.5 26 22.7 12.6 86 75.2 41.7 46 127.7 70.8 06 180.2 99.9 66 232.6 129.0 27 23.6 13.1 87 76.1 42.2 47 128.6 71.3 07 181.0 100.4 67 233. 5 129.4 28 '24.5 13.6 88 77.0 42.7 48 129.4 71.8 08 181.9 100.8 68 234.4 129.9 29 25.4 14.1 89 77.8 43.1 49 130.3 72.2 09 182.8 101.3 69 235.3 130.4 30 31 26.2 14.5 90 78.7 43.6 50 131.2 72.7 10 183.7 101.8 70 236.1 130.9 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 1.33. 8 37 32.4 17.9 97 84.8 47.0 57 137.3 76.1 17 189.8 105.2 77 242.3 134.3 38 33.2 18.4 98 85.7 47.5 58 138.2 76.6 18 190.7 105.7 78 243.1 134.8 39 34.1 18.9 99 86.6 48.0 59 139.1 77.1 19 191.5 106.2 79 244.0 135. 3 40 ' 35.0 19.4 100 87.5 48.5 60 139.9 140.8 77.6 20 192.4 106.7 80 244.9 245.8 135.7 41 35.9 19.9 101 88.3 49.0 161 78.1 221 193.3 107.1 281 136.2 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. 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 90 253.6 140.6 141.1 51 44.6 24.7 111 97.1 53.8 171 149.6 82.9 231 202.0 112.0 291 254.5 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 1 258.0 143.0 56 49.0 27.1 16 101.5 56.2 76 153. 9 85.3 36 206.4 114.4 96 1 258.9 143.5 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 425 Difference of Latitude and Departure for 29° (151°, 209°, 331° ). Dist. Lat. Dep. Dist. Lat. Dep. Dist. ' Lat. Dep. Dist. 481 Lat. Dep. Dist. Lat. Dep. 301 263.2 145.9 361 315. 7 175.0 421 368.2 204.1 420.7 233.2 541 473. 2 262.3 02 264.1 146.4 62 316.6 175. 5 22 369.1 204.6 82 421.6 233.7 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 10 311 271.1 150.3 150.8 70 323.6 324.5 179.4 30 376.1 376.9 208.5 90 428.5 429.4 237.6 50 481.0 266.6 272.0 371 179.9 431 209.0 491 238.0 551 481.9 267.1 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 2.39. 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 78 230.6 183.3 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 j212.8 99 436.4 241.9 59 488.9 271.0 20 321 279.8 280.7 155. 1 80 332.3 333. 2 184.2 40 384.8 1213.3 500 437.3 242.4 60 489.8 271.5 155. 6 381 184.7 441 1 385.7 1213.8 501 438.2 242.9 561 490.6 272.0 22 281.6 156.1 82 334.1 185.2 42 386.6 i214.3 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 27 286.0 158. 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 30 288.6 160.0 160.5 90 341.1 341.9 189.1 50 393. 5 218.2 218.7 10 511 446.1 247.3 70 498.5 276.3 31 289.5 391 189.6 451 394.4 447.0 247.8 571 499.4 276.8 32 290.3 161.0 92 .342. 8 190.0 52 395.3 219.1 12 447.8 248.2 72 500.3 277.3 33 291.2 161.4 93 343. 7 190. 5 53 396.2 219.6 13 448.6 248.7 73 501.1 277.8 34 292.1 161.9 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. 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 19 253.9 251.6 79 506.4 280.7 40 297.3 298.2 164.8 165.3 400 401 349.8 350. 7 193.9 194.4 60 461 402.3 403.2 223.0 20 454.8 252. 1 80 507.2 281.2 341 223.5 521 455.6 252.6 581 508.1 ! 281.7 1 42 299.1 165.8 02 351.6 194.9 62 404.0 224.0 22 456.5 253. 1 82 509. 282. 2 I 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. 24 458.3 1254.0 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 10 358.6 359.4 198.8 199. 3 70 471 411.0 411.9 227.9 228. 3 30 531 463. 5 i 256. 9 90 516.0 286.0 351 307.0 170.2 411 464.4 257.4 591 516.9 286.5 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 i 203.6 80 419.8 232.7 40 472.3 261.8 600 524.8 290.9 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 6 1° (119°, 241°, 299°) Page 426 TABLE 2. • Difference of Latitude and Departure for 30° (150°, 210 °, 330° ). Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Di.st. Lat. Dep. Dist. Lat. Dep. 1 0.9 0.5 61 52.8 30.5 121 104.8 60.5 181 156.8 90.5 241 208.7 120.5 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. 123.0 7 6.1 3.5 ^7 58.0 33.5 27 110.0 63.5 87 161.9 93.5 47 213.9 123.5 8 6.9 4.0 B8 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 8.7 5.0 70 60.6 35. 30 112.6 65.0 90 164.5 95.0 50 216. 5 125.0 125.5 11 9.5 5.5 71 61.5 35.5 131 113. 4 65. 5 191 165.4 95.5 251 217.4 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 i 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 i 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 i 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 i 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 1 69.5 99 172. 3 99.5 59 224.3 129.5 20 17.3 10.0 10.5 80 69.3 70.1 40.0 40 121.2 ' 70.0 122.1 70.5 200 201 173.2 174.1 100.0 100. 5" 60 261 225.2 130.0 21 18.2 81 40.5 141 226.0 130.5 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. 134.5 30 26.0 15.0 15. 5 90 77.9 78.8 45.0 50 129.9 130.8 75.0 10 181.9 105.0 70 271 233. 8 234.7 135.0 135.5 31 26.8 91 45.5 151 75. 5 211 182.7 105.5 32 27.7 16.0 92 79.7 46.0 52 131.6 76.0 12 183.6 106.0 72 233. 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 76 239.0 138.0 37 32.0 18.5 97 84.0 48.5 57 136. 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. 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 41 34.6 35.5 20.0 20.5 100 101 86.6 50.0 50.5 60 138.6 139.4 80.0 80.5 20 190.5 191.4 110.0 80 242.5 243.4 140.0 140.5' 87.5 161 221 110.5 281 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 53.0 66 143.8 83.0 26 195. 7 113.0 86 247.7 143. 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 10 111 95.3 96.1 55. 70 147.2 85.0 30 199.2 115.0 115.5 90 291 251.1 252. 145. 51 44.2 25.5 55. 5 171 148.1 85.5 231 200.1 145. 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 10 100. 5 58.0 76 152. 4 88.0 36 204.4 118. 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 2.58. 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 Dist. 52.0 30.0 20 103.9 60.0 80 155. 9 90.0 40 207.8 120.0 300 259.8 150.0 Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 80° (120°, 240°, 300°). TABLE 2. [Page 427 Difference of Latitude and Departure for 30 ° (150°, 210°. .330°). Dist. Lat, Dep. Dist. 1 Lat. 1 Dep. Dist. Lat. Dep. Dist. Lilt. : 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 i 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 j 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 j 367.2 212.0 84 419.2 242.0 44 471.1 272. 05 264. 1 152.5 65 316. 1 182.5 25 , 368. 1 212.5 85 420. 242.5 45 472.0 272.5 0() 265.0 153.0 66 317.0 183. 26 368.9 213.0 86 420. 9 243. 46 472.9 273.0 07 2(i5. 9 153. 5 67 317.8 183. 5 27 . 369. 8 1 213. 5 87 421.8 243. 5 47 473.7 273. 5 08 266. 7 154.0 68 318. 7 184.0 28 1 370. 7 1 214. 88 : 422.6 244.0 48 474.6 274.0 09 267.6 154.5 6!) 319.6 184. 5 29 371.5 i214.5 89 ; 423.5 244.5 49 475.5 274. 5 10 268.5 155.0 70 320. 4 185. 30 ! 372.4 215.0 215. 5 90 491 424.4 245.0 245. 5 50 551 476.3 477.2 275.0 311 269.3 155. 5 371 321. 3 185. 5 431 373.3 425.2 275. 5 12 270.2 156.0 72 322. 2 i 186. 32 374.1 ,216.0 92 426.1 246.0 52 478.1 276.0 13 271.1 156.5 73 323. 186.5 33 375.0 216. 5 93 426.9 246.5 53 478.9 276. 5 14 271.9 157.0 74 32.3.9 187.0 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 I 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 i 378.5 218.5 97 430. 4 248. 5 57 482. 4 278.5 18 275. 4 ! 159. 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 1 380.2 219.5 99 432.2 249.5 59 484.1 279.5 20 321 277.1 160.0 80 .329. 1 381 330. 190.0 40 381. 1 220.0 500 433. ! 250. 60 561 485.0 485.9 280.0 278. 1 160. 5 190. 5 441 381.9 220.5 501 433. 9 250. 5 280.5 22 278.9 161.0 82 .330. 8 191.0 42 382. 8. 221. 02 434.8 251. 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 1 162. 84 332. 6 192.0 44 384.5 ,222.0 04 1 436.5 252. 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. 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. 1 224. 08 \ 440.0 254.0 68 491.9 284.0 29 284.9 164.5 89 336. 9 194.5 49 388. 9 2^4. 5 09 ' 440.8 2.54. 5 69 492.8 284.5 30 331 285.8 286.7 165.0 90 337. 8 195.0 195. 5 50 389. 7 451 390.6 225.0 10 i 441. 7 511 1 442.6 255.0 70 571 493.6 494.5 285.0 285. 5 165. 5 391 338.6 225.5 255.5 32 287.5 166.0 92 339. 5 196.0 52 391.5 226.0 12 i 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. 94 341.2 ; 197.0 54 393. 2 ' 227. 14 445.2 257. 74 497.1 287.0 35 290.1 167.5 95 342. 1 197. 5 55 394.0 227.5 15 I 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 34.3.8 198. 5 57 395.8 '228.5 17 1 447.8 258. 5 77 499.7 288. 5 38 292.7 169.0 98 344.7 199.0 58 396. 6 229. 18 448.6 i 2.59.0 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 40 341 294.5 295. 3 170.0 400 .346. 4 200.0 200.5 60 461 398. 4 1 230. 20 521 450. 3 j 260. 80 581 502.2 503. 1 290.0 290.5 170.5 401 347.3 399.2 230.5 451. 2 1 260. 5 42 296.2 171.0 02 348.1 201.0 62 400. 1 ; 231. 22 452.1 1261.0 82 504. 291.0 43 297.1 171.5 03 .349.0 201. 5 63 401.0 231.5 23 i 452. 9 1 261. 5 83 504.9 291.5 44 297.9 172.0 04 349. 9 202.0 64 401.8 1232.0 24 453.8 1 262.0 84 505. 8 292.0 45 298.8 172.5 05 350.7 202. 5 65 i 402.7 232.5 25 454.7 |262.5 85 506.6 292.5 46 299.7 173.0 06 351. 6 203. 66 403.6 233.0 26 455.5 263.0 86 507.5 293.0 47 300. 5 173.5 07 352.5 203. 5 67 404.4 2.33.5 27 456.4 263.5 87 508.4 293. 5 48 301.4 174.0 08 353.3 i 204.0 68 405. 3 234. 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 "304. 175.0 10 355. 1 205.0 205. 5 70 407.0 471 407. 9 235. 30 i 459.0 265.0 90 591 511.0 511.8 295.0 175. 5 411 355.9 235. 5 531 j 459.9 265.5 295.5 52 304. 8 176.0 12 356.8 1206.0 72 408.8 236.01 32 ' 460.7 266.0 92 512.7 296.0 53 305.7 176.51 13 357.7 J206.5 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. 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 5(3 308. 3 178.0 16 360.3 208.0 76 412.2 238.0 36 464. 2 1 268. 96 516.2 298.0 57 309.2 178.5 17 361.1 I-208.5 77 413.1 238.5 37 465.1 1268.5 97 517.0 298.5 58 310.0 179.0 18 .362.0 209.0 78 414.0 239.0 38 465.9 269.0 98 517.9 299.0 59 310.9 179.5 19 i 362.9 209.5 79 ! 414.8 239.5 39 466.8 269.5 99 518.8 299.5 60 311. 8 180. 0' 20 1 363.7 i 210.0 80 j 415. 7 240.0 40 467.7 270.0 600 519.6 300.0 Dist. Dep. Lat. Dist. j Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 6 0° (120°, 240°, 300° ). Page 428 TABLE 2. Difference of latitude and Departure for 31° (149°, 211°, 329° ). Dlst. 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. 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 21 106.3 63.9 84 157. 7 94.8 44 209.1 125.7 5 4.3 2.6 65 55.7 33.5 25 107.1 64.4 85 158.6 95.3 45 210.0 126.2 6 5.1 3.1 ^ 56.6 34.0 26 108.0 64.9 86 159.4 95.8 46 210.9 126.7 7 6.0 3.6 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 71 60.0 60.9 36.1 30 111.4 112; 3 67.0 90 162.9 97.9 50 214.3 128.8 129.3 11 9.4 5. 7 36.6 131 67.5 191 163.7 98.4 251 215.1 12 10.3 6.2 72 61.7 37.1 32 118:1 68.0 92 164.6 98.9 52 216. 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 10.8 80 81 68.6 69.4 41.2 40 120.0 120.9 72.1 200 171.4 103.0 60 261 222.9 223.> 133. 9 134.4 21 18.0 41.7 141 72.6 201 172.3 103.5 22 18.9 11.3 82 70.3 42.2 42 121. 7 73.1 02 173. 1 104. 62 224.6 134. 9 23 19.7 11.8 83 71.1 42.7 43 122. 6 73.7 03 174. 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 22H. 3 136. 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 I 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 16.0 90 . 77.1 46.4 46.9 50 ' 128.6 151 ; 129.4 77.3 10 180.0 !l08.2 180.'9 108.7 70 271 231.4 139.1 31 26.6 91 78.0 77.8 211 232.3 139.6 32 27.4 16.5 92 78.9 47.4 52 1 130.3 78.3 12 181.7 lo;-^. 2 72 233. 1 140.1 33 28.3 17.0 93 79.7 47.9 53 : 131. 1 78.8 13 182.6 109.7 73 234. 140.6 34 29.1 17.5 94 80.6 48.4 54 132.0 79.3 14 183. 4 110.2 74 234. 9 141.1 35 30.0 18.0 95 81.4 48.9 55 i 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 21. i" 100 101 85.7 51.5 60 137.1 82.4 82. 9~ 20 221 188.6 113. 3 80 240.0 144.2 41 35.1 86.6 52.0 161 138.0 "189. 4 113. 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 43 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 70 145.7 146.6 87.6 30 197.1 198.0 118.5 90 291 248.6 149.4 51 43.7 26.3 111 95.1 57.2 171 88.1 231 119.0 249.4 149.9 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 53 45.4 27.3 13 96.9 58.2 73 148.3 89.1 33 199.7 120.0 93 251.2 150.9 54 46.3 27.8 14 97.7 58.7 74 149.1 89.6 34 200.6 120.5 94 252.0 151.4 55 47.1 28.3 15 98.6 59.2 75 150.0 90.1 35 201.4 121.0 95 252. 9 151.9 56 48.0 28.8 16 99.4 59.7 76 150. 9 90.6 36 202.3 121.5 96 253.7 152.5 57 48.9 29.4 17 100.3 60.3 77 '-151.7 91.2 37 203. 1 122.1 97 254.6 153.0 58 49.7 29.9 18 101.1 60.8 78 152.6 91.7 38 204.0 122.6 98 255.4 153.5 59 50.6 30.4 19 102.0 61.3 79 153. 4 92.2 39 204.9 123.1 99 256.3 154.0 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. 39° (121°, 239 °,. 301° ). ^■- TABLE 2. [Page 429 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 1248.8 43 465.4 279.7 04 260.6 156.6 64 312.0 187 5 24 363.4 218.4 84 414.9 1249.3 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 10 311 265. 7 266.6 159.7 70 317.2 190.6 30 431 368.6 369.4 221.5 90 420.0 1252.4 420.9 ,252.9 50 551 471.4 472.3 2B3.3 160.2 371 318. 191.1 222.0 491 283.8 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 1 253. 9 53 474.0 284.8 14 269.2 161.7 74 320.6 192.6 34 372. 223.5 94 423.4 254. 4 54 474.9 285. 3 15 270. 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. 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. 59 479.2 287.9 20 321 274.3 275. 2~ 164.8 80 325.7 195.7 40 441 377.2 378. 226.6 500 428.6 257.5 60 480. i 288. 4 | 165. 3 381 326. 6 196.2 227.1 501 429.4 258.0 561 480.9 288.9 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 1 291.0 26 279.4 167.9 86 3S0.9 198.8 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 i 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 i 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 "170. 5 90 391 334.3 335.2 200.9 50 385.7 231.8 .10 437.2 262.7 70 488.6 ' 293.6 331 283.7 201.4 451 386.6 232.3 511 438.0 263. 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 1 295. 1 34 286.3 172.0 94 337.7 202.9 54 1 389.2 233.8 14 440.6 264.7 74 492. 295. 6 35 287.2 172.5 95 338.6 203.4 55 1 390.0 234.3 15 441.4 265.2 75 492.9 296.1 36 288.0 173.1 96 339. 4 204.0 56 1 390.9 234. 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. 3 236.9 237. 4 20 521 445. 7 267.8 80 497.2 298.7 299.2 341 292.3 175.6 .401 343.7 206.5 461 395. 2 446.6 268.3 581 498.0 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. 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 1271.4 87 503. 2 302.3 48 298.3 179. 2 08 349.7 210.1 68 : 401.2 241.0 28 452.6 i271.9 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. 4 352.3 211.2 211.7 70 402.9 471 403! 7 242.1 242. 6 30 531 454.3 273.0 90 591 505.7 303.9 304. 4 351 300.9 180.8 411 455. 2 273.5 506.6 52 301.7 181.3 12 353.2 212.2 72 404.6 243.1 32 456. 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. 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 1 462.0 277.6 99 513. 4 308.5 60 ■ 308.6 185.4 20 360.0 216. 3 80 411.4 247.2 40 462.9 278.1 600 514.3 309.0 Dist. Dep. ! Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. K 9° (121°, 239°, 301° ). Page 430 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. i 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. 97.5 44 206.9 129.3 5 4.2 2.6 ^ 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 60.2 37.1 30 110.2 68.9 90 161.1 162. 100.7 101:2 50 212.0 212.9 132.5 11 9.3 5.8 71 37.6 131 111.1 69.4 191 251 133.0 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 21 17.0 10.6 80 67.8 42.4 40 118.7 74.2 200 169.6 106.0 60 220.5 137. 8 17.8 11.1 81 68.7 42.9 141 119.6 74.7 201 170. 5 1 106. 5 261 221.3 138.3 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. 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 66 225.6 141.0 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 !lll.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 36 29.7 18.5 95 80.6 50.3 55 131.4 82.1 15 182.3 113.9 /o 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. 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 21.7 100 84.8 53.0 60 135.7 136.5 84.8 85.3 20 221 186.6 187. 4" 116.6 80 237.5 238. 3 148.4 41 34.8 101 85.7 53.5 161 117. 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. 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 27.0 10 93.3 94.1 58.3 70 144.2 90.1 30 195.1 195.9 121.9 90 245. 9 153.7 154. 2 51 43.3 111 58.8 171 145.0 90.6 231 122.4 291 246. 8 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 Lat. DIst. Dep. Lat. Dlst. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. )8° (1 22°, 2.38 °, 302° )• TABLE - 2. [Page (431 Difference of Latitude and Departure for 32° (148°, 212 °, 328= )• IDist. 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. 9 254.9 641 458.8 286.7 02 256.1 160.0 62 307. 191.8 22 357.9 223.6 82 408.8 255. 4 42 459. 6 287.2 03 257.0 160.5 63 307.9 192.3 23 358. 7 224.1 83 409.6 255.9 43 460.5 287.7 04 257.8 161.1 64 308.7 192.9 24 359. 6 224.7 84 410. 5 256. 5 44 461.3 288. 3 05 258.7 161.6 65 309. 5 193.4 25 360.4 225.2 85 411.3 257. 45 462. 2 288.8 06 259.5 162.1 66 310. 4 193.9 26 361.3 225. 7 86 412.2 257. 5 46 463. 289.3 07 260.4 162.7 67 311. 2 194.5 27 362.1 226. 3 87 413. 258. 1 47 463.9 289.9 08 261.2 163.2 68 312. 1 195. 28 363.0 226.8 88 41,3. 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 49 465. 6 290.9 10 311 262.9 263. 8 164.3 164.8 70 371 313. 8 314.6 196.0 196. 6" 30 431 364.7 365. 5 227.8 228.4 90 415.6 259.6 50 466.4 467.3 291.5 491 416.4 260.2 551 292.0 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 55 470.7 294.1 16 268.0 167.4 76 318.9 199.2 36 369.8 231.0 96 420.6 262.8 56 471.5 294.6 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 59 474.1 296.2 20 321 271.4 272. 2 169.6 170". 1 80 381 322.3 201.3 40 373.2 233. 1 500 424.0 424.9 26.5.0 "265. 5 60 561 474.9 475. 8 296.7 297. 3 323.1 201.9 441 374.0 233.7 501 22 273.1 170.6 82 324. 202.4 42 374.8 234.2 02 425. 7 266.0 62 476.6 297.8 23 273.9 171.1 83 324. 8 202.9 43 375.7 234.7 03 426. 6 266. 5 63 477.5 298.3 24 274.8 171.7 84 325. 7 203.5 44 376.5 235.3 04 427. 4 267.1 64 478.3 298.9 25 275.6 172.2 85 326. 5 204.0 45 377.4 235. 8 05 428. 3 267.6 65 479.2 299.4 26 276.5 172.7 86 327.4 204. 5 46 378.2 236. 3 06 i 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 t 431.7 269.7 69 482.6 301.5 30 279.9 280.7 *174. 9 90 330.8 331.6 206.6 50 381.6 382.5 238.4 10 432.5 1270.3 433.4 1270.8 70 483.4 .302. 1 331 175.4 391 207.2 451 239.0 511 571 484. 3' 302.6 32 281.6 175.9 92 332.5 207.7 52 383.3 239.5 12 434. 2 271.4 72 485. 1 303.2 33 282.4 176.4 93 333.3 208.2 53 384.2 240.0 13 435. 1 271.9 73 486.0 303.7 34 283.3 177.0 94 334. 2 208.8 54 385. 240.6 14 435. 9 272.4 74 486.8 304.2 35 284.1 177.5 95 335.0 209.3 55 385. 9 241.1 15 436. 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 76 488.5 305.3 37 285.8 178.6 97 336. 7 210.4 57 387.6 242.2 17 i 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. 79 491.1 306.8 40 341 288.3 180.2 400 339.2 211.9 60 390.1 391.0 243.8 20 441.0 275. 6 80 581 491.9 492.8 307.4 289.2 180.7 401 340.1 212.5 461 244.3 521 441.9 276.1 307.9 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 64 393.5 245.9 24 444.4 277.7 84 495.3 309. 5 45 292.6 182.8 05 343. 5 214.6 65 394.4 246.4 25 445. 3 278.2 85 496.2 310.0 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. 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 90 500.3 312.6 361 297.7 186.0 411 348.6 217.8 471 399.4 249.6 531 450. 3 281.4 591 501. 2 313.2 52 298.5 186.5 12 349.4 218.3 72 400.3 250.1 32 451.1 281.9 92 502.0 313.7 53 299.4 187.0 13 350.3 218.8 73 401.1 250.6 33 452.0 282.4 93 502.9 314.2 54 300.2 187.6 14 351.1 219.4 74 402.0 251.2 34 452.8 283.0 94 503. 7 314.8 55 301.1 188.1 15 352.0 219.9 75 402.8 251.7 35 453.7 283. 5 95 504.6 315. 3 56 301.9 188.6 16 :^2.8 220.4 76 403.7 252.2 36 454. 5 284.0 96 505. 4 315.8 57 302. 8 189.2 17 353. 6 221.0 77 404.5 252.8 37 455.4 284.6 97 506.2 316.4 58 303.6 189.7 18 354. 5 221.5 78 405.4 253. 3 38 456.2 285.1 98 507.1 316.9 59 304.5 190.2 19 355.3 222.0 79 406.2 253.8 39 457.1 285.6 99 508.0 317.4 60 305.3 190.8 20 356.2 222.5 80 407.1 254.3 40 467.9 286.2 600 508.8 318.0 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. •Dist. Dep. Lat. Dist. Dep. Lat. 5 8° (1 22°, 238 = , 302° ). / Page 432] 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 0.8 0.5 61 51.2 33.2 121 101.5 65.9 181 151. 8 98.6 241 202.1 131. 3 2 1.7 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 3.4 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 3.3 m 55.4 35.9 26 105.7 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. 5 136.2 136.7 11 9.2 6.0 71 59.5 38.7 131 109.9 71.3 191 160.2 104.0 251 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. 94 162.7 105.7 54 213.0 138.3 15 12.6 8.2 75 62.9 40.8 35 i 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 / 1 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 40 117.4 118.3 76.2 200 201 167. 7 108. 9 168.6 109.5 60 261 218.1 218.9 141.6 142.2 21 17,6 11.4 81 67.9 44.1 141 76.8 22 18.5 12.0 82 68.8 44.7 42 119. 1 77.3 02 169.4 1110.0 62 219. 7 142.7 23 19.3 12.5 83 69.6 45.2 43 119.9 77.9 03 170.3 1110.6 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 1 122.4 79.5 06 172.2 112.2 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 16.9 90 75.5 76.3 49.0 50 125.8 81.7 82.2 10 211 176.1 177.0 114.4 70 226.4 147.1 147.6 91 49.6 151 126.6 114.9 271 227. 3 32 26.8 17.4 92 77.2 50.1 52 1 127.5 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 j 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. 152. 40 33.5 21.8 100 83. 9 54. 5 60 134.2 135. 87.1 20 184.5 119.8 80 234.8 235.7 152. 5 153.0 41 34.4 22.3 101 84.7 55.0 161 87.7 221 185.3 120.4 281 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. 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 93.1" 59.9 60. 5 " 70 142.6 92.6 30 192.9 193.7 125. 3 90 291' 243.2 244.1 157.9 42.8 27.8 111 171 143. 4 93.1 231 125. 8 158.5 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.^- ' 38 199. 6 129.6 98 249.9 162.3 59 49.5 32.1 19 99.8 64.8 79 150.1 97.5 39 200.4 130.2 99 250. 8 162.8 60 50.3 32.7 20 100.6 65.4 80 151.0 98.0 40 201.3 130.7 300 251.6 163.4 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. lAt. Dist. Dep. Lat. e. 7° (123°, 237°, 303° . TABLE 2. [Page 433 | 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. 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 22 353.9 229.8 82 404.2 262. 5 42 454.6 295. 2 03 254.1 165.0 63 304. 4 197.7 23 354.7 230. 4 83 405. 1 263. 1 43 455. 4 295.7 04 255. 165. 5 64 305. 3 198.2 24 355. 6 230. 9 84 405. 9 263. 6 44 456.2 296.2 05 255. 8 166.1 65 306.1 198. 8 25 356.4 231. 4 85 406.7 264.1 45 457.1 296.8 06 256.6 166. 6 66 307. 199.3 26 357.3 232.0 86 407.6 264.7 46 457.9 297.3 07 257. 5 167.2 67 307.8 199.8 27 358.1 232. 5 87 408.4 265.2 47 458.8 297. 9 08 258.3 167.7 68 308.6 200.4 28 359.0 233.1 88 409.3 265.8 48 1 459.6 298.4 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 10 311 260.0 260.8 168.8 169.3 70 371 310. 3 311.2 201.5 30 360.6 361.5 234.2 90 411.0 266.8 50 461.3 299.5 202.0 431 234.7 491 411.8 267.4 551 462.1 300. 1 12 261.7 169.9 72 312. 202.6 32 362.3 235.2 92 412.6 267.9 52 463.0 300.6 13 262.5 170.4 73 312. 8 203. 1 33 363.1 235.8 93 413. 5 268. 5 53 463. 8 301.2 14 263.3 171.0 74 313. 7 203.7 34 364.0 236.3 94 414.3 269.0 54 464. 6 301.7 15 264.2 171.5 75 314.5 204.2 35 364.8 236.9 95 415. 1 269.6 55 465. 5 302.3 16 265.0 i 172.1 76 315.3 204.7 36 365.7 237.4 96 416.0 270.1 56 466. 3 302. 9 17 265.9 172.6 77 316.2 205.3 37 366. 5 238.0 97 416.8 270.7 57 467.2 303.4 18 266.7 173.2 78 317. 205.8 38 367.3 238. 5 98 417.6 271.2 58 468.0 303. 9 19 267.5 173.7 79 317.9 206.4 39 368.2 239.1 99 418.5 271.8 59 468.8 304.5 20 321 268.4 174.2 269.2 174.8 80 381 318.7 206.9 40 369.0 239.6 5C0 501 419.3 420.2 272.3 60 561 469.7 470.5 305. 319.5 207.5 441 369. 9 240.1 272.8 305.5 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 1 175. 9 83 [ 321.2 208.6 43 371. 5 241.2 03 421.9 273.9 63 472.2 306.6 24 271.7 176.4 84 322.1 209.1 44 372.4 241.8 04 422.7 274.5 64 473.0 307. 2 25 272. d 177.0 85 322.9 209.6 45 373. 2 242.3 05 423. 5 275. 65 473.8 307.7 26 273.4 177.5 86 323. 7 210.2 46 374. 1 242.9 06 424.4 275. 6 66 474.7 308. 3 27 274.2 178.1 87 324.6 210.7 47 374. 9 243.4 07 425. 2 276.1 67 475. 5 308.8 28 275.1 178. 6 88 325.4 211.3 48 375. 7 244.0 08 426.0 276.7 68 476.4 309.4 29 275.9 179.1 89 326.2 211.8 49 376.6 244.5 09 426.9 277.2 69 477.2 309.9 30 331 276.8 277.6 179.7 90 327.1 212.4 212.9 50 1 377.4 245.1 10 427.7 277.8 70 478.0 310.4 311.0 180.2 391 327.9 451 378.2 245. 6 511 428.5 278.3 571 478.9 32 278.4 180.8 92 328.8 213.5 52 379.1 246.1 12 429.4 278.8 72 479.7 311.5 33 279.3 181.3 93 329.6 214.0 53 379.9 246.7 13 430.2 279.4 73 480.6 312.0 34 280.1 181.9 94 330.4 214.6 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 55 381.6 247.8 15 431.9 280.4 75 482.2 313.1 36 281.8 183. 96 332. 1 215.6 56 382.4 248.3 16 432.7 281.0 76 483.1 313.7 37 282.6 183.5 97 333.0 216.2 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 59 385.0 250. 19 435. 3 282.6 79 485.6 315. 3 40 285.2 286.0 185.1 185. 7 400 401 335. 5 217.8 60 461 385.8 386.6 250. 5 20 436.1 436.9 283. 2 80 486.4 487. 2 315. 9 341 336. 3 218.4 251.0 521 283.7 581 316.4 42 286.8 186.2 02 337.1 218.9 62 387. 5 251.6 22 437.8 284.3 82 488.1 317.0 43 287.7 186.8 03 338.0 219. 5 63 388.3 252. 1 23 438.6 284.8 83 488.9 317.5 44 288.5 187.3 04 338.8 220.0 64 389.1 252.7 24 439.4 285.4 84 489.8 318.1 45 289.3 187.9 05 339.7 220.5 65 390.0 253.2 25 440.3 285.9 85 490.6 318.6 46 290.2 188.4 06 340.5 221.1 66 390.8 253.8 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 68 392.5 254.9 28 442.8 287.5 88 493.1 320.2 49 292. 7 190.0 09 343.0 222.7 69 393.3 255. 4 29 443.6 288.1 89 494.0 320.8 50 293.5 190.6 10 343. 9 344.7 223. 3 223. 8 70 471 394.2 395.0 255.9 30 444.5 288.6 289.2 90 494.8 321.3 351 294.4 191.1 411 256.5 531 445.3 591 495.7 321.9 52 295.2 191.7 12 345. 5 224.4 72 395. 8 257.0 32 446.1 289.7 92 496. 5 322.4 53 296.1 192.2 13 346.4 224.9 73 396.7 257.6 33 447.0 290.3 93 497. 3 322. 9 54 296.9 192.8 14 347.2 225.4 74 397. 5 258.1 34 447.8 290.8 94 498.1 323.5 55 297.7 193.3 15 348.1 226.0 75 398.3 258.7 35 448.7 291.4 95 499.0 324.1 56 298.6 193.9 16 348.9 226.5 76 399.2 259.2 36 449.5 291.9 96 499.8 324.6 57 299.4 194.4 17 349.7 227.1 77 400.0 259.8 37 450.3 292. 5 97 500.6 325. 1 58 300.2 194.9 18 350.6 227.6 78 400. 9 260.3 38 451.2 293. 98 501.5 325. 7 59 301.1 195.5 19 351.4 228.2 79 401. 7 260.9 39 452.0 293.6 99 502.3 326.2 60 301. 9 196. 20 352.2 228.7 80 402.6 261.4 40 452.9 294.1 600 503.2 326.8 Dist. Dep. 1 Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 57° (123°, 237' ', 303°) . 22489—03 28 Page 434; TABLE 2. Difference of Latitude and Departure for 34° (146°, 214°, 326° )■ DIst. Lat. Dep. Dist. Lat. Dep. Dist. 1 Lat. Dep. Dist. Lat. Dep. Dist. t 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 1 101.1 68.2 82 150.9 101.8 42 ' 200.6 135.3 3 2.5 1.7 63 52.2 35.2 23 1 102. i 68. 8 1 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 5 4.1 2.8 i 53.9 36.3 25 103. 6 69. 9 85 153.4 103. 5 45 1 203. 1 137.0 6 5.0 3.4 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. 104.6 47 204. 8 138.1 » 8 6.6 4.5 68 56.4 38.0 28 106.1 i 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 1 72.1 89 156.7 105.71 49 206. 4 139.2 10 8.3 5.6 70 58.0 58.9 39.1 30 107.8 1 72.7 90 157.5 158. 3 106.2 50 207. 3 139.8 11 9.1 6.2 71 39.7 131 108.6 1 73.3 191 106.8 251 208.1 140.4 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 i 74.4 93 160. 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 i 75. 5 95 161.7 109.0 55 1 211.4 142.6 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 i 77. 7 99 165. 111.3 59 ; 214. 7 144.8 20 21 16.6 17.4 11.2 11.7 80 81 66.3 44.7 40 116. 1 78.3 78.'8 200 165.8 111.8 166.6 ill2.4 60 215.5 261 216.4 145.4 145. 9 67.2 45.3 141 1 116.9 201 22 18.2 12.3 82 68.0 45.9 42 117.7 1 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. 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 1 115. 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 73.0 49.2 48 1 122. 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 i 223.0 150.4 30 24.9 16.8 90 74.6 75.4 50.3 50 124.4 1 83.9 10 174.1 174.9 117.4 70 ! 223.8 151.0 151.5 31 25.7 17.3 91 50.9 151 125.2 1 84.4 211 118.0 271 224.7 32 26.5 17.9 92 76.3 51.4 52 i 126.0 1 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 ill9. 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 1 131.0 ' 88.4 18 180.7 121.9 78 230. 5 155. 5 39 32.3 21! 8 99 82.1 55. 4 59 1 131.8 1 88.9 19 181.6 122.5 79 231.3 156.0 40 33.2 22.4 100 82.9 83.7 55.9 60 161 132.6 1 89.5 20 182.4 123.0 80 232.1 156.6 157.1 41 34.0 22.9 101 56.5 133.5 1 90.0 221 183.2 123.6 281 233.0 42 34.8 23.5 02 84.6 57.0 62 134.3 ! 90.6 22 184.0 124.1 8S ' 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 1 234.6 158. 3 44 36.5 24.6 04 86.2 58.2 64 136. 91. 7 24 185. 7 125. 3 84 1 235.4 158.8 45 37.3 25.2 05 87.0 58.7 65 136.8 t 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 92.0 61.5 70 140.9 95.1 30 190.7 128.6 90 240.4 162.2 162.7 51 42.3 28.5 111 62.1 171 141.8 95.6 231 191.5 129.2 291 241.2 52 43.1 29.1 12 92.9 62.6 72 i 142.6 96.2 32 192.3 fl29.7 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 1 242.9 163.8 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 1 131. 4 95 244.6 165.0 56 46.4 31.3 16 96.2 64.9 76 1 145. 9 1 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. 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 Dist. Dep. ■Lat. Dist. Dep. ' Lat. Dist. 1 Dep. Lat. Dist. Dep. '■ Lat. Dist. Dep. Lat. 56° (124°, 236", 304°). TABLE 2. [Page 435 Difference of Latitude and Departure for 34° (146°, 214 =, 326° ). Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. 1 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 1 304. 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 1 353. 2 238.2 86 402.9 271.8 46 452.6 305.3 07 254.5 171.7 67 304.3 205.2 27 1 354.0 238.8 87 403.8 i 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 1 272.8 48 1 454.3 306.4 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 30 356.5 240.4 90 406.2 274.0 50 456.0 307. 5 311 257.8 173.9 371 307.6 207.5 431 357.3 241.0 491 407.1 274.6 551 456.8 308.1 ^?. 258.7 174.5 72 308.4 208.0 32 358.1 241.6 92 407.9 [ 275.1 52 457.6 308.7 13 259.5 175.0 73 ; 309.2 208.6 33 359. 242. 1 93 408.7 ; 275.7 53 458.4 309.2 14 260.3 175.6 74 1 310. 1 209.1 ■ 34 ; 359. 8 242. 7 94 409.5 i 276.2 54 459. 3 309.8 15 261.2 176.1 75 310.9 209.7 35 i 360.6 243.2 95 410.4 1 276.8 55 460.1 310.3 16 262.0 176.7 76 311.7 210.3 36 361. 5 243. 8 96 411. 2 1 277.4 56 460.9 310.9 17 262.8 177.3 77 312.6 210.8 37 362.3 !244.4 97 412.0 1 277.9 57 461. 7 311.5 18 263.7 177.8 78 313.4 211.4 38 363.1 244.9 98 412.8 1 278.4 58 462.6 312.0 19 264.5 178.4 79 314.2 211.9 39 364.0 245.5 99 413.7 279.0 59 463.4 312.6 20 265.3 266.1 178.9 80 315.0 212.5 213.0 40 \ 364.8 441 365. 6 246.0 500 501 414.5 415.3 279.6 280.1 60 464.2 313.1 313.7 321 179.5 381 315.9 246.6 561 465. 1 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 1 317.5 214.2 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 j 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 J 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 i 469.2 316.5 27 271.1 182.9 87 320.8 216.4 47 ; 370. 6 250. 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 1 372.2 251.1 09 421.9 284.6 69 471. 7 318.2 30 273.6 274.4 184.5 90 323.3 324.2 218.1 218.6 50 373. 1 251. 6 451 i 373. 9 1 252. 2 10 422. 8 285.2 70 472.6 571 473.4 318.7 319.3 331 186.1 391 511 423.6 285.8 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 28r.4 74 475.9 321.0 35 277.7 187.3 95 327.5 220.9 55 377.2 i254.4 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 i -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 1 480.0 323.8 40 281.9 190.1 400 331.6 332.4 223.7 224.2 60 461 381.3 257.2 382.2 '257.8 20 431.1 290.8 80 480.8 324.3 324.9 341 282.7 190.7 401 521 431.9 291.3 581 481.6 42 283.5 191.2 02 333.3 224.8 62 383.0 1258.3 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. 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. i 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 i 441.9 298. 93 491.6 331.6 54 293.5 198.0 14 343. 2 231. 5 74 393.0 265.0 34 442.7 298.6 94 492.5 332.2 55 294.3 198.5 15 344.1 232.1 75 393.8 265.6 35 443.6 299.1 95 493.3 332.7 56 295. 1 199.1 16 344.9 232.6 76 394.6 266.2 36 444.4 299.7 96 494.1 333.3 57 296.0 199.6 17 345.7 233.2 77 395.5 266.7 37 445.3 300.2 97 494.9 333. 8 58 296.8 200.2 18 346. 5 233.7 78 396.3 267.3 38 446.1 300.8 98 495.8 334.4 59 297.6 200.7 19 347.4 234. 3 79 397.1 267.9 39 446.9 301.4 99 496.6 334. 9 60 298.5 201.3 20 348.2 234.9 80 397.9 268.4 40 447.7 302.0 600 497.4 335. 5 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 56° (124°, 236°, 304° )• Page 436] 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 «B 54.1 37.9 26 103.2 72.3 86 152.4 106.7 46 201. 5 141.1 7 5.7 4.0 67 54.9 38.4 27 104.0 72.8 87 153. 2 i 107. 3 47 202.3 141.7 8 6.6 4.6 68 55.7 39.0 28 104.9 73.4 88 154. ; 107. 8 48 203.1 142.2 9 7.4 5.2 69 56.5 39.6 29 105.7 74.0 89 154.8 108.4 49 204.0 142.8 10 8.2 5.7 70 71 57.3 58.2 40.2 30 106.5 74.6 75.1 90 191 155.6 109.0 50 204.8 205.6 143.4 144.0 11 9.0 6.3 40.7 131 107.3 156.5 109. H 251 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 12.0 80 65.5 45.9 40 114.7 115.5 80.3 200 201 163.8 164:"6 114.7 60 213.0 149.1 149.7 21 17.2 81 66.4 46.5 141 80.9 115.3 261 213.8 22 18.0 12.6 82 67.2 47.0 42 116.3 81.4 02 165. 5 115.9 62 214.6 150.3 23 18.8 13.2 83 68.0 47.6 43 117.1 82.0 03 166.3 116.4 63 215.4 150.9 24 19.7 13.8 84 68.8 48.2 44 118.0 82.6 04 167.1 117.0 64 216.3 151.4 25 20.5 14.3 85 69.6 48.8 45 118.8 83.2 05 167.9 117.6 65 217.1 152.0 26 21.3 14.9 86 70.4 49.3 46 119.6 83.7 06 168.7 118.2 66 217.9 152.6 27 22.1 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 17.8 90 91 73.7* 74.5 51.6 52.2 50 151 122.9 123.7 86.0 86.6 10 211 172.0 172. 8 120.5 70 221.2 222.0 154.9 155.4 31 25.4 121.0 271 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 20 180.2 126.2 80 229.4 160.6 41 33.6 23.5 101 82.7 57.9 161 131.9 92.3 221 181.0 126.8 281 230.2 161.2 42 34.4 24.1 02 83.6 58.5 62 132.7 92.9 22 181.9 127.3 82 231.0 161.7 43 35.2 24.7 03 84.4 59.1 63 133. 5 93.5 23 182.7 !127.9 83 231.8 162.3 44 36.0 25.2 04 85.2 59.7 64 134.3 94.1 24 183. 5 128.5 84 232.6 162.9 45 36.9 25.8 05 86.0 60.2 65 135.2 94.6 25 184.3 129.1 85 233.5 163. 5 46 37.7 26.4 06 86.8 60.8 66 136.0 95.2 26 185.1 129.6 86 234.3 164.0 47 38.5 27.0 07 87.6 61.4 67 136.8 95.8 27 185.9 130.2 87 235.1 164.6 48 39.3 27.5 08 88.5 61.9 68 137.6 96.4 28 186.8 130.8 88 235.9 165.2 49 40.1 28.1 09 89.3 62.5 69 138.4 96.9 29 187.6 131.3 89 236. 7 165.8 50 41.0 28.7 10 90.1 63.1 70 139.3 97.5 30 188. 4. 189.2 131.9 90 237.6 166.3 51 41.8 29.3 111 90.9 63.7 171 140.1 98.1 231 132.5 291 238.4 166.9 52 42.6 29.8 12 91.7 64.2 72 140.9 98.7 32 190. 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 1.34. 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 67 46.7 32.7 17 95.8 67.1 77 145.0 101.5 37 194.1 135. 9 97 243. 3 170.4 58 47.5 33. 3 18 96.7 67.7 78 145.8 102.1 38 195.0 136. 5 98 244.1 170.9 59 48.3 33.8 19 97.5 68.3 79 146.6 102.7 39 195. 8 137.1 99 244.9 171.5 60 49.1 34.4 20 98.3 68.8 80 147.4 103.2 40 196.6 137.7 300 245.7 172.1 DIst. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. )5° (1 25°, 235 °, 305° )■ TABLE ± [Page 437 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. JOl 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 08 252.3 176.6 68 301.5 211.1 28 350.6 245. 5 88 399.8 279.9 48 448.9 314.3 09 253. 1 177.2 69 302.3 211.6 29 351.4 246.0 89 400.6 280.5 49 449.7 314.9 10 253.9 177.8 70 303.1 212.2 30 352.2 353. 1 246.6 247.2 90 491 401.4 402.2 281.0 281.6 50 551 450.5 1 315.4 451.4 1 316.0 311 254.8 178.4 371 303.9 212.8 431 12 255. 6 178.9 72 304.7 213.4 32 I 353.9 247.8 92 403.0 282.2 52 452.2 1 316.6 13 256.4 179.5 73 305.6 213. 9 33 i a54. 7 248.3 93 403.9 282. 8 53 453.0 i 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 20 321 262.1 263. 183.5 184. 1 80 381 311.3 312.1 217.9 40 360.4 361.3 252.4 252. 9 500 501 409.6 410.4 286.8 60 458.7 321.2 218.5 441 287.4 561 459.6 321.8 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 1 314.6 220.2 44 363.7 254. 7 04 412.9 289.1 64 462.0 323.5 25 266.2 186.4 85 315.4 220.8 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 1 318.7 223.1 49 367.8 257.5 09 417. 291.9 69 466.1 326.4 30 331 270.3 271. r 189. 3 189.8 90 ■391 319.5 223.7 50 368.6 369.4 258.1 258. 7 10 511 417.8 418.6 292.5 70 466.9 326. 9 1 320.3 224. 3 451 293.1 571 467.8 327. 5 1 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 1226.5 55 372.7 261.0 15 421.9 295.4 75 471.0 329.8 36 275.2 192.7 96 324.4 1227.1 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. 38 276.9 193. 9 98 326.0 228.3 58 375.2 262.7 18 424.3 1297.1 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 40 341 278.5 279.3 195.0 400 327.7 |229.4 60 461 376.8 377.6 263.8 20 426.0 298.3 80 475. 1 ! 332. 7 476.0 333.3 195.6 401 328.5 230.0 264. 4 521 426.8 298.8 581 42 280.2 196.1 02 329.3 230.6 62 378.5 265.0 22 427.6 299.4 82 476. 8 i 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 1 380.9 266.7 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 j 336. 1 47 284.3 199.0 07 333.4 233.4 67 1 382.6 267.8 27 431.7 302.3 87 480. 9 \ 336. 7 48 285.1 199.6 08 334.2 234. 68 1 383.4 268.4 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 50 351 286: 7 287.5 200.7 201.3 10 411 335. 9 336.7 235.1 235. 7 70 1 385.0 471 , 385.8 269.6 270. 1 30 434.2 304.0 90 483.3 338.4 484.2 339.0 531 435.0 304.5 591 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. 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 I 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. j Lat. , >5° (125°, 235°, 305°). Page 438 ] 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 1 71.7 82 147.2 107.0 42 i 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 i 196.6 142.8 4 3.2 2.4 64 51.8 37.6 24 100.3 1 72.9 84 148.9 108.2 44 I 197.4 143.4 5 4.0 2.9 65 ■ 52.6 38.2 25 101.1 1 73.5 85 149.7 108.7 45 1 198.2 144.0 6 4.9 3.5 6» 53.4 .38. 8 26 101.9 1 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 1 74.6 87 151.3 109.9 47 199. 8 145.2 8 6.5 4.7 68 ,55; 40. 28 103.6 1 75.2 88 152. 1 110.5 48 200.6 145.8 9 7.3 5.3 ■ 69 55. 8 ■' 40. (5 29 104.4 75.8 89 152.9 111.1 49 201.4 146. 4 10 8.1 5.9 70 56. 6 i 41. 1 30 105.2 76.4 90 153. 7 111.7 112.3 50 i 202.3 251 203. i 146.9 11 8.9 6.5 71 57.4 i 41.7 131 1 106.0 77.0 191 154. 5 147.5 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 1 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 1 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 n.2 79 63.9 1 46.4 39 112.5 81.7 99 161.0 117.0 59 209. 5 152.2 20 21 16.2 11.8 12.3 80 81 64.7 47.0 40 113.3 82.3 200 161.8 162.6 117.6 118.1 60 261 210. 3 152.8 17.0 65.5 47.6 141 114.1 ' 82.9 201 211.2 153.4 22 17.8 12.9 82 66. 3 i 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. 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. 45 117.3 85.2 05 165.8 120.5 G5 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 16&.3 122.3 68 216. 8 157.5 29 23.5 17.0 89 72. 52. 3 49 120.5 ; 87.6 09 169.1 122.8 69 217. 6 158.1 30 31 24.3 17.6 90 72. 8 52. 9 50 121.4 88.2 8'8.8 10 211 169.9 170.7 123.4 70 218.4 219.2 158.7 159.3 25.1 18.2 91 73.6 1 53.5 151 122.2 124.0 271 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 i 89. 9 13 172.3 125. 2 73 220.9 160. 5 34 27.5 20.0 94 76.0 i 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 2L7 97 78.5 57.0 57 127.0 i 92.3 17 175. 6 127. 5 77 224.1 162.8 38 30.7 22.3 98 79. 3 i 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 1 58. 2 59 128.6 93.5 19 177.2 128.7 79 225.7 164.0 40 32.4 33.2 23.5 100 80. 9 i 58. 8 60 129.4 j 94.0 20 178.0 178.8 129.3 129."9 80 226. 5 281 227.3 164.6 165.2 41 24.1 101 81.7 59.4 161 130.3 i 94.6 221 42 34.0 24.7 02 82.5 60.0 62 131.1 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 j 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 1 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 j 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 i 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 j 63.5 68 135. 9 98. 7 28 184.5 134.0 88 233. 169. 3 49 39.6 28.8 09 88. 2 1 64. 1 69 136. 7 99. 3 29 185.3 134.6 89 233.8 169.9 50 5i 40.5 41.3 29.4 10 89.0 64.7 65.2 70 137.5 1 99.9 30 186.1 135. 2 135. 8 90 234.6 291 235.4 170.5 171.0 30.0 111 89.8 171 138.3 100. 5 231 186.9 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 i 66.4 73 140.0 101.7 33 188.5 137.0 93 ' 237. 172,2 54 43.7 31. 7 14 92.2 1 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 48.5 35.3 20 97.1 70.5 80 145.6 105.8 40 194.2 141.1 300 242.7 176.3 Dist. Dep. Lat. Dist. Dep. j Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. i4° (1 26°, 234°, 306° )■ TABLE . 2. [Page 439 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 09 250.0 181.6 69 298.5 216.9 29 347.1 252.2 89 395.6 1287.4 49 444.2 322.7 10 250.8 251.6 182.2 182. 8 70 299.3 217.5 30 347. 9 252.8 90 396. 4 288. 50 445.0 323.3 311 371 300.2 218.1 431 348.7 253.3 491 397.3 288.6 551 445.8 323.8 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 20 321 258.9 188.1 80 307.4 308.2 223.4 40 356.0 356.8 258.6 500 404.5 405.3 293.9 60 453.1 329.1 259.7 188.7 381 224.0 441 259.2 501 294.5 561 453.9 329.7 22 260.5 189.3 82 309.1 224.5 42 357.6 259.8 02 406.1 295.0 62 454.7 330.3 23 261. 3 189.9 83 309.9 225. 1 43 358.4 260.4 03 407.0 295.6 63 455.5 330.9 24 262.1 190.5 84 310.7 225. 7 44 359. 2 261.0 04 407.8 296.2 64 456.3 331.5 25 262.9 191.0 85 311.5 226.3 45 360.0 261.6 05 408.6 296. 8 65 457.1 332.1 26 263.7 191.6 86 312.3 226.9 46 360.8 262.2 06 409.4 297.4 66 457.9 332.7 27 264.6 192.2 87 313. 1 227.5 47 361.6 262.8 07 410.2 298.0 67 458.7 333.3 28 265.4 192.8 88 313.9 228.1 48 362.4 263. 3 08 411.0 298.6 68 459.5 333.8 29 266.2 193.4 89 314.7 228.7 49 363.3 263. 9 09 411.8 299.2 69 460.3 334.4 30 267.0 194.0 90 315.5 229.2 50 364.1 364.9 264.5 10 412.6 299.8 70 461.1 335.0 331 267.8 194.6 391 316.3 229.8 451 265.1 511 413.4 300.3 571 462.0 335. 6 32 268.6 195.2 92 317.1 230.4 52 365.7 265.7 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 35 271.0 196.9 95 319.6 232.2 55 368.1 267.5 15 416.7 302.7 75 4a5.2 338.0 36 271.8 197.5 96 320.4 2.32. 8 56 368.9 268.0 16 417.5 303.3 76 466.0 338. 5 37 272.6 198.1 97 321.2 233.4 57 369.7 268.6 17 418.3 303.9 77 466.8 339.1 38 273.5 198.7 98 322.0 233.9 58 370.5 269.2 18 419.1 304.4 78 467.6 339.7 39 274.3 199. 3 99 322.8 234.5 59 371.3 269. 8 19 419.9 305. 79 468.4 340.3 40 275.1 199.9 400 323.6 235. 1 60 372. 2 270.4 20 420.7 305.6 80 469.3 340.9 341 275. 9 200.4 401 324.4 235. 7 461 373.0 271.0 521 421.5 306.2 581 470.1 341.5 42 276.7 201.0 02 325. 2 236. 3 62 373. 8 271.6 22 422.3 306.8 82 470.9 342.1 43 277. 5 201.6 03 326.0 236.9 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 29 428.0 310.9 89 476.5 346.2 50 351 283.2 205.7 10 331.7 241.0 70 380.2 276.3 30 428.8 311.5 90 477.3 346.8 284.0 206.3 411 332.5 241.6 471 381.1 276.9 531 429.6 312.1 591 478.2 347.4 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. 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. 246. 3 79 387. 5 • 281.6 39 436.1 316.8 99 484.6 352.1 60 291.3 211.6 20 339. 8 246.9 80 388.3 282.1 40 436.9 317.4 600 485.4 352.7 Dist. Dep. Lat. Dist. Dep. Lat. DLst. Dep. Lat. Difct. Dep. Lat. Dist. Dep. Lat. 54° (1 26°, 234 °, 306° )• Page 440] TABLE ± Difference of Latitude and Departure for c !7° (143°, 217°, 323° ). Diet. 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 m 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 50 199.7 200.5 150.5 151.1 11 8.8 6.6 71 56.7 42.7 131 104.6 78.8 191 152.5 114.9 251 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 15.2 11.4 79 63.1 47.5 39 i 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 84.9 200 201 159.7 120.4 60 ! 207.6 156.5 21 16.8 12.6 81 64.7 48. 7 141 160.5 121.0 261 208.4 157.1 22 17.6 13.2 82 65.5 49.3 42 113.4 85.5 02 161.3 121.6 62 209.2 157.7 23 18.4 13.8 83 66.3 50.0 43 114. 2 86.1 03 162.1 122.2 63 210.0 158.3 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 03 166.9 125.8 69 214.8 161.9 30 24.0 18.1 18.7 90 71.9 54.2 50 119.8 90.3 10- 167.7 126.4 127.0 70 271 215. 6 216.4 162.5 163.1 31 24.8 91 72.7 54.8 151 120.6 90.9 211 168.5 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. 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 32.7 24.1 100 79.9 60.2 60 127.8 96.3 20 175.7 132.4 133.0 80 281 223.6 224.4 168.5 169. 1 41 24.7 101 80.7 60.8 161 128.6 96.9 221 176.5 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 ^.5 09 87.1 65.6 69 135. 101.7 29 182.9 137.8 89 230.8 173.9 50 39.9 30.1 10 87.8 66.2 70 135.8 136.6 102.3 30 183. 7 138.4 90 231.6 174.5 175. 1 51 40.7 30.7 111 88.6 66.8 171 102.9 231 184. 5 139. 291 232.4 52 41.5 31.3 12 89.4 67.4 72 137.4 103.5 32 185. 3 i 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. 96 236.4 178.1 57 45.5 34.3 17 93.4 70.4 77 141.4 106.5 37 189. 3 142. 6 97 237.2 178.7 58 46.3 34.9 18 94.2 71.0 78 142.2 107.1 38 190. 1 143. 2 98 238.0 179.3 59 47.1 35.5 19 95.0 71.6 79 143.0 107.7 39 190.9 143.8 99 238. 8 179.9 60 47.9 36.1 20 95.8 72.2 80 143.8 108.3 40 191.7 144.4 300 239.6 180.5 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep-. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 53° (127°, 23S t°, 307= ). TABLE ± [Page 441 Difference of Latitude and Departure for 37° (143°, 217°, 323 '). Dlst. Lat. Dep. Dist. Lat. Dep. Dist. Lat. { Dep. i Dist. Lat. Dep. Dist. i Lat. Dep. 301 240.4 181.1 361 288. 3 217.3 421 336.2 1 253. 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. 82 384.9 290.0 42 432.8 326.2 03 242.0 182.4 63 289.9 218.5 23 1 337.8 254. 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 i 340.2 1 256. 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. 87 388.9 293.0 47 436.8 329.1 08 245.9 185.4 68 293.9 221.5 28 1 341.8 257. 6 88 389.7 293.6 48 437.6 329.7 09 246.7 186.0 69 294.7 222.1 29 342.6 1 258. 2 89 390.5 .294.2 49 438.4 330. 3 10 311 247.5 248.3 186.6 18772 70 295.5 222.7 30 343.4 344. 2 ; 258. 8 259.4 90 491 391.3 294.8 50 439.2 330.9 371 296.3 223.3 431 392.1 295.4 551 1 440.0 331.5 12 249.1 187.8 72 297.1 223.9 32 345. 260. 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 1 348.2 i 262. 4 96 396.1 298. 5 56 444.0 334.6 17 253.1 190.8 77 301.1 226.9 37 i 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 i 350.6 264.2 99 398.5 300.3 59 446.4 336.4 20 321 255.5 256.3 192.6 80 381 303. 4 304.2 228.7 40 351.4 352. 2~ 264.8 500 399.3 400.1 300.9 60 447.2 337.0 193.2 229. 3 441 265.4 501 301.5 561 448.0 337.6 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. 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 6.5 451. 2 340. 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 I 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 90 311.4 312.2 234.7 235.3 50 359.4 451 360.1 270.8 271.4 10 511 407. 3 408.1 306.9 307.5 70 , 455.2 343.0 571 456.0 343.6 331 199.2 391 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 34.5.5 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. 346. 7 37 269.1 202.8 97 317.0 238.9 57 364.9 275. 17 412.9 311.2 77 460.8 347.3 38 269.9 203.4 98 317.8 239. 5 58 365. 7 ^75.6 18 413.7 311.8 78 461.6 347.9 39 270.7 204.0 99 318.6 240.1 59 366.5 276.2 19 414. 5 312.4 79 462.4 348.5 40 341 271. 5 272.3 204.6 400 401 319. 4 320.2 240.7 241.3 60 367.3 461 368. 1 276.8 277. 4 20 521 415.3 416. 1 313.0 313.6 80 463. 2 349. 1 581 464. 349. 7 205.2 42 273.1 205.8 02 321.0 241.9 62 368.9 278.0 22 416. 9 314.2 82 464.8 3.50.3 43 273.9 206.4 03 321.8 242.5 63 369. 7 278.6 23 417.7 314.8 83 46.5.6 3,50.9 44 274.7 .207. (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 1 372. 1 280.4 26 420.1 316.6 86 468. 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 j 373. 7 281.6 28 421.7 317.8 88 469.6 3.53.9 49 278.7 210.0 09 326.6 246.1 69 374.5 282.3 29 422. 5 318.4 89 470.4 3.54.5 50 351 279.5 280.3 210.6 10 327.4 328. 2 246.7 247. 3 70 1 375.3 282.9 30 423. 3 424.1 319.0 319. 6 90 471. 2 355. 1 .591 472. 3.55. 7 211.2 411 471 376. 1 283. 5 531 52 281.1 211.8 12 329.0 247.9 72 376. 9 ' 284. 1 32 424.9 320.2 92 , 472.8 3.56.3 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. 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. 358. 7 57 285.1 214.8 17 333. 251. 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 i 287. 7 38 429.7 323.8 98 477.6 3.59.9 59 286.7 216.1 19 334.6 252. 2 79 382.5 288.3 39 430.5 324.4 99 { 478.4 i 360.5 60 287.5 216.7 20 335.4 252.-8 80 ' 383. 3 1 288. 9 40 431.3 325.0 Lat. 600 i 479. 2 361. 1 Dist. Dep. Lat. Dlst. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Dist. j Dep. Lat. 5 3° (127°, 233°, 307° . Page 442] TABLE 2. Difference of Latitude and Departure for 38° (142°, 218°, 322' )• Dlst. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. DLst. Lat. Dep. 1 i 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 «6 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 43.7 30 131 102.4 80.0 90 149.7 150. 5 117.0 50 251^ 197.0 197.8 153.9 11 8.7 6.8 71 55.9 103.2 80.7 191 117.6 154.5 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 59 204.1 159.5 20 15.8 12.3 12.9 80 63.0 63.8 49.3 40 110.3 86.2 200 201 157.6 123.1 60 204.9 205.7 160.1 21 16.5 81 49.9 141 111.1 86.8 158.4 123.7 261 160.7 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 64 208.0 162.5 25 19.7 15.4 85 67.0 52.3 45 114.3 89.3 05 161.5 126. 2 65 208.8 163.2 26 20.5 16.0 86 67.8 52.9 46 115.0 89.9 06 162. 3 126.8 66 209.6 163.8 27 21.3 16.6 87 68.6 53.6 47 115.8 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. 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 10 165.5 166.3 129.3 70 212.8 166.2 31 24.4 91 71.7 56.0 151 93.0 211 129.9 271 213.6 166.8 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 20 221 173.4 135.4 80 220.6 221.4 172.4 173.0 41 32.3 25.2 101 79.6 62.2 161 126.9 99.1 174.2 136. 1 281 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 51 39.4 40.2 30.8 10 86.7 87. 5" 67.7 70 134.0 104.7 30 181.2 182.0 141.6 142.2 90 29r 228.5 229.3 178.5 179.2 31.4 111 68.3 171 134. 7 105.3 231 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. 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. 5 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. Dlst. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 52' (128 °, 232°, 308°). tablp: 2. [Page 443 1 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. 801 237.2 185.3 361 284.5 222.3 421 331.8 259.2 481 379.0 296.2 .541 426. 3 333. 1 02 238.0 185.9 62 285.3 1222.9] 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 43 427.9 334.3 04 239.6 187.2 64 286.8 224.1 24 334. 1 261.0 84 381.4 298.0 44 428.7 335. 05 240.3 187.8 65 287.6 224.7 25 334.9 261.7 a5 382.2 298.6 45 429. 5 335.6 06 241.1 188.4 66 288.4 225. 3 26 3.35. 7 262.3 86 383. 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. 10 244.3 190.9 70 291.6 227.8 228.4 30 338.8 264.7 90 386.1 301. 7 302.3 50 433.4 338.6 311 245.1 191.5 371 292.4 431 339.6 265.4 491 386.9 551 434.2 339.3 12 245.9 192.1 72 293.1 229.0 32 340.4 266.0 92 387.7 302.9 52 435. 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. 5 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 i 269. 1 97 391.6 ,306. 57 438.9 343.0 18 250.6 195.8 78 297.9 232.7 38 345. 2 1 269. 7 98 392.4 306.6 58 439.7 343. 6 19 251.4 196.4 79 298.7 2,33. 3 39 345. 9 1 270. 3 99 393.2 .307. 2 59 440.5 344.2 20 252.2 197.0 197.6 80 299.4 234.0 234. 6 40 346. 7 270.9 500 394.0 307. 8 308.4 60 561 441.3 442.1 344.8 321 253.0 381 300.2 441 347.5 271.5 501 394.8 345.4 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 23 254.5 198.9 83 301.8 235.8 43 .349. 1 272.7 03 396.4 309.7 63 443.7 346.6 24 255.3 199.5 84 302.6 236.4 44 349.9 273.4 04 397.2 310. 3 64 444.4 347. 2 25 256. 1 200.1 85 303.4 2.37. 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 66 446.0 348.5 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 3-50. 3 30 260.0 203.2 90 307.3 240.1 50 451 354.6 355.4 277.1 10 401.9 314.0 70 449.2 350.9 351.6 331 260.8 203.8 391 308.1 240.7 277.7 511 402.7 314.6 571 450.0 32 261.6 204.4 92 308.9 241.3 52 356. 2 278.3 12 403.5 315. 2 72 450. 7 .352. 2 33 262. 4 1 205. 93 309.7 242.0 53 .357. 278.9 13 404.2 315.8 73 451.5 352.8 34 263.2 205. 6 94 310.5 242.6 54 357.8 279.5 14 405. 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 75 453.1 354. 36 264.8 206.9 96 312.1 243.8 56 359. 3 280.7 16 406.6 ,317. 7 76 453. 9 354. 6 37 265.6 207.5 97 312.8 244.4 57 360.1 1281.4 17 407.4 318. 3 77 454.7 3.55. 2 38 266.3 208.1 98 313. 6 245. 58 360. 9 j 282. 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 60 362.5 363.3 283.2 20 409.8 320.2 80 457.1 457.8 357.1 357.7 341 268.7 209.9 401 316.0 246.9 461 283.8 521 410.6 320.8 581 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 4.59. 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. 5 45 271.9 212.4 05 319.1 249.3 65 366.4 286.3 25 413.7 323.2 85 461.0 360. 2 46 272.7 213. 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 I 214. 3 08 321.5 251.2 68 368.8 288.1 28 416.1 .325. 1 88 463. 3 362.0 49 275. 214. 9 09 322. 3 251.8 69 369.6 288.7 29 416.9 325. 7 89 464.1 362. 6 50 351 275.8 276.6 215.5 10 323.1 252.4 70 370. 4 289.3 290. 30 531 417.6 326.3 90 464.9 363.2 216.1 411 323.9 253.0 471 371.2 418.4 326.9 591 465.7 363.8 52 277.4 ;216.7 12 324.7 253. 7 72 371.9 290.6 32 419.2 327.5 92 466.5 364.4 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 54 279.0 218.0 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. 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 97 470.5 367. 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 Dist. 283.7 221.6 20 331.0 258.6 80 378.2 295.5 40 425.5 332.5 600 472.8 369.4 Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 52° (128°, 232°, 308° ). Page 444J TABLE / '2. Difference of Latit d and Departure for 39° (141°, 219°, 321° )• Dist. Lat. Dep. 0.6 Dist. Lat. Dep. 38.4 Dist. j Lat. Dep. Dist. Lat. Dep. 140.7 113.9 Dist. 241 Lat. Dep. 1 0.8 61 47.4 121 94. 76.1 181 187.3 151.7 2 1.6 1.3 62 48. 2 39. 1 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 ill5.2 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 1117.1 46 191.2 154. 8 7 5.4 4.4 67 52. 1 ! 42. 2 27 98.7 79.9 87 145.3 ill7. 7 47 192.0 155.4 8 6.2 5.0 68 52.8 I 42.8 28 99.5 80.6 88 146.1 ;il8.3 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 71 54. 4 44. 1 55. 2 44. 7 30 131 101. 81.8 90 147.7 119.6 50 194.3 157.3 11 8.5 6.9 101.8 82.4 191 148.4 120.2 251 195.1 158.0 12 9.3 7.6 72 56. 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 ( 1 59.8 48.5 37 106.5 86.2 97 153.1 124.0 57 199.7 161.7 18 14.0 11.3 78 60.6 49.1 38 107.2 86.8 98 153.9 124.6 58 200.5 162.4 19 14.8 12.0 79 61.4 49.7 39 108.0 87.5 99 154.7 125.2 59 201.3 163.0 20 15.5 16.3 12.6 13. 2" 80 62.2 50.3 51.0 40 108.8 88.1 200 155.4 125.9 60 261 202.1 202.8 163.6 21 81 62.9 141 109.6 88.7 201 156.2 126.5 164.3 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 10 163.2 164.0 132.2 70 209.8 169.9 170.5 31 24.1 19.5 91 70. 7 57. 3 151 117.3 95.0 211 132. 8 271 210.6 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 36 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 i 61.0 57 122. 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 41 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 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. 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 70 132.1 107.0 107.6 30 231 178.7 179.5 144.7 90 225.4 182.5 51 39.6 32.1 111 86.3 69.9 171 132.9 145. 4 291 226.1 183. 1 52 40.4 32.7 12 87.0 70.5 72 133.7 108.2 32 180.3 146.0 92 226.9 183. 8 53 41.2 33.4 13 87.8 71.1 73 134.4 108.9 33 181.1 146.6 93 227.7 184.4 54 42.0 34.0 14 88.6 71.7 74 135.2 109.5 34 181.9 147.3 94 228.5 185. 55 42.7 34.6 15 89.4 72.4 75 136.0 110.1 35 182.6 147.9 95 229.3 185. 6 56 43. 5 35.2 16 90.1 73.0 76 136.8 110.8 36 183.4 148.5 96 230.0 186. 3 57 44.3 35.9 17 90.9 73.6 77 137.6 111.4 37 184.2 149.1 97 230.8 186.9 58 45.1 36.5 18 91.7 74.3 78 138.3 112.0 38 185.0 149.8 98 231.6 187.5 59 45.9 37.1 19 92.5 74.9 79 139.1 112.6 39 18.5.7 150. 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 Lat. 300 Dist. 233. 1 Dep. 188.8 Dist. I)ep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 51° (129°, 23 1°, 309' '). TABLE 2. [Page 445 Difference of Latitude and Departure for 39° (141°, 219°, 321°). 1 Dlst. ' Lat. 1 Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. ! Dep. 1 Dist. Lat. Dep. 1 301 233.9 189.4 361 280.6 227.1 421 327. 2 264.9 481 373.8 .302.6 541 420.4 i 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 1303.9 43 422.0 1 341.7 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 : 237.0 191.9 65 283.7 229.7 25 ' 330.3 267.4 85 376. 9 305. 2 45 423.5 : 342.9 0(3 237.8 192.5 66 1 284.4 230.3 26 331.1 268.0 86 377.7 1305.8 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 i 240. 1 194.4 69 286.8 232.2 29 333. 4 269.9 89 380. ; 307. 7 49 426.6 I 345.5 10 311 240.9 i 241.7 195.0 70 287.6 288.3 232.8 233.4 30 431 334.2 1270.6 335. : 271. 2 90 491 380.8 381.6 308.3 308. 9' 50 551 427. 4 1 346. 1 428. 2 1 346. 7 195.7 371 12 i 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 i273. 1 94 383. 9 310.8 54 430.5 1 348.6 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 96 385.5 312.1 56 432. 1 349. 9 17 246.4 199.5 77 293.0 237.2 37 339. 6 275. 97 386.2 312. 7 57 432.8 350.5 18 247.1 200.1 78 293.8 237. 8 38 340.4 275.6 98 387. 313. 3 58 433.6 351.1 19 247.9 200.7 79 294.5 238.5 39 341.2 276.2 99 387. 8 314. 59 434.4 351.7 20 321 248.7 249. 5 201. 3 80 295.3 296.1 239.1 40 342.0 276.9 342.7 277.5 500 501 388.6 389.4 314. 7 60 561 4.35.2 i 352.4 435.9 353.0 202.0 381 239.7 441 315. 3 22 250.3 202.6 82 296.9 240.4 42 343.5 278.1 02 390.1 ;315.9 62 436. 7 353. 6 23 251.0 203.2 83 297.7 241.0 43 344.3 278.7 03 390.9 316.5 63 437.5 354.3 24 251.8 203.9 84 298.4 241.6 44 345.1 |279.4 04 391.7 317.1 64 438. 3 354. 9 25 252.6 204.5 85 299.2 242.2 45 345.8 280.0 05 392.5 317.8 65 439. 1 355. 5 26 253. 4 205.1 86 300. 242.9 46 346.6 [280.6 06 393.2 318.4 66 439.8 356.2 27 254.1 205.7 87 300. 8 243.5 47 347. 4 281.3 07 394.0 1319.0 67 440. 6 356. 8 28 254.9 206.4 88 301.5 244.1 48 348.2 281.9 08 394.8 1319.6 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 i 358. 1 30 256.5 257.2 207.6 90 303.1 ,245.4 50 349.7 283.2 283. 8" 10 511 396.3 397.1 320.9 70 443. I 358. 7 443. 7 359. 3 331 208.3 391 303.9 246.0 451 350. 5 321. 6 571 32 258.0 208.9 92 304.7 246.7 52 351.3 284.4 12 397.9 i322.2 72 444. 5 359. 9 33 258.8 209. 5 93 305.4 247.3 53 352.1 1285.0 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 i 361.2 35 260.4 210.8 95 307.0 248.5 55 353. 6 286.3 15 400.2 324.1 75 446.9 1 361.8 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 i 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 40 341 264.2 213.9 400 310. 9 251.7 60 357. 5 289.4 20 404.1 i327.2 80 450.7 365. 265.0 214.6 401 311.6 252. 3 461 35873 '290. 1 521 404.9 327.8 581 451.5 365. 6 42 265.8 215.2 02 312.4 252.9 62 359.1 290.7 22 405.7 328.5 82 452. 3 366.2 43 266. 6 215.8 03 313.2 253.6 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. 5 45 268.1 217. 1 05 314.8 254.8 65 361.4 292. 6 25 408.0 330. 4 85 454. 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 88 457. 370.0 49 271.2 219.6 09 317.9 257.3 69 364.5 295. 1 29 411.1 332. 9 89 457. 8 370.6 50 351 272.0 272. 8 220.2 220. 8 10 411 318.6 I 258.0 70 365.3 295. 7 30 411. 9 ! 333. 5 90 i 458.5 371.3 319.4 258.6 471 366.0 296.4 531 412.6 j334. 1 591 459.3 371.9 52 273.6 221.5 12 320.2 259.2 72 366.8 297.0 32 413. 4 1 334. 8 92 460. 1 372.5 53 274.3 222.1 13 321.0 259.9 7.i 367.6 297.6 33 414. 2 1 335. 4 93 460.9 373.2 54 275. 1 222.7 14 321.8 260.5 74 368.4 298.3 34 415. 336. 1 94 461.6 373.8 55 275.9 223.4 15 322. 5 261.1 75 369.2 298.9 35 415.8 336.7 95 462.4 374.4 56 276.7 224.0 16 323. 3 261.8 76 369.9 299. 5 36 416. 5 337. 3 96 463.2 375.1 57 277.5 ! 224.6 17 324. 1 262.4 77 370.7 300.1 37 417.3 337.9 97 464.0 375. 7 58 278.2 225.3 18 324.9 263.0 78 371.5 300.8 38 418.1 338.5 98 464.8 1 376. 3 59 279.0 225.9 19 325.6 263.6 79 372.3 301.4 39 418. « 339.1 99 465.5 ' 376. 9 60 279.8 226.5 20 326. 4 ' 264. 3 80 373.0 302.0 40 419. 6 '• 339. 8 600 466. 3 | i 377. 6 Dist. Dep. Lat. Dist. Dep. I Lat. Dist. Dep. Lat. Dist. Dep. ' Lat. Di.st. j Dep. j Lat. e c ►1° (11 29°, 231°, 309°). Page 446J TABLE 2. ■ Difference of Latitude and Departure for 40° (140°, 220°, 320°). Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 0.8 0.6 61 46.7 39.2 121 92.7 77.8 181 138.7 116.3 241 184.6 154.9 2 1.5 i 1.3 62 47.5 39.9 22 93.5 78.4 82 139.4 117.0 42 1&5.4 155.6 3 2.3 i 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 i 2.6 64 49.0 41.1 24 95.0 79.7 84 141.0 118. 3 - 44 186.9 156.8 5 3.8 ; 3.2 65 49.8 41.8 25 95.8 80.3 85 141.7 118.9 45 187.7 157.5 6 4.6 1 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 8 6.1 5.1 68 52.1 43.7 28 ! 98.1 82.3 88 144.0 120.8 48 190.0 159. 4 9 6.9 5.8 69 52.9 44.4 29 98.8 82.9 89 144.8 121.5 49 190. 7 160.1 10 7.7 6.4 70 53.6 54.4 45.0 30 99.6 100.4 83.6 84.2 90 145.5 122.1 50 251 191.5 160.7 11 8.4 7.1 71 45.6 131 191 146.3 122.8 192.3 161.3 12 9.2 /. 1 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 54 194.6 163.3 15 11.5 9.6 75 57.5 48.2 35 103.4 86.8 95 149.4 125.3 55 195.3 163. 9 16 12. 3 10. 3 76 58.2 48.9 36 104.2 87.4 96 150.1 126.0 56 196.1 164.6 17 13.0 10.9 77 59.0 49.5 37 104.9 88.1 97 150.9 126.6 57 196.9 165.2 18 13.8 11.6 78 59.8 50.1 38 105.7 88.7 98 151.7 127.3 58 197.6 165.8 19 14.6 12.2 79 60.5 50.8 39 106.5 89.3 99 152.4 127.9 59 198.4 166. 5 20 15.3 12.9 80 61.3 51.4 40 107.2 90.0 200 "201 153.2 128.6 60 199.2 199.9 167.1 167. 8 21 16.1 13.5 81 62.0 52.1 141 108.0 90.6 154.0 129.2 261 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 91 68.9 69.7 57.9 50 114.9 96.4 10 160.9 135.0 70 206.8 207.6 173.6 174.2 31 23.7 19.9 58.5 151 115. 7 1 97. 1 211 161.6 135.6 271 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 1 100. 9 17 166.2 139.5 77 212.2 178. 1 38 29.1 24.4 98 75.1 6.3.0 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 41 30. 6 31.4 25.7 26.4 100 76.6 64.3 60 161 122.6 102.8 20 168.5 141.4 80 214. 5 180.0 180. 6 101 77.4 64.9 123.3 103.5 221 169.3 142.1 281 215.3 42 32.2 27.0 02 78.1 65.6 62 124.1 104.1 22 170.1 142.7 82 216.0 181.3 43 32.9 27.6 03 78.9 66.2 63 124.9 104.8 23 170.8 143. 3 83 216.8 181.9 44 33.7 28.3 04 79.7 66.8 64 125.6 105.4 24 171.6 144.0 . 84 217.6 182.6 45 34.5 28.9 05 80.4 67. 5 65 126.4 106.1 25 172.4 144.6 85 218.3 183.2 46 35.2 29.6 06 81.2 68.1 66 127.2 106.7 26 173. 1 145.3 86 219.1 183.8 47 36.0 30.2 07 82.0 68.8 67 127.9 107.3 27 173. 9 145.9 87 219.9 184.5 48 36.8 30.9 08 82.7 69.4 68 128.7 108.0 28 174.7 146.6 88 220.6 185.1 49 .37.5 31.5 09 83.5 70.1 69 129. 5 108.6 29 175.4 147.2 89 221.4 185.8 50 38.3 ' 39.1 32.1 10 84.3 85.0 70.7 70 130.2 131.0 109.3 30 176.2 147.8 90 222.2 222. 9 186.4 51 32.8 111 71.3 171 109.9 231 177.0 148.5 291 187.1 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 i 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. 55 42.1 i 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 j 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. 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. 1 Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. ' >0° (130°, 230°, 310° . - TABLE 2. [Page 447 Difference of Latitude and Departure for 40° (140°, 220 °, 320° ). Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 230.6 193.5 361 276. 5 232.1 421 322.5 270.6 481 368.5 309.2 541 414.4 347.7 02 231.3 194.1 62 277.3 232.7 22 323. 3 271.3 82 369. 2 309.8 42 415.2 348.4 03 232.1 194.8 63 278.1 233.3 23 324. 271.9 83 I 370.0 310. 5 43 416.0 349.0 04 232.9 195.4 64 278.8 234.0 24 324.8 272.6 84 370. 8 311.1 44 416. 7 349. 7 | 05 233.6 196.1 65 279.6 234.6 25 325. 6 273. 2 85 371.5 311.7 45 417.5 350. 3 06 234.4 196.7 66 280.4 235. 3 26 326.3 273.8 86 372.3 312.4 46 418.3 351.0 07 235.2 197.3 67 281.1 235.9 27 327.1 274. 5 87 373.1 313.0 47 419.0 351.6 08 235.9 198.0 68 281.9 236.6 28 327.9 275. 1 88 373.8 313.6 48 419.8 1 352.2 09 236.7 198. 6 69 282.7 237.2 29 328.6 275. 8 89 374.6 314.3 49 420.6 352.9 10 237.5 199.3 70 283.4 237.8 30 329.4 276.4 90 375.4 314.9 50 421.3 353.5 311 238.2 199.9 371 284.2 238.5 431 330.2 277.1 491 376.1 315.6 551 422.1 354.2 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 37?. 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 i 356.8 16 242.1 203.1 76 288.0 241.7 36 334. 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 80 291.1 291. '9 244.3 40 337.1 282.8 500 383. 321.4 60 429.0 i 360.0 321 245.9 206.3 381 244.9 441 337.8 283. 5 501 383. 8 322. 561 429.8 1 360.6 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 i 389.2 326.5 68 435.1 365.1 29 252.0 211.5 89 298.0 250.1 49 344.0 288. 6 09 389.9 327. 1 69 435.9 365.8 30 252.8 212.1 90 298.8 250. 7 50 344.7 345.5 289.3 10 390. 7 391. 5 327.8 70 571 436.6 366.4 437.4 367.0 331 253.6 212.8 391 299.5 251.3 451 289.9 511 328.4 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. 291.2 13 393. 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. 35 256.6 215.3 95 302.6 253.9 55 348.6 292.5 15 394. 5 331. 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 i 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 i 396.8 332. 9 78 442.8 ( 371.5 39 259.7 217.9 99 305.7 256.5 59 351.6 295.0 19 1 397.6 333. 6 79 443.5 372.2 40 341 260.5 218.6 400 306.4 257.1 60 352. 4 295.7 20 i 398.3 521 i 399. 1 334. 2 334. 9 80 581 444.3 372.8 445. 1 373. 5 261.2 219. 2 401 307.2 257.8 461 353.1 296.3 42 262.0 219.8 02 308.0 258.4 62 353.9 297.0 22 399.9 335. 5 82 445.8 1 374.1 43 262.8 220.5 03 308.7 259. 1 63 354.7 297.6 23 1 400.6 336. 1 83 446. 6 374. 8 44 263. 5 221.1 04 309. 5 259.7 64 355. 4 298.3 24 401.4 336.8 84 447. 4 375. 4 45 264. 3 221.8 05 310.2 260.3 65 356.2 298.9 25 402. 2 337. 4 85 448.1 376.0 46 265.1 222.4 06 311.0 261.0 66 357.0 299.5 26 402. 9 338.1 86 448.9 376.7 47 265.8 223.1 07 311.8 261.6 67 357.7 300. 2 27 403. 7 338.7 87 449.7 377.3 48 266.6 223.7 08 312.5 262.3 68 358.5 300.8 28 404.5 339. 4 88 450.4 378.0 49 267.4 224.3 09 313. 3 262.9 69 359. 3 301. 5 29 1 405.2 340,0 89 451. 2 378. 6 50 268.1 225.0 225.6 10 411 314.1 314.8 263.6 264.2 70 471 360.0 360.8 302. 1 302.8 30 406.0 531 i 406.8 340. 6 "341.3 90 452.0 379.2 351 268.9 591 452. 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 1 380.5 53 270.4 226.9 13 316.4 265.5 73 362.3 304. 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 1 409. 1 343. 2 94 455.0 1 381.8 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 7^ 366.9 307.9 39 ! 412.9 346.4 99 458. 9 385. 60 275.8 231.4 20 321.7 270.0 80 367.7 308.5 40 ' 413. 7 347.1 600 459.6 385.7 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 50° (1 30°, 230 °, 310° )• Page 448] TABLE 2. Difference of Latitude and Departure for 41° (139°, 221°, 319° ). Dirt. 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 4.5 3.9 » 66 49.8 43.3 26 95.1 82.7 86 140.4 122.0 46 185.7 161.4 7 5.3 4.6 67 50.6 44.0 27 95.8 83.3 87 141.1 122.7 47 186.4 162.0 8 6.0 5.2 68 51.3 44.6 28 96.6 84.0 88 141.9 123. 3 48 187.2 162.7 9 6.8 5.9 69 52.1 45.3 29 97.4 84.6 89 142.6 124.0 49 187.9 163.4 10 7.5 6.6 70 52.8 45.9 30 98.1 98.9 85.3 90 143.4 124.7 50 188.7 164.0 11 8.3 7.2 71 53.6 46.6 131 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 '201 150.9 151.7 131.2 60 196.2 170.6 171.2 21 15.8 13.8 81 61.1 53.1 141 106.4 92.5 131.9 261 197.0 22 16.6 14.4 82 61.9 53.8 42 107.2 93.2 02 152. 5 132.5 62 197.7 171.9 23 17.4 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. 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 68.7 59.0 50 113.2 114.0 98.4 10 158.5 137.8 138.4 70 271' 203.8 204.5 177.1 177.8 31 23.4 20.3 91 59.7 151 99.1 211 159.2 32 24.2 21.0 92 69.4 60.4 52 114. 7 99.7 12 160.0 1.39. 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 1^3.0 141.7 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. 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 60 120.8 121.5 105.0 105.6 20 221 166.0 166.8 144.3 145. 0~ 80 281 211.3 212.1 183.7 41 30.9 26.9 101 76.2 66.3 161 184.4 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. 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 70 128.3 111.5 112. 2 30 231 173.6 174.3 150.9 90 218.9 219.6 190.3 190. 9" 51 38.5 33.5 111 83.8 72.8 171 129.1 151.5 291 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. Dist. Dep. Lat. 49° (1 31°, 229 °, 311° ). TABLE 2. [Page 449 | Difference of Latitude and Departure for 41° (139°, 221 °, 319° )• Dist. 301 Lat. Dcp. Dist. 361 Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 227.2 197.5 272.5 236.9 421 317.7 276.2 481 363.0 315. 6 541 408.3 354. 9 02 227.9 198.1 62 273.2 237.5 22 318. 5 276.9 82 363.8 316.2 42 409.0 355.6 03 228.7 198.8 63 274.0 238.2 23 319. 2 277.5 83 364.5 316.9 43 409.8 356.2 04 229.4 199.4 64 274.7 238.8 24 320.0 278.2 84 365. 3 317. 5 44 410.6 356.9 05 230.2 200.1 65 275.5 239.5 25 320. 8 278.8 85 366.0 318.2 45 411.3 357.5 08 230.9 200.8 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 10 234.0 234.7 203.4 70 279.2 242.7 30 431 324. 5 282.1 90 369.8 370.6 321.5 322.1 50 551 415.1 360.8 811 204.0 371 280.0 243.4 325.3 282.8 491 415.8 361.5 12 235.5 204.7 72 280.8 244.1 32 326. 283.4 92 371.3 322.8 52 416.6 362.1 13 236.2 205.4 73 281.5 244.7 33 326.8 284.1 93 372.1 323.4 53 417. 3 362.8 14 237.0 206.0 74 282.3 245.4 34 327. 5 284.7 94 372.8 324.1 54 418.1 363.4 15 237.7 206.7 75 283.0 246.0 35 328.3 285.4 95 373.6 324.7 55 418.9 364.1 16 238.5 207.3 76 283.8 246.7 36 329.1 286.0 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 3^5. 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 80 286.8 287.5 249.3 40 332.1 288.7 500 501 377. 3 378.1 328.0 60 422.6 367.4 321 242.3 210.6 381 250.0 441 332. 8 i 289. 3 328.7 561 423.4 368.0 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 6.5 426.4 370.7 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 30 331 249.1 216.5 90 294.3 255.9 256. 5 50 339.6 295.2 10 384.9 385.7 334.6 335.2 70 571 430. 2 374.0 249.8 217.2 391 295.1 451 340.4 295.9 511 430.9 374.6 32 250.6 217.8 92 295.8 257.2 52 341. 1 296.5 ■ 12 386.4 335.9 72 431.7 375. 3 33 251.3 218,5 93 296.6 257.8 53 341. 9 297.2 13 387.2 336.5 73 432.4 375. 9 34 252.1 219.1 94 297.4 258. 5 54 342.6 297.9 14 387.9 337.2 74 433.2 376.6 35 252.8 219.8 95 298.1 259. 2 55 343.4 298.5 15 388.7 337.9 75 434. 377.2 36 253.6 220.4 96 298.9 259.8 56 344. 1 299.2 16 389.4 338.5 76 434.7 377.9 37 254. 3 221.1 97 299.6 260.5 o/ 344.9 299.8 17 390.2 339.2 1 1 435.5 378. 5 38 255.1 221.8 98 300.4 261. 1 58 345. 7 300.5 18 390.9 339. 8 78 436.2 379.2 39 255.8 222.4 99 301.1 261.8 59 346.4 301.1 19 391.7 340.5 79 437.0 379.8 40 256. 6 257.4 223.1 400 301.9 262.4 60 461 347.2 347.9 301.8 302.5 20 392.4 393. 2 341.1 80 437.7 380.5 341 223.7 401 302.6 263.1 521 341. 8 581 438.5 381.2 42 258.1 224.4 02 303.4 263.7 62 348.7 303. 1 22 394.0 342.5 82 439.2 381.8 43 258.9 225.0 03 304.2 264.4 63 349.4 303.8 23 394.7 343.1 83 440.0 382.5 44 259.6 225.7 04 304.9 265.1 64 350. 2 304.4 24 395. 5 343.8 84 440.7 383.2 45 260.4 226.3 05 305.7 265. 7 65 350.9 305. 1 25 396.2 344.4 85 441.5 383.8 46 261.1 227.0 06 306. 4 266.4 66 351. 7 305. 7 26 397.0 345.1 86 442.3 384.5 47 261.9 227.7 07 307.2 267.0 67 352. 5 306.4 27 397.7 345. 7 87 443.0 385. 1 48 262.6 228. 3 08 307.9 267.7 68 353. 2 307.0 28 398.5 346.4 88 443.8 385.8 49 263.4 229.0 09 308.7 268.3 69 354.0 307.7 29 399.2 347.0 89 444.5 386.4 50 264.2 264. 9 229.6 10 309.4 269.0 269.6 70 471 354.7 355:5 308.4 30 531 400.0 400.7 347.7 90 445.3 387.1 351 230.3 411 310.2 309.0 348.4 591 446.0 387.7 52 265.7 230.9 12 310.9 270.3 72 356. 2 309. 7 32 401.5 349. 92 446.8 388.4 53 266.4 231.6 13 311.7 271.0 73 357. 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. 350. 3 94 448.3 389.7 55 267.9 232.9 15 313.2 272.3 75 358. 5 311.6 35 403.8 351. 95 449.1 390.4 56 268.7 233.6 16 314. , 272. 9 76 359.2 312. 3 36 404.5 351.6 96 449.8 391.0 57 269.4 234.2 17 314.7 273.6 77 360.0 312.9 37 405.3 352. 3 97 450.6 391. 7 58 270.2 234.9 18 315.5 274.2 78 360.8 313.6 38 406.0 352. 9 98 451. 3 392. 3 59 270.9 235. 5 19 316. 2 274.9 79 361.5 1314.3 39 406.8 353. 6 • 99 452.1 393.0 60 271.7 236.2 20 317.0 275.6 80 362.3 314.9 40 407.5 354.3 600 452.8 393.6 Dist. Dep. Lat. Diet. Dep. Lat. Dist. Dep. 1 Lat. Dist. Dep. Lat. Dist. Dep. Lat. 49° (1 31°, 229°, 311° )• 22489—03- -29 Page 450 1 TABLE '2. Difference of Latitude and Departure for 42° (138°, 222°, 318° ). Dist. Lat. Dep. Dist. Lat. Dep. Dist. 1 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 i 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. ! 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 7.4 70 71" 52.0 46.8 30 96.6 97.4 87.0 90 141.2 141.9 127.1 50 251 185.8 186.5 167.3 11 8.2 52.8 47.5 131 87.7 191 127.8 168.0 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 1129.8 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 93.7 200 148.6 149.4 133.8 134.5 60 261 193.2 194.0 174.0 21 15.6 14.1 81 60.2 54.2 141 104.8 94.3 201 174.6 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 64 196.2 176.7 25 18.6 16.7 85 63.2 56.9 45 107.8 97.0 05 152. 3 137.2 65 196.9 177.3 26 19.3 17.4 86 63.9 57.5 46 108.5 97.7 06 153. 1 137.8 66 197.7 178.0 27 20.1 18.1 87 64.7 58.2 47 109.2 98.4 07 153.8 138.5 67 198.4 178. 7 28 20.8 18.7 88 65.4 58.9 48 110.0 99.0 08 154. 6 139.2 68 199.2 179.3 29 21.6 19.4 89 66.1 59.6 49 110.7 99.7 09 155.3 139.8 69 199.9 180.0 30 31 22.3 20.1 90 66.9 67.6 60.2 50 111.5 112.2 100.4 10 156.1 156.8 140.5 70 200.6 180.7 23.0 20.7 91 60.9 151 101.0 211 141.2 271 201.4 181.3 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 1 115.2 103.7 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 41 29.7 26.8 100 101 74.3 66.9 60 118.9 107.1 20 163. 5 164.2 147.2 80 281 208.1 208.8 187.4 188.0 30.5 27.4 75.1 67.6 161 119.6 107.7 221 147.9 42 31.2 28.1 02 75.8 68.3 62 120.4 108.4 22 165.0 148.5 82 209.6 1"88.7 43 32.0 28.8 03 76.5 68.9 63 121.1 109.1 23 165.7 149.2 83 210.3 189.4 44 32.7 29.4 04 77.3 69.6 64 121.9 109.7 24 166.5 149.9 84 211.1 190.0 45 33.4 30.1 05 78.0 70.3 65 122.6 110.4 25 167.2 150.6 85 211.8 190.7 46 34.2 30.8 06 78.8 70.9 66 123. 4 111.1 26 168.0 151.2 86 212.5 191.4 47 34.9 31.4 07 79.5 71.6 67 124.1 111.7 27 168.7 151.9 87 213.3 192.0 48 35.7 32.1 08 80.3 72.3 68 124. 8 ' 112. 4 28 169.4 152.6 88 214.0 192.7 49 36.4 32.8 09 81.0 72.9 69 125. 6 i 113. 1 29 170.2 153. 2 89 214.8 193.4 50 51 37.2 37.9 33.5 10 81.7 73.6 70 126.3 127.1 113.8 30 170.9 171.7 153.9 90 215.5 194.0 194.7 34.1 111 82.5 74.3 171 114.4 231 154.6 291 216.3 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. 1 Lat. Dist. Dep. Lat. Dist. Dep. Lat. 48° (132°, 228°, 312). 1 TABLE 2. [Page 451 | Difference of Latitude and Departure for 42° (138°, 222°, 318° ). Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. ; Dep. Dist. Lat. Dep. Dist. Lat. 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. 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 i 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 48 318.1 286.4 88 362.7 326.6 48 407.2 366.7 09 229.6 206.8 69 274.2 246.9 29 318.8 287.1 89 363. 4 327.2 49 408.0 367.4 10 311 230.4 231.1 207.4 208.1 70 275.0 247.6 30 319.6 287.7 90 .364.1 :327.9 50 408.7 368. 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. 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 20 321 237.8 214.1 80 282.4 254.3 40 327.0 294.4 295.1 500 371.6 334.6 60 416.2 416.9 374.7 238.6 214.8 381 283.1 254.9 441 327.7 501 372.3 335.3 561 375. 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 i 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 50 451" 334.4 335.2 301.1 10 379.0 341.3 70 423.6 424.3 381.4 331 246.0 221.5 391 290.6 261.6 301.8 511 379.7 341.9 571 382.1 32 246.7 222.2 92 291.3 262. 3 52 335.9 302.5 12 380.5 342.6 72 425.1 382.8 33 247.5 222.8 93 292.1 263.0 53 336.6 303.1 13 381.2 343.3 73 425.8 383.4 34 248.2 223.5 94 292.8 263.6 54 337.4 1303.8 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. 77 428.8 386.1 38 251.2 226.2 98 i 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 40 341 252.7 253.4 227.5 400 297. 3 267.7 60 341.8 307.8 20 386.4 348.0 80 431.0 388.1 228.2 401 i 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 i 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 1 299.5 269.7 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 6(5 346.3 311.8 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. ()A 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. 314.5 315.2 30 393. 9 i 354. 6 90 438.4 394. 8 351 260.8 234.9 411 305. 4 275.0 471 531 394.6 355.3 591 439.2 395.4 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 57 265.3 238.9 17 309. 9 279.0 77 354.5 319.2 37 399.1 359.3 97 443.7 399.5 58 266.0 239.6 18 i 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 i 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. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 48° (1 32°, 228°, 312° ). Page 452 TABLE 2. Difference of Latitude and Departure for 43° (137°, 223 °, 317° )• Dist. Lat. Dep. Dist. Lat. Dep. Dist. { Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 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 1 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 i 90.0 83.9 83 133.8 124.8 43 177.7 165.7 4 2.9 2.7 64 46.8 43.6 24 : 90.7 84.6 84 134.6 125.5 44 178.5 166.4 5 3.7 3.4 65 47.5 44.3 25 i 91.4 85.2 85 135. 3 126.2 45 179.2 167.1 6 4.4 4.1 ^6 48.3 45.0 26 92.2 85.9 86 136.0 126.9 46 179.9 167.8 7 5.1 4.8 67 49.0 45.7 27 92.9 86.6 87 136. 8 127.5 47 180.6 168.5 8 5.9 5.5 68 49.7 46.4 28 93.6 87.3 88 137.5 128.2 48 181.4 169.1 9 6.6 6.1 69 50.5 47.1 29 94.3 88.0 89 138.2 128.9 49 182.1 169.8 10 7.3 6.8 70 51.2 47.7 30 95.1 95.8 88.7 89.3 90 139.0 129.6 50 182.8 170.5 11 8.0 7.5 71 51.9 48.4 131 191 139.7 130.3 251 183.6 171.2 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 i 97.3 90.7 93 141.2 131.6 53 185.0 172.5 14 10.2 9.5 74 54.1 50.5 34 98.0 91.4 94 141.9 132.3 54 185.8 173.2 15 11.0 10.2 75 54.9 51.1 35 98.7 92.1 95 142.6 133.0 55 186.5 173.9 16 11.7 10.9 76 55.6 51.8 36 99.5 92.8 96 143.3 133.7 56 187.2 174.6 17 12.4 11.6 77 56.3 52.5 37 100.2 93.4 97 144.1 134.4 57 188.0 175.3 18 13.2 12.3 78 57.0 53.2 38 100.9 94.1 98 144.8 135.0 58 188.7 176.0 19 13.9 13.0 79 57.8 53.9 39 i 101.7 94.8 99 145.5 135.7 59 189.4 176.6 20 14.6 13.6 80 58.5 54.6 40 102.4 103.1 95.5 96.2 200 146.3 136.4 60 190.2 177.3 21 15.4 14.3 81 59.2 55.2 141 201 147.0 137.1 261 190.9 178.0 22 16.1 15.0 82 60.0 55.9 42 1 103.9 96.8 02 147.7 137.8 62 191.6 178.7 23 16.8 15.7 83 60.7 56.6 43 { 104.6 97.5 03 148.5 138.4 63 192.3 179.4 24 17.6 16.4 84 61.4 57.3 44 105.3 .98.2 04 149.2 139.1 64 ! 193.1 180.0 25 18.3 17.0 85 62.2 58.0 45 106.0 98.9 05 149.9 139.8 65 193.8 180.7 26 19.0 17.7 86 62.9 58.7 46 106.8 99.6 06 150.7 140.5 66 i 194.5 181.4 27 19.7 18.4 87 63.6 59.3 47 ' 107.5 100.3 07 151.4 141.2 67 1 195.3 182.1 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 09 152.9 142.5 69 196. 7 i 183. 5 1 30 21.9 20.5 90 65.8 61.4 50 109.7 102.3 10 153.6 143.2 70 197.5 198.2 184.1 31 22.7 21.1 91 66.6 62.1 151 110.4 103.0 211 154.3 143.9 271 184.8 32 23.4 21.8 92 67.3 62.7 52 111.2 103.7 12 155.0 144.6 72 198.9 185.5 33 24.1 22.5 93 68.0 63.4 53 111.9 104.3 13 155.8 145.3 73 199.7 186.2 34 24.9 23.2 94 68.7 64.1 54 112.6 105.0 14 156.5 145.9 74 200.4 186.9 35 25.6 23.9 95 69.5 64.8 55 113.4 105.7 15 157.2 146.6 75 201.1 187.5 36 26.3 24.6 96 70.2 65.5 56 114.1 106.4 16 158.0 147.3 76 201.9 188.2 37 27.1 25.2 97 70.9 66.2 57 114.8 107.1 17 158.7 148.0 77 202.6 188.9 38 27.8 25.9 98 71.7 66.8 58 115. 6 107.8 18 159.4 148.7 78 203.3 189.6 39 28.5 26.6 99 72.4 67.5 59 116.3 108.4 19 160.2 149.4 79 204.0 190.3 40 29.3 27.3 100 73.1 68.2 60 117.0 117.7 109.1 20 160.9 150.0 80 281 204.8 191.0 41 30.0 28.0 101 73.9 68.9 161 109.8 221 161.6 150.7 205.5 191.6 42 30.7 28.6 02 74.6 69.6 62 118.5 110.5 22 162.4 151.4 82 206.2 192.3 43 31.4 29.3 03 75.3 70.2 63 119.2 111.2 23 163.1 152.1 83 207.0 193.0 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 65 120.7 112.5 25 164.6 153.4 85 208.4 194.4 46 33.6 31.4 06 77.5 72.3 66 121.4 113.2 26 165.3 154.1 86 209.2 195.1 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 70 171 124.3 115.9 30 168.2 156. 9 157.5 90 212.1 197.8 51 37.3 34.8 111 81.2 75.7 125.1 116.6 231 168.9 291 212.8 198.5 52 38.0 35.5 12 81.9 76.4 72 125.8 117.3 32 169.7 158.2 92 213.6 199.1 53 38.8 36.1 13 82.6 77.1 73 126.5 118.0 33 170.4 158.9 93 214.3 199.8 54 39.5 36.8 14 83.4 77.7 74 127.3 118.7 34 171.1 159.6 94 215.0 200.5 55 40.2 37.5 15 84.1 78.4 75 128.0 119.3 35 171.9 160.3 95 215.7 201.2 56 41.0 38.2 16 84.8 79.1 76 128.7 120.0 36 172.6 161.0 96 216.5 201.9 57 41.7 38.9 17 85.6 79.8 77 129.4 120.7 37 173. 3 161.6 97 217.2 202.6 58 42.4 39.6 18 86.3 80.5 78 130.2 121.4 38 174.1 162.3 98 217.9 203.2 59 43.1 40.2 19 87.0 81.2 79 130. 9 122.1 39 174.8 163.0 99 218.7 203.9 60 43.9 40.9 20 87.8 81.8 80 131.6 122.8 40 175.5 163.7 300 219.4 204.6 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. t7° (133°, 227 °, 313° ). TABLE 2. [Page 453 Dist. Difference of Latitude and Departure for 43° (137°, 223°, 317° ). Lat. Dep. Dist. Lat. Dep. Dist. Lat. 1 Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 220.1 205.3 361 264.0 246.2 421 307. 9 287. 1 481 351.8 328.1 541 395. 7 369. 02 220.9 206.0 62 264.8 1246.9 22 308. 6 j 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. 291.9 88 356.9 332.8 48 400.8 373.7 09 226.0 210.7 69 269.9 251.7 29 313.8 292.6 89 357.7 333.5 49 401.5 374.4 10 311 226.-7 227.5 211.4 70 270.6 252.3 30 431" 314.5 293.3 90 358.4 334.2 50 402.2 403.0 375.1 375.8 212.1 371 271.3 253.0 315.2 293.9 491 359.1 334.9 551 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 57 407.4 379.9 18 232.6 216.9 78 276.5 257.8 38 320.3 298.7 98 364.2 1339.6 58 408.1 380.6 19 233.3 217.6 79 277.2 258.5 39 321.1 299.4 99 364.9 1340.3 59 408.8 381.2 20 321 234.0 218.2 80 381 277.9 278.7 259.2 259. 8 40 321.8 300.1 300.8 500 365.7 i 341.0 60 409.6 381.9 382.6 234.8 218.9 441 1 322.5 501 366.4 341.7 561 410.3 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 90 285.2 286.0 266.0 50 451 329.1 306.9 10 373.0 347.8 70 416.9 388.7 389.4 331 242.1 225.7 391 266.7 329.9 307.6 511 373.8 348.5 571 417.6 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 1349. 9 73 419.1 390.8 34 244.3 227.8 94 288.2 268.7 54 332.1 309.6 14 376. { 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 i351.2 75 420.5 392.2 36 245.7 229.2 96 289.6 270.1 56 333.5 311. 16 377.4 351.9 76 421.3 392.8 37 246.5 229.8 97 290.4 270.8 57 334.3 311.7 17 378.2 352.6 77 422.0 393.5 38 247.2 230. 5 98 291.1 271.4 58 335.0 312.4 18 378.9 353.3 78 422.7 394.2 39 247.9 231.2 99 291.8 272.1 59 335.7 313.0 19 379.6 354.0 79 423.5 394.9 40 248.7 249.4 231.9 232.6 400 292.6 272.8 60 336.5 337.2 313.7 20 380.3 354.6 80 424.2 395.6 341 401 293.3 273.5 461 314.4 521 381.1 355.3 581 424.9 396.2 42 250.1 233.2 02 294.0 274.2 62 337.9 315.1 22 381.8 356.0 82 425.7 396.9 43 250.9 233.9 03 294.7 274.9 63 338.7 315.8 23 382.6 356.7 83 426.4 397.6 44 251.6 234.6 04 295.5 275.5 64 ! 339.4 316.5 24 383.3 357. 4 84 427.1 398.3 45 252. 3 235.3 05 296.2 276.2 65 340.1 317.1 25 384.0 358.1 85 427.9 399.0 46 253.1 236.0 06 296.9 276.9 66 340.8 317.8 26 384.7 358.7 86 428.6 399.6 47 253.8 236.7 07 297.7 277.6 67 341.6 318.5 27 385.5 359.4 87 429.3 400.3 48 254.5 237.3 08 298.4 278.3 68 342.3 319.2 28 386.2 360.1 88 430.1 401.0 49 255.3 238.0 09 299. 1 278.9 69 343.0 319.9 29 386. 9 360.8 89 430.8 401.7 50 256.0 238.7 10 299.9 279.6 70 343.7 320.5 321. 2 30 387.6 388. 4 361.5 90 431.5 402.4 351 256.7 239.4 411 300.6 280.3 471 344.5 531 362.1 591 432.3 403.1 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 95 435.2 405. 8 56 260.4 242.8 16 304.3 283.7 76 348.1 324.6 36 392.0 365.5 96 435.9 406.5 57 361.1 243.5 17 305.0 284.4 77 348.9 325.3 37 392.8 366.2 97 436.7 407.2 58 261.8 244.2 18 305.7 285.1 78 349.6 326.0 38 393.5 366.9 98 437.4 407.8 59 262.6 244.8 19 306.4 285.8 79 350.3 326.7 39 394.2 367.6 99 438.1 408.5 60 263.3 245.5 20 307.2 286.4 80 ! 351.1 327.4 40 394.9 368.3 600 438.8 409.2 Dist. Dep. Lat. Dist. Dep. Lat. Dist. j Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 4 7° (133°, 227°, 313° )• Page 454 1 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 i 131. 6 1 127. 1 43 174.8 168.8 4 2.9 2.8 64 46. 1 44. 5 1 24 89.2 86.1 84 132. 4 127. 8 44 175.5 169.5 6 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 13.3.8 129.2 46 177.0 170.9 7 5.0 4.9 67 48.2 46.5 27 91.4 88.2 87 134.5 129.91 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. 10 7.2 6.9 70 50.4 48.6 30 93.5 94.2 90.3 90 136.7 137.4 132.0 132.7 50 251 179.8 180.6 173.7 11 7.9 7.6 71 51.1 49.3 131 91.0 191 174.4 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 95 140.3 135.5 55 183.4 177.1 16 11.5 11.1 76 54.7 52.8 36 97.8 94.5 96 141.0 136.2 56 184.2 177.8 17 12.2 11.8 77 55.4 53.5 37 98.5 95.2 97 141.7 136.8 57 184.9 178.5 18 12.9 12.5 78 56.1 54.2 38 99.3 95.9 98 142.4 137.5 58 185.6 179.2 19 13.7 13.2 79 56.8 54.9 39 100.0 96.6 99 143.1 138.2 59 186.3 179.9 20 14.4 13.9 80 57.5 55.6 40 100.7 97.3 200 143.9 144.6 138.9 60 187. 187.7 180.6 21 15.1 14.6 81 58.3 56.3 141 101.4 97.9 201 139.6 261 181.3 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 1 105. 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 j 107.2 103.5 09 150.3 145.2 69 193.5 186.9 30 21.6 20.8 21.5 90 64.7 62.5 50 ! 107.9 104.2 10 151.1 145. 9 Y46. 6 70 271 194.2 187.6 31 22.3 91 65.5 63.2 151 108. 6 104.9 211 151.8 194.9 188.3 32 23.0 22.2 92 66.2 63.9 52 109. 3 105.6 12 152. 5 i 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. 73 196.4 189.6 34 24.5 23.6 94 67.6 65.3 54 110.8 107.0 14 153. 9 1 148. 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. 76 198.5 191.7 37 26.6 25.7 97 69.8 67.4 57 112.9 109.1 17 156.1 150.7 77 199.3 192.4 38 27.3 26.4 98 70.5 68.1 58 113. 7 109.8 18 156.8 151.4 78 200.0 193.1 39 28.1 27.1 99 71.2 68.8 59 114.4 110.5 19 157. 5 152. 1 79 200.7 193.8 40 28.8 27.8 28.5 100 101 71.9 72.7 69.5 60 115.1 115.8' 111.1 111.8 20 158.3 152.8 80 201.4 194.5 41 29.5 70.2 161 221 159.0 153. 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 36.7 34.7 10 79.1 79.8 76.4 70 122.3 118.1 30 165.4 166.2 159.8 90 208.6 201.5 51 35.4 111 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 1 124.4 120.2 33 167.6 1161.9 93 210.8 203. 5 54 38.8 37.5 14 82.0 79.2 74 i 125.2 120.9 34 168. 3 162. 6 94 311.5 204.2 55 39.6 38.2 15 82.7 79.9 75 125.9 121.6 35 169. 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 i 164. 6 97 213.6 206.3 58 41.7 40.3 18 84.9 82.0 78 128.0 123.6 38 171.2 |165.3 98 214.4 207.0 59 42.4 41.0 19 85.6 82.7 79 128.8 124.3 39 171.9 166.0 99 215.1 207.7 60 43.2 41.7 20 86.3 83.4 80 129. 5 125.0 40 172.6 166.7 300 215.8 208.4 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 16° (134°, 226 °, 314° )• TABLE 2. [Page 455 Dist. Difference of Latitude and Departure for 44° (136°, 224°, 316 '). Lat. Dep. Dist. Lat. Dep. Di.st. Lat. Dep. Dist. Lilt. Dep. Dist. 1 Lat. Dep. 801 216. 5 209. 1 361 259.7 250. 8 421 302. 8 292.5 481 346.0 334. 1 541 1 i 389.2 375.8 02 217.2 209.8 ()2 260.4 251. 5 22 303.6 293.2 82 346.7 334. 8 42 389.9 376.5 03 218.0 210.5 (53 261.1 252. 2 23 304.3 293.8 83 347.4 335. 5 43 390.6 377.2 04 218.7 211.2 64 261.8 252. 9 24 305. 294.5 84 348.2 336.2 44 391.3 377.9 05 219. 4 211.9 65 262.6 253. 6 25 305. 7 295.2 85 348.9 336. 9 45 392.0 378.6 06 220.1 212.6 66 263.3 254. 3 26 306.4 295.9 86 349. 6 337. 6 46 392.8 379.3 07 220.8 213.3 67 264. "0 254. 9 27 307.2 296.6 87 ! 350.3 338.3 47 393.5 380.0 08 221.6 214.0 68 264.7 255. 6 28 307.9 297.3 88 351.0 339.0 48 394.2 380. 7 09 222. 3- 214.7 69 265.4 256. 3 29 308.6 298.0 89 351.7 339.7 49 394.9 381.4 10 311 223.0 223.7 215.4 70 266.2 266.9 257.0 30 431 309.3 310.0 298.7 299.4 90 491 352.5 353.2 340.4 341.1 50 551 395.6 396.4 382.1 382.7 216.0 371 257.7 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 1 356. 1 343.9 55 399.2 385.5 16 227. 3 219.5 76 270.5 261.2 36 313. 6 302. 9 96 i 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 1 357.5 345.2 57 400.7 386.9 18 228.8 220.9 78 271.9 262.6 38 315.1 304.3 98 358.2 345.9 58 401.4 387.6 19 229.5 221.6 79 272.6 263.3 39 315.8 305.0 99 358.9 346. 6 59 402.1 388.3 20 321 230.2 230.9 222.3 80 273.4 264.0 264.7 40 441 316. 5 305.7 500 359.7 360.4 347.3 348.0 60 561 402.8 403.6 389.0 389.7 223.0 381 274.1 317. 2 306. 4 501 22 231.6 223.7 82 274.8 265.4 42 318. 307.0 02 361.1 348.7 62 404.3 39D.4 23 232.3 224.4 83 275.5 266.1 43 318. 7 307.7 03 361.8 349.4 63 405.0 391.1 24 233.1 225.1 84 276.2 266.8 44 319.4 308.4 04 362.5 350.1 64 405. 7 391.8 25 233.8 225.8 85 276.9 267.5 45 320. 1 309.1 05 363.3 350.8 65 406.4 392.5 26 234.5 226.5 86 377.7 268.1 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. 311.9 09 366.1 353.6 69 409.3 395.3 30 331 237.4 238.1 229.2 229.9 90 391 280. 5 270.9 50 323.7 312.6 10 366. 9 354.3 70 410.0 410.7 396.0 396.7 281.3 271.6 451 324.4 313.3 511 367.6 355.0 571 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. 94 283.4 273.7 54 326. 6 315.4 14 369.7 357. 1 74 412.9 398.7 35 241. 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. 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 78 415.8 401.5 39 243.9 335.5 99 287.0 277.2 59 330. 2 318.9 19 373.3 360.5 79 416.5 402.2 40 244.6 2.36. 2 400 287.7 288.5 277.9 60 330.9 319.6 20 374.1 361.2 80 417.2 417.9 402.9 403.6 341 245.3 236.9 401 278.6 461 331.6 320.2 521 374. 8 361.9 581 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. 04 290.6 280.7 64 333. 8 322.3 24 376.9 364.0 84 420.1 405.7 45 248.2 239.7 05 291.3 281.3 65 334.5 323.0 25 377.7 364.7 85 420.8 406.4 46 248.9 240.4 06 292.1 282.0 66 335.2 323.7 26 378.4 365.4 86 421.5 407.1 47 249.6 241.1 07 292.8 282.7 67 335.9 324.4 27 379.1 366.1 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. 408.5 49 251.1 242.4 09 294.2 284.1 69 337.4 325.8 29 380.5 367.5 89 423. 7 409.1 50 251.8 243.1 10 294.9 284.8 70 338. 1 326.5 30 381.2 368.2 90 424.4 409.9 351 252.5 243.8 411 295.7 285.5 471 338.8 327.2 531 382.0 368.9 591 425.1 410.5 62 253.2 244.5 12 296.4 286.2 72 339.5 327.9 32 382.7 369.6 92 425.9 411.2 53 253.9 245.2 13 297.1 286.9 73 340.3 328.6 33 383.4 370. 3 93 426.6 411.9 54 254.6 245.9 14 297.8 287.6 74 341.0 329.3 34 384. 1 371.0 94 427.3 412.6 55 255.4 246.6 15 298.5 288.3 75 341.7 330.0 35 384.8 371. 7 95 428.0 413.3 56 256.1 247.3 16 299. 2 289.0 76 342. 4 330.7 36 385. 6 372.4 96 428.7 414.0 57 256.8 248.0 17 300.0 289.7 77 343. 1 331.4 37 386.3 373.1 97 429.5 414.7 58 257.5 248.7 18 300.7 290.4 78 343. 8 332. 1 38 387.0 373.7 98 430.2 415. 4 59 258.2 249.4 19 301.4 291.1 79 344.6 332.7 39 387.7 374.4 99 430.9 416.1 60 259. 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. j Lat. 1 46° (134°, 226°, 314°). Page 456J TABLE 2. Difference of Latitude and Departure for 46° (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 11 7.1 7.1 70 49.5 49.5 30 91.9 91.9 90 134.4 134.4 135.1 50 251 176.8 177.6 176.8 7.8 7.8 71 50.2 50.2 131 92.6 92.6 191 136.1 177.5 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 I 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 60 183.8 184.6 183.8 21 14.8 14.8 81 57.3 57.3 141 99.7 99.7 201 142.1 142.1 261 184.6 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. 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 1 149. 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 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 20 155.6 156.3 155.6 80 198.0 198.0 41 29.0 29.0 101 71.4 71.4 161 113.8 113.8 221 156.3 281 198.7 198.7 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 51 35.4 35.4 10 77.8 77.8 70 120.2 120.2 30 162.6 163. 3 162.6 90 205.1 205.1 36.1 36.1 111 78.5 78.5 171 120.9 120.9 231 163.3 291 205.8 205.8 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 5° (i; J5°, 225°, 315° . TABLE 2. [Page 457 Difference of Latitude and Depart are 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. 1 541 382.5 382.5 02 213.5 213.5 62 256.0 256.0 22 298.4 298.4 82 340. 8 ' 340. 8 42 383.2 383.2 03 214.3 214.3 63 256.7 256. 7 23 299.1 299.1 83 .341.5 341.5 43 383. 9 383.9 04 215.0 215.0 64 257. 4 257. 4 24 299.8 299.8 84 342.2 342.2 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 45 385.4 385.4 06 216.4 216.4 66 258.8 258.8 26 301.2 301.2 86 343.6 343.6 46 386.1 386.1 07 217.1 217.1 67 259.5 259. 5 27 301.9 301.9 87 344.3 344.3 47 386. 8 386.8 08 217.8' 217.8 68 260.2 260.2 28 302.6 302.6 88 345.1 34.5.1 48 387.5 387.5 09 218.5 218.5 69 260.9 260.9 29 303. 4 303.4 89 345.8 345.8 49 388.2 388.2 10 219.2 219.2 70 371 261.6 262.3 261.6 30 304.1 304.1 90 346.5 347.2 346.5 50 388.9 388.9 311 219.9 219.9 262.3 431 304.8 304.8 491 347.2 551 389.6 389.6 12 220.6 220.6 72 263.0 263.0 32 305. 5 305.5 92 347.9 347.9 52 390.3 390.3 13 221.3 221.3 73 263.8 263.8 33 306.2 306.2 93 348.6 348.6 53 391.0 391.0 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 75 265.2 265.2 35 307.6 307.6 95 350.0 350.0 55 392.4 392.4 16 223.4 223.4 76 265.9 265.9 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 97 351.4 351.4 57 393.9 393.9 18 224.9 224.9 78 267.3 267.3 38 309.7 309.7 98 352.1 352.1 58 394.6 394.6 19 225.6 225.6 79 268.0 268. 39 310.4 310.4 99 352.8 352.8 59 395.3 395.3 20 226.3 227.0 226.3 80 268.7 268.7 269.4 40 311.1 31178 311.1 311.8 500 501 353.5 353.5 354.3 60 561 396. ! 396. | 321 227.0 381 269.4 441 354.3 396.7 396.7 22 227.7 227.7 82 270.1 270.1 42 312.5 312.5 02 355.0 355.0 62 397.4 397.4 23 228.4 228.4 83 270.8 270.8 43 313.3 313.3 03 355.7 355.7 63 398.1 398.1 24 229.1 229.1 84 271.5 271.5 44 314.0 314.0 04 356.4 356.4 64 398.8 1 398.8 25 229.8 229.8 85 272.2 272.2 45 314.7 314.7 05 357.1 357.1 65 399. 5 399. 5 26 230.5 230.5 86 272.9 272.9 46 315. 4 315.4 06 357.8 357. 8 66 400. 2 400. 2 27 231.2 231.2 87 273.7 273.7 47 316.1 316.1 07 358.5 358.5 67 400.9 400.9 28 231.9 231.9 88 274.4 274.4 48 316.8 316.8 08 359.2 359.2 68 401.6 * 401.6 29 232.6 232.6 89 275.1 275.1 49 317.5 317.5 09 359.9 359.9 69 402.3 , 402.3 30 233.3 233.3 90 275.8 276.5 275.8 50 318.2 318.2 10 511 360.6 360.6 70 403.0 403.8 403.0 331 234.1 234.1 391 276.5 451 318.9 318. 9 361.3 361.3 571 403.8 32 234.8 234.8 92 277.2 277.2 52 319.6 319.6 12 362.0 362.0 72 404.5 i 404.5 33 235. 5 235. 5 93 277.9 277.9 53 320.3 320. 3 13 362.7 362.7 73 405.2 , 405.2 34 236.2 236.2 94 278.6 278.6 54 321.0 321.0 14 363. 5 363. 5 74 405.9 405.9 35 236.9 236. 9 95 279.3 279.3 55 321.7 321.7 15 364. 2 364. 2 75 406.6 406.6 36 237.6 237.6 96 280.0 280.0 56 322.4 322.4 16 364.9 364.9 76 407.3 407.3 37 238.3 238.3 97 280.7 280.7 57 323.2 323.2 17 365.6 !365.6 77 408.0 408.0 38 239.0 239.0 98 281.4 281.4 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 1367.0 79 409.4 409.4 40 240.4 240.4 400 282.8 283.6 282.8 60 325. 3 326.0 325.3 326. 20 521 367.7 1367:7 368.4 368.4 80 581 410.1 410.8 410.1 341 241.1 241.1 401 283.6 461 410.8 42 241.8 241.8 02 284.3 284.3 62 326.7 326.7 22 369.1 j 369.1 82 411.5 411.5 43 242.5 242.5 03 285.0 285.0 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 [370.5 84 412. 9 412. 9 45 244.0 244.0 05 286.4 286.4 65 328.8 328.8 25 371.2 1371.2 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 I 372. 6 87 415. 1 415. 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 '. 416.5 50 247.5 248.2 247.5 10 289.9 289.9 290.6 70 332.3 332. 3 30 374.8 374.8 90 591 417.2 417.9 417.2 417.9 351 248.2 411 290.6 471 333. 1 333.1 531 375.5 375.5 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 54 250.3 250.3 14 292.7 292.7 74 335. 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 95 420.7 420.7 56 251.7 251.7 16 294.2 294.2 76 336. 6 336. 6 36 379.0 379.0 96 421.4 421.4 57 252.4 252.4 17 294.9 294.9 77 337. 3 337.3 37 379.7 379.7 97 422.1 422.1 58 253.1 253.1 18 295.6 295.6 78 338.0 338.0 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 1381.1 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 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 45° (■ L35°, 22. )°, 315< '). 1 Page 458] TABLE 3. Meridional Parts, or Increased Latitudes. Comp 1 293.465 M. 0° 1° 20 go 4° 5° 6° JO 8° 90 M. 0.0 59.6 119.2 178.9 238.6 298.3 358.2 418.2 478.3 538.6 1 1.0 60.6 20.2 79.9 39.6 99.3 59.2. 19.2 79.3 39.6 1 2 2.0 61.J 62;b 21.2 80.8 40.6 300.3 60.2 20.2 80.3 40.6 2 3 3.0 22.2 81.8 41.6 01.3 61.2 21.2 81.3 41.6 3 4 4.0 63.6 23.2 82.8 42.5 02.3 62.2 22.2 82.3 42.6 4 5 5.0 64.6 124.2 183.8 243.5 303.3 363.2 423.2 483.3 543.6 5 6 6.0 65.6 25.2 84.8 44.5 04.3 64.2 24.2 84.3 44.6 6 7 7.0 66.5 26.2 85.8 45.5 05.3 65.2 25.2 85.3 45.6 7 8 7.9 67.5 27.2 86.8 46.5 06.3 66.2 26.2 86.3 46.6 8 9 8.9 68.5 28.2 87.8 47.5 07.3 67.2 27.2 87.3 47.6 9 10 9.9 69.5 129.1 188.8 248.5 308.3 368.2 428.2 488.3 548.6 10 11 10.9 70.5 30.1 89.8 49.5 09.3 69.2 29.2 89.3 49.6 11 12 11.9 71.5 31.1 90.8 50.5 10.3 70.2 30.2 90.4 50.6 12 13 12.9 72.5 32.1 91.8 51.5 11.3 71.2 31.2 91.4 51.7 13 14 13.9 73.5 33.1 92.8 52.5 12.3 72.2 32.2 92.4 52.7 14 15 15 14.9 74.5 134.1 193.8 253.5 313.3 373.2 433.2 493.4 553.7 16 15.9 75.5 35.1 94.8 54.5 14.3 74.2 34.2 94.4 54.7 16 17 16.9 76.5 36.1 95.8 55.5 15.3 75.2 35.2 95.4 55.7 17 18 17.9 77.5 37.1 96.8 56.5 16.3 76.2 36.2 96.4 56.7 18 19 18.9 78.5 38.1 97.8 57.5 17.3 77.2 37.2 97.4 57.7 19 20 19.9 79.5 139.1 198.8 258.5 318.3 378.2 438.2 498.4 558.7 20 21 20.9 80.5 40.1 99.7 59.5 19.3 79.2 39.2 99.4 59.7 21 22 21.9 81.5 41.1 200.7 60.5 20.3 80.2 40.2 500.4 60.7 22 23 22.8 82.4 42.1 01.7 61.5 21.3 81.2 41.2 01.4 61.7 23 24 23.8 83.4 43.1 02.7 62.5 22.3 82.2 42.2 02.4 62.7 24 25 24.8 84.4 144.1 203. 7 263.5 323.3 383.2 443.2 503.4 563.7 25 26 25.8 85.4 45.1 04.7 64.5 24.3 84,2 44.2 04.4 64.7 26 27 26.8 86.4 46.0 05.7 65.5 25.3 85.2 45.2 05.4 65.7 27 28 27.8 87.4 47.0 06.7 66.5 26.3 86.2 46.2 06.4 66.8 28 29 28.8 88.4 48.0 07.7 67.4 27.3 87.2 47.2 07.4 67.8 29 30 29.8 89.4 149.0 208.7 268.4 328.3 388.2 448.2 508.4 568.8 30 31 30.8 90.4 50.0 09.7 69.4 29.3 89.2 49.2 09.4 69.8 31 32 31.8 91.4 51.0 10.7 70.4 30.3 90.2 50.2 10.4 70.8 32 33 32.8 92.4 52.0 11.7 71.4 31.3. 91.2 51.2 11.4 71.8 33 34 33.8 93.4 53.0 12.7 72.4 273.4 32.3 92.2 52.2 12.4 72.8 34 35 34.8 94.4 154.0 213.7 333.3 393.2 453.2 513.4 573.8 35 36 35.8 95.4 55.0 14.7 74.4 34.3 94.2 54.3 14.5 74.8 36 37 36.7 96.4 56.0 15.7 75.4 35.3 95.2 55.3 15.5 75.8 37 38 37.7 97.3 57.0 16.7 76.4 36.2 96.2 56.3 16.5 76.8 38 39 38.7 98.3 58.0 17.7 77.4 37.2 97.2 57.3 17.5 77.8 39 40 40 39.7 99.3 159.0 218.7 278.4 338.2 398.2 458.3 518.5 578.8 41 40.7 100.3 60.0 19.7 79.4 39.2 99.2 59.3 19.5 79.9 41 42 41.7 01.3 61.0 20.6 80.4 40.2 400.2 60.3 20.5 80.9 42 43 42.7 02.3 62.0 21.6 81.4 41.2 01.2 61.3 21.5 81.9 43 44 43.7 03.3 63.0 22.6 82.4 42.2 02.2 62.3 22.5 82.9 44 45 44.7 104.3 164.0 223.6 283.4 343.2 403.2 463.3 523. 5 583.9 45 46 45.7 05.3 65.0 24.6 84.4 44.2 04.2 64.3 24.5 84.9 46 47 46.7 06.3 66.0 25.6 85.4 45.2 05.2 65.3 25.5 85.9 47 48 47.7 07.3 67.0 26.6 86.4 46.2 06.2 66.3 26.5 86.9 48 49 48.7 08.3 68.0 27.6 87.4 47.2 07.2 67.3 27.5 87.9 49 50 49.7 109.3 168.9 228.6 288.4 348.2 408.2 468.3 528.5 588.9 50 51 50.7 10.3 69.9 29.6 89.4 49.2 09.2 69.3 29.5 89.9 51 52 51.6 11.3 70.9 30.6 90.4 50.2 10.2 70.3 30.5 90.9 52 53 52.6 12.3 71.9 31.6 91.4 51.2 11.2 71.3 31.5 91.9 53 54 53.6 13.2 72.9 32.6 92.4 52.2 12.2 72.3 32.5 93.0 54 55 54.6 114.2 173.9 233.6 293.4 353.2 413.2 473.3 533.5 594.0 55 56 55.6 15.2 74.9 34.6 94.4 54.2 14.2 74.3 34.6 95.0 56 57 56.6 16.2 75.9 35.6 95.4 55.2 15.2 75.3 35.6 96.0 57 58 57.6 17.2 76.9 36.6 96.3 56.2 16.2 76.3 36.6 97.0 58 59 58.6 18.2 77.9 37.6 97.3 57.2 17.2 77.3 37.6 98.0 59 M. 0° 1° 2° 8° 4° 5° 6° 7° 8° 9° M. TABLE 3. [Page 459 | Meridional Parts, or Increased Latitudes. Comp 1 293.465 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 1091.0 1153. 9 1 GOO.O 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 t 8 07.1 67.7 28.6 89.7 51.0 12.6 74.6 36.8 99.4 62.3 8 9 08.1 68.7 29.6 90.7 52.0 13.7 75.6 37.8 1100.4 63.3 9 10 609.1 669.8 730.6 791.7 853.1 914.7 976.6 1038. 9 1101.4 1164. 4 10 11 10.1 70.8 31.6 92.7 54.1 15.7 77.7 39.9 02.5 65.4 11 12 11.1 71,8 32.7 93.8 55.1 16.8 78.7 40.9 03.5 66.5 12 13 12.1 72.8 33.7 94.8 56.1 17.8 79.7 42.0 04.6 67.5 13 14 13.1 73.8 34.7 95.8 57.2 18.8 80.8 43.0 05.6 68.6 14 15 614.1 674.8 735.7 796.8 858.2 919.8 981.8 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 24.0 925.0 85.9 987.0 48.2 10.9 73.9 19 20 . 619. 2 679.9 740.8 801.9 863.3 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 35 33.3 94.1 55.0 16.2 77.7 39.4 01.5 63.9 1064. 9" 26.6 89.7 1190. 7 34 35 634.3 695.1 756.0 817.3 878.7 940.5 1002.5 1127.6 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 1196,0 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 55 654.6 715.4 776.4 837.7 899.3 961.1 1023. 3 1085. 8 1148. 6 1211.8 55 56 55.6 16.4 77.4 38.7 900.3 62.1 24.3 86.8 49.7 12.9 56 57 56.6 17.4 78.5 39.8 01.3 63.2 25.3 87.9 50.7 14.0 57 58 57.6 18.4 79.5 40.8 02.3 64.2 26.4 88.9 51.8 15.0. 58 59 58.6 19.4 80.5 41.8 03.4 65.2 27.4 89.9 17° 52.8 16.1 59 M. 10° 11° 12° 13° 14° 15° lfi° 1S° 1J.° M. Page 460] TABLE 3. Meridional Parts, or Increased Latitudes. Comp. 293.466 M. 2©° 210 22° 28° 24° 26° 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 % 19.3 82.^ 84.^ 47.1 11.6 76.7 42.3 08.4 75.1 42.4 10.4 2 3 20.3 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 1 77.4 44.7 12.6 4 5 1222. 4 1286. 1 1350. 3 1414. 9 1480. 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. 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 1 90.8 58.2 26.3 16 17 35.1 98.9 63.2 27.9 93.1 58.8 25.0 91.9 59.4 27.5 17 18 36.2 1300.0 64.2 29.0 94.2 59.9 26.2 93.0 '60.5 28.6 18 19 37.3 01.1 65.3 30.0 95.2 61.0 27.3 94.1 61.6 29.7 19 20 20 1238. 3 1302. 1 1366.4 1431. 1 1496. 3 1562. 1 1628. 4 1695. 3 1762. 7 1830. 9 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 36.4 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 30 1248. 9 1312. 8 1377. 1 1442.0 1507. 3 1573. 1 1639. 5 1706.5 1774. 1 1842.3 31 50.0 13.9 78.2 43.0 08.4 74.2 40.6 07.6 75.2 43.4 31 32 51.0 14.9 79.3 44.1 09.4 75.3 41.7 08.7 76.3 44.6 32 33 52.1 16.0 80.4 45.2 10.5 76.4 42.8 09.8 77.4 45.7 33 34 53.2 17.1 81.5 46.3 11.6 77.5 43.9 10.9 78.6 46.9 34 35 1254. 2 1318. 2 1382. 5 1447.4 1512. 7 1578. 6 1645.0 1712. 1 1779.7 1848. 35 36 55.3 19.2 83.6 48.5 13.8 79.7 46.2 13.2 80.8 49.2 36 37 56.4 20.3 84.7 49.5 14.9 80.8 47.3 14.3 82.0 50.3 37 38 57.4 21.4 85.8 50.6 16.0 81.9 48.4 15.4 83.1 51.4 38 39 58.5 22.4 86.8 51.7 17.1 83.0 49.5 16.6 84.2 52.6 39 40 1259. 5 1323. 5 1387. 9 1452. 8 1518. 2 1584. 1 1650. 6 1717.7 1785.4 1853.7 40 41 60.6 24.6 89.0 53.9 19.3 85.2 51.7 18.8 86.5 54.9 41 42 61.7 25.6 90.1 55.0 20.4 86.3 52.8 19.9 87.6 56.0 42 43 62.7 26.7 91.1 56.1 21.5 87.4 53.9 21.1 88.8 57.2 43 44 63.8 27.8 92.2 57.1 22.6 88.5 55.1 22.2 89.9 58.3 44 45 1264.9 1328. 9 1393. 3 1458.2 1523. 7 1589. 6 1656.2 1723. 3 1791. 1 1859.5 45 46 65.9 29.9 94.4 59.3 24.8 90.7 57.3 24.4 92.2 60.6 46 47 67.0 31.0 95.5 60.4 25.9 91.8 58.4 25.5 93.3 61.8 47 48 68.0 32.1 96.5 61.5 27.0 92.9 59.5 26.7 94.5 62.9 48 49 69.1 33.1 97.6 62.6 28.0 94.1 60.6 27.8 95.6 64.0 49 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 54 55 1275. 5 1339. 6 1404. 1 1469. 1 1534. 6 1600. 7 1667. 3 1734. 5 1802. 4 1870. 9 55 56 76.6 40.6 05.2 70.2 35.7 01.8 68.4 35.7 03.5 72.1 56 57 77.6 41.7 06.2 71.3 36.8 02.9 69.5 36.8 04.7 73.2 57 58 78.7 42.8 ■ 07.3 72.4 37.9 04.0 70.7 37.9 05.8 74.4 58 59 79.7 43.8 08.4 73.5 39.0 05.1 71.8 39.1 07.0 75.5 59 M. 20° 21° 22° 28° 24° 26° 26° 27° 28° 29° M. TABLE 3. [Page 461 | Meridional Parts, or Increased Latitudes. Comp. 1 293.465 M. 80° 31° 82° 38° 34° 35° 36° 87° 38° 39° 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 2243.0 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 ^91.9 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 35 15.8 85.5 56.0 27.3 99.4 72.3 46.2 2347. 5 21.1 97.0 73.9 34 1917.0 1986. 7 2057. 2 2128. 5 2200.6 2273. 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 25.1 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 1934. 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 2372. 3 46.3 2447.5 22.5 99.8 2601. 1 54 55 55 1940. 2 2010. 1 2080. 8 2152. 4 2224. 8 2298. 1 2523. 8 56 41.3 11.3 82.0 53.6 26.0 99.3 -^73.6 48.8 25.1 02.4 56 57 42.5 12.5 83.2 54.8 27.2 2300. 5 74.8 50.1 26.4 03.7 57 58 43.6 13.6 84.4 56.0 28.4 01.8 76.1 51.3 27.6 05.0 58 59 44.8 14.8 85.6 57.2 29.6 03.0 77.3 52.6 28.9 06.3 59 M, 30° 81° 32° 88° 34° 35° 36° 87° 88° 39° M. Page 462J TABLE 3. Meridional Parts, or Increased Latitudes. \ Con^P- 29065 M. 40° 41° 42° 48° 44° 45° 46° 47° 48° 49° M. 2607.6 2686.2 2766. 2847.1 2929.5 3013. 4 3098. 7 3185. 6 3274. 1 3364. 4 1 08.9 87.6 67.4 48.5 30.9 14.8 3100.1 87.1 75.6 65.9 1 2 10.2 88-9 68.7 49.9 32.3 16.2 01.6 88.5 77.1 67.4 2 3 11.5 90.2 70.1 51.2 33.7 17.6 03.0 ! 90.0 78.6 69.0 3 4 12.8 91.5 71.4 52.6 35.1 19.0 04.4 91.4 80.1 70.5 4 5 2614. 1 2692. 8 2772. 8 2853. 9 2936. 5 3020. 4 3105. 9 3192. 9 3281. 6 3372.0 5 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 i 95.8 84.6 75.1 7 8 18.1 96.8 76.8 58. 40. 6 24.7 10.2 ; 97.3 86.1 76.6 8 9 19.4 98.1 2699. 5 78.1 59. 4 42. 26.1 11. 6 : 98. 8 87.6 78.1 9 10 2620. 7 2779. 5 2860.8 2943.4 3027. 5 3113.1 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 I 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 2627.2" 04.8 84.8 66.2 1 49.0 33.2 18.8 1 06.1 95.0 85.7 14 15 2706.1 2786. 2 2867. 6 2950. 4 3034. 6 3120. 3 3207. 6 3296. 5 3387. 3 15 16 28.5 07.4 87.5 69.0 51.8 36.0 21.7 09.0 98.0 88.8 16 17 29.8 08.7 88.9 70.3 53.2 37.4 23.2 10.5 99.5 90.3 17 18 31.1 10.1 90.2 71.7 54.5 38.8 24.6 j 12.0 3301. 91.8 18 19 20 32.4 11.4 91.6 73.1 55.9 40.2 26.0 1 13.4 02.5 93.4 19 20 2633. 7 2712. 7 2792. 9 2874.4 ! 2957.3 3041. 7 3127.5 ! 3214.9 3304. 3394. 9 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 2640. 2 18.0 98.3 79.9 62.9 47.3 33.3. 20.8 10.0 3401.0 24 25 2719. 3 2799. 7 2881. 3 2964.3 3048. 7 3134. 7 3222. 3 3311.5 3402. 6 26 41.6 20.7 2801.0 82.7 65.7 50.2 36.2 23.7 13.0 04.1 26 27 42.9 22.0 02.4 84.0 67.1 51.6 37.6 25.2 14.5 05.6 27 28 44.2 23.3 03.7 85.4 68.5 53.0 39.0 26.7 16.0 07.2 28 29 45.5 24.7 05.1 86.8 i 69.9 . 54.4 40.5 28.2 17.5 08.7 29 30 30 2646. 8 2726. 2806. 4 2888.2 2971.3 3055. 9 3141. 9 3229. 6 3319. 3410. 2 31 48.1 27.3 07.8 89.5 1 72.7 57.3 43.4 31.1 20.5 11.8 31 32 49.4 28.6 09.1 90. 9 1 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 52.0 31.3 11.8 93.7 76.9 61.5 47.7 35.6 25.1 16.4 34 35 2653. 3 2732. 6 2813. 2 2895. 2978. 3 3063. 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 1 82.5 67.2 53.5 41.5 31.1 22.5 38 39 58.6 38.0 18.6 2900.5 83.9 68.7 55.0 42.9 32.6 24.1 39 40 2659. 9 2739. 3 2820. 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 45 46 67.8 47.3 28.1 10.2 93.7 78.7 65.2 53.3 43.2 34.9 46 47 69.1 48.6 29.4 11.6 95.1 ! 80.1 66.6 54.8 44.7 36.4 47 48 70.4 50.0 30. 8 13. 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 2922. 6 04.9 90.1 76.8 65.2 55. 3 47.2 54 55 2679. 6 2759. 3 2840. 3 3006.3 3091.5 3178. 3 3266. 7 3356. 8 3448. 8 55 56 81.0 60.7 41.7 ^4.0 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 I 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. TABLE 3. [Page 463 | Meridional Parts, or Increased Latitudes. Com p. 1 293.465 M. 50° 51° 62° 58° 54° 55° 56° 67° 58° 59° M. 3456. 5 3550. 6 3646. 7 3745. 1 3845. 7 3948. 8 4054. 5 4163. 4274. 4 4389. 1 1 58.1 52.2 48.4 46.7 47.4 50.5 56.3 64.8 76.3 91.0 1 2 59.6 53.8 50.0 48.4 49.1 52.3 58.1 66.6 78.2 92.9 2 3 61.2 55.4 51.6 50.0 50.8 54.0 59.8 68.5 80.1 94.9 3 4 62.7 56.9 53.2 51.7 52.5 55.7 61.6 70.3 82.0 96.8 4 5 3464. 3 3558.5 3654. 8 3753. 4 3854. 2 3957. 5 4063. 4 4172. 1 4283. 9 4398. 8 5 6 65.9 60.1 56.5 55.0 55.9 59.2 65.2 74.0 85.7 4400. 7 6 ,7 67.4 61.7 58.1 56.7 57.6 61.0 67.0 75.8 87.6 02.6 7 8 69.0 63.3 59.7 58.3 59.3 62.7 68.8 77.7 89.5 04.6 8 9 70.5 64.9 61.3 60.0 61.0 64.5 70.6 79.5 91.4 06.5 9 10 3472. 1 3566. 5 3663. 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 73.3 74.6 78.5 84.9 94.2 06.6 22.1 17 18 84.5 79.2 76.0 75.0 76.3 80.2 86.7 96.1 08.5 24.1 18 19 86.1 80.8 77.6 76.7 78.1 82.0 88.5 97.9 10.4 26.1 19. 20 3487. 7 3582. 4 3679. 3 3778. 3 3879. 8 3983. 7 4090. 3 4199. 8 4312. 3 4428. 20 21 89.2 84.0 80.9 80.0 81.5 85.5 92.1 4201. 6 14.2 30.0 21 22 90.8 85.6 82.5 81.7 83.2 87.2 93.9 03.5 16.1 31.9 22 23 92.4 87.2 84.2 83.3 84.9 89.0 95.7 05.3 18.0 33.9 23 24 93.9 88.8 85.8 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 55 3542. 7 3638. 6 3736. 8 3837. 2 3940. 1 4045. 6 4153. 8 4265. 4379. 4 4497.1 56 44.3 40.3 38.4 38.9 41.8 47.4 55.7 66.9 81.3 99.1 56 57 45.9 41.9 40.1 40.6 43.6 49.1 57.5 68.8 83.2 4501. 1 57 58 47.4 43.5 41.7 42.3 45.3 50.9 59.3 70.7 85.2 03.1 58 59 49.0 45.1 43.4 45.0 47.0 52.7 61.1 72.5 87.1 05.1 59 M. 60° 51° 52° 53° 54° 55° 66° 67° 58° 59° M. Page 464j TABLE 3. Meridional Parts, or Increased Latitudes. Comp 1 293.46.5 M. 60° 61° 02° 03° 04° 05° 66° 67° 68° 69° M. 4507. 1 4628. 7 4754. 3 4884. 1 5018. 4 5157. 6 5302. 1 5452. 4 5609. 1 5772. 7 1 09.1 30.8 56.4 86.3 20.6 59.9 04.6 55.0 11.8 75.5 1 2 11.1 32^9 34ri9 58.6 88.5 22.9 62.3 07.0 57.6 14.4 78.3 2 3 13.1 60.7 90.7 25.2 64.7 09.5 60.1 17.1 81.1 3 4 15.1 37.0 62.8 92.9 27.5 67.0 11.9 62.7 19.8 83.8 4 5 5 4517.1 4639. 4764.9 4895. 1 5029.8 5169. 4 5314. 4 5465. 2 5622. 4 5786. 6 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 / 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 9%Ji 9 10 10 4527. 1 4649. 4 4775. 6 4906. 1 5041. 2 5181. 3 5326. 7 5477. 1 5635. 9 5800.7 11 29.1 51.5 77.8 08.3 43.5 83.7 29.2 80.7 38.5 03.5 11 12 31.1 53.5 79.9 10.5 45.8 86.0 31.7 83.2 41.2 06.3 12 13 33.1 55.6 82.0 12.8 48.1 88.4 34.2 85.8 43.9 09.1 13 14 35.1 57.7 84.2 15.0 50.4 90.8 36.6 88.4 46.6 11.9 14 15 4537.1 4659. 7 4786. 3 4917. 2 5052. 7 5193. 2 5339. 1 5491.0 5649. 3 5814. 7 15 16 39.2 61.8 88.5 19.4 55.0 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 4547. 2 4670. 1 4797. 1 4928. 3 5064.2 5205. 1 5351. 5 5503. 9 5662. 8 5828. 9 20 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 40.2 24 25 4557. 3 4680. 6 4807. 8 4939. 4 5075. 7 5217. 1 5364. 5516. 9 5676. 4 5843. 25 26 59.3 82.6 10.0 41.7 78.1 19.5 66.5 19.5 79.1 45.9 26 27 61.4 84.7 12.1 43.9 80.4 21.9 69.0 22.1 81.8 48.7 27 28 63.4 86.8 14.3 46.1 82.7 24.3 71.5 24.7 84.5 51.6 28 29 65.4 88.9 16.5 48.4 85.0 26.7 74.0 27.3 87.3 54.4 29 30 4567. 4 4691. 4818. 6 4950. 6 5087. 3 5229. 1 5376. 5 5529. 9 5690. 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 35.2 95.4 63.0 32 33 73.5 97.3 25.1 57.3 94.3 36.4 84.0 37.8 98.2 65.9 33 34 75.6 99.4 27.3 59.6 96.6 38.8 86.5 40.4 5700. 9 68.7 34 35 4577. 6 4701. 5 4829. 5 4961.8 5098. 9 5241. 2 5389. I 5543. 5703. 6 5871. 6 35 36 79.6 03.6 31.6 64.1 5101.3 43.6 91.6 45.6 06.4 74.4 36 37 81.7 05.7 33.8 66.3 03.6 46.0 94.1 48.3 09.1 77.3 37 38 83.7 07.8 36.0 68.6 05.9 48.5 96.6 50.9 11.9 80.2 38 39 85.7 09.9 38.1 70.8 08.3 50.9 99.1 53.5 14.6 83.1 39 40 4587. 8 4712. 4840. 3 4973. 1 5110. 6 5253. 3 5401. 6 5556. 1 5717. 3 5885. 9 40 41 89.8 14.1 42.5 75.3 12.9 55.7 04.2 58.8 20.1 88.8 41 42 91.8 16.2 44.7 77.6 15.3 58.2 06.7 61.4 22.8 91.7 42 43 93.9 18.3 46.8 79.8 17.6 60.6 09.2 64.0 25.6 94.6 43 44 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. 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 50 06.1 31.0 59.9 93.4 31.7 75.2 24.4 79.9 42.1 11.9 49 4608. 2 4733. 1 4862. 1 4995. 6 5134. 5277. 6 5427. 5582. 5 5744. 9 5914. 8 50 51 10.2 35.2 64.3 97.9 36.4 80.1 29.5 85.2 47.7 17.7 51 52 12.3 37.3 66.5 5000.2 38.7 82.5 32.0 87.8 50.4 20.6 52 53 14.3 39.4 68.7 02.4 41.1 85.0 34.6 90.5 53.2 23.5 53 54 16.4 41.6 70.9 04.7 43.4 87.4 37.1 93.1 56.0 26.4 54 55 4618. 5 4743. 7 4873. 1 5007. 5145. 8 5289. 8 5439. 7 5595. 8 5758. 8 5929. 3 55 56 20.5 45.8 75.3 09.3 48.1 92.3 42.2 98.4 61.5 32.2 56 57 22.6 47.9 77.5 11.5 50.5 94.7 44.8 5601. 1 64.3 35.1 57 58 24.6 50.0 79.7 13.8 52.8 97.2 47.3 03.8 67.1 38.1 58 59 26.7 52.2 81.9 16.1 55.2 99.7 49.9 06.4 69.9 41.0 59 M. «0° 61° 62° 68° 64° 65° 66° 67° 68° 09° M. TABLE 3. [Page 465 IMeridional Parts, or Increased Latitudes. Comp. 1 ^ '293.4d5 M. 70° 71° 72° 78° 74° 1 75° 76° 77° 78° 79° M. 5943. 9 6123. 5 6312. 5 6512. 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. 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 vj«.3 51.3 41.8 42.9 56.0 ' 82.6 24.7 84.6 65.2 70.2 9 10 5973. 2 6154. 4 6345. 6546. 4 6759. 7 6986. 5 7228. 9 7489. 1 7770. 1 8075. 5 10 11 76.2 57.5 48.3 49.8 63.3 90.4 33.1 93.6 74.9 80.8 11 12 79.1 60.6 51.6 53.3 67.0 : 94.3 37.3 98.1 79.8 86.1 12 13 82.1 63,7 54.8 56.7 70.7 ! 98.3 41.5 7502. 6 84.7 91.5 13 14 85.0 66.8 58.1 60.2 74.3 7002.2 45.7 07.1 89.6 96.8 14 15 5988. 6169. 9 6361. 4 6563. 7 6778. 7006.1 7249. 9 7511.7 7794. 5 8102. 2 15 16 90.9 73.0 64.7 67.1 81.7 10.0 54.1 16.2 99.4 07.5 16 17 93.9 76.1 67.9 70.6 85.4 14.0 58.3 20.7 7804. 3 12.9 17 18 96.9 79.2 71.2 74.1 89.1 17.9 62.5 25.3 09.3 18.3 18 19 99.8 82.3 74.5 77.6 92.8 21.8 66.7 29.8 14.2 23.7 19 20 6002.8 6185. 5 6377. 8 6581. 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 6815.0 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 6032. 6 6216. 8 6410. 9 6616. 1 6833. 7 7065. 5 7313. 5 7580. 3 7868. 9 8183. 5 30 31 35.6 20.0 14.2 19.6 37.4 69.5 17.8 84.9 74.0 89.0 31 32 38.6 23.1 17.6 23.1 41.2 73.5 22.1 89.5 79.0 94.5 32 33 41.6 26.3 20.9 26.6 44.9 77.5 26.4 94.2 84.0 8200.0 33 34 44.6 29.4 24.2 30.2 48.7 81.5 30.7 98.8 89.1 05.5 34 35 6047. 6 6232. 6 6427.6 6633. 7 6852. 4 7085. 5 7335.0 7603. 4 7894. 1 8211. 1 35 36 50.6 35.8 30.9 37.2 56. 2 89. 5 39.3 08.1 99.2 16.6 36 37 53.6 38.9 34.2 40.8 60. 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 45 74.8 61.2 57.7 65.7 86.4 21.8 74.0 45.5 39.9 61.2 44 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. 6280. 4 6478. 6687. 1 6909. 3 7146. 2 7400. 2 7673. 9 7970. 7 8295. 50 51 96.0 83.6 81.4 90.7 13.1 50.3 04.6 78.6 75.9 8300. 7 51 52 99.1 86.8 84.8 94.3 16.9 54.4 09.0 83.4 81.0 06.4 52 53 6102. 1 90.0 88.2 97.9 20.8 58.5 13.4 88.1 86.2 12.0 53 54 05.2 93.2 91.6 6701. 5 24.6 62.6 17.8 92.9 91.4 17.7 54 55 6108. 2 6296. 4 6495. 6705. 1 6928. 4 7166. 7 7422. 2 7697. 7 7996. 6 8323. 4 55 56 11.3 99.6 98.4 08.7 32.3 70.8 26.6 7702. 5 8001.8 29.2 56 57 14.3 6302. 9 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 M. 70° 71° 72° 78° 74° 75° 76° 77° 78° 79° M. 22489—03- -BO- Page 466] TABLE 4. 1 Length of a Degree in Latitude and . Longitude. Degree of Long. Degree of Lat. 1 Lat. Naut. miles. statute miles. Meters. Naut. miles. Statute miles. Meters. 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.^1 59. { 86 9.130 1 253 .662 .705 569 2 3 9.078 1 169 .663 .706 570 3 4 9.922 9.005 1 051 .664 .708 573 4 5 59. 840 68. 911 110 900 59. 666 68. 710 110 576 5 6 9.741 8.795 715 .668 .712 580 6 7 9.622 8.660 497 .670 .715 584 7 8 9.487 8.504 245 .673 .718 589 8 9 9.333 8.326 109 959 .676 .721 595 9 10 59. 161 68.129 109 641 59. 680 68. 725 110 601 10 11 8.971 7.910 9 289 .684 .730 608 11 12 8.764 7.670 8 904 .687 .734 616 . 12 13 8.538 7.410 8 486 .692 .739 624 13 14 8.295 7.131 8 036 .697 .744 633 14 15 58. 034 66. 830 107 553 59. 702 68. 751 110 643 15 16 7.756 6.510 7 036 .707 .757 653 16 17 7.459 6.169 6 487 .713 .764 663 17 18 7.146 5.808 5 906 .719 .771 675 18 19 6.816 5.427 5 294 .725 .778 686 19 20 56. 468 65.026 104 649 59. 732 68. 786 110 699 20 21 6.102 4.606 3 972 .739 .794 712 21 22 5.720 4.166 3 264 .746 .802 725 22 23 5.321 3.706 2 524 .754 .811 739 23 24 4.905 3.228 1 754 .761 .820 68.829 753 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 .858 815 28 29 2.578 0.548 7 441 .804 .869 832 29 30 52.064 59. 956 96 488 59. 813 68. 879 110 849 30 31 1.534 9.345 5 506 .822 .890 866 31 32 0.989 8.716 4 495 .831 .901 883 32 33 0.428 8.071 3 455 .841 .912 901 33 34 49.851 7.407 2 387 .851 .923 919 34 35 49. 259 56. 725 91 290 59. 861 68. 935 110 938 35 36 8.653 6.027 166 .871 .946 956 36 37 8.031 5.311 89 014 .881 .958 975 37 38 7.395 4:579 7 835 .891 .969 994 38 39 6.744 3.829 6 629 .902 .981 111 013 39 40 46. 079 53.063 85 396 59. 912 68. 993 111 033 40 41 5.399 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 45 TABLE 4. [Page 467 | Length of a Degree in Latitude and Longitude. Degree of Long. Degree of Lat. Lat. Naut. miles. Statute miles. Meters. Naut. miles. Statute miles. Meters. 46 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 50 38. 688 44.552 71 698 60. 019 69. 115 111 229 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 Page 468] TABLE 5A. Distance of an Object by Two Bearings. Difference between Difference between the course and first bearing?, in points. the course and second bearing, in points. 2 2K 2H 2 % » 1 8Ji ^% 1 3 1.96 1.09 3i 1.57 0.94 '2.19 1.31 3J 1.32 0.84 1.76 1.12 2.42 1. 58 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 4J 0.81 0.63 1.00 0.77 1.23 0.95 1.53 1.18 1.91 1.48 2.45 1.90 3.25 2.51 4| 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 5\ 0.64 0.55 0.77 0.66 0.92 0.79 1.09 0.94 1.30 1.11 1.56 1.34 1.88 1.62 5J 0.60 0.53 0.72 0.63 0.85 0.75 1.00 0.88 1.18 1.04 1.39 1.23 1.66 1.46 5| 0.57 0.52 0.68 0.61 0.79 0.72 0.93 0.84 1.08 0.98 1.26 1.14 1.48 1.34 6 0.54 0.50 0.64 0.59 0.74 0.69 0.86 0.80 1.00 0.92 1.16 1.07 1.35 1.24 6} 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 7k 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 n 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 n 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 8J 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 8f 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 n 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 n 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 91 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 lOJ- 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.&5 0.59 m 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 10| 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 0.51 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 iij 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 12i 0.42 0.28 0.46 0.31 0.50 0.34 0.54 0.36 0.57 0.38 0.61 0.41 0.64 0.42 12J 0.43 0.28 0.47 0.30 0.51 0.32 0.55 0.35 0.58 0.37 0.61 0.39 0.65 0.41 12| 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 n\ 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 l^ 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 13| 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 TABLE 5A. [Page 469 | Distance of an Object by Two Bearings. Difference between the course Difference between the course and first bearing, in points. and second bearing, in points. 8K 4 *V* 4M *r* 5 5K 1 4f 3.44 2.76 5 2.76 2.30 3.62 3.01 5i 2.31 1.98 2.91 2.50 3.80 3.26 5^ 1.99 1.76 2.44 2.15 3.05 2.69 3.96 3.49 5f 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 6^ 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 6| 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 8i 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 8i 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 8| 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.&5 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 m 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 lU 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 lU 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 0.70 111 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 m 0.68 0.43 0.71 0.45 0.74 0.47 0.77 0.49 0.80 0.51 0.84 0.53 0.87 0.55 12| 0.68 0.41 0.71 0.43 0.74 0.44 0.77 0.46 0.80 0.48 0.83 0.50 0.86 0.51 13 0.69 0.38 0.72 0.40 0.75 0.42 0.78 0.43 0.80 0.45 0.83 0.46 0.86 0.48 131^ 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 13J 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 o% oVa 6 «^ 6^ 6K ' 1 6J 4.52 4.33 6| 3.63 3.52 4.63 4.49 7 3.04 2.98 3.72 3.65 4.74 4.64 7i 2.62 2.59 3.11 3.08 3.80 3.76 4.83 4.77 7i 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 8i 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 8f 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 9i 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 9| 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 lOi 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 1.36 101 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 lU 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 12J 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 13i 0.88 0.45 0.91 0.47 0.93 0.48 0.96 0.49 0.99 0.51 1.01 0.52 1.04 0.54 13J 0.88 0.42 0.91 0.43 0.93 0.44 0.95 0.45 0.98 0.46 1.00 0.47 1.02 0.48 13| 0.88 0.38 0.90 0.39 0.92 0.40 0.95 0.41 0.97 0.41 0.99 0.42 1.01 0.43 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 Page 470] TABLE 5A. Distance of an Object by Two Bearings. Difference between Difference between the course and first bearing, in points. the course and second bearing, in points. IK J^ 7K 8 W* »% m 9 8i 5.07 5.06 • ' 8J 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 n 2.58 2.51 2.95 2.87 3.44 3.34 4.12 3.39 5.12 4.97 H 2.31 2.21 2.60 2.49 2.96 2.84 3.44 3.30 4.11 3.93 5.10 4.88 n 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 10^ 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 10^ 1.66 1.46 1.79 1.58 1.94 1.71 2.12 1.87 2.34 2.06 2.60 2.29 2.94 2.59 3.38 2.98 10| 1.56 1.34 1.67 1.43 1.80 1.54 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 lU 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 lu 1.34 1.03 1.41 1.09 1.49 1.15 1.58 1.22 1.68 1.30 1.79 1.38 1.92 1.49 2.08 1.61 111 1.28 0.95 1.34 1.00 1.41 1.05 1.49 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 m 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 12i 1.15 0.73 1.20 0.76 1.24 0.79 1.29 0.82 1.35 0.86 1.41 0.89 1.47 0.93 1.55 0.98 12| 1.12 0.67 1.16 0.69 1.20 0.72 1.25 0.74 1.29 0.77 1.34 0.80 1.40 0.83 1.46 0.87 13 1.09 0.61 1.13 0.63 1.16 0.65 1.20 0.67 1.24 0.69 1.29 0.72 1.34 0.74 1.39 0.77 m 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 m 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 0.60 131 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 »K 95^ 9% 10 lOK im lOK » 1 lOi 4.97 4.50 10^ 3.99 3.52 4.91 4.33 101 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 lU 2.27 1.75 2.50 1.93 2.79 2.16 3.18 2.46 3.72 2.88 4.52 3.49 111 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 m 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 1.82 121 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 m 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 m 1.31 0.62 1.35 0.64 1.40 0.66 1.46 0.69 1.52 0.72 1.59 0.75 1.67 0.79 1.76 0.83 13| 1.25 0.54 1.29 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 UK 11 'A llji 12 I'zy, 1 t'2% 12'/i u 1 12i 4.12 2.77 i m 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 m 2.10 1.08 2.29 1.18 2.55 1.31 2.91 1.50 3.44 1.77 13i 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 TABLE 5B. [Page 471 | Distance of an Object by Two Bearings. Difference between the course and second bearing. Difference between the course and first bearing. 20° 22° 24° 26° 28° 80° a 2° 30° 1.97 0.98 32 1.64 0.87 2.16 1.14 34 1.41 0.79 1.80 1.01 2.34 1.31 36 1.24 0.73 1.55 0.91 1.96 1.15 2.52 1,48 38 1.11 0.68 1.36 0.84 1,68 1.04 2.11 1,30 2.70 1.66 40 1.00 0.64 1.21 0.78 1.48 0.95 1.81 1,16 2.26 1,45 2.88 1.85 42 0.91 0.61 1.10 0.73 1.32 0.88 1.59 1.06 1.94 1,30 2.40 1.61 3.05 2,04 44 0.84 0.58 1.00 0.69 1.19 0.83 1.42 0.98 1.70 1.18 2.07 1.44 2.55 1,77 46 0.78 0.56 0.92 0.66 1.09 0.78 1.28 0.92 1.52 1.09 1.81 1.30 2.19 1,58 48 0.73 0.54 0.85 0.64 1.00 0.74 1.17 0.87 1.37 1.02 1.62 1.20 1,92 1,43 50 0.68 0.52 0.80 0.61 0.93 0.71 1.08 0.83 1.25 0.96 1.46 1.12 1.71 1.31 52 0.65 0.51 0.75 0.59 0.87 0.68 1.00 0.79 1.15 0.91 1.33 1.05 1.55 1.22 54 0.61 0.49 0.71 0.57 0.81 0.66 0.93 0.76 1.07 0.87 1.23 0.99 1.41 1.14 56 0.58 0.48 0.67 0.56 0.77 0.64 0.88 0.73 1.00 0.83 1.14 0.95 1.30 1.08 58 0.56 0.47 0.64 0.54 0.73 0.62 0.83 0.70 0.94 0.80 1.07 0.90 1.21 1.03 60 0.53 0.46 0.61 0.53 0.69 0.60 0.78 0.68 0.89 0.77 1.00 0.87 1.13 0.98 62 0.51 0.45 0.58 0.51 0.66 0.58 0.75 0.66 0.84 0,74 0.94 0.83 1.06 0.94 64 0.49 0.44 0.56 0.50 0.63 0.57 0.71 0.64 0.80 0.72 0.89 0.80 1.00 0.90 66 0.48 0.43 0.54 0.49 0.61 0.56 0.68 0.62 0.76 0.70 0.85 0.78 0.95 0.87 68 0.46 0.43 0.52 0.48 0.59 0.54 0.66 0.61 0,73 0.68 0.81 0,75 0.90 0.84 70 0.45 0.42 0.50 0.47 0.57 0.53 0.63 0.59 0.70 0.66 0.78 0.73 0.86 0.81 72 0.43 0.41 0.49 0.47 0.55 0.52 0.61 0.58 0.68 0.64 0.76 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 0.60 0.67 0.66 0.74 0.72 80 0.39 0.39 0.44 0.44 0.49 0.48 0.54 0.53 0.60 0.59 0.65 0.64 0.71 0.70 82 0.39 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 0.35 0.55 0.37 140 0.39 0.25 0.42 0.27 0.45 0.29 0.48 0.31 0.51 0. 33 0.53 0.34 0.56 0.36 142 0.40 0.25 0.43 0.27 0.46 0.28 0.49 0.30 0.51 0.32 0.54 0.33 0.56 0.35 144 0.41 0.24 0.44 0.26 0.47 0.28 0.50 0.29 0.52 0.31 0.55 0.32 0.57 0.34 146 0.42 0.24 0.45 0.25 0.48 0.27 0.51 0.28 0.53 0.30 0.56 0.31 0.58 0,32 148 0.43 23 0.46 0.25 0.49 0.26 0.52 0.27 0.54 0.29 0.57 0,30 0.59 0.31 150 0.45 0.22 0.48 0.24 0.50 0.25 0.53 0.26 0.55 0.28 0.58 0,29 0.60 0.30 152 0.46 0.22 0.49 0.23 0.52 0.24 0.54 0.25 0.57 0.27 0.59 0,28 0.61 0.29 154 0.48 0.21 0.50 0.22 0.53 0.23 0.56 0.24 0.58 0.25 0.60 26 0. 62 0.27 156 0.49 0.20 0.52 0.21 0.55 0.22 0.57 0.23 0.60 0.24 0.62 25 0.64 0.26 158 0.51 0.19 0.54 0.20 0.57 0.21 0.59 0.22 0.61 0.23 0.63 0.24 0.66 0.25 160 0.53 0.18 0.56 0.19 0.59 0.20 0.61 0.21 0.63 0,22 0.65 0.22 0.67 0.23 1 Page 472] TABLE 5B. Distance of an Object by Two Bearings. Difference between the cours* and secoiu bearing. Difference between the course and first bearing. a:° Z6° i> 8° 40° 42° 44° 46° 44° 3.22 i 2.24 46 2.69^ 1.93 3.39 2.43 48 2.31 1 1.72 2.83 2.10 3.55 2.63 50 2. 03 i 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 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 0.87 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 1 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 1 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 1 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 i 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 1 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 1 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 I 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 TABLE 5B. [Page 473 | Distance of an Object by Two Bearings. Difference Difference between the course and first bearing. between the course and second bearing. 48° 50° 5 2° 54° 56° 58° 60° 58° 4.28 3.63 60 3.57 3.10 4.41 3.82 62 3.07 2.71 3.68 3.25 4.54 4.01 64 2.70 2.42 3.17 2.85 3.79 3.41 4.66 4.19 66 2.40 2.20 2.78 2.54 3.26 2.98 3.89 3.55 4.77 4.36 68 2.17 2.01 2.48 2.30 2.86 2.65 3.34 3.10 3.99 3.71 4.88 4.53 70 1.98 1.86 2.24 2.10 2.55 2.39 2.94 2.76 3.43 3.22 4.08 3.83 4.99 4.69 >72 1.83 1.74 2.04 1.94 2.30 2.19 2.62 2.49 3.01 2.86 3.51 3.33 4.17 3.96 74 1.70 1.63 1.88 1.81 2.10 2.02 2.37 2.27 2.68 2.58 3.08 2.96 3.58 3.44 76 1.58 1.54 1.75 1.70 1.94 1.88 2.16 2.10 2.42 2.35 2.74 2.66 3.14 3.05 78 1.49 1.45 1.63 1.60 1.80 1.76 1.99 1.95 2.21 2.16 2.48 2.43 2.80 2.74 80 1.40 1.38 1.53 1.51 1.68 1.65 1.85 1.82 2.04 2.01 2.26 2.23 2.53 2.49 82 1.33 1.32 1.45 1.43 1.58 1.56 1.72 1.71 1.89 1.87 2.08 2.06 2.31 2.29 84 1.26 1.26 1.37 1.36 1.49 1.48 1.62 1.61 1.77 1.76 1.93 1.92 2.13 2.12 86 1.21 1.20 1.30 1..30 1.41 1.41 1.53 1.52 1.66 1.65 1.81 1.80 1.98 1.97 88 1.16 1.16 1.24 1.24 1.34 1.34 1.45 1.45 1.56 1.56 1.70 1.70 1.84 1.84 90 1.11 1.11 1.19 1.19 1.28 1.28 1.38 1.38 1.48 1.48 1.60 1.60 1.73 1.73 92 1.07 1.07 1.14 1.14 1.23 1.23 1.31 1.31 1.41 1.41 1.52 1.52 1.63 1.63 94 1.03 1.03 1.10 1.10 1.18 1.17 1.26 1.26 1.35 1.34 1.44 1.44 1.55 1.54 96 1.00 0.99 1.06 1.06 1.13 1.13 1.21 1.20 1.29 1.28 1.38 1.37 1.47 1.47 98 0.97 0.96 1.03 1.02 1.10 1.08 1.16 1.15 1.24 1.23 1.32 1.31 1.41 1.39 100 0.94 0.93 1.00 0.98 1.06 1.04 1.12 1.11 1.19 1.18 1.27 1.25 1.35 1.33 102 0.92 0.90 0.97 0.95 1.03 1.01 1.09 1.06 1.15 1.13 1.22 1.19 1.29 1.27 104 0.90 0.87 0.95 0.92 1.00 0.97 1.06 1.02 1.12 1.08 1.18 1.14 1.25 1.21 106 0.88 0.84 0.92 0.89 0.97 0.94 1.03 0.99 1.09 1.04 1.14 1.10 1.20 1.16 108 0.86 0.82 0.90 0.86 0.95 0.90 1.00 0.95 1.05 1.00 1.11 1.05 1.17 1.11 110 0.84 0.79 0.88 0.83 0.93 0.87 0.98 0.92 1.02 0.96 1.08 1.01 1.13 1.06 112 0.83 0.77 0.87 0.80 0.91 0.84 0.95 0.88 1.00 0.93 1.05 0.97 1.10 1.02 114 0.81 0.74 0.85 0.78 0.89 0.82 0.93 0.85 0.98 0.89 1.02 0.93 1.07 0.98 116 0.80 0.72 0.84 0.75 0.88 0.79 0.92 0.82 0.96 0.85 1.00 0.90 1.04 0.94 118 0.79 0.70 0.83 0.73 0.86 0.76 0.90 0.79 0.94 0.83 0.98 0.86 1.02 0.90 J 20 0.78 0.68 0.82 0.71 0.85 0.74 0.89 0.77 0.91 0.80 0.96 0.83 1.00 0.87 122 0.77 0.66 0.81 0.68 0.84 0.71 0.87 0.74 0.90 0.77 0.95 0.80 0.98 0.83 124 0.77 0.63 0.80 0.66 0.83 0.69 0.86 0.71 0.90 0.74 0.93 0.77 0.96 0.80 126 0.76 0.61 0.79 0.64 0.82 0.66 0.85 0.69 0.88 0.71 0.91 0.74 0.95 0.77 128 0.75 0.59 0.78 0.62 0.81 0.64 0.84 0.66 0.87 0.69 0.90 0.71 0.93 0.74 130 0.75 0.57 0.78 0.60 0.81 0.62 0.83 0.64 0.86 0.66 0.89 0.68 0.92 0.71 132 0.75 0.56 0.77 0.57 0.80 0.59 0.83 0.61 0.85 0.64 0.88 0.66 0.91 0.68 134 0.74 0.54 0.77 0.55 0.80 0.57 0.82 0.59 0.85 0.61 0.87 0.63 0.90 0.65 136 0.74 0.52 0.77 0.53 0.80 0.55 0.82 0.57 0.84 0.58 0.87 0.60 0.89 0.62 138 0.74 0.50 0.77 0.51 0.79 0.53 0.81 0.54 0.84 0.56 0.86 0.58 0.89 0.59 140 0.74 0.48 0.77 0.49 0.79 0.51 0.81 0.52 0.83 0.54 0.86 0.55 0.88 0.57 142 0.74 0.46 0.77 0.47 0.79 0.49 0.81 0.50 0.83 0.51 0.85 0.52 0.87 0.54 144 0.75 0.44 0.77 0.45 0.79 0.46 0.81 0.48 0.83 0.49 0.85 0.50 0.87 0.51 146 0.75 0.42 0.77 0.43 0.79 0.44 0.81 0.45 0.83 0.46 0.85 0.47 0.87 0.49 148 0.76 0.40 0.77 0.41 0.79 0.42 0.81 0.43 •0.83 0.44 0.85 0.45 0.87 0.46 150 0.76 0.38 0.78 0.39 0.80 0.40 0.81 0.41 0.83 0.42 0.85 0.42 0.87 0.43 152 0.77 0.36 0.78 0.37 0.80 0.38 0.82 0.38 0.83 0.39 0.85 0.40 0.87 0.41 154 0.77 0.34 0.79 0.35 0.81 0.35 0.82 0.36 0.84 0.37 0.85 0.37 0.87 0.38 156 0.78 0.32 0.80 0.32 0.81 0.33 0.83 0.34 0.84 0.34 0.86 0.35 0.87 0.35 158 0.79 0.30 0.81 0.30 0.82 0.31 0.83 0.31 0.85 0.32 0.86 0.32 0.87 0.33 160 0.80 0.27 0.82 0.28 0.83 0.28 0.84 0.29 0.85 0. 29 0.86 0.30 0.88 0.30 Page 474] TABLE 5B. Distance of an Object by Two Bearings. Difference between the course Difference between the course and first bearing. and second bearing. 62° «4° 66° 68° 70° 72° 74° 76° 72° 5.08 i 4.84 \ 74 4.25 4.08 5.18 4.98 76 3.65 3.54 4.32 4.19 5.26 5.10 78 3.20 3.13 3.72 3.63 4.39 4.30 5.34 5.22 80 2.86 2.81 3.26 3.21 3.78 3.72 4.46 4.39 5.41 5.33 82 2.58 2.56 2.91 2.88 3.31 3.28 3.83 3.80 4.52 4.48 5.48 5. 42 84 2.36 2.34 2.63 2.61 2.96 2.94 3.36 3.35 3.88 3.86 4.57 4.55 5.54 5.51 86 2.17 2.17 2.40 2.39 2.67 2.66 3.00 2.99 3.41 3.40 3. 93 3.92 4.62 4.61 5.59 5.57 88 2.01 2.01 2.21 2.21 2.44 2.44 2.71 2.71 3.04 3.04 3.45 3.45 3.97 3.97 4.67 4.66 90 1.88 1.88 2.05 2.05 2.25 2.25 2.48 2.48 2.75 2.75 3.08 3.08 3.49 3.49 4.01 4.01 92 1.77 1.76 1.91 1.91 2.08 2.08 2.28 2.28 2.51 2.51 2.78 2.78 3.11 3.11 3.52 3.52 94 1.67 1.66 1.80 1.79 1.95 1.94 2.12 2.11 2.31 2.30 2.54 2.53 2.81 2.80 3.14 3.13 96 1.58 1.57 1.70 1.69 1.83 1.82 1.97 1.96 2.14 2.13 2.34 2. 33 2.57 2.55 2.84 2.82 98 1.50 1.49 1.61 1.59 1.72 1.71 1.85 1.84 2.00 1.98 2.17 2.15 2.36 2.34 2.59 2.56 100 1.43 1.41 1.53 1.51 1.63 1.61 1.75 1.72 1.88 1.85 2.03 2.00 2.19 2.16 2.39 2.35 102 1.37 1.34 1.46 1.43 1.55 1.52 1.66 1.62 1.77 1.73 1.90 1.86 2.05 2.00 2.21 2.16 104 1.32 1.28 1.40 1.36 1.48 1.44 1.58 1.53 1.68 1.63 L79 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. lo 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 0.87 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 TABLE 5B. [Page 475 Distance of an Object by Two Bearings. Difference Difference between the course and first bearing. between the course and second bearing. 78° 80° 82° 84° 86° 88° 90° 92° 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 1.37 1.11 1.43 1.15 1.48 1.20 1.55 1.26 1.62 1.31 1.70 1.38 1.79 1.45 128 1.28 1.01 1.33 1.04 1.38 1.08 1.43 1.13 1.49 1.17 1.55 1.23 1.62 1.28 1.70 1.34 130 1.24 0.95 1.29 0.98 1.33 1.02 1.38 1.06 1.44 1.10 1.49 1.14 1.56 1.19 1.62 1.24 132 1.21 0.90 1.25 0.93 1.29 0.96 1.34 0.99 1.39 1.03 1.44 1.07 1.49 1.11 1.55 1.16 134 1.18 0.85 1.22 0.88 1.26 0.90 1.30 0.93 1.34 0.97 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 1 2. 96 3.93 3.33 124 2.00 1.65 2.12 1.76 2.26 1.87 2. 42 i 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 1.23 0.65 1.26 0.67 1.29 0.69 1.33 0.70 1.36 0.72 1.40 0.74 1.44 0.76 1.48 0.78 150 1.20 0.60 1.23 0.61 1. 26 ' 0. 63 1.29 0.64 1.32 0.66 1.35 0.67 1.38 0.69 1.42 0.71 152 1.18 0.55 1.20 0.56 1.22 0.57 1. 25 ! 0. 59 1.28 0.60 1.31 0.61 1.34 0.63 1.37 0.64 154 1.15 0.50 1.17 0.51 1.19 0.52 1. 22 0. 53 1.24 0.54 1.27 0.56 1.29 0.57 1.32 0.58 156 1.13 0.46 1.15 0.47 1.17 0.47 1. 19 i 0. 48 1.21 0.49 1.23 0.50 1.2510.51 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 Page 476J TABLE 5B. Distance of an Object by Two Bearings. Difference between the course and second bearing. Difference between the course and first bearing. 110° 112° 114° 116° 118° 120° 122° 120° 5.41 4.69 1 ' 122 4.52 li 5.34 4.53 124 3.88 4.46 3.70 15.26 4.36 126 3.41 2! 76 3.83 3.10 14.39 3.55 5.18 4.19 128 3.04 2.40 3.36 2.65 13.78 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 h 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 1 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 1 0.46 1.38 0.47 124° 126° 128° 130° 132° 134° 136° 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 3.68 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° 144° 1 14«° 148° 150° 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 1 TABLE 6. [Page 477 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 4.3.8 15 4.4 5.1 190 15.8 18.2 1,200 39.6 45.6 16 4.6 5.3 200 16.2 18.7 1,300 41.3 47.6 17 4.7 5.4 210 16.6 19.1 1,400 42.9 49.4 18 4.9 5.6 220 17.0 19.6 1,500 44.4 51.1 19 5.0 5.8 230 17.4 20.0 1,600 45.8 52.8 20 5.1 5.9 240 17.7 20.4 1,700 47.2 54.4 21 5.3 6.1 250 18.2 20.9 1,800 48.6 56.0 22 5.4 6.2 260 18.5 21.3 1,900 49.9 57.5 23 5.5 6.3 270 18.9 21.7 2,000 51.2 59.0 24 5.6 6.5 280 19.2 22.1 2, 100 52.5 60.5 25 5.7 6.6 290 19.6 22.5 2,200 53.8 61.9 26 5.8 6.7 300 19.9 22.9 2,300 55.0 63.3 27 6.0 6.9 310 20.1 23.2 2,400 56.2 64.7 28 6.1 7.0 320 20.5 23.6 2,500 57.3 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 73.5 35 6.8 7.8 390 22.7 26.1 3,200 64.9 74.7 36 6.9 7.9 400 22.9 26.4 3,300 65.9 75.9 37 6.9 8.0 410 23.2 26.7 3,400 66.9 77.0 38 7.0 8.1 420 23.5 27.1 3,500 67. 8 78.1 39 7.1 8.2 430 23.8 27.4 3,600 68. 8 79.2 40 7.2 8.3 440 24.1 27.7 3,700 69.7 80.3 41 7.3 8.4 450 24.3 28.0 3, 800 70.7 81.4 42 7.4 8.5 460 24.6 28.3 3,900 71.6 82.4 43 7.5 8.7 470 24.8 28.6 4,000 72.5 83.5 44 7.6 8.8 480 25.1 28.9 4,100 73.4 84.5 45 7.7 8.9 490 25.4 29.2 4,200 74.3 85.6 46 7.8 9.0 500 25.6 29.5 4,300 75.2 86.6 47 7.9 9.0 520 26.1 30.1 4,400 76.1 87.6 48 7.9 9.1 540 26.7 30.7 4, 500 76.9 88.5 49 8.0 9.2 560 27.1 31.2 4,600 77.7 89.5 50 8.1 9.3 580 27.6 31.8 4,700 78.6 90.5 55 8.5 9.8 600 28.0 32.3 4,800 79.4 91.4 60 8.9 10.2 620 '28.6 32.9 4,900 80.2 92.4 65 9.2 10.6 640 29.0 33.4 5,000 81.0 93.3 70 9.6 11.0 660 29.4 33.9 6,000 88.8 102.2 75 9.9 11.4 680 29.9 34.4 7,000 96.0 110.5 80 10.3 11.8 700 30.3 34.9 8,000 102.6 118.1 85 10.6 12.2 720 30.7 35.4 9,000 108. 7 125.2 90 10.9 12.5 740 31.1 35.9 10,000 114.6 132.0 95 11.2 12.9 Page 478] TABLE 7 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. S. ' M. S. ' M. S. ' M. S. / M. S. II s. ^ " s. A II s. A " 8. A " s. A II S. rfB 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 h, 4 12 123 8 12 183 12 12 243 16 12 303 20 12 4 16 64 4 16 124 8 16 184 12 16 244 16 16 304 20 16 5 20 65 4 20 125 8 20 185 12 20 245 16 20 305 20 20 6 24 66 4 24 126 8 24 186 12 24 246 16 24 306 20 24 7 28 67 4 28 127 8 28 187 12 28 247 16 28 307 20 28 8 32 68 4 32 128 8 32 188 12 32 248 16 32 308 20 32 9 36 69 4 36 129 8 36 189 12 36 249 16 36 309 20 36 10 40 70 4 40 130 8 40 190 12 40 250 16 40 310 20 40 11 44 71 4 44 131 8 44 191 12 44 251 16 44 311 20 44 12 48 72 4 48 132 8 48 192 12 48 252 16 48 312 20 48 13 52 73 4 52 133 8 52 193 12 52 253 16 52 313 20 52 14 56 74 4 56 134 8 56 194 12 56 254 16 56 314 20 56 15 1 75 5 135 9 195 13 255 17 315 21 16 1 4 76 5 4 136 9 4 196 13 4 256 17 4 316 21 4 17 1 8 77 5 8 137 9 8 197 13 8 257 17 8 317 21 8 18 1 12 78 5 12 138 9 12 198 13 12 258 17 12 318 21 12 19 1 16 79 5 16 139 9 16 199 13 16 259 17 16 319 21 16 20 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 40 325 21 40 26 1 44 86 5 44 146 9 44 206 13 44 266 17 44 326 21 44 27 1 48 87 5 48 147 9 48 207 13 48 267 17 48 327 21 48 28 1 52 88 5 52 148 9 52 208 13 52 268 17 52 328 21 52 29 1 56 89 5 56 149 9 56 209 13 56 269 17 56 329 21 56 30 2 90 6 150 10 210 14 270 18 330 22 31 2 4 91 6 4 151 10 4 211 14 4 271 18 4 331 22 4 32 2 8 92 6 8 152 aO 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 40 220 221 14 40 14 44 280 18 40 340 22 40 41 2 44 101 6 44 161 10 44 281 18 44 341 22 44 42 2 48 102 6 48 162 10 48 222 14 48 282 18 48 342 22 48 43 2 52 103 6 52 163 10 52 223 14 52 283 18 52 343 22 52 44 2 56 104 6 56 164 10 56 224 14 56 284 18 56 344 22 56 45 3 105 7 165 11 225 15 285 19 345 23 46 3 4 106 7 4 166 11 4 226 15 4 286 19 4 346 23 4 47 3 8 107 7 8 167 11 8 227 15 8 287 19 8 347 23 8 48 3 12 108 7 12 168 11 12 228 15 12 288 19 12 348 23 12 49 3 16 109 7 16 169 11 16 229 15 16 289 19 16 349 23 16 50 51 3 20 110 7 20 170 11 20 230 15 20 290 19 20 350 23 20 3 24 111 7 24 171 11 24 231 15 24 291 19 24 351 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 44 356 23 44 57 3 48 117 7 48 177 11 48 237 15 48 297 19 48 357 23 48 58 3 52 118 7 52 178 11 52 238 15 52 298 19 52 358 23 52 59 3 56 119 7 56 179 11 56 239 15 56 299 19 56 359 23 56 60 4 120 8 180 12 240 16 300 20 360 24 Note. — When turning seconds of arc into time, and vice versa, it should be remembered that the fractions are sixtieths; thufi, the value in time oi 42" is not 2^48, but 2»U=2".8. TABLE 8. [Page 479 Sidereal into Mean Solar Time. "3 To be subtracted from a sidereal time interval. Oh Ih 2. Sh 4h oh 6" 7" For seconds. m. in. 8. TO. «. m. «. TO. 8. TO. S. TO. 8. TO. 8. m. 8. 8. 8. 0.000 9.830 19.659 29. 489 39. 318 49. 148 58. 977 1 8. 807 1 0. 164 9.993 19.823 29.653 39.482 49. 312 59. 141 1 8. 971 1 0.003 2 0. 328 10. 157 19. 987 29. 816 39. 646 49. 475 59. 305 1 9. 135 2 .005 3 0. 491 10. 321 20. 151 29. 980 39. 810 49. 639 59. 469 1 9. 298 3 .008 4 0. 655 10.485 20. 314 30. 144 39. 974 49. 803 59. 633 1 9.462 4 .011 5 0. 819 10.649 20. 478 30. 308 40. 137 49. 967 59. 796 1 9.626 5 .014 6 0. 983 10. 813 20. 642 30. 472 40. 301 50. 131 59. 960 1 9.790 6 .016 7 1. 147 10.976 20. 806 30. 635 40. 465 50. 295 0.124 1 9. 954 7 .019 8 1.311 11. 140 20. 970 30. 799 40. 629 50. 458 0.288 1 10.118 8 .022 9 10 1.474 11. 304 21. 134 30. 963 40. 793 50. 622 0.452 1 10.281 9 .025 1.638 11.468 21. 297 31. 127 40. 956 50. 786 0.616 1 10.445 10 .027 11 1.802 11. 632 21.461 i 31.291 41. 120 50. 950 0.779 1 10.609 11 .030 12 1.966 11. 795 21. 625 31. 455 41. 284 51. 114 0.943 1 10.773 12 .033 13 2. 130 11.959 21.789 1 31.618 41. 448 51. 278 1.107 1 10. 937 13 .035 14 2. 294 12. 123 21. 953 31. 782 41.612 51.441 1.271 1 11.100 14 .038 15 2. 457 12. 287 22. 117 1 31. 946 41. 776 51. 605 1.435 1 11.264 15 .041 16 2. 621 12. 451 22. 280 32. 110 41. 939 51. 769 1.599 1 11.428 16 .044 17 2. 785 12. 615 22. 444 32. 274 i 42. 103 51. 933 1.762 1 11.592 17 .046 18 2. 949 12. 778 22. 608 32. 438 i 42. 267 52. 097 1.926 1 11.756 18 .049 19 3. 113 12. 942 1 22. 772 i 32. 601 I 42. 431 52. 260 2.090 1 11.920 19 .052 20 3.277 13. 106 22. 936 i 32. 765 42. 595 52. 424 2.254 1 12.083 20 .055 21 3. 440 13. 270 23. 099 i 32. 929 42. 759 52. 588 2.418 1 12.247 21 .057 22 3. 604 13.434 23. 263 ; 33. 093 42. 922 52. 752 2.582 1 12.411 22 .060 23 3. 768 13.598 23. 427 33. 257 43. 086 52. 916 2.745 1 12.575 23 .063 24 3. 932 13. 761 23. 591 33. 420 43. 250 53. 080 2.909 1 12.739 24 .066 25 4. 096 13.925 23. 755 33. 584 43. 414 53. 243 3.073 1 12.903 25 .068 26 4. 259 14.089 23. 919 33. 748 43. 578 53. 407 3.237 1 13.066 26 .071 27 4. 423 14. 253 24. 082 33. 912 43. 742 53. 571 3.401 1 13.230 27 .074 28 4. 587 14.417 24. 246 34. 076 43.905 53. 735 3.564 1 13.394 28 .076 29 4. 751 14.581 24. 410 34. 240 44. 069 53. 899 54. 063 3.728 1 13.558 29 .079 30 4.915 14. 744 24. 574 34. 403 44. 233 3.892 1 13.722 30 .082 31 5. 079 14.908 24. 738 34. 567 44. 397 54. 226 4.056 1 13.886 31 .085 32 5. 242 15.072 24. 902 34. 731 44. 561 54. 390 4.220 1 14.049 32 .087 33 5. 406 15.236 25.065 34. 895 44. 724 54. 554 4.384 1 14.213 33 .090 34 5. 570 15.400 25. 229 35. 059 44. 888 54. 718 4.547 1 14.377 34 35' .093 .096 35 5. 734 15. 563 25. 393 35. 223 45. 052 54. 882 4.711 1 14.541 36 5. 898 15. 727 25. 557 35. 386 45. 216 55. 046 4.875 1 14.705 36 .098 37 6.062 15. 891 25. 721 35. 550 45. 380 55. 209 5.039 1 14.868 37 .101 38 6. 225 16. 055 25. 885 35. 714 45. 544 55. 373 5.203 1 15.032 38 .104 39 6. 389 16. 219 16.383 26. 048 35. 878 45. 707 55. 537 5.367 1 15.196 39 .106 40 6. 553 26. 212 36. 042 45. 871 55. 701 5.530 1 15.360 40 .109 41 6. 717 16.546 26. 376 36. 206 46. 035 55. 865 5.694 1 15.524 41 .112 42 6. 881 16. 710 26. 540 36. 369 46. 199 56. 028 5.858 1 15.688 42 .115 43 7.045 16. 874 26. 704 36. 533 46. 363 56. 192 6.022 1 15.851 43 .117 44 7. 208 17.038 26. 867 36. 697 46. 527 56. 356 6.186 1 16.015 44 .120 45 7.372 17.202 27. 031 36. 861 46. 690 56. 520 6.350 1 16.179 45 .123 46 7.536 17.366 27. 195 37. 025 46. 854 56. 684 6.513 1 16.343 46 .126 47 7. 700 17. 529 27. 359 37. 188 47. 018 56. 848 6.677 1 16.507 47 .128 48 7.864 17.693 27. 523 37. 352 47. 182 57. Oil 6.841 1 16.671 48 .131 49 8. 027 17.857 27. 687 37. 516 47. 346 57. 175 7.005 1 16.834 49 .134 50 8. 191 18.021 27. 850 37.680 47. 510 57. 339 7.169 1 16.998 50 .137 51 8.355 18. 185 28.014 37. 844 47. 673 57. 503 7.332 1 17. 162 51 .139 52 8.519 18. 349 28. 178 38. 008 47. 837 57. 667 7.496 1 17.326 52 .142 53 8. 683 18. 512 28. 342 38. 171 48. 001 57. 831 7.660 1 17.490 53 .145 54 8. 847 18.676 28. 506 38. 335 38.499 48. 165 57. 994 7.824 1 17.654 54 .147 55 9. 010 18. 840 28. 670 48. 329 58. 158 7.988 1 17.817 55 .150 56 9. 174 19.004 28. 833 38. 663 48. 492 58. 322 8.152 1 17.981 56 .153 57 9. 338 19. 168 28. 997 38. 827 48. 656 58. 486 8.315 1 18.145 57 .156 58 9. 502 19. 331 29. 161 38. 991 48. 820 58. 650 8.479 1 18.309 58 .158 59 9. 666 19. 495 29. 325 39. 154 48. 984 58. 814 8.643 1 18.473 59 0.161 Page 480] TABLE 8. Sidereal into Mean Solar Time. S To be subtracted from a sidereal time interval. 8h flh lOi- llh Igk 18* 14h IS" For seconds.! m. VI. s. TO. S. m. ». m. s. TO. 8. VI. D. TO. «. TO. S. s. «. 1 18.636 1 28.466 1 38.296 1 48. 125 57. 955 2 7. 784 2 17. 614 2 27.443 1 1 18.800 1 28.630 1 38.459 1 48.289 58. 119 2 7. 948 2 17. 778 2 27. 607 1 0.003 2 1 18.964 1 28.t94 1 38.623 1 48.453 58. 282 2 8.112 2 17.941 2 27. 771 2 .005 3 1 19.128 1 28.958 1 38.787 1 48.617 58. 446 2 8. 276 2 18. 105 2 27. 935 3 .008 4 1 19.292 1 29. 121 1 38.951 1 48. 780 1 48.944 58. 610 58. 774 2 8.440 1 2 18.269 2 8.603 2 18.433 2 28. 099 2 28. 263 4 5 .011 .014 5 1 19.456 1 29.285 1 39. 115 6 1 19.619 1 29.449 1 39.279 1 49. 108 58. 938 2 8. 767 2 18. 597 2 28. 426 6 .016 7 1 19.783 1 29. 613 1 39.442 1 49.272 ! 1 59. 101 2 8.931 2 18. 761 2 28. 590 7 .019 8 1 19.947 1 29. 777 1 39.606 1 49.436 1 59. 265 2 9.095 2 18. 924 2 28. 754 8 .022 9 1 20.111 1 29.940 1 30. 104 1 39. 770 1 49.600 1 1 49. 763 1 59. 429 59. 593 2 9.259 2 19.088 2 28. 918 9 .025 10: 1 20,275 1 39.934 2 9.423 2 19.252 2 29. 082 10 .027 11 1 20. 439 1 30.268 1 40.098 1 49.927 1 59. 757 2 9.586 2 19.416 2 29. 245 11 .030 12 1 20.602 1 30.432 1 40.261 1 50.091 1 59. 921 2 9.750 2 19.580 2 29. 409 12 .033 13 1 20. 766 1 30.596 1 40.425 1 1 50.255 2 0.084 2 9. 914 2 19. 744 2 29. 573 13 .035 14 1 20.930 1 30.760 1 40.589 1 1 50.419 2 0.248 2 10.078 2 19.907 2 29. 737 14 .038 15 1 T 21. 094 1 30.923 1 40. 753 1 50. 583 2 0.412 2 10. 242 t 2 20. 071 2 29.901 15 .041 16 1 21.258 1 31. 087 1 40. 917 1 50. 746 2 0.576 2 10. 405 2 20. 235 2 30.065 16 .044 T7 i 21.422 1 31. 251 1 41.081 1 50.910 2 0.740 2 10. 569 2 20. 399 2 30. 228 17 .046 18 i 21.585 1 31.415 1 41.244 1 51.074 2 0.904 2 10. 733 2 20. 563 2 30. 392 18 .049 19 1 21.749 1 31.579 1 41.408 1 51.233 2 1.067 2 10. 897 i 2 20. 727 2 11.061 2 20.890 2 30. 556 19 .052 20 1 21.913 1 31. 743 1 41.572 1 51.402 2 1.231 2 30. 720 20 .055 21 1 1 22. 077 1 31.906 1 41.736 1 51.565 2 1. 395 2 11. 225 2 21. 054 2 30. 884 21 .057 22! 1 22.241 1 32. 070 1 41.900 1 51.729 2 1.559 2 11. 388 ; 2 21. 218 2 31. 048 22 .060 23 1 1 22.404 1 32. 234 1 42. 064 1 51. 893 2 1.723 2 11.552 2 21.382 2 31.211 23 .063 24 ! 1 22. 568 1 32.398 1 42.227 1 52.057 2 2 1.887 2.050 2 11. 716 2 21. 546 2 11. 880 2 21. 709 2 31. 375 2 31. 539 24 .066 25 i 1 22. 732 1 32. 562 1 42. 391 1 52. 221 25 .068 26 1 1 22. 896 1 32.726 1 42. 555 1 52. 385 2 2.214 2 12.044 2 21.873 2 31. 703 26 .071 27 1 1 23. 060 1 32.889 1 42. 719 1 52. 548 2 2.378 2 12.208 2 22.037 2 31.867 27 .074 28 1 1 23.224 1 33.053 1 42. 883 1 52. 712 2 2.542 2 12.371 2 22.201 2 32. 031 28 .076 29 30 1 23.387 1 23.551 1 33.217 1 33.381 1 43. 047 1 52. 876 2 2.706 2 12.535 2 22. 365 2 32. 194 29 .079 1 43.210 1 53.040 . 2 2.869 2 12.699 2 22.529 2 32. 358 30 .082 31 1 23. 715 1 33.545 1 43. 374 1 53. 204 2 3.033 2 12.863 2 22. 692 2 32. 522 31 .085 32 1 23.879 1 33. 708 1 43. 538 : 1 53. 368 2 3.197 2 13. 027 i 2 22. 856 2 32. 686 32 .087 33 1 24.043 1 33.872 1 43. 702 i 1 53. 531 2 3.361 2 13. 191 1 2 23. 020 2 32. 850 33 .090 34 1 24.207 1 34.036 1 43.866 1 53.695 2 3.525 2 13.354 2 23. 184 2 33.013 34 .093 35 1 24.370 1 34.200 1 44. 029 1 53.859 2 3.689 2 13.518 2 23. 348 2 33. 177 35 .096 36 1 24. 534 1 34.364 1 44.193 1 54.023 2 3. 852 2 13.682 2 23.512 2 33.341 36 .098 37 1 24.698 1 34.528 1 44. 357 1 54. 187 2 4.016 2 13.846 2 23.675 2 33.505 37 .101 38 1 24.862 1 34.691 1 44.521 1 54.351 2 4.180 2 14.010 2 23. 839 2 33.669 38 .104 39 1 25.026 1 34.855 1 44. 685 1 54.514 2 4.344 2 14.173 2 14.337 2 24. 003 2 24. 167 2 33. 833 39 .106 40 1 25. 190 1 35.019 1 44.849 1 54. 678 2 4.508 2 33. 996 40 .109 41 1 25.353 1 35. 183 1 45.012 1 54.842 2 4.672 2 14.501 2 24. 331 2 34. 160 41 .112 42 1 25.517 1 35.347 1 45.176 1 55.006 2 4. 835 2 14. 665 ! 2 24. 495 2 34. 324 42 .115 43 1 25.681 1 35.511 1 45.340 1 55. 170 2 4.999 2 14. 829 i 2 24. 658 2 .34. 488 43 .117 44 1 25.845 1 35.674 1 45.504 1 55.333 2 5.163 2 14. 993 i 2 24. 822 2 34. 652 44 .120 45 1 26.009 1 35.838 1 45.668 1 55.497 2 5.327 2 15. 156 2 24. 986 2 34. 816 45 .123 46 1 26. 172 1 36.002 1 45.832 1 55.661 2 5.491 2 15. 320 2 25. 150 2 34. 979 46 .126 47 1 26.336 1 36. 166 1 45.995 1 55.825 2 5.655 2 15.484 2 25. 314 2 35. 143 47 .128 48 1 26.500 1 36.330 1 46. 159 1 55.989 2 5.818 2 15.648 2 25.477 2 35. 307 48 .131 49 1 26.664 1 36.493 1 46.323 1 56. 153 2 5.982 2 15.812 2 25. 641 2 35. 471 49 .134 50 1 26. 828 1 36.657 1 46.487 1 56.316 2 6.146 2 15.976 2 25. 805 2 35. 635 50 .137 51 1 26.992 1 36.821 1 46.651 1 56.480 2 6.310 2 16.139 2 25.969 2 35. 798 51 .139 52 1 27. 155 1 36.985 1 46.815 1 56.644 2 6.474 2 16.303 2 26. 133 2 35. 962 52 .142 53 1 27. 319 1 37. 149 1 46.978 1 56.808 2 6.637 2 16.467 2 26. 297 2 36.126 53 .145 54 1 27.483 1 37.313 1 47.142 1 56.972 2 6.801 2 16.631 2 26.460 2 36. 290 64 .147 55 1 27.647 1 37.476 1 47.306 1 57.136 2 6.965 2 16. 795 2 26. 624 2 36. 454 55 .150 56 1 27.811 1 37. 640 1 47. 470 i 1 57. 299 2 7.129 2 16.959 2 26. 788 2 36.618 56 .153 57 1 27.975 1 37.804 1 47.634 1 57.463 2 7.293 2 17. 122 2 26. 952 2 36. 781 57 .156 58 1 28. 138 1 37.968 1 47.797 1 57.627 2 7.457 2 17.286 2 27. 116 2 36. 945 58 .158 59 1 28.302 1 38. 132 1 47. 961 1 57. 791 2 7.620 2 17.450 2 27. 280 2 37. 109 59 0.161 TABLE 8. [Page 481 Sidereal into Mean Solar Time. "3 2 "2 m. 1 2 3 4 5 6 7 8 9 To be subtracted from a sidereal time interval. m. s. 2 37. 273 2 37. 437 2 37. 601 2 37. 764 2 37. 928 2 38. 092 2 38. 256 2 38. 420 2 38. 584 2 38. 747 17h m. s. 2 47. 102 2 47. 266 2 47. 430 2 47. 594 2 47. 758 2 47. 922 2 48. 085 2 48.249 2 48. 413 2 48. 577 181- 19«> ao" •21h 2 SI" 2S^ For seconds.! m. s. 2 56. 932 2 57. 096 2 57. 260 2 57.424 2 57. 587 m. 3 3 3 3 3 6.762 6.925 7.089 7.253 7.417 m. s. 3 16.591 3 16. 755 3 16.919 3 17.083 3 17.246 m. 8. 3 26.421 3 26. 585 3 26. 748 3 26. 912 3 27. 076 TO. 8. 3 36. 250 3 367414 3 36. 578 3 36. 742 3 36.906 TO. «. 3 46. 080 3 46. 244 3 46. 407 3 46. 571 3 46. 735 1 2 3 4 8. 0. 003 .005 .008 .011 2 57. 751 2 57.915 2 58. 079 2 58. 243 2 58. 406 3 3 3 3 3 7.581 7.745 7.908 8.072 8.236 3 17.410 3 17.574 3 17. 738 3 17.902 3 18.066 3 27. 240 3 27.404 3 27.568 3 27. 731 3 27.895 3 37. 069 3 37. 233 3 37.397 3 37.561 3 37. 725 3 46. 899 3 47. 063 3 47. 227 3 47. 390 3 47. 554 5 6 7 8 9 .014 .016 .019 .022 .025 10 11 12 13 14 2 38. 911 2 39. 075 2 39. 239 2 39. 403 2 39. 566 2 48. 741 2 48. 905 2 49. 068 2 49. 232 2 49. 396 2 58. 570 2 58. 734 2 58. 898 2 59. 062 2 59. 226 3 3 3 3 3 8.400 8.564 8.728 8.891 9.055 3 18.229 3 18.393 3 18.557 3 18. 721 3 18.885 3 28. 059 3 28. 223 3 28. 387 3 28. 550 3 28. 714 3 37. 889 3 38. 052 3 38. 216 3 38. 380 3 38. 544 3 47. 718 3 47. 882 3 48. 046 3 48. 210 3 48. 373 10 11 12 13 14 .027 .030 .033 .035 .038 15 16 17 18 19 2 39. 730 2 39.894 2 40. 058 2 40. 222 2 40. 386 2 49.560 2 49. 724 2 49. 888 2 50. 051 2 50. 215 2 59. 389 2 59. 553 2 59. 717 2 59.881 3 0.045 3 3 3 3 3 9.219 9.383 9.547 9.710 9.874 3 19.049 3 19.212 3 19. 376 3 19.540 3 19. 704 3 28.878 3 29.042 3 29. 206 3 29. 370 3 29. 533 3 38. 708 3 38. 871 3 39.035 3 39. 199 3 39. 363 3 48. 537 3 48. 701 3 48. 865 3 49. 029 3 49. 193 15 16 17 18 19 .041 .044 .046 .049 .052 20 21 22 23 24 2 40. 549 2 40. 713 2 40. 877 2 41.041 2 41. 205 2 50. 379 2 50. 543 2 50. 707 2 50. 870 2 51. 034 3 3 3 3 3 0.209 0.372 0. 536 0.700 0.864 3 3 3 3 3 10. 038 10. 202 10. 366 10. 530 10. 693 3 19.868 3 20.032 3 20. 195 3 20. 359 3 20. 523 3 29. 697 3 29. 861 3 30.025 3 30. 189 3 30. 353 3 39.527 3 39. 691 3 39. 854 3 40. 018 3 40. 182 3 49. 356 3 49. 520 3 49. 684 3 49. 848 3 50.012 20 21 22 23 24 .055 .057 .060 .063 .066 25 26 27 28 29 2 41.369 2 41.532 2 41.696 2 41.860 2 42. 024 2 51. 198 2 51. 362 2 51.526 2 51. 690 2 51.853 3 3 3 3 3 1.028 1.192 1. 355 1.519 1.683 3 3 3 3 3 10. 857 11. 021 11. 185 11. 349 11.513 3 20.687 3 20. 851 3 21.014 3 21. 178 3 21. 342 3 30. 516 3 30. 680 3 30. 844 3 31.008 3 31. 172 3 40.346 3 40. 510 3 40. 674 3 40. 837 3 41.001 3 50. 175 3 50. 339 3 50. 503 3 50. 667 3 50. 831 25 26 27 28 29 .068 .071 .074 .076 .079 30 31 32 33 34 2 42. 188 2 42. 352 2 42. 515 2 42. 679 2 42. 843 2 52.017 2 52. 181 2 52. 345 2 52. 509 2 52. 673 3 3 3 3 3 1.847 2.011 2.174 2.338 2.502 3 3 3 3 3 11.676 11. 840 12. 004 12. 168 12. 332 3 21. 506 3 21. 670 3 21. 834 3 21. 997 3 22. 161 3 31. 336 3 31.499 3 31. 663 3 31. 827 3 31.991 3 41. 165 3 41. 329 3 41. 493 3 41. 657 3 41. 820 3 50. 995 3 51. 158 3 51. 322 3 51. 486 3 51. 650 30 31 32 33 34 35 36 37 38 39 .082 .085 .087 .090 .093 35 36 37 38 39 2 43. 007 2 43. 171 2 43. 334 2 43. 498 2 43. 662 2 52. 836 2 53. 000 2 53. 164 2 53. 328 2 53. 492 3 3 3 3 3 2.666 2.830 2.994 3. 157 3.321 3 3 3 3 3 12. 496 12. 659 12. 823 12. 987 13. 151 3 22. 325 3 22. 489 3 22. 653 3 22.817 3 22. 980 3 32. 155 3 32. 318 3 32. 482 3 32. 646 3 32. 810 3 41. 984 3 42. 148 3 42. 312 3 42. 476 3 42. 639 3 51.814 3 51. 978 3 52. 141 3 52. 305 3 52. 469 .096 .098 .101 .104 .106 40 41 42 43 44 2 43. 826 2 43.990 2 44. 154 2 44. 317 2 44. 481 2 53. 656 2 53. 819 2 53. 983 2 54. 147 2 54. 311 3 3 3 3 3 3. 485 3. 649 3.813 3.977 4.140 3 3 3 3 3 13. 315 13. 478 13. 642 13. 806 13. 970 3 23. 144 3 23. 308 3 23. 472 3 23.636 3 23. 800 3 32.974 3 33. 138 3 33. 301 3 33.465 3 33. 629 3 42. 803 3 42. 967 3 43. 131 3 43. 295 3 43. 459 3 52. 633 3 52. 797 3 52. 961 3 53. 124 3 53. 288 3 53. 452 3 53. 616 3 53. 780 3 53. 943 3 54. 107 40 41 42 43 44 45 46 47 48 49 .109 .112 .115 .117 .120 .123 .126 .128 .131 .134 45 46 47 48 49 2 44. 645 2 44. 809 2 44. 973 2 45. 137 2 45. 300 2 54. 475 2 54. 638 2 54. 802 2 54. 966 2 55. 130 3 3 3 3 3 4.304 4.468 4.632 4.796 4.960 3 3 3 3 3 14. 134 14.298 14.461 14. 625 14. 789 3 23.963 3 24.127 3 24. 291 3 24. 455 3 24. 619 3 33. 793 3 33. 957 3 34. 121 3 34. 284 3 34. 448 3 43.622 3 43. 786 3 43. 950 3 44. 114 3 44. 278 50 51 52 53 54 2 45.464 2 45. 628 2 45. 792 2 45. 956 2 46. 120 2 55. 294 2 55. 458 2 55. 621 2 55. 785 2 55.949 3 3 3 3 3 5.123 5.287 5.451 5.615 5.779 3 3 3 3 3 3 3 3 3 3 14. 953 15. 117 15. 281 15. 444 15.608 15. 772 15. 936 16. 100 16. 264 16. 427 3 24. 782 3 24.946 3 25.110 3 25. 274 3 25. 438 3 34. 612 3 34. 776 3 34.940 3 35. 104 3 35. 267 3 44. 442 3 44. 605 3 44. 769 3 44. 933 3 45.097 3 54. 271 3 54. 435 3 54. 599 3 54. 763 3 54. 926 50 51 52 53 54 .137 .139 .142 .145 .147 55 56 57 58 59 2 46.283 2 46. 447 2 46. 611 2 46. 755 2 46. 939 2 56. 113 2 56. 277 2 56. 441 2 56. 604 2 56. 768 3 3 3 3 3 5.942 6.106 6.270 6.434 6.598 3 25.602 3 25. 765 3 25.929 3 26. 093 3 26. 257 3 35.431 3 35. 595 3 35. 759 3 35. 923 3 36. 086 3 45. 261 3 45. 425 3 45. 588 3 45. 752 3 45. 916 3 55. 090 3 55. 254 3 55. 418 3 55. 582 3 55. 746 55 56 57 58 59 .150 .153 .156 .158 0.161 22489—03- -31 Page 482] TABLE 9. Mean Solar into Sidereal Time. To be added to a mean time interval. 1 Oh Ik 21. 8" 4b oh [«" Jh For seconds. 1 m. 1 2 3 4 m. 0.000 0.164 0. 329 0.493 0.657 m. B. 9.856 10.021 la 185 10.349 10.514 m. s. 19. 713 19.877 20. 041 20. 206 20. 370 m. s. 29. 569 29. 734 29. 898 30. 062 30. 227 m. s. 39. 426 39.590 39. 754 39.919 40. 083 40. 247 40. 412 40. 576 40. 740 40. 904 in. s. 49. 282 49. 447 49. 611 49. 775 49. 939 m. s. 59. 139 59. 303 59. 467 59. 632 59. 796 TO. 8. 1 8.995 1 9.160 1 9. 324 1 9. 488 1 9. 652 s. 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 20. 534 20.699 20. 863 21. 027 21. 191 30. 391 30. 555 30. 719 30. 884 31.048 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 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. 849 22. 013 31.212 31. 376 31. 541 3i. 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 15 16 17 18 19 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 52. 568 52. 732 52. 896 53. 061 53. 225 53. 389 53. 554 53. 718 53. 882 54. 046 ^- 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 1 12.281 1 12.445 1 12.609 1 12.774 1 12.938 1 13.102 1 13.266 1 13.431 1 13.595 1 13.759 15 16 17 18 19 20 21 22 23 24 25" 26 27 28 29 .041 .044 .047 .049 .052 .6.55 .057 .060 .063 .066 .068 .071 .074 .077 .079 20 21 22 23 24 3.285 3.450 3.614 3.778 3.943 13. 142 13.306 13.471 13.635 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 2.424 2.589 2.753 2.917 3.081 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 1 3.246 3. 410 3.574 3.739 3.903 30 31 32 33 34 35 36 37 38 39 4.928 5.093 5.257 5. 421 5.585 5. 750 5. 914 6.078 6.242 6.407 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 45. 176 45. 340 45. 504 45. 668 45. 833 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 1 14.745 1 14.909 1 15.073 1 15.238 1 15.402 30 31 32 33 34 35 36 37 38 39 .082 .085 .088 .090 .093 .096 .099 .101 .104 .107 15.606 15. 770 15.935 16.099 16. 263 25.463 25. 627 25. 791 25. 955 26. 120 26. 284 26. 448 26. 612 26. 777 26.941 35. 319 35. 483 35. 648 35. 812 35. 976 55. 032 55. 196 55. 361 55. 525 55. 689 4.888 5.053 5.217 5.381 5.546 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 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 1.5.895 1 16.059 1 16.223 40 41 42 43 44 .110 .112 .115 .118 .120 45 46 47 48 49 7.392 7.557 7.721 7.885 8.049 17.249 17.413 17. 577 17. 742 17.906 18.070 18. 234 18.399 18.563 18. 727 18. 892 19.056 19. 220 19. .384 19.549 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 57. 496 57. 660 57. 825 57. 989 58. 153 6.531 6.695 6.860 7.024 7.188 1 16.388 1 16.552 1 16.716 1 16.881 1 17.045 45 46 47 48 49 50 51 52 53 54 .123 .126 .129 .131 .134 .137 .140 .142 .145 .148 50 51 52 53 54 55 56 57 58 59 8.214 8.378 8.542 8.707 8.871 27. 927 28. 091 28. 255 28.420 28. 584 28. 748 28. 912 29.077 29. 241 29. 405 37. 783 37. 947 38. 112 .38. 276 38. 440 38. 605 38. 769 .38. 933 39. 097 39. 262 47. 640 47. 804 47. 968 48. 132 48. 297 0' 48. 461 48. 625 48. 790 48. 954 49. 118 7.353 7.517 7.681 7.845 8.010 1 17.209 1 17.373 1 17.538 1 17.702 1 17.866 9.035 9.199 9.364 9.528 9.692 58.317 58. 482 58. 646 58. 810 58.975 8.174 8.338 8.502 8.667 8. 831 1 18.0.30 1 18.195 1 18. 359 1 18.523 1 18.688 55 56 57 58 59 .151 .153 .156 .159 0.162 TABLE 9. [Page 483 Mean Solar into Sidereal Time. c g S To be added to a mean time interval. 8h flh lOh lli> 12h ISh 14h 15'' For seconds.! m. m. s. m. 8. m. s. 7/1. S. m. s. m. 8. m. s. m. s. s. s. 1 18.852 1 28.708 1 38.565 1 48.421 1 58. 278 2 8.134 2 17.991 2 27. 847 1 1 19.016 1 28.873 1 38. 729 1 48.585 1 58. 442 2 8.298 2 18. 155 2 28.011 1 0.003 2 1 19.180 1 29.037 1 38.893 1 48.750 1 58. 606 2 8.463 2 18.319 2 28. 176 2 .005 3 1 19.345 1 29.201 1 39.058 1 48.914 1 58. 771 2 8.627 2 18.483 2 28.340 3 .008 4 5 1 19.509 1 19.673 1 29.365 1 29.530 1 39.222 1 39.386 1 49.078 1 49. 243 1 1 58. 935 59.099 2 2 8.791 8.956 2 18.648 2 18.812 2 28. 504 2 28. 668 4 5 .011 .014 () 1 19.837 1 29.694 1 39.550 1 49.407 1 59. 263 2 9.120 2 18.976 2 28. 833 6 .016 7 1 20.002 1 29.858 1 39.715 1 49.571 1 59. 428 2 9.284 2 19.141 2 28. 997 7 .019 8 1 20.166 1 30.022 1 39.879 1 49. 735 1 59. 592 2 9.448 2 19.305 2 29. 161 8 .022 9 1 20.330 1 30. 187 1 40.043 1 49.900 1 59. 756 2 9.613 2 19.469 2 29. 326 9 .025 10 1 20.495 1 30.351 1 40.207 1 50.064 1 59. 920 2 9.777 2 19.633 2 29. 490 10 .027 11 1 20.659 1 30.515 1 40.372 1 50. 228 2 0.085 2 9.941 2 19,798 2 29.654 11 .030 12 1 20.823 1 30.680 1 40.536 1 50. 393 2 0.249 2 10. 105 2 19.962 2 29. 818 12 .033 13 1 20.987 1 30.844 1 40. 700 1 50.557 2 0.413 2 10. 270 2 20. 126 2 29. 983 13 .036 14 1 21.152 1 31.008 1 40.865 1 41.029 1 50.721 1 50. 885 2 0.578 0.742 2 10. 434 2 20. 290 2 30. 147 14 . 038 15 1 21. 316 1 31.172 2 10. 598 2 20.455 2 30. 311 15 .041 16 1 21.480 1 31.337 1 41. 193 1 51.050 2 0.906 2 10.763 2 20. 619 2 30. 476 16 .044 17 1 21.644 1 31.501 1 41.357 1 51.214 2 1.070 2 10. 927 2 20. 783 2 30. 640 17 .047 18 1 21.809 1 31.665 1 41.522 1 51.378 2 1.235 2 11.091 2 20. 948 2 30. 804 18 .049 19 20 1 21.973 1 31. 829 1 31.994 1 41.686 1 51.542 2 1.399 2 11.255 2 21.112 2 30. 968 2 31. 133 19 20 .052 .055 1 22.137 1 41. 850 1 51. 707 2 1. 563 2 11. 420 2 21.276 21 1 22.302 1 32. 158 1 42.015 1 51.871 2 1.727 2 11.584 2 21. 440 2 31. 297 21 .057 22 1 22.466 1 32.322 1 42. 179 1 52.035 2 1.892 2 11. 748 2 21.605 2 31.461 22 .060 23 1 22.630 1 32.487 1 42.343 1 52.200 2 2.056 2 11.912 2 21. 769 2 31.625 23 .063 24 25 1 22. 794 1 22.959 1 32.651 1 42. 507 1 42.672 1 52. 364 2 2.220 2 12. 077 2 21. 933 2 31. 790 24 25 .066 1 32.815 1 52.528 2 2.385 ; 2 12. 241 2 22. 098 2 31.954 .068 2(5 1 23.123 1 32.979 1 42.836 1 52.692 2 2.549 2 12. 405 2 22. 262 2 32. 118 26 .071 27 1 23.287 1 33. 144 1 43.000 1 52.857 2 2. 713 2 12. 570 2 22. 426 2 32. 283 27 .074 28 1 23.451 1 33.308 1 43. 164 1 53.021 2 2.877 ' 2 12. 734 2 22.590 2 32. 447 28 .077 29 30 1 23.616 1 33.472 1 43.329 1 43.493 1 53. 185 2 3.042 , 2 12. 898 2 22. 755 2 32. 611 29 .079 1 23.780 1 33.637 1 53.349 2 3.206 1 2 13. 062 2 22. 919 2 32. 775 30 .082 31 1 23.944 1 33. 801 1 43.657 1 53.514 2 3.370 2 13. 227 2 23. 083 2 32.940 31 .085 32 1 24. 109 1 33.965 1 43.822 1 53.678 2 3.534 2 13. 391 2 23. 247 2 33. 104 32 .088 33 1 24.273 1 34. 129 1 43.986 1 53. 842 i 2 3.699 2 13. 555 2 23. 412 2 33. 268 33 .090 34 35 1 24.437 1 24.601 1 34. 294 1 34.458 1 44. 150 1 44. 314 1 54.007 ; 2 1 54. 171 ; 2 3.863 2 13. 720 2 23. 576 2 33.432 34 35 .093 4.027 2 13. 884 2 23. 740 2 33. 597 .096 36 1 24.766 1 34.622 1 44.479 1 54.335 2 4.192 2 14. 048 2 23. 905 2 33. 761 36 .099 37 1 24.930 1 34. 786 1 44.643 1 54.499 2 4.356 2 14.212 2 24.069 2 33. 925 37 .101 38 1 25.094 1 34.951 1 44.807 1 54.664 2 4.520 2 14. 377 2 24. 233 2 34.090 38 .104 39 40 1 25.259 1 35. 115 1 44. 971 1 54.828 2 4.684 2 14. 541 2 24. 397 2 34. 254 2 34.418 39 .107 1 25.423 1 35.279 1 45. 136 1 54. 992 2 4.849 2 14. 705 2 24. 562 40 .110 41 1 25. 587 1 35.444 1 45.300 1 55. 156 2 5.013 2 14. 869 2 24. 726 2 34. 582 41 .112 42 1 25. 751 1 35.608 1 45.464 1 55. 321 2 5.177 i 2 15. 034 2 24. 890 2 34. 747 42 .115 43 1 25.916 1 35. 772 1 45. 629 1 55. 485 2 5.342 ! 2 15. 198 2 25. 054 2 34.911 43 .118 44 45 1 26.080 1 26.244 1 35.936 1 36. 101 1 45. 793 1 45.957 1 55. 649 1 55. 814 2 2 5. 506 1 2 15. 362 5.670 2 15.527 2 25.219 2 25. 383 2 35. 075 2 35.239 44 .120 45 .123 46 1 26.408 1 36.265 1 46. 121 1 55.978 2 5. 834 2 15. 691 2 25. 547 2 35. 404 46 .126 47 1 26.573 1 36.429 1 46.286 1 56. 142 2 5. 999 2 15. 855 2 25. 712 2 35. 568 47 .129 48 1 26.737 1 36.593 1 46.450 1 56. 306 2 6.163 2 16. 019 2 25. 876 2 35. 732 48 .131 49 1 26.901 1 36. 758 1 36. 922 1 46.614 1 46. 778 1 56.471 2 6.327 2 16. 184 2 26. 040 2 35. 897 49 50 .134 50 1 27.066 1 56.6;^ 2 6.491 2 16. 348 2 26. 204 2 36. 061 .137 51 1 27.230 1 37.086 1 46.943 1 56. 799 2 6.656 2 16.512 2 26. 369 2 36. 225 51 .140 52 1 27.394 1 37.251 1 47.107 1 56.964 2 6.820 2 16. 676 2 26. 533 2 36. 389 52 .142 53 1 27.558 1 37.415 1 47. 271 1 57. 128 2 6.984 2 16. 841 2 26. 697 2 36.554 53 .145 54 1 27. 723 1 37.579 1 47.436 1 57.292 2 7.149 2 2 17.005 17. 169 2 26. 861 2 27. 026 2 36. 718 54 .148 55 1 27.887 1 37. 743 1 47. 600 1 57.456 2 7.313 2 36. 882 55 .151 56 1 28. 051 1 37.908 1 47. 764 1 57.621 2 7.477 2 17. 334 2 27. 190 2 37. 047 56 .153 57 1 28.215 1 38.072 1 47.928 1 57. 785 2 7.641 2 17. 498 2 27. 354 2 37.211 57 .156 58 1 28.380 1 38.236 1 48.093 1 57. 949 2 7.806 2 17. 662 2 27.519 2 37. 375 58 .159 59 1 28.544 1 38.400 1 48.257 1 58. 113 2 7.970 o 17. 826 2 27.683 2 37.5.39 59 0.162 Page 484j TABLE 0. Mean Solar into Sidereal time. c ai To be added to a mean time Interval. leh l**" ISh ISk 20'J 211. in. s. 22h ash For seconds. m. m. s. m. 8. m. s. m. s. TO. 8. m. 8. tn. 8. 8. ! 8. 2 37. 704 2 47. 560 2 57. 417 3 7.273 3 17. 129 3 26.986 3 36.842 3 46. 699 1 2 37. 868 2 4^. 724 2 57. 581 3 7. 437 3 17.294 3 27. 150 3 37.007 3 46. 863 1 i 0. 003 2 2 38.032 2 47. 889 2 57. 745 3 7.602 3 17.458 3 27.315 3 37. 171 3 47. 027 2 .005 3 2 38. 196 2 48. 053 2 57.909 3 7.766 3 17. 622 3 27. 479 3 37. 335 3 47. 192 3 .008 4 2 38. 361 2 48. 217 2 58. 074 3 7. 930 3 17. 787 3 27. 643 3 37. 500 3 47. 356 3 47.520 4 5 i .011 :oi4 5 2 38. 525 2 48. 381 2 58. 238 3 8.094 3 17.951 3 27.807 3 37. 664 6 2 38.689 2 48. 546 2 58. 402 3 8.259 3 18. 115 3 27.972 3 37. 828 3 47. 685 6 ! .016 7 2 38. 854 2 48. 710 2 58. 566 3 8.423 3 18.279 3 28. 136 3 37.992 3 47. 849 7 .019 8 2 39. 018 2 48. 874 2 58. 731 3 8.587 3 18.444 3 28.300 3 38. 157 3 48.013 8 .022 9 2 39. 182 2 49. 039 2 58. 895 3 8.751 3 18.608 3 28.464 3 38. 321 3 48. 177 9 .025 10 2 39. 346 2 49. 203 2 59. 059 3 8.916 3 18. 772 3 28. 629 3 38. 485 3 48. 342 10 j .027 11 2 39.511 2 49. 367 2 59. 224 3 9.080 3 18.937 3 28. 793 3 38. 649 3 48. 506 11 ! .030 12 2 39. 675 2 49. 531 2 59. 388 3 9.244 3 19. 101 3 28.957 3 38. 814 3 48. 670 12 ! .033 13 2 39.839 2 49. 696 2 59. 552 3 9.409 3 19.265 3 29. 122 3 38. 978 3 48. 834 13 ; .036 14 15 2 40.003 2 49. 860 2 59. 716 3 9.573 3 19.429 3 29. 286 3 39. 142 3 39. 307 3 48. 999 14 i .038 2 40. 168 2 50. 024 2 59. 881 3 9.737 3 19.594 3 29. 450 3 49. 163 15 .041 16 2 40. 332 2 50. 188 3 0.045 3 9.901 3 19. 758 3 29. 614 3 39.471 3 49. 327 W .044 17 2 40. 496 2 50. 353 3 0.209 3 10.066 3 19.922 3 29. 779 3 39.635 3 49. 492 17 .047 18 2 40. 661 2 50. 517 3 0.373 3 10.230 3 20.086 3 29.943 3 39. 799 3 49. 6;56 18 .049 19 2 40. 825 2 50. 681 2 50. 846 3 0.538 3 10. 394 3 20.251 3 30. 107 3 30. 271 3 39. 964 3 40. 128 3 49.820 3 49. 984 19 .052 20 2 40. 989 3 0.702 3 10.559 3 20.415 20 . 055 21 2 41. 153 2 51.010 3 0.866 3 10.723 3 20. 579 3 30.436 3 40. 292 3 50. 149 21 : .057 22 2 41.318 2 51. 174 3 1.031 3 10.887 3 20. 744 3 30. 600 3 40. 456 3 50. 313 22 .060 23 2 41. 482 2 51. 338 3 1.195 3 11.051 3 20. 908 3 30. 764 3 40. 621 3 50. 477 23 .063 24 2 41. 646 2 51. 503 3 1.359 3 11.216 3 21.072 3 30. 929 3 40. 785 3 40.949 3 50. 642 3 50.806 24 25 .066 25 2 41.810 2 51. 667 3 1.523 3 11.380 3 21.236 3 31. 093 : .068 26 2 41.975 2 51. 831 3 1.688 3 11.544 3 21. 401 3 31.257 3 41.114 3 50. 970 26 .071 27 2 42. 139 2 51.995 3 1.852 3 11.708 3 21. 565 3 31.421 3 41.278 3 51.134 27 .074 28 2 42. 303 2 52. 160 3 2.016 3 11.873 3 21. 729 3 31. 586 3 41.442 3 51. 299 28 .077 29 2 42. 468 2 52. 324 3 2.181 3 12.037 3 21. 893 3 31. 750 3 41. 606 3 41.771 3 51.463 29 .079 30 2 42. 632 2 52.488 3 2.345 3 12.201 3 22.058 3 31.914 3 51.627 30 .082 31 2 42. 796 2 52. 653 3 2.509 3 12.366 3 22.222 3 32. 078 3 41.935 3 51. 791 31 .085 32 2 42. 960 2 52. 817 3 2.673 3 12.530 3 22.386 3 32.243 3 42. 099 3 51. 956 32 .088 33 2 43. 125 2 52. 981 3 2.838 3 12.694 3 22.551 3 32.407 3 42. 264 3 52. 120 33 .090 34 2 43. 289 2 53.145 3 3.002 3 12.858 3 22.715 3 32.571 3 42. 428 3 52. 284 34 .093 35 2 43.453 2 53.310 3 3.166 3 13.023 3 22. 879 3 32. 736 3 42. 592 3 52. 449 35 .096 36 2 43. 617 2 53. 474 3 3. 330 3 13. 187 3 23.043 3 32.900 3 42. 756 3 52. 613 36 .099 37 2 43. 782 2 53. 638 3 3.495 3 13.351 3 23.208 3 33.064 3 42. 921 3 52. 777 37 .101 38 2 43. 946 2 53. 803 3 3.659 3 13.515 3 23.372 3 33. 228 3 43. 085 3 52. 941 38 .104 39 40 2 44. 110 2 44. 275 2 53. 967 3 3.823 3 13.680 3 23. 536 3 33. 393 3 43. 249 3 53. 106 39 40 .107 .110 2 54. 131 3 3.988 3 13.844 3 23. 7UU 3 33.557 3 43. 413 3 53. 270 41 2 44. 439 2 54. 295 3 4.152 3 14.008 3 23. 865 3 33. 721 3 43.578 3 53.434 41 .112 42 2 44. 603 2 54. 460 3 4.316 3 14. 173 3 24. 029 3 33. 886 3 43. 742 3 53. 598 42 .115 43 2 44. 767 2 54. 624 3 4.480 3 14.337 3 24. 193 3 34. 050 3 43. 906 3 53. 763 43 .118 44 2 44. 932 2 54. 788 3 4.645 3 14.501 3 24. 358 3 34. 214 3 44. 071 3 53. 927 3 54. 091 44 45 .120 .123 45 2 45. 096 2 54. 952 3 4.809 3 14.665 3 24. 522 3 34. 378 3 44. 235 46 2 45. 260 2 55.117 3 4.973 3 14.830 3 24. 686 3 34. 543 3 44. 399 3 54. 256 46 .126 47 2 45. 425 2 55. 281 3 5.137 3 14.994 3 24. 850 3 34. 707 3 44. 563 3 54.420 47 .129 48 2 45. 589 2 55. 445 3 5. 302 3 15. 158 3 25. 015 3 34.871 3 44. 728 3 54. 584 48 . 131 49 2 45. 753 2 55. 610 3 5. 466 3 15.322 3 25. 179 3 35. 035 3 44. 892 3 54. 748 3 54.913 49 50 .134 .137 50 2 45'. 917 2 55. 774 3 5. 630 3 15.487 3 25. 343 3 35. 200 3 45. 056 51 2 46. 082 2 55. 938 3 5. 795 3 15.651 3 25. 508 3 35. 364 3 45. 220 3 55. 077 51 .140 52 2 46. 246 2 56. 102 3 5.959 3 15.815 3 25. 672 3 35. 528 3 45. 385 3 55. 241 52 .142 53 2 46. 410 2 56. 267 3 6.123 3 15.980 3 25. 836 3 35. 693 3 45.549 3 55. 405 53 .145 54 2 46. 574 2 56. 431 3 6.287 3 16: 144 3 26. 000 3 35. 857 3 45. 713 3 55. 570 54 55 .148 55 2 46. 739 2 56.595 3 6.452 3 16.308 3 26. 165 3 36. 021 3 45. 878 3 55. 734 . 151 56 2 46. 903 2 56. 759 3 6.616 3 16.472 3 26. 329 3 36. 185 3 46. 042 3 55. 898 56 .153 57 2 47. 067 2 56. 924 3 6.780 3 16.637 3 26.493 3 36. 350 3 46. 206 3 56. 063 57 .156 58 2 47. 232 2 57. 088 'J 6.944 3 16.801 3 26. 657 3 36. 514 3 46. 370 3 56. 227 58 .159 59 2 47. 396 2 57. 252 3 7.109 3 16.965 3 26.822 3 36. 678 3 46. 535 3 56. 391 59 0.162 ^ 3 ^ -i 2 TABLE 10. Mean Time of Sun's Visible Rising and Setting. [Page 486 «» •ajBp xoaddv i;Z; cdacP^oQPj'ccpjccp^GQTiJoQPH'aQl^oQPj'cQQ^aQiPciaQp^aJM .r-irr'^t^-^aoc-iOi-^c^ascct^iricot^ig^c^c^i-i !o ■ajBp ■xoiddv .^;2; iOO»AOiOOiraO'^^H|Tj'^x»0'0?cicX'^asc^Of-'(MOcox'^t— (o SS2 ■^OiCSi-iCJC^OecCit r*r>-tDX»CO"^rHC^(N— (C^ xor^r^^XiC^-^o locpa>r*xxr*g»500 CO^C^Mi-tCOO'^OSiC ii2 COiC Oi iC O "^ «-H CC 5 .-ICC.-" c- i-HCOr-lCC CO iC (O i/^ OicCOtOi-i i-icc(Nc»5m CO iC CO lO o c^t-rHi>oxa>c?xo!xrHt-c^cocmcco'fT»< lOCOiCCOiCCOiCCOiCCOUOcOiC^iCCOi^COiOCO gco'^iort'iQiO'^cp'g'to ^iCCOiOcOiC^OiOcOiCcO kccoiccoi^coiccrutico ~^t>-iOcOiOcO»C»ftcp»Ct" ^lOcOvCcOiCCOiCCOiOCO ■^xcococooc^^i-HO i-(^oc^aic^xccx-^ iCCOvftCO^OCOiCCOiCCO lOCOiCCOiOCOiCsOiC^ OSi-HXC^t^C^COCO^Tf lO CO i^ CO iC CO lO CO lO CO »i^tct^icr-cpcocpcot>- : ic o lO o ic o ic o »c o aiCCOiC'^iCCOiCcOiCCO iCX'^X'^^CO^C^OXcpXcpxt>-t^t-*t^X »iOcOiOcOiCtOiCcO»CcO gX>CXiCO?"^05 7pOCCrHCO'-iCSC^C^C^r-tcC iCCOiCCOiOcOi^COiOcO iCCO»CCO»OcOiCCOOCO lO CO iC t^oxoiOixor-T iir5cccoc^t>-f-ixoa>g>o 5 to iC CO ift CO >C c ? COiC COiOcO lOCOiO iC-^COCC cOiC COiC t^M X .— OS ,_, -rr »-i -^ .-I CO iC COlO CO lO CO iC incocctCco-^t^-^x Oi^X iC cOiO COii^COiCCOiCCOiCCO iC T-H lO iC COiO i-H iS rH -^ CO iC CO iC iC Oi CO X CO ;aii>o>tN-^t^Qor^xxi fttOCOiO'>OiOCOtOCO»CCO ^xr»gicog>cootOO lOr^-^i-H-^c^qoMc^cc f^cOiCCCiCCOiCCOiCCO »OCO»CCO^COiCcOiC^ CO COM iC CO iC CO iC CO if^ Tf< ^ lr^ Q lO f-l iC r-. 25 T-l CO Lt CO ir: CO sssg xoxoxosx icO«OcO:OCOcOiCcOiCco'iCcOiCCOiCcOiCcOiOCO'iCCOiCCOi^ lO o i.-; siotoio CO iC CO iC CO g.-< i^ .-I r* tH t^ c^ ^* CJ iftCOiCcOiOcOi^COiOcO CD C^ CO i?5 .-" lit) COCOCOiCCOiC'^iO- i-iiC rHiC CCiCCOiC CO iC CO iC CO :0000000c acOCOCOCOCOCO^C itOCO SS8 CO CO CO OOOOr-. .-t0^25rH CO CO CO CO CO 1-^lCrHiJf^r-^lOr^lCrH COCOiCcDiOCOiCCOiOsO XlMXMXCOXCOt^COt^CO lO to iC c ; CO »C CO iC .-1 iC ^ iC 1-1 CO iC CO iC CO •gsg i to to to to to to S2§2 to to to to 'MO--iO.HO- to to to to to to to to to ■«* to to to i-.Oi-lO>-l to CO to to CO OrHO'-iOr-lOrHOr.l CO to to to to CO CO to to to Or-IO to to to T-HOr-lOr to to to to t fi r_ai6 (BPiaiPi zD fi w Oiw(Axf^mPixPix\oiaifi!K^'£c^:n!^w\Pi(aPit^('ixPiaiCiia-leiai -^^ '-^-^ ic CO r* X OS o Page 486] TABLE 10. Mean Time of Sun's Visible Rising and Setting. o 3 •^Z •xojdav ^'A ¥» •xojddv 5^ i-l«0?-^>0 tOt-OOOlO >-llMM'*>0 tor- we^cslNe^ iNNe5 »c in O>0OiSoOOOi.0O 05 oD eS aj OS aj oi aa 05 tfi 05 cc 05 to 05 of 05 oi 05 oi tpr^-^O'HC^OliCCOCO CO^HO'^l^I^'^Qi-lCO ift O »0 ^ U5 fH Tf rH -n* t-< -^ (N -^ C>l CO C^ CO CO CO CO rHC^r-tCOi-HCCr-ITr'THTrO'VO'^O'VOiQOlO u-« . CO r* ic lO r* CO o> ft ?5 CC i-H CC i-< 00 i-l CO rH -^ i-t -^ O "^ O Tf O ■«* O ''5' (MCOC^COfHCOrHCOt-lCO g'coo5;^'-<0(Nas-^i>co lMC^(NCO(NCOi-HCOrHCO COO>ir4r-(OCOGOlC^O f-lCOrHTj^i-H-^O-^O-^ iHC0iHC0rH-<9-^Oi!NQi-H(NasC0 C^Cicaicooc^c^ ocoai»or*50(Doo^oi C» iM iM "N CO IN CO - • -" "" "* "' " (MCOi-HCOr-tCOrHCOrHCO T»'i-l^'00t^tD©COCO ■*r-C*i-iCO.-ICOC5cOO ■^O-^O-^i-HCOr-ICOiH ) CO t^ icin CO c^i o o CO SopCJOOCOGCiOtOI^ C0O>i-IC^O5'*COtO'*» u0e0l0C0i0OiCC0"^<0 t^tO-*30lMQQCO0piC ocooo>otoi~3iai'3i-i COfH.-HiM^^'QOtOtoao lOcOOtOiOOtOCOiCtO ■*Qe4(MO-^00!0!000 I00l00i0t0-^CO"^«0 «INC^lNIMlM!NC-4O■* O»«OO0t~5O00 ■COt^ COCC^ S*?OIN»OCO"^-^COlCC^tO eoc^coc^icoo)cO(Ncoe4 ,^ioeo>0!0>n«oiOtDoto i-tt^OQ0050^t^O50.H COlNCOC^OllNCJCOlNCO gonr- lO CO iC ^ lO 1-4 -^ T-f - CONCOCT CO cOOCT>rHCOlNl^CO COCJCOCOC^COC^COOCO lOtOiOtOiOtOiOtOiOtO "t t^-^ooeo cocqcOiMco lO to lA to lO N CO CO CO CO to lO to lO to •<}< H •«(< IM Tj" C^ C lO to iC to lO to 1 ;■* [t^ic t~- tot ireo-^oco-ie^c^oaco SiCtOiOtOOtOiOtO 1 1^ IC t^ ■»** 00 I C^ CO C^ COS I to if^ to 1/t) to i-iCO<— l-rJ 'CMiOIMlOC^tOiHtOi-lt^ :idHio 1-tio iiotoifl toic 1-t tC T-t lO rH to in to lo to Ol^ QCCOIOD iC to iC to lO to inOlOr-l Tr 0> 00 (35 ijir-l^r-l in to lO to ic toio toin a in to in to ic in CO in CO to i-llOrHini-H to in to in to »t~'^ t^-* to : lO rH in .-H l75 • in to in to in ■^ to "^ to in oin toin to »05coo>coo»cooicocoeo sinrHinfHin fin to in to in iHini-iini-H to in to in to eotooitocioc^t-r \fi r^ ^ T^ ^fi T-i in o in to in to iniHinrH in to in to CO IN CO rH-* C^r-( oinininininiOinino into'*to'^to-^toTi-^r-IC3COO'^ o-^O'fOinoinoin intointointointointo . . J" ^ to 00 00 to Q Tjl T-l rHTTO-^o-^oinoin in to in to in to in to in to iniNcoeoiNinot^gocc ooo»t~i-iiniN'O>00iHr~lN H'*r1T}< intointointointointo tO')<' iNCOINCOe^COINeOlNCO intointointointointo oc^oocot-'^tominto COCOiNCOiNCOC^COC5cO intointointointointo COO>iNO<-It-IOC-IC:»CO COINCOCOCOCOCOCOCMCO intointointointointo i^r^tpocinooicoQ corH05rHOOO OrHin in to in inrH to in to ine1 cc (^aifiiaafiicapiaifiitn oj cc pj cc P4 cc pj co pj oq g'MCOlN'^fil'i-l'i'r-llC OiOOOOOiOOiOi— I S't-i-HTfiCOOOtOiMC^tO ^ ^ t^ ^ t^ ^ t^ ^ t^ ^ t^ 5 coooino-*i-icoc^ coaocoGOcoxccxcccc;ccoo c«ra> c^ a» c^ os c-i ai MOOCOCOCOOOCOXCOTO rHT(IO^OinOlS>ftO — OiC00C^-HO»M >-li-IOOiO-^OOi-H^I^«5 «>tOMOlOMtOtOCOO 01INC^O)C^eOrHMr-ITr 50C^C^C^)COi-l05 M»Hciir-ICOlNC4c5ciN sss iC O-^ O "^O- ,^-^t~T»lt~T)lt~^t C^(Na>'S>0(NcocOrtico>r- (NMOior-goiooc^co lOOiOOfO-^r-ITl'i-l SsooeooooiOMO ■*t~eOt~M00M00COO0 JOCOiOt^QC oooo iCt~o»eoo50>r^!DOco i -iOi-it ■* t^ ^ t~ coc^ostCiOosiH-^r-^os t^OiUJi-tCOCO^H? t- It t- ■* r~ -^ r- g" ^ !-» 2 00 OO p --O iH -r O -f o 55 o SoS — ■lOCO'TiOe^tOiHOOC Si-ITf»' 1-1 ■* 1-1 ^ T-l !ii«t~eoooMpfHT S (M CO c5 CO 6j ^ e^ ' Sc5SlNCO t^iootoi^r^^os iNCoSc iC?o»o t SsjcocOcO j; lO to lO «0 C^NrHCOQ'^OQUJ S* t^ OS to OS ki C0lMeOC4C ^iC to iC to u A iC lO O kO o to T)< to Tt< t- -Tji t- tOr-ICOCOOtOt-OS-^C^iHOI^CTi •^i-|-*rH-*r-ICO. ^ t^ ■^ t>. ^ t>. 00 1-1 to OiOO iCtOiO CO ^iflejt^QOS to iC to IC to iC to SoSc (Nt^oos^i-n^eom- iHrfrl lOtOi/S lO O tC O ^ to kC to lO to iC to sss intoio l-3o ^ O iO p lC O to ■-co-^ to^oo l>1^t^ inpinp t^Tfint^c) — mom S to ■"too mom m torn to sss? mt^imt r^totor^mos-^pc^rH HOTC^eoc'icoc^^NiS" mtomtomtomtomto s^joototor^-mos stomtomtomto COpi-l(N mtomto omo m torn CQCCCCOOCQCOCCOOCOOO _i tp CO ift ■^ '»»' !M "^ 61 '^ 5^ liO coo CO lO o gS2S2 ,c;m to mto CO 00 CO m 1-1 in mtom r-imi-l torn to g'Qomoom m 1—1 m rH .fl* m to m to QO moo t mtom t oocor"COt>.T»i mtomtomtomtomto mSmc m tom t 5 OS CO 00 t >mtom to TtOI-VCO m tomo poo>- \0'^^'£> ^^ *z g g oj g ca ^ to to to to gCO'NC r-(Or to to to t IC^COOJCOOICOi-tCOi-tCO jOi-lOi-lOrHOi-lOrt itotototototototo to to rH OJ CO -^ m to -* -^r KS< ■* ■* I -T 05 02 a; 03 05 CO Pf 03 05 OQ 1-hCO^HOO— ^COi-H^i— (■"J* Oi-l O to to to i-IOi-i to to to Oi-lOi-l to to to to 1-1 •*P'* Oi-iOi-l to to to to g3g OtOtO mpm ^-* O 1— I to to to 05o3'o5oco5a}pjo305o3bjaQ05os05;cOiGCQ5o3 X OS P r- ^'l CO -"t l?f"^| t$^ (^ ^5 OS p^ ^^m mi-'^mmmmmmmto Page 488] TABLE 10. Mean Time of Sun's Visible Rising and Setting. Xi u. ^z o T-i c^ ec 'xojdd V iOoo'^op?©oo«p QO^oo^aD'^aotpao^ootp CiCCaiaOOJOOOiCOOiOO aOqOX'OOQOOOODXXQOCCOC jsQCCOaOQGOQQCOXOOSQOiQOaOa'-OiOs 00OG0Q00Q00O0Di-HQ0»-i iCtOiOOiC^CiC^DiCO GCC^OOC^CCC^XCOt^CCI^CC ^iC^iCCOiOCOiC^iCtO iCCOiOOiC^dCtOiCtO co^oot'-t^r*t^t^r*oocox g^ai50asr*QOt^Gcoo gt^QOOOQOOO^QOO t^Or-r-l?Oi-f!CC^iOC^iCCO O^OOOSOOOi-tOCM iC^iCiOiOtOiJStD»CiMXCOOD'<1* t^fNt^COCC'^iO'^iOiC'^'C iC^iCtOificOiCOi^^OiCtO TTi-ITf^i-C'S'rHTri-l-^i-H-Tfr ^iCCCiCtOiCtCi»0^«C^ ,iCcOiCtOiCcO»C«vC«D •.DC£JCOl-*iOGO"^OOCCOaCOO iCtO»C^iCCO»C?DiC'Oir20 »acoxr^r^t^xix?Das SiOOiCOOOiOOiCO fliOtOiCCOiCeOiO«OiO^ Sot^QOi-^QCoci^-ai^o . icoiJ5oicoicoi?5i-i ^:OtOiO?OintOiCiOiOCO OOiOOiOi-tiOrHi5r-l ^tO«0»Cfrc^!iOfHi-* iCCO'^TfCC'^OiMt^i-taOOOi tpi^OiOt^eoooc^Oit-i.— I QC^Q0CCt>-^tO iC(0iCt0iC(0iCOi.0?0 _ . _ CO coicr iO:OiOOiO?OiCOiO«OiC', ^(0':0':00':0-^ii^'-OiCcO SS2 O— 1^ CO oc in to to to iC to iC to iOt~--9iaOMOr-.HQCO lOi-llCrHiCC^lCC^liSC^ iCtOiCtOiCtOiOtOlOtO lOtC r* toto^«•- •* c^-^iN- iO toiA to L 5MOIi-ir-lOMaCiCtOtOiCQOMS SiOtokntOiOtOiCtOiCtOtOtOiftt iCtOtOtOLCtOintOlCtO lOtO lO tOiC to marl—' ^ CO ^ CO UD tOiO to OCOX'^tOtOiCopcOOiC^^ ■^ coco CO CO CO CO CO CO coco -T intOiOtOvCtOintOiOtOiCtO Sg2 ^ ^ :o t-t»C •sO'-DiC 00 c**^ coco 1-1 iC i-H i?5 i-H CO iC CO iC CO -pj"r*Mai— iT-*Oi-sxTt< ic t-* cox tC CO iC CO XCCt^iCiCt^COXi-tOOC^ COCQC0C0C0C0eCCCCC*^CC-^ irscoirrcoiccoiCcoiccoiCico dlBp •xojddv 2-^' ^55 S to tOiTi i-(id-iin.-i to iC to lA to T-.IC lO to ic rHift Ol tOtC to 00?J tO"* lOtOiC to S8§ .MtOtO 00^t--i-liCCOCO'* iCOiCr-tiOr- (iCi—l iCtOintOiAtOiAto c^too ic toiC toic to tOrH-*eO lOtoioto 5 CO t~ C4 OS I ■'T fN -^ 04 ; ic toio to -^ CO CO CO in to lO to tO-^iCtOCOOOrHOsasrHt^CO cocococococococooa^c^-* lOtoictointointointoiCto •VC^COOJ in to in to t^QiCIN CO CO CO CO in to lO to eOTj<(Ntoooooco»toi-ii-intot~'«)'ooc^o>- in to in to COMCOC^ in to in to ■*00(NO CO ?1 CO CO in to in to QC^OOrftOtO-^CCC^OOC^ COCOC- 3 vi u~t ^ O O ^ n t, '.r3 *;z; •ajBp xojddv ?i (M CJ CJ C^I C-l iM CO s ^ P^OSC^GOp^OQf^COpjX P4 X C^ OD plj (Xl 0^ TjO p^ CO p< X p^ CO p^ GQ Q^ CO P^ CC C^ CO Ct^ 00 OEh CC pE^ CO pg ^ ^iCiCidOiCiCiOiCiCiC lOiOiO^Ci^UtiiOiOiCiC »0 iC »C- iC tC tO iC lO iCiC j»C lO »C iC i-C iC iC iC iC «c S'«Otpi^cpcOt*iCt^iCX'iOQO-^GO-<*'OS'^OCOai ccoiNOCMi-irH^^c^'orNoeoaiocoi'^cO'^ S"«pi^iOOi»aO"^o^OTr'-HccrHcoc^c^c^c^coi.-HcC'-^'^ooosiC'as^cO'-or^t-'t^»«o«'Xio> TfH^'^.-H^f-ITPr-l-n^r-H -frH'^i-C^.-H^i-CtJ^rH iJOf-'Mi-HCCr-lfCrHCCr-t :COiC»-''n".--C0C4C0C0 «c^coc^cccslccc^ccc-u5tDcoict^'^xccaik^Oi-^r-*Qc^aic<50Q3;t^iO?ct^w^ocMffic^ ^c^"^c^"^c^coc5o5mcoc^o5c^co^^coc^ccc^IjCOcoccccmccc^ccc5ccc^w S'^HCQO'*o>iOx«pr*t^ ^C^COCM«C4CC5«55cC ig '-• T? c^ ?? w rr! T? ^■^coic^?oooDOio>h-Q«D^-?'eoeO'n*?^«o COCCeO«COCCiCCCo5lCOC^^(N^'M'.WCDC5iOii^C05O(NGO CCCOCOCiCsCOOTCCCCCC SSCOCCCCCOCOCOPOCCCO^ S'lOt^MOOfMOQ^OiCO CQ?Sco6lCCMCOMCO«iCOCC0O«c1cOC^COC^W 65C0C^-rCM'^C^-^tN*3* »OtOiOtOiOX>iC*^iOO i0:DiCOiC?0iC?0iC'-0 iC:3iC?DiC^iCOift'-0 CCCCMC^COCCCOCCCCJC^CO?iMrJCOC5^C^'VC^'#C^'TfrH'^rHTf<^-^ lO ?0 iC ?OiC « ^ ^ lO to lO ^ iC to 'NCOi-lXasO>0Q^t>-(NiCW^iC5^tOi-OXritOMiOiCMtOMXOOSCii-Ht^CO iCCOi^tOiCtOiOCDiCcOiCtOinftOiOtOiOtOiC*© iCTMtOr-iX^QXfN rHiAfHlSr-iiOOOOO iotoictoiOtoicr*ior^ oac^r*co«OiO"^^c^QO ^^oiOi— 'XcctO'^'^to ?1 -^ M -^ Csj ^ C^ TP IN -^r C^ -^ C^ iC iH »C ri lO 1-t J5 lOtOiCtOiC^OiCtOiOtO lOtOiOtOiO^OiCtOiCtO i^^<;o-c^<5s.-i<-i lO^LCtOiAtOiOtOtOtO owr-'^iOtpMooi-HO lOtOi/StOOtOiCtOiOt* 2S28SgSo3S OOOOOOOOOrH t^ i-t m t^ ec Q ^ M © 31 i-(U5.-iiCrHO^OOO OOOOmO — K^i-H g§S coX'^oeoioxcOQ OiC<:OiC^kOCOiOCO tOiCtOiCtOiCtOiCtO ^COiO i-t O MX*C to to »0 C^ lO T-» lO r-^ iC to lO to iC to iC to -^XClOOCOcCiOtOt^ ■ ^ CO -f Oi iO?OiC Sr* lO ic r* CO OS r-t iC i-H iC r-i iC to iC to lA to lC to ^Hi-H^COt^tOiftXC^O fiOOOOOOOOrH S3 > iC -^ t^ C^ Oi O 11 3 to iC to lO to iC t* XTptOtpcOXi-t^-XCO OOOOOOOr-tLf*,-! S*iOu5COt^i-tO>Oi»Ht^CO C^iAtOiOtOiAtOiCtOiOtO iCOOOO to vC to lO t'- iC t>- 'ftp'NOiOlT-th*'^'rtO OOOOiCrtiC'i-HiC-l iC eo lO =. gaCOCOiCWMiOQOC r^icu; X c^ o SOO ^ -^ OC -^ iC o r-l to ^ T ^ -rr a ^l^f t~ r^.H'?''.}'.— t^oGOiCcc •* M ■* M C ■^ r* -^ t^ •" = ■00 0D-«O — -MOiiC I'J^r^-^O^C^Osi OOiOO O iC t^ lO r-» ■ ^ !>■ ^ t^ ^ t^ ^ t^ P4!»pjaipJGCQ^3SP4:c -H IM CO -^ iC iM M r) C^l CnI C4 00 Ci; «j Pi en Cti GO ;i{ CO Cl4 0SPJ3QQicCCEHCOP£cC .— (T^ CO -^ 15 CO CO CO CO CO OHCceiasQJaJoiaiaJaj to r^ oC' ff> o CO CO CO CO T Page 490] ^ N a 3 o TABLE 10. Mean Time of Sun's Visible Rising and Setting. ^'^ •xoiddv Q"^ p^cdaiccO^aQp^agpduD pdaQpHOQpjaQpjastfcceiHCCpHail^aS^ceOicnpiScAQjaiojcoOHCCPdai 7 II CO o O bo •73 m 3 C -J r* i^ t* 1^ w r* t^ CO r^ oo - I t 2 §. ; O ^ iC 5;] »o g^i lO^iCiCiCiCU^iOiOiC kCtCiAiCiCtdCiOiOiA iCLOiCiCiCtOiOOiC^ S5S .-(t^C^ CO i-H 00 ^H CO »~< 00 f-H OO rH ,^OOOiHO>rHOO'MQOeOGCCOt>-COt;r*^^"5^'^^5'-^3I'^S!2*^£2^£3^ g^^^r^eOi-HCOr-tCCiH55i-^COi-HCOrHCOi-tCOrHCOi-tOOTHCOi-ICOrHCOTH 05i-tCOrHCO»-H0OiH0Oi-t g'lCO'^OCO^^C^C^C^CO T-ICOO'«t<5>iQOQ«DCCr* ffS 5l W ?l CO IM CO 5^ CO C^ CO C5 CO C^ C^ C^ C^ iN C^ C^COC^COrHCOilCOiHCO ^c^5«?coo-^»oic-^oc^t*;f-(ooooaoi-Ht^coic-^ gC^C0C^COCslC0CSlC0CJC0tMS5(N-^rH'<»'rH'^rH"^ ftO^COC^loOC^TpCa-^rHTj* rH^rHTPT-(*^i-H-9"rHlO i-(iCOiCOiCO^OO cii-t'MOCOGO'^t^OiCt-; Sc^'^tN'^rH'^'H-^T-lTj* t* 00 o r- 00 ic o -^ »-H c^j M f;,-H^i-H-^^HTri-HiCi— (iC '^OC^t-Oa>g?»-lt^C0lidCC0I:>-i-40iQ0^(0C0 rH'^i-H-'TrHTrOiOOiCjOlOOOOlClOOlOO S^t-TPkCI^WOiO(N iCGOCOOrHC^Oi-' O lO O O O O »-C < lO O »C t^ iC t^ -^ I: ■^-^iHC^OQ-^lCt^COO lOOiCrH-^rHTPi-H-^C^ rHTt*a>-.pi>ocicocooi»-t'g^aootosO'q*»-if-(ooix<©icaic^c^aiOX'ai i-HOO»COiCOOOOjOOiOO>50»C>»-ii/it-H Ti«rH-t«i-(TrO*CO(MCOCOt* t>-0>tO*-«C0C0Q^C0l'* ,«©ococ^r-iioaooo>co ifti-HtCi-Hi/ii-HTjirH-^C^ 2 « Or^OSOit^t-H^COCOtrt'i-Ht^OsaiOi-H-^'^F-HtDOiOi^'MCOvOOOO i-Hu5i-HiOOiCOOOO . . rH-^^ |OOOOiOOiCrHiOi-H »0 I>iOt^'^t>'^t^"^l>" •^c^coc^oococococ^co :3i-HC0iOai00iQC^i-HtO COCOCOCO?4COC5'VW'^ sssssssssss !0C^«liOOC0I>.H-^iO|O00O01WOC0'-HC0i2 ^ t^ rf t^ Tj< i> -^ t> •* i> M" r- ^ r» ^ t^ rf r- ■.>< t~ •ajwp •xojddv «z; *2: BJxMcccs'uaaJccaSoiiQiaoaSMSJxaJccaia! aJaJaJxaSaiMcfiaSM TABLE 10. Mean Time of Sun's Visible Rising and Setting. [Page 491 p a •^^ •xojdd V flj 02 C^' CO C4 CO p5 CG Ph' OQ pHMP^copt^MpiHaip^QQpiHcdaHCOpt^cociix'CiicoaSaic^coP^cotf i0TfOTl■C^00C0'O>Ol0t^CC00r-' ■<5'lC•^lC•^^S"^Oc0 ,occocoocoocoocc irjTpiO'^iOTriS'rrioeoiCicooccocoocooeo gCO»-HC^O^OrfiCI>!t^'--OQC'Tt* O«i-Hr-iC0O 'Tj'iO-^O'^iCCQiOCOi/SCOiOCOOCOOWiOCO ■■ r'-^'^*0"^iocoiccc;»ccotocctcccic*ooco ss t^(NXi'-»aiaiQocr)t^'co*^-^'^cpcot-»rHa>o Tr-^Tj"»j5wiocoiCcoiocoi5«iCcciioeo 8Q0Cl(^COtO-^'«J*«OCOt*.-H tDC^t^r-taOOiaiQOiHt^iC^:pOO'0'^CO':p(NI--i-t 20>O00r-<(0!N»O^'Ttoooai aia>ooQi-ir~c^t$coir5 ■TCoiceoiccoiocOiCieo OS 0004^00 OJt-CS to Tf'^S'iSCOiOOOiCCCtCCO ;i-ta>iM00C^t*CCt>--^5O.iOiOiO"^«DC0t-CC00C^ ' ac^ocooiccoo'^oog'r* iCOiOiCO-n'l^-TfOOeO'aOINOl^Q'-''— '0<-H0a c^r*cctp'^>oiOT5'^00iriC0,i0t^«Ot^':0Or*(0XiO lO . _ . ,iOOiO»OidO»COidC cc2ja>3jaicoQcooc^ T-t CS 1-1 r-( C^ lO ^ lO ^ »o iC ^ iG lA 40 O CO O CO OS Tj< o> ■V u5 -^ lO CO iC CO lO lO lO iC iC iC lO coO-^OrfOaiCOs 5 00OQCO 5 i/5 iC ifS iC lO i^' iC iC ^ iC iC lO iC L? t g CO r-( CO rH C^ W IM Q O Ol t^ 5 O iC iC t^ Ci r* ao t^ c .ooccoc r* oa I Tj» -r TT '^ ''T iiC iC i^ iCift lO lC 11^ lAiC • C^ iC CM »0 C^ »0 -H t-O 1-t 'O I-" *o Q r'- -■■* — -— — ■-— — - - -^iC^^C^ S ift tC lO lO 3 ift lO O lO »C I O (^ 15 I- 3S CO 0» COQO OC lO iC iC iC lO u H -^ ^H -^ C^ TT» C^ CO iC ^ tCiO tC ij O lO lO »o iC i— ao— tX)»-iX': lO »C iC iC iC iC lO iC iC' »/5 Sd 01 01 01 ■*r '^ "^ -^ iC lO »C lO iC QOOOOrH lO 4C lO tOCO«OCO<£>COI^CO|. lO irt lO iC^ iC -V iC • cor*cot^CMr^cMQOCM aoc^oo'NoO'-'0>r-io>i-i,oi ' iC ■**" »C Tp — ^ - - - -._..-..__.-„_ 5 ITS iC iC iC f< lO ^ iC ■^ iC C iC u^ tC lO lO ^ lO lO iO lA lO ^ lO Ida > t^ in Tf .C t* TJ< iC ^ iC I iC U^ lO »C iC I J tO lO iC ^ •n* 00^ x>^ QCv X cococo ca CO o»co ioi n CiCM a> vC' iC »0 t/2 iC i"^ lib ■Tj' ic iC lO iC »c >a iC ■^ 1/5 -^ iC tf2 iC lO lO lO lO iC iC lO »o iTJ TT lO -^ iC iC lO lO lO '^J^ iC iC iC lO •xoidd V .^^ iiC lO QOiOQOiOOOiCOOUJ OQi^GCiCOCOopiCXtO iC lO lO lO iC iCii^ iC iC ^ iC ^ »0 TT* I lO '^ lO T u XiOXiCXift^X-^QO-^X ^ lO 'f lO f iC lO lO »C i/i iC "^ »C -^ lit li^ lil lO i£^ iC iO O lO lOiO iC lO lO iC ■^ X rf lO -V iC ; OS COS 5 50 0> '^ J> O " iC "-X04JO»-'CMCOTf iOcOI> 00 Ol "^"^ Page 492] TABLE 10. 'Mean Time of Sun's Visible Rising and Setting. S^ •xoaddv «» « ° 53 ?3 c5 IN S dzfloixpiwfiixPizB ecejecwccfioii-iTri-i s s s s tfcdp^xpjxtfxc^^ "-• ^ S3 3! "2 CQ CO CO OO CO a^c^p(HCCPdGCpc^u3p^ t* ^ t^ -^ i> -^ i> -^ r* -^ S' c^c^c>5p-tcoi-tcci-^cOf-4 ,cci-(C0O'^O'OT^l0^lC■VlCic■^ ^CDiO«OiC«Ci»ft«ClfttOiC |:0^C^lC^0^C«SlO^O4C kD'^«0'^0-^tD'n<':0'*f ■^O-^OTpOCOt-tCO St^ir5Tf-1rHr-lT--oiiO!CO"«rioco;oi-Hooa>ooo Tf -^ ?0 C^ 00 O Q Oi C^ O C^ O ?5 O M iC COiO ^^tpcO»CtCCOOi-HOOo « i-ll-~lMCD-*iO CO^COiACOi/^cOiC Sop. irerecoirecoire t— ooiosot— Mcpeo-^ i-ii-i-hC>mo^10'^OCOOC^Ii-ii-*OI'-*COOCOO>^OQ iScO»CCOiCCOOCCOCOOCOOCOOCOOC^O?S t'-'^aOCO^C^Of-lrHO SCO CO ^ lO O lO'n'iCCOiCCOiSCO cc t-* r» r>- r- <© 00 «e cc ic oi-^o-^^co^coc^c^ lO CO iC CO iC CO iC CO iC CO iCCO oco oco o coocc ocoocooeooiMOc^ COC^'^C^'«J r-l O 1-1 00 ^ iC -^ iC*^ iC ^ i-iXi-HQO(NooiMooc^ooc^t^dr*cor-cot^coco ■xojdd V SCI Q(M iC lO iC i/S iC lO Id is ic i!5 ic O* ■'J* Oi "^ 0> ^ OS ^ lO iC id ^ gi-lQrHi-Hi-«r^.-t^i-t ^iH^i-Hi-HQi-HQfNO iC i?ti lO lO iCiCiCiO O iC iC lOiC lO ift iC ut iCui lO iQ iC "^ iO "^ ij3 iC iC iC »0 iCiC iC ^iCiC 00 <0 00 CO •^ ic "^ iS iC iC lO lO 00 to 00 «o ^ iC ^ lO Q^!XiC^u^Oi-oot--oot>- C iC iC lO »C »C iCi lOiCiC iC iCift tO iC »0 iCiO iC lO &H95pt^C»Q^CX2p4c»tf GO pC^CGpjxPjCOpCHCOtfU^ Oh C» Qh GO C^h C/5 P4 CC P^ CC OO OS SCOOCOOCOQ iC lO lC iC lO lC ^ oot^oot^t^i^r^t^t^r* «£> r* oQ OS Q r-t eg c9 '^ uS"^ ^0 r* wcJCiJico cococococo coco •^ u^ TABLE 10. Mean Time of Sun's Visible Rising and Setting. [Page 493 x o I d d V tftBpSwpjoopjtnBia! sjuipjcnKaiQjcnpjGCi Oi ZD fiiUl Pi ViOi'Xi fix a^ CC P4 en p4 I» (4 GO M r» S*^«^r*OiO ^j lO !>• o 5? -^ co o> co cc ©t^t^o-^coc<»o^«p i-lMf-l?IC^C^C^(NC^»H COi-ICCi-ICOO-^O-^iC tCOiOiOO-VOCCi-tCO rlC^C^C^COr-C^OlOtS c^ CO ■^ in to t~ lO ic »o 1/5 »c ic iOO>Cli-c<1>r-CT-liCOOio xci5Gccoaoc030Mooco'»«accooo«aoe<5a>c^ OCCOMi-HiNi-IHr-IC^ iCOOir^c^coooQO '^c^oor^cocoooooMfio .-(l^^I-lI-l6^■-^l^^l-lMO«lOcOlC■^lO■*^lO■^ S'lOOOr-iCOMMOOt^ iOCOiOOSOMOS60(N iC-^»COOiOCOiCCOOCO fJiHOin'>5'U5T»-*t~-*i~ect~cot~e<5t-eoooeoooe<3XMooei5aocOQOc<5 Ol'riN-^iOt^OtMO OC^r-IC^rti-li-lr-imi-l cooceoioo>iNc^«om 00400)004 gt-^-^^HOicr-oj'^oi »50eOi-(Oli-(r-(04i-l t^MOOCCOOeOOOMOOM 04 O CO O CO >i5 « ift ■* ■* ■* -Wi to CO O OS O 04 iH « l> •* t~ ■* t~ CO C~ 05 t~ CO t^ 05 l~ 05 00 05 00 05 ao CO a>t-H05ooi^^f-Ho»ciC rti-IO)0 04 005 005u5 t~rl't^'>J0 04«OtD050»O>05 iCt—rH 04t*tOOI»-tr>"t^OI0150 i0 05O01O04O04O0)rHr-(rHr-lrHO05O0IO 05>O05lO'9'-C05 :0'^r^'»i<»^'^t^*^t^"^ |I>'i^t-»ra«t^'^t»'^l^^ t*O5t^O5t^O5t^O5t*O0 OO'OiOQOtpiOOjaQ -.J'iC'^'^iO-^iiScOOOS t^eor-o5r-o5i>coooo5 !SOt^01ir5T)<05t^r-ia!00 >-t'c9i^i-ipaoo5iC'!eMg5ooo5>otOi-(Ooo 5iC05iCC0O0)O0l|O0)Or-lr-lr-li-(i-l03O SOD04<:p»C05t^O ^■^■^coir5co»r5o5iC05 gr-cofto-^oooeO'* 04C50400JrH.-ir-li-l ■^^000^05iO00OC0»O oiooiiocciocc*-*-* t^'.tt^COI^COt^COt^CO iHr-l0»O-^r-o5t^eo cOllO'fCO^THQQOiOt^ S05iOCO'C05iOCO'niTj"'<9> S'0»0>Ot^01U5-1*'^^01 Ol4O«0iO05ifta5iC05iO oiiO-foot~i-ias JO 04 to •^"^•^•^■'J^'^M'COiOCO tO^tO'^tO'^tO'^tOTj* 305t~OOt-05T)-'*t-'5"'r-'^t~'*t-'^t»'*t-"i' 0CQO0p04t0-^C0t^^ OT«0>tO'*05f-pOI^05-tt^i-lOt>-'*'*000 ■^05>OCOiraCOK5eOOOJ004004rHr-lr-lrHr-Ci-l o-*tO'^to-*tO'*r»'^t^'*t>-'*r-'^r-Tj-'^-*t>T-ioaoMioto>-iooo T»'-4'»J'-^'*05ir505in05>(5 05O04O04O04rHi-( o.s<;o-*tO'j'tO'^tO'^tO'*t^"rt-'Vf-'^r-->!(< gO4t~05u'5iO-1ai-jr»05tou9"jit^oi 04ir5CO»i5CC005»CCOii5 to-j'-js-^to-^to-^to-^ 05 0r-IOOCOlOin0500i-l'rt00 05l(5t0 04a>5>04tO io5ira-*'«'^-^'*'<>'-^'^|ioeoiC05iSo5ir504 04 i*^^t0^t0^t0^tO^'t0^t0^tO'TTHO^c^^ 040040040COiOCO>0 tOiCOiCtOiOtO-^tO-^ Tfi to to ■.f 00 Ol 00 04 t^ o5ioeoioeoio-3>0'*^ to^to-^to^o^to^ lCiCr»04Q004t>-i5'i-tOO|040^C0r^iC^t03<00C0 erHi-lrHT-lr-(rti-(TH04i-( .dtOLCtoiCtootoictoic i^ooiooiSoiioiS :0»ntOiC!0»00»CtOiO !o>i-i'H©coaoi!itof-'^ M0 05 0COii5cOiC05iA tOiOtOiCtO-^tO-^tO"^ 3>04^0)o5r-to>caooj to^to^to.s*to^to^ tfOlOS05»'*»'t^tOtOt^U5 ,fl* to iC to iC to »C to iC '^ lO 00^0>0IO.-IJ4O05® tOtCtOiCtOiCtOiCtOiO S005004i-lrH04po50> 00)i-l04rH04>-l04i-(r-( ^tOir5tOiCtO>CtOi/5tOiC ■'j'ooicr^totoooicos'.^ tOi(5:OiOtOiOtOiCOir5 iOt~tOlS00-Jgiic^-* I004004004004 ^tOiAtOiCtOLCtOiCtOlC O05rH^01.H05O'*0> i-(04i-IO4i-104i-l04r-li-H tOtOtOiCtOiCtOlCtOtC t^t^OOtOOstOOCO rlrlrli-lr-lr-COlr-t tOU5tO»OtO»CtO>(5 oioiccoi0^f^*oo»o 04r-C01i-l04 04 04 totntotctotctoictoio a3'043 o«o«oco©ecoe5 ~ t* lO ■^ »0 "^ lO ■^ lO Tf< •xojddy aocooeoocoQccoco - lO r^ "5 '^ r lo Tj< lit) ■^ 5 iC lO iC lO lO ■^ lO ^ ©050COQCOQCOOCC I0»0i0i0i0i00»0i0i0 iC lO iCi iC tOGOtOQOtoccoostoqs 3 lO tO lO tC O lO ^ lO Pi CB C^ cc p4 03 p4 02 P:5 CO ' tf' oi P5 !» pi OQ Ph' cc pti cc c4 o^ Page 494] TABLE 10. Mean Time of Suit's Visible Rising and Setting. ^ -S 1^ w .15 3 ^^ •xojddv xoiddy 5"^ ^OQpjinadcQcdaOP^aQ ^ ■«< rt •g< rH -^ 1-1 -a" 1-1 ^ .H -31 r-l CO T-l eO 1-1 eC r-l CC r-l SSi-HOrHOrHOr-lOi-l O 1-1 O i-( O r-l O ■-( O rt pjaQPjtspjccQjcntf cQ pd co P4 % pj cc tf «: cj c» pj co pj aa oj oi PJ en pj co SIh co $SOr-tOrHOt-IOT-»Ot-( Or-tOi— lOr^OfHOi— I O-HOrlOrHOr-lOrH ?0 O -IOT-lOiHO.-40rH CO ^ ^ CO >0 CO O to CO CO OrHOiHOr-cOi-lOrt COCOCOCOCOCOCOCOCOCO S"cc-oi OrHOi-IOr-(OrHOi-lOi-IOrHOT-IOi-IOr-l .tfCOCOCOCOCOcOCOcOCOCOcOCOCOCOCOCOCOCOcocO Oi-IOi-IOr-IOi-HOrHOi-lOr-l,-lrti-li-lr-(iH ^COCOCOCOCOCOCOCOCOCO.COCOCOCOCOCOCOCOCOCO .: 00 CO 30 ic 01 10 a> •<»< a» ■* o -.»< o « ^h m ih co i-m oj c^ c^ .-i « i-i co o ■* o SOr-IOi-IO-HOr-IO.-l T-HtHr-lrtr-lrHrtT-lrHr-l •Hi-HrHi-li-li-li-li-lrHi-t ^COCOCOCOCOCOCOCOCOCO COCOCOCOCOCOCOCOCOCO COCOCOCOCOCOCOCOCOCO Si-ieO»HC0^«THeCi-IC«i-HrorHM^«i-IMrHeCrf .HOr-IO.-tOr-IOrHlc5i-(Oi-IO^Oi-IOrtOrt COCOCOCOCOCOCOCOCOCCCOCOCOCOCOCOCOCOCOCOCOCO rtOrtOrHOi-lOrHOTH cocococococococococococo CO C^ CO C^ CO t-l t^ r-l r^ r-l t^ r-( r* rH t^ O 1^ O t^ O t^ O OrHOi-IOi-lOi-lOrH O 1-I O f-H O i-H O ■-I O tH O rH COCOCOCOCOCOCOCOCOCO cocococococococococococo Or.lOr-lSr-l©i-lO.HOTHOrHOi-(OrHi-lrHi-li-l COCOCOCOCOCOCOCOCOCOCOCO CO COCOCOCOCOCOCOCOCO Y-(0!-lrti-trHi-(rHTH,.Hi-(r-li-liHOr-lOr-tOi-'0 COCOCOCOCOCOCOCOCOCO CO CO CO CO CO CO CO CO CO CO CO CO rH (N .-I >-l ^ 1-1 C^ •-I C^ O MOMOC5 0sC0»'^^-^cr0 1-1 i-H rH r-( rH 1-1 iH r-l i-H rH rH i-t >-l i-l rH O r-l O rH O rH O CO CO CO cococococococo cocococococococococococo ~;xc0«iC00si0O>OO-*N-l'^'-'=^^"C^C^50^Wi-l'*r^-*OiCOiffiS COWCOOOt^aOt^l^OOt^QCCO SOr-IOr-<0"-li-tt-li-li-li-lr-o.Hic^-*c^-*c-i>oocoocoo>t^gji^ooooQoa>t^aj«50cooin ^COCOCOCOCOCOCOCOCOCO cocococococococococococococococococococolcocococococococococococo ss 05I^OCO-HCOi-liOO)iC|J^'*CO-*Tt<05-*CliCrH|COi-ICOOt^OX35CCX|Oi9COH^OCO.HvOC-cNI>COcO-.lOI^COo Oi^OXr-H^C-lCpCOlC COCOCOCOCOCOCOCOCOCO OXi-ll-»!NCpCCiO"*-J< C^OCIOC-IOC^OMO COCOCOCOCOCOCOCOCOCO COCOCOCOCOCOCOCOCOCO g'OXC^t^MCC^iOiC-* ^COCOCOCOCOCOCOCOCOCO gOX'-icos^incOTj'Tjico ^COCOCOCOCOCOCOCOCOCO l^r-ICOCCOCOClt^>-lXrH COCOCOCOCOCOCOCOCOOCOCO -»(< T)< lO CO CO C^ t- T r^OCMOlMOC^OlNOC^liO cocococococococococDcoic lOMCOC^XiHOlQOCnT-HX C02)t~i-l0>pO0Ji-I^OCC{N>CCOCOiOC^cOQ C^iCCOiCCOiCCOlCCOincOlS COiCCOiOCOiCCOlCcOiCCOiO c* X CO O lO »-* -^ S O .-I rH ,-1 r-l rt ^ CO CO CO CO CO CO CO CO CO CO :x t^05 CO o ^ > CO CO CO CO CO CO -t~mo5-*oc^c^^eoos SOi-IOrHrHrHi-lrHrHO ^COCOCOCOCOCOCOCOCOCO ■^XcOt^t^iCOi-fJ^OC^ -5.HO.-IOi-(OlMO 3COCOCOCOCOCOCOCO ^ CO CO CO CO CO CO o^c^ X CO CO CO CO CO CO tC lO CO CO CO CO ^ CO CO CO CO CO CO OOr-l(5 CO CO CO CO IN^COC^ CO CO CO CO S* PXiH CpCOlC 000000 ^ CO CO CO CO CO CO 0000 CO CO coco giOOiTSoiOiO • lO CO lO CO U3 10 Olt^rt CD lO iC o ira iCiOcOiO pjccoSccpiccaScosJaJ O O — • 7i :o "^ cocox «o>o CO CO CO CO CO CO lOi-i coosxr- i-IOrHiCr-(iO CO CO CO lC CO IC C^COCO-HlOptQOOXt^ (MOC COlOCOiOCOiCcOiOCOiC cr>rH005C^t^'*cgcDTfr^c^ e^>oco-«>cO'*co-*eo-*co-* coiCCOiCcOiCcOiQcOiCcoiC Xt^QcOe^'^COlNiOOl^X SS'^eo'^cOTj'cO'^eo-^eoco COinCOinCOiCCOlCCDUtlCOlC ) .^ CD CO 10 lO CO 5 1-1 in th 10 rt lO s CD >c CO in CO in coi-ixoox^coeo-* inc<)t»oo'o5'-i^-''S>ninco 1-1 in iH ■nl ?» ^ 6) ■* W* M ■>9< 5cCiScOiC ?5iCC t^ OS GO 1^1 Oi 00 5 CCiScCiCCOiOCCiCWiO iCiM'^^«OQr*O10DQ0 cciO«»cccii5eo'^cC'^ » »c c^ :o C^ l^ f )GOO|0>030QCi-lt*T^':pC^iO QC 1— 1 1* T^ 'X' C^ I iS JO tO CO »5 CO I coi''^eo»cc^oiQCor*f-i?£>iMtio S'i>r-taco QOOl Oioooi> 1-1 1>- w ?p cc iO "^ '<*' »^ CO WOC^OC^iCCNiScOtC COiCCCiScOiCCCiOCOiC OfNr-i-HQQQOiOsOt^ OOiCCOiOCOilCCO'^'^*^ r-( to C^ »0 CC -^iC PO CO i-H S'csQOair-l00iMt-C0:0l'^iJ?::iCi-^c0C0r*C^GCT-i QQa>i-Hr-co-C^00r-lOSO4rH00C0«D ■^'^'^■^'^COiCOOiCCO :0iC^iO?0iO^iC?0iC iC'^<:OC^t>-r-IOSOOGQ ■rj«-^'<5-^OSOif-IOD tOiC^iOcOiO«Oi/5C^»C OSOSrH00C^«O^»5«DC0 ^COiOCOiCCOiOCO^ftCO i:OiC«OiO«OiCi«OiCOti:5 t>-^HOlOSrH00005OiC'^ ;oiOtoict>-ior*»cr^iO rHX'COlCiOCOCp.-iOOOS iCCOiCCOiCCOiOCOiOC^ ^O^iitlCOiOCOLn^iC CCC0iOTHt»O>OS0Qi-(«O iCCCiCC0iCf^iC?JOtM «OiC?D»OcOiO«OU5r*iO Soctjc^i'^coc^aoo cc-^iCwr^o^r*rtiO OWOC^OC^O*H.-tiH SOOCOOiOr-'COCO'NiCO cooDXt^QiCc^eocoi-i TrM-^ccizScoioeoicco tOUO«OiCCOiO«OiOOiC S04t>-I>OSlOi-C^CCC^ ?iOrHOr-l»Ht-liHi-l SaiCCi^C^C^Q***OS«Ot^ C0^1*^^'^^C0^C0 ^cOiC^iCtOiAOLAXiiO t^inoico^H^cooiict^ ■^SS-^coiccoicJ^icc^ COiC'OiC?C»0^iC^iO SCO ^ ^ CO OS lO t* C^ O 'M O 1-t O 1-t cOift:DiOt*iCI>iCt*iO S CO ^^CO'S'CO^OO^ CO opfHpoic^r-'^iO'Cco COiC«DiO?OiCtDiCtO»C SS82g t^-iOiCt^COC^OC^QO'^ T-*Or-tOi-l 1 lO I> »C I> »c 1-ii-lOrH - .— .— . — O O 1—t O 1—1 O rH t^ lO t» »o C* Ut) t^ ■OrHOrHO to lO t^ >c t* Id f- TJI t~ -^ Sf-.-ll3SO».Ht^C0iCiOCC g{I^HOOOOOOOtO Tj'iH-^rH-^i-l'^OlOO pHODtfajaSajSiHCcPScc aSaJtfasCSaJtfaQpScc > t^ M ira lO c^ 00 c OOOOO j lO r-l ■* e^ -^ •* t^ -^ 1-- -* SMOOO O lO O iC CCiC«OiO CO TJI t>. ^ t^ ^ t^ (M •* Id i-H 00 C anuctfoiWaJPiccB^aQWcftOSaJPHaJtfGcBJaQ cc as o , ^- CI CO -7" ic '— 1^ 00 d o Page 496] TABLE 10. Mean Time of Sun's Visible Rising and Setting. o3 to *- a 0) CI O II 5 ^z o 5 -^ cj eo ■xojddv S=» pi^'xsiic'aiKisiaiiidx aixi:s^'cc3icca^u}p^ui pjcctfcctfos^cfitfai ^ PH & ^ & T-l ^ ^?c ^ too SS2S2 to -.o o to o — ' O I-* tototctototototo totototototototo rf*tO»CtOiOtOiCtOiCtOift ^tOiCtOiOtOlOtOiCtOiC tOiOtOiCtOiCtOiOtOO 0--.0r-. to to to to ooo© to to to to toMr»cci-»2J*£J*'-' -- to to to to to to to to tOiCtOiAtOiCtOtA rH!C— 'OT^M-:''*^- rH O i-H O to to to to Oi-iOi-i to '-O to to I-* OS t^ ^ oooo to to to to CO ^p w 3? to to to to BncoiSHCcipjcQPJaQP^aQ S3838 OrH OrH to to to to t r-mit^m t o© oot to to to to t Tloo©oo 3 to to to to to to to to to r-«OrH to to to CO CO CO CO O ;sss8§ > to to to to t oi r-i OS .-I <» c^ qo N t~ ec to StOiCtO^tO^tOtO ^ to lO to lO lO to iQ r- ■* ^ QO ci O' c^ o r-* <-! o tOintOiCtOiCtOiCtOiCtOiOtOiCtO»OtOiOtO>C totot~-toociC5R'^9;OT tOiCtO^tOlAtOiCtOtO gt-)r-M.-irmq<5o5C> lOeoiCcoiiScoifteo'* tOLOtOlCtOtCtOiCtO^ S'c^MMC^MrH-*0"5Qtoi3»r»ooaot~-a>too>iS ^tOLOtOiCtO^tOOtOiAtOiOtOiCtO^tOtAtOO vcoQtot^t^toooinQ'^ tO^toUSCOiOtOiCtOiC r-(e<5(NMeor-(2©too» tOiOtoirsto&ctoiotoiA «r-lU50lt-01COOOaitOrHlOC^< S"toot^3»ooaoost-otOi-iiciM-«'coM5;. _ ^ ^ - ^tOiCtOiCtOiOtOlCtOiOltOiOtOiOtOiCtOiCtOiOtOif^tOiCtOiCtOiCtOiC -ffcCiOt^tOtOt^ipOS^ totCtOtfttO^tOiCtOiC rHCOe^rHCOOinOltOt; ■^ ^ ■^ ^ ^ Tf< ^« CC M* CO toiAtoiatoicto^toio r-t~o>toQ'*c^co-5'r-i ■^CO-.TCOtCCOiCCOOCO tOiOtOLCtOiCtOiOtOiO SMtoor»oooitOr-i'j< eo>neoioci tOiCtOiCtOi^tOiCl^iO gs t^-i-HcocmoeocoM'C^ CO^COOCOlOCOiOCOiC I-n^^OCOCOr-IOOOOiOS jtOiTScOvCCOiCcOif^COiO iCTHl>OGOaiOr*rHO ^^^Tf*^00'9'CO»O CO cOiOCOii^cOiCCOiCCOiO 5 r* (N CO CO '«!t - ;Gooa>oiQr-(McDcoio rTpTT-^CCiiOCCiOOOUOCC ;coiCcOiOcoir5cOiCcO»C . ,. "if^CCCOrH COiCCOiT^COiAcCOCO COiCCOiCcOiCcOiCcOiO iCCCcOf-taOOOiOQ^CO !iCCCiCCCkS55iC>c50C^ COiOCOiOcOiOCOifit^ift COiOcO CCiQCC if^COO COiCcOiO iOCO»C CO tC CO ic t* »c t* id> »c eoinincor*pHQso*fHco s'i^t-cOiOiC'^coc^arrH ;iOcoiCi«iCco»5coiceo *COiCCOiOcOiOCO»CCOiC :iceoiccoioccoc3oc^ »coocoiccoior*ict>ic 05ffii-ir*cocoiC"^t^c^ cceoiC i-lrHr-l iC COGO-H ■^M'tOr-lOJOli-ltP'^CO rHrH.-Hr-i,-lOC^OC<0 .iotocogOr-<©asc^t^ OIN oc5 ■.J'r)©rHt~-'.r" (MOINO lOSO^rHOOCOtO't'^t 3 o © 00 mo in ■* t^,i-H rfStoiot~iOt^ict^ioi^iojt-int^mt>inr»iot (M©c^©c5o?S©eom .-(00COmtOCJO»Ol(N C^©C^©IMO t* lO i> lO r* 4/3 HiceoS r»rHOoo?2'2t~^©*' ■ (NOCOiftCOiO icr* ■^ r* ■^ coio-v* -^lOt^r-HrHOO'l'-^OpO C0iOC0»O'«iJ*-^TT*'.t'-^TI< S*eotoin"rr»cn'*t~i-H©mjio OMOC-IOC^OC^i-(r-l|iHrHrHi-HrHrHe^©CMO 65o (N ©COiS COiCCOiO -^ -f -^ "V -^ "^ lO CO lO CO S"t^MO»©i-i«cotomcot~.-i©g>(Mtoioe2cc^ ©C^©(Nrtr-li-lrHr-(rH|r-li-(f3 0(N0C^©Sl© r-IOO'}'l5r-IM©OC-*lO eoiocoineoiorr^'^''*' g©t~INiC-»"COf-i-<0»» C^ltOTj'COt^rHOCCeOlC C^OOJ©01©CCiScOift toopcomto.-(©oo ^■*o£C::^ — i; 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to to to oooo to to to to ooo to to to ggggggg to to to to to to to lOt^iCC^iCt^iCt^iO Soco .cjtotco 8 iC to iC to to to to to oooooooo totototototototototoior-ict^ic ^ '->ooooooooo to to to to to to t , to to to to to to to to to to r-ir*c^r^c^i^oitocot rHiOi-l to to to IC Trt tO r-4 IC rH lO lO to lO to lO to iC OO-H to to to — i0t-(0000 O.HOi-iOi-(0 to to to to to to to OOO to to to xoidd V ^M 1^ SS8S «; to to to Cs ^ Oi '^ C5 ^ CS OO OOOOO to to to to to to to sss to to to ooo to to to 383 to to to to OS^^iOOiiC^iOOiiOC SOOOO I > to to to to to to to St^ -^ r* Tj« i^ -^ OOOOOO to to to to to to to yoo^ oo»cooic 00 >ooooooo > to to to to to to to C0^00^COrH';Oi-'COr^lcO»-fCO^HC0»-*C0f-tCOC^ CO^COC^COC4CO!MCOC^icOC^COr42^C^2JC^C4C^ a Ort o ^ to to to ) rt 0.-1 1 -o tO'tO Oi-lOrl to to to to O^O' to to to t S5;::;Srto;^ to to to to to to to P5aia;cc3iccPi3ccW73 o "S^'^^^'^'i" fim(i'^I>'^l^-^t^-^t^'^t^'^t^'^XCOXCCX«3OCOXtOXC^C30COCOCO SO'»'O'^r-l'»'iH'*i-ie0 S'WQiC0Ct>*«OOSCC(Ni— I t-l C^ C<5 lO lO iC s iC iO O C"^<;oxcO'-i t^'^l>'^l>-^t>'^l>-'^'l^'^l>'^I>'^C^COGCCo|xCOCOCOXCC»CC0DCO t>-Ttft:^Ti«i:^TfTt«i>''^I>'^l>'^ W^C^COXCOaOCOOOCO * 00 CO iCi-l i-» L C^M-NC^CTlC^COr-tCCrH '*<3>oo-g«ccosGO-^'^oo t>.Tj*C^Tft^COt->-CC00CC Sosr-^DOcocoOiCt^ xi -^ c^ ^ lO tt g; S'OiTT'-'C^COOiOXX^ Q'^C^i-HiOOiXOOCClcOO*X>t^CT>'^CCr-t!;Or* to OS X r^ O Tt* CO C^ ifi Oi X «D t-^ "9* "^ ^^ t^ X O ^ ^ ^H !>• t^ ^h cCiC O Cs lO iTSimCiCOOOiCO'^O'^^-^T-i-^rH cocoes C^CCC^C^COCIWC^CCi-i OOfH'-J'r-i'^OlQOiOlO coc^co^icoi-i'^i-iTpo -^i(;i:OiCtOiOOid<:OiO !(0'^t^*^t^'^l>''^t>-'* t>-'-'^ ^ !;0 lA ^ in ^ lO CO lC <:0 kO O lA e& iC ^ iC O iC CO lO ^rH iooioo55o25iooiooico25t-(TrT-i'^i-tTr oio«oiCOicoiC(Oio cO'^i>'*r*'^i*'^t*-^ c^«(^^co5^cccccocococ«5c5coc^coc^coc^coc4'^cs■^c^'^rH"^rH'^1H|^ ^(OiOtOiC500^iCitOin «OiC?D»C?OiOcOtC(Oif2 Uo i/5tOu^tDin?DiOOicUDifttDi0^inCOOW«-lrHfiOO-^OS *jCOCCCOCCCCCOCOCOiM ;o^cou^^u:>:oicoiC iCt*O-f-Ht>-QXQXOiClXaiXpr^'-C^Oi!c^X?cxir)Xi^X'oxy?xtDao^x toxtpxtot^^r^tot;- Soooooooooo 0000000000 0000000000 0000000000 ■^tOOtOCOCOcOtOCOtOcO ^OtOCDCOCOcOCOtOCOJtOCOtOCOtOiOtOcOCOtO|OtOtOcDtOtOCOtOtOCO •a}Bp •xojddv Or-lOiHOrH&r-lOr-l rHi-lrHrHt-IQlNOC^O» .-OrtOr-lOi-lOr-liO Oi-IC>r-lOi-(Oi-IO.-l ! , ........ « cB 03 03 oj cc oi ai 05 (» i 03 02 ci oQ ej 00 Oh' aJ aj CO ; oj ai 0; 03 ci CO oJ tc oi CO f-iCOi-'CO^HeOr-ITj'rHTjl i-HTfQ-^O-^OiCOiO Or-lO>-HO-^0-HO«0«Oi-lOr-lOr-0'-' O -H OJ « 5^ -^tp^tpS iC»bift»cS SiOioiOeo Page 600] TABLE 10. Mean Time of Sun's Visible Rising and Setting. J S o &< f, 45 ti 00 S a 03 ^ Ti P o o 3 9 P Tl 3 i" 3 5 a Oi-ic^w^ io«t^ooo> Oi-fnco-* i««5i-ooai : o J d d 1 'xojdd V ^^ ftiai03MC!^«ia?aiai'/J 0^x'9Jx2^^a4c»2^a5pHcc^xP^ajC4cc^c» c^xSE^xfiSMQ^coC^yJoix :'^iaiOiOiOiCi«>C«JiO lOJSiriiCtCiCiOiftiOiO OtOi«iOiC>0"3»QiCiO iOiC?2>ClCift04t5u5iOiO»C aiftiCiOiCiCidCiOiCiO lOiCJiOiOiCiOiCiOiCiO uOiOiCtOidOiOiCiftiC iC^»ftiftiC»CiOutiiC»f5iCiC ; i35 iC »c 3 lO i« » lif »0 lO lO i'^ lO » ^^ 0> W Ol C^ OS : ifl ic lO lo »c iC ; lO iC lO »CiC iC iCtOiOift kOiOiO^iCiOiCiQiOiO liOiC^»?l»«iOiOiOi/i;ift iCi«»QiC»CidOiOiC»OtOiO : C^ Q 00 Q CO o e lO CO O ^ l£2 to '^0'^oiijo»oos^Oioa>--ooo-^ccr*r*Gor^GO?pootolaoooi';oasioai>coiftQ'^ »0 O »C O kO 0»0»0»C»CiCiCiOiC lOOiOiCvOiOiOiCiOiO |»C iOiOiC!>0>0»CiOOiOOiC iCtOi0^iC^idOiOiCiOiO»0»0 V5iO»OidCiCiOiO»CiO iOiOiCiOiOidOtCOiOtOiC • »0 1^ lO O i« o lOOiOOUCOiOiCLOiOiCiOiOiO iCiOiOiOiCiOiC*COiQ iCOiC^OiOcOiOiOiOiOiOiCidC >CiCiOiCiCiCi»C>iC50ift OicoicoifboiiS^iicoiib tOiOtOi^OiOCOiOtOiC^iC iiccoic^coM ; 40 O iC O >« O » lO CO tC CD iC CO OiCO kCOiCOiOiOiCiCidC OiOOiCOiCOiQOiCiO'OOiOOiCOvftOiOOiO ii550»C^»CtOin«0^iC^iCiOiO ?OiCCOiC«OiCOiO:0»cUoiO«Oi0^inO»0«OiC- (N 35 '-' lOOiCO iooi00oooico55 lO^OiOCO^OO^tC^iO «;t^if5r*TfGio«QOcoasc^ giOOmOiOOLOOiOO -£ii050iCtDiO:OiCO»C^ -;t^iCQO-3*as^aicooco StOOiSOiCOiOOOO -iiceoiosoiAcoiCOOco oooooi>ooic ?0'iO(OC050«00':OOiC OOOOOOOOOvO C0':0«0C0C0'OOOc0iC "^acc^i^coh*coco-*5ol'g«»oiCioo-Tr'»'COi>?or^(N &iOOiCOiOO»COiO'0»CO>COiCOiOOiCOiO C0i0t0iC-Tfr^icOipohP'f^t^>0'Xi"^oDcc(^c^O'r) Oi.cou:>oiooi?5o»ooiooiooi6oinoici-iic ?OiO«0»COiCcOiOOiC«0»0«OiC<0»COiC50»ncOiC SXi^t^Cpt^b^'^Ot^iC iCOiCOiCOiCiOtO oioo»c?oiO':oir5!Oin g*X?pOl»CQiCQ^'-oi>oooooin OCOOtO^^OO^OiC -JOO^OfOtOO^OtOtOtO Soot^r'-GOt^^co^iO iOOiCO»COiCO>C OiOtOiCcOiCOiC^iO tOiOOiOtOiCtOiCCOiO^OiO r-HiOrHii5i-H»OrH4jOi-HtC^-*iC io»0!OiOtoic^»coio«Oir; ~ — — — — - ^iCOuOOtOi— tiftrHlOr-tlOi—^irai— liOrHiCi-HlOi—t^ :otoococo;o:ocotOiO :Oooooooooo i^o^ooto^ootoocoo oooi>oooooic tOiriSOiOtOOtOiC^OiC Oi-O^iO^^tOiCCOiC^OiC eoooooooooo ^50:00^t0'^50^^<0 iCCCOiMt^t-tCCOOsCi ooooooooouo iO:OtOOO!:OOOcOiO OGCi-Ht^iMtOCOiC'^Tt' iOCCOC^GO'-ia>QO c^i 00 CO r^ ■:** ^ If: iC oooooooooo ^tocooco^co^^^oco oooooooooo ^^tootoooco^oto Scoi^'^ioD'-H^ooas OO&OOOOf-iiC tOO^O'lOOtD'OOOiC i-(oO!Nr^cO'y3iC»oO'fh*coaoc^ai005i'>iaccor* !0»C^mOU^«0iCtDiC 'COiC^iCOiCtOiC^iOtOO r^coxc^^t-tOQC^o OOOOOOiHOr-iiC COeO«0?0«0«0^?0'-OiC «i*!MOCCCO'^t^iC'©cpiC $:0i-(00000000 ^CO«OOtOX>0';OtOCO«0 COTff^COO"— 'i-HOCOOi OOOOrHOiHOrHiC OCO^OO'^OOtOiC coQO'^i^tccoso**'t^co c^MOT-^.-40ic^a0'^r^ic*o CO»OOiOCOt0^i0^iC ;?OO^iOOvO:OiOOtCO>C '^0D»0t-«0»0G0'^0lC0Oi-teG£ju5iq>5?o o t^ t^ CO go ^ oooooSo CO CO CO CO CO CO CO fHOi— tOt-<0»— (iC»— liO COCOCOCOCOCOCOiCCOiO t^-COOC^OOTrHi-ICOO COiOCOlOCOlOCO^CCOiCi sgs§ ^COCOCO GO »c r^ ^ iC GO "^ ooooooo CO CO CO CO CO CO CO OOrH CO CO CO — I C^ OS ^ GO lO CO O rH to r-t iC •— * »0 CO CO to CD O CO IC moiiOoocococcioo>co.-icq COtCCOiOCOLOCOtCCOiCCOtC COLOCOtOCOtCCOlCCOLnCOtO CO lC CO >0 CO to CO to CO to CO to CO to CO to CO tO CO to CO tO SooS ^cococo t^*^ CO CO - - -. ooooooo CO CO CO CO CO CO CO lO t- CO 0> iH rt ioOrt :COCOCO CO CO tO CO to CO to r~coo»iNp©c^«'*co CO to t^ M g> rH .-I o ec GO to CO ■-HtOr-iiorii/sc^'j'c^'V ijTfffqTjifjTrco-^coaSoiSm COtOCOtOCOtOCOtOCOtO COtOCOtOCOtOCOtOCOtOCOtO S'OGOrH ©oo ^- CO CO CO gg3gg§g to to to to to to to S8S CO CO CO lO to iC to iC to ift gsss S^^ CO CO rH -^ OS OOOOOiO CO to CO to to CO ^ §ioS CO toco coo-*-^ r)«0 tO r-t tO r-< tO f— I tO tO CO to CO tO CO tO p^QQMcQpi^aaQjaQajco pijaopiJcApjoBp^aop^oD adxp^xajoopfcfip^co COi-HOOOOOOflcOCC-^ lOC^t^OOJOO—'l^COiOiQCO COtOCOtOCOtOCOtOCOtO cOiOCOtOCOtOCOtOCOtOCOtO ioo»r-t~ootoococ^c^i'?'OcooOGCcoQtCJe^'*o CO to CO to CO lO CO lO CO to CO to CO to CO to CO tO CO tO CO to OHCcp^oopjQQp^cnp^ccMai a o & .2 OQ el S 1 3 5 r ^ TABLE 10. Mean Time of Sun's Visible Rising and Setting. [Page 501 •xojdd V ^^ r^ C^ Cvj CJ IN C^ M C^ CO CO '^ la <© i-^ Qi CO CO 00 CO CO o PJOQP^XP^CIQQJ^^CIQ QHXpijxp^coQ^coc^GCpi^xpiHaQPi^oDQi^cQp^x QjcQp^asp^GCPQ0^G0"r!*OS'^(J>C0QCO i^-}(,HCOC^CO^C^?^CSl gCOQC^Q'MrHCqr-IW QOCOCOCOOOC^OO'MOiNOSTHOrHQi-lOf-iOO OiOOiCOiOOiOOiO COOi-^Oi-^Oi-3'OOiCCO COC^COrHCOi-f^fH-^Q -^COCOCOCosi340>oooooot^ i-iC005C0G0 a> '^ QO »o op «o c* iC o ic «o vC -iO(D<©iO C^CO!NCOC^COC^0OiMCO C^'QQQ0r^Q*.O^iOC^CO c^coc^cococococococo .(OU5COiCCOiOCOiO«OiC 0»C— I'^S^COCOf-H^O cocococococOcococOco tOiCtO»C«OiCcOincOiC coc;C^ococO'-' cocococococOcocococo COiCCOvCCOiCcOiCCOiC it^QOipOt>-C^COCO'^ ]COCOCOC^'<»'CStJiCt*t>a • CO^CO^COCOCOCOOOCO aCOtOCOvOCOlOCOiOCOiA CQ CC CC CC CO CO CO CC CO cococococococcco ooi-it^eo«c-^-*ocot^-^ CO CO CO toicto .-I 00 CO to toiotDin tda<:DiCcOLCOiCO^ lOiCtOCOOOC^OOi-HOO ko»OtOiO«DiC;Oi^(0»0 tOiOCO OJCOt- to ic to in ooc^<50iN05' to in >e^Qts>inr»t>-toos'.ji :co^cocococococococo itointointoiotointoin « CO -^ CO 5 in to in ■.I* a> to t^ t-* in ■* CM -9" ?J ■■»' cJi to in to in to in s t>-t~-in > in to in to in coin CMO'^OOtOtOCC'^OCM inCMiOrlinrHinrHSi-l toictointointoint^in to to op to in to in to in c-Jr-i-5io> inNinrH to in to in iCOiccoicr^ict^iot^tc OSC0.-li-HCOOa»CQ0r-CO COiCCOtCcOiOCOiAcOiC o>*rr-ii-tcoaicpt>-GO"3< iCi-(OrHOOOOOO COiCt^iCI>iCI>iCI.^iC iCOCOCOCOCOCOCOcO^CO IcOiOCOiOCOiOCOiCCOift )in-J3in to to 00 •>»< o c< ■<>• CM ■«" CM 35 CM to in to in to in COiCcOiCcOiCCOiCt>-iC lO O CO c^ p 1/2 1^ lO r» ic jiCcOr-iCOiCOp^iNp -cocococococo^co'^c^ aCOiCCOiCCOiCcOlCCO^ »f*^OQMPOC^OD^CO :COCOCOCO"*COTfC^'^.cOu^04C0i— ii-rcO^ lAi— (iCrHiCrHOT- in to in SOCMOC^tO CMinrHinrH to in to in to lO t^-^o»CMf-int^ r^ to-^ oi CM in r-H in I— ' in TT t- Tf l- ■<»< »t**-(a>a>»-it^coininco :cceocofjTt-H to CO ■'J' in CM to in to in to in Soot^-coininc^ooQ -hOOOOOOOO toint^int^ini>int^in ot^cointocM^Oij^to f-linr-l in« tji fM ■ ^ l^ ^ t^ TJI "tOOQOOtOO-^CMCM'Tj'O :COCMeOCM-^CM-*CMTj ^T-H'^T— tin.— iici— (tno tointointointointoin i^toO'<>cMr-iino>r~tp inoooooomoin tcini>'ini>.int»'.jit>-^ |0 -^ CO ^ to U-HinT-iini-i |t>. Tji r» rji t- 00 05 in pi CM ■* — TfCM -91 ■.}* t^ Tji r* -^ 91 I tfcQrtccpiHCCpaccffJccOHCoeJaQDJodKoDpHCO tfcoPJaQP^cntfuipHCCP^oaPJastfaQpjcoCdcQ CMNcMCMCQ CMCM^flCO Page 502] TABLE 10. Mean Time of Sun's Visible Rising and Setting. S CO o 1 •xojddv •xojddv ^^ 5S 5 in to t- «!»pl5M«OptfCO(J5M St^ t^ t^ r^ r^ t^ t^ QO r* 00 r* cc r* go t^ ao t^ cc so ao TI" iC ■<)' IC -^ >0 -"t "3 tC iO -^ >C -^ is Tf> iS TP is -^ i3 ^»CiOlC»C»OlOiO»OidCiO»OiCiOif5iOiniC»CiC S 3 lO o dHaQpHSOpjcQpjcfifriJaQ pcJagPnOQpcJcopdccpjaQ iOiO»OiOiOiCidCift»fl ^» l> 00 a Q lO lO »0 CD e^ccp^ccf:cjcof:^ci!}p^cG iC iC »C lO *C iC lO lO iQ iC lO lO iC iC iC lO »C »C lO »5i Ma»0*GOCCGOCCt^-3«t^ O-^O-rr OtI^O-"?*©^ rH 'Tf i-i tJ« rH tP rH '^ rH Tf* i-HCOT-twSrHCOi-lCOiHW -OiCcOiCOiOCOin<^iO (N C^ CCiM ■<*« 1-^ -^ O »C Ol 1:0 go t^ CC 00 1^ 00 CO OitO to »0 «0 lO ?D iC CO iC O iC :0 iC !0 iC CD iC CO lO CO lO COiOcOiOCOiC-COiCCOiC t^ccoooOiJit^aicoOic i-H"»tccc«5Tfc^ir5t--co a> COiCCD i-HiOfHiCrH liT CD iC CO iC gcooot^r^aicoo"^-Hco COC^COC^CO(N'^(N'^« O lO I ^ i-( -^ iH L(5 rl S CO lO CD lO CO iC goiO(N'«tcoc^iCi-icoai ^COiOCOiCCDvCCDiCcOiC XOOOCOrH-^COlMiOO COiCcOiOcOiCcOu^^iiO COrH 10 iCi-HiO COiC CD OiCOOO iOCDiCI>iO i-iOicot^-'^iLCcocoaor-t ooco01-<(^^ol^I•>. 5iO cOiO lC O »C O vS o CDiO CO iC CDiC iOGCt^iCasC0 »o O iC i-H iC I— ( lO I> -^ l>- -7< I> Tj< t-ooot.cD'M^'^c^r-ai COiOI> s CD C^ -^ vCtH X OOi-HlO rH iC iH rf !N 'Sf I> -^ l--"^ t^ 'fj^ ;iCrJcO'-Hao COiCcO OiQ 00i-t CD t-H lO »— I lO I— I iC CD iC CD lO i-tCDiCO'^iCC^t-^OOiOO'-HC liCrHiCOOO OOOOOiOr-itOi-HiC ^ CO lO i^ ic t^ lO i^ ic c^ -^ t^ -^ i> Ti< cOt— iaoaii-*r^-^-hi^.— (OoocoiccorHcsOO OOOiOr-nOi-HiCi— l»CC^-^C^Tj'C^)Tj<«5C0 »c c^ -^ C^l ■^ 00 ^ r* "^ i-^ Tt r* rt< 1-tOOcO lO iH lO ':oiOco cO-^"^CDC^ lO CD »0 COiO ;cocDiC-*t-(MaiOr-foc ?:iOr-( .j^COiO iCrHlC CDiOCO a 00 CO ■^ ITS r-t ^COiO §-go ^OOOOOOOOrHO i-ILSi-liOrtiCOJlSOJTr ^ t^ »c t> lO i> 10 1^ lO t^ 10 r^ -^ t^ -^ t^ Tj< r* tH t>- Tj4 » 00 0000 i-tiCi-HiOr-llCT-liOC^T)! < 1-1 00 •* -»" 00 Q < f~ ■* t~ TJ> 1^ -^ COcgvO'^OOOOffiCOt^ OT('00^^00-#inoO(M O O O O i-H 10 I-H lO i-HiOr f lO (M Tf (M Tf C^ Tf • --T* t^ -^ t^ -^ t^ -^ iHOaiCOOOT-HC^t^t^CO ooe^i-HOcot~'j5-*aic^ci05ioooocOT-taiiO'0 JCslfN CO OrfrHOOm ■* IN lO C^ lO i-( t^ ''t t* -^ t^ -^ ■OOOOrHOfHiCrHlC 3 t^OO'i'rt Ol :rHOrH5rHOrHlAe^in O>--t(M 003-^t~-^t^-(-*lN,-(iOW0l'OC^iOC^iSC^-*f<-*COTPCOC 00 -^ 00 Ci oc )r-liCT-( CO -^ 00 -^00 w iH r:* i^ cc CO a> r-< O rt lO C^ rf 00 ■* 00 00 00 00 JeOT(Oi-iiomnN'*cO'ji 5-^OOOOOOCOOOCOOOOO ; 00 CO .-I -H ■* 00 t^ lO Q IN COQOt~iOOrH3 rt< t~ -SI I> ■* I> Tj< S*C<10iiC50Q0C0i-HO'^=0 QOCOiHOiiCiOOirHCOt^ (N-^fNTj^cN-^CO-^OOOO O0CO'^ClinTH ^ t> -^ t^ -^ t- Tj< i> Tji t- T)< t^ "^ t^ -"^ r>. "a< t- ij< t- -^ HOOOrHiHCO^rtr 10 Clio -*<00t)I OOrHO 00-* 00-^ OOOOC^OOt^COlNOOOOCO lOi-HOOOOr-liBiHlC t^-a<00'*«'-^ODCOOOCO ;tocoaoO'Ht^Tjicoooo ■HomtNoiooco-^oco -INTt<(NTj -"l^ t^ -^ t^ rH I> Tt t>. '•^ I> •«*< t^ TjH |> -"^ t^ T}< rioa>ootOi-i(Nioosooio jINCOCJCOCOCOOOiNeOlN P^ccPhcqPhcoP^coPJco sss SCOlO c i-H lO r I -^ ooco c iNiN«500Q-*'^roOliO QHQQPjCQI^OQpljUipHOQ 'Ti' •»»• "^ iC 00-* 00 10 ■* Oi O ■* ^3 00 in rH -T C^ •^ IN CO CO 00 CO 00 CO 00 CO !iC ' 00 CO -^ (N in rH 1 00 00 00 CO 00 00 >t^t^OTf(Ninr-lOO )ooooccoococococnc<5 Sr-tp-^t^oinoo-^ai sco^c^Tj^^^LOooin iOOOOCOOOCOODCOOSC^ Oi5t»p4=op!3a6c4(»Wc»picotfa3pi;ooa3a3pia> rt IN C3 ■^ tQ ^S '"" OS "^ ininininin inuoinin TABLE 10. Mean Time of Sun's Visible Rising and Setting. [Page 503 o a •xoaddy P5 aj 03 CO « 73 rt cfj rt CO Wco'McoCKHCBPiccMccPSMtfcoPiGdrtccOHCC :iCOiooiao-*OTjio n coocoocoocoocco d:h cd piH CO a; cc jii aJ si X* Cij x' C^?1C5cCC^CQN0trHCCi-IC0 ;ooo ;oaDOaoigcot>-r-iiCC^ iC CC iC CC »d >OG0C5giC5Ot;THO_^coc^ irjiCiCidOcoiccoiOco ;OQ0 OiCl CO Ol ; '^ Tj* CO Tf4 CO Tf » lO lO ^ lO o »c t^QcO^ COOCOiC iC lO iC ifl iCC^iCCO-^TfCOiC COiOCOiCCOiCCOiO 'MCO COiS COiCCOi : ga 05 GO o t^ .-H J lO iCiC CO O CO ■^'^COiOi-t lOCOiC COiC CO O t^ Ol ^ 00 o O C^ O i-( O rH r-t CO ir5 CO lO CO li^ CO ic CO -^ -3" c^ iC CDi/3 CO iC 0(NO(N Oi-H O CO ift CO uC CO IC CO cOC^iOCO'^'tCOiC'McO.— tl lO CO iC CO o O C^ O C^J O CM o CO lit; CO ic :o i/t CO sOOD O i^ »C LC ooor-i-i COiO COiC \ft ifi \^ lO CO CM CO CO iC -^ -^ ift COiOCOiCCOiOCOiC COiSoOiCCOiCCMiCC^O lOiOiCiOiCiCiOiCiOCO t^»-'COCMiCCOTj<-5*cO»CC^lcO r-j o c-i o C'J ^^ '^ f^ '^ f"^ '^^ '^ iC CO iC CO iC OCM O CM OCMO CO iC' CO lO CO >C CO :-<^'*fff CO Iff O OC CI t>- CO t^ -^ O CM O Ct O CI O CO iff CO Iff CO Iff CO 71 CO 00 CO 00 CO iff CO iff CO iff Iff Iff Ifflff S CO iff Iff Iff iff CO Iff cocoiffr^-t'^-cooccoaa COiffCOiffCOiffCOiffCOiff ifflfflfflfflfflfflfflfflfflff I01CJO»-*^^0.— I^CJCICO CO Iff CO iff Iff iff CO iff OCOO CI OCMO CO Iff CO iff CO iff CO Tf S«iff CO iff iff CO Iff iff Oicoo^'^oQ'^r^iff iff Iff iff o5 Iff I"- CO CO CO CO 1-- Iff 30 -^ 00 iCOiffCOiffCOiffCOiffCOiff Ifflfflfflfflfflfflfflfflfflff ^ Oi CO d CI CO iff CO iff CO iff ■ Iff lO Iff Iff SCJ rH -H ^ ,-. CM CO O CO Occ o CO iff CO Iff CO Iff CO •xojddy aCO rH ^ : TPiff ' j^ CM^ C^CM >* iff rr Iff ■«1« Iff D iff Iff iff iff iff «— < CO O CO o "^ Iff -^ Iff ■^ iff iff iff iff iff Iff CO iff Iff Iff Iff CQiri Iff Iff t>-co»^r»cot-.cooo CO Iff CO iff CO iff COiff Ifflfflfflfflfflfflfflff Iff QOiff Oi -^ CO Iff CO iff CO Iff iff iff Iff iff OS -r o CO Q CO r-. Iff CO O CO O CO o iff iff CO iff CO iff CO I-^lff ' " CI CO CM CO CO >* Iff ■ TT Iff -^ Iff ; iff iff Iff Iff Iff CM CO CI -^ 1—1 ^Iff Tf iff Tf iff Iff iff iff iff -l^rHlff Iff Iff Oco TT iff Iff Iff aicoost>aot^oooo COiffCOiffCOiffCOiff ifflfflfflfflfflfflfflff sSco OiCOOicoCicOQiffC Iff CO Iff CO < iff Iff Iff Iff Iff Iff iff Iff Iff. c ^CM'^CM'TfCM'^CO'' 5 -^ iff -^ S iff iff Iff iff -^ iff iff iff Iff Iff Iff coco CO -^ CM ■^ Iff Tt^ Iff TJ< Iff Iff Iff Iff Iff •^ CI Iff Iff -^ Iff rH CO O CO O t^ O I- TflffTflffTTlffM'lff' Ifflfflfflfflfflfflfflff Oir^Oi* 00 CO iff CO iff CO iff iff iff iff iff SSS; Jiff CO : -n" Iff Iff 25 Iff Iff iff iff CO Iff ■^ iff ■^ iff Tf Iff Tflff Iff Iff Iff Iff Iff ■«(Ji Iff ■^ iff Tt* iff iff iff iff iff '^ --5 Iff Iff ■V iff -^ iff Iff iff COC - - . Iff Tj< Iff Tf Iff j iff iff Iff Iff Iff ■ iffcoiffeoiff cococicocMcocMi--cMt^:r-(t-r-tooo — „ -I ... J .... .^ ^ .. -I ... .- - .^ JJ-J ^ ^^ ^ Iff Iff Iff Iff Iff X OOO iff -riff 05001 ■^ iff flff Iff Iff Iff Iff ;co^ ITf Iff -ifflff co-rcO'^cO'^co'^ ■^iffrt»cot^cp ^Iff'^lff'^lff'^lff-^lff Ifflfflfflfflfflfflfflfflfflff 00 CO 00 ■^ Iff TJ< iff Iff Iff CO 00 CD 00 CO Iff •* iff 'Tiff iff Iff Iff Iff iff ifft^-ifft^ifft-ifft-'Tr^- ■< iff -* Iff : Iff Iff. Iff -•r iff "^f iff Lff Iff Iff Iff CO CO CO CO CO Tf Iff '^ Iff f Iff Iff iff Iff Iff CO CO CO iff ■^ Iff Iff lO Iff CO CO CO CO -J* iff -T iff iff iff iff iff X CD ■rr Iff Tj« Iff Tj< Iff iff Iff Iff Iff GO CO X CD X CO — ^ iff ■^ Iff Iff Iff iff X CD X CO -riff n- Iff Iff Iff Iff iff ;si:6pit^pi:£Qico^^\^:Qp^!^ci^^^oi:^\pi^^'^pi':^^f^^z6(^r^ "3S vs t* 00 ^^"^ O r- CM '^5r^r Iff CO t^ X OS o Page 504] TABLE 10. Mean Time of Sun's Visible Rising and Setting. i § V so 01 O 5 I O^ II 0) OQ T S £ " a 3 55 .^=^ •xojadv ■xojddv S5 § ? CO CO CO CO C:i:^PCt^^:nC^a^:^z6iO^:c0^^^a!iO^^Xa^m!£p^rnP^iXiPia^P^m g*»Ci-HC0C0»HiO^t^t^Q tHCOOCOOCOO-^O-^ O -^ iC tI< tC 35 lA ift 4C lO Cc!coft5cc0^cQtfajPc5a5 0it^y5OC0C0Q- C0<— 'COC^OOCS "■ ~' '^i>-^r*'-j*t^Tj.'^t^ COC^ iM?l oit^i>-o-^^ri3"Oit>.qsococoo'©r*a>'^M tfiOTpO^O'^OCOOCO.-lCOrHCOi-HC^i-tC^IC^I a;0030'N^-^3*--5ri3o'ooccr)?p'n*co-^i-ioo ^i-H«OC0OC0OC0OC0.O"^»C'^i0' COiCCOOCOOCOOC^O ^iH?5oc^owc5c^ocojo »H»-(ascor*?Dioopc^Q >cor-.iOioooc^ooco KiCCOiTiCOiOCOOCOO ^^■^tOTfO-^t^-" Si-tC^OCJOr)065oC^ OC^OoSiCCOiOCOiCCO SScoiceO"^-^-^''?''^'^ (NGOOf-HOOCOiOiOCOOO '^'^'^lOCOiCCOiOCOiO SiMt^OOSQOOt^C^iO"^ CO iC W r>- Q 30 CO o r* c^ iQtCOSO^QOOlOt^W locoiocoicco"^'^'^-^ iC'^COCOiHOOOQrHCOCO '^'^TT'^'Tj^-vCOiOCOiC SgCOiCT-HOOXiXCSt^fH S£Tj-C0C0-^(M'X>Or-ai04l>O«pC^'-t"C0C0»Cr-i-Xi ^vCcdCtOiC^iCOiCtO iO^»CtOiC':0»COiC50 » as GO 00 OS t^OOi-tirs CO lO :0 lO CO lO ?D t^T-liCCOCO-Tf^CDQX* tncOiOCO^COiCCOiOCO coo'^M-f'^i-tt^aiOi SXCCOtC-HTfCOCOiC C^iOCOiCCOiCCOiOCO 1— It^OsCll-^i— (iCCOCOiC iCC0'c^ OC^OC^iC(N»OCOt?5cO iCCOiOCOiCCOrf'CO'^'^ iCcoco-^c^cpor^OiOs iC?0»CtO»CtOiCcO^?D lOCOiCCOOCOiCCOiOCO TfT^-COiCr-ltOOaOCftOS t^O«Pi-HiCCOCO'^C lO ?o iC ^ iC ^ COC^uOCO'^'^CO'X'C^t-* i0(0iO(0iC«0iCC0iO':0 OOOOlOlCCi-Mt^MiOCO : c^ ocC0«O"^idO iCCOiCtOiCCOiCtOiOtO >'CiCiCiC"^^COt^ooa>i-HQOc^i>.co iCcOiCOiOOiOOiOcO COtOCMt>.i-IXOai^i-* i-tiHi-ti-li-trHr-lrHOC^ iCCCiCcO^COiAtOiOCO tO"*j.c^x THrHi-l»-lrHrHr->«-1i-1i-l iCtOiCOiO':OiO<;OiO«0 •i-HOp'-i OsC^GOCOt^-^COiOiCtO rHrHi-lrHrHTHr-(i-(r-li-l iCCOiCtOiCcDiCCOiOCO '^t^COOOlNOS— lOOtH r-()-(i-lrHi-lr-(i-l(NT-ICS OCOiO^OlOCOiCCOiflCO ICOOS^OO'^t^iO *QCOfliCOOS^*^ ^.^-„^ .-_^ ^ jiTDtOiCXi'iCOiC^i-t'O i-C^iO:OiCcOiCOiOcD 3 T^ ^ CO OS >c^T-i?qc^^coQcoO'«*' ai'^ai»ooQcpi>r*tDt>- :COOCOOCOOCOOCOO C^OtMOC^OiMOC^O ^iC^iCtCiCcOiO'-Ot^tC iCtOiCCOiCcOiCtOiCcO JjOJNi-I^C^OC^OSCO iCeOiOcOiCOiOcOift-co •OOOiCOlTf*OCOOCO^-l lOCOiOcDiCcDiCCOiOtC oOTfr^io?D^iCt^-^oo i^OiOOiCtOiCCDiCCO iC?OiCCDiCtOiCtOiCCO »ift^-lTj<.— |-^COCO :cooccocoocoocoo,coocoocoocoocoo BiC(DiC:OiCcCiCOiCcOiCOiC:OiC:OiC!^iCCO OicpOSt^OOCCt^QOcOOi tOOiCi-H-t^CO(MCOCO tCt0iC«0»CC0iOtOiC«O jr^Q'-OQCOi-Hifii-liOCq.iC^'^C^-^COCOCOCO'^ :coocoocoocoocoO:Coocoocoocoocoo JiCcDiO':OiCOif5cDi^50 lOOiOcOiOCOiCcOiCCO ri -^ CI tc 1-1 cooeooco iC CO iC O iC COQcpOl^ owocoo CDiC CO lA CO Sr*aoGOooast^a>t^o iCCOiOcOiC^OiCCOiOCO *55aiaiOiCiQCOQQO»HQOrHt^i— (t^C^^OC<|yDM :c*tOcoiCcoocoocoocoocoocoocoocoo iiOiOiCvdCcO'CcOiftiCO iC cOiCcOiOcOOcOiOcO COCOiCCOiQ CO O CO O CO irj CO iC CO iC OCOOCOC5 CO »C COiC CO •^■^"fJ^lOCOlCCOcOC^COrHt^^r* " COOCOOCCOCOOCOO lOcOiCcOiCCOiCCOiCcO ii-H!Xn-HQ0»-l0a.-H0SOaS|O0". OQOiOOaQOi^-t S-TftCTriiS-'fiO'^iCi'^iCj-^iO-^OCOOCOOCOO *iOidCiO»COtCiCidOU3iCu0c0iCCOiCC0iCC0 coocoococ lO COiC CO lO C t^cccococc^iCTriCto ccocoocoocoocoo iCcDiCcDiCcOiCcOi^CO j-^Qc-^GO'^aO'^X'COGOcooDcoasc^aiMasc^o iCCOiC ?o iC COiC cOiC CO »co^*cot^co^*co^*col^^ct^lCGOlCQplCaclftap lC LO iC iC lC 00 ^ qo ^ X' lO '^ O ^ lO iC lO tO iC lO rH^HOr-IO-MCl^JOSCil ■^O'^O'^OCOOCOO iCCOiCCOiCcOiOCOiC.^ -'*«OS'*OiTtC0CSC0Oi iOS^OC'COQOCOXCOOOCpCOCOCOt^ODl^OOr^GOt* D t>- 00 1^ 00 1>- 00 r^ 00 1^ 00 r^ 00 1^ t^ t^ t-. r-- r^ f* lC lO lO ^ lA iC^ iC ^ »c iC iC ^ lO iC WcoPtHCoOiccPtHCcPtHCop^ai^tfc/itfa^SiccCtHaDD^cotfo^QScdCd rt C^ CO c^ 5^ ri cs tr^ CO r- X 31 o ^th" (M CO Hf^'^'p C4 C^rJC^JC^CO COCOCOCOCO PcHCoPCHxP^ccP^GCPcHa^ CD^ l^ ^^"^ ^ O CO CO CO CO Tf* TABLE 10. Mean Time of Sun's Visible Rising and Setting. [Page 505 s i .H e^ CO 5 ^ 00 Oi <5-^ N CO ■^ "CMC •xojddy s I aixaiaici^oixxx qjccq^ccpihssOhccp^hoq tf-fcoo*-Di^ocofaioc»rec^iO'^0'--'-'ic^o iC lO lO o rt aj OS cc 03 CO pi aj OS aj ra aj DJ MJ pi 02 c4 as as cc ■*i-H4^?5r-icoocoo->j'iOirtTi'Ocoi-i ,^-^t^'^i^'^r*'^t^Tj*t^-^t^cot^cor^coi^coGCcooocooocooocooocooocoaDcoaowoonciriOi ^•^t>-^r*-^t^-^t^-^t^ -^i^-^t^cot^cct^cor* ■^iCCOOCOOMi-Ht^Ni-HC^OCOS-TiSiS-^iO cot~coaocoocco«co«'co»coooc^aoo4aoc^oc M 1-1 e^ >-< i-i 1-1 ^ c^ 1-H c^ oc5ocoocoincoio-* .^ Tjl t>. ^ t~ ■^ t~ ^ I^ ■* t>. 'J' t^ ■>>• t^ ■* t~ CO t^ CO t~ rfS Tj" b- -.jf i> -3ir5 3' __ _ j"^'-ir-iNo6j3coin'* ?5t>-coc-eot-coaoco«.coaoeoooeoaoe^acecoi>cor*cooocooDcooocOQOcoaocoao S'QQoQcoiC'OC^wocs^iireiC'Nooosc^iOiONOiaocoeot^OJC^Tf^Oi— hjitoooe^j^gceof^c^ «o?ioc4oe^OrtrH !-n-i«T-(Oc^oc^oc4>cco>ocO'^-*-*Tic^i ^■-^r~'^t^-^c»Tft~-T)-'^t~Tj'*r~cot-cot-cot~cor»eot~eot~coaccoQOeoooeooD S*CO»OrH000QQ^COC^^ coiocoinfioMOOJO peoiceoocoin5)iOOiC"*QOOOCON-i005CCOQO>'*'^OCr-l i-(Or-irH>-lrHrtrtOO) O0)l0C0lOe0iBC0'*'»J "^ t- ■* t^ Tj< t~ CO t~ CO r~ CO t~ CO t^ CO t» CO t^ CO t^ CO GO eo 00 ■"j'S'T-itooO'^iccocqtOiOOOiOcortt^t^-^coiOlooocoiOocorJicc-i-i Tt.f-'jS'Sooo>'^'^o>o>'»eo COlOCOlOC^iCC^OlNO C^Oi-ti-lr-frHi-tf-(OC^ OC^iOC^lCCO'^COTP'^ ^co*^^£)-t^oso>t^»-'iftcocoiOf-0»QCCC^t0C0i0iOC0tOrt00 05Or~C^>O3' OM>oeo3eoiftco>ocO|iOcoinm'^'^')'-*^'s" COlOCOiCCOiS«lCC^Opl«55SOr1r1i-lri.-ci-l ^^•^TTCOiCCO^COkO r-002iiC>2'-iac«t-i C04C?IOC50PJOi-lr-( Soc^oc^oc-ioco»ccoSco35o5»5winwiO'^i-^'rr^^'n<-^'n''n'-^u5jwir5S535coSc^oc^o t^ 1-1 '*■ IH QD S'OSC^OOCOt'-lft^SD'^t^CO^i— 'QQC^GC'^^^K^t^COOS^HrHOiCOt^lS oe-)Ocsloc5oc^ONOoiOMoeoiScoiocoioco>ncoio-^'*'*'*'-iJit>-OiCC^COO>iiHrHO>COt^iO»CODCOO grHS-iriSi-ce^Ssqoc^oMoc^oe^iotNoco oeoiocoiocoincoineo i/5irii'-*ir-*ifv*S S't^eoi^r^toociftWcoo l-li-ii-lr-lr-(r1i-lrHi-l(M f)i- 00 C^i-lfJi-dNr-lMi-ifJi-l i^i-lC^i-IIMi-lSi-li-li-i ^iC too tCiC tOiO tO^ to in to lC to iA to O to lO to I^-HiHNO-U'OJiQt'O i-ie^i-ie^-^cjoiNOc< latOiCtOiCtOiCtOiOtO ?SofJOcoocooco U3tOiCtO»Oto»OtoiCto t^OOtOOiiCp^^COC^ rt^l-l1-.rt?4lHC^llH^^ iCtCiCtOiCtDLCtOiCtO C4'^i-liQOtOOOI^l--a> iCtOii^tOiC'-OiCtOtAtO SiCtor-'^osci^Qeo coiccoiftcom-rio-* ■^tO-OitO-TtO-JitO-litO lin.QS'C^Mcoputact^ oeoocoocoocoicco lOtOiCtOiCtOiCtO^tO COOSt^PiOf-l'^C^COCO rHi-li-l«i-CCMi-l6050500Qi-ir*^^t^C^tOC^iOCOiO-^ eOOCOS!NO!Ni-l?i— ik^i-KNi-KNi-iOJi-iC^i^ .^iCtOiStOiOtOiCtOiCtOiOtOiCtOtOtOiCtOiOtO rJ-iOCOtOC^t^i-IOOpoO iCtOiOtOiOtOifltOiCtO aiQ>OT}'iO"5>tccot^coi^;jt^MoC'-gpogjQO fteoocooeoocoocoo coocoocoocoOMi-i ^iCtOiCtOLStOiCtOiCtO OtOtCtOiCtOiCtOtOtO 3»oa>i-iocc^t^c^tceo 5Ni-(C^i-tC^^HC4i-t!N^ iCtOiStOiStO»J^tOi/ttO i-l?iiHC^i-ICMi-loSi-l(N lOtOlfttOiOtOiOtOiCtO tO-^iCO'^tCCOt^I^OO |C-0DO^C^ peic»POr-lO.->OrHOr-lOrHO.-IOiHOrHOi-10r-cOrHC5-HOrlO>-IOi-IO.-lO.-lO>-IOnOC^ ^!0?00?OCOtO?OtO?0 l?0<0-OtO'-0 0':CCSO:0:OCO Oi-(Oi-iOrHOSo55jOMOMO(NOOJOC10C^ ^ O O O O ^ ^ O ^ ^ 5© ^ 5fl ^^ ^ C3 ;5 tc CO !0 O ^ Or-«©f-tOi-'Oi-tOi^ S O rH O r-( O tH O rt O 1-1 O i-H O ?5 O C^ O C^ O 6l ^ ?0 CO O to <:0 O ^ O ?S ^ ;0 to CO ^ CO O to O ?0 O i-HOrHOr-^Oi-tOi-l COOOOIOCOtOCO^CO tOCOO^OCOCOCOCOCOOiOCO cooox'O^ioaaico-3'O CDCOCOCO^COtOtOCOO CO«000 CO lO CO iC CO i« CO O CO -aOoO^OOasOiCCOt^OCOfHC I »C (M -^ CO CO ■* ^cocococococococococo'cocococococococococo -iOCO^QCdOiOUOl'-O cOi— tcp?^*cco-^^coiO ^COCOCOCOCOCOCOCOCOCO COCOCOCOCOCOCOCOCOCO rJ-TfClif^f-iCOpl-QX a>XXail:^OCOi-iiO'-"CM OCIOCMOC^OC^OC^ iOOCOiCCOiCCOiCCO cOcOCOCOCOCOiCcOvOCOOcOvCCOOCOiOCOiOCOiCCO OC^Oc5»C(MiOcOiOCO COCOCOCOtOcOiOCOiOCO t^»H COC^lC co'^'^coiC'McO'-ir^ iCCOiOCOiOCOiCCOiOCOiOCO iCcO»CCOiOCOiOCOiCCO»i5CO -;oxa>o»xpt>-'-H coiM ic co^ -rcoic^co^t- ; p^ CO CO CO CO CO CO CO CO CO CO COCOCOCOCOCOCOCOCOCO Sco-^-^cococ^t^i-^xoci COiAcCiOCOiCCOiCCOiOCO kocOtCCOiOcOiCCOtCCOiCcO ptfCOCOCOCOcOcOcOCOtOCO ^COCOCOCOCOCOCOCOCOCO COCOCOCOCOCOCOCOCOCO lOCO-^-^COCOC^t^rHX COCOCOCOCOCOCOCOCOCO SaiOSOXrHCOC^lCCC C^iOCOiOCOiOCOiOCO COCCiCcOiCcOOcOvOcO ■^Tj^coicc^t^i-'ocoiaixo iCCO»OCOiCCOiCCO"^CC"rp-^ iCCOiOCOu^COiOCOiCCOiOCO OiQXf-'t-C^iOCOTP-rf iCCOiCCOiCCOOCOiCCO lOCOiOCOiCcOiOcOi^CO jxaioaxi-ico-M S*Oxq50iXor*i-iiC(N ^COCOCOCOCOCOCOCOCOCO '^'^C0>C»-cco COOiCC^-fCOI^-ffHCO ioco»ccciAoo»ocoicco iOCOiCCO»CCOif^CO^CO Oii^xoicooirtii— I'^cotN'^ "■ " "" " '■^ -^ -^ tP "^ COiC COlC CO S" X CO 1^ t^-co Oi ■3' o CO n ^(OCOCOCOCOCOCOCCCDCO rHCCp 0. t^ CO Oi C^ U5 -M lO C^ »C C^ CO lO CO lO CO iC CO ■^OCOiMC^COQTjOlCO lOCOiCcoocoiocoTrco iCCOOCOiOCOiOCOiCCO I^t>»COOi"^rHC^C^i-l'^a> '^COtJ'CO'*'^'' " — — — lO CO lO CO »0 CO t rt* Tf ^ 00 '^ CO iC CO lO CO S"t^lC^t^^XCOp^rH ^COCOCOCOCOCOCOCOCOCO gcox CO coo '^ t>. CO lO t^ -^ Oi C^ lO 1?^ iC OJ lO w CO lO CO iC CO lO CO !NQi-i(NClC0X^cOCO lOcoioeO'^co-^co-^cc lOCOiOCO^CCOiOcOiOCO : iC X CC Ol 1— i rH O CO GC Tf t>. CO '^ CO'^CO'^ COiC CCiO CO ,cifl CO lO CO iC ■tH CO -^ ^"^ CD »0 CO iTi CO ^CDCO xoir-^iCcocoTf lOCOiCCOiCCOiCCO CM COQ lO rH lO »r3 cDiC t^ X Ol CD 1-1 iC CO iH -^ r-l ^ C>» -^ CM CO iC CO lO CO lO CD lCOlflr-'t--OSXI>Ol5CM |'^c5' CO rH CO ^-( CO coo CO lO CO QJ 00 P^ CO Clj CC P^' CC p^ OD !fi4 «} p4 C» QJ CQ 0:^ GG p^ OQ 1^ cS"^~^h" cm CO -^ ifl XD t^ x"* Oi p TABLE 10. Mean Time of Sun's Visible Rising and Setting. [Page 507 a s C^ C< iM M ■aiBp •xojddv a fimPilxOicDe^CBfilXl (sjodaSajOSaQPSajP^co Or-IOiHOr-lOrH Or-I O r-( O rH O rH O i-H O r^ PJGQOjoQP^aJP^cQP^cc Oi.^OrHOi-iO.HOrH -JM-fw-i'cofco-^c^-^ n-*cj'»-Hio^iOT-iin.-iii5 jj 5S o O O O O O O O O o --0 o --o O O O O O 'O ■oo-oooooooo S' til to C^ O 5S O 2) to rH O OiHOi-IOr-lOr-IOr-l .c^tootototoootototo Oi-iOiHO-hS.-hS.-I totototstootootoo tOtOiCtOiOOiCtOOtO 0.-I0r-(0.-I0rt0i-I ^ otototototototototo ga>ooo>oo>oo>.-i tOtOtOtOtCOiOtOiCtO iCtOiOtOiOtOiOtOiOtO .cftotototototototo<>to iCMSlNiOCSiiniNiOlM iCtOiOtOiCtOiCOiOtO t^-^-O'.i'touoiou^ioto iCtOlCtOiOtOiOtOiOtO WaJWasp^cotfaJOHCo C9MMM?3C^UM01C-J"00'* ^COtOtOtOiOtOiOtOtCtO SiCI-*>Ot^tOtOtOtOt>. irstoiCiOiCtoiotoioto iOc^io(Miraoiioc^iCco lOtOiOtOiOtOiOtOiOtO lO CCU3 CO lO toio o SCO CO ic to in to lO to S'OilOCO»CQOtOt^tOl^t>- inC>lSc^lSc^>0(NiOCM ^LQOiAtOlOtOiOtOOtO S*coi^r^r*i^oQtooQicai ^>CtO»CtO»CtO»AtOirttO Sl^-toOOCOO-^OJ-^O ^jiSc^ioiMiONinco ]iOtOiCtOiCtOiCtO>i5tO lioo-'j'oco.-icie^c^co I lO CO iC CO >C CO »C CO iC CO jiCtOiAOiCtOiCtOLCtO COOCOt-iMI^i-hCMOCO lOMOCOincOOOOiCCO i^tOiOtOiOtOiCtOutltO CO ■'J' CO vn tomo GC iC t^ to t>" t-* ^ CO ".I* Co "^ CO liD to >n to »o to «"tco5to«?iOQin^'»'CJ SOC^iScOiOCOiOCOiOCO ,«»iCtOiCtOiCtOiOtOirttO COOJiMCOi-l-^QlOOtO iCCOiOCO»CCOiOCOi^CO lOtOiCtOOtOiCtOtOtO -iiO^'« iocoii5eo-^co-*cO'.i-oof^t^90t^oitoo ^CO^CO^CO^CO^f^ lOtoiCtoir^tototoicto t^oto.-iiijo)3jeoco3| LctoiotoiotointoiAto §iAcoSSSc<5ibOTiOco .«»iCtOLCtOiOtO>OtOiOtO gooo>o>goor-rHtO'M|iOco^:.r-^ioc3t5rHt^ CO ^ CO "^ "^ ^ ""S^ ^ ^ -" ~ " " — lOOiOtOLOtOiAtOiCtO t^ t- to 00 to oi ic o 3; rH tJ'CO^^COtJ^CO'^^^^ lOtOiCtOlAtOOtOiCtO lO.^^oicococ^-^i-'ijrs lOtou^toiCtointoicto e^ic^toQr*o^oooca> __ . .-^lOC^tOtHt^QOOOOOll^OtOC^i-ICO '^TI'^^lO'.J*-'^^'^.^* ^■^CO^COiOCOiOCOiO LCOOtOtf^tOiOtOi^tOu^tOU^tOiAtOiCtOiCtO jSC0i0C^t0r-lf»Oa00>05 fticco>oeoincoSco^co .<»iCtOiOtOLCtOiCtOiCtO incoSco'*cO'*^T>i'.)< ^lOOiOtOlOtOlfltOiOtO OQQt^.HtOJJiOCO-*-!' lAtOiOtOtCtOtftltOOtO '»'-<5<-9<'*^'SOei5'Ocoioeoirtco>o »CtOiGtOir5tO»r5tOlCtO»OtOiCtO»OtOlOtOiOeO to oi lO CO ■.»" 3j CO to ?J t^ I o oc o? en iftOiOtOiCOiOtOiOtO _ 00Qt~)tOrt«5>aj00i-( ■*-.)> co-*MiScoiOcoiocoiOcoiccoiO?jireoio ictoiotOiCto»i5tokato i»cto»ctoioto»otoiot* S'00^0»QOO'-t|-*'MiOCO ,aj i^ to ic to i.c to »o to *£; to ■^■.J-COiO-Mt^OXasOilgOrH iC50»^tOiOtO»CtO»OtO ;^ 00 O 1^ ^H to CO iC 2* CO iC ^i?3tOiCtO»CtOifttOii5tO C^tOrJOOOaiOCi-Ht^Ol ^^•).^COTJOOOtON COiCCOiCMiCoSOC^O tctoiotoutitotot^icr* r-l0OO»Ol«O.-ltOCO'»'3l lOtOii^tOiCt^i/^t^iOt* 0Qi-ltO«>->"2'C-ltO-^CO S 31 CO to .-I OCMOO ) i> in r- lO CCOJOt^iH t>-in t*ict^ •cjiotoiotoictointointo QCi-itoc-ii/jcocoice^t^ coiocotneoiccoincoo iotoLOtoLCto>nto>cto Qcoooot^ojioeocoic eoioc^oi^oojoe^o iOo»ot^iot^iot^»nr» r^coini-ttooooGocii^^H 55^^Tj<^.q«TT"cO^COiO •cjictoictoictoictointo coiccoiocoincoicc- in i^ ic t^ • oinrjco jt~-ini^in ■*i-nogao r-inr-int- S'<-itpasr>"t>-oito^H-.*j-int*iOt*int^ ■.fcOf-iinoat^r-Oiinji ■IrHi-lO D t^in t^ in in t^ in t^ O^ioOOtO^-l'THC^CC MOi-lOrHOrH,-lr-lf-l int*int»im--int^int» o>int^ooinocje< Oi-IO>HO ic t^ in t-* in c^ £> c4 o S t-*in t>-in t^ 2 I «« •xoiddy rfiin XMOJi-l ^ CO ^ CO toin oio mwSSin to in to in to tOtO-»'COC^OO'N002'' in to in to in r* in t^ in t^ j-n^ooc^^^ocot^inin >iHOi-HT-li-lTHOrHO • int^int^int~"ioi> iin r«.io t»in CO i^ in in 00 c^in c^ in c^ CO ^in to in to in c^ to CO ■^ m iniin to in to in to c^i^ooiooi-itoco'^in c^ine5inr-ioi-iorHo lOtoictoinc^int^int^ ootoo-^ tomtom e^iM-^ioto mNinc^m to m to m to S?}^S^S s tomtom Stoo-*^ r^m rH m tom tom to i-lOrH m r*m .H O rH O rH O T-< t^m t^m t*m t^ )Oi^c^inmo«»a>o >cjmo)mc>»miM'Vco ^ T}< t~ .* t^ m t^-n* t^-^ xaotoQ-^c^i-i-a'Oto i-HmrHOi-lOi-IOOO mtomt~-mt^mt~mi> 23S8S r«.Oift CO tM ic 000000 iOtOiCtOiCt^tOt>id:>- mt^m 1-1 C^ •.Ji o> to t- o> I— tOrnmi— tmr-i t^ m t~ -^ r» -^ t^ -r-tC^-^Olt^tOOCOCO jiMmiN-a" e li' t~ 1-* 00 o m CO (M coco coco t^ ■^ t^ ^ l^ 3*mi— icocOTHm^t>»t^o rfS'm torn torn Tfin.-i momommmino mtomtomto-^to-^t^ co-fo mom O ^ O ^ i.^ ^ i-H 1^ ■* r~ ■^ t» ■^ t~ McKOJoQQ^aaajccKccpHKP^copjccPJccPdcc to t^ 00 a> ^5^ ^ cS~c5 ■.»' m c^fje^cico cocococoeo > I^ to oco (i-HCOlNCO < l~. Tf t^ -.J" .^ ■* I- ■* t~ »5coe3c»OHa3P:5cca3ai Page 508] J3 ! •^ s. ^ a TABLE 10. Mean Time of Sun's Visible Rising and Setting. .iSaJ cojdd dv MOQPJQQpliCQtfa^OHCC p; OS B< OQ PlJ CO tf Ui 04 OQ -^ u5 ic to ^ l6 ic Oscopjccpjccp^cntfccfficcKaiajcnpHcctfco 0<-tO<-iOi-iOr-lOrt ^-j.O'J'O^QUSOiO Oi-iO>HC>>-l*i-(OrH O t— t O rH lO rl lO F-^ »C I-H UO i.^ lO ^H IC rl in ?H lO f-i iO*-*iCtHiOi— »lOC4l«C^ ^t0OC0;0»0Ou'3t0i0<0UCOiCeCiC?Di0O»C?0 iCtOiCOiCeO»OtO»0?0 lO?Oi050iC«OiC5CiC«0 S•^•,_lt~,Hto.-lOe^t©e^lnNlOeo■^elS^T^<•5l■^c5•a5ocg>«o u5c^>ocr ^l/5«OiOOiCtO»COiC0«OiOtOi0^iO^ S"C3>-C0OC^rH •^CO'^CO"^CO'V^'^--y .^iO^i0:0iC^»Ot0iOec i-ic<©coo>^oou5r»o ^Tj^^^co^co^cO'^ I0^i0«0i0*^l0t0i0«0 ®«ico>cooc^i-(i-ieo M'<»-CO X t>-CO OS rHOi-lO lOt'-iot^iOt^ioc^ict* S'O^OOit^COOOt^OliOO -^fHCOCOiH^Q^OOt^ t^OJiOOCOC^C^I'g'O^pOCQOtCO'^C^I^H-^CStD •^■^CO-^CO-n'CO'^COiC COiCCOiCCOlAcOirSC^iC C^iCT^OrJOC^OfMON-lOi-trrtT-tT-Hr^r-lOi-l ^i05Cio«oiceoic«ovc«o»ccoiotoic«»oo»cto»coiCt^ict^iCt^icr^ict^iOr*ici>ict^ict^ ~" r-Q tc th ■* oi cocoes ico to oicot^oiio^'* CO M^jo-^p 0000 too-* C<1 SC04ScOi^CCiOCOlCCOiCCOlOC^iCC^iCnOC>10|T^OC^OfHOi-lr-tr-l^ ^ictoicoictoiotoictoictoiotoictoict^ict^ict^ict^irsi^iftc^ict^ i-lrti-HrtOrHOCMOlN ic r^ »m^ o t> ic t^ ic t^ g'e0'7'r^>c^t>.osooooo eoineoicccioc^ioejo ^lOtoiocDirstoiotoict^ tOf-i-fcocoic^Htpoaoor*oioc^co-*r-itoasai' coinc-i>cc^oe^ono c^oc^Oi-iOi-i^i-ii-i ^ lO to lO to »o i^ ic t^ ic t^ ic t^ lO t^ tc !> lO r* »o t* :i-HCO-?-oa>ocotDS^'<»<'flt-wiC'^Mtoo>g>t^c>) (NiOCOiCCOiCCO-^'^ ■>J>>lDO0Ct~MC0iCO01 »OCOiOCO-^'^"OT-lt^O»0>t~C^'ai-*Mr~OS05tSCMCOii5QOO C40CSOi-lO>Hrtr^rt|rHrH.-lt-lO.-lOCaOC^OCJi054i5cOiCCOiCM ^ict^»ot^»ot~-»ct*icr- |iot^>ot*ioi>»ot— lot* iOt^'*t~-»Ot*iCt^iCt^iOt* ^i-^CJt^OlQtOMCOiC i^CO-^M^^Tf-^-^fCOiC cotoasOTf^ajoivc-^ COiSC^OC^OrHOrtiH ■»l't^'»(<00'^00'^CiOTj<00 OJOit^'M-^iOf-'OQOOrH ICC^IOCOIOCOIOCO-^-^ ■oco ■^■^i-ltO«CJ>iOCO'MtO lOCOiCCO'^CO'J'-^-^'V co-^mScoiOc^ocJo XOCOiCXO^iCt^^ t-i»-(r-(»-(OC^OC^iCCO ■>*i«-^00'*WM<00COO0 ft©M ©C^iO i>r-OJ'^ !N Seoioco t^ -.J" t>- r)l r- wxiC'-ioi'*O5 00iC>-; ■^CO^^^^CO^COiO Minooos-^corotinTa C0iC-'rc^3it^cocot^© i-iT-iOc^icc^iCco-^-r ■*0CT><«COaCCOOCC0 00 OS O iC CO C^ to Oa TABLE 11. [Page 509 For reducing the Time of the Moon's passage over the Meridian of Greenwich to the Time of its pass- 1 age over anv other Meridian. The numbers taken from this Table are to be added to the Time at 1 Greenwich in West Longitude, subtracted in East Longitude. Longi- tude. Daily variation of the moon's pa.ssing the meridian. Longi- tude. 40" 42m 44m^ 46m 48™ oO-» 52" 64m 66" 68" 60" 1 62" i 64" 66" o m. m. m. m. ■m. TO. TO. TO. TO. TO. TO. TO. 1 TO. TO. o ! : 5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 10 1 1 1 1 1 1 1 1 2 2 2 1 2 ■■ 2 2 10 15 2 2 2 3 2 2 2 2 2 2 2 3 3 3 15 20 2 2 2 2 3 3 3 3 3 3 3 3 4 4 20 25 3 3 3 3 3 3 4 4 4 4 4 4 4 5 25 30 3 3 4 4 4 4 4 4 5 5 5 5 5 5 30 35 4 4 4 4 5 5 5 5 5 6 6 6 6 6 35 40 4 5 5 5 5 6 6 6 6 6 7 7 7 7 40 45 5 5 5 6 6 6 6 7 7 7 7 8 8 8 45 50 6 6 6 6 7 7 7 7 8 8 8 9 9 9 50 55 6 6 7 7 7 8 8 8 9 9 9 9 10 10 55 60 7 7 7 8 8 8 9 9 9 10 10 10 11 11 60 65 7 8 8 8 9 9 9 10 10 10 11 11 12 12 65 70 8 8 9 9 9 10 10 10 11 11 12 12 12 13 70 75 8 9 9 10 10 10 11 11 12 12 12 13 13 14 75 80 9 9 10 10 11 11 12 12 12 13 13 14 14 15 80 85 9 10 10 11 11 12 12 13 13 14 14 15 15 16 85 90 10 10 11 11 12 12 13 13 14 14 15 15 16 16 90 95 11 11 12 12 13 13 14 14 15 15 16 16 17 17 95 100 11 12 12 13 13 14 14 15 16 16 17 17 18 18 100 105 12 12 13 13 14 15 15 16 16 17 17 18 19 19 105 110 12 13 13 14 15 15 16 16 17 18 18 19 20 20 110 115 13 13 14 15 15 16 17 17 18 19 19 20 20 21 115 120 13 14 15 15 16 17 17 18 19 19 20 21 21 22 120 125 14 15 15 16 17 17 18 19 19 20 21 22 22 23 125 130 14 15 16 17 17 18 19 19 20 21 22 22 23 24 130 135 15 16 16 17 18 19 19 20 i 21 22 22 23 24 25 135 140 16 16 17 18 19 19 20 21 1 22 23 23 24 25 26 140 145 16 17 18 19 19 20 21 22 ' 23 23 24 25 26 27 145 150 17 17 18 19 20 21 22 22 i 23 24 25 26 27 27 150 155 160 17 18 19 20 21 21 22 22 23 i 24 25 26 27 28 28 155 18 19 20 20 22 23 24 1 25 26 27 28 28 29 160 165 18 19 20 21 22 23 24 1 25 i 26 i 27 27 28 29 30 165 170 19 20 21 22 23 24 25 25 26 27 28 29 30 31 170 175 19 20 21 22 23 24 25 26 27 1 28 29 30 31 32 175 180 20 21 22 23 24 25 26 ! 27 28 1 29 1 30 31 32 33 180 40m 42in 1 44". 1 46"- 4S"> 1 60" 52" 64" I 66" 1 68" 60" 62" 64" 66" Page 510] TABLE 12. For finding the Variation of the Sun'e 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. 1 2 3 4 5 6 7 8 9 10 Horary motion. M. 1" 2" 8" .4" 5" 6" 7" 8" 9" 10" 11" 12" 13" 14" 15" 16" 17" 18" 19" 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 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 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 7 7 7 7 7 -. 1 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 5 5 5 5 5. 5 5 5 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 8 8 8 8 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 5 6 6 6 6 6 6 6 7 7 7 7 7 7 8 8 8 8 8 8 8 9 9 9 9 2 2 I 2 2 3 3 3 3 3 3 4 4 4 4 4 t 5 5 5 5 5 6 6 6 6 6 6 7 7 7 7 7 7 8 8 8 8 8 8 9 9 9 9 9 9. 10 10 10 10 2 2 2 2 2 3 3 3 3 3 3 4 2 2 2 2 2 3 3 3 3 3 4 4 4 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 4 5 1 1 1 1 2 2 2 2 3 1 1 1 1 2 2 2 2 3 1 1 1 1 1 1 1 2 1 1 1 2 2 2 3 3 3 3 4 4 4 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 • 18 19 20 2 2 2 3 3 2 2 2 3 3 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 1 1 2 2 2 2 2 2 2 2 2 2 2 3 3 3 4 4 4 4 5 5 5 3 3 3 4 4 3 3 4 4 4 3 4 4 4 5 4 5 5 5 5 5 5 5 5 6 5 5 5 6 6 5 5 6 6 6 4 4 4 4 5 5 5 5 5 6 6 6 6 6 6 7 7 7 7 7 8 8 8 8 8 8 9 9 9 9 9 10 10 10 10 10 10 11 11 11 4 4 5 5 5 5 5 6 6 6 6 6 7 7 7 7 7 8 8 8 8 8 9 9 9 9 9 10 10 10 10 10 11 11 11 11 11 12 12 12 5 5 5 5 5 6 6 6 6 7 7 7 7 7 8 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 - 5 5 5 6 6 6 6 7 7 7 7 7 8 8 8 8 9 9 9 9 10 10 10 10 11 11 11 11 11 12 12 12 12 13 13 13 13 14 14 14 5 6 6 6 6 7 7 7 7 8 8 8 8 9 9 9 9 10 10 10 10 11 11 11 11 12 12 12 12 13 13 13 13 14 14 14 14 15 15 15 6 6 6 6 7 7 7 7- 8 8 8 9 9 9 9 10 10 10 10 11 11 11 11 12 12 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 26 27 28 29 30 7 8 8 8 9 8 8 8 9 9 8 9 9 9 10 31 32 33 34 35 9 9 9 10 10 10 10 11 11 11 9 10 10 10 11 10 10 10 11 11 31 32 33 34 35 36 37 38 39 40 11 11 11 12 12 11 12 12 12 13 36 37 38 39 40 41 42 43 44 45 41 42 43 44 45 •} 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 12 12 12 12 13 12 13 13 13 14 13 13 14 14 14 46 47 48 49- 50 51 52 53 54 55 56 57 58 59 60 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 12 13 13 13 13 14 14 14 14 15 15 15 15 16 16 13 13 14 14 14 14 14 14 15 15 15 15 15 16 16 16 16 17 17 17 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 14 15 15 15 16 16 16 16 17 17 15 16 16 16 17 17 17 17 18 18 18 18 18 19 19 TABLE 12. [Page 511 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" 24" 25" 26" 27" 28" 29" 80" 81" 82" 88" 84" 85" 86" 1 2 3 4 5 1 1 1 2 2 3 3 3 1 1 1 2 2 2 3 3 4 1 1 1 2 2 3 3 3 4 1 1 2 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 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 16 17 18 19 20 4 4 4 5 5 5 6 6 6 7 4 4 5 5 5 6 6 6 7 7 7 8 8 8 9 9 9 10 10 11 11 11 12 12 12 13 13 13 14 14 4 4 5 5 6 6 6 7 7 7 8 8 8 9 9 10 10 10 11 11 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 4 5 5 5 6 4 5 5 6 6 5 5 5 6 6 5 5 6 6 7 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 7 8 9 6 7 8 8 9 7 7 8 8 9 11 12 13 14 15 6 7 7 7 8 8 8 9 9 10 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 6 7 7 8 8 8 9 9 10 10 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 7 7 8 8 8 7 7 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 11 12 12 13 13 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 9 9 9 10 10 10 11 11 11 12 12 12 13 13 13 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 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 31 32 33 34 35 36 37 38 39 40 11 11 12 12 13 13 13 14 14 15 15 15 16 16 17 11 12 12 13 13 13 14 14 15 15 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 14 14 15 15 16 14 15 15 16 16 15 15 16 16 17 16 16 17 17 18 16 17 17 18 18 19 19 20 20 21 17 17 18 18 19 19 20 20 21 21 17 18 18 19 19 20 20 21 21 22 18 18 19 19 20 20 21 22 22 23 18 19 19 20 20 21 22 22 23 23 19 19 20 20 21 22 22 23 23 24 16 16 16 17 17 16 17 17 18 18 17 17 18 18 19 17 18 18 19 19 18 19 19 20 20 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 17 18 18 18 19 19 20 20 20 21 18 18 19 19 20 20 20 21 21 22 18 19 19 20 20 21 21 22 22 23 23 23 24 24 25 19 20 20 21 21 20 20 21 21 22 21 21 21 22 22 22 22 23 23 23 22 22 23 23 24 23 23 24 24 25 2Z 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 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 25 26 26 27 28 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 21 22 22 23 23 22 23 23 23 24 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 31 32 32 31 31 32 32 33 51 52 53 54 55 56 57 58 59 60 19 19 19 20 20 20 20 20 21 21 21 21 21 22 22 21 22 22 23 23 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 Page 512] 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. I 2 3 4 5 6 7 8 9 10 87" 88" 89" 1 1 2 3 3 40" 1 1 2 3 3 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 41" 42" 48" 44" 45" 46" 47" 48" 49" 50" 51" 52" 58" 1 2 3 4 5 1 1 2 2 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 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 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 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 8 8 9 10 10 11 12 12 13 14 14 15 16 16 17 18 18 19 20 21 21 22 23 23 24 4 5 6 6 7 8 8 9 10 11 11 12 13 13 14 15 15 16 17 18 18 19 20 20 21 4 5 6 6 7 4 5 6 7 7 5 5 6 7 8 5 5 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 11 12 13 14 15 8 9 9 10 11 11 12 13 14 14 15 16 16 17 18 19 19 20 21 22 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 13 14 15 16 17 11 12 13 14 14 15 16 17 10 10 11 12 13 10 11 11 12 13 11 12 13 14 15 16 17 18 19 20 10 10 11 12 12 12 12 13 14 15 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 14 15 16 16 17 14 15 16 17 18 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 13 14 14 15 15 16 17 17 18 19 15 16 17 18 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 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 31 32 33 34 35 19 20 20 21 22 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 29 30 30 31 32 25 26 27 28 29 26 27 28 28 29 30 31 32 33 33 26 27 28 29 30 31 31 32 33 34 27 28 29 29 30 27 28 29 30 31 32 33 34 34 35 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 22 23 23 24 25 25 26 27 27 28 '28 29 30 30 31 31 32 33 33 34 35' 35 36 36 37 24 25 25 26 27 27 28 29 29 30 31 31 32 33 33 34 35 35 36 37 37 38 39 39 40 25 25 26 27 27 28 29 29 30 31 31 32 33 33 34 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 31 32 33 31 32 33 34 35 36 37 38 39 40 29 29 30 31 32 32 33 34 34 35 29 30 31 32 32 33 34 34 35 36 30 31 32 32 33 31 32 32 33 34 31 32 33 34 35 32 33 34 34 35 36 37 38 38 39 33 34 34 35 36 33 34 35 36 37 34 35 36 37 38 35 36 37 37 38 39 40 41 42 43 36 36 37 38 39 40 41 42 42 43 36 37 38 39 40 41 42 42 43 44 41 42 43 44 45 46 47 48 49 50 34 34 35 36 37 35 35 36 37 38 35 36 37 38 38 37 38 38 39 40 38 38 39 40 41 38 39 40 41 42 35 36 36 37 38 "38 39 40 40 41 36 36 37 38 39 39 40 41 41 42 37 37 38 39 39 40 41 42 42 43 37 38 39 40 40 38 39 40 41 41 39 40 41 41 42 40 41 42 42 43 41 42 42 43 44 42 42 43 44 45 43 43 44 45 46 43 44 45 46 47 44 45 46 47 48 45 46 47 48 49 51 52 53 54 55 56 57 58 59 60 41 42 43 43 44 42 43 44 44 45 43 44 44 45 46 44 45 45 46 47 45 46 46 47 48 46 47 47 48 49 47 48 48 49 50 48 48 49 50 51 49 49 50 51 52 49 50 51 52 53 56 57 58 59 60 TABLE 12. [Page 513 For finding the Variation of the Sun's Kight Ascension or Declination, or of the Equation of Time, in 1 any number of minutes of time, the Horary Motion bemg 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 1 Moon's Declination or Right Ascension in seconds of time. the motion in one minute being given 1 at the top, and the numbers in the side column being taken for seconds 1 M. Horary motion M. 54" 66" 1 66" 1 1 5S" 1 69" 1 60" 61" 02" 6S" 64" 65" 66" 67" 68" 69" 70" 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 9 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 4 5 5 5 5 6 5 5 5 5 5 5 5 6 5 6 6 6 6 6 5 6 5 6 6 6 6 6 6 6 6 7 - 7 7 7 7 7 6 7 6 6 ! 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 7 8 7 7 7 8 8 8 8 8 8 8 9 9 9 9 9 9 9 8 9 8 8 8 9 9 9 9 9 9 9 10 10 10 10 10 10 11 9 10 11 9 10 9 10 9 10 10 10 10 11 10 10 10 10 11 11 12 11 11 11 11 12 12 10 11 11 11 11 12 12 12 12 12 13 13 11 12 11 11 11 11 12 12 12 12 12 13 13 13 13 13 14 14 14 12 13 12 12 12 12 13 13 13 13 13 14 14 14 14 15 15 15 15 13 14 13 13 13 13 14 14 14 14 14 15 15 15 15 16 16 16 16 14 15 14 14 14 15 14 15 14 15 15 15 15 15 16 16 16 16 17 17 17 17 18 15 16 16 15 16 16 16 17 17 17 17 18 18 18 18 19 17 15 16 16 16 16 17 17 17 18 18 18 18 19 19 19 20 20 17 18 16 17 17 17 17 18 18 18 19 19 19 20 20 20 20 21 21 18 19 17 17 18 18 18 19 19 19 20 20 20 21 21 21 22 22 22 19 20 18 18 19 19 20 19 20 20 20 21 21 21 22 22 22 23 23 23 20 21 21 19 19 20 20 21 21 21 22 22 22 23 23 23 24 24 25 22 20 20 21 21 21 22 22 22 23 23 23 24 24 25 25 25 26 22 23 21 21 21 22 22 23 23 23 24 24 25 25 25 26 26 26 27 23 24 22 22 22 23 23 24 24 24 25 25 26 26 .26 27 27 28 28 24 25 23 23 23 24 23 24 24 25 24 25 25 25 25 26 26 27 27 28 28 29 28 29 29 30 29 25 26 26 26 26 27 27 28 28 29 30 26 27 24 25 25 26 26 27 27 27 28 28 29 29 30 30 31 31 32 27 28 25 26 26 27 27 28 28 28 29 29 30 30 31 31 32 32 33 28 29 26 27 27 28 28 29 29 29 30 30 31 31 32 32 33 33 34 29 30 31 27 28 28 28 28 29 29 29 29 30 30 30 30 31 31 31 32 32 33 33 33 34 34 35 35 30 32 32 33 34 34 35 35 36 36 31 32 29 29 30 30 31 31 32 33 33 34 34 35 35 36 36 37 37 32 33 30 30 31 31 32 32 33 34 34 35 35 36 36 37 37 38 39 33 34 31 31 32 32 33 33 34 35 35 36 36 37 37 38 39 39 40 34 35 36 32 32 32 33 33 34 33 34 M 35 34 35 35 36 36 37 36 37 37 37 38 39 39 40 39 40 41 40 41 41 42 35 38 38 40 36 37 33 34 35 35 36 36 37 38 38 39 39 40 41 41 42 43 43 37 38 34 35 I 35 36 37 37 38 39 39 40 41 41 42 42 43 44 44 38 39 35 36 i 36 37 38 38 39 40 40 41 42 42 43 44 44 45 46 39 40 36 37 37 38 I 38 38 39 39 40 39 40 40 41 41 42 41 42 42 43 43 44 45 45 46 46 47 47 48 40 41 41 37 43 44 44 45 46 42 38 39 1 39 40 41 41 42 43 43 44 45 46 46 47 48 48 49 42 43 39 39 40 41 42 42 43 44 44 45 46 47 47 48 49 49 50 43 44 40 40 1 41 42 43 43 44 45 45 46 47 48 48 49 -50 51 51 44 45 46 41 41 41 42 42 43 43 44 44 44 44 45 45 46 46 47 47 48 49 49 50 51 50 51 51 52 52 53 53 54 45 47 48 48 50 46 47 42 43 44 45 45 46 47 48 49 49 50 51 52 52 53 54 55 47 48 43 44 45 46 46 47 48 49 50 50 51 52 53 54 54 55 56 48 49 44 45 46 47 47 48 49 50 51 51 52 53 54 55 56 56 57 49 50 51 45 46 46 47 47 48 48 48 48 49 49 50 50 51 51 52 53 53 54 53 54 55 56 56 57 58 59 58 60 50 51 52 54 55 57 58 52 47 48 49 49 50 51 52 53 54 55 55 56 57 58 59 60 61 52 53 48 49 49 50 51 52 53 54 55 56 57 57 58 59 60 61 62 53 54 49 50 50 51 52 53 54 55 56 57 58 59 59 60 61 62 63 54 55 56 50 50 50 51 51 52 52 53 53 54 54 55 55 56 56 57 57 58 58 59 60 61 61 6'2 61 63 62 63 63 64 64 65 55 56 59 60 57 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 57 58 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 58 59 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 59 60 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 60 22489 -(18- Page 514] 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. 71" 72" 1 2 4 5 6 7 8 10 11 12 13 14 16 17 18 78" 1 2 4 5 6 74" 76" 76" 77" 78" 79" 80" 81" 82" 88" 84" 85" 86" 87" 1 2 3 4 5 1 2 4 5 6 f 2 4 5 6 1 3 4 5 6 1 3 4 5 6 1 3 4 5 6 1 3 4 5 7 1 3 4 5 7 1 3 4 5 7 1 3 4 5 7 1 3 4 5 7 1 3 4 6 7 1 3 4 6 7 1 3 4 6 7 1 3 4 6 7 1 3 4 6 7 1 2 3 4 5 6 7 8 9 10 7 8 9 11 12 7 9 10 11 12 13 15 16 17 18 19 21 22 23 24 26 27 28 29 30 32 33 34 35 37 38 39 40 41 43 44 45 46 47 49 50 51 52 54 55 7 9 10 11 12 8 9 10 11 13 8 9 10 11 13 8 9 10 12 13 8 9 10 12 13 8 9 11 12 13 8 9 11 12 13 8 9 11 12 14 8 10 11 12 14 8 10 11 12 14 8 10 11 13 14 9 10 11 13 14 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 14 15 16 17 19 14 15 16 18 19 14 15 16 18 19 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 16 18 19 21 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 21 22 23 25 20 21 23 24 25 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 25 26 28 22 24 25 27 28 23 24 26 27 28 23 24 26 27 29 23 25 26 28 29 16 17 18 19 20 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 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 35 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 35 31 32 33 34 36 37 38 39 40 41 33 34 35 36 38 33 34 35 37 38 33 34 35 35 36 36 37 38 39 39 34 36 37 38 40 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 39 40 41 43 44 45 46 48 49 ^0 51 53 54 55 56 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 45 46 48 49 44 45 47 48 50 44 46 47 49 50 45 46 48 49 51 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 43 44 45 46 47 49 50 51 52 53 54 56 57 58 59 60 62 63 64 65 '66' 67 69 70 71 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 50 51 53 54 55 50 52 53 55 56 51 52 54 55 57 52 53 54 56 57 52 54 55 57 58 36 37 38 39 40 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 56 57 59 60 62 57 58 59 61 62 57 59 60 62 63 58 60 61 62 64 59 60 62 63 65 59 61 62 64 65 41 42 43 44 45 56 57 58 60 61 62 63 64 66 67 68 69 71 72 73 57 58 59 60 62 63 64 65 67 68 69 70 72 73 74 58 59 60 61 63 64 65 66 68 69 70 71 73 74 75 58 60 61 62 63 59 60 62 63 64 60 61 62 64 65 66 68 69 70 72 61 62 63 65 66 67 68 70 71 72 61 63 64 65 67 68 69 71 72 73 62 63 65 66 68 69 70 72 73 74 63 64 66 67 68 70 71 72 74 75 64 65 66 68 69 71 72 73 75 76 64 66 67 69 70 7l 73 74 76 77 65 67 68 69 71 66 67 69 70 72 67 68 70 71 73 46 47 48 49 50 51 52 53 54 55 65 66 67 68 70 65 67 68 69 71 72 74 75 77 78 73 75 76 77 79 74 75 77 78 80 56 57 58 59 60 71 72 73 75 76 72 73 74 76 77 73 74 75 77 78 74 75 76 78 79 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 85 80 82 83 85 86 81 83 84 86 87 56 57 58 59 60 TABLE 12. [Page 515 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 cohmm. 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. 1 M. 88" 89" 90" 91" 92" 98" 94" 95" 96" 1 97" 98" 99" 100" 101" 102" 103" 104" 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 1 3 4 6 7 9 10 12 13 15 16 18 19 21 22 23 25 26 28 29 31 32 34 35 37 1 3 4 6 7 9 10 12 13 15 16 18 19 21 22 24 25 27 28 30 31 33 34 36 37 39 40 42 43 45 2 3 5 6 8 9 11 12 14 15 17 18 20 21 23 24 26 27 29 30 32 33 35 36 38 39 41 42 44 45 2 3 5 6 8 9 11 12 14 15 17 18 20 21 23 24 26 27 29 30 32 33 35 36 38 2 3 5 6 8 9 11 12 14 15 17 18 20 21 23 25 26 28 29 31 32 34 35 37 38 2 3 5 6 8 9 11 12 14 16 17 19 20 22 23 2 3 5 6 8 2 3 5 6 8 2 3 i 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 10 12 14 15 17 2 3 5 7 9 1 2 3 4 5 6 7 8 9 10 9 11 13 14 16 17 19 20 22 24 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 16 17 17 19 21 22 24 18 19 21 22 24 18 19 2i 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 27 29 31 32 34 19 21 22 24 26 19 21 23 24 26 11 12 13 14 15 25 26 28 29 31 33 34 36 37 39 25 27 28 30 31 25 27 29 30 32 26 27 29 30 32 26 27 29 31 32 26 28 29 31 33 34 36 38 39 41 26 28 30 31 33 35 36 38 40 41 27 28 30 32 33 27 29 30 32 34 27 29 31 33 34 28 29 31 33 35 16 17 18 19 20 33 34 36 38 39 33 35 36 38 40 34 35 37 38 40 34 36 37 39 40 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 38 40 41 43 44 39 41 42 44 46 40 41 43 44 46 40 42 43 45 47 41 42 44 45 47 41 43 44 46 48 42 43 45 461 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 26 27 28 29 30 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 47 49 50 52 53 55 56 58 59 61 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 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 61 62 64 65 67 68 70 71 73 74 62 63 65 66 68 69 71 72 74 75 62 64 65 67 68 70 71 73 74 76 63 64 66 67 69 71 72 74 75 77 T8~ 80 81 83 84 86 87 89 90 92 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 67 69 70 72 73 71 73 74 76 78 79 81 82 84 85 87 88 90 91 93 72 74 75 77 78 80" 81 83 85 86 88 89 91 92 94 73 74 76 78 79 74 75 77 78 80 74 76 78 79 81 75 77 78 80 82 76 78 79 81 83 77 78 80 82 83 85 87 88 90 92 77 79 81 82 84 78 80 82 83 85 79 81 82 84 86 80 81 83 85 87 46 47 48 49 50 51 52 53 54 55 51 52 53 54 55 56 57 58 59 60 75 76 78 79 81 82 84 85 87 88 76 77 79 80 82 83 85 86 88 89 77 78 80 81 83 84 86 87 89 90 77 79 80 82 83 85 86 88 90 91 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 86 88 89 91 93 87 88 90 92 94 88 89 91 93 94 88 90 92 94 95 8J 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 Page 516] 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, anH the number of minutes of time in tlie 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. 1 2 3 4 5 Horary motion. M. 105" 106" 107" 108" 109" 1 110" f 111" 112" 113" 114" 115" 116" 117" 118" 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 13 14 15 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 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 n 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 44 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 51 53 55 48 50 52 54 56 49 50 52 54 56 49 51 53 55 57 49 51 53 55 57 50 52 54 56 58 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 31 32 33 34 35 54 56 58 60 61 63 65 67 68 70 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 65 58 60 62 63 65 58 60 62 64 66 59 61 63 65 67 59 61 63 65 67 60 62 64 66 68 60 62 64 66 68 61 63 65 67 69 36 37 38 39 40 64 65 67 69 71 64 66 68 70 71 65 67 68 70 72 74 76 77 79 81 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 72 74 75 77 79 72 74 76 78 80 73 75 77 78 80 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 46 47 48 49 50 81 82 84 86 88 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 98 100 102 103 105 90 92 94 95 97 99 101 102 104 106 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 60 100 102 103 105 107 101 103 104 106 108 102 104 105 107 109 103 105 106 108 110 104 105 107 109 111 105 106 108 110 112 105 107 109 111 113 106 108 110 112 114 107 109 111 113 115 108 110 112 114 116 109 111 113 115 117 110 112 114 116 118 56 57 58 59 60 TABLE 12. [Page 517 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" 180" 131" 132" 1 2 3 4 5 6 7 8 9 10 2 4 6 8 10 12 14 16 18 20 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 11 2 4 6 8 11 2 4 6 9 11 2 4 6 9 11 2 4 7 9 11 2 4 7 9 11 2 4 7 9 11 1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 12 14 16 18 20 12 14 16 18 20 12 14 16 18 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 22 24 26 28 30 22 24 26 28 30 22 24 26 28 30 22 24 26 28 31 33 35 37 39 41 43 45 47 49 51 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 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 61 63 65 67 69 32 34 36 38 40 42 44 46 48 50 32 34 36 38 40 42 44 46 48 50 33 35 37 39 41 43 45 47 49 51 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 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 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 65 67 69 71 74 55 57 59 61 64 66 68 70 72 74 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 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 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 41 42 43 44 45 71 73 75 77 79 72 74 76 78 80 73 75 77 79 81 73 75 77 79 81 83 85 87 89 92 94" 96 98 100 102 104 106 108 110 112 74 76 78 80 82 84 86 88 90 92 94 96 98 100 103 105 107 109 111 113 74 76 79 81 83 85 87 89 91 93 75 77 79 81 83 76 78 80 82 84 76 78 80 83 85 77 79 81 83 85 u 80 82 84 86 78 80 82 85 87 79 81 83 85 87 79 81 84 86 88 36 37 38 39 40 81 83 85 87 89 82 84 86 88 90 83 85 87 89 91 85 88 90 92 94 86 88 90 92 95 87 89 91 93 95 87 90 92 94 96 88 90 92 95 97 89 91 93 95 98 90 92 94 96 98 90 92 95 97 99 101 103 106 108 110 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 91 93 95 97 99 101 103 105 107 109 92 94 96 98 100 93 95 97 99 101 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 46 47 48 49 50 102 104 106 108 110 103 105 107 109 111 105 107 110 112 114 106 108 110 113 115 107 109 111 113 116 108 110 112 114 116 109 111 113 115 117 110 112 114 116 118 111 113 115 117 119 111 114 116 118 120 112 114 117 119 121 51 52 53 54 55 56 57 58 59 60 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 Page 618] 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 l)eing given at the top of the page in seconds, and the number of minutes of time in the side cohimn. 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. 188" 134" 2 4 7 9 11 185" 186" 4 187" 188" 189" 140" 141" 142" 148" 144" 145" 146" 1 2 3 4 5 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 6 7 8 9 10 13 16 18 20 22 13 16 18 20 22 14 16 18 20 23 14 16 18 20 23 14 16 18 21 23 14 16 18 21 23 14 16 19 21 23 14 16 19 21 23 14 16 19 21 24 14 17 19 21 24 14 17 19 21 24 14 17 19 22 24 15 17 19 22 24 15 17 19 22 24 6 7 8 9 10 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 35 26 28 30 33 35 26 28 31 33 35 26 28 31 33 36 26 29 31 33 36 26 29 31 34 36 27 29 31 34 36 27 29 32 34 37 11 12 13 14 15 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 50 53 55 58 60 51 53 56 58 60 51 54 56 58 61 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 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 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 75 78 80 83 85 36 37 38 39 40 80 82 84 86 89 80 83 85 87 89 81 83 86 88 90 82 84 86 88 91 82 84 87 89 91 83 85 87 90 92 83 86 88 90 93 84 86 89 91 93 85 87 89 92 94 85 88 90 92 95 86 88 91 93 95 86 89 91 94 96 87 89 92 94 97 88 90 92 95 97 36 37 38 39 40 41 42 43 44 45 91 93 95 98 100 92 94 96 98 101 92 95 97 99 101 93 95 97 100 102 94 96 98 100 103 94 97 99 101 104 95 97 100 102 104 96 98 100 103 105 96 99 101 103 106 97 99 102 104 107 98 100 102 105 107 98 101 103 106 108 99 102 104 106 109 100 102 105 107 110 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 56 57 58 59 60 124 126 129 131 133 125 127 130 132 134 126 128 131 133 135 127 129 131 134 136 128 130 132 135 137 129 131 133 136 138 130 132 134 137 139 131 133 135 138 140 132 134 136 139 141 133 135 137 140 142 133 136 138 141 143 134 137 139 142 144 135 138 140 143 145 136 139 141 144 146 TABLE 12. [Page 519 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. 147" 148" 149" 160" 161" 152" 153" 164" 166" 166" 157" 168" 169" 160" 1 2 3 4 5 6 7 8 9 10 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 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 11 12 13 14 15 11 12 13 14 15 27 29 32 34 37 27 30 32 35 37 27 30 32 35 37 28 30 33 35 38 28 30 33 35 38 28 30 33 35 38 28 31 33 36 38 28 31 33 36 39 28 31 34 36 39 29 31 34 36 39 29 31 34 37 39 29 32 34 37 40 29 32 34 37 40 29 32 35 37 40 16 17 18 19 20 39 42 44 47 49 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 58 61 64 66 56 59 61 64 67 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 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 79 81 84 86 89 66 69 71 74 77 67 69 72 74 77 67 70 72 75 78 68 70 73 75 78 68 71 73 76 79 68 71 74 76 79 69 72 74 77 80 69 72 75 77 80 31 32 33 34 35 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 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 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 91 93 96 98 101 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 1 41 42 43 44 45 41 42 43 44 45 100 103 105 108 110 101 104 106 109 111 102 104 107 109 112 103 105 108 110 113 115 118 120 123 125 128 130 133 135 138 103 106 108 111 113 104 106 109 111 114 105 107 110 112 115 105 108 110 113 116 106 109 111 114 116 107 109 112 114 117 107 110 113 115 118 108 111 113 116 119 109 111 114 117 119 109 112 115 117 120 46 47 48 49 50 51 52 53 54 55 113 115 118 120 123 113 116 118 121 123 114 117 119 122 124 127 129 132 134 137 116 118 121 123 126 117 119 122 124 127 117 120 122 125 128 118 121 123 126 128 119 121 124 127 129 120 122 125 127 130 120 123 126 128 131 121 124 126 129 132 122 125 127 130 133 123 125 128 131 133 46 47 48 49 50 51 52 53 54 55 125 127 130 132 135 126 128 131 133 136 128 131 133 136 138 129 132 134 137 139 130 133 135 138 140 131 133 136 139 141 132 134 137 140 142 133 135 138 140 143 133 136 139 141 144 134 137 140 142 145 135 138 140 143 146 136 139 141 144 147 56 57 58 59 60 137 140 142 145 147 138 141 143 146 148 139 142 144 147 149 140 143 145 148 150 141 143 146 148 151 142 144 147 149 152 143 145 148 150 153 144 146 149 151 154 145 147 150 152 155 146 148 151 153 156 147 149 152 154 157 147 150 153 155 158 148 151 154 156 159 149 152 155 157 160 56 57 58 59 60 Page 520] TABLE 13. For finding the Su a's change of Right Ascension for any given number of hours. 1 Hourly Number of hours Hourly tion. 1 2 3 4 5 6 7 8 10 j 11 1 12 tion. 8. «. s. s. B. g. 8. s. c. *. «. 8. ! 8. 8. 8.50 8.5 17.0 25.5 34.0 42. b 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 8.8 17.4 1775 26.1 26:3" 34.8 35.0' 43.5 43. 8 52.2 52.5 60.9 61.3 69.6 70. 78.3 7"8.8 87.0 87.5 95.7 96.3 104.4 105. 8.70 8.75 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 9.0 17.9 18.0 26.9 27.0 35.8 36.0 44.8 53.7 62.7 63.0 71.6 80.6 81.0 89.5 98.5 99.0" 107.4 8.95 9. 00 9.00 45.0 54.0 72.0 90.0 108.0 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 9.25 9.2 9.3 18.4 18.5 27.6 27.8 36.8 37.0 46.0 55.2 64.4 64.8 73.6 82.8 83.3 92.0 101.2 101.8 110.4 111.0 9.20 9:25 46.3 55.5 74.0 92.5 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 19.0 28.4 37.8 47.3 47.5 56.7 57.0 66.2 75.6 85.1 94.5 104.0 104. 5 113.4 9.45 9.50 9.5 28.5 38.0 66.5 76.0 85.5 95.0 114.0 9.50 9.55 9.6 19.1 28.7 38.2 47.8 57.3 66.9 76.4 86.0 95.5 105.1 114.6 9.55 9.60 9.6 19.2 28.8 38.4 48.0 57.6 67.2 76.8 86.4 96.0 105.6 115.2 9.60 9.65 9.7 19.3 29.0 38.6 48.3 57.9 67.6 77.2 86.9 96.5 106.2 115. 8 9.65 9.70 9.7 19.4 29.1 29.3 38.8 39.0 48.5 58.2 58.5 67.9 77.6 87.-3 87.8 97.0 106.7 116.4 9.70 9.75 9.8 19.5 48.8 68.3 78.0 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 50.0 59.7 60.0 69.7 70.0 79.6 80.0 89.6 90.0" 99.5 109.5 119.4 9.95 10.00 10.0 30.0 40.0 100.0 110.0 120.0 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 41.0 51.0 61.2 71.4 81.6 91.8 92. 3 102.0 102.5 112.2 122.4 10.20 10.25 20.5 30.8 51.3 61.5 71.8 82.0 112.8 123.0 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 52.5 62.7 6.3.0 73.2 73.5 83.6 94.1 94.5 104.5 105. 0' 115.0 115.5 125.4 126.0 10. 45 10.50 10.5 21.0 31.5 42.0 84.0 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 32.3 42.8 43.0 5.3.5 53.8 64.2 74.9 85.6 86.0 96.3 96.8 107.0 107.5 117.7 118.3 128.4 129.0 10.70 10.75 1Q.8 21.5 64.5 75.3 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 22.0 32.9 43.8 44.0 54.8 55.0 65.7 66.0" 76.7 77.0 87.6 88.0 98.6 109.5 110.0 120. 5 121.0 131.4 10. 95 11.00 11.00 11.0 33.0 99.0 132.0 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 45.0 56.0 56.3 67.2 67.5 78.4 89.6 100.8 101.3 112.0 112.5 123.2 123.8 134.4 11.20 11.25 22.5 78.8 90.0 135.0 11.25 11.30 11.3 22.6 33.9 45.2 56.5 67.8 79.1 90.4 101.7 113. 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 TABLE 13. [Page 521 For finding the Sun's change of Right Ascension for any given number of hours. Hourly varia- tion. Number of hours. Hourly varia- tion. 13 14 15 16 1 17 18 19 20 21 s. 22 23 24 s. s. s. s. .«. s. *. s. s. s. s, s. 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 8.70 113.1 121.8 122.5 130.5 131.3 139.2 147.9 156.6 157.5 165.3 166.3 174.0 175.0 182.7 183. 8 191.4 192. 5^ 200.1 201.3 208.8 8.70 8.75 8.75 113.8 140.0 148.8 210.0 8.80 114.4 123. 2 132. 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 9.00 116.4 117.0 125. 3 134.3 135. 143.2 144.0 152.2 153.0 161.1 162.0 170.1 171.0 179.0 188.0 196.9 205. 9 214.8 8.95 126.0 180.0 189.0 198. 207.0 216.0 9.00 9.05 117.7 126.7 135.8 144.8 153.9 162. 9 172.0 181.0 190.1 199.1 208.2 217.2 9.05 9.10 118.3 127.4 136.5 145.6 154.7 163. 8 172.9 182.0 191.1 200.2 209.3 218.4 9.10 9.15 119.0 128.1 137.3 146.4 155.6 164.7 173.9 183.0 192.2 201. 3 210.5 219.6 9.15 9.20 119.6 120.3 128.8 138.0 147.2 148.0 156.4 157. 3 165.6 166.5 174.8 175.8 184.0 185.0 193.2 194. 3 202.4 203.5 211.6 220.8 9.20 9.25 129.5 138. 8 212.8 222.0 9.25 9.30 120.9 130. 2 139.5 148.8 158.1 167.4 176.7 186.0 195. 3 204.6 213.9 223.2 9.30 9. 35 121.6 130.9 140.3 149. 6 159. 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 9.50 122.9 132.3 133.0 141.8 151.2 160.7 161.5 170.1 171.0 179.6 180.5 189.0 190.0 198.5 199.5 207.9 209.0 217.4 226.8 9.45 123.5 142.5 152.0 218. 5 228.0 9.50 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 9.70 126.1 135.8 136.5 145.5 146.3 155.2 156.0 164.9 165.8 174.6 175.5 184.3 185.3 194.0 203.7 204.8 213.4 223.1 232.8 9.70 9.75 126.8 195.0 214.5 224.3 -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 9.95 129.4 139.3 140.0 149.3 150.0 159.2 160.0 169.2 170.0 179.1 189.1 199.0 200.0 209.0 210.0 218.9 220.0 228.9 230. 238.8 9.95 10.00 130.0 180.0 190.0 240.0 10.00 10.05 130.7 140.7 150.8 160.8 170.9 180.9 191.0 201.0 211.1 221.1 231.2 241.2 10.05 10.10 131.3 141.4 151.5 161.6 171.7 181.8 191.9 202.0 212.1 222.2 232.3 242.4 10.10 10. 15 132.0 142.1 152.3 162.4 172.6 182.7 192.9 203.0 213.2 223.3 233.5 243.6 10.15 10.20 132.6 142.8 153.0 163.2 173. 4 174.3 183.6 184.5 193.8 194.8 204.0 205.0 214.2 215.3 224.4 225.5 234.6 235. 8 244.8 10.20 10.25 133.3 143.5 153. 8 164.0 246.0 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. 3 165.6 176.0 186.3 196.7 207.0 217.4 227.7 238.1 248.4 10.35 10.40 135.2 145.6 156.0 166.4 176. 8 187.2 197.6 208.0 218.4 228.8 239.2 249.6 10.40 10.45 10.50 135.9 136.5 146.3 147.0 156.8 167.2 177.7 -178.5 188.1 198.6 199.5 209.0 210.0 219.5 229.9 231.0 240.4 250. 8 252.0 10.45 157. 5 168.0 189.0 220.5 241.5 10.50 10.55 137. 2 147.7 158. 3 168.8 179.4 189.9 200.5 211.0 221.6 232. 1 242.7 253.2 10.55 10.60 137.8 148.4 159.0 169.6 180.2 190.8 201.4 212.0 222.6 233.2 243.8 254.4 10.60 10.65 138.5 149.1 159.8 170.4 181.1 191.7 202.4 213.0 223. 7 234. 3 245.0 255.6 10. 65 10.70 139.1 149.8 150.5 160.5 171.2 181.9 182.8 192.6 193.5 203.3 204.3 214.0 224.7 235.4 236.5 246.1 247.3 256.8 10.70 10.75 139. 8 161.3 172.0 215.0 225.8 258.0 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. 95 142.4 153.3 164.3 165.0 175.2 186.2 197.1 198.0 208.1 209.0 219.0 230.0 240.9 242. 251.9 253. 262.8 10.95 11.00 143.0 154.0 176.0 187.0 220.0 231.0 264.0 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 11.20 145.6 146.3 156.8 157.5 168.0 179.2 180.0 190.4 201.6 212.8 224.0 235.2 246.4 247.5 257.6 258.8 268.8 270.0 11.20 11.25 168.8 191. 3 202.5 213.8 225.0 236.3 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 11.45 148. 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 Page 522] TABLES 14, 15, 16. TABLE 14. Dip of the Sea Horizon. Height of Dip of the the Eye. Horizon Feet. 59 2 1 23 3 1 42 4 1 58 5 2 11 6 2 24 7 2 36 8 2 46 9 2 56 10 3 06 11 3 15 12 3 24 13 3 32 14 3 40 15 3 48 16 3 55 17 4 02 18 4 09 19 4 16 20 4 23 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 5 22 31 5 27 32 5 33 33 5 38 34 5 43 35 5 48 36 5 53 37 5 58 38 6 02 39 6 07 40 1 6 12 45 6 36 50 6 56 55 7 16 60 7 35 65 7 54 70 8 12 75 8 29 80 8 46 85 9 02 90 9 18 95 9 33 100 ; 9 48 Dlst. of Land in Sea Miles. TABLE 15. Dip of the Sea at different Distances from the Observer. u n 2 2J 3 H 4 5 10 11 6 4 3 23 12 Height of the Eye above the Sea in Feet. 80 I 15 34 17 12 20 45 23 15 12 10 8 26 57 28 19 15 12 10 85 34 23 17 14 12 40 27 20 16 14 11 6 40 91 45 30 23 19 16 12 10 Note to Table 15. — The numbers of this Table below the black lines are the same as are given in Table 14, the visible horizon corresponding to those heights not being so far distant as the land. TABLE 16. The Sun's Parallax in Altitude. Altitude. Parallax. o // 9 10 9 20 8 30 8 40 7 50 6 55 5 60 4 65 4 70 3 75 2 80 2 85 1 90 TABLE 17. Parallax in Altitude of a Planet. [Page 523 •apmmv COOO»opeO«005(MiCOO^^I:^0!M'*'©0005!N(Ml>)i-H,-H,-l,-(^T-lT-lr-IT-l t^i^meo-io-<*icoc<)i-ioioci-i-^iC'+aot^cocoic*'*< ec CO (M i-l r-l o 6 FN t^t^«OvO'*CCC<)(MT-lOOOiaOt^t^COiCiC't<-t0^(MT-lt-lO (£)CDiC-*C0(M*eCC0SqMi— It— lOO OOCOiMrHT— iOO050i00l--l>-^5DlO"*-*-*C0OToooooot^i^cDcoio»o-^rt!t 050500a0t^l>-t>'iX>^C0i0»b'^'*'^C0e«5(MC S^ o o 2 4 6 8 J) 's Hor. Parallax. W • !»' 16' 17' 1 80" 0" 80" 0" 80" 0" 53' 57' 81' 1 1 o 2 4 6 8 // 0.1 0.6 1.0 1.5 2.0 // 0.1 0.6 1.1 1.6 2.1 0.1 0.7 1.2 1.7 2.3 // 0.1 0.7 1.3 1.9 2.4 II 0.2 0.8 1.4 2.0 2.6 II 0.2 0.8 1.5 2.1 2.7 II 0.0 0.0 0.1 0.1 0.2 // 0.0 0,0 0.1 0.1 0.2 II 0,0 0.0 0.1 0.1 0.2 10 12 14 16 18 2.4 2.9 3.4 3.8 4.3 2.6 3.1 3.6 4.1 4.6 2.8 3.3 3.9 4.4 4.9 3.0 3.6 4.1 4.7 5.2 3.2 3.8 4.4 5.0 5,6 3.4 4.0 4.7 5.3 5.9 10 12 14 16 18 0.3 0.5 0.6 0.8 1.0 0.3 0.5 0.7 0.9 1.1 0.4 0.5 0.7 0.9 1.1 20 22 24 26 28 4.7 5.2 5.6 6.0 6.5 5.1 5.5 6.0 6.5 6.9 5.4 5.9 6.4 6.9 7.4 5.8 6.3 6.8 7.4 7.9 6.1 6.7 7.3 7.8 8.4 6.5 7.1 7. 7 8.3 8.9 20 22 24 26 28 1.2 1.5 1.7 2.0 2.3 1.3 L6 1.9 2.2 2.5 1.4 1.7 2.0 2.3 2.6 30 32 34 36 38 6.9 7.3 7.7 8.1 8.4 7.3 7.8 8.2 8.6 9.0 7.9 8.3 8.8 9.2 9.7 8.4 8.9 9.4 9.8 10.3 8.9 9.4 10.0 10.5 10.9 9.5 10.0 10.6 11.1 11.6 30 32 34 36 38 2.6 2.9 3.3 3.6 4.0 2.8 3.1 3.5 3.9 4.3 3.0 3.4 3.8 4.1 4.6 40 42 44 46 48 8.8 9.2 9.5 9.8 10.2 9.4 9.8 10.2 10.5 10.9 10.1 10.5 10.9 11.3 11.6 10.7 11.2 11.6 12.0 12.4 11.4 11.9 12.3 12.8 13.2 12.1 12.6 13.1 13.6 14.0 40 42 44 46 48 4.3 4.7 5.0 5.4 5.8 4.6 5.0 5.4 5.8 6.2 5.0 5.4 5.8 6.2 6.6 50 52 54 56 58 10.5 10.8 11.1 11.3 11.6 11.2 11.5 11.8 12.1 12.4 12.0 12.3 12.7 13.0 13.3 12.8 13.1 13.5 13.8 14.1 13.6 14.0 14.4 14.7 15.1 14.4 14.9 15.3 15.6 16.0 50 52 54 56 58 6.1 6.5 6.8 7.2 7.5 6.6 7.0 7.4 7.7 8.1 7.1 7.5 7.9 8.3 8.6 60 62 64 66 68 11.8 12.1 12.3 12.5 12.7 12.7 12.9 13.2 13.4 13.6 13.5 13.8 14.1 14.3 14.5 14.4 14.7 15.0 15.2 15.5 15.4 15.7 16.0 16.2 16.5 16.3 16.6 16.9 17.2 17.5 60 62 64 66 68 7.8 8.1 8.4 8.7 9.0 8.4 8.8 9.1 9.4 9,7 9.0 9.4 9.7 10.0 10.3 70 72 74 76 78 12.9 13.0 13.1 13.3 13.4 13.8 13.9 14.1 14.2 14.3 14.7 14.9 15.0 15.2 15.3 15.7 15.9 16.0 16.2 16.3 16.7 16.9 17.1 17.2 17.4 17.7 17.9 18.1 18.3 18.4 70 72 74 76 78 9.2 9.5 9.7 9.8 10.0 9,9 10.2 10.4 10.6 10.8 10.6 10.9 11.1 11.3 11.5 80 82 84 86 88 13.5 13.5 13.6 13.6 13.7 14.4 14.5 14.6 14.6 14.6 15.4 15.5 15.6 15.6 15.6 16.4 16.5 16.6 16.6 16.7 17.5 17.6 17.6 17.7 17.7 18.6 18.7 18.7 18.8 18.8 80 82 84 86 88 10.1 10.3 10.3 10.4 10.4 10.9 11.0 11.1 11.2 11.2 11.7 11.8 11.9 12.0 12.0 90 13.7 14.6 15.6 16.7 17.7 18.8 90 10.5 11.3 12.0 TABLE 20A. [Page 525 | Mean Refraction. [Barometer, 30 inches. Fahrenheit's Thermometer, 50°.J Apparent Mean Re- Apparent Mean Re- Apparent Mean Re- Apparent Mean Re- Apparent Altitude. Mean Re- Altitude. fraction. Altitude. fraction. Altitude. fraction. Altitude. fraction. fraction. o / ' o / 9 30 5 35. 1 o / 15 00 3 34.1 o / 25 00 2 4.4 42 00 1 04.7 00 36 29. 4 35 5 32.4 10 3 31.7 10 2 3.4 20 1 03.9 1 00 24 53. 6 40 5 29. 6 20 3 29.4 20 2 2.5 40 1 03.2 2 00 18 25. 5 45 5 27.0 30 3 27.1 30 2 1.6 43 00 1 02.4 3 00 14 25. 1 50 5 24.3 40 3 24.8 40 2 0.7 20 1 01.7 4 00 11 44.4 55 5 21.7 50 3 22.6 50 1 59.8 40 1 01.0 5 00 9 52.0 10 00 5 19.2 16 00 3 20.5 26 00 1 58.9 44 00 1 00.3 06 9 44.0 05 5 16.7 10 3 18.4 10 1 58.1 20 59. 6 10 9 36.2 10 5 14.2 20 3 16.3 20 1 57.2 40 58.9 15 9 28.6 15 5 11.7 30 3 14.2 30 1 56.4 45 00 58.2 20 9 21.2 20 5 9.3 40 3 12.2 40 1 55.5 20 57.6 25 9 14.0 25 5 6.9 50 3 10.3 50 1 54.7 40 56.9 5 30 9 7.0 10 30 5 4.6 17 00 3 8.3 27 00 1 53.9 46 00 56.2 35 9 0.1 35 5 2.3 10 3 6.4 10 1 53.1 20 66.6 40 8 53.4 40 5 0.0 20 3 4.6 20 1 52.3 40 55.0 45 8 46.8 45 4 57.8 30 3 2.8 30 1 61.5 47 00 54.3 50 8 40.4 50 4 55.6 40 3 1.0 40 1 50.7 20 53.7 55 8 34.2 55 4 53.4 50 2 59.2 50 1 50.0 40 53.1 6 00 8 28.0 11 00 4 51.2 18 00 2 57.5 28 00 1 49.2 48 00 62.5 05 8 22.1 05 4 49.1 10 2 55.8 20 1 47.7 49 00 50.6 10 8 16.2 10 4 47.0 20 2 54.1 40 1 46.2 50 00 48.9 15 8 10.5 15 4 44.9 30 2 52.4 29 00 1 44.8 51 00 47.2 20 8 4.8 20 4 42.9 40 2 50.8 20 1 43.4 52 00 46.5 25 7 59.3 25 4 40.9 50 2 49.2 40 1 42.0 53 00 43.9 6 30 7 53.9 11 30 4 38.9 19 00 2 47.7 30 00 1 40.6 54 00 42.3 35 7 48.7 35 4 36.9 10 2 46.1 20 1 39.3 66 00 40.8 40 7 43.5 40 4 35.0 20 2 44.6 40 1 38.0 56 00 39.3 45 7 38.4 45 4 33. 1 30 2 43.1 31 00 1 36.7 57 00 37.8 ■ 50 7 33.5 50 4 31.2 40 2 41.6 20 1 35.5 68 00 36.4 55 7 28.6 55 4 29.4 50 2 40.2 40 1 34.2 59 00 35.0 7 00 7 23.8 12 00 4 27.5 20 00 2 38.8 32 00 1 33.0 60 00 33.6 05 7 19.2 05 4 25. 7 10 2 37.4 20 1 31.8 61 00 32.3 10 7 14.6 10 4 23.9 20 2 36.0 40 1 30.7 62 00 31.0 15 7 10.1 15 4 22.2 30 2 34.6 33 00 1 29.5 63 00 29.7 20 7 5.7 20 4 20.4 40 2 33. 3 20 1 28.4 64 00 28. 4 25 7 1.4 25 4 18.7 50 2 32.0 40 1 27.3 65 00 27.2 7 30 6 57.1 12 30 4 17.0 21 00 2 30.7 34 00 1 26. 2 66 00 25.9 35 6 53. 35 4 15.3 10 2 29.4 20 1 25. 1 67 00 24.7 40 6 48.9 40 4 13.6 20 2 28.1 40 1 24.1 68 00 23.6 45 6 44.9 45 4 12.0 30 2 26.9 35 00 1 23.1 69 00 22.4 50 6 41.0 50 4 10.4 40 2 25.7 20 1 22.0 70 00 21.2 55 6 37.1 55 4 8.8 50 2 24.5 2 23.3 40 36 00 1 21.0 1 20.1 71 00 72 00 20.1 18.9 8 00 6 33.3 13 00 4 7.2 22 00 05 6 29.6 05 4 5.6 10 2 22.1 20 1 19.1 73 00 17.8 10 6 25.9 10 4 4.1 20 2 20.9 40 1 18.2 74 00 16.7 15 6 22.3 15 4 2.6 30 2 19.8 37 00 1 17.2 75 00 16.6 20 6 18.8 20 4 1.0 40 2 18.7 20 1 16.3 76 00 14.6 25 6 15.3 25 3 59.6 50 2 17.5 40 1 15.4 77 00 13.5 8 30 6 11.9 13 30 3 58.1 23 00 2 16.4 38 00 1 14.5 78 00 12.4 35 6 8.5 35 3 56.6 10 2 15.4 20 1 13.6 79 00 11.3 40 6 5.2 40 3 55. 2 20 2 14.3 40 1 12.7 80 00 10.3 45 6 2.0 45 3 53.7 30 2 13.3 39 00 1 11.9 81 00 9.2 50 5 58.8 50 3 52.3 40 2 12.2 20 1 11.0 82 00 8.2 55 5 55.7 55 3 50.9 50 2 11.2 40 1 10.2 83 00 84 00 7.2 6.1 9 00 5 52.6 14 00 3 49.5 24 00 2 10.2 40 00 1 9.4 05 5 49.6 10 3 46. 8 10 2 9.2 20 1 8.6 85 00 5.1 10 5 46.6 20 3 44.2 20 2 8.2 40 1 7.8 86 00 4.1 15 5 43.6 30 3 41.6 30 2 7.2 41 00 1 7.0 87 00 3.1 20 5 40.7 40 3 39.0 40 2 6.2 20 1 6.2 88 00 2.0 25 5 37.9 50 3 36. 5 50 2 5.3 40 1 5.4 89 00 1.0 9 30 5 35.1 15 00 3 34.1 25 00 2 4.4 42 00 1 4. 7 90 00 0.0 Page 526] TABLE 20B. Correction of the Sun's Apparent Altitude for Refraction and Parallax. [Barometer, 30 inches. Fahrenheit's Thermometer, 50°.] Apparent Altitude. Mean Re- fraction and Parallax 0. Apparent Altitude. Mean Re- fraction and Parallax 0. Apparent Altitude. Mean Re- fraction and Parallax ©. Apparent Altitude. Mean Re- fraction and Parallax ©. Apparent Altitude. Mean Re- fraction and Parallax 0. o / / // O / ' II o / / // o / 1 II 1 ' II 9 30 5 26 15 00 3 25 25 00 1 56 42 00 58 00 36 20 35 5 23 10 3 24 10 1 55 20 57 1 00 24 45' 40 5 21 20 3 21 20 1 55 40 56 2 00 18 17 45 5 18 30 3 19 30 1 54 43 00 55 3 00 14 16 50 5 15 40 3 17 40 1 53 20 55 4 00 11 35 55 5 13 50 3 15 50 1 52 40 54 5 00 9 43 10 00 5 10 16 00 3 13 26 00 1 51 44 00 53 05 9 35 05 5 8 10 3 10 10 1 50 20 53 10 9 27 10 5 5 20 3 8 20 1 49 40 52 15 9 20 15 5 3 30 3 6 80 1 48 45 00 52 20 9 12 20 5 40 3 4 40 1 48 20 52 25 9 5 25 4 58 50 3 2 50 1 47 40 51 5 30 8 58 10 30 4 56 17 00 3 27 00 1 46 46 00 50 35 8 51 35 4 53 10 2 58 10 1 45 20 50 40 8 44 40 4 51 20 2 57 20 1 44 40 49 45 8 38 45 4 49 30 2 55 30 1 44 47 00 48 50 8 31 50 4 47 40 2 53 40 1 43 20 48 55 8 25 55 4 44 50 2 51 50 1 42 40 47 6 00 8 19 11 00 4 42 18 00 2 50 28 00 1 41 48 00 47 05 8 13 05 4 40 10 2 48 20 1 40 49 00 45 10 8 7 10 4 38 20 2 46 40 1 38 50 00 43 15 8 2 15 4 36 30 2 44 29 00 1 37 51 00 41 20 7 56 20 4 34 40 2 43 20 1 35 52 00 40 25 7 50 25 4 32 50 2 41 40 1 34 53 00 39 6 30 7 45 11 30 4 30 19 00 2 40 30 00 1 33 54 00 37 35 7 40 35 4 28 10 2 38 20 1 31 55 00 36 40 7 35 40 4 26 20 2 37 40 1 30 56 00 34 45 7 29 45 4 24 30 2 35 31 00 1 29 57 00 33 50 7 25 50 4 22 40 2 34 20 1 28 58 00 32 55 7 20 55 4 20 50 2 32 40 1 26 59 00 31 7 00 7 15 12 00 4 19 20 00 2 31 32 00 1 25 60 00 30 05 7 10 05 4 17 10 2 29 20 1 24 61 00 28 10 7 6 10 4 15 20 2 28 40 1 23 62 00 27 15 7 1 15 4 13 30 2 27 33 00 1 22 63 00 26 20 6 57 20 4 11 40 2 25 20 1 20 64 00 24 25 6 52 25 4 10 50 2 24 40 1 19 65 00 23 7 30 6 48 12 30 4 8 21 00 2 23 34 00 1 18 66 00 22 35 6 44 35 4 6 10 2 21 20 1 17 67 00 21 40 6 40 40 4 5 20 2 20 40 1 16 68 00 21 45 6 36 45 4 3 30 2 19 35 00 1 15 69 00 19 50 6 32 50 4 1 40 2 18 20 1 15 70 00 18 55 6 28 55 4 50 2 17 40 1 14 71 00 17 8 00 6 24 13 00 3 58 22 00 2 15 36 00 1 13 72 00 16 05 6 21 05 3 57 10 2 14 20 1 12 73 00 16 10 6 17 10 3 55 20 2 13 40 1 11 74 00 15 15 6 13 15 3 54 30 2 12 37 00 1 10 75 00 14 20 6 10 20 3 52 40 2 11 20 1 9 76 00 13 25 6 6 25 3 51 50 2 10 40 1 8 77 00 78 00 12 10 8 30 6 3 13 30 3 49 • 23 00 2 8 38 00 1 8 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 TABLE 21. [Page 527 1 Correction of the Mean Refraction for the Height of the Barometer. Barom. Mean refraction. Barom. Add. 1 1 ' 2 8' j A ' 1 6' 6' 1' 8' 1 9' |l0' Subtract. 0" 80" j 0" 80" 0" 80" 0" 80" 0" 80" 0" 80" 0" 80" 0" 80" 0" 80" 0" 80" 0" II If 1 " „ „ „ „ II II „ „ „ „ „ n // // II II ;; 27.50 2 5 7 10 12 15 17 20 23 25 28 30 33 35 38 40 43 45 48 51 27.55 2 5 7 10 12 15 17 20 22 25 27 30 32 35 37 40 42 45 47 50 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 16 18 21 23 25 28 30 32 35 37 39 42 44 47 27.75 13 16 18 20 23 25 27 29 32 34 36 39 41 43 46 27.80 2 4 7 9 11 13 15 18 20 22 24 27 29 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 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 37 34 j36 39 42 2 4 38 41 28.05 2 4 6 8 10 12 14 16 18 20 22 24 25 27 29 31 33 35 37 39 28.10 2 4 6 8 9 11 13 15 17 19 21 23 25 27 29 31 33 34 36 38 28.15 2 4 6 7 9 11 13 15 17 19 20 22 24 26 28 30 32 34 36 37 28.20 2 4 5 7 9 11 13 14 16 18 20 22 24 25 27 29 31 33 35 36 28.25 2 3 5 7 9 10 12 14 16 18 19 21 23 25 26 28 30 32 34 35 28.30 2 3 5 7 8 10 12 14 15 17 19 21 22 24 26 27 29 31 33 34 28.35 2 3 5 7 8 10 12 13 15 17 18 20 22 23 25 27 28 30 32 33 28.40 2 3 5 6 8 10 11 13 14 16 18 19 21 23 24 26 27 29 31 32 28.45 2 3 3 5 4 6 6 8 7 9 9 11 10 12 12 14 14 16 15 17 17 19 18 20 20 22 21 23 23 25 24 27 26 28 27 30 31 29 30 28.50 31.50 28.55 3 4 6 7 9 10 12 13 15 16 17 19 20 22 23 25 26 28129 31.45 28.60 3 4 6 7 8 10 11 13 14 15 17 18 20 21 23 24 25 27128 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 4 5 6 8 9 10 12 13 14 16 17 18 20 121 22 24 25126 31.30 28.75 2 4 5 6 7 9 10 11 13 14 15 16 18 19 20 21 23 24 25 31.25 28.80 2 4 5 6 7 8 10 11 12 13 14 16 17 18 19 21 22 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 9 11 10 12 11 13 14 15 16 17 18 19 20 21 31.05 29.00 2 3 4 5 6 7 8 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 29.25 2 3 4 4 5 6 7 8 8 9 10 11 11 12 13 14 14 15 30.75 29.30 2 3 3 4 5 6 6 7 8 8 9 10 11 11 12 13 13 14 30.70 29.35 2 3 3 4 5 5 6 7 7 8 9 9 10 10 11 12 13 13 30.65 29.40 2 2 3 4 4 5 5 6 7 7 8 8 9 10 10 11 12 12 30.60 29.45 29.50 -Y 2 2 2 3 3 4 4 5 6 6 7 7 8 8 9 9 10 11 11 30.55 2 3 3 4 5 5 6 6 7 7 8 8 9 9 10 10 30.50 29.55 2 2 3 3 4 4 5 5 5 6 6 7 7 8 8 9 9 30. 45 29.60 2 2 2 3 3 4 4 4 5 5 6 6 6 7 7 8 8 30.40 29.65 2 2 2 3 3 4 4 4 5 5 5 6 6 6 7 7 30.35 29.70 1 2 2 2 3 3 3 4 4 4 5 5 5 5 6 6 30.30 29.75 1 1 2 2 2 3 3 3 3 4 4 4 4 5 5 5 30.25 29.80 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 30.20 29.85 1 1 1 1 1 2 2 2 2 2 2 2 3 3 3 3 30.15 29.90 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 30.10 29.95 1 1 1 1 1 1 1 1 1 1 1 30.05 30.00 ; U 30.00 Subtract. 0" 30" 0" 80" 0" 80" 0" 80" 0" 80" 0" 83" 0" 80" 1 C" 80" 0" | 80" 0" 1 80" 0" A^d. 0' 1' 2' 1 8' 4' 5' C 1 V \ 8' 9' 10' ^lean refraction. Page 528J TABLE ^. Correct ion of tl e Mean Refraction for the Height of the Thermometer. Mean refraction. Ther. Ther. Add. o 0' I' 1/ "' 4' 5' 1 8' ; 7' 8' 9' 10' Add. 0" 80" II 0" II 80" II 0" 80" II 0" 80" II 0" II 80" II 0" 80" II 0' II 80" 0" 80" j 0" 80" II 0" II 80" 0" 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 •2 15 19 23 27 31 36 40 44 48 53 :58 62 \ 67 72 n 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 i 62 66 71 76 80 — 4 — 2 3 3 _7_ 7 10 lb 14 13 17 16 21 20" 24 23 28 27 31 30 35 34 39 37 43 41 47 45 51 49 55 53 59 57 64 I 68 61 65 72 77 69 74 — 2 2 3 6 9 12 16 19 22 25 29 32 36 39 43 47 50 54 58 62 66 i 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 i 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 20 2 2 4 4 6 6 8 8 10 9 12 11 14 13 16 15 18 17 20 19 22 22 24 24 27 26 29 28 31 30 34 33 36 35 39 37 41 40 44 42 19 20 21 2 4 5 7 9 11 13 15 17 19 21 23 25 27 29 31 34 36 38 41 21 22 2 3 5 7 9 11 12 14 16 18 20 22 24 26 28 30 32 35 37 39 22 23 2 3 5 7 8 10 12 14 15 17 19 21 23 25 27 29 31 33 36 38 23 24 2 3 5 6 8 10 11 13 15 17 18 20 22 24 26 28 30 32 34 36 24 25 2 3 5 6 8 9 11 13 14 16 18 19 21 23 25 27 29 31 33 35 25 26 3 4 6 7 9 11 12 14 15 17 19 20 22 24 26 28 29 31 33 26 27 3 4 6 7 9 10 12 13 15 16 18 19 21 23 25 26 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 32 33 2 3 4 5 6 7 8 10 11 12 13 14 15 17 18 19 21 22 23 33 34 2 3 4 5 6 7 8 9 10 11 12 13 14 16 17 18 19 21 22 34 35 2 3 4 5 6 6 7 8 9 10 11 13 14 15 16 17 18 19 20 35 36 2 3 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 36 37 2 2 3 4 5 6 6 7 8 9 10 11 12 13 14 15 16 17 18 37 38 2 3 4 4 5 6 7 7 8 9 10 11 12 13 13 14 15 16 38 39 2 3 3 4 5 5 6 7 8 8 8 9 8 10 9 11 10 11 10 12 11 13 12 14 13 15 13 39 40 40 2 2 3 4 4 5 6 6 7 41 2 2 3 3 4 4 5 6 6 7 7 8 9 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 t 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" 80" 0" 80" 0" 80" 0" 80" 0" 80" 0" 80" 0" 80" 0" 80" 0" 80" 0" 80" i 0" Add. i Add. c V 1' 2' 3' 4' 5' 1 V 7' 8' 9' 10' Ther. Ther. Mean refraction. TABLE 22. [Page 529 Correction of the Mean Refraction for the Height of the Thermometer. Ther. Subt. Mean refraction. Ther. Subt. 0' V 2' 8' 4' 6' 6' 7' 8' 9' 10' 0" 80" 0" 30" 0" 80" 0" 80" 0" 80" 0" 80" 0" 80" 0" 80" II 1 2 3 4 5 6 6 7 8 9 10 11 12 13 0" II 1 2 3 4 5 6 7 8 9 10 11 12 13 14 80" 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 0" 80" 0" o 50 51 52 53 54 55 56 57 58 59 II II 2 2 II 0_ 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 II 2 2 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 5 5 5 II 1 1 1 1 2 2 2 2 3 3 3 3 3 4 4 4 4 5 5 5 5 5 6 6 6 6 6 II 1 1 1 1 2 2 2 3 3 3 3 4 4 4 5 5 5 5 6 6 6 7 7 7 7 8 8 8 II 1 1 1 2 2 2 3 3 3 \ 5 5 II 1 1 2 2 2 3 3 4 4 4 5 5 6 II 1 1 2 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 II 1 1 2 2 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 // 1 1 2 2 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 II 1 1 2 3 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 II 1 1 2 3 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 II 1 2 2 3 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 II 1 2 2 3 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 " 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 53 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 56 II 1 3 4 5 o 50 51 52 53 54 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 60 61 62 63 64 65 66 67 68 69 5 6 6 6 6i 7 6: 7 7i 8 14 |15 15 il6 16 117 16 !18 17 |l9 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 7 7 8 8 8 8 9 9 9 10 8 8 9 9 10 10 10 11 11 11 18 19 20 21 22 20 20 21 22 23 70 71 72 73 74 22 124 23 |25 24 126 25 127 26 28 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 7 7 7 7 7 7 7 8 8 8 .8 7 7 7 7 8 8 8 8 8 9 9 9 9 9 10 10 10 10 10 11 11 8 9 9 9 9 10 10 10 10 11 11 11 11 12 12 12 12 13 13 13 13 10 10 11 11 11 12 12 12 13 13 13 14 14 14 14 15 15 15 16 16 12 12 13 13 13 14 14 14 15 15 16 16 16 17 17 17 18 18 18 19 14 14 14 15 15 16 16 17 17 17 18 18 19 19 19 20 20 21 21 21 22 15 16 16 17 17 18 18 19 19 20 20 21 21 22 22 22 23 23 24 24 25 17 18 18 19 19 20 20 21 21 22 23 23 24 24 25 25 26 26 27 27 28 19 20 20 21 21 22 23 23 24 24 25 25 26 27 27 28 28 29 29 30 31 21 21 22 23 23 24 25 25 26 27 "27 28 29 29 m_ 30 31 32 32 33 34 23 24 24 25 26 26 27 28 28 29 30 31 31 32 33 33 34 35 35 36 37 25 26 26 27 28 29 29 30 31 32 32 33 34 35 35 36 37 38 38 39 40 27 29 28 130 28 131 29 i31 30 32 31 32 33 34 35 36 37 38 38 39 40 41 42 43 44 45 46 47 48 49 50 80 81 82 83 84 31 32 32 33 34 35 36 37 37 38 39 40 41 41 42 43 33 34 35 36 37 38 39 39 40 41 42 43 44 44 45 46 43 44 45 46 48 49 50 51 52 53 54 55 56 58 59 60 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 95 96 97 98 99 100 16 19 100 Subt. Then 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' 5' 6' V 8' 9' 10' Mean refraction. 22489—03- -34 Page 530] TABLES 23, 24. TABLE 23. Correction of the Moon's Altitude for parallax and re- fraction corresponding to a mean value of the hori- zontal parallax, 57^ ?>W. Moon's alt. Corr. Moon's alt. Corr. Moon's alt. Corr. Moon's p alt. C°'^'^- » o , 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 TABLE 24. Correct] on of tV [B£ le Mooi irometer I's Apparent Altitude 30 inches.— Fahrenheit's 1 or Par rhermon allax and Refr aeter, 50°.] action. Moon's app. alt. Horizontal parallax. § Correction for seconds of parallax.— Add. Corr. for minutes of alt. 54' 55' 56' 57' 58' 59' 60' 61' 0" 2" 4" 6" 8" o r , // / II ' // / // ' II / II 1 II / // // II II II II „ 5 43 56 44 56 45 56 46 56 47 56 48 55 49 55 50 55 2 4 6 8 10 44 11 45 11 46 11 47 11 48 11 49 10 50 10 51 10 10 10 12 14 16 18 20 25 25 25 25 25 24 24 24 20 20 22 24 26 28 30 89 39 38 38 38 38 37 37 30 30 32 34 86 38 40 52 51 51 51 51 51 51 51 40 40 42 44 46 48 50 45 4 46 3 47 3 48 3 49 3 50 3 51 3 52 3 52 13 50 50 1 52 2 54 4 56 6 58 8 6 45 15 46 15 47 14 48 14 49 14 50 13 51 13 10 26 1 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 1 46 45 45 45 44 44 44 30 30: 32 34 36 38 40 55 55 55 54 54 54 53 53 40 40 1 42 44 46 48 50 7 46 46 4 12 47 3 48 3 49 3 50 3 50 12 51 2 51 11 52 1 53 1 50 50 52 2 54 4 56 6 58 8 47 12 48 12 49 12 52 11 53 10 10 21 20 20 20 19 18 18 18 10 10 12 14 16 18 20 29 28 28 27 27 26 25 25 20 20 22 24 26 28 30 36 36 35 35 34 34 34 33 30 30 32 34 36 38 40 43 42 42 41 41 40 40 40 40 40 42 44 46 48 50 50 49 48 48 48 47 46 46 50 50 52 54 56 58 Add. 8 46 56 47 56 48 55 49 54 50 54 51 54 52 53 53 53 01 2 4 6 8 V \" 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 8 2 30 13 13 12 11 11 10 10 9 30 30 i 32 34 36 38 4 2 40 19 18 17 17 16! 16 15 • 14 40 40 42 44 46 48 5 3 50 9 24 23 22 49 26 22 50 26 21 20 19 53 24 19 50 50 52 2 54 4 56 6 58 8 6 4 7 4 47 28 48 27 51 25 52 24 54 23 10 33 32 31 30 30 29 28 27 10 10 12 14 16 18 8 5 20 37 36 35 34 34 33 32 32 20 20 22 24 26 28 9 5 30 41 41 40 39 38 37 37 36 30 30 32 34 36 38 40 45 44 43 43 42 41 40 39 40 40 42 44 46 48 50 49 48 47 46 46 45 44 44 50 49 51 53 55 57 TABLE 24. [Page 531 1 Correction of the Moon'tj Apparent Altitude for Parallax and Refraction. 1 [Barometer 30 inches.— Fahrenheit's Thermometer 50°.] 1 Moon's Horizontal parallax. Correction for seconds of parallax. — Add. Corr. for app. alt. minutes of alt. 54' 56' 66' 67' 58' 59' 60' 61' 0" 2" 4" 6" 8" O ' ' // / // / // ' // / // / // / // / II II // II II II ,/ Add. 10 47 53 48 52 49 51 50 50 51 50 52 48 53 48 54 47 2 4 6 8 V ^' 10 56 55 54 53 52 51 50 50 10 10 12 14 16 18 2 1 20 59 58 57 56 55 55 54 53 20 20 22 24 26 28 3 1 30 48 2 49 1 50 59 58 57 56 55 30 29 31 33 35 37 4 1 40 5 4 2 51 2 52 1 53 59 58 40 39 41 43 45 47 5 2 50 11 7 48 10 6 5 4 4 2 54 1 55 50 49 51 2 53 4 55 6 57 8 6 2 7 2 49 9 50 8 51 7 52 7 53 5 54 4 55 3 10 12 11 10 9 j 9 7 6 5 10 10 12 14 16 18 8 2 20 15 14 12 12 ! 11 9 8 7 20 20 22 24 26 28 9 3 30 17 16 14 13 13 11 10 9 30 29 31 33 35 37 40 19 18 17 15 15 13 12 11 40 39 41 43 45 47 50 21 20 49 21 18 17 17 52 17 15 14 13 50 49 51 2 53 4 55 6" 57 8 12 48 22 50 19 51 18 53 17 54 15 55 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 25 27 30 27 26 24 23 22 20 19 18 30 29 31 33 35 37 40 28 27 25 24 23 21 20 19 40 39 41 43 45 47 50 29 28 26 50 27 25 24 22 21 20 50 49 51 2 53 4 55 6 57 8 1 13 48 30 49 29 51 26 52 25 53 23 54 22 55 20 10 31 30 28 27 26 24 22 21 10 10 12 14 16 18 2 20 32 31 29 27 26 24 23 21 20 19 21 23 25 27 3 30 33 32 30 28 27 25 23 22 30 29 31 33 35 37 4 40 34 32 30 29 28 26 24 22 40 39 41 43 45 47 5 50 35 33 31 30 28 26 25 23 50 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 55 23 10 35 34 32 30 28 26 25 23 10 10 12 14 16 18 8 20 36 34 32 30 29 27 25 24 20 19 21 23 25 27 9 30 36 34 32 30 29 27 25 23 30 29 31 33 35 37 40 36 34 32 30 29 27 25 23 40 39 41 43 45 47 50 15 36 34 32 30 29 27 25 54 25 23 55 23 50 49 51 2 53 4 55 6 57 8 48 36 49 35 50 33 51 31 52 29 53 27 10 36 35 32 30 28 26 24 22 10 10 12 14 16 18 20 36 35 32 30 28 26 24 22 20 19 21 23 25 27 30 36 34 31 29 28 25 23 21 30 29 31 38 35 37 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 19 50 49 51 2 53 4 55 6 57 8 16 49 32 50 29 51 27 52 25 53 23 54 20 55 18 10 34 32 29 27 25 23 20 18 10 10 12 13 15 17 20 34 32 29 27 25 22 20 17 20 19 21 23 25 27 30 33 31 28 26 24 21 19 16 30 29 31 33 35 36 40 33 31 28 25 23 21 18 16 40 38 40 42 44 46 50 32 30 27 24 22 20 17 15 50 48 50 2 52 4 54 6 56 8 Sub. 17 48 31 49 29 50 26 51 23 52 21 53 18 54 16 55 13 10 30 28 25 22 20 17 14 12 10 10 12 13 15 17 2 20 28 26 23 20 18 15 12 10 20 19 21 23 25 27 3 30 27 25 22 19 17 14 11 9 30 29 31 33 34 36 4 40 26 24 21 18 16 13 10 7 40 38 40 42 44 46 5 1 50 26 48 24 23 20 17 15 52 13 12 53 10 9 6 50 48 50 2 52 4 53 6 55 8 6 1 7 1 18 49 21 50 18 51 15 54 7 55 4 10 23 20 17 14 12 9 6 3 10 10 11 13 15 17 8 1 20 22 19 16 13 11 8 5 2 20 19 21 23 25 27 9 1 30 21 18 15 12 10 6 3 30 29 30 32 34 36 40 20 17 14 10 8 4 1 54 58 40 38 40 42 44 46 50 19 18 15 12 9 51 7 6 52 4 2 53 59 56 50 48 50 2 51 4 53 6 55 8 48 16 49 13 50 10 53 53 57 54 55 10 15 12 8 5 2 52 59 55 53 10 10 11 13 15 17 20 13 10 6 3 57 53 51 20 19 21 23 25 27 30 12 8 5 2 51 58 55 51 49 30 29 30 32 34 36 40 10 6 3 56 53 49 47 40 38 40 42 44 46 50 9 5 2 50 58 55 51 48 45 50 48 50 51 53 55 Page 532] TABLE 21. 1 Correction of the Moon's Apparent Altitude for Parallax and Refraction. | [Barometer 30 inches.— Fahrenheit's Thermometer 50°.] 1 Moon's Horizontal parallax. "f d Correction for seconds of . parallax.— Add. Corr. for app. alt. C c 1^ minutes of alt. Sub 64' 66' 56' 57' 58' 69' 60' 61' 0" II 2" II 4" II 6" II 8" o / 1 II 1 11^ / II / // / II / // / // ' II II 20 48 6 49 3 49 59 50 56 51 52 52 49 53 45 54 42 2 4 6 8 V ^' 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 1 30 1 48 58 53 50 46 42 38 35 30 28 30 32 34 36 4 1 40 59 56 52 48 44 40. 36 33 40 38 39 41 43 45 5 1 50 57 47 55 54 50 46 42 51 39 38 34 53 31 30 50 47 49 2 51 4 53 6 54 7 6 1 7 1 21 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 1 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 14 50 47 49 50 52 54 22 47 42 48 37 49 33 50 29 51 25 52 20 53 16 54 11 2 4 6 7 10 40 35 30 26 22 17 13 8 10 9 11 13 15 17 20 37 32 I 27 23 19 14 10 5 20 19 20 22 24 26 30 34 30 i 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 25 , 20 48 22 ! 49 17 15 11 6 52 3 1 53 57 50 46 48 2 50 4 52 6 54 7 23 47 27 50 13 51 8 52 58 53 54 10 25 20 1 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 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 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 51 47 48 45 40 49 37 35 50 31 29 51 26 23 52 20 18 50 46 47 2 49 4 51 5 53 7 6 2 7 2 46 58 48 42 53 14 10 50 45 39 33 28 22 16 10 10 9 11 13 14 16 8 2 20 46 41 35 29 24 18 12 6 20 18 20 22 24 25 9 3 30 43 38 32 26 20 14 8 3 30 27 29 31 33 34 40 40 34 28 23 17 11 5 52 59 40 36 38 40 42 43 50 37 46 34 31 i 25 19 49 16 14 7 1 56 50 45 47 49 51 52 26 47 28 48 22 50 10 51 4 51 58 52 52 2 4 5 7 10 31 25 19 13 7 1 54 48 10 9 11 13 14 16 20 27 21 15 9 3 50 57 50 44 20 18 20 22 23 25 30 24 18 12 6 49 59 53 46 40 30 27 29 31 32 34 40 20 14 8 ,2 55 49 42 36 40 36 38 39 41 43 50 17 11 47 7 4 48 58 51 49 48 45 38 32 52"28 50 45 47 2 48 4 50 5 52 7 1 27 46 14 48 1 48 54 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 r 47 40 33 27 20 20 18 20 21 23 25 3 1 30 3 46 57 50 43 36 29 23 16 30 27 28 30 32 34 4 1 40 45 59 53 46 39 32 25 19 12 40 36 37 39 41 43 5 2 50 56 45 53" 49 46 46 42 47 38 35 48 31 28 21 15 8 50 44 46 48 50 52 6 2 7 3 28 49 24 50 17 51 11 52 4 2 4 5 7 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 26 46 22 19 47 15 11 4 49 49 57 49 53 49 42 50 44 46 2 48 4 49 5 51 7 29 45 30 48 7 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 TABLE 24. [Page 533 1 Correction of the Moon 's Apparent Altitude for Parallax and Refraction. 1 [Barometer 30 inches .—Fahrenheit's Thermometer 50°.] 1 Moon's Horizontal parallax -5^ Correction for seconds of paraillax.— Add. Corr. for app. alt. is minutes of alt. 54' 66' 56' 57' 58' 69' 60' 61' 0" 2" 4" II 6" II 8" o / / // / II / // / // / // / // / II / // „ // II II Sub. 30 45 6 45 57 46 50 47 42 48 34 49 26 50 18 51 10 2 3 5 7 V 0'' 10 2 54 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 5 2 50 31 45 44 41 38 29 21 12 4 49 55 47 50 42 50 43 45 2 47 3 49 5 50 7 6 3 7 3 45 33 46 24 47 16 48 7 48 59 49 50 10 37 29 20 12 2 54 45 37 10 9 10 12 14 15 8 4 20 33 24 15 7 47 58 49 40 32 20 17 19 21 22 24 9 4 30 28 20 11 2 54 45 36 27 30 26 27 29 31 32 40 24 16 7 46 58 49 40 31 22 40 34 36 38 39 41 50 20 . 11 2 53 44 35 26 49 22 17 50 13 50 43 44 2 46 3 48 5 50 7 32 44 15 45 7 45 58 46 49 47 40 48 31 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 25 27 29 30 32 40 43 58 48 39 29 20 11 1 52 40 34 35 37 39 41 50 54 44 34 24 15 6 48 56 47 50 42 44 2 46 3 47 5 49 7 1 33 43 48 44 39 45 29 46 19 47 10 48 48 50 49 41 10 44 34 25 15 5 47 55 45 36 10 8 10 12 13 15 2 1 20 40 30 20 10 50 40 31 20 17 18 20 22 23 3 1 30 35 25 15 5 46 55 45 35 25 30 25 27 28 30 32 4 2 40 30 20 10 50 40 30 20 40 33 35 37 38 40 5 2 50 34 25 15 5 45 55 45 35 24 14 50 42 43 45 47 48 6 3 7 3 43 21 44 11 45 45 50 46 40 47 30 48 19 49 9 2 3 5 7 10 16 6 44 55 45 34 24 14 3 10 8 10 12 13 15 8 4 20 11 1 50 40 29 19 9 48 58 20 17 18 20 21 23 9 4 30 6 43 56 45 35 24 13 3 52 30 25 26 28 30 31 40 1 51 40 30 19 8 47 58 47 40 33 35 36 38 40 50 42 56 46 35 24 14 3 46 58 52 42 50 41 43 2 44 3 46 5 48 7 35 42 52 43 41 44 30 45 19 46 9 47 47 48 36 10 47 36 25 14 3 52 41 30 10 8 10 11 13 15 20 42 31 20 9 45 58 47 • 36 25 20 16 18 20 21 23 30 37 26 15 3 52 41 30 19 30 24 26 28 29 31 40 32 21 10 44 58 47 36 25 14 40 33 34 36 38 39 50 27 16 4 53 42 30 46 25 19 8 48 2 50 41 42 2 44 3 46 5 47 6 36 42 22 43 11 43 59 44 48 45 37 47 14 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 45 51 44 33 50 40 42 2 43 3 45 5 47 6 5 3 6 3 37 41 51 42 39 43 27 44 15 45 3 46 39 47 27 10 46 34 21 9 44 57 45 33 21 10 8 10 11 13 14 7 4 20 41 29 16 4 52 40 27 15 20 16 17 19 21 22 8 4 30 35 23 11 43 58 46 34 21 9 30 24 25 27 29 30 9 5 40 30 18 5 53 40 28 15 3 40 32 33 35 37 38 50 25 41 19 12 42 59 47 34 44 29 22 45 16 9 46 3 46 57 46 51 50 40 41 2 43 3 45 5 46 6 38 42 7 42 54 43 41 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 45 32 30 23 25 27 28 30 40 40 58 45 32 18 6 52 39 26 40 31 33 35 36 38 50 52 39 26 42 20 13 43 7 43 54 46 44 40 33 20 50 39 41 2 42 3 44 5 46 6 39 40 47 41 33 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 15 17 19 20 22 2 1 30 30 17 3 49 36 22 8 45 54 30 23 25 26 28 29 3 2 40 25 11 41 57 43 30 16 2 48 40 31 32 34 36 37 4 2 50 19 5 51 37 23 9 44 55 42 50 39 40 42 43 45 5 3 Page 534] TABLE 24. 1 Correction of the Moon's Apparent Altitude for Parallax and Eefraction. | [Barometer 30 inches.— Fahrenheit's Thermometer 50°.] Moon's app. alt. Horizontal parallax. - Correction for .seconds of parallax. — Add. Corr. for minutes of alt. 54' 56' 56' 57' 58' 59' 60' 61' 0" // 2" II 4" II 6" II 8" II / / // 1 II / // 1 II / // / II ' II / II Sub. 40 40 14 41 9 41 46 42 32 43 18 44 4 44 60 45 36 2 3 6 6 6' W 10 8 40 54 39 26 11 43 57 43 29 10 8 9 11 12 14 7 4 20 2 48 33 19 6 50 36 22 20 15 17 18 20 21 8 5 30 39 66 42 28 13 42 59 44 30 16 30 23 24 26 27 29 9 6 40 50 36 22 7, 53 38 24 9 40 30 32 34 35 37 50 45 30 16 1 47 32 18 44 11 3 60 38 40 2 41 3 43 5 44 6 41 39 39 40 24 41 10 41 55 42 41 43 26 44 56 10 33 18 4 49 34 19 4 49 10 8 9 11 12 14 20 27 12 40 58 43 28 13 43 58 43 20 16 17 18 20 21 30 21 6 51 36 22 7 51 37 30 23 24 26 27 29 40 16 45 30 16 46 30 40 30 32 33 35 36 50 10 39 54 39 24 9 42 63 38 43 31 23 50 38 39 1 41 3 42 4 44 6 42 39 4 39 48 40 33 41 17 42 2 42 47 44 16 10 38 58 42 27 11 41 66 41 25 10 10 7 9 10 12 13 1 1 20 52 36 21 6 60 34 18 3 20 16 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 6 49 40 30 31 33 34 36 4 2 50 34 18 2 46 30 14 42 68 42 50 37 38 1 40 3 41 4 43 6 5 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 45 29 10 7 9 10 12 13 7 4 20 16 38 59 43 27 11 41 64 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 6 40 4 47 30 14 40 58 41 24 8 •40 29 31 32 34 36 50 37 57 37 51 41 38 35 24 7 51 34 17 42 10 1 50 37 38 1 39 3 41 4 42 6 44 39 18 40 1 40 44 41 27 42 54 10 45 28 11 39 54 37 20 3 46 10 7 9 10 11 13 20 38 21 4 47 30 13 41 56 39 20 14 16 17 19 20 30 32 15 38 58 41 24 7 49 32 30 21 23 24 26 27 40 26 9 51 34 17 42 25 40 29 30 31 33 34 50 20 2 44 27 10 40 63 35 41 28 18 42 11 60 0" 36 37 1 39 3 40 i 41 1 1 45 37 14 37 56 38 38 39 21 40 3 40 46 4 6 10 7 49 31 14 39 66 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 26 7 49 30 21 23 24 25 27 4 3 40 48 30 11 38 64 36 18 42 40 28 30 31 32 34 5 3 50 4(5 41 23 4 47 29 11 40 52 34 50 35 37 1 38 3 39 4 41 6 6 4 7 5 36 35 37 17 37 58 38 40 39 22 40 4 40 45 41 27 10 29 10 51 33 16 39 67 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 6 30 21 22 23 25 26 40 9 50 32 13 38 54 36 17 40 58 40 28 29 30 32 33 50 47 2 35 56 43 36 37 25 37 18 6 47 28 9 50 50 35 36 1 37 3 39 4 40 6 37 59 38 40 39 21 40 2 40 43 10 49 30 11 52 34 14 39 66 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 69 40 21 30 20 22 23 24 26 40 30 10 50 31 12 62 32 13 40 27 29 30 31 33 50 23 35 16 3 35 56 43 36 36 24 5 46 26 39 17 5 39 58 60 34 35 1 37 3 38 4 39 5 1 1 48 37 17 37 57 38 37 10 10 50 30 10 50 30 10 60 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 66 34 30 20 21 23 24 26 4 3 40 49 29 9 48 28 8 48 27 40 27 28 29 31 32 5 3 50 49 42 34 35 22 35 15 1 41 21 40 19 50 33 35 1 36 3 37 39 6 4 7 6 35 64 36 34 37 13 37 53 38 32 39 11 4 5 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 6 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 TABLE 24. [Page 635 Correction of the Moon's Apparent Altitude for Parallax and Refraction. 1 [Barometer 30 inches.— Fahrenheit's Thermometer 50°.] Moon's app. alt. Horizontal parallax. o 2 Correction for seconds of parallax.— Add. Corr. for minutes of alt. 54' 55' 56' 57' 68' 59' 60' 61' 0" 2" 4" 6" 8" o » ' // ' It ' // ' 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 34 57 36 14 36 53 31 9 20 13 14 15 17 18 30 33 11 49 28 6 45 23 1 30 19 20 22 23 24 40 26 4 42 20 35 58 37 15 37 53 40 26 27 28 29 31 50 19 33 57 35 34 28 13 51 29 7 45 50 32 33 1 35 3 36 4 37 5 Sub. 51 33 12 33 50 35 6 35 44 36 22 36 59 37 37 10 5 43 21 34 58 36 14 51 29 10 6 8 9 10 11 2 1 20 32 58 36 13 50 28 6 43 21 20 13 14 15 16 18 3 2 30 51 29 6 43 21 35 58 36 13 30 19 20 21 23 24 4 3 40 44 22 33 59 36 14 50 28 5 40 25 26 28 29 30 5 4 50 37 14 51 33 44 28 6 34 58 42 20 36 12 36 57 36 49 50 31 33 1 34 2 35 4 36 5 6 4 7 5 52 32 30 33 7 34 21 35 35 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 47 31 7 43 19 34 11 34 55 32 8 50 31 32 1 33 2 34 4 35 5 53 32 23 32 59 33 35 34 47 35 24 36 10 39 15 51 27 3 39 15 35 51 10 6 7 8 10 11 20 32 8 44 20 33 56 31 7 43 20 12 13 14 16 17 30 25 36 12 48 23 34 59 35 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 31 38 21 32 57 32 7 43 34 35 19 50 30 31 1 32 2 34 4 35 5 54 31 3 32 13 32 49 33 24 33 59 35 10 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 33 45 28 34 19 50 29 30 1 32 2 33 3 34 5 55 30 18 30 52 31 27 32 1 32 36 33 10 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 56 40 14 48 30 40 22 31 14 31 55 29 3 32 55 37 50 28 30 1 31 2 32 3 33 4 29 33 30 7 31 47 32 21 33 28 10 25 29 59 32 6 39 13 46 20 10 6 7 8 9 10 20 18 51 24 30 58 31 4 37 11 20 11 12 13 14 16 30 10 43 16 50 23 31 56 29 2 30 17 18 19 20 21 1 1 40 3 36 9 42 15 48 21 32 54 40 22 23 24 25 27 2 2 50 28 55 28 1 34» 7 40 12 45 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 3 32 36 10 39 12 45 17 50 22 31 55 27 10 5 6 7 9 10 5 4 20 32 5 37 9 42 14 47 19 20 11 12 13 14 15 6 5 30 24 28 57 29 1 33 6 38 10 30 16 17 18 19 21 7 5 40 17 49 21 29 53 25 30 57 29 1 40 22 23 24 25 26 8 6 50 58 9 41 13 45 17 49 21 3152 50 27 28 1 29 2 30 3 31 4 9 7 28 1 28 33 29 5 29 37 30 9 30 41 31 12 3144 10 27 53 25 28 57 28 32 4 35 10 5 6 7 8 9 20 45 17 49 • 20 29 52 23 30 55 26 20 10 12 13 14 15 30 38 9 41 12 44 15 46 17 30 16 17 18 19 20 40 30 1 33 4 35 6 38 9 40 21 22 23 24 25 50 22 27 14 27 53 27 45 24 28 55 27 29 58 29 49 29 30 20 50 26 27 1 28 2 29 3 30 4 59 28 16 28 47 29 18 30 51 10 6 37 7 38 9 40 11 42 10 5 6 7 8 9 20 26 58 29 27 59 30 1 31 2 33 20 10 11 12 13 14 30 51 21 51 22 28 53 23 29 54 24 30 15 16 17 18 19 40 43 13 43 14 44 14 45 15 40 20 21 22 23 24 50 35 5 35 5 36 6 36 A 50 25 26 27 29 30 Page 536] TABLE 24. Dorrection of the Moon's Apparent Altitude for Parallax and Refraction. [Barometer 30 inches.— Fahrenheit's Thermometer 50°.] Moon's app. alt. Horizontal parallax. §2 Correction for seconds of parallax.— Add. Corr. for minutes 64' 55' 56' 57' 58' 59' 60' 61' IS 0" 2" II 4" II 6" II 8" II of alt. o / / It / // ' II ' II / // ' // ' II ' II II // 60 26 26 26 67 *^7 27 27 57 28 27 28 57 29 27 29 67 1 2 3 4 10 19 49 19 49 19 49 18 48 10 6 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 16 16 17 18 19 40 25 55 24 26 63 23 27 63 22 28 61 21 40 20 21 22 23 24 50 47 16 46 14 44 13 42 12 50 26 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 26 28 54 10 5 6 7 8 9 20 23 26 62 20 49 18 47 16 45 20 10 11 12 12 13 30 16 43 12 40 10 38 7 35 30 14 16 16 17 18 40 7 36 4 32 1 29 27 58 26 40 19 20 21 22 23 50 24 59 27 25 65 24 26 62 20 49 17 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 28 8 10 42 10 38 6 34 2 30 27 68 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 26 26 27 63 24 2 24 29 24 56 26 23 25 51 26 18 26 45 27 12 1 2 3 4 10 23 54 21 48 15 42 9 36 3 10 4 5 6 7 8 20 46 13 39 6 33 27 26 64 20 9 10 11 12 13 30 37 4 31 24 68 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 26 3 26 3 64 23 12 23 39 24 6 24 32 24 58 26 24 25 50 26 17 10 4 31 23 67 23 49 16 41 8 10 4 6 6 7 8 20 22 56 22 48 14 40 6 32 26 58 20 9 10 10 11 12 30 47 13 39 5 31 24 57 22 48 30 13 14 16 16 16 40 39 5 30 23 56 22 48 13 39 40 17 18 19 20 21 50 31 22 67 22 48 13 39 4 24 55 30 25 21 60 22 23 1 23 2 24 2 25 3 Sub. 65 22 23 22 48 23 13 23 39 24 4 24 30 10 14 40 5 30 23 56 20 46 11 10 4 6 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 16 16 3 3 40 49 14 39 4 28 23 63 18 43 40 17 18 18 19 20 4 4 50 41 6 30 22 55 19 44 8 33 60 21 22 1 23 2 23 2 24 3 5 5 6 5 66 21 32 21 57 22 21 22 46 23 10 23 35 23 59 24 23 10 24 48 12 37 1 25 49 14 10 4 6 6 7 7 7 6 20 15 39 3 28 22 52 16 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 67 21 45 40 16 17 18 19 20 50 50 20 41 14 21 5 37 1 25 22 15 48 22 39 12 23 2 36 50 20 21 1 22 2 23 2 24 3 67 21 28 21 52 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 63 16 39 2 24 47 40 16 16 17 18 18 50 19 59 21 44 7 20 68 30 21 21 21 52 15 37 50 19 20 1 21 1 22 2 22 3 68 19 50 20 13 20 36 21 43 22 6 22 28 10 42 4 27 49 12 34 21 66 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 16 37 21 59 30 11 12 13 13 14 40 16 38 22 44 5 27 49 40 16 16 16 17 18 50 7 29 19 21 19 51 19 42 13 20 4 34 20 25 20 56 17 21 8 39 21 30 60 18 19 1 20 1 21 2 21 3 69 18 59 20 47 10 50 12 33 19 65 16 37 20 59 20 10 4 4 5 6 6 20 42 3 24 45 7 28 49 10 20 7 8 8 9 10 30 33 18 64 15 36 19 57 18 39 30 11 11 12 13 13 40 24 45 6 27 48 9 29 20 50 40 14 16 16 16 17 50 16 37 18 67 18 39 20 41 50 18 18 19 20 20 TABLE 24. [Page 537 1 Correction of the Moon's Apparent Altitude for Parallax and Refraction. [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' 55' 56' 57' 58' 59' 60' 61' 0" 2" 4" 6" 8" o / 1 II / II ' H / // ' II / // / II / // II // II // II II 70 18 7 18 28 18 48 19 9 19 30 19 50 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 51 11 20 7 7 8 9 9 30 41 1 21 41 1 21 41 1 30 10 11 11 12 13 40 32 17 53 12 32 18 52 12 32 19 52 40 13 14 15 15 16 50 24 44 17 35 3 23 18 14 43 3 18 53 22 42 50 17 17 1 18 1 19 2 19 3 71 17 15 17 54 18 34 19 12 19 32 10 6 26 45 5 24 43 3 22 10 3 4 4 5 6 20 16 57 17 36 17 55 14 33 18 53 12 20 6 7 8 8 9 30 48 8 27 46 5 24 43 2 30 10 10 11 12 12 40 40 16 59 18 37 17 56 15 34 18 52 40 13 13 14 15 15 50 31 50 9 28 47 17 37 5 24 42 50 16 17 1 17 1 18 2 19 2 72 16 22 16 41 17 17 18 17 55 18 14 18 32 10 13 32 16 50 9 27 46 4 22 10 3 4 4 5 5 20 5 23 41 16 59 18 36 17 54 12 20 6 7 7 8 8 30 15 57 14 32 50 9 27 45 3 30 9 10 10 11 11 40 48 5 23 41 16 59 17 35 17 53 40 12 13 13 14 14 50 39 15 56 14 32 16 22 50 16 40 7 25 43 17 33 50 15 16 1 16 1 17 2 18 2 73 15 30 15 47 16 5 16 58 17 15 10 21 38 15 56 13 30 48 5 23 10 3 3 4 5 5 20 12 29 47 4 21 39 16 56 13 20 6 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 53 40 11 12 13 13 14 50 45 2 14 53 19 35 15 52 15 42 9 26 42 50 14 15 15 16 2 17 2 Sub. 74 14 36 15 9 15 26 15 59 16 16 16 32 1 1 10 28 44 17 33 49 6 22 10 3 3 4 4 5 Y 1// 20 19 35 14 51 8 24 40 15 56 12 20 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 52 40 11 11 12 12 13 4 4 50 75 13 52 8 23 39 14 55 10 26 42 50 13 14 1 14 1 15 16 5 5 6 6 13.43 13 59 14 14 14 29 14 45 15 1 15 16 15 32 2 2 10 34 50 5 20 36 14 52 7 22 10 3 3 4 4 5 7 7 20 25 41 13 56 11 27 42 14 57 12 20 5 6 6 7 7 8 8 30 16 32 46 1 17 32 47 2 30 8 8 9 9 10 9 9 40 7 22 37 13 52 7 22 37 14 51 40 10 11 11 12 12 50 12 58 13 28 42 13 57 13 47 12 27 41 50 13 13 14 1 14 1 15 2 76 12 49 13 4 13 18 13 33 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 5 5 6 6 7 30 23 37 12 51 5 19 33 47 1 30 7 8 8 8 9 40 14 27 41 12 55 9 23 36 13 50 40 9 10 10 11 11 50 5 18 32 45 12 59 13 26 40 50 12 12 13 13 14 77 11 56 12 9 12 22 12 36 12 49 13 3 13 16 13 30 1 1 2 10 47 13 27 40 12 53 7 20 10 2 3 3 4 4 20 38 11 51 4 17 30 43 12 57 10 20 4 5 5 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 12 4 26 12 16 39 50 11 11 12 1 12 1 13 2 78 11 1 11 14 11 26 11 39 11 52 12 29 10 10 52 5 17 30 42 11 54 6 19 10 2 2 3 3 4 20 43 10 55 8 20 32 44 11 56 8 20 4 4 5 5 6 30 34 46 10 58 10 22 34 46 11 58 30 6 6 7 7 8 40 25 37 48 12 24 36 48 40 8 8 9 9 10 50 79 16 28 39 10 51 3 15 26 38 50 10 10 11 1 11 1 12 1 10 7 10 19 10 30 10 42 10 53 11 5 11 16 11 28 10 9 58 9 21 32 43 10 55 6 17 10 2 2 3 3 3 20 49 11 22 33 44 10 56 7 20 4 4 4 5 5 30 40 9 50 1 12 23 34 45 10 56 30 6 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 Page 538] TABLE 24. Correction of the Moon's Apparent Altitude for Parallax and Refraction. [Barometer 30 inches.— Fahrenheit's Thermometer 50°.] Moon's app. alt. Horizontal parallax. •a .2 5g Correction for seconds of parallax.— Add. Corr. for minutes 54' 55' 66' 57' 58' 69' 60' 61' ■ji "^ 0" 2" 4" 6" 8" of alt. o / ' n ' "•! ' II / // / // / // / // / // II II II II 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 55 5 20 3 4 4 4 5 30 45 8 55 5 15 25 35 45 9 54 30 5 5 6 6 6 40 36 46 8 55 5 15 25 35 44 40 / 7 7 8 8 50 27 37 46 8 37 8 56 6 15 25 9 14 34 50 8 9 9 1 9 1 10 1 81 8 18 8 27 8 46 8 56 9 5 9 24 10 9 18 27 36 46 8 55 4 13 10 1 2 2 2 3 20 7 59 8 17 26 36 45 8 54 3 20 3 3 4 4 4 30 50 7 59 8 17 26 35 44 8 52 30 4 5 5 5 6 40 41 50 7 59 8 17 25 34 42 40 6 6 6 7 7 50 32 41 49 7 58 7 15 24 8 13 32 50 7 8 8 1 8 1 9 1 82 7 23 7 31 7 40 7 48 7 57 8 5 8 22 10 14 22 30 38 47 7 55 3 11 10 1 2 2 2 2 20 4 12 20 28 37 45 7 52 20 3 3 3 3 4 30 6 55 3 11 19 27 35 42 7 50 30 4 4 5 5 5 40 46 6 54 2 10 17 25 32 40 40 5 6 6 6 6 50 37 45 6 52 6 50 1 15 7 5 22 7 12 30 50 7 7 7 7 1 8 1 Sub. 83 6 28 6 35 6 43 6 57 7 20 10 19 26 33 40 47 6 54 2 9 10 1 1 2 2 2 V V 20 9 16 23 30 37 44 6 51 6 58 20 2 3 3 3 3 2 2 30 1 13 20 27 34 41 48 .30 3 4 4 4 4 3 3 40 5 51 5 58 4 11 18 24 31 38 40 5 5 5 5 6 4 4 50 42 49 5 39 5 55 1 8 14 21 27 50 6 6 6 6 1 7 1 5 5 6 6 84 5 33 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 50 5 55 20 2 2 2 3 3 8 8 30 5 10 16 22 28 34 39 45 30 3 3 3 3 4 9 9 40 4 56 1 1 13 18 24 29 35 40 4 4 4 4 5 50 85 47 4 52 4 58 4 48 3 4 53 8 14 19 25 50 5 5 5 5 6 1 4 37 4 43 4 58 5 4 5 9 5 14 10 28 33 38 43 48 4 53 4 58 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 86 3 51 3 56 5 9 3 59 13 18 22 50 4 4 4 5 5 1 3 42 3 46 3 50 3 55 4 3 4 7 4 11 10 33 37 41 45 49 3 53 3 57 1 10 1 1 1 1 1 20 23 27 31 35 39 43 46 3 50 20 1 1 2 2 2 30 14 18 21 25 29 33 36 40 30 2 2 2 2 2 40 5 9 12 16 19 23 26 30 40 3 3 3 3 3 50 2 56 2 59 3 2 53 6 9 13 16 19 50 3 3 3 4 4 87 2 47 2 50 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 57 1 59 2 2 2 4 2 6 10 42 43 45 47 49 1 51 1 53 1 55 10 20 32 34 36 38 39 41 43 44 20 1 1 1 1 1 30 23 25 26 28 29 31 32 34 30 1 1 1 1 ] 40 14 15 16 19 20 21 22 24 40 1 1 1 1 1 50 5 6 7 9 10 11 12 13 1 3 50 0" 1 1 1 2 2 89 56 57 58 59 1 1 1 1 2 10 46 47 48 49 50 51 51 52 10 20 37 37 38 39 40 40 41 42 20 30 28 28 28 29 30 30 31 31 30 40 19 19 19 19 20 20 21 21 40 50 9 10 ■ 10 10 10 10 10 10 50 1 1 1 1 1 TABLE 25 [Page 539 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. It the change move the body toward 1 the elevated pole, apply the correction L to the altitude with the signs m the Table; otherwise, | change the signs. a o "S a 1 Q o o o Latitude of same name as declination. Latitude of different name from declination. < d .2 % c 1 70° 60° 60° 40° 80° 20° 10° 0° 10° 20° 30° 40° 50° 60° 70° 94 87 76 64 50 34 17 17 It 34 50 64 76 II 87 94 o o 10 95 88 78 65 51 35 18 18 35 51 65 78 88 95 10 ?.o 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 i 65 45 22 22 45 65 84 100 40 fSO 100 78 53 27 27 53 78 100 50 60 100 68 35 35 68 100 60 70 50 100 34 51 17 51 100 70 94 87 77 64 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 ?, 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 43 - 8 59 108 64 70 94 87 77 64 50 34 17 17 34 50 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 60 117 88 56 23 -12 47 81 112 60 70 127 81 32 -19 70 119 70 94 87 77 65 50 34 17 17 34 50 65 77 87 94 10 94 87 76 64 49 33 16 - 2 20 37 53 67 80 90 98 10 20 97 89 78 65 50 33 15 - 4 22 40 57 73 86 96 104 20 1 1 30 103 94 83 69 52 34 14 - 6 26 46 64 81 95 107 30 1 1 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 95 65 118 72 22 18 -29 80 129 70 87 77 50 35 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 1 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 6^ 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 1 1 30 100 91 80 65 49 30 10 -10 30 50 69 86 100 30 10 40 100 87 70 51 31 8 -15 38 60 81 100 40 10 50 100 81 58 33 6 -21 48 75 100 50 60 100 71' 39 5 -31 66 100 60 70 100 53 3 -48 100 70 96 89 78 66 51 35 18 18 35 51 66 78 89 96 10 94 86 76 63 48 32 14 — 4 22 39 56 70 83 94 101 10 20 94 86 76 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 1 a 70 134 91 44 -6 -58 110 70 1 B 6 70° 60° 60° 40° 80° 20° 10° 0° 10° 20° 80° 40° 50° 60° 70° 0) 3 I latitude of same name as 6 eclinat tion. Latitude of different name from declination. O < < Q Page 640] 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. Declination. Altitude. Latitude of same name as declination. Latitude of different name from declination. < c 1 70° 60° ^o 40° 80° 20° 10° 0° 10° 20° 80° 40° 60° 60° 70° 14 o 10 20 30 40 50 60 70 // 97 94 94 97 106 n 89 86 86 89 96 109 II 79 76 75 77 82 93 115 II 66 63 61 62 66 73 89 125 II 52 48 46 45 46 50 60 82 II 35 31 27 26 25 25 27 35 II 18 14 10 6 2 - 2 - 7 -16 II - 4 - 9 - 14 - 21 - 30 - 43 - 69 II 18 23 28 35 44 58 79 121 II 35 40 45 55 67 85 114 // 52 57 64 74 88 110 II 66 72 80 91 107 II 79 85 93 106 II 89 95 104 II 97 103 o 10 20 30 40 50 60 70 10 20 30 40 50 60 70 o 14 16 18 20 22 24 26 1 OS c 16 10 20 30 40 50 60 70 98 94 94 96 104 90 86 85 87 94 106 80 76 74 75 80 90 110 67 63 61 61 63 70 84 117 52 48 45 44 44 47 54 73 53 48 44 42 41 43 49 64 36 31 27 25 22 21 21 25 18 13 9 4 - 6 -14 -26 - 5 - 10 - 17 - 24 - 34 - 50 - 79 18 23 30 37 48 62 86 132 36 41 48 58 70 90 121 52 58 66 77 92 115 67 73 82 94 111 80 86 95 109 90 97 106 98 104 18 20 10 20 30 40 50 60 70 10 20 30 40 50 60 70 99 95 93 95 102 100 95 93 94 100 91 87 85 86 92 103 81 76 74 74 78 87 105 68 63 60 59 61 66 79 108 36 31 26 23 20 17 16 16 36 31 25 21 17 13 10 6 18 13 8 ■ 2 - 3 -10 -20 -36 - 6 - 12 - 19 - 27 - 39 - 56 - 89 18 24 31 40 51 67 93 143 36 42 50 60 74 95 128 53 59 68 79- 96 121 68 74 84 97 116 81 88 98 112 91 98 109 99 106 10 20 30 40 50 60 70 92 87 85 85 90 100 82 76 74 73 76 83 100 68 63 60 58 59 63 74 100 53 48 43 40 39 39 43 56 18 12 6 - 6 -15 -26 -46 - 6 - 13 - 21 - 31 - 43 - 63 -100 18 25 33 42 55 72 100 36 43 52 63 78 100 53 60 70 82 100 68 76 86 100 82 89 100 92 100 100 10 20 30 40 50 60 70 22 10 20 30 40 50 60 70 96 93 94 98 110 93 88 85 85 88 97 117 83 77 73 72 74 80 95 131 69 63 59 57 57 60 68 92 •54 48 43 39 36 36 38 47 37 30 25 19 14 9 4 - 3 19 12 5 - 2 - 9 -19 -33 -56 ^ 7 - 15 - 23 - 34 - 48 - 70 -111 19 26 35 45 58 77 107 37 45 54 66 82 106 54 62 72 86 104. 69 78 88 103 83 91 103 93 102 101 10 20 30 40 50 60 70 24 10 20 30 40 50 60 70 97 93 93 97 107 95 88 85 84 86 93 112 84 77 73 71 72 77 91 123 70 64 59 56 54 56 64 83 55 48 42 38 34 .32 32 38 37 30 24 18 12 5 - 2 -13 19 11 4 - 4 -12 -23 -39 -67 - 8 - 16 - 26 - 37 - 53 - 77 -122 19 27 36 48 62 83 115 37 46 56 69 86 111 55 63 74 89 109 70 79 91 107 84 93 105 95 104 103 10 20 30 40 50 60 70 0" 10 20 30 40 50 60 70 26 10 20 30 40 50 60 70 98 95 93 96 105 96 89 85 83 85 92 108 85 78 73 70 70 74 86 115 72 64 59 54 52 53 58 75 56 48 41 36 32 28 27 29 38 30 23 16 9 1 - 8 -23 19 11 3 - 6 -16 -28 -46 -78 - 9 - 18 - 28 - 41 - 58 - 84 -134 19 28 38 50 66 88 123 38 47 58 72 91 117 56 65 77 92 114 72 81 94 111 85 95 108 96 106 105 © c "3 OJ 1 < 70° 60° 50° 40° 80° 20° 10° 0° 10° 20° 80° 40° 50° 60° 70° 6 Latitude of same name as declination. L atitud eof d iflerent name from declination. TABLE 26. [Page 641 Variation of Altitude in one minute from meridian passage Declination of the same name a.s the latitude; npper transit; reduction additive. Lati- tude. 0° Lati- tude. 1° .2° 3° 40 5° 6° 70 8° 9° 10° 11° o II II II II // II II // II II II II 28.1 22.4 18.7 16.0 14.0 12.4 11.1 10.1 1 28.0 22.4 18.6 16.0 13.9 12.4 11.1 1 2 28.0 22.3 18.6 15.9 13.9 12.3 2 3 27.9 22.3 18.5 15.8 13.8 3 4 5 28.1 22. 4^ 27.8 22.2 18.5 15.8 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 11.1 13.9 12. 4 15.9 18.5 22.2 18.5 27.7 22.1 9 10 10 13.9 15.8 27.6 11 10.1 11.1 12.3 13.8 15.8 18.4 22.0 27.4 11 12 9.2 10.1 11.1 12.3 13.8 15.7 18.3 21.9 27.3 12 13 8,5 9.2 10.0 11.0 12.2' 13.7 15.6 18.2 21.7 27.1 13 14 15 7.9 8.5 9.2 10.0 10.9 12.1 10.9 13.6 12.1 15.5 18.0 21.6 26.9 14 15 7.3 7.8 8.4 9.1 9.9 13.5 15.4 17.9 21.4 26.7 16 6.8 7.3 7.8 8.4 9.1 9.8 10.8 12.0 13.4 15.3 17.8 21.3 16 17 6.4 6.8 7.2 7.8 8.3 9.0 9.8 10.7 11.9 13.3 15.2 17.6 17 18 6.0 6.4 6.8 7.2 7. 7 8.3 8.9 9.7 10.6 11.8 13.2 15.0 18 19 5.7 6.0 6.3 6.7 6.3 7.2 7.6 8.2 8.9 9.6 10.6 9.5 11.7 13.1 19 20 20 5.4 5.7 6.0 6.7 7.1 7.6 8.1 8.8 10.5 11.6 21 5.1 5.4 5.6 5.9 6.3 6.6 7.0 7.5 8.1 8.7 9.5 10.4 21 22 4.9 5.1 5.3 5.6 5.9 6.2 6.6 7.0 7.5 8.0 8.6 9.4 22 23 4.6 4.8 5.0 5.3 5.5 5.8 6.1 6.5 6.9 7.4 7.9 8.5 23 24 4.4 4.6 4.8 5.0 5.2 5.5 5.8 6.1 6.4 6.8 7.3 7.8 24 25 25 4.2 4.4 4.6 4.7 5.0 5.2 5.4 5.7 6.0 6.4 6.8 7.2 26 4.0 4.2 4.3 4.5 4.7 4.9 5.1 5.4 5.7 6.0 6.3 6.7 26 27 3.9 4.0 4.1 4.3 4.5 4.7 4.9 5.1 5.3 5.6 5.9 6.2 27 28 3.7 3.8 4.0 4.1 4.3 4.4 4.6 4.8 5.0 5.3 5.5 5.8 28 29 3.5 3.7 3.8 3.9 4.1 4.2 4,4 4.6 4.7 5.0 5.2 5.5 5.1 29 30 80 3.4 3.5 3.6 3.7 3.9 4.0 4.2 4.3 4.5 4.7 4.9 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 34 35 2.8 2.9 3.0 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.9 35 36 2.7 2.8 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 36 37 2.6 2.7 2.7 2.8 2.9 2.9 3.0 3.1 3.2 3.3 3.4 3.5 37 38 2.5 2.6 2.6 2.7 2.8 2.8 2.9 3.0 3.0 3.2 3.2 3.3 38 39 2.4 2.5 2.5 2.6 2.7 2.7 2.8 2.9 2.9 3.0 3.1 3.2 39 40 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 41 2.3 2.3 2.4 2.4 2.5 2.5 2.6 2.6 2.7 2.8 2.8 2.9 41 42 2.2 2.2 2.3 2.3 2.4 2.4 2.5 2.5 2.6 2.6 2.7 2.8 42 43 2.1 2.1 2.2 2.2 2.3 2.3 2.4 2.4 2.5 2.5 2.6 2.7 43 44 2.0 2.0 2.1 2.1 2.1 2.2 2.1 2.2 2.3 2.3 2.4 2.4 2.5 2.5 44 45 2.0 2.0 2.1 2.2 2.2 2.2 2.3 2.3 2.4 2.4 45 46 1.9 1.9 2.0 2.0 2.0 2.1 2.1 2.2 2.2 2.2 2.3 2.3 46 47 1.8 1.9 1.9 1.9 2.0 2.0 2.0 2.1 2.1 2.1 2.2 2.2 47 48 1.8 1.8 1.8 1.9 1.-9 1.9 2.0 2.0 2.0 2.1 2.1 2.1 48 49 50 1.7 1.6 1.7 1.8 1.8 1.8 1.8 1.9 1.8 1.9 1.9 2.0 1.9 2.0 2.1 49 1.7 1.7 1.7 1.8 1.8 1.8 1.9 1.9 2.0 50 51 1.6 1.6 1.6 1.7 1.7 1.7 1.7 1.8 1.8 1.8 1.9 1.9 51 52 1.5 1.6 1.6 1.6 1.6 1.6 1.7 1.7 1.7 1.8 1.8 1.8 52 53 1.5 1.5 1.5 1.5 1.6 1.6 1.6 1.6 1.7 1.7 1.7 1.7 53 54 1.4 1.4 1.5 1.5 1.5 1.5 1.5 1.5 1.6 1.6 1.6 1.6 1.7 54 55 1.4 1.4 1.4 1.4 1.5 1.5 1.5 1.5 1.6 1.6 1.6 55 56 1.3 1.3 1.4 1.4 1.4 1.4 1.4 1.4 1.5 1.5 1.5 1.5 56 57 1.3 1.3 1.3 1.3 1.3 1.4 1.4 1.4 1.4 1.4 1.4 1.5 57 58 1.2 1.2 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.4 1.4 1.4 58 59 1.2 1.2 1.2 1.2 1.2 1.3 1.3 1.3 1.3 1.3 1.3 1.3 59 60 1.1 1.1 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.3 1.3 60 0° 1° 2° 3° 4° 5° 6° 70 8° 90 10° 11° De elinatio n of the same name as the latitude; upper tra nsit; red) etion add Itire. Page 542J TABL?: 26. Variation of Altitude in one minute from meridian passage. Lati- tude. Declination of the same name as the latitude; upper transit reduction addltlre. Lati- tude. 12° 18° 14° 15° 16° 17° 18° 19° 20° 21° 22° 28° 24° c 9.2 8.5 7.9 II 7.3 6.8 6.4 II 6.0 5.7 II 5,4 II 5.1 4.9 II 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 «.2 8.4 7.8 7.2 6.8 6.3 6.0 5.6 5.3 5.0 4.8 9 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 15.7 12.2 13.7 10.9 9.9 9.1 8.3 7.7 7,2 6.7 6.3 5,9 5.5 5.2 4 5 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 / 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 9.5 8.7 8.0 7.4 6.8 9 10 10 26.9 21.4 17.8 15.2 13.2 11.7 10,5 9.5 8.6 7.9 7.3 11 26.7 21.3 17.6 15.0 13.1 11,6 10.4 9.4 8,5 7.8 11 12 26.5 21.1 17.5 14,9 13,0 11.5 10.3 9,3 8.4 12 13 26.2 20.9 17,3 14.8 12.8 11.3 10,1 9.2 13 14 26.0 20.7 17.1 14.6 12.7 11,2 10.0 14 15 25.7 20.4 16.9 14,4 12.5 11.1 15 16 26.5 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 9.0 11.1 12.4 14.1 16.3 19,5 24.2 24 25 7.7 8.3 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 12.8 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 14.9 30 31 5.1 5.3 6.6 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 2,0 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 56 1.5 1.6 1.6 1.6 1.6 1.7 1.7 1,7 1.8 1,8 1.8 1.9 1,9 56 57 1.5 1.5 1.5 1.5 1.6 1,6 1.6 1,6 1.7 1.7 1.7 1.8 1,8 57 58 1.4 1.4 1.5 1.5 1.5 1.5 1.5 1,6 1.6 1.6 1.6 1.7 1.7 58 59 1.4 1.4 1.4 1.4 1.4 1.5 1.5 1.5 1.5 1,5 1.6 1.6 1.6 59 60 1.3 1.3 1.3 1.3 1.4 1.4 1.4 1,4 1.4 1.5 1.5 1.5 1.5 60 12° 18° 14° 15° 16° 17° 18° 19° 20° 21° 22° 23° 24° De< jlinatior I of the t ame nai ne as th 3 latitud e; uppei transit; reducti on addit l¥e. TABLE 26. [Page 543 Variation of Altitude in one minute from meridian passage. Declination of the same name as the latitude; upper transit reduction additive. Lati- tude. Lati- tude. 26° 26° 27° 28° 29° 30° 31° 32° 83° 34° 35° 36° 37° o 4.2 4.0 3.9 3.7 3.5 3.4 3.3 3.1 3.0 2.9 2.8 2.7 2.6 o 1 4.4 4.2 4.0 3.8 3.7 3.5 3.4 3.2 3.1 3.0 2.9 2.8 2.7 1 2 4.6 4.3 4.1 4.0 3.8 3.6 3.5 3.3 3.2 3.1 3.0 2.8 2.7 2 3 4.7 4.5 4.3 4.1 3.9 3.7 3.6 3.4 3.3 3.2 3.0 2.9 2.8 3 4 5 5.0 4.7 4.5 4.3 4.1 3.9 3.7 3.5 3.4 3.3 3.1 3.0 3.1 2.9 4 5.2 4.9 4.7 4.4 4.2 4.0 3.8 3.7 3.5 3.3 3.2 3.0 5 6 5.4 6.1 4.9 4.6 4.4 4.2 4.0 3.8 3.6 3.5 3.3 3.2 3.0 6 7 5.7 5.4 5.1 4.8 4.6 4.3 4.1 3.9 3.7 3.6 3.4 3.3 3.1 7 8 6.0 5. 7 5.3 5.0 4.8 4.5 4.3 4.1 3.9 3.7 3.5 3.4 3.2 8 9 6.4 6.0 5.6 5.3 5.0 4.7 4.4 4.2 4.0 3.8 3.6 3.5 3.3 9 10 6.8 6.3 5.9 5.5 5.2 4.9 4.6 4.4 4.2 3.9 3.8 3.6 3.4 10 11 7.2 6.7 6.2 5.8 5.5 5.1 4.8 4.6 4.3 4.1 3.9 3.7 3.5 11 12 7.7 7.1 6.6 6.2 5.8 5.4 5.1 4.8 4.5 4.3 4.0 3.8 3.6 12 13 8.3 7.6 7.1 6.5 6.1 5.7 5.3 5.0 4.7 4.4 4.2 4.0 3.8 13 14 15 9.1 9. 9 8.2 7.6 7.0 6.4 6.0 5.6 5.2 4.9 4.6 4.4 4.1 3.9 4.0 14 8.9 8.1 7.4 6.9 6.4 5.9 5.5 5.2 4.8 4.5 4.3 15 16 10.9 9.8 8.8 8.0 7.3 6.8 6.3 5.8 5.4 5.1 4.8 4.5 4.2 16 17 12.2 10.8 9.6 8.7 7.9 7.2 6.7 6.2 5.7 5.3 5.0 4.7 4.4 17 18 13.9 12.1 10.6 9.5 8.6 7.8 7.1 6.6 6.1 5.6 5.2 4.9 4.6 18 19 16.1 13.7 11.9 10.5 9.4 8.4 7.7 7.0 6.4 6.0 5.5 5.1 4.8 19 20 19.2 15.9 13.5 11.7 10.3 9.2 8.3 7.5 6.9 6.3 5.8 5.4 5.0 20 21 23.8 18.9 15.6 13.3 11.5 10.2 9.1 8.2 7.4 6.8 6.2 5.7 5.3 21 22 23. 5 18.6 15.4 13.1 11.3 10.0 8.9 8.0 7.3 6.6 6.1 5.6 22 23 23.1 18.3 15.1 12.8 11.1 9.8 8.7 7.9 7.1 6.5 6.0 23 24 22.7 18.0 14.9 12.6 10.9 9.6 8.6 7.7 7.0 6.4 24 25 22.3 17.7 14.6 12.4 10.7 9.4 8.4 7.5 6.8 25 26 21.9 17.4 14.3 12.1 10.5 9.2 8.2 7.4 26 27 21.5 17.0 14.0 11.9 10.3 9.1 8.1 27 28 . 21.1 16.7 13.8 11.7 10.1 8.9 28 29 22.3 20.6 16.3 13.5 11.4 9.9 29 30 17.7 21.9 20.2 16.0 13.2 11.1 30 31 14.6 17.4 21.5 19.8 15.6 12.9 31 32 12.4 14.3 17.0 21.1 19.3 15.3 32 33 10.7 12.1 14.0 16.7 20.6 18.9 33 34 9.4 10.5 11.9 13.8 16.3 20.2 34 35 8.4 9.2 10.3 11.7 13.5 16.0 19.8 35 36 7.5 8.2 9.1 10.1 11.4 13.2 15.6 19.3 36 37 6.8 7.4 8.1 8.9 9.9 11.1 12.9 15.3 18.9 37 38 6.2 6.7 7.2 7.9 8.7 9.6 10.9 12.6 14.9 18.4 38 39 5.7 5.3 6.1 6.5 7.1 7.7 8.5 9.4 10.6 9.2 12.2 14.5 17.9 39 40 5.6 6.0 6.4 6.9 7.5 8.2 10.4 11.9 14.1 17.4 40 41 4.9 5.2 5.5 5.8 6.2 6.7 7.3 8.0 8.9 10.1 11.6 13.8 17.0 41 42 4.5 4.8 5.0 5.3 5.7 6.1 6.6 7.1 7.8 8.7 9.8 11.3 13.4 42 43 4.2 4.4 4.6 4.9 5.2 5.5 5.9 6.4 6.9 7.6 8.5 9.5 11.0 43 44 3.9 4.1 4.3 4.5 4.8 5.1 5.4 5.8 6.2 6.7 7.4 8.2 9.3 44 45 3.7 3.8 4.0 4.2 4.4 4.7 4.9 5.2 5.6 6.0 6.6 7.2 8.0 45 46 3.5 3.6 3.7 3.9 4.1 4.3 4.5 4.8 5.1 5.4 5.9 6.4 7.0 46 47 3.3 3.4 3.5 3.6 3.8 4.0 4.2 4.4 4.6 4.9 5.3 5.7 6.2 47 48 3.1 3.2 3.3 3.4 3.5- 3.7 3.9 4.0 4.3 4.5 4.8 5.1 5.5 48 49 50 2.9 3.0 3.1 3.2 3.3 3.4 3.6 3.7 3.9 4.1 4.4 4.6 5.0 49 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.5 3.6 3.8 4.0 4.2 4.5 50 51 2.6 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.4 3.5 3.7 3.9 4.1 51 52 2.4 2.5 2.6 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.4 3.6 3.7 52 53 2.3 2.3 2.4 2.5 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.3 3.4 53 54 2.2 2.2 2.3 2.3 2.4 2.5 2.5 2.6 2.7 2.8 2.9 3.0 3.2 54 55 2.0 2.1 2.1 2.2 2.3 2.3 2.4 2.4 2.5 2.6 2.7 2.8 2.9 55 56 1.9 2.0 2.0 2.1 2.1 2.2 2.2 2.3 2.4 2.4 2.5 2.6 2.7 56 57 1.8 1.9 1.9 2.0 2.0 2.0 2.1 2.2 2.2 2.3 2.3 2.4 2.5 57 58 1.7 1.8 1.8 1.8 1.9 1.9 2.0 2.0 2.1 2.1 2.2 2.3 2.3 58 59 1.6 1.7 1.7 1.7 1.8 1.8 1.9 1.9 1.9 2.0 2.0 2.1 2.2 59 60 1.6 1.6 1.6 1.6- 1.7 1.7 1.7 1.8 1.8 1.9 1.9 2.0 2.0 60 25° 26° 27° 28° 29° 80° 31° 32° 88° 34° 85°| 86° 87° De 3linatlor 1 of the same na me as th e latltuc le; uppe r transit reduct on addl tlve. Page 544 TABLE 26. Variation of Altitude in one minute from meridian past^age. Declination of the same name a« the latitude; upper transit reduction additive. Lati- tude. Lati- tude. o 88° 89° 40° 41° 42° 48° 44° 46° 46° 47° 48° 49° 60° o 2.5 2.4 2.3 2.3 2.2 2.1 2.0 It 2.0 1.9 1.8 1.8 II 1. 7 1.7 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 5 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 2.8 2.7 2.6 2.5 2.4 2.3 2.2 2.2 2.1 2.0 1.9 1.9 1.8 5 6 2.9 2.8 2.7 2.6 2.5 2.4 2.3 2.2 2.1 2.0 2.0 1.9 1.8 6 7 3.0 2.9 2.7 2.6 2.5 2.4 2.3 2.2 2.2 2.1 2.0 1.9 1.8 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 2.7 2.5 2.4 2.3 2.2 2.2 2.1 2.0 1.9 9 10 3.3 3.1 3.0 2.8 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 2.1 14 15 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 16 4.0 3.8 3.6 3.4 3.2 3.0 2.9 2.8 2.6 2.5 2.4 2.3 2.2 16 17 4.1 3.9 3.7 3.5 3.3 3.1 3.0 2.8 2.7 2.6 2.4 2.3 2.2 17 18 4.3 4.1 3.8 3.6 3.4 3.2 3.1 2.9 2.8 2.6 2.5 2.4 2.3 18 19 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 2.5 2.4 21 4.9 4.6 4.3 4.0 3.8 3.6 3.4 3.2 3.0 2.9 2.7 2.6 2.4 21 22 5.2 4.8 4.5 4.2 4.0 3.7 3.5 3.3 3.1 2.9 2.8 2.6 2.5 22 23 5.5 5.1 4.7 4.4 4.1 3.9 3.6 3.4 3.2 3.0 2.9 2.7 2.6 23 24 25 5.8 5.4 5.0 4.6 4.3 4.0 3.8 3.5 3.3- 3.1 3.0 2.8 2.6 2.7 24 25 6.2 5.7 5.3 4.9 4.5 4.2 3.9 3.7 3.5 3.3 3.1 2.9 26 6.7 6.1 5.6 5.2 4.8 4.4 4.1 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 3.5 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 4.5 4.2 3.9 3.6 3.3 31 32 12.6 10.6 9.2 8.0 7.1 6.4 5.8 5.2 4.8 4.4 4.0 3.7 3.5 32 33 14.9 12.2 10.4 8.9 7.8 6.9 6.2 5.6 5.1 4.6 4.3 3.9 3.6 33 34 35 18.4 14.5 11.9 10.1 8.7 7.6 6.7 6.0 5.4 4.9 4.5 4.1 3.8 34 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 5.5 5.0 4.5 37 38 16.5 13.0 10.7 9.0 7.7 6.8 6.0 5.3 4.8 38 39 16.0 12.6 10.3 8.7 7.5 6.5 5.8 5.1 39 40 15.5 12.2 10.0 8.4 7.2 6.3 5.6 40 41 15.0 11.8 9.7 8.1 7.0 6.1 41 42 16.5 14.5 11.4 9.3 7.9 6.7 42 43 13.0 16.0 14.0 11.0 9.0 7.6 43 44 10.7 12.6 15.5 13.6 10.6 8.7 44 45 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 4.8 5.1 5.6 6.1 6.7 7.6 8.7 10.2 12.6 50 51 4.3 4.6 5.0 5.4 5.9 6.5 7.3 8.4 9.9 12.1 51 52 3.9 4.2 4.5 4.8 5.2 5.7 6.3 7.0 8.0 9.5 11.6 52 53 3.6 3.8 4.0 4.3 4.6 5.0 5.4 6.0 6.7 7. 7 9.1 11.1 53 54 55 3.3 3.5 3.7 3.9 3.5 4.1 3.7 4.4 4.8 5.2 5.8 6.5 7.4 8.7 7.1 10.6 54 55" 3.0 3.2 3.3 4.0 4.3 4.6 5.0 5.5 6.2 8.3 56 2.8 2.9 3.1 3.2 3.4 3.6 3.8 4.1 4.4 4.8 5.3 5.9 6.8 56 57 2.6 2.7 2.8 2.9 3.1 3.2 3.4 3.6 3.9 4.2 4.6 5.0 5.6 o/ 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° 50° De .'linatior 1 of the «anie nai Tie as th e latitiid c; uppei transit red net i on addit hi'. TABLE 26. [Page 545 Variation of Altitude in one minute from meridian passage. Declination of the same name as the latitude; upper transit reduction additive. Lati- tude. Lati- tude. 51° 52° oS° 54° 55° 56° 67° 58° 69° 60° 61° 62° 68° n II II II II II II II II II II II II 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 L7 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 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 2.0 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 2.2 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 20 2.3 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 30 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 2.8 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 35 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 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 40 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 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 4.6 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° 52° 53° 54° 55° 56° 57° 58° 69° 60° 61° 62° 68° De ^linatioi 1 of the liame nai ne as th e latitat e; uppe r transit reduct on addll Ive. 22480—03- Page 546] TABLE 26. Variation of Altitude in one minute from meridian passage Lati- tnde. Declination of a different name from the latitude ; upper transit; reduction additive. Lati- tude. 0° 1° go 8° 4° 5° 6° 70 8° 9° 10° 11° o II // II II // II II II II II II II 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 22] 4 22.4 18.7 16.0 14.0 12.5 11.2 10.2 9.3 8.6 2 3 28.1 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 11.2 10.2 9.3 8.6 8.0 7.4 4 5 22.4 18.7 16.0 14.0 12.5 10.2 9.3 8.6 8.0 7.4 7.0 5 6 18.7 16.0 14.0 12.5 11.2 10.2 9.3 8.6 8.0 7.5 7.0 6.6 6 7 16.0 14.0 12.4 11.2 10.2 9.3 8.6 8.0 7.5 7.0 6.6 6.2 7 8 14.0 12.4 11.2 10.2 9.3 8.6 8.0 7.5 7.0 6.6 6.2 5.9 8 9 12.4 11.2 10.2 9.3 8.6 8.0 7.4 7.5 7.0 6.6 6.2 5.9 5.6 5.3 9 10 10 11.1 10.1 9.3 8.6 8.0 7.0 6.6 6.2 5.9 5.6 11 10.1 9.3 8.6 8.0 7.4 7.0 6.6 6.2 5.9 5.6 5.3 5.1 11 12 9.2 8.5 7.9 7.4 7.0 6.5 6.2 5.9 5.6 5.3 5.0 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 5.0 4.8 4.6 4.4 14 15 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 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. 4.8 4.6 4.4 4.2 4.1 3.9 17 18 6.0 5.7 5.5 5.2 5. 4. 8 4.0 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 3.0 3.7 3.6 3.5 3.4 21 22 4.9 4.7 4.5 4.3 4.1 4.0 3.9 3.7 3.6 3.5 3.4 3.3 22 23 4.6 4.4 4.3 4.1 4.0 3.8 3.7 3.6 3.5 3.4 3.3 3.2 23 24 4.4 4.2 4.1 3.9 3.8 3.7 3.6 3.5 3.4 3.3 3.2 3.1 24 25 4.2 4.1 3.9 3.8 3.7 3.5 3.4 3.3 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 3.0 2.9 2.8 2.8 2.7 2.6 29 30 3.4 3.3 3.2 3.1 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 2.5 2.5 2.4 32 33 3.0 2.9 2.9 2.8 2.7 2.7 2.6 2.5 2.5 2.4 2.4 2.3 33 34 2.9 2.8 2.8 2.7 2.6 2.6 2.5 2.5 2.4 2.4 2.3 2.3 34 35 2.8 2.7 2.7 2.6 2.5 2.5 2.4 2.4 2.3 2.3 2.2 2.2 35 36 2.7 2.6 2.6 2.5 2.5 2.4 2.4 2.3 2.3 2.2 2.2 2.1 36 37 2.6 2.5 2.5 2.4 2.4 2.3 2.3 2.2 2.2 2.2 2.1 2.1 37 38 2.5 2.5 2.4 2.4 2.3 2.3 2.2 2.2 2.1 2.1 2.1 2.0 38 39 2.4 2.4 2.3 2.3 2.2 2.2 2.1 2.1 2.1 2.0 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 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 45 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 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 1.5 48 49 1.7 1.7 1.7 1.6 1.6 1.6 1.6 1.5 1.5 1.5 1.5 1.5 49 50 1.6 1.6 1.6 1.6 1.6 , 1.5 1.5 1.5 1.5 1.5 1.4 1.4 50 51 1.6 1.6 1.6 1.5 1.5 1.5 1.5 1.5 1.4 1.4 1.4 1.4 51 52 1.5 1.5 1.5 1.5 1.5 1.4 1.4 1.4 1.4 1.4 1.4 1.3 52 53 1.5 1.5 1.4 1.4 1.4 1.4 1.4 1.4 1.3 1.3 1.3 1.3 53 54 1.4 1.4 1.4 1.4 1.4 1.3 , 1.3 1.3 1.3 1.3 1.3 1.3 1.3 54 55 1.4 1.4 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 50 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° 3° 4° 5° 6° 70 8° 9° 10° 11° Declir lation 0: a differ ent name from th s latitude ; upper tr ansit; rer luction a( Iditire. TABLE 26. [Page 547 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° 13° 14° 15° 16° 17° 18° 19° 20° 21° 22° 23° 24° o 1 2 3 4 9.2 8.5 7.9 7.4 7.0 8.5 7.9 7.4 6.9 6.5 II 7.9 7.4 •6.9 6.5 6.2 5.8 5.5 5.3 5.0 4.8 II 7.3 6.9 6.5 6.1 5.8 5.5 5.3 5.0 4.8 4.6 II 6.8 6.5 6.1 5.8 5.5 5.2 5.0 4.8 4.6 4.4 II 6.4 6.1 5.8 5.5 5.2 II 6.0 5.7 5.5 5.2 5.0 II 5.7 5.4 5.2 4.9 4.7 II 5.4 5.1 4.9 4.7 4.5 II 5.1 4.9 4.7 4.5 4.3 II 4.9 4.7 4.5 4.3 4.1 II 4.6 4.4 4.3 4.1 4.0 II 4.4 4.2 4.1 3.9 3.8 1 2 3 4 5 6 7 8 9 6.5 6.2 5.9 5.6 5.3 6.2 5.8 5.6 5.3 5.0 5.0 4.8 4.6 4.4 4.2 4.8 4.6 4.4 4.2 4.1 4.5 4.4 4.2 4.0 3.9 4.3 4.2 4.0 3.9 3.8 4.2 4.0 3.9 3.7 3.6 4.0 3.9 3.7 3.6 3.5 3.8 3.7 3.6 3.5 3.4 3.7 3.6 3.5 3.4 3.3 5 6 7 8 9 10 11 12 13 14 5.0 4.8 4.6 4.4 4.2 4.8 4.6 4.4 4.3 4.1 4.6 4.4 4.3 4.1 3.9 4.4 4.2 4.1 3.9 3.8 4.2 4.1 3.9 3.8 3.7 4.1 3.9 3.8 3.7 3.5 3.9 3.8 3.7 3.5 3.4 3.8 3.6 3.5 3.4 3.3 3.6 3.5 3.4 3.3 3.2 3.5 3.4 3.3 3.2 3.1 3.4 3.3 3.2 3.1 3.0 3.3 3.2 3.1 3.0 2.9 3.2 3.1 3.0 2.9 2.8 10 11 12 13 14 15 16 17 18 19 4.1 3.9 3.8 3.7 3.5 3.9 3.8 3.7 3.5 3.4 3.8 3.7 3.5 3.4 3.3 3.7 3.5 3.4 3.3 3.2 3.5 3.4 3.3 3.2 3.1 3.4 3.3 3.2 3.1 3.0 3.3 3.2 3.1 3.0 2.9 3.2 3.1 3.0 2.9 2.9 3.1 3.0 2.9 2.9 2.8 3.0 2.9 2.8 2.8 2.7 2.9 2.8 2.8 2.7 2.6 2.8 2.8 2.7 2.6 2.6 2.8 2.7 2.6 2.5 2.5 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 3.4 3.3 3.2 3.1 3.0 3.3 3.2 3.1 3.0 2.9 3.2 3.1 3.0 2.9 2,8 3.1 3.0 2.9 2.8 2.8 3.0 2.9 2.8 2.8 2.7 2.9 2.8 2.8 2.7 2.6 2.9 2.8 2.7 2.6 2.5 2.8 2.7 2.6 2.6 2.5 2.7 2.6 2.6 2.5 2.4 2.6 2.6 2.5 2.4 2.4 2.6 2.5 2.4 2.4 2.3 2.5 2.4 2.4 2.3 2.3 2.4 2.4 2.3 2.3 2.2 20 21 22 23 24 2.9 2.8 2.7 2.6 2.6 2.8 2.7 2.7 2.6 2.5 2.7 2.7 2.6 2.5 2.4 2.4 2.3 2.2 2.2 2.1 2.1 2.0 2.0 1.9 1.9 2.7 2.6 2.5 2.5 2.4 2.6 2.5 2.5 2.4 2.3 2.5 2.5 2.4 2.3 2.3 2.5 2.4 2.4 2.3 2.2 2.4 2.4 2.3 2.2 2.2 2.4 2.3 2.2 2.2 2.1 2.3 2.3 2.2 2.1 2.1 2.3 2.2 2.1 2.1 2.0 2.2 2.1 2.1 2.1 2.0 2.2 2.1 2.1 2.0 2.0 25 26 27 28 29 30 31 32 33 34 2.5 2.4 2.3 2.3 2.2 2.4 2.4 2.3 2.2 2.2 2.3 2.3 2.2 2.1 2.1 2.3 2.2 2.2 2.1 2.0 2.2 2.2 2.1 2.1 2.0 2.0 1.9 1.9 1.8 1.8 2.2 2.1 2.1 2.0 2.0 2.1 2.1 2.0 2.0 1.9 2.1 2.0 2.0 1.9 1.9 2.0 2.0 1.9 1.9 1.9 2.0 2.0 1.9 1.9 1.8 2.0 1.9 1.9 1.8 1.8 1.9 1.9 1.8 1.8 1.8 30 31 32 33 34 35 36 37 38 39 35 36 37 38 39 40 41 42 43 44 2.2 2.1 2.0 2.0 1.9 2.1 2.1 2.0 1.9 1.9 2.0 2.0 1.9 1.9 1.8 2.0 1.9 1.9 1.8 1.8 1.9 1.9 1.8 1.8 1.7 1.9 1.8 1.8 1.8 1.7 1.8 1.8 1.8 1,7 1.7 1.8 1.8 1.7 1.7 1.6 1.8 1.7 1.7 1.7 1.6 1.7 1.7 1.7 1.6 1.6 1.7 1.7 1.6 1.6 1.6 1.9 1.8 1.8 1.7 1.7 1.8 1.8 1.7 1.7 1.6 1.8 1.8 1.7 1.7 1.6 1.8 1.7 1.7 1.6 1.6 1.7 1.7 1.7 1.6 1.6 1.7 1.7 1.6 1.6 1.5 1.7 1.6 1.6 1.6 1.5 1.7 1.6 1.6 1.5 1.5 1.6 1.6 1.6 1.5 1.5 1.6 1.6 1.5 1.5 1.5 1.6 1.5 1.5 1.5 1.4 1.6 1.5 1.5 1.4 1.4 1.5 1.5 1.5 1.4 1.4 1.4 1.3 1.3 1.3 1.2 40 41 42 43 44 45 46 47 48 49 1.6 1.6 1.5 1.5 1.4 1.6 1.6 1.5 1.5 1.4 1.6 1.5 1.5 1.4 1.4 1.5 1.5 1.5 1.4 ■ 1.4 1.5 1.5 1.4 1.4 1.4 1.5 1.5 1.4 1.4 1.3 1.5 1.4 1.4 1.4 1.3 1.5 1.4 1.4 1.4 1.3 1.4 1.4 1.4 1.3 1.3 1.4 1.4 1.3 1.3 1.3 1.4 1.4 1.3 1.3 1.3 1.4 1.3 1.3 1.3 1.2 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 1.4 1.4 1.3 1.3 1.2 1.4 1.3 1.3 1.3 1.2 1.4 1.3 1.3 1.3 1.2 1.3 1.3 1.3 1.2 1.2 1.3 1.3 1.3 1.2 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 1.1 1.3 1.2 1.2 1.2 1.1 1.3 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 1.2 1.1 1.1 1.1 1.1 1.0 1.0 1.0 0.9 0.9 50 51 52 53 54 55 56 57 58 59 60 1.2 1.2 1.1 1.1 1.1 1.0 1.2 1.1 1.1 1.1 1.0 1.0 13° 1.2 1.1 1.1 1.1 1.0 1.0 1.2 1.1 1.1 1.1 1.0 1.0 1.1 1.1 1.1 1.0 1.0 1.0 1.1 1.1 Ivl 1.0 1.0 1.0 1.1 1.1 1.1 1.0 1.0 1.0 1.1 1.1 1.0 1.0 1.0 0.9 1.1 1.1 1.0 1.0 1.0 0.9 1.1 1.1 1.0 1.0 1.0 0.9 1.1 1.0 1.0 1.0 1.0 0.9 1.1 1.0 1.0 1.0 0.9 0.9 12° 14° 16° 16° 17° 18° 19° 20° 21° 22° 23° 24° Declination of a different name from the latitude: upper transit; reduction additive. Page 548] TABLE 26. Variation of Altitude in one minute from meridian passage. Lati- tude. Declination of a different name from the latitude; upper transit; reduction addltlre. 1 Lati- tude. 26° 26° 27° 28° 29° 80° 81° 820 88° 84° 85° 86° 87° o 1 2 3 4 4.2 4.1 3.9 3.8 3.7 II 4.0 3.9 3.8 3.6 3.5 II 3.9 3.7 3.5 3.4 II 3.7 3.6 3.5 3.4 3.3 II 3.5 3.4 3.3 3.2 3.2 II 3.4 3.3 3.2 3.1 3.0 II 3.3 3.2 3.1 3.0 2.9 II 3.1 3.1 3.0 2.9 2.8 n ■ 3.0 2.9 2.9 2.8 2.7 II 2.9 2,8 2,8 2,7 2.6 II 2.8 2.7 2.7 2.6 2.6 II 2.7 2.6 2.6 2.5 2.5 II 2,6 2,6 2.5 2.4 2.4 o 1 2 3 4 5 6 7 8 9 5 6 7 8 9 3.6 3.4 3.3 3.2 3.1 3.4 3.3 3.2 3.1 3.0 3.3 3.2 3.1 3.0 2.9 3.2 3.1 3.0 2.9 2.9 3.1 3.0 2.9 2.8 2.8 3.0 2.9 2.8 2.7 2.7 2.9 2.8 2.7 2.7 2.6 2.8 2.7 2.6 2.6 2.5 2.7 2.6 2,5 2.5 2.4 2.6 2,5 2.6 2,4 2,4 2.5 2.4 2.4 2.3 2.3 2.4 2.4 2.3 2.3 2.2 2.3 2.3 2.2 2,2 2,2 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 3.1 3.0 2.9 2.8 2.7 3.0 2.9 2.8 2.7 2.7 2.9 2.8 2.7 2.7 2.6 2.8 2.7 2.6 2.6 2.5 2.7 2.6 2.6 2.5 2.4 2.6 2.5 2.5 2.4 2.4 2.5 2.5 2.4 2.4 2.3 2.5 2.4 2-. 3 2.3 2.3 2.4 2.3 2.3 2.2 2.2 2,3 2,3 2,2 2,2 2,1 2.2 2.2 2,2 2,1 2.1 2.2 2,1 2,1 2.1 2.0 2,1 2,1 2.0 2.0 2.0 10 11 12 13 14 2.7 2.6 2.5 2.5 2.4 2.6 2.5 2.5 2.4 2.4 2.5 2.5 2.4 2.4 2.3 2.5 2.4 2.3 2.3 2.2 2.4 2.3 2.3 2.2 2.2 2.3 2.3 2.2 2.2 2.1 2.3 2.2 2.2 2.1 2.1 2.2 2.2 2.1 2.1 2.0 2.1 2.1 2.1 2.0 2.0 2.1 2.0 2.0 2.0 1.9 2,0 2,0 2,0 1,9 1.9 2.0 1.9 1.9 1.9 1.8 1.9 1.9 1.9 1.8 1.8 15 16 17 18 19 2.4 2.3 2.3 2.2 2.2 2.3 2.3 2.2 2.2 2.1 2.3 2.2 2.2 2.1 2.1 2.2 2.1 2.1 2.1 2.0 2.1 2.1 2.1 2.0 2.0 2.1 2.0 2.0 2.0 1.9 2.0 2.0 2.0 1.9 1.9 2.0 2.0 1.9 1.9 1.8 1.9 1.9 1.9 1.8 1.8 1.9 1.9 1.8 1,8 .1,8 1.9 1.8 1.8 1.8 1.7 1,8 1,8 1,7 1,7 1.7 1.8 1.7 1.7 1.7 1.6 20 21 22 23 24 25 26 27 28 29 2.1 2.1 2.0 2.0 1.9 2.1 2.0 2.0 1.9 1.9 2.0 2.0 1.9 1.9 1.9 2.0 1.9 1.9 1.9 1.8 1.9 1.9 1.9 1.8 1.8 1.9 1.9 1.8 1.8 1.7 1.8 1.8 1.8 1.7 1.7 1.8 1.8 1.7 1.7 1.7 1.8 1.7 1.7 1.7 1.6 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 1.6 1.5 1.5 25 26 27 28 29 30 31 32 33 34 30 31 32 33 34 1.9 1.8 1.8 1.8 1.7 1.8 1.8 1.8 1.7 1.7 1.8 1.8 1.7 1.7 1.7 1.8 1.7 1.7 1.7 1.6 1.7 1.7 1.7 1.6 1.6 1.7 1.7 1.6 1.6 1.6 1.7 1.6 1.6 1.6 1.5 1.6 1.6 1.6 1.5 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 1.5 1,4 1,5 1,5 1,5 1,4 1,4 1.5 1.5 1.4 1.4 1.4 35 36 37 38 39 1.7 1.6 1.6 1.6 1.5 1.7 1.6 1.6 1.5 1.5 1.6 1.6 1.6 1.5 1.5 1.6 1.6 1.5 1.5 1.5 1.6 1.5 1.5 1.5 1.4 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 1.5 1.4 1.4 1.4 1.4 1.4 1,4 1,4 1,4 1,3 1,4 1,4 1,4 1,3 1,3 1.4 1.4 1.3 1.3 1.3 1.4 1.3 1.3 1.3 1.3 35 36 37 38 39 40 41 42 43 44 1.5 1.5 1.4 1.4 1.4 1.5 1.4 1.4 1.4 1.4 1.5 1.4 1.4 1.4 1.3 1.4 1.4 1.4 1.3 1.3 1.4 1.4 1.4 1.3 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 1.2 1.3 1.3 1.3 1.2 1.2 1,3 1,3 1.2 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 40 41 42 43 44 45 46 47 48 49 1.3 1.3 1.3 1.2 1.2 1.3 1.3 1.3 1.2 1.2 1.3 1.3 1.2 1.2 1.2 1.3 1.3 1.2 1.2 1.2 1.3 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.1 1.2 1.2 1.2 1.1 1.1 1.2 1.2 1.2 1.1 1.1 1.2 1.2 1.1 1.1 1.1 1,2 1.2 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 1.1 1.1 45 46 47 48 49 50 51 52 53 54 1.2 1.2 1.1 1.1 1.1 1.2 1.1 1.1 1.1 1.0 1.2 1.1 1.1 1.1 1.0 1.1 1.1 1.1 1.1 1.0 1.1 1.1 1.1 1.0 1,0 1.1 1.1 1.1 1.0 1.0 1.1 1.1 1.0 1.0 1.1 1.1 1.0 1,1 1,0 1.1 50 51 52 53 54 55 56 57 58 59 60 1.0 1.0 1.0 1.0 0.9 1.0 1.0 1.0 0.9 1.0 1.0 1.0 1.0 1.0 1.0 55 56 57 58 59 60 0.8 0.8 0,8 25° 2G° 27° 28° 29° 80° 31° 82° 88° 84° 85° 86° 87° Declination of the Hanie name as the latitude; lower transit; reduction subtraotlve. TABLE 26. [Page 549 Variation of Altitude in one minute from meridian passage. Declination of a different name from the latitude; upper transit; reduction additive. Lati- tude. o Lati- tude. 88° 89° 40° 41° 42° 48° 44° 45° 46° 47° 48° 49° 60° II II " 1 II II II II II II II II II II o 2.5 2.4 2.3 2.3 2.2 2.1 2.0 2.0 1.9 1.8 1.8 1.7 1.7 1 2.5 2.4 2.3 2.2 2.1 2.1 2.0 1.9 1.9 1.8 1.7 1.7 1.6 1 2 2.4 2.3 2.3 2.2 2.1 2.0 2.0 1.9 1.8 1.8 1.7 1.7 1.6 2 3 2.4 2.3 2.2 2.1 2.1 2.0 1.9 1.9 1.8 1.8 1.7 1.6 1.6 3 4 2.3 2.2 2.2 2.1 2.0 2.0 1.9 1.8 1.8 1.7 1.7 1.6 1.6 4 5 5 2.3 2.2 2.1 2.1 2.0 1.9 1.9 1.8 1.8 1.7 1.6 1.6 1.5 6 2.2 2.2 2.1 2.0 2.0 1.9 1.8 1.8 1.7 1.7 1.6 1.6 1.5 6 7 2.2 2.1 2.0 2.0 1.9 1.9 1.8 1.8 1.7 1.6 1.6 1.5 1.5 7 8 2.1 2.1 2.0 1.9 1.9 1.8 1.8 1.7 1.7 1.6 1.6 1.5 1.5 8 9 2.1 2.0 2.0 1.9 1.9 1.8 1.8 1.7 1.6 1.6 1.6 1.5 1.5 9 10 2.1 2.0 1.9 1.9 1.8 1.8 1.7 1.7 1.6 1.6 1.5 1.5 1.4 10 11 2.0 2.0 1.9 1.8 1.8 1.7 1.7 1.6 1.6 1.6 1.5 1.5 1.4 11 12 2.0 1.9 1.9 1.8 1.8 1.7 1.7 1.6 1.6 1.5 1.5 1.4 1.4 12 13 1.9 1.9 1.8 1.8 1.7 1.7 1.6 1.6 1.6 1.5 1.5 1.4 1.4 13 14 1.9 1.9 1.8 1.8 1.7 1.7 1.6 1.6 1.5 1.5 1.4 1.4 1.4 14 15 1.9 1.8 1.8 1.7 1.7 1.6 1.6 1.6 1.5 1.5 1.4 1.4 1.4 15 16 1.8 1.8 1.7 1.7 1.7 1.6 1.6 1.5 1.5 1.4 1.4 1.4 1.3 16 17 1.8 1.8 1.7 1.7 1.6 1.6 1.5 1.5 1.5 1.4 1.4 1.4 1.3 17 18 1.8 1.7 1.7 1.6 1.6 1.6 1.5 1.5 1.4 1.4 1.4 1.3 1.3 18 19 1.7 1.7 1.7 1.6 1.6 1.5 1.5 1.5 1.4 1.4 1.4 1.3 1.3 19 20 1.7 1.7 1.6 1.6 1.6 1.5 1.5 1.4 1.4 1.4 1.3 1.3 1.3 20 21 1.7 1.6 1.6 1.6 1.5 1.5 1.5 1.4 1.4 1.4 1.3 1.3 1,3 21 22 1.7 1.6 1.6 1.5 1.5 1.5 1.4 1.4 1.4 1.3 1.3 1.3 1.2 22 23' 1.6 1.6 1.6 1.5 1.5 1.4 1.4 1.4 1.3 1.3 1.3 1.3 1.2 23 24 1.6 1.6 1.5 1.5 1.5 1.5 1.4 1.4 1.4 1.3 1.3 1.3 1.2 1.2 24 25 1.6 1.5 1.5 1.4 1.4 1.4 1.3 1.3 1.3 1.2 1.2 1.2 25 26 1.6 1.5 1.5 1.5 1.4 1.4 1.4 1.3 1.3 1.3 1.2 1.2 1.2 26 27 1.5 1.5 1.5 1.4 1.4 1.4 1.3 1.3 1.3 1.2 1.2 1.2 1.2 27 28 1.5 1.5 1.4 1.4 1.4 1.3 1.3 1.3 1.3 1.2 1.2 1.2 1.1 28 29 1.5 1.4 1.4 1.4 1.4 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.1 29 30 1.5 1.4 1.4 1.4 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.1 1.1 30 31 1.4 1.4 1.4 1.3 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.1 1.1 31 32 1.4 1.4 1.3 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.1 1.1 1.1 32 33 1.4 1.4 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.1 1.1 1.1 1.1 33 34 1.4 1.3 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.1 1.1 1.1 1.1 34 35 1.3 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.1 1.1 1.1 1.1 35 36 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.1 1.1 1.1 1.1 36 37 1.3 1.3 1.2 1.2 1.2 1.2 1.2 1.1 1.1 1.1 37 38 1.3 1.2 1.2 1.2 1.2 1.2 1.1 1.1 1.1 38 39 1.2 1.2 1.2 1.2 1.2 1.1 1.1 1.1 39 40 1.2 1.2 1.2 1.2 1.1 1.1 1.1 40 41 1.2 1.2 1.2 1.1 1.1 1.1 . 41 42 1.2 1.2 1.1 1.1 1.1 42 43 1.2 1.1 1.1 1.1 43 44 1.1 1.1 1.1 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 55 56 57 58 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 0~9' 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.7 0.8 0.8 0.7 0.7 0.8 0.7 0.7 0.7 0.7 0.7 0.7 0.7 55 56 57 58 0.8 0.8 0.8 0.8 0.8 0.8 59 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.7 0.7 0.7 0.7 0.7 0.7 59 60 0.8 0.8 0.8 0.8 0.8 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 60 38° 89° 40° 41° 42° 48° 44° 45° 46° 47° 48° 49° 50° Dec lination of the N ime nan 16 as the latitude ; lower transit; reductio n Hnbtrii ctlve. Page 550] TABLE 26. Variation of Altitude in one minute from meridian passage. Declination of a different name from the latitude: uuner transit: reduction additlre. Lati- tude. o Lati- tude. 61° 62° 58° 64°. 66° 56° 57° 68° 59° 60° 61° 62° 68° 1.6 1.5 1.5 II 1.4 II 1.4 II 1.3 II 1.3 \%^ II 1.2 ! 1.1 II 1.1 1.0 1.0 1 1.6 1.5 1.5 1.4 1.4 1.3 1.3 1.2 1.1 1.1 1.0 1.0 1 2 1.5 1.5 f.4 1.4 1.3 1.3 1.3 1.2 1.2 1.1 1.1 1.0 1.0 2 3 1.5 1.5 1.4 1.4 1.3 1.3 1.2 1.2 1.1 1.1 1.1 1.0 1.0 3 4 1.5 1.5 1.4 1.4 1.3 1.3 1.2 1.2 1.1 1.1 1.1 1.0 1.0 4 5 1.5 1.4 1.4 1.3 1.3 1.3 1.2 1.2 1.1 1.1 1.0 1.0 1.0 5 6 1.5 1.4 1.4 1.3 1.3 1.2 1.2 1.2 1.1 1.1 1.0 1.0 1.0 6 7 1.4 1.4 1.4 1.3 1.3 1.2 1.2 1.1 1.1 1.1 1.0 1.0 0.9 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 30 1.1 1.1 1.0 1.0 31 1.1 1.0 1.0 31 32 33 34 1.1 1.1 1.0 32 33 34 0.8 0.7 0.8 35 36 37 38 39 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 35 36 37 38 39 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 40 41 42 43 44 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.7 0.7 0.8 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 40 41 42 43 44 45 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 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 1 0.7 0.7 0.7 0.7 0.7 0.7 0.6 0.6 0.6 0.6 0.6 54 55 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 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 1 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° 58° 64° 55° 56° 67° 58° 59° 60° 61° 62° 68° D eclinatl( )n of the same nc ime as t be latitu de; low€ r transi I reduc ion subt ractlre. TABLE 27. ■ [Page 551 Reduction to be a pplied to Altitudes near the Meridian. Var. Time from meridian passage. Var. 1 min. (Table (Table TO. S. TO. 8. TO. S. TO. 8. TO. 8. TO. 8. TO. 8. TO. 8. TO. 8. TO. 8. TO. 8. TO. 8. TO. 8. 26.) 30 1 1 30 2 2 30 3 3 30 4 4 30 5 o 30 6 6 30 26.) II / II / II / // / // / // 1 II / // 1 II ' II / II ' II ' // ' II II 0.1 1 1 1 2 2 2 3 4 4 0.1 0.2 1 1 2 3 3 4 5 6 7 8 0.2 0.3 1 1 2 3 4 5 6 7 9 11 13 0.3 0.4 00 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 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 36 1 41 2 5 2 31 3 3 31 5.0 6.0 6.0 1 6 13 24 37 54 1 13 2 1 2 30 3 1 3 36 4 13 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 44 1 2 1 30 2 3 2 40 2 56 3 23 4 10 5 2 6 7 2 10.0 11.0 3 11 25 1 9 1 39 2 15 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 1.3.0 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 4 1 34 2 15 3 4 4 5 3 6 15 7 34 9 10 34 15.0 16.0 16.0 4 16 36 1 40 2 24 3 16 4 16 5 24 6 40 8 4 9 36 11 16 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 14 47 20.0 21.0 21.0 5 21 47 1 24 2 11 3 9 4 17 5 36 7 5 8 45 10 35 12 36 22.0 5 22 49 1 28 2 17 3 18 4 30 5 52 7 25 9 10 11 5 13 12 15 29 22.0 23.0 6 23 52 1 32 2 24 3 27 4 42 6 8 7 46 9 35 11 36 13 48 16 12 23.0 24.0 6 24 54 1 36 2 30 3 36 4 54 6 24 8 6 10 12 6 14 24 16 54 24.0 25.0 6 25 56 1 40 2 36 3 45 5 6 6 40 8 26 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 Page 662] TABLE 27. Reduction to be applied to Altitudes near the Meridian. Var. 1 min. Time from meridian passage. Var. (Table m. 8. m. s. m. s. m. g. m. s. m. s. m. s. m. «. m. 8. m. ». m. s. m. s. m. K. (Table 26.) 7 7 SO 8 H SO » 9 30 10 10 30 11 11 30 12 12 30 13 26.) 0.1 5 6 6 7 8 ' " 9 10 11 / II 12 13 14 1 II 16 1 II 17 0.1 0.2 10 11 g 13 19 14 16 18 20 22 24 26 29 31 34 0.2 0.3 15 17 22 24 27 30 33 36 40 43 47 51 0.3 0.4 0.5 20 24 23 28 26 32 29 32 36 40 44 48 53 58 1 12 1 2 1 18 1 8 0.4 36 40 45 50 55 1 1 6 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 8 59 9 22 10 19 10 40 11 44 12 2 13 30 14 51 15 2 16 33 16 40 18 22 20 10 22 2 24 26 2 28 10 10.0 11.0 11.0 13 15 18 20 20 13 22 11 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 l4 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 TABLE 27. [Page 553 Reduction to be applied to Altitudes near the Meridian Var. Time from meridian passage. Var. 1 mln. (Table (Table m. «. m. 8. TO. S. m. 8. TO. 8. m. 8. TO. «. TO. 8. TO. 8. m. 8. TO. 8. m. s. TO. 8. 26.) 18 30 14 14 30 15 15 80 16 16 80 17 17 30 18 18 80 19 19 30 26.) „ / II / II / II / II / // / II / // / // 1 II / II / II / II ' II „ 0.1 18 20 21 22 24 26 27 29 31 32 34 36 38 0.1 0.2 36 39 42 45 48 51 54 58 1 1 1 5 1 8 1 12 1 16 0.2 0.3 55 59 1 3 1 7 112 117 122 127 132 137 143 148 154 0.3 0.4 1 13 1 18 124 130 136 1 42 149 156 2 2 2 10 2 17 2 24 2 32 0.4 0.5 131 138 145 152 2 2 8 2 16 2 24 2 33 2 42 2 51 3 1 3 10 0.5 0.6 149 158 2 6 2 15 2 24 2 34 2 43 2 53 3 4 3 14 3 25 3 37 3 48 0.6 0.7 2 8 2 17 2 27 2 37 2 48 2 59 3 11 3 22 3 34 3 47 4 4 13 4 26 0.7 0.8 2 26| 2 37 2 48 3 312 3 25 3 38 3 51 4 5 4 19 4 34 4 49 5 4 0.8 0.9 2 44 2 56 3 9 3 22 3 36 3 50 4 5 4 20 4 36 4 52 5 8 5 25 5 42 0.9 1.0 1.0 3 2 i 3 16 3 30 3 45 4 4 16 4 32 4 49 5 6 5 24| 5 42 6 1 6 20 2.0 6 4 1 6 32 7 7 30 8 8 32 9 4 9 38 10 12 10 48 11 24 12 2 12 40 2.0 3.0 9 7 9 48 10 30 1115 12 1 12 48 13 38 14 27 15 19 16 12 17 7 18 3 19 1 3.0 4.0 12 9 13 14 14 1 15 16 1 17 4 18 9 19 16 20 25 2136 22 49 24 4 25 21 4.0 5.0 15 11 16 20 17 31 18 45 20 1 2120 22 41 24 5 25 31 27 28 31 5.0 6.0 18 13 19 36 21 2 22 30 24 1 25 36 27 13 6.0 7.0 21 16 22 52 24 32 26 15 28 1 7.0 8.0 24 18 26 8 28 2 8.0 9.0 27 20 9.0 Var. T ime fror a meridi anpasss ge. Var. 1 mill. (Table m. s. m. «. m. s. m. 8. TO. 8. TO. 8. TO. 8. TO. 8. TO. 8. TO. 8. TO. 8. TO. 8. TO. 8. (Table 26.) 20 20 80 21 21 80 22 22 30 23 23 30 24 24 30 25 25 80 26 26.) II / II ' // ' H ' II ' n / n / // / II / II / II ' // / // / // II 0.1 40 42 44 46 48 51 53 55 58 1 1 2 1 6 1 8 0.1 0.2 120 124 128 132 137 141 146 150 155 2 2 5 2 10 2 15 0.2 0.3 2 2 6 2 12 219 2 25 2 32 2 39 2 46 2 53 3 3 7 3 15 3 23 0.3 0.4 2 40 2 48 2 56 3 5 3 14 3 22 3 32 3 41 350 4 4 10 4 20 4 30 0.4 0.5 3 20 3 30 3 41 3 51 4 2 4 13 4 24 4 36 4 48 5 5 12 5 25 5 38 0.5 0.6 4 4 12 4 25 4 37 4 50 5 4 5 17 5 31 5 46 6 615 6 30 6 46 0.6 0.7 4 40 4 54 5 9 5 24 5 39 5 54 6 10 6 27 6 43 7 7 17 7 35 7 53 0.7 0.8 5 20 5 36 5 53 6 10 6 27 6 45 7 3 7 22 7 41 8 8 20 8 40 9 1 0.8 0.9 6 6 18 6 37 6 56 7 16 7 36 7 56 8 17 8 38 9 9 22 9 45 10 8 0.9 1.0 1.0 6 40 7 7 21 7 42 8 4 8 26 8 49 9 12 9 36 10 10 25 10 50 1116 2.0 13 20 14 14 42 15 24 16 8 16 52 17 38 18 24 19 12 20 20 50 2140 22 32 2.0 3.0 20 21 22 3 23 7 24 12 25 19 26 27 27 37 28 48 30 3.0 4.0 26 40 28 1 29 24 4.0 Page 554] TABLE 28A. For finding the Latitude of a place by Altitudes of Polaris. [A=l8t correction. Argument, the star's hour angle (or 24i>— the star's hour angle).] Qh ih 2h j 3h 1 41. 5h 12 00.0 11 59.9 11 59.8 11 59.6 11 59.3 11 58.9 11 58.5 11 58.0 11 57.4 11 56.7 10 11 12 13 14 15 16 17 18 19 -1 11 55.9 ' 11 55.0 11 54.1 11 53.1 11 52.0 -1 11 50.8 11 49.5 1148.1 11 46.7 11 45.2 20 21 22 23 24 25 26 27 28 29 11 43.6 11 41.9 11 40.1 11 38.3 11 36.3 11 34.3 11 32.2 11 30.0 11 27.8 11 25.5 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 -1 11 23.1 11 20.6 11 18.0 11 15.3 11 12.6 -1 11 09.7 11 06.8 11 03.8 11 00.8 ^057^ -1 10 54.4 10 51.1 10 47.7 10 44.2 10 40.7 -1 10 37.0 10 33.3 10 29.5 10 25.6 10 21.7 -1 10 17.6 10 13.5 10 09.3 10 05.0 10 00.7 -1 09 56.2 09 51.7 09 47.1 09 42.4 09 37.7 -1 09 32.8 .0 .1 .1* .3 .4 -1 -1 -1 09 32.8 09 27.9 09 22.9 09 17.9 09 12.7 09 07.4 09 02.1 08 56.7 08 51.3 08 45.8 08 40.2 08 34.4 08 28.6 08 22.7 08 16.8 08 10.8 08 04.7 07 58.5 07 52.3 07 46.0 07 39.6 07 33.1 07 26.5 07 19.9 07 13.1 07 06.3 06 59.5 06 52.5 06 45.5 06 38.4 06 31.2 06 24.0 06 16.7 06 09.3 06 01.8 05 54.2 05 46.6 05 38.9 05 31.1 05 23.3 05 15.3 05 07.3 04 59.3 04 51.1 04 42.9 04 34.6 04 26.2 04 17.8 04 09.3 04 00.7 — 1 llh 03 52.0 03 43.3 03 34.5 03 25.6 03 16.6 03 07.6 02 58.6 02 49.4 02 40.2 02 30.8 02 21.4 4.9, 5.0 5.0; 5.2, 5.3 5.3 m; 5.4' 5.5| 5.6, 5.8 5.8| 5.9; 5.9 6.0 6.1; 6.2' 6.2, 6.3, G.4 G.5 6.6; 6.6 6.8 6.8 6.8 7.0' 7.0' 7.1' 7.2 7.2 7.3! 7.4' 7.5' 7.6' 7.6 7.7^ 7.8! 7.8 8.0 8.0' 8.0! 8.2' 8.31 8.4|- 8.4, 8.5 8.6; 8.7;- 8.7: ■ 9.0 9.0; 9.0: 9.2 9.2| 9.4 9.4 -1 02 21 02 11. 02 02. 0152. 0143. -1 01 33. 0123. 0113. 0103. 00 53. 4 — ' ^ 9.5 9.5 9.6 9.7^ -1 00 43. 00 33. 00 23. 00 12. 00 02. -0 59 52, 59 41 59 31. 59 20. 59 09. -0 58 58, 58 48, 58 37, 58 26 58 15, -0 58 04 57 52 57 41 57 30 57 18 -0 57 56 56 56 44 56 32. 56 21. -0 56 09. 55 57. 55 45. 55 33. 55 21. -0 55 09. 54 57. 54 45. 54 32. 54 20. -0 54 08. 53 55. 53 43. 53 30. 53 18. -0 53 05 52 52 52 39 52 26 52 13 -0 52 00 5147 5134 5121 5108, -0 50 54, 9.8: 9.9; 10.0' I 10.1 10.2 10.21 IO.3I 10.3: 10.5| 10.5 10.6 10.6; 10.7; 10.8 10.9' 10.9! 10.9 11.1 ll.l| 11.2' 11.2; 11.3 11.4' I 11.4 11.6 11.6 11.6 11.7' 11.8 11.8: 11.9 12.0' 12.0 12.1 12.1 12.2 12.3| 12.3 12.4! 12.5j 12.5, 12.6 12.6 12.7 12.8 12.8; 12.9 13.0 13.0 13.0 13.1 13.2 13.3 13.3 -0 50 54. 50 41. 50 28. 50 14. 50 01. -0 49 47. 49 33. 49 20. 49 06. 48 52. -0 48 38. 48 24. 48 10. 47 56. 47 42. -0 47 28. 47 14, 47 00. 46 45. 46 31, -0 46 17 46 02 45 48 45 33 45 18 -0 45 04 44 49 44 34 44 19 44 04 -0 43 50 43 35 43 20 43 05 42 49 -0 42 34 42 19 42 04 4148 4133 -0 41 18 4102 40 47 40 31 4016 -0 40 00, 39 44 39 28 39 13 38 57 -0 38 41 38 25 38 09 37 53 37 37 -0 37 21 37 05 36 48 36 32 36 16 -0 36 00 13.3 13.4; 13..5 13.5 13.6; 13.7, 13.71 13.7 13.8: 13.9, 14.0 14.0 14.0 14.1 14.1 14.2 14.2 14.3; 14.4, •14.4 14.5 14.5; 14.6] 14.6 14.7| 14.8 14.8! 14.8; 14.9 i 14.9 15.0 15.0! 15.0' 15.1! 15.2; 15.2J 15.3 15.3; 15.3: 15.4 15.5; 15.5 15.6' 15.6| 15.71 15.7 15.7; 15.8; 15.8 15.9 15.9 16.0 16.0 16.1 16.1 16.2 16.2 16.3 16.3 I6.3! -0 36 00 35 43 35 27 35 10. 34 54. -0 34 38. 34 21. 34 05. 33 48. 33 3 1. -0 33 15^ 32 58. 32 41, 32 24. 32 07, -0 31 50, 31 34, 31 27, 31 10, 30 53, -0 30 36, 30 18, 30 01, 29 44, 29 17, -0 29 00, 28 42, 28 25 28 08 27 50 -0 27 33 27 16 26 58 26 41 26 23 -0 26 05 25 48 25 30 25 13 24 55 -0 24 37 24 20 24 02 23 44 23 26 -0 23 08 22 50 22 33 22 15 2157 -0 21 39 2121 2103 20 45 20 27 -0 20 09 19 50 19 32 19 14 18 56 -0 18 38 16.3 16.4 16.4 16.4 16.4 16.5 16.6; 16.6 16.7 16.7 16.8 16.8 16.8 16.8 16.9 I6.9; 16.9 17.0 17.1; 17.0 17.1 17.2 17.2 17.2 17.2 17.3j 17.3; 17.4; 17.4 17.4 17.5 17.5: 17.5; 17.6 17.6 17.6 17.6 17.7 17. 17.7 17.8 17.8! 17.8 17.8' 17.9 17.9 17.9 17.9 18.0 18.0 18.0 18.0, 18.1 18.1 18.1 18.1 18.2 I8.2' 18.2 4 .0 .5 5 9 3 .7 .1 A .7 ,-- — -0 18 38. 18 20. 18 01. 17 43. 17 25. -0 17 06. 16 48. 16 30. 16 11. 15 53. -0 15 35 15 16. 14 58. 14 39 14 21, -0 14 03 13 44 13 26, 13 07 12 48 -0 12 30. 12 11, 1153. 1134. 1115. -0 10 57 10 38 10 20 10 01 09 42 -0 09 24 09 05 08 46 08 27 08 09 -0 07 50 07 31 07 12, 06 54 06 35 lOh 9h Sh Ih 06 16 05 57 05 39 05 20 05 01 -0 04 42 04 23 04 05 03 46 03 27 -0 03 08 02 49 02 30 02 12 01 53 -0 01 34 0115 00 56 00 37 00 18 -0 00 00, 01' 18.2 18.2 18.3 18.3 18.3 18.3 18.3 18.4 18.4 18.4' 18.4! I8.4! 18.4' 18.4J 18.5! I8.5; 18.5 18.5 18.6; 18.6- 18.6| 18.6 18.6 18.6 18.7 18.6 18.6 18.6 I8.7' 18.7- 18.7| 18.71 I8.7' 18.7 18.7; 18.71 18.7; 18.8! 18.8 18.7 18.8' 18.8; 18.8, 18.8; 18.8' 18.8! 18.8 18.8 18.8 18.9 18.8; 18.8 18.9 18.8 18.8 18.9 18.8 18.9 18.9 18.9 60 59 58 57 5<> 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 16 15 14 13 12 Jl_ 10 Change the sign to + when the argument is found at tlie bottom. TABLE 28B. [Page 555 For finding the Latitude of a L place by Altitudes of Polaris. [B=the 2d correction. This correction is always additive.] Star's Star's altitude. 1 star's hour angle. hour angle. 10° 15° 16° 17° 18° ^ 19° 20° 21° 22° 23° h. m. // // II II II // // II II // ' h. m. 00 0.0 0.0 0.0 0.0 n 0.0 0-0.0 0-0.0 0-0.0 0.0.0 0-0.0 12 00 10 0.0 ', 0.0? 0.0 ', 0.0 1 0.0 1 0.0 " 0.0 1 0.0 " 0.0 1 0.0 1 11 50 20 0.1- 0.1- 0.1- 0.1 \ 0.1 •; 0.1 •; 0.1 0.1 \ 0-1 \ 0.1 \ 40 30 0.2 \ 0.2' 0.2' 0.2 0.2 \ 0.2 1 0.3-2 0.3-5 0.3-3 0.3-3 30 40 0.3- 0.3 2 0.4" 0.4 0.4'^ 0.5-3 0.5-3 0.5-3 0-63 0-6-3 20 50 0.4- 0.5 t, 0.6' 0.6 3 0.7 -J 0.8-3 0.8 3 0.8-3 0-9-3 0.9 -, 10 1 00 0.5- 0._8- 1.1 ! 0.9- 0.9 3 1.0- 1-1 ■, 1-1 1-1 ■ 1.2' 1.3' 00 10 0.7-; 1.2-3 1-8 1 2.3-5 2.8- 3- 2' 1.2 1.3-4 1.4-^ 1-45 1.5-5 1.6 -J 1-75 10 50 20 1.1 'll 1.8 •: 1.4 -'l 2.2-! 1.6 1.7-1 2.6 -J 3-1 1 3.6- 1-8-6 1-9 1 2-0 -J 2-1 1 2-7- 2-2-6 40 30 2.0 i 2.3-, 2-4 -5 2-5-6 2-8-6 30 40 2.4 2-8 1 2-9-6 3-1 1 3.7- 4.4-^ 3-2 •« 3.8-; 4.5-^ a 3-4-6 20 50 1.7- 2.0"' 2.3-^ 2.6-4 3.5 -J 2.9 3-3 -fi 3.9- 3-5-6 4.0-5 10 2 00 3.4 ts 4.1- 4.7- 00 10 3.7 -fi 4.3- 4.8 -J 5.3-! 5-9 -« 7-0 1 8.7-, 3.9 6 6 6 4.9 -J 5.5 -J 6.7-; 7.4-^ 4-5 fi 5.1- 5.8-' 6.4- 7.1-; 8.4-? 9.1- 9.8 •' 10.4 -; 4.8-; 5.4- 6.1 -; 6.8-, 7.5-; 8.3-^ 5.0-5 5.7-; 6.4-; 8.7-^ 9.4 -J 10.2 -, 10.9 -, 11.6 -, 5.3-5 6-0 •; 6.8-5 8.3 -J 9.1 •* 5.6-" 7-1 8 7-9-8 8-7-8 9 50 20 2.6-: 4.0 •; 4.5 40 30 2.9'^ 4.5-^ 5.1 30 40 3.3 t 5.0-:^ 5.7 20 50 3.6'^ 5.5 -J 6.3 10 3 00 4.0-'' 6.0-^ 6.9 6 6 5 6 6 00 10 4.3 -J 6.6-^ 7.5 8-0 •« 8.9-2 9-6 -« 10.4-^ 9.9 -J 10. 7 -J 10.4 -' 11-3-8 12-1-8 12.9-^ 8 50 20 4.7-^ 7.1 -J 8.1 8.6-' 40 30 5.0-^ 7.6-; 8.6 9.2-5 11.5 -, 30 40 5.3 -J 8.1 •; 9.2 9-9 I 11.0 •? 12.2 -J 20 50 5.7-^ 8.6-^ 9.2-^ 9.8 10.5-^ 11.1 •! 11. 7-' 12.3 •; 13.0-5 13. 7-! 10 4 00 6.0-^ 9.1-^ 9.7-^ 10.4 h 11.0-^ 11.7-'^ 12.3-" 13.0-^ 13.7-^ 14.4-^ 00 10 6.3-^ 9.6-;; 10.2-^ 10.9 11.6-^ 12.2-^ 13.0-^ 13.6-^ 14-3 -' 15.0-5 7 50 20 6.6, 10.0'^ 10.7-^ 11.3 12.1 1 12.8 ■. 13.6-° 14.3-^ 14.9-^ 15-7 -„ 40 30 6.8-^ 10.4-^ 11. 1-! 11.7 12:5 -f 13.3-^ 14. 0-* 14.8 -, 15.6 •! 16.3-^ 30 40 7.0- 10.8 -J 11.4^ 12.1 13.0 -, 13.8 -, 14.5-^ 15.3-^ 16.1 -l 16.9-° 20 50 7.3-^ 11.1 -l 11.8 -J 12.5 4 13.4 -J 14.2 J 15.0-^ 15.8 , 16.6-^ 17.5-^ 10 5 00 7.5-^ 11.4-^ 12.1 -^ 12.9 13.7 -^ 14.5 -^ 15.4-^ 16.2-^ 17.1 -^ 17.9-^ 00 10 7.6-; 11.6-^ 12.4 -J 13.2 14.0 -J 14.8-^ 15.7-^ 16.5-^ 17.4-3 18.3-^ 6 50 20 7.8 -f 11.7-^ 12.6 , 13.4 2 14.2 ■; 15.1 -l 16.0-^ 16.8-^ 17.7-^ 18.6-^ 40 30 7.9-, 11.9 f 12.7 ■, 13.6 14.4-2 15.3-2 16.2 -; 17.1-.' 18.0 -^ 18.9 -f 30 40 7.9-^ 12.0 "I 12.9 -f 13.7 14.6 -^ 15.5-2 16.4-2 17.3-2 18.1 -^ 19.0 -, 20 50 7.9-^ 12.1 -^ 13.0 -^ 13.8 14. 7 -^ 15.6 -^ 16.5-^ 17.3 •« 18.2-1 19.1 ■] 10 6 00 7.9-^ 12.2-^ 13.0 •" 13.9-^ 14.7-° 15.6-0 16.5 •" 17.3-0 18.3 -1 19.2-1 6 00 TABI .E 28C. [C=the 3d correction. Hor. Arg. the star's declination. Vert. Arg., B=the 2d correct ion.] B. 88° 47' 88° 48' 88° 49' 1 20" 30" 40" 50" 0" 10" 20" 80" 40" 50" 0" 10" 20" // // « II II II 1 " II II II II II II II 0.0 0.0 0.0 0.0 o.c ) 0.0 0.0 0.0 0.0 0.0 .0 0.0 0.0 10 +0.2 +0.1 +0.1 + 0.0 0.( ) -0.0 -0.1 -0.1 -0.2 - -0.2 -0 .3 —0.4 -0.4 20 0.4 0.3 0.2 0. 1 0. ( ) 0.1 t 0.2 ; 0.3 0.4 0.5 .6 0.7 0.8 30 0.6 0.5 0.3 0.1 o.c ) 0.1 0. 3 0. 5 0.6 0.7 .8 1.1 1.2 40 0.8 0.6 0.4 0.2 o.c ) 0.2 0.4 0.6 0.8 1.0 1 .2 1.5 1.6 50 +1.0 4-0.7 +0.5 + 0.2 o.c ) -0.2 0.5 -0.9 -1.0 - -1.2 -1 .5 -1.7 -2.1 Note. — Below 15° B is nearly proportional to the altitude. Page 656] TABLE 28B For finding the Latitude of a place by Altitudes of Polaris. [B=the 2d correction. This correction is always additive.] Star's hour Star's altitude. 1 SUir's hour angle. 24° 26° 26° 27° 28° 28° 80° 31° 82° Z9fi angle. h. m. » II II // II // // // II II II h. in. 00 0.0 „ 0-0.0 0.0 . 0.0 l 0.2 •; 0.4 l 0.7 l 1-1 1 1.5 •" 0.0 ^ 0.0 -l 0.2 -i 0.4 l 0.7 -^ 1.1 4 1.5 -^ 0.0 „ 0.0 •° 0.2 -i 0.4 'l 0.7 l 1-1 1 1.6 -^ 0.0 „ 0.0 •° 0.2 -t 0.4 'l 0.7 l 1.1 -J 1.7 ■' 2.3 -^ 2.9 ■; 3.6 •; 0.0 ^ 0.0 •° 0.2 -t 0.4 'l 0.8 , 1.2 -J 1.7 -^ 0.0 ^ 0.0 •" 0.0 „ 0.0 ,, 12 00 10 0.0 -J 0. o*-? 0.0 •; 0.0 -° 11 50 20 0.1 • 0.1 i 0.2 •; 0.5 5 0.2 -2 0.2 -2 40 80 0.3 •: 0.3 -^ 0.5 \ 0.5 -, 30 40 0.6 ■, 0.6 . 0.8 ■: 1.3 -^ 0.8 z 1.3 -l 0.9 -. 20 50 1.0 ■' 1.0 J 1.4 'X 10 1 00 1.4 ■' 1.4 •' 1.9 •; 1.8 •' 1.9 •'^ 1.9 -' 00 10 1.8 ■' 2.0 i 2.1 -^ 2.2 -J 2.8 •; 3.5 l 4.3 -^ 5.1 -l 2.3 ■; 3.0 -J 3.8 -l 4.7 -^ 5.6 'l 6.5 -^ 7.51-° 2.4 -^ 2.5 -^ 2.6 -: 10 50 20 2.3 ■: 2.4 -l 2.5 , 2.7 -^ 3.2 -J 3.3 'l 3.4 'l 40 30 2.9 ! 3.1 ■; 3.8 •; 3.2 ■; 3.4 ! 4.0 -l 4.1 -^ 4-3/0 30 40 3.6 •: 4.0 -i 4.7 •! 4-1 ■« 4.5 -l 5.3 ■; 4.9 •; S-Oi'o 5.31-° 20 5f) 4.3 •: 4.5 -l 4.9 -^ 5.8 -J 6.0 -J 6.2,-; 10 2 00 5.0 ■' 5.3 -^ 5.5 ■« 5.8 -^ 6.0 -^ 6.2 -^ 6.8l-° 7.0i-° 7. 3 1-1 00 10 5.8 -J 6.1 •; 6.4 -^ 6.7 'l 7.0l-° 7.2i-° 7.91-1 8. 2 1-2 8.51-2 9 50 20 6.6 'l 7.0 -^ 7.3 -l 7.6 -^ 7-9,n 8.3-1 8.61-; 8.9 -J 9.31-1 9.6-1 40 30 i.b 7.9 -l 8.2 -^ 8-5/n 8.9 ■; 9.3 -J 9.6 •° 10.0 1-1 10.4 - 10.81-2 30 40 8. 3- 'l 8.7 -^ 9.1 'l 9.51-° 10.0 11 10.4 1 10.8 -J 11.21-2 11.6-2 12.0 1-2 20 50 9.2 'l 9.6 'l 10.0 •„ 10.51° ii.oi° 11.41° 11. 9 1- 12.4!-^ 12. 9 i-„ 13. 3 1-^ 10 3 00 10.0 -^ 10.5 -^ 11.01° 11. 5 1-° 12.0l° 12. 5 11 13.0 1-1 13.61-2 14.11-2 14. 6 1-** 00 10 10.9 'l 11-4/2 12.0;° 12.51° i3.di° 13.611 T4.2i-'f 14. 7 1-1 I5.4I-5 16. oj-; 8 50 20 11.8 'l 12.41° 13.0i° 13.5 O 14. 1 11 14.7 ■ 15.3 • 15.9-2 16.61-2 17.3 -^ 40 30 12.6 'l 13.3 -l 13.9 -l 14.5 -J 15.ll° 15.8-1 16.4 ■ 17.1 1-2 17.8-2 18.5-2 30 40 13.5 •; 14.2 J 14.8 -^ 15.51° 16-1 n 16. 8 1-° 17.5-1 18. 2 1-1 19. 1-2 19.7-2 20 50 14.3 'l 15.0 'l 15.7 -l 16.4 -l 17.1 ^ 17.8 •" 18.5 -^ 19.4-2 20. 1 1-1 20. 9 1-2 10 4 00 10 15.1 •*' 15.9 -t 15.8 •'^ 16.6 -^ 16.5 -^ 17.3 •« 17.3 -^ 18.1 •* 18. 1 1-° 18. 8 1-° 19.7 -l 19.61-1 20.41° 21.41-° 21. 2 1-1 22. 3 1-1 22.0 1-1 00 19.0 'l 20. 6 1-° 23. 1 1-1 7 50 20 16.6 •; 17.3 ! 18.1 -Z 19.0 •; 19.8 •« 20.6 'l 21.5 -l 22.41-° 23.2 -„ 24.1 -° 40 30 17.2 J 18.0 -J 18.8 -^ 19.7 ! 20.5 -l 21.4 •" 22.3 -Z 23.2 'l 24.1 \ 25.li-° 30 40 17.8 i 18.6 'l 19.5 -l 20.3 -^ 21.2 •: 22.1 -l 23.0 -^ 24.0 i 24.9 'l 25.9 -^ 20 50 18.3 i 19.2 -^ 20.1 -^ 21.0 ! 21.9 •' 22.8 -l 23.7 -' 24.6 •_ Ih.l -_ 26.7 -l 10 5 00 18.8 -^ 19.2 -f 19.7 -5 20.6 -^ 21.1 •; 21. { 22.4 -^ 23.4 -^ 23.9 -^ 24.4 •' 24.9 -f 25.3 .5 26.4 .6 27.4 •' 28.0 -^ 00 10 20.1 ■] 22. ( 22.9 ••' 25.8 27.0 6 50 20 19.5 i 20.5 -^ 21.4 l 22.4 -^ 23.3 -t 24.3 -t 25.4 •; 26.2 -^ 27.4 -^ 28.5 -5 40 30 19.8 -l 20.7 • 21.7 -l 22.6 -l 23.6 'l 24.6 -^ 25.7 -l 26.6 -J 27.8 -t 28.8 l 30 40 20.0 -2 20.9 f 21.9 -^ 22.8 -2 23.9 -^ 24.9 -f 25.9 -2 26.9 -^ 28.0 -2 29.1 -^ 20 50 20.1 -^ 21.0 -1 22.0 -1 23.0 ■] 24.0 1 25.0 -1 26.0 -1 27.0 -1 28.2 -2 29.3 ■; 10 6 00 20.2 -^ 21.1 -1 22.0 •" 23.1 1 24.1 -1 25.1 -1 26.1 -1 27.1 -1 28.3 1 29.4 •' 6 00 TABLE 28C [C=the 3d c orrection. Her. Arg., the star's declinatio n. Vert. Arg., B=th€ 2d correct ion.] B. 88° 4 V 88 ° 48' 88-^ 49' 1 20" 80" 40" 50" 0" 10" 20" 80" 40" 50" 0" 10" 20" II w // II II II II II II II II / 1 II ii 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 .0 0.0 0.0 10 +0.2 +0.1 +0.1 ■+ 0.0 0.0 -0.0 -0.1 -0.1 -0.2 -0.2 -0 .3 -0.4 -0.4 20 0.4 0.3 0.2 0.1 0.0 0.1 0.2 0.3 0.4 0.5 .6 0.7 0.8 30 0.6 0.5 0.3 0.1 0.0 0.1 0.3 0.5 0.6 0.7 .8 1.1 1.2 40 0.8 0.6 0.4 0.2 0.0 0.2 0,4 0.6 0.8 1.0 1 .2 1.5 1.6 50 +1.0 +0.7 +0.5 4 -0.2 0.0 -0.2 -0:5 -0.7 -1.0 -1.2 -1 .5 -1.7 -2.1 TABLE 28B. For finding the Latitude of a place by Altitudes of Polaris. [B = the 2d correction. This correction is always additive.] [Page 557 star's hour angle. h. in. 00 10 20 30 40 50 1 00 10 20 30 40 50 00 10 20 30 40 50 3 00 10 20 30 40 50 4 00 10 20 30 40 50 5 00 10 20 30 40 50 6 00 Star's altitude. 0.0 0.1 0.2 0.5 0.9 1.5 2.0 S.8 10.0 11.3 12.6 13.9 15.2 16,6 17.9 2 20.5 21.7 22.8 24.0 25.0 26.1 27.0 27.8 28.4 29.1 29.6 30.0 30.3 30.5 30.5 24.9 26.0 27.1 27.9 28.8 29.6 30.2 30.7 31.1 31.4 31.6 31.7 38° 89° 0.0 0.1 0.3 0.6 1. 1 1.7 2.4 3.3 4.3 5.3 6.6 7.8 9.2 10.6 12.1 13.6 15.1 16.7 18.3 19.9, 21.5, 23.1, 24.6; 26.1, 27.5 28.8 40° 0.0 0.1 0.3 0.6 1.1 1.8 2.5 3.4 4.5 5.6 6.8 8.1 9.5 29.9 31.2 32.4 33.5 34.4 35.3 36.1 36.8 37.3 37.6 37.8 37.9 0.0 0.1 0.3 0.7 1.2 1.9 2.7 3.6 4.6 5.8 7.0 8.3 11.3 13.0 14.6 16.2 18.0 19.7 21.4 23.1 24.7 26.4 27.9 29.5 30.9 32.3 33.5 34.7 35.8 36.7 37.5 38.2 38.6 39.0 39.3 39.4 42° 11.7: 13.4 15.1 16.8 18. 5: 20.3: 38.8 39.5 40.0 40.4 40.7 40.8 48° 9.0: 10.5: 12.1; 13.9; 15.6: 26.5: 28.3: 30. 0: Star's hour angle. /(. ?;(. 12 00 11 50 40 30 20 10 00^ 10 50 40 30 20 10 00 6 50 40 30 20 10 6 00 TABLE 28C. [C = the 3d correction. Hor. Arg., the star's declination. Vert. Arg.j B = the 2d correction.] B. 10 20 30 40 50 20' 0.0 +0.2 0.4 0.6 0.8 +1.0 88° 47' 80' 0.0 +0.1 0.3 0.5 0.6 +0.7 40' 0.0 +0.1 0.2 0.3 0.4 +0.5 60' 0.0 +0.0 0.1 0.1 0.2 +0.2 88° 48' 0.0 0.0 0.0 0.0 0.0 0.0 10' 0.0 -0.0 0.1 0.1 0.2 -0.2 20" 0.0 80' 0.0 -0.1 0.3 0.5 0.6 -0.7 40' 0.0 -0.2 0.4 0.6 0.8 -1.0 50' 0.0 -0.2 0.5 0.7 1.0 -1.2 0.0 -0.3 0.6 0.8 1.2 -1.5 88° 49' 10" 0.0 -0.4 0.7 1.1 1.5 -1.7 20' 0.0 -0.4 0.8 1.2 1.6 -2.1 Page 558] TABLE 28B. For finding the Latitude of a place by Altitudes of Polaris. [B=the 2d correction. This correction is always additive.] star's hour Star's altitude. 1 star's liour angle. 44° 45° 46° 47° 48° 49° 50° 51° 52° angle. h. m. „ // „ II // „ „ „ „ //. m. 00 0.0 1 0.0 , 0.0 , 0.0 1 0.0 1 0.0 1 0.0 , 0.0 , 0.0 , 12 00 10 0.1 o 0.1. -2 0.1 2 0.1 2 0.1 .3 0-1 :3 0.1 :3 0.1 -3 0.1 i 11 50 20 0.3 1 0.3 4 0.3-5 0.3 5 0.4 .5 0.4 5 0.4 5 0.4 6 0.4 i .] 40 30 0.7 (i 0.7 \ 0.8 % 0.8 ; 0.9 6 0.9 ; 0.9 7 1.0 7 1.0 8 30 40 1.3 7 1.4 •; 1.4 % 1.5 \ 1-5 8 1.6 8 1-6 :9 1.7 9 1. 8 i-,3 20 50 2.0 9 2-1 :9 2.2i: 2.3 9 2.3i 2. 4 1.1 2. 5 1.1 2.61: 2.8 • 10 1 00 2.9 3.0^^ ^•2io 3.2^„ ^•^1 3.5,. •^•^3 3-7i3 3.9 • 00 10 4.0 1 4.iil.2 4.2 :3 4.4 :3 4.5 : 4.7 :4 4.9 4 5.0 1:6 5.3 • 10 50 20 5.1 ^ ^' ^ 1.3 5. 5 1.4 5- 7 1.4 5. 9 1.5 6.1 1.5 6. 3 1.6 6. 6 1.6 6. 8 ;•- 40 30 6.4 4 6.61.5 6.9i4 ' • 1 1.6 7. 4 1.0 7.61.7 7. 9 1.7 8. 2 1.8 8.5 •; 30 40 7.8, 8-1 1.5 8. 3 1.7 8. 7 1.7 H-2l-7 9. 3 1.8 9. 6 1.9 10.0 1.9 10-3 20 20 50 9.3t f) 9.61.7 10. 1 7 10- 4 1.8 10. 7 1.9 11.1 1.9 11.5 2.0 11.9 2.0 12. 3 22 10 2 00 10 10.9 12. 6 T 7 11.3 13. 0^:; 11.' U.8 >iq 12-2is 12.6 1.9 13-0 2.0 I5.O21 13-5 2.1 15.621 13.9, 2 a 14-5'- 00 13. J 14.0 : 14.5 16.1 2 16.7^2 19-0 25 9 50 20 14.3, q 14. 9 1.9 15.4i:9 16.0 2.0 16.5 2.1 17.1 2.2 17.7 2.3 18.42:3 40 30 16.2, ^ 16. 8 1.9 17.3 2.1 18.0 2.0 18. 621 ly. *j 2 2 20.0 2.3 20. 7 2 4 21.5;' 23.9^' 30 40 18.1, 8 18.7 2.0 19.4 2.0 20.0,, 20. 7 20 Zl, t) 2 2 22.3 2.3 23.12:4 20 50 19.9^ n 20. 7 1.9 21.4 2.0 22.12:1 22. 9 22 23, 7 2.3 24.62.4 25.524 26.4 2 28. 9 ^-"^ 31-5 25 34. ,- 36. 5 ^J 10 3 00 21.9 22.6,^ 23-4„o 24.2_ 25-122 26.0,3 27-023 27- 9 06 00 10 23. 7 1 <» 24.62:0 25.4;:; 26. 4 21 97 3 ■^'. •'2.2 ^o* ^00 .^y. *^ 2 4 30.4 24 8 50 20 25. 6 , q 26. 61 9 27. 5 2.0 28. 5 2 29.52 1 30. 5 2 2 31.7 22 32. 8 "4 40 80 27. 5 1 8 28. 5 1.9 29. 5 1.9 30. 5 2 1 31.621 32. 7 22 00, y 2 3 35.22:3 30 40 29.3, 8 30. 4 1.8 31. 4 1.9 32.61:9 33. 7 20 34.9 2.1 36. 2 2 1 37. 5 2.3 38.9 2, 41. 2 20 50 31.1, 6 32.2i7 33. 3 19 34.5,0 35. 7 20 37.0 2.0 38. 3 2.1 OU, ^01 10 4 00 32.7 6 33.9/^ 35.2 • 36. 4 ^-g 37.7^3 39.0,^ 40.4,, 41.9,-, 00 10 34.3, 35. 6 1 g 36. 9 1:6 38.2,'7 39. 5 18 41. 0^8 42.5^:8 44.01:9 45-5 2-; 47.5;-; 49.4 ! 51. 1 ;■! 52.7 • 54. ^-^ 7 50 20 35. 9 , 1 37. 2 1.4 38. 5 1.5 39. 9 1:5 41- 3 1.5 42.81.6 44. 3 1.7 45. 9 1.8 40 30 37. 3 , S 38. 6 1 3 4o.o;-4 41.4;.4 42.81.6 44. 4 1.5 46.0 1.6 47. 7 1.6 30 40 38.6, '> oy. y 1 41.4 42.81.3 44.41.3 45. 9 1.4 47.61.4 49. 3 1.5 20 50 39.8 q 4i.ii:i 42.61.1 44.1 1.2 45. 7 1.2 47. 3 1.3 49.0 1.3 50. 8 1 10 5 00 40.7 9 e 42.2 •„ 43.7 • 45-3io 46-9io 48-6ii 50.3,, 52.1,-, 00 10 41.6 43.1 8 44.6 \ 46.3'-° 47. 9 'g 49.7 . 51.5 .9 53. 2 1 Q 55.2 1-2 6 50 20 42.4 " 43.9 \ 45.4 7 47.1 6 48.7 7 50.5 7 52.4 7 54. 2 7 56.1 'l 40 30 42.9 1 44.5 4 46.1 "4 47.7 \ 49.4 -5 51.2 \ 53.1 -5 54.9 'e 56.9 'l 30 40 43.3 3 44.9 2 46.5 \ 48.1 3 49.9 "2 51.7 ■; 53.6 55.5 2 57.5 'l 20 50 43.6 45.1 46.7 ■, 48.4 1 50.1 ■, 51.9 '0 53.9 ■-, 55.7 \ 57.8 -f 10 6 00 43.7 "^ 45.3 ■ 46.8 ■ 48.5 ■ 50.2 ■ 52.1 ■ 54.0 ■ 55.9 ■ 57.9 -1 6 00 TABLE 28C. [C =the 3d correction. Hor. Arg., the star's declination. Vert. Arg., B=t he 2d corre( Jtion.] B. 88° 47' 88° 48' 88° 49' 1 20" 80" 40" 50" 0" 10" 20" 80" 40" 60" 0" 10" 20" 30 +0.6 +0.5 II +0.3 II +0.1 0.0 -0.1 II -0.3 -0.5 II -0.6 II -0.7 II 0.8 II -1.1 -1.2 40 0.9 0.6 0. 4 1 0. 2 0.0 0.2 0.4 0.6 0.9 1.0 1.2 1.4 1.6 50 1.0 0.7 0.5 0.2 0.0 0.2 0.5 0.7 1.0 1.2 1.5 1.7 i 2.0 60 1.2 0.9 0.6 0.2 0.0 0.2 0.6 0.9 1.2 1.5 1.8 2.1 2.5 70 1.5 1 1-1 0.7 0.4 0.0 0.4 0.7 1.1 1.5 1.8 2.1 2.5 2.8 80 +1.6 +1.2 +0.8 +0.4 0.0 -0.4 -0.8 -1.2 -1.6 -2.1 ■2.5 -2.8 -3.3 TABLE 28B. [Page 559 For finding the Latitude of a place by Altitudes / /' / n / „ / ,, , ,/ / // h. m. 00 0.0 0.1 0.0 0.1 0.0 0.1 0.0 0.2 0. 2 O.Ooo 0. 0. 2 12 00 10 0. 1 0.4 0-1 0.4 0-1 0.4 0.2o3 0.2 0:3 0.2 0:4 0-2 0:4 0.2o4 11 .50 20 0-'^0.6 0-5 0.5 0-5 0.6 0.5o6 0.0 0.7 0-60.6 0.60.7 0.60.7 40 30 1-0 0.8 1-0 0.8 1-1 0.8 I-I09 1-2 0.9 1-2 1.0 1-3 0.9 1-3 1.0 30 40 1-8 1.0 1-«1.1 1-9 1.1 2.O11 2.1 1.1 2- 2 1.2 2. 2 1.3 2.3i3 20 50 2.81.2 2. 9 1.3 3.0 1.3 3.1i4 3. 2 1.5 3- 4 1.5 3. 5 1.5 3.617 10 1 00 4.0- . 4.2, , 4.3,^ 4.5,, 4.7 4. 9 5.0 5.3 00 1.4 1 fi 5.8;-7 T 6.1-^8 6. 3 1:9 6.61:8 6.8 2'o 7.1^:2 10 5.4 5.6/7 10 50 20 7.0 1.8 7. 3 1:8 7. 5 2.0 7.^19 8-2 2.0 8.4 2.2 0. 9.1 24 40 30 ^- ^ 1.9 ^- 1 2.0 9. 5 20 9. 8 2.1 10.22.3 10.624 11.02:4 11-5 2.5 30 40 10.7 2.1 11-12.2 11.5 2.3 11.9.4 12.5 2.3 13.02:5 13.4 2.6 14.02? 20 50 12. 8 2.2 13. 3 2.3 13. 8 2.3 14.3,., 14.82.6 15. 5 2 6 16.0 2.8 16. 7 2 9 10 2 00 15.0.,, 15. 6„, 16. 1 „ . 16. 8„, 17. 4„, 18. 1 „ 18.8 ° 19.6 00 22.632 10 17.324 18. 2 5 18.6" 19. 3 2 8 20. 1 28 020.830 21.7 9 50 20 19.7 2.5 20.52:6 21.32:7 22.1,8 22. 9 2.9 23. 8 go 24.83 25. 8 33 40 30 ZZ, '^2 6 23.1 2.6 ^!-^-7 24.9, « 25. 8 3 26.83.1 27.93.2 29.1 33 30 40 24. 8 2.C 25.7 2.7 26.7 2.8 27. V,, 28. 8 3 29.93.1 31.1 3.2 32.434 20 50 27.4 2.7 28.4 2.7 29. 5 2.8 30. 6 2 q 31. 8 3 33.0 32 34. 3 33 35. 834 10 ' 3 00 30. 1 „ ^ 31.1„., 32. 3„, 33. 5 ■„ 34. 8 " 36. 2 37. 6 „ 39. 2 00 42.6^J 10 32.626 33. 8 27 35. 1 2 8 36. 5 ;■; 037.93:0 39.4^7 40.9 3.3 8 50 20 35. 2 2.6 36. 5 2*7 37.9 2.8 39.428 40.9 2.9 42.53 44.232 46.0 33 40 30 37.82.5 39. 2 2 6 40.7 2.6 42.2,, 43. 8 2.9 45.63:0 47.43:1 49. 3 3 3 30 40 40.3 2.4 41-82.5 43. 3 2.6 45.0,7 46. 7 2 9 48.629 50. 5 3 52.631 20 50 42.7 2.3 44.3 2.4 45.9 2.5 47. V, 6 49.62:6 51.5 28 53. 5 2.9 55. 7 3 1 10 ' 4 00 - 45.0^2 46.7^,3 ^A4 2 4 50.3.,, 52.2 54.3^" 56. 9 \\ 56. 4 59.2,7 1 1.6 • 00 10 47.2 21 49. "\ 50. 8 ;l 52. 8 ;■, 54.824 7 50 20 49.32:0 51.12:0 53. 1 21 55. loo 57.22:3 59.4 24 1 1.9.^-J 1 4.4^^ 40 30 51. 3 1.8 53.1 1.9 55. 2 1:9 57. 3,9 59.52 1 1 \.%^\ 1 4.3 •* 1 6.92:3 30 40 53.1 1.5 o5.0i6 ^Hl-7 5y-2i8 1 1-6 1.8 1 3.9 2.0 1 6.52:0 1 9.2 2^ 20 50 54.61.5 56-61.5 . ^^•^•5 l-Oifi ^ ^-^-6 1 5.9i7 1 8.5i^^ lll-3i8 10 5 00 56.1^., ^^•^3 1 ^-^3 ^•So 1 ^-014 1 6.4i2 1 7.6 110.3 •; 1 11.8ii 113.1 -^ 00 10 57. 3 0.9 59.4^:0 1 1-6 : 3.9- 1 9.0 :2 114.7 • 6 50 20 5|^- 2 0.8 1 0-4 0.8 } f-Io-8 5-O09 1 7.60.9 110.2 ^ 1 13.1 0:9 1 16.1 0:9 40 30 59.0 0.6 } }-h-^ 1 3. 5 0.7 5-^07 1 8- 5 0.7 1 11- 2 0.6 114.0^8 1 17. Oj-^ 30 40 59.60.3 1 1-80.3 1 4. 2 0.3 6-604 1 9. 2 0.4 1 11.80.4 1 14.8j° 117.804 20 50 59.9oi 1 2.I02 1 4.5oo 7.001 1 9.601 1 12. 2 02 1 12.4"- 1 15. 2 J-^ 1 15.4 • 118. 2 02 1 18.4 10 6 00 1 0.0°-^ 1 2.3 1 4.7°- 7.1°-^ 1 9.7°-^ 6 00 TABLE 28C. [C = the 3d correction. Hor. Arg., the star's declination. Vert. Arg., B = the 2d corr ection.] B. 88° 47' 88° 48' 88° 49' 1 20" 80" 40" 50" 0" 10" 20" 8 tO" 40" 50" 0" 10" 20" „ „ „ „ „ „ II // „ „ „ „ II „ 30 -rO.6 +0.5 +0.3 +0.1 0.0 -0.1 -0.3 - 0.5 -0.6 -0.7 -0.8 -1.1 -1.2 40 0.9 0.6 0.4 0.2 0.0 0.2 0.4 0.6 0.9 1.0 1.2 1.4 1.6 50 1.0 0.7 0.5 0.2 0.0 0.2 0.5 0.7 1.0 1.2 1.5 1.7 2.0 60 1.2 0.9 0.6 0.2 0.0 0.2 0.6 0.9 1.2 1.5 1.8 2.1 2.5 70 1.5 1.1 0.7 0.4 0.0 0.4 0.7 1.1 1.5 1.8 2.1 2.5 2.8 80 +1.6 +1.2 +0.8 +0.4 0.0 -0.4 -0.8 — 1.2 -1.6 -2.1 -2.5 -2.8 -3.3 Page 660] TABLE 28D. For finding the Latitude of a place by Altitudes of Polaris. [D=the 4th correction. (D has the same sign as A when the Dec. <88°48', the oppo.^ite sign when the Dec. >88° 48'.)] [Vertical Argument, A = the 1st correction. Horizontal Argument, the star's declination.] A. 10 12 14 16 18 20 22 24 68 70 72 20 40 1 00 1 20 1 40 2 00 Declination, 88° 47' 20" 25 0.0 1.1 2.2 3.3 4.4 5.6 6.7 7.8 8. 9 10.0 11.1 12.2 13.3 27.8 28.9 30.0 31.1 32. 2 33.3 34.4 35.6 36.7 37.8 38.9 40.0 0.0 1.0 1.9 2.9 3.9 4.9 5.8 6.8 7.8 8.8 9.7 10.7 11.7 12.7 13.6 14.6 15.6 16.6 17.5 18.4 19.4 20.4 21.4 22.3 23.3 24.3 25.3 26.2 27. 2 28.2 29.2 30.1 31^1 32. 1 33.0 34.0 35.0 «0" o.t 0.8 1.7 2.5 3.3 4.2 5.0 5.8 ^•1 7.5 8.3 9.2 10^ 10.8 11.7 12.5 13.3 14.2 15.0 15.8 16^7 "17. 6 18.3 19.2 20.0 20.8 21.7 22.5 23.3 24.2 25.0 25.8 26.7 27.5 28.3 29.2 30.0 85' 0.0 0.7 1.4 2.1 2.8 11.8 12.5 13.2 13.9 14.6 15.3 16.0 16.7 17.3" 18.0 18.8 19.4 20.1 20.8 21.5 22.2 "22.9 23.6 24.3 25.0 40" 0.0 0.6 1.1 1.7 2.2 2.8 3.3 3.9 4.4 6.0 5.5 6.1 6.7 7.2 7.8 8.3 8.9 9.4 10.0 10.6 11.1 11.7 12.2 12.8 13.3 13. 9" 14.4 15.0 15.6 16.1 16.7 17.2 17.8 18.3 18.9 19.4 20.0 45' 0.0 0.4 0.8 1.2 1.7 2.1 2.5 2.9 3.3 3.8 4.2 4.6 AO 5.4 5.8 6.2 7.9 8.3 8.8 9.2 9.6 10.0 10.4 10.8 11.2 11.7 12.1 12.5 12.9 13.3 13.8 14.2 14.6 15.0 2.5 2.8 3.0 3.3 3.6 3.9 4.2 4.4 4.7 5.0 5.3 5.6 5.8 6.1 6.4 6.7 6.9 7.2 7.5 7.8 8.0 8.3 8.6 _8^9 9.2 9.4 9.7 10.0 0.0 0.1 0.3 0.4 06 0.7 0.8 1.0 1.1 1.2 1.4 1.6 1.7 1.8 1.9 2.1 2^2 "2.3 2.5 2.7 2.8 2.9 3.0 3.2 3.3 3.4 3.6 3.8 3.9 4.0 4.2 4.3 4.4 4.6 4.7 4.9 5,0 88° 48' 0.0 1.2 0.0 1.4 0.0 1.6 0.0 1.7 0.0 1.8 0.0 1.9 0.0 2.1 0.0 2.2 0.0 0.0 0.0 0^0 0.0 0.0 0.0 OJ) 0.0" 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.1 0.3 0.4 0^ 0.7 0.8 1.0 1.1 2.3 2.5 2.7 2.8 2.9 3.0 3.2 3.3 3.4 3.6 3.8 3.9 4.0 4.2 4.3 4.4 4.6 4.7 4.9 5.0 10" 15 4.7 5.0 5.3 5.6 5.8 6.1 6.4 6.7 6.9 7.2 7.5 7.8 8.0 8.3 8.6 8.9 9. 2 4 9.7 10.0 0.0 0.4 0.8 1.2 1.7 2.1 2.5 2.9 3.3 3.8 4.2 4.6 5.0 5.4 5.8 6.2 6.7 7.1 7.5 7.9 8.3 9.2 9.6 10.0 10.4 10.8 11.2 11.7 12.1 12.5 12.9 13.3 13.8 14.2 14.6 X5.0 20' 0.0 0.6 1.1 1.7 2.2 2.8" 3.3 3.9 4.4 25" 0.0 0.7 1.4 2.1 2.8 5.0 5.5 6.1 6.7 3.4 4.1 4.9 5.5 7.2 7.8 8.3 9.4 10.0 10.6 11.1 11.7 12.2 12.8 13.3 13.9 14.4 15.0 15.6 16.1 16.7 17.2 17.8 18.3 18.9 19.4 20.0 6.2 6.9 7.7 8.3 9.0 9.7 10.4 11.1 Proportional parts. 0.0 0.0 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.2 0.3 0.3 0.3 11.8 12.5 13.2 13.9 14.6 15.3 16.0 16.7 0.4 0.4 0.4 0.4 0.5 0.5 0.5 0.6 0.6 0.6 0.6 0.7 17.3 0.7 18.0 0.7 18.810.7 19.410.8 20.1 20.8 21.5 22.2 0.8 0.8 0.9 0.9 0.0 0.0 0.1 0.2 0.2 0.3 0.3 0.4 0.4 0.5 0.6 0.6 0.7 0.7 0.8 0.8 0^ "0.9 1.0 1.1 1.1 22.9 0.9 23.6 0.9 24.3 1.0 25.0 1.0 1.2 1.2 1.3 1^3 1.4 1.4 1.5 jL6 1.6 1.7 1.7 L_8 1.8 1.9 1.9 2.0 0.0 0.1 0.2 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.1 1.3 1.3 1.4 1.5 1.6 1^ 1.7 1.8 1.9 2^^ '2.1 2.2 2.2 2.^ 2.4 2.5 2.6 2^ "2.8 2.8 2.9 3.0 4' 0.0 0.1 0.2 0,3 0.4 0.6 0.6 0.8 0.9 1.0 1.1 1.3 1.4 2.3 2.4 2.6 2.6 2.8 2.9 3.0 3.1 Proportional parts. 0.2 0.4 0.6 0.7 0.9 1.1 „ „ „ „ „ „ „ „ n „ II II 0.2 0.1 0.1 0.1 0.1 0.0 0.0 0.0 0.0 0.0 0.1 0.1 0.3 0.3 0.2 0.2 0.1 0.0 0.0 0.0 0.0 0.0 0.1 0.2 0.5 0.4 0.4 0.3 0.2 0.1 0.1 0.0 0.1 0.1 0.2 0.3 0.7 0.5 0.5 0.4 0.2 0.1 0.1 0.0 0.1 0.1 0.2 0.4 0.8 0.7 0.6 0.5 0.3 0.2 0.1 0.0 0.1 0.2 0.3 0.5 1.0 0.8 0.7 0.6 0.4 0.2 0.1 0.0 0.1 0.2 0.4 0.6 0.1 0.2 0.4 0.5 0.6 0.7 TABLE 28D. [Page 561 | For finding the Latitude of a place by Altitudes of Polaris. [D= the 4th correction. (D has the same sign as A when the Dec. <88° 48', the oppo.site sign when the Dec >88°48'.)] [Vertical Argument A=the 1st correction. Horizontal Argument, the star's declination.] A. Declination, 88° 48' 88° 49' 1 Proportional parts. 1 80" 36" 40" 45" 60" 65" 0" 5" 10" 16" 20" 1" 2" 8" 4" 0.0 0.0 0.0 II 0.0 II 0.0 0.0 II 0.0 II 0.0 0.0 0.0 II 0.0 II 0.0 0.0 0.0 0.0 2 0.8 1.0 1.1 1.2 1.4 1.6 1.7 1.8 1.9 2.1 2.2 0.0 0.1 0.1 0.1 4 1.7 1.9 2.2 2.5 2.8 3.1 3.3 8.6 8.9 4.2 4.4 0.1 0.1 0.1 0.2 6 2.5 2.9 3.3 3.8 4.2 4.6 5.0 5.3 5.8 6.2 6.7 0.1 0.2 0.2 0.8 8 8.3 3.9 4.4 5.0 5.6 6.1 6.7 7.2 7.8 8.3 8.9 0.1 0.2 0.3 0.4 10 4.2 4.9 5.6 6.2 6.9 7.6 8.3 9.0 9.7 10.4 11.1 0.1 0.3 0.4 0.6 12 5.0 5.8 6.7 7.5 8.3 9.2 10.0 10.8 11.7 12.5 13.3 0.2 0.3 0.5 0.7 14 5.8 6.8 7.8 8.8 9.8 10.8 11.8 12.7 13.7 14.6 15.6 0.2 0.4 0.6 0.8 16 18 6.7 7.8 8.9 10.0 11.1 12.2 13.3 14.4 15.6 16.7 17.8 0.2 0.2 0.4 0.7 0.9 7.5 8.8 10.0 11.2 12.5 13.8 15.0 16.2 17.5 18.8 20.0 0.5 0.7 1.0 20 8.3 9.7 11.1 12.5 13.9 15.3 16.7 18.1 19.4 20.9 22.2 0.3 0.6 0.8 1.1 22 9.2 10.7 12.2 13.8 15.3 16.8 18.3 19.8 21.4 22.9 24.4 0.3 0.6 1.0 1.3 24 10.0 11.7 13.3 15.0 16.7 18.4 20.0 21.7 23.8 25.0 26.7 0.3 0.4 0.7 1.0 1.4 26 10.8 12.7 14.4 16.2 18.0 19.9 21.7 23.5 25.3 27.1 28.9 0.7 1.1 1.4 28 11.7 13.6 15.6 17.5 19.4 21.4 23.3 25.3 27.2 29.2 31.1 0.4 0.8 1.2 1.6 80 12.5 14.6 16.7 18.8 20.8 22.9 25.0 27.1 29.2 31.2 38.3 0.4 0.8 1.2 1.6 32 13.3 15.6 17.8 20.0 22.2 24.4 26.0 26.7 28.4 28.9 31.1 83.8 35.5 0.4 0.9 1.3 1.8 84 14.2 16.6 18.9 21.2 23.6 30.7 33.1 35.4 37.8 0.5 0.9 1.4 1.9 86 15.0 17.5 20.0 22.5 25.0 27.5 30.0 32.5 35.0 37.5 40.0 0.5 1.0 1.5 2.0 88 15.8 18.4 21.1 23.8 26.4 29.0 81.6 34.2 87.0 39.6 42.2 0.5 1.1 1.6 2.2 40 42 16.7 19.4 22.2 25.0 27.8 30.6 83.3 36.1 88.9 41.7 44.4 0.6 1.1 1.7 2.2 17.6 20.4 23.3 26.2 29.2 32.1 85.0 37.9 40.8 48.8 46.7 0.6 1.2 1.8 2.4 44 18.3 21.4 24.4 27.5 30.6 33.7 36.8 39.8 42.8 45.9 48.9 0.6 1.2 1.8 2.4 46 19.2 22.3 25.6 28.8 32.0 35.1 38.3 41.5 44.8 47.9 51.1 0.6 1.3 1.9 2.6 48 50 20.0 23.3 26.7 30.0 33.3 36.7 88.2 40.0 43.8 45.1 46.7 50.0 58.3 0.7 1.3 2.0 2.7 20.8 24.3 27.8 31.2 34.7 41.7 48.6 52.1 55.5 0.7 1.4 2.1 2.8 52 21.7 25.3 28.9 32.5 36.1 39.7 43.3 46.9 50.5 54.2 57.8 0.7 1.4 2.2 2.9 54 22.5 26.2 30.0 33.8 37.5 41.2 45.0 48.7 52.5 56.2 60.0 0.7 1.5 2.2 8.0 56 58 23.3 27.2 31.1 35.0 88.9 42.8 46.7 50.5 52. 3 54.4 58.8 62.2 0.8 1.6 2.3 3.1 24.2 28.2 32.2 36.2 40.3 44.3 48.8 56.4 60.4 64.4 0.8 1.6 2.4 3.2 60 25.0 29.2 33.3 37.5 41.7 45.9 50.0 54.2 58.3 62.5 66.7 0.8 1.7 2.5 3.8 62 25.8 30.1 34.4 38.8 43.0 47.3 51.7 56.0 60.3 64.6 68.9 0.9 1.7 2.6 3.4 64 66 26.7 31.1 35.6 40.0 44.4 48.9 53.3 57.8 62.2 66.7 71.1 0.9 1.8 2.7 2.7 3.6 27.5 32.1 36.7 41.2 45.8 50.4 55.0 59.6 64.2 68.8 73.3 0.9 1.8 3.6 68 28.3 33.0 37.8 42.5 47.2 52.0 56.7 61.3 66.1 70.9 75.5 0.9 1.9 2.8 3.8 70 29.2 34.0 38.9 43.8 48.6 53.5 58.3 63.1 68.0 72.9 77.7 1.0 1.9 2.9 3.9 72 20 30.0 35.0 40.0 45.0 50.0 55.0 60.0 65.0 70.0 75.0 80.0 1.0 2.0 3.0 4.0 Proportional parts. 0.1 0.1 0.1 II 0.2 0.2 0.3 0.3 0.3 0.3 0.3 0.4 40 0.2 0.3 0.4 0.4 0.5 0.5 0.6 0.6 0.6 0.7 0.7 100 0.4 0.5 0.6 0.6 0.7 0.8 0.8 0.9 0.9 1.0 1.1 120 0.5 0.7 0.7 0.8 0.9 1.1 1.1 1.2 1.3 1.4 1.5 140 0.6 0.8 0.9 1.0 1.1 1.3 1.4 1.5 1.6 1.7 1.8 2 00 0.8 1.0 1.1 1.2 1.4 1.6 1.7 1.8 1.9 2.1 2.2 22489—03- -36 Page 562] TABLE 29. Conversion Tables for Nautical and Statute Miles. XmUical miles into statute miles. Statute miles into naiUical miles. 1 nautical mile or knot = 6,080 feet. 1 statute mile = 5,280 feet. 1 statute mile =6,280 feet. 1 nautical mile or knot = 6,080 feet. ' Nautical Statute Nautical Statute Nautical statute Statute Nautical Statute Nautical Statute Nautical miles. miles. miles. miles. miles. miles. miles. miles. miles. miles. miles. miles. 1.00 1.151 8.75 10. 075 16.50 18. 999 1.00 0.868 ^00 7.815 17.00 14. 763 1.25 1.439 9.00 10. 363 16.75 19. 287 1.25 1.085 9.25 8.032 17.25 14.980 1.50 1.727 9.25 10.651 17.00 19. 575 1.50 1.302 9.50 8.249 17.50 15. 197 1.75 2.015 9.50 10. 939 17.25 19. 863 1.75 1.519 9.75 8.467 17.75 15.414 2.00 2.303 9.75 11.227 17.50 20. 151 2.00 1.736 10.00 8.684 18.00 15. 632 2.25 2.590 10.00 11.515 17.75 20. 439 2.25 1.953 10.25 8.901 18. 25 15. 849 2.50 2.878 10.25 11.803 18.00 20. 727 2.50 2.170 10.50 9.118 18.50 16. 066 2.75 3.166 10.50 12. 090 18.25 21.015 2.75 2.387 10.75 9.335 18.75 16. 283 3.00 3.454 10.75 12. 378 18.50 21. 303 3.00 2.604 11.00 9.552 19.00 16.500 3.25 3.742 11.00 12. 666 18.75 21. 590 3.25 2.821 11.25 9.769 19.25 16.717 3.50 4.030 11.25 12. 954 19.00 21.878 3.50 3.038 11.50 9.986 19.50 16. 934 3.75 4.318 11.50 13. 242 19.25 22. 166 3.75 3.256 11.75 10. 203 19.75 17.151 4.00 4.606 11.75 13. 530 19.50 22. 454 4.00 3.473 12.00 10. 420 20.00 17. 369 4.25 4.893 12.00 13. 818 19.75 22. 742 4.25 3.690 12.25 10. 638 20.25 17. 586 4.50 5.181 12.25 14. 106 20.00 23. 030 4.50 3.907 12.50 10. 855 20.50 17. 803 4.75 5.469 12.50 14. 393 20.25 23. 318 4.75 4.124 12.75 11. 072 20.75 18. 020 5.00 5.757 12.75 14. 681 20.50 23. 606 5.00 4.341 13.00 11. 289 21.00 18. 237 5.25 6.045 13.00 14. 969 20.75 23. 893 5.25 4.559 13.25 11. 507 21.25 18. 454 5.50 6.333 13.25 15. 257 21.00 24. 181 5.50 4.776 13. 50 11. 724 21.50 18. 671 5.75 6.621 13.50 15. 545 21.25 24. 469 5.75 4.994 13.75 11. 941 21.75 18.888 6.00 6.909 13.75 15. 833 21.50 24. 757 6.00 5.211 14.00 12. 158 22.00 19. 105 6.25 7.196 14.00 16. 121 21.75 25.045 6.25 5.428 14.25 12. 376 22.25 19. 322 6.50 7.484 14.25 16.409 22.00 25. 333 6.50 5.645 14.50 12. 593 22.50 19. 539 6.75 7.772 14.50 16. 696 22.25 25. 621 6.75 5.862 14.75 12. 810 22.75 19. 756 7.00 8.060 14.75 16.984 22.50 25. 909 7.00 6.079 15.00 13. 027 23.00 19. 973 7.25 8.348 15.00 17. 272 22.75 26. 196 7.25 6.296 15.25 13.244 23.25 20. 191 7.50 8.636 15.25 17. 560 23.00 26. 484 7.50 6.513 15.50 13. 461 23.50 20. 408 7.75 8.924 15.50 17. 848 23.50 27. 060 7.75 6.730 15.75 13. 678 23.75 20. 625 8.00 9.212 15.75 18. 136 24.00 27. 636 8.00 6.947 16.00 13. 895 24.00 20.842 8.25 9.500 16.00 18. 424 24.50 28. 212 8.25 7.164 16.25 14. 112 24.25 21. 060 8.50 9.787 16.25 18.712 25.00 28. 787 8.50 7.381 16.50 14. 329 24.50 21. 277 8.75 7.598 16.75 14. 546 25.00 21.711 TABLE 30. [Page 563 Conversion Tables for Metric and English Linear Measure. Metric to Eiiglwi. 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 .003 106 844 .003 728 213 .004 349 582 .004 970 950 .005 592 319 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 .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 3, 218. 70 4, 828. 05 6, 437. 40 1, 853. 25 3, 706. 50 5, 559. 75 7, 413. 00 5 6 7 8 9 1.524 003 1.828 803 7 2.133 604 3 2.438 404 9 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 Page 564] TABLE 31. Conversion Tables for Thermometer Scales. [F°=Fahrenheit temperature; C°=Centigrade temperature; R°=R6aumur temperature.] Equivalent temperatures— Fahr., Cent., Mail R°=* C°=i (F°- -32°). C 3=JRO = g (F°- -32°). S F°. C°. R°. r C°. R°. 1 -17.2 -13.8 51 +10.6 + 8.4 2 16.7 13.3 52 11.1 8.9 Equivalent temperatures— Centigrade and Fahrenheit. 3 4 16.1 15.6 12.9 12.4 53 54 11.7 12.2 9.3 9.8 F°= 1 C°-h32°. 5 6 7 15.0 14.4 13.9 12.0 11.6 11.1 55 56 57 12.8 13.3 13.9 10.2 10.7 11.1 C°. pa C°. F°. c° F°. c°. F°. C°. F°. 8 13.3 10.7 58 14.4 11.6 -10 14.0 32.0 10 50.0 20 68.0 30 86.0 9 12.8 10.2 59 15.0 12.0 — 9 15.8 1 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 11.1 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— Riaumitr and Fahrenheit. 28 2.2 1.8 78 2.5.6 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 R°. F°. R°. F°. R°. F°. R°. F°. 31 32 33 34 35 36 37 38 39 40 41. 42 -0.6 0.0 + 0.6 1.1 1.7 2.2 2.8 3.3 3.9 4.4 5.0 5.6 -0.4 0.0 + 0.4 0.9 1.3 1.8 2.2 2.7 3.1 3.6 4.0 4.4 81 82 83 84 85 86 87 88 89 90 91 92 27.2 27.8 28.3 28.9 29.4 30.0 30.6 31.1 31.7 32.2 32.8 33.3 21.8 22.2 22.7 23.1 23.6 24.0 24.4 24.9 25.3 25.8 26.2 26.7 1 2 3 4 5 6 7 8 9 -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 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 6! 7 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 TABLE 32. [Page 565 To obtain the True Force and Direction of the Wind from its Apparent Force and Direction on a Moving Vessel. •atBOS ^jojiiBaa 'aojoj orux C<105iOC0'*iO-^iOtOmtOt~!Ot~00l>'3DCC0000a>CCO>O0>Oi-IOt-lT-lr-(iHC^C^C^(N0JC^IM Moq am no s;u{od 'uoTjoajip aiux COCO^^OO^O^CD^OCO^^^^j^^COtOO^OtDtOO^OtOCOOOkOeO^OSOCDO^eOO •aiBOS jjojnBag 'aoaoj arux N«iOmTfOOO^Oi-(rHi-li-lc^iMC^C^~104C^ ■Moq aqi J90 s^uiod 'uoijoajip atux CO'5iCi^i/2iCiO»Cif5Uci05DiOiClOtCiCiO ■81B08 :)jojnB8a 'aajoj atux C^CCOCO-^iO-^iCOiOOt^^t^oDt^OOOOQOODOsaOCSOOSOOOr-li-iUHT-lc^C^C^C^KMC^C^ •Moq aqj yo sjuiod 'uoijaaiip arux iOOCOii^iCiOiCiOi^iCiOiC»C»0»CiCiCiC"^iC'^-^idO"^iCiC'^-^»C •^TT'iC'^'^-f-^-^T^ •ajBas :)jojn'Baa 'aaaoj atux c^cciocO'^iC'^icto»ceot^«ot^oot*t^cct*ooa^oO'35ascsoooi-*i-iU-ii-(c^c^e^c^(NMej ■Aioq aqi jjo s^uiod 'uojiaajip arux iootoidninTjiiom"»''*iO'*'*-*Tf9jiTj<..ji.^ij< «-»<■<>' cc^'«/5t0t~«Or"t^t»t»00t~0Ca000 050>05OOOOr-tr-li-mC^e^C^C^C^C^ 'Aioq aqi yo s^ujod 'uopoajip arux li^iOtO-^iOiC't'^iO^'^-^M'^'V M-^-^MM-^MMMMMMMMM MMMC)MMe^MMI^lc^Mc^lMMc^IMc^INN(^J^^l^^c^<^^M^^ •aiBas jjojn'Baa; 'aajoj arux INMTt0D0000ai0>0»OOOOr-li-li-li-liMC^iM(N:^ •Avoq aqj BO sjaiod 'uoijoajjp arux lOmiO'"»"fl<>OMM-*<«MMe^C4MC^e^Mr-ie>«C^rHe^drHi-ICooooooo>o>o»oooi-<>-i!-ii-i(N-IOT-l.-IOO'-liOOi-lOOOOOO •aXBOS '4J0jnBaa 'aoJOj arux CJM'^C^M'<1*M'^iC'^-^iC-^iCtOu050«OtOt*l:^t^t^00000005C>CiOSOOOt-lT--rHC^C^M • Avoq aqj BO sjurod 'uoi:>aajrp arux miOiOM-^-^e-lMMi-HMMOfHC^l Or-IC^OO^mO-HOJOOO>00 OS0500>OSOO>C50> 'ai^Ds ^jojnBaa 'aajoj arux C4o9^eOOOaOi 0000O>0000OS«GC00 •axBos laojnBaa 'aojoj arux cOiOtD«o«oi~«ct»ooooooo»aooooo>a>r-(^0(NC-i!ooosoooo>ot-.ooo>t~ooo»t~xoot»t~aot-t»oot~t>-t» •a[BOs iiojn'Bag 'aajoj arux 4C^-»101000?^r-'r-l •AVoq aqi bo s-juiod 'uorjoaarp arux io>nme^"»'"*oc^MaoorJooo»oi-~-ooot~ooo>tot»aotot»ootDtoi»totot-«i;ct-;ctoto •aiBDS jjojnBag 'aojoj arux i-(iMTtir-ic^MiHe^MNCo>ooooOr-ir-i-H •M.oq aqj bo sjniod 'uoijaaarp arux iOiCiCC^-1''^P>C^M30OC^t-CCO 50t^05 0t>-OOiCOt>»C!OCOidC«OidC«OiCiCiO-V»CiO •aiBos jjojnBag 'aojoj arux l-IC^'<)"M«>lO"9coo5C^C^-<«"MC^lO-<)<-<(tOlO»t~tDOSOOOOOO>3S-H — O •Aioq aqj go sjutod 'uoijoaJlp arux lO'^OM-^iCt-C^-^iOOOC^-^^Oa MlOt~M'^iCMM^MM'^CMMMCMMMC^MMC^e^M •aXBDs iJojUBag 'aajoj arux r-ie^MOrHC^OOe^rlOrHC^rHO MPjTH'*MC^iO-*MtDr-lr-IO •Avoq aq:> bo sjurod 'uor^aajrp arux «ototOT)ntoM>oweceocjr( NMUtC^C4Mrt(NINrtC^C^r-(rHC^ •aiBos ^jojnBag aojoj arux iHC^MOr-IC^OOrtr-IOOC^rHO MCJO-»J OiOOt>OOiOir-'t— 'O Moqaq^ Bosjnrod 'uopoai}p arux cooec^o^otooooooo ooooooooooooooo ooooooooo •s^ouj[ 'xassaA jo paadg OiOOOiCOOiCOOiOOOiOO r-li-l(NrH^!NiHT-IC^i-(i-ie^i-(r-lC^ oireoo>oooioooiooo>oo rHi-lC^i-lrH(Ni-li-IOJi-lT-l(NrtrH(M oioooinooiao O rH C^ M 00 o> Page 566] TABLE 33. Distance by Vertical Angle. 05 Q CC t^ ^ Vi N e^ M T-- r-l ^ iOeO(NrH OCPJMOOQ I-Hr-IOIOT OlOOOlN ■Ir-lrtr-l 00000 ^ ^ CC CQ CC 00000 00000 i-lrHSc ■^t^ i-Ht^ CC i-I>-ItHOO 3 tir~ooo ^.-lOOO OkOiC-^ -^ r-(0000 ~ (MT)'0(NiOCC(Nr-IO o OTjiece^ . CCOOOl-* ^ li5o -^ "^ "^ 00000 > t^t^o SrHOO ■.^ ■f54TjcS-<}2t~0 CCtHOiO in 1-lr-IOO occc>iT)> O r-CCO)rH iCt-H rH CCI> Mi-lOiO-* tHi-Ii-HOO O OCCI^i-l . 00O5 CCiO CC ■'T »r5 c^ » oxj-r » r-lCC'^.-l O iONtHiH Til (N CC tH O ■<)< cq r-l rH O •<9' (M r-( r-l ^ cocci/sr* *■ T) 00 00 1^ O) (N tH tH .H r-l ocoooo •O v(5 CC 51 r-( ooooo ooQor* co^ lO CC C-1 p o> ooooo OCt^l^tOiftiO 000000 ooooo t>- CO iCiC ■*** -^ 000000 i-HOOOl-tD «0 lO ■* '<' CC c^ ooooo 000000 ec?i>Hoo ooooo ooooo rH rH 001 Oi lO-q'CClN^lOOOlOOOO >o»occaOT)iot~-* jJOoot^iC'^ccoii-io >eq00>0 'J' Tfi TT CC CC CCCC(N04lN 'C^M!NQDt^t^«00 t^tOlO ooooo t^toic -^cc ooooo ooooo OrHCqCC^ lO-^CCCCO) OOOOO 10 or* 00 OS OSOOOD t^t^ ooooo T-IOOOOOO OOOOO OOOOO o a>oo t>-i^ OOOOO 00 X t^ to in ooooo I^ tOiO-^ -^ ooooo to »o '^ -^ CC ooooo ■*Tf CClMffJ ooooo CCCCOIOt-I ooooo i-<-HOOO ooooo Or-lC^CC* to iCiC ■'I* ■^ OOOOO a>oo t^toio OOOOO Tj* ^ CC CC C^ r^ 000000 CO t^ tO>OTj< ooooo t- to lO ■«<" CC ooooo to 10 "* CC CC ooooo in-^cocc^j ooooo ^CCC^Ni-l ooooo CCC4C^r-IO ooooo iC-^ ^ cccc c^ ooooo o CCCCOCJi-H ooooo ooooo .-I rHOOO ooooo 1-1 000105 ooooo 0>0>0>0000 0000© iCCOI~*00O> ONtJIOOO CC CC C^ C< i-H r-l 000000 CC CJ C^ rH 1-1 O 000000 C^rH— 1000 000000 ON'* to 000 TABLE 33. Distance bv Vertical Angle. [Page 567 CO O 55 - r-i C^ O 00 =0000 CO O t0 51000 rHC05irHT-t|C^CClO(NiO 0»T»((NQO OiOCOINrH OOiCOOC^ rl 0)10 0110 ,-(005 OS 00 tOi-ltOMOO lOt^Olt^O^ t^COOOOtOi-*050Ii-<0 01c3c4rHrH,i-lTHiHr-li-l -T^QcccOT-txaiOicco lO Tj<0r-I001i0 1'i0001 01 -^rHOOOf'oi^-lOOOJ C-leCiOOKM COr-ITlooao ■^ .-* Ice O CC l^ r-l •^ (M ^>-l Ol i-H M O) 00 Ol lOOlOCOr-IO 55 Ol |iH r-l rH i-H rH 05 lOC^OJ _ OOTt-IOO> 01(?J .-(rHiHr-l lOOlOlOOi ■*lMC001i-l (NOOiOO lOOirHrl OlOOiOOt^ tH rt lO OOOM o>oot-t-«> lO O Ol O Ol OJ'^OCOO 00t>t-«O5O OOrHOJin rHr-< ooojo> r»^iO'*»j' CO -^ O cc O iO'^T)CJ>O0O0t~ ■*i-ICOt^iO TJi rH -^ ^ lO 00 GC t^ t^ CO rHlOC0»-llO ?0 lO lO lO "^ 00 t^ OiOl t^ C0i-li0'*0» lO lO -^ -^ -^ 0-^ CO Tl lO ■>J< ?l *-0 O lO iC iC iOlOiO"iJ<')'Ujc.JiTjiT>iC0 ■J5 -* CO 0> OJ i-fOiOT»-i>H OS OS O 1-1 -r t^ r-( CO ^^ CO c TCOCOOIr-liOOlOiO'^' 0)0101010) O) O) 1-1 r-( .H r .^^1^,-tCO r-*^C0COOS OiO-*'>1-l ^©■"tOlO lOrfcOOlOl eocoo)oioi iC »-(t^cOO 1-1 iH o o o lO OS CO -* OS CO iC CO 1— I lO COOIO) Olr-I r-QOOco t^ TTCOCOOlr-l ^ OSiOOO-^ COOsiOt^ ^ OlOlCOrH -' — -• — O COOOiO'* ^ r* CO OS o ^ COiOiH O Q lO t^ lO ■^ COOsiO t^ CO oS-^oioio COO)0101rH 0)Qt~Ot~ 1-1^1-1 0-* COOlOlOlrH » lOOi-icg •cP CO o ^ Q ^ t* us CO SeoQ COOJOliHrH lOCOt^OOOs leoioooc >C0Oli-lr CO 0)0)1-10 Oi-IOlCO'* Olt^COQt r-tO OOi 1-liHOO SOt^COiH O iCiO to HOOO St^COQOO SiOiOiO^ HOOOO lO i-IJ^ -nj" rH 5C ol O) rt iH 1-1 S i-liOOOCOQC'jCOOSiOi-II^I'I'OOCOOS-.^f "i-iooioiif'^' — ^^' — " Ol OIOIO "'J"'^CO:COO)01rHi-( 010)i-li-liH r»^i-iosr- - lOlOTjlTjl OOOOO ■^ 1-1 OSI>iO lO lO ij' 'J' ■«< OOOOO 1-1 00 CO 31 o) OOOOO 3D CO-* 0)0 COO)0)0)i-i S;^SSS OOiOCOi-IQO t-*C0Ot^iO OOOOiOjiOiOiO'^Tji Hr-(i-lO OOOOO - I<0)Q0S OOOOO -* CO CO CO w OOOOO r-l t^ -r 1-1 0> !■- i-IOOOiOiO T-li-lr-lrtOO t^ -* 1-1 OS r^ »o lO lO lO ^ *1i * OOOOOO O)00st-i0'* ■* 'J' CO 95 CO CO OOOOOO ociocoi-iooQr-coio-*co eocOeococop)oiO)0«o)o5 OOOOO OOOOOO C0'*0)000 t^CO-«iC0O)i-c COCOCOCOOl 010101010)C< OOOOO OOOOOO ■^ 0)000 1> CO CO CO O) O) OOOOO aot~co- 1 Log. A. Log. B. Log. A. Log. B. Log. A. Log. B. Log. A. Log. B. Log. A. Log. B. Log. A. Log. B. m. 9. 4059 9. 4059 9. 4072 9. 4034 9. 4109 9. 3959 9. 4172 9. 3828 9.4260 9. 3635 9. 4374 9. 3369 1 .4059 .4059 .4072 .4034 .4110 .3957 .4173 . 3825 .4261 .3631 . 4376 .3364 2 .4059 .4059 .4073 .4033 .4111 .3955 .4174 .3822 .4263 .3627 .4378 . 3358 3 . 4059 .4059 .4073 .4032 .4112 .3953 .4175 .3820 .4265 .3624 .4380 .3353 4 .4059 .4059 9. 4059 .4074 .4031 .4113 .3952 .4177 .3817 9. 3814 .4266 .3620 .4383 .3348 5 9. 4059 9. 4074 9. 4030 9.4113 9. 3950 9. 4178 9. 4268 9. 3616 9. 4385 9. 3343 6 .4060 .4059 .4074 .4029 .4114 .3948 .4179 .3811 .4270 .3612 .4387 .3337 7 .4060 .4059 .4075 .4028 .4115 .3946 .4181 . 3809 .4272 .3608 .4389 .3332 8 .4060 .4059 . 4075 .4027 .4116 .3944 .4182 .3806 .4273 .3604 .4391 .3327 9 10' .4060 9. 4060 .4059 9. 4059 .4076 9. 4076 .4026 "9. 4025 .4117 .3943 .4183 .3803 9. 3800 .4275 9. 4277 .3600 .4393 9. 4396 .3221 9. 3316 9. 4118 9. 3941 9. 4184 9. 3596 11 .4060 .4059 .4077 .4024 .4119 .3939 .4186 .3797 .4279 .3592 .4398 .3311 12 .4060 . 4058 .4077 . 4023 .4120 .3937 .4187 .3794 .4280 .3588 .4400 .3305 13 .4060 . 4058 .4078 .4022 .4121 .3935 .4188 . 3792 .4282 .3584 .4402 .3300 14 15 .4060 .4058 .4078 .4021 .4121 .3933 .4190 .3789 9. 3786' .4284 9. 4'286 .3580 .4405 .3294 9. 4060 9. 4058 9. 4079 9. 4020 9. 4122 9. 3931 9. 4191 9. 3576 9. 4407 9. 3289 16 .4060 .4058 .4079 .4019 .4123 .3929 .4193 .3783 .4288 .3572 .4409 .3283 17 .4060 .4057 .4080 .4018 .4124 .3927 .4194 .3780 .4289 . 3568 .4411 .3278 18 .4061 .4057 .4080 .4017 .4125 .3925 .4195 . 3777 .4291 .3564 .4414 .3272 19 20 .4061 .4057 .4081 .4016 9. 4015 .4126 .3923 .4197 .3774 .4293 9. 4295 .3559 .4416 .3266 9. 4061 9. 4057 9. 4081 9. 4127 9. 3921 9. 4198 9. 3771 9. 3555 9.4418 9. 3261 21 .4061 .4056 .4082 .4014 .4128 .3919 .4199 . 3768 .4297 .3551 .4420 .3255 22 .4061 .4056 .4083 .4013 .4129 .3917 .4201 .3765 . 4299 .3547 .4423 .3249 23 .4061 .4056 . 4083 .4012 .4130 .3915 .4202 .3762 .4300 .3542 .4425 .3244 24 25 .4061 .4055 .4084 9. 4084 .4010 9.4009 .4131 .3913 .4204 .3759 .4302 . 3538 .4427 .3238 9. 4062 9. 4055 9. 4132 9. 3911 9. 4205 9. 3756 9. 4304 9.3534 9.4430 9. 3232 26 .4062 .4055 .4085 .4008 .4133 .3909 .4207 .3752 .4306 . 3530 .4432 .3226 27 .4062 .4054 .4086 .4007 .4134 .3907 .4208 .3749 .4308 .3525 .4434 . 3220 28 .4062 .4054 .4086 .4006 .4135 .3905 .4209 .3746 .4310 .3521 .4437 .3214 29 30 .4062 9. 4062 .4054 9. 4053 .4087 .4004 9.4003 .4136 .3903 .4211 .3743 .4312 .3516 .4439 .3208 9. 4087 9. 4137 9.3900 9. 4212 9.3740 9. 4314 9. 3512 9.4441 9. 3203 31 . 4063 .4053 .4088 .4002 . 4138 .3898 .4214 .3737 .4315 .3508 .4444 .3197 32 .4063 .4052 .4089 .4001 .4139 . 3896 .4215 .3733 .4317 . 3503 .4446 .3191 33 .4063 .4052 .4089 . 3999 .4140 .3894 .4217 .3730 .4319 .3499 .4448 .3185 34 . 4063 .4051 .4090 9. 4091 . 3998 9. 3997 .4141 .3892 .4218 9. 4220 .3727 .4321 . 3494 .4451 .3178 35 9. 4064 9. 4051 9. 4142 9. 3889 9. 3723 9. 4323 9.3490 9.4453 9. 3172 36 .4064 .4050 . 4091 . 3995 .4144 .3887 .4221 .3720 .4325 .3485 .4456 .3166 37 .4064 . 4050 .4092 . 3994 .4145 .3885 .4223 .3717 .4327 .3480 .4458 .3160 38 .4064 .4049 .4093 .3993 .4146 .3882 .4224 .3713 .4329 .3476 .4460 .3154 39 . 4065 .4049 .4093 . 3991 .4147 9. 4148 .3880 9. 3878 .4226 9. 4227 .3710 9. 3707 .4331 9. 4333 .3471 .4463 .3148 40 9. 4065 9. 4048 9. 4094 9. 3990 9. 3467 9.4465 9. 3142 41 .4065 .4048 . 4095 .3988 .4149 .3875 .4229 .3703 .4335 .3462 .4468 .3135 42 .4065 .4047 .4095 .3987 .4150 .3873 .4231 .3700 .4337 .3457 .4470 .3129 43 .4066 .4047 .4096 .3985 .4151 .3871 .4232 .3696 .4339 .3453 .4473 .3123 44 45 .4066 .4046 9. 4045 .4097 .3984 .4152 .3868 .4234 .3693 9. 3690 .4341 9. 4343 .3448 .4475 .3116 9. 4066 9. 4097 9. 3982 9. 4154 9. 3866 9. 4235 9. 3443 9. 4477 9.3110 46 .4067 .4045 .4098 .3981 .4155 .3863 .4237 .3686 .4345 . 3438 .4480 . 3103 47 .4067 .4044 .4099 .3979 . 4156 .3861 .4238 .3683 .4347 .3433 .4482 .3097 48 .4067 .4043 .4100 .3978 .4157 .3859 .4240 . 3679 .4349 .3429 .4485 . 3091 49 50 .4068 .4043 .4100 9. 4101 .3976 9."3975 .4158 9. 4159 .3856 9. 3854 .4242 . 3675 9. 3672 .4351 "9. 4353' .3424 .4487 .3084 9. 4068 9. 4042 9. 4243 9. 3419 9. 4490 9. 3078 51 .4068 .4041 .4102 . 3973 . 4161 .3851 .4245 .3668 . 4355 .3414 .4492 .3071 52 .4069 .4041 .4103 . 3972 .4162 .3849 .4246 . 3665 .4357 .3409 .4494 .3064 53 .4069 .4040 . 4103 .3970 .4163 .3846 .4248 .3661 . 4359 .3404 .4497 . 3058 54 55 .4069 9. 4070 .4039 9. 4038 .4104 9. 4105 .3969 .4164 9.4165 .3843 9. 3841 .4250 .3657 9. 3654 . 4361 9. 4363 .3399 .4500 9. 4503 .3051 9. 3967 9. 4251 9. 3394 9. 3044 56 .4070 .4038 .4106 .3965 .4167 .3838 .4253 .3650 .4366 .3389 .4505 .3038 57 .4071 .4037 .4107 .3964 .4168 .3836 .4255 .3646 . 4368 . 3384 .4508 .3031 58 .4071 .4036 .4107 .3962 .4169 . 3833 .4256 .3643 .4370 .3379 .4510 . 3024 59 60 .4071 9. 4072 .4035 9. 4034 .4108 9.'4T09 .3960 9. 3959 .4170 . 3830 9. 3828 .4258 .3639 .4372 .3374 .4513 .3017 9.4172 9. 4260 9. 3635 9. 4374 9. 3369 9. 4515 9. 3010 Page 572] TABLE 37. Log. A and Log. B. [For Computing the Equation of Equal Altitudes. For Noon, A-; for Midnight, A + ; for Noon or Midnight, B+. | Argument=Elapsed Time.] h 7 h - I 1 10^ 1 Ilk 1 Log. A. Log.B. Log. A. Log.B. Log. A. Log. B. Log. A. Log.B. Log. A. Log.B. Log. A. Log.B. m. 9. 4515 9. 3010 9^4685 9. 2530 9. 4884 9. 1874 9.5115 9. 0943 9. 5379 8. 9509 9. 5680 8. 6837 1 .4518 .3003 .4688 .2520 .4888 .1861 .5119 .0925 .5384 .9478 .5685 .6770 2 .4521 .2996 .4691 .2511 .4892 .1848 .5123 .0906 .5389 .9447 .5691 .6701 3 . 4523 .2989 .4694 .2502 .4895 .1835 .5127 .0887 .5393 .9416 .5696 .6632 4 5 .4526 9. 4528 .2982 .4697 .2492 .4899 9. 4902 .1822 9. 1809 .5132 9. 5136 .0867 .5398 .9384 .5701 .6560 8. 6488 9. 2975 9. 4701 9. 2483 9. 0848 9.5403 8. 9352 9. 5707 6 .4531 .2968 .4704 .2473 .4906 .1796 .5140 .0828 .5408 .9320 . 5712 .6414 7 .4534 .2961 .4707 .2463 .4910 .1782 .5144 .0809 .5412 .9287 .5718 .6339 8 .4536 .2954 .4710 .2454 .4913 .1769 .5148 .0789 .5417 .9254 .5723 .6262 9 10 .4539 .2947 .4713 .2444 9. 2434 .4917 .1756 9. 1742 .5153 .0769 .5422 .9221 .5728 .6183 9. 4542 9. 2940 9. 4716 9. 4921 9. 5157 9. 0749 9. 5427 8.9187 9.5734 8. 6103 11 .4544 .2932 .4719 . 2425 .4924 .1728 . 5161 .0729 .5432 .9153 . 5739 .6021 12 .4547 .2925 .4723 .2415 .4928 .1715 . 5165 .0708 .5436 .9118 .5745 .5937 13 .4550 .2918 .4726 .2405 .4932 .1701 .5169 .0688 .5441 .9083 .5750 .5852 14 .4552 .2911 9. 2903 .4729 .2395 .4935 .1687 .5174 .0667 .5446 .9048 .5756 .5764 15 9. 4555 9. 4732 9. 2385 9. 4939 9. 1673 9.5178 9. 0646 9. 5451 8. 9013 9. 5761 8. 5674 16 .4558 .2896 .4735 .2375 . 4943 .1659 .5182 .0625 .5456 .8977 .5767 .5583 17 .4561 .2888 .4738 .2365 .4946 .1645 .5186 .0604 .5461 .8940 .5772 .5488 18 .4563 .2881 .4742 .2355 .4950 .1630 .5191 .0583 . 5466 .8903 .5778 .5392 19 20 .4566 .2873 '9. 28*66 .4745 .2344 .4954 9. 4958 .1616 . 5195 .0561 .5470 .8866 .5783 .5293 9. 4569 9. 4748 9. 2334 9. 1602 9.5199 9. 0540 9. 5475 8. 8829 9. 5789 8. 5192 21 .4572 . 2858 .4751 .2324 .4961 .1587 .5204 .0518 .5480 .8791 .5794 .5088 22 . 4574 .2850 .4755 .2313 .4965 .1573 . 5208 .0496 .5485 .8752 .5800 .4981 23 .4577 .2843 .4758 .2303 .4969 .1558 .5212 .0474 .5490 .8713 .5806 .4871 24 .4580 .2835 .4761 .2292 .4973 .1543 .5217 .0452 . 5495 9. 5500 .8674 .5811 . 4758 25 9. 4583 9. 2827 9. 4764 9. 2282 9. 4977 9. 1528 9. 5221 9. 0429 8. 8634 9. 5817 8. 4641 26 .4585 .2819 .4768 . 2271 .4980 .1513 .5225 .0406 .5505 .8594 .5822 .4521 27 .4588 .2812 .4771 . 2261 .4984 .1498 .5230 .0383 .5510 . 8553 .5828 . 4397 28 .4591 .2804 .4774 .2250 .4988 .1483 .5234 .0360 .5515 . 8512 .5834 .4270 29 30 .4594 .2796 9. 2788 .4778 .2239 .4992 9. 4996 .1468 .5238 9. 5243 . 0337 .5520 .8470 .5839 . 4138 9. 4597 9. 4781 9. 2228 9. 1453 9. 0314 9. 5525 8. 8427 9. 5845 8. 4001 31 .4600 .2780 .4784 .2217 .5000 .1437 .5247 .0290 .5530 .8384 .5851 .3860 32 .4602 .2772 .4788 .2206 .5003 .1422 .5252 .0266 . 5535 .8341 .5856 .3713 33 .4605 .2764 .4791 .2195 .5007 .1406 .5256 .0242 . 5540 .8297 .5862 . 3561 34 .4608 . 2756 .4794 .2184 9. 2173 .5011 .1390 5261 9. 5265 .0218 .5545 9. 5550 .8253 .5868 . 3403 8. 3239 35 9. 4611 9. 2747 9. 4798 9. 5015 9. 1375 9. 0194 8. 8208 9. 5874 36 .4614 .2739 .4801 .2162 .5019 .1359 .5269 .0169 .5555 .8162 .5879 .3067 37 .4617 .2731 .4804 .2151 .5023 .1343 .5274 .0144 .5560 .8115 .5885 .2888 38 .4620 .2723 .4808 .2140 .5027 .1327 .5278 .0119 .5565 .8068 .5891 .2701 39 40 .4622 9. 4625 .2714 9. 2706 .4811 .2128 .5031 .1310 .5283 9.5287 .0094 .5570 .8020 .5897 .2505 9.4815 9.2117 9. 5035 9.1294 9. 0069 9. 5576 8. 7972 9. 5902 8. 2299 41 .4628 .2698 .4818 .2105 .5038 .1278 .5292 .0043 .5581 .7923 .5908 .2082 42 .4631 .2689 .4821 .2094 .5042 .1261 . 5296 .0017 .5586 .7873 .5914 .1853 43 . 4634 .2681 .4825 .2082 .5046 .1244 .5301 8. 9991 .5591 .7823 .5920 .1611 44 45 .4637 .2672 .4828 .2070 9.2059 .5050 .1228 .5305 .9965 8. 9938 . 5596 9. 5601 .7772 .5926 .1354 9. 4640 9.2664 9. 4832 9. 5054 9.1211 9. 5310 8.7720 9. 5931 8. 1080 46 .4643 .2655 .4835 .2047 . 5058 .1194 .5315 .9911 .5606 .7668 .5937 .0786 47 .4646 .2646 .4839 .2035 .5062 .1177 . 5319 .9884 .5612 .7614 .5943 .0470 48 .4649 .2638 .4842 .2023 .5066 .1159 .5324 .9857 .5617 .7560 .5949 .0128 49 50 .4652 .2629 9. 2620 .4846 .2011 .5070 .1142 9. 1125 .5328 .9830 8. 9802 .5622 .7505 8. 7449 .5955 7. 9756 9. 4655 9.4849 9. 1999 9. 5074 9. 5333 9. 5627 9. 5961 7. 9348 51 .4658 .2611 .4853 .1987 .5078 .1107 .5337 .9774 .5632 .7392 .5967 .8897 52 .4661 .2602 .4856 .1974 .5082 .1089 .5342 .9745 .5638 .7335 . 5973 .8391 53 .4664 .2593 .4860 .1962 .5086 .1072 .5347 .9717 .5643 .7276 .5979 .7817 54 .4667 .2584 9. 2575 .4863 9. 4867 .1950 .5091 .1054 .5351 .9688 8. 9659 .5648 9.5654 .7217 8. 7156 .5985 .7154 55 9. 4670 9. 1937 9. 5095 9. 1036 9. 5356 9. 5991 7. 6368 56 .4673 .2566 .4870 .1925 .5099 .1017 .5361 .9630 .5659 .7094 .5997 .5405 57 .4676 .2557 .4874 .1912 .5103 .0999 . 5365 .9600 .5664 .7032 .6003 .4162 58 .4679 .2548 .4877 .1900 .5107 .0981 .5370 .9570 .5669 .6968 .6009 .2407 59 60 .4682 .2539 9. 2530 .4881 . 1887 .5111 .0962 9. 0943 .5375 9. 5379 .9540 8.9509 .5675 9. 5680 .6903 .6015 6. 9591 9. 4685 9. 4884 9. 1874 9. 5115 8. 6837 9.6021 Inf. f OF THE ^ X %£^LypnBKa>._^ / TABLE 37. [Page 573 Log. A and Log. B. [For Computing the Equation of Equal Altitudes. For Noon, A — ; for Midnight, A +; for Noon or Midnlgh t, B-. Argument = Elapsed Time. 1 ■ . lai" 18" 14h loh itt- 1 7" Log. A. Log. B. Inf. Log. A. Log. B. Log. A. Log. B. Log. A. Log. B. Log. A. Log. B. Log. A. Log. B. in. 9. 6021 9.6406 8. 7563 9. 6841 9. 0971 9. 7333 9. 3162 9. 7895 9.4884 9. 8539 9. 6383 1 .6027 6. 9608 .6412 .7641 . 6848 .1014 .7:342 . 3194 .7905 .4911 .8550 .6407 9 .6038 7. 2431 . 6419 .7718 .6856 . 1057 . 7351 . 8225 .7915 .4937 . 8562 .6431 8 .6039 .4198 .6426 .7794 .6864 .1099 .7360 .8256 .7925 .4963 .8573 .6455 4 5 .6045 . 5453 7. 6428 . 6438 9.6440 .7868 .6872 .1141 9. 1183 .7369 9. 7378 .8287 .7935 .4990 .8585 .6478 9. 6051 8. 7942 9. 6879 9. 3319 9. 7945 9. 5016 9. 8597 9. 6502 B . 6057 .7226 .6447 . 8015 .6887 .1224 . 7386 .3350 . 7955 .5042 .8608 .6526 7 . 6063 .7902 . 6454 .8087 . 6895 . 1265 .7395 .3880 .7965 . 5068 .8620 .6550 8 .6069 .8488 .6461 .8158 .6903 .1806 .7404 .8411 .7975 .5094 . 8632 . 6573 9 10 . 6075 .9005 .6467 9.6474 .8227 8. 8296 .6911 9. 6919 .1347 9. 1887 .7418 .3442 9. 8472 .7986 9. 7996' .5120 9. 5146 .8644 .6597 9. 6082 7. 9469 9. 7422 9. 8655 9. 6621 n .6088 .9889 .6481 .8364 .6926 .1428 .7431 . 8503 .8006 .5171 .8667 .6644 12 .6094 8. 0273 .6488 . 8482 .6934 .1468 .7440 . 3533 .8016 .5197 .8679 . 6668 18 .6100 .0627 .6495 .8498 .6942 .1507 .7449 .3563 .8027 . 5223 .8691 .6691 14 15 .6106 9.6112 .0955 8. 1260 .6502 9. 6509 . 8564 8. 8628 .6950 9. 6958 .1547 9. 1586 .7458 . 3593 9.8628 . 8037 9. 8047' .5248 . 8708 .6715 9. 6738 9. 7467 9. 5274 9.8715 16 .6119 . 1547 .6516 .8692 .6966 .1625 .7476 .3653 .8058 .5800 .8727 .6762 17 .6125 .1816 . 6523 .8756 .6974 .1664 . 7485 . 3688 .8068 .5325 .8789 .6785 18 .6131 .2071 .6580 .8818 .6982 .1703 .7494 .3713 .8078 .5851 .8751 .6809 19 .6137 . 2312 . 6538 .8880 .6990 9. 6998 .1741 .7503 . 3742 9. 3772^ .8089 9. 8099 .5376 9. 5401 .8763 9. 8775 .6832 20 9.6144 8. 2541 9. 6545 8. 8941 9. 1779 9. 7512 9. 6856 21 .6150 .2759 . 6552 .9002 .7006 .1817 .7522 .3801 .8110 .5427 .8787 .6879 22 .6156 .2967 .6559 .9062 .7014 .1855 .7531 .3831 .8120 .5452 .8799 .6903 28 .6163 .3166 .6566 .9121 .7022 .1893 .7540 .8860 .8131 .5477 .8812 .6926 24 25 .6169 .8357 .6573 9. 6580 .9180 8. 9288 .7030 9. 7088 .1930 .7549 . 3889 9. 3918 .8141 9. 8152 .5502 9. 5528 .8824 .6949 9. 6973 9.6175 8. 3540 9. 1967 9. 7558 9. 8836 26 .6182 .3717 .6588 .9295 .7047 .2004 .7568 .3947 .8162 .5553 .8848 .6996 27 .6188 .3887 . 6595 . 9852 .7055 .2041 .7577 .3976 .8173 . 5578 .8861 .7019 28 .6194 . 4051 .6602 .9408 .7063 .2078 .7586 .4005 .8184 . 5603 .8873 .7043 29 80 .6201 9. 6207 .4210 8. 4363 .6609 .9464 8. 9519 .7071 9. 7079 .2114 9. 2150 .7595 .4083 9. 4062 .8194 . 5628 .8885 .7066 9. 6616 9. 7605 9. 8205 9. 5653 9. 8898 9. 7089 81 . 6214 .4512 .6624 .9573 .7088 .2186 .7614 .4090 .8216 .5677 .8910 .7112 82 .6220 . 4657 . 6631 .9627 .7096 .2222 .7624 .4119 .8227 .5702 .8923 .7186 88 .6226 .4796 . 6638 .9681 .7104 .2258 .7638 .4147 .8237 .5727 . 8935 .7159 34 85 .6233 9. 6239 . 4932 8. 5064 . 6645 . 9734 8. 9787 .7112 .2293 .7642 .4175 .8248 .5752 .8948 .7182 9. 6653 9. 7121 9. 2329 9. 7652 9. 4204 9. 8259 9. 5777 9. 8961 9. 7205 86 .6246 .5192 .6660 . 9889 .7129 .2364 .7661 .4232 .8270 .5801 .8973 .7228 87 .6252 .5318 .6667 .9891 .7137 .2399 .7671 .4260 .8281 .5826 .8986 .7251 88 .6259 .5440 .6675 .9942 .7146 .2434 .7680 .4288 .8292 .5850 .8999 .7275 39 40 .6265 . 5559 .6682 9. 6690 . 9993 .7154 .2468 .7690 .4316 .8803 .5875 .9011 .7298 9. 6272 8. 5675 9. 0043 9. 7162 9. 2508 9. 7699 9. 4348 9. 8314 9. 5900 9. 9024 9. 7821 41 .6279 .5788 .6697 .0093 .7171 . 2587 .7709 .4371 .8325 .5924 . 9037 .7344 42 .6285 .5899 .6704 .0142 .7179 .2571 .7718 .439^ . 8336 . 5948 .9050 .7367 48 .6292 .6008 .6712 .0191 .7187 .2605 .7728 .4426 .8347 .5973 .9063 .7390 44 45 .6298 .6114 8. 6218 .6719 .0240 .7196 9. 7204 .2639 .7788 .4454 .8358 .5997 9.6022 .9075 .7413 9. 6305 9. 6727 9. 0288 9. 2673 9. 7747 9.4481 9. 8369 9. 9088 9. 7436 46 .6311 .6320 .6734 .0336 .7213 .2706 . 7757 .4509 .8380 .6046 .9101 .7459 47 .6318 .6419 .6742 .0384 .7221 .2740 .7767 .4536 . 8391 .6070 .9114 .7482 48 .6325 .6517 .6749 .0431 .7230 . 2773 .7776 .4563 .8402 .6094 .9127 .7505 49 50 .6381 9. 6338 .6613 8. 6707 .6757 9. 6764 .0478 9. 0524 .7238 .2806 .7786 .4590 .8414 .6119 .9140 .7529 9. 7247 9. 2839 9. 7796 9.4617 9. 8425 9. 6143 9. 9154 9. 7552 51 .6345 .6799 .6772 .0570 .7256 .2872 .7806 .4644 .8486 .6167 .9167 .7575 52 .6351 .6890 .6779 .0616 .7264 .2905 .7815 .4671 .8447 .6191 .9180 .7598 53 . 6358 .6979 .6787 .0662 .7273 .2937 .7825 .4698 .8459 .6215 .9193 .7621 54 .6365 .7067 .6795 9. 6802 .0707 9. 0752 .7281 .2970 9. 8002 . 7835 .4725 9. 4752 .8470 9.8481 .6239 .9206 .7644 55 9. 6372 8. 7153 9. 7290 9. 7845 9. 6263 9. 9220 9. 7667 56 .6378 .7237 .6810 .0796 .7299 . 8034 .7855 . 4778 .8493 .6287 .9233 .7690 57 .6385 .7321 .6818 .0840 .7307 .3066 .7865 .4805 .8504 .6311 .9246 .7713 58 .6392 .7402 .6825 .0884 .7316 .3098 .7875 .4831 .8516 .6335 .9260 .7736 59 .6399 . 7483 .6833 .0928 .7324 .3130 .7885 .4858 .8527 .6359 .9273 .7759 60 9.6406 8. 7568 9.6841 9.0971 9. 7333 9. 3162 9. 7895 9.4884 9. 8539 9. 6383 9. 9287 9. 7782 Page 574 TABLE 37. Log. A and Log. B. [For Computing the Equation of Equal Altittide.s . For Noon, A — ; for Midnight, A +; for Noon or Midnight, B -. 1 Argument = Elapsed Time.] fa l| 18" IS" 200 2ih 221- o jh Ivog. A. Log.B. Log. A. Log.B. Log. A. Log.B. Log. A. 0. 2623 Log.B. Log. A. Log. B. Log. A. Log. B. m. 9. 9287 9. 7782 • 0. 0172 9. 9167 0. 1249 0. 0625 0. 2279 0. 4523 0. 4372 0. 7689 0. 7652 1 .9300 .7804 . 0188 .9190 .1269 .0650 .2649 .2309 .4562 .4414 . 7765 .7729 2 .9314 .7827 . 0204 . 9213 .1290 .0676 .2676 . 2339 .4601 .4455 .7842 .7807 3 . 9327 .7850 .0221 .9237 .1310 .0701 .2702 .2370 .4640 .4497 .7920 .7886 4 5 .9341 9.9355 .7873 .0237 .9260 . 1330 .0727 .2729 .2401 0.2431 .4680 0. 4720 . 4540 .8000 0. 8081 .7967 9. 7896 0. 0253 9. 9284 0.1351 0. 0753 0. 2756 0. 4582 0.8049 6 .9368 .7919 .0270 .9307 .1371 .0779 . 2783 .2462 .4761 .4625 .8163 .8133 7 .9382 .7942 .0286 .9331 .1392 .0805 .2810 .2493 .4801 .4668 .8247 .8218 8 .9396 .7965 .0303 . 9355 .1412 .0830 .2838 . 2524 .4842 .4711 . 8333 .8305 9 .9410 .7988 .0319 0. 0336 .9378 . 1433 0. 1454 .0856 .2865 . 2556 0.2587 .4884 0. 4926 .4755 .8420 . 8393 0. 8483 10 9. 9424 9.8011 9. 9402 0. 0882 0. 2893 0.4799 0. 8508 11 .9437 .8034 . 0353 .9426 .1475 .0909 .2921 .2619 .4968 .4844 . 8599 .8574 12 .9451 .8057 .0370 .9449 .1496 .0935 .2949 .2650 .5010 .4889 .8691 .8667 13 .9465 .8080 .0386 .9473 .1517 .0961 .2977 .2682 .5053 .4934 .8786 .8763 14 15 .9479 .8103 .0403 .9497 .1538 .0987 .3005 .2714 0. 2746 .5097 .4980 .8882 .8860 9. 9493 9. 8126 0. 0420 9. 9520 0. 1559 0. 1013 0. 3034 0. 5140 0. 5026 0. 8980 0. 8959 16 .9508 .8149 .0437 .9544 .1581 .1040 .3063 .2778 .5184 .5072 .9080 .9060 17 .9522 .8172 .0454 .9568 .1602 .1066 . 3091 .2811 . 5229 .5118 .9183 .9164 18 .9536 .8195 .0472 .9592 .1623 .1093 .3120 .2843 .5274 .5165 .9288 .9270 19 20 .9550 9.9564 .8218 9. 8241 .0489 .9616 .1645 .1119 . 3150 .2876 "0. 2909 . 5319 0. 5365 . 5213 0. 5261 . 9396 .9378 0. 0506 9.9640 0. 1667 0. 1146 0. 3179 0. 9506 0. 9489 21 .9579 .8264 .0523 .9664 .1689 .1173 .3208 .2942 ■ . 5411 .5309 .9618 .9603 22 .9593 .8287 .0541 .9687 .1711 .1200 .3238 .2975 . 5458 .5358 .9734 .9719 23 .9607 .8310 .0558 .9711 .1733 .1226 .3268 .3008 .5505 .5407 .9853 .9839 24 25 .9622 9. 9636 .8333 . 0576 .9735 .1755 .1253 0. 1280 .3298 .3041 . 5553 .5457 .9975 .9961 9. 8356 0. 0593 9. 9760 0. 1777 0. 3328 0. 3075 0. 5601 0. 5507 1.0100 1.0087 26 .9651 .8379 .0611 .9784 .1799 .1308 .3359 .3109 .5649 .5557 .0228 .0216 27 .9665 .8402 .0628 .9808 .1821 .1335 .3389 .3143 .5698 .5608 .0361 .0350 28 .9680 .8425 .0646 .9832 .1844 .1362 .3420 .3177 .5748 .5660 .0497 .0487 29 30 .9695 9. 9709 .8448 .0664 .9856 .1867 .1389 0. 1417 .3451 0. 3482 .3211 0. 3245 .5798 0.5848 .5712 .0638 .0628 9. 8471 0. 0682 9. 9880 0. 1889 0.5764 1 1. 0783 1. 0774 31 .9724 .8494 .0700 .9904 .1912 .1444 .3514 .3280 . 5899 .5817 .0934 .0925 32 .9739 . 8517 .0718 .9929 .1935 .1472 .3545 .3315 . 5951 .5871 .1089 .1081 33 .9754 .8540 .0736 .9953 .1958 .1499 .3577 .3350 .6003 .5925 .1250 .1242 34 .9769 .8563 .0754 .9977 .1981 .1527 0. 1555 .3609 .3385 0. 3420' .6056 .5979 .1416 .1409 35 9.9784 9. 8586 0. 0772 0.0002 0. 2004 0. 3641 0. 6110 0.6034 1. 1590 1. 1583 36 .9798 .8609 .0790 .0026 .2028 .1582 .3674 .3456 .6164 .6090 .1770 .1764 37 .9813 .8632 .0809 .0051 .2051 .1610 .3706 .3491 .6218 .6147 .1958 .1952 38 .9829 .8655 .0827 .0075 .2075 .1638 .3739 .3527 .6273 .6204 .2154 .2149 39 40 .9844 .8678 . 0845 .0100 .2098 .1667 .3772 .3563 .6329 .6261 0. 6319 .2359 . 2354 1. 2569 9. 9859 9. 8701 0.0864 0. 0124 0. 2122 0. 1695 0. 3805 0. 3599 0. 6386 1. 2573 41 .9874 .8724 .0883 .0149 .2146 .1723 .3839 .3636 .6443 .6378 .2799 .2795 42 .9889 .8748 .0901 .0173 .2170 .1751 .3873 .3673 .6501 .6438 .3037 .3033 43 .9904 .8771 .0920 .0198 .2194 .1780 .3907 .3710 .6560 .6498 .3288 .3285 44 45 .9920 9. 9935 .8794 .0939 0. 0958 .0223 .2218 .1808 .3941 .3747 0. 3784 .6619 0.6679 .6559 .3554 .3552 9. 8817 0. 0248 0. 2243 0. 1837 0. 3975 0. 6621 1. 3837 1.3835 46 .9951 .8840 .0976 .0272 .2267 .1866 .4010 .3822 .6740 .6684 .4140 .4138 47 .9966 .8863 .0995 .0297 .2292 .1895 .4045 .3859 .6802 .6747 .4465 .4463 48 .9982 .8887 .1015 .0322 .2316 .1924 .4080 .3897 .6865 .6811 .4815 .4814 49 50 .9998 .8910 .1034 .0347 .2341 .1953 .4115 .3936 0. 3974 .6928 0. 6993 .6876 .5196 1. 5613 .5195 0.0013 9. 8933 0. 1053 0. 0372 0. 2366 0. 1982 0. 4151 0. 6942 1.5612 51 .0029 .8956 .1072 .0397 .2391 .2011 .4187 .4013 .7058 .7008 .6074 .6073 52 .0044 .8980 .1092 .0422 .2416 .2040 .4223 . 4052 .7124 .7076 .6588 .6587 53 .0060 .9003 .1111 .0447 .2442 .2070 .4260 .4091 .7191 .7144 .7171 .7171 54 .0076 .9026 .1131 .0473 .2467 .2099 .4297 .4130 0. 41 70 .7259 0. 7328' .7214 .7844 .7843 55 0.0092 9. 9050 0. 1150 0. 0498 0. 2493 0.2129 0. 4334 0. 7284 1. 8638 1. 8638 56 .0108 .9073 .1170 .0523 .2518 .2159 . 4371 .4210 .7398 . 7355 .9610 .9610 57 .0124 .9096 .1190 .0548 .2544 .2189 .4408 .4250 .7469 .7428 2. 0863 2. 0863 58 .0140 .9120 .1209 . 0574 . 2570 .2219 .4446 .4291 .7541 .7501 .2627 .2627 59 60 .0156 0. 0172 .9143 .1229 . 0599 .2596 .2249 . 4485 . 4331 .7615 .7576 2.5640 2.5640 9. 9167 0. 1249 0. 0625 0. 2623 0. 2279 0. 4523 0. 4372 0. 7689 0.7652 Inf. Inf. TABLE 38. [Page 575 1 Error in Longitude due to one minute Error of Latitude. 2 3 — Latitude. • 03 d 00 -a 3 0° 5° 10° 15° •20° •25° 30° 35° 40° 45° 60° 66° 60° 66° 70° 75° o / 1 1 , , , 1 / / , / / / 1 / O o 10 110 .4 .4 .4 .5 .5 .6 .7 .8 1.0 1.8 L8 2.9 110 10 ?.o .4 .4 .5 .6 .7 .8 1.0 1.2 1.6 2.6 20 80 .4 . .6 .7 .9 1.1 1.5 2.3 30 40 .5 .6 .8 1.0 1.3 40 50 .7 .9 1.2 50 60 10 .9 .8 .9 1.2 1.8 3.0 105 60 10 105 .8 .8 .3 .3 .4 .4 .5 .6 9.0 .8 .8 .4 .4 .5 .6 .7 .9 1.2 L6 2.7 20 80 .8 .4 .5 .6 .7 .8 1.1 1.5 2.4 30 40 .4 .5 .6 . t 1.0 1.3 40 50 .4 .6 .8 1.2 50 60 .6 .9 60 15 100 .2 .2 .2 .3 .3 .4 .4 .5 .6 .8 1.1 1.6 2.9 100 15 20 .2 ,2 .8 .3 .4 .5 .5 .7 .9 1.1 1.6 2.7 20 80 .2 .8 .8 .4 .5 .6 .8 1.1 1.5 2.4 30 40 .2 .3 .4 .6 .7 .9 1.3 2.1 40 50 .8 .4 .6 .8 1.2 50 60 .8 .6 .9 .5 .6 .8 1.1 1.7 3.0 95 60 15 15 95 .1 .1 .2 .2 .3 .3 .4 20 .1 .2 . 2 .8 .3 .4 .5 .6 .8 1.1 1.6 2.8 20 80 .2 .2 .3 .4 .5 .6 .8 LO L5 2.5 80 40 .2 .3 .4 .5 .7 .9 1.3 2.1 40 50 .3 .4 .6 .8 1.1 50 60 .2 .3 .6 .9 60 20 90 .0 .0 .1 .1 .1 .2 .2 .3 .4 .6 .7 1.1 1.6 3.0 90 20 80 .0 .1 .1 .2 .2 .3 .4 .5 .7 1.0 L5 2.7 80 40 .0 .1 .2 .3 .8 .5 .6 .9 1.3 2.2 40 50 .0 .1 .2 .4 .5 .8 1.1 50 60 .0 .2 .3 .5 .9 60 70 .0 .2 .6 1.1 LO L6 3.1 70 20 85 .1* .1* .0 .0 .0 .1 .1 .2 .3 .3 .5 .7 85 20 80 .1* .0 .0 .1 .1 .2 .2 .4 .5 .7 LO L5 2.7 30 40 .1* .0 .0 .1 .2 .3 .4 .6 .9 1.3 2.3 40 50 .1* .0 .1 .2 .8 .5 .7 1.1 50 60 .2* .0 .1 .3 .5 .9 60 70 20 .3* .0 .2 .6 1.1 .1 .1 .2 TT .5 .9 1.5 3.1 70 80 .2* .2* .1* .1* .1* .0 .0 .0 80 20 80 .2* .2* .1* .0 .0 .1 .1 .2 .3 .4 .6 .9 1.5 2.8 30 40 .2* .2* .1* .0 .1 .2 .3 .4 .6 .9 1.3 2.4 40 50 .8* .2* .1* .1 .2 .3 .5 .7 1.1 50 60 .4* .2* .0 .1 .3 .5 .9 60 70 20 75 .6* .3* .0 .2 .6 1.2 .1* .0 To" .1 .2 .3 .6 1.2 70 .3* .3* .2* .2* .2* .1* .1* .1* 75 20 80 .8* .3* .2* .2* .1* .1* .0 .1 .1 .2 .4 .6 .9 1.5 3.0 30 40 .4* .3* .2* .1* .1* .0 .1 .2 .4 .5 .8 1.3 2.5 40 50 .4* .3* .2* .1* .0 .1 .3 .5 .7 1.1 50 60 .6* .4* .2* .1* .1 .3 .5 .9 60 70 20 1.2* .6* .3* .0 .2 .6 1.2 .2* .2* .2* .2* .2* .2* .2* .2* 70 70 20 70 .4* .4* .3* .8* .8* .3* .2* .2* 80 .4* .4* .3* .3* .2* .2* .1* .1* .0 .0 .1 .2 .6 .8 L5 3.1 30 40 .5* .4* .3* .8* .2* .1* .0 .1 .2 .3 .5 .8 1.3 2.6 40 50 .6* .5* .3* .2* .2* .0 .1 .3 .4 .7 1.1 50 60 .9* .6* .4* .3* .1* .1 .2 .5 .9 60 70 1.2* .6* .3* .1* .2 .6 L2 70 •h H *^ s 0° 6° 10° 15° 20° 26° 80° 86° 40° 46° 60° 66° 60° 65° 70° 76° «g Ph Latitude. Page 576] TABLE 39. Amplitudes. Declination. Lati- tude. Lati- tude. o°.o 0°.6 1°.0 1°.5 2^.0 2°. 5 8°.0 8°. 6 4°.0 4°. 5 5°.0 o°.5 6°.0 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 1.5 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 9.3 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 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 8.7 9.4 9.6 0.2 54 55 0.0 0.9 1.7 2.6 3.5 4.4 5.2 6.1 7.0 7.9 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 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 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 S.O 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 5.0 6.5 6.7 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 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 577 Amplitud es. Declination. Lati- tude. Lati- tude. 6°.0 6°. 6 ;°.o 7°. 5 8°,0 j 8°.o j 9°.0 , 9°, 5 10°.0 10°. 5 11°.0 11°. 5 12°.0 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 1 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 1 9.6 : 10.1 0.7 1.2 1.7 2. 3 2. 8 1 20 25 30 6.6 7.1 7.7 8.3 8.8 9.4 1 9.9 0.5 1.1 1.6 2.2 2.8 3.3 25 30 6.9 7.5 8.1 8.7 9.3 9.8 10.4 11.0 11.5 12.1 12.7 13.3 13.9 82 7.0 7.7 8.3 8.8 9.5 10.0 0.6 1.2 1.8 2.4 3.0 3.6 4.2 32 34 7.2 7.8 8.5 9.0 9.7 0. 3 0. 8 1.5 2.1 2.7 3.3 3.9 4.5 34 36 7.4 8.0 8.7 9.3 9.9 0.5 1 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. 3.8 4.5 5.2 5.9 6.7 7.4 46 48 50 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 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 i 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 6.3 i 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 i 3.1 58 59 60 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 24.6 59 60 12.1 13.1 14.1 15.1 16.2 17.2 i 18.2 19.3 20.3 21.4 22.4 23.5 61 2.5 3.5 4.6 5.6 6.7 7.8 i 8.8 9.9 1.0 2.1 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 1 3.9 5.2 6.3 62 63 3.4 4.4 5.6 6.7 7.9 9. 20. 1 1.3 2.5 3.7 4.8 6.1 i 7.2 63 64 3.9 14.4 5.0 6.2 7.3 8.5 9. 7 0. 9 2.1 3.3 4.6 5.7 7.1 28.2 8.3 64 65.0 15.5 16.8 18.0 19.3 20.5 21.7 23.0 24.2 25.6 1 26.8 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 67. 5 5.5 6.8 8.2 9.5 19.9 0.9 2.2 3.6 5.0 6.4 7.8 9.2 29.9 0.7 2.1 31.4 .32.9 7.0 15.9 17.2 18.6 21.3 22.7 24.1 25.5 27.0 28.4 67.5 8.0 6.2 7.6 9.0 20.4 1.8 3. 2 4. 7 6.1 7.6 9.1 30.6 2. 2 3. 7 8.0 8.5 6.6 8.0 9.4 0.9 2.3 3. 8 5. 3 6.8 8.3 9.8 1.4 3. 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. 6. 5 25. 6 ; 27. 2 8.1 28.8 9.7 1.4 3.0 4.7 6.4 9.5 70.0 70.0 17.8 19.3 20.9 22.4 24.0 .30.5 32.2 33.9 35.7 1 37.4 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. 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 1 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 1 2.4 4.4 6.5 8.6 40.8 3. 5. 3 3.0 3.5 1.6 3.5 5.4 7.4 9.3 1.4 1 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 1 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 1 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 '2US9—0S- -37 Page 578] TABLE 39. Amplitudes. Lati- tude. Declination. Lati- tude. 12°.0 1 12°. 6 18°.0 1S°.5 14°.0 14°. 5 15°.0 15°. 6 1«°.0 16°. 5 17°.0 17°, 5 18°.0 o o c o o o o o 1 o . o o o o o o 12.0 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0 16.5 17.0 17.5 18.0 10 2.2 2.7 3.2 3.7 4.2 4.7 5.3 5.8 6.3 6.8 7.3 7.9 8.3 10 15 2.5 2.9< ► 3.5 4.0 4.5 5.0 5.6 6.1 6.6 7.1 7. 7 8.2 8.7 15 20 2.8 3.3 3.8 4.4 4.9 5.5 6.0 6.5 7.1 7.6 8.1 8.7 9.2 20 25 3.3 3.8 4.4 4.9 5.5 6.1 6.6 7.1 7.7 8.3 8.8 9.4 9.9 25 80 13.9 14.5 15.0 15.6 16.2 16.8 17.4 18.0 18.6 19.2 19.7 20.3 20.9 30 32 4.2 4.8 5.3 6.0 6.6 7.2 7.8 8.4 9.0 9.6 20.2 0.8 1.4 32 34 4.5 5.1 5.7 6.4 7.0 7.6 8.2 8.8 9.5 20.0 0.7 1.3 1.9 34 36 4.9 5.5 6.1 6.8 7.4 8.0 8.7 9.3 20.0 0.5 1.2 1.8 2.5 36 38 5.3 6.0 6.6 7.2 7.9 8.5 9.2 9.8 0.5 1.1 1.8 2.4 3.1 38 40 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 41 6.0 6.7 7.3 8.0 8.7 9.4 20.0 0.8 1.4 2.1 2.8 3.5 4.2 41 42 6.2 6.9 7.6 8.3 9.0 9.7 0.4 1.1 1.8 2.5 3.2 3.9 4.6 42 43 6.5 7.2 7.9 8.6 9.3 20.0 0.7 1.4 2.2 2.9 3.6 4.3 5.0 43 44 45 6.8 17.1 7.5 8.2 18.5 8.9 9.6 0.4 20.7 1.1 1.8 2.6 3.3 4.0 4.7 25. 2 5.4 44 17.8 19.3 20.0 21.5 22.2 23.0 23.7 24.4 25.9 45 46 7.4 8.2 8.9 9.6 0.4 1.1 1.9 2.6 3.4 4.1 4.9 5.7 6.4 46 47 7.7 8.5 9.3 20.0 0.8 1.5 2.3 3.1 3.8 4.6 5.4 6.2 6.9 47 48 8.1 8.9 9.7 0.4 1.2 2.0 2.8 3.6 4.3 5.1 5.9 6.7 7.5 48 49 8.5 9.3 20.1 0.8 1.6 2.4 3.2 4.1 4.9 5.7 6.5 7.3 8.1 28.7 49 50 18.9 19.7 20.5 21.3 22.1 22.9 23.7 24.6 25.4 26.2 27.0 27.9 50 51 9.3 20.1 0.9 1.8 2.6 3.5 4.3 5.1 6.0 6.8 7.6 8.5 9.4 51 52 9.7 0.6 1.4 2.3 3.1 4.0 4.9 5.7 6.6 7.5 8.3 9.2 30.1 52 53 20.2 1.1 1.9 2.8 3.7 4.6 5.5 6.4 7.3 8.2 9.0 30.0 0.9 53 54 0.7 1.6 2.5 3.4 4.3 5.2 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 30.5 1.5 2.5 3.6 56 57 2.4 3.4 4.4 5.4 6.4 7.4 8.4 9.4 30.4 1.4 2.5 3.5 4.6 57 58 3.1 4.1 5.1 6.1 7.2 8.2 9.2 30.3 1.3 2.4 3.5 4.6 5.7 58 59 3.8 4.8 5.9 6.9 8.0 9.1 30.2 1.3 2.3 3.5 4.6 5.7 6.9 59 60 24.6 25.6 26.7 27,8 28.9 30.1 31.2 32.3 33.4 34.6 35.8 36.9 38.2 60 61 5.4 6.5 7.6 8.8 9.9 1.1 2.2 3.5 4.6 5.8 7.1 8.3 9.6 61 62 6.3 7.5 8.6 9.8 31.0 2.2 3.4 4.7 5.9 7.2 8.5 9.8 41.2 62 63 7.2 8.5 9.7 31.0 2.2 3.5 4.7 6.1 7.4 8.7 40.1 41.5 2.9 63 64 8.3 9.6 30.9 2.2 3.5 4.8 6.2 7.6 9.0 40.4 1.8 3.3 4.8 64 65.0 29.5 30.8 32.2 33.5 34.9 36.3 37.8 39.2 40.7 42.2 43.8 45.4 47.0 65.0 5.5 30.1 1.5 2.9 4.3 5.7 7.1 8.6 40.1 1.6 3.2 4.8 6.5 8.2 5.5 6.0 0.7 2.2 3.6 5.0 6.5 8.0 9.5 1.1 2.7 4.3 5.9 7.7 9.4 6.0 6.5 1.4 2.9 4.3 5.8 7.3 8.9 40.5 2.1 3.8 5.4 7.1 8.9 50.8 6.5 7.0 2.1 3.6 5.1 6.7 8.2 9.8 1.5 3.2 4.9 6.6 8.4 50.3 2.3 7.0 67.5 32.9 34.4 36.0 37.6 39.2 ,^.8 42.6 44.3 46.1 47.9 49.8 51.8 53.9 67.5 8.0 3.7 5.3 6.9 8.6 40.2 1.9 3.7 5.5 7.4 9.3 51.3 3.4 5.6 8.0 8.5 4.6 6.2 7.9 9.6 1.3 3.1 4.9 6.8 8.8 50.8 2.9 5.1 7.5 8.5 9.0 5.5 7.2 8.9 40.7 2.5 4.3 6.2 8.2 50.3 2.4 4.6 7.0 9.6 9.0 9.5 70.0 6.4 ! 8.2 40.0 1.8 43.0 3.7 5.6 7.6 9.7 1.9 4.2 6.5 9.1 61.9 9.5 37.4 39.3 41.1 45.0 47.0 49.2 51.4 53.7 56.1 58.7 61.5 64.6 70.0 0.5 8.5 40.4 2.4 4.4 6.4 8.6 50.8 3.2 5.7 8.3 61.1 4.3 7.8 0.5 1.0 9.7 1.7 3.7 5.8 8.0 50.3 2.6 5.2 7.9 60.7 3.9 7.5 71.7 1.0 1.5 40.9 3.0 5.1 7.4 9.7 2.1 4.6 7.4 60.3 3.5 7.1. 71.4 6.9 1.5 2.0 2.3 43. 7 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 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 5.3 7.7 50.3 3.0 5.9 8.9 62.2 6.1 70.6 6.3 90.0 3.0 3.5 7.0 9.6 2.3 5.3 8.4 61.8 5.6 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 ; 4.9 9.5 75.5 90.0 4.5 TABLE 39. [Page 579 | Amplitudes. Declination. Lati- tude. Lati- tude. 18°.0 18°. 5 19°.0 19°. 5 20°. 20°. 5 21°.0 21°. 6 22°.0 22°. 6 28°. 28°. 5 24°.0 o Q 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 30 9.9 20.9 20.5 21.5 1.1 22.1 1.6 2.2 2.7 1 3.3 3.9 4.4 5.0 5.5 6.1 6.7 25 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 5.0v 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 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 40 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 35.1 45 46 6.4 7.2 7.9 8.7 9.5 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 28.7 8.9 9.7 30.6 1.4 2.3 3.1 4.0 4.8 5.7 6.5 37.4 7.4 8.3 49 50 29.6 30.4 31.3 32.1 33.0 33.9 34.8 35.6 36.5 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 52 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 54 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 55 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 60.0 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 38.2 39.4 40.6 41.9 43.2 44.5 45.8 47.2 48.6 49.9 51.4 i 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 62.5 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 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 65.0 5.9 7.5 9.2 50.9 2.6 4.5 6.4 8.4 60.5 62.5 2.8 5.2 7.8 70.9 74.4 4.5 47.0 48.7 50.4 52.2 54.0 56.0 58.0 60.2 64.9 67.6 70.6 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 1.5 2.0 90.0 2.0 Page 580] TABLE 39. Amplitudes. Declination. Lati- tude. Lati- tude. 24°.0 24°. 5 25°.0 25°. 6 26°. 26°. 6 27°.0 27°.5 28°. 28°. 6 29°. 29°.5 80°. o 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 t.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 32.1 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 20 22 6.0 6.6 7.1 7. 7 8. 2 8.8 9.3 9.9 0.4 1.0 1.5 2.1 2.6 22 24 6.4 7.0 7.6 8.1 8.7 9.2 9.8 30.4 0.9 1.5 2.0 2.6 3.2 24 26 6.9 7.5 8.1 8.6 9.2 9.7 30.3 0.9 1.5 2.1 2.6 3.2 3.8 26 28 7.4 8.0 8.6 9.2 9.8 30.3 0.9 1.5 2.1 2.7 3.3 3.9 4.5 28 30 28.0 28.6 29.2 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 35 9.4 29.8 30.0 0.6 31.3 1.9 32.3 2.6 33.0 3.2 3.8 4.5 5.1 5.8 6.4 7.1 34 30.4 31.1 31.7 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 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 41 2.6 3.3 4.1 4.8 5.5 6.2 7.0 7.7 8.5 9.2 40.0 0.7 1.5 41 42 3.2 3.9 4.7 5.4 6.1 6.9 7.7 8.4 9.2 9.9 0.7 1.5 2.3 42 43 3.8 4.5 5.3 6.1 6.8 7.6 8.4 9.2 9.9 40.7 1.5 2.3 3.1 43 44 4.4 5.2 6.0 6.8 7.5 8.3 9.1 40.0 40.7 1.6 2.4 3.2 4.0 44 45 35.1 35.9 36.7 37.5 38.3 39.1 39.9 40.8 41.6 42.5 43.3 44.1 45.0 45 46 5.8 6.6 7.5 8.3 9.1 40.0 40.8 1.7 2.5 3.4 4.3 5.1 6.0 46 47 6.6 7.4 8.3 9.1 40.0 0.9 1.7 2.6 3.5 4.4 5.3 6.2 7.1 47 48 7.4 8.3 9.2 40.0 0.9 1.8 2.7 3.6 4.6 5.5 6.4 7.4 8.3 48 49 50 8.3 39.2 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 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.v5 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 I 5.9 80.1 9.5 60.0 54.4 56.0 57.7 59.4 61.2 63.2 65.2 67.4 69.9 72.6 75.8 80.0 90.0 60.0 0.5 5.7 7.4 9.1 61.0 2.9 5.0 7.2 9.6 72.4 5.8 9.9 90.0 0.5 1.0 7.0 8.8 60.7 2.6 4.7 7.0 9.5 72.3 5.5 9.8 90.0 1.0 1.5 8.5 60.3 2.3 4.4 6.7 9.2 72.0 5.4 9.7 90.0 1.5 2.0 60.0 61.7 2.0 4.2 6.5 9.0 71,9 5.2 9.6 90.0 2.0 62.5 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 581 Correction of the Amplitude as observed on the Apparent Horizon. Declination. . Lati- tude. Lati- tude. 0° 5° 10° 12° 14° 16° 18° 20° 22° 24° 26° 28° 30° 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 24 .2 .2 2 .2 .2 .2 .3 .3 .3 .3 .3 .3 .3 0.4 20 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.4 24 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 . 32 36 .5 .5 .5 .5 .5 .5 .5 .5 .6 .6 .6 .6 .6 36 38 40 .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 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 50 .7 0.8 .8 .8 .8 .8 .8 .8 .9 .9 1.0 1.0 1.0 .1 48 50 0.8 0.8 0.8 0.9 0.9 0.9 0.9 1.0 1.1 1.1 1.1 1.3 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 58 .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 Page 582] TABLE 41. Natural Sines and Cosines. Prop. 0° 1 3 2° 8° 4 o Prop. parts 29 parts 8 M. N. sine. N.cos. N. sine. N. COS. N. sine. N. COS. N. sine. N. COS. 99863 N. sine N.,cos. 00000 100000 01745 99985 03490 99939 05234 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 1(^)000 01832 99983 03577 99936 05321 99858 07063 99750 57 2 2 4 00116 lOOOiX) 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 036tM 99933 05408 99854 071.50 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 997.38 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 13 00349 00378 99999 99999 02094 02123 99978 99977 03839 99926 05582 05611 99844 99842 07324 07353 99731 99729 48 2 6 03868 99925 47 2 7 14 00407 99999 02152 99977 03897 99924 05640 99841 07.382 99727 46 2 7 15 00436 99999 02181 99976 03926 99923 05669 998.39 07411 99725 45 2 8 16 00465 99999 02211 99976 0.3955 99922 05698 99838 07440 99723 44 8 17 00495 99999 02240 99975 03984 99921 05727 99836 07469 99721 43 9 18 19 00524 00553 99999 02269 02298 99974 99974 04013 04042 99919 057.36 05785 99834 99833 07498 99719 42 41 1 , 9 99998 99918 07527 99716 10 20 00582 99998 02327 99973 04071 99917 0.5814 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 0,5873 99827 07614 99710 38 11 23 00669 99998 02414 99971 04159 99913 05902 99826 07643 99708 37 12 24 00698 99998 99997 02443 99970 99969 04188 04217 99912 99911 05931 05960 99824 99822 07672 07701 99705 99703 36 35 12 25 00727 02472 13 26 00756 99997 02501 99969 04246 99910 05989 99821 07730 99701 34 13 27 00785 99997 02530 99968 04275 ' 99909 06018 99819 07759 99699 33 14 28 00814 99997 02560 99967 04304 I 99907 06047 99817 07788 99696 32 14 29 00844 99996 02589 99966 04333 1 99906 06076 99815 07817 99694 31 15 15 30 31 00873 99996 02618 99966 04362 j 99905 06105 06134 99813 99812 07846 99692 30 29 00902 99996 02647 99965 04391 99904 07875 99689 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 04565 99897 99896 06279 99803 99801 08020 99678 24 18 37 01076 99994 02821 99960 06308 08049 99676 23 18 38 01105 99994 02850 99959 04594 j 99894 06337 99799 08078 99673 22 19 39 01134 99994 02879 99959 04623 1 99893 06366 99797 08107 99671 21 1 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 06482' 99792 99790 08194 08223 99664 18 21 43 01251 99992 02996 04740 99888 99661 17 21 44 01280 99992 03025 99954 04769 99886 06511 99788 08252 99659 16 1 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 06656 99780 99778 08368 99649 99647 12 U 24 49 01425 99990 03170 99950 04914 99879 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 050.30 99873 06773 99770 08513 99637 7 26 27 54 55 01571 01600 99988 99987 03316 99945 99944 050-59 05088 99872 99870 06802 99768 99766 08542 08571 99635 99632 6 5 03345 06831 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 N. sine. 06976 99756 N. sine. 08716 99619 N. COS. N. sine. N. COS. N. sine. N. COS. N. COS. N. COS. N. sine. M. 89° 88° 87° 86° 8 j° TABLE 41. [Page 583 Natural Sines and Cosines. Prop. parts 29 5 o 6° 7 o 8 o 9° Prop, parts 4 M. N. sine. N. COS. N. sine. N. COS. N.sine. N.cos. N. sine. N. COS. N. .sine. N. cos. 08716 99619 10453 99452 12187 99255 13917 99027 15643 98769 60 4 1 08745 99617 10482 99449 12216 99251 13946 99023 15672 1 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 7 08889 08918 99604 99602 10626 99434 12360 12389 99233 99230 14090 99002 15816 15845 98741 54 53 4 4 3 10655 99431 14119 98998 98737 4 8 08947 99599 10684 99428 12418 99226 14148 98994 15873 98732 52 3 4 9 08976 99596 10713 99424 12447 99222 14177 98990 15902 98728 51 3 5 10 09005 99594 10742 99421 12476 99219 14205 98986 15931 98723 50 3 5 11 09034 99591 10771 99418 12504 99215 14234 98982 15959 98718 49 3 6 12 09063 99588 10800 10829 99415 99412 12533 99211 14263 14292 98978 15988 98714 98709 48 47 3 3 6 13 09092 99586 12562 99208 98973 16017 7 14 09121 99583 10858 99409 12591 99204 14320 98969 16046 98704 46 3 7 1 15 09150 99580 10887 99406 12620 99200 14349 98965 16074 98700 45 3 8 1 16 09179 99578 10916 99402 12649 99197 14378 98961 16103 98695 44 3 8 1 17 09208 99575 10945 99399 12678 99193 14407 98957 16132 98690 43 3 9 18 9 19 09237 99572 99570 10973 11002 99396 99393 12706 99189 14436 14464 98953 16160 16189 98686 42 41 3 3 09266 12735 99186 98948 98681 10 i 20 09295 99567 11031 99390 12764 99182 14493 98944 16218 98676 40 3 10 ' 21 09324 99564 11060 99386 12793 99178 14522 98940 16246 98671 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 24 09411 99556 11147 99377 12880 99167 14608 98927 16333 98657 36 35 2 2 12 25 09440 99553 11176 99374 12908 99163 14637 98923 16361 98652 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 1 98ft43 33 9 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 1 98633 31 2 15 30 15 31 09585 99540 11320 99357 13053 99144 14781 14810 98902 98897 16505 98629 30 29 2 09614 99537 11349 99354 13081 99141 16533 98624 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 i 34 09700 99528 11436 99344 13168 99129 14896 98884 16620 98609 26 2 17 35 09729 99526 11465 99341 13197 99125 14925 98880 16648 98604 25 2 17 36 18 ! 37 09758 09787 99523 11494 99337 99334 13226 99122 14954 14982 98876 98871 16677 16706 98600 24 2 99520 11523 13254 99118 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 42 43 09932 99506 11667 99317 13399 13427 99098 15126 98849 98845 16849 98570 18 17 21 09961 99503 11696 99314 99094 15155 16878 j 98565 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 i 47 10077 99491 11812 99300 13543 99079 15270 98827 16992 ! 98546 13 J 23 i 48 24 49 10106 99488 11840 99297 99293 13572 13600 99075 15299 98823 17021 17050 98541 12 10135 99485 11869 99071 15327 98818 98536 11 24 50 10164 99482 11898 99290 13629 99067 15356 98814 17078 ! 98531 10 25 j 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 27 55 10279 99470 12014 99276 13744 13773 99051 15471 98796 17193 98511 6 5 10308 99467 12043 99272 99047 15500 98791 17222 98506 27 i 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. sine. N. COS. i N. sine. M. 1 8 JO 88 o 8 2° 8 1° 80° Page 584] TABLE 41. Natural Sines and Cosines. Prop. 10° 1 11 o 12° 1 18° 1 14° 1 Prop. parts 28 1 1 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 98476 19109 98157 20820 97809 22523 97430 24220 97023 59 6 1 2 17422 98471 19138 98152 20848 97803 22552 97424 24249 97015 58 6 1 3 17451 98466 19167 98146 20877 97797 22580 97417 24277 97008 57 6 2 4 17479 •98461 19195 98140 20905 97791 22608 97411 24305 97001 56 6 2 5 17508 98455 19224 98135 20933 97784 22637 97404 24333 96994 55 6 3 6 17537 98450 19252 98129 20962 97778 97772 22665 22693 97398 97391 24362 24390 96987 '96980' 54 5 3 7 17565 98445 19281 98124 20990 53 5 4 8 17594 98440 19309 98118 21019 97766 22722 97384 24418 96973 52 5 4 9 17623 98435 19338 98112 21047 97760 22750 97378 24446 96966 51 5 5 10 17651 98430 19366 98107 21076 97754 22778 97371 24474 96959 50 5 5 11 17680 98425 19395 98101 21104 97748 22807 97365 24503 96952 49 5 6 12 13 17708 98420 19423 98096 98090 21132 21161 97742 22835 97358 97351 24531 96945 48 47 5 6 17737 98414 19452 97735 22863 24559 96937 5 7 14 17766 98409 19481 98084 21189 97729 22892 97345 24587 96930 46 5 7 15 17794 98404 19509 98079 21218 97723 22920 97338 24615 96923 45 5 7 16 17823 98399 19538 98073 21246 97717 22948 97331 24644 96916 44 4 8 17 17852 98394 19566 98067 21275 97711 22977 97325 24672 96909 43 4 8 18 1 17880 98389 19595 98061 98056 21303 97705 23005 97318 24700 24728 96902 96894 42 41 4 9 19 17909 98383 19623 21331 97698 23033 97311 4 9 20 17937 98378 19652 98050 21360 97692 23062 97304 24756 96887 40 4 10 21 17966 98373 19680 98044 21388 1 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 j 97673 23146 97284 24841 96866 37 4 11 12 24 25 18052 98357 19766 19794' 98027 98021 21474 97667 97661 23175 97278 24869 24897 96858 96851 36 35 4 18081 98352 21502 23203. 97271 4 12 26 18109 98347 19823 98016 21530 j 97655 23231 97264 24925 96844 34 3 13 27 18138 98341 19851 98010 21559 97648 23260 97257 24954 96837 33 3 13 28 18166 98336 19880 98004 21587 1 97642 23288 97251 24982 96829 32 3 14 29 18195 98331 19908 97998 21616 1 97636 23316 97244 25010 96822 31 3 14 14 30 31 18224 98325 19937 19965 97992 97987 21644 97630 97623 23345 23373 97237 97230 25038 25066 96815 96807 30 29 3 18252 98320 21672 3 15 32 18281 98315 19994 97981 21701 1 97617 23401 97223 25094 96800 28 3 15 33 18309 98310 20022 97975 21729 1 97611 2.3429 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 25179 1 96778 25 3 17 17 36 37 18395 18424 98294 20108 97958 97952 21814 i 97592 21843 ; 97585 23514 23542 97196 97189 25207 96771 25235 1 96764 24 23 2 2 , 98288 20136 18 38 18452 1 98283 20165 97946 21871 97579 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 2.3627 97169 25320 96742 20 2 19 41 18538 98267 20250 97928 21956 97560 23656 97162 25:348 96734 19 2 20 20 42 43 18567 18595 98261 20279 97922 97916 21985 \ 97553 23684 97155 97148' 25376 96727 25404 96719 18 17 2 98256 20307 1 22013 97547 23712 2 21 44 18624 [ 98250 20336 97910 22041 97541 23740 97141 25432 i 96712 16 2 21 45 18652 ; 98245 20364 97905 22070 97534 23769 97134 25460 96705 15 2 21 46 18681 98240 20393 97899 22098 97528 23797 97127 25488 96697 14 22 47 18710 98234 20421 97893 22126 97521 23825 97120 25516 96690 13 22 23 48 49 18738 18767 98229 98223 20450 20478 97887 ,'97881 22155 97515 97508 23853 23882 97113 97106 25545 96682 25573 : 96675 12 11 22183 23 50 18795 98218 20507 97875 22212 97502 23910 97100 25601 96667 10 24 51 18824 98212 20535 t 97869 22240 97496 23938 97093 25629 96660 9 24 52 18852 98207 20563 : 97863 22268 97489 23966 , 97086 25657 96653 8 25 53 18881 98201 20592 ! 97857 22297 i 97483 23995 ' 97079 25685 96645 / 25 26 54 55 18910 98196 20620 20649 i 97851 97845 22325 22353 97476 97470 24023 24051 1 97072 97065 25713 96638 6 5 18938 98190 25741 96630 26 56 18967 98185 20677 97839 22382 97463 24079 97058 25769 1 96623 4 27 57 18995 , 98179 20706 97833 22410 i 97457 24108 97051 25798 I 96615 3 1 27 58 19024 j 98174 20734 97827 22438 97450 24136 97044 25826 96608 2 28 59 19052 1 98168 20763 97821 22467 I 97444 24164 i 97037 25854 i 96600 1 28 60 19081 98163 20791 97815 22495 ! 97437 24192 ; 97030 25882 96593 N. CO.". 1 N. sine. N. COS. j N.sine. N. COS. j N. sine. N. cos. N. sine. N. COS. N. sine. M. 7«° 7 s° 77° 7 fl° 75° TABLE 41. [Page 585 Natural Sines and Cosines. Prop. parts 27 1 5° 16 o 1' o 18° 19° Prop. parts 9 M. N. sine. N. COS. N. sine. N. CCS. N.siiie. N.co.s. N. sine. N.cos. N. sine. N. COS. 25882 96593 27564 96126 29237 95630 30902 95106 32557 94552 60 9 1 25910 96585 27592 96118 29265 95622 30929 95097 32584 94542 59 9 1 2 25938 96578 27620 96110 29293 95613 30957 95088 32612 94533 58 9 1 3 25966 96570 27648 96102 29321 95605 30985 95079 32639 94523 57 9 2 4 25994 96562 27676 96094 29348 95596 31012 95070 32667 94514 56 8 2 5 26022 96555 27704 96086 29376 95588 31040 95061 32694 i 94504 55 8 3 6 26050 96547 96540 27731 96078 96070 29404 95579 95571 31068 31095 95052 95043" 32722 94495 94485 54 53 8 8 3 7 26079 27759 29432 32749 4 8 26107 96532 27787 96062 29460 95562 31123 95033 32777 94476 52 8 4 9 26135 96524 27815 96054 29487 95554 31151 95024 32804 94466 51 8 5 10 26163 96517 27843 96046 29515 95545 31178 95015 32832 94457 50 8 5 11 26191 96509 27871 96037 29543 95536 31206 95006 32859 94447 49 7 5 12 26219 96502 96494 27899 27927 96029 29571 95528 31233 31261 94997 32887 32914 94438 94428 48 47 7 7 6 13 26247 96021 29599 95519 94988 6 14 26275 96486 27955 96013 29626 95511 31289 94979 32942 94418 46 7 ' 7 15 26303 96479 27983 96005 29654 95502 31316 94970 32969 94409 45 7 7 16 26331 96471 28011 95997 29682 95493 31344 94961 32997 94399 44 7 8 17 26359 96463 28039 95989 29710 95485 31372 94952 33024 i 94390 43 6 8 18 19 26387 96456 28067 95981 29737 95476 31399 31427 94943 94933 33051 33079" 94380 42 6 6 9 26415 96448 28095 95972 29765 95467 94370 41 9 20 26443 96440 28123 95964 29793 95459 31454 94924 33106 ( 94361 40 6 9 21 26471 96433 28150 95956 29821 95450 31482 94915 33134 ' 94351 39 6 10 22 26500 96425 28178 95948 29849 95441 31510 94906 33161 94342 38 6 10 23 26528 96417 28206 95940 29876 95433 31537 94897 33189 94332 37 6 11 24 26556 96410 28234 28262 95931 95923 29904 29932 95424 95415 31565 94888 94878 33216 94322 36 35 5 5 11 25 26584 96402 31593 33244 94313 12 26 26612 96394 28290 95915 29960 95407 31620 94869 33271 94303 34 5 12 27 26640 96386 28318 95907 29987 95398 31648 94860 33298 ; 94293 33 5 13 28 26668 96379 28346 95898 30015 95389 31675 94851 33326 , 94284 32 5 13 29 26696 96371 28374 95890 30043 95380 31703 94842 33353 94274 31 5 14 14 30 31 26724 96363 28402 95882 30071 95372 95363 31730 31758 94832 94823 33381 94264 33408 94254 30 29 5 26752 96355 28429 95874 30098 4 14 32 26780 96347 28457 95865 30126 95354 31786 94814 33436 ; 94245 28 4 15 33 26808 96340 28485 95857 30154 95345 31813 94805 33463 ; 94235 27 4 15 34 26836 96332 28513 95849 30182 95337 31841 94795 33490 i 94225 26 4 16 35 26864 96324 28541 95841 30209 95328 31868 94786 33518 , 94215 25 4 16 17 36 37 26892 96316 28569 28597 95832 95824 30237 30265 95319 95310 31896 31923 94777 33545 ; 94206 33573 1 94196 24 23" 4 26920 96308 94768 3 17 38 26948 96301 28625 95816 30292 95301 31951 94758 33600 , 94186 22 3 18 39 26976 96293 28652 95807 30320 95293 31979 94749 33627 94176 21 3 18 40 27004 96285 28680 95799 30348 95284 32006 94740 33655 94167 20 3 18 41 27032 96277 28708 95791 30376 95275 32034 94730 33682 94157 19 3 19 19 42 43 27060 96269 96261 28736 28764 95782 95774 30403 95266 95257 32061 94721 94712 33710 33737 94147 18 3 3 27088 30431 32089 94137 17 20 44 27116 96253 28792 95766 30459 95248 32116 94702 33764 ! 94127 16 2 20 45 27144 96246 28820 95757 30486 95240 32144 94693 33792 94118 15 2 21 46 27172 96238 28847 95749 30514 95231 32171 94684 33819 94108 14 2 21 47 27200 96230 28875 95740 30542 95222 32199 94674 33846 94098 13 2 22 48 27228 96222 28903 95732 95724 30570 95213 95204 32227 32254 94665 94656 33874 94088 12 2 22 49 27256 96214 28931 30597 33901 94078 11 2 23 50 27284 96206 28959 95715 30625 95195 32282 94646 33929 94068 10 23 51 27312 96198 28987 95707 30653 95186 32309 94637 33956 94058 9 23 52 27340 96190 29015 95698 30680 95177 32337 94627 33983 94049 8 24 53 27368 96182 29042 95690 30708 95168 32364 94618 34011 94039 7 24 25 54 55 27396 96174 96166 29070 29098 95681 95673 30736 95159 95150 32392 32419 94609 '94599 34038 94029 6 27424 30763 34065 94019 5 25 56 27452 96158 29126 95664 30791 95142 32447 94590 34093 94009 4 26 57 27480 96150 29154 95656 30819 95133 32474 94580 34120 93999 3 26 58 27508 96142 29182 95647 30846 95124 32502 94571 34147 93989 2 27 59 27536 96134 29209 95639 30874 95115 32529 94561 34175 93979 1 27 60 27564 96126 29237 95630 30902 95106 32557 94552 34202 93969 N. COS. N. sine. N. COS. N. sine. N. COS. N. sine. X. COS. N. sine. N. COS. N. sine. M. 7 t° 7S t° 7 i° 71° 70° Page 586] TABLE 41. Natural Sines and Cosines. Prop. parts 87 M. 20' 21° 1 22° 28° 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 3 4 4 5 5 5 1 2 3 4 5 6 7 8 9 10 11 12 34202 34229 34257 34284 34311 34339 34366 34393 34421 34448 34475 34503 34530 93969 93959 93949 98939 93929 93919 93909 93899 93889 93879 93869 93859 93849 35837 35864 358^1 35918 35945 35973 36000 36027 36054 36081 36108 36135 36162 93358 93348 93337 93327 93316 93306 93295 37461 37488 37515 37542 37569 37595 37622 92718 92707 92697 92686 92675 926(>4 92653 92642 92631 92620 92609 92598 92587 39073 39100 39127 39153 39180 39207 39234 92050 92039 92028 92016 92005 91994 91982 40674 40700 40727 40753 40780 40806 40833 91355 9i:i43 91331 91319 91307 91295 91283 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 11 11 11 10 10 10 10 10 10 9 9 9 9 9 8 8 8 8 8 93285 93274 93264 93253 93243 93232 37649 37676 37703 37730 37757 37784 39260 39287 39314 39341 39367 39394 91971 91959 91948 91936 91925 91914 40860 40886 40913 40939 40966 40992 91272 91260 91248 91236 91224 91212 91200 91188 91176 91164 91152 91140 6 6 7 7 8 8 9 9 9 10 10 11 11 12 12 13 13 14 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 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55^ 56 57 58 59 60 34557 34584 34612 34639 34666 34694 93839 93829 93819 93809 93799 93789 36190 36217 36244 36271 36298 36325 36352 36379 36406 36434 36461 36488 93222 93211 93201 93190 93180 93169 93159 93148 93137 93127 93116 93106 37811 37838 37865 37892 37919 37946 37973 37999 38026 38053 38080 38107 38134 38161 38188 38215 38241 38268 38295 38322 38349 38376 38403 38430 38456 38483 38510 38537 38564 38591 38617 38644 38671 38698 38725 38752 92576 92565 92554 92543 92532 92521 92510 92499 92488 92477 92466 92455 92444 92432 92421 92410 92399 92388 92377 92366 92355 92343 92332 92321 92310 92299 92287 92276 92265 92254 92243 92231 92220 92209 92198 92186 39421 39448 39474 39501 39528 39555 39581 39608 39635 39661 39688 39715 91902 91891 91879 91868 91856 91845 91833 91822 91810 91799 91787 91775 91764 91752 91741 91729 91718 91706 91694 91683 91671 91660 91648 91636 41019 41045 41072 41098 41125 41151 34721 34748 34775 34803 34830 34857 93779 93769 93759 93748 93738 93728 41178 41204 41231 41257 41284 41310 91128 91116 91104 91092 91080 91068 41 i 8 40 ! 7 39 ' 7 38 7 37 7 36 7 34884 34912 34939 34966 34993 35021 93718 93708 93698 93688 93677 93667 36515 36542 36569 36596 36623 36650 93095 93084 93074 93063 93052 93042 93031 93020 93010 92999 92988 92978 39741 39768 39795 39822 39848 39875 39902 39928 39955 39982 40008 40035 41337 41363 41390 41416 41443 41469 91056 91044 91032 91020 91008 90996 35 34 33 32 31 30 6 6 6 6 6 6 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 35048 35075 35102 35130 35157 35184 93657 93647 93637 93626 93616 93606 36677 36704 36731 36758 36785 36812 41496 41522 41549 41575 41602 41628 90984 90972 90960 90948 90936 90924 29 28 27 26 25 24 5 5 5 5 5 4 35211 35239 35266 35293 35320 35347 93596 93585 93575 93565 93555 93544 36839 36867 36894 36921 36948 36975 92967 92956 92945 92935 92924 92913 92902' 92892 92881 92870 92859 92849 92838 92827 92816 92805 92794 92784 40062 40088 40115 40141 40168 40195 40221 40248 40275 40301 40328 40355 40381 40408 40434 40461 40488 40514 40541' 40567 40594 40621 40647 40674 91625 91613 91601 91590 91578 91566 41655 41681 41707 41734 41760 41787 90911 90899 90887 90875 90863 90851 90839 90826 90814 90802 90790 90778 90766 90753 90741 90729 90717 90704 23 22 21 20 19 18 4 4 4 4 3 3 35375 35402 35429 35456 35484 35511 93534 93524 93514 93503 93493 93483 37002 37029 37056 37083 37110 37137 91555 91543 91531 91519 91508 91496 91484 91472 91461 91449 91437 91425 41813 41840 41866 41892 41919 41945 41972 41998 42024 42051 42077 42104 17 16 15 14 13 12 3 3 3 3 2 2 35538 35565 35592 35619 35647 35674 93472 93462 93452 93441 93431 93420 37164 37191 37218 37245 37272 37299 38778 38805 38832 38859 38886 38912 92175 92164 92152 92141 92130 92119 11 10 9 8 7 6 2 2 2 35701 35728 35755 35782 35810 35837 93410 93400 93389 93379 93368 93358 37326 37353 37380 37407 37434 37461 92773 92762 92751 92740 92729 92718 38939 38966 38993 39020 39046 39073 92107 92096 92085 92073 92062 92050 91414 91402 91390 91378 91366 91355 421.30 42156 42183 42209 42235 42262 90692 90680 90668 90655 90643 90631 5 4 3 2 1 — N. coe. N. sine. N. cos. N. sine. N. COS. N. sine. N. COS. N. sine. N. COS. N. sine. M. 09° 68° 67° 66° 65° ! 1 TABLE 41. [Page 587 Natural Sines and Cosines. Prop. ' s •5° 26° 27° 28° 29° Prop. parts 14 26 M. N. sine. N. COS. N. sine. N. COS. X. sine. j. N. cos. N. sine. N. COS. N. sine. N. COS. 42262 90631 43837 89879 45399 89101 46947 88295 48481 87462 60 14 1 42288 90618 43863 89867 45425 1 89087 46973 88281 48506 87448 59 14 1 2 42315 90606 43889 89854 45451 i 89074 46999 88267 48532 87434 58 14 1 3 42341 90594 43916 89841 45477 ' 89061 47024 88254 48557 87420 57 13 2 1 4 42367 90582 43942 89828 45503 89048 47050 88240 48583 87406 56 13 2 i 5 42394 90569 43968 89816 45529 89035 47076 88226 48608 87391 55 13 3 j 6 3 ; 7 42420 90557 90545 43994 89803 45554 ! 89021 47101 88213 88199 48634 48659 87377 54 13 42446 44020 89790 45580 89008 47127 87363 53 12 3 i 8 42473 90532 44046 89777 45606 88995 47153 88185 48684 87349 52 12 4 9 42499 90520 44072 89764 45632 88981 47178 88172 48710 87335 51 12 4 10 42525 90507 44098 89752 45658 88968 47204 88158 48735 87321 50 12 5 1 n 42552 90495 44124 89739 45684 88955 47229 88144 48761 87306 49 11 5 12 42578 90483 44151 89726 45710 88942 47255 47281 88130 48786 87292 87278 48 11 6 1 13 42604 90470 44177 89713 45736 ( 88928 88117 48811 47 11 6 14 42631 90458 44203 89700 45762 88915 47306 88103 48837 87264 46 11 7 1 15 42657 90446 44229 89687 45787 88902 47332 88089 48862 87250 45 11 7 ' 16 42683 90433 44255 89674 45813 88888 47358 88075 48888 87235 44 10 7 ! 17 42709 90421 44281 89662 45839 88875 47383 88062 48913 87221 43 10 8 I 18 8 19 42736 90408 44307 89649 45865 1 88862 47409 88048 88034 48938 48964 87207 42 41 10 42762 90396 44333 89636 45891 i 88848 47434 87193 10 9 20 42788 90383 44359 89623 45917 ; 88835 47460 88020 48989 87178 40 9 9 j 21 42815 90371 44385 89610 45942 88822 47486 88006 49014 87164 39 9 10 22 42841 90358 44411 89597 45968 ' 88808 47511 87993 49040 87150 38 9 10 i 23 42867 90346 44437 89584 45994 88795 47537 87979 49065 87136 37 9 10 24 25 42894 90334 90321. 44464 89571 89558 46020 i 88782 46046 88768 47562 47588 87965 87951 49090 49116 87121 87107 36 8 35 ; 8 n 42920 44490 11 26 42946 90309 44516 89545 46072 88755 47614 87937 49141 87093 34 1 8 12 27 42972 90296 44542 89532 46097 88741 47639 87923 49166 87079 33 1 8 12 i 28 42999 90284 44568 89519 46123 88728 47665 87909 49192 87064 32 7 13 • 29 43025 90271 44594 89506 46149 88715 47690 87896 49217 87050 31 7 13 ! 30 43051 90259 44620 89493 46175 88701 47716 47741 87882 49242 87036 87021 30 7 29 7 13 1 31 43077 90246 44646 89480 46201 j 88688 87868 49268 14 ! 32 43104 90233 44672 89467 46226 ' 88674 47767 87854 49293 87007 28 ' 7 14 ! 33 43130 90221 44698 89454 46252 i 88661 47793 87840 49318 86993 27 1 6 15 ; 34 43156 90208 44724 89441 46278 ! 88647 47818 87826 49344 86978 26 6 15 35 43182 90196 44750 89428 46304 88634 47844 87812 49369 86964 25 6 16 36 43209 43235 90183 90171 44776 89415 89402 46330 88620 47869 87798 49394 49419 86949 24 23 6 16 37 44802 46355 i 88607 47895 87784= 86935 5 16 38 43261 90158 44828 89389 46381 88593 47920 87770' 49445 86921 22 5 17 39 43287 90146 44854 89376 46407 88580 47946 87756 49470 86906 21 5 17 40 43313 90133 44880 89363 46433 ; 88566 47971 87743 49495 86892 20 5 18 41 43340 90120 44906 89350 46458 1 88553 47997 87729 49521 86878 19 4 18 42 43366 43392 90108 44932 89337 89324 46484 46510 88539 48022 87715 87701 49546 49571 86863 18 . 4 17 4 19 43 90095 44958 88526 48048 86849 19 44 43418 90082 44984 89311 46536 88512 48073 87687 49596 86834 16 4 20 45 4:W45 90070 45010 89298 46561 88499 48099 87673 49622 86820 15 4 20 i 46 43471 90057 45036 89285 46587 ; 88485 48124 87659 49647 86805 14 3 20 ' 47 43497 90045 45062 89272 46613 88472 48150 87645 49672 86791 13 3 21 ' 48 21 49 43523 90032 45088 45114 89259 46639 i 88458 48175 87631 49697 49723 86777 12 3 43549 90019 89245 46664 88445 48201 87617 86762 11 3 22 50 43575 90007 45140 89232 46690 88431 48226 87603 49748 86748 10 2 22 51 43602 89994 45166 89219 46716 88417 48252 87589 49773 86733 -9 2 23 ; 52 43628 89981 45192 89206 46742 88404 48277 87575 49798 86719 8 2 23 53 43654 89968 45218 89193 46767 88390 48303 87561 49824 86704 7 2 23 1 54 24 i 55 43680 43706 89956 89943 45243 89180 46793 88377 88363 48328 48354 87546 87532 49849 49874 86690 86675 6 1 5 1 45269 89167 46819 24 56 43733 89930 45295 89153 46844 i 88349 48379 87518 49899 86661 4 1 25 57 43759 89918 45321 89140 46870 88336 48405 87504 49924 86646 3 j 1 25 58 43785 89905 45347 89127 46896 88322 48430 87490 49950 86632 2 26 59 43811 89892 45373 89114 46921 88308 48456 87476 49975 86617 1 ! 26 60 43837 89879 45399 89101 46947 88295 48481 87462 50000 86603 N. COS. N. sine. N. COS. N. sine. N. cos. N. sine. N. cos. N. sine. N. COS. N. sine. M. 64 1° 6 i° 62° 61° 60° Page 588] TABLE 41. Natural Sines and Cosines. Prop. 80° ■ 1 81° 1 82° 1 88° 1 3^ [° ! Prop. parts. 25 1 parts. 16 M. N. sine. N. COS. N. sine. N. COS. N.*ine. N. COS. N. sine. N. COS. N. sine. N. COS. 50000 86603 51504 85717 52992 84805 54464 83867 55919 82904 60 16 1 50025 86588 51529 85702 53017 ! 84789 | 54488 83851 55943 82887 59 16 1 2 50050 86573 51554 85687 53041 84774 54513 83835 55968 82871 58 15 1 3 50076 iS559 51579 85672 53066 84759 54537 83819 55992 82855 57 15 2 4 50101 86544 51604 85657 53091 84743 54561 83804 56016 82839 66 15 2 5 50126 86530 51628 85642 53115 84728 54586 83788 56040 82822 55 15 3 6 50151 86515 51653 85627 85612 53140 84712 54610 83772 83756 56064 82806 82790 54 53 14 14 3 7 50176 86501 51678 53164 84697 54635 56088 3 8 50201 86486 51703 85597 53189 84681 54659 83740 56112 82773 52 14 4 9 50227 86471 51728 85582 53214 84666 54683 83724 56136 82757 51 14 4 10 50252 86457 51753 85567 53238 84650 54708 83708 56160 82741 50 13 5 11 50277 86442 51778 85551 53263 84635 54732 83692 56184 82724 49 13 5 5 12 13 50302 50327 86427 51803 85536 85521 53288 53312 84619 84604 54756 '54781 83676 56208 82708 48 13 86413 51828 83660 56232 82692 47 13 6 14 50352 86398 51852 85506 53337 84588 54805 83645 56256 82675 46 12 6 15 50377 86384 51877 85491 53361 84573 54829 83629 56280 82659 45 12 7 16 50403 86369 51902 85476 53386 84557 54854 83613 56305 82643 44 12 7 17 50428 86354 51927 85461 53411 84542 54878 8.3597 56329 82626 43 11 8 8 18 19 50453 50478 86340 86325 51952 51977 85446 85431 53435 84526 84511 54902 83581 56353 82610 82593 42 11 53460 54927 83565 56377 41 11 8 20 50503 86310 52002 85416 53484 84495 54951 83549 56401 82577 40 11 9 21 50528 86295 52026 85401 53509 84480 54975 83533 56425 82561 39 10 9 22 50553 86281 52051 85385 53534 84464 54999 83517 56449 82544 38 10 10 23 50578 86266 52076 85370 53558 84448 55024 83501 56473 82528 37 10 10 24 50603 86251 52101 85355 53583 84433 84417 55048 83485 56497 56521 82511 36 35 10 9 10 25 50628 86237 52126 85340 53607 55072 ■ 83469 82495 11 26 50654 86222 52151 85325 53632 84402 55097 83453 56545 82478 34 9 11 27 50679 86207 52175 85310 53656 84386 55121 83437 56569 82462 33 9 12 28 50704 86192 52200 85294 53681 84370 55145 83421 56593 82446 32 9 12 29 50729 86178 52225 85279 53705 ! 84355 55169 i 8.3405 56617 82429 31 8 13 30 50754 86163 52250 85264 53730 84339 55194 ! 83389 56641 82413 30 29 8 8 13 31 50779 . 86148 52275 85249 53754 84324 55218 83373 56665 82396 13 32 50804 86133 52299 85234 53779 84308 55242 83356 56689 82380 28 7 14 33 50829 86119 52324 85218 53804 84292 55266 83340 56713 82363 27 7 14 34 50854 86104 52349 85203 53828 " • 84277 55291 83324 56736 82347 26 / 15 35 50879 86089 52374 85188 53853 84261 55315 83308 56760 82330 25 ( 15 15 36 37 50904 ' 50929 86074 86059 52399 85173 53877 84245 84230' 55339 83292 83276 56784 82314 24 23 6 6 52423 85157 53902 55363 56808 82297 16 38 50954 86045 52448 85142 53926 84214 55388 83260 56832 82281 22 6 16 39 50979 86030 52473 85127 53951 84198 55412 83244 56856 82264 21 6 17 40 51004 86015 52498 85112 53975 84182 55436 83228 56880 82248 20 o 17 41 51029 86000 52522 85096 54000 84167 55460 83212 56904 82231 19 18 42 43 51054 51079 85985 85970 52547 85081 54024 54049 84151 55484 83195 56928 82214 18 17 o 5~ 18 52572 85066 84135 55509 83179 56952 82198 18 44 51104 85956 52597 85051 54073 84120 55533 83163 56976 82181 16 4 19 45 51129 85941 52621 85035 54097 84104 55557 83147 57000 82165 15 4 19 46 51154 85926 52646 85020 54122 84088 55581 83131 57024 82148 14 4 20 47 51179 85911 52671 85005 54146 84072 55605 83115 57047 82132 13 3 20 48 51204 85896 52696 84989 54171 84057 84041 55630 8.3098 57071 82115 12 11 3 3 20 49 51229 85881 52720 84974 54195 55654 83082 57095 82098 21 50 51254 85866 52745 84959 54220 i 84025 55678 83066 57119 82082 10 3 21 51 51279 85851 52770 84943 54244 , 84009 55702 j 83050 57143 82065 9 2 22 52 51304 85836 52794 84928 54260 ! 83994 55726 i 83034 57167 82048 8 2 22 53 51329 85821 52819 84913 54293 83978 55750 i 8.3017 57191 82032 7 2 23 23 54 55 51354 85806 52644 52869 84897 54317 54342 83962 83946 55775 55799' 83001 57215 57238 82015 6 5 2 1 51379 85792 84882 82985 81999 23 56 51404 85777 52893 84866 54366 83930 55823 82969 57262 81982 4 1 24 57 51429 85762 52918 84851 54391 83915 55847 82953 57286 81965 3 1 24 58 51454 85747 52943 84836 54415 83899 55871 829.36 57310 81949 2 1 25 59 51479 85732 52967 84820 54440 83883 55895 82920 57334 81932 1 25 60 51504 85717 52992 84805 54464 . 83867 55919 82904 57358 81915 N. COS. N. sine. N. COS. N. sine. N. COS. N. sine. N. COS. N. sine. N. COS. N. sine. M. 59° 5 *° 67° 56° 5 6° TABLE 41. [Page 589 [ Natural Sines and Cosines. Prop. 85° 1 86° 1 S', ° 38° 89° Prop. parts 23 t parts 18 M. N. sine. N. COS. X. sine. ] N. COS. X. .sine. N. COS. X. sine. N. COS. N. sine. N. cos. 57358 81915 58779 80902 60182 79864 61566 78801 62932 77715 60 18 1 57381 81899 58802 80885 60205 79846 61589 78783 62955 77696 59 18 1 9 57405 81882 58826 80867 60228 79829 61612 78765 62977 77678 58 17 1 3 57429 81865 58849 80850 60251 79811 61635 78747 63000 77660 57 17 2 4 57453 81848 58873 80833 60274 79793 61658 78729 63022 77641 56 17 2 o 57477 81832 58896 80816 60298 79776 61681 78711 63045 77623 55 17 2 3 6 7 57501 81815 58920 80799 60321 60344 79758 61704 78694 78676 63068 63090 77605 77586 54 16 57524 81798 58943 80782 79741 61726 53 16 3 8 57548 81782 58967 80765 60367 79723 61749 78658 63113 77568 52 16 3 9 57572 81765 58990 80748 60390 79706 61772 78640 63135 77550 51 15 4 10 57596 81748 59014 80730 60414 79688 61795 78622 63158 77531 50 15 4 11 57619 81731 59037 80713 60437 79671 61818 78604 63180 77513 49 15 5 12 57643 81714 59061 80696 80679 60460 60483 79653 61841 78586 63203 63225 77494 48 47 14 5 13 57667 81698 59084 79635 61864 78568 77476 14 5 14 57691 81681 59108 80662 60506 79618 61887 78550 63248 77458 46 14 6 15 57715 81664 59131 80644 60529 79600 61909 78532 63271 77439 45 14 6 16 57738 81647 59154 80627 60553 79583 61932 78514 63293 77421 44 13 7 17 57762 81631 59178 80610 60576 79565 61955 78496 63316 77402 43 13 7 7 18 19 57786 81614 59201 80593 80576 60599 79547 61978 62001 78478 63338 77384 42- 13 57810 81597 59225 60622 79530 78460 63361 77366 41 12 8 20 57833 81580 59248 80558 60645 79512 62024 78442 63383 77347 40 12 8 21 57857 81563 59272 80541 60668 79494 62046 78424 63406 77329 39 12 8 22 57881 81546 59295 80524 60691 79477 62069 78405 63428 77310 38 11 9 23 57904 81530 59318 80507 60714 79459 62092 78387 63451 77292 37 11 9 24 57928 81513 59342 59365 80489 80472 60738 79441 62115 62138 78369 78351 63473 77273 36 11 10 25 57952 81496 60761 79424 6:3496 77255 35 11 10 26 57976 81479 59389 80455 60784 79406 62160 78333 63518 77236 34 10 10 27 57999 81462 59412 80438 60807 79388 62183 78315 6;?540 77218 33 10 11 28 58023 81445 59436 80420 60830 79371 62206 78297 63563 77199 32 10 11 29 58047 81428 59459 80403 60853 79353 62229 78279 63585 77181 31 9 12 30 58070 81412 . 59482 59506 80386 80368 60876 60899 79335 79318 62251 62274 78261 63608 63630 77162 30 29 9 9 12 31 58094 81395 78243 77144 12 32 58118 81378 59529 80351 60922 79300 62297 78225 63653 77125 28 8 13 33 58141 81361 59552 80334 60945 79282 62320 78206 63675 77107 27 8 13 34 58165 81344 59576 80316 60968 79264 62342 78188 63698 77088 26 8 13 35 58189 81327 59599 80299 60991 79247 62365 78170 63720 77070 25 8 14 36 58212 81310 59622 80282 61015 61038 79229 62388 62411 78152 63742 77051 77033 24 23 7 7 14 37 58236 81293 59646 80264 79211 78134 63765 15 38 58260 81276 59669 80247 61061 79193 62433 78116 63787 77014 22 7 15 39 58283 81259 59693 80230 61084 79176 62456 78098 63810 76996 21 6 15 40 58307 81242 59716 80212 61107 79158 62479 78079 63832 76977 20 6 16 41 58330 81225 59739 80195 61130 79140 62502 78061 63854 76959 19 6 16 42 58354 81208 59763 80178 61153 79122 79105 62524 62547 78043 78025 63877 76940 76921 18 17 5 5 16 43 58378 81191 59786 80160 61176 63899 17 44 58401 81174 59809 80143 61199 79087 62570 78007 63922 76903 16 5 17 45 58425 81157 59832 80125 61222 79069 62592 77988 63944 76884 15 5 18 46 58449 81140 59856 80108 61245 79051 62615 77970 63966 76866 14 4 18 47 58472 81123 59879 80091 61268 79033 62638 77952 63989 76847 13 4 18 19 48 49 58496 81106 59902 80073 61291 79016 62660 77934 64011' 76828 76810 12 11 4 58519 81089 59926 80056 61314 78998 62683 77916 64033 3 19 50 58543 81072 59949 80038 61337 78980 62706 77897 64056 76791 10 3 20 51 58567 81055 59972 80021 61360 78962 62728 77879 64078 76772 9 3 20 52 58590 81038 59995 80003 61383 78944 62751 77861 64100 76754 8 2 20 53 58614 81021 60019 79986 61406 78926 62774 77843 64123 76735 7 2 21 21 54 55' 58637 58661 81004 60042 79968 61429 "61451 78908 62796 62819 77824 77806' 64145 76717 6 2 80987 60065 79951 78891 64167 76698 5 2 21 56 58684 80970 60089 79934 61474 78873 62842 77788 64190 76679 4 1 22 57 58708 80953 60112 79916 61497 78855 62864 77769 64212 76661 3 1 22 58 58731 80936 60135 79899 61520 78837 62887 77751 64234 76642 2 1 23 59 58755 80919 60158 79881 61543 78819 62909 77733 64256 76623 1 23 60 58779 80902 60182 79864 61566 78801 62932 77715 64279 76604 N. COS. N. sine. K. COS. N. sine. K. COS. N. sine. N. COS. N. sine. N. cos. X. sine. M. 5 1° bS ° 5 >o 5 1° Q< 0° Page 590] TABLE 41. Natural Sines and Cosines. Prop. 40° 1 41° 1 42° 1 48 o 44 o Prop. parts 22 1 parts 19 19 M. N. sine. N.cos. N. sine. 65606 N. COS. N.sine. N. COS. N.sine. N. COS. N. sine. N. COS. 64279 76604 75471 66913 74314 68200 73135 69466 71934 60 1 64301 76586 65628 75452 66935 74295 68221 73116 69487 71914 59 19 1 2 64323 7fi567 65650 75433 66956 74276 68242 73096 69508 71894 58 18 1 3 64346 76548 65672 75414 66978 74256 68264 73076 69529 71873 57 18 1 4 64368 76530 65694 75395 66999 74237 68285 73056 69549 71853 56 18 2 5 64390 76511 65716 75375 67021 74217 68306 73036 69570 71833 55 17 2 3 6 64412 76492 76473 65738 75356 75337 67043 74198 74178 68327 73016 69591 71813 71792 54 53 17 7 64435 65759 67064 68349 72996 69612 17 3 8 64457 76455 65781 75318 67086 74159 68370 72976 69633 71772 52 16 3 9 64479 76436 65803 75299 67107 74139 68391 72957 69654 71752 51 16 4 10 64501 76417 65825 75280 67129 74120 68412 72937 69675 71732 50 16 4 11 64524 76398 65847 75261 67151 74100 68434 72917 69696 71711 49 16 4 5 12 13 64546 64568 76380 65869 75241 75222 67172 67194 74080 68455 72897 69717 69737 71691 71671 48 47 15 15 76361 65891 74061 68476 72877 5 14 64590 76342 65913 75203 67215 74041 68497 72857 69758 71650 46 15 6 15 64612 76323 65935 75184 67237 74022 68518 72837 69779 71630 45 14 6 16 64635 76304 65956 75165 67258 74002 68539 72817 69800 71610 44 14 6 17 64657 76286 65978 75146 67280 73983 68561 72797 69821 71590 43 14 7 7 18 19 64679 64701 76267 76248 66000 66022 75126 75107 67301 73963 68582 72777 72757 69842 69862 71569 71549 42 41 13 67323 73944 68603 13 7 20 64723 76229 66044 75088 67344 73924 68624 72737 69883 71529 40 13 8 21 64746 76210 66066 75069 67366 73904 68645 72717 69904 71508 39 12 8 22 64768 76192 66088 75050 67387 73885 68666 72697 69925 71488 38 12 8 23 64790 76173 66109 75030 67409 73865 68688 72677 69946 71468 37 12 9 24 64812 76154 66131 75011 67430 73846 68709 68730 72657 72637 69966 69987 71447 36 11 11 9 25 64834 76135 66153 74992 67452 73826 71427 35 10 26 64856 76116 66175 74973 67473 73806 68751 72617 70008 71407 34 11 10 27 64878 76097 66197 74953 67495 73787 68772 72597 70029 71386 33 10 10 28 64901 76078 66218 74934 67516 73767 68793 72577 70049 71366 32 10 11 29 64923 76059 66240 74915 67538 73747 68814 72557 70070 71.345 31 10 11 11 30 31 64945 64967 76041 76022 66262 74896 74876 67559 73728 73708 68835 72537 72517 70091 70112 71325 30 29 10 9 66284 67580 68857 71305 12 32 64989 76003 66306 74857 67602 73688 68878 72497 70132 71284 28 9 12 33 65011 75984 66327 74838 67623 73669 68899 72477 70153 71264 27 9 12 34 65033 75965 66349 74818 67645 73649 68920 72457 70174 71243 26 8 13 35 65055 75946 66371 74799 67666 73629 68941 72437 70195 71223 25 8 13 14 36 37 65077 75927 66393 74780 67688 67709 73610 68962 72417 72397 70215 71203 24 23 8 7 65100 75908 66414 74760 73590 68983 70236 71182 14 38 65122 75889 66436 74741 67730 73570 69004 72377 70257 71162 22 7 14 39 65144 75870 66458 74722 67752 73551 69025 72357 70277 71141 21 7 15 40 65166 75851 66480 74703 67773 73531 69046 72337 70298 71121 20 6 15 41 65188 75832 66501 74683 67795 73511 69067 72317 70319 71100 19 6 15 16 42 65210 75813 66523 66545 74664 67816 67837 73491 69088 72297 70339 71080 71059 18 17 6 43 65232 75794 74644 73472 69109 72277 70360 16 44 65254 75775 66566 74625 67859 73452 69130 72257 70381 71039 16 5 17 45 65276 75756 66588 74606 67880 73432 69151 72236 70401 71019 15 5 17 46 65298 75738 66610 74586 67901 73413 69172 72216 70422 70998 14 4 17 47 65320 75719 66632 74567 67923 73393 69193 72196 70443 70978 13 4 18 18 48 49 65342 65364 75700 66653 74548 67944 73373 69214 69235 72176 72156 70463 70484 70957 12 4 75680 66675 74528 67965 73353 70937 11 3 18 50 65386 75661 66697 74509 67987 73333 69256 72136 70505 70916 10 3 19 51 65408 75642 66718 74489 68008 73314 69277 72116 70525 70896 9 3 19 52 65430 75623 66740 74470 68029 73294 69298 72095 70546 70875 8 3 19 53 65452 75604 66762 74451 68051 73274 69319 72075 70567 70855 / 2 20 20 54 55 65474 75585 66783 66805 74431 68072 73254 73234 69340 72055 72035 70587 70608 70834 70813" 6 5 2 2 65496 75566 74412 68093 69361 21 56 65518 75547 66827 74392 68115 73215 69382 72015 70628 70793 4 I 21 57 65540 75528 66848 74373 68136 73195 69403 71995 70649 70772 3 1 21 58 65562 75509 66870 74353 68157 73175 69424 71974 70670 70752 2 1 22 59 65584 75490 66891 74334 68179 73155 69445 71954 70690 70731 1 22 60 65606 75471 66913 74314 68200 73135 69466 71934 70711 70711 — N.cos. i 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 591 Logarithms of Numbers. No. 1 100. Log. 0.00000 ^2.00000. 1 No. Log. No. Log. No. Log. No. Log. No. Log. 1 0.00000 21 1. 32222 41 1.61278 61 1. 78533 81 1. 90849 2 0. 30103 22 1. 34242 42 1. 62325 62 1. 79239 82 1.91381 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 6 0. 69897 25 "26 1.39794 45 46 1. 65321 65 1. 81291 85 1. 92942 0. 77815 1. 41497 1. 66276 66 1. 81954 86 1. 93450 7 0. 84510 27 1.43136 47 1. 67210 67 1. 82607 87 1. 93952 8 0. 90309 28 1.44716 48 1. 68124 68 1. 83251 88 1.94448 9 0. 95424 29 1. 46240 49 1. 69020 69 1. 83885 89 1.94939 10 1. 00000 30 1.47712 50 1. 69897 70 1. 84510 90 1. 95424 11 1. 04139 31 1. 49136 51 1. 70757 71 1. 85126 91 1. 95904 12 1.07918 32 1.50515 52- 1. 71600 72 1. 85733 92 1. 96379 13 1.11394 33 1. 51851 53 1. 72428 73 1. 86332 93 1. 96848 14 1. 14613 34 1. 53148 54 1. 73239 74 1. 86923 94 1. 97313 15 1. 17609 35 1. 54407 55 1. 74036 75 1. 87506 95 1.97772 16 1. 20412 36 1. 55630 56 1. 74819 76 1. 88081 96 1. 98227 17 1. 23045 37 1.56820 57 1. 75587 77 1. 88649 97 1. 98677 18 1. 25527 38 1.57978 58 1. 76343 78 1. 89209 98 1. 99123 19 1. 27875 39 1.59106 59 1. 77085 79 1. 89763 99 1. 99564 20 1. 30103 40 1. 60206 60 1. 77815 80 1. 90309 100 2. 00000 Page 592] TABLE 42. Logarithms of Numbers. No. 100 1600 Log. 00000- —20412. No. 1 '■ i 8 00130 00561 00988 01410 01828 02243 02653 03060 03463 03862 04258 04650 05038 05423 05805 4 5 7 8 9 100 101 102 103 104 105 106 107 108 109 OOOOO 00432 008t)0 01284 01703 00043 00475 00903 0132^ 01745 02160 02572 02979 03383 03782 04179 04571 04961 05346 05729 00087 00518 00945 01368 01787 02202 02612 03019 03423 03822 04218 04610 04999 05385 05767 00173 00604 01030 01452 01870 02284 02694 03100 03503 03902 04297 04689 05077 05461 05843 00217 ' 00260 00647 00689 00303 00732 01157 01578 01995 02407 02816 03222 03623 04021 04415 04805 05192 05576 05956 06333 06707 07078 07445 07809 00346 00775 01199 01620 02036 02449 02857 03262 03663 04060 00389 00817 01242 01662 , 02078 02490 02898 1 03302 03703 04100 4S ! 42 01072 01494 01912 02325 02735 03141 03543 03941 01115 01536 01953 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 02119 02531 02938 03:342 03743 02366 02776 03181 03583 03981 110 111 112 113 114 115 116 117 118 119 04139 04532 04922 05308 05690 06070 06446 06819 07188 07555 04336 04727 05115 05500 05881 06258 06633 07004 07372 07737 08099 08458 08814 09167 09517 09864 10209 10551 10890 11227 11561 11893 12222 12548 12872 04376 04766 05154 05538 05918 06296' 06670 07041 07408 07773 08135 08493 08849 09202 09552 04454 04844 05231 05614 05994 04493 04883 05269 05652 06032 T 2 3 4 5 6 7 8 9 41 4 8 12 16 21- 25 29 33 37 40 4 8 12 16 • 20 24 28 32 36 06108 06483 06856 07225 07591 07954 08314 08672 09026 09377 06145 06521 06893 07262 07628 06183 06558 06930 07298 07664 08027 08386 08743 09096 09447 06221 06595 06967 07335 07700 08063 08422 08778 09132 09482 06371 06744 07115 07482 07846 06408 06781 07151 07518 07882 120 121 122 123 124 125 126 127 128 129 07918 08279 08636 08991 09342 09691 10037 10380 10721 11059 11394 11727 12057 12385 12710 13033 13354 13672 13988 14301 07990 08350 08707 09061 09412 08171 08529 08884 09237 09587 08207 08565 08920 09272 09621 08243 08600 08955 09307 09656 10003 10346 10687 11025 11361 2 3 4 5 6 7 8 9 89 4 8 12 16 20 23 27 31 35 88 4 8 11 15 19 23 27 30 34 09726 10072 10415 10755 11093 11428 11760 12090 12418 12743 09760 10106 10449 10789 11126 09795 10140 10483 10823 11160 09830 10175 10517 10857 11193 09899 10243 10585 10924 11261 09934 10278 10619 10958 11294 09968 10312- 10653 10992 11327 11661 11992 12320 12646 12969 130 131 132 133 134 135 136 137 138 139 11461 11793 12123 12450 12775 11494 11826 12156 12483 12808 11528 11860 12189 12516 12840 13162 13481 13799 14114 14426 14737 15045 15351 15655 15957 11594 11926 12254 12581 12905 11628 11959 12287 12613 12937 11694 12024 12352 12678 13001 87 36 1 2 3 4 5 6 7 8 9 4 7 11 15 19 22 26 30 33 4 7 11 14 18 22 25 29 32 13066 13386 13704 14019 14333 13098 13418 13735 14051 14364 13130 13450 13767 14082 14395 13194 13513 13830 14145 14457 14768 15076 15381 15685 15987 13226 13545 13862 14176 14489 13258 13577 13893 14208 14520 13290 13609 13925 14239 14551 13322 13640 13956 14270 14582 14891 15198 15503 15806 16107 16406 16702 16997 17289 17580 17869 18156 18441 18724 19005 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 14613 14922 15229 15534 15836 16137 16435 16732 17026 17319 14644 14953 15259 15564 15866 14675 14983 15290 15594 15897 14706 15014 15320 15625 15927 16227 16524 16820 17114 17406 14799 15106 15412 15715 16017 14829 15137 15442 15746 16047 16346 16643 16938 17231 17522 17811 18099 18384 18667 18949 19229 19507 19783 20058 20330 14860 15168 15473 15776 16077 16376 16673 16967 17260 17551 1~ 2 3 4 5 6 7 8 9 85 "4" 7 11 14 18 21 25 28 32 84 3 7 10 14 17 20 24 27 31 16167 16465 16761 17056 17348 17638 17926 18213 18498 18780 16197 16495 16791 17085 17377 16256 16554 16850 17143 17435 16286 16584 16879 17173 17464 17754 18041 18327 18611 18893 19173 19451 19728 20003 20276 16316 16613 16909 17202 17493 17609 17898 18184 18469 18752 17667 17955 18241 18526 18808 17696 17984 18270 18554 18837 17725 18013 18298 18583 18865 17782 18070 18355 18639 18921 19201' 19479 19756 20030 20303. 17840 18127 18412 18696 18977 2 3 4 5 '6 7 8 88 32 3 7 10 13 17 20 23 26 30 3 6 10 13 16 19 22 26 29 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 19257 19535 19811 20085 20358 8 19285 19562 19838 20112. 20385 No. 1 2 s 4 5 1 6 7 ^ TABLE 4:2. Logarithms of Nximbers. [Page 593 N( -2200 Log. 20412 -34242. 1 No. 1 2 8 4 5 6 7 « 9 160 161 162 163 164 165 166 167 168 169 20412 20683 20952 21219 21484 20439 20710 20978 21245 21511 20466 20737 21005 21272 21537 20493 20763 21032 21299 21564 21827 22089 22350 22608 22866 20520 20790 21059 21325 21590 21854 22115 22376 22634 22891 20548 20817 21085 21352 21617 21880 22141 22401 22660 22917 23172 23426 23679 23930 24180 20575 20844 21112 21378 21643 21906 22167 22427 22686 22943 23198 23452 23704 23955 24204 24452 24699 24944 25188 25431 25672 25912 26150 26387 26623 26858 27091 27323 27554 27784 28012 28240 28466 28691 28914 29137 29358 29579 29798 30016 30233 30449 30664 30878 31091 31302 31513 31723 31931 32139 20602 20871 21139 ^405 21669 21932 22194 22453 22712 22968 23223 23477 23729 23980 24229 20629 20898 21165 21431 21696 21958 22220 22479 22737 22994 23249 23502 23754 24005 24254 20656 20925 21192 21458 21722 1 2 3 4 5 6 7 8 9 31 3 6 9 12 16 19 22 25 28 30 3 6 9 12 15 18 21 24 27 21748 22011 22272 22531 22789 21775 22037 22298 22557 22814 21801 22063 22324 22583 22840 21985 22246 22505 22763 23019 23274 23528 23779 24030 24279 170 171 172 173 174 175 176 177 178 179 23045 23300 23553 23805 24055 24304 24551 24797 25042 25285 23070 23325 23578 23830 24080 24329 24576 24822 25066 25310 23096 23350 23603 23855 24105 24353 24601 24846 25091 25334 23121 23147 23376 23401 29 28 23629 23880 24130 24378 24625 24871 25115 25358 23654 23905 24155 1 2 3 4 5 6 7 8 9 3 6 9 12 15 17 20 23 26 3 6 8 11 14 17 20 22 25 24403 24650 24895 25139 25382 24428 24674 24920 25164 25406 25648 25888 24477 24724 24969 25212 25455 25696 25935 26174 26411 26647 26881 27114 27346 27577 27807 28035 28262 28488 28713 28937 29159 29380 29601 29820 30038 30255 30471 30685 30899 31112 31323 31534 31744 31952 32160 32366 32572 32777 32980 33183 33385 33586 33786 33985 34183 24502 24748 24993 25237 25479 25720 25959 26198 2frl35 26670 26905 27138 27370 27600 27830 28058 28285 28511 28735 28959 29181 29403 29623 29842 30060 30276 30492 30707 30920 31133 31345 31555 31765 31973 32181 32387 32593 32797 33001 33203 33405 33606 33806 34005 34203 24527 24773 25018 25261 25503 180 181 182 183 184 25527 25768 26007 26245 26482 25551 25792 26031 26269 26505 25575 25816 26055 26293 26529 25600 25624 25840 25864 25744 25983 26221 26458 26694 1 2 3 4 5 6 7 8 9 27 3 5 8 11 14 16 19 22 24 26 26316 26M0 26364 26553 26576 | 26600 26788 26811 26834 27021 27045 1 27068 27254 27277 27300 27485 27508 ; 27531 27715 27738 27761 3 5 8 10 13 16 18 21 23 185 186 187 188 189 26717 26951 27184 27416 27646 26741 26975 27207 27439 27669 27898 28126 28353 28578 28803 29026 29248 29469 29688 29907 30125 30341 30557 30771 30984 26764 26998 27231 27462 27692 27921 28149 28375 28601 28825 29048 29270 29491 29710 29929 30146 30363 30578 30792 31006 26928 27161 27393 27623 27852 28081 28307 28533 28758 28981 29203 29425 29645 29863 30081 190 191 192 193 194 27»75 28103 28330 28556 28780 27944 27967 28171 28194 28398 1 28421 28623 28646 28847 ' 28870 29070 29092 29292 29314 29513 29535 29732 29754 29951 29973 30168 30190 30384 30406 30600 30621 30814 30835 31027 31048 31239 31260 31450 ' 31471 31660 31681 31869 31890 32077 i 32098 27989 28217 28443 28668 28892 29115 29336 29557 29776 29994 30211 30428 30&43 30856 31069 31281 31492 31702 31911 32118 25 24 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 3 5 8 10 13 15 18 20 23 2 5 7 10 12 14 17 19 22 195 196 197 198 199 29003 29226 29447 29667 29885 200 201 202 203 204 30103 30320 30535 30750 30963 30298 30514 30728 30942 31154 23 ~2" 5 7 9 12 14 16 18 21 22 2 4 7 9 11 13 15 18 20 205 206 207 208 209 210 211 212 213 214 31175 31387 31597 31806 32015 31197 31408 31618 31827 32035 31218 31429 31639 31848 32056 31366 31576 31785 31994 32201 32408 32613 32818 33021 33224 33425 33626 33826 34025 34223 32222 32428 32634 32838 33041 32243 32449 32654 32858 33062 33264 33465 33666 33866 34064 32263 32469 32675 32879 33082 33284 33486 33686 33885 34084 32284 ' 32305 \ 32325 32490 1 32510 32531 32346 32552 32756 32960 33163 32695 32715 32899 32919 33102 33122 32736 32940 33143 1 2 3 4 5 6 7 8 9 21 "2~ 4 20 2 4 215 216 217 218 219 33244 33445 33646 33846 34044 33304 33506 33706 33905 34104 33325 33526 33726 33925 34124 33345 33546 33746 33945 34143 33365 33566 33766 33965 34163 6 6 8 ! 8 11 ! 10 13 12 15 14 17 16 No. 1 2 3 ' 4 5 6 7 « 9 19 18 22489—03- -38 Page 594] TABLE 42. Logarithms ( 3f Numbers. Xo. 2200 280C . Log. 34242- — M716. Ko. « 1 1 i 2 3 4 5 1 34341 1 7 8 9 220 34242 34262 34282 34301 34321 34361 34380 34400 34420 221 34439 34459 34479 34498 34518 34537 34557 34577 34596 34616 20 222 34635 34655 34674 34694 34713 34733 34753 34772 34792 34811 1 2 223 34830 348o0 ;34869 34889 34908 34928 34947 34967 34986 35005 2 4 224 35025 35044 1 35064 35083 35102 35295 35122 35315 35141 35334 35160 35353 35180 35199 35392 3 4 6 8 225 35218 35238 35257 35276 35372 226 35411 35430 35449 35468 35488 35507 35526 35545 35564 35583 5 10 227 35603 35622 35641 35660 35679 35698 35717 35736 35755 35774 6 12 228 35793 35813 35832 35851 35870 35889 35908 35927 35946 35965 V 14 229 35984 36003 36192 36021 36040 36059 36078 36097 36116 36135 36154 8 9 16 18 230 36173 36211 36229 36248 36267 36286 36305 36324 Sfi.^l9 231 36361 36380 36399 36418 36436 36455 36474 36493 36511 ! 36530 19 232 36549 36568 36586 36605 36624 36642 36661 36680 36698 36717 1 2 233 36736 36754 36773 36791 36810 36829 36847 36866 36884 36903 9 4 234 36922 36940 36959 36977 36996 37014 37033 37051 37070 37088 3 4 6 8 235 37107 37125 37144 37162 37181 37199 37218 37236 37254 37273 236 37291 37310 37328 37346 37365 37383 37401 37420 37438 37457 5 10 237 37475 37493 37511 37530 37548 37566 37585 37603 37621 37639 6 11 238 37658 37676 37694 37712 37731 37749 37767 37785 37803 37822 7 13 239 37840 37858 37876 37894 37912 37931 37949 37967 37985 38003 8 9 15 17 240 241 38021 38202 38039 38220 38057 38238 38075 38256 38093 38274 38112 38292 38130 38310 38148 38328 38166 ; 38184 38346 1 38364 18 242 38382 38399 38417 38435 38453 38471 38489 38507 38525 38543 1 2 3 4 2 4 5 7 243 38561 38578 38596 38614 38632 38650. 38668 38686 38703 38721 244 38739 38757 38775 38792 38810 38828 38846 , 38863 38881 38899 245 38917 38934 38952 38970 38987 39005 39023 39041 39058 39076 246 39094 39111 39129 39146 39164 39182 39199 39217 39235 39252 5 Q 247 39270 39287 39305 39322 39340 39358 39375 39393 39410 39428 6 11 248 39445 39463 39480 39498 39515 39533 39550 39568 39585 39602 7 13 249 39620 39637 39655 39672 39690 39707 . 39724 39742 39759 39933 39777 8 9 It 250 39794 39811 39829 39846 39863 39881 39898 39915 39950 251 39967 39985 40002 40019 40037 40054 40071 40088 40106 40123 252 40140 40157 40175 40192 40209 40226 40243 40261 40278 40295 253 40312 40329 40346 40364 40381 40398 40415 40432 40449 40466 1 2 254 40483 40500 40518 40688 40535 40705 40552 40722 40569 40586 40603 40773 40620 40637 2 3 3 5 255 40654 40671 40739 40756 40790 40807 256 , 40824 40841 40858 40875 40892 40909 40926 40943 40960 40976 4 7 257 40993 41010 41027 41044 41061 41078 41095 41111 41128 41145 5 9 258 41162 41179 41196 41212 41229 41246 41263 41280 41296 41313 6 10 259 41330 41347 41363 41380 41397 41414 41430 41447 41464 41481 7 8 9 12 14 15 260 41497 41514 41531 41547 41564 41581 41597 41614 41631 41647 261 262 41664 41830 41681 41847 41697 41863 41714 41880 41731 41896 41747 41913 41764 41780 41 797 41814 41929 41946 41963 41979 16 263 41996 42012 42029 42045 42062 42078 42095 42111 42127 42144 1 2 264 42160 42177 42193 42210 42226 42243 42259 42423 42275 42292 42308 2 3 3 5 265 42325 42341 42357 42374 42390 42406 42439 42455 42472 266 42488 42504 42521 42537 42553 42570 42586 42602 42619 42635 4 6 267 42651 42667 42684 42700 42716 42732 42749 42765 42781 42797 5 8 268 42813 42830 42846 42862 42878 42894 42911 42927 42943 42959 6 10 269 42975 42991 43008 43024 43040 43056 43217 43072 43233 43088 43249 43104 43120 7 8 11 13 270 43136 43152 43169 43185 43201 43265 43281 271 272 43297 43457 43313 43473 43329 43489 43345 43505 43361 43521 43377 43537 43393 43553 43409 43569 43425 43584 43441 43600 9 14 15 273 43616 43632 43648 43664 43680 43696 43712 43727 43743 43759 1 2 274 43775 43791 43807 43823 43838 43854 44012 43870 44028 43886 44044 43902 43917 2 3 3 5 275 43933 43949 i 43965 43981 i 43996 44059 i 44075 276 44091 44107 44122 44138 ! 44154 44170 44185 44201 , 44217 44^32 4 6 277 44248 44264 44279 i 44295 44311 44326 44342 44358 44373 44389 5 8 278 44404 44420 44436 44451 44467 44483 44498 44514 44529 44545 6 9 279 44560 44576 44592 44607 44623 i , 44638 44654 44669 44685 44700 8 9 11 12 ,14 No. 1 2 3 4 5 6 7 8 9 TABLE 42. Logarithms of Numbers. [Page 595 No. 2800 3400. Log. 44716 53148. No. 1 2 3 4 5 6 7 8 » 1 280 281 282 283 284 285 286 287 288 289 44716 44871 45025 45179 45332 44731 44886 45040 45194 45347 44747 44902 45056 45209 45362 45515 45667 45818 45969 46120 44762 44917 45071 45225 45378 44778 44932 45086 1 45240 ! 45393 1 45545 45697 45849 46000 46150 44793 44948 45102 45255 45408 45561 45712 45864 46015 46165 44809 44963 45117 45271 45423 44824 44979 45133 45286 45439 45591 45743 45894 46045 46195 44840 44855 44994 45010 45148 45163 45301 45317 45454 1 45469 16 1 2 3 4 5 6 7 8 9 2 3 5 6 8 10 11 13 14 45484 45637 45788 45939 46090 45500 45a52 45803 45954 46105 45530 45682 45834 45984 46135 45576 45728 45879 46030 46180 45606 45758 1 45909 46060 46210 46359" 46509 46657 46805 46953 45621 45773 45924 46075 46225 290 291 292 293 294 295 296 297 298 299 46240 46389 46538 46687 46835 46255 46404 46553 46702 46850 46270 46419 46568 46716 46864 47012 47159 47305 47451 47596 46285 46434 46583 46731 46879 47026 47173 47319 47465 47611 46300 46449 46598 46746 . 46894 47041 47188 47334 47480 47625 46315 46464 46613 46761 46909 47056 47202 47349 47494 47640 46330 46479 46627 46776 46923 56345 46494 46642 46790 46938 46374 46523 46672 46820 46967 47114 47261 47407 47553 47698 1 15 1 2 3 4 5 6 7 8 9 2 3 5 6 8 9 11 12 14 46982 47129 47276 47422 47567 46997 47144 47290 47436 47582 47070 47217 47363 47509 47654 47085 47232 47378 47524 47669 47100 47246 47392 47538 47683 300 301 302 303 304 47712 47857 48001 48144 48287 47727 47871 48015 48159 48302 47741 47885 48029 48173 48316 47756 47900 48044 48187 48330 47770 47914 48058 48202 48344 47784 47929 48073 48216 48359 47799 47943 48087 48230 48373 47813 47958 48101 48244 48387 47828 47842 47972 47986 48116 48130 48259 48273 48401 i 48416 1 305 306 307 308 309 48430 48572 48714 48855 48996 48444 48586 48728 48869 49010 48458 48601 48742 48883 49024 48473 48615 48756 48897 49038 48487 48629 48770 48911 49052 48501 48643 48785 48926 49066 48515 48657 48799 48940 49080 48530 48671 48813 48954 49094 49234 49374 49513 49651 49790 49927 50065 50202 50338 50474 50610 50745 50880 51014 51148 48544 1 48558 14 48827 48968 49108 49248 49388 49527 49665 49803 49941 50079 50215 50352 50488 50623 50759 50893 51028 51162 51295 51428 51561 51693 51825 51957 52088 52218 52349 52479 52608 52737 52866 52994 53122 48841 48982 49122 492(32 49402 49541 49679 49817 49955 50092 50229 50365 50501 50637 50772 50907 51041 51175 51308 51441 51574 51706 51838 51970 52101 52231 52362 52492 52621 52750 52879 53007 53135 1 2 3 4 5 6 7 8 9 1 3 4 6 7 8 10 11 13 310 311 312 313 314 49136 49276 49415 49554 49693 49150 49290 49429 49568 49707 49164 49304 49443 49582 49721 49859 49996 50133 50270 50406 49178 49318 49457 49596 49734 49872 50010 50147 50284 50420 49192 49332 49471 49610 49748 49206 49346 49485 49624 49762 49220 49360 49499 49638 49776 315 316 317 318 319 49831 49969 50106 50243 50379 49845 49982 50120 50256 50393 50529 50664 50799 50934 51068 49886 50024 50161 50297 50433 50569 50705 50840 50974 51108 49900 50037 50174 50311 50447 49914 50051 50188 50325 50461 1 18 1 2 3 4 5 6 7 8 9 1 3 4 5 7 8 9 10 12 320 321 322 323 324 50515 50651 50786 50920 51055 50542 50678 50813 50947 51081 50556 50691 50826 50961 51095 50583 50718 50853 50987 51121 50596 50732 50866 51001 51135 51268' 51402 51534 51667 51799 325 326 327 328 329 51188 51322 51455 51587 51720 51202 51335 51468 51601 51733 51215 51348 51481 51614 51746 51228 51362 51495 51627 51759 51891 52022 52153 52284 52414 51242 51375 51508 51640 51772 51255 51388 51521 51654 51786 51282 51415 51548 51680 51812 51943 52075 52205 52336 52466 1 330 331 332 333 334 51851 51983 52114 52244 52375 51865 51996 52127 52257 52388 51878 52009 52140 52270 52401 51904 52035 52166 52297 52427 51917 52048 52179 52310 52440 51930 52061 52192 52323 52453 1 2 3 4 5 6 7 8 9 12 1 2 4 5 6 7 8 10 11 335 336 337 338 339 52504 52634 52763 52892 53020 52517 52647 52776 52905 53033 52530 52660 52789 52917 53046 52543 52673 52802 52930 53058 52556 52686 52815 52943 53071 52569 52699 52827 52956 53084 52582 52711 52840 52969 53097 52595 52724 52853 52982 53110 No. 1 2 3 4 5 6 7 8 9 Page 596] TABLE 42. Logarithms of Numbers. No. S400 lOOC . Log. 53148 60206. 1 No. 1 2 3 4 5 G 7 8 9 1 340 :^i 342 343 344 345 346 347 348 349 350 351 352 353 354 53148 53275 1 53403 53529 53^56 53782 1 53908 ' 54033 ! 54158 ' 54283 . 54407 54531 54654 54777 54900 53161 53288 53415 535* 53668 53794 53920 54045 54170 54295 54419 54543 54667 54790 54913 53173 53301 53428 53555 53681 53807" 53933 54058 54183 54307 54432 54555 54679 54802 54925 53186 53314 53441 53567 53694 ' 53820 1 53945 : 54070 54195 54320 53199 53326 53453 53580 53706 5.3832 53958 54083 54208 54332 53212 53339 5;i466 53593 53719 53845 5.3970 54095 54220 54345 53224 53352 53479 5.3605 53732 53857 53983 54108 54233 .54357 53237 53364 5,3491 53618 53744 53870 5,3995 54120 54245 54370 54494 54617 5-^741 54864 54986 55108 55230 55352 5,5473 55594 53250 53377 53504 53631 53757 53882 ,54008 ,54133 54258 54382 54506 54630 54753 54876 54998 55121 55242 55364 55485 55606 53263 53390 ,5.3517 53643 53769 53895 54020 ,54145 54270 54394 54518 54642 54765 54888 55011 Vi 1 2 3 4 5 / 8 9 1 3 4 5 7 8 9 10 12 54444 54568 54691 54814 54937 : 54456 54580 54704 54827 54949 54469 54593 54716 548.39 .54962. 55084 55206 55328 55449 55570 54481 54605 54728 54851 54974 55096 55218 55;i40 55461 55582 355 356 357 358 359 55023 ,55145 55267 55388 55509 550;i5 55157 55279 55400 55522 55047 55169 55291 55413 55534 55060 55182 55303 55425 55546 55072 55194 55315 55437 55558 55133 55255 55376 55497 55618 55739 55859 55979 56098 56217^ 1 2 3 4 5 6 7 8 9 12 1 2 4 5 6 7 8 10 11 360 361 362 363 364 55630 55751 1 55871 55991 ' 56110 i 55642 55763 55883 56003 56122 55654 55775 55895 56015 56134 55666 55787 55907 i 56027 56146 55678 55799 55919 56038 56158 55691 55811 55931 56050 56170 55703 55823 55943 56062 56182 55715 55835 55955 56074 56194 56312 5&431 56549 56667 56785 55727 ,55847 55967 56086 56205 365 366 367 368 369 56229 , 56348 56467 56585 56703 ' 56241 56360 56478 56597 56714 56832 56949 57066 57183 57299 56253 56372 56490 56608 56726 56844 56961 57078 57194 57310 56265 56384 56502 56620 56738 56277 56396 56514 56632 56750 56289 56407 56526 56644 56761 56301 56419 56538 56656 56773 56324 56443 56561 56679 56797 56914 57031 57148 57264 57380 57496 57611 57726 57841 57955 56336 56455 56573 56691 56808 370 371 372 373 374 56820 56937 57054 57171 57287 56855 56972 57089 57206 57322 56867 56984 57101 57217 57334 56879 56996 57113 57229 57345 56891 57008 57124 57241 57357 56902 57019 57136 57252 57368 56926 57043 57159 57276 57392 57507 57623 57738 57852 57967 11 1 2 3 4 5 6 7 8 9 1 2 3 4 6 7 8 9 10 375 376 377 378 379 57403 57519 57634 57749 57864 57415 57530 57646 57761 57875 57426 57542 57657 57772 57887 57438 57553 57669 57784 57898 57449 57565 57680 57795 57910 57461 57576 57692 57807 57921 57473 57588 57703 .57818 579,33 57484 57600 ,57715 57830 57944 380 381 382 383 384 57978 58092 58206 58320 58433 57990 58104 58218 58331 58444 58001 58115 58229 58343 58456 58013 58127 58240 58354 58467 58024 581.38 58252 58365 58478 58035 58149 58263 58377 58490 58047 58161 58274 58388 58501 58058 58172 58286 58399 .58512 58070 58184 58297 ,58410 58524 58081 58195 58309 58422 58535 5864? 58760 58872 58984 59095 385 386 387 388 389 58546 58659 58771 58883 58995 58557 58670 58782 58894 59006 58569 58681 58794 58906 59017 58580 58692 58805 58917 59028 58591 58704 58816 58928 59040 58602 58715 58827 58939 59051 58614 58726 58838 58950 59062 58625 58737 58850 58961 59073 58636 58749 58861 58973 59084 10 390 391 392 393 394 59106 59218 59329 59439 59550 59660" 59770 59879 59988 60097 59118 59229 59340 59450 59561 59671 59780 59890 59999 60108 1 59129 59240 59351 59461 59572 59682 59791 59901 60010 60119 59140 59251 59362 59472 59583 59693' 59802 59912 60021 60130 59151 59262 59373 59483 59594 59704' 59813 59923 60032 60141 59162 59273 59384 59494 59605 i 59715 59824 59934 60043 60152 59173 59284 59.395 .59506 ,59616 "59726 59835 59945 60054 60163 59184 59295 59406 59517 59627 59737 59846 59956 60065 60173 59195 59306 59417 59528 59638 59207 ,59318 59428 59539 59649 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 395 396 397 398 399 59748 59857 59966 60076 60184 59759 59868 59977 60086 60195 No. 2 S 4 o G 7 8 ! » 1 No. TABLE 42. Logarithms of Numbers. [Page 597 4000 1600. Log. 60206 66276. 1 No. 1 2 3 4 5 6 7 8 9 1 400 401 402 403 404 60206 60314 60423 60531 60638 60746 60853 60959 61066 61172 6f278 61384 61490 61595 61700 60217 60325 60433 60541 60649 60756 60863 60970 61077 61183 60228 60336 60444 60552 60660 60239 60347 60455 60563 60670 60249 60358 60466 60574 60681 60260 60369 60477 60584 60692 60271 60379 60487 60595 60703 60282 60390 60498 60606 60713 60293 60401 60509 60617 60724 60304 60412 60520 60627 60735 60842" 60949 61055 61162 61268 61374 61479 61584 61690 61794 61899 62003 62107 62211 62315 11 1 2 3 4 5 6 7 8 9 1 2 3 4 6 7 8 9 10 405 406 407 408 409 60767 60874 60981 61087 61194 60778 60885 60991 61098 61204 60788 60895 61002 61109 61215 60799 60906 61013 61119 61225 60810 60917 61023 61130 61236 60821 60927 61034 61140 61247 60831 60938 61045 61151 61257 410 411 412 413 414 61289 61395 61500 61606 61711 61300 61405 61511 61616 61721 61310 61416 61521 61627 61731 61321 61426 61532 61637 61742 61331 61437 61542 61648 61752 61342 61448 61553 61658 61763 61868 61972 62076 62180 62284 62387 62490 62593 62696 62798 61352 61458 61563 61669 61773 61878 61982 62086 62190 62294 62397 62500 62603 62706 62808 62910 63012 63114 63215 63317 61363 61469 61574 61679 61784 61888 61993 62097 62201 62304 62408 62511 62613 62716 62818 62921 63022 63124 63225 63327 63428 63528 63629 63729 63829 63929 64028 64128 64227 64326 415 416 417 418 419 420 421 422 423 424 61805 61909 62014 62118 62221 62325 62428 62531 62634 62737 61815 61920 62024 62128 62232 62335 62439 62542 62644 62747 61826 61930 62034 62138 62242 62346 62449 62552 62655 62757 62859 62961 63063 63165 63266 63367 63468 63568 63669 63769 61836 61941 62045 62149 62252 62356 62459 62562 62665 62767 62870 62972 63073 63175 63276 61847 61951 62055 62159 62263 62366 62469 62572 62675 62778 62880 62982 63083 63185 63286 61857 61962 62066 62170 62273 62377 62480 62583 62685 62788 62418 62521 62624 62726 62829 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 425 4^6 427 428 429 430 431 432 433 434 62839 62941 63043 63144 63246 62849 62951 63053 63155 63256 63357' 63458 63558 63659 63759 62890 62992 63094 63195 63296 62900 63002 63104 63205 63306 62931 63033 63134 63236 63337 63438 63538 63639 63739 63839 63347 63448 63548 63649 63749 63377 63478 63579 63679 63779 63387 63488 63589 63689 63789 63397 63498 63599 63699 63799 63899 63998 64098 64197 64296 63407 63508 63609 63709 63809 63909 64008 64108 64207 64306 63417 63518 63619 63719 63819 63919 64018 64118 64217 64316 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 63849 63949 64048 64147 64246 . 63859 63959 64058 64157 64256 63869 63969 64068 64167 64266 63879 63979 64078 64177 64276 63889 63988 64088 64187 64286 63939 64038 64137 64237 64335 64345 64444 64542 64640 64738 64355 64454 64552 64650 64748 64365 64464 64562 64660 64758 64375 64473 64572 64670 64768 64865 64963 65060 &5157 65254 64385 64483 64582 64680 64777 64875 64972 65070 65167 65263 64395 64493 64591 64689 64787 64404 64503 64601 64699 64797 64414 64513 64611 64709 64807 64424 64523 64621 64719 64816 64914 65011 65108 65205 65302 65398 65495 65591 65686 65782 64434 64532 64631 64729 64826 64924" 65021 65118 65215 65312 65408 65504 65600 65696 65792 64836 64933 65031 65128 65225 64846 64943 65040 65137 65234 64856 64953 65050 65147 65244 64885 64982 65079 65176 65273 6t895 64992 65089 65186 65283 6^904 65002 65099 65196 65292 1 2 3 4 5 6 7 8 9 9 450 451 452 453 454 65321 65418 65514 65610 65706 65331 65427 65523 65619 65715 65341 65437 65533 65629 65725 65350 65447 65543 65639 65734 65360 65456 65552 65648 65744 65369 65466 65562 65658 65753 65379 65475 65571 65667 65763 65389 65485 65581 65677 65772 1 2 3 4 5 5 6 7 8 455 456 457 458 459 65801 65896 65992 66087 66181 65811 65906 66001 66096 66191 65820 65916 66011 66106 66200 65830 65925 66020 66115 66210 65839 65935 66030 66124 66219 65849 65944 66039 66134 66229 65858 65954 66049 66143 66238 65868 65963 66058 66153 66247 65877 65973 66068 66162 66257 65887 65982 66077 66172 66266 No. 1 2 3 4 5 6 7 8 9 1 Page 598] TABLE 42. Logarithms of Numbers. No. 4600 5200. « Log. 66276- ^71600. No. . 1 2 8 4 fi 7 8 9 460 461 66276 66370 66285 66380 6()295 66389 66304 66398 66314 66408 66323 66417 66332 66427 66342 66436 66351 66445 66361 66455 •10 1 1 2 462 66464 66474 66483 66492 66502 66511 66521 66530 66539 66549 1 463 66558 6659r 66577 66586 66596 66605 66614 66624 66633 66642 2 464 66652 66661 66755^ 66671 66764 66680 66773" 66689 66783 66699 66792 66708 66801 66717 66727 66820 66736 66829 3 4 5 6 3 4 5 465 66745 66811 466 66839 66848 66857 66867 66876 66885 66894 66904 (>6913 66922 467 66932 66941 66950 66960 66969 66978 (56987 66997 67006 67015 1^ 468 67025 67034 67043 67052 67062 67071 67080 67089 67099 67108 8 9 1 469 67117 67127 67136 67145 67237 67330 67154 67164 67173 67182 67274 67191 67284 67201 67293 8 9 470 67210 67219 67228 67247 67339 67256 67265 471 67302 6731 1 67321 67348 67357 67367 67376 67385 472 67394 {)7403 67413 67422 67431 67440 67449 67459 67468 67477 473 67486 67495 67504 67514 67523 67532 67541 67550 67560 67569 474 475 67578 67669^ 67587 67679 67596 67688 67605 67697 67614 67706 67624 67715 67633 67724' 67642 677^3 67651 67742 67660 67752 476 67761 67770 67779 67788 67797 67806 67815 67825 67834 67843 477 67852 67861 67870 67879 67888 67897 67906 67916 67925 67934 478 67943 67952 67961 67970 67979 67988 67997 68006 68015 68024 479 68034 68124 68043 68133 68052 68142 68061 68151 68070 68160 68079 68169" 68088 68178 68097 68187 68106 68196 68115 68205 480 481 68215 68224 68233 68242 68251 68260 68269 68278 68287 68296 482 68m5 68314 68323 68332 68341 68350 68:^59 68368 68377 68386 483 484 485 486 68395 68485 68574 68664 68404 68494 68583' 68673 68413 68502 68592 68681 68422 68511 68431 68520 68440 68529 68449 68538 68628 68717 68458 68547 68467 68556 68476 68565 9 68601 68690 68610 68699 68619 68708 68637 68726 68646 68735 68655 68744 1 1 487 68753 68762 68771 68780 68789 68797 68806 68815 68824 68833 9 2 488 68842 68851 68860 68869 68878 68886 68895 68904 68913 68922 ;] o 489 490 68931 68940 69028 68949 69037 68958 69046 68966 69055 68975 69064 68984 69073 68993 69082 69002 69090 69011 4 5 4 5 69020 69099 491 69108 69117 69126 69135 69144 69152 69161 69170 69179 69188 6 5 492 69197 69205 69214 69223 69232 69241 69249 69258 69267 69276 7 6 493 69285 69294 69302 69311 69320 69329 69338 69346 69355 69364 8 7 494 69373 69381 69390 69399 69408 69417 69425 69434 69443 69452 9 8 495 496 69461 69548 69469 69557 69478 69566 69487 69574 69496 69583 69504 69592 69513 69601 69522 69609 69531 69618 69539 69627 497 69636 69644 69653 69662 69671 69679 69688 69697 69705 69714 498 69723 69732 69740 69749 69758 69767 69775 69784 69793 69801 499 69810 69897 69819 69827 69836 69845 69854 69940 69862 69949 69871 69958 69880 69966 69888 69975 500 69906 69914 69923 69932 501 69984 69992 70001 70010 70018 70027 70036 70044 70053 70062 502 70070 70079 70088 70096 70105 70114 70122 70131 70140 70148 503 70157 70165 70174 70183 70191 70200 70209 70217 70226 70234 504 70243 70252 70260 70269 70278 70286 70295 70381' 70303 70389 70312 70398 70321 505 70329 70338 70346 70355 70364 70372 70406 506 70415 70424 70432 70441 70449 70458 70467 70475 70484 70492 507 70501 70509 70518 70526 70535 70544 70552 70561 70569 70578 508 509 70586 70672 70595 70680 70603 70689 70612 70697 70621 70706 70629 70714 70800 70638 70723 70808 70646 70731 70817 70655 70740 70825 70663 70749 „ 8 510 70757 70766 70774 70783 70791 70834 511 70842 70851 70859 70868 70876 70885 70893 70902 70910 70919 1 1 512 70927 70935 70944 70952 70961 70969 70978 70986 70995 71003 ?. 2 513 71012 71020 71029 71037 71046 71054 71063 71071 71079 71088 3 2 514 71096 71105 71113 71122 71130 71139 71147 71155 71240 71164 71248 71172 71257 4 5 3 4 515 71181 71189 71198 71206 71214 71223 71231 516 71265 71273 71282 71290 71299 71307 71315 71.324 71332 71341 6 5 517 71349 71357 71366 71374 71383 71391 71399 71408 71416 71425 7 6 518 71433 71441 71450 71458 71466 71475 71483 71492 71500 71508 8 6 519 71517 71525 71533 71542 71550 71559 71567 71575 71584 71592 9 7 No. 1 2 « 4 5 6 7 8 9 1 TABLE 42. Logarithms of Numbers. [Page 699 No 5200 5800. Log. 71600 76343. No. 1 2 3 4 5 6 7 8 9 1 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 71600 71684 71767 71850 71933 71609 71692 71775 71858 71941 71617 71700 71784 71867 71950 71625 71709 71792 71875 71958 71634 71717 71800 71883 71966 71642 71725 71809 71892 71975 71650 71734 71817 71900 71983 71659 71742 71825 71908 71991 71667 71750 71834 71917 71999 72082 72165 72247 72329 72411 72493 72575 72656 72738 72819 72900 72981 73062 73143 73223 71675 71759 71842 71925 72008 72090 72173 72255 72337 72419 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 5 6 7 8 72016 72099 72181 72263 72346 72428 72509 72591 72673 72754 ~ 72835 72916 72997 73078 73159 72024 72107 72189 72272 72354 72032 72115 72198 72280 72362 72041 72123 72206 72288 72370 72049 72132 72214 72296 72378 72057 72140 72222 72304 72387 72066 72148 72230 72313 72395 72074 72156 72239 72321 72403 72436 72518 72599 72681 72762 72444 72526 72607 72689 72770 72452 72534 72616 72697 72779 72460 72542 72624 72705 72787 72469 72550 72632 72713 72795 72477 72558 72640 72722 72803 72485 72567 72648 72730 72811 72501 72583 72665 72746 72827 72908 72989 73070 73151 73231 72843 72925 73006 73086 73167 72852 72933 73014 73094 73175 7^860 72941 73022 73102 73183 72868 72949 73030 73111 73191 73272 73352 73432 73512 73592 72876 72957 73038 73119 73199 73280 73360 73440 73520 73600 73679 73759 73838 73918 73997 72884 72965 73046 73127 73207 73288 73368 73448 73528 73608 72892 72973 73054 73135 73215 73296 73376 73456 73536 73616 73239 73320 73400 73480 73560 73247 73328 73408 73488 73568 73255 73336 73416 73496 73576 73263 73344 73424 73504 73584 73304 73384 73464 73544 73624 73312 73392 73472 73552 73632 8 73640 73719 73799 73878 73957. 74036 74115 74194 74273 74351 73648 73727 73807 73886 73965 73656 73735 73815 73894 73973 73664 73743 73823 73902 73981 73672 73751 73830 73910 73989 73687 73767 73846 73926 74005 73695 73775 73854 73933 74013 73703 73783 7.3862 73941 74020 74099 74178 74257 74335 74414 74492 74570 74648 74726 74803 73711 73791 73870 73949 74028 74107 74186 74265 74343 74421 1 2 3 4 5 6 7 8 9 1 2 2 3 4 5 6 6 7 74044 74123 74202 74280 74359 74052 74131 74210 74288 74367 74060 74139 74218 74296 74374 74068 74147 74225 74304 74382 74076 74155 74233 74312 74390 74084 74162 74241 74320 74398 74092 74170 74249 74327 74406 74429 74507 74586 74663 74741 74437 74515 74593 74671 74749 74445 74523 74601 74679 74757 74453 74531 74609 74687 74764 74461 74539 74617 74695 74772 74468 74547 74624 74702 74780 74476 74554 74632 74710 74788 74484 74562 74640 74718 74796 74500 74578 74656 74733 74811 74889 74966 75043 75120 75197 75274 75351 75427 75504 75580 74819 74896 74974 75051 75128 74827 74904 74981 75059 75136 74834 74912 74989 75066 75143 74842 74920 74997 75074 75151 74850 74927 75005 75082 75159 74858 74935 75012 75089 75166 74865 74943 75020 75097 75174 74873 74950 75028 75105 75182 74881 74958 75035 75113 75189 75266 75343 75420 75496 75572 '75648 75724 75800 75876 75952 75205 75282 75358 75435 75511 75587 75664 75740 75815 75891 75213 75289 75366 75442 75519 75595 75671 75747 75823 75899 75220 75297 75374 75450 75526 75603 75679 75755 75831 75906 75228 75305 75381 75458 75534 75610 75686 75762 75838 75914 75236 75312 75389 75465 75542 75618 75694 75770 75846 75921 75243 75320 75397 75473 75549 75626 75702 75778 75853 75929 75251 75328 75404 75481 75557 75633 75709 75785 75861 75937 75259 75335 75412 75488 75565 75641 75717 75793 75868 75944 7 570 571 572 573 574 75656 757.32 75808 75884 75959 1 2 3 4 5 6 7 8 9 1 1 2 3 4 4 5 6 6 575 576 577 578 579 75967 76042 76118 76193 76268 75974 76050 76125 76200 76275 75982 76057 76133 76208 76283 75989 76065 76140 76215 76290 75997 76072 76148 76223 76298 76005 76080 76155 76230 76305 76012 76087 76163 762.38 76313 76020 76095 76170 76245 76320 76027 76103 76178 76253 76328 76035 76110 76185 76260 76335 No. 1 8 » 4 5 « 7 8 9 1 Page 600J TABLE 42. Logarithms of Numbers. No. 5800 WOO. Log. 76343 80618. 1 No. 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 1 • i 3 4 5 6 7 76395 76470 76545 76619 76693 "76768 76842 76916 76989 77063 77137 77210 77283 77357 77430 8 1 76343 76418 76492 76567 76641 76716 76790 76864 76938 77012 "77085" 77159 77232 77305 77379 1 76360 76425 76500 765y 76649 ; 76723 ' 76797 76871 7«>945 77019 " 77093" ■ 77166 77240 77313 77386 76358 76433 76507 76582 7(5656 "76730" 76805 76879 76953 77026 "77100" 77173 77247 77320 77393 76365 76440 76515 76589 76664 76373 76448 76522 76597 76671 76380 76455 76530 76604 76678 76388 76462 76537 76612 76686 76403 76477 76552 76626 76701 76775 76849 76923 76997 77070 77144 77217 77291 77364 77437 76410 76485 76559 76634 76708 8 1 2 3 4 6 6 7 8 9 1 2 2 3 4 6 6 6 7 76738 76812 76886 76960 77034 76745 76819 76893 76967 77041 76753 76827 76901 76975 77048 76760 76834 76908 76982 77056 77129 77203 77276 77349 77422 76782 76856 76930 77004 77078 77151 77225 77298 77371 77444 77107 77181 77254 77327 77401 77115 77188 77262 77335 77408 77122 77195 77269 77342 77415 595 596 597 598 599 77452 77525 77597 77670 77743 77459 77532 77605 77677 77750 77466 77539 77612 77685 77757 77474 77546 77619 77692 77764 77481 77554 77627 77699 77772 77488 77561 77634 77706 77779 77495 77568 77641 77714 77786 77503 77576 77648 77721 77793 77866" 77938 78010 78082 78154 77510 77583 77656 77728 77801 77873" 77945 78017 78089 78161 78233 78305 78376 78447 78519 77517 77590 77J563 77735 77808 77880 77952 78025 78097 78168 600 601 602 603 604 77815 77887 77960 78032 78104 77822 77895 77967 78039 78111 78183" 78254 78326 78398 78469 77830 77902 77974 78046 78118 78190 78262 78333 78405 78476 78547 78618 78689 78760 78831 77837- 77909 77981 78053 78125 77844 77916 77988 78061 78132 77851 77924 77996 78068 78140 78211 78283 78355 78426 78497 77859. 77931 78003 78075 78147 7 605 606 607 608 609 78176 78247 78319 78390 78462 78197 78269 78340 78412 78483 78204 78276 78347 78419 78490 78219 78290 78362 78433 78504 ^ 78226 78297 78369 78440 78512 78240 78312 78383 78455 78526 1 2 3 4 5 6 -7 8 9 1 1 2 3 4 4 5 6 6 610 611 612 613 614 615 616 617 618 619 78533 78604 78675 78746 78817 78888 78958 79029 79099 79169 78540 78611 78682 78753 78824 78554 78625 78696 78767 78838 78909 78979 79050 79120 79190 78561 78633 78704 78774 78845 78569 78640 78711 78781 78852 78923 78993 79064 79134 79204 78576 78647 78718 78789 78859 78930 79000 79071 79141 79211 78583 78654 78725 78796 78866 78937 79007 79078 79148 79218 78590 78661 78732 78803 78873 78944 79014 79085 79155 79225 78597 78668 78739 78810 78880 78951 79021 79092 79162 79232 78895 78965 79036 79106 79176 78902 78972 79043 79113 79183 78916 78986 79057 79127 79197 620 621 622 623 624 625 62(5 627 628 629 79239 79309 79379 79449 79518 79246 79316 79386 79456 • 79525 79253 79323 79393 79463 79532 79260 79330 79400 79470 79539 79267 79337 79407 79477 79546 79274 79344 79414 79484 79553 79281 79351 79421 79491 79560 79288 79358 79428 79498 79567 79295 79365 79435 79505 79574 79644 79713 79782 79851 79920 79989 80058 80127 80195 80264 80332 80400 80468 80536 80604 79302 79372 79442 79511 79581 79588 79657 79727 79796 79865 799;?4 80003 80072 80140 80209 8d277 80346 80414 80482 80550 79595 79664 79734 79803 79872 79602 79671 79741 79810 79879 79609 79678 79748 79817 79886 79616 79685 79754 79824 79893 79623 79692 79761 79831 79900 79630 79699 79768 79837 79906 79637 79706 79775 79844 79913 79982 80051 80120 80188 80257 80325 80393 80462 80530 80598 79650 79720 79789 79868 79927 6 630 631 632 633 634 635 636 637 638 639 79941 80010 80079 80147 80216 80284 80353 80421 80489 80557 79948 80017 80085 80154 80223 80291 80359 80428 80496 805^4 79955 80024 80092 80161 80229 79962 80030 80099 80168 80236 79969 80037 80106 80175 80243 80312" 80380 80448 80516 80584 79975 80044 80113 80182 80250 80318 80387 80455 80523 80691 79996 80065 80134 80202 80271 80339" 80407 80475 80543 80611 1 2 3 4 5 6 7 8 9 1 1 2 2 3 4 4 5 5 80298 80366 80434 80502 80570 80305 80373 80441 80509 80577 No. 1 2 3 4 o 6 7 8 9 1 TABLE 42. [Page 601 Logarithms of Numbers. No . 6400 7000. Log. 80G18 84510. 1 No. 1 2 3 4 5 6 7 8 9 640 641 80618 80686 80625 80693 80632 80699 80638 80706 80645 80713k 80652 80720 80659 80726 80665 80733 80672 80740 80679 80747 1 ' 1 642 80754 80760 80767 80774 80781 80787 80794 80801 80808 80814 1 1 1 643 80821 80828 80835 80841 80848 80855 80862 80868 80875 80882 2 i 1 644 645 80889 80895 80902 80909 80916 80922 80929 80936 80943 80949 3 ; 2 4 i 3 5 4 6 1 4 7 i 5 8 ; 6 9 6 ■ 80956 80963 80969 80976 80983 80990 80996 81003 81010 81017 646 81023 81030 81037 81043 81050 81057 81064 81070 81077 81084 647 81090 81097 81104 81111 81117 81124 81131 81137 81144 81151 648 81158 81164 81171 81178 81184 81191 81198 81204 81211 81218 649 81224 81231 81238 81245 81251 81258 81265 81271 81278 81285 650 81291 81298 81305 81311 81318 81325 81331 81338 81345 81351 651 81358 81365 81371 81378 81385 81391 81398 81405 81411 81418 652 81425 81431 81438 81445 81451 81458 81465 81471 81478 81485 653 81491 81498 81505 81511 81518 81525 81531 81538 81544 81551 654 81558 81564 81571 81578 81584 81591 81598 81604 '81671 81611 81677 81617 655 81624 81631 81637 81644 81651 81657 81664 81684 656 81690 81697 81704 81710 81717 81723 81730 81737 81743 81750 657 81757 81763 81770 81776 81783 81790 81796 81803 81809 81816 658 81823 81829 81836 81842 81849 81856 81862 81869 81875 81882 659 81889 81895 81902 81968 81908 81974 81915 81981 81921 81987 81928 81935 81941 82007' 81948 82014 660 81954 81961 81994 82000 661 82020 82027 82033 82040 82046 82053 82060 82066 82073 82079 662 82086 82092 82099 82105 82112 82119 82125 82132 82138 82145 663 82151 82158 82164 82171 82178 82184 82191 82197 82204 82210 664 665 82217 82223 82230 82236 82243 82249 82256 82263 82269 82334 82276 82282 82289 8229"5 82302 82308 82315 82321 82328 82341 666 82347 82354 82360 82367 82373 82380 82387 82393 82400 82406 667 82413 82419 82426 82432 82439 82445 82452 82458 82465 82471 668 82478 82484 82491 82497 82504 82510 82517 82523 82530 82536 669 82543 82549 82556 82562 82569 82575 82582 82588 82595 82601 670 82607 82614 82620 82627 82633 82640 82646 82653 82659 82666 671 82672 82679 82685 82692 82698 82705 82711 82718 82724 82730 672 - 82737 82743 82750 82756 82763 82769 82776 82782 82789 82795 673 82802 82808 82814 82821 82827 82834 82840 82847 82853 82860 674 82866 82872 82879 82885 82892 82898 82905 82911 82918 82982 82924 675 82930 82937 82943 82950 82956 82963 82969 82975 82988 676 82995 83001 83008 83014 83020 83027 83033 83040 83046 83052 677 83059 83065 83072 83078 83085 83091 83097 83104 83110 83117 678 83123 83129 83136 83142 83149 83155 83161 83168 83174 83181 679 680 83187 83193 83200 83206 83213 83219 83225' 83289 83232 83296 83238 83302 83245 83308 83251 83257 83264 83270 83276 83283 681 83315 83321 83327 83334 83340 83347 83353 83359 83366 83372 682 83378 83385 83391 83398 83404 83410 83417 83423 83429 83436 683 83442 83448 83455 83461 83467 8.3474 83480 8.3487 83493 83499 684 685 83506 83569 83512 83575 83518 83525 83531 83537 83601 83544 83607 83550 83613 83556 83620 83563 83626 83582 83588 83594 686 83632 83639 83645 83651 83658 83664 83670 83677 83683 83689 687 83696 83702 83708 83715 83721 83727 83734 83740 83746 83753 688 689 83759 83822 83765 83828 83771 83835 83778 83841 83784 83847 83790 83853 83797 83860 83803 83866 83809 83872 83816 83879 ! 6 690 83885 83891 83897 83904 83910 83916 83923 83929 83935 83942 691 83948 83954 83960 83967 83973 83979 83985 83992 83998 84004 1 1 692 84011 84017 84023 84029 84036 84042 84048 84055 84061 84067 2 1 693 84073 84080 84086 84092 84098 84105 84111 84117 84123 84130 3 2 694 84136 84142 84148 84155. 84161 84167 84173 84180 84186 84248 84192 84255 4 2 5 3 695 84198 84205 84211 84217 84223 84230 84236 84242 696 84261 84267 84273 84280 84286 84292 84298 84305 84311 84317 6 , 4 697 84323 84330 84336 84342 84348 84354 84361 84367 84373 84379 7 ! 4 698 84386 84392 84398 84404 84410 84417 84423 84429 84435 84442 8 5 699 84448 84454 84460 84466 84473 84479 84485 84491 84497 84504 9 ; 5 No. 1 2 3 4 5 6 7 8 9 Pag e602] TABLE 42. IjOgarithms of Numbers. No. 7000 7600. Log. 84510 88081. 1 No. 1 i 8 1 4 6 1 6 7 1 8 1 700 701 702 703 704 84510 84572 84634 84696 84757 84516 84578 84640 84796 84763 84522 84584 84646 84708 84770 84528 84590 84652 84714 84776 84535 84597- 84658 1 84720 84782 84541 84603 84665 84726 84788 84547 84553 84609 84615 84671 84677 84733 84739 84794 ! 84800 84559 84566 1 1 7 84621 ! 84683 i 84745 ! 84807 ; 84628 84689 84751 84813 1 2 i 3 I .4 5 ! 6 i 7 -i 8 9 1 1 2 3 4 4 5 6 6 705 706 707 708 709 710 711 712 713 714 84819 84880 ■ 84942 85003 85065 84825 { 84887 84948 85009 85071 ' 84831 84893 84954 85016 85077 85138 85199 85260 85321 85382 84837 84899 84960 • 85022 85083 84844 84905 84967 85028 85089 84850 1 84911 ' 84973 ' 85034 < 85095 i 85156 85217 85278 85339 85400 84856 i 84862 84917 ! 84924 84979 84985 85040 85046 85101 ! 85107 85163 85169 84868 : 84930 i 84991 85052 85114 84874 84936 84997 85058 85120 85126 85187 85248 85309 85370 85132 85193 85254 85315 85376 85144 85205 85266 85327 85388 85150 85211 85272 85333 85394 85175 85236 85297 85358 85418 85181 85242 85303 85364 85425 85224 ' 85285 85345 85406 85291 85352 85412 715 716 717 718 719 85431 85491 85552 85612 85673 85437 85497 85558 85618 85679 85443 85503 85564 85625 85685 85449 85509 85570 85631 85691 85455 85516 85576 85637 85697 85461 85522 85582 85643 85703 85467 85473 85528 85534 85588 85594 85649 1 85655 85709 i 85715 85479 1 85540 85600 85661 85721 85485 85546 85606 85667 85727 720 721 722 723 724 725 726 727 728 729 85733 85794 85854 85914 85974 85739 85800 85860 85920 85980 85745 85806 85866 85926 85986 85751 85812 85872 85932 85992 86052 86112 86171 86231 86291 85757 85818 85878 85938 85998 85763 85824 85884 85944 86004 86064 86124 86183 86243 86303 85769 : 85775 85830 1 85836 85890 1 85896 85950 85956 85781 85842 85902 85962 86022 85788 85848 85908 85968 86028 86088 86147 86207 86267 86326 86386 86445 86504 86564 86623 86010 86070 ■' 86130 86189 86249 86308 86016 1 2 3 4 5 6 7 8 9 6 1 1 2 2 3 4 4 5 5 86034 86094 86153 86213 86273 86040 86100 86159 86219 86279 86046 86106 86165 86225 86285 86058 86118 86177 86237 86297 86076 86136 86195 86255 86314 86082 86141 86201 86261 86320 730 . 731 732 733 734 86332 86392 86451 86510 86570 86338 86398 86457 86516 86576 86635 86694 86753 86812 86870 86344 86404 86463 86522 86581 86641 86700 86759 86817 86876 86935 86994 87052 87111 87169 86350 86410 86469 86528 86587 86646 86705 86764 86823 86882 86356 86415 86475 86534 86593 86362 86421 86481 86540 86599 86368 i 86374 86427 ■ 86433 86487 86493 8a546 86552 86605 86611' 86380 86439 86499 86558 86617 735 736 737 738 739 86629 86688 86747 86806 86864 86652 86711 86770 86829 86888 86658 86717 86776 86835 86894 86664 86670 i 86676 86682 86741 86800 86859 86917 86723 86782 .86841 86900 86729 86735 86788 86794 86847 1 86853 86906 1 86911 740 741 742 743 744 86923 86982 87040 87099 87157 86929 86988 87046 87105 87163 86941 86999 87058 87116 87175 86947 87005 87064 87122 87181 86953 87011 87070 87128 87186 86958 87017 87075 87134 87192 86964 87023 87081 87140 87198 1 86970 87029 1 87087 87146 87204 86976 87035 87093 87151 87210 87268 87326 87384 87442 87500 745 746 747 748 749 87216 87274 87332 87390 87448 87221 87280 87338 87-396 87454 87227 87286 87344 87402 87460 87233 87291 87349 87408 87466 87239 87297 87355 87413 87471 87245 87303 87361 87419 87477 87251 87309 87367 87425 87483 87256 87315 87373 87431 87489 87262 87320 87379 87437 87495 1 2 3 4 5 6 7 8 9 5 750 751 752 753 754 87506 87564 87622 87679 87737 87512 87570 87628 1 87685 87743 87518 87576 87633 87691 87749 87523 87581 87639 87697 87754 87529 87587 87645 87703 87760 87535 87593 87651 87708 87766 87541 87599 87656 87714 87772 87547 87604 87662 87720 87777 87552 87610 87668 87726 87783 875"58 87616 87674 87731 87789 1 1 2 2 3 3 4 4 5 755 756 757 758 759 87795 87852 87910 87967 88024 87800 87858 87915 87973 88030 87806 87864 ; 87921 ! 87978 88036 87812 87869 87927 87984 88041 87818 87875 87933 87990 88047 87823 87881 87938 87996 88053 87829 87887 87944 88001 88058 87835 87892 87950 88007 88064 87841 87898 87955 88013 88070 87846 87904 87961 88018 88076 No. 1 1 ^ 8 4 5 6 ' 8 » 1 TABLE 42. [Page 603 Logarithms of Numbers. No. 7600 8200. Log. 88081 91381. 1 No. 1 2 8 * 5 6 7 8 9 760 761 88081 88138 88087 88144 88093 88150 88098 88156 88104 88161 88110 88167 88116 88173 88121 88178 88127 88184 88133 88190 1 6 762 88195 88201 88207 88213 88218 88224 88230 88235 88241 88247 1 1 763 88252 88258 88264 88270 88275 88281 88287 88292 88298 88304 2 1 764 765 88309 "88366 88315 88"372 88321 88326 88332 88338 88343 88349 88406 88355 88412 88360 88417 3 i 2 A O 88377 88383 88389 88:395 88400 5 6 7 3 4 4 766 88423 88429 88434 88440 •88446 88451 88457 88463 88468 88474 767 88480 88485 88491 88497 88502 88508 88513 88519 88525 88530 768 88536 88542 88547 88553 88559 88564 88570 88576 88581 88587 769 88593 88598 88604 88610 88615 88672 88621 88677 88627 88683 88632 88689 88638 88694 88643 88700 9 1 5 770 88649 88655 88660 88666 771 88705 88711 88717 88722 88728 88734 88739 88745 88750 88756 772 88762 88767 88773 88779 88784 88790 88795 88801 88807 88812 773 88818 88824 88829 88835 88840 88846 88852 88857 88863 88868 774 775 88874 88930 88880 88885 88891 88897 88902 88908 88913 88919 88975 88925 88936 88941 88947 88953 88958 88964 88969 88981 776 88986 88992 88997 89003 89009 89014 89020 89025 89031 89037 777 89042 89048 89053 89059 89064 89070 89076 89081 89087 89092 778 89098 89104 89109 89115 89120 89126 89131 89137 89143 89148 779 89154 89159 89165 89170 89176 89182 89237 89187 89193 89198 89204 89260 780 89209 89215 89221 89226 89232 89243 89248 89254 781 89265 89271 89276 89282 89287 89293 89298 89304 89310 89315 782 89321 89326 89332 89337 89343 89348 89354 89360 89365 89371 783 89376 89382 89387 - 89393 89398 89404 89409 89415 89421 89426 784 89432 89437 89443 89448 89454 89459 89515 89465 89520 89470 89526 89476 89531 89481 89537 785 89487 89492 89498 89504 89509 786 89542 89548 89553 89559 89564 89570 89575 89581 89586 89592 787 89597 89603 89609 89614 89620 89625 89631 89636 89642 89647 788 89653 89658 89664 89669 89675 89680 89686 89691 89697 89702 789 790 89708 89713 89719 89724 89730 89735 89741 89746 89752 89757 89763 89768 89774 89779 89785 89790 89796 89801 89807 89812 791 89818 89823 89829 898^4 89840 89845 89851 89856 89862 89867 792 89873 89878 89883 89889 89894 89900 89905 89911 89916 89922 793 89927 89933 89938 89944 89949 89955 89960 89966 89971 89977 794 89982 89988 89993 89998 90004 90009 90015 90069 90020 90075 90026 90080 90031 90086 795 90037 90042 90048 90053 90059 90064 796 90091 90097 90102 90108 90113 90119 90124 90129 90135 90140 797 90146 90151 90157 90162 90168 90173 90179 90184 90189 90195 798 90200 90206 90211 90217 90222 90227 90233 90238 90244 90249 799 800 90255 90309 90260 90266 90271 90325 90276 90282 90287 90293 90:347 90298 90352 90;304 90358 90314 90320 90331 90336 90342 801 90363 90369 90374 90380 90385 90390 90396 90401 90407 90412 802 90417 90423 90428 90434 90439 90445 90450 90455 90461 9046() 803 90472 90477 90482 90488 90493 90499 90504 90509 90515 90520 804 90526 90531 90536 90542 90547 90553 90558 90563 90617 90569 90623" 90574 90628 805 90580 90585 90590 90596 90601 90607 90612 806 90634 90639 90644 90650 90655 90660 90666 90671 90677 90682 807 90687 90693 90698 90703 90709 90714 90720 90725 90730 907:36 808 809 90741 90795 90747 90800 90752 90806 90757 90811 90763 90816 90768 90822 90773 90827 90779 90832 90886 90784 90838 90891 90789 90843 5 810 90849 90854 90859 90865 90870 90875 90881 90897 811 90902 90907 90913 90918 90924 90929 90934 90940 90945 90950 1 1 812 90956 90961 90966 90972 90977 90982 90988 90993 90998 91004 2 1 813 91009 91014 91020 91025 91030 91036 91041 91046 91052 91057 3 2 814 91062 91068 91073 91078 91132^ 91084 91137 91089 91142 91094 91148 91100 91153 91105 91110 4 5 2 3 815 91116 91121 91126 91158 91164 816 91169 91174 91180 91185 91190 91196 91201 91206 91212 91217 6 3 817 91222 91228 91233 91238 91243 91249 91254 91259 91265 91270 7 4 818 91275 91281 91286 91291 91297 91302 91307 91312 91318 91323 8 4 819 91328 91334 91339 91344 91350 91355 91360 91365 91371 91376 9 5 No. 1 2 3 4 5 « 7 8 9 1 Page 604] TABLE 42. Logarithms of Numbers. No. 8200 8800. Log. 91381 94448 No. 1 2 S 4 5 6 7 8 9 1 820 821 91381 91434 91387 91440 91392 91445 91397 91450 91403 91466 91408 91461 91413 91466 91418 91424 91429 91482 6 91471 91477 822 91487 91492 91498 91503 91608 91514 91619 91524 91629 91535 1 1 823 91540 9154» 91551 91556 91561 91566 91572 91577 91682 91687 1 824 91593 91598 91603 91609 91614 91619 91624 91630 91635 91640 3 4 2 3 4 4 6 5 825 91645 91661 91656 91661 91666 91672 91677 91682 91687 91693 826 91698 91703 91709 91714 91719 91724 91730 91735 91740 91745 6 827 91751 91756 91761 91766 91772 91777 91782 91787 91793 91798 828 91803 91808 91814 91819 91824 91829 91834 91840 91845 91850 8 9 829 91855 91861 91866 91871 91876 91882 91887 91892 91897 91903 830 91908 91913 91918 91924 91929 91934 91939 91944 91950 91955 831 91960 91965 91971 91976 91981 91986 91991 91997 92002 92007 832 92012 92018 92023 92028 92033 92038 92044 92049 92054 92059 833 92065 92070 92075 92080 92085 92091 92096 92101 92106 92111 834 92117 92122 92127 92132 92137 92143 92148 92153 92158 92205' 92210 92163 835 92169 92174 92179 92184 92189 92195 92200 92215 836 92221 92226 92231 92236 92241 92247 92252 92257 92262 92267 837 92273 92278 92283 92288 92293 92298 92304 92309 92314 92319 838 92324 92330 92335 92340 92345 92360 92355 92361 92366 92371 839 92376 92381 92387 92392 92397 92402 92454 92407 92459 92412 92418 92464 92469 92423 92474 840 92428 92433 92438 92443 92449 841 92480 92485 92490 92495 92500 92505 92511 92616 92521 92526 842 92531 92536 92542 92547 92552 92557 92562 92567 92572 92578 843 844 92583 92634 92588 92639 92593 92645 92598 92650 92603 92655 92609 92660 92614 J 92665 92619 92624 92670 92676 92722 92727 92629 92681 5 845 92686 92691 92696 92701 92706 92711 92716 92732 846 92737 92742 92747 92752 92758 92763 92768 92773 92778 92783 1 2 1 1 9 847 92788 92793 92799 92804 92809 92814 92819 92824 92829 92834' 848 92840 92845 92860 92855 92860 92865 92870 92876 92881 92886 849 92891 92896 92901 92906 92911 92916 92921 92927 92932 92983 92937 4 5 2 3 850 92942 92947 92952 92967 92962 92967 92973 92978 92988 851 92993 92998 93003 93008 93013 93018 93024 93029 93034 93039 6 3 852 93044 93049 93054 ~ 93059 93064 93069 93075 93080 93085 93090 7 4 853 93095 93100 93106 93110 93115 93120 93125 93131 93136 93141 8 4 854 93146 93151 93156 93161 93166 93217 93268 93171 93222 93273 93176 93181 93186 93192 9 5 855 856 93197 93247 93202 93252 93207 93258 93212 93263 93227 93278 93232 93237 93283 93288 93242 93293 857 93298 93303 93308 93313 93318 93323 93328 93334 93339 93344 858 93349 93354 93359 93364 93369 93374 93379 93384 93389 93394 859 93399 93404 93409 93414 93420 93425 93430 93435 93440 93490 93445 860 93450 93455 93460 93465 93470 93475 93480 93486 93495 861 93500 93505 93510 93515 93520 93526 93631 93536 : 93541 93546 862 93551 93556 93561 93566 93571 93576 93581 93586 93591 93596 863 93601 93606 93611 93616 93621 93626 93631 93636 93641 93646 864 865 93651 93702 93656 93707 93661 93712 93666 93717 93671 93722 93676 93727 93682 93687 93692 93737 93742 93697 93747 93732 866 93752 93757 93762 93767 93772 93777 93782 93787 93792 93797 867 93802 93807 93812 93817 93822 93827 93832 93837 93842 93847 868 869 93852 93902 93857 93907 93862 93912 93962 93867 93917 93967 93872 93922 93877 93927 93882 93932 93982 93887 93892 93937 93942 9398; "93992 93897 93947 4 870 93952 93957 93972 93977 93997 871 94002 94007 94012 94017 94022 94027 94032 94037 i 94042 94047 1 872 94052 94057 94062 94067 94072 94077 94082 94086 94091 94096 2 1 873 94101 94106 94111 94116 94121 94126 94131 94136 1 94141 94146 3 1 874 94151 94156 94161 94166 94171 94176 94181 94186 94191 94240 94196 94245 4 5 2 2 875 94201 94206 94211 94216 94221 94226 94231 94236 876 94250 94255 94260 94265 94270 94275 94280 94285 94290 94295 6 2 877 94300 94305 94310 94316 94320 94325 94330 94335 94340 94345 7 3 878 94349 94354 94359 94364 94369 94374 94379 94384 94389 94394 8 3 879 94399 94404 94409 94414 94419 94424 94429 6 94433 94438 94443 9 4 No. 1 ■ 2 3 4 5 i ' ' 8 9 1 TABLE 42. [Page 605 Logarithms of Numbers. No. 8800 9400. L og. 94448 97313 No. 94448 94498 1 2 3 4 9 6 7 8 9 1 880 881 94453 94503 94458 94507 94463 94512 94468 94517 94473 94522 94478 94527 94483 94532 94488 94537 94493 94542 5 882 94547 94552 94557 94562 94567 94571 94576 94581 94586 94591 1 1 883 94596 94601 94606 94611 94616 94621 94626 94630 94635 94640 2 1 884 8'85 94645 94694 94650 94699 94655 94704 94660 94709 94665 94670 94675 94724 94680 94729 94685 94734 94689 94738 3 4 5 6 7 8 9 2 2 3 3 4 4 5 94714 94719 886 94743 94748 94753 94758 94763 94768 94773 94778 94783 94787 887 94792 94797 94802 94807 94812 94817 94822 94827 94832 94836 888 94841 94846 94851 94856 94861 94866 94871 94876 94880 94885 889 890 94890 94939 94895 94900 94905 94910 94915 94919 94924 94929 94934 94983 94944 94949 94954 94959 94963 94968 94973 94978 891 94988 94993 94998 95002 95007 95012 95017 95022 95027 95032 892 95036 95041 95046 95051 95056 95061 95066 95071 95075 95080 893 95085 95090 95095 95100 95105 95109 95114 95119 95124 95129 894 95134 95139 95143 95148 95153 95158 95163 95168 95173 95221 95177 95226 895 95182 95'187 95192 95197 95202 95207 95211 95216 896 95231 95236 95240 95245 95250 95255 95260 95265 95270 95274 897 95279 95284 95289 95294 95299 95303 95308 95313 95318 95323 898 95328 95332 95337 95342 95347 95352 95357 95361 95366 95371 899 900 95376 95381 95386 95390 95395 95400 95405 95410 95415 95419 95424 95429 95434 95439 95444 95448 95453 95458 95463 95468 901 95472 95477 95482 95487 95492 95497 95501 95506 95511 95516 902 95521 95525 95530 95535 95540 95545 95550 95554 95559 95564 903 95569 95574 95578 95583 95588 95593 95598 95602 , 95607 95612 904 95617 95622 95626 95631 95636 95641 95646 95650 95655 95703 95660 95708 905 95665 95670 95674 95679 95684 95689 95694 95698 906 95713 95718 95722 95727 95732 95737 95742 95746 i 95751 95756 907 95761 95766 95770 95775 95780 95785 95789 95794 1 95799 95804 908 95809 95813 95818 95823 95828 95832 95837 95842 1 95847 95852 909 ' 95856 95861 95866 95914 95871 95918 95875 95923 95880 95885 95890 ! 95895 95938 95942 95899 95947 910 95904 95909 95928 95933 911 95952 95957 95961 95966 95971 95976 95980 95985 I 95990 95995 912 95999 96004 96009 96014 96019 96023 96028 96033 96038 96042 913 96047 96052 96057 96061 96066 96071 96076 96080 96085 96090 914 96095 96099 96104 96109 96114 96118 96123 96128 96133 96137 915 96142 96147 96152 96156 96161 96166 96171 96175 96180 96185 916 96190 96194 96199 96204 96209 96213 96218 96223 t 96227 96232 917 96237 96242 96246 96251 96256 96261 96265 96270 96275 96280 918 96284 96289 96294 96298 96303 96308 96313 96317 96322 9(i327 919 96332 96336 96341 96388 96346 96393 96350 96398 96355 96402 96360 96407 96365 96369 96374 920 96379 96384 96412 96417 96421 921 96426 96431 96435 96440 96445 96450 96454 96459 ! 96464 96468 922 96473 96478 96483 96487 96492 96497 96501 96506 96511 96515 923 96520 96525 96530 96534 96539 96544 96548 96553 96558 96562 924 925 96567 96572 96577 96581 96586 96591 96595 96600 96605 96609 96614 96619 96624 96628 96633 96638 96642 96647 96652 96(556 926 96661 96666 96670 96675 96680 96685 96689 96694 96699 96703 927 96708 96713 96717 96722 96727 96731 96736 96741 96745 96750 928 929 930 96755 96802 96759 96806 96853 96764 96811 96858 96769 96816 96862 96774 96820 96778 96825 96783 96830 96788 96834 96881 96792 96839 96886 96797 96844 4 96848 96867 96872 96876 96890 931 96895 96900 96904 96909 96914 96918 96923 96928 96932 96937 1 : 932 96942 96946 96951 96956 96960 96965 96970 96974 96979 96984 2 1 933 96988 96993 96997 97002 97007 97011 97016 97021 97025 97030 3 1 934 935 97035 970.39 97044 97049 97053 97058 97063 97067 97072 97118 97077 97123" 4 5 2 • 2 97081 97086 97090 97095 97100 97104 97109 97114 936 97128 97132 97137 97142 97146 97151 97155 97160 97165 97169 6 2 937 97174 97179 97183 97188 97192 97197 97202 97206 97211 97216 7 3 938 97220 97225 97230 97234 97239 97243 97248 97253 97257 97262 8 3 939 No. 97267 97271 97276 97280 97285 97290 97294 97299 97304 97308 ^ 4 1 o 3 4 5 6 7 8 9 1 Page 606] TABLE 42. Logarithms of Numbers. No. 9400 10000. Log. 97313- 99996. No. 1 i 8 4 5 * 1 8 1 » 940 97313 97317 97322 97327 97331 97336 97340 97345 1 97350 97354 5 941 97359 97364 97368 97373 97377 97382 97387 97391 97396 97400 942 97405 97410 97414 97419 97424 97428 97433 97437 97442 97447 1 1 943 97451 97456 97460 97465 97470 97474 97479 97483 97488 97493 2 1 944 945 97497 97502 97506 97511 97516 97520 97525 97529 97534 97539 97585 3 ! 2 4 1 2 97543 97548 97552 97557 97562 97566 97571 97575 97580 946 97589 97594 97598 97603 97607 97612 97617 97621 97626 \ 97630 5 1 3 947 97635 97640 97644 97649 97653 97658 97663 97667 97672 97676 6 i 3 948 97681 97685 97690 97695 97699 97704 97708 97713 97717 ! 97722 7 ! 4 949 950' 97727 97731 , 97736 97740 97745 97791 97749 97795 97754 97800 97759 97804 97763 i 97768 97809^ 97813 8 ; 4 9 i 5 97772 97777 97782 97786 951 97818 97823 97827 97832 97836 97841 97845 97850 97855 ' 97859 952 97864 97868 97873 97877 97882 97886 97891 97896 97900 97905 953 97909 97914 97918 97923 97928 97932 97937 97941 97946 i 97950 954 97955 97959 97964 97968 97973 97978 97982 98028 97987 98032 97991 1 97996 955 98000 98005 98009 98014 98019 98023 9803.7 1 98041 956 98046 98050 98055 98059 98064 98068 98073 98078 98082 ! 98087 957 98091 98096 98100 98105 98109 98114 98118 98123 98127 1 98132 958 98137 98141 98146 98150 98155 98159 98164 98168 98173 1 98177 959 98182 98227 98186 98191 98195 98200 98245 98204 98209 98214 98218 ! 98223 98263 98268 960 98232 98236 98241 98250 98254 98259 961 98272 98277 98281 98286 98290 98295 98299 98304 98308 98313 962 98318 98322 98327 98331 98336 98340 98345 98349 98354 98358 963 98363 98367 98372 98376 98381 98385 98390 98394 98399 98403 964 965 98408 98453 98412 98457 98417 98421 98426 98430 98435 98439 98444 , 98448 98462 98466 98471 98475 98480 98484 98489 98493. 966 98498 98502 98507 98511 98516 98520 98525 98529 98534 98538 967 98543 98547 98552 98556 98561 98565 98570 98574 98579 1 98583 968 98588 98592 98597 98601 98605 98610 98614 98619 98623 98628 969 970 98632 98637 98641 98646 98650 98655 98659 98664 98709 98668 : 98673 98713 98717 98677 98682 98686 98691 98695 98700 98704 971 98722 98726 98731 98735 98740 98744 98749 98753 98758 98762 972 98767 98771 98776 98780 98784 98789 98793 98798 98802 98807 973 98811 98816 98820 98825 98829 98834 98838 98843 98847 : 98851 974 98856 98860 98865 98869 98874 98878 98883 98887 98892 98896 98941 975 9890'0 98905 98909 98914 98918 98923 98927 98932 98936 976 98945 98949 98954 98958 98963 98967 98972 98976 98981 98985 977 98989 98994 98998 99003 99007 99012 99016 99021 99025 99029 978 99034 99038 99043 99047 99052 99056 99061 99065 99069 99074 979 99078 99083 99127 99087 99092 99096 99140 99100 99145 99105 99149 99109 99154 99114 99118 99162 980 99123 99131 99136 99158 981 99167 99171 99176 99180 99185 99189 99193 99198 99202 99207 982 99211 99216 99220 99224 99229 99233 99238 99242 99247 99251 983 99255 99260 99264 99269 99273 99277 99282 99286 99291 99295 984 99300 99304 99308 99313 99317 99322 99326 99330 99335 99339 985 99344 99348 99352 99357 99361 99366 99370 99374 99379 99383 986 99388 99392 99396 99401 99405 99410 99414 99419 99423 99427 987 99432 99436 99441 99445 99449 99454 99458 99463 99467 99471 988 989 990 99476 99520 99480 99524 99484 99528 99489 99533 99493 99537 99498 99542 99502 99546 99506 99550 99511 1 99515 99555 99559 99603 4 99564 99568 99572 99577 99581 99585 99590 99594 99599 991 99607 99612 99616 99621 99625 99629 99634 99638 99642 99647 1 ' 992 99651 99656 99660 99664 99669 99673 99677 99682 99686 99691 2 1 993 99695 99699 99704 99708 99712 99717 99721 99726 99730 99734 3 1 994 995 99739 99782' 99743 99787 99747 99791 99752 99795 99756 99760 99804~ 99765 99808 99769 99813 99774 99817 99778 99822 4 2 5 i 2 99800 996 99826 99830 99835 99839 99843 99848 99852 99856 99861 99865 6 2 997 99870 99874 99878 99883 99887 99891 99896 99900 99904 99909 7 3 998 99913 99917 99922 99926 99930 99935 99939 99944 99948 99952 n ! 999 99957 99961 99965 99970 99974 99978 99983 99987 99991 99996 9 ; 4 No. 1 2 8 4 5 a 7 8 TABLE 43. [Page 607 Logarithmic Sines, Tangents, and Secants to every Point and Quarter Point of the Compass. Points. Sine. 1 Cosine. 1 Tangent. Cotangent. Secant. Cosecant. 1 Inf. neg. 10. 00000 Inf. neg. 8.69080 9.99948 j 8.69132 8.99130 i 9.99790 8.99340 9.16652 9.99527 i 9.17125 infinite. 11. 30868 11.00660 10. 82875 10.00000 10.00052 10. 00210 10. 00473 Infinite. 11. 30920 11. 00870 10. 83348 8 71 1 u 9. 29024 9. 38557 9. 46282 9. 52749 9. 99157 9. 98679 9. 98088 9. 97384 9. 29866 9. 39879 9. 48194 9. 55365 10. 70134 10. 60121 10. 51806 10. 44635 10. 00843 10. 01321 10. 01912 10. 02616 10. 70976 10. 61443 10. 53718 10. 47251 7 6| 6J 6i 2 2i 21 9. 58284 9. 63099 9. 67339 9. 71105 9. 96562 9. 95616 9. 94543 9. 93335 9. 61722 9. 67483 9. 72796 9. 77770 10. 38278 10. 32517 10. -27204 10. 22230 10. 03438 10. 04384 10. 05457 10. 06665 10.41716 10. 36901 10. 32661 10. 28895 6 5^ 5i 3 3i 31 9.74474 9. 77503 9. 80236 9. 82708 9. 91985 9. 90483 9. 88819 9. 86979 9. 82489 9. 87020 9.91417 9. 95729 10. 17511 10. 12980 10. 08583 10. 04271 10. 08015 10. 09517 10. 11181 10. 13021 10. 25526 10.22497 10. 19764 10. 17292 5 4| ^ 4i 4 9. 84949 9. 84949 10.00000 10. 00000 10. 15051 10. 15051 4 Cosine. Sine. Cotangent. Tangent. Cosecant. Secant. Points. Page 608j TABLE U. Log. Sines, Tangents, and Secants. 0" 179° M. Hour A. M. Hour p. M. Sine. Diff. 1'. Cosecant. Tangent. Diff. 1'. Cotangent. Secant. Cosine. M. 12 Inf. neg. lniinit«. Inf. neg. Infinite. 10. 00000 10.00000 60 1 11 59 52 8 6.46373 30103 13. 53627 6. 46373 30103 13.53627 00000 00000 59 2 59 44 16 76476 17609 23524 76476 17609 23524 00000 00000 58 3 59 3t5 24 94085 12494 05915 94085 12494 05915 00000 00000 57 4 59 28 3? 40 7.06579 j 9691 7. 16270 7918 12. 93421 7. 06579 9691 12. 93421 12. 83730 00000 00000 56 55 5 11 59 20 12. 83730 7. 16270 7918 10.00000 10. 00000 6 59 12 48 24188 6694 75812 24188 6694 75812 00000 00000 54 7 59 4 56 30882 1 5800 69118 .30882 5800 69118 00000 00000 53 8 58 56 1 4 36682 5115 63318 36682 5115 63318 00000 00000 52 9 10 58 48 11 58 40 1 12 41797 4576 58203 41797 4576 58203 00000 00000 51 50 1 20 7. 46373 4139 12. 53627 7. 46373 4139 12. 53627 10. 00000 10. 00000 11 58 32 1 28 50512 3779 49488 50512 3779 49488 00000 00000 49 12 58 24 1 36 54291 3476 45709 54291 3476 45709 00000 00000 48 13 58 16 1 44 57767 3218 42233 57767 3219 42233 00000 00000 47 14 15 58 8 1 52 60985 2997 39015 60986 2996 39014 00000 00000 10. 00000 46 45 11 58 2 7. 63982 2802 12. 36018 7. 63982 2803 12. 36018 10. 00000 16 57 52 2 8 66784 2633 33216 66785 2633 33215 00000 00000 44 17 57 44 2 16 69417 2483 30583 69418 2482 30582 00001 9. 99999 43 18 57 36 2 24 71900 2348 28100 71900 2348 28100 00001 99999 42 19 20 57 28 11 57 20 2 32 2 40 74248 7. 76475 2227 2119 25752 12. 23525 74248 7. 76476 2228 25752 00001 99999 41 '40 2119 12. 23524 10. 00001 9. 99999 21 57 12 2 48 78594 2021 21406 78595 2020 21405 00001 99999 39 22 57 4 2 56 80615 1930 19385 80615 1931 19385 00001 99999 38 23 56 56 3 4 82545 1848 17455 82546 1848 17454 00001 99999 37 24 56 48 3 12 3 20 84393 1773 15607 12. 13834 84.394 1773 1704 15606 00001 99999 36 35 25 11 56 40 7.86166 1 1704 7. 86167 12. 13833 10. 00001 9. 99999 26 56 32 3 28 87870 1 1639 12130 87871 1639 12129 00001 99999 34 27 56 24 3 36 89509 ! 1579 10491 89510 1579 10490 00001 99999 33 28 56 16 3 44 91088 1524 08912 91089 1524 08911 00001 99999 32 29 56 8 3 52 92612 1472 07388 92613 1473 07387 00002 99998 31 30 11 56 4 7. 94084 1424 12. 05916 7. 94086 1424 12. 05914 10. 00002 9. 99998 30 31 55 52 4 8 95508 137£i 04492 95510 1379 04490 00002 99998 29 32 55 44 4 16 96887 1336 03113 96889 1336 03111 00002 99998 28 33 55 36 4 24 98223 1297 01777 98225 1297 01775 00002 99998 27 34 55 28 4 32 99520 1259 00480 99522 1259 00478 00002 99998 9. 99998 26 25 35 11 55 20 4 40 8.00779 1 1223 11. 99221 8. 00781 1223 11.99219 10. 00002 36 55 12 4 48 02002 -1190 97998 02004 1190 97996 00002 99998 24 37 55 4 4 56 03192 1158 96808 03194 1159 96806 00003 99997 23 38 54 56 5 4 04350 1128 95650 04353 1128 95647 00003 . 99997 22 39 54 48 5 12, 5 20 05478 1100 94522 05481 1100 94519 00003 99997 21 40 11 54 40 8. 06578 1072 11. 93422 8. 06581 1072 11. 93419 10. 00003 9. 99997 20 41 54 32 5 28 07650 1046 92350 07653 1047 92347 00003 99967 19 42 54 24 5 36 08696 1022 91.304 08700 1022 91300 00003 99997 18 43 54 16 5 44 09718 999 90282 09722 998 90278 00003 99997 17 44 45 54 8 5 52 10717 976 89283 10720 976 89280 00004 99996 16 11 54 6 8. 11693 954 11. 88307 8. 11696 955 11. 88304 10. 00004 9. 99996 15 46 53 52 6 8 12647 934 87353 12651 934 87349 00004 99996 14 47 53 44 6 16 13581 914 86419 13585 915 86415 00004 99996 13 48 53 36 6 24 14495 896 85505 14500 895 85500 00004 99996 12 49 53 28 6 32 15391 877 84609 15395 878 84605 00004 99996 11 10 50 11 53 20 6 40 8. 16268 860 11. 83732 8. 16273 860 11. 83727 10. 00005 9. 99995 51 53 12 6 48 17128 843 82872 17133 843 82867 00005 99995 9 52 53 4 6 56 17971 827 82029 17976 828 82024 00005 99995 8 53 52 56 7 4 18798 812 81202 18804 812 81196 00005 99995 / 54 55 52 48 7 12 19610 797 80390 19616 797 80384 00005 99995 6 11 52 40 7 20 8. 20407 782 11. 79593 8. 20413 782 11. 79587 10. 00006 9. 99994 5 56 52 32 7 28 21189 769 78811 21195 769 78805 00006 99994 4 57 52 24 7 36 21958 755 78042 21964 756 78036 00006 99994 3 58 52 16 7 44 22713 743 77287 22720 742 77280 00006 99994 2 59 52 8 7 52 23456 730 76544 23462 730 76538 00006 99994 1 60 M. 52 8 24186 . 717 75814 24192 718 75808 00007 99993 Hour p. M. Hour A. M. Cosine. Dlff.l'. Secant. Cotangent. Diflf.l'. Tangent. Cosecant. Sine. M. 90° 89° - TABLE 44. [Page 609 1° l,og. Sines, Tangents, and Secants 178° M. Hour A. M. Hour p. M. Sine. Dia. 1'. Cosecant. Tangent. Diff. 1'. Cotangent. Secant. Cosine. M. 11 52 8 8.24186 717 11. 75814 8. 24192 718 11. 75808 10. 00007 9. 99993 60 1 51 52 8 8 24903 706 75097 24910 706 75090 00007 99993 59 2 51 44 8 16 25609 695 74391 25616 696 74384 00007 99993 58 3 51 36 8 24 26304 684 73696 26312 684 73688 00007 99993 57 4 5 51 28 8 32 26988 673 73012 26996 673 73004 00008 10. 00008 99992 56 55 11 51 20 8 40 8. 27661 663 11. 72339 8. 27669 663 11. 72331 9. 99992 6 51 12 8 48 28324 653 71676 28332 654 71668 00008 99992 54 7 51 4 8 56 28977 644 71023 28986 643 71014 00008 99992 53 8 50 56 9 4 29621 634 70379 29629 634 70371 00008 99992 52 9 10 50 48 9 12 30255 624 69745 30263 625 69737 00009 99991 51 11 50 40 9 20 8. 30879 616 11. 69121 8. 30888 617 11.69112 10. 00009 9. 99991 50 11 50 32 9 28 31495 608 68505 31505 607 68495 00009 99991 49 12 50 24 9 36 32103 599 67897 32112 599 67888 00010 99990 48 13 50 16 9 44 32702 590 67298 32711 591 67289 00010 99990 47 14 50 8 9 52 33292 583 66708 33302 584 66698 00010 99990 46 45 15 11 50 10 8. 33875 575 11. 66125 8. 33886 575 11.66114 10. 00010 9. 99990 16 49 52 10 8 34450 568 65550 34461 568 65539 00011 99989 44 17 49 44 10 16 35018 560 64982 35029 561 64971 00011 99989 43 18 49 36 10 24 35578 553 64422 35590 553 64410 00011 99989 42 19 20 49 28 11 49 20' 10 32 10 40 36131 547 63869 36143 546 63857 00011 99989 41 8. 36678 539 11. 63322 8. 36689 540 11. 63311 10. 00012 9. 99988 40 21 49 12 10 48 37217 533 62783 37229 533 62771 00012 99988 39 22 49 4 10 56 37750 526 62250 37762 527 62238 00012 99988 38 23 48 56 11 4 38276 520 61724 38289 520 61711 00013 99987 37 24 48 48 11 12 38796 514 61204 38809 514 61191 00013 99987 36 25 11 48 40 11 20 8. 39310 508 11. 60690 8. 39323 509 11. 60677 10.00013 9. 99987 35 26 48 32 11 28 39818 502 60182 39832 502 60168 00014 99986 34 27 48 24 11 36 40320 496 59680 40334 496 59666 00014 99986 33 28 48 16 11 44 40816 491 59184 40830 491 59170 00014 99986 32 29 48 8 11 52 41307 485 58693 41321 486 58679 00015 99985 31 30 11 48 12 8. 41792 480 11. 58208 8. 41807 480 11. 58193 10. 00015 9. 99985 30 31 47 52 12 8 42272 474 57728 42287 475 57713 00015 99985 29 32 47 44 12 16 42746 470 57254 42762 470 57238 00016 99984 28 33 47 36 12 24 4.3216 464 56784 43232 464 567()8 00016 99984 27 34 35 47 28 12 32 43680 459 56320 43696 460 56304 00016 99984 26 11 47 20 12 40 8.44139 455 11. 55861 8. 44156 455 11. 55844 10. 00017 9. 99983 25 36 47 12 12 48 44594 450 55406 44611 450 55389 00017 99983 24 37 47 4 12 56 45044 445 54956 45061 446 54939 00017 99983 23 38 46 56 13 4 45489 441 54511 45507 . 441 54493 00018 99982 22 39 40 46 48 13 12 45930 436 54070 45948 437 54052 00018 To. 00018 99982 9. 99982 21 20 11 46 40 13 20 8. 46366 433 11, 53634 8. 46385 432 11. 53615 41 46 32 13 28 46799 427 5.3201 46817 428 53183 00019 99981 19 42 46 24 13 36 47226 424 52774 47245 424 52755 00019 99981 18 43 46 16 13 44 47650 419 52350 47669 420 52.331 00019 99981 17 44 46 8 13 52 48069 416 51931 48089 416 51911 00020 99980 16 15 45 11 46 14 8. 48485 411 11.51515 8. 48505 412 11. 51495 10. 00020 9. 99980 46 45 52 14 8 48896 408 51104 48917 408 51083 oa)2i 99979 14 47 45 44 14 16 49304 404 50696 49325 404 50675 00021 99979 13 48 45 36 14 24 49708 400 50292 49729 401 50271 00021 99979 12 49 45 28 14 32 50108 396 49892 50130 397 49870 00022 99978 11 10 50 11 45 20 14 40 8. 50504 393 11. 49496 8. 50527 393 11. 49473 10. 00022 9. 99978 51 45 12 14 48 50897 390 49103 50920 390 49080 00023 99977 9 52 45 4 14 56 51287 386 48713 51310 386 48690 00023 99977 8 /53 44 56 15 4 51673 382 48327 51696 383 48304 00023 99977 / 54 44 48 15 12 52055 379 47945 52079 380 47921 00024 99976 6 55 11 44 40 15 20 8. 52434 376 11. 47566 8. 52459 376 11. 47541 10. 00024 9. 99976 5 56 44 32 15 28 52810 373 47190 52835 373 47165 00025 99975 4 57 44 24 15 36 53183 369 46817 53208 370 46792 00025 99975 3 58 44 16 15 44 53552 367 46448 53578 367 46422 00026 99974 2 59 44 8 15 52 53919 363 46081 53945 363 46055 0002(1 99974 1 60 44 16 54282 360 45718 54308 361 45692 00026 99974 M. Hour p. M. Hour A. M. Cosine. Diff. 1'. Secant. Cotangent. Diff. 1'. Tangent. Cosecant. Sine. M. 91° 88° 1 22489—03- -39 Page 610] TABLE 44. 2° Log. Sines, Tangents, and Secants 177° M. Hour A. M. Hour p. M. Sine. Diff.l'. Cosecant. Tangent. Diff. 1'. Cotangent. Secant. Co.slne. M. 11 44 16 8. 54282 360 11. 45718 8. 54308 361 11.45692 10. 00026 9. 99974 60 1 43 52 16 8 54642 357 45358 54669 358 45331 00027 99973 59 2 43 44 16 16 54999 355 45001 55027 355 44973 00027 99973 58 3 43 36 16 24 55354 351 44646 55382 352 44618 00028 99972 57 4 5 43 28 16 32 55705 349 44295 55734 349 44266 00028 99972 56 11 43 20 16 40 8. 56054 346 11. 43946 8. 56083 346 11.43917 10. 00029 9. 99971 55 6 43 12 16 48 56400 343 43600 5t>429 344 . 43571 00029 99971 54 1 43 4 16 56 56743 341 43257 56773 341 43227 00030 99970 53 8 42 56 17 4 57084 337 42916 57114 338 42886 00030 99970 52 9 10 42 48 17 12 57421 336 42579 57452 336 42548 00031 99969 51 11 42 40 17 20 8. 57757 332 11. 42243 8. 57788 333 11.42212 10. 00031 9. 99969 50 11 42 32 17 28 58089 330 41911 58121 330 41879 00032 99968 49 12 42 24 17 36 58419 328 41581 58451 328 41549 00032 99968 48 13 42 16 17 44 58747 325 41253 58779 326 41221 00033 99967 47 14 42 8 17 52 59072 323 40928 59105 323 40895 00033 99967 46 45 15 11 42 18 8. 59395 320 11. 40605 8. 59428 321 11. 40572 10. 00033 9. 99967 16 41 52 18 8 59715 318 40285 59749 319 40251 00034 99966 44 17 41 44 18 16 60033 316 39967 60068 316 39932 00034 99966 43 18 41 36 18 24 60349 313 39651 60384 314 39616 00035 99965 42 19 20 41 28 18 32 60662 311 39338 60698 311 39302 00036 99964 41 40 11 41 20 18 40 8. 60973 309 11. 39027 8. 61009 310 11. 38991 10. 00036 9. 99964 21 41 12 18 48 61282 307 38718 61319 307 38681 00037 99963 39 22 41 4 18 56 61589 305 38411 61626 305 38374 00037 99963 38 23 40 56 19 4 61894 302 38106 61931 303 38069 00038 99962 37 24 25 40 48 19 12 62196 301 37804 62234 301 37766 00038 99962 36 35~ 11 40 40 19 20 8. 62497 298 11. 37503 8. 62535 299 11. 37465 10. 00039 9. 99961 26 40 32 19 28 62795 296 37205 62834 297 37166 00039 99961 34 27 40 24 19 36 63091 294 36909 63131 295 36869 00040 99960 33 28 40 16 19 44 63385 293 36615 63426 292 36574 00040 99960 32 29 30 40 8 19 52 63678 290 36322 63718 291 36282 00041 99959 31 11 40 20 8. 63968 288 11. 36032 8. 64009 289 11. 35991 10. 00041 9. 99959 30 31 39 52 20 8 64256 287 35744 64298 287 35702 00042 99958 29 32 39 44 20 16 64543 284 35457 64585 285 35415 00042 99958 28 33 39 36 20 24 64827 283 35173 64870 284 35130 00043 99957 27 34 39 28 20 32 65110 281 34890 65154 281 34846 00044 99956 26 35 11 39 20 20 40 8. 65391 279 11. 34609 8. 65435 280 11. 34565 10. 00044 9. 99956 25 36 3i^ 12 20 48 65670 277 34330 65715 278 34285 00045 99955 24 37 39 4 20 56 65947 276 34053 65993 276 34007 00045 99955 23 38 38 56 21 4 66223 274 33777 66269 274 33731 00046 99954 22 39 38 48 21 12 66497 272 33503 66543 273 33457 00046 99954 9. 99953 21 20 40 11 38 40 21 20 8. 66769 270 11. 33231 8. 66816 271 11. 33184 10. 00047 41 38 32 21 28 67039 269 32961 67087 269 32913 00048 99952 19 42 38 24 21 36 67308 267 32692 67356 268 32644 00048 99952 18 43 38 16 21 44 67575 266 32425 67624 266 32376 00049 99951 17 44 38 8 21 52 67841 263 32159 67890 264 32110 00049 99951 16 45 11 38 22 8. 68104 263 11. 31896 8. 68154 263 11. 31846 10. 00050 9. 99950 15 46 37 52 22 8 68367 260 31633 68417 261 31583 00051 99949 14 47 37 44 22 16 68627 259 31373 68678 260 31322 00051 99949 13 48 37 36 22 24 68886 258 31114 68938 258 31062 00052 99948 12 49 37 28 22 32 69144 256 30856 69196 257 30804 00052 99948 9. 99947 11 10 50 11 37 20 22 40 8. 69400 254 11. 30600 8. 69453 255 11. 30547 10. 00053 51 37 12 22 48 69654 253 30.346 69708 254 30292 00054 99946 9 52 37 4 22 56 69907 252 30093 69962 252 30038 00054 99946 8 53 36 56 23 4 70159 250 29841 70214 251 29786 00055 99945 7 54 36 48 23 12 23 20 70409 249 29591 70465 249 29535 00056 99944 6 55 11 36 40 8. 70658 247 11. 29342 8. 70714 248 11. 29286 10.00056 9. 99944 5 56 36 32 23 28 70905 246 29095 70962 246 29038 00057 99943 4 57 36 24 23 36 71151 244 28849 71208 245 28792 00058 99942 3 58 36 16 23 44 71395 243 28605 71453 244 28547 00058 99942 2 59 36 8 23 52 71638 242 28362 71697 243 28303 00059 99941 1 60 36 24 71880 240 28120 71940 241 28060 00060 99940 M. Hour p. M. Hour A. M. Cosine. Diff. 1'. Secant. Cotangent. Diff.l'. Tangent. Cosecant. Sine. M. 92° 87° TABLE 44. [Page 611 3° Log. Sines, Tangents, and Secants 176° M. Hour *. M. Hour P. M. Sine. Difl. 1'. Cosecant. Tangent. Diff. 1'. Cotangent. Secant. Cosine. M. 11 36 24 8. 71880 240 11. 28120 8. 71940 241 11. 28060 10. 00060 9. 99940 60 1 35 52 24 8 72120 239 27880 72181 239 27819 00060 99940 59 ?. 35 44 24 16 72359 238 27641 72420 239 27580 00061 99939 58 8 35 36 24 24 72597 237 27403 72659 237 27341 00062 99938 0/ 4 35 28 24 32 72884 235 27166 72896 236 27104 00062 99938 56 55 5 11 35 20 24 40 8. 73069 234 11. 26981 8. 73132 234 11. 26868 10. 00068 9. 99937 6 35 12 24 48 73303 232 26697 73366 234 26634 000«)4 99986 54 7 35 4 24 56 73535 232 26465 73600 232 26400 000(>1 99936 53 8 34 56 25 4 73767 230 26233 73832 231 26168 00065 99935 52 9 34 48 25 12 73997 229 26003 74063 229 25937 11. 25708 00066 10. 00066 99934 51 50 10 11 34 40 25 20 8. 74226 228 11. 25774 8. 74292 229 9. 99934 11 34 32 25 28 74454 226 25546 74521 227 25479 00067 99933 49 12 34 24 25 36 74680 226 25320 74748 226 25252 00068 99982 48 13 34 16 25 44 74906 224 25094 74974 225 25026 00068 99932 47 14 34 8 25 52 75130 223 24870 75199 224 24801 00069 99931 '9. 99930 46 45 15 11 34 26 8. 75353 222 11.24647 8. 75423 222 11. 24577 ! 10. 00070 18 33 52 26 8 75575 220 24425 75645 222 24355 00071 99929 44 17 33 44 26 16 75795 220 24205 75867 220 24183 00071 99929 43 18 33 36 26 24 76015 219 23985 76087 219 23913 00072 99928 42 19 33 28 26 82 76234 217 23766 76306 219 23694 00073 99927 41 40 ?.o 11 33 20 26 40 8. 76451 216 11. 23549 8. 76525 217 11. 23475 10. 00074 9. 99926 21 33 12 26 48 76667 216 23333 76742 216 23258 00074 99926 39 22 33 4 26 56 76883 211 23117 76958 215 23042 00075 99925 38 28 82 56 27 4 77097 213 22903 77173 214 22827 00076 99924 37 24 32 48 27 12 77310 212 22690 77387 213 22613 00077 99923 36 35 2o 11 82 40 27 20 8. 77522 211 11. 22478 8. 77600 211 11. 22406 10. 00077 9. 99923 26 32 32 27 28 77733 210 22267 77811 211 22189 00078 99922 34 27 32 24 27 36 77943 209 22057 78022 210 21978 00079 99921 33 28 32 16 27 44 78152 208 21848 78232 209 21768 00080 99920 32 29 32 8 27 52 78360 208 21640 78441 208 21559 00080 99920 31 30 80 11 32 28 8. 78568 206 11. 21432 8. 78649 206 11.21351 1 10. 00081 9. 99919 81 31 52 28 8 78774 205 21226 78855 206 21145 00082 99918 29 82 31 44 28 16 78979 204 21021 79061 205 20989 00088 99917 28 88 31 36 28 24 79188 203 20817 79266 204 20784 00083 99917 27 84 31 28 28 82 79386 202 20614 79470 203 20580 i 00084 99916 9. 99915 26 25 85 11 31 20 28 40 8. 79588 201 11.20412 8. 79673 202 11.20827110.00085 8fi 31 12 28 48 79789 201 20211 79875 201 20125; 00086 99914 24 87 31 4 28 56 79990 199 20010 80076 201 19924 00087 99918 23 88 30 56 29 4 80189 199 19811 80277 199 19728 00087 99913 22 89 30 48 29 12 80388 197 19612 80476 198 19524 00088 99912 21 40 11 30 40 2v^ 20 8. 80585 197 11.19415 8. 80674 198 11.19326 10.00089 9.99911 20 41 30 32 29 28 80782 196 19218 80872 196 19128 00090 99910 19 42 30 24 29 36 80978 195 19022 81068 196 18982 00091 99909 18 48 30 16 29 44 81173 194 18827 81264 195 18736 00091 9<>909 17 44 30 8 29 52 30 81367 8.81560' 193 18633 81459 194 18541 00092 99908 16 45 11 30 192 11. 18440 8. 816.53 193 11.18847 10.00098 9. 99907 15 46 29 52 30 8 81752 192 18248 81846 192 18154 00094 99906 14 47 29 44 30 m 81944 190 18056 82038 192 17962 00095 99905 18 48 29 36 30 24 82134 190 1 7866 82280 190 17770 00096 99904 12 49 50 29 28 11 29 20 80 82 80 40 82824 8.82513 189 17676 82420 190 17580 00096 99904 11 188 11.17487 8. 82610 189 11. 173V.0 10. 00097 9. 99903 10 51 29 12 - 80 48 82701 187 17299 82799 188 17201 00098 99902 9 52 29 4 30 56 82888 187 17112 82987 188 17013 00099 99901 8 58 28 56 31 4 83075 186 16925 83175 186 16825 00100 99900 / 54 55 28 48 11 28 40 31 12 31 20 83261 185 16739 88361 186 16689 00101 99899 6 5 8. 88446 184 11.16554 8. 83547 185 11.16458 10.00102 9. 99898 56 28 32 81 28 83680 188 16370 88732 184 16268 00102 99898 4 57 28 24 31 m 83813 183 16187 83916 184 16084 00108 99897 3 58 28 16 31 44 88996 181 16004 84100 182 15900 00104 99896 2 59 28 8 31 52 84177 181 15828 84282 182 15718 00105 99895 1 60 M. 28 32 S4:ioS 181 15642 84464 182 15536 00106 99894 Hour p. M. Hour A. M. Cosine. Diff. 1'. Secant. Cotangent. Diff. 1'. Tangent. Cosecant. Sine. M. 93° 86° 1 Page 612] TABLE 44. 4° Log. Sines, Tangents, and Secants 175° M. Hour A. M. Hour p. K. Sine. Diff.l'. Cosecant. Tangent. Diff.l'. 1 Cotangent. Secant. Cosine. M. 11 28 32 8. 84358 181 11. 15642 8.84464 182 11. 15536 10. 00106 9. 99894 60 1 27 52 32 8 84539 179 15461 84646 180 15354 00107 99893 59 2 27 44 32 16 84718 179 15282 84826 180 15174 00108 99892 58 3 27 36 32 24 84897 178 15103 85006 179 14994 00109 99891 57 4 27 28 32 3f 85075 177 14925 85185 . 178 14815 00109 99891 56 55 5 11 27 20 32 40 8. 85252 177 11. 14748 8. 85363 177 11. 14637 10. 00110 9. 99890 6 27 12 32 48 85429 176 14571 85540 177 14460 00111 99889 54 7 27 4 32 56 85605 175 14395 8.5717 176 14283 00112 99888 53 8 26 56 33 4 85780 175 14220 85893 176 14107 00113 99887 52 9 10 26 48 11 26 40 33 12 85955 173 14045 86069 174 13931 00114 99886 51 50 33 20 8. 86128 173 11. 13872 8. 86243 174 11. 1.3757 10. 00115 9. 99885 11 26 32 33 28 86301 173 13699 86417 174 13583 00116 99884 49 12 26 24 33 36 86474 171 13526 86591 172 13409 00117 99883 48 13 26 16 33 44 86645 171 13355 86763 172 13237 00118 99882 47 14 26 8 33 52 86816 171 13184 86935 171 13065 00119 99881 46 45 15 11 26 34 8. 86987 169 11. 13013 8. 87106 171 11. 12894 10. 00120 9. 99880 16 25 52 34 8 87156 169 12844 87277 170 12723 00121 99879 44 17 25 44 34 16 87325 169 12675 87447 169 12553 00121 99879 43 18 25 36 34 24 87494 167 12506 87616 169 12384 00122 99878 42 19 20 25 28 11 25 20 34 32 87661 168 12339 87785 168 12215 00123 99877 41 40 34 40 8. 87829 166 11.12171 8. 87953 167 11. 12047 10. 00124 9. 99876 21 25 12 34 48 87995 166 12005 88120 167 11880 00125 99875 39 22 25 4 34 56 88161 165 11839 88287 166 11713 00126 99874 38 23 24 56 35 4 88326 164 11674 88453 165 11547 00127 99873 37 24 24 48 35 12 88490 164 11510 88618 165 11382 00128 99872 36 35 25 11 24 40 35 20 8. 88654 163 11. 11346 8. 88783 165 11. 11217 10. 00129 9. 99871 26 24 32 35 28 88817 163 11183 88948 163 11052 00130 99870 34 27 24 24 35 36 88980 162 11020 89111 163 10889 00131 99869 33 28 24 16 35 44 89142 162 • 10858 89274 163 10726 00132 99868 32 29 24 8 35 52 89304 160 10696 89437 161 10563 00133 99867 31 30 11 24 36 8. 89464 161 11. 10536 8. 89598 162 11. 10402 10. 00i;34 9. 99866 30 31 23 52 36 8 89625 159 10375 89760 160 10240 00135 99865 29 32 23 44 36 16 89784 159 10216 89920 160 10080 00136 99864 28 33 23 36 36 24 89943 159 10057 90080 160 09920 00137 99863 27 34 35 23 28 36 32 90102 158 09898 90240 159 09760 001.38 99862 26 11 23 20 36 40 8. 90260 157 11. 09740 8. 90399 158 11. 09601 10. 00139 9. 99861 25 36 23 12 36 48 90417 157 09583 90557 158 09443 00140 99860 24 37 23 4 36 56 90574 156 09426 90715 157 09285 00141 99859 23 38 22 56 37 4 90730 155 09270 90872 157 09128 00142 99858 22 39 22 48 37 12 90885 155 09115 91029 156 08971 00143 99857 21 40 11 22 40 37 20 8. 91040 155 11. 08960 8. 91185 155 11. 08815 10. 00144 9. 99856 20 41 22 32 37 28 91195 154 08805 91340 155 08660 00145 99855 19 42 22 24 37 36 91349 153 08651 91495 155 08505 00146 99854 18 43 22 16 37 44 91502 153 08498 91650 153 083.50 00147 99853 17 44 22 8 37 52 91655 152 08345 91803 154 08197 00148 99852 16 15 45 11 22 38 8.91807 152 11.08193 8. 91957 153 11.08043 10. 00149 9. 99851 46 21 52 38 8 91959 151 08041 92110 152 07890 00150 99850 14 47 21 44 38 16 92110 151 07890 92262 152 07738 00152 99848 13 48 21 36 38 24 92261 150 07739 92414 151 07586 00153 99847 12 49 21 28 38 32 92411 150 07589 92565 151 07435 00154 99846 11 50 11 21 20 38 40 8. 92561 149 11.074.39 8. 92716 150 11. 07284 10. 001.55 9. 99845 JO 51 21 12 38 48 92710 149 07290 92866 150 07134 00156 99844 9 52 21 4 38 56 92859 148 07141 93016 149 06984 00157 99843 8 53 20 56 39 4 93007 147 06993 93165 148 0683.5 00158 99842 7 54 20 48 39 12 93154 147 06846 93313 149 06687 00159 99841 6 55 11 20 40 39 20 8. 93301 147 11. 06699 8. 93462 147 11.06538 10. 00160 9. 99840 5 56 20 32 39 28 93448 146 06552 93609 147 06.391 00161 99839 4 57 20 24 39 36 93594 146 06406 93756 147 06244 00162 99838 3 58 20 16 39 44 93740 145 06260 93903 146 06097 00163 99837 2 59 20 8 39 52 93885 145 06115 94049 146 05951 00164 998.36 1 60 20 40 94030 144 05970 94195 145 05805 00166 99834 M. Hour p. M. Hour A. M. Cosine. Diff.l'. Secant. Cotangent. Diff.l'. Tangent. Cosecant. Sine. M. 94° 85° 1 TABLE 44. [Page 613 Log. Sines, Tangents, and Secants. 6° A A B B C C 174° M. Hour A. M. Hour p. M. Sine. Difl. Cosecant. Tangent. Diff. Cotangent. Secant. Diff. Cosine. M. 11 20 00 40 00 8. 94030 11.05970 8. 94195 11. 05805 10. 00166 9. 99834 60 1 19 52 40 08 94174 2 05826 94340 2 05660 00167 99833 1 59 ">, 19 44 40 16 94317 4 05683 94485 4 05515 00168 99832 58 w 19 36 40 24 94461 7 05539 94630 7 05370 00169 99831 57 4 5 19 28 11 19 20 40 32 94603 9 05397 94773 9 05227 00170 93830 56 40 40 8. 94746 11 11. 05254 8. 94917 11 11. 05088 10.00171 9. 99829 55 (\ 19 12 40 48 94887 13 05113 95060 13 04940 00172 99828 54 7 19 04 40 56 95029 15 04971 95202 15 04798 00173 99827 53 8 18 56 41 04 95170 18 04830 95344 18 04656 00175 99825 52 9 18 48 41 12 95310 20 04690 95486 8.95627 20 22 04514 11.04873 00176 99824 51 50" 10 11 18 40 41 20 8. 95450 22 11.04550 10.00177 i 9. 99823 n 18 82 41 28 95589 24 04411 95767 24 04233 00178 99822 49 1^ 18 24 41 36 95728 26 04272 95908 27 04092 00179 99821 48 ia 18 16 41 44 95867 29 041.33 96047 29 03953 00180 99820 47 14 15 18 08 41 52 96005 31 03995 96187 31 03813 00181 10.00183 99819 19.99817 46 45 11 18 00 42 00 8. 96143 33 11.03857 8. 96325 83 11.08675 18 17 52 42 08 96280 35 03720 96464 35 08536 00184 99816 44 17 17 44 42 16 96417 37 03583 96602 38 03398 00185 99815 48 IS 17 36 42 24 96553 89 03447 96739 40 03261 00186 99814 42 19 17 28 42 82 96689 42 44 08311 11.03175 96877 42 44 03123 00187 99813 41 90 11 17 20 42 40 8. 96825 8. 97013 11.02987 10. 00188 9. 99812 40 ?A 17 12 42 48 96960 46 03040 97150 46 02850 00190 99810 39 22 17 04 42 56 97095 48 02905 97285 49 02715 00191 99809 38 28 16 56 43 04 97229 50 02771 97421 51 02579 00192 99808 37 24 16 48 43 12 97368 53 55 02637 97556 53 02444 00193 99807 36 35 2ft 11 16 40 43 20 8. 97496 11.02504 8. 97691 55 11. 02309 10.00194 1 9.99806 26 16 32 43 28 97629 57 02371 97825 58 02175 00196 1 99804 34 27 16 24 43 36 97762 59 02238 97959 60 02041 00197 1 99803 88 28 16 16 43 44 97894 61 02106 98092 62 01908 00198 99802 32 29 80 16 08 43 52 98026 64 01974 11. 01843 98225 &4 01775 00199 99801 31 30 11 16 00 44 00 8. 98157 66 8. 98358 66 11.01642 10. 00200 9. 99800 81 15 52 44 08 98288 68 01712 98490 69 01510 00202 99798 29 82 15 44 44 16 98419 70 01581 98622 71 01378 00203 99797 28 88 15 36 44 24 98549 72 01451 98753 73 01247 00204 99796 27 34 15 28 44 82 98679 75 01321 98884 75 01116 11.00985 00205 99795 26 25 85 11 15 20 44 40 8. 98808 77 11.01192 8. 99015 77 10. 00207 9. 99793 86 15 12 44 48 98937 79 01068 99145 80 00855 00208 99792 24 87 15 04 44 56 99066 81 00934 99275 82 00725 00209 99791 23 88 14 56 45 04 99194 83 00806 99405 84 00595 00210 99790 22 39 14 48 45 12 99322 86 00678 99534 86 89 00466 00212 99788 21 20 40 11 14 40 45 20 8. 99450 88 11.00550 8. 99662 11.00888 10. 00213 9. 99787 41 14 32 45 28 99577 90 00423 99791 91 00209 00214 99786 19 42 14 24 45 36 99704 92 00296 99919 93 00081 00215 99785 18 48 14 16 45 44 99880 94 00170 9.00046 95 10. 999,54 00217 99783 17 44 45 14 08 45 52 99956 96 00044 10. 99918 00174 9.00301 97 100 99826 00218 To. 00219 1 1 99782 1 9.99781 16 15 11 14 00 46 00 9. 00082 99 10.99699 46 18 52 46 08 00207 101 99793 00427 102 99573 00220 1 1 99780 14 47 18 44 46 16 00332 108 99668 00553 104 99447 00222 1 i 99778 13 48 13 36 46 24 00456 105 99544 00670 106 99321 00223 99777 12 49 50 13 28 11 18 20 46 32 46 40 00581 9.00704 107 110 99419 10. 99296 00805 9. 00930 108 111 99195 00224 10. 00225 99776 9. 99775 11 10 10. 99070 51 13 12 46 48 00828 112 99172 01055 113 98945 00227 99773 9 52 13 04 46 56 00951 114 99049 01179 115 98821 00228 99772 8 58 12 56 47 04 01074 116 98926 • 01303 117 98697 00229 99771 7 54 55 12 48 47 12 47 20 01196 9.01318 118 121 98804 10. 98682 01427 120 122 98578 10.98450 00231 99769 99768 6 5 11 12 40 9. 01550 10. 00232 56 12 32 47 28 01440 123 98560 01673 124 98827 00233 99767 4 57 12 24 47 36 01561 125 98439 01796 126 98204 00235 1 j 99765 3 58 12 16 47 44 01682 127 98318 01918 128 98082 00236 99764 2 59 12 08 47 52 01808 129 98197 02040 131 97960 00237 99763 1 60 12 00 48 00 01923 132 98077 02162 133 97838 00239 99761 M. Hour p. M. Hour A. M. Cosine. Diff. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. Sine. M. 96° A A B B C C 84° 1 Seconds of time 1» •.'= j 8b 4' 5- i C 7. 1 Prop, parts of cols. -; B (c 16 17 33 49 66 33 50 66 1 82 83 1 99 100 1 115 116 1 Page 614] TABLE U. Log. Sines, Tangents, and Secants. 6° A A B B C C 178° M. Hour A. M. Hour p. m. Sine. Diflf. Cosecant. Tangent. Diff. 1 Cotangent. Secant. 10. 00239 Diff. Cosine. M. 60 11 12 00 48 00 9.01923 10. 98077 9.02162 10.97838 9. 99761 1 11 52 48 08 02043 i 2 97957 02283 1 2 97717 00240 99760 59 2 11 44 1 48 16 02163 : 4 97837 02404 j 4 97596 00241 99759 58 3 11 36 48 24 02283 ! 6 97717 02525 1 6 97475 00243 99757 57 4 11 28 48 321 02402 7 9 97598 02645 8 9 97355 10^97234 00244 10. 00245 99756 9. 99755 56 55 5 11 11 20 48 40 9. 02520 10. 97480 9. 02766 6 11 12 48 48 02639 1 11 97361 02885 1 11 97115 00247 99753 .54 7 11 04 48 56 02757 ! 13 97243 03005 13 96995 00248 99752 53 8 10 56 49 04 02874 15 97126 03124 15 96876 00249 9975] 52 9 10 10 48 49 12 049 20 02992 17 97008 03242 9. 03361 17 19 96758 10. 96639 00251 10. 00252 0" 99749 51 11 10 40 9. 03109 19 10. 96891 9. 99748 50 11 10 32 49 28 03226 20 96774 03479 21 96521 00253 99747 49 12 10 24 49 36 03342 22 96658 03597 23 96403 00255 99745 48 13 10 16 49 44 03458 24 96542 03714 i 24 96286 00256 99744 47 14 15 10 08 49 52 03574 26 96426 03832 1 26 96168 00258 10. 00259 99742 46 45 11 10 00 50 00 9. 03690 28 10. 96310 9.03948 28 10. 96052 9. 99741 16 9 52 50 08 03805 30 96195 04065 1 30 95935 00260 99740 44 17 9 44 50 16 03920 31 96080 04181 1 32 95819 00262 99738 43 18 9 36 50 24 04034 33 95966 04297 1 34 95703 00263 99737 42 19 9 28 50 32 50 40 04149 35 95851 04413 36 95587 00264 99736 41 40 20 11 9 20 9. 04262 37 10. 95738 9.04528 ! 38 10. 95472 10. 00266 9. 99734 21 9 12 50 48 04376 39 95624 04643 39 95357 00267 99733 39 22 9 04 50 56 04490 41 95510 04758 41 95242 00269 99731 38 23 8 56 51 04 04603 43 95397 04873 43 95127 00270 99730 37 24 8 48 51 12 04715 44 95285 04987 i 45 95013 00272 99728 36 35 25 11 8 40 1 51 20 9.04828 1 46 10.95172 9.05101 1 47 10. 94899 10. 00273 9. 99727 26 8 32 51 28 04940 48 95060 05214 i 49 94786 00274 99726 34 27 8 24 51 36 05052 50 94948 05328 1 51 94672 00276 99724 33 28 8 16 1 51 44 05164 52 94836 05441 ! 53 94559 00277 99723 32 29 8 08 i 51 52 05275 9. 05386 54 56 94725 05553 54 94447 00279 99721 9. 99720 31 30 30 11 8 00 52 00 10. 94614 9.05666 56 10.94334 10. 00280 31 7 52 52 08 05497 57 94503 05778 1 58 1 94222 00282 99718 29 32 7 44 52 16 05607 59 94393 05890 1 60 94110 00283 99717 28 33 7 36 52 24 05717 61 94283 06002 62 93998 00284 99716 27 34 7 28 52 32 05827 63 94173 06113 64 93887 00286 99714 26 35 11 7 20 52 40 9.05937 65 10.94063 9.06224 66 10.93776 10. 00287 9. 99713 25 36 7 12 52 48 06046 67 93954 06335 68 93665 00289 99711 24 37 7 04 52 56 06155 69 93845 06445 69 93555 00290 99710 23 38 6 56 53 04 06264 70 93736 06556 71 93444 00292 99708 22 39 40" 6 48 53 12 06372 9. 06481" 72 93628 06666 73 93334 00293 99707 21 20 11 6 40 53 20 74 10.93519 9. 06775 75 10. 93225 10. 00295 9. 99705 41 6 32 53 28 06589 i 76 93411 06885 77 93115 00296 99704 19 42 6 24 53 36 06696 78 93304 06994 79 93006 00298 99702 18 43 6 16 53 44 06804 80 93196 07103 81 92897 00299 99701 17 44 45 6 08 53 52 06911 81 93089 07211 83 84 92789 00301 99699 9. 99698 16 15 11 6 00 54 00 9. 07018 83 10. 92982 9. 07320 10. 92680 fo. oote' 46 5 52 54 08 07124 85 92876 07428 86 92572 00304 99696 14 47 5 44 54 16 07231 87 92769 07536 88 92464 00305 99695 13 48 5 36 54 24 07337 89 92663 07643 90 92357 00307 99693 12 49 . 5 28 54 32 07442 91 92558 07751 92 92249 10. 92142 00308 99692 9. 99690 11 10 50 11 5 20 54 40 9. 07548 93 10. 92452 9. 07858 94 10. 00310 51 5 12 54 48 07653 94 92347 07964 96 92036 00311 99689 9 52 5 04 54 56 07758 96 92242 08071 98 91929 . 00313 99687 8 53 4 56 55 04 07863 98 92137 08177 99 91823 00314 99686 7 54 4 48 55 12 07968 100 92032 08283 101 91717 00316 99684 6 5 55 11 4 40 55 20 9. 08072 102 10. 91928 9. 08389 103 10.91611 10. 00317 1 9. 99683 56 4 32 55 28 08176 104 91824 08495 105 91505 00319 99681 4 57 4 24 55 36 08280 106 91720 08600 107 91400 00320 99680 3 58 4 16 55 44 08383 107 91617 08705 109 91295 00322 99678 2 59 4 08 55 52 08486 109 91514 08810 111 91190 00323 99677 1 60 4 00 56 00 08589 111 91411 08914 113 91086 00325 99675 M. M. Hour p. M. Hour A. M. Cosine. Diflf. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. Sine. 96° A A B B c C 88° Seconds of time Prop, parts of cols. < 2» 28 28 6' 83 84 1 TABLE U. [Page 615 Log. Sines, Tangents, and Secants. 7° A A B B C C 172° M. Hour A. M. Hour P. M. 56 Sine. DiflF. Cosecant. Tangent. DiS. i Cotangent. Seeant. Diff. Cosine. M. 60 n 4 9. 08589 10.91411 9. 08914 10. 91086 10. 00325 9. 99675 1 3 52 56 8 08692 2 91308 09019 2 90981 00326 99674 59 2 3 44 56 16 08795 3 91205 09123 3 i 90877 00328 99672 58 8 3 36 56 24 08897 5 91103 09227 5 1 90773 00330 99670 57 4 5 3 28 56 32 08999 6 8 91001 rd."90899 09330 9.09434 7 8 i 90670 00331 99669 56 11 3 20 56 40 9. 09101 [10. 90566 10. 00333 9. 99667 55 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 10 2 48 11 2 40 57 12 57 20 09506 9. 09606 14 16" 90494 10. 90394 09845 9. 09947 15 16 90155 10. 90053 00339 99661 51 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 90093 10252 21 89748 00345 99655 47 14 2 8 57 52 10006 22 89994 10353 23 89647 00347 99653 9. 99651" 46 45 15 11 2 58 9. 10106 24 10. 89894 9. 10454 24 10. 89546 10. 00349 16 1 52 58 8 10205 26 89795 10555 26 89445 00350 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 58 40 10501 9. 10599 30 89499 10856 31 89144 00355 99645 41 20 11 1 20 32 110.89401 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 89205 11155 36 88845 00360 99640 38 23 56 59 4 10893 37 89107 11254 37 88746 00362 99638 37 24 25' 48 59 12 10990 38 1 89010 lia53 39 88647 00363 10. 00365 99637 9. 99635 36 35 11 40 59 20 9. 11087 40 [10.88913 9. 11452 41 10. 88548 26 32 59 28 11184 42 ! 88816 11551 42 88449 00367 1 99633 34 27 24 59 36 11281 43 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 10. 88057 00371 10. 00373 99629 9. 99627 31 30 30 11 1 9. 11570 48 110.88430 9.11943 49 31 10 59 52 8 11666 i 50 88334 12040 51 87960 00375 99625 29 32 59 44 16 11761 51 88239 12138 52 87862 00376 99624 28 33 59 36 24 11857 53 1 88143 12235 54 87765 00378 99622 27 34 35 59 28 32 11952 54 ! 88048 12332 9. 12428 55 57 87668 00380 10. 00382 99620 26 10 59 20 1 40 9. 12047 56 10.87953 10. 87572 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 87283 8/187 00387 99613 22 39 58 48 1 12 12425 62 i 87575 12813 64 00388 99612 21 20 40 10 58 40 1 1 20 9. 12519 64 (10.87481 9. 12909 65 10. 87091 10.00390 9.99610 41 58 32 1 28 12612 66 ! 87388 13004 67 86996 00392 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 99(W5 17 44 45 58 8 1 52 12892 70 1 87108 13289 72 86711 00397 99603 16 15 10 58 1 2 9. 12985 72 10.87015 9. 13384 73 10. 86616 10. 00.399 9. 99()01 46 57 52 2 8 13078 74 86922 13478 to 86522 00400 99(i00 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 50 57 28 10 57 20 2 32 1 2 40 13355 9. 13447 78 80 86645 10. 86553 13761 9. 13854 80 81 86239 10. 86146 00405 99595 9. 99593 11 10 10. 00407 51 57 12 2 48 13539 82 8<>461 13948 i 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 55 56 48 3 12 13813 87 : 86187 88 110.86096 14227 1 88 9.14320 1 90 85773 10. 85680 00414 10. 00416 2 2 99586 9. 99584 6 5 10 56 40 1 3 20 9. 13904 56 56 32 3 28 13994 90 8600(i 14412 91 85588 00418 2 99582 4 57 56 24 3 36 14085 91 85915 14.504 i 93 85496 00419 2 9958 1 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 AHU. Cosine. Diff. Secant, i Cotangent. Diff. Tangent. Cosecant. Diff. Sine. M. 97^ A A B B C C 82° 1 Seconds of time 1' 2' -8' 4' b> 6^ 1 7. Prop, parts of cols. < B 12 12 24 36 24 37 1 48 49 1 60 61 1 72 84 73 86 1 1 Page 616] TABLE 44. Log. Sines, Tangente, and Secants. 8° A A B B C C I'iV M. Hour A. M. Hour p. M. Sine. JDifl. Cosecant. Tangent. Dili. Cotangent. Secant. Difif. Cosine. M. 10 56 14 9.14356 1 10.85644 9. 14780 10. 85220 10. 00425 9. 99575 60 1 55 52 4 8 14445 : 1 1 85555 14872 1 85128 00426 99574 59 9 55 44 ■ 4 16 14535 3 i 85465 14963 1 3 85037 00428 99572 58 3 55 36 I 4 24 14624 4 85376 15054 4 84946 00430 99570 57 4 5 55 28 1 4 32 10 55 20 I 1 4 40 14714 i 6 85286 9.14803 7 10,85197 15145 6 84855 9.15236 ! 7 10.84764 00432 10.00434 99568 56 55 9. 99566 6 55 12 : 4 48 14891 1 8 85109 15327 9 1 84673 00435 99565 54 7 55 4 4 56 14980 1 10 85020 15417 10 i 84583 00437 99563 53 8 54 56 ! 5 4 15069 11 84931 15508 12 84492 00439 ; 99561 52 9 54 48 1 5 12 15157 13 84843 15598 , 13 84402 00441 99559 51 50 10 10 54 40 1 1 5 20 9.15245 14 10.84755 9.15688 14 10.84312 10.00443 9. 99557 11 54 32 ' 5 28 15333 16 84667 15777 16 84223 00444 99556 49 12 54 24 5 36 15421 17 84579 15867 1 17 ! 84133 00446 99554 48 13 54 16 5 44 15508 \ 18 84492 15956 19 ! 84044 00448 99552 47 14 54 8 1 5 52 15596 20 84404 16046 20 ' 83954 00450 99550 46 15 10 54 1 6 9. 15683 21 10. 84317 9.1613.5 i 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 X 24 84143 15944"^ 25 84056 16312 25 I "83688 00455 99545 48 18 53 36 6 24 16401 26 ' 83599 00457 99543 42 19 20 53 28 1 6 32 16030 27 83970 16489 27 83511 10. 83423 00459 1 99541 41 40 10 53 20 1 6 40 9. 16116 28 10. 83884 9. 16577 29 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 1 32 j 83626 16841 33 83159 00467 1 99533 37 24 52 48 1 7 12 16460 1 34 1 83540 16928 35 83072 00468 1 99532 36 25 10 52 40 1 7 20 9. 16545 , 35 ilO. 83455 9. 17016 36 10.82984 10. 00470 1 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 10 52 7 52 18 16886 41 83114 17363 42 82637 00478 99522 9. 99520 31 30 9. 16970 42 10. 83030 9. 17450 43 10. 82550 10. 00480 31 51 52 i 8 8 17055 1 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 i 47 82777 17708 48 82292 00485 99515 27 34 35 51 28 8 32 17307 48 82693 10. 82609 17794 49 82206 00487- 99513 26 25 10 51 20 1 8 40 9. 17391 49 9.17880 50 10. 82120 10. 00489 9.99511 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 40 50 48 1 9 12 17724 55 82276 18221 56 81779 00497 99503 21 10 50 40 1 9 20 9. 17807 56 10.82193 9. 18306 58 10.81694 10. 00499 1 9.99501 20 41 50 32 I 9 28 17890 58 82110 18391 59 81609 00501 1 99499 19 42 50 24 ! 9 36 17973 i 59 82027 18475 61 81525 00503 1 99497 18 43 50 16 9 44 18055 61 81945 18560 62 . 81440 00505 1 ! 99495 17 44 50 8 9 52 1 10 18137 62 81863 9.18220 i 63 10.81780 18644 63 81356 00506 1 i 99494 16 15 45 10 50 9. 18728 65 10.81272 10. 00508 1 19.99492 46 49 52 : 10 8 18302 i 65 ! 81698 18812 66 81188 00510 99490 14 47 49 44 10 16 18383 66 81617 18896 1 68 81104 00512 1 99488 13 48 49 36 I 10 24 18465 68 81535 18979 i 69 81021 00514 2 99486 12 49 50 49 28 1 10 32 18547 1 69 81453 9.18628 71 ;iO. 81372 19063 9.19146 71 80937 72 10780854 00516 10. 00518 2 2 99484 9. 99482 11 10 10 49 20 i 1 10 40 51 49 12 10 48 18709 1 72 81291 19229 74 80771 00520 2 99480 9 52 49 4 10 56 18790 73 ; 81210 19312 75 • 80688 ■ 00522 2 1 99478 8 53 48 56 11 4 18871 75 81129 19395 76 80605 00524 2 i 99476 7 54 55 48 48 11 12 18952 76 ■ 81048 19478 i 78 1 80522 00526 2 j 99474 6 10 48 40 i 1 11 20 9.19033 i 78 10.80967 9.19561 ' 79 10.80439 10. 00528 2 9. 99472 5 56 48 32 11 28 19113 79 ! 80887 19643 1 81 1 80357 00530 2 \ 99470 4 57 48 24 11 36 19193 80 i 80807 19725 82 j 80275 00532 2 99468 3 58 48 16 11 44 19273 82 I 80727 19807 84 80193 00534 2 i 99466 2 59 48 8 i 11 52 19353 83 80647 19889 85 80111 00536 2 99464 1 60 M. 48 12 19433 85 80567 19971 87 80029 00538 2 99462 M. Hour p. M. j Hoxir a. m. Cosine. Dlfif. Secant. Cotangent. ^ Diff. Tangent. Cosecant. DiflE. Sine. 98° A A . B B C C 81° Seconds of time 1" 2» 8- j 4« o' «• <• fA 11 Prop, parts of cols. -JB 11 [C 1 21 22 32 42 32 43 1 [ 1 53 54 1 63 65 1 74 76 2 TABLE U. [Page 617 Log. Sines, Tangents, and Secants. 9° A A B B C C 170° M. Hour A. M. Hour p. M. Sine. Diff. Cosecant. Tangent. Diff. Cotangent. Secant. Diff. 1 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 10.80170 20297 5 79703 10. 79622 00546 10. 00548 99454 56 55 5 10 47 20 1 12 40 9. 19830 6 9. 20378 6 9. 99452 H 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 10 46 40 13 12 1 13 20 20145 9. 20223 11 13 79855 20701 12 13 79299 00556 99444 51 50 10. 79777 9. 20782 ' 10. 79218 10. 00558 9.99442 11 46 32 13 28 20302 14 79698 20862 1 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 79.542 21022 17 78978 00564 99436 47 14 46 8 13 52 20535 18 79465 21102 18 78898 00566 99434 46 45 15 10 46 1 14 9. 20613 19 10. 79387 9.21182 19 10. 78818 10. 00568 9. 99432 K) 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 45 28 14 32 20922 24 79078 21499 25 78501 00577 99423 41 20 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 15 12 21306 9. 21382 30 78694 21893 31 78107 00587 99413 36 25 10 44 40 1 15 20 31 10. 78618 9. 21971 32 10. 78029 10. 00589 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 30 44 8 15 52 21685 37 78315 10. 78239 22283 38 77717 10. 77639 00598 99402 31 10 44 1 16 9. 21761 38 9. 22361 39 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 35 43 28 16 32 22062 43 77938 22670 44 77330 00608 99392 26 10 43 20 1 16 40 9. 22137 44 10. 77863 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 42 48 17 12 22435 9. 22509 49 50 77565 10. 77491 23054 9. 23130 50 52 76946 00619 99381 21 40 10 42 40 1 17 20 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 45 42 8 17 52 22805 55 57 77195 10. 77122 23435 57 76565 00630 2 99370 16 15 10 42 1 18 9. 22878 9. 23510 58 10. 76490 10. 00632 2 9. 99368 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 00(i36 2 99364 13 48 41 36 18 24 23098 60 76902 23737 62 76263 00638 2 99362 12 49 41 28 18 32 23171 9. 23244 62 63 76829 23812 63 65 76188 00641 2 99359 11 10 50 10 41 20 1 18 40 10. 76756 9. 23887 10.76113 10. 00643 2 9,99357 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 00(>47 2 99353 8 53 40 56 19 4 23462 67 76538 24112 69 75888 00649 2 99351 i 54 55 40 48 10 40 40 19 12 23535 9. 23607 68 76465 24186 70 75814 00652 2 99348 6 1 19 20 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 M. 40 20 23967 76 76033 24632 78 75368 00665 2 99335 -M. Hour p. M. Hour A. M. Co.sine. Diff. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. } Sine. 99° A A B B C C 80° 1 Seconds of time 1« 2» 3^ 4. 5' 6» 7» Prop, parts of cols. •! B Ic 9 19 28 10 19 29 1 i 1 38 39 1 47 49 1 57 58 2 66 68 2 Page 618] TABLE 44. Log. Sines, Tangents, and Secants. 10° A A B B C C 169° M. Hour A. M. Hour p. M. Sine. Diff. 1 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 52 20 8 24039 1 i 75961 24706 1 1 75294 00667 99333 59 2 39 44 20 16 24110 2 1 75890 24779 2 75221 00669 99331 58 :^ 39 36 20 24 24181 3 75819 24853 4 75147 00672 99328 57 4 39 28 20 3i 24253 5 75747 10. 75676 24926 5 6 75074 10. 75000 00674 i 99326 i 9. 99324 56 55 5 10 39 20 1 20 40 9. 24324 6 9. 25000 10. 00676 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 10 38 48 21 12 24607 10 75393 25292 11 12 74708 00685 99315 51 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 i 14 74490 00692 i 99308 48 13 38 16 21 44 24888 15 75112 25582 15 74418 00694 99306 47 14 38 8 21 52 24958 16 75042 25655 16 74345 00696 99304 46 15 10 38 1 22 9. 25028 17 10. 74972 9. 25727 18 10. 74273 10. 00699 9. 99301 45 1(1 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 37 28 22 32 25307 22 74693 26015 22 73985 00708 99292 41 20 10 37 20 1 22 40 9. 25376 23 10. 74624 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 25 36 48 23 12 25652 27 74348 26372 28 73628 00719 99281 9. 99278 36 35 10 36 40 1 23 20 9. 25721 28 10. 74279 9. 26443 29 10. 73557 10. 00722 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 34 74005 26726 34 35 73274 00731 99269 31 30 10 36 1 24 9. 26063 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 73665 27078 40 72922 00743 99257 26 35 10 35 20 1 24 40 9. 26403 40 10. 73597 9. 27148 41 10. 72852 10. 00745 9. 99255 25 3H 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 34 48 25 12 26672 44 73328 27427 46 72573 00755 2 99245 21 40 10 34 40 1 25 20 9. 26739 45 10. 73261 9. 27496 47 10. 72504 10. 00757 2 9. 99243 20 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 1 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 72398 28391 62 71609 00788 2 99212 7 54 32 48 27 12 27668 61 72332 28459 63 71541 00791 2 2 99209 9. 99207 5' 55 10 32 40 1 27 20 9. 27734 63 10. 72266 9. 28527 65 10. 71473 10. 00793 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 Diff. 99195 M. Hour P.M. Hour A. M. Cosine. Diff. Secant. Cotangent. Diff. Tangent. Cosecant. Sine. M. 100^ A A B B C C 79° 1 Seconds of time 1. 2- 8" 4" 5» 6» 7' Prop, parts of cols, i B 9 9 17 18 1 26 26 1 34 35 1 43 44 1 51 53 2 60 62 2 TABLE U. [Page 619 Log. Sines, Tangents, and Secants. 11° A A B B C C 168° M. Hour A. M. Hour p. M. Sine. Difl. Cosecant. Tangent. Diflf. 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 8 31 36 28 24 28254 3 71746 29067 3 70933 00818 99187 57 4 81 28 28 32 28319 4 71681 29184 4 70866 00815 99185 9. 99182 56 55 5 10 31 20 1 28 40 9. 28384 5 10. 71616 9. 29201 5 10. 70799 10. 00818 6 31 12 28 48 28448 6 71552 29268 6 70732 00820 99180 54 7 31 4 28 56 28512 7 71488 29335 8 70665 00823 99177 58 8 30 56 29 4 28577 8 71423 29402 9 70598 00825 99175 52 9 10 30 48 29 12 28641 9 71359 29468 10 70532 00828 99172 51 50 10 80 40 1 29 20 9. 28705 10 10. 71295 9. 29585 11 10. 70465 10. 00830 9.99170 n 30 82 29 28 28769 11 71281 29601 12 70399 00833 99167 49 12 30 24 29 36 28833 1 12 71167 29668 13 70332 00835 99165 48 18 30 16 29 44 28896 13 71104 29734 14 70266 00838 99162 47 14 30 8 29 52 28960 14 71040 29800 15 16 70200 00840 99160 9. 99157 46 45 15 10 30 1 30 9. 29024 16 10. 70976 9. 29866 10. 70134 10. 00843 IB 29 52 30 8 29087 17 70913 29932 17 70068 00845 99155 44 17 29 44 30 16 29150 18 70850 29998 18 70002 00848 99152 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 9. 99145 41 40 20 10 29 20 1 80 40 9. 29340 21 10. 70660 9. 30195 22 10. 69805 10. 00855 21 29 12 80 48 29403 22 70597 30261 23 69739 00858 99142 39 22 29 4 80 56 29466 23 70534 30326 24 69674 00860 99140 38 28 28 56 31 4 29529 24 70471 30.391 25 69609 00863 99137 87 24 28 48 31 12 1 31 20 29591 25 70409 30457 26 69543 10. 69478 00865 99135 36 35 25 10 28 40 9. 29654 26 10. 70346 9. 30522 27 10. 00868 9. 99182 26 28 32 81 28 29716 27 70284 30587 28 69413 00870 99130 34 27 28 24 31 36 29779 28 70221 30652 29 69.348 00873 99127 38 28 28 16 31 44 29841 29 70159 30717 30 69283 00876 99124 32 29 80 28 8 31 52 29903 30 70097 30782 31 32 69218 10. 69154 00878 99122 9. 99119 31 30 10 28 1 82 9. 29966 31 10. 70034 9. 30846 10. 00881 81 27 52 82 8 30028 32 69972 30911 33 69089 00883 99117 29 82 27 44 32 16 30090 33 69910 30975 35 69025 00886 99114 28 88 27 36 82 24 80151 34 69849 31040 36 68960 00888 99112 27 34 85 27 28 32 32 30213 35 69787 81104. 37 68896 00891 1 99109 9. 99106 26 25 10 27 20 1 32 40 9. 30275 36 10. 69725 9. 31168 38 10. 68832 10. 00894 2 86 27 12 32 48 30336 37 69664 31233 39 68767 005?&6 2 99104 24 87 27 4 32 56 80898 38 69602 31297 40 68703 00899 2 99101 23 88 26 56 33 4 30459 89 69541 31361 41 68689 00901 2 99099 22 39 26 48 83 12 30521 40 69479 31425 42 68575 00904 2 2 99096 9. 99093 21 20 40 10 26 40 1 33 20 9. 30582 41 10. 69418 9. 31489 43 10.68511 10. 00907 41 26 32 83 28 30643 42 69357 31552 44 68448 00909 2 99091 19 42 26 24 33 36 30704 43 69296 31616 45 68384 00912 2 99088 18 48 26 16 33 44 80765 45 69235 31679 46 68321 00914 2 99086 17 44 45 26 8 33 52 30826 46 47 69174 31743 47 68257 00917 2 2 99083 16 15 10 26 1 34 9. 30887 10.69113 9. 81806 49 10. 68194 10. 00920 9. 99080 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 86 34 24 31068 50 68932 31996 52 68004 00928 2 99072 12 49 25 28 34 82 31129 51 68871 32059 53 67941 00980 2 99070 11 10 50 10 25 20 1 34 40 9. 31189 52 10. 68811 9. 32122 54 10. 67878 10. 00938 2 9. 99067 51 25 12 34 48 31250 53 68750 32185 55 67815 00936 2 99064 9 52 25 4 34 56 31310 54 68690 82248 56 67752 00938 2 99062 8 58 24 56 35 4 31370 55 68630 32311 57 67689 00941 2 99059 7 54 55 24 48 35 12 31480 56 68570 32373 58 67627 00944 2 2 99056 6 10 24 40 1 35 20 9. 31490 57 10. 68510 9. 32436 59 10. 67564 10. 00946 9. 99054 5 56 24 32 35 28 31549 58 68451 32498 60 67502 00949 2 99051 4 57 24 24 35 36 31609 69 68391 32561 61 67439 00952 2 99048 3 58 24 16 35 44 81669 60 68331 32628 63 67877 00954 2 99046 2 59 24 8 35 52 81728 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. Diff. Sine. M. 101° A A B B C C 78° 1 Seconds of time ■ 1* 2' 3» 4' 5» 1 6» 7' Prop, parts of cols. •{B ic 8 a 16 16 1 23 24 1 31 32 1 39 1 47 40 1 49 2 ! 2 54 57 2 Page 620] TABLE U. Log. Sines, Tangents, and Secants. 129 A A B B C C 167° M. Hour A. M. Hour p, M. Sine. Difl. Cosecant. Tangent. DiS. Cotangent. Secant. • Difl. j Cosine. M. 60 10 24 1 36 9. 31788 10. 68212 9. 32747 10. 67253 10. 00960 9.99040 1 23 52 36 8 31847 1 68153 32810 1 67190 00962 99088 59 2 23 44 36 16 31907 2 68093 32872 2 67128 00965 : 99085 58 8 23 36 36 24 31966 3 68034 32933 3 67067 00968 99082 57 4 5 23 28 10 23 20 36 3t 1 36 40 82025 j 4 67975 10. 67916 32995 9.33057 4 5 67005 00970 10. 0097'3 '• 99080 9.99027 56 55 9. 32084 5 10. 66943 B 23 12 1 36 48 32143 6 67857 33119 6 66881 00976 99024 54 7 23 4 1 36 56 82202 7 67798 33180 7 66820 00978 99022 53 8 22 56 37 4 82261 8 67739 33242 8 66758 00981 99019 52 9 22 48 37 12 82319 9 67681 33803 9 66697 00984 10. 00987 ; 99016 9. 99013 51 50 10 10 22 40 1 37 20 9.32378 1 10 10. 67622 9. 88365 10 10.66635 1 11 22 32 37 28 82437 10 67563 33426 11 66574 00989 1 99011 49 12 22 24 37 36 82495 11 67505 33487 12 66513 00992 1 99008 48 18 22 16 37 44 32553 12 67447 33548 13 66452 00995 1 99005 47 14 22 8 37 52 32612 13 14 67388 38609 14 66391 00998 1 99002 46 45 15 10 22 1 38 9. 32670 10. 67880 9. 33670 15 10.66380 10. 01000 1 9.99000 16 21 52 38 8 32728 15 67272 38731 16 66269 01003 1 98997 44 17 21 44 38 16 82786 16 67214 33792 17 66208 01006 1 98994 43 18 21 36 38 24 32844 17 67156 33853 18 66147 01009 1 i 98991 42 19 20 21 28 38 32 32902 18 67098 33913 19 66087 01011 10.01014 1 98989 1 9.98986 41 40 10 21 20 1 38 40 9. 32960 19 10. 67040 9. 38974 20 10.66026 21 21 12 38 48 33018 20 66982 34034 21 65966 01017 1 98983 .39 22 21 4 38 56 38075 21 66925 34095 22 65905 01020 1 98980 38 28 20 56 39 4 33133 22 66867 34155 28 65845 01022 1 98978 37 24 20 48 39 12 88190 28 66810 34215 24 65785 10. 65724 01025 10.01028 1 98975 36 35 25 10 20 40 1 39 20 9. 33248 24 10. 66752 9. 34276 25 1 9.98972 26- 20 32 39 28 38805 25 66695 34336 26 I 6o664 01031 1 98969 34 27 20 24 39 36 33362 26 66638 34396 27 1 65604 01033 1 98967 83 28 20 16 39 44 83420 27 66580 34456 28 65544 01086 1 ' 98964 32 29 20 8 39 52 33477 ! 28 66523 84516 29 65484 01089 1 98961 31 80 10 20 1 40 9.33534 29 10. 66466 9. 34576 30 10. 65424 10. 01042 1 9.98958 80 81 19 52 40 8 33591 29 66409 34635 31 65365 01045 1 98955 29 82 19 44 40 16 88647 30 66358 84695 32 ! 65305 01047 1 98958 28 38 19 36 40 24 83704 31 66296 84755 83 65245 01050 2 98950 27 34 85 19 28 40 32 33761 32 66239 34814 34 65186 01053 2 98947 26 25 10 19 20 1 40 40 9.33818 33 10. 66182 9. 34874 35 10.65126 10. 01056 2 9.98944 36 19 12 40 4^ 33874 34 66126 .34933 36 65067 01059 2 98941 24 87 19 4 40 56 38931 35 66069 34992 37 i 65008 01062 2 98988 23 88 18 56 41 4 33987 36 66013 35051 38 64949 01064 2 98936 22 39 18 48 41 12 34043 i 87 65957 8.5111 39 64889 01067 2 98933 9. 98930 21 20 40 10 18 40 1 41 20 9. 34100 38 10. 65900 9. 35170 40 10.64830 10.01070 2 41 18 32 41 28 34156 39 65844 85229 41 ! 64771 01073 2 98927 19 42 18 24 41 36 34212 40 65788 85288 42 64712 01076 2 98924 18 48 18 16 41 44 34268 1 41 65782 35347 43 64653 01079 2 98921 17 44 45 18 8 41 52 34324 ; 42 65676 85405 44 45 64595 01081 2 98919 9. 98916 16 15 10 18 1 42 9. 34380 43 10. 65620 9. 35464 10. 64536 10. 01084 2 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 9.84658 1 48 10. 65342 9. 35757 50 110.64243 10. 01099 2 9. 98901 10 51 17 12 42 48 34713 48 65287 35815 51 641^5 01102 2 98898 9 52 17 4 42 56 34769 49 65231 85873 52 64127 01104 2 98896 8 53 16 56 43 4 34824 50 65176 35981 53 64069 01107 2 98893 7 54 16 48 43 12 34879 51 65121 85989 64 64011 OHIO 3 3' 98890 9. 98887 6 5 55 10 16 40 1 43 20 9. 34934 52 10. 65066 9. 36047 55 10.63953 10.01113 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 8 98878 2 59 16 8 43 52 35154 56 64846 36279 59 63721 01125 3 98875 1 60 16 44 35209 57 64791 36836 60 63664 01128 3 Difl. 98872 M. Hour p. M. Hour A. M. Cosine, j Diflf. Secant. Cotangent. Difif. Tangent. Cosecant. Sine. M. 102 o A A B B C C 77° 1 Seconds of time Prop, parts of cols. -{B C TABLE U. [Page 621 I Mg. Sines, Tangents, and Secants. 13° A A B B C C 166° M. Hour A.M. Hour P. M. Sine. 9. 35209 Diff. Cosecant. Tangent. Diff. Cotangent. Secant. Diff. Cosine. M. 60 10 16 1 44 10. 64791 9. 36336 10. 63664 10.01128 9. 98872 1 15 52 44 8 35268 1 64737 36394 1 63606 01181 ! 98869 1 59 ?< 15 44 44 16 35818 2 64682 86452 2 68548 01183 98867 58 8 15 86 44 24 85373 3 &4627 36509 3 63491 01186 98864 57 4 15 28 44 32 35427 4 64578 10. 64519 36566 4 5 63484 10. 63876 01189 98861 56 55 5 10 15 20 1 44 40 9. 85481 4 9. 36624 10. 01142 9. 98858 fi 15 12 44 48 35536 5 64464 86681 6 68319 01145 98855 54 7 15 4 44 56 35590 6 64410 36738 6 63262 01148 98852 53 8 14 56 45 4 85644 7 64356 36795 7 63205 01151 98849 52 9 14 48 45 12 35698 8 64302 36852 8 63148 01154 98846 51 10 10 14 40 1 45 20 9. ;^752 9 10. 64248 9. 36909 9 10. 63091 10.01157 9. 98848 50 n 14 82 45 28 35806 10 64194 36966 10 63034 01160 98840 49 12 14 24 45 86 35860 11 64140 37023 11 62977 01163 98887 48 i;s 14 16 45 44 85914 11 64086 37080 12 62920 01166 98834 47 14 14 8 45 52 85968 12 64082 37137 13 62868 01169 98831 46 45 15 10 14 1 46 9. 86022 13 10. 63978 9. 37193 14 10. 62807 10.01172 9. 98828 ifi 18 52 46 8 36075 14 63925 87250 15 62750 01175 98825 44 17 18 44 46 16 36129 15 68871 87306 16 62694 01178 98822 43 18 18 86 46 24 36182 16 68818 37363 17 62637 01181 98819 42 19 18 28 46 32 86236 17 63764 37419 18 62581 01184 98816 41 20 10 18 20 1 46 40 9. 36289 18 10. 63711 9. 37476 19 10. 62524 10.01187 9. 98813 40 21 13 12 46 48 36842 18 63658 37532 19 62468 01190 98810 39 22 13 4 46 56 36895 19 68605 37588 20 62412 01193 98807 88 28 12 56 47 4 36449 20 63551 37644 21 62356 01196 98804 37 24 25 12 48 47 12 36502 21 6,3498 37700 22 62300 01199 98801 36 35 10 12 40 1 47 20 9. 36555 22 !l0.6;i445 9. 37756 23 10. 62244 10. 01202 9. 98798 2rt 12 82 47 28 36608 23 68392 37812 24 62188 01205 98795 34 27 12 24 47 86 36660 24 68340 37868 25 62182 01208 98792 38 28 12 16 47 44 36713 25 63287 37924 26 62076 01211 98789 32 29 30 12 8 47 52 36766 25 63284 37980 27 62020 01214 10. 01217 2 98786 31 10 12 1 48 9. 86819 26 110.63181 9. 38035 28 10. 61965 9. 98788 30 81 11 52 48 8 36871 27 68129 38091 29 61909 01220 2 98780 29 82 11 44 48 16 36924 28 68076 38147 30 61858 01223 2 98777 28 88 11 86 48 24 36976 29 6.8024 38202 31 61798 01226 2 98774 27 84 85 11 28 48 32 37028 30 62972 38257 32 61743 10. 61687 01229 10. 01232 2 2 98771 26 25 10 11 20 1 48 40 9. 37081 31 10. 62919 9. 38813 32 9. 98768 m 11 12 48 48 87183 32 62867 38868 ! 33 61632 01235 2 98765 24 87 11 4 48 56 37185 32 62815 88423 1 34 61577 012.38 2 98762 23 88 10 56 49 4 87237 33 62763 38479 i a5 61521 t)1241 2 98759 22 89 10 48 49 12 87289 34 62711 38534 36 61466 01244 2 98756 21 40 10 10 40 1 49 20 9. 87841 35 10. 62659 9. 38589 37 10. 61411 10.01247 2 9. 98758 20 41 10 32 49 28 87893 36 62607 88644 88 61856 01250 2 98750 19 42 10 24 49 86 87445 37 62555 88699 39 61301 01254 2 98746 18 48 10 16 49 44 37497 38 62503 88754 40 61246 01257 2 98748 17 44 45 10 8 49 52 37549 9. 37600 39 62451 88808 42 61192 10. 61137 01260 10. 01263 2 2 98740 16 15 10 10 1 50 39 10.62400 9. 38863 9. 98787 46 9 52 50 8 37652 40 62348 38918 43 61082 01266 2 98784 14 47 9 44 50 16 37703 41 62297 38972 44 61028 01269 2 98731 13 48 9 36 50 24 37755 42 62245 39027 45 60973 01272 2 98728 12 49 50 9 28 50 32 37806 9.37858 43 44 62194 10. 62142 39082 45 60918 01275 2 98725 11 10 10 9 20 1 50 40 9. 39136 46 10. e0864 10. 01278 3 9. 98722 51 9 12 50 48 37909 45 62091 39190 47 60810 01281 3 98719 9 52 9 4 50 56 37960 46 62040 39245 48 60755 01285 3 98715 8 58 8 56 51 4 38011 47 61989 39299 49 60701 01288 3 98712 7 54 8 48 51 12 38062 47 61988 39353 50 60647 01291 3 98709 6 55 10 8 40 1 51 20 9.88113 48 10. 61887 9. 39407 51 10. 60593 10. 01294 3 9. 98706 5 56 8 32 51 28 88164 49 61836 39461 52 60589 01297 3 98703 4 57 8 24 51 86 38215 50 61785 39515 53 60485 01300 3 98700 3 58 8 16 51 44 38266 51 61784 39569 54 60431 01303 3 98697 2 59 8 8 51 52 38817 52 61683 39623 55 60377 01306 3 98694 1 60 M. 8 52 38368 53 61682 39677 56 Diff. 60323 Tangent. 01310 3 98690 M. Hour P. M. Hour A. M. Cosine. Diff. Secant. Cotangent. Cosecant. Diff. Sine. 103° A A B B C C 76° 1 Seconds of time 1« i 2' 3s ^ 4, ^ 5» j 6' 7» Prop, parts of cols. < B Ic 7 7 13 14 1 20 26 21 28 1 2 33 39 8.5 42 2 2 46 49 3 Page 622] TABLE 44. Log. Sines, Tangents, and Secants. 14° A A B B C C 16o° M. Hour A. M. Hour p. M. Sine. Diff. Cosecant. Tangent. Diff. Cotangent. 10. 60323 Secant. Diff. Cosine. 10 8 1 52 9. 38368 10. 61632 9. 39677 10. 01310 9. 98690 60 1 7 52 52 8 3S418 1 ! 61582 39731 1 60269 01313 98687 59 2 7 44 52 16 38469 2 61531 39785 9 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 98(>78 56 55 5 10 7 20 1 52 40 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 599t8 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 10 10 6 40 1 53 20 9. 38871 8 10. 61129 9.40212 i 9 10. 59788 10. 01341 9. 98659 50 11 6 32 53 28 38921 9 61079 40266 10 59734 01344 98656 49 12 6 24 53 36 38971 10 61029 40319 1 10 59681 01348 98652 48 13 6 16 53 44 39021 11 60979 40372 j 11 59628 01351 98649 47 14 6 8 53 52 39071 11 60929 40425 1 12 59575 01354 98646 46 15 15 10 6 1 54 9. 39121 12 ilO. 60879 9.40478 i 13 10. 59522 10. 01357 9. 98643 16 5 52 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 20 5 28 10 5 20 54 32 39319 15 60681 10. 60631 40689 17 59311 01370 — J- 98630 9. 98627 41 40 1 54 40 9. 39369 16 9.40742 : 17 10. 59258 10. 01373 21 5 12 54 48 39418 17 60582 40795 1 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 1 55 20 39566 S. 39615 20 60434 40952 ! 21 59048 01386 98614 36 25 10 4 40 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 4 8 55 52 39811 24 60189 41214 25 58786 01403 2 98597 31 30 10 4 1 56 9. 39860 24 10.60140 9.41266 26 10.58734 10. 01406 2 9. 98594 30 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 2 98581 9. 98578 26 25 35 10 3 20 1 56 40 9. 40103 29 10.59897 9.41526 30 10. 58474 01422 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 1 33 58319 01432 2 98568 22 39 2 48 57 12 40297 32 59703 41733 1 34 58267 01435 2 98565 21 40 10 2 40 1 57 20 9. 40346 33 10. 59654 9.41784 35 110.58216 10. 01439 2 9. 98561 20 41 2 32 57 28 40394 33 59606 41836 36 58164 01442 2 98558 19 42 2 24 57 36 40442 34 59558 41887 ! 36 58113 01445 2 98555 18 43 2 16 57 44 40490 36 59510 41939 i 37 58061 01449 2 98551 17 44 2 8 57 52 40538 36 59462 41990 38 58010 01452 2 985^8 16 15 45 10 2 1 58 9. 40586 37 10. 59414 9. 42041 39 10. 57959 10. 01455 2 9. 98545 46 1 52 58 8 40634 37 59366 42093 40 i 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 3 98531 9. 98528 11 10 50 10 1 20 1 58 40 9. 40825 41 :i0. 59175 9.42297 : 43 10. 57703 10. 01472 51 1 12 58 48 40873 42 59127 42348 i 44 57652 01475 3 98525 9 52 1 4 58 56 40921 42 59079 42399 i 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 48 57499 01485 3 98515 9.98511 6 5 55 10 40 1 59 20 9. 41063 45 10.58937 9. 42552 10. 57448 10. 01489 3 56 32 59 28 41111 46 58889 42603 49 57397 01492 3 98508 4 57 24 59 36 41158 46 58842 42653 50 57347 01495 3 98505 3 58 16 59 44 41205 47 58795 42704 50 57296 01499 3 98501 2 59 8 59 52 41252 48 58748 42755 51 57245 01502 3 98498 1 60 2 41300 49 58700 42805 52 57195 01506 3 98494 M. Hour p. M. Hour A. M. Cosine. Diff. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. Sine. M. 104° A A B B C c 76° Seconds of time 1« 2« 3» 4» 5> «• 7» fA Prop, parts of cols, i B IC 6 7 12 13 1 18 20 1 24 26 2 31 83 2 37 39 2 43 40 3 TABLE 44. [Page 623 Log. Sines, Tangents, and Secants. 15° A A B B C C 164° M. Hour A.M. 10 Hour P.M. Sine. Diff. Cosecant. Tangent. Diff. Cotangent. Secant. Diff. Cosine. M. 2 9.41300 10. 58700 9. 42805 10. 57195 10. 01506 ! 9. 98494 60 1 9 59 52 8 41347 1 58653 42856 1 57144 01509 98491 59 2 59 44 16 41394 2 5860(5 42906 2 57094 01512 1 98488 1 58 1 8 59 36 1 24 41441 2 58559 42957 2 57043 01516 98484 ! 57 I 4 59 28 32 41488 3 58512 43007 3 56993 01519 98481 56 5 9 59 20 2 40 9. 41535 4 10. 58465 9. 43057 4 10. 56943 10. 01523 9.98477 55 6 59 12 48 41582 5 58418 43108 5 56892 01526 1 98474 54 7 59 4 56 41628 5 58372 43158 6 56842 01529 1 98471 53 8 58 56 ; 14' 41675 6 58325 43208 7 56792 01533 ; 98467 52 9 10 58 48 ! 1 12 41722 7 58278 43258 7 56742 01536 98464 9. 98460 51 50 9 58 40 2 1 20 9. 41768 8 10. 58232 9. 43308 8 10. 56692 10. 01540 1 n 58 32 1 28 41815 8 58185 43358 9 56642 01543 98457 49 12 58 24 1 36 41861 9 58139 43408 10 56592 01547 98453 48 13 58 16 , 1 44 41908 10 58092 43458 11 56542 01550 98450 47 14 15 58 8 9 58 1 52 41954 9. 42001 11 11 58046 43508 11 56492 01553 10. 01557 98447 9. 9844;^ 46 45 2 2 10. 57999 9. 43558 12 110.56442 16 57 52 i 2 8 42047 12 57953 43607 13 56393 01560 98440 44 17 57 44 2 16 42093 13 57907 43657 14 56343 01564 98436 43 18 57 36 2 24 42140 14 57860 43707 15 56293 01567 98433 42 19 57 28 2 32 42186 14 57814 43756 9. 43806 16 56244 01571 10. 01574 98429 41 20 9 57 20 i 2 2 40 9. 42232 15 10. 57768 16 10. 56194 1 9. 98426 1 40 | 21 57 12 j 2 48 42278 16 57722 43855 17 56145 01578 1 98422 39 22 57 4 2 56 42324 17 57676 43905 18 56095 01581 1 98419 38 23 56 56 3 4 42370 17 576.30 43954 19 i 56046 01585 1 , 98415 37 24 25 56 48 3 12 42416 18 57584 44004 20 55996 01588 1 98412 1 36 9 56 40 i 2 3 20 9. 42461 19 10. 57539 9. 44053 20 10. 55947 10. 01591 1 9.98409 1 35 26 56 32 3 28 42507 20 57493 44102 21 55898 01595 2 98405 34 27 56 24 3 36 42553 21 57447 44151 2-2 55849 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 9. 42690 22 23 57356 10.57310 44250 24 55750 01605 2 98395 31 9 56 2 4 9. 44299 25 ilO. 55701 10. 01609 2 9.98391 i 30 31 55 52 4 8 42735 24 57265 44.348 25 55652 01612 2 98388 t 29 32 55 44 4 16 42781 24 57219 44397 26 55603 01616 2 ' 98384 28 33 55 36 1 4 24 42826 25 57174 44446 27 55554 01619 2 i 98381 27 34 55 28 i 4 32 42872 26 57128 10. 57083 44495 9. 44544 28 55505 01623 2 98377 26 25 35 9 55 20 2 4 40 9.42917 27 29 10. 55456 10. 01627 2 9.98373 36 55 12 4 48 42962 27 57038 44592 29 55408 016.30 2 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 55310 01637 2 98363 22 39 40 54 48 9 54 iO' 5 12 43098 30 30 56902 44738 9. 44787 32 33 55262 10. 55213 01641 10. 01644 2 98359 1 21 2 9. 98356 i 20 2 5 20 9. 43143 10. 56857 41 54 32 5 28 43188 31 56812 44836 34 55164 01648 2 98352 19 42 54 24 5 36 43233 32 56767 44884 34 55116 01651 2 98349 18 43 54 16 5 44 43278 33 56722 44933 35 55067 01655 3 98345 17 44 54 8 5 52 43323 9. 43367 33 34 56677 44981 9. 45029 36 37 55019 10. 54971 01658 10. 01662 3 98342 t 16 45 9 54 2 6 10. 56633 3 9. 98338 15 1 46 53 52 6 8 4.3412 35 56588 45078 38 54922 01666 3 98.334 14 I 47 53 44 6 16 43457 36 56543 45126 38 54874 01669 3 98331 13 48 53 36 i 6 24 43502 36 56498 45174 39 54826 01673 3 98327 12 49 50 53 28 6 32 2 6 40 43546 37 56454 45222 9. 45271 40 41 54778 10. 54729 01676 10. 01680 3 3 98324 11 10 9 53 20 9. 43591 38 10. 56409 9. 98320 51 53 12 i 6 48. 43635 39 56365 45319 42 54681 01683 3 98317 9 52 53 4 ■ 6 56 43680 39 56320 45367 43 54633 01687 3 98313 8 53 52 56 7 4 43724 40 56276 45415 43 54585 01691 3 98309 7 54 55 52 48 9 52 40 7 12 2 7 20 43769 9743813 41 42 56231 45463 9.45511 44 45 54537 01694 10.01698 3 3 98306 9. 98302 6 5 10. 56187 10. 54489 56 52 32 7 28 43857 43 56143 45559 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 54.346 01709 3 98291 2 59 52 8 7 52 43990 45 56010 45702 48 54298 01712 3 98288 1 60 52 8 440.34 46 55966 45750 49 54250 01716 4 98284 M. Hour p. M. Hour A. x. Cosine. Diff. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. Sine. M. 105° A A B B C C 74° 1 .Seconds of time ; 1» '2' \ 3' 4» 5» 6' 1' A 6 Prop, parts of cols. B 6 Ic 11 12 1 17 18 1 23 28 25 31 2 2 34 40 37 43 3 3 Page 624] TABLE 44. Log. Sines, Tangents, and Secants. 1S° A A B B C C 163° M. Hour A. M Hour p. M. Sine. Diff. Cosecant. Tangent. Diff. Cotangent. Secant. Diff. Cosine. M. 9 52 2 8 9. 44034 10. 55966 9. 45750 10. 542.50 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 2 541.55 01723 98277 58 8 51 36 8 24 44166 2 55834 45892 2 54108 01727 98273 57 4 51 28 8 ^2 44210 3 9. 44253 4 557f;0 10. 55747 45940 9. 45987' 3 4 54060 10. 54013 01730 10. 61734 98270 9.98266 56 55 5 9 51 20 2 8 40 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 10. 5.5528 46177 9. 46224 7 8 53823 10. 53776 01749 1 98251 1 9.98248 51 ,50 9 50 40 2 9 20 9. 44472 7 10.01752 11 50 32 9 28 44516 8 55484 46271 9 53729 017.56 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 15 50 8 9 50 9 52 44646 10 9.44689 1 11 553.54 10.5.5311 46413 9. 46460 11 12 5.3587 01767 98233 9. 98229 46 45 2 10 10. ,53540 10.01771 16 4 ) 52 10 8 447.33 1 11 55267 46507 12 53493 01774 98226 44 17 49 44 10 16 44776 12 55224 46554 13 53446 01778 98222 43 18 4 J 36 10 24 44819 13 55181 46601 14 53399 01782 98218 42 19 20 49 28 9 49 20 10 32 2 10 40 44862 14 14 55138 10. 55095 46648 9.46694 15 15 53352 10. 53306 01785 10.01'78'9 98215 41 9. 44905 9.98211 40 21 49 12 10 48 44948 1 15 5.5052 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 1 98200 37 24 48 48 11 12 46077 17 54923 46881 19 53119 01804 98196 36 25 9 48 40 2 11 20 9.45120 18 10. .54880 9. 46928 19 10. 53072 10.01808 2 9.98192 35 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 30 48 8 11 52 2 12 45292 21 9.453.34 21 54708 47114 22 52886 01823 2 98177 31 30 9 48 10.54666 9. 47160 23 10. 52840 10. 01826 2 9.98174 31 47 52 12 8 45377 i 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 2 12 40 45504 : 24 9.4.5547 25 54496 10. 54453 47346 9. 47392 26 27 52654 10. 52608 01841 2 98159 26 25 35 9 47 20 10.01845 2 9.981.55 36 47 12 12 48 4.5589 26 54411 47438 28 52562 01849 2 98151 24 37 47 4 12 56 45632 26 54368 47484 29 52516 018,53 2 98147 23 38 46 56 13 4 45674 27 54326 47.530 29 52470 01856 2 98144 22 39 46 48 40 9 46 40 13 12 2 13 20 45716 28 28' 54284 10. .54242 47576 9. 47622 30 31 52424 01860 10.01864 2 2 98140 9»98136 21 20 9. 45758 10. 52378 41 46 32 13 28 45801 29 54199 47668 32 52.332 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 45 9 46 13 52 2 14 4,5927 31 54073 10. .54031 47806 9. 47852 34 35 .52194 10. ,52148 01879 10. 01883 3 3 98121 9.98117 16 15 9. 45969 32 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 i 34 53905 47989 37 52011 01894 3 98106 12 49 45 28 14 32 461.36 1 35 53864 48035 38 51965 01898 3 98102 11 50 i 9 45 20 2 14 40 9.46178 .36 10. 53822 9. 48080 39 10.51920 10.01902 3 9. 98098 10 51 45 12 14 48 46220 i 36 53780 48126 39 51874 01906 3 98094 9 52 j 45 4 14 56 46262 37 53738 48171 40 51829 01910 3 98090 8 53 I 44 56 15 4 46303 38 53697 48217 41 51783 01913 3 98087 7 54 44 48 15 12 46.345 38 53655 10.53614 48262 9. 48.307 42 43 51738 01917 3 3 98083 6 5 55 9 44 40 2 15 20 9.46386 39 10. 51693 10. 01921 9. 98079 56 44 32 15 28 46428 40 53572 48353 43 5ia47 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 51.5-57 01933 4 98067 2 59 44 8 15 52 46552 1 42 5.3448 48489 46 51511 01937 4 98063 1 60 M. 44 16 46594 43 53406 Secant. 48534 46 51466 01940 4 Diff 98060 M. Hour p. M. Hour A. M. Casine. Diff. Cotangent Diff. Tangent. Cosecant. Sine. 106° A A B B C C 73° Seconds of time 1" «• 3« 4' &> 6< 7" Prop, parts of cols. (1 5 6 11 12 1 16 17 1 21 •23 2 27 29 2 32 35 3 37 41 3 TABLE 44. [Page 625 Log. Sines, Tangents, and Secants. 17° A A B B C C 162° M. Hour A. M. Hour p. M. Sine. Diff. Cosecant. Tangent. Diff. Cotangent. Secant. Difl. Cosine. M. 9 44 2 16 9. 46594 10. 53406 9. 48584 10. 51466 10. 01940 9.98060 60 1 48 52 16 8 46685 1 53365 48579 1 51421 01944 98056 59 2 48 44 16 16 46676 1 53324 48624 1 51376 01948 98052 58 8 48 86 16 24 46717 2 53283 48669 2 51331 019.52 98048 57 4 5 43 28 16 32 46758 3 54242 48714 3 51286 01956 98044 56 55 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 4()S41 4 53159 48804 4 51196 01964 98036 54 1 43 4 16 56 4(i8S2 5 53118 48849 5 51151 01968 98032 58 8 42 56 17 4 46923 5 53077 48894 6 51106 01971 98029 52 9 10 42 48 17 12 46964 6 7 53036 10. 52995 48939 7 51061 01975 98025 51 9 42 40 2 17 20 9. 47005 9. 48984 7 10. 51016 10. 01979 9. 98021 50 11 42 32 17 28 47045 7 52955 49029 8 50971 01983 1 1 98017 49 12 42 24 17 36 47086 8 52914 49073 9 50927 01987 1 1 98013 48 13 42 16 17 44 47127 9 52873 49118 i 10 50882 01991 1 1 98009 47 14 15 42 8 17 52 2 18 47168 9 52832 10. 52791 49163 10 50837 01995 1 1 98005 1 9.98001 46 45 9 42 9. 47209 10 9. 49207 11 110.50793 10. 01999 16 41 52 18 8 47249 11 52751 49252 12 50748 02008 97997 44 17 41 44 18 16 47290 11 52710 49296 12 50704 02007 97998 43 18 41 36 18 24 47830 12 52670 49341 13 50659 02011 97989 42 19 41 28 18 32 47371 13 52629 49385 14 50615 02014 1 ' 97986 41 20 9 41 20 2 18 40 9.47411 13 10. 52589 9. 49430 15 10. 50570 10.02018 1 9.97982 40 21 41 12 18 48 47452 14 52548 49474 15 50526 02022 1 I 979.78 39 22 41 4 18 56 47492 15 52508 49519 16 50481 02026 1 97974 38 28 40 56 19 4 47533 15 52467 49563 17 50487 02080 2 97970 37 24 40 48 19 12 47573 16 52427 49607 18 50393 02084 10. 02038 2 97966 2 9.97962 36 35 25 9 40 40 2 19 20 9. 47613 17 10. 52387 9. 49652 18 10. 50848 2(5 40 32 19 28 47654 17 52346 49696 19 50304 02042 2 97958 34 27 40 24 19 36 47694 18 52306 49740 20 50260 02046 2 97954 33 28 40 16 19 44 47734 19 52266 49784 21 50216 02050 2 97950 32 29 40 8 19 52 47774 19 20 52226 49828 21 22 50172 02054 2 2 97946 31 30 80 9 40 2 20 9.47814 10.52186 9. 49872 10. 50128 10. 02058 9. 97942 81 39 52 20 8 47854 21 52146 49916 23 50084 02062 2 97938 29 82 39 44 20 16 47894 21 52106 49960 24 50040 02066 2 97934 28 88 39 36 20 24 47934 22 52066 50004 24 49996 02070 2 97930 27 34 85 39 28 20 32 47974 j 23 52026 50048 9. 50092 25 26 49952 10. 49908 02074 2 97926 26 25 9 39 20 2 20 40 9. 48014 23 10. 51986 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 51906 50180 27 49820 02086 2 97914 23 38 38 56 21 4 48133 25 51867 50223 28 49777 02090 3 97910 22 39 40 38 48 21 12 2 21 20 48173 26 51827 50267 29 49733 02094 3 i 97906 3 9.97902 21 20 9 38 40 9. 48213 27 10. 51787 9.50311 29 ilO. 49689 10. 02098 41 38 32 21 28 48252 27 51748 50.355 30 1 49645 02102 3 j 97898 19 42 38 24 21 86 48292 28 51708 50398 31 49602 02106 3 ; 97894 18 43 38 16 21 44 48332 29 51668 50442 32 49558 02110 3 97890 17 44 45 38 8 21 52 2 22 48371 29 30 51629 10. 51589 50485 32 49515 02114 3 3 97886 9. 97882 16 15 9 38 9.48411 9. 50529 33 10.49471 10.02118 46 87 52 22 8 48450 31 51550 50572 34 49428 02122 3 97878 14 47 37 44 22 16 48490 31 51510 50616 35 49884 02126 3 97874 13 48 37 36 22 24 48529 32 51471 50659 35 49341 02130 3 97870 12 49 50 37 28 9 37 20 22 32 2 22 40 48568 33 33 51432 10. 51393 50703 9. 50746^ 36 49297 02134 3 97866 11 10 9. 48607 37 10. 49254 10. 02139 3 9.97861 51 37 12 22 48 48647 '34 51353 50789 37 49211 02143 3 97857 9 52 37 4 22 56 48686 35 51314 50833 38 49167 02147 3 97853 8 58 36 56 23 4 48725 35 51275 50876 39 49124 02151 4 97849 t 54 55 36 48 9 36 40 23 12 2 23 20 48764 36 51236 50919 9. 50962 40 40 49081 02155 4 97845 6 5 9. 48803 37 10.51197 10. 49038 10. 02159 4 9. 97841 56 36 32 23 28 48842 37 51158 51005 41 48995 02163 4 97887 4 57 36 24 23 36 48881 38 51119 51048 42 48952 02167 4 97888 3 58 36 16 23 44 48920 39 51080 51092 43 48908 02171 4 97829 2 59 36 8 23 52 48959 39 51041 511.35 43 48865 02175 4 97825 1 60 36 24 48998 40 51002 51178 44 48822 02179 4 97821 M. Hour p. M. Hour A. M. Cosine. Diff. Secant. Cotangent.] Diflf. Tangent. Cosecant. Diff. Sine. M. 107° A A B B C C 72° 1 Seconds of time Prop, parts of cols. -{B C 10 11' \ 30 33 L3 22489-03- 40 Page 626] TABLE U. Log. Sines, Tangents, and Secants. 18° A A B B C C 161° M. Hour A.M. 9 36 Hour p. M. Sine. Diff. Cosecant. Tangent. Diff. Cotangent. Secant. Diff. Cosine. 1 M. 2 24 9. 48998 10. 51002 9.51178 10. 48822 10. 02179 I 9. 97821 1 60 1 35 52 24 8 49037 1 50963 51221 1 48779 02183 97817 59 2 85 44 24 16 49076 1 50924 51264 1 48736 02188 97812 58 8 35 36 24 24 49115 2 50885 51806 2 48694 02192 97808 57 4 5 35 28 24«82 49158 3 50847 51349 8 48651 02196 97804 56 55 9 35 20 2 24 40 9. 49192 8 10. 50808 9. 51392 3 10. 48608 10. 02200 9. 97800 6 85 12 24 48 49281 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 34 48 25 12 49347 6 50653 51563 6 48437 02216 97784 51 50 10 9 34 40 2 25 20 9. 49385 6 10. 50615 9. 51606 7 10. 48394 10. 02221 9. 97779 11 84 32 25 28 49424 7 50576 51648 8 48352 02225 97775 49 12 34 24 25 86 49462 8 50538 51691 8 48309 02229 97771 48 18 34 16 25 44 49500 8 50500 51784 9 48266 02233 97767 47 14 84 8 25 52 49539 9 50461 51776 10 48224 02237 97763 46 45 15 9 34 2 26 9. 49577 9 10. 50428 9. 51819 10 10.48181 10. 02241 9. 97759 1« 38 52 26 8 49615 10 50385 51861 11 48139 02246 97754 44 17 83 44 26 16 49654 11 50346 51903 12 48097 02250 97750 43 18 33 36 26 24 49692 11 50308 51946 18 48054 02254 97746 42 19 33 28 26 32 49730 9. 49768 12 13 50270 10. 50232 51988 9. 52031 18 48012 02258 97742 41 40 20 9 88 20 2 26 40 14 10. 47969 10. 02262 9. 97738 21 . 33 12 26 48 49806 13 50194 52073 15 47927 02266 97734 39 22 83 4 26 56 49844 14 50156 52115 15 47885 02271 2 97729 38 23 82 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 25 9 32 40 2 27 20 9. 49958 16 10. 50042 9. 52242 10. 47758 10. 02283 2 9. 97717 85 26 32 82 27 28 49996 16 50004 52284 18 47716 02287 2 97713 84 27 82 24 27 86 50084 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 82 8 27 52 50110 18 49890 52410 20 47590 02300 2 97700 81 30 9 82 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 82 31 44 28 16 50228 20 49777 52536 22 47464 02313 2 97687 28 83 31 36 28 24 50261 21 49739 52578 28 47422 02317 2 > 97688 27 34 81 28 28 82 50298 21 49702 52620 24 47380 02321 2 97679 26 25 85 9 81 20 2 28 40 9. 50336 22 10. 49664 9. 52661 24 10. 47389 10. 02326 2 9. 97674 86 31 12 28 48 50374 23 49626 52708 25 47297 02880 3 97670 24 37 81 4 28 56 50411 23 49589 52745 26 47255 02334 3 97666 23 88 30 56 29 4 50449 24 49551 52787 27 47213 02838 3 97662 22 39 40 30 48 29 12 50486 25 49514 52829 27 47171 10. 47130 02848 3 97657 21 20 9 30 40 2 29 20 9. 50523 25 10. 49477 9. 52870 28 10. 02847 3 9. 97653 41 30 32 29 28 50561 26 49489 52912 29 47088 02351 3 97649 19 42 30 24 29 86 50598 26 49402 52953 29 47047 02355 3 97645 18 43 30 16 29 44 50635 27 49865 52995 80 47005 02360 3 97640 17 44 30 8 29 62 50673 28 49327 58087 31 46963 02864 3 97636 16 45 9 30 2 30 9. 50710 28 10. 49290 9. 58078 31 10. 46922 10. 02868 8 9. 97682 15 46 29 52 30 8 50747 29 49253 53120 82 46880 02372 8 97628 14 47 29 44 30 16 50784 80 49216 53161 83 46889 02377 3 97623 18 48 29 36 30 24 50821 30 49179 53202 34 46798 02381 3 97619 12 49 29 28 30 32 50858 31 49142 58244 84 46756 02385 8 4 97615 9. 97610 11 10 50 9 29 20 2 30 40 9. 50896 31 10. 49104 9. 58285 35 10. 46715 10.02390 51 29 12 30 48 50988 82 49067 53327 36 46673 02394 4 97606 9 52 29 4 30 56 50970 38 49030 53368 36 46632 02398 4 97602 8 53 28 56 31 4 r^007 88 48998 53409 37 46591 02408 4 97597 / 54 55 28 48 9 28 40 31 12 2 31 20 51043 84 85 48957 10. 48920 58450 9. 53492 38 88 46550 10. 46508 02407 10. 02411 4 4 97593 9. 97589 6 5 9. 51080 56 28 82 31 28 51117 85 48888 53533 89 46467 02416 4 97584 4 57 28 24 81 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 87 48773 53656 41 46344 02429 4 97571 i 60 28 82 51264 88 48736 53697 42 46303 02488 4 97567 M. M. Hour p. M. Hour A. M. Cosine. Diff. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. Sine. 108 3 A A B B C C 71°| Seconds of time 1» 2« 8» 4' 5> 6» T Prop, parts of cols. 59 4 8 1 55 52 57326 32 ; 42674 60605 ; 36 39395 03278 5 I 96722 1 60 4 56 57358 32 42642 60641 1 37 39359 03283 5 1 96717 i M. Hour P.M. Hour A. M. Cosine. Difl. Secant. Cotangent. Biff. Tangent. Cosecant. Difif. 1 Sine. M. 111° A A B B C C 68° 1 Second of time 1' 2' 3» 4« 5» 6» 7» Prop, parts of cols. t 4 5 1 8 9 1 12 14 16 19 2 ■ 20 23 3 24 28 4 28 32 4 1 Page 630] TABLE 44. Log. Sines, Tangents, and Secants. 22° A A B B C c 157° M. Hour A. M. Hour p. M. Sine. Diff. Cosecant. Tangent. Diff. Cotangent. Secant. Diff. Cosine. M. 60 9 4 2 56 9. 57358 10. 42642 9. 60&41 10. 39359 10. 03283 9. 96717 1 3 52 56 8 57389 1 42611 60677 1 39323 03289 96711 59 2 3 44 56 16 57420 1 i 42580 60714 1 39286 03294 96706 58 3 3 36 56 24 57451 2 ! 42549 60750 2 39250 03299 96701 57 4 3 28 56 32* 57482 2 ' 42518 60786 2 .3 39214 10.39177 03304 10. 03309 0' 96696 9. 96691 56 55 5 9 3 20 2 56 40 9. 57514 3 |lO. 42486 9. 60823 6 3 12 56 48 57545 3 1 42455 60859 4 39141 03314 96686 54 t 3 4 56 56 57576 4 ! 42424 60895 4 39105 03319 96681 53 8 2 56 57 4 57607 4 42393 60931 5 39069 03324 96676 52 9 2 48 57 12 57638 5 42362 60967 5 39033 03330 10.03335 96670 51 50 10 9 2 40 2 57 20 9. 57669 5 ilO. 42331 9. 61004 6 10. 38996 9. 96665 11 2 32 57 28 57700 6 42300 61040 1 38960 03340 96660 49 12 2 24 57 36 57731 6 42269 61076 / 38924 03345 96655 48 13 2 16 57 44 57762 7 42238 61112 8 38888 03350 96650 47 14 15 2 8 57 52 57793 7 i 42207 61148 8 9 38852 03355 96645 9. 96640 46 45 9 2 2 58 9. 57824 8 110.42176 9.61184 10. 38816 10. 03360 16 1 52 58 8 57855 8 i 42145 61220 10 • 38780 03366 96634 44 17 1 44 58 16 57885 9 42115 61256 10 38744 03371 96629 43 18 1 36 58 24 57916 9 42084 61292 11 38708 03376 2 96624 42 19 1 28 58 32 57947 10 42053 61328 11 38672 03381 2 96619 9.96614 41 40 20 9 1 20 2 58 40 9. 57978 10 ilO. 42022 9. 61364 12 10. 38636 10. 03386 2 21 1 12 58 48 58008 11 ! 41992 61400 13 38600 03392 2 96608 39 22 1 4 58 56 58039 11 41961 61436 13 38564 03397 2 96603 38 23 56 59 4 58070 12 41930 61472 14 38528 03402 2 96598 37 24 48 59 12 58101 12 41899 61508 14 38492 10. 38456 03407 2 2 96593 9. 96588 36 35 25 9 40 2 59 20 9. 58131 13 10.41869 9. 61544 15 10. 03412 2(j 32 59 28 58162 13 41838 61579 15 38421 o:^i8 2 96582 34 27 24 59 36 58192 14 ! 41808 61615 16 38385 03423* 2 96577 33 28 16 59 44 58223 14 41777 61651 17 38349 03428 2 96572 32 29 8 59 52 58253 15 41747 61687 17 38313 10. 38278 03433 3 96567 31 30 80 9 3 9. 58284 15 10.41716 9. 61722 18 10. 03438 3 9. 96562 31 8 59 52 8 58314 16 41686 61758 18 38242 03444 3 96556 29 32 59 44 16 58345 16 41655 61794 19 38206 03449 3 96551 28 33 59 36 24 58375 17 41625 61830 20 38170 03454 3 96546 27 34 59 28 32 58406 17 1 41594 61865 20 21 38135 03459 10. 03465 3 3 96541 9. 96535 26 25 35 8 59 20 3 40 9. 58436 18 jlO. 41564 9. 61901 10. 38099 36 59 12 48 58467 18 1 41533 61936 21 38064 03470 3 96530 24 37 59 4 56 58497 19 41503 61972 22 38028 03475 3 96525 23 38 58 56 1 4 58527 19 41473 62008 23 37992 03480 3 96520 22 39 40 58 48 1 12 58557 20 ! 41443 62043 23 37957 03486 3 96514 21 20 8 58 40 3 1 20 9. 58588 20 ilO. 41412 9. 62079 24 10. 37921 10. 03491 3 9. 96509 41 58 32 1 28 58618 21 i 41382 62114 24 37886 03496 4 96504 19 42 58 24 1 36 58648 21 1 41352 62150 25 37850 03502 4 96498 18 43 58 16 1 44 58678 22 41322 62185 26 37815 03507 4 96493 17 44 58 8 1 52 58709 22 41291 62221 26 27 37779 03512 4 4 96488 16 15 4o 8 58 3 2 9. 58739 23 10. 41261 9. 62256 10. 37744 10.03517 9. 96483 46 57 52 2 8 58769 23 41231 62292 27 37708 03523 4 96477 14 47 57 44 2 16 58799 24 41201 62327 28 37673 03528 4 96472 13 48 57 36 2 24 58829 24 41171 62362 29 37638 03533 4 96467 12 49 57 28 2 32 58859 25 41141 62398 29 37602 03539 4 96461 9. 96456 11 10' 50 8 57 20 3 2 40 9. 58889 25 10.41111 9. 62433 30 10. 37567 10. 03544 4 51 57 12 2 48 58919 26 41081 62468 30 37532 03549 4 96451 9 52 57 4 2 56 58949 26 41051 62504 31 37496 03555 5 96445 8 53 56 56 3 4 58979 27 41021 62539 32 37461 03560 5 96440 7 54 56 48 3 12 59009 27 40991 62574 32 33 37426 03565 5 96435 6 5 55 8 56 40 3 3 20 9. 59039 28 10. 40961 9. 62609 10. 37391 10. 03571 5 9. 96429 56 56 32 3 28 59069 28 40931 62645 33 37355 03576 5 96424 4 57 56 24 3 36 59098 29 40902 62680 34 37320 03581 5 96419 3 58 56 16 3 44 59128 29 ! 40872 62715 35 37285 03587 5 96413 2 59 56 8 3 52 59158 30 40842 62750 35 37250 03592 5 96408 1 60 56 4 59188 31 4081.2 62785 36 37215 03597 5 96403 M. Hour p. M. Hour A. M. Cosine. Diff. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. Sine. M. 11 2° A A B B C C 67° Seconds of time 1» 2» 3* 4' 5- 6- ?• fA Prop, parts of cols, i B Ic 4 4 1 8 9 1 11 13 2 15 18 3 19 22 8 23 27 4 27 81 5 TABLE 44. [Page 631 Log. Sines, Tangents, and Secants. •23° A A B B C C 156° M. Hour A. M. Hour p. M. Sine. Diff. Cosecant. . Tangent. Diff. Cotangent: Secant. Difl. Cosine. M. 8 56 3 4 9. 59188 10. 40812 9. 62785 10. 87215 10. 08597 9. 96403 60 1 55 52 4 8 59218 40782 62820 1 37180 03608 96.397 59 2 55 44 4 16 59247 1 40758 62855 1 37145 03608 96392 58 S 55 86 4 24 59277 1 40723 62890 2 37110 03613 96387 57 4 5 55 28 "8 55 20 4 32 59307 9. 59836 2 2 40698 10. 40664 62926 9. 62961 2 37074 03619 96381 9. 96376 56 55 3 4 40 3 10. 37039 10. 03624 « 55 12 4 48 59866 3 40634 62996 3 37004 03680 96370 54 7 55 4 4 56 59896 3 40604 63081 4' 36969 03635 96365 58 8 54 56 5 4 59425 4 40575 68066 5 36934 03640 96360 52 9 54 48 5 12 59455 4 40545 63101 5 .36899 03646 96854 9. 96849 51 50 10 8 54 40 8 5 20 9. 59484 5 10. 40516 9. 63135 6 10. 36865 10. 08651 11 54 82 5 28 59514 5 40486 68170 6 36880 08657 96843 49 1^ 54 24 5 36 59543 6 40457 68205 7 36795 03662 96388 48 1H 54 16 5 44 59573 6 40427 63240 7 36760 03667 96833 47 14 15 54 8 5 52 59602 7 7 40398 10. 40368 68275 8 86725 03673 96327 46 45 8 54 3 6 9. 59632 9. 68310 9 10. 36690 10. 03678 9. 96822 16 53 52 6 8 59661 8 40389 63345 9 86655 03684 96316 44 17 58 44 6 16 59690 8 40810 63879 10 36621 03689 2 96.311 48 18 58 36 6 24 59720 9 40280 63414 10 36586 03695 2 96805 42 19 20 53 28 6 32 59749 9 40251 63449 11 I 36551 03700 2 96300 41 8 53 20 3 6 40 9. 59778 10 10. 40222 9. 63484 12 10.36.516 10. 03706 2 9. 96294 40 21 53 12 6 48 59808 10 40192 63519 12 1 86481 03711 2 96289 39 22 53 4 6 56 59837 11 40163 63.553 13 36447 03716 2 96284 38 2S 52 56 7 4 59866 11 40134 6;i588 13 36412 03722 2 96278 37 24 25 52 48 8 52 40 7 12 59895 12 40105 63623 14 .36377 03727 10. 087.33 2 2 . 96273 36 35 3 7 20 9. 59924 12 10. 40076 9. 63657 14 10, 36843 9. 96267 26 52 32 7 28 59954 13 40046 63692 15 36308 087.38 2 96262 84 27 52 24 7 86 59983 13 40017 63726 16 36274 03744 2 96256 83 28 52 16 7 44 60012 14 89988 63761 16 86239 03749 3 96251 32 29 52 8 7 52 60041 14 39959 10. 39930 68796 17 36204 03755 3 96245 31 30 80 8 52 3 8 9. 60070 15 9. 63880 17 10.36170 10. 03760 3 9. 96240 81 51 52 8 8 60099 15 39901 63865 18 i 361.35 03766 3 96234 29 82 51 44 8 16 60128 15 89872 6.3899 1 18 86101 03771 3 ■ 96229 28 88 51 36 8 24 60157 16 89848 68934 19 36066 03777 3 96228 27 34 85 51 28 8 32 60186 9. 60215 16 17 39814 63968 20 36032 03782 10. 03788 3 3 96218 26 8 51 20 3 8 40 10. 39785 9.64003 20 |10. 3.5997 9. 96212 25 86 51 12 8 48 60244 17 39756 64037 21 1 35968 03798 3 96207 24 87 51 4 8 56 60273 18 89727 64072 ! 21 i .35928 03799 3 96201 23 88 50 56 9 4 60302 18 89698 64106 22 .85894 03804 3 96196 22 39 40 50 48 9 12 60331 19 ! 39669 64140 22 35860 0.3810 4 4 96190 9. 96185 21 20 8 50 40 3 9 20 9. 60359 19 [10.39641 9. 64175 23 10.35825 10. 03815 41 50 32 9 28 60888 20 89612 64209 24 j a5791 03821 4 96179 19 42 50 24 9 36 60417 20 89583 64243 24 .35757 03826 4 96174 18 48 50 16 9 44 60446 21 39554 64278 25 35722 03832 4 96168 17 44 "45 50 8 9 52 60474 21 39526 64812 25 35688 03838 4 96162 16 8 50 3 10 9. 60503 22 10.89497 9.64346 1 26 10.3.56.54 10. 08843 4 9.961.57 15 46 49 52 10 8 60582 22 89468 64381 26 3.5619 03849 4 96151 14 47 49 44 10 16 60561 28 89489 64415 27 .35585 08854 4 96146 18 48 49 86 10 24 60589 28 89411 64449 28 85.551 08860 4 96140 12 49 50 49 28 8 49 20 10 32 3 10 40 60618 24 39882 64483 28 3.5517 08865 10. 03871 4 5 96135 9.96129 11 10 9. 60646 ! 24 10. 39:^4 9.64517 29 10. 35483 51 49 12 10 48 60675 i 25 89325 64552 29 1 35448 03877 5 96128 9 52 49 4 10 56 60704 i 25 39296 (M586 30 35414 03882 5 96118 8 58 48 56 11 4 60782 26 39268 64620 81 35380 03888 5 96112 / 54 55" 48 48 8 48 40 11 12 60761 9. 60789 26 27 39239 10.39211 64654 9. 64688 31 32 .35.346 10. .8.5812 08893 10.03899 5 5 /96107 9.96101 6 5 8 11 20 56 48 32 11 28 60818 27 39182 64722 32 35278 08905 5 96095 4 57 48 24 11 36 60846 28 89154 64756 38 .35244 03910 5 96090 8 58 48 16 11 44 60875 28 89125 64790 38 .35210 03916 5 96084 2 59 48 8 11 52 60903 29 39097 64824 .34 .35176 03921 5 96079 1 60 M. 48 12 60981 29 39069 64858 35 35142 03927 6 96073 Hour p. M. Hour A.M. Cosine. Diff. Secant. Cotangent. Diff Tangent. .;Cosecant. Diff. Sine. M. 113^ A A B B C C 66° 1 Seconds of time Prop, parts of cols. -< B p age 632j TABLE 41. Log. Sines, Tangents, and Secants. 24° A A B B C C 165° M. 60 M. Hour A. M. Hour p. 3C. Sine. 1 Diff. j Cosecant. Tangent. Diff. Cotangent. Secant. Diff. Cosine. 8 48 3 12 9.60931 i 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 1 39012 64926 1 35074 03938 96062 58 3 47 36 12 24 61016 1 i 38984 64960 2 35040 03944 96056 57 4 5 47 28 12 3g 61045 9. 61073 2 2 38955 64994 2 35006 03950 96050 56 55 8 47 20 3 12 40 10. 38927 9. 65028 3 10.34972 10. 03955 9. 96045 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 10 46 48 13 12 61186 4 38814 65164 5 34836 03978 96022 51 50 8 46 40 3 13 20 9. 61214 5 10.38786 9. 65197 6 10. 34803 10. 03983 9.96017 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. 6i;i54 / 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 20 45 28 8 45 20 14 32 3 14 40 61466 9 38534 9 10.38506 65501 1 11 9.65535 i 11 34499 04035 2 2 95965 41 40 9. 61494 10. 34465 10. 04040 9. 95960 21 45 12 14 48 61522 10 i 38478 65568 12 i 34432 04046 2 95954 39 22 45 4 14 56 61550 10 38450 65602 1 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 i 34331 04063 2 95937 36 35 25 8 44 40 3 15 20 9. 61634 12 10. 38366 9. 65703 14 ilO. 34297 10. 04069 2 9. 95931 26 44 32 15 28 61662 12 38338 65736 15 34264 04075 2 95925 34 27 44 24 15 36 61689 12 38311 65770 15 34230 04080 3 95920 33 28 44 16 15 44 61717 13 38283 65803 16 34197 04086 3 95914 32 29 30 44 8 15 52 61745 13 38255 65837 16 34163 04092 3 95908 31 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 35 43 28 16 32 61883 \ 16 ! 38117 66004 19 ! 33996 04121 3 95879 26 25" 8 43 20 3 16 40 9. 61911 16 ilO. 38089 9. 66038 20 10. 33962 10. 04127 3 9. 95873 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 20 40 8 42 40 3 17 20 9.62049 1 18 10.37951 9.66204 22 10.33796 10. 04156 4 9. 95844 41 42 32 17 28 62076 i 19 37924 66238 1 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 1 24 33696 04173 4 95827 17 44 42 8 17 52 62159 20 37841 66337 25 33663 04179 4 95821 9. 95815 16 15 45 8 42 3 18 9. 62186 21 10. 37814 9. 66371 25 10. 33629 10. 04185 4 46 41 52 18 8 62214 21 37786 66404 26 33596 04190 4 95810 14 47 41 44 18 16 62241 22 37759 66437 26 33563 04196 5 95804 13 48 41 36 18 24 62268 22 37732 66470 27 33530 04202 5 95798 12 49 50 41 28 8 41 20 18 32 62296 23 37704 66503 9. 66537 27 28 33497 04208 5 95792 11 10 3 18 40 9. 62323 1 23 10. 37677 10. 33463 10. 04214 5 9. 95786 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 55 40 48 8 40 40 19 12 3 19 20 62432 25 37568 9.62459 1 25 10.37541 66669 9. 66702 30 31 33331 04237 5 5 95763 6 5 10. 33298 10. 04243 9. 95757 56 40 32 19 28 62486 ■ 26 37514 66735 31 33265 04249 5 95751 4 57 40 24 19 36 62513 ; 26 37487 66768 32 33232 04255 5 95745 3 58 40 16 19 44 62541 27 37459 66801 32 33199 04261 6 95739 9 59 40 8 19 52 62568 27 37432 66834 33 33166 04267 6 95733 1 60 40 20 '62595 28 37405 66867 33 Diff. 33133 04272 6 95728 M. M. Hour p. M. Hour A.M Cosine. Diff. Secant. Cotangent. Tangent. Cosecant. Diff. Sine. 114° A A B B C C 65° .Seconds of time 1» i' ){• 4' 5* 17 21 4 C 21 2.'i 4 7« 24 29 Prop, parts of colp.-fE 5 1 7 8 1 10 13 2 14 17 3 TABLE 44. Page 633 Log. Sines, Tangents, and Secants. 25° A A B B C C 154° M. Hour A. M. Hour P. M. Sine. Diff. Cosecant. Tangent. Diff. Cotangent. Secant. Diff. Cosine. M. 8 40 3 20 9. 62595 10. 87405 9. 66867 10. 33133 10. 04272 9. 95728 60 1 39 52 20 8 62622 87378 66900 1 38100 04278 95722 59 9, 39 44 20 16 62649 1 37351 66933 1 38067 04284 95716 58 8 39 36 20 24 62676 1 37824 66966 2 33034 04290 95710 57 4 5 39 28 20 32 62703 2 87297 66999 2 33001 04296 95704 56 55 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 H 38 56 21 4 62811 4 87189 67131 4 32869 04320 95680 52 9 10 38 48 21 12 62838 4 87162 67163 5 5 32837 04326 95674 51 8 38 40 3 21 20 9. 62865 4 10.37135 9. 67196 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 87082 67262 7 32738 04343 95657 48 18 38 16 21 44 62945 6 87055 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. 67860 8 10. 32640 10. 64361 2 9. 95639 45 16 37 52 22 8 63026 7 36974 67393 9 32607 04367 2 95683 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 37 28 22 32 63106 8 36894 67491 10 32509 04385 2 95615 41 40 20 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 i 36841 67556 11 32444 04397 2 95603 39 22 37 4 22 56 63186 10 ! 36814 67589 12 32411 04403 2 95597 38 28 36 56 23 4 63213 10 36787 67622 12 32378 04409 2 95591 37 24 36 48 23 12 63239 11 36761 67654 13 32346 04415 2 955a5 36 25 8 36 40 3 23 20 9. 63266 11 10.36734 9. 67687 14 10.32813 10. 04421 3 9. 95579 35 26 36 32 23 28 63292 11 36708 67719 14 32281 04427 3 95.573 34 27 36 24 23 36 63319 12 36681 67752 15 32248 04433 3 95567 83 28 36 16 23 44 63345 12 36655 67785 15 32215 04439 3 95561 32 29 80 36 8 23 52 63372 9. 63398 13 36628 67817 16 32183 04445 3 95555 31 30 8 36 3 24 13 10. 36602 9. 67850 16 :10. 32150 10. 04451 3 19.95549 81 35 52 24 8 63425 14 36575 67882 17 32118 04457 3 95543 29 82 35 44 24 16 63451 14 36549 67915 17 32085 04463 3 95537 28 88 35 36 24 24 63478 15 86522 67947 18 32053 04469 3 95531 27 34 35 28 24 32 63504 15 36496 67980 18 32020 04475 3 95525 26 25 85 8 35 20 3 24 40 9. 63531 15 10.36469 9. 68012 19 10. 31988 10. 04481 4 9. 95519 86 35 12 24 48 63557 16 .36443 68044 20 31956 04487 4 95513 24 87 35 4 24 56 68583 16 86417 68077 20 31928 04493 4 95507 23 88 34 56 25 4 63610 17 1 36390 68109 21 31891 04500 4 95500 22 39 34 48 25 12 63636 17 1 36364 68142 21 31858 04506 4 95494 21 20 40 8 34 40 3 25 20 9. 63662 18 ;iO. 36338 9. 68174 22 10. 31826 10. 04512 4 9. 95488 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. 68794 .20 10.36206 9. 68336 24 10.31664 10. 04542 5 9. 95458 15 46 33 52 26 8 68820 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 86128 68432 26 31568 04560 95440 12 49 33 28 26 32 68898 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 ilO. 31503 10. 04573 5 9. 95427 51 33 12 26 48 63950 23 36050 68529 28 31471 04579 5 95461 9 52 33 4 26 56 63976 23 36024 68.561 28 31489 04585 5 95415 8 53 32 56 27 4 64002 23 35998 68593 29 31407 04591 5 95409 7 54 32 48 27 12 64028 24 35972 68626 29 30 31374 10. 31342 04597 5 95403 6 5 55 8 32 40 3 27 20 9. 64054 24 10. 35946 9. 68658 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 85894 68722 31 31278 04616 6 95384 3 58 32 16 27 44 64132 26 1 85868 68754 31 1 31246 04622 6 95378 2 59 32 8 27 52 64158 26 85842 68786 32 31214 04628 6 95372 1 60 32 28 64184 26 85816 68818 33 31182 04634 6 95366 M. Hour p. M. Hour A. M. Cosine. Diff. Secant. Cotangent. Diff. Tangent. Cosecant. Diflf. Sine. M. 115° A A B B C C 64° 1 Seconds of time ! 1» 2. 1 3. 4" 5« 1 6» 7« f A 1 3 Prop, parts of cols, -j B ] 4 vC 1 7 8 2 10 12 2 13 16 3 17 20 20 24 4 5 23 28 5 Page 634] TABLE U. Log. Sines, Tangents, and Secants. 26° M. A A B B C c 153° Hour A. M. Hour p. M. Sine. Diff. Cosecant. Tangent. Diff. Cotangent. Secant. Diff. Cosine. M. 8 32 3 28 9.64184 10. 35816 9. 68818 10.31182 10. 04634 9.95366 60 1 31 52 ! 28 8 64210 35790 68850 1 31150 04640 95360 59 2 31 44 28 16 64236 1 35764 68882 1 31118 04646 95354 58 8 31 36 28 24 64262 1 35738 68914 2 31086 04652 95348 57 4 5 31 28 28 32< 64288 9.64313 2 ~2' 35712 10735687 68946 9. 68978 2 3 31054 10.31022 04659 10. 04665 . 95341 1 9.95335 56 55 8 31 20 3 28 40 6 31 12 ' 28 48 64;«9 3 :i5661 69010 3 30990 04671 1 i 95329 54 7 31 4 i 28 56 64365 3 35635 69042 4 30958 04677 1 ! 95323 53 8 30 56 29 4 64391 3 35609 69074 4 3092f) 04683 1 1 95317 52 9 10 30 48 29 12 3 29 20 64417 4 4 35583 10. 35558 69106 5 5 30894 10. 30862 04690 10. 04696 1 95310 1 9.95304 51 50 8 30 40 9.64442 9. 69138 11 30 32 1 29 28 64468 5 35532 69170 6 30830 04702 1 I 95298 49 12 30 24 29 36 64494 5 35506 69202 6 30798 04708 1 95292 48 13 30 16 29 44 64519 5 35481 69234 7 ' 30766 04714 1 1 95286 47 14 30 8 29 52 64545 6 35455 69266 8 30734 10. 30702 04721 1 1 95279 46 45" 15 8 30 ! 3 30 9. 64571 6 10. 35429 9. 69298 10. 04727 2 i 9. 95273 16 29 52 30 8 64596 7 35404 69329 8 30671 04733 2 1 95267 44 17 29 44 1 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 ; 95254 42 19 20 29 28 30 32 64673 9.64698 8 35327 69425 10 30575 04752 10. 04758 2 2 95248 41 40 8 29 20 3 30 40 8 10. 35302 9. 69457 11 10. 30543 9. 95242 21 29 12 30 48 64724 9 35276 69488 11 30512 04764 2 95236 39 22 29 4 1 30 56 64749 9 35251 69520 12 30480 04771 2 95229 38 23 28 56 31 4 64775 10 35225 69552 12 30448 04777 2 1 95223 37 24 28 48 31 12 64800 10 11 35200 10. 35174 69584 13 13 30416 10. 30385 04783 10.04789 3 1 95217 36 35 25 8 28 40 3 31 20 9. 64826 9. 69615 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 95198 33 28 28 16 31 44 64902 12 35098 69710 15 30290 04808 3 95192 32 29 30 28 8 31 52 64927 12 35073 10. 35047 69742 15 16 30258 10. 30226 04815 3 ' 95185 31 30 8 28 i 3 32 9. 64953 13 9. 69774 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 i 32 24 65029 14 34971 69868 17 30132 04840 3 95160 27 34 "35" 27 28 32 32 65054 14 15 •34946 10. 34921 69900 18 30100 10. 30068 04846 4 95154 26 25 8 27 20 3 32 40 9. 65079 9. 69932 18 10.04852 4 9.95148 36 27 12 32 48 65104 15 34896 69963 19 30037 04859 4 95141 24 37 27 4 ! 32 56 65130 16 34870 69995 20 30005 04865 4 95135 23 38 26 56 33 4 65155 16 34845 70026 20 29974 04871 4 95129 22 39 26 48 33 12 65180 16 34820 70058 21 29942 04878 4 1 95122 21 40 8 26 40 ! 3 33 20 9. 65205 17 10. 34795 9.70089 ! 21 10.29911 10. 04884 4 9.95116 20 41 26 32 33 28 65230 17 34770 70121 22 29879 04890 4 95110 19 42 26 24 33 36 65255 18 34745 70152 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. 29753 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 25 29691 04929 5 95071 13 48 25 36 34 24 65406 20 34594 70341 25 29659 04935 5 9.5065 12 49 50' 25 28 34 32 8 25 20 3 M 40 65431 "9.65456 21 "21 34569 10. 34544 70372 26 26 29628 10. 29596 04941 10.04948 5 95059 5 9.95052 11 10 9. 70404 51 25 12 i M 48 65481 22 34519 70435 27 29565 04954 5 95046 9 52 25 4 I M 56 65506 22 34494 70466 27 29534 04961 5 95039 8 53 24 56 : 35 4 65531 22 34469 70498 28 29502 04967 6 95033- 7 54 24 48 1 35 12 65556 23 34444 70529 28 29471 04973 6 ! 95027 6 00 8 24 40 i 3 35 20 9. 65580 23 10. 34420 9. 70560 29 10. 29440 10. 04980 6 9.95020 5 56 24 32 35 28 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 05005 6 i 94995 1 60 M. 24 36 65705 25 Difl. 34295 70717 32 29283 05012 6 94988 Hour p. M. 1 Hour a. m. Cosine. Secant. Cotangent. Diff. Tangent. Cosecant. Difl. j Sine. M. 116° A A B B C C 68° Seconds of time !•• 2« 8* 4« &• 6> 7« (A Prop, parts of cols. < B (C 8 6 4 8 1 2 10 12 2 13 16 3 16 19 20 24 4 6 22 28 6 TABLE 44. [Page 635 Log. Sines, Tangents, and Secants. 27° A A B B C C 152° M. •Hour A.M. Hour P. M. Sine. i Diff. Cosecant. Tangent. Diff. Cotangent. Secant. Diff. Cosine. M. 60 8 24 3 36 9.65705 i 10. 34295 9. 70717i 10. 29283 10. 05012 9. 94988 1 23 52 36 8 65729 34271 70748 1 29252 05018 94982 59 ?, 23 44 36 16 65754 1 34246 70779 1 29221 05025 1 94975 58 n 23 36 36 24 65779 1 34221 70810 2 29190 05081 94969 57 4 23 28 36 32 65804 2 34196 70841 9. 70873 2 3 29159 10. 29127 05088 94962 56 55 5 8 23 20 3 36 40 9.65828 i 2 10. 34172 10.05044 9. 94956 H 23 12 36 48 65853 i 2 34147 70904 3 29096 05051 94949 54 7 23 4 36 56 65878 3 34122 70935 4 29065 05057 94948 58 8 22 56 37 4 65902 i 3 34098 70966 4 29034 05064 94986 52 9 To 22 48 37 12 3 37 2b 65927 9.65952 4 34073 70997 5 29008 05070 94980 9. 94928 51 50 8 22 40 4 10. 34048 9. 71028 5 10. 28972 10. 05077 n 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 1 94911 48 18 22 16 37 44 66025 5 33975 71121 / 28879 05096 1 • 94904 47 u 22 8 37 52 66050 6 33950 71153 / 28847 10. 28816 05102 10. 05109 2 2 94898 46 45 15 8 22 3 38 9.66075 1 6 10. 33925 9. 71184 8 9. 94891 IH 21 52 38 8 66099 6 33901 71215 8 28785 05115 2 94885 44 17 21 44 38 16 66124 ! 7 38876 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 10 28692 05135 10. 05142 2 2 94865 9. 94858 41 40 20 8 21 20 3 38 40 9. 66197 8 10. 33803 9. 71339 10.28661 21 21 12 38 48 66221 8 33779 71370 11 28630 05148 2 94852 39 9.2 21 4 38 56 66246 9 33754 71401 11 28599 05155 2 94845 88 23 20 56 39 4 66270 9 33730 71431 12 28569 05161 3 94839 87 24 2o 20 48 8 20 40 39 12 3 39 20 66295 I 10 9.66319 10 33705 10. 33681 71462 12 13 28538 10. 28507 05168 3 94832 36 9. 71493 10. 05174 3 9. 94826 .35 2<5 20 32 39 28 66348 11 33657 71524 13 28476 05181 3 94819 .84 27 20 24 39 36 66368 11 33632 71555 14 28445 05187 3 94813 33 28 20 16 39 44 66392 11 33608 71586 14 28414 05194 3 94806 32 29 20 8 89 52 66416 12 33584 71617 15 28883 05201 3 94799 31 80 8 20 3 40 9. 66441 12 10. 83559 9. 71648 15 10. 28852 10. 05207 3 9. 94793 30 81 19 52 40 8 66465 13 33535 71679 16 28321 05214 3 94786 29 82 19 44 40 16 66489 13 33511 71709 16 28291 05220 4 94780 28 88 19 36 '40 24 66513 13 83487 71740 17 28260 05227 4 94773 27 34 85 19 28 8 19 20 40 32 3 40 40 66537 14 9. 66562 14 33463 71771 17 28229 10. 28198 05233 10. 05240 4 4 94767 9. 94760 26 25 10. 33438 9. 71802 18 86 19 12 40 48 66586 15 33414 71833 19 28167 05247 4 94753 24 87 19 4 40 56 66610 15 83390 71863 19 28137 05253 JL 94747 23 88 18 56 41 4 66634 15 83366 71894 20 28106 05260 4 94740 22 89 40" 18 48 8 18 40 41 12 66658 16 16 33342 10. 83318 71925 9. 71955 20 21 28075 05266 4 4 947.34 21 20 3 41 ao 41 f8 9. 66682 10. 28045 10. 05273 9. 94727 41 18 32 66706 17 33294 71986 21 28014 05280 4 94720 19 42 18 24 41 36 66731 17 88269 72017 22 27988 05286 5 94714 18 48 18 16 41 44 66755 17 33245 72048 22 27952 05293 5 94707 17 44 18 8 41 52 66779 18 83221 72078 23 27922 05300 5 94700 9. 94694 16 15 45 8 18 8 42 9.66803 ; 18 10. 88197 9. 72109 23 10. 27891 10. 05306 5 4H 17 52 42 8 66827 19 33173 72140 24 27860 05313 5 : 94687 14 47 17 44 42 16 66851 19 83149 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 42 32 66899 20 20 33101 10. 33078 72231 9. 72262 25 26 27769 10727738 05333 10. 05;340 5 5 94667 11 8 17 20 3 42 40 9. 66922 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 58 16 56 43 4 66994 21 33006 72354 27 27646 05360 6 94640 7 54 55 16 48 8 16 40 43 12 67018 22 9. 67042 22 32982 10. 32958 72384 9. 72415 28 28 27616 10. 27585 05366 6 94634 6 5 3 48 20 10. 05373 6 9.94627 5(> 16 32 43 28 67066 23 329:^ 72445 29 27555 05380 6 94620 4 57 16 24 43 36 67090 i 23 32910 72476 29 27524 05386 6 94614 8 58 16 16 43 44 67118 i 23 32887 72506 30 27494 05393 6 94607 2 59 16 8 43 52 67137 I 24 32863 72537 30 27463 05400 6 94600 1 60 M. 16 44 67161 24 32839 72567 31 27433 05407 / 94593 Hour p. M. Hour A.M. Cosine. ' Diff. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. Sine. M. 117° A A B B C C 62° j Seconds of time 1» 2« 3« 4» 5' 6' 7' Prop, parts of cols. -(B Ic 3 6 4 8 1 2 9 12 2 12 15 3 15 19 4 18 23 5 21 27 6 Page 636] TABLE 44. Log. Sines, Tangents, and Secants. 28° A A B B C C 151° M. Hour A. M. Hour p. M. Sine. DiS. Cosecant. Tangent. Diflf. ! Cotangent. Secant. Diff. Cosine. M. 60 8 16 3 44 9. 67161 10. 32839 9.72567 1 10.27438 10. 05407 9. 94593 1 15 52 44 8 67185 32815 72598 1 1 27402 05413 94587 59 2 15 44 44 16 67208 1 32792 72628 1 27372 1 05420 94580 58 8 15 36 44 24 67232 1 32768 72659 2 27341 05427 94573 57 4 5^ 15 28 8 15 20 44 32^ 3 44 40 67256 9.67280 2 2 32744 72689 2 3 27311 05433 94567 56 55 10. 32720 9. 72720 10. 27280 10. 05440 9. 94560 H 15 12 44 48 67303 2 32697 72750 3 27250 05447 94553 54 7 15 4 44 56 67327 3 32678 72780 4 27220 05454 94546 58 S 14 56 45 4 67350 3 32650 72811 4 27189 05460 94540 52 9 10 14 48 45 12 67374 9. 67398 3 4 32626 10. 32602 72841 5 27159 05467 94533 51 50 8 14 40 3 45 20 9.72872 5 10. 27128 10. 05474 9. 94526 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 18 14 16 45 44 67468 5 32532 72963 7 27037 05494 94506 47 14 14 8 45 52 67492 5 32508 72993 7 27007 05501 2 94499 46 45 15 8 14 3 46 9. 67515 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 78084 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 28 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 8 94431 36 35 25 8 12 40 3 47 20 9. 67750 10 10. 32250 9. 73326 18 10. 26674 10. 05576 8 9.94^4 26 12 32 47 28 67773 10 32227 73356 18 26644 05583 3 94417 34 27 12 24 47 36 67796 10 32204 73386 14 26614 05590 8 94410 88 28 12 16 47 44 67820 11 32180 73416 14 26584 05596 3 94404 32 29 12 8 47 52 67848 11 32157 78446 9. 73476 15 26554 05603 3 94397 81 30 80 8 12 3 48 9. 67866 12 10. 32134 15 10. 26524 10. 05610 3 9. 94390 81 11 52 48 8 67890 12 32110 73507 16 26493 05617 4 94383 29 82 11 44 48 16 67913 12 32087 73537 16 26463 05624 4 94376 28 88 11 36 48 24 67936 13 32064 73567 17 26438 05631 .4 94369 27 34 11 28 48 32 67959 13 32041 73597 17 26403 05638 10. 05645 4 4 94362 26 ;i5 8 11 20 3 48 40 9. 67982 14 10. 32018 9. 73627 18 10. 26873 9. 94355 25 86 11 12 48 48 68006 14 31994 73657 18 26343 05651 4 94349 24 87 11 4 48 56 68029 14 31971 78687 19 26318 05658 4 94342 23 88 10 56 49 4 68052 15 31948 73717 19 26283 05665 4 94335 22 39 10 48 49 12 68075 15 81925 73747 20 26253 05672 4 94828 21 20 40 8 10 40 3 49 20 9. 68098 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 94307 18 48 10 16 49 44 68167 17 31833 78867 22 26133 05700 5 94300 17 44 10 8 49 52 68190 17 31810 73897 9. 73927 22 23 26103 10. 26073 05707 5 94293 9. 94286 16 15 45 8 10 3 50 9. 68213 17 10. 31787 10. 05714 5 46 9 52 50 8 68237 18 31763 78957 23 26043 05721 5 94279 14 47 9 44 50 16 68260 18 31740 78987 24 26013 05727 5 94278 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 94259 11 8 9 20 3 50 40 9. 68328 19 10.31672 9. 74077 25 10. 25923 10. 05748 6 9. 94252 10 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 58 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 5 55 8 8 40 3 51 20 9. 68443 21 10. 31557 9. 74226 28 10. 25774 10. 05783 6 9.94217 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 8 58 8 16 51 44 68512 22 31488 74316 29 25684 05804 / 94196 2 59 8 8 51 52 68534 23 31466 74345 30 25655 05811 / 94189 1 60 8 52 68557 23 31443 74375 30 25625 05818 7 94182 M M. Hour p. M. Hour A. M. Cosine. DIfl. Secant. Cotangent, j Diff. Tangent. Cosecant. Diff. Sine. 118° A A B B c C 61° 1 Seconds of time 1" 2« 8- 1 4» 5' 6» 7- fA Prop, parts of cols, i B Ic 8 4 1 6 8 2 9 12 11 15 3 3 15 19 4 17 23 5 20 26 6 TABLE 44. [Page 637 Log. Sines, Tangents, and Secants. 29° A A B B C C 160° M. Hour A. M. Hour p. M. Sine. DifF. 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 ?. 7 44 52 16 68603 1 31397 74435 1 25565 05832 94168 58 8 7 36 52 24 68625 1 31375 74465 1 25535 05839 94161 57 4 7 28 52 32 68648 1 31352 74494 9. 74524 2 2 25506 05846 94154 56 55 5 8 7 20 3 52 40 9. 68671 2 10. 31329 10. 25476 10. 05853 9. 94147 fi 7 12 52 48 68694 2 31306 74554 3 25446 05860 94140 54 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 10 8 6 40 3 53 20 9. 68784 4 10. 31216 9. 74673 5 10. 25327 10. 05888 9.94112 50 n 6 32 53 28 68807 4 31193 74702 5 25298 05895 94105 49 ii> 6 24 53 36 68829 4 31171 74732 6 25268 05902 94098 48 18 6 16 53 44 68852 5 31148 74762 6 252.38 05910 2 94090 47 14 15 6 8 53 52 68875 5 31125 74791 9. 74821 7 25209 0.5917 10. 0.5924 2 2 94083 46 45 8 6 3 54 9. 68897 6 10. 31103 7 10. 25179 9. 94076 16 5 52 54 8 68920 6 31080 74851 8 25149 05931 2 94069 44 17 5 44 54 16 68942 6 31058 74880 8 25120 05938 2 94062 43 1« 5 36 54 24 68965 7 31035 74910 9 25090 05945 2 94055 42 19 5 28 54 32 68987 7 31013 74939 9 25061 05952 2 94048 41 90 8 5 20 3 54 40 9. 69010 7 10. 80990 9. 74969 10 10. 25031 10. 05959 2 9. 94041 40 9^ 5 12 54 48 69032 8 30968 74998 10 25002 05966 3 94034 39 99 5 4 54 56 69055 8 30945 75028 11 24972 05973 3 94027 38 9'^ 4 56 55 4 69077 9 30923 75058 11 24942 05980 3 94020 37 24 4 48 55 12 69100 9 9 30900 75087 12 24913 0.5988 3 94012 36 9h 8 4 40 3 55 20 9. 69122 10. 30878 9. 75117 12 10. 24883 10. 05995 3 9. 94005 3b 9f\ 4 32 55 28 69144 10 . 30856 75146 13 24854 06002 3 93998 34 91 4 24 55 36 69167 10 30833 75176 13 24824 06009 3 93991 33 ?8 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 80 8 4 3 56 9. 69234 11 10. 30766 9. 75264 15 10. 24736 10. 06030 4 9. 93970 30 81 3 52 56 8 69256 12 30744 75294 15 24706 06037 4 93963 29 82 3 44 56 16 69279 12 30721 75323 16 24677 06045 4 93955 28 88 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 10. 06066 4 4 9.3941 26 85 8 3 20 3 56 40 9. 69345 13 10. 30655 9.75411 17 10. 24-589 9. 93934 25 86 3 12 56 48 69368 13 30632 75441 18 24559 06073 4 93927 24 87 3 4 56 56 69390 14 30610 75470 18 24530 06080 4 93920 23 88 2 56 57 4 69412 14 30588 75500 19 24500 06088 5 93912 22 39 40 2 48 57 12 69434 15 30566 75529 19 24471 06095 5 93905 21 20 8 2 40 3 57 20 9. 69456 15 10. 30544 9. 75558 20 10. 24442 10. 06102 6 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 48 2 16 57 44 69523 16 30477 75647 21 24353 06124 5 93876 17 44 45 2 8 57 52 69.545 16 17 30455 75676 22 24324 06131 5 93869 .16 15 8 2 3 58 9. 69567 10. 30433 9. 75705 22 10. 24295 10. 06138 5 9. 93862 46 1 52 58 8 69589 17 30411 75735 23 24265 06145 5 93855 14 47 1 44 58 16 69611 17 30889 75764 23 24236 06153 6 93847 13 48 1 36 58 24 69633 18 30867 75793 24 24207 06160 6 93840 12 49 1 28 58 32 69655 18 19 30845 75822 24 24178 06167 6 938.33 11 10 50 8 1 20 3 58 40 9. 69677 10. 30323 9. 75852 25 10. 24148 10. 06174 6 9. 93826 51 .1 12 58 48 69699 19 30801 75881 25 24119 06181 6 93819 9 52 1 4 58 56 69721 19 30279 75910 26 24090 06189 6 9.3811 8 53 56 59 4 69743 20 30257 75939 26 24061 06196 6 93804 7 54 55 48 59 12 69765 20 30235 75969 27 24031 06203 6 93797 6 8 40 3 59 20 9. 69787 20 10. 30213 9. 75998 27 10. 24002 10. 06211 7 9. 93789 5 56 32 59 28 69809 21 30191 76027 28 23973 06218 7 93782 4 57 24 59 36 69831 21 30169 76056 28 28944 06225 7 98775 3 58 16 59 44 69853 22 30147 76086 29 23914 06232 7 93768 2 59 8 59 52 69875 22 30125 76115 29 23885 06240 7 93760 1 60 M. 4 69897 22 30103 76144 29 23856 06247 7 93753 Hour p. M. Hour A. M. Cosine. Diff. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. Sine. M. 119° A A B B C C 60° 1 Seconds of time Prop, parts of cols.-jB C Page 638j TABLE 44. Log. Sines, Tangents, and Secants. 80° A A B B C C 1490 M. Hour A.M. Hour p. M. Sine. Diflf. Cosecant. Tangent. Diff. Cotangent. Secant. Diff. Cosine. M. 8 4 9. 69897 10. 30103 9. 76144 10. 23856 10. 06247 9. 93753 60 1 7 59 52 8 69919 30081 76173 23827 06254 ^i 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 5 59 28 7 59 20 m 4 40 69984 9. 70006 1 2 30016 10. 29994 76261 2 23739 06276 10. 06283 ' 93724 9. 93717 56 55 9. 76290 2 10. 23710 6 59 12 48 70028 2 29972 76319 3 23681 06291 93709 54 7 59 4 56 70050 3 29950 76348 3 23652 06298 1 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 93087 51 10 7 58 40 4 1 20 9. 70115' 4 10. 29885 9. 76435 5 10. 23565 10. 06320 9. 93680 50 11 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 936()5 48 18 58 16 1 44 70180 5 29820 76522 6 23478 06342 2 93658 47 14 58 8 1 52 70202 5 5 29798 10. 29776 76551 7 23449 10. 23420 06350 2 93650 9. 93643 46 45 15 7 58 4 2 9. 70224 9. 76580 7 10. 06357 2 16 57 52 2 8 70245 6 29755 76609 8 23391 063(>4 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 4 2 40 70310 7 29690 76697 9 23303 06386 2 93614 9. 93606 41 40 20 7 57 20 9. 70332 7 10. 29668 9. 76725 10 10. 23275 10. 06394 2 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 10. 23130 06423 3 93577 36 25 7 56 40 4 3 20 9. 70439 9 10. 29561 9. 76870 12 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 93539 9. 93532 31 30 30 7 56 4 4 9. 70547 11 10. 29453 9. 77015 14 10. 22985 10. 06468 4 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 9.70654 12 29367 77130 16 22870 06498 4 93502 26 35 7 55 20 4 4 40 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 54 48 5 12 70739 14 29261 77274 19 22726 06535 5 93465 21 20 40 7 54 40 4 5 20 9. 70761 14 10. 29239 9. 77303 19 10. 22697 10. 0a543 5 9. 93457 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 16 29154 10.29133 77418 21 22582 10. 22553 06573 5 93427 9. 93420 16 15 45 7 54 4 6 9. 70867 9. 77447 22 10. 06580 6 46 53 52 6 8 70888 16 29112 77476 22 22524 06588 6 93412 14 47 53 44 6 16 70909 17 29091 77505 23 22495 06595 6 93405 13 48 53 36 6 24 70931 17 29069 77533 23 22467 06603 6 93397 12 49 50 53 28 7 53 20 6 32 70952 9.70973 18 18 29048 10. 29027 77562 9. 77591 24 22438 06610 6 " 6 93390 9. 93382 11 10 4 6 40 24 10. 22409 10.06618 51 53 12 6 48 70994 18 29006 77619 25 22.381 06625 6 93375 9 52 53 4 6 56 71015 19 28985 77648 25 22352 06633 6 93367 8 53 52 56 7 4 71036 19 28964 77677 26 22323 06640 7 93360 7 54 55 52 48 7 12 71058 19 28942 77706 26 26 22294 10. 22266 06648 7 93352 6 5 7 52 40 4 7 20 9. 71079 20 10. 28921 9. 77734 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. M. Cosine. Diff. Secant. Cotangent. Diff. Tangent. Cosecant. jDiff. Sine. M. 120^ A A B B C C 69° 1 Seconds of time 1« 2- 8* 4« &• 6« J' A Prop, parts of cols.^B Ic 3 4 1 5 7 2 8 11 3 11 14 4 13 18 5 16 22 6 19 25 7 TABLE 44. [Page 639 Log. Sines, Tangents, and Secants. 31° A A B B C C 148° M., Hour A. M. Hour P.M. Sine. Diflf. Cosecant. Tangent. Diff. Cotangent. Secant. Diff. Cosine. M. 7 52 4 8 9.71184 10. 28816 9. 77877 10. 22123 10. 06693 9. 93307 60 1 51 52 8 8 71205 28795 77906 22094 06701 98299 59 9, 51 44 8 16 71226 1 28774 77935 1 22065 06709 93291 58 8 51 36 8 24 71247 1 28753 77963 1 22087 06716 93284 57 4 51 28 8 32 71268 1 28732 77992 2 22008 06724 93276 56 55 5 7 51 20 4 8 40 9. 71289 2 jlO. 28711 9. 78020 2 10. 21980 10. 06731 1 i 9. 93269 1 fi 51 12 8 48 71310 2 1 28690 78049 3 21951 06739 93261 54 7 51 4 8 56 71331 2 ! 28669 78077 3 21923 06747 93253 58 S 50 56 9 4 71352 3 28648 78106 4 21894 06754 93246 52 9 10 50 48 9 12 4 9 20 71378 3 28627 •3 110.28607 78135 1 4 21865 06762 93238 51 50 7 50 40 9. 71393 9. 78168 5 10. 21887 10. 06770 1 9.93280 11 50 32 9 28 71414 4 ' 28586 78192 5 21808 06777 1 ; 93223 49 12 50 24 9 36 71435 4 28565 78220 6 21780 06785 2 93215 48 IS 50 16 9 44 71456 i 4 ! 28544 78249 6 21751 06793 2 93207 47 14 50 8 9 52 71477 5 5 28523 78277 9. 78306 7 21723 06800 10. 06808 2 93200 2 9.93192" 46 45 15 7 50 4 10 9. 71498 10. 28502 t 10. 21694 16 49 52 10 8 71519 5 28481 78334 8 21666 06816 2 93184 44 17 49 44 10 16 71539 6 ; 28461 78863 8 21637 06823 2 , 93177 43 18 49 36 10 24 71560 6 1 28440 78391 9 21609 06831 2 93169 42 19 20 49 28 10 32 71581 9. 71602 7 7 28419 78419 9 9 21581 06839 2 93161 41 40 7 49 20 4 10 40 10. 28398 9. 78448 10. 21552 10. 06846 3 9.93154 ?.\ 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 28 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 35 25 7 48 40 4 11 20 9. 71705 9 10. 28295 9. 78590 12 10. 21410 10. 06885 3 9.93115 26 48 32 11 28 71726 9 [ 28274 78618 12 21382 06892 3 93108 34 27 48 24 11 36 71747 9 28253 78647 13 21358 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 10. 28191 78704 14 14 21296 06916 4 4 93084 31 30 80 7 48 4 12 9. 71809 10 9. 78732 10. 21268 10. 06923 9. 93077 81 47 52 12 8 71829 11 1 28171 78760 15 21240 06931 4 93069 29 82 47 44 12 16 71850 11 1 28150 78789 ; 15 21211 06939 4 93061 28 88 47 36 12 24 71870 11 1 28130 78817 16 21188 06947 4 98053 27 34 47 28 12 32 71891 12 I 28109 78845 i 16 21155 06954 4 5 93046 26 25 85 7 47 20 4 12 40 9. 71911 12 110.28089 9.78874 ! 17 10. 21126 10. 06962 9. 98038 86 47 12 12 48 71932 12 1 28068 78902 17 21098 06970 5 93030 24 87 47 4 12 56 71952 13 28048 78930 17 21070 06978 5 93022 23 88 46 56 13 4 71973 13 28027 78959 18 21041 06986 5 93014 22 39 46 48 13 12 71994 13 1 28006 78987 t 18 21013 10. 20985 06993 10. 07001 5 5 93007 21 40 7 46 40 4 13 20 9.72014 1 14 10.27986 9.79015 19 9. 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 48 46 16 13 44 72075 15 27925 79100 20 20900 07024 6 ; 92976 17 44 46 8 13 52 72096 15 i 27904 79128 21 9. 79156 21 20872 07032 6 ! 92968 16 15 45 7 46 4 14 9. 72116 15 10. 27884 10. 20844 10. 07040 6 9. 92960 46 45 52 14 8 72137 16 27863 79185 22 20815 07048 6 1 92952 14 47 45 44 14 16 72157 16 27848 79213 22 20787 07056 6 1 92944 13 48 45 36 14 24 72177 16 27823 79241 23 20759 07064 6 1 92936 12 49 50 45 28 7 45 20 14 82 4 14 40 72198 17 27802 79269 1 23 20731 07071 6 92929 11 10 9.72218 i 17 10.27782 9.79297 1 24 10. 20703 10. 07079 6 9.92921 51 45 12 14 48 72238 1 18 1 27762 79326 1 24 20674 07087 7 1 92913 9 52 45 4 14 56 72259 18 27741 79354 25 20646 07095 7 ! 92905 8 58 44 56 15 4 72279 1 18 27721 79382 25 20618 07103 7 92897 1 54 55 44 48 15 12 4 15 20 72299 19 27701 19 10.27680 79410 26 20590 10. 20562 07111 10.07119 7 I 92889 7 19.92881 6 5 7 44 40 9. 72320 9. 79438 26 56 44 32 15 28 72340 i 19 27660 79466 26 205;w 07126 7 92874 4 57 44 24 15 36 72360 ; 20 27640 79495 27 20505 07134 7 92866 3 58 44 16 15 44 72381 20 27619 79523 27 20477 07142 7 92858 2 59 44 8 15 52 72401 1 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. DiflF. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. Sine. M. 121° A A B B C C 58° 1 Seconds of time 1» 2" 3« 4» 5« 6' 7" Prop, parts of cols. B 1 c 3 5 8 4 i 7 11 1 2 3 10 13 14 18 4 h 15 j 18 21 1 25 6 ' 7 Page 640] TABLE 44. Log. Sines, Tangents, and Secants. 82° A A B B C C 147° M. Hour A. M. Hour p. M. Sine. 1 Diff. Cosecant. Tangent. Diff. Cotangent. Secant. Diff. Cosine. M. 60 7 44 4 16 9. 72421 10. 27579 9.79579 10. 20421 10. 07158 9. 92842 1 48 52 16 8 72441 27559 79607 20398 07166 92834 59 9 48 44 16 16 72461 1 27539 79635 1 20365 07174 92826 58 8 43 86 16 24 72482 1 27518 79663 1 20337 07182 92818 57 4 5 43 28 16 3» 72502 1 27498 79691 2 20309 07190 1 92810 56 55 7 43 20 4 16 40 9. 72522 2 10. 27478 9. 79719 2 10. 20281 10. 07197 1 9. 92803 H 43 12 16 48 72542 2 27458 79747 8 20258 07205 1 92795 54 7 48 4 16 56 72562 2 27438 79776 3 20224 07213 1 92787 53 8 42 56 17 4 72582 3 27418 79804 4 20196 07221 1 92779 52 9 10 42 48 17 12 72602 3 27398 79832 i 4 20168 07229 1 92771 9. 92768 51 50 7 42 40 4 17 20 9. 72622 3 10. 27878 9. 79860 5 10. 20140 10. 07237 1 11 42 32 17 28 72643 4 27857 79888 5 20112 07245 1 92755 49 12 42 24 17 36 72668 ; 4 27887 79916 6 20084 07258 2 92747 48 18 42 16 17 44 72688 4 27317 79944 ; 6 20056 07261 2 92739 47 14 15 42 8 17 52 72708 5 5 27297 79972 '9. 80000 7 7 20028 07269 10. 07277 2 2 92731 9. 92728 46 45 7 42 4 18 9. 72723 10. 27277 10.20000 U) 41 52 18 8 72743 5 27257 80028 7 19972 07285 2 92715 44 17 41 44 18 16 72768 6 27237 80056 8 19944 07293 2 92707 48 18 41 36 18 24 72788 6 27217 80084 8 19916 07301 2 92699 42 19 20 41 28 7 41 20 18 32 72808 6 27197 80112 9 19888 07309 3 92691 41 40 4 18 40 9.72828 7 10. 27177 9.80140 1 9 10. 19860 10. 07817 3 i 9. 92683 21 41 12 18 48 72848 7 27157 80168 1 10 19832 07325 3 ! 92675 39 22 41 4 18 56 72863 7 27137 80195 10 19805 07338 3 ' 92667 38 28 40 56 19 4 72883 , 8 27117 80223 11 19777 07:341 8 ; 92659 87 24 40 48 19 12 72902 8 27098 80251 11 19749 07349 8 i 92651 36 25 7 40 40 4 19 20 9.72922 8 10. 27078 9.80279 12 10. 19721 10. 07857 8 i 9. 92648 35 26 40 82 19 28 72942 9 27058 80307 12 19693 07365 8 ! 926:35 34 27 40 24 19 36 72962 9 27038 80335 13 19665 07873 4 92627 33 28 40 16 19 44 72982 i 9 27018 80868 13 19687 07381 4 92619 32 29 80 40 8 19 52 78002 10 10 26998 10. 26978 80391 18 9.80419 14 19609 07389 4 92611 9. 92603 31 80 7 40 4 20 9. 73022 10. 19581 10. 07397 4 81 39 52 20 8 73041 : 10 26959 80447 14 19553 07405 4 92595 29 82 39 44 20 16 78061 ; 11 26989 80474 15 19526 07413 4 92587 28 88 89 36 20 24 78081 11 26919 80502 , 15 19498 07421 4 92579 27 34 39 28 20 82 78101 11 26899 80580 : 16 19470 07429 5 ! 92571 26 85 7 39 20 4 20 40 9.78121 12 10. 26879 9.80558 1 16 10. 19442 10. 07487 5 (9.92568 25 86 39 12 20 48 78140 12 26860 80586 17 19414 07445 5 ! 92555 24 87 89 4 20 56 73160 12 26840 80614 17 19886 07454 5 1 92546 23 88 38 56 21 4 73180 1 13 26820 80642 1 18 19358 07462 5 ! 92538 22 89 40 38 48 21 12 73200 i 13 26800 80669 18 9.80697 j 19 19831 07470 5 5~ 92580 21 7 38 40 4 21 20 9. 78219 13 10. 26781 10. 19808 10. 07478 9. 92522 20 41 88 82 21 28 73239 14 26761 80725 1 19 19275 07486 6 1 92514 19 42 88 24 21 86 73259 ! 14 26741 80753 1 20 19247 07494 6 92506 18 48 88 16 21 44 78278 : 14 26722 80781 : 20 19219 07502 6 92498 17 44 45 38 8 "7'38 21 52 4 22 73298 15 26702 80808 20 19192 07510 6 92490 16 9.73818 15 10. 26682 9.80886 1 21 10. 19164 10. 07518 6 9. 92482 15 46 37 52 22 8 78387 15 26663 80864 i 21 19136 07527 6 92478 14 47 37 44 22 16 78857 1 16 26643 80892 i 22 19108 07535 6 92465 13 48 87 36 22 24 78377 ' 16 26628 80919 ! 22 19081 07543 6 92457 12 49 37 28 22 32 73396 16 26604 80947 j 28 19058 07551 7 "^7" 92449 11 10 50 7 37 20 4 22 40 9.73416 17 10. 26584 9.80975 1 28 10. 19025 10. 07559 9. 92441 51 87 12 22 48 73435 1 17 26565 81003 24 18997 07567 / 92483 9 52 37 4 22 56 7:3455 i 17 26545 81030 24 18970 07575 7 92425 8 58 36 56 23 4 73474 18 26526 81058 25 18942 07584 7 92416 7 54 36 48 23 12 73494 i 18 26506 81086 25 18914 07592 7 92408 6 5 55 7 36 40 4 28 20 9.73518 ; 18 10. 26487 9.81113 26 10. 18887 10. 07600 7 9. 92400 56 36 32 28 28 78533 19 26467 81141 26 18859 07608 8 92392 4 57 86 24 23 36 78552 i 19 26448 81169 26 18831 07616 8 92884 8 58 36 16 23 44 78572 19 26428 81196 27 18804 07624 8 1 92376 2 59 36 8 23 52 73591 20 26409 81224 27 18776 07638 8 92367 1 60 M. 36 24 73611 20 26389 81252 ! 28 18748 07641 8 92359 Hour p. M. Hour A. M. Cosine. Dili. Secant. Cotangent. Diff. Tangent. Ccsecant. Diff. Sine. M. 1-220 A A B B C C 57° Seconds of time 1» 2» 8> 4» 6< 6> 7' fA Prop, parts of cols. iB Ic 2 3 1 6 7 2 7 10 3 10 14 4 12 17 5 15 21 6 17 24 7 TABLE U. [Page 641 Log. Sines, Tangents, and Secants. 83° A A B B C C 146° M. Hour A. M. Hour P. M. Sine. Diff. Cosecant. Tangent. Difl. Cotangent. Secant. Difl. 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 '? 35 44 24 16 73650 1 26350 81307 1 18693 07657 92343 58 8 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 1 92326 56 5 7 35 20 4 24 40 9. 73708 2 10. 26292 9. 81390 2 10. 18610 10. 07682 1 9. 92318 55 6 35 12 24 48 73727 2 26273 81418 3 18582 07690 1 92310 54 7 35 4 24 56 73747 2 26253 81445 3 18555 07698 1 92302 53 8 34 56 25 4 73766 3 26234 81473 4 18527 07707 1 92293 52 9 10 34 48 25 12 73785 3 26215 81500 4 18500 07715 1 92285 51 50 7 34 40 4 25 20 9. 73805 3 10. 26195 9. 81528 5 10. 18472 10. 07723 1 9. 92277 n 34 32 25 28 73824 3 26176 81556 5 18444 07731 2 92269 49 12 34 24 25 36 73843 4 26157 81583 5 18417 07740 2 92260 48 18 34 16 25 44 73863 4 26137 81611 6 18389 07748 2 92252 47 14 15 34 8 25 52 73882 4 26118 81638 6 18362 07756 2 92244 46 7 34 4 26 9. 73901 5 10. 26099 9. 81666 7 10. 18334 10. 07765 2 9. 92235 45 Ifi 33 52 26 8 73921 • 5 26079 81693 7 18307 07773 2 92227 44 17 33 44 26 16 73940 5 26060 81721 8 18279 07781 2 92219 43 18 33 36 26 24 73959 6 26041 81748 8 18252 07789 3 92211 42 19 20 33 28 26 32 73978 6 26022 81776 9 18224 07798 3 92202 41 7 33 20 4 26 40 9.73997 6 10. 26003 9. 81803 9 10. 18197 10. 07806 3 9. 92194 40 21 33 12 26 48 74017 7 25983 81831 10 18169 07814 3 92186 39 22 33 4 26 56 74036 7 25964 81858 10 18142 07823 3 92177 38 28 32 56 27 4 74055 7 25945 81886 11 18114 07831 3 92169 37 24 32 48 27 12 74074 8 25926 81913 11 18087 07339 3 92161 36 25 7 32 40 4 27 20 9.74093 8 10. 25907 9. 81941 11 10. 18059 10. 07848 3 9. 92152 35 26 32 32 27 28 74113 8 25887 81968 12 18032 07856 4 92144 34 27 32 24 27 36 74132 9 25868 81996 12 18004 07864 4 92186 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 80 7 32 4 28 9. 74189 10 10. 25811 9. 82078 14 10. 17922 10. 07889 4 9.92111 30 81 31 52 28 8 74208 10 25792 82106 14 17894 07898 4 92102 29 82 31 44 28 16 74227 10 25773 82133 15 17867 07906 4 92094 28 88 31 36 28 24 74246 10 25754 82161 15 17839 07914 5 92086 27 34 31 28 28 32 74265 11 25735 82188 16 17812 07923 5 92077 26 85 7 31 20 4 28 40 9. 74284 11 10.25716 9. 82215 16 10. 17785 10. 07931 5 9. 92069 25 8H 31 12 28 48 74303 11 25697 82243 16 17757 07940 5 92060 24 87 31 4 28 56 74322 12 25678 82270 17 17730 07948 5 92052 23 88 30 56 29 4 74341 12 25659 82298 17 17702 07956 5 92044 22 39 30 48 29 12 74360 12 25640 82325 18 17675 07965 6 92035 9. 92027 21 20 40 7 30 40 4 29 20 9. 74379 13 10. 25621 9. 82352 18 10. 17648 10. 07973 6 41 30 32 29 28 74398 13 25602 82380 19 17620 07982 6 92018 19 42 30 24 29 36 74417 13 25583 82407 19 17593 07990 6 92010 18 48 30 16 29 44 74436 14 25564 82435 20 17565 07998 6 92002 17 44 45 30 8 29 52 74455 14 25545 82462 I 20 17538 10. 17511 08007 6 91993 16 7 30 4 30 9. 74474 14 10. 25526 9. 82489 21 10. 08015 6 9. 91985 15 46 29 52 30 8 74493 15 25507 82517 21 17483 08024 6 91976 14 47 29 44 30 16 74512 15 25488 82544 22 17456 08032 / 91968 13 48 29 36 30 24 74531 15 25469 82571 22 17429 08041 7 91959 12 49 29 28 30 32 74549 16 25451 82599 22 17401 08049 / 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 51 29 12 30 48 74587 16 25413 82653 23 17347 08066 / 91934 9 52 29 4 30 56 74606 17 25394 82681 24 17319 08075 7 91925 8 53 28 56 31 4 74625 17 25375 82708 24 17292 08083 / 91917 / 54 55 28 48 31 12 74644 17 25356 82735 25 17265 08092 8 91908 9. 91900 6 7 28 40 4 31 20 9. 74662 17 10. 25338 9. 82762 25 10. 17238 10. 08100 8 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 91888 3 58 28 16 31 44 74719 18 25281 82844 27 17156 08126 8 91874 ' 2 59 28 8 31 52 74737 19 25263 82871 i 27 17129 08134 8 91866 1 60 28 32 74756 19 25244 82899 27 17101 08143 8 91857 M. Hour P. M. Hour A. M. Cosine. Diff. Secant. Cotangent. Difl. Tangent. Cosecant. Difl. Sine. M. 1 123= A A B B c C 66° 1 Seconds of time 1' 2» 3» 4" 5» 6« 7« fA Prop, parts of cols. 3 1 •1 7 6 8 10 13 4 5 10 16 6 12 20 7 14 23 8 Page 646] TABLE 44. Log. Sines, Tangents, and Secants. 88° A A B B C C 141° M. Hour A. M. Hour p. M. Sine. Difl. Cosecant. Tangent. Difl. Cotangent. Secant. Difl. Cosine. M. 6 56 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 o 55 44 4 16 1 78967 1 21033 89333 1 10667 10367 89633 58 3 55 36 4 24 78983 1 21017 89359 1 10641 10376 1 89624 57 4 55 28 4 32 1 78999 1 1 21001 10. 20985 89385 2 10615 10. 10589 10386 10. 10396 1 1 89614 9.89604 56 55' 5 6 55 20 5 4 40 9. 79015 9. 89411 2 6 55 12 4 48 79031 2 20969 89437 3 10563 10406 1 89594 54 7 55 4 4 56 79047 2 20953 89463 3 10537 10416 1 89584 53 8 54 56 5 4 79063 2 20937 89489 3 10511 10426 1 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 15 54 8 5 52 79160 4 4" 20840 89645 6 6 10355 10486 10. 10496 2 3 89514 46 >45 6 54 5 6 9. 79176 10. 20824 9. 89671 10. 10329 9. 89504 16 53 52 6 8 79192 4 20808 89697 7 10303 10505 3 89495 44 17 53 44 6 16 79208 20792 89723 / 10277 10515 3 89485 43 18 53 36 6 24 79224 20776 89749 8 10251 10525 3 89475 42 19 53 28 6 32 79240 5 20760 89775 8 10225 10535 3 3 89465 41 20 6 53 20 5 6 40 9. 79256 5 10. 20744 9. 89801 9 10. 10199 10. 10545 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 1 89879 10 10121 10575 4 89425 37 24 52 48 7 12 79319 6 20681 89905 10 10095 10585 4 89415 36 35 25 6 52 40 5 7 20 9. 79335 7 10. 20665 9. 89931 11 10. 10069 10. 10595 4 9. 89405 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 / 20617 90009 12 09991 10625 5 89375 32 29 30 52 8 7 52 79399 8 20601 10. 20585 90035 13 09965 10636 5 89364 31 30 6 52 5 8 9. 79415 8 9. 90061 13 10. 09939 10. 10646 5 9. 89354 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 61 12 8 48 79510 10 20490 90216 16 09784 10706 6 89294 24 37 51 4 8 56 79526 10 20474 90242 16 09758 10716 6 89284 23 38 50 56 • 9 4 79542 10 ' 20458 90268 16 09732 10726 6 89274 22 39 40 50 48 6 50 40 9 12 5 9 20 79558 10 20442 90294 17 09706 10736 7 89264 9. 89254 21 20 9. 79573 11 10. 20427 9. 90320 17 10. 09680 10. 10746 7 41 50 32 9 28 79589 11 20411 90346 18 09654 10756 7 89244 19 42 50 24 9 36 79605 11 20395 90371 18 09629 10767 7 89233 18 43 50 16 9 44 79621 11 ! 20379 90397 19 09603 10777 7 89223 17 44 50 8 9 52 79636 12 \ 20364 90423 19 09577 10787 7 89213 16 15 45 6 50 5 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 10 50 6 49 20 5 10 40 9. 79731 13 10. 20269 9. 90578 22 10. 09422 10. 10848 8 9. 89152 51 49 12 10 48 79746 14 20254 90604 22 09396 10858 9 89142 9 52 49 4 10 56 79762 14 20238 90630 22 09370 10868 9 89132 8 53 48 56 11 4 79778 14 20222 90656 23 09344 10878 9 89122 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. M. Hour p. M. Hour A. M. Cosine. Difl. Secant. Cotangent. Difl. Tangent. Cosecant, Difl. Sine. 128' A A B B C C 51° Seconds of time 1« 2' 8< 4» &> 6» 7' Prop, parts of cols.-jB Ic 2 3 1 4 6 3 6 10 4 8 13 5 10 16 6 12 19 8 14 23 9 TABLE 44. [Page 647 Log. Sines, Tangents, and Secants. 89° M. A A B B C C 140° Hour A. M. Hour P. M. Sine. Difl. Cosecant. Tangent. , Difl. , Cotangent. Secant. Diff. Cosine. M. 6 48 5 12 9. 79887 10. 20113 9. 90837 10.09163 10. 10950 9. 89050 60 1 47 o2 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 1 89020 57 4 5 47 28 6 47 20 12 32 5 12 40 79950 9.799(55 1 1 20050 10.20035" 90940 2 09060 9.90966 2 10.09034 10991 10. 11001 1 89009 56 55 1 9. 88999 6 47 12 12 48 79981 2 20019 90992 3 ' 09008 11011 1 88989 54 7 47 4 12 56 79996 2 20004 91018 3 1 08982 11022 1 88978 53 8 46 56" 13 4 80012 2 19988 91043 3 08957 11032 1 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 15 46 8 13 52 80105 9. 80120 4 4 19895 10. 19880 91198 1 6 08802 11094 2 3 88906 9. 88896 46 45 6 46 5 14 9.91224 1 6 10. 08776 10. 11104 16 45 52 14 8 80136 4 19864 91250 ; 7 08750 11114 3 88886 44 17 45 44 14 16 80151 4 19849 91276 1 7 08724 11125 , 3 88875 43 18 45 36 14 24 80166 5 19834 91301 1 8 08699 11135 3 88865 42 19 20 45 28 6 45 20 14 32 5 14 40 80182 9.80197 5 5 19818 10. 19803 91327 i 8 9.91353 i 9 • 08673 11145 3 3 88855 9. 88844 41 40 10. 08647 10.11156 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 1 08570 11187 4 88813 37 24 25 44 48 6 44 40 15 12 5 15 20 80259 6 6 19741 91456 9. 91482 10 08544 11197 10. 11207 4 4 88803 9788793 36 35 9. 80274 10. 19726 11 10. 08518 26 44 32 15 28 80290 7 19710 91507 11 08493 11218 5 88782 34 27 44 24 15 36 80305 7 19695 91533 12 08467 11228 5 88772 33 28 44 16 15 44 80320 7 19680 91559 12 08441 11239 5 88761 32 29 44 8 15 52 80336 7 19664 91585 12 08415 11249 5 88751 31 30 6 44 5 16 9. 80351 8 10. 19649 9. 91610 13 10. 08390 10. 11259 5 9. 88741 30 31 43 52 16 8 80366 8 19634 91636 13 08364 11270 5 88730 29 32 43 44 16 16 80382 8 19618 91662 14 08338 11280 6 88720 28 33 43 36 16 24 80397 8 19603 91688 14 08312 11291 6 88709 27 34 35 43 28 6 43 20 16 32 5 16 40 80412 9. 80428 9 9 19588 10. 19572 91713 15 08287 11301 6 6 88699 9. 88688 26 25" 9.91739 15 10. 08261 10. 11312 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 1 08209 11332 6 88668 23 38 42 56 17 4 80473 10 19527 91816 16 i 08184 11343 7 88657 22 39 40 42 48 17 12 80489 9. 80504 10 10 19511 10. 19496 91842 9. 91868 17 ! 08158 17 10.08132 11353 / 88647 21 20 6 42 40 5 17 20 10. 11364 7 9. 88636 41 42 32 17 28 80519 10 19481 91893 18 ! 08107 11374 / 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 6 42 17 52 5 18 80565 9. 80580 11 19435 91971 19 08029 11406 8 88594 16 12 10. 19420 9. 91996 19 10.08004 10. 11416 8 9. 88584 15 46 41 52 18 8 80595 12 19405 92022 20 07978 11427 8 88573 14 47 41 44 18 16 80610 12 19390 92018 20 07952 11437 8 88563 13 48 41 36 18 24 80625 12 19375 92073 21 07927 11448 8 88552 12 49 50 41 28 6 41 20 18 32 5 18 40 80641 9. 80656 13 13 19359 10. 19344 92099 21 07901 11458 10.11469 9 9 88542 11 10 9. 92125 21 10. 07875 9. 88531 51 41 12 18 48 80671 13 19329 92150 22 i 07850 11479 9 88521 9 52 41 4 18 56 80686 13 19314 92176 22 07824 11490 9 88510 8 53 40 56 19 4 80701 14 19299 92202 23 07798 11501 9 88499 7 54 55 40 48 6 40 40 19 12 5 19 20 80716 14 14 19284 92227 23 07773 11511 9 88489 6 5 9. 80731 10. 19269 9. 92253 24 :10. 07747 10. 11522 10 9. 88478 56 40 32 19 28 89746 14 19254 92279 24 07721 11532 10 88468 4 57 40 24 19 36 80762 15 19238 92304 24 07696 11543 10 88457 3 58 40 16 19 44 80777 15 19223 92330 25 07670 11553 10 88447 2 59 40 8 19 52 80792 15 19208 92356 25 07644 11564 10 88436 1 60 40 20 80807 15 19193 92381 26 07619 11575 10 88425 M. Hour p. M. Hour A. M. Cosine. Difl. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. Sine. M. 129° A A B B C C 50° j Seconds of time 1» 2» 3' 4» 5» 6» 7« Prop, parts of cols.^B 2 3 1 4 6 3 6 10 4 8 13 6 10 16 7 12 19 8 13 23 9 Page 648J TABLE 44. Log. Sines, Tangents, and Secants. 40° A A B B C C 189° M. Hour A.M. Hour p. M. Sine. DIff. j Cosecant. Tangent. Diff. 1 Cotangent. decant. Diff. Cosine. M. 6 40 0, 6 20 9. 80807 1 10. 19193 9. 92381 10.07619 10. 11575 9. 88425 60 1 39 52 20 8 S0822 19178 92407 07593 11585 88415 59 2 39 44 20 16 80837 19163 92433 1 07567 11596 88404 58 3 39 36 20 24 S0852 1 19148 92458 1 07542 11606 1 88394 57 4 39 28 20 32^ 80867 1 1 i 19133 92484 2 07516 10.07490 11617 10.11628 1 1 88383 9. 88372 56 55 5 6 39 20 5 20 40 9.80882 i 1 10. 19118 9. 92510 2 6 39 12 20 48 80897 1 1 19103 92535 3 07465 11638 1 88362 54 7 39 4 20 56 80912 2 I 19088 92561 3 07439 11649 1 88351 53 8 38 56 21 4 80927 2 1 19073 92587 3 07413 11660 1 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 ilO. 07362 10. 11681 2 9. 88319 50 11 38 32 21 28 80972 3 ' 19028 92663 o 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 52 81017 i 3 18983 92740 6 07260 11724 10. li7:S4 3 3 88276 9. 88266 46 45 15 6 38 5 22 9.81032 i 4 10. 18968 9. 92766 6 10.07234 16 37 52 22 8 81047 ' 4 18953 92792 7 07208 11745 3 88255 44 17 37 44 '22 16 81061 4 18939 92817 t 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 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 5 18864 92945 9 07055 11809 4 88191 38 23 36 56 23 4 81151 6 18849 92971 10 07029 11820 4 88180 37 24 36 48 23 12 81166 6 18834 92996 10 07004 11831 4 88169 36 35 25 6 36 40 5 23 20 9.81180 6 10. 18820 9. 93022 11 10. 06978 10. 11842 4 9. 88158 26 36 32 23 28 81195 6 18805 93048 11 06952 11852 5 88148 34 27 36 24 23 36 81210 i 18790 93073 12 06927 11863 5 88137 33 28 36 16 23 44 81225 i 18775 93099 12 06901 11874 5 88126 32 29 "30 36 8 23 52 81240 7 18760 10. 18746 93124 12 13 06876 11885 10.11895 5 5 88115 31 30 6 36 5 24 9. 81254 7 9. 93150 10. 06850 9. 88105 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 15 06748 11939 6 88061 26 25 35 6 35 20 5 24 40 9. 81328 9 10. 18672 9. 93278 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 34 48 25 12 81387 10 18613 93380 17 06620 10. 06594 11993 7 88007 21 20 40 6 34 40 5 25 20 9. 81402 10 10. 18598 9. 93406 17 10. 12004 7 9. 87996 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 45 34 8 25 52 81461 9. 81475 11 11 18539 10.18525 93508 1 19 06492 12047 8 87953 9. 87942 16 15" 6 34 5 26 9. 93533 19 10. 06467 | 10. 12058 8 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 5 26 40 81534 9. 81549 12 18466 93636 21 06364 12102 10.12113 9 9 87898 11 10 50 6 33 20 12 10. 18451 9. 93661 21 10. 06339 | 9. 87887 51 33 12 26 48 81563 13 18437 93687 22 06313 12123 9 87877 9 52 33 4 26 56 81578 13 18422 93712 22 06288 12134 9 87866 8 53 32 56 27 4 81592 13 18408 93738 23 0 4» 1 5" 6» 7» Prop, parts of cols. ■{ B 2 3 1 4 6 3 6 10 4 7 13 6 9 16 11 19 8 12 22 10 Page 650] TABLE 44. Log. Sines, Tangents, and Secants. 42° A A B B C C 187° M. Hour A. H. Hour p. M. Sine. Difif. Cosecant. Tangent. Difl. Cotangent. Secant. Diff. 1 Cosine. M. 6 24 5 36 9. 82551 10. 17449 9. 95444 10. 04556 10. 12893 9. 87107 60 1 23 52 36 8 82565 17435 95469 04531 12904 87096 59 2 23 44 36 16 82579 17421 95495 1 04505 12915 87085 58 3 23 36 36 24 82593 17407 95520 1 04480 12927 87073 57 4 5' 23 28 36 ^ 82607 17393 95545 2 2 04455 12938 10.12950 "r 87062. 56 55 6 23 20 5 36 40 9. 82621 10. 17379 9. 95571 10. 04429 9. 87050 6 23 12 36 48 82635 17365 95596 3 04404 12961 1 \ 87039 54 7 23 4 36 56 82649 2 17351 95622 3 04378 12972 1 ; 87028 53 8 22 56 37 4 82(563 2 17337 95647 3 i 04353 12984 2 87016 52 9 10 22 48 37 12 82677 2 17323 95672 4 i 04328 12995 2 87005 51 6 22 40 5 37 20 9. 82691 2 10. 17309 9. 95698 4 10. 04302 10. 13007 2 9. 86993 50 11 22 32 37 28 82705 3 17295 95723 5 04277 13018 2 86982 49 12 22 24 37 36 82719 3 17281 95748 5 04252 13030 2 86970 48 13 22 16 37 44 82733 3 17267 95774 5 04226 1.3041 3 86959 47 14 15 22 8 37 52 5 38 82747 3 17253 95799 9. 95825 6 04201 13053 3 3" 86947 46 45 6 22 9. 82761 3 10. 17239 6 10.04175 10.13064 9. 86936 16 21 52 38 8 82775 4 17225 95850 7 i 04150 13076 3 86924 44 17 21 44 38 16 82788 4 17212 95875 7 04125 13087 3 86913 43 18 21 36 38 24 82802 4 17198 95901 8 1 04099 13098 3 86902 42 19 20 21 28 6 21 20 38 32 82816 4 17184 95926 8 j 04074 13110 4 86890 41 40 5 38 40 9. 82830 5 10. 17170 9. 95952 8 10.04048 10. 13121 4 9. 86879 21 21 12 38 48 82844 5 17156 95977 9 1 04023 13133 4 86867 39 22 21 4 38 56 82858 5 17142 96002 9 03998 13145 4 86855 38 23 20 56 39 4 82872 5 17128 96028 10 03972 13156 4 86844 37 24 20 48 39 12 82885 6 17115 96053 10 11 03947 10. 03922 13168 5- 5 86832 9. 86821 36 35 25 6 20 40 5 39 20 9. 82899 6 10. 17101 9. 96078 10.13179 26 20 32 39 28 82913 6 17087 96104 11 03896 13191 5 86809 34 27 20 24 39 36 82927 6 17073 96129 11 03871 13202 5 86798 33 28 20 16 39 '44 82941 6 17059 96155 12 03845 13214 5 86786 32 29 30 20 8 39 52 82955 7 17045 96180 12 03820 13225 6 86775 31 30^ 6 20 5 40 9. 82968 7 10. 17032 9. 96205 13 10. 03795 10. 13237 6 ! 9. 86763 31 19 52 40 8 82982 t 17018 96231 13 03769 13248 6 86752 29 32 19 44 40 16 82996 7 17004 96256 14 03744 1.3260 6 86740 28 33 19 36 40 24 83010 8 16990 96281 14 03719 13272 6 86728 27 34 35 19 28 40 32 5 40 40 83023 8 8 16977 96307 14 03693 13283 7 86717 26 6 19 20 9. 83037 10. 16963 9. 96332 15 110.03668 10. 13295 7 9. 86705 25 36 19 12 40 48 83051 8 16949 96357 15 03643 13306 1 86694 24 37 19 4 40 56 83065 8 16935 96383 16 03617 13318 1 86682 23 38 18 56 41 4 83078 9 16922 96408 16 03592 13330 7 86670 22 39 40 18 48 6 18 40 41 12 83092 9 16908 96433 16 03567 13341 10. 13353 8 8 86659 21 20 5 41 20 9. 83106 9 10. 16894 9. 96459 17 10. 03541 9. 86647 41 18 32 41 28 83120 9 16880 96484 17 03516 13365 8 86635 19 42 18 24 41 36 83133 10 16867 96510 18 03490 13376 8 86624 18 43 18 16 41 44 83147 10 16853 965.35 18 03465 1,3388 8 86612 17 44 45 18 8 6 18 0^ 41 52 83161 9. 83174 10 10 16839 96560 19 03440 13400 10.13411 8 9 86600 9. 86589 16 15 5 42 10. 16826 9. 96586 19 10.03414 46 17 52 42 8 83188 11 16812 96611 19 I 03389 13423 9 86577 14 47 17 44 42 16 83202 11 16798 96636 20 03364 13435 9 86565 13 48 17 36 42 24 83215 11 16785 96662 20 03338 1.3446 9 86554 12 49 17 28 42 32 83229 11 11 16771 96687 21 21 03313 10. 03288 1.3458 10. 13470 9 To 86542 11 10 50 6 17 20 5 42 40 9. 83242 10. 16758 9. 96712 9. 86530 51 17 12 42 48 83256 12 16744 96738 22 03262 13482 10 86518 9 52 17 4 42 56 83270 12 16730 96763 22 03237 13493 10 86507 8 53 16 56 43 4 83283 12 16717 96788 22 03212 13505 10 ! 86495 7 54 55 16 48 6 16 40 43 12 83297 12 13 16703 10. 16690 96814 23 03186 13517 10 fl 86483 6 5 43 20 9. 8.3310 9. 96839 23 10. 03161 10. 1.3528 9. 86472 5 56 16 32 43 28 83324 13 16676 96864 24 03136 13540 11 1 86460 4 57 16 24 43 36 83338 13 16662 96890 24 03110 13552 11 86448 3 58 16 16 43 44 83351 13 16649 96915 25 03085 13564 11 86436 9 59 16 8 43 52 83365 14 16635 96940 25 03060 13575 11 86425 1 60 M. 16 44 83378 14 16622 96966 25 03034 13587 12 86413 M. Hour P.M. Hour A. M. Cosine. Diff. Secant. Cotangent. Difl. Tangent. Cosecant. Diff. Sine. 182 A A B B C C 47° Seconds of time 1> 2> 3« 4' 5' 6' 7' Prop, parts of cols. < B Ic 2 3 1 3 6 3 6 10 4 7 13 6 9 16 10 19 9 12 •22 10 TABLE U. [Page 651 Log. Sines, Tangents, and Secants. 43° A A B B C C 136° M. Hour A. M. Hour P.M. Sine. Diff. Cosecant. Tangent. Diff. Cotangent. Secant. Diff. Cosine. M. 60 6 16 5 44 9. 88378 10. 16622 9. 96966 10. 03034 10. 13587 9. 86413 1 15 52 44 8 88392 16608 96991 08009 13599 86401 59 2 15 44 44 16 88405 16595 97016 1 02984 13611 86889 58 8 15 36 44 24 88419 1 16581 97042 1 02958 13623 86877 57 4 15 28 44 82 88432 1 16568 97067 2 02933 13634 86366 9. 86354 56 55 5 6 15 20 5 44 40 9. 88446 1 10. 16554 9. 97092 2 10. 02908 10. 13646 6 15 12 44 48 88459 1 16541 97118 3 02882 13658 86342 54 7 15 4 44 56 88473 2 16527 97143 3 02857 13670 86330 58 H 14 56 45 4 83486 2 16514 97168 3 02832 13682 2 86818 52 9 14 48 45 12 83500 2 16500 97193 4 4 02807 18694 2 86806 51 50 10 6 14 40 5 45 20 9. 83513 2 10. 16487 9. 97219 10. 02781 10. 13705 2 9. 86295 11 14 32 45 28 83527 2 16478 97244 5 02756 13717 2 86288 49 12 14 24 45 86 83540 8 16460 97269 5 02731 18729 2 86271 48 18 14 16 45 44 83554 3 16446 97295 5 02705 18741 3 86259 47 14 15 14 8 45 52 88567 9. 83581 3 3 16488 97320 6 02680 10. 02655 18753 10.13765 3 86247 46 45 6 14 5 46 10. 16419 9. 97345 6 3 9. 86235 16 13 52 46 8 83594 4 16406 97871 7 02629 13777 3 86223 44 17 13 44 46 16 83608 4 16892 97896 7- 02604 13789 3 86211 48 18 13 36 46 24 83621 4 16379 97421 8 02579 13800 4 86200 42 19 20 13 28 6 18 20 46 82 83634 4 16366 10.16352 97447 "9. 97472 8 02553 13812 4 86188 41 40 5 46 40 9. 83648 4 8 10. 02528 10. 13824 4 9. 86176 21 18 12 46 48 88661 5 16839 97497 9 02503 13836 4 86164 39 22 13 4 46 56 83674 5 16326 97528 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 9. 97598 10 02427 13872 10. 13884 5 86128 36 25 6 12 40 5 47 20 9. 88715 6 10. 16285 11 10. 02402 5 9.86116 35 26 12 32 47 28 83728 6 16272 97624 11 02376 13896 5 86104 84 27 12 24 47 36 88741 6 16259 97649 11 02351 13908 5 86092 88 28 12 16 47 44 88755 6 16245 97674 12 02326 13920 6 86080 82 29 12 8 47 52 83768 6 7 16282 97700 12 02300 13982 6 86068 9. 86056 31 80 80 6 12 5 48 9. 83781 10. 16219 9. 97725 13 10. 02275 10. 18944 6 81 11 52 48 8 83795 7 16205 97750 18 02250 13956 6 86044 29 82 11 44 48 16 83808 7 16192 97776 13 02224 13968 6 86082 28 33 11 36 48 24 83821 / 16179 97801 14 02199 18980 7 86020 27 34 85 11 28 6 11 20 48 32 83834 8 8 16166 97826 14 02174 10. 02149 18992 7 86008 9. 85996 26 25 5 48 40 9. 83848 10. 16152 9. 97851 15 10. 14004 7 m 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 88887 8 16118 97927 16 02073 14040 8 85960 22 39 40 10 48 6 10 40 49 12 83901 9 9 16099 10. 16086 97953 9.97978 16 17 02047 14052 10. 14064 8 85948 21 5 49 20 9. 83914 10. 02022 8 9. 85986 20 41 10 32 49 28 83927 9 16073 98003 17 01997 14076 8 85924 19 42 10 24 49 86 83940 9 16060 98029 18 01971 14088 8 85912 18 48 10 16 49 44 83954 10 16046 98054 18 01946 14100 9 85900 17 44 45 10 8 49 52 88967 10 10 16088 98079 19 01921 10. 01896 14112 9 85888 9. 85876 16 15 6 10 5 50 9. 88980 10. 16020 9. 98104 19 10. 14124 9 46 9 52 50 8 88993 10 16007 98180 19 01870 14136 9 85864 14 47 9 44 50 16 84006 10 15994 98155 20 01845 14149 9 85851 18 48 9 36 50 24 84020 11 15980 98180 20 01820 14161 10 85839 12 49 50 9 28 50 32 84033 11 15967 98206 21 21 01794 14173 10 85827 9. 85815 11 10 6 9 20 5 50 40 9. 84046 11 10. 15954 9. 98281 10. 01769 10. 14185 10 51 9 12 50 48 84059 11 15941 98256 22 01744 14197 10 85803 9 52 9 4 50 56 84072 12 15928 98281 22 01719 14209 10 85791 8 58 8 56 51 4 84085 12 15915 98307 22 01693 14221 11 85779 7 54 8 48 51 12 84098 12 15902 98382 23 01668 14234 11 85766 6 55 6 8 40 5 51 20 9. 84112 12 10. 15888 9. 98357 23 10. 01648 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 84188 18 15862 98408 24 01592 14270 11 85780 8 58 8 16 51 44 84151 13 15849 98438 24 01567 14282 12 85718 2 59 8 8 51 52 84164 13 15886 98458 25 01542 14294 12 85706 1 60 8 52 84177 IS 15823 98484 25 01516 14307 12 85693 M. Hour p. M. Hour A. M. Cosine. Diflf. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. Sine. M. 133° A A B B C C 46°n Seconds of time 1» 2s 3» 4» 6» 6' T Prop, parts of cols.