^ AVmKimSaxi .irva>tayaig*' A f No. 9 S>ri»e 11.85^ American Practical Navigator An Epitome of Navigation and Nautical Astronomy By NATHANIEL BOWDITCH. LL. D., Etc. HYDROGRAPHIC OFFICE *^ OF TH€ UNIVERSITY OF Washington : : : Government Printing Office : : : 1910 \ a ORDERS RELATING TO REVISION. Bureau of Navigation, Navy Department^ January i, 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. William D. Whiting, . '• Xi-l '.i -" Chief of Bureau. Bureau of Equipment, Navy Department^ March 18-, 1903. A revision of Bowditch's American Practical Navigator having become neces- sary, the work has been oCMipleted by Lieut. G. W. Logan, U. S. Navy, under the supervision of the Hydrographer to the Bureau of Equipment. The revision was approved by a Board consisting of Capt. Colby M. Chester, U. S. Navy, Commander C. J. Badger, U. S. Navy, and Lieut. Commander C. C. Rogers, U. S. Navy. It is directed that this revised edition be substituted for all former editions. R. B. Bradford, Chief of Bureau. I>REF^OE. 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 by Lfeut. T. A. Kearney, U. S. Navy; the chapters on Winds and Cyclonic Storms were contributed by Mr. James Page, nautical expert, Hydrographic Office. There has been an extensive rewriting of the text, with the object of amplifying those matters that are of the greatest importance in the modern practice of navigation, and of omitting or condensing those of lesser importance; and the revision of the tables has proceeded along similar lines. This has involved, among other things, a much wider treatment of the subject of the compass; an extension of the traverse table for 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 in an appendix, that i]b 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, Oornmander^ U. S. Navy^ Ilydrographer. Hydrographic Office, Bureau of Equipment, Navy Department, Washington^ D. 6*., March 19^ 1903. 3 204618 NOTE. This edition is a reprint of the revised edition, 1903, with no change made in the text or tables of that edition except the correction of such errors as have been discovered in it to the present date. John J. Knapp, Captain^ U. S. Navy^ Ilydrographer. ^ Hydkographic Office, Bureau of Navigation, Navy Department, Washington, D. C. , July <§, 1910. 4 P^RT I TEXT AND APPENDICES. ooisrTEisrTs of i>a.iit i. Page. Orders relating to revision 2 Preface 3 Abbreviations 9 Chapter I. Definitions relating to Navigation H II. Instruments and Accessories in Navigation 13 III. The Compass Error • ?9 IV. Piloting 42 V. The Sailings 50 VI. Dead Reckoning 60 VII. Definitions relating to Nautical Astronomy 63 VIII. Instruments employed in Nautical Astronomy 66 IX. Time and the Nautical Almanac 74 X. Correction of Observed Altitudes 82 XI. The Chronometer Error 87 XII. Latitude 94 XIII. Longitude 103 XIV. Azimuth 109 XV. The Sumner Line 114 XVI. The Practice of Navigation at Sea 124 XVII. Marine Surveying 131 XVIII. Winds 142 XIX. Cj'clonic Storms 147 XX. Tides 153 XXI. Ocean Currents 158 •Appendix I. Extracts from the American Ephemeris and Nautical Almanac for the year 1879, which have reference to examples for that year given in this work 163 II. A collection of Forms for working Dead Reckoning and various Astronomical Sights, with 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. (or;i) 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 jae. G. M. T Greenwich mean time. G. S. T Greenwich sidereal time. h Altitude. H Meridian altitude. H. A. (or t) Hour angle. H. D Hourly difference. H. P. (or Hor. par. ) . . .Horizontal parallax. Hr-s Hour-s. H. W High water. I. C Index correction. L. (or 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. TO Meridional difference. Merid Meridian or noon. Mag Magnetic. M. D Minute's difference. Mid Middle. Mid. L Middle latitude. M. T Meantime. 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 jo) Polar distance. P. L. (oT 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 Variation. Vert Vertex or vertical. W., Wly West, westerly. W. T Watch time z Zenith distance. Z Azimuth. SYMBOLS. (^ The Sun. ° Degrees. - .Gamma. Oo.... . Omicron. /IS. .Delta. nTi.... .Pi. E e . .Epsilon. Pp. ... .Rho. ZS. .Zeta. 26{<;). .Sigma. Htf. .Eta. Tt .... .Tau. (ye . .Theta. Tv.... .Upsilon. It .. .Iota. $ (p .Phi. Kk. .Kappa. xx--.. .Chi. AX. .Lambda. w^.... .Psi. Mju. .Mu. £1 00 .Omega. DEFINITlONy RELATING TO NAVIGATION., u CHAPTER I. DEFINITIONS EELATING TO NAVIGATION. 1. That science, generally termed Navigation, which affords the knowledge necessary to conduct a ship from point to point upon the earth, enabling the mariner to determine, with a sufficient degree of accuracy, the position of his vessel at any time, is properly divided into two branches: Navigation and Nautical Astronomy. 2. Navigation, in its limited sense, is that branch which treats of the 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 S3a, 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 Astronomy 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*ion 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 fii'ttened 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 Axis 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 circles PQP^, PMP^, PM'P^, formed by the intersection with the earth's surface of planes secondary to the equator (that is, passing through its poles and therefore perpendicular to its plane) . Parallels of Latitude are small circles NTn, N^n^'T'', formed by the intersection with the earth's surface of planes passed parallel to the equator. The Latitude of a place on the surface of the earth is the arc of the meridian intercepted between the equator and that place. Latitude is reckoned North and South, from the equator as an origin, through 90° to the poles; thus, the latitude of the point T is MT, north, and of the point T^, M^T^, north. The Difference of Latitude between any two places is the arc of a meridian intercepted between their parallels of latitude, and is called North or South, according to direction-; thus, the difference of latitude between T and T^ is Tr/ or T^n, north from T or south from T\ The Longitude of a place on the surface of the earth is the arc of the equator intercepted between its meridian and that of some place from which the longitude is reckoned. Longitude is measured East or West through 180° from the meridian of a designated place, such meridian being termed the Prime Meridian; the prime meridian used by most nations, including the United States, is that of Greenwich, England. If, in the figure, the prime meridian be PGQP^, then the longitude of the point T is QM, east, and of T^, QM^, east. The Difference of Longitude between any two places is the arc of the equator inter- cepted between their meridians, and is called East or West, according to direction; thus, the difference of longitude between T and T'' is MM^, east from M or west from M^. The Departure is the linear distance, measured on a parallel of latitude, between two meridians; unlike the various quantities previously defined, departure is reckoned in miles; the departure between two meridians varies with the parallel of latitude upon which it is measured; thus, the departure between the meridians of T and T' is the number of miles corresponding to the distance Tn in the latitude of T, or to n^T' in the latitude of T^. Fig. 1. 12 DEFINITIONS EELATING TO NAVIGATION. ^ The curved line which joins any two places on the earth's surface, cutting all the meridians at the same angle, is called the Rhumb Line, Loxodromic Curve, or Equiangular Spiral. In the figure, this line is represented by TrT''. The constant angle which this line makes with the meridians is called the Course; and the length of the line between any two places is called the Distance between those places. The unit of linear measure employed by navigators is the Nautical or Sea Mile, or Knot. It is equal to one minute of latitude — that is, to the length of that portion of a meridian which subtends at the earth's center the angular measure of one minute; since, however, on account of the fact that the earth is not a perfect sphere, this distance is not exactly the same in all latitudes, a mean value is adopted for the length of the knot, and it is regarded as equal to 6,080.27 feet. For the purposes of navigation, the variation from this value in different latitudes is so small that it may be neglected, and the knot may be assumed equal to a minute of latitude in all parts of the earth; hence, when a vessel changes her position to the north or south by one nautical mile, it may always be considered that the latitude has changed 1^. Owing to the fact that the meridians all converge toward the poles, the difference of longi- tude produced by a change of position of one mile to the east or west will vary with the latitude; thus a departure of one mile will equal a difference of longitude of 1''.0 at the equator, of 1''.! in the latitude of 30°, and of 2^0 in the latitude of 60°. The Great Circle Track or Course between any two places is the route between those places along the circumference of the great circle which joins them. In the figure, this line is represented by TgT', From the properties of a great circle (which is a circle upon the earth's surface formed by the inter- section of a plane passed through its center) the distance between two points measured on a great circle track is shorter than the distance upon any other line which joins them. Except when the two points are on the same meridian or when both lie upon the equator, the great circle track will always differ from the rhumb line, and the great circle track will intersect each intervening meridian at a different angle. INSTRUMENTS AND ACCESSORIES IN NAVIGATION. 13 CHAPTER II. INSTRUMENTS AND ACCESSORIES IN NAVIGATION. DIVIDERS OB, COMPASSES. 7. This instrument consists of two legs movable about a joint, so that the points at the extremities of the legs may be set at any required distance from each other. It is used to take and transfer dis- tances and to describe arcs and circles. When used for the former purpose it is termed dividers, and the extremities of both legs are metal points; when used for describing arcs or circles, it is called a com- pass, and one of the metal points is replaced by a pencil or pen. PABAIiliEL BXJIiEBS. §. Parallel rulers are used for drawing lines parallel to each other in any direction, and are particu- larly useful in transferring the rhumb-line on the chart to the nearest compass-rose to asfcertain the course, or to lay off bearings and courses.- PROTRACTOR. 9. This is an instrument used for the measurement ©Wangles upon paper; there is a wide variation in the material, size, and shape in which it may be made. (For a description of the Three Armed Protractor, see art. 432, Chap. XVII. ) THE CHIP LOG. 10. This instrument, for measuring the rate of sailing, consists of three parts; viz, the log-chip, the log-line, and the log-glass. A light substance thrown from the ship ceases to partake of the motion of the vessel as soon as it strikes the water, and will be left behind on the surface; after a certain inter- val, if the distance of the ship from this stationary object be measured, the approximate rate of sailing will be given. The log-chip is the float, the log-line is the measure of the distance, and the log-glass defines the interval of time. The log-chip is a thin wooden quadrant of about 5 inches radius, loaded with lead on the circular edge sufficiently to make it swim upright in the water. There is a hole in each corner of the log- chip, and the log-lijie is knotted in the one at the apex ; at about 8 inches from the end there is seized a wooden socket; a piece of line of proper length, being knotted in the other holes, has seized into its bight a wooden peg to fit snugly into the socket before the log-chip is thrown; as soon as the line is checked this peg pulls out, thus allowing the log-chip to be hauled in with the least resistance. The log-line is about 150 fathoms in length, one end made fast to the log-chip, the other to a reel upon which it is wound. At a distance of from 15 to 20 fathoms from the log-chip a permanent mark of red bunting about 6 inches long is- placed to allow sufficient stray line for the log-chip to clear the vessel's eddy or wake. The rest of the line is divided into lengths of 47 feet 3 inches called knots, by pieces of fish-line thrust through the strands, with one, two, three, etc., knots, according to the number from stray-line mark; each knot is further subdivided into five equal lengths of two-tenths of a knot each, marked by pieces of white rag. The length of a knot depends upon the number of seconds which the log-glass measures; the length of each knot must bear the same ratio to the nautical mile (^V o^ ^ degree of a great circle of the earth or 6,080 feet) that the time of the glass does to an hour. In the United States Navy all log-lines are marked for log glasses of 28 seconds, for which the proportion is: 3600 :6080 = 28» :a;, X being the length of the knot. Hence a; = 47".29, or47f'3*°. The speed of the ship is estimated in knots and tenths of a knot. The log-glass is a sand glass of the same shape and construction as the old hour-glass. ^ Two glasses are used, one of 28 seconds and one of 14 seconds; the latter is employed when the ship is going at a high rate of speed, the number of knots indicated on a line marked for a 28-second glass being doubled to obtain the true rate of speed. 11. The lojg in all its parts should be frequently examined and adjusted; the peg must be found to fit sufficiently tight to keep the log-chip upright; the log-line shrinks and stretches and should often be verified; the log-glass should be compared with a watch. One end of the glass is stopped with a cork, by removing which the sand may be dried or its quantity corrected. 12. A ground log consists of an ordinary log-line, with a lead attached instead of a chip; in shoal water, where there are no well-defined objects available for fixing the position of the vessel and the course and speed are influenced by a tidal or other current, this Tog is sometimes used, its advantage being that the lead marks a stationary point to w^hich motion may be referred, whereas the chip would drift with the stream. The speed, which is marked in the usual manner, is the speed over the ground, and the trend of the line gives the course actually made good by the vessel. 14 INSTRUMENTS AND ACCESSORIES IN NAVIGATION. THE PATENT liOG. 1 3. This is a mechanical contrivance for registering the distance actually run by a vessel through the water. There are various types of patent logs, but for the most part they act upon the same principle, consisting of a registering device, a fly or rotator, and a log or tow line; the rotator is a small sj>indle with a number of wings extending radially in such manner as to form a spiral, and, when drawn through the water in the direction of its axis, rotates about that axis after the manner of a screw pro- peller; the rotator is towed from the vessel by means of a log or tow line from 20 to 50 fathoms in I'^ngth, made fast at its apex, the line being of special make so that the turns of the rotator are transmitted through it to the worm shaft of the register, to which the inboard end of the line is attached; the regis- tering device is so constructed as to show upon a dial face the distance run, according to the number of turns of its worm shaft due to the motion of the rotator; the register is carried at some convenient point on the vessel's quarter; it is frequently found expedient to rig it out upon a small boom, so that the rotator will be towed clear of the wake. 14. Though not a perfect instrument, the patent log affords the most accurate means available for determining the vessel's speed through the water. It will usually be found that the indications of the log are in error by a constant percentage, and the amount of this error should be determined by careful experiment and applied to all readings. Various causes may operate to produce inaccuracy of working in the patent log, such as the bending of the wings of the rotator by accidental blows, fouling of the rotator by sea weed or refuse from the ship, or mechanical wear of parts of the register. The length of the tow-line has much to do with the working of the log, and by varying the length the indications of the instrument may sometimes be adjusted when the percentage of error is small; it is particularly important that the line shall not be too short. The readings of the patent log can not be depended upon for accuracy at low speeds, when the rotator does not tow horizontally, nor in a head or a following sea, when the effect depends upon the wave motion as well as upon the speed of the vessel. 15. Electrical registers for patent logs are in use, the distance recorded by the mechanical register being communicated electrically to some point of the vessel which is most convenient for the purposes of those charged with the navigation. 16. A number of instruments based upon different physical principles have been devised for recording the speed of a vessel through the water and have been used with varying degrees of success. 17. The revolutions of the screw propeller afford in a steamer a valuable check upon the patent log and a means of replacing it if necessary. To be of service the number of revolutions per knot must be carefully determined for the vessel by experiment under varying conditions of speed, draft, and foul- ness of bottom. THE LEAD. 1§. This device, for ascertaining the depth of water, consists essentially of a suitably marked line, having a lead attached to one of its ends. It is an invaluable aid to the navigator in shallow water, particularly in thick or foggy weather, and is often of service when the vessel is oxit of sight of land. Two leads are used for soundings — the hand-lead, weighing from 7 to 14 pounds, with a line marked to about 25 fathoms, and the deep-sea lead, weighing from 30 to 100 pounds, the line being 100 fathoms or upward in length. Lines are generally marked as follows: 2 fathoms from the lead, with 2 strips of leather. 3 fathoms from the lead, with 3 strips of leather. 5 fathoms from the lead, with a white rag. 7 fathoms from the lead, with a red rag. 10 fathoms from the lead, with leather having a hole in it. 13 fathoms from the lead, same as at 3 fathoms. 15 fathoms from the lead, same as at 5 fathoms. Fathoms which correspond with the depths marked are called marks; the intermediate fathoms are called deeps; the only fractions of a fathom used are a half and a quarter. A practice sometimes followed is to mark the hand-lead line in feet around the critical depths of the vessel by which it is to be used. Lead lines should be measured frequently while wet and the correctness of the marking verified. The distance from the leadsman's hand to the water's edge should be ascertained in order that prober allowance may be made therefor in taking soundings at night. 19. The deep-sea lead may be armed by filling with tallow a hole hollowed out in its lower end, by which means a sample of the bottom is brought up. THE SOUNDING MACHINE. 20. This machine possesses advantages over the deep-sea lead, for which it is a substitute, in that soundings may be obtained at great depths and with rapidity and accuracy without stopping the ship. It consists essentially of a stand holding a reel upon which is wound the sounding wire, and which is controlled by a suitable brake. Crank handles are provided for reeling in the wire after the sounding has been taken. Attached to the outer end of the wire is the lead, which has a cavity at its lower end for the reception of the tallow for arming. Above the lead is a cylindrical case containing the depth- registering mechanism; various devices are in use for this purpose, all depending, however, upon the increasing pressure of the water with increasing depths. 21. In the Lord Kelvin machine a slender glass tube is used, sealed at one end and open at the other, and coated inside with a chemical substance which changes color upon contact with sea water; this tube is placed, closed end up, in the metal cylinder; as it sinks the water rises in the tube, the contained air being compressed with a force dependent upon the depth. The limit of discoloration is marked by a clearly defined line, and the depth 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, wiLh 1 knot. 30 fathoms from the lead, with 3 knots. 35 fathoms from the lead, with 1 knot. 40 fathoms from the lead, with 4 knots. And so on. INSTRUMENTS AND ACCESSORIES IN NAVIGATION. 15 22. A tube whose inner surface is gYound 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 when accurate results are required. The correction consists in increasing the indicated depth by a fractional amount according to the following table: Bar. reading. Increase. // 29.75 30.00 30.50 30.75 One-fortieth. One-thirtieth. One-twentieth. One-fifteenth. THE mariij:eb,'s compass. 25. The Mariner's Compass is an instrument consisting either of a single magnet, or, more usually, of a series of magnets, which, being attached to a graduated circle pivoted at the center and allowed to ' ' 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 course and of all visible objects, terrestrial or celestial. 16 INSTRUMENTS AND ACCESSOEIES 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 11^° each, called points, the latter being further divided into half-points and quarter-points; still finer subdivisions, eighth-points, are sometimes used, though not indicated on the card. A system of numbering the degrees from 0° to 360°, always increasing toward the right, is shown in the figure. This system is in use by the mariners of some nations, and its general adoption would carry with it certain undoubted advantages. 27. Boxing the Compass is the process of naming the points in their order, and is one of the first things to be learned by the young mariner. The four principal points are called cardinal points and are named North, South, Ea^, and West; each differs in direction from the adjacent one by 90°, or 8 points. Midway between the cardinal points, at an angular distance of 45°, or 4 points, are the inter-cardinal points, named according to their position Northeast, Southeast, etc. 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 11 J°, from each cardinal and inter- cardinal point (and therefore midway between it and the 22J°-division last described), is a point which bears the name of that cardinal or inter-cardinal point joined by the word by to that of the cardi- nal point in the direction of which it lies: North Vjy 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. ^ N. and NNE. ^ 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. ^ E., N. by E. ^ E., NNE. ^ E., NE. ^ N., etc. Some mariners, however, make it a prac- tice to box from each cardinal and inter-cardinal point toviard a 22^°-point (NNE., ENE., etc.); as N. i E., N. by E. ^ E., NE. by N. i N., NE. J N., etc. The names of the whole points, together with fractional points (according to the nomenclature of the United States Navy), are given in the following table, which shows also the degrees, minutes, and seconds from North or South to which each division corresponds: N. to E. North: N. iE N. ^E N. f E N. byE N. byE. iE. N. byE. JE. N. byE. fE. NNE NNE. JE.... NNE. ^E.... NNE. |E.... NE. byN NE. t N NE. ^N NE. JN NE NE. I^E NE. ^E NE. I E NE. bvE NE. by E. J E NE. by E. I E NE. by E. f E ENE ENE. iE.... ENE. JE.... ENE. |E..-. E. byN E. ^N E. iN E. iN East N. toW. North: N. i W N. ^ W N. J W N.byW N. byW. iW. N. by W. JW. N. by W. f W. NNW NNW. i W... NNW. JW... NNW. f W... NW. byN NW. IN NW. iN NW. iN NW NW. i W NW. ^W NW. t W NW. by W NW.byW.iW NW. byW. iW NW.byW.fW WNW WNW. i W... WNW. ^ W... WNW. f W... W.byN W. IN W. ^N W. iN West S. to E. South: S. iE S. JE S. f E S. byE S. by E. i E . . . S. byE. ^E... S. by E. f E... SSE SSE. iE SSE. JE SSE. |E SE. byS SE. f S SE. ^S SE. iS SE SE.iE SE. JE SE.f E SE. byE SE. by E. iE.. SE. byE. ^E.. SE. byE. IE.. ESE ESE. iE ESE. ^E ESE. JE E.byS E. |S E. JS E. iS East S. to W. South: S. i W S. JW S.f w S. by W S. by W. iW.. S. by W.J W.. S. by W. f W.. SSW SSW. i W SSW. J w SSW. I w SW. byS SW. IS SW. fS SW. iS SW SW. i w SW. JW SW. f w SW. by W SW. by W. i W SW. by W. J W SW. by W. J W WSW WSW. i W.... WSW. JW.... WSW. f W.... W. byS W. |S W.JS W. iS.. West Pts. Angular measure. 1 li H If 2 2i 2J 2| 3 3i 3.} 31 4 4i 4i 4f 5 5i 5i 51 6 6i 6J 61 7 7i 7i 71 2 48 45 5 37 30 8 26 15 11 15 00 14 03 45 16 52 30 19 41 15 22 30 00 25 18 45 28 07 30 30 56 15 33 45 00 36 33 45 39 22 30 42 11 15 45 00 00 47 48 45 50 37 30 53 26 15 56 15 00 59 03 45 61 52 30 64 41 15 67 30 00 70 18 45 73 07 30 75 56 15 78 45 00 81 33 45 84 22 30 87 11 15 90 00 00 28. The compass card is mounted in a bowl which is carried in gimbals, thus enabling the card to retain a horizontal position while the ship is pitching and rolling. A vertical black line called the lub- ber's line is marked on the inner surface of the bowl, and the compass is so mounted that a line joining 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, Steering, Check, or Boat Compass. INSTRUMENTS AND ACCESSORIES IN NAVIGATION. 17 30. There are two types of compass in use, the wet or liquid and the dry; in the former the bowl is filled with liquid, the card being thus partially buoyed, with consequent increased ease of working on the pivot, and the liquid further serving to decrease the vibrations of the card when deflected by reason of the motion of the vessel or other cause. On account of its advantages the liquid compass is used in the United States Navy. 31. The Navy Service 7J-inch Liquid Compass. — This consists of a skeleton card 7^ inches in diameter, made of tinned brass, resting on a pivot in liquid, with provisions for two pairs of magnets symmetrically placed. The magnet system of the card consists of four cylindrical bundles of steel wires; these wires are laid side by side and magnetized as a bundle 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 because they are more homogeneous, can be more perfectly tempered, and for the same weight 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 of the card. The card is of a curved annular type, the outer ring being convex on the upper and inner side, and' is graduated to read to one-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 card. The pivot is fastened to the center of the bottom of the bowl by a flanged plate and screws. Through this plate and the bottom of the bowl are two small holes which communicate with the expansion chamber and admit of a circulation of the liquid between it and the bowl. The pivot is of gun metal with an iridium cap. The card is mounted in a bowl of cast bronze, the glass cover of which is closely packed with rubber, preventing the evaporation or leakage of the liquid, which entirely fills the bowl. This liquid is com- posed of 45 per cent pure alcohol and 55 per cent distilled water, and remains liquid below —10° F. The lubber's line is a fine line drawn on an enameled plate on the inside of the bowl, the inner surface of the latter being covered with an insoluble white paint. Beneath the bowl is a metallic self-adjusting expansion chamber of elastic metal, by means of which the bowl is kept constantly full without the show of bubbles or the development of undue pressure caused by the change in volume of the liquid due to changes of temperature. The rim of the compass bowl is made rigid and its outer edge turned strictly to gauge to receive the azimuth circle. 32. The Dry Compass. — The Lord Kelvin Compass, which may be regarded as the standard for the nonliquid tj'pe, consists of a strong paper card with the central parts cut away and its outer edge stiffened by a thin aluminum ring. The pivot is fitted with an iridium point, upon which rests a small light aluminum boss fitted with a sapphire bearing. Radiating from this boss are 32 silk threads whose outer ends are made fast to the inner edge of the compass card; these threads sustain the weight of the suspended card, and, as they possess Some elasticity, tend to decrease the shocks due to motion. Eight small steel wire needles, 3 J 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 (b) 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. 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 provided for the protection of the compass and for lighting it at night. Binnacles must be rigidly secured to the deck of the vessel in such position that the lubber's line of the compass gives true indications of the direction of the ship's head. The position of the various binnacles on shipboard and the height at which they carry the compass must be chosen with regard to the purpose which the compass is to serve, having in mind the magnetic conditions of the ship. 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 6583—06 2 18 INSTRUMENTS AND ACCESSORIES IN NAVIGATION. semicircular deviation, placed in a magnet chamber lying immediately beneath the compass chamber, so arranged as to permit variation in the height and direction of the magnets employed; (6) a pair of arms projecting horizontally from the compass chamber and supporting masses of soft iron for quad- 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 securing a vertical soft iron rod, or "Flinders bar," used in certain cases for correction of a part of the semicircular deviation. An explanation of the various terms here used, together with the method of compensating the compass, will be given in Chapter III. THE PELORirS. 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. Revolving about a common center, which is also the center of the plate, are (a) a dumb com- pass card, usually engraved on metal, whose face is level with the raised periphery of the plate on which are marked the scores, and (6) a pivoted horizontal bar carrying at its extremities a pair of sight vanes so arranged that the line of sight always passes through the vertical axis of the instrument, and having an index showing the point at which the line of sight cuts the dumb compass. The dumb compass and the sight-vane bar can each be rigidly clamped. The 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 utitil 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 process of correction to which the bearings shown by compass are subject. It will at once be evident that the indications of the pelorus will be accurate only when bearings are taken at an instant when the ship is heading exactly in the direction for which it is set, and care must be taken accordingly in its use. The most modern types of pelorus are fitted for illuminating the dumb compass, thus greatly facili- tating night work. THE 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 includes the outline of the adjacent land, together with the surface forms and artificial features that are useful as aids to navigation, and sets forth the depths of water, especially in the near approaches to the land, by soundings that are fixed in position by accurate determinations. Except in charts of harbors or other localities so limited that the curvature of the earth is inappreciable on the scale of construction, a nautical chart is always framed over with a network of parallels of latitude and meridians of longitude in relation to which the features to be depicted on the chart are located and drawn; and the mathematical relation between the meridians and parallels of the chart and those of the terrestrial sphere determines the method of measurement that is to be employed on the chart and the special uses to which it is adapted. 37. There are three principal systems of projection in use: (a) the Mercator, (b) i\xe jwlyconic, and (c) the gno7nonic; 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. 38. The Mercator Projection. — The Mercator Projection, so called, may be said to result from the development, upon a plane surface, of a cylinder which is tangent to the earth at the equator, the various points of the eartn's surface having been projected upon tne cylinder in such manner that the loxodromic curve or rhumb line (art. 6, Chap. I) appears as a right line preserving the same angle of bear- ing with respect to the intersected meridians as does the ship's track. In order to realize this condition, the line of tangency, which coincides with the earth's equator, being the circumference of a right section of the cylinder, will appear as a right line on the develop- ment; while the series of elements of the cylinder corresponding to the projected terrestrial meridians will appear as equidistant right lines, parallel to each other and perpendicular to the equator of the chart, maintaining the same relative positions and the same distance apart on that equator as the meridians have on the terrestrial spheroid. The series of terrestrial parallels will also appear as a system of right lines parallel to each other and to the equator, and will so intersect the meridians as to form a system of rectangles whose altitudes, for successive intervals of latitude, must be variable, increasing from the equator in such manner that the angles made by the rhumb line with the meridian on the chart may maintain the required equality with the corresponding angles on the spheroid. 39. Meridional Parts. — At the equator a degree of longitude is equal to a degree of latitude, but in receding from the equator and approaching the pole, while the degrees of latitude remain always of the same length (save for a slight change due to the fact that the earth is not a perfect sphere), the degrees of longitude become less and less. INSTRUMENTS AND ACCESSORIES IN NAVIGATION. 19 Since, in the Mercator projection, the degrees of longitude are made to appear everywhere of the same length, it becomes necessary, in order to preserve the 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 Mercator pro- jection and for solving problems in Mercator 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, f preferably the lowest parallel to be drawn on the chart. The distance of any other parallel of latitude rom 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. Example: Let a projection be required for a chart of 14° extent in longitude between the parallels of latitude 20° 30^ and 30° 25^, and let the space allowable on the paper between these parallels measure 10 inches. Entering the column in Table 3 headed 20°, and running down to the line marked 30^ in the side column, will be found 1248.9; then, entering the column 30°, and running down to the line 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, for which V of arc of the equator is taken as the unit. On the intended projection, 10'° therefore, V of arc of longitude will measure __^ ' = 0.0152 inch, which will be the scale of the chart. 656.6 For the sake of brevity call it 0.015. By this quantity all the values derived from Table 3 will have tp 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 distance on the chart between 20° 30^ and 21° 00^. On the meridians lay off distances equal to 0.478 inch, and through the three points thus obtained draw a straight line, which will be the parallel of 21° 00^. Proceed in the same manner to lay down all the parallels answering to full degrees of latitude; the distances will be respectively: 0'".015X (1344.9—1248.9) ==1.440 inches, 0'°.015X (1409.5—1248.9) =2.409 inches, 0'".015X(1474.5~-1248.9)=3.384 inches, etc. Thus will be shown the parallels of latitude 22° 00^ 23° 00^ 24° 00^ etc. Finally, lay down in the same way the parallel of latitude 30° 25^, which will be the northern inner neat line of the chart. A degree of longitude will measure on this chart 0'". 015x60=0'". 9. 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 f;enerally be found sufficiently exact to make even subdivisions of the degrees, as in the case of the ongitude. 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 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° 00'' 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 and other positions are plotted on the chart by their latitude and longitude. A chart may be transferred from any other projection to that of Mercator by drawing a system of corre- sponding parallels of latitude and meridians over both charts so close to each other as to form minute squares, and then the lines and characters contained in each square of the map to be transferred may be copied by the eye in the corresponding squares of the Mercator projection. Since the unit of measure, the mile or minute of latitude, has a different value in every latitude, there is an appearance of distortion in a Mercator chart that covers any large extent of surface; for instance, an island near the pole will be represented as being much larger than one of the same size near the equator, due to the different scale used to preserve the character of the projection. 42. The Polyconic Projection. — This projection is based upon the development of the earth's surface on a series of cones, a different one for each parallel of latitude, each one having the parallel as its base, and its vertex in the point where a tangent to the earth at that latitude intersects the earth's axis. The degrees of latitude and longitude on this chart are projected in their true length, and 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 Pkojection. — 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 linee where the visual rays passing through them intersect the plane of projection. In a gnomonic chart, a straight line between any two points is projected as an arc of a great circle, and is therefore the shortest line between those points. Excepting in the Polar regions, for which latitudes the Mercator projection can not be constructed, the gnomonic charts are not used for general navigating purposes. Their greatest application is to afford a ready means of finding the course and distance at any time in great circle sailing, the method of doing which will be explained in Chapter V. 44. Meridians Employed in Chart Construction. — The United States, England, Germany, Italy, Russia, Norway, Sweden, Denmark, Holland, Austria, Portugal, and Japan adopt as a prime meridian the meridian of GreenvAch. France adopts the meridian of Paris in Long. 2° 20' 14". 5 E. of Greenwich. Spain adopts the meridian of San Fernando, Cadiz, in Long. 6° 12' 20" W. of Greenwich. The Pulkowa Observatory of fet. Petersburg (sometimes referred to in Russian charts) is in Long. 30° 19' 39". 6 E. of Greenwich. The Royal Observatory of Naples (sometimes referred to in Italian charts) is in Long. 14° 14' 06" E. of Greenwich. The meridian of Genoa is 8° 55' 21" E.; of Lisbon, 9° 08' 36" W.; of Rio de Janeiro, 43° 10' 21".2 W.; of Amsterdam, 4° 53' 03".8 E.; of Washington, 77° 03' 56".7 W. 45. Quality of Bottom. — The following table shows the qualities of the bottom, as expressed on charts of various nations: United States. Clay C. Coral Co. Gravel G. Mud M. Rocky rky. Sand S. Shells Sh. Stone St. Weed Wd. Fine fne. Coarse crs. Stiff stf. Soft sft. Black bk. Red rd. Yellow yl. Gray gy. English. Clay cl. Coral crl. Gravel g. Mud m. Rock rk. Sand 8. Shells sh. Stones St. Weed wd. Fine f. Coarse c. Stiff stf. Soft sft. Black blk. Red rd. Yellow y. French. Italian. Argile A. Corail Cor. Gravier Gr. Vase V. Roche R. Sable S. Coquille ....Cog. Pierre P. Herb H. Fin fin. Gros g. Dure d. Molle m. Noire n. Rouge r. Jaune j. Argila Cor&llo Rena or Ghiaja Fango Roccia S&bia or Ar6na Conchiglia Pietre Alga Fino Grosso Tenace Molle Nero Rosse Giallo Spanish. Arcillo or Barro Coral cl. Casc&jo Co. Fango or Luno . . . F. Piedra or Roca . . .P. Arena A. Conchuela ca. Piedra P. Alga A. Fina ...f. Gruesa Tenaz Muelle Ne|rro Rojo Amarillo German. Lehm L. Korallen K. Grob sand g. s. Schlemm Sch. Fels F. Sand 8. Muschel M. Stein. Gras G. Fein f. Grob g. Zahe Z. Welch W. Schwarz schw. Roth. Gelb. 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: Austrian fathom (klafter ) . . Danish and Norwegian fathom (farn) . . Dutch fathom (vaden).. p . /fathom ( brasse ) . . ^"^^^^^^ \meter( metre)... Portuguese fathom (bra^a) . . Prussian fathom (faden) . . Russian fathom ( sajen ) . . Spanish fathom (braza) . . Swedish fathom (famn) . . English feet. 6.222 6.175 5.575 5.329 3.281 6.004 5.906 6.000 5.492 5.843 English 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 metre are identical. A pied usael=13.124. inches, or 1.094 feet. A mHre is 3 pieds; a. pied du roi=12.7896 inches; brasse is used upon old French charts instead of metre. Upon 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 classes 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 mercury in the tube will fall until the top of the column 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 column of mercury thus left standing in the tube is equal to the pressure by which it is held in position — namely, that of the atmospheric air — it follows that the height of the column is subject to variation upon variation of that pressure; hence the 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 parts 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 ' W. ' M ^y^ rack and pinion, the latter having a milled head accessible to the observer, ' by which the adjustment is made. In the middle of the brass tube is fixed a thermometer, the bulb of which is covered from the outside but open toward the mercury, and which, being nearly in contact with the glass tube, indicates the temperature of the mercury and not that of the external air; the central position of the column is selected in order that the mean temperature may be obtained — a matter of importance, as the temperature of the mercurial column must be taken into account in every accurate application of its reading. 50. In the arrangement of further details mercurial barometers are di- vided into two classes, according as they are to be used as Standards (fig. 4) on shore, or as Sea Barometers ( fig. 3) on shipboard. In the Standard Barometer the scale and vernier are so graduated as to enable an observer to read the height of the mercurial column to the nearest 0.002 inch, while in the Sea Barometer the reading can not be made closer than 0.01 inch. The instruments also differ in the method of obtaining the true height of the mercurial column at varying levels of the liquid in the cistern. It is 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 -p o rise of level will occur. As the height of the mercurial column is required pj^j 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 INSTEUMENTS AND ACCE8S0BIES IN NAVIGATION. head of the screw projecting from the bottom of the instrument and thus placing it under control of the observer. By this means the surface of the mercury in the cistern (which is visible through a glass casing) may be raised or lowered until it exactly coincides with that level which is chosen as the zero of the scale, and which is indicated by an ivory pointer in plain view. In the Sea Barometer there is no provision for adjusting the level of the cistern to a fixed point, but compensation for the variable level is made in the scale graduations; a division representing an inch on the scale is a certain fraction short of the true inch, proper allowance being thus made for the rise in level which occurs with a fall of the column, and for the reverse condition. Further modification is made in the Sea Barometer to adapt it to the special use for which intended. The tube toward its lower end is much contracted to prevent the oscillation of the mercurial column known as "pumping," which arises from the motion of the ship; and just below this point is a trap to arrest any small bubbles of air from finding their way upward. The instrument aboard ship is sus- pended in a revolving center-ring, in gimbals, supported on a horizontal brass arm which is screwed to the bulkhead; a vertical position is thus maintained by the tube at all times. t 51. The vernier is an attachment for facilitating the exact reading of the scale of the barometer, and is also applied to many other instruments of precision, as, for example, the sextant and theodolite. It consists of a metal scale similar in general construction to that of the instrument to which it is fitted, and arranged to move alongside of and in contact with the main scale. The general principle of the vernier requires that its scale shall have a total length exactly equal to some whole number of divisions of the scale of the mstrument 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 coincidfence, 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 accuracy is not attainable in observing the height of a barometer on a vessel at sea, nor is it essential. The Standard Barometer on shore, however, is capa- ble of very exact reading; hence each scale division is made equal to half a tenth, or 0.05 inch, while a vernier covering 24 such divisions is divided into 25 parts; hence the column 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 vernier by day, while a small bull's-eye lamp held behind the instrument enables the observer to get a correct reading at night. When observing the barometer it should hang freely, not being inclined by holding or even by touch, because any inclina- tion will cause the column to rise in the tube. 54. Other things being equal, the mercury will stand higher in the tube when it is warm than when it is cold, owing to expansion. For the purposes of comparison, all barometric observations are reduced to a standard which assumes 32° F. as the 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. IN8TBUMENTS AND ACCESSORIES IN NAVIGATION. 23 the plus sign showing that the correction is to be added to the reading of the ship's barometer and the minus sign that it is to be subtracted: Tempera- ture. Correction. Tempera- ture. Correction. Tempera- ture. Correction. Tempera- ture. Correction. o Inch. o Inch. o 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 96 -0.18 38 -0.03 58 -0.08 78 -0.13 98 -0.18 As an example, let the observed reading of the mercurial barometer be 29.95 inches, and the tem- perature as given by the attached thermometer 74°; then we have: 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, though not completely, exhausted, the box is hermetically sealed. When the pressure of the atmosphere increases the inclosed air is compressed, the capacity of the box is diminished, and the two flat ends approach each other; when the pressure of the atmosphere decreases, the ends recede from one another in consequence of the expansion of the inclosed air. By means of a combination of levers, this motion of the ends of the box is communicated to an index pointer which travels over a graduated dial plate, the mechanical arrangement being such that the motion of the ends of the box is 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 deiangement 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 INSTEUMENTS AND ACCESSOEIES IN NAVIGATION. between them. An approximate rule is to allow 0.0011 inch for each difference in Jevel of one foot, or, more roughly, 0.01 inch for every 9 feet. A very exact method is afforded by Babinet's formula. If B^ and B represent the barometric pres- sure (corrected for all sources of instrumental error) at the lower and at the upper stations respectively, and to and i the corresponding temperatures of the air; then, Diff. in height=CX Bq-B. B.+B' if the temperatures be taken by a Farhenheit thermometer, C (infeet) = 62,494(^l+*^±^^; if a centigrade thermometer is used, C (in meters) =16,000^1+?^^^^^ 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 oi 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 Centigrade, in which the freezing point is at 0° and the boiling point at 100°; and the Reaumur, in which these points are at 0° and 80°, respectively. The Fahrenheit thermometer is generally used in the United States and England. Tables will be found in this work for the interconversion of the various scale readings (Table 31). 59. The thermometer is a valuable instrument for the mariner, not only by reason of the aid it affords him in judging meteorological conditions from the temperature of the air and the amount of moisture it contains, but also for the evidences it furnishes at times, through the temperature of the sea water, of the ship's position and the probable current that is being encountered. 60. The thermometers employed in determining the temperature of the air (wet and dry bulb) and of the water at the surface, should be mercurial, and of some standard make, with the graduation etched upon the glass stem; they should be compared with accurate standards, and not accepted if their read- ings vary more than 1° from the true at any point of the scale. 6 1 . 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, which is always somewhat less than the temperature of the free air. From the difference of these two temperatures the observer may determine the proximity of the air to saturation; that is, how near the air is to that point at which it will be obliged to precipitate some of its moisture (water vapor) in the form of liquid. With the envelope of the wet bulb removed, the two ther- mometers should read precisely the same; otherwise they are practically useless. The two thermometei-s, the wet and the dry bulb, should be hung within a few inches of each other, and the surroundings should be as far as possible identical. In practice the two thermometers are generally inclosed within a small lattice case, such as that shown in figure 6; the case should be placed in a position on deck remote from any source of artificial heat, sheltered from the direct rays of the sun, and from the rain and spray, but freely exposed to the circulation of the air; the door should be kept closed except during the proc- ess of reading. The cloth envelope of the wet bulb should be a single thickness of fine muslin, tightly stretched over the bulb, and tied with a fine thread. 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 be at all times thoroughly moist, but not dripping. When the temperature of the air falls to 32° F. the water in the wick freezes, the capillary action is at an end, the bulb in consequence soon becomes quite dry, and the thermometer no longer shows the temperature of evaporation. At such times the bulb 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 INSTRUMENTS AND ACCESSORIES IN NAVIGATION. 25 this process the temperature of the wet bulb is temporarily raised above that of the dry, but only for a brief time, as the water quickly freezes; and inasmuch as evaporation takes place from the surface of the ice thus formed precisely as from the surface of the water, the thermometer will act in the same way fts if it had a damp bulb. The wet-bulb thermometer can not properly read higher than the dry, and if the reading of the wet bulb should be the higher, it may always be attributed to imperfections in the instruments. 62. Knowing the temperature of the wet and dry bulbs, the relative humidity of the atmosphere ftt the time of observation may be found from the following table: Tempera- ture of the air, dry- Difference between dry-bulb and wet-bulb readings. bulb ther- mometer. 1° 2° 3° 4° 5° 6° 7° 8° 9° 10° o Per ct. Per ct. Per ct. Per ct. Per ct. Per ct. Per ct. Per ct. Per ct. Perct. 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 fi.^ 53 44 35 27 36 91 82 73 64 65 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 81 76 71 67 63 58 54 70 95 90 86 81 77 72 68 64 60 55 72 95 91 86 82 77 73 69 65 61 57 74 95 91 86 82 78 74 70 66 62 58 76 95 91 87 82 78 74 70 66 63 59 78 96 91 87 83 79 75 71 67 63 60 80 96 92 87 83 79 75 72 68 64 61 82 96 92 88 84 80 76 72 69 65 62 84 96 92 88 84 80 77 73 69 66 63 86 96 92 88 84 81 77 73 70 67 63 88 96 92 88 85 81 77 74 71 67 64 90 96 92 88 85 81 78 74 71 68 65 The table may be readily understood. For example, if the temperature of the air (dry bulb) be <50°, and the temperature of evaporation (wet bulb) be 56°, the difference being 4°, look in the column headed "Temperature of the air" for 60°, and for the figures on the same line in column headed 4°; here 78 will be found, which means that the air is 78 per cent saturated with water vapor; that is, that the amount of water vapor present in the atmosphere is 78 per cent of the total amount that it could carry at the given temperature (60°). This total amount, or saturation, is thus represented by 100, and if there occurred any increase of the quantity of vapor beyond this point, the excess would be precipi- tated in the form of liquid. Over the ocean's surface the relative humidity is generally about 90 per cerjt, or even higher in the doldrums; over the land in dry winter weather it may fall as low as 40 per cent. 63. The sea water of which the temperature is to be taken should be drawn from a depth of 3 feet below the surface, the bucket used being weighted in order to sink it. The bulb of the thermome- ter should remain immersed in the water at least three minutes before reading, and the reading should be made with the bulb immersed. THE LOG BOOK. 64. The 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 observations, which should be made not only for the purpose of foretelling the weather during the voyage, but also for contribution to the general fund of knowledge of marine meteorology. 65. A convenient form for lecording 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 oflScers, appears upon the oj)posite page. 26 INSTRUMENTS AND ACCESSORIES IN NAVIGATION. State of sea by symbols. 00 1 6 as° •Sa QO t >4 1 Barometer. a3 a S2 Id 1 I'll "sa 1^. Ill O o Reading of patent log. •a CO o a o m ^i-i(MeoTj+^ QG OQ OQ tX2 Oa "3 Is 13 S S ac 6C b£' s P X! O . iS O « O cS J h:; J t-^ (-:! T3 el o P5 g O be o PI o .S 2 I is -^ s^ i^ 0) T5 O O be i u d ,o Ph 01 01 o o C (3 c^ 03 Lrf ^ Q P O ►-] iJ > C be be a a ^ 'S (D 0) o o Oi 01 be be c3 ra o S o a 72 72 CC o 5 Ph - s a " 'S H ;> H 1 a a -r) 'O Fi '? o o ^ 1 o ^ a o 01 -S ^ a) 05 K ^P= be '73 a j: £ I a oj c8 O O INSTRUMENTS 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 century sailing full and by; in the higher grades, from the amount of sail which the same vessel could carry when closehauled. The scale, with the estimated velocity of the wind in both statute and nautical miles per hour, is as follows: Conditions. Velocity. Mean pressure in pounds per square foot. Force of vyind. Statute miles per hour. Nautical miles per hour. 0._Calm Full-rigged ship, all sails set, no headway . Just sufficient to give steerage way Speed of 1 or 2 knots, ' • full and by " Speed of 3 or 4 knots, " full and by " Speed of 6 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 66.4 66.1 78.1 and over. 0.03 0.23 2.— Light breeze 3.— Gentle breeze 4.— Moderate breeze . . 0.62 1.2 1.9 2.9 6. —Strong breeze 7.— Moderate gale 8. — Fresh gale 9.— Strong gale 10.— Whole gale 11. — Storm Topgallantsailsover single-reefed topsails Double-reefed topsails 4.2 5.9 Treble-reefed topsails (or reefed upper- topsails and courses). Close-reefed topsails and courses (or lower topsails and courses). Close-reefed main topsail and reefed fore- sail (or lower main topsail and reefed foresail). 8.4 11.6 16.5 20.6 20.6 6§. When steaming or sailing with any considerable speed,xthe apparent direction and force of the wind, as determined from a vane, flag, or 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 pennant 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 will be found. 69. W^EATHER. — 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. — Drizzling, or light rain. /. — Fog, or foggy weather. g. — (xloomy, or dark, stormy-looking weather, /i.— Hail. I. — Lightning, m. — -'Misty weather. 0. — Overcast. p. — Passing showers of rain. q. — Squally weather. r. — Rainy weather, or continuous rain. s. — Snow, or snowv weather. «.— Thunder. u. — Uglj^ appearances, or threatening weather. V. — Visibility of distant objects. VK — Wet, or heavy dew. z. — Hazy. To indicate great intensity of any feature, its symbol may be underlined; thus: r., heavy rain. TO. Clouds. — The following are the principal forms of clouds, named in the order of the altitude above the earth at which they usually occur, beginning with the most elevated. The symbols by which each is designated follows its name: 1. Cirrus, (Oi. ). — 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 le&s distinctly, a formation like a tangled web. This sheet often produces halos around the sun and moon. 3. CiRRO-CuMULUs, {Ci.-Ou.). — 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-Stkatus, (A.-S.). — A thick sheet of a gray or bluish color, showing a brilliant patch in the neighborhood of the sun or moon, and which, without causing halos, may give rise to coronse. This form goes through all the changes like the Cirro-Stratus, but its altitude is only half so great. 6. Stkato-Cumulus, (S.-Cu.). — Large globular masses or rolls of dark cloud, frequently covering the whole sky, especially in winter, and occasionally giving it a wavy appearance. The layer of Strato- Cumulus is not, as a rule, very thick, and patches of blue sky are often visible through the intervening spaces. All sorts of transitions between this form and the Alto-Cumulus are noticeable. It may be distinguished from Nimbus by its globular or rolled appearance and also because it does not bring rain. 7. Nimbus, (N.). — Rain clouds; a thick layer of dark clouds, without shape and with ragged edges, from which continued rain or snow generally falls. Through the openings of these clouds an upper layer of Cirro-Stratus or Alto-Stratus may almost invariably be seen. If the layer of Nimbus separates into shreds or if small loose clouds are visible floating at a low level underneath a large nimbus, they may be described as Fracto-Nimbus (Fr.-N. ), the "scud" of sailors. 8. Cumulus, (Cw. ). — 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 (i^.-Cu. ). 9. CuMULo-NiMBus, (Ou.-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. E. — Rough sea. G. — Ground swell. S. — Smooth sea. H. — Heavy sea. T. — Tide-ripe. L. — Long rolling sea. THE COMPASS ERROR. "^ 29 CHAPTER III THE COMPASS EEEOE. CAUSES OF THE ERROF. 73. When two magnets are near enough together to exert a mutual influence, 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- liood of the geographical pole, though not exactly comcident 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 l)e parallel to the lines of magnetic force in that plane created by the earth's magnetic poles, the end which we name north pointing to the north, and the south end in the opposite direction. The north end of the compass — north-seeking, as it is sometimes designated for clearness — will be that end which has 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 compass. 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 been 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 must 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 proximity to vessels, docks, machinery, or other masses of iron or steel. It is also encountered at sea in localities where the mineral substances 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 mariner, but, fortunately, the number of localities subject to local attraction is limited. The amount of this error can seldom, if ever, be determined; if known, it might 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; [b) 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 by the compass on a given heading of the ship, and must be corrected for the deviation on that heading for conversion to magnetic, and for both deviation and variation for conversion to true bearings or courses. The process of applying the errors under all 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 bearing 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. T§. 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 ^vest, or marked — . Figures 7 and 8 represent, respectively, examples of easterly and westerly errors. In both cases consider that the circles rep- resent the observer's horizon, N and S being the correct north and south points in each case. If N^ and S^ repre- sent the corresponding points indicated by a compass whose needle is deflected by a com- E pass error, then in the first case, the north end of the needle being drawn to the right or east, the error will be easterly or positive, and in the second case, the north end of the needle being drawn to the left or west, the com- pass error w'ill be westerly or negative. Considering figure 7, if Fig. Fig. 8. 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 the correct direction is to the right, the error is e.\st. 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 easterly deviation, he would know that to obtain the result the error must be applied to the right; if it were desired to change a correct course to the one indi- cated by compass, the error being westerly, the converse presents itself — the correct must be to the left — the uncorrected will therefore be to the right; if a correct bearing is to be compared with a com- pass bearing to find the compass error, when the correct is to the right the error is east, or the reverse. §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 N. 76° E. ; variation, 5° W. ; required the true bearing. N. 71° E. A bearing taken by a similar compass is NW. bv W. i W. ; variation, I pt. W. ; required the true bearing. NW. by W. | W. A vessel steers S. 27° E. by compass; deviation on that heading, 3° W. ; variation in the localitv, 12° E.; required the true course. S. 18° E. A vessel steers S. bv W. i W. ; deviation, } pt. W. ; variation, 1 pt. E. ; required the true course. ssw.nv. 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. I N. ; variation 1|^ 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 by compass is S. 89° E. ; it is found by calculation to be N. 84° E. (true) ; variation, 8° W.; required the deviation. 1° E. FINDING THE COMPASS EBBOR. 82. The variation of the compass for any given locality is found from the charts. A nautical chart always contains information from which the navigator is enabled to ascertain the variation for any place within the region embraced and for any year. Beside the information thus to be acquired from local charts, special charts are published showing the variation at all points on the earth's surface. §3. The deviation of the compass, varying as it does for every ship, for every heading, and for every geographical locality, must be determmed 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 explained hereafter), whence the deviations on exact points may be found. §4. In swinging ship for deviations the vessel should be on an even keel and all movable masses of iron in the vicinity of the compass secured as for sea. The vessel, upon being placed on any heading, should be steaciied 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 requisite time on each heading), or at anchor, by means of springs and hawsers. §5. The deviation of all compass^es 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 constructed as explained in article 94. 86. There are four methods for ascertaining the deviations from swinging; namely, by reciprocal hearings, by hearings of the sun, by ranges, and by a distant object. 87. Reciprocal Bearings. — One observer is stationed on shore with a spare compass placed in a position free from disturbing magnetic influences; a second observer is at the standard compass on board ship. At the instant when ready for observation a signal is made, and each notes the bearing of the other. The bearing by the shore compass, reversed, is the magnetic bearing of the shore station from the ship, and the difference between this and the bearing by the ship's standard compass 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 by 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 op 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, and which when in line lie on a known magnetic bearing. By steaming about on different headings and noting the compass bearing of the ranges each time of crossing the line that they mark, a series of deviations may be obtained,. the deviation of each heading being equal to the difference between the compass and the magnetic bearing. 90. Distant 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 may be assumed to be the mean of the compass bearings. 32 THE COMPASS ERROK. In choosing an object for use in this method care must be taken that it is at such a distance that its bearing from the ship does not practically differ as the vessel swings in azimuth. If the ship is swung at anchor, the distance should be not less than 6 miles. If swung under way, the object must be so far that the parallax (the tangent of which may be considered equal to half the diameter of swinging divided by the distance) shall not exceed about 30'. 91. In all of the methods described it will be found convenient to arrange the results in tabular form. In one column record the ship's head by standard compass, and abreast it in successive columns the observations from which the deviation is determined on that heading, and finally write the deviation itself. When the result of the swing has been worked up another table is constructed showing simply the headings and the corresponding deviations. This is known as the Deviation Table of the compass. If compensation is to be attempted, this table is the basis of the operation; if not, the deviation tables of the standard and steering compass shotild be posted in such place as to be accessible to all persons concerned with the navigation of the ship. 92. Let it be assumed that a deviation table has been found and that the values are as follows: Deviation table. Ship's head by standard compass. Devia- tion. Ship's head by standard compass. Devia- 1 tion. 1 Ship's head by standard compass. Devia- tion. Ship's head by standard compass. Devia- tion. North o / - 1 00 - 1 50 - 3 00 - 5 15 - 7 10 -10 15 -13 05 -17 10 East E.byS... ESE..... SE. by E . SE 1 SE.byS.. ! SSE S.byE... o r -19 55 '-22 00 1-23 30 -24 00 -23 30 -20 30 -16 00 - 8 50 South 00 +10 20 +17 00 +21 50 +24 30 +26 20 +25 00 +23 30 West W.byN... WNW NW.byW. NW o / +19 30 +17 00 +13 00 +11 10 + 7 40 N. by E . . . NNE NE.by N.. NE S. by W . . . ssw SW.byS.. sw SW. by W . WSW W.byS... NE.byE.. ENE E. by N . . . NW. by N . NNW N.bv W... + 5 05 + 3 00 + 1 00 We have from the table the amount of deviation on each compass heading; therefore, knowing the ship's head by compass, it is easy to pick out the corresponding deviation and thus to obtain the mag- netic heading. But if we are given the magnetic direction in which it is desired to steer and have to find the 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 table just given, suppose it is required to determine the compass heading corresponding to N. 79° W., magnetic. The deviation corresponding to N. 79° W., per compass, is + 17° 00'. If we apply this to N. 79° W., magnetic, we have S. 84° W. as the compass course. But, consulting the table, it may be seen that the deviation corresponding to S. 84° W., per compass, is + 21^°, and therefore if we steer that course the magnetic direction will be N. 74J° W., 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 N. 79° W. P- c F rst trial. N. 79° W. 17° E. S. 84° W. 2U °E. Trial comp. course Dev. onS. 84° W., p. c. Mag. course made good N. 74 J° W. Since this assumption carries the course 4J° too far to the right, assume next a deviation on a course 5° farther to the left than the one used here. Mag. course required . Try dev. on S. 79° W. p. c. Second trial. N. 79° W. 23J° E. Trial comp. course Dev. on S. 77^° W., p. c. S. 77F W. 24° E. Mag. course made good N. 78^° W. This is as close to the required course as the ship can be steered. It may occur that further trials will be necessary in some cases. 93. The Napier Diagram. — A much more expeditious method for the solution of this problem is afforded by the Napier Diagram, and as that diagram also 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. i UNIVERSITY OF THE COMPASS EEROR. 38 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 Avestern semicircles. The vertical line is of a convenient length and divided into thirty-two equal parts corresponding to the points of the compass, beginning at the top with North ind continuing around to the right; it is also divided into 360 degrees, which are appropriately marked. DEVIATION WEST DEVIATIOH EAST DEVIATION WEST DEVIATION EAST Fig. 9. The vertical line is intersected at each compass point by two lines inclined to it at an angle of 60°, that line which is inclined upward to the right being drawn plain and the other dotted. To plot a curve on the Napier diagram, if the deviation has been observed with the ship's head ou given TOwijoass 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. 6583—06 3 34 THE COMPASS ERROR. To obtain a complete curve, a sufficient number of observations should be taken while the ship swings through an entire circle. Generally, observations on every alternate point are enough to estab- lish a good curve, but in cases where the maximum deviation reaches 40° it is preferable to observ^e on every point. The curve shown in the full line on figure 9 corresponds to the table of deviations given in article 92. From a 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 cf intersection draw another line parallel to the plain lines; the point on the scale where this last line cuts the vertical line is the magnetic course sought. The correctness of this solution will be apparent when we consider that the C0° triangles are equilateral, and therefore the distance measured along the vertical side will equal the distance measured along the inclined sides — that is, the deviation; and the direction will be correct, for the construction is such that magnetic directions will be to the right of compass directions when the deviation is easterly and to the left if westerly. From a given magnetic course to find the corresponding compass course, the process is the same, excepting that the first line drawn should follow, or be parallel to, the plain lines, and the second, or return line, should be parallel to the dotted; and a proof similar to that previously employed will show the correctness of the result. As an example, the problem given in article 92 may be solved by the diagram, and the result will be found to accord with the solution previously given. THE THEORY OF DEVIATION. « 95. Features of the Earth's Magnetism. — It has already been stated that the earth is an immense natural magnet, with a pole in each hemisphere which is not coincident with the geographical pole; it has also a magnetic equator which lies close to, but not coincident with, the geographical equator. A magnetic needle freely suspended at a point on the earth's stirface, 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 eartli'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 ol the earth's total force, and are usually designated as H and Z. The angle CAB, which the line of direction makes with the plane of the horizon, is called the magnetic inclination or dip, and denoted by 6. It is clear that the horizontal component will reduce to zero at the magnetic poles, where 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 immediately imparted to the former, which itself becomes magnetic and continues to remain so as long as it is within the sphere of influence of the permanent magnet; the magnetism that it acquires under these circumstances is said to be induced, and the properties of induc- tion are such that that end or region which is nearest the pole of the influencing magnet will take up a polarity opposite thereto. If the magnet is withdrawn, the induced magnetism is soon dissipated. If the magnet is brought into proximity again, but with its opposite pole nearer, magnetism will again be 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 acquires and parts with its magnetic qualities under the varying influences to which it is subjected. 97. Magnetic Properties Acquired by an Iron or Steel Vessel in Building. — The inductive action of the earth's magnetism affects all iron or steel within its influence, and tlie 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 oi hammering, bending, and twisting that it undergoes. Fig. 10. a As it is probable that the student will not have practical need of a knowledge of the theory of deviation and the compensation of the compass until after he has mastered all other subjects pertaining to Navigation and Nautical Astronomy, it may be considered preferable to omit the remafnder of this chapter at first and return to it later. THE COMPASS ERROR. 35 An iron bar held in the line of the earth's total force instantly becomes magnetic; if held at an angle thereto it 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 poles of the earth and all influence would be neutralized. If, while such a bar is in a magnetic state through inductive action, it should be hammered or twisted, a certain mag- netism of a permanent character is impressed upon it, which is never entirely lost unless the bar i& subjected to causes equal and opposite to those that produced the first effect. A sheet of iron is affected by induction in a similar way, the magnetism induced by the earth diffusing itself over the entire plate and separating itself into regions of opposite jiolarity 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 vertif^al components of the earth's force in the locality and upon the direction of the keel in building; its permanency will depend upon the amount of mechanical violence to which the metal has been subjected by the riveting and other inci- dents of construction, and upon the nature of the metal employed. 9§. Causes that Produce Deviation. — There are three influences that operate to produce devia- tion; namely, (a) suhpermanent magnetism; [b) transient magnetism induced in vertical soft iron, and (c) transient magnetism induced in horizontal soft iron. Their effect will be explained. Suhpermanent magnetism is the name given to that magnetic force which originates ih 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 rnaterial 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 suhpermanent. The vessel will then approximate to a permanent magnet, in which the north polarity will lie in that region which was north in building, and the south polarity (that which exerts an attracting influence on the north pole of the compass needle), in the region which was south in building. Transient magnetism induced in vertical soft iron is that developed in the soft iron of a vessel through the inductive action of the vertical component only of the earth's total force, and is transient in nature. Its value or force 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 do not usually lie in the horizontal plane of the compass needle, but as this needle is constrained to act in a horizontal plane, its movements will be affected solely by the horizontal components of these forces, and its direction will be determined by the resultant of those components. The earth's force operates to retain the compass needle in the plane of the magnetic meridian, but the resultant of the three remaining forces, when without this plane, deflects the needle, and the amount of such deflection constitutes the deviation. 99. Classes 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, qaadrantal, 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 suhpermanent 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 18D°, 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 semicircidar deviation. In figure 9, a curve is depicted which shows the deviations of a semicircular nature separated from those due to other disturbing causes, and from this the reason for the name will be apparent. 101. Returning to the two distinct sources from which the semicircular deviation arises, it may be seen that the force due to suhpermanent magnetism remains constant regardless of the geographical position of the vessel; but since the horizontal force of the earth, which tends to hold the needle in the magnetic meridian, varies with the magnetic latitude, the deviation due to suhpermanent 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 \ertical 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 sin & deviation arising from this cause on change of latitude is ^^^^c, or tan 6. If, then, we consider the change in the semicircular deviation due to a change of magnetic latitude, it will be necessary to separate the two factors of the deviation and to remember that the portion pro- duced by subpermanent magnetism varies as , and that due to vertical induction as tan 0. But for rl any consideration of the effect of this class of deviation in one latitude only, the two parts may be joined together and regarded as having a single resultant. 102. If we now resume our former assumption, that all the forces tending to produce semicircular deviation are concentrated in a single pole exerting an attracting influence upon the north pole of the compass, we may consider a line to be drawn joining that theoretical pole with the center of the com- pass, then the angle made by this line with the keel line of the vessel, measured from right ahead, around to the right is called the starboard 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 pole of the compass) is in the direction given by the starboard angle; if, therefore, a magnet be placed with its center in the ver- tical axis of the 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 stiirboard 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 Ob and Oc, respectively, represent, on the same scale, the resolved directions of that force in the keel line and in the transverse line of the ship. Each of these resolved forces will exert a maximum effect when acting at right angles to the needle, the athwartship one when the ship heads north or south by compass, and the longitu- dinal one when the heading is east or west. On any other heading than those named the deviation produced 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: ,0c tan a=_; or (what may be shown to be the same thing): tan a=«!^; sinB and when the maximum deviations are small, this becomes: tan or==-, a Since the starboard angle is always measured to the right, it will be seen that, for positive values of B and C, a will be between 0° and 90°; for a negative B and a positive C, between 90° and 180°; for a It should be remarked that in a mathematical analysis of the deviations, it would be necessary to distinguish between the approximate coefficients, B and C, here described, as also A, D, and E, to be mentioned later, and the 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 difference need not be entered into. THE COMPASS ERROR. 37 n^ative values of both B and C, between 180° and 270°; and for a positive B and negative C, 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 previouslygiven(art. 92), Bisenualto -19° 55', or to —19° 30', 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 ^ (-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 latitudfe; 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 ditferent 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 Ftinders bar. Having thus opposed to each of the component forces a corrector of magnetic character identical with its own, a change of latitude will make no difference in the effectiveness of the compensation, for in every case the modified conditions will produce identical results in the disturbing and in the correcting force. 106. Quadrantal D(;viatlon IS thsit which arises from horizontal induction in the soft iron of the vessel through the action of the horizontal component of the earth's total force. Let us consider, in figure 12, the effect of any piece of soft iron which is symmetrical with respect to the compass — that is, which lies wholly within a plane passing through the center of the needle in either a fore-and-aft or an ath wart- ship direction. It may be seen (a) that such iron produces no deviation on the cardinal points (for on north and south headings the fore-and-aft iron, though strongly magnetized, has no tendency to draw the needle from a north-and-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 (h) the direction of the deviation produced is opposite in successive quadrants. The action of unsymmetrical soft iron is not quite so readily apparent, but investigation shows that part of its effect is to produce a deviation which becomes zero at the inter-cardinal points and is of 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 quadraidal deviatiom^. 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 considered positive when it produces easterly deviations in the quadrant between North and East; the coefficient of deviations arising from unsymmetrical soft iron is called E, and is reckoned as positive when it produces easterly deviations in the quadrant between NW. and NE. ; this latter attains inaportance only when there is some marked inequality in the distribution of metal to starboard and to port, as in the case of a compass placed off the midship line. 10§. D 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 I (-7° 10' + 24° 30') = + 8° 40'; or to \ (+23° 30' - 7° 40') = + 7° 55'; or to i ( + 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 equal to the mean of the deviations on North and South; or to the mean of those on East and West with sign reversed; or to the mean of those means. In the example, E is equal to i (-1°00'±0°00') =-0° 30'; or to * (+ 19° 55' - 19° 30') =+0° 13'; or to i (-0° 30'H-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. Fig. 12. 88 THE COMPASS EEEOR. 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 deviation, represented by the coefticient E; another effect is the constant deviation, so called because it is uniform in amount and direction on every heading of the ship. If plotted on a Napier diagram, it would appear as a straight line parallel with the initial line of the diagram. 112. Like other classes of deviation, the effect of the disturbing force is represented by a coeffi- cient; this coefficient is designated as A, and is considered plus for easterly and minus for westerly errors. It is approximately equal to the mean of the deviations on any number of equidistant headings. In the case previously given, it might be found from the four headings, North, East, South, and West, and would then be equal to i (-1° 00^-19° 55'±0° 0(y+19° 300=-0° 2V; or from all of the 32 headings, when it would equal -|-0° 16'. For the same reason as in the case of E, the value of A is usually so small that it may be neglected; it only attains a material size when the compass is placed off the midship line, or for some similar cause. 113. Like quadrantal deviation, since its force varies with the earth's horizontal force, the con- stant deviation will remain uniform in amount in all latitudes. No attempt is made to compensate this class of error. 114. Coefficients. — The chief value of coefficients is in mathematical analyses of the deviations and their causes. It may, however, be a convenience to the practical navigator to find their approxi- mate values by the methods that have been given, in order that he may gain an idea of the various sources of the' error, with a view to amellDrating the conditions, when necessary, by moving the bin- nacle or altering the surrounding iron. The following relation exists between the coefficients and the deviation : rf=A + B sin 2' + C cos z' + D sin 2z' + E cos 2z', where d is the deviation, and z^ the ship's heading by compass, measured from compass North. 115. Mean Directive Fokce. — The effect of the disturbing forces is not confined to causing devi- ations; it is only those components acting at right angles to the needle which operate to produce deflection; the effect of those acting in the direction of the needle is exerted either in increasing or diminishing the directive force of the compass, according as the resolved component is northerly or southerly. It occurs, with the usual arrangement of iron in a vessel, that the mean effect of this action throughout a complete swing of the ship upon all headings is to reduce the directive force — that is, while it varies with the heading the average value upon all azimuths is minus or southerly. The result of such a condition is unfavorable from the fact that the compass is thus made more "sluggish," is easily disturbed and does not return quickly to rest, and a given deflecting force produces a greater deviation when the directive force is reduced. The usual methods of compensation largely correct this fault, but do not entirely do so; it is therefore the case that the mean combined horizontal force of earth and ship to north is generally less than the horizontal force of the earth alone; but it is only in extreme cases that this deficiency is serious. 116. Heeling Error. — This is an additional cause of deviation that arises when the vessel heels to one side or the other. Heretofore only those forces have been considered which act when the vessel is on an even keel; but if there is an inclination from the vertical certain new forces arise, and others previously inoperative become effective. These forces are (a) the vertical component of the subperma- nent magnetism acquired in building; (b) the vertical component of the induced magnetism in vertical soft iron, and (c) the magnetism induced by the vertical component of the earth's total force in iron which, on an even keel, was horizontal. The first two of these disturbing causes are always present, but, when the ship is upright, have no tendency to produce deviation, simply exerting a downward pull on one of the poles of the needle; the last is a new force that arises when the vessel heels. The maximum disturbance due to heel occurs when the ship heads North or South. When heading East or West there will be no deviation produced, although the directive force of the needle will be increased or diminished. The error will increase with the amount of inclination from the vertical. 117. For the same reason as was explained in connection with semicircular deviations, that part of the heeling error due to subpermanent magnetism will vary, on change of latitude, as ^, while that due to vertical induction will vary as tan 6. In south magnetic latitude the effect of vertical induction will be opposite in direction to what it is in north. 118. The heeling error is corrected by a permanent magnet placed in a vertical position directly under the center of the compass. Such a magnet has no effect upon the compass when the ship is upright; but since its force acts in an opposite direction to the force of the ship which causes heeling error, is equal to the latter in amount, and is exerted under the same conditions, it affords an effective compensation. For similar reasons to those affecting the compensation of B and C, the correction by means of a permanent magnet is not general, and must be rectified upon change of latitude. PRACTICAL COMPENSATION. 119. In the course of explanation of the different classes of deviation occasion has been taken to state generally the various methods of compensating the errors that are produced. The practical methods of applying the correctors will next be given. 120. Order of Correction. — The following is the order of steps to be followed in each case. It is assumed that the vessel is on an even keel, that all surrounding masses of iron or steel are in their normal positions, all correctors removed, and that the binnacle is one in which the semicircular deviation is corrected by two sets of permanent magnets at right angles to each other. 1 . Place quadrantal correctors by estimate. 2. Correct semicircular deviations. THE COMPASS ERROR. 39 3. Correct quadrantal deviations. 4. Swing ship for residual deviations. The heehng corrector inay be placed at any time after the semicircular and quadrantal errors are corrected. A Flinders bar can be put in place only after observations in two latitudes. 121. The ship is first placed on some magnetic cardinal point. If North or South, the only force (theoretically speaking) which tends to produce deflection of the needle will be the athwartship com- ponent of the semicircular force, whose effect is represented by the coefficient C. If East or AVest, the only deflecting force will be the fore-and-aft component of the semicircular force, whose effect is repre- sented by the coefficient B. This will be apparent from a consideration of the direction of the forces producing deviation, and is also shown by the equation connecting the terms (where A and E are zero) : f? = B sin / -f C cos z' + J) sin 2z^ If the ship is headed North or South, z^ being equal to 0° or 180°, the equation becomes d = =h C. If on East or West, z^ being 90° or 270°, we have d = ± B. This statement is exact if we regard only the forces that have been considered in the problem, but experience has demonstrated that the various correctors when in place create certain additional forces by their mutual action, and in order to correct the disturbances thus accidentally produced, as well as those due to regular causes, it is necessary that the magnetic conditions during correction shall approxi- mate as closely as possible to those that exist when the compensation is completed; therefore the quad- rantal correctors should first be placed on their arms at the positions which it is estimated that they will occupy later when exactly located. An error in the estimate will have but slight effect under ordinary conditions. It should be understood that the placing of these correctors has no corrective effect while the ship is on a cardinal point. Its object is to create at once the magnetic field with which w^e shall have to deal when compensation is perfected. This having been done, proceed to correct the semicircular deviation. If the ship heads North or South, the force producing deflection is, as has been stated, the athwartship component of the semi- circular force, which is to be corrected by permanent magnets placed athwartships; therefore enter in the binnacle one or more such magnets, and so adjust their height that the heading of the ship by compass shall agree with the magnetic heading. When this is done all the deviation on that azimuth will' be corrected. Similarly, if the ship heads East or West, the force producing deviation is the fore-and-aft com- ponent of the semicircular force, and this is to be corrected by entering fore-and-aft permanent magnets in the binnacle and adjusting the height so that the deviation on that heading disappears. With the deviation on two adjacent cardinal points corrected, the semicircular force has been com- pletely compensated. Next correct the quadrantal deviation. Head the ship NE., SE., SW., or NW. The coefficients B and C having been reduced to zero by compensation, and 22^, on the azimuths named, being equal to 90° or 270°, the equation becomes d = ±D. The soft-iron correctors are moved in or out from the positions in which they were placed by estimate until the deviation on the heading (all of which is due to quadrantal force) disappears. The quadrantal disturbing force is then compensated. 122. Determination of Magnetic Headings. — To determine when the ship is heading on any given magnetic course, and thus to know when the deviation has been corrected and the correctors are in proper position, four methods are available: (a) Swing the ship and obtain by the best available method the deviations on a sufficient number of compass courses to construct a curve on the Napier diagram for one quadrant, and thus find the com- pass headings corresponding to two adjacent magnetic cardinal points and the intermediate intercardinal point, as North, NE., and East, magnetic. « Then put the ship successively on these courses, noting the corresponding headings by some other compass, and when it is desired to head on the various magnetic azimuths during the process of correction the ship may be steadied upon them by the auxiliary com- pass. Variations of this method will suggest themselves and circumstances may render their adoption convenient. The compass courses corresponding to the magnetic directions may be obtained from observations made with the auxiliary compass itself, or while making observations with another com- pass the headings by the auxiliary may be noted and a curve for the latter constructed, as explained in article 94, and the required headings thus deduced. (b) By the methods to be explained hereafter (Chap. XIV), ascertain in advance the true bearing of the sun at frequent intervals during the period which is to be devoted to the compensation of the compasses; apply to these the variation and obtain the magnetic bearings; record the times and bearings in a convenient tabular form; set the watch accurately for the local apparent time; then when it is required to steer any given magnetic course, set that point of the pelorus for the ship's head and set the sight vanes for the magnetic bearing of the sun corresponding to the time by watch. Maneuver the ship with the helm until the sun comes on the sight vanes, when the azimuth of the ship's head will be that w'hich is required. The sight vanes must be altered at intervals to accord with the table of times and bearings. (c) Construct a table showing times and corresponding magnetic bearings of the sun, and also set the watch, as explained for the previous method. Then place the sight vanes of the azimuth circle of the compass at the proper angular distance to the right or left of the required azimuth of the ship's head; leave them so set and maneuver the ship with the helm until the image of the sun comes on with the vanes. The course will then be the required one. As an example, suppose that the table shows that the magnetic azimuth of the sun at the time given by the watch is N. 87° E., and let it be required to head magnetic North; w^hen placed upon this heading, therefore, the sun must bear 87° to the right, or east, of the direction of the ship's head; when steady on any course, turn the sight vane to the required bearing relative to the keel. If on N. 11° W., for example, turn the circle to N. 76° E. ; leave the vane fi This is all that is required for the purposes of compensation, but if there is opportunity it is always well to make a complete swing and obtain a full table of deviations, which may give interesting information of the existing magnetic conditions. 40 THE COMPASS ERKOE. undisturbed and alter course until the sun comes on. The magnetic heading is then North, and adjust- ment may be made accordingly. (d) When ranges are available, they may be utilized for determining magnetic headings. 123. Summary of Ordinary Corrections. — To summarize, the following is the process of correct- ing a compass for a single latitude, where magnets at right angles are employed for compensating the semicircular deviation and where the disturbances due to unsymmetrical soft iron are small enough to be neglected: First. All correctors being clear of the compass, place the quadrantal correctors in the position which it is estimated that they will occupy when adjustment is complete. • The navigator's experience will serve in making the estimate, or if there seems no other means of arriving at the probable position they may be placed at the middle points of their supports. Second. Steady the ship on magnetic North, East, South, or West, and hold on that heading by such method as seems best. By means of permanent magnets alter the indications of the compass until the heading coincides with the magnetic course. If heading North, magnets must be entered N. ends to starboard to correct easterly deviation and to port to correct westerlj^, and the reverse if heading South. If heading East, enter N. ends forward for easterly and aft for westerly deviations, and the reverse if heading West. (Binnacles differ so widely in the methods of carrying magnets that details on this point are omitted. It may be said, however, that the magnetic intensity of the correctors may be varied by altering either their number or their distance from the compass; generally speaking, several magnets at a distance are to be preferred to a small number close to the compass. ) Third. Steady the ship on an adjacent magnetic cardinal point and correct the compass heading by permanent magnets to accord therewith in the same manner as described for the first heading. Fourth. Steady the ship on an intercardinal point (magnetic) and move the quadrantal correctors away from or toward the compass, keeping them at equal distances therefrom, until the compass and magnetic headings coincide. 124. The compensation being complete, the navigator should proceed immediately to swing ship and make a table of the residual deviations. Though the remaining errors will be small, it is seldom that they will be reduced to zero, and it must never be assumed that the compass may be relied upon without taking the deviation into account. Observations on eight equidistant points will ordinarily suffice for this purpose. 125. To Correct Semicircular Deviation with a Single Magnet. — In certain binnacles provision is made for correcting the semicircular deviation by a single magnet (or series of magnets) in the star- board angle, the magnet tray having motion in azimuth as well as vertically. In this case the process of correcting semicircular deviation is somewhat different from that described for correction by rectangular magnets. Either of the two following methods may be employed: (o) By computation determine the starboard angle. An approximate method for doing this is given in article 103, and a more exact one may be found in works treating this subject mathematically. Head the ship on a cardinal point (magnetic); enter the magnets in the tray and revolve it until their N. ends lie at an angular distance from ahead (measured to the right) equal to the starboard angle; raise or lower the tray until the deviation disappears. (6) Head the ship on a cardinal point (magnetic), enter the magnets, and turn the tray to an east- and-west position, the N. ends in such direction as will tend to reduce the deviation; raise or lower the tray until the deviation disappears. Alter course 90° and head on an adjacent magnetic cardinal point; observe the amount of deviation that the compass shows; correct half of this by altering the starboard angle and the other half by raising or lowering the tray. Return to first course, note deviation, and correct one-half in each way, as before. Continue the operation, making a series of trials until the deviations disappear on both headings, when the compensation will be correct. This operation may be considerably hastened by finding the first position of the magnets from a rough calculation of the starboard angle (art. 103). 126. Correcting the Heeling Error. — The heeling error may be corrected by a method involving computation, together with certain observations on shore. A more practical method, however, is usually followed, though its results may be less precise. The heeling corrector is placed in its vertical tube, N. end uppermost in north latitudes, as this is almost invariably the required direction; the ship being on a course near North or South and rolling, observe the vibrations of the card, which, if the error is material, will be in excess of those due to the ship's real motion in azimuth; slowly raise or lower the corrector until the abnormal vibrations disappear, when the correction will be made for that latitude; but it must be readjusted upon any considerable change of geographical position. In making this observation care must be taken to distinguish the vessel's "yawing" in a seaw^ay, from the apparent motion due to heeling error; for this reason it may be well to have an assistant to watch the ship's head and keep the adjuster informed of the real change in azimuth, by which means the latter may better judge the effect of the heeling error. In the case of a sailing vessel, or one which for any reason maintains a nearly steady heel for a continuous period, the amount of the heeling error may be exactly ascertained by observing the azi- muth of the sun, and corrected with greater accuracy than is possible with a vessel which is constantly rolling. 127. Flinders Bar. — The simplest method that presents itself for the placing of the Flinders bar is one which is available only for a vessel crossing the magnetic equator. Magnetic charts of the world show the geographical positions at which the dip becomes zero — that is, where a freely suspended needle is exactly horizontal and where there exists no vertical component of the earth's total magnetic force. In such localities it is evident that the factor of the semicircular deviation due to vertical induc- tion disappears and that the whole of the existing semicircular deviation arises from subpermanent magnetism. If, then, when on the magnetic equator the compass be carefully compensated, the effect of the subpermanent magnetism will be exactly opposed by that of the semicircular correcting magnets. Later, as the ship departs from the magnetic equator, the semicircular deviation will gradually acquire a material value, which will be known to be due entirely to vertical induction, and if the Flinders bar be so placed as to correct it, the compensation of the compass will be general for all latitudes. THE COMPASS ERROR. 41 In following this method it may usually be assumed that the soft iron of the vessel is symmetrical with respect to the fore-and-aft line and that the Flinders bar may be placed directly forward of the compass or directly abaft it, disregarding the effect of components to starboard or port. It is tiierefore merely necessary to observe whether a vertical soft iron rod Tuust be placed forward or abaft the compass to reduce the deviation, and, having ascertained this fact, to find by experiment the exact distance at which it completely corrects the deviation. The Flinders bar frequently consists of a bundle of soft iron rods contained in a case, which is secured in a vertical position near the compass, its upper end level with the plane of the needles; in this method, the distance remaining fixed, the intensity of the force that it exerts is varied by increasing or decreasing the number of rods; this arrangement is more convenient and satisfactory than the employment of a single rod at a variable distance. 12§. When it is not possible to correct the compass at the magnetic equator there is no ready practical method by which the Flinders bar may be placed; the operation will then depend entirely upon computation, and as a mathematical analysis of deviations is beyond the scope laid out for this work the details of ])rocedure will not be gone into; the general principles involved are indicated, and students seeking more must consult the various works that treat the subject fully. It has been explained that each coefficient of semicircular deviation (B and C) is made up of a sub- permanent factor varying as jr and of a vertical induction factor varying as tan 6. If we indicate by the subscripts ^ and ,., respectively, the parts due tp each force, we may write the equations of the coefficients: B=B, X y + B,. X tan 6; and C = C,Xg+C, XtanG. Now if we distinguish by the subscripts i and 2 the values in the first and in the second position of observation, respectively, of those quantities that vary with the magnetic latitude, we have: Bi = B, Xg--fB,.Xtanei, Bj = B, X if + Bv X tan 6.^; and Ci = C,x4-+CvXtanei, C2 = C, Xfr + Cv X tan 02. The values of the coefficients in both latitudes are found from the observations made for deviations; the values of the horizontal force and of the dip at each place are known from magnetic charts; hence we may solve the first pair of equations for B^ and B,., and the second pair for C, and C,.; and having found the values of these various coefficients, we may correct the effects of B^ and C^ by permanent mag- nets in the usual way and correct the remainder — that due to B^ and C^. — by the Flinders bar. Strictly, the Flinders bar should be so placed that its repelling pole is at an angular distance from ahead equal to the "starboard angle" of the attracting pole of the vertical induced force, this angle depending upon the coefficients B^ and Cv; but since, as before stated, horizontal soft iron may usually be regarded as symmetrical, Cy is assumed as zero and the bar placed in the inidship line. 129. To Correct Adjustment on Change of Latitude. — The compensation of quadrantal devia- tion, once properly made, remains effective in all latitudes; but unless a Flinders bar is used a correction of the semicircular deviation made in one latitude will not remain accurate when the vessel has materially changed her position on the earth's surface. With this in mind the navigator must make frequent observations of the compass error during a passage and must expect that the table of residual deviations obtained in the magnetic latitude of compensation will undergo considerable change as that latitude is departed from. The new deviations may become so large that it will be found convenient to readjust the semicircular correcting magnets. This process is very simple. When correctors at right angles are used, provide for steadying the ship, by an auxiliary compass or by the pelorus, upon two adjacent magnetic cardinal points (art. 122). Put the ship on heading North or South (magnetic), and raise or lower the athwartship magnets or alter their number until the deviation disappears; then steady on East or West (magnetic) and similarly adjust the fore-and-aft magnets. Swing ship for a new table of residual deviations. ' When correctors in the starboard angle are used, arrange as before for heading on two adjacent cardinal magnetic courses. Steady on one of these, observe amount of compass error, correct half by changing the starboard angle and half by raising or lowering magnets; steady on the adjacent cardinal point and repeat 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 sen?e given the word by modern and popular usage, is the art of conducting a vessel in channels and harbors and along coasts, where landmarks and aids to navigation are available for fixing the position, and where the depth of water and dangers to navigation are such as to require a constant watch to be kept upon the vessel's course and frequent changes to be made therein. 131. Requisites. — As requisites to successful piloting, the navigator should be provided with the best available chart of the locality to be traversed, together with the sailing directions and descrip- tions of aids to navigation; and all of these should be corrected for the latest information, published in notices to mariners or otherwise, that bear upon the locality. The ves.sel should be equipped with the usual instruments employed in navigation. The deep-sea pounding-machine, if provided, should be ready for use when there is a chance that it may be needed. The lead lines should be correctly marked, and 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 ]5arallel 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 w^hich it leads to be assured that it clears all dangers. 133. Methods of Fixing Position. — A navigator in sight of objects whose positions are shown upon the chart may locate his vessel by either of the following methods: {a) cross bearings of two known objects; {h) the bearing and distance of a known ol^ject; (r) the bearing of a known object and the angle between two known objects; { Draw a circle with that object as a center and of such radius that no neighboring dangers lie beyond its circumference; note, from Table 33, the vertical angle which is subtended by the known height at the distance chosen as a radius, and, by frequent observations in passing, make .^ure 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. Consideration^ 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 5LA, clear of the danger at all points, and note its direction by the compass rose; then let frequent bearings be taken as the ship proceeds, and so long as the bearings, YA, ZA, are to the right of XA he may be assured that he is on the left or safe side of the line. If, as in the case given, there is but one object in sight and that nearly ahead, it would be very difficult to get an exact position, but this method would always show whether or not the ship was on a good course, and would, in consequence, be of the greatest value. And even if there were other objects visible by which to get an accurate fix it would be a more simple matter to note, by an occasional glance over the sight-vane of the pelorus or compass, that the ship was making good a safe course than to be put to the 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. Soundings. — 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 ship moving with speed through the water, or the tide may cause a discrepancy, or the chart itself may lack perfection; but the soundings should agree in a general way, and a marked departure from the characteristic bottom shown on the chart should lead the navigator to verify his position and proceed with caution; especially is this true if the water is more shoal than expected. 160. But if the soundings in shallow water when landmarks are in sight serve merely as an auxiliary guide, those taken (usually with the patent sounding machine or deep-sea lead) when there exist no other means of locating the position, fulfill a much more important purpose. In thick weather, when approaching or running close to the land, and at all times when the vessel is in less than 100 fathoms of water and her position is in doubt, soundings should be taken continuously and at regular intervals, and, with the character of the bottom, systematically recorded. By laying the soundings on tracing paper, along a line which represents the track of the ship according to the scale of the chart, and then moving the paper over the chart, keeping the various courses parallel to the corresponding directions on the chart, until the observed soundings agree with those laid down, the ship's position will in general be quite well 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 moi'e than thaf the time has come when he must anchor or lie off till conditions are more favorable. 161. Lights. — Before coming within range of a light the navigator should acquaint himself with its characteristics, so tha,t 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 immediately 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 must be taken to avoid being deceived on first sighting a light, as there are various errors into which the inexperienced may fall. The glare of a powerful light is often seen beyond the distance of visibility of its direct rays by the reflection downward from particles of mist in the air; the same mist may also cause a white light to have a distinctly reddish tinge, or it may obscure a light except within short distances. When a light is picked up at the extreme limit at which the height of the observer will permit, a fixed light may appear flashing, as it is seen when the ship is on the crest of a wave, and lost when in the 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 must not be positively assumed, on sighting a light, even in perfectly clear weather, that a vessel's distance is equal to the range of visibility; it may be either greater or less, as the path of a ray of light near the horizon receives extraordinary deflection under certain circumstances; the conditions governing this deflection are discussed in article 301, Chapter X. 162. Buoys. — While buoys are valuable aids, the mariner should always employ a certain amount of caution in being guided by them. In the nature of things it is never possible to be certain of finding buoys in correct position, or, indeed, of finding them at all. Heavy seas, strong currents, ice, or collisions with passing vessels may drag them from their places or cause them to disappear entirely, and they are especially uncertain in unfrequented waters, or those of nations that do not keep a good lookout upon their aids to navigation. When, therefore, a buoy marks a place where a ship must be navigated with caution, it is well to have a danger angle or bearing as an additional 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 })uoys to be left on the starboard hand of a vessel going out of a harbor or fairway, and red buoys (the color of the port side light) on the port hand. In these various systems the color and character of the buoy are such as to denote the special purpose for which it is employed. 163. Fogs and Fog Signals. — As with lights, the navigator should, in a fog, acquaint himself with the characteristics of the various sound signals which he is likely to pick up, and when one is heard, its periods should be timed and compared with those given in the light lists to insure its proper identity. Experiment has demonstrated that sound is conveyed through the atmosphere in a very uncertain way; that its intensity is not always increased as its origin is approached, and that areas within its range at one time will seem silent at another. Add to these facts the possibility that, for some cause, the signal may not be working as it should be, and we have reason for observing the rule to proceed with the utmost caution when running near the land in a fog. The best guide is the lead, and that should be kept going constantly. The method of plotting soundings described in article 160 will give the most reliable position that is obtainable. Moreover, the lead will warn the navigator of the approach to shallow water, when, if his position is at all in doubt, it is wisest to anchor before it becomes too late. When running slowly in a fog (which caution, as well as the law, requires that one should do) it must be borne in mind that the relative effect of current is increased; for instance, the angle of deflec- tion from the course caused by a cross-set is greater at low than at high speed. It is worth remembering that when in the vicinity of a bold blu^ shore vessels are sometimes warned of a too close approach by having their own fog signals echoed back from the cliffs; indeed, from a knowledge of the velocity of sound (art. 314, Chap. XI) it is possible to gain some rough idea of the distance in such a case. 164. Tides and Currents. « — The information relating to the tides given on the chart and in other publications should be studied, as it is of importance for the navigator to know not only the height of the tide above the plane of reference of the chart, but also the direction and force of the tidal current. The plane of reference adopted for soundings varies with different charts; on a large number it is that of mean low water, and as no plane of reference above that of mean low water is ever employed, the navigator may with safety refer his soundings to that level when in doubt. When traversing waters in which the depth exceeds the vessel's draft by but a small margin, account must be taken of the fact that strong winds or a high barometer may cause the water to fall below even a very low plane of reference. On coasts where there is much diurnal inequality in the tides, the amount of rise and fall can not be depended upon, and additional caution is necessary. A careful distinction should be made between the vertical nse and jail of the tide, which is marked at the transition periods by a stationary height, or stand, and the tidal current, which is the horizontal transfer of water as a result of the difference of level, producing the flood and ebb, and the intermediate condition, or slack. It seldom occurs that the turn of the tidal stream is exactly coincident with the high and low water, and in some channels the current may outlast the vertical movement which pro- duces it by as much as three hours, the effect being that when the water is at a stand the tidal stream is at its maximum, and when the current is slack the rise or fall is going on with its greatest rapidity. Care must be taken to avoid confounding the two. Usually, more complete data is furnished in charts and tide tables regarding the rise and fall, and it frequently occurs that the information regarding the tidal current is comparatively meager; the mariner must therefore take every means to ascertain for himself the direction and force of the tidal and other currents, either from the set shown between suc- cessive well-located positions of the ship, or by noting the ripple of the water around buoys, islets, or shoals, the direction in which vessels at anchor are riding, and the various other visible effects of the current. Current arrows on the chart must not be regarded as indicating absolutely the conditions that are to be encountered. They represent the mean of the direction and force observed, but the observations upon which they are based may not be complete, or there may be reasons that bring about a departure from the normal state. Generally speaking, the rise and fall and strength of current are at their minimum along straight stretches of coast upon the open ocean, while bays, bights, inlets, and large rivers operate to augment the tidal effects, and it is in the vicinity of these that one finds the highest tides and stronge.st currents. The navigator need therefore not be surprised, in cruising along a coast, to notice that his vessel is set more strongly toward or from the shore in passing an indentation, and that the evidences of tide will appear more marked as he nears its mouth. 165. Charts. ^ — The chart should be carefully studied, and among other things all of its notes should be read, as valuable information may be given in the margin which it is not practicable to place upon the chart abreast the locality affected. The mariner will do well to consider the source of his chart and the authority upon which it is based. He will naturally feel the greatest confidence in a chart issued by the Govenmient of one of the more important maritime nations which maintains a well-equipped office for the especial purpose of acquiring and treating hydrographic information. He should note the character of the survey from which the chart has been constructed; and, finally, he should be especially careful that the chart is of recent issue or bears correction of a recent date — facts that should always be clearly shown upon its face. It is well to proceed with caution when the chart of the locality is based upon an old survey, or one whose source does not carry with it the presumption of accuracy. Even if the original survey was a good one, a sandy bottom, in a region where the currents are strong or the seas heavy, is liable to undergo in time marked changes; and where the depth is affected by the deposit or removal of silt, as in the vicinity of the estuaries of large river systems, the behavior is sometimes most capricious. Large blank spaces on the chart, where no soundings are shown, may be taken as an indication that no sound- aSee also Chapter XX. 6See aLso article 36 and following articles, Chapter II. PILOTING. 49 ings were made, and are to be regarded with suspicion, espeeiallj' if the region abounds in reefs or pin- nacle rocks, in which case only the the closest sort of a survey can l)e considered as revealing all the dangers. All of these facts must be duly weighed. When navigating by landmarks the chart of the locality which is on the largest scale should be used. The hydrography and topography in such charts appear in greater detail, and — a most important consideration — bearings and angles may be plotted with increased accuracy. 166. Records. — It will be found a profitable practice to pay careful attention to the recording of the various m.atter relating to the piloting of the ship. A notebook should be kept at hand on deck or on the bridge, in which are to be entered all bearings or angles taken to fix the position, all changes of course, important soundings, and any other facts bearing upon the navigation. (This book should be different from the one in which astronomical sights and offshore navigation are worked. ) The entries, though in memorandum forin, should be complete; it should be clear whether bearings and cour-ses are true, magnetic, or by compass; and it is especially important that the time and patent log reading should be given for each item recorded. The value of this book will make itself apparent in various directions; it will afford accurate data for the writing of the ship's log; it will furnish interesting information for the next run over the same ground; it will provide a means by which, if the ship be shut in by fog, rain, or darkness, or if there be diflftculty in recognizing landmarks ahead, the last accurate fix can be plotted and brought forward; and, finally, if there should be a mishap, the notebook would furnish evidence as to where the trouble has been. The chart on which the work is done should also be made an intelligible record, and to this end the pencil marks and lines should not be needlessly numerous, heavy, or long. In plotting bearings, draw lines only long enough to cover the probable position. Mark intersections or positions by drawing a small circle around them, and writing neatly abreast them the time and patent log reading. Indicate the courses and danger bearings by full lines and mark them appropriately, preferably giving both magnetic (or true) and compass directions. A great number of lines extending in every direction may lead to confusion; however remote the chance may seem, the responsibilities of piloting are too serious to run even a small risk. Finally, on anchoring, record and plot the position by bearings or angles taken after coming to; observe that the berth is a safe one, or, if in doubt, send a boat to sound in the vicinity of the ship to make sure. 6583—06 1 50 THT^: SAILINGS. CHAPTER V. THE SAILINGS. lev. In considering a ship's position at sea with reference to any other place, either one that has been left or one toward which the vessel is bound, five terms are involved — the Course, the Distance, the Difference of Latitude, the Difference of Longitude, and the Departure. (^ The solutions of the various problems that arise from the mutual relation of these quantities are called Sailings. 16§. Kinds of Sailings — When the only quantities involved are the course, distance, difference of latitude, and departure, the process is denominated Plane Sailing. In this method the earth is regarded as a plane, and the operation proceeds as if the vessel sailed always on a perfectly level sur- face. When two or more courses are thus considered, they are combined by the method of Traverse Sailing. _ It is evident that the number of miles of latitude and departure canthus be readily deduced; but, while one mile always equals one minute in difference of latitude, one mile of departure corre- sponds to a difference of longitude that will vary with the latitude in which the vessel is sailing. Plane sailing, therefore, furnishes no solution where difference of longitude is considered, and for such solu- tion resort must be had to one of several methods, which, by reason of their taking account of the spherical figure of the earth, are called Spherical Sailings. When a vessel sails on an east or west course along a parallel of latitude, the method of converting departure into difference of longitude is called Parallel Sailing. When the course is not east or west, and thus carries the vessel through various latitudes, the conversion may be made either by Middle Latitude Sailing, in which it is assumed that the whole run has been made in the mean latitude, or by Mercator Sailing, in which the principle involved in the construction of the Mercator chart (art. 38, Chap. II) is utilized. Great Circle Sailing deals with the courses and distances between any two points when the track followed is a great circle of the terrestial sphere. A modification of this method which is adopted under certain circumstances is called Composite Sailing. PLANE SAILING. 169. In Plane Sailing, the curvature of the earth being neglected, the relation between the elements X' of the rhumb track joining any two points may be considered from the plane right triangle formed by the meridian of the place left, the parallel of the place arrived at, and the rhumb line. In figure 23, T is the point of departure; T', the point of destination; Tn, the meridian of departure; T^?), the parallel of destination; and TT^, the rhumb line between the points. Let C repre- sent the course, T^Tn; Dist., the distance, TT^; DL, the difference of latitude, Tn; and Dep., the departure, T^n. Then from the triangle TT^n, we have the following: sinC=^; Dist. Fig. 23. cos C := tan C DL Dist. From these equations are derived the following formulae for working the various problems that may arise in Plane Sailing: Given. Course and distance . Difference of latitude and departure. Course and difference of latitude. Required. (Difference of latitude . \Departure {Course .. Distance. {Distance. . Departure Formulae. D L =Dist. cos C. Log D L =log Dist. + log cos C. Dep. = Dist. sin C. Log Dep. =log Dist. -|- log sin C. Log tan C= log Dep.— log D L. Log Dist. = log Dep.— log sin C. Log Dist. =log D L —log cos C. Log Dep. =log D L+log tan C. Dist. -= Dep. DL cos C D L tan C. "For the definition of thiese terms, see article 6, Chapter I. THE SAILINGS. 51 Given. Required. Course and departure. j I Distance ilDifference of latitude Distance and difference ijt^oiirse . .. of latitude. i| Departure Distance and departure.. I Course Difference of latitude. Formulae. Dist. Dep. D L = CosC= sin C Dep. tan C DL Dist." Log Dist. = log Dep. —log sin C. Log D L = log Dep.— log tan C. Log cos C=log D L —log Dist. Dep. = Dist. sin C. LogDep. = log Dist. -flog sin C. Sin C=^^ Dist Log sin C= log Dep. — log Dist. D L =::Dist. cos C. Log D L :=log Dist. +log cos C. 1 yo. The solution of the plane right triangle may be accomplished either by Plane Trigonometry, by Traverse Tables, or by -construction. If the former method is adopted, the logarithms of numbers may be found in Table 42, and of the functions of angles in Table 44. A more expeditious method is avail- able, however, in tlie Traverse Tables, which give by inspection the various solutions. Table 1 contains values of the various parts for each unit of Dist. from 1 to 300, and for each quarter-point (2° 49''), of C; Table 2 contains values for each unit of Dist. from 1 to 600, and for each degree of C. The method of solving by construction consists in laying down the various given terms by scale upon a chart or plain paper, and measuring thereon the terms required. 171. Of the various problems that may arise, the first two given in the foregoing table are of much the most frequent occurrence. In the first, the given quantities are course and distance, and those to be found are difference of latitude and departure; this is the case where a navigator, knowing the distance run on a given course, desires to ascertain the amount made good to north or south and to east or west. In the second case the conditions are reversed; this arises where the course and distance between two points are to be obtained from their known difference of latitude and departure. Example: A ship sails SW. by W., 244 miles. Required the difference of latitude and the departure made good. By Computation. By Inspection. Dist. C DL Dist. C Dep. 244 56° 15' 135.6 244 56° 15' 202.9 log 2.38739 log cos 9.74474 2.13213 log _^__ log 2.38739 log sin 9.91985 In Table 1, find the course SW. by W. (5 points); it occurs at the bottom of the page, therefore take the names of the columns from the bottom as well; opposite 244 in the Dist. column will be seen Lat. 135.6 and Dep. 202.9. og 2.30724 Example: A ship sails N. 5° E., 188 miles. By Computation. Required the difference of latitude and the departure. Br/ Inspection. Dist. C DL Dist. C Dep. 188 5° 187.3 188 5° 16.4 log 2.27416 log cos 9.99834 log 2.27250 In Table 2, find the course 5°; it occurs at the top of the page, therefore take the names of the columns from the top; opposite 188 in the Dist. column will be seen Lat. 187.3 and Dep. 16.4. log 2.27416 log sin 8.94030 1.21446 Example: A vessel is bound to a port which is 136 miles to the north and 203 miles to the west of her position. Required the course and distance. By Computation. By Inspection. Dep. 203 log 2.30750 Enter Table 1 and turn the pages until a course DL 136 log 2.13.354 is found whereon the numbers 136 and 203 are found abreast each other in the columns marked respectively J^at. and Dep. This occurs most nearly at the course for 5 points, the angle being taken Dep. 203 log 2.30750 from the bottom, because the appropriate names C 56° 11' log sin 9.91951 of the columns are found there. The course is therefore NW. by W. Interpolating for interme- Dist. 244.3 log 2.38799 diate values, the corresponding number in the Dist. column is about 244.3. C (N.) 56° 11' (VV.) log tan 0.17396 52 THE SAILINGS. Example: As the result of a day's run a vessel changes latitude 244 miles to the south and makes a departure of 171 miles to the east. What is the course and distance made good? Bij Inspection. Enter Table 2 and the nearest agreement will be found on course (S.) 35° (E. ), the appropriate names being found at the top of the page. The nearest corresponding Dist. is 298 miles. By Computai ion. Dep. 171 DL 244 log 2.23300 log 2.38739 C (S.) 35°02' (E.) log tan 9.84561 Dep. 171 C 35° 02' log 2.23300 log sin 9.75895 Dist. 297.9 log 2.47405 TRAVERSE SAILING. 172. A Traverse is an irregular track made by a ship in sailing on several different courses, and the method of Traverse Sailing consists in hnding the difference of latitude and departure corresponding to several courses and distances and reducing all to a single equivalent course and distance. This is done by determining the distance to north or south and to east or west made good on each course, taking the algebraic sum of these various differences of latitude and departure and finding the course and distance corresponding thereto. The work can be most expeditiously performed by adopting a tabular form for the computation and using the traverse tables. Example: A ship sails SSE., 15 miles; SE., 34 mibs; W. by S., 16 miles; WNW., 39 miles; S. by E., 40 miles. Required the course and distance made good. Courses. Dist. N. s. E. w. SSE. SE. W. by S. WNW. S. by E. S. by W. 15 34 16 39 40 14.9 13.9 24.0 3.1 39.2 5.7 24.0 7.8 15.7 36.0 66.8 14.9 80.2 14.9 37.5 51.7 37.5 65.3 14.2, The result of the various courses is, therefore, to carry the vessel S. by W., 66.8 miles from her original position. PARAIiLEL SAILING. ITS. 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 Tand 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 -^I)roportional to the radii of the circles, we have: TT' MM' OT. CM' From the triangle COT, r = R cos L; hence Yr~- = — = — ; or, DLo = Dep. sec. L; or, Dep. = DLo cos L. DlliO R 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, tlie computation can be made by logarithms; but the traverse tables maj' more conveniently be employed. Remembering that those tables are based upon the formulae, DL=Dist. cos C, and Dist.=DL sec C, we may substitute for the column marked Lat. the departure, for that marked Dist. the difference of longitude, and for the courses at top and bottom of the page the latitude. The tables then become available for making the required conversions. Example: A ship in the latitude of 49° 30' sails directly east until making good a difference of longitude of 3° 30'. Required the departure. By Inspection. Enter Table 2 with the latitude as C and the difference of longitude as Dist. As the table is calculated only to single degrees, we must find the numbers in the pages of 49° and 50° and take the mean. Corresponding to Dist. 210 in the former is Lat. 137.8, and in the latter Lat. 135.0. The mean, which is the required departure, is 136.4. L DLo By Computation. 49° 30' log cos 9.81254 210' log 2.32222 Dep. 136.4 log 2.13476 Example: A ship in the latitude of 38° sails due west a distance of 215.5 miles, difference of longitude. Required the By Computation. By Inspection. L Dep. DLo I 38° 215.5 273' °33' log sec log log 0.10347 2.33345 2.43692 Entering Table 2 with the latitude, 38°, as a coiirse, corresponding with the number 215.5 in column of Lat., is 273.5 in the column of Dist. This is therefore the required difference of longitude, being equal to 4° 33'. 5. MIDDLE LATITUDE SAILING. 175. When a ship follows a course obliquely across the meridian the latitude is constantly changing, and the method of converting departure and difference of longitude by Parallel Sailing, just described, ceases to be applicable. In figure 25, T is the point of departure; T', the point of destination; P, the earth's pole; TT', the rhumb track; n^TT', the course; Tn, rijT', the respective parallels of latitude; and MM', the equator. The difference of longitude between T and T' is MPM', which may be measured by the arc of the equator, MM', intercepted between their meridians. This corresponds to a departure Tn in the latitude of T, and to the smaller departure T'«i 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 nmst have some intermediate value between these extremes. Dividing the total difference of longitude into a number of equal parts MP/nj, jHiPm^, 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 lOther. These will be d-i r-^ in the latitude T, d^ r<^ in the latitude r■^, etc. Hence we have: MM'=cZi 1\ sec MT + dj ^2» sec ni^ rj + dg r^, sec m,^ r^, + etc. Now, if LL' be a parallel of latitude lying midway between Tn and T'nj, 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 may be 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 method of conversion based upon this assumption is denominated Middle Latitude Sailing, and by reason of its convenience and simplicity is usually employed for short distances, such as those covered by a vessel in a day's run. 176. In Middle Latitude 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 may be remarked that the Middle Latitude should not be used when the latitudes are of opposite name; if of different names and the distance is small, the departure may be assumed equal to the difference of longitude, since the meridians are sensibly parallel near the equator; but if the distance is great the two portions of the track on opposites of the equator must be treated separately. \ 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. Fig. 25. Latitude left, DL, 42° 30'.0 N. 4 09 .4 S. Latitude left, 42° 30' N. Latitude arrived at, 38 21 N. Latitude arrived at, 38 20 .6 N. 2)80 51 Mid. latitude, 40 25 N. 54 THE SAILINGS. Enter Table 2 with the middle latitude, 40°, as a course; the difference of longitude (Dist. ) cor- responding to the departure (Lat. ) 166.7 is 217.6; entering with 41°, it is 220.9; the mean is 219.2 (3° 39''.2). Longitude left, 58° 51^0 W. DLo, 3 39 .2 E. Longitude arrived at, 55 11 .8 W. Example: A ship in Lat. 39° 42^ S., Long. 3° 31^ E., sails S. 42° W., 236 miles. Required the lati- tude and longitude arrived at. From Table 2: Course, S. 42° W., Dist., 236 miles; we find Lat., 175.4 H. (2° 55^4), Dep., 157.9 W. Latitude left, 39° 42'.0 S. Latitude left, 39° 42^ S. DL, 2 55 .4 S. Latitude arrived at, 42 37 S. Latitude arrived at, 42 37 .4 S. 2)82 19 Mid. latitude, 41 09 S. From Table 2: Mid. Lat. (course), 41°, Dep. (Lat.), 157.9; we find DLo (Dist.), 209.3 (3° 29^3), Longitude left, 3° 31^0 E. DLo, 3 29 .3 W. and arrives at Lat. 47° 18^ N., l^ong. 20= W. W. Longitude arrived at, 01 .7 Example: A vessel leaves Lat. 49° 57^ N., Long. 15° 16^ W. 10^ W. Required the course and distance made good. Latitude left, 49° 57^ N. Longitude left, 15<= Latitude arrived at, 47 18 N. Longitude arrived at, 20 fWW\^ ^. r"4^54^ t 159 4^- ^^' \ 294^ 2)97^5^ N. 48 38 N. (course), 49°, DLo (Dist.), 294; we find Dep. (Lat.), 192.9. Dep. 192.9 W., we find course S. 51° W., Dist., 251 miles. DL, w. Mid. latitude, From Table 2: Mid. Lat. i From Table 2: DL 159 S. 178. The assumption upon which Middle Latitude sailing is based — that the conversion may be made as if the whole distance were sailed upon a parallel midway between the latitudes of departure and destination — while sufficiently accurate for moderate distances, may be materially in error where the distances are large. In such case, either the method of Mercator 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: T I cos Lc=— , TO where Lc represents the latitude of conversion, and I and m are respectively the differences of latitude and of meridional parts (art. 39, Chap. II) between the latitudes of departure and destination. « Mid. Lat. Difference of latitude. Mid. Lat. 1° a° 3° 4° 6° 6° 7° 8° 9° 10° 12° 14° 16° 18° 20° o 15 18 21 -86 -67 -54 / / -85 -84 -67 -66 -54 -53 / -83 -65 -52 f -81 -63 -51 -41 -28 -19 / -79 -61 -49 / -76 -59 -47 / -73 -56 -44 / -69 -53 -42 / -65 -50 -39 / -56 -43 -32 / -46 -34 -24 -34 -23 -15 / -21 -12 - 5 / - 6 1 7 . 15 18 21 24 30 35 -44 -31 -23 —44 -30 -22 -44 -29 -21 -42 -29 -21 -40 -26 -18 -38 -24 -17 -36 -23 -15 -33 -20 -12 -31 -18 -10 -24 -12 - 5 -17 - 6 2 - 8 1 10 1 11 18 12 21 28 24 30 35 40 45 50 -17 -12 - 8 -16 —11 - 8 -15 -11 - 7 -14 -10 - 6 - 3 - 1 - 1 -13 - 8 - 5 - 2 1 -12 - 7 - 3 -10 - 5 - 1 - 8 - 3 1 - 6 - 1 3 — 4 1 6 2 7 12 8 14 20 16 22 28 25 31 38 34 41 49 40 45 50 55 58 60 62 64 66 68 70 72 -5—5 -4-3 - 3 - 3 - 4 - 3 - 2 2 3 2 4 5 5 7 8 7 10 11 10 13 14 17 18 20 17 20 22 25 29 32 35 39 43 46 51 55 58 64 69 55 58 60 - 3 - 2 -2-1 - 2 - 1 - 1 1 2 2j 4 3 5 4 6 7 8 9 9 11 12 13 14 16 25 27 30 35 38 42 46 50 55 60 65 71 75 81 89 62 64 66 68 70 72 - 1 — 1 1 1 2 2 3 4 5 5 6 7 8 10 10 12 13 14 16 18 18 20 23 22 25 28 33 37 41 46 51 57 61 67 76 78 87 97 98 109 123 a The statement often made, that the latitude of conversion is always greater than the middle latitude, is not correct when the compression of the earth is taken into account, as an inspection of the table will show; that statement is based upon an assumption that the earth is a perfect sphere, and it was upon that assumption that a table which appeared in early editions of this work was computed. The value of the compression adopted for this table is 293.465' THE SAILINGS. 55 Example: A vessel sails from Lat. 10° 13^ S. to Lat. 20° 2V 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°, Correction, —65'. Mid. latitude, ' 15 17 S. Correction, — 1 05 Lc, 14 12 S. Lc 14° 12' log sec .01348 Dep. 432 log 2.63548 DLo 445'. 6 log 2.64896 • MERCATOR SAILING. 179. Mercator Sailing is the method by which values of the various elements are determined from considering them in the relation in which they are plotted upon a chart constucted according to the Mercator projection. 180. Upon the Mercator chart (art. 38, Chap. II), the meridians being parallel, the arc of a par- allel of latitude is shown as equal to the corresponding arc of the equator; the length of every such arc is, therefore, expanded; and, in order that the rhumb line may appear as a straight line, the merid- ians are also expanded by such amount as is neces.sary 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 Mercator chart may be constructed and all problems of Mercator Sailing may be solved. In the triangle ABC (fig. 26), the angle ACB is the course, C; the side AC, the b distance, Dist.; the side BC, the difference of latitude, DL; and the side AB, the departure, Dep. Then corresponding to the difference of latitude BC in the lati- tude under consideration, if CE be laid off to represent the meridional difference of latitude, m, completing the right triangle CEF, EF will repre^^ent 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. 182. To solve the triangle CEF by the traverse tables it is only necessary to substitute merid- ional difference for Lat., and difference of longitude for Dep. Where long distances are involved, carrying the computation beyond the limits of the traverse table, as frequently occurs in this method, either of two means may be adopted : the problems may be worked by the trigonometrical formulae, using logarithms, or the given quantities involved may all be reduced by a common divisor until they fall within the traverse table, and the results, when obtained, correspondingly increased. The former method is generally preferable, especially when the distances are quite large and accurate results are sought. The formulae for the various conversions are as follows: tan C= DLo DLo=m tan C; m=DLo cot C. Example: A ship in Lat. 42° 3( ' N., Lon-. 58° 51' W., sails SE. by S., 300 miles, latitude and longitude arrived at. From Table 1: Course, SE. by S., Dist., 300; we find Lat. 249.4 S. (4° 09/4). Latitude left, 42° 30'.0 N. Merid. parts, +2806.4 DL, 4 09 .4 S. Required the Latitude arrived at, 38 20 .6 N. Merid. parts, -2480.4 By Computation. DLo 326.0 33° 45' f 217'.8 13° 37'.8 log 2.51322 log tan 9.82489 log 2.33811 TO, 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 -^ (Dep.), 108.9; hence DLo=217'.8 or 3° 37'.8. Longitude left, DLo, 58' 3 51'.0 W. 37 .8 E. Longitude arrived at, 55 13 .2 W. 56 THE SAILINGS. Example: A ship in Lat. 4° 3?^ S., Long. 21° 05^ W., sails N. 14° W., 450 miles. Kequired the latitude and longitude arrived at. From Table 2: Course, (N.) 14° (W.), Dist., 450; we find Lat. 436.6 N. (7° 16^6). Latitude left, 4° 37^0 S. DL, 7 16 .6 N. Merid. parts, +275.4 Latitude arrived at, 2 39 .6 X. Merid. parts, +159.0 m, 434.4 tation. By Inspection. m 434.4 log 2.63789 From Table 2: Course, 14°, m (Lat.), 434.4, we find C . 14° log tan 9.39677 DLo (Dep.) 108^3 W., or 1° 48^3. T^T / 108^3 log 2.03466 DLo |io48/.3 . Longitude left, 21° 05^0 W. DLo, 1 48 .3 W. Longitude arrived at, 22 53 .3 W. Example: Required the course and distance by rhumb line from a point in Lat. 42° 03^ N., Long. 70° 04^ W., to another in Lat. 36° 59^ N., Long. 25° 10^ W. Lat. departure, 42° 03^ N. Merid. pts., +2770.1 Long, departiire, 70° 04^ W. Lat. destination, 36 59 N. Merid. pts., —2377.3 Long, destination, 25 10 W. DL { ^"got^js. m, 392.8 DLo {^^2694^}^ DLo 2694 log 3.43040 rn 392.8 log 2.59417 C (S.) 81° 42^ (E.) log tan .83623 log sec .84056 DL 304^ log 2.48287 Dist. 2106 log 3.32343 The course is therefore S. 81° 42^ E., and the distance is 2,106 miles. Since the figures involved are so large, it is best to employ only the method by computation. The formula by which the Dist. is obtained comes from Plane Sailing. GREAT CIRCLE SAILING. 1§3. The shortest distance 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 Great C'-rcle Sailing. 1§4. 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 su(;h a case a certain parallel should be fixed upon as a limit of latitude, and a route laid down such that a great circle is followed as far as the limiting parallel, then the parallel itself, and finally another great circle to the port of destination. Such a modification of the great circle method is called Composite Sailing. I §5. The rhumb line (art. 6, 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 points, intelligent navigators of the present day use the latter wherever practicable. On the Mercator chart, however, the arc of a great circle joining two points (unless both are on the equator or both on the same meridian) will not be projected as a straight line, but as a curve which seems to be longer than the thumb line; hence the shortest route appears as a circuitous one, and this is doubtless the reason that a wider use of the great circle has not been made. It should be clearly understood that it is the rhumb line which is in fact the indirect route, and that in following the great circle the vessel is always heading for her port, exactly as if it were in sight, while on the course which is shown as a straight line on the Mercator chart the vessel never heads for her port until at the very end of the voyage. 1§6. The method of great circle sailing is of especial value to steamers, as such vessels need not, in the choice of a route, have regard for the winds to the same extent as must a sailing vessel ; but even in navigating vessels under sail a knowledge of the great circle course may prove of great value. For example, suppose a ship to be bound from Sydney to V^alparaiso; 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 SAILIT^GS. 57 jtreat circle is followed throughout, though this would lead to a latitude of 61° S.). With the wind at E. ^ S. the ship would lie nearer to the Mercator course on tlie starboard tack, assuming that she sailed within six points of the wind; but if she took that tack she would be increasing her distance from th-^ port of destination by 4^ miles in every 10 that she sailed; while on the port tack, heading one point farther from the rhumb, the gain toward the port would be 9^ miles out of every 10. Any course between East and SSW. Avould 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. 187. As the great circle makes a different angle with each meridian that is crossed, it becomes necessary to make frequent changes of the ship's course; in practice, the course is a series of chords joining the various points on the track line. If, while endeavoring to follow a great circle, the ship is driven from it, as by unfavorable weather, it will not serve the purpose to return to the old track at convenience, but it is required that another great circle be laid down, joining the actual position in which the ship finds herself with the port of destination. 188. The methods of determining the great circle course may be divided generally into four classes; namely, by Great Circle Sailing Oiarts, by Computation, by the methods of the Time Azimuth, and by Graphic Approximations. 189. 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 gnomonic projection (art. 43, Chap. II), all great circles are represented as straight lines, and it is only necessary to join any two points by such a line to represent the great circle track between them. The courses and distance are readily obtainable by a method explained on the charts. The track may be transferred to a chart on the 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 Computation. — 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; AVE, the great circle joining them, with its vertex at V; and P, the pole of the earth. Let Ca = PAB, the initial course; Cb = PBA, the final course; La,Lv,Lb = the latitudes of the respective 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, respectivelv, = APB, APV, BPV. D = the great circle distance between A and B; and ^ = an auxiliary angle introduced for the computation. We then have: tan 9> = cos Loab cot Lb; cot Ca = cot Loab cos (La + '''; all sextants, however, are not so closely graduated. Whatever the limits of subdivision, all sextants are fitted with verniers which contain one more division than the length of scale covered, and in which, therefore, scale-readings and vernier-readings increase in the same direction — toward the left hand. To read any sextant, it is merely necessary to observe the scale division next below, or to the right of, the zero of the vernier, and to add thereto the angle corresponding to that division of the vernier scale which is most nearly in exact coincidence with a division of the instrument scale. 242. 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 firttand its last direction is equal to twice the inclina- tion of the reflecting 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 being CD; then ADC is the angle between its first and last directions, and we desire to prove that ADC = 2 CFB. From the equality of the angles of incidence and ^iq 32 reflection: From Geometry: ABE^EBC, and ABC = 2 EBC; BCF = FCD, and BCD = 2 BCF. ADC = ABC -BCD = 2 (EBC -BCF) = 2 CFB, which is the relation that was to be proved. 243. In the sextant, since the index mirror is immovably attached to liie index arm, which also carries the vernier, it follows that no change can occur in the inclination between the index mirror and the horizon mirror, excepting such as is registered by the travel of the vernier upon the scale. If, when the index mirror is so placed that it is nearly parallel with the horizon mirror, an observer direct the telescope toward some well-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 by moving the index bar, it will be seen that while one of the images remains fixed the other moves. The fixed image is the direct one seen through the unsilvered part of the horizon glass, while the movable image is due to rays reflected by the index and horizon mirrors. When the two images coincide these mirrors must be parallel (assuming that the object is sufficiently distant to disregard the space which separates the mir- rors) ; in this position of the index mirror the vernier indicates the true zero of the scale. If, however, instead of observing a single object, the instrument is so placed that the direct ray from one object appears in coincidence with the reflected ray of a second object, then the true angle between the objects will be twice the angle of inclination between the mirrors, or twice the angle measured by the vernier from the true zero of the scale. To avoid the necessity of doubling the angle on the scale, the latter is so marked that each half degree appears as a whole degree, whence its indications give the whole ane-le directly. 244. Adjustments op the Sextant. — The theory of the sextant requires that, for accurate indi- cations, the following conditions be fulfilled: (rt) The two surfaces of each mirror and shade glass must be parallel planes. {h) The graduated arc or limb must be a plane, and itn graduations, as well as those of the vernier, must be exact. (c) The axis must be at the center of the limb, and perpendicular to the plane thereof. (d) The index and horizon glasses must be perpendicular, and the line of sight parallel, to the plane of the limb. Of these, only the last named ordinarily require the attention of the navigator who is to make use of the sextant; the' others, which may be called the permanent adjustments, should be made before the instrument leaves the hands of the maker, and with careful use will never be deranged. 245. The Adjustment of the Index Mirror consists in making the reflecting surface of this mirror truly perpendicular to the plane of the sextant. In order to test this, set the index n^^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 forv/ard. The adjustment is made by the screws at the back of the mirror. 246. The Ad,justment of the Horizon Mirror consists in making the reflecting surface of this mirror perpendicular to the plane of the sextant. The index mirror having been adjusted, if, in revolving it by means of the index arm, there is found one position in which it is parallel to the horizon glass, then the latter must also be perpendicular to the plane of the sextant. In order to test this, put in the tele- scope and direct it toward a star; move the index until the reflected image appears to pass the direct image; if one passes directly over the other the mirrors must be parallel; if one passes on either side of the other the horizon glass needs adjustment, which is accomplished by means of the screws attached. 68 INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY. The sea horizon may also be used for making this a(lju-?tment. 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 but a small angle with the horizon; if the images still coincide the glasses are parallel; if not, the horizon glass needs adjustment. 247. The Adjustment of the Telescope must be so made that, in measuring angular distances, the line of sight, or axis of the telescope, shall be parallel to the plane of the instrument, as a deviation in that respect, in measuring large angles, will occasion a considerable error. To avoid such error, a telescope is employed in whicli are placed two wires, i)arailel to each other and equidistant from the center of the telescope; by means of these wires the adjustment may be made. Screw on the telescope, and turn the tube containing the eyeglass till the wires are parallel to the plane of the instrument; then select two clearly-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 coincidence with the direct image of the other at the inner wire; then, by altering slightly the position of the instru- ment, make the objects appear on the other wire; if the contact still remains perfect, the axis of the telescope is in its right situation; but if the two objects appear to separate or lap over at the outer wire the telescope is not parallel, and it must be rectified by turning one of the two screws of the ring into which the telescope is screwed, having previously unturned the other screw; by repeating this operation a few times the contact will be precisely the same at both wires, and the axis of the telescope will be parallel to the plane of the instrument. Another method of making this adjustment is to place the sextant upon a table in a horizontal position, look along the plane of the limb, and make a mark upon a wall, or other vertical surface, at a distance of about 20 feet; draw another mark above the first at a distance equal to the height of the axis of the telescope above the plane of the limb; then so adjust the telescope that the upper mark, as viewed through the telescope, falls midway between the wires. Some sextants are accompanied by small sights whose height is exactly equal to the distance between the tt lescope and the plane of the limb; by the use of these, the necessity for employing the second mark is avoided and the adjustment can be very accurately made. 248. The errors which arise from defects in what have been denominated the permanent adjustments of the sextant may be divided into three classes, namely: Errors due to faulty centering of the axis, called eccentricity; errors of graduation; and errors arising from lack of parallelism of surfaces in index mirror and in shade glasses. The errors due to eccentricity and faulty graduation are constant for the same angle, and should be determined once for all at some place where proper facilities for doing the work are at hand; these errors can only be ascertained by measuring known angles with the sextant. If angles of 10°, 20°, 30°, 40°, etc., are first laid off with a theodolite or similar instrument and then measured by the sextant, a table of errors of the sextant due to eccentricity and faulty graduation may be made, and the error at any intermediate angle found by interpolation ; this table will include the error of graduation of the theodolite and also the error due to inaccurate reading of the sextant, but such errors are small. Another method for determining the combined errors of eccentricity and graduation is by measuring the angular distance between stars and comparing the observed and the computed arc between them, but this process is liable to inaccuracies by reason of the uncertainty of allowances for atmospheric refraction. Errors of graduation, when large, may be detected by "stepping off " distances on the graduated arc with the vernier; place the zero of the vernier in exact coincidence with a division of the arc, and observe whether the final division of the vernier also coincides with a division of the arc; this should be tried at numerous positions of the graduated limb, and the agreement ought to be perfect in every case. The error due to a prismatic index mirror may be found by measuring a certain unchangeable angle, then taking out the glass and turning the upper edge down, and measuring the angle again; half the dif- ference of these two measures will be the error at that angle due to the mirror. From a number of meas- ures of angles in this manner, a table similar to the one for eccentricity and faulty graduation can be made; or the two tables may be combined. When possible to avoid it, however, no sextant should be used in which there is an index mirror which produces a greater error than that due to the probable error of reading the scale. Mirrors having a greater angle than 2^^ between their faces are rejected for use in the United States Navy. Index mirrors may be roughly tested by noting if there is an elongated image of a well-defined point at large angles. Since the error due to a prismatic horizon mirror is included in the index correction (art. 249), and consequently applied alike to all angles, it may be neglected. Errors due to prismatic shade glasses can be determined by measuring angles with and without the shade glasses and noting the difference. They may also be determined, where the glasses are so arranged that they can be turned through an angle of 180°, by measuring the angle first with the glass in its usual position and then reversed, and taking the mean of the two as the true measure. 249. Index Error. — The Index Error of a sextant is the error of its indications due to the fact that when the index and horizon mirrors are parallel the zero of the vernier does not coincide with the zero of the scale. Having made the adjustments of the index and horizon mirrors and of the telescope, as previously described, it is necessary to find that point of the arc at which the zero of the vernier falls when the two mirrors are parallel, for all angles measured by the sextant are reckoned from that point. If this point is to the left of the zero of the limb, all readings will be too great; if to the right of the zero, all readings will be too small. If desirable that the reading should be zero when the mirrors are parallel, place the zero of the vernier on zero of the arc; then, by means of the adjusting screws of the horizon glass, move that glass until the direct and reflected images of the same object coincide, after which the perpendicularity of the horizon glass should again be verified, as it may have been deranged by the operation. This adjust- ment is not essential, since the correction may readily be determined and applied to the reading. In certain sextant work, however, such as surveying, it will be very convenient to be relieved of the INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY. 69 necessity of correcting each angle observed. The sextant should never be relied upon for maintaining a constant index correction, and the error should be ascertained frequently. It is a good practice to verify the correction each time a sight is taken. 250. The Index Correction may be found (a) by a star, {b) by the sea horizon, and (c) by the sun. (a) Bring the direct and reflected images of a star into coincidence, and read off the arc. The index correction is numerically equal to this reading, and is positive or negative according as the read- ing is on the right or left of the zero. (6) The samq method may be employed, substituting for a star the sea horizon, though this will be found somewhat less accurate. (c) Measure the apparent diameter of the sun by first bringing the upper limb of the reflected image to touch the lower limb of the direct image, and then bringing the lower limb of the reflected image to touch the upper limb cf the direct image. Denote the readings in the two cases by r and r^; then, if S = apparent diameter of the sun, and E. = the reading of the sextant when the two images are in coincidence, we have: r =Il + S, K = R - S, R=:^(r + rO. As R represents the error, the correction will be — R. Hence the rule: Mark the readings when on the arc with the negative sign; when ojf, with the positive sign; then the index correction is one-half the algebraic sum of the two readings. Example: The sun's diameter is measured for index correction as follows: On the arc, 31^ 20^^; off the arc, 33'' 10^^. Required the correction. On the arc, - 31^ 20^^ Off the arc, +33 10 2)+ 1 50 I. C, + 55 251. From the equations previously given, it is seen that: S = i {r-r^y, hence, if the observations are correct, it will be found that the sun's semidiameter, as given in the Nautical Almanac for the day of observation, is equal to one-half the algebraic difference of the readings. If required to obtain the index correction with great precision, several observations should be taken and the mean used, the accuracy being verified by comparing the tabulated with the observed semidiameter. If the sun is low, the horizontal semidiameter should be observed, to prevent the error that may arise from unequal refraction. 253. Use op the Sextant. — To measure the angle between any two visible objects, point the tele- scope toward the lower one, if one is above the other, or toward the left-hand one, if they are in nearly the same horizontal plane. Keep this object in direct view through the unsilvered part of the horizon glass, and move the index arm until the image of the other object is seen by a double reflection from the index mirror and the silvered portion of the horizon glass. Having gotten the direct image of one object into nearly exact contact with the reflected image of the other, clamp the index arm and, by means of the tangent-screw, complete the adjustment so that the contact may be perfect; then read the limb. In measuring the altitude of a celestial body above the sea horizon, it is necessary that the angle shall be measured to that point of the horizon which lies vertically beneath the object. To determine this point, the observer should move the instrument slightly to the right and left of the vertical, swinging it about the line of sight as an axis, taking care to keep the object in the middle of the field of view. The object will appear to describe the arc of a circle, and the lowest point of this arc marks the true vertical. The shade-glasses should be employed as may be necessary to protect the eye when observing objects of dazzling brightness, such as the sun, or the horizon when the sun is reflected from it at a low altitude. Care must be taken that the images are not too bright or the eye will be so affected as to interfere with the accuracy of the observations. 253. Choice op Sextants. — The choice of a sextant should be governed by the kind of work which is required to be done. In rough work, such as surveying, where angles need only be measured to the nearest 30^'' the radius may be as small as 6 inches, which will permit easy reading, and the instrument can be correspondingly lightened. Where readings to 10'^ are desired, as in nice astronomical work, the radius should be about 7Hnches, and the instrument, to be strongly built, should weigh about 3 J pounds. The parts of an instrument should move freely, without binding or gritting. The eyepieces should move easily in the telescope tubes; the bracket for carrying the telescope should be made very strong. It is frequently found that the parallelism of the line of sight is destroyed in focusing the eyepiece, either on account of the looseness of the fit or because of the telescope bracket being weak. The vernier should lie close to the limbs to prevent parallax in reading. If it is either too loose or too tight at either extremity of its travel, it may indicate that the pivot is not perpendicular. The balls of the tangent- screvv should fit snugly in their sockets, so that there may be no lost motion. Where possible, the sextant should always be submitted to expert examination and test as to the accuracy of its permanent adjustments before acceptance by the navigator. 254. Resilvering Mirrors. — Occasion may sometimes arise for resilvering the mirrors of a sextant, as they are always liable to be damaged by dampness or other causes. For this purpose some 70 ' INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY. clean tin foil and mercury are required. Upon a piece of glass about 4 inches square lay a piece of tin foil whose dimensions exceed by about a quarter of an inch in each direction those of the glass to be silvered; smooth out the foil carefully by rubbing; jjut a small drop of mercury on the foil and spread it with the finger over the entire surface, being careful that none shall find its way under the foil; then put on a few more drops of mercury until the whole surface is fluid. The glass which id to be silvered having been carefully cleaned, it should be laid upon a ])iece of tissue paper whose edge just covers the edge of the foil and transferred carefully from the paper to the tin foil, a gentle pressure being kept upon the glass to avoid the formation of bubbles; finally, place the mirror face downward and leave it in an inclined position to allow the surplus mercury to flow off, the latter operation being hastened by a strip of tin foil at its lower edge. After five or six hours the tin foil around the edges may be removed, and the next day a coat of varnish made from spirits of wine and red sealing wax should be applied. For a horizon mirror care must be taken to avoid silvering the plain half. The mercury drawn from the foil should not be placed with clean mercury with a view to use in the artificial horizon or the whole will be spoiled. 255. Octants and Quintants. — Properly speaking, a sextant is an instrument whose arc covers one-aixth of a complete circle, and which is therefore capable of measuring an angle of 120°. Other instruments are made which are identical in principle with the sextant as heretofore described, and which differ from that instrument only in the length of the arc. These are the octant, an eighth of a circle, bv which angles may be measured to 90°, and the qalnlant, a fifth of a circle, Avhich measures angles up to 144°. The distinction between these instruments is not always carefully made, and in such matters as have been touched upon in the foregoing articles the sextant may be regarded as the type of all kindred reflecting instruments. THE ARTIFICIAL. HORIZON. 256. The Artificial Horizon is a small, rectangular, shallow basin of mercury, over which, to protect the mercury from agitation by the wind, is placed a roof consisting of two plates of glass at right angles to each other. The mercury affords a perfectly horizontal surface which is at the same time an excellent mirror. The different parts of an artificial horizon are furnished in a compact form, a metal bottle being provided for containing the mercury when not in use, together with a suitable funnel for pouring. If MN, in figure 33, is the horizontal surface of the mercury; S'B a ray of light from a celestial object, incident to the surface at B; BA the reflected ray; then an observer at A will receive the ray BA as if it proceeded from a point S'^, whose angular depression, MBS'''', below the horizontal plane is equal to the altitude, MBS^, of the object above that plane. If, then, SAis a direct ray from the object parallel to S^B, an observer at A can measure with the sextant the angle SAS''= S^BS'^= 2 S'BM, by bringing the image of the object reflected by the index 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 limb of the other. Half the cor- rected instrumental reading will be the apparent altitude of the sun's loiver or upper limb, according as the lower or upper limb of the reflected image was the one employed in the observation. In observations of the sun with the artificial horizon, the eye is protected by a single dark glass over the eyepiece of the telescope through which direct and reflected rays must pass alike, thereby avoiding the errors that might 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 dll prismatic, the observed altitude will be erroneous. The error may be removed by observing a second altitude with the roof reversed, and, in general, by taking one half of a set of obser- vations with the roof in one position and the other half with the roof reversed. On the rare occasions when the atmosphere is so calm that the unsheltered mercury will remain undisturbed, most 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 placed that its longer edge lies in the direction in which the observed body will bear at the middle of the observations. The spot selected for taking the sights should be as free as possible from causes which will produce vibration of the mercury, and precautions should be taken to shelter the horizon from the wind, as the mere placing of the roof will not ordinarily be suf- ficient to accomplish this. Embedding the roof in earth serves to keep out the Avind, 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 shocks, and also aids in keeping out the moisture from the ground. In damp climates the roof should be kept dry by wiping, or the moisture deposited from the inclosed air will form a cloud upon the glass. Molasses, oil, or other viscous fluid may, when necessary, be employed as a substitute for mercury INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY. 7l 25§. 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-mtasurer, 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 y the others. 260. Care of Chronometers on Shipboard. — The box in which the chronometers are kept should have a permanent place as near as practicable to the center of motion of the ship, and where it will be free from excessive shocks and jars, such as those that arise from the engines or from the firing of heavy guns; the location should be one free from sudden and extreme changes of temperature, and as far removed as possible from masses of vertical iron. The box should contain a separate compart- ment for each chronometer, and each compartment should be lined with baize cloth padded with curled hair, for the double purpose of reducing shocks and equalizing the temperature within. An outer cover of baize cloth should be provided for the box, and this should be changed or dried out frequently in damp weather. The chronometers should all be placed with the XII mark in the same position. For transportation for short distances by hand, an instrument should be rigidly clamped in its gimbals, for if left free to swing, its performance may be deranged by the violent oscillations that are imparted to it. For transportation for a considerable distance, as by express, the chronometer should be allowed to run down, and should then be dismounted and the balance corked. 261. Since it is not possible to make a perfect instrument which will be 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 Avatch upon the variable rate of the chronometer. The error of the chronometer is the difference between the time indicated and the standard time to which it is referred — usually Greenwich mean time. The amount the chronometer gaiyis or loses daily is the daily 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 rewinding, and an indicator on the face always shows how many hours have elapsed since the last winding. To insure a uniform rate, they must be wound regularly every day, and, in order to avoid the serious conse- quences of their running down, the navigator should take some means to guard against neglecting this duty through a fault of memory. To wind, turn the chronometer gently on its side, enter the key in its hole and push it home, steadying the instrument with the hand, and wind to the left, the last half turn being made so as to bring up gently against the stop. After winding, cover the keyhole and return the instrument to its natural position. Chronometers should always be wound in the same order to prevent omissions, and the precaution taken to inspect the indicators, as a further assurance of the proper performance of the operation. After winding each day, the comparisons should be made, and, with the readings of the maximum- and-minimum thermometer and other necessary data, recorded in a book kept for the purpose. The maximum-and-minimum thermometer is one so arranged that its highest and lowest readings are marked by small steel indices that remain in place until reset. Every chronometer box should be provided with such an instrument, as a knowledge of the temperature to which chronometers have been subjected is essential in any analysis of the rate. To draw down the indices for the purpose of resetting, a magnet is used. This magnet should be kept at all times at a distance from the chronometers. 263. Comparison of Chronometers. — The instrument believed to be the best is regarded as the Standard, and each other is compared with it. It is usual to designate the Standard as A, and the others as B, C, etc. Chronometers are made to beat half-seconds, and any two may be compared by following the lieat of one with the ear and of the other with the eye. To make a comparison, say of A and B, open the boxes of these two instruments and close all others. Get the cadence and, commencing when A has just completed the beat of some even 5-second division of the dial, count "half-one-half-two-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 accurac) 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. 264. The following form represents a convenient method of recording comparisons: Stand. A, No. 777. Chro. B, No. 1509. Chro. C, No. 1802. Date, 1903. Designation of comparisons. Chro. B witti Stand. A. 2d diff. Chrt). C with Stand. A. 2d diff. Therm. Bar. Remarks. Max. Min. Air. January 1 Stand. A. B and C. h. 1)1. s. 1 13 40 1 12 21.5 s. h. m. s. 1 14 20 2 04 11 s. o 63 o 59 o 60 It 30.07 Found errors by time- ball. Difference. 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 H 4'.5 and — 0\5, respectively; it would at once be suspected that the irregularity was in B, and that that chronometer had lost 3^* on its normal rate during the preceding day. Suppose, however, the second differences were +4^5 and +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. With all available data a temperature curve should be constructed which will indicate graphically the performance of the instrument. It is most convenient to employ for this purpose a piece of "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 cf tem- perature, numbered at the left edge, from the bottom up; draw a vertical line in red ink to represent the zerQ 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. 268. Hack or Comparing Watch. — In order to avoid derangement, the chronometers should never be removed from the permanent box in which they are kept on shipboard. When it is desired to mark a certain instant of time, as for an astronomical observation or for obtaining the chronometer error by signal, the time is marked by a "hack " (an inferior chronometer used for this purpose only), or by a comparing watch. Careful comparisons are taken — preferabl j' 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" W. T., -2 36 30^ 45.5 C-W, 2 50 44.5 If then a sight is taken when the watch shows 3'' 01" 27.* 5, we have: W. T., C-W, S^Ol" 2 50 21\b 44.5 Chro.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 tnean 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 possibility 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^ Comparison Sight |W, -11 42 35 [C-W, 11 15 03 fW, 11 50 21 |C-W,+11 15 03 [C, 11 05 24 w, 11" 42"' 35« c, -c, -10 57 38 w- 44 57 w, 11 50 21 w- -c,- - 44 57 c, 11 05 24 74 TIME AND THE NAUTICAL ALMANAC, CHAPTER IX. TIME AND THE NAUTICAL ALMANAC. 270. The subjects of Time and the Nautical Almanac are two of the most important ones to be mastered in the study of Nautical Astronomy, as they enter into every operation for the astronomical determination of a ship's position. They will be treated in conjunction, as the two are interdependent. METHODS OF RECKONING TIME. 271. The instant at which any point of the celestial sphere is on the meridian of an observer is termed the transit, culmination, or meridian passage of that point; when on that half of the meridian which contains the zenith, it is designated as superior or upper transit; when on the half containing the nadir, as inferior or lower transit. 272. Three different kinds of time are employed in astronomy — (a) apparent or solar time, (6) mean time, and (c) sidereal time. These depend upon the hour angle from the meridian of the points to which they respectively refer. The point of reference for apparent or solar time is the Center of the Sun; for mean time, an imaginary point called the Mean Sun; and for sidereal time, the Vernal Equinox, also called the First Point of Aries. The unit of time is the Bay, which is the period between two successive transits over the same branch of the meridian of the point of reference. The day is divided into 24 equal parts, called Hours; these into 60 equal parts, called Minutes, and these into 60 equal parts, called Seconds. 273. Apparent or Solar Time. — The hour angle of the center of the sun affords a measure of Apparent or Solar Time. An Apparent or Solar Day is the interval of time between two successive transits over the same meridian of the center of the sun. It is Apparent Noon when the sun's hour circle 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 returns of the sun to the same meridian are not equal, apparent time can not be taken as a standard. The apparent day varies in length from two causes: first, the sun does not move in the equator, the great circle perpendicular to the axis of rotation of the earth, but in the ecliptic; and, secondly, the sun's motion in the ecliptic is not uniform. Sometimes the sun describes an arc of 57^ of the ecliptic, and sometimes an arc of 61^ in a day. At the points where the ecliptic and equinoctial intersect, the direction of the sun's apparent motion is inclined at an angle of 23° 27'' to the equator, while at the solstices it moves in a direction parallel to the equator. 274. Mean Time. — To avoid the irregularity of time caused by the want of uniformity in the sun's motion, a fictitious sun, called the Mean Sun, is supposed to move in the equinoctial with a uniform velocity that equals the mean velocity of the true sun in the ecliptic. This mean sun is regarded as being in coincidence with the true sun at the vernal equinox, or First Point of Aries. Mean Time is the hour angle of the mean sun. A Mean Day is the interval between two successive transits of the mean sun over the meridian. Mean Noon is the instant when the mean sun's hour circle coincides with the meridian. Mean time lapses uniformly; at certain times it agrees with apparent time, while sometimes it is behind, and at other times in advance of it. It is this time that is measured by the clocks in ordinary use, and to this the chronometers used by navigators are regulated. 275. The difference between apparent and mean time is called the Equation of Time; by this quantity, the conversion from one to the other of these times may be made. Its magnitude and the direction of its application may be found for any moment from the Nautical Almanac. 276. Sidereal Time. — Sidereal Time is the hour angle of the First Point of Aries. This point, which is identical with the vernal equinox, is the origin of all coordinates of right ascension. Since the position of the point is fixed in the celestial sphere and does not, like the sun, moon, and planets, have actual or apparent motion therein, it shares in this respect the properties of the fixed stars. It may therefore he said that intervals of sidereal time are those which are measured by the stars. A Sidereal Day is the interval between two successive transits of the First Point of Aries across the same meridian. Sidereal Noon is the instant at which the hour circle of the First Point of Aries coincides with the meridian. In order to 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 Bight Ascension of the Mean Sun. 277. Civil and Astronomical Time. — 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 cf 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 interconverting these times. For example: January 9, 2 a. m., civil time, is January 8, 14'', astronomical time. January 9, 2 p. m., civil time, is January 9, 2*', astronomical time. 278. HouK Angle. — The hour angle of a heavenly body is the angle at the pole of the celestial concave between the d eclination circle of the heavenly body and the celestial - p • i meridian. It is measured by the arc of the celestial equator between the decli- ^\ /• ^-♦vm' nation circle and the celestial meridian. / \ ^ft-v^..^*. In figure 34 let P be the pole of the celestial sphere, of which VMQ is the equator, PQ, the celestial meridian, and PM, PS, PV, the declination circles of the mean sun, a heavenly body, and the First Point of Aries, respectively. Then QPM, or its arc, QM, is the hour angle of the mean sun, or the mean time; QPS, or QS, the hour angle of the 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 equivalent to the sidereal time; VPS, or VS, the right ascension of the heavenly body; and VPM, or VM, the right ascension of the mean sun. 279. Time at Different Meridians. — The hour angle of the true sun at any meridian is called the local apparent lime; that of the mean sun, the local mean time; that of the First Point of Aries, the local sidereal time. The hour angles of the same body and points from Greenwich are respectively the Green- vnch apparent^ mean, and sidereal times. The difference between the local time at any meridian and the Greenwich time is equal to the longitude of that place from Greenwic^h 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 PM and PM'' represent the celestial meridians of two places; PS, the declination circle through the sun, and PG, the Greenwich meridian- let Tg = 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: Fig. 35. Lo = Tg — Tm; and Lo' = To— Tm-; 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 formulae must be reckoned westward, always from their respective meridians and from 0** to 24''; in other words, it is the astronomical time which should be used in all astronomical computations. The formula Lo = Tg — Tm is true for any kind of time, solar or sidereal; or, in general terms, Tg and Tm are the hour angles of any point of the sphere at the two meridians whose difference of longitude is Lo. S may be the sun (true or mean) or the vernal equinox. 2§0. Finding the Greenwich Time. — Since nearly every computation made by the navigator requires a knowledge of the Greenwich date and time as a preliminary to the use of the Nautical Almanac, the first operation necessary is to deduce from the local time the corresponding Greenwich date, either exact or approximate, and thence the Greenwich time expressed astronomically. The formula is: Tg-Tm+Lo, remembering that west longitudes are positive, east longitudes are negative. Hence the following rule for converting local to Greenwich time: Having expressevl tlie local time astronomically, add the longitude if west, subtract it iieasi; the result is the corresponding Greenwich time. Example: In longitude 81° 15^ VV. the local time is, 1879, April, 15^ 10'' 17"' 30' a. m. Required the Greenwich time. Local Ast. time, April, W^ 22" 17'" 30' Longitude, + 5 25 00 Greenwich time, 15 3 42 30 Example: In longitude 81° 15^ E. the local time is, August, 5'^ 2'' 10"' 30' p. m. Required the Green- wich time. Local Ast. time, 5" 2" lO-" 30' Longitude, - 5 25 00 Greenwich time, 4 20 45 30 76 TIME AND THE NAUTICAL ALMANAC. Example: In longitude 17° 28'' W. the local time is, May, 1* 3'' 10"" p. m. Required the Greenwich tinae. Local Ast. time, 1* S^ lO-" 00^ Longitude, + 1 09 52 Greenwich time, 1 4 19 52 Example: In longitude 125° 3CK E. the local time is. May, 1* 8" 10" 30^ a. m. Required the Green- wich time. Local Ast. time, April, 3(fi 20" 10"' 30^ Longitude, — 8 22 00 Greenwich time, 30 11 48 30 2§1. From the preceding article we have: Tg = Tm + Lo; hence, Tm = Tg - Lo; thus it will be seen that, to find the local time corresponding to any Greenwich time, the above process is simply reversed. Since all observations at sea are referred to chronometers regulated to Greenwich mean time, and as these instruments are usually marked on the dial from O*" 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 15'', S^ 21" 45 Longitude, -r 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. « 2S2. The American Ephemeris and Nautical Almanac is divided into four parts, as follows: Part I, Ephemeris for the meridian of Greenwich, gives the ephemerides of the sun and moon, the geocentric and heliocentric positions of the major planets, the sun's coordinates, and other fundamental astronom- ical data for equidistant intervals of Greenwich mean time; Part II, Ephemeris for the meridian of Washington, gives the ephemerides of the fixed stars, sun, moon, and major planets for transit over the meridian of Washington; Part III, Phenomena, contains predictions of phenomena to be observed, with data for their computation; and Part IV, Star Numbers and other data, contains matter relating to cer- tain fixed stars. Tables are also appended for the 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; solarand lunar eclipses are described, and the tables for the interconversion of mean and sidereal time and for finding the latitude by Polaris are included. The elements dependent upon the sun and moon are placed at the beginning of the book, arranged according to the months of the year; eighteen pages are devoted to each month, numbered in Roman notation from I to XVIII. Of these, page I contains the Apparent Right Ascension and Declina- tion of the sun and the Equation of Time for the instant of Greenwich apparent noon; throughout the remaining seventeen pages Greenwich viean time forms the basis of reckoning. Page I is used in com- putations from observations that depend upon the time of the sun's meridian passage, at which instant the local apparent time is 0", and the Greenwich apparent time is equal to the longitude, if west, or to 24" minus the longitude, if east; this page therefore affords a means for reducing the elements for such observations from a knowledge of the longitude alone. In all other observations the calculation is made for some definite instant o^ Greenwich mean time (usually as noted by the chronometer) , in which case Pages II to XVIII are employed. 283. Reduction of Elements. — The reduction of elements in the Nautical Almanac is usually accomplished by Interpolation, but in certain cases where extreme precision is necessary the method of Second Differences must be used. a See extracts 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 Almanac gives the value of the required element, nothing more is necessary than to employ that value. But if the time falls between the Almanac times, the required quantity must be found by interpolation. The Almanac contains the rate of change or difference of each of the principal quantities for some unit of time, and, unless great precision is required, the first differences only need be regarded. In order to, use the difference columns to advantage, the Greenwich date should be expressed in the unit of time for which the difference is given. Thus, for using the hourly differences, the Greenwich 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 the quantities in the Almanac are approximate numbers, given to a certain decimal, any inter- polation of a lower order than that decimal is unnecessary work. Moreover, since, in computations at sea, the Greenwich time is more or less inexact, too great refinement need not be sought in reducing the Almanac elements. Simple interpolation assumes that the differences of the quantities are proportional to the differences of the times; in other words, that the differences given in the Almanac are constant; this is seldom the case, but the error arising from the assumption 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 table may be used. Yet, as it is proper to seek always the greatest attainable accuracy, the use of the table showing the exact positions is recommended. That table is, however, published in the "Ephemeris and Nautical Almanac" only, and is omitted from the abridged " Nautical Almanac; " hence, where the larger book is not at hand, the table of mean places must be employed. 2§4. To find from the Nautical Almanac a required element for any given time and place, it is first necessary to express the time astronomically and to convert it to Greenwich time and date. Then take from the Almanac, for the nearest given preceding instant, the required quantity, together with its corresponding " Diff. for l*" " or " Diff. for 1"'," noting the name or sign in each case; for the sun use Page I of the proper month in the Almanac when apparent time is to be the basis for correction, but otherwise use Page II. Multiply the "Diff. for 1''" by the number of hours and fraction of an hour, or the "Diff. for 1'"" by the number of minutes and fraction of a minute, corresponding to the interval between the time for which the quantity is given in the Almanac and the time for which required; apply the correction thus obtained, having regard to its sign. A modification of this rule may be adopted if the time for which the quantity is desired falls 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 apparent noon. Long. =81° 15' W. G. A. T. Dec, 171 Corr., 0\ 5h25n> > + + + 10° 26' 42".3 N. 4 46 .2 Dec, 171 10 31 28. .5 N. H. D., G. A. T., 52". 80 5^42 Corr., / 286". 18 14'46".18 17^ 5" 25™ = = 17^ l-L, 5\42. Eq. t: Corr., , 1?» Oh, , 17* 5^25°' > T., + + + 0° '24« 3 .46 .18 Eq.t., 27 .64 H. D. G. A. 0^.587 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. 1 Dec, 17'» 0\ Corr., ( + ) + 10 ° 26' 42". 3 N. 4 46 .2 Dec, 16* 18" 35°>: 10 21 56 .1 N. H. D., G. A. T., 52". 80 5". 42 Cor.., ; 286". 18 \4' 46". 18 .6* 18" Eq. t. Corr., 35™ = 17* - , 17* 0^ , 16* 18" 35" - 5". 42 on, ' 24^46 3.18 Eq. t. S 21 .28 H. D. G. A. + 0^587 5".42 Corr., 3M82 78 TIME AND THE T^AUTICAL ALMANAC. Example: April 16, 1879, at 11** 55™ 30* a. m., local mean time, in Long. 81° 15' W., required the declination and semidiameter of the sun, the equation of time, and the right ascension, declination horizontal parallax, and semidiameter of the moon and Jupiter. Local mean time, 15" 23'' 65™ 30" Longitude, — 5'' 25'" 00" [161 5" 20™ 30' Greenwich mean time, \ 16"* 5'' 20™.5 116'' 5\34 For (lie Sim. Dec, 0^ ( + ) 10° 05' Corr., + 4 30". 44 . 1 N. S. D., 15' 58". 3 (Same as at G. A. Noon.) Eq. t.; Corr. , Eq. t. H. D. G. M. 0™ 10-". 15 + 3.22 Dec, 10 10 14 . 4K 13 . 37 H. D., + G. M. T., + 53". 5". 24 34 + 0^ 604 - b\ 34 Corr., + 1 284". 30 4' 44". 30 For the Moon. R.A., 6», 2-2h 14n ' 39».29 Dec, 5h, (-) 7°59'36".1S. Hor.Par.,Oh, Corr., + 38.31 Corr., Dec, M. D., + 4 27 .1 Corr., R. A., 22 15 17 .CO 7 55 09 .0 a. Hor. Par., M. D. 1«.869 13".03 H. D., No. min., + 20'".5 No. mill., + 20'".5 ' G. M. T., Corr. , + 3". 22 {Add to mean time.) 55' 13".6 55 06 .4 l."34 5».34 S.D.,Oh, Corr., S. D., 15' 04". 7 1 .=: 15 02 .9 H. D., G. M. T., + Corr., Corr., J 267". 12 Corr., I 4'27".l 7". 15 Corr., 0".34 5h.34 1".81 For Jupiter. R. A.,0^ 22" 26™ 35^54 Corr., + 9.71 R. A., D. M. 't. + 22 26 45 . 25 H. G. l^ 5" 819 . 34 Corr. , 9". 71 Dec, 0", Corr., + Dec, H. D., + G. M. T., + Corr., + ) 10° 40' 28". OS. 53 . 6 10 39 34 . 4 S. 10". 03 5". 34 53". 6 Hor. Par., 16^ 1". 6 S. D., 16^ 16".9 2§5. Should greater precision be required than that attainable by simple interpolation, resort musi be had to the reduction for second differences. The differences between successive values of the quantities given in the Nautical Almanac are called the first differences; the differences between successive first differences are called the second differences. Simple interpolation, which satisfies the necessities of sea computations, assumes the first differences to be constant; but if the variation of the first differences be regarded, a further interpolation is required for the second difference. The difference for a unit of time in the American Nautical Almanac abreast any element expresses the rate at which the element is changing at that precise instant of Greenwich time. Now, regarding the second difference as constant, the first difference varies uniformly with the Greenwich time; there- fore its value may be found for any intermediate time by simple interpolation. Hence the following rule for second differences: Employ the interpolated value of the first differ- ence which corresponds to the middle of the interval for which the correction is to be computed. Example: For the Greenwich date 1879, April, 10'^ 18" 25™ 30", find the moon's declination. Dec, 18", (-)26= Corr., -f 19' 41". 1 S. 2 .1 First diff. Corr. , .044 039 Second diff., + 0". 181 Interval, +0".213 Dec 26 19 39 .0 S. M. D., +0 .083 No. min., +25™. 5 Corr. 0".039 Corr. , 2". 12 The difference for one minute being 4-0".044 at 18", and -j-0".225 at 19", the difference for one minute undergoes a change of + 0".181 during one hour. The time for which it is desired to obtain the difference is at the middle instant between 18" 0™ and 18" 25™. 5 — that is, at 18" 12™. 75, or its equivalent, 18" 213. With a change of + 0".181 in one hour, the change in 0".213 is readily obtainable; correcting the minute's difference at 18". accordingly, the process of correcting the declination becomes the same SIS in simple interpolation. TIME AND THE NAUTICAL ALMANAC. 79 CONVERSION OF TIMES. 2§6. Conversion of Time is the process by which any instant of time that is defined according to one system of reckoning may be defined according to some other system; and also by which any interval of time expressed in units of one system may be con- verted into units of another. 287. Sidereal and Mean Times. — Mean time is the hour angle of the Mean Sun; sidereal time is the hour angle of the First Point of Aries. Since the Right Ascension of the Mean Sun is the angular distance 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 Mean Sun. This is explained in figure 36, which represents a" projection of the celestial sphere upon the equator. If P be the pole; QPQ^, the meridian; V, the First Point of Aries; M, the position of the mean sun (west of the meridian ) ; then QPV, or the arc QV, is the sidereal time; QPM, or the arc QM, is the mean time; and VPM, or the arc VM, is the Right Ascension of the Mean Sun. From this it will appear that: QV=QM+VM, or Sidereal t'.me=Mean time+Right Ascension of Mean Sun. If the mean sun be on the opposite side of the meridian, at M', then the mean time equals 24"— M^Q. In this case: QV=VM^-M^Q, or Sidereal tiine= 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 Right Ascension of the Mean Sun, but the former must be increased by 24'' when necessary to make the subtraction possible. 2§8. Apparent and Mean Times. — Apparent time is the angle between the meridian and the hour circle which contains the center of the sun; mean time is the angle between the meridian and the hour circle which contains the mean sun. Since the equation of time represents the angle between the hour circles of the mean and apparent suns, it is clear that the conversion of mean time to apparent time may be accomplished by the application of the equation of time, with its proper sign, to the mean time; and the reverse operation 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 QM will be the mean time; QV, the apparent time; and VM, the equation of time; whence ve have as before: QV = QM + VM, or Apparent time = Mean time + Equation of time; the equation of time will be positive or negative according to the relative position of the two suns. 289. Sidereal and Mean Time Intervals. — The sidereal year consists of 366.25636 sidereal days or of 365,25636 mean solar days. If, therefore, M be any interval of mean time, and S the corresponding interval of sidereal time, the relations between the two may be expressed as follows: j_ 366.25636 _ , M~ 365.25636 ~^-""^^'^^^' M_ 365.25636 _ S ~ 366.25636 ~ '^-y^^^^^^- 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 + 9^8565M; 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 be found in the Nautical Almanac. 80 TIME AND THE NAUTICAL ALMANAC. 290. To Convert Mean Solar into Sidereal Time. — Apply to the local mean time the longitude, adding if west and subtracting if east, and thus obtain the Greenwich mean time. Take from the Nau- tical Almanac the Right Ascension of the Mean Sun at Greenwich mean noon, and correct it for the Greenwich mean time by Table 9 or by the hourly difference of 9^857. Add to the local mean time this corrected right ascension, rejecting 24'' if the sum is greater than that amount. The result will be the local sidereal time. Example: April 22, 1879, in Long. 81° 15^ W., the local mean time is 2"; 00™ 00' p. m. Required the corresponding local sidereal time: L. M. T., 22^ 2" 00'" 00' Long., -r 5 25 00 R. A. M. S., 22'^ 0\ 2" 00-" 41\24 Red. for 7" 25'" (Tab. 9), -f 1 13 .10 L. M. T., 2" 00-" OO'' R.A.M.S., + 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, local sidereal time. in Long. 75° E., the local mean time is 4" 00"' 00' a. m. Required the L. M. T., 21'! 16h 00°' 00^ Long., - 5 00 00 R. A M. S. 21'» 0^ 1" 56'" 44^69 Red. for 11" (Tab. 9), + 1 48 .42 L.M.T., 21-1 16" 00'" 00'' R.A.M.S.,+ 1 58 33.11 G. M. T., 21 11 00 00 R. A. M. S., IP, 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 Convert Sidereal into Mean Solar Time. — Take from the Nautical Almanac the Right Ascension of the Mean Sun for Greenwich mean noon of the given astronomical day, and apply to it the reduction for longitude, either by Table 9 or by the hourly difference of 9^857, and the result will be the Right Ascension of the Mean Sun at local mean noon, which is equivalent to the local sidereal time at that instant. Subtract this from the given local sidereal time (adding 24" to the latter if necessary), and the result will be the interval from local mean noon, expressed in units of sidereal time. Convert this sidereal time interval into a mean time interval by subtracting the reduction as given by Table 8 or by the hourly difference of 9^830; the result will be the local mean time. Example: April 22, 1879, a. m., in Long. 75° E., the local sidereal time is 17" 58™ 33M1. What is the local mean time? Astronomical day, April 21. L. S. T., R. A M. S., 17"58™33M1 - 1 55 55 .41 R. A. M. S., Gr. 21i 0", 1" 56"' 44^69 Red. for -5" long. (Tab. 9), - 49 .28 Sid. interval from L. M. noon, 16 02 37 .70 Red. for sid. interval (Tab. 8), 2 37 .70 R. A. M. S., local 0", 1 55 55 .41 16 00 00.00 L. M. T., 21", 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., -2 01 34.63 Sid. interval from L. M. Noon, 2 00 19 .71 Red. for sid. interval (Tab. 8), — 19 .71 L. M. T., 22^ 2 00 00 .00 R. A. M. S , Gr. 22^ 0", 2" 00™ 4P.24 Red. for +5" 25™ long. (Tab. 9), + 53 .39 R. A. M. S., local 0", 2 01 34 .63 292. To Covert Mean into Apparent Time and the Reverse. — Find the Greenwich time corre- sponding to the given local time. If apparent time is given, find the Greenwich apparent time and take the equation of time from Page I of the Almanac. If mean time, find the Greenwich mean time and take the equation of time from Page II. Correct the equation of time for the required instant and apply it with its proper sign to the given time. Example: April 21, 1879, in Long. 81° 15' W., find the local apparent time corresponding to a local mean time of 3" 05™ 00^ p. m. ™ 00' L. M. Eq. t., + L. M. T., 21'»3"05™00' Long., + 5 25 00 G, M. T., 21 8 30 00 L. A. T., 21" 3" 05™ 00^ 1 22.01 Eq. t., 0", 1™ 17.61 Corr., + 4.40 21 3 06 22.01 Eq.t., 1 22.01 H.D., -f 0'.518 G.M.T.,+ 8".5 Corr., "T 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. ,. A. T., .ong.. 2'i 20^ 45" - . 5 25 '00' 00 L. A. T., Eq. t., + L. M. T., 2'' 20" 45"' 00' 3 30.90 Eq. t., Corr., Eq. t., H. D. G. M. Corr., {A, 0", ddt 3" 42'. 46 - 11 .56 i. A. T., 2 15 20 00 2 20 48 30.90 3 30 .90 - 0'.754 - 15". 33 — 11'.56 o apparent time. ) 293. To Find the Hour Angle of a Body from the Time, and the Reverse. — 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: QV =QM + VM, = V M^ - M^ Q; QM =QV-VM; M' Q = V M^ - V Q, or (24" - M^ Q) = (24>' + Q V) - V M^ Substituting, therefore, hoiir angle of the body for mean time, and right ascension of the body for Right Ascension of the Mean Sun, the rules previously given for the conversion of mean and sidereal times will be applicable for the conversion of hour angle and sidereal time. Thus, the sidereal time is equal to the sum of the right ascension of the body and its hour angle, subtracting 24" 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" lO"' 30' (astronomical) mean time, find the hour angle of Sirius. L. M. 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. Tl, 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 6583—06- L. S. T., 11 42 29 .] 82 COKRECTION OF OBSERVED ALTITUDES. CHAPTER X. OOEEEOTIOl^ OF OBSEEVED ALTITUDES. ^ ^ 294. The true altitude of a heavenly body at any place on the earth's surface is the altitude of its center, as it would be measured by an observer at the center of the earth, above the plane passed through the center of the earth at right angles to the direction of the zenith. The observed altitude of a heavenly body, as measured at sea, may be converted to the true altitude by the application of the following-named corrections: Index Correction, Dip, Refraction, Parallax, and Semidiameter. The corrections for parallax and semidiameter are of inappreciable magnitude in observations of the fixed stars, and with planets are so small that they need only be regarded in refined calculations. In observations with the artificial horizon there is no correction for dip. For theoretical accuracy, the corrections should be applied in the order in which they are named, but in ordinary nautical practice the order of application makes no material difference, except in the case of the parallax of the moon as explained in article 306. INDEX CORRECTION. 395. This correction is fully explained in articles 249 and 250, Chapter VIII. REFRACTION. 396. It is known by various experiments that the rays of light deviate from their rectilinear course in passing obliquely from one medium into another of 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 rsiy; 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 diffe,rence of the direction of the ray before entering the atmosphere and this la.«t 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 BiS 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. 39§. The refraction for a mean state of the atmosphere (barometer 30'", Fahr. thermometer 50°) is given in Table 20 A; the combined refraction and sun's parallax in Table 20 B; and the combined refraction and moon's parallax in Table 24. Since the amount of the refraction depends upon the density of the atmosphere, and the density varies with the pressure and the temperature, which are indicated by the barometer and thermometer, the true refraction is found by applying to the mean refraction the corrections to be found in Tables 21 and 22; these are deduced from Bessel's formula?, and are regarded as the most reliable tables constructed. It should be remembered, however, that under certain conditions of the atmosphere a very extraordinary defiection occurs in rays of light which reach the observer's eye from low altitudes Fig. 37. COEEECTION OF 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 Dip (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' b2" The correction for height of barometer is, + 13 The correction for the temperature, -j- 42 True refraction. 10 47 299. The correction for refraction should always be subtracted, as also that for combined refraction and parallax of the sun; the correction for combined refraction and parallax of the moon is invariably additive. DIP. /. 300. Dip of ilte 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- inore 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 Visible or Sea Horizon. The Dip of the Horizon is H A H^'', 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, Avhen 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, ancl 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 densjties, 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 '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. nA sextant attachment devised by Lieutenant-Commander J. B. Blish, U. S. Navy, enables an observer to measure the actual dip at any time. 84 COERECTIOlSr OF OBSERVED ALTITUDES. ^ (b) The error in the tabulated value of the dip will increase with an increase in the difference oi temperature, and will diminish with an increase in the force of the wind. (c) The error will decrease with the height of the observer's eye; hence it is expedient, especially when error is suspected, to make the observation from the most elevated position available. (d) When the sea water is colder than the air the visible horizon is raised and the dip is decreased; therefore the true altitude is greater than that giv^en by the use of the ordinary dip table. When the water is warmer than the air, the horizon is depressed and the dip is increased. At such times the altitude is really less than that found from the use of the table. The same cause, it may be mentioned here, affects the kindred matter of the visibility of objects. When the air is warmer, terrestrial objects are sighted from a greater distance and appear higher above the horizon than under ordinary conditions. When the water is warmer than the air, the distance of visibility is reduced, and terrestrial objects appear at a less altitude. 302. What has been said heretofore about the dip supposes the horizon to be free from all 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 w'ill 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 point on its surface. The zenith distance of a body, S (fig. 40), seen from A, on the surface of the earth, is Zx\S; seen from C it is ZCS; the parallax is the difference of these angles, ZAS— ZCS= ASC. Parallax in altitude is, then, the angle at the heavenly body subtended by the radius of the earth. If the heavenly body is in the horizon as at H', the radius, being at right angles to AH^, subtends the greatest possible angle at the star for the same distance, and this angle is called the horizontal parallax. The parallax is less as the bodies are farther from the earth, as will be evident PiG^ 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 sin 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 j^ in the above, sin par. = sin H. P. sin Z. If h = SAH', the apparent altitude of the heavenly body, then Z — 90° — h; 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. CORRECTION 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 j\m moon, but subtractive for the sun. As the correction for parallax of the moon is so large, it is essential that it be taken from the table with considerable accuracy; the corrections for index correction, semidiameter, and dip should there- fore be applied first, and the "approximate altitude" thus, obtained should be used as an argument in entering Table 24 for parallax and refraction. SEMIDIAMETER. 307. The semidiameter of a heavenly body is half the angle subtended by the diameter of the j 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 j 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 'm Almanac. ??0§. 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 subtract! ve for the upper. Example: May 6, 1879, the observed altitude of the sun's upper limb was 62° 10' 40^'; I. C, + 3' lO''; 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. (Naut. Aim.), - 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, — 1' 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), + 0' 04" Hor. Par. (Naut. Aim.), 7" Corr., - 2 32 I. C, + 2 30 53 23 38 + 2 34 dip (Tab. 14), - 4' 23" ref. (Tab. 20 A),— 43 Corr., 86 COERECTION OF OBSERVED ALTITTTDES. Example: May 6, 1879, at 13" 24" G. M. T., the observed altitude of the moon's lower limb was 25° 30^ 3(K^; I. C, —V 30'^; height of eye, 20 feet. Required the true altitude. Obs. alt.C, 25° 30' 30^' 1st corr., 10 57 S. D. (Naut. Aim.), + 16' 42'' Hor. Par.(Naut. Aim.) 61' 10" Aug. (Tab. 18), -f 08 Approx. alt., 25 41 27 p. &r. (Tab. 24), + 53 07 True alt., 26 34 34 dip (Tab. 14), I. C, 1st corr.. Or, the following modification may be adopted: + 16 50 - 4' 23" - 1 30 - 5 53 + 10' 57" Obs. alt.C, 1st corr., Approx. alt., par., True alt.. 25° 30' 30'' 8 56 25 39 26 55 08 26 34 34 S. D., Aug., dip, ref., I. C. + 16' 42" + 08 -4- 16 50 - 4' 23" - 2 01 - 1 30 H. P., 3670" App. alt., 25° 39' log 3. 56467 cos 9. 95494 par. / 3308" \55' 08" log 3.51961 - 7 64 1st corr., + 8' 56" THE CHEONOMETER ERROR. 87 CHAPTER XI. THE OHEONOMETEK EEROR. 309. It has already been explained (art. 261, Chap. YIII) that the error of a chronometer is the difference between the time indicated by it and the correct standard time to which it is referred; and that the daily rate is the amount that it gains or loses each day. In practice, chronometer errors are usually stated with reference to Greenwich mean time. It is not required that either the error or the rate shall be zero, but in order to be enabled to determine the correct time it is essential that both rate and error be known, and that the rate shall have been uniform since its last determination. 310. Determining the Rate. — Since all chronometers are subject to some variation in rate under the changeable conditions existing on shipboard, it is desirable to ascertain a new rate as often as possible. The process of obtaining a rate involves the determination of the error on two different occasions 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 wag 0'" 48^0 fast of G. M. T. What was the rate? Error, March lO-^ 0\ + 0°' 32^ 5 Error, March 20<^ 0\ -f- 48 . Change in 10 days, i 15 . 5 Daily rate, 4- 1'.55 The chronometer is therefore gaining 1\55 per day. 311. Determining Error from Rate. — The error on any given day being known, together with the daily rate, to find the error on any other day it is only necessary to multiply the rate by the number of days that may have elapsed, and to apply the product, with proper sign, to the given error. Example: On December 17 a chronometer is 3'" 27'.5 slow of G. M. T. and losing 0'.47 daily. What is the error on December 26? Error Deo. 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 slow of G. M. T. on December 26, 3™ 3P.7. 312. It is necessary to distinguish between the signs of the chronometer correction and of the chronometer error. A chronometer fast of the standard time is considered as having a positive error, since its readings are positive to (greater than) those of an instrument showing correct time; but the same chronometer has a negative correction, as the amount must be subtracted to reduce chronometer readings to correct readings. 313. Numerous methods are available for determining the error of a chronometer in port. The principal of these will be given. BY TIME SIGNALS. 314. In nearly all of the important ports of the world a time signal is made each day at some defined instant. In many cases this consists in the dropping of a time-ball — the correct instant being given telegraphically from an observatory. In a number of places where there is no time-ball a signal may be received on the instruments at the telegraph offices, whereby mariners may ascertain the errors of their chronometers. Such signals are to be had in almost every port of the United States. The time signal may be given by a gun-fire or other sound, in which case allowance must be made by the observer for the length of time necessary for the sound to travel from the point of origin to his position. Sound travels 1,090 feet per second at 32° F., and its velocity increases at the rate of 1.15 feet per second with each degree increase of temperature. If V be the velocity of sound in feet per second at the existing temperature, and D the distance in feet to be traversed, y is the number of seconds to be subtracted from the chronometer reading at the instant of hearing the signal, to ascertain the reading at the instant the sijjnal was made. This method of obtaining the chronometer error consists in taking the difference between the standard time and chronometer time at the time of observation and marking the result with appropriate 88 THE CHRONOMETEE ERROE. Example: A time-ball drops at 5'' 0'" 0', G. M. T., and the reading of a chronometer at the same moment is 4*' 57™ 52^5. AVhat is the chronometer error? G. M. T., 5hOO"'00'' Chro. t., 4 57 52 .5 Chro. error, — 2 07 .5 That is, chronometer sloiv 2'" 07^5; chronometer correction additive. BY TRANSITS. 315. The most accurate method of finding the chronometer correction is by means of a transit instrument well adjusted in the meridian, noting the times of transit of a star or the limbs of the sun across the threads of the instrument. At the instant of the body's passage over tlie meridian wire, mark the time by the chronometer. The hour angle at the instant is 0^; therefore the local sidereal time is equal to the right ascension of the body in the case of a star, or the local apparent time is 0'' in the case of the sun's center. By con- verting this sidereal or apparent time into the corresponding mean time and applying the longitude, the Greenwich mean time of transit is given. By comparing with this the time shown by chronometer the error is found. Example: 1879, May 9 (Ast. day), in Long. 44° 39' E., observed the transit of Arcturus over the middle wire of the telescope, the time noted by a chronometer regulated to Greenwich mean time being 8'' 05'" 33^.5. Required the error. L. S. T. (R. A. *), ' 14" ]0"> IP. 71 Long., - 2 58 36 G. S. T., R. A. M. S., 9'! 0\ - Sid. int. from 0'', Reduction (Tab. 8), - G. M. T., Chro. t., Chro. fast, 2 59 . 75 Example: June 25, 1879, in Long. 60° E., observed the transit of both limbs of the sun over the meridian wire of the telescope, noting the times bv a chronometer. Find the error of the chronometer on G. M. T. Transit of western limb, S*- 04'" 02^ 5 Eq. t., 2"» 16^ 72 Tran-it of eastern limb, 8 06 20 . — — — H. D., + 0^532 Chro. time, loc. app. noon, 8 05 11 .25 Long., — 4*" 11 3 11 07 35 42, .71 .69 8 03 1 53, 19. ,02 ,27 8 8 02 05 33. 33. .75 ,50 8 05 11 . ,25 O'' 00™ 2 ' 00^ 14 .59 4 02 00 14 00 .59 8 8 02 05 14 11 , .59 ,25 L. A. T., loc. app. noon, 0" 00™ 00^ Corr., — 2M28 Eq. t., Eq. t., 2"' 14^59 L. M. T., lo(;. app. noon, 02 14 .59 Add to apparent thxsie. Long., G. M. T., loc. app. noon, Chro. time, loc. app. noon, Chro. fast, 2 56 . 66 BY A SINGLE ALTITUDE (TIME SIGHT). 316. The problem involved in this solution, by reason of its frequent application in determining the longitude at sea, is one of the most important ones in Nautical Astronomy. It consists in finding the hour angle from given values of the altitude, latitude, and polar distance. The hour angle thus obtained is converted by means of the longitude and equation of time in the case of the sun, or longi- tude and right ascension in the case of other celestial bodies, into Greenwich mean time; and this, com- pared with the chronometer time, gives the error. SIT. It should be borne in mind that the most favorable position of the heavenly body for time observations is when near the prime vertical. When exactly in the prime vertical a small error in the latitude produces no appreciable effect. Therefore, if the latitude is uncertain, good results may be obtained by observing the sun or other body when bearing east or west. If observations are made at the same or nearly the same altitude on each side of the meridian and the mean of the results is taken, various errors are eliminated of which it is otherwise impossible to take account, and a very accurate determination is thus afforded. 318. With a sextant and artilicial horizon or good sea horizon, several altitudes of a body should be observed in quick succession, noting in each case the time as shown by a hack chronometer or com- paring watch whose error upon the standard chronometer is known. Condensing the observation into THE CHRONOMETER ERROR. 89 a brief interval justifies ttie assumption that the altitude varies uniformly with the time. A very satis- factory method is to set the sextant in advance at definite intervals of altitude and note the time as con- tact is observed. 319. Correct the observed altitude for instrumental and other errors, reducing the apparent to the true altitude. If the sun, the moon, or a planet is observed, the declination is to be taken from the Nautical Almanac for the time of the observation. If the chronometer correction is not approximately known and it is therefore impossible to determine the Greenwich mean time of observation with a fair degree of accu- racy, the first hour angle found will be an approximate one; the declination corrected by this new value of the time will produce a more exact value of the hour angle, and the operation may be re- peated until a sufficiently ]irecise value is determined. 3 20. In figure 41 there are given: AO = h, the altitude of the body O; Fig. 41. DO = d, the declination; and QZ = L, the latitude of the place. In the astronomical triangle POZ there may be found from the foregoing: ZO = z, the zenith distance of the body, = 90° — h; PO =p, the polar distance, = 90° ± d; and PZ = co-L, the co-latitude of the place, =90° — L. From this data it is required to find the angle OPZ, the hour angle of the body,= t. oy the formula: . cos I {h+'L+p) sin ^ {Ij + p — h) ^^^ *^- cosLsinja If we let .s = J {h + h-\-p), this becomes: /" / r \ / /* \ 1 / 2 \ JXa^ ■^ * \ »^-^ P / This is given sin 5 < = s/ sec L cosec p cos s ein (s — ^). The polar distance is obtained by adding the declination to 90° when of different name from the latitude and subtracting it from 90° when of the same name. Like latitude and altitude it is always positive. If the sun is the body observed, the resulting hour angle is the local apparent time and is to be taken from the a. m. or p. m. column of Table 44 according as the altitude is observed in the forenoon or afternoon. If the moon, a star, or a planet be taken, the hour angle is always found in the p. m. column. Local apparent time as deduced from an observation of the sun is converted to local .mean time by the application of the equation of time; then, by adding the longitude if west, and subtracting it if east, the Greenwich mean time is obtained. The hour angle of any other body, added to its right ascension when it is west of the meridian at observation or subtracted Iherefrom when east, gives the local sidereal time, which may be reduced to Greenwich sidereal time by the application of the longitude, and thence to Greenwdch mean time by methods jireviously explained. A comparison of the Greenwich mean time with the chronometer time of sight gives the error of the chronometer. Example: January 20, 1879, p. m., in Lat. 48° 41^ 00^^ S., Long. 69° 03^ 00^^ E., observed a series of altitudes of the sun with a sextant and artificial horizon; mean double altitude, 59° 03^ 10^^, images approaching; mean of times by comparing watch, 4*" 40"" 56^; C — W, 7'' 23'" 25*; index correction,— 1^30^''; approximate chronometer correction, —0"' 10^ What was the exact chronometer error? Obs. 2 alt. Q, 59° 03^ 10'^ \\\\' ^v. W. T., C— W, T. 4h 40ni 5gs 7 23 25 Obs. I. C. Chro. t., App. C. C, 0. 04 21 - 10 Corr App. G M. 04 11 S. D., p. & r. Corr., — 1 30 2)59 01 40 29 + 30 50 14 43 29 45 33 + 16^ 17'^ - V ?>\" Dec, 20° 08^ 26'''. 6 S. Eq. t, ll-" 14^60 H. D., G. M. T. + 32'^. 5 0\07 H. D., + 0^74 G. M. T., 0\07 Corr., -f 2". 21h Corr., + 0».052 Dec, 20° 08' 24''. 3 S. 69° 51' 36" Eq. t, ll"- 14^7 ( Jrfd to apparent time. ) + 14' 43" 90 THE CHEONOMETER ERROR. h L 29° 48 69 45^ 33'^ 41 00 51 36 sec cosec cos sin .18031 .02740 9.43631 9.84483 L. A. T., Eq. t., L. M. T., Long. , G. M. T., Chro. t, Chro. slow. 4h + 29™ 11 '46'. 7 14.7 P 4 —4 41 36 01.4 12.0 ■2)148 18 09 8 »—h 74 44 09 05 23 32 04 04 49.4 21.0 2) 19.48885 , 00 28.4 'L. A.T., 4''29'»46\7 sin ^ t 9.74442 Example: May 18, 1879, p. m., in Lat. 8° 03^ 22'^ S., Long. 34° 5r 57'^ W., observed a series of altitudes of the star Arcturus, east of the meridian, using artificial horizon; mean double altitude, 60° 10^; mean watch time, 6" 50"' 32^; C— W, 2" 20"" 59^5; I. C, +2^ OO'''. Find the true error of the chronometer. W. T., 6" 50"' 32' Obs. 2 alt. *, 60° 10^ 00''' E. A. *, 14'> 10-" 1P.7 C— W, 2 20 59.5 I. C, -f 2 00 Dec. *, 19° 48^ 33''''.5 N. Chro. t., 9 11 31.5 2)60 12 00 30 06 00 ref., - 1 41 p, 109° 48^ 34" h, 30 04 19 h 30° 04^ 19''' R. A. *, 14»' lO-" 11».7 L 8 03 22 sec .00431 H. A., - 3 35 41 p 109 48 34 cosec .02650 L S T 2)147 56 15 Long., "' 73 58 08 cos 9.44116 G. S. T., 43 53 49 sin 9.84096 R. A. M. S., 0^ H. A. 3" 35'° 41» E. sin J t 9.65647 2)19.31293 Sid. int. from 0^, Red. (Tab. 8), G. M. T., Chro. t.. 10 + 2 34 19 30.7 27.8 12 - 3 53 43 58.5 11.7 9 10 1 46.8 30.2 9 9 09 11 16.6 31.5 Chro. fast, 2 14 .9 BY EaUAL AliTITTJDES. 321. The method of observing eqrml altitudes of the same body on opposite sides of the meridian is usually employed for accurate determinations of the chronometer error when the method of transits is not available. In the case of a star, the mean of the two chronometer times corresponding to the equal altitudes is the chronometer time of transit; but in the case of the sun the mean of these times differs somewhat from the time of transit, since, in consequence of the change of the sun's declination between the observations, the equal altitudes do not occur at equal intervals before and after the transit. The small correction necessary, when the sun is observed, to reduce the mean of the times to the time of transit is called the equation of equal altitudes. 322. Equal Altitudes op the Sun.« — On shore, at a place whose longitude is accurately known, and whose latitude is approximately know^n, observe, with an artificial horizon, the same altitude both before and after meridian passage, as near the prime vertical as convenient when the altitude is more than 10°, noting the times. In low latitudes the method of equal altitudes will often give very accurate results, even when the observations are quite near the meridian. It is most convenient, as w^ell as conducive to accuracy, to take the observations in series, setting the sextant in advance of the altitude and marking the time at the instant that the contact is observed; about five or seven sights may compose a series, and several series may be observed, with the images of the sun alternately approaching and separating; thus the mean of the results (working each series of sights separately) will eliminate various possible errors. Ten minutes of double altitude will usually be found a convenient interval for observing. The sights may be taken on opposite sides of the meridian for either upper or lower transit. If at upper transit, the first altitudes are taken in the forenoon and the times recorded; then in the afternoon the times corresponding to the same altitudes are observed, the last altitude taken in the morning being the first to come on in the afternoon; series taken with separating images in the forenoon should be observed with approaching images in the afternoon, and the reverse. If the time of lower transit i.s to be determined, the first set of sights is taken in the afternoon of one day and the second set in the forenoon of the next, care being taken as before to observe with images moving in opposite directions on opposite sides of the meridian. a Chauvenet's method. THE CHKONOMETER ERROE. 91 323. The mean of the a. m. times call the A. M. Chronometer Time, the mean of the p. m. times, the P. M. Chronometer Time. If, instead of noting the times by the chronometer, a watch is used (compared with the chronometer both before and after each observation), it will generally be found necessary to make an allowance for its gain or loss on the chronometer, so as to obtain the exact difference between the watch and chronometer at the instant of observation. The difference applied to the mean of the watch times gives the mean chronometer time the same as would have been found by employing the chronometer directly. The half sum of the A. M. and P. M. Chronometer Times is the Middle Chronometer Time; the P. M. minus the A. M. time in the cas3 of observations for upper transit, or the A. M. minus the P. M. time for lower transit, gives the Elapsed Time. Twelve hours should be added to the chronometer time at second observation in any case where the chronometer has passed XII'' during the interval between sights. Take from the Nautical Almanac, page I, the sun's declination, the hourly difference of declination, and the equation of time, reducing each to the instant of local apparent noon by applying the differences due to the longitude. Mark north latitude and declination +, south latitude and declination — . Mark hourly difference of declination when toward north +, when toward south — . Enter Table 37 with the elapsed time, and take out log A and log B, prefixing to each its proper sign as given in the taV)le 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). Pretix 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 observ^ations 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*' O" 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 with a ciironometer regulated to Greenwich mean time. What is the error of the chronometer? A. M. COMPARISONS. Chro., Watch, 0-W, Chro., Watch, C-W, 2h 22m 30 Chro., 8 52 02 Watch, 5 30 28 C-W, 2t' 56" >30' Chro., 9 26 02 Watch, 5 30 28 C-W, WATCH, A . M. ALTS. 9h 12.1. '30^ 91° 00' 12 65 10 13 20 20 13 45 30 14 10 40 p. M. COMPARISONS. 81' 04° 1, 2 34 -SO" 01 Dec, H. D. at Long., Corr. , Dec, 9°00'54".1N. noon,+ 54".32 + 5''.43 5 30 29 8h 33" \, 3 03 '30» 01 , |294".9« 1 4'.55".0 5 30 29 9° 05' 49" N. H. D. (13th),+54".40 H. D. (14th), +54 .03 Diff., 24hrs.,~ .37 Diff., 1 hr., -0".015 Diff., 5''.43, -0 .03 H.D.atnoon,+54",32 Mean, W. T., A. M., C-W, A. M. Chro. T., r. M. Chro. T., Mid. Chro. T., Eq. eq. nit., Chro. t. L. A. Noon, Kq. t., Chro. t. L. M. Noon, Long., Chro. fast. 9hl3" 20' + 5 30 28 2 43 48 + 8 15 24 2)10 59 12 5 29 3G 7.1 5 29 28.9 - 31.5 5 28 57.4 — 5 25 42.0 WATCH, P. M. 2h 45m 45h 45 20 44 55 Tab. 37 log A(-)9.4445 44 30 H. D. +54".32 log (4-)1.7350 44 05 Lat. +30° 2.5' tan (+) 9.7687 rf 4 9°6' Mean, W. T., P. M., 2'' 44™ 55» 1st Part— «».88 log (-)0.9482 C-W, + 5 30 29 2d Part+l .81 P, M. Chro. T., A. M. Chro. T.. 8.15 24 Kq.eq.l 7 ^ - 2 43 48 alt. i Klapsed Time, 5 31 36 Eq. t., H. D., Long., Om 35».02 + 0».65 + 5h.43 logB( + )9.3193 log ( + ) 1.7350 tan ( + )9.2045. log ( + ) 0.2688 Corr., Kq. t., {Minus to viean time.) 03 15.4 92 THE CHRONOMETER ERROR. 324. A quicker method of solving the same problem « is available when results are not required to be accurate to the fraction of a second. If // is the change of altitude in minutes of arc, due to the total change in declination in the time elapsed between sights (the latitude and hour angle remaining the same), and V the number of seconds it requires for the sun to change its altitude one minute of arc, then: Equation of equal altitudes = o ^^^ 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 t\ When the sights are taken on opi>osite sides of the upper meridian t^ is minus; for the lower meridian it is plus. When the artificial horizon is used, if t^ is computed on a basis of the change of the double altitude, its value is only half of the true one and the second term of the equation becomes // X t^ instead of as given above. The example given in illustration of the preceding method when worked by this method is as follows: Change in declination between sights = H. D. X elapsed time = 54'''.32 X 5''.53 — 300'''. Change in altitude due to 100^'' declination (Tab. 25) = + 56'^. 56X30Q_^^ " ~ ' 100 X 60 ~ ' " •*"• / _ 2''45"'4 5^ - 2'^44»'05^ ^ W^ _ ^ - ~ 91° 4^" — 91° OO' " ~ 40' ~ ~ ^'•^• „ Eq. equal alt. = + 2.80 X — 2^5 = — 7«.-00. 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 of 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 equai 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. Exajiple:— 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. Altitudes. Chro. P. M. 7" 32'" 10^5 125° 30' 11" 34"' 20^3 7 32 35.0 40 11 33 56.0 7 32 59.3 50 11 33 32.0 A. M. Chro. t., 7 32 34.9 P. M. Chro. t., 11 33 56.1 F. M. Chro. t, 11 33 56.1 2)19 06 31.0 L. S. T.(R. A. *), 16" 22'" 03\5 ' Long., — 1 13 54.7 Chro. t Transit, 9 33 15 .5 G. M. T. Transit, 9 59 30.9 G. S. T., 15 08 OS. 8 R. A. M. S., 0", — 5 05 59.4 Chro. slow. 26 15 .4 Sid. int. from 0", 10 02 09 .4 Red. (Tab. 8), — 1 38.5 G. M. T., 10 00 30 .9 a Suggested by Commander W. E. Sewell, U. S. Navy. THE CHKONOMETER ERROR. 93 32§. Degree of Dependence. — An error of h' 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 will still be correct. Hence, we conclude that by this method the chronometer may be accurately rated at a place whose latitude and longitude are both imperfectly known. The chief source of error is in the observation itself. The best observers with the sextant can not depend on the noted time of a 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 meridian 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 tlience be found. Let 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 equatir, but south of the zenith; QA — d, its declination; AS = h, itd altitude; and ZA = 2 = 90°— /i, its zenith distance. From the figure we have: QZ = QA + L^rf + 2. AZ, By 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', k.". In case the body is below the pole, as at kf" — 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=J9+/l. 330. A common practice at eea 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 is 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. 0. (sign reversed), Chro. time, C-W, Watch time noon, 0^ 00"' 00» L. S. T. transit. Long. (+ if west), G. S. T., K. A. M. S., 0^ Sid int. from '', Red. (Tab. 8), G. M. T., C. C. (sign reversed), 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 from the Nautical Almanac for the time of meridian passage, having regard for its proper sign or name. The algebraic sum of the declination and zenith distance will be the latitude. Therefore, add together the zenith distance and the declination if they are of the same name, but take their difference if of opposite names; this sum or difference will be the latitude, which will be of the same name as the greater. Example: At sea, June 21, 1879, in Long. 60° W., the observed meridian altitude of the sun's lower limb was 40° 4^; sun bearing south; I. C., + 3^ 0'^; height of the eye, 20 feet; required the latitude. Obs. alt., 40° 04^ 00'^ S. D., + 15^ 46^'' Dec, 23° 27^ 20^''.5 N. ah ^J. >M»«-n. Corr., + 13 21 I. C, + 3 00 • H. D., + 0'^.32 Long., 4^ h, 40 17 21 dip p. <&r.. + 18 46 2, 49° 42^ 39''' N. 23 27 22 N. - 4' 23'^ , - 1 02 Corr., + F''.28 L, 73 10 01 N. — 5 25 Corr., + 13' 21'' Dec, 23° 27' 22" Example: At sea, April 14, 1879, in Long. 140° E., the observed meridian altitude of the sun's lower limb was 81° 15' "30"; sun bearing north; I. C.,— 2' 30"; height of the eye, 20 feet. Obs. alt, 81° 15' 30" S. D., + 15' 59" Dec, 9° 22' 35".4 N. Corr., + 8 59 dip, — 4 23 H. D., + 54'^.03 h, 81 24 29 p.&r.,— 07 Long.,— 9\33 LC, Zy 8° 35' 31" S. ^ f 504".l d, 9 14 11 N. - 7 00 ^^^^■' \8' 24".l 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 2, 59° 34' 48" S. d, 18 50 49 N. L, 40 43 59 S. Corr., + 12' 02" Example: January 1, 1879, the observed meridian altitude of Sirius was 58° 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 LC, dip, ref., Corr., + 5' 00" - 4' 02" - 43 h, 53 23 55 d, 36° 16 36' 05" N. 33 04 S. - 4 45 + 0' 15" L, 20 03 01 N. Example: June 13, 1879, in Long. 65° W., and in a high northern latitude, the meridian altitude of the sun's lower limb was 8=" 16' 10", below the pole; height of the eye, 20 feet; I. C, 0' 00". Greenwich apparent time of lower culmination, June 13, 16'' 20"" ( =Long. +12''). Obs. alt, 8° 16' 10" S. D., + 15' 47" Dec, 23° 13' 03".8 N. Corr., + 5 12 dip, - 4 23 H. D., 8 21 22 p.&r., - 6 12 G. M. T. z, 81° 38' 38" S. - 10 35 p^^^ , / 180°-tZ, 156 44 36 N. ^^^^'^ "^ I Corr., + 5 12 75 05 58 N. Dec, 23° 15' 24" N. Alternative method. h, 8° 21' 22" p, p, 66 44 36 8".58 16" .33 { 2' 140".5 20". 5 23° 15' 24" 66° 44' 36" 75 05 58 N. 180°-(7, 156° 44' 36" 96 LATITUDE, h, 59° 18' 00" N. S. N. Obs. alt., . I. C, S. D., Aug., dip, 1st Corr., Approx. alt., p.cfcr. (Tab. 24), h, 59° 06' 40" d, 30° 42' 00' 4 51 06 + 2' 00" — 16' 03" 14 4 16 L, 25 50 54 - 20 33 - 18' 33" 58° 48' 07" + 29 53 59 18 00 G. M. T., Gr. trans., b^ 27^.0 Corr. for Long (Tab. 11),+ 11 .0 L. M. T., local trans., 5 38 .0 Long., + 5 20 .0 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, + 2' (Y'; height of the eye, 19 feet. Dec. (lib), 4°51'36".5 S. M. D., - No. min., — Corr., + Dec, Hor. Par., G. M. T., local trans., + 10 58 .0 15" 2" '.07 .0 30'''.1 58' 46".3 Example: At sea, September 16, 1879, in Long. 75° E., the observed meridian altitude of Jupiter was 51° 25^ 24^^ bearing north; I. C, +3' (V'; height of the eye, 16 feet. G. M. T., Gr. trans., lO*- 49'>'.8 Corr. for Long., + .9 Obs. alt., 51° 25' 24' par.. + 0' 01" Corr, - 1 41 'S. I.e., dip, + 3 + 3 -3' 00 h, 51 23 43 01 z, 38° 36' 17" 55" d, 10 44 59 S. s. ref., -4 47 L, 49 21 16 42 — — Corr., , - 1' 41" L. M. T., local trans., 10 50.7 Long., - 5 00 .0 G. M. T. local trans., 5 50 .7 Dec, 10°44'20".5 S. H. D., G. M. T., - 6".58 5h.84 Corr., 38".43 Dec, H. P., par. (Tab. 17) , 10° 44' 53" S. 2".2 1" 333. Constant. — In working a meridian altitude, especially the daily noon observation of the sun, it is frequently a convenience to so arrange the terms of the problem 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 being necessary only to add or subtract the altitude. It is assumed that the noon longitude will be sufficiently accurately known in advance to enable the navigator to correct the declination ; also the approximate meridian altitude to correct the parallax and refraction; if the latter is not known, it may readily be found from the declination and approximate latitude. Generally speaking, Lat. = Zenith distance + Dec, = 90° — True alt. + Dec, = 90° - (Obs. alt. + Corr.) + Dec, = (90° + Dec - Corr.) - Obs. alt., in which the quantity (90° + Dec. — Corr.) may be termed a Constant for the meridian altitude of the day, as it remains the same regardless of what the observed altitude may prove to be. The constant having been worked up before the observation is made, the latitude will be known as soon as the observed altitude is applied. To avoid the confusion that might arise from the necessity of combining the terms algebraically according to their different names, it may be convenient to divide the problem into four cases and lay down rules for the arithmetical combination of the terms, disregarding their respective names as follows: Case I. Lat. and Dec. same name, Lat. greater, + 90° + Dec. — Corr. — Obs. alt. Case II. Lat. and Dec. same name, Dec. greater, — 90° + Dec + Corr. -|- Obs. alt. Case III. Lat. and Dec. opposite names, + 90° — Dec — Corr. — Obs. alt. Case IV. Lat. and Dec. same name, lower transit,-]- 90° — Dec. + Corr. + Obs. alt. The correctness of such an arrangement will become readily apparent from an inspection of figure 42. The assumption has been made that the correction to the observed altitude is positive; when this is not true the sign of the correction must be reversed. As examples of this method, the first, second, third, and fifth of the examples previously given illustrating the meridian altitude will be worked, using the constant; the details by which Corr. and Dec. are obtained are omitted, being the same as in the originals. Dec, Corr. 1st Example. Case I. + 90° 00^ 00'' + 23 27 22 - 13 21 Dec, Corr. , 2d Example. Case II. -90°.00^00" + 9 14 11 + 8 59 Dec, Corr., 3d Example. Case III. +90° 00' 00''' -18 50 49 - 12 02 Dec, Corr. , 5th Example. Case I r. +90° 00' 00" -23 15 24 5 12 Constant, +113 14 01 Obs. alt., — 40 04 00 Constant, Obs. alt.. -80 -81 36 50 15 30 Constant, + 70 57 09 Obs. alt., -30 13 10 Constant, +66 49 48 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 tlie 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; /i = 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 = /; -]- af; 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 af corresponding to the a thus found and to the interval, in minutes and seconds, from meridian passage. This quantity will represent the amount necessary to reduce the corrected altitude at the time of observation to the corrected altitude at the meridian passage; it is always additive when the body is near upper transit, and always to be subtracted when near lower transit. If the mean of a number of sights is to be taken, determine each reduction separately, take the mean of all the reductions, and apply it to 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 fcorrection 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 ob.'^ervation 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 between watch time of transit and watch time of observation gives the watch time — that is, the mean time — elapsing between transit and observation. A fixed star covers in that time an angle corresponding to the sidereal and not to the mean time interval, and a reduction should be made accordingly to give its true hour angle at the instant of observation. A planet's hour angle should be corrected in the same way (for we may disregard its very small change in right ascension). The correction may be entirely neglected in the case of the sun, as the difference between mean and apparent time intervals is immaterial. The reduction of the hour angle in the case of the moon becomes rather cumbersome, so much so that it is better to find the hour angle of this body by the more usual method of converting watch time to G. M. T., and thence to L. S. T., and finding the difference between the latter and the R. A.; an additional reason for this is that the G. M. T. of observation must be known exactly, with the moon, for the correction of the declination (art. 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 a are given when the altitudes are above 86° or below 6°, as the method of reduc- tion to the meridian is not accurate when the body transits very near the zenith, and the altitudes themselves are questionable when very low. In case it is desired to find the change of altitude in one minute from noon for conditions not given in the tables, it may be computed by the formula: _ 1^^9635 cos L cos d sin (L — d) In working sights by this method where great accuracy is required, as in determining latitudes on shore for surveying purposes, it is well to compute the a rather than to take it from the table, as one is thus enabled to employ the value as found to the second decimal place. Due regard must be paid to the names of the declination and latitude in working this formula; if they are of opposite names, the declination is negative, and L and d should be added together to obtain I^d. 337. Table 27 contains values of af up to the limits within which the method is considered to apply with a fair degree of accuracy. It must not be understood that the plan of reduction to the meridian is not available for wider limits, but it would seem preferable to employ the " will have different directions of application according to the position of the body relatively to the observer. From a knowledge of the approximate latitude, the method of com- bining them will usually be apparent; it is better, however, to have a definite plan for so doing, and this may be based upon the following rule: Mark q)" north or south, according to the name of the declination; mark q)' north or south, accord- ing to the name of the zenith distance, it being north if the body bears south and east or south and west, and south if the body bears north and east or north and west. Then combine cp" and '^ for declination and q/ for zenith distance, the problem takes the form of a meridian altitude; indeed, the method resolves itself into the finding of the zenith distance and declination of that point on the meridian at which the latter is intersected by a perpendicular let fall from the observed body. The time should be noted at the instant of observation, from which is found the local time, and thence the hour angle of the celestial object. 100 LATITUDE. If the sun is observed, the hour angle is the L. A. T. in the case of a p. m. sight, or 12'' - L. A. T. for an a. m. sight. If any other body, the hour angle may be found as hitherto explained. Example: June 7, 1879, in Lat. 30° 25' N., Long. 81° 25' 30" W., by account; chro. time, 6'' 22"' 52'; obs. 75° 13', bearing south and east; I. C. — 3' 00"; height of the eye, 25 feet; chro. corr. —2"' 36'. Find the latitude. Chro.t., C.C, 6" 22-" 52' - 2 36 Obs. alt. Q, 75° Corr., + 13' 00" 7 40 Dec, H.D.. G. M. T. Corr., Dec, .01310 9.62317 + , + 22° 45' 09". 9 N. 14". 6 6''.3 G.M.T., Eq.t, 6 20 16 + 1 26 /(, 75 20 40 S.D., + dip, — p. & r., — I.e., 15' 48" 4' 54" 14 3 00 91". 98 1' 32" 22° 46' 42" N. G.A.T., Long., 6 21 42 - 5 25 42 L.A.T.= , / 0" 56"' 00» E. ~^' \14° 00' 00" t d h Cf/ Lat. - 8 08 Corr., + 14° 00' 00" 22 46 42 75 20 40 23 24 07 N. 7 02 30 N. 30 26 37 N. 7' 40" sec tan tan cosec .41210 9.63627 » sin 9.98563 sin 9.59898 cos 9.99671 Eq.t., H.D., - G.M.T.,+ 1"' 28'. 85 0'.46 6\3 Corr., — 2'. 85 Eq.t., 1"'26'. {Add to 7Hea?i time. ) Example: May 28, 1879, p. m., in Lat. 6° 20' S. by account. Long. 30° 21' 30" W.; chro. time, 7" 35™ 10'; observed altitude of moon's upper limb, 75° 33' 00", bearing north and east; 1. C, —3' 00"; height of eye, 26 feet; chro. fast of G. M. T., 1"" 37'. 5. Required the latitude. Chro. t., C. C, 7>"35" - 1 '10» 37.5 G. M. T., R. A. M. S., Red. (Tab. 9), 7 33 + 4 22 + 1 32.5 37.3 14.5 G. S. T., R. A. C- 11 57 -10 22 24.3 17 H. A. from Gr. Long., 1 35 2 01 07 26 Obs. alt.'^, S. D., Aug., dip, I. C, 1st Corr., Approx. alt., p. cfcr.(Tab.24), + 75° 33' 00" - 15' 51" - 16 5 00 - 3 00 - 24 07 75° 08' ,53" + 14 37 R. A. C lOb 21'" 07=.78 Dec, M. D., + No. mill., 2».06 33'>'.54 R. A., 69^.09 lm093 lOh 22"> 17' M. D., No. mill., Corr., Dec, 6° 49' 52". 4 N. 14". 46 33"'.54 _f 485" I 8' 05" 6° 41' 47" Oh 26>n 19» E. 6° 34' 45" 75 23 30 Hor. Par., 68' 03" h Lat. 6° 34' 45" 6 41 47 75 23 30 6 44 26 N. 13 05 40 S. sec tan .00286 9.06973 cosec .93324 tan 9.07259 sin sin 9.98573 9.06959 9.98856 6 21 14 S. Example: August 6, 1879, p. m., in Lat. 52° 47' S. by D. R., Long. 146° 32' E., observed altitude of Achernar, near lower transit, 24° 01' 20" bearing south and vi'est; watch time, 6'' 48"' 22'; C— W, 9" 46"" 27'; chro. corr. on G. M. T., + 1"' 57'; height of eve, 18 feet; I. C. + T 00". Find the latitude. Watch time, C-W, Chro. t., C. C, G. M. T., 5^ R. A. M. S., Red. (Tab. 9), G. S. T., R. A. *, H. A. from Gr., Long., H. A., 6" 48"' 22' + 9 46 27 + 4 34 1 49 57 + -1- 16 36 8 54 2 46 39.8 43.7 1 34 1 33 09.5 15.3 00 9 46 54 W. 08 E. 9 47 02 W. Obs. alt. Corr., *, 24° 01' 20" - 5 19 R. A. *, 1" 33"* 15'. 3 Dec, 57° 50' 28" S. h 23 56 01 LC, dip, ret, + 1' 00" - 4' 09" - 2 10 6 19 Corr., — 5' 19" 2" 12"' 58' 33° 14' 30" t d 33° 57 23 -cf/' 117 64 14^ 30^^ 50 28 56 01 44 18 S. 54 15 N. LATITUDE. sec .07760 tan .20153 coeec sin sin cos .07233 h 180°- tan .27913 9. 60818 9. 94699 Cf/ 9. 62750 Lat. 52 50 03 S. 101 BY THE POLE STAR. 340. This method, confined to northern latitudes, is available when the star Polaris and the hori- zon are distinctly visible, the time of the observation being noted at the moment the altitude is measured. Two methods will be given. The first is sufficiently precise for nautical purposes, involving the computation of the formula: Jj — h — p cos t, in which, h = true altitude, deduced from the observed altitude; p = polar distance = 90° — d, the apparent declination being taken from the Nautical Almanac for the date; t = star's hour angle. Find the right ascension and declination of Polaris from the Nautical Almanac; then find the hour angle in the usual way. To the log cosine of the hour angle add toe logarithnj of the polar distance in minutes; the number corresponding to the resulting logarithm will be a correction in minutes to be subtracted from the star's true altitude to find the latitude. Attention must be paid to the sign of the correction p cos t. If t is more than 6'' and less than 18**, the sign of cos < is — ; hence the formula becomes arithmetically: L = /i + p cos t. Example: June 11, 1879, from an observed altitude of Polaris the true altitude was found to be 29° 5' 55'^ The time noted by a Greenwich chronometer was 13'' 41"' 26'; chro. corr. — 2" 22"; Long. 5h 25." 42S w. h, 29° 05^ 55'^ E. A. >j<, 1" 14'° 04» ;) cos t, + 1 19 54 Dec, 88° 39^ 47^^ N. Chro. time, C. C, + + > 13" 41"' 2 '26' 22 G. M. T., ll'i, R.A.M.S., Red. (Tab. 9) , 13 39 5 17 2 04 49 15 G.S.T., B.A. *, 18 59 1 14 08 04 H. A. from Gr. Long., 17 45 5 25 04 W. 42 W. H. A., 12 19 22 W. t. 11" 40" 1 75° 09^ ' 38' E. .30'^ Lat., 30 25 49 N. r 1° 20^ P' \ 8(y.2 p, 80^2 log 1. 90417 13^' .90 i, 175° 09^ 30^'' cos ( ~) 9. 99845 [ \ J ""i ; /,\ ^"'c %•' LATITUDE. mean of the times may be used. The means of these two corrections may always be used for finding the third and fourth corrections; and these four quantities may be combined with the mean of the altitudes. If the nearest 1(K^ suffices for each, the corrections may be taken out for the nearest arguments without interpolation, and all but the first may thus be taken out when a precision of 3^'' is required. If a precision of V is sufficient for each correction, as is ordinarily the case at sea, an hour angle within 3" will suflBce for A; C and D may be neglected, and B used only when the altitude exceeds 47°. Example: January 1, 1903, about 9 p. m., Longitude 79° 54^ 07^^ W., observed double altitude of Polaris with artificial horizon, 81° 57' 20^''; chro. time l*" 55™ 12^; chro. corr. on G. M. T. -f 1" 07'; I. C. — O'SO^''. (The necessary quantities, taken from the Nautical Almanac for 1903, are given below.) Required the latitude. Chro. time, 1" 55™ 12' Obs. 2 alt. *, 81° 57' 20^' R. A. *, 1" 24™ 33'.3 C. C, + 1 07 I. C - 50 ^ Dec, 88° 47' 42" N. G. M. T., 13 56 19 R. A. M. S., +18 39 50.9 Red. (Tab. 9), + 2 17.4 ref . , G. S. T., 8 38 27.3 R. A. *, 1 24 33.3 h, A, H.A.fromGr., 7 13 54 W. B, Long., 5 19 37 W. C, H. A., 1 54 17 W. 2)81 56 30 40 58 15 — 1 07 40 57 08 — 1 03 13.9 + 08.9 00.0 — 15.7 TaL, 89 53 47 N- LONGITUDE. 1 03 CHAPTER XIIL LONGITUDE. 342. The longitude of a position on the earth's surface is measured bv the arc of the equator intercepted between the prime meridian and the meridian passing through the place, or by the angle at the pole between those two meridians. Meridians are great circles of the terrestrial sphere passing through the poles. The prime meridian is that one assumed as the origin, passing through the location of some principal observatory, such as Greenwich, Paris, or Washington. That of Greenwich is the prime mendian not only for English but also for American navigators, and those of many other nations. Secondary meridians are those connected with the primary meridian, directly or indirectly, by exchange of telegraphic time signals. Tertiary meridians are those connected with secondaries by carrying time in the most careful manner with all possible corrections. Longitude is found by taking the difference between the hour angle of a celestial body from the | prime meridian and its hour angle, at the same instant, from the local meridian. In determinations | ashore the hour angle from the prime meridian may be found either from chronometers or from I telegraphic signals; the local hour angle may be found by transit instruments or by sextant. In determinations at sea the chronometer and sextant give the only means available. DETERMINATION ASHORE. 343. Telegraphic Determination of Secondary Meridians. — In order to locate with accuracy ^ the positions of prominent points on the coasts, it is necessary to refer them, by chronometric measure- ments, to secondary meridians of longitude which have been determined with the utmost degree of care- Before the establishment of telegraphic cables, this was attempted principally through the observa- tion of moon culminations, which seemed always to carry with them unavoidable errors, or by trans- porting to and fro a large number of chronometers between the principal observatory and the position to be located; and in this method it (tan be conceived that errors would be involved, no matter how thorough the theoretical compensation for error of the instruments. By the aid of the electric telegraph, differences of longitude are determined with great accuracy, and an ever-increasing number of secondary meridional positions are thus established over the world; these afford the necessary bases in carrying on the surveys to map correctly the various coast lines, and render possible the publication of reliable and accurate navigators' charts. 344. To determine telegraphically the difference of longitude between two points, a small observa- "^ tory containing a transit instrument, chronograph, break-circuit sidereal chronometer, and a set of telegraph instruments is established at each of the two points, and, being connected by a temporary wire with the cable or land line at each place, the two observatories are placed in telegraphic com- munication with each other. By means of transit observations of stars, the error of the chronometer at each place on its own local sidereal time is well determined, and the chronometers are then accurately compared by signals sent first one way and then the other, the times of sending and receiving being very exactly noted at the respective stations. The error of each chronometer on local sidereal time being applied to its reading, the difference between the local times of the two places may be found, and consequently the difference of longitude. The time of transmission over the telegraph line is eliminated by sending signals both ways. By the employment of chronometers keeping sidereal time, the computation is simplified, though mean-time chronometers may be used. 345. Establishment of Tertiary Meridians. — Let it be supposed that the meridional distance ^ between A and B is to be measured, of which A is a secondary meridional position accurately deter- mined, and B a tertiary meridional position to be determined. If possible, two sets of observations should be taken at A to ascertain the errors and rates of the chro- nometers. The run is then made to B, and observations made to determine local time, and hence the difference of longitude; and on the same spot altitudes of the sun, or of a number of pairs of stars, or both, should be taken to determine the latitude. Now, if chronometer rates could be relied on to be uniform, this measurement would suffice, but since variations may always arise, the run back to A should he made, or to another secondary meridio- nal position, C, and new rates there obtained. Finally, the errors of the chronometers on the day when the observations were made at the tertiary position should be corrected for the loss or gain in rate, and for the difference of the errors as thus determined. When opportunity does not permit obtaining a rate at the secondary meridional station or stations, both before and after the observations at B, the navigator may obtain the errors only, and assume that the rate has been uniform between those errors. A modification of the foregoing method that may sometimes prove convenient is to make the first and third sets of observations at the position of the tertiary meridian, and the intermediate one at the second- ary meridian ; in this case the error will be obtained at the secondary station, and the rate at the tertiary. 104 LONGITUDE. Example: A vessel at a station A, of known longitude, obtained chronometer errors as follows: May 27, noon, chro. slow, 7'" 18^9, June 3, noon, chro. slow, 7 12 .7; then proceeding to a station B a series of observations for longitude was taken on June 17; after which, returning to A, the following errors were obtained: July 3, noon, chro. slow, 7" 00^7, July 10, noon, chro. slow, 6 59 .8. Required the correct error on June 17. May 27, —7"' 18^9 June 3, —7 12.7 July 3, -7"' 00^7 July 10, -6 59 .8 Change, + 6.2 Daily rate, + 0^.89 Change, + .9 Daily rate, + 0M3 Therefore, assuming that these rates were correct at the middle of the periods for which they were determined, we have, May 30, Midnight, Rate, -r0^89 July 6, Midnight, Rate, +0.13 Change of rate, 37 days, —0 .76 Daily change of rate, — 0^021 Change of rate for 3^ days, — 0^07; rate June 3, noon, 4-0^89— 0^07=+0^82 Change of rate for 17^ daye, —0^.37; rate June 17, noon, -f ,89—0 .37=+0 .52 Mean daily rate, June 3 to 17, Total change of error, June 3 to 17, Error, June 3, Error, June 17, -rO.67 +0™ 09«.38 -7 12.7 -7 03.3 346. Single Altitudes. — The determination of lon^tudes ashore by single altitudes of a celestial body is identical in principle with the determination at sea by that method, which will be explained hereafter (art. 349). It may be remarked, however, that by taking observations on opposite sides of the meridian, at altitudes as nearly equal as possible, a means is afforded, which is not available at sea, of eliminating certain constant errors of observation. 347. Equal Altitudes. — The method of equal altitudes, explained in article 321, Chapter XI, is available for the determination of longitudes as well as for chronometer error. In the case of the sun, the sight gives the chronometer time of L. A. noon or midnight; applying the chronometer correction and equation of time (the latter with its sign for mean time), we obtain the G. A. T., which equals the longitude, if west, or 24^ minus the longitude, if east. For any other body, the sight gives the chro- nometer time of transit; apply the chronometer correction and there results G. M. T., which may be reduced to G. S. T.; the difference between the latter and the R. A. of the body (this being L. S. T.), is the longitude. Example: April 20 p. m. and April 21 a. m., 1879, in Lat. 30° 25' N., Long, (approx.) 81° 26' W., chro. corr. —3" 11^4, observed times and equal altitudes of the sun as stated below; C — W for p. m. sights, 5" SI" 58\5, and for a. m. sights, 5*" 32"' 01\ Required the longitude. ATCH, P. M. ALTS. 2h5ii. ,40» 90° 0' 52 05 89 50 52 30 40 52 55 30 53 20 20 WATCH, A. M. 8h59moo» Dec, 58 34 .5 58 09 .5 H.D.atMid., + 57 46 .0 Long. +12i>, 57 20 .0 Mean, W.T., P.M., 2i>52m30».0 Mean, VV.T., A.M., 8i'58™10» C - W, +5 31 58 .5 C - W, +5 32 01 P.M. Chro. T., 8 24 28.5 A.M. Chro. T.+ri^, 26 30 11.0 A.M.Chro.,T.+12h,26 30 11.0 P. M. Chro. T., 8 24 28.5 Corr., Dec, 11° 29' 17".l N. H. D. (20th), +51". 45 ^^^^— H. D. (;21.st), +50 .97 51". 10 17>'.43 Difl. 24h, - .48 Diff. Ih, - 0".02 Diff. 17i'.43, - 0".36 H. D. at Mid., +.51".10 f 890".7 ■*" (14' 51" 11° 44' 08" N. 2)10 54 39 .5 Elapsed Time, 18 05 42 .5 Mid. Chro. T., Eq. eq. alt., 5 27 19 .75 + 19 .35 Eq. t., 1">04».9 Tab. 37 log A ( + )9.9364 " H.D.+51".101Og (+)1.7084 Chro.t.,L.A.Mid., 5 27 39.1 H. D., Eq. t., + 1 14 .3 Long. + 12!', Chro. t.,L.M. Mid., 5 28 53 .4 Corr., C. C. , - 3 11 .4 Eq. t., Long., W., logB(-)9.7912 log ( + )1.7084 Ob.54 Lat. 30° 25' tan ( + )9.7687 fZ+ll°44'tan ( + )9.3176 17^.43 1st Part +25".911og( + )1.4135 9, 4 2d Part - 6 .56 log (-) 0.8171 f 5i>25°>42».0 l81°25' 30" (Plusto mean time.) LONGITUDE. 105 34§. In the same example the equation of equal altitudes may be found by the less exact method *^ heretofore given (art. 324), as follows: Change in declination between sights = H. D. X Elapsed time = 51^^.10 X 18'*.1 = 925^''. Change in altitude due to 100^^ declination (Tab. 25) = +53^^. ¥ V = Oo X 925 j_ o/ 1 Q 100X60 - + «-^^- 2'' 53'" 20' — 2" 51"' 40^ 90° 00^ - 89° 20^ Eq. eq. alt. = — 8.19 X 2^5 = 100^ 40^ 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 time sight, sometimes called the cJironometer 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 (Treenwich 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 w-as observed, the name of the longitude will be indicated in combining the quantities. 350. As has been stated, the most favorable position of the celestial body for finding the hour angle from its altitude is when nearest the prime vertical, provided the altitude is not so small as to be seriously affected 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. R., the following altitudes of the sun's lower limb were observed, and times noted by a watch compared with the Green- wich chronometer. Chro. corr., + 4'" 59^2; I. C, — 30^^; height of the eye, 23 feet; C- AV, 2'» 17'" 06^ Required the true longitude. W. T., 7h 20>" ISs 20 47 21 14 Mean, 7 20 45.3 C-W, + 2 17 06 Chro. t., 9 37 51.3 C. C, , 17* + 4 59.2 G. M. T., . 21 42 50.6 Eq. t., + 3 47.9 Obs. alt. Q, 29° 35' 30" 41 20 46 10 Mean, Corr., Dec, 19° 32' 01".8 N. Eq. t., 3m 47».68 G. A. T., 21 4G 38.4 S. D., dip, p. & r., I.e., 29 41 00 + 9 05 29 50 05 + 15' 51" _ 4' 42" - 1 34 — 30 - 6 46 H. D., + 33".09 G. M.T., - 2h.3 H. D., - 0«.09 G.M.T., - 2''.3 Corr., Dec, P, f 76". 1 tl' 16" 19° 30' 46" N. 70° 29' 14" Corr., + 0*.21 Eq. t., 3'" 47» .9 [Plus to mean time.) 9' 05" h L P 29° 41 70 50^ 05'^ 33 00 29 14 sec cosec cos sin .12588 .02569 2)141 52 19 8 8—h » 70 41 56 09 06 04 9.51406 9.81782 G. A. T. 21" 46™ 38» L. A. T. 19 32 07 2)19.48345 sin i t 9.74172 Long. / 2" 14-" 31' \33° 37^ 45' ;-} w. 106 LONGITUDE. Example: At sea, April 16, 1879, p. m., in Lat. 11° 47^ S., Long. 0° 20^ E., hy D. R., observed an altitude of the star Aldebaran, west of the meridian, 23° 13'' 20'''; chronometer time, 6'' 56™ 32*; chro- nometer fast of G. M. T., 2" 27^ I. C. Chro. t., CO., 6'^ 56" 32^ 2 27 G. M. T., R. A. M. S., +1 Red. (Tab. 9),+ G. S. T., R. A. *, H.A.fromGr., 4 03 15 W. 6 54 05 1 37 01.9 1 08.0 8 32 14.9 4 28 59.6 -2' OO''; height of eye, 26 feet. What was the longitude? R. A. >fc, 4" 28" 59^. 6 Dec. Obs.alt.*, Corr., 23° 13' 9 20" 16 h, 23 04 04 I.e., dip, ref.. — 2' 5 2 00" 00 16 p, 16° 15' 59" K 106° 15' 59" Corr. , — 9 16 h L P 23° 04' 04" 11 47 00 106 15 59 sec cosec cos sin 2) sini« .00925 . 01774 8 s — h 2)141 07 03 70 33 32 47 29 28 9. 52223 9. 86757 Gr.H. H. A. A. 4" 03™ 15' W. 4 05 50 W. 19. 41679 9. 70839 T ^r,„ JO*' 02™ 35' \p Long. JQo 38, 45//|E. 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»; — W, 2" 05™ 42'; C. C, +2™ 18«; I. C, +1' 30"; height of eye, 18 feet. Required the longitude. W.T., C— w, Chro. t., CO., G.M.T.,164, R.A.M.S.,01', Red. (Tab. 9), G.S.T., R.A. *, H.A.fromGr. 5i> 48"' 02 • 2 05 42 7 63 44 + 2 18 19 56 02 + 1 37 01.9 + 3 16.5 21 36 20.4 22 27 11.6 50 51 E. Obs. alt. *, Corr., h, I.e., dip, ref., Corr., 45° 40' 00" 3 36 46 36 24 1' 30" 4' 09" 57 3' 36" R.A. (17 '•lOh), 221' 27- '19».0 Dec. (17* Oh), H.D., G.M.T., Corr.. Dec, P. , 10° 36 ' 28".l 8. H.D., G.M.T.; Corr., + 1'.8 4t'.l 7'. 4 + 10".0 4i'.l 41*. R.A., 221- 27°' 11».6 10° 37' 09" S. 79° 22' 51" h L P 45° 36' 24" 25 12 00 79 22 51 2)150 11 15 sec cosec . 04343 .00750 i-h 75 05 38 29 29 14 cos sin Gr. H. A. O** 50™51'E. H. A. 2 57 21 E. 9.41032 9. 69217 2)19.15342 sini< 9.57671 Long. f 2'>06™30'\-jT. 131 ° 37' 30"/ ^* LONGITUDE. 107 Example: Afsea, June 26, 1879, p. m., in Lat. 49° 5(y N., Long. 6° 16^ W., by account, observed an altitude of the moon's lower limb 21° 18' W^, 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« Obs. alt C. C, + 42 S. D., G. M. T., 2 27 40 Aug., R. A. M. S.. + 6 16 57.5 Red. (Tab. 9), + 24.3 G, S. T., 8 45 01.8 dip, R. A. d, 11 38 39.3 I. C, H. A. from Gr., 2 53 37 E. 1st eorr. 21° 18' 10" h 15' 59" h 6 16 05 4' 36" 1 45 6 21 9' 44" Approx. alt., 21° 27' 54" p.&r. (Tab. 24), + 52 06 R. A., M. D., No. min., Corr. , R. A., Hor. par.. 11" 37"' 41».96 2^07 27"'. 7 . 57«.34 11" 38°' 39«.3 Dec. 2° 3.5' 36".4 S. M. D., No. min., 15".l 27"'.7 Corr., Dec, p. -{ 419".3 6' 59".3 2° 42' 36" S. 92° 42' 36" 58' 36" 8—h 22° 2(y 0(/' 49 50 00 92 42 36 2)164 52 36 82 26 18 60 06 18 Gr. H. A. H. A. Long. 2" 53"' 37^ E. 3 19 04 E. r O^ 25™ 27^1 ^ t 6°21M5''/"^- .19043 .00049 9.11923 9.93799 2)19.24814 sin i t 9.62407 sec cosee cos sin 352. Equal Altitudes. — The method of finding the longitude at sea by observation of equal alti- tudes of a heavenly body is one that may be conveniently employed when applicable, though the limits of applicability are narrow. If, on board a vessel which is either stationary in position or moving at a uniform rate of speed in a true east or west direction, equal altitudes of the sun, a planet, or a star be 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 a." equal to the mean of the times of observation, no matter what course may have been steered by th< vessel in the interval. But if the azimuth of the body is less than 80° from the north or south point of the horizon the method is not available for vessels making a material amount of northing or southing; and if the hour a,ngle 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 should not yield to the temptation offered by the simplicity of this method to follow it beyond the limits within which it may properly be considered to apply. 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'' minus 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^ N., Long. 86° 00^ E., by D. R., observed equal altitudes of Q before and afternoon, using same sextant and same height of eye. Watch: a. m., 11'' 52'" 37*; p.m., 12" 07"° 22^; C — W, 6" 17" 48%- C. C, + 2°' 32^ Vessel steering west between sights. Required the longi- tude at noon. W. T.,A. M., Ilh52'"37» Eq. t, 3'" 42'. 5 W. T., P. M., 12 07 22 H. D., - 0^75 2)23 59 59 G. M.T., - 5^7 W. T.,L. A.,noon, 11 59 59.5 Corr., + 4^3 C-W, + 6 17 48 Eq. t., 3'" 46^8 Chro. t., L. A.,noon, 6 17 47.5 {Subtract irom mean time.) C. C, + 2 32 G. M. T., L. A.,noon,l'i, 18 20 19.5 Eq. t., - 3 46.8 G. A. T.,L. A., noon, - 18 16 33 f 5'' 43"' ''7*' ) Longitude, { 8b° 5V lo'^ \ ^- Example: August 6, 1879, p. m., in Lat. 25° 55^ S., by obs., and Long. 36° 58^ W., by account, observed equal altitudes of the star Antares, the chronometer times before and after passage being 9''42"-38« and lO'' 00'" 26% and the true azimuths S. 81° E. and S. 81° W., respectively; chro.' fast of G. M. T., 1"" 27^ The ship was steaming on a course SSW. What was the longitude? Chro. time before, 9" 42'" 38'' Chro. time after, 10 00 26 Chro. time passage, C. C, G. M. T. passage, R. A. M. S., Red. (Tab. 9), G. S. T. passage, L. 8. T. passage (R. A. >{<; 2)19 43 04 9 51 - 1 32 27 9 50 4- 8 58 + 1 05 36.3 36.9 18 50 , 16 22 18.2 03.4 {9h Ogm 158"! 37° 03' 45'''|^- AZIMUTH. 109 CHAPTER XIV. AZIMUTH. L d True amp. E. 23° OF N. sin 9. 59223 Obsd. amp. E. 81 00 N. Error, 8°. E. Error, 7° 59^ E. w^ 354. The azimuth of a body has been defined (art. 223, Chap. VII) as the arc of the horizon 5»t. interceptea between tlie meridian and the vertical circle passing through the body; and the amplitude (art. 224) as the arc measured between the position of the body when its true altitude is zero and the east or west point of the horizon. The amplitude is measured from the east point at rising and the west point at setting, and, if added to or subtracted from 90°, will agree with the azimuth of the body when in the true horizon. The azinmth is usuallj'^ measured from the north point of the horizon in north latitude, and from the south point in south latitude, through 180° to the east or west; thus, if a body bore N. by E., its azimuth would be nametl N. ll]f° PI in north, or S. 168J° E. in south latitude. The determination of the azimuth of a celestial body is an operation of frequent necessity. At sea, the comparison of the true bearing with a bearing by compass affords the only means of ascertain- ing the error of the compass due to variation and deviation; on shore, the azimuth is required in order to furnish a knowledge of the variation, and is further essential in all surveying operations, the true direction of the base line being thus obtained. 355. There are various methods of obtaining the true azimuth of a celestial body, which will be described as follows: («) Amplitudes, (b) Time Azimuths, (c) Altitude Azimuths, {d) Time and Altitude Azimuths. A further method, by means of the Sumner line, will be explained later (Chap. XV). Still another operation pertains to this subject, namely: (e) The determination of the True Bearing of a Terrestrial Object. AMPIilTTJDES. 356. The method of obtaining the compass error by amplitudes consists in observing the compass bearing of the sun or other celestial body when its center is in the true horizon, the true bearing, under such conditions, being obtained by a short calculation. Since the true horizon is not marked by any visible line (differing as it does from the visible horizon by reason of the effects of refraction, parallax, and dip), allowance may be made for the difference by an estimate of the eye, or else the observation may be made in the visible horizon and a correction applied. 35T. When the center of the sun is at a distance above the horizon equal to its own diameter it is almost exactly in the true horizon; at such a time, note its bearing by compass, and also note (as in all observations for determining compass error) the ship's head by compass, and the angle and direction of the ship's heel. Or, note the bearing at the instant at which the center of the body is in the visible horizon; in the case of the sun and moon, the correct bearing at that time may be most accurately ascertained by taking the mean of the bearings when the upper and the lower limbs of the disk are just appearing or disap- pearing. 35§. To find the true amplitude by computation there are given the latitude, L, and declination, d. The quantities are connected by the formula, sin Amp. =sec L sin d, from a solution of which the amplitude is obtained. To find the true amplitude by inspection enter Table 39 with the declination at the top and the lati- tude in the side column; under the former and opposite the latter will be given the true amplitude. To obtain accurate results, interpolate for minutes of latitude and declination. To reduce the observed amplitude when taken in the visible horizon to what it would have been if taken in the true horizon, enter Table 40 with the latitude and declination to the nearest degree and apply the correction there found to the observed amplitude; the result will be the corrected amplitude by compass, which, by comparison with the true amplitude, gives the compass error. When the body observed is the sun, a star, or a planet, apply the correction, at rising in north latitude or at setting in south latitude, to the 7-igJtt, and at setting in north latitude or at rising in south latitude, to the^left. For the moon, apply half the correction in a contrary direction. Example: At sea, in Lat. 11° 29^ N., the observed bearing of the sun, at the time of.rising when its center was estimated to be one diameter above the visible horizon, was E. 31° N. ; corrected declination 22° 32^ N. Required the compass error. By computation. By inspection {Table 39). 11° 29^ sec . 00878 L, 11°. 5 N.l Trueamn E 23° N 22 32 sin 9.58345 d, 22 .5 N.K"^®^'"P- *^- "^-^ • " ^- Obsd. amp. E. 31 .0 N. dro '0' 110 AZIMUTH. Example: At sea, in Lat. 25° 03^ S., the observed bearing of Venus when in the visible horizon at rising was E. 18° 30^ N., its declination being 21° 44' N. Required the compass error. By computation. By inspection ( Table 39). L 25° 03' sec .04290 L, 25°.0S.1t, E 24° 1 N d 21 44 sin 9.56854 d, 21 . 7 N.) "^^^ ^™P- J^-^-i-1^- Obsd. amp. E. 18°.5N. 1^ tt ic axr True amp. E. 24° 08' N. sin 9.61144 Corr. (Tab. 40) 0. 3 left.} *"^™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, 40°.5N.l^ W 28° 4 S d 21 12 sin 9.55826 d, 21 . 2 S. J "^ "^"^ '™P- " • ^» •* fc*- Obsd. amp. W. 17°.0S. 1 p, w ia 7 a True amp. W. 28° 22' S. sin 9.67689 Corr. (Tab. 40) 0.3 right, f ^o^P-amP- ^^ ^^ ■' ^• Comp. amp.W. 16 42 S. Error, 11°40'W. Error, 11°.7W. TIME AZIMUTHS. 359. In this method are given the hour angle at time of observation, t, the polar distance, p, and the latitude, L; to find the azimuth, Z. Any celestial bodj^ 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 be taken with their corresponding times, and the means taken. 361. First prepare the data as follows: (a) Find the Greenwich time corresponding to the local time of observation. ^[^ {b) Take out the declination of the body from the Nautical Almanac; if the method of computation j±- is employed the polar distance and the co-latitude should be noted. ^irnun s (c) Find the hour angle of the body by rules heretofore given. >l Scfq This having been done, the true azimuth may be determined either by Time Azimuth Tables, by the ' / i ETanhic method of an Azimuth Diaaram. or bv Solution of the Astronomical Trianale. Owinef to the nos- graphic method of an Azimuth Diagram, or by Solution of the Astronomical Triangle. Owing to the pos- Yi^fj'o 'Of, • gibility of more expeditious working, either of the first-named two is to be considered preferable to the ■^ t * «> last, and the navigator is recommended to supply himself with a copy of a book of Azimuth Tables, or , . with an Azimuth Diagram; an explanation of the method of use accompanies each of these. /'• 362. To solve the triangle: Let S = J .snm of polar distance and co-Lat. D = I difference of polar distance and co-Lat. \t = \ 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 Case. — If the half-sum of the polar distance and co-Lat. is greater than 90°: always take the difference of X and Y, which subtract from 180°, and the result will be the true azimuth. In either case, mark the true azimuth N. or S. according to the latitude, and E. or W. according to the hour angle. It may sometimes be convenient to use the supplement of the true azimuth, by subtracting it from 180° and reversing the prefix N. or S., in order to make it correspond to the compass azimuth when the latter is less than 90°. The cotangent of half the hour angle may be found from Table 44 abreast the whole hour angle in the column headed "Hour P. M." AZIMUTH. Ill Example: December 3, 1879, a. m., in Lat. 30° 25^ N., Long. 5" 25™ 42* W., the observed bearing of sun's center was N. 135° 30^ E., and the Greenwich mean time, December 3, 2'' 36" 11'. The corrected declination of the sun was 22° 07' S. ; the equation of time (additive to mean time) , 10" 03'. Required the error of the compass. G.M.T. (Dec.3), Long., 2" 36™ 11' 5 25 42 co-Lat. P, 59° 3y 112 07 L.M.T. (Dec.2), 21 10 29 Eq.t., + 10 03 L.A.T., 21 20 32 t, 2" 39'»28« J9+CO-L, 171 42 S, 85 51 t S D X Y 2h39m28« cot it .44051 85° 5r cosec .00114 26 16 50 44 88 19 sin 9.64596 tan .08761 cot it .44051 sec 1.14045 cos 9.95267 tan 1.53363 ^-co-L, 52° 32' X+Y 139 03 D, 26 16 True azimuth, N. 139° 03' E. Comp. azimuth, N. 135 30 E. Compass error, 3 33 E. Example: April 9, 1879, in Lat. 2° 16' N., the observed bearing of the sun's center was N. 85° 15' E: sun's hour angle, 3'' 44™ 16', and its declination, 7° 38' N. Required the compass error. co-Lat. , P, 87° 82 44' 22 t S D X Y Y-5 True a Comp. Compa 3" 44™ 85° 03' 2 41 5 03 87 22 16' N. , N. cot it . 27372 cosec .00162 sin 8. 67039 COt^i sec cos tan t .27372 1. 06406 9. 99952 jo+co-L, 170 06 tan 8. 94573 82° 19' E. 85 15 E. s, 85 03 1. 33730 co-L —p, 5° 22' :82 19 zimuth, azimuth 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., 73° 28' p, 113 12 JO + co-L, 186 40 s, 93 20 p — co-L, 39° 44' t S D -X 4h 27™ 31' 93° 20' 19 52 27 16 87 40 cot i I cosec sin tan t .18022 .00074 9. 53126 cot i sec cos tan t .18022 1. 23549 9. 97335 X Y 9. 71222 1.38906 Y- 60 24 D, 19 52 Z 119° 36' True azimuth, S. 119° 36' W. Comp. azimuth, S. 124 00 W. Compass error, 4 24 W. ALTITUDE AZIMUTHS. 363. This method is employed when the altitude of the body is observed at the same time as the azimuth; in such a case the hour angle need not be known, though the time of observation should be recorded with sufficient accuracy for the correction of the declination of the sun, moon, or a planet. There are given the altitude, h, the polar distance, p, and the latitude, L; to find the azimuth, Z. 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''cos s cos {s—p)sec L sec h, in which s = i (/i + L+p). The resulting azimuth is to be reckoned from the north in north .latitude and from the south in south latitude. /^ ^ \12 AZIMUTH. It may occur that the term (s—p) will have a negative value, but since the cosine of a negative angle less than 90° is positive, the result will not be affected thereby. Example: December 3, 1879, in Lat. 30° 25^ N., the observed bearing of the sun's center was N. 135° 30^ E., and its corrected altitude 24° 59^; the approximate G. M. T. was 2^.6, the declination at that time being 22° 07^ S. Required the compass error. h 24° 59^ sec . 04267 L 30 25 sec .06431 p 112 07 2)167 31. True azimuth, N. 139° 00^ E. Comp. azinmth, N. 135 30 E. 83 45 cos 9.0.3690 s—p —28 22 cos 9.94445 Compass error, 3 30 E. 2 ) 19. 08833 *Z 69 30 cos 9.54416 'Z 139 00 TIME AND ALTITUDE AZIMUTHS. 366. When, at the time of observing the compass bearing of a celestial body, the altitude is meas- ured and the exact time noted, the true azimuth may be very expeditiously determined, a knowledge of the latitude being unnecessary. • In view of the simplicity of the computation this method strongly commends itself to observers not provided with an azimuth table or diagram. 367. The observation is identical with that of the altitude azimuth (art. 364), with the exception that the times of observation must be exactly instead of approximately noted. 36§. Ascertain the declination of the body at time of sight, and correct the observed altitude; com- pute the hour angle. We then have: sin Z=sin t cos d sec h, from which the azimuth may be found. This method has a defect in that there is nothing to indicate whether the resulting azimuth is measured from the north or the south point of the horizon; but as the approximate azimuth is always known, cases are rare when the solution will be in question. 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.) t 39° 52' sin 9. 80686 True azimuth, N. 139° 04' E. d 22 07 cos 9. 96681 Comp. azimuth, N. 135 30 E. h 24 59 sec .04267 3 34 E. Z S. 40° 56' E. sin 9. 81634 TRUE BEARING OF A TERRESTRIAL OBJECT. 369. Thus far, sea observations for combined variation and deviation have been discussed, but if it becomes necessary, as in surveying, to ascertain the True Bearing of a Terrestrial Object, or to find the variation at a shore station, more accurate methods than the foregoing must be resorted to. The most reliable method is that by an Astronomical Bearing. This consists in finding the true bearing of some well-defined object by taking the angle between it and the sun or other celestial body with a sextant or a theodolite, and simultaneously noting the time by chronometer, or measuring the altitude, or observing both time and altitude. It should always be noted whether the object is right or left of the sun. 370. By Sextant. — Measure the angular distance between the object and the sun's limb; and if there is a second observer, measure the altitude of the sun at the same moment and note the time. In the absence of an assistant, first measure the altitude of the sun; next, the angular distance between the sun and the object; then, a second altitude of the sun, noting the time of each observation. Also measure the altitude of the defined point above the sea or shore horizon. By Theodolite. — This instrument is far more convenient than the sextant, for, being leveled, the horizontal angle between the sun and the object is at once given, no matter what may be the altitudes of the objects. In case the altitude of the sun is needed, it may be read accurately enough from the vertical circle, although not as finely graduated as the limb of the sextant. The error in altitude must, how- ever, be found by the level attached to the telescope, since it will usually be found to differ from the levels of the horizontal circle. If, in directing the telescope to the sun, there is no colored eye-piece, an image of the sun may be cast on a piece of white paper held at a little distance from the eye-piece, and by adjusting the focus the shadow of the cross-wires will be seen. It should be understood that any celestial body may be used as well as the sun, and there are, in fact, certain advantages in the use of the stars; the sun is chosen for illustration, because it will usually be found most convenient to employ that body. AZIMUTH. 113 371. Find the true azimuth of the celestial body by any; one of the methods previously explained in this chapter and apply to it the azimuth difference, or horizontal angle between the celestial and the terrestrial body, having regard to the direction of one from the other. To find the azimuth difference from sextant observations, change the observed altitudes of the bodies into appar^nf 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. + App. Alt. Object) , we have: cos i Az. Diff. = \/sec App. Alt. O 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 a correction for semidiameter (S. D. X sec h), but it is usual to eliminate this correction by taking the mean of observations of both limbs. Example: December 10, 1879, a. m., in Lat. 30° 25^ 24^-' N., Long. 81° 25^ 24'^ W., made observa- tions with a sextant and obtained the following data for finding the true bearing of a station: Watch time, 11" 22™ 36' Obs. Ang. Dist. 0, 117° 07^ Left. C-W, 5 21 18 Obs. 20, 71° 37^ 20''' Chro. corr., + 2 16 Obs. alt. Station, 20' " zero. Dec. S. , 22° '56' 27" Eq. t., 4- ym 00' S.D., 16' 17" L C, Kequired the true bearing of the object. W. T., C-W, Chro. t, C. C, 11" 22" 36' 5 21 18 + 43 2 54 16 G.M.T.,Dec.lO, 4 Eq. t. G. A. T., Long., L. A. T., + 10 00 2 0, 71= ' 37' 20' 0, 35 S. D., + 48 40 16 17 App. Alt., 36 p. & r., — 04 57 1 13 4 53 5 25 10 42 h, 36 03 44 23 27 28 it 8° 08' 00" 22 56 27 36 03 37 9° 17' E. 170 43 E. 7 sin 9.15069 cos 9.96422 sec .09239 sin 9.20730 1 8° 08' 00" Obs. Ang. Dist., O's S. D., App. Ang. Dist., 117° 07' 00" 16 17 117 23 17 App. Dist. App. Alt. O App. Alt. Object S — App. Dist. i Az, DifE. Az. DiflF. 117° 23' 8C 05 20 2)153 48 76 54 ■40 29 '62° 30' 125 00 sec 0.09250 sec 0.00001 cos 9.35536 cos 9.88115 2)19.32902 cos 9.66451 True bearing 0, Az. Diff., N. 170° 43' E. 125 00 Left. True bearing object, N. 45° 43' E. Example: Same date and place and same objects as in the preceding example; measurement made with a theodolite, angular distance (|), 123° 17'; object left of sun. Watch time, 11" 16" 34'.5; watch slow of L. A. T., 4'" 53'.5. Dec. 0, 22° 56' S. Required the true bearing. W.T., W. SlOW; 11" 16" ,+ 4 '34' 53 .5 .5 .0 co-Lat., 59° p, 112 35' t 0" 38"' 32' 56 S 86° 15' D ''6 11 cot i t cosec sin tan 1.07435 .00093 9.65230 cot J t sec cos tan 1.07435 1.18440 9 95110 L. A. T., 23 21 28 p + co-lj, 172 31 "V 70° Ol/ .72758 t. 38 i 583—06— 32 —8 S, 86 15 Y 89 39 2.20985 ji — co-L, 53 21 X + Y169 03 D, 26 True be; Az. Diff True be; 41 aring0, X. 169° 03' E. 123 17 Left. 6 aring object, N. 45 46 E. 114 THE SUMNER LINE. chaptp:r XV. THE SUMNER LINE. DESCRIPTION OF THE LIITE. 3T2. The method of navigation involving the use of the Sumner line takes its name from Capt. Thomas H. Sunmer, an American shipmaster, who discovered it and published it to the world. As a proof of its value, the incident which led to its discovery may be related: " Having sailed from Charleston, S. C, 25th November, 1837, bound for Greenock, a series of heavy gales from the westward promised a quick passage; after passing the Azores the wind prevailed from the southward, with thick weather; after passing longitude 21° W. no observation was had until near the land, but soundings were had not far, as was supposed, from the bank. The weather was now more boisterous, and very thick, and the wind still southerly; arriving about midnight, 17th December, within 40 miles, by dead reckoning, of Tuskar light, the wind hauled SE. true, making the Irish coast a lee shore; the ship was then kept close to the wind and several tacks made to preserve her position as nearly as possible until daylight, when, nothing being in sight, she was kept on ENE. under short sail with heavy gales. At about 10 a. m. an altitude of the sun was observed, and the chronometer time noted; but, having run so far without observation, it was plain the latitude by dead reckoning was liable to error and could not be entirely relied upon." The longitude by chronometer was determined, using this uncertain latitude, and it was found to be 15^ E. of the position by dead reckoning; a second latitude was then assumed 10^ north of that by dead reckoning, and toward the danger, giving a position 27 miles ENE. of the former position; a third latitude was assumed 10' farther north, and stdl 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 points and at Smalls light and at the ship at the same instant." Then followed the conclusion that, although the absolute position of the ship was uncertain, she must be somewhere on that line. The ship was kept on the course ENE., and in less than an hour Smalls light was made, bearing ENE. J F,. and close aboard. The latitude by dead reckoning was found to be 8' in error, and if the position given by that latitude had been assumed correct the error would have been 8 miles too far S. and 31' 30'' of longitude too far W., and the result to the ship might have been disastrous had this wrong position been adopted. This represents one of the practical applications of the Sumner line. The properties of the line thus found will now be explained. 373. Circles of Equal 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 EP^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 body, is termed the circle of illumination, and from any point on its circumference the true altitude of the center of the body will be zero. If, now, we con- sider any small 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 other point of the same circle; thus, the altitude of the bodj' at B is equal to its altitude at B' or B", and its altitude at D is the same as at D' or D". It therefore follows that at any instant of time there is a series of positions on the earth at which a celestial body appears at the same given altitude, and these positions lie in the circumference of a circle described upon the earth's surface whose Fig. 43. center is at that position which has the body in the zenith, and whose radius depends upon the zenith distance, or — what is the same thing — upon the altitude. Such circles are termed circles of eqiial altitude. THE SUMNER LINE. 115 374. The data for an astronomical sight comprise merely the time, declination, and altitude. The first two fix the position of the body and may be regarded as giving the latitude and longitude of that point on the earth in whose zenith the body is found ; the zenith distance (the complement of the altitude) mdicates the distance of the observer's zenith from that point; but „here 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 body 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 sight 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 w"hen 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 k' upon the earth, the zenith / \ ^' distances corresponding respectively to the radii AO / \\ and A^O. / W-"'"" 375. The Sumner Line. — In practice, under / ___— — -— ?nC ""^X the conditions existing at sea, it is never necessary . — """ ~^/\\ ^\ to determine the whole of a circle of equal altitude, I "* / /' \ \ as a very small portion of it will suffice for the pur- \ I P^ \ \ poses oi navigation; the position is always known \ /" ^' 1 within a distance which will seldom exceed thirty \ I / ^ / miles under the most unfavorable conditions, and \ V/ / whichisusually very much less; in the narrow limits \^ y\ / thus required, the arc of the circle will practically X.^^^ ^^ \^^^ y^ coincide with the tangent at its middle point, and ..^--''''^ -''^ may be regarded as a straight line. Such a line, jtjq 44 comprising so much of the circle of equal altitude as covers the probable limits of position of the observer, is called a Sumner line or Line of position. 376. Since the direction of a circle at any point — that is, the direction of the tangent — must be perpendicular to the radius at that point, it follows that the Sumner line always lies in a direction at right angles to that in which the body bears from the observer. Thus, in figure 44, it may be seen that m m^ and n n', the extended Sumner lines corresponding to the bodies at A and A'', are respectively perpendicular to the bearings of the bodies OA and OA'. This fact has a most important application m the employment of the Sumner line. 377. Uses of the Sumner Line. — The Sumner line is valuable because it gives to the navigator a knowledge of all of the probable positions of his vessel, while a sight worked with a single assumed latitude or longitude gives but one of the probable positions; it must be recognized that, in the nature of things, an error in the assumed coordinate will almost invariably exist, and its possible effect should be taken into consideration; the line of position reveals the difference of longitude due to an error in the latitude, or the reverse. Since the Sumner line is at right angles to the bearing, it may be seen that when the body bears east or west — that is, when it is on the prime vertical — the resulting line runs north and south, 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 Sumner line inclined to both meridians and parallels; if the line agrees in direction more nearly with the meridian, latitude should generally be assumed and the longi- tude worked; if it is nearer a parallel, the reverse course is usually preferable. The values of the assumed coordinates may vary from ICK to 1°, according to circumstances. 37§. The greatest benefit to be derived from the Sumner method is when two lines are worked and their intersections found. The two lines may be given by different bodies, which is generally preferable, or two different lines may be obtained from the same body from observations taken at different times. The position given by the intersection of two lines is more accurate the more nearly the 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 position of the ship at the time of first sight must be brought forward to that at the second in considering the intersection; if, for example, a certain line is determined, and the ship then runs NW. 27 miles, it is evident that her new position is on a line parallel with the first and 27 miles to the NW. of it; a second line being obtained, the inter- section of this with the first line, as corrected for the run, gives the ship's position. Besides the employment of two lines for intersections with each other, a single line may be made to serve various useful purposes for the navigator. These are described in article 400, Chapter XVI. METHODS OF DETERMINATION. 379. Any line may be defined in either of two ways — by two of its points, or by one point and the direction. There are thus two methods by which a Sumner line may be determined: (a) Assume two values of one coordinate and find the corresponding values of the other. Two values of the latitude may be assumed and the longitudes determined, as was done by Captain Sumner on the occasion that led to the discovery of the method; or else two values of the longitude may be assumed and the latitudes determined. Two points are fixed in this way, and the line joining them is the line of position. (6) Assume either one latitude or one longitude and determine the corresponding coordinate. This gives one point of the line. The azimuth of the body is then ascertained, and a line is drawn through 116 THE SUMNER LINE. the determined point at right angles to the direction in which the ])ody 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. E., 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, + V 3(y^; 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., CSO" 51' E.; h, 45° 36' 24^''; p, 79° 22' 51''. Assume values of Lat. 25° 02' and 25° 22' S. h P 45° 36' 24" 25 02 00 79 22 51 sec cosec .04284 .00750 L, 25° 22' 00" sec cosec .04403 .00750 Gr. H H. A 2)150 01 15 cos 9.41270 sin 9.69105 «2 75 10 38 s.,—h 29 34 14 «i 75 00 38 Si—h 29 24 14 cos 9.40794 sin 9.69328 1. A. O*- 50™ 51' E. 2)19.15409 Gr. H. A. 0" 50™ 51^ H. A., 2 57 12 2)19.15275 .1 2 57 29 E. sin 1 35" 10"; observed altitude of moon's upper limb, 75° 33' 00", bearing north and east; I. C., — 3' 00"; height of eye, 26 feet; chro. fast of G. M. T., 1"' 37'.5. Required the Sumner line. From a solution of the same problem with a single longitude (art. 339, Chap. XII), the following values were obtained: H. A. from Greenwich, l"- 35™ 07^ W.; h, 75° 23' 30"; d, 6° 41' 47" N. Assume the longitudes 30° 10' and 30° 30' W. Gr. H. A. 1" 35™ 07^ W. Long.i 2 00 40 W. Gr. H. A. l** 35'" 07' Long., 2 02 00 >33™50« i -2 41 00 h 7 10 h at./ 61° 57' 01" + 2 08^ H, 61 59 09 d 28 00 51 21 59 27 L, 50 00 18 N. . r50° 00' 18" N. ^"^2^40 15 00 W. 118 THE SUMNER LINE. This shows that the Sumner hne Ues so nearly in a due east-and-west direction that a difference of longitude of 30^ makes a difference of latitude of only V. From an azimuth table or diagram, it is found that the azimuth of the sun corresponding to Lat. 50° N. Dec. 22° N. and H. A. G'" 10^ E., is N. 177° E. Therefore, using the values given by the earlier solution, the line is defined as follows: ^^{'oTorN. Line runs N. 87° E. The direction of the line thus given and the one found from the double coordinates may be 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. 3§2. Graphic Methods. — Each line may be plotted upon the chart of the locality in which the ship is being navigated and the intersection thus found. The details of the plotting will be obvious, whether the line is defined by two of its points, or by one point and its direction. This plan will com- mend itself especially when the vessel is near shore, as the chart in use will then probably be one of conveniently large scale, and it will be an advantage to see where the position falls with reference to soundings and landmarks. 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 by the latitude and longitude of two points of each, and consider that they are plotted on a chart which is constructed upon a sheet of elastic rubber. It is evident that if, while 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 positions of the various {)oints in terms of the new coordinates which have been created, namely, those in which a minute of atitude is equal to a minute of longitude. Thus, if on the true chart a point is m minutes north and n minutes east of anothei', on the stretched one it will still be m 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 m minutes north and n minutes east (on the original scale) of some definite point of one of the lines, the intersection on the stretched chart will lie TO minutes north and n minutes (of the new scale) to the east of the same point. A stricter mathematical conception of the stretched chart and its properties may perhaps be obtained by considering the chart of the locality to be projected (with the eye at the zenith) upon a plane which passes through one of the meridians and makes an angle with the plane of the horizon which is equal to the latitude; each minute of longitude will then be increased by multiplying it by the secant of the latitude, and thus becomes equal to a minute of latitude. From a consideration of the properties of this hypothetical chart it may be seen that the following rule may be laid down: If two or more Sumner lines be plotted by their latitude and longitude upon any sheet of paper, using a scale whereon latitude and longitude are equal regardless of the latitude of the locality, the intersection of those lines, measured by coordinates on the scale employed, correctly represents the intersection of the lines as it would be measured upon a true chart. It follows from this that we may plot Sumner lines upon any piece of paper, measuring the coordi- nates with an ordinary scale ruler, and assigning any convenient length for the mile; the larger the scale the more accurate will be the determination. Or, what is even more convenient, we may employ "profile paper," whereon lines are ruled at right angles to each other and at equal distances apart, in which case no scale ruler is needed. One caution must be observed in using this method; all longitudes employed on the paper for any purpose must be those of the scale, namely, one minute of longitude equals one minute of latitude. For instance, if the two Sumner lines be taken at different times, in bringing the first up to the position of the second by the intermediate run, that run must be laid down to scale; that is, the easting or westing must appear as so many minutes of longitude, not so many miles. To do this enter the traverse table with course and distance run, and pick out latitude and departure; then, by means of the middle latitude, convert departure into minutes' of longitude and bring the first line to the second by laying off so many minutes of latitude north or south, and so many of longitude east or west. In the case where the Sumner is defined by one position and its line of direction, it is not correct to lay down the angle to the meridian on the hypothetical chart, for all angles are distorted thereon. The best way is to find another position on the line by assuming a second latitude ten or twenty miles removed from that of the point given, entering the traverse table with the angle that the line makes with the meridian as a course, and'abreast the latitude taking out the departure; convert departure into differ- ence of longitude, and plot the second point by its coordinates from the first. Example: Let it be required to find the intersection, by each of the methods, of the following lines: . /40° 00' N. i ;40° 20' N. ^H63 15 W. ^463 07 W. T,/40 05 N. V./40 15 N. ^H63 03 W. ■'^^SS 12 W. a 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: Az :i~:i" ' t ~ ~ : I j^:: iii-i- _ 23::: t z ZZZlZZ.lZJl."." z _.vi : : : ___ _^^ : : :::: :2^^ :-::;;__;l_:l _ — ::: : \ : :: ::: .t. \_:- 1.. _..?^__ [ : :s::_ __::::^.::: ::::.! / .»L_ I""::/::::: _. : t :_ 83' \o' /^* L5' 12- 10' OT' 03' 63'' 2,0' Ai 10' 63* Imile - .06in.cK Fig. 45. T . ,. /40° 12^8 N. Intersection :|g3 ^g g ^ Suppose, in the example just given, the first line had been defined as follows: ^63° 15^ W ^^"® ™"*^ ^- ^"° ^• To find a second coordinate bv which to plot it, proceed as follows: In Table 2, for 17°: Lat. 20^ N., Dep. 6.1 m. E. For Mid. Lat: 40°, Dep. 6.1 m., diff. long. 8^0 E. Hence, as previously given: . /40° 00^ N. ^H63 15 W. r40° 20^ N. 463 07 W. 3§4. Methods by Computation. « — The finding of the intersection of two Sumner lines by compu- tation may be divided into two cases: Case I. When one line lies in a NE.-SW. direction, and the other in a NW.-SE. direction. Case II. When both lie in a NE.-SW., or both in a NW.-SE. direction. Suppose, first, that the lines are defined by the latitude and longitude of two points of each, and for the simplification of the problem consider the lines projected on a plane passing through one of the meridians and making an angle with the plane of the horizon equal to the latitude, the properties of which were explained under the graphic method, (art. 383); this saves the necessity of 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 positions, the results are as exact as if the longer method be followed of dealing with minutes of latitude and longitude of unequal length. 385. Case I One line NE.-SW., and the other NW.-SE.— Suppose the two lines, projected as described, are as shown in figure 46, Aj Aj and Bj B^! f^r the present assume that the two points, Aj and Bj, have a common latitude. Drop the perpen- dicular PO from the intersection; then the latitude of the inter- section will be a distance OP above the common latitude of Aj and Bi, and its longitude will be a distance AjO to the right of Ai and BjO to the left of Bj. Find the angles ex and fi from the traverse table (Table 2), they being taken out with the difference of latitude between the two points of the same line in the column Lat. and the differ- ence of longitude in the column Dep. (Do not overlook the fact that we are dealing now with the plane of projection and that a and /3 are not the angles made by the Sumner line with meridians on the earth's surface. ) The solution may now be accomplished by either of two methods: (a) Observe that the case is the same as if a ship were steaming along the line Ai Bj and took the first bearing of the point P when at Aj, at an angle from the course equal to 90°— cr, and the second bearing when at Bj, at an angle from the course equal to 90°+/?, with an intervening run equal to the difference of longitude Aj Bj; or, she may be considered as steaming from Bj to Aj, in which case the first angle is 90°— /3 and the second 90° -fa. Picking out of Table 5 B, corresponding to the angles given, the quantity in the second column, we shall have the ratio of the distance of passing abeam, OP, to the distance Ai Bi; multiply the difference of longitude by this ratio, and we shall have the actual length of OP. Then entering the traverse table with this as a latitude and a: as a course, we find in the departure column the distance AiO by which the longitude of OP is defined; it is recommended also to pick out B,0, using the angle fi, which affords a proof of the correctness of all work done after the finding of a and yS. aSugKested by Lieut. G. W. Logan, U. 8. Navy. 120 THE SUMNEK LINE. (6) The second method is to find by trial and error some latitude such that its departure correspond- ing to a, plus its departure corresponding to /?, equals the difference of longitude Aj Bj-, then the point will be defined by the latitude, and by its longitude from Aj and Bj, the agreement of the longitude as established from the different points furnishing a check upon the operation. Example: Find the intersection of the following Sumner lines: 40^ N. 55.3 W. 40 N. 32.5 W. /50° 00^ N. A.A 7 20.0 W. (50 I 6 00 N. 11.3 W. +20^ lat. +24.7 long. +20 lat. —21.2 long. Line runs NW. «r=51°. -SE. Line runs NE.-SW. ^=47°. Longitude Ai B,=22^8. Fig. 47. Hence, intersection: (6) To solve by Table 2: First draw a rough sketch (fig. 47) to illustrate the direction of coordinates. Notice that Aj is west of Bj. The line through Aj runs NW.-SE. That through Bj, NE.-SW. The intersection is therefore south of both, east of Ai, and west of B,. (a) To solve by Table 5 B: First bearing (90°— a) =39°; second bearing (90°+/J) = 137°. Corresponding ratio, 0.43, mul- tiplied by 22^ 8 = 9^ 8 lat. ( The angles 90° - ^ and 90° ^ a would have given the same ratio, 0.43.) Then (Table 2) with a: = 51°, lat. =9'.8, dep. =12M; and with /i = 47°, lat. =9^8, dep. = 10^5. 9^8 S. of lat. 49= 12 .1 E. of long. 6 10.5W. of long. 6 Assuming lat 5' Dep. for 51° 6.2 Dep. for 47° 5.3 40^ 55.3 32.5 N. =49° 30^.2 N. W. = 6° 43 .2 W.\ , W. = 6° 43 .0 W.r 8^ 10^ 9^9 9.7 12.3 12.2 8.5 10.7 10.6 check. Hence, intersection: Sum. .11.5 18.2 23.0 22.8 9^9 S. of 49° 40' =49° 30''. 1. 12 .2 E. of 6 55.3= 6 43 .11 , . 10 .6 W. of 6 32.5= 6 43 .l/^^^^^* It may be seen that the results by the two methods substantially agree. 386. Case II. Both lines NE.-SW., or both NW.-SE.— Consider the lines as drawn in figure 48, and p continue the assumption that A^ and Bj have a common " latitude. The differences from the first case by both methods simply involve a change of signs. (a) If the ship is steaming from A^ toward Bj, the first angle from the keel line is 90° — a, and the second, 90° — ^; if steaming from Bj toward Aj, the first angle is 90° + /J, and the second 90° + a; in other words, either add both angles to 90° or subtract both from 90° and enter with the smaller angle as the first bearing. (b) It may be seen that O Aj — OBj = Aj Bj ; in other words, to solve by the second method, the values must be so found that the difference of the corresponding depar- tures equals the difference of longitude, instead of their Fig. 48. sums, as before. Example: Find the intersection of the Sumner lines defined below: , / 49° 30^ N. ^H 5 24.8 W. , f49°5y ^H 5 21.5 +20^ lat. —3.3 long. Line runs NE.-SW a=9°. ,, r49 30 N. •^H 5 25.8 W. R 149 50 ■"='\ 4 52.1 +20 lat. —33.7 long. Line runs NE.-SW. /?=59°. Ai Bi=F.O. In this case (fig. 49) Bj is west of Aj, the lines both ruQ NE.-SW., and /3 is the greater angle; there- fore intersection lies to the north and east of both points. (a) By Table 5 B: First course (90° -Lor) = 99°; second course (90° + /3)= 149°; ratio 0.67 XKO = 0^7; or, first course (90° — ^) = 31°; second course (90°-a) = 81°; ratio = 0.67, as before. Fig. 49. lat. =0^.7, dep. =0M; and /i = 59°, lat. =0^7, dep. =1^2. THE SUMNER LINE. 121 HeiJce, intersection: (b) By Table 2: 0^7N. of 49°3(y N. =49°3(y.7N. .1 E. of 5 24 .8 W. = 5 24 .7 W. \ , , 1 .2 E. of 5 25 .8 W. = 5 24 .6 W. /<^^ecK. Assuming lat 2^0 0^5 0^6 Dep. for 9° 0.3 0.1 0.1 Dep. for 59° 3 .3 0.9 1 .1 Difference 3.0 0.8 1 .0 Hence, intersection: 0^.6 N. of 49° 30' .1 E. of 5 24 1 .1 E. of 5 25 :49° 30^6 = 5 24 >} check. 3§7. In discussing these cases, we have assumed that there was a point of one line which had a common latitude with a point of the other line; this would be the case if two lines were worked from time sights taken at the same time. It may occur, however, either that they have not a common lati- tude, but do have a common longitude, as in the case of two lines worked from q)^ cf/' (latitude) sights taken at the same time; or that they have neither a common latitude nor a common longitude, as with one time sight and one latitude sight, or with two sights taken at different times. In case there is a (;om- mon longitude (fig. 50) , which will be rather a rare one, the problem is worked with OP as a longitude co- ordinate; the modification of the other method will B suggest itself, the principal change rendered necessary being due to the fact that the angles from the course in Table 5 B will be complementary to what they were before, as we are now dealing with angles to the meridian instead of angles to the parallel. When there is no common coordinate of either latitude or longitude, the simplest way of solving is first to find some point on one line which corresponds in latitude with one of the points on the other line, then solve as before. Thus, in figure 51, given Aj A2 and Bj B2, find ex and /3, and thence the longitude of a point A3 corresponding to the difference of latitude between A^ and Bj on the course a; then find intersection of A3 Aj and B^ Bj in the usual way. Example: Let it be required to find the intersection of. Sumner lines as follows: 30' S. , / 25° 50' S. +20' lat. Line runs SE.-NW. 22 E. "^^IIS 40 E. A I 25^ +18 long. a=42°. ■R / 25 15 S. ^M115 37 E. B, / 25 35 S. •4115 30 E. 20 lat. - 7 long. Line runs NE.-SW. Find where Bj B.^ crosses parallel 25° 30' S. yS=19°, lat. = +15', dep. = — 5'.1. Hence, the line B3 B^ becomes: 25° 30' S. , T> _Q/ Q Line runs NE.-SW. 115 31.9 E. Ai^3-y-y /i=:i9°: B. The directions of the lines (fig. 52) require us to follow Case I. Aj is west of B3. The line through A, runs SE.-NW., and that through B3, SW.-NE. Therefore, /^ o, the intersection is south of Ai and B3, east of A,, and west "^ ' ofB3. (a) By Table 5 B. (90°- a) =48°, (90° 4- /J) =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 7.6 9.9 122 THE 8UMNEE LINE. Intersection: 8^ S. of 25° 30^ = 25° 38^ 7.2 E. of 115 22 =115 29.21 2.7 W. of 115 31.9=115 29.21 •check. 38§. The following is a summary of the method when lines are given by coordinates of two points of each: (a) By Table 5 B. . (b) By Table 2. 1. Write down lines; find oc and /S. 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° - /5) and (90° + a). Cose//, angles (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 a and ft with latitude; this gives differences of longitude to the point of intersection from the re- spective points of common latitude. a) and (90° + yS) or (90° a) and (90° + /S) or (90° 1. Write down lines; 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 2, at pages a and /J; 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 P; reduce the difference of longitude Aj B^ to departure, and use this in miles instead of the Aj B, in minutes; and when A^O and BjO are found, being in miles of departure, they must be reduced to min- utes of loHgitude before being applied to the longitude of A^ and Bj. Example: The Sumner lines of the last example being expressed by a single point and the direction, as given below, find the intersection. f 25° 40^ 1115 31 r 25 1115 s. E. 25 S. 33.5 E. Line runs (a =) N. 39° W. Line runs (/3 = ) N. 18° E. First bring second line up to Lat. 25° 40^ S. /3 5'. 4; hence we have: 18°; lat. = + 15^ dep. = — 4.9 m. ; diff. long. = "{ 25° 40^ S. 115 28.1 E. Line runs (/3=) N. 18° E. Fig. 53. Intersection: (6) By Table 2: AB' = 2^9 = 2.6 miles. B' being west of A (fig. 53), and the lines through the two points running respectively NE. and NW., the intersection is north of both, east of B', and west of A. (a) By Table 5 B. (90° - a) = 51°; (90° + ft) = 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. 2^3 N. of 25° 40^ S. = 25° 37^7 S. 2 .0 W. of 115 ^ E. = 115 29 Klj^^^j^^ .8 E. of 115 28.1 E. = 115 28 .9 E. Assuming lat ¥ 2' 2^3 Dep.for39° 3.2 1.6 1.9 = 2M Dep.forl8° 1.3 0.7 0.7=0.8 Sum 4.5 2.3 '2.6 = 2.9 Intersection : 2^3 N. of 25° 40^ = 25= 2 .1 W. of 115 31 = 115 0.8E. of 115 28.1 = 115 37^7 28 28 ^check. THE SUMNEK LINE. 123 The following summary gives the various steps when the lines are each given by the coordinates of one point with the direction: (a) By Table 5 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 /, angles (90° -a) and (90°+/?) or {^°—fi) and (90°+a). Case II, angles (90°+a) and (90°+/S) or (90°— /i) and (90°— a). Take out ratio from second column, and multiply l)y 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 difference of latitude, and con- vert to difference of longitude; this gives differences of long:itude to the point of intersection from the respective points of common latitude. (6) By Table 2. 1. Write down lines as given. 2. If the points have not a common latitude, reduce one point to latitude of the other. 3. Write down difference of longitude and con- vert it to departure. 4. Draw rough sketch to illustrate direction of point of intersection. 5. Enter Table 2 at pages a and ft; find by 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 froni 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. Suppose, now, that after an observation the vessel sails a given distance in a given direction; it is clear that while her exact position is still undetermined it must be at one of the series of points comprised in a line 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 PRACTICE 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 azimuth from astronomical observations, it will be the aim of the present chapter to describe the conditions ^which govern the choice and employment of the various problems, together with certain qonsiderations by which the navigator may be guided in his practical work at sea. 392. Departure 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, Avhich, 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 from the ship. It is a good plan to record the time by chip'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. EouTiNE 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 amplified as circumstances render expedient. 394. Morning Sights. — The morning time sight and azimuth should be observed, if possible, when the sun is on the prime vertical. As the body bears east at that time, the resulting Sumner line is due north and south, and the longitude will thus be obtained without an accurate knowledge of the latitude. Another reason for so choosing the time is that near this point of the sun's apparent path the body is changing most slowly in azimuth, and an error in noting the time will have the minimum effect in its computed bearing. The time when the sun will be on the prime vertical — that is, when its azimuth is 90° — may be found from the azimuth tables or the azimuth diagram. Speaking generally, during half the year the sun does not rise until after having crossed the prime vertical, and is therefore never visible on a bearing of east. In this case it is best to take the observation as soon as it has risen above the altitude of uncertain atmospheric effects — between 10° and 15°. A series of several altitudes should be taken, partly because the mean is more accurate than a single sight, and partly because an error in the reading of the watch or sextant may easily occur when there is no repetition. If the sextant is set in advance of the altitude on even five or ten minute divisions of the arc, and the time marked at contacts, the method will be found to possess various advantages. As the sight is being taken the patent 4og should be read and ship's time recorded. It is well, too, to make a practice of noting the index correction of the sextant each time that the sextant is used. The bearing of the sun by compass should immediately afterward be observed, and the heading by compass noted, as also the time (by the same watch as was used for the sight). Before working out the sight, the dead reckoning is brought up to the time of observation, and the latitude thus found used as the approximate latitude at sight. It is strongly recommended that every sight he worked for a Sumner line, either by assuming two latitudes, or by using one latitude and the 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 ch'inge 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 9/ q/' sight, according to circumstances, a second Sumner hne obtained, and the intersection of the earUer Sumner with it will give the ship's position. 396. Noox Sights. — Between 11 and 11.30 o'clock (allowing for gain or loss of time due to the day's run) the ship's clocks should be set for the L. A. T. of the prospective noon position. The noon longitude may be closely estimated from the morning sight and the probable run. The navigator should also set his own watch for that time, to the nearest minute, and note exactly the number of seconds that it is in error. He may now compute the constant (art. 333, Chap. XII) for the meridian altitude. The daily winding of the chronometer is a most important feature of the day's routine, ami may well be performed at this hour. At a convenient time before noon, the observations for meridian altitude are commenced and continued until the watch shows L. A. noon, at which time the meridian altitude is measured and the latitude deduced. If the weather is cloudy and there is doubt of the sun being visible on the meridian, an altitude may be taken at any time within a few minutes of noon, the time noted, and the interval from L. A. noon found from the known error of the watch. It is then the work of less than a minute to take out the a from Table 26, the a/^ 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 foriner plan needs no explanation. There are a number of variations in the methods of computation, one of which will be given as a type. By the ship's run, work back the noon latitude to the latitude at a. m. time sight. If the Sumner line was found from two assumed latitudes which differed + vi minutes, while the corresponding longi- tudes differed d= n minutes, then V difference of latitude causes dz — minutes difference of longitude. If m the true latitude at sight is i a; minutes from one of the assumed latitudes, then =h a; X — is the corre- Vfi spending difference of longitude. If the Sumner line was found from one assumed latitude and an azimuth, Z, it makes an angle with the meridian equal to 90°— Z. Enter the traverse table with this as a course and with the difference between the true and assumed latitudes as a latitude, and the departure will be found; convert this into difference of longitude at the latitude of observation, and apply the result with its proper 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 up the longitude for the run between the sight and neon. 39§. CiREENT AND RuN. — The currcut may be fouud by Comparing the noou positious 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. Afternoon Sights. — 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 imperatively necessary that a more frequent determination of the latitude and longitude be made. If the vessel is near the land or in the vicinity of off-lying dangers, if she is running a great circle course requiring frequent changes, if she is making deep-sea soundings, if she has just come through a period of foggy or cloudy weather, or if the indications are that she is about to enter upon such a period, it is obviously inexpedient to await the coming of the next noon for a fix. The responsibilities resting upon the navigator require that he shall earlier find -his ship's position; and, generally speaking, the greater the speed made by the vessel the more absolute is this requirement. The key to all such determinations will lie in the Sumner line, and a clear understanding of the properties of such a line will greatly facilitate the solutions. The mariner must keep in mind two facts: First, that a single observation of a heavenly body can never, by itself, give the point occupied by an observer on the earth's surface; and second, that whenever any celestial body is visible, together with enough of the horizon to permit the measuring of its altitude, an observer may thereby determine a line which passes through his own position on the earth's surface in a direction at right angles to the bearing of the body. It may readily be seen that if two Sumner lines are determined the observer's position must be at their intersection, and that that intersection will be most clearly marked when the angle between the lines equals 90°; hence, if two heavenly bodies are in sight at the same time the position may be found from the intersection of their Sumner lines, the angle of intersection being equal to the horizontal angle between the bodies. If only one body is in sight, as is generally the case when the sun is shining, one line of position may be gotten from an altitude taken at one tim?, and a second line from another altitude taken when it has changed some 30° in azimuth — usually, a couple of hours later. Bringing forward the first line for the intervening run, the intersection may be found. With the general principles of the Sumner line clearly before him, the navigator will find no diffi- culty in making the choice of available bodies. If about to take a star sight, and sky and horizon are equally good in all quarters, two bodies should be taken whose azimuths differ as nearly as possible by 90°. if one l)ody can be taken on or near the meridian, its bearing being practically north or south, the resulting Sumner line will be east and west — that is, it may be said that whatever the longitude (within its known limits) the latitude will be the same; the other sight may then be worked as a time sight with this single latitude and time will thus be saved. The same is true if Polaris is observed, and it is a very convenient practice to take an altitude of that star at dawn and obtain a latitude for working 126 THE PRACTICE OF NAVIGATION AT SEA. the a. m. time sight of the sun. A similar case arises when a body is observed on the prime vertical; its Sumner line then runs north and south and coincides with a meridian; if the other body is favorably located for a cp^ (p" sight, it may be worked with a single longitude and the latitude thus found directly. If it is not possible to obtain two lines and thus exactly locate the ship, the indications of a single line may be of great value to the navigator. A Sumner line and a terrestrial bearing will give the ship's position by their intersection in the same manner as two lines of position or two bearings; or the posi- tion of the ship on a line may be shown with more or less accuracy by a sounding or a series of soundings. If the body be observed when it bears in a direction at right angles to the trend of a neighboring shore line, the resulting line will be parallel with the coast and thus show the mariner his distance from the land, which may be of great importance even if his exact position on the line remains in doubt. If the bearing be parallel to the coast line, then the Sumner line will point toward shore; the value of a line that leads to the point that the vessel is trying to pick up is amply demonstrated by the experience of Captain Sumner that led to the discovery of the method (art. 372, Chap. XV). For especially accurate work three Sumner lines may be taken, varying in azimuth about 120°; if they do not intersect in a point, the most probable position of the ship is at the center of the triangle that they form. If two pairs of lines be determined, each pair based upon observation of two bodies bearing in nearly opposite directions and at about the same altitude, the mean position that results from the inter- section of the four lines will be as nearly as possible free from 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 Stars, Planets, and Moon. — It may be judged that the employment in navigation of other heavenly bodies than the sun is considered ot the utmost importance, and mariners are urged to familiarize themselves with the methods by which observations of stars, planets, and the moon may be utilized to reveal to them 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 obtained 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 strongly recommended 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, will enable the navigator to recognize the more important constellations and single stars by their situation with relation to each other, and to the pole and the equator. It may occur, however, that occasion will arise for observing a body whose name is not known, either because it has not been learned, or because the surrounding stars by which it is usually identified are obscured by clouds or 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 onlv 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 be approximately deduced by applying the compass error. The method « to be described then affords a convenient means of identification. The quantities given are the corrected altitude of observation, h, the (approximate) true azimuth of the body, Z, and the latitude bv dead reckoning, L; those to be determined are the declination, d, and the hour angle, t. From the"^ astronomical triangle we have: sin Z sin t ~. r; or, sin Z cos /i.=sin I cos d. sin -p cosh The value of sin Z cos h (calculated from the given azimuth and altitude) must therefore equal sin t cos d, whatever the values of t and d may 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 h, the trial values of the hour angle and declination are the correct ones; if not, other trials may 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 " Suggested by Lieut. G. W. Logan, U. S. Navy. THE PRACTICE OF NAVIGATIOISr 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 haveto 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 D. 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 h. Z 107^^ h 38= sin 9. 981 cos 9. 897 sin Z cos /( log 9. 878 Now suppose the observer estimates from the position of the body that its declination is 3° S. Look in the azimuth table on the page of latitude 5° (declination contrary name to latitude ) , and find the hour angle (p. m. ) corresponding to Dec. 3° and Az. 107°; this is about l** 40""; then with d=3°, t=l^ 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*^. ) ( 1' 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 assumption 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 d log 9. 826 The logarithm is not yet quite large enough; assume declination 10° S.; the hour angle is 3'' 20"". t 3" 20" sin 9. 884 d 10° cos 9. 993 sin < cos d log 9. 877 This is practically identical with the logarithm of sin Z cos h, and the correct values are, therefore, t!=3'' 20", d=10° S. We now have: G. S. T. 12" 53"° Long. J 53^ W. L. S. T. 10 00 H. A. J 20 E. R. A. 13 20 From the Nautical Almanac it is found that the right ascension of Spica is 13'' 19" and the decli- nation 10° 32'' S. This is therefore the bodv observed. Example: March 18, 1879, in Lat. 26° S., Long. 5" 42" E., by D. R., the altitude of a body is 41° and i<^s azimuth S. 84° E., the Greenwich sidereal time being lO" 52". Required the name of the body. 84° 41° sin 9.998 cos 9.878 sin Z cos Mog 9.876 Assume first an hour angle of 3'' 00'". The corresponding declination is 23° (same name as lati- tude). t 3" 00" sin 9.849 d 23° cos 9.964 sin t cos d log 9.813 Next assume an hour angle of 3" 30". The declination is then 21° S. t 3" 30" sin 9.899 d 21° cos 9.970 ein t cos d log 9.869 1.28 THE PRACTICE OF NAVIGATION AT SEA. Assume hour angle 3^ 35". Declination is still nearest to 21° S t 3" 35" sin 9.907 d 21° cos 9.970 sin < cos rf log 9.877 The last assumption is therefore correct. We then have: G. S. T. 10" 52" Long. ^ 42E. L. S. T. 16 34 H. A. J 35 E. R. A. 20 09 As there is no fixed star corresponding to these coordinates the tables for the planets should be consulted. On March 18, 1879, the right ascension of Mars is 20'' 09", and the declination 21° 06^ S. This is therefore the body that was observed. 404. The following is a summary of the method employed: 1. Reduce time of observation to "Greenwich sidereal time and find the true altitude to the nearest degree. (These operations must be performed before any sight can be worked; they are, therefore, not strictly a part of the process of identification. ) 2. Correct the observed azimuth for deviation and variation. 3. Find the logarithm of sin Z cos h to the third place. 4. Assume a declination and find the corresponding hour angle that will produce the given azimuth at the given latitude; orassume an hour angle and find the corresponding declination. ( Use an azimuth table or diagram for the purpose.) 5. Find the logarithm of sin t cos d to the third place. 6. Observe whether this agrees with the logarithm of sin Z cos h, and if it does not, repeat trials until an agreement is found. 7. Having found the hour angle and dechnation, convert the Greenwich sidereal time into local sidereal time and subtract the hour angle if west, or add it if east; the result is the right ascension of the observed body, by which, with the declination and magnitude, the identification is accomplished. 405. The exactness with which the comparison of logarithms is carried out will depend upon the possibility of errors of identification in the region of the heavens involved. It will not usually be necessary to find the correspondence as closely as has been done in the examples given, and the cases will be rare when, with a fair estimate of hour angle or declination at beginning, a sufficiently accurate knowledge of the values can not be arrived at after the second approximation; and frequently the first will suffice for identificaton. 406. Value op the Moon in Observations. — Next to the sun, the most conspicuous body in the heavens is the moon, and it may therefore frequently be employed by the mariner with advantage. Owing to its nearness to the earth and the rapidity with which it changes right ascension and declina- tion, the various corrections entailed render observations of this body somewhat longer to work out, with consequent increased chances of error; and errors in certain parts of the work will have more serious results than with 'other bodies; the navigator will therefore usually pass the moon by if a choice of celestial bodies is offered for a determination of position; but so many occasions present themselves when there is no available substitute for the moon that the extra time and care necessary to devote to it are well repaid. During hours of daylight it is often clearly visible, and its line of position may cut with that of the sun at a favorable angle, giving a good fix from two observations taken at the same time, when the only other method of finding the position would be to take two sights of the sun sepa- rated by a time interval in which an imperfect allowance for the true run intervening would affect the accuracy of the result, or a clouding-over of the heavens would preventany definite result whatever being reached; and during the night, the gleam upon the water directly below the moon may define the horizon and give opportunity for an altitude of that body when it is impossible to take an observation of any other. Navigators are therefore recommended to make use of the moon with complete confidence whenever it will serve their purposes. It has been the purpose of this work to point out the features of the various sights wherein the practice with the moon differs from that of the sun, stars, or planets; care and intelligent consideration will render these quite clear. Besides its availability for determining Sumner lines of position, which it shares with other bodies, the moon affords a means for ascertaining the Greenwich meantime independently of the chronometer, thus rendering it possible to deduce the longitude and chronometer error. This is accomplished by the method of lunar distances, which is fully explained in Appendix V. If the Greenwich time given by an observation of lunar distance could be relied upon for accuracy, the method would be a great boon to the navigator; but this is not the case. The most practiced observer can not be sure of obtaining results as close as modern navigation demands, and the errors to which the method is subject are larger than the errors that may be expected in the chronometer, even when the instrument is only a moder- ately good one and its rate is carried forward from a long voyage. The method is not, therefore, recom- mended for use except where the chronometer is disabled or where it is known to have acquired some extraordinary error; and when lunar distances are resorted to care must be taken to navigate with due allowance for possible inaccuracy of the results. In this connection it is appropriate to say that the best safeguard against the dire consequences that may result from a disabled or unreliable chronometer is for every vessel to carry two — or, far better, three — of those instruments, the advantages of which plan are stated in article 265, Chapter VIII. 40T. Employment of Bodies dependent upon their Position. — The practical navigator will soon observe that there are certain conditions in which bodies are especially well adapted for the finding of latitude, and others where the longitude is obtained most readily. THE PRACTICE OF NAVIGATION AT SEA. 129 Taking the sun for an example, when a vessel is on the equator and the declination is zero, that body will rise due east of the observer and continue on the same bearing until noon, when for an instant it will be directly overhead, with a true altitude of 90°, and will then change to a bearing of west, which it will maintain until its setting. In such a case any observation taken throughout the day will give a true north-and-south Sumner line, defining longitude perfectly, but giving no determination of the latitude, excepting for a moment only when the body is on the meridian. With the exception noted, all efforts to determine the latitude will fail. The reduction to the meridian takes the form y. , becoming inde- terminate, and in the q/ cf/' sight the cosine of q/ will assume a value that corresponds alike to any angle within certain wide limits — the limits within which the circle of equal altitude has practically a north-and-south direction. In conditions approximating to this we may obtain a longitude position more easily than one for latitude, even within a few minutes of noon. As the latitude and declination separate, conditions become more favorable for finding latitude and less so for longitude; the intermediate cases cover a wide range, wherein longitude may be well determined by observations three to five hours from the meridian, and latitude by those within two hours of meridian passage. As extreme conditions are approached the accuracy of longitude determinations con- tinues to decrease; at a point in 60° north latitude, when the sun is near the southern solstice, its bear- ing differs only 39° from the meridian at rising; or, in other words, even if observed at the most favorable position, the resulting Sumner line is such that V in latitude makes a difference of 1.3 miles of departure, or 2^.6 of longitude, and is far better for a latitude determination than for longitude. And in higher latitudes still this condition is even more marked. Having grasped these general facts, the navigator must adapt his time for taking sights to the cir- cumstances that prevail, and when the sun does not serve for an accurate determination of either latitude or longitude the ability to utilize the stars, planets, and moon as a substitute will be of the greatest advantage. 40§. Use of Various Sights. — Having taken a sight, the navigator may sometimes be in doubt as to the best method of working it. No rigorous rules can be laid down, and experience alone must be his guide. In a general way it may be well, when the body is nearer to the prime vertical than to the meridian, to work it for longitude, assuming latitude, and using the time sight; and when nearer the meridian to work it for latitude, assuming longitude, by the q/ q/' method. The time sight is more generally used than the other, it has wider limits of accurate application and is probably a little quicker; but as the meridian is approached and the hour angle decreases small errors in the terms make large ones in the results. The q/ q/' or latitude method should not ordinarily be employed beyond three hours from the meridian, and then only when the body is within 45° of azimuth from the meridian and has a declination of at least 3°; with an hour angle of &" (90°) or a declination of 0° the trigo»ometric functions assume such form that the method is not available; nor does it give definite results when the azimuth is 90° or thereabouts. When the body is close enough to the meridian for the method of reduction to the meridian to be applicable, that method is to be preferred because of its quickness and facility. It should be noted, however, that, though close enough to employ the reduction, it may not be sufficiently correct to assume that the body bears due north or south, and the sight should be worked with two longitudes, or the Sumner line determined by the azimuth, unless the bearing nearly coincides with the direction of the meridian. In cases where a body transits near the zenith, a good fix both in latitude and longitude may be obtained by sights, a few minutes apart, near its meridian passage. Various special methods have been devised for doing this, but it seems simpler to treat the problem as an ordinary one for Sumner lines, except where it falls within the narrow limits of application of the equal altitude method (art. 352, Chap. XIII). The solution is possible, because in the condition where it is available (that of a high transit) the body makes a very rapid change of azimuth (from nearly east to nearly west) in a short space of time, and two observations separated by a short interval give Sumntr lines that cut at a favorable angle. The time sight or latitude sight may be used according as the body's bearing is greater or less than 45° from the meridian. If one observation be taken when the bearing is about SE. and the other when it is about SW., the intersection, allowing for intervening run, will not only give the longitude, but will also afford a good check upon the meridian observation for latitude, which, in the case of high transits, it is difficult to make with perfect accuracy. 409. Working to Skconds and Accuracy of Determinations. — The beginner who seeks counsel from the more experienced in matters- pertaining to navigation will find that he receive.s conflicting advice as to whether it is more expedient to carry out the terms to seconds of arc, or to disregard seconds jand work with the nearest whole minute. It is a well-recognized fact that exact results are not attainable in navigation at sea; the chro- nometer error, sextant error, error of refraction, and error of observation are all uncertain; it is impos- sible to make absolutely correct allowance for them, and the uncertainty increases if the position is obtained by two observations taken at different times, in which case an exactly correct allowance for the intervening run of the ship is an essential to the correctness of the determination. No navigator should ever assume that his position is not liable to be in error to some extent, the precise amount depending upon various factors, such as the age of the chronometer rate, the quality of the various instruments, the reliability of the observer, and the conditions at the time the sight was taken; perhaps a fair allowance for this possible error, under favorable circumstances, will be 2 miles; therefore, instead of plotting a position upon the chart, and proceeding with absolute confidence in the belief that the ship's position is on the exact point, one may describe, around the point as a center, a circle whose radius is 2 miles — if we accept that as the value of the possible error — and shape the future courses with the knowledge that the ship's position may be anywhere within the circle. It is on account of this recognized inexactness of the determination of position that some navigators assume that the odd seconds may be neglected in dealing with the different terms of a sight; the average possible error due to this course is probably about one minute, though under certain conditions it may 6583—06 9 130 THE PEACTICE OF NAVIGATION AT SEA. be considerably more. It is possible that, in a particular case, the error thus introduced through one term would be' offset by that from others, and the result would be the same as if the seconds had been -taken into account; but that does not affect the general fact that the neglect of seconds as a regular thing renders any determination liable to be in error about one minute. Those that omit the seconds argue, however, that since, in the nature of things, any sight may be in error two minutes, it is imma- terial if we introduce an additional possibility of error of one minute, because the new error is as liable to decrease the old one as to increase it; but the fallacy of the argument will be apparent when we return to the circle drawn around our plotted point. The eccentricity of the sextant may exactly offset the improper allowance for refraction, and the mistake in the chronometer error may offset the observer's personal error, but unless we know that such is the case — which we never can — we have no justification for doing otherwise than assume that the ship may be any place within the 2-mile circle. If, now, we increase the possible error by 1 mile, our radius of uncertainty must be increased to 3 miles, and the diameter of the circle, representing the range of uncertainty in any given direction, is thereby increased from 4 to 6 miles. It is deemed to be the duty of the navigator to put forth every effort to obtain the most probable position of the ship, which requires that he shall eliminate possible errors as completely as it lies within his power to do. By neglecting seconds he introduces a source of error that might with small trouble be avoided. This becomes of still more importance since modern instruments and modern methods constantly tend to decrease the probability of error in the observation, and to place it within the power of the navigator to determine his ship's position with greater accuracy. 410. There is a more exact way of defining the area of the ship's possible position than that of describing a circle around the most probable point, as mentioned in the preceding article, and that is to draw a line on each side of each of the Sumner lines by which the position is defined, and at a uniform distance therefrom equal to the possible error that the navigator believes it most reasonable to assume under existing conditions; the parallelogram f( rmed by these four auxiliary lines marks the limit to be assigned for the ship's position; this method takes account of the errors due to poor intersections, and warns the navigator of the^ direction in which his position is least clearly fixed and in which he must therefore make extra allowance for the uncertainty of his determination. It must be remembered in this connection that no position can ever be obtained except from the intersection of two Sumner lines, whether or not the lines ar6 actually plotted; thus, a meridian altitude gives a Sumner line that extends due east and west, and a sight on the prime vertical a line that extends north and south, though it may not have been considered necessary to work the former with two longitudes or the latter with two latitudes. 411. The Work Book and Fobms for Sights. — The navigation work book, or sight book, being the official record of all that pertains to the navigation of the ship when not running by bearings of the land, should be neatly and legibly kept, so that it will be intelligible not only to the person who per- formed the work, but also to any other who may have reason to refer to it. Each day's work should be begun on a new page, the date set forth clearly at the top, and prefer- ably, also, a brief statement of the voyage upon which the ship is engaged. It is a good plan to have the dead reckoning begin the space alfotted for the day, and then have the sights follow in the order in which taken. The page should be large enough to permit the whole of any one sight to be contained thereon without the necessity of carrying it forward to a second page. No work should be commenced at the bottom of a page if there is not room to complete it. Every operation pertaining to the working of the sights should appear in the book, and all irrelevant matter should be excluded. It is well to observe a systematic form of work for each sight, always writing the different terms in the same position on the page; this practice will conduce to rapidity and lessen the chances of error. In order to facilitate the adoption of such a method, there are appended to this work (Appendix II) a series of forms that are recommended for dead reckoning, and for time sights, meridian altitudes, and latitude sights (both by (f/ q/' formula and method of reduction to the meridian), for the sun, stars, planets, and moon, respectively. . For beginners, these are deemed of especial importance, and it is recommended that, until perfect familiarity with the different sights is acquired, the first step in work- ing out an observation be to write down a copy of the appropriate blank form, indicating the proper sign of application of each quantity (for which the notes will be a guide), and not to put in any figures until the scheme has been completely outlined; then the remainder of the work will consist in writing down the various quantities in their jproper places and performing the operations indicated. MARINE SURVEYING. 131 chaptp:r xvii. maeine surveying. 412. Definitions. — Surveying is the art of representing upon paper the surface of the earth, giving its characteristic features, such as, on land, the position of prominent objects, heights, and depressions, and on water, the depth, character of bottom, and position of shoals. Topographical Surveying delineates the land, and Hydrographic Surveying, the water. Geodesy is a higher kind of surveying, which takes into account the curvature of the earth. To points determined by a geodetic survey other surveys are referred. It is not deemed appropriate to include in this work a complete treatise on Marine Surveying. The scope of this chapter will be to set forth such general information regarding the principles of surveying and the instruments therein employed as will give the navigator an intelligent understanding of the subject sufficient to enable him to comprehend the methods by which marine charts are made, and, if occasion should arise, to conduct a survey with such accuracy as the instruments ordinarily at hand on shipboard may permit. For a more detailed discussion of Marine Surveying, the student is referred to the various publications which treat the subject exhaustively. INSTRUMENTS EMPLOYED IN MARINE SURVEYING. 413. The Theodolite AND Transit. — The Theodo- lite ( fig. 54 ) is an i"nstrument for the accurate measure- ment of horizontal and ver- tical angles. While these instruments vary in detail as to methods of construc- tion, the essential principles are always identical. A telescope carrying cross- hairs in the common focus of the object-glass and eye- piece is so mounted as to have motion about two axes at right angles to one an- other; graduated circles and verniers are provided by which angular motion in azimuth and (usually) in altitude may be measured; and the instrument is capa- ble of such adjustment by levels that the planes of mo- tion about the respective axes will correspond exactly with the horizontal and the vertical. The telescope is carried in appropriate supports upon a horizontal plate which has, immovably at- tached to it, one or more verniers, and which revolves just over a graduated circle that is marked upon the periphery of a second hori- zontal plate, a means of measuring the motion of the upper plate relatively to the lower one being thus provided. Thumb- screws are fitted by which the up- per plate may be clamped to the lower, and (except- ing in some simpler forms of the instrument) others by which the lower plate may be made immovable in azi- muth, or allowed free mo- ^ _ tion, at will; all clamping ^^" ^ ' arrangements include slow-motion tangent-screws for finer control. 132 MARINE SURVEYING. A vertical graduated circle, or arc, with a vernier, clamps, and tangent-screws, is fitted to most theodolites, for the measurement of the angular motion of the telescope in altitude. The theodolite usually carries a magnetic needle, with a graduated circle and vernier for compass bearings. The instrument is mounted upon a tripod, and levels and leveling-screws afford a means of bringing the instrument to a truly horizontal position. The Transit used in surveying is a modified form of the theodolite, and is generally employed where less accuracy is required; it takes its name from the fact that the telescope may be turned completely about its horizontal axis, or transited, without removal from its supports. 414. The line ofcoUimation of a telescope is an imaginary line passing through the optical center of the object-glass in a direction at right angles to that of its axis of rotation. This is also called the axis ofcoUimation. The line of sight ib an imaginarv line passing through the optical center of the object- glass and the point of intersection of the cross-hairs. A theodolite or transit, before it can be used for the accurate measurement of angles, must be in adjustment in the following respects: (a) The vertical axes of revolution of the upper and lower hori- zontal plates must be coincident; (b) the axis must be vertical and the plates horizontal when the bubbles of the levels are in their central positions; (c) the vertical cross hair must be perpendicular to the horizontal axis of the telescope; (d) the line of collimation must coincide with the line of sight; (e) the horizontal axis of the telescope must be perpendicular to the vertical axis of the instrument; (/) the bubble of the telescope level must stand at the middle of its scale, and the vertical circle must read zero, when the line of collimation is horizontal. The last-named condition may be disregarded if vertical angles are not to be measured. 415. The instrument being in adjustment, to observe angles it should be set up, leveled, and focused. This involves placing the tripod so that a plumb bob from the center of the instrument shall hang directly over the spot at which the measurement is to be made. The legs of the tripod should be firmly placed in such manner that the height shall be convenient for the observer and the instrument shall be nearly level. Then the horizontal plates are brought to a true level by means of the leveling screws and bubbles. The telescope should next be focused by moving the object glass and eyepiece in such manner that the object sighted and the cross hairs may be plainly seen and that the object will not appear to have motion relatively to the cross hairs as the eye is moved to the right or left in front of the eyepiece. This last condition insures the cross hairs being at the common focus of the eyepiece and objective. To observe a horizontal angle with a theodolite or transit, clamp the upper plate to the lower at zero, leaving the lower plate imclamped; swing the telescope so that its vertical cross hair bisects one of the objects, and clamp the lower plate; unclamp the upper plate and bring the telescope to bisect the other object, and the reading of the vernier on the scale will give the required angle. (The final nice motion by which the cross-hair is brought exactly upon a point is always given by the tangent screw. ) In taking a round of angles, this operation is repeated successively upon each object to be observed about the horizon, the upper plate being always swung, while the lower is kept where set upon the first object, or origin. The result will give the angular distance of each object from the origin, and, if the observations have been accurately made, upon finally sighting back to the origin, the reading should be zero. To repeat an angle, having made the first measurement of it in the usual way, unclamp the lower circle and swing back the telescope until it again points to the first object, and clamp it; then unclamp the upper circle, swing to the second object, and clamp. The scale-reading should now be double that of the first angle. Repeat as often as the importance of the angle requires, and the accepted value will be the final reading divided by the number of measurements. All angles of the main triangulation, and others of importance in the survey, are repeated. Defects in adjustment of the instrument may be eliminated by taking one series of angles with the telescope direct and another with the telescope reversed. To reverse the telescope, revolve it about its horizontal axis through 180°, then swing it about its vertical axis through 180° — in other words, invert it. Vertical angles are measured on the same principle as that described for horizontal ones. The process of setting up the instrument at a station and observing the angles between the various objects that are visible is called occupying the station. 416. The Plane Table. — This is an instrument by which positions are plotted in the field directly upon a working sheet. It consists (fig. 55) of a drawing board mounted upon a tripod in such manner as to be capable of motion in azimuth, and with facilities for being brought to a perfect level; in con- nection with it is employed an alidade, consisting of a straightedge ruler, upon which is mounted a telescope with cross-hairs whose line of sight is exactly parallel to the vertical plane through the edge of the rule. It is evident that if a sheet representing a chart be placed upon such a board and turned so that the true meridians, as portrayed thereon, lie in the direction of the earth's meridian at that place, then all lines of bearings on the chart will coincide with the corresponding lines on the earth's surface; from which it follows that if the alidade be so placed that its rule passes through the spot on the chart representing the position of the observer, while th6 telescope is directed to some visible object, the position of that object on the chart lies somewhere upon the line drawn along the edge of the rule. Upon this general principle depend the various applications of the plane table. The drawing board is usually made of several pieces of well-seasoned wood, tongued and grooved together, with the grain running in different directions to prevent warping; about its edge are several metal clips for securing the paper in place. It is supported upon three strong brass arms, to which it is attached by screws, thus permitting its removal at will. The arms are attached to a horizontal plate which revolves upon a second horizontal plate lying immediately below it; a clamp and tangent screw are fitted, by which the upper plate, and with it the drawing board, may be secured to the lower plate, or may be given a fine motion in azimuth. Three equidistant lugs of brass, grooved on the under side, project down from the lower plate, resting on screws in the top of the tripod, by which the instrument 18 leveled; when adjusted in this respect it is firmly clamped in position, and, as the tripod is made unusually large, the adjustment is not easily deranged. MAEINE SURVEYING. 133 The alidade is a metal straightedge with a vertical column at its center, at the top of which are the supports which carry the telescope; a vertical arc and vernier are provided for measuring the motion of the telescope in altitude. The telescope is usually so fitted that it may he revolved in azimuth through an arc of exactly 180°, for the purpose of adjusting the line of collimation. On top of the rule near Its center is the level — sometimes replaced by two levels at right angles — by means of which it may be seen when the table is in a true horizontal position. A magnetic needle mounted in a rectangular metal box, whose outer straightedge is parallel to the- zero line of a graduated scale over which the needle swings, is provided for drawing the north-and-south line on the chart; this is called a dedinatoire. Fig. 55. 417. To be in correct adjustment, a plane table must comply with the following conditions: (a) The fiducial edge of the rule must be perfectly straight. (6) The level must have the bubble in its central position when the table is truly horizontal, (c) The vertical cross hair must be perpendic- ular to the horizontal axis of the telescope, {d) The line of collimation must coincide with the line of sight, (e) The horizontal axis of the telescope must be parallel to the plane of the table. (/) The vertical circle should read zero when the line of collimation is horizontal. 418. The results derived from the use of the plane table, like all others dependent upon graphic methods, must be regarded as less accurate than those deduced by computation, and even less accurate than those derived from the careful plotting of theodolite angles. Hence it is that, in a careful marine survey, this instrument would be employed only for the topography and shore line. For whatever purpose used, the plane table would not ordinarily be called into requisition until the survey had so far progressed that a chart could be furnished the observer showing certain stations whose positions were already established; with this chart, the first step would be to occupy one of the determined points. The table must be set up with the point on the chart directly over the center of the station; it must then be leveled and the telescope focused as described for the theodolite or transit; and finally it must be oriented, that is, so turned in azimuth that all lines of the chart are parallel to similar lines of the earth's surface. To orient, unclamp the table and swing it until the north-and-south lineof the chart is approximately parallel to that of the earth, one means of doing which is afforded by the dedi- natoire; place the alidade so that the edge of the rule passes through the points on the chart representing the station occupied and some second- station which is clearly in view; then, sighting through the tele- scope, per/ect the adjustment of the table by swinging it until the second station is exactly bisected by the vertical cross hair, the final slow motion being obtained by clamping the table and working the tangent screw. If the adjustment has been correctly made, the rule may be laid along the line joining the station occupied and any other on the chart, and the telescope will point exactly to that other station. Being properly oriented, if the alidade be so placed that the edge of the rule pass through the station occupied, and the telescope point directly to some unknown object whose position is to be determined, 134 MARINE SURVEYING. then a line drawn along the rule will contain the point which represents the position of that object. If, now, the plane table be set up at a second station, oriented for its new position, and a line be simi- larly drawn from that station toward the one to be established, it will intersect the first line in the required point. This is the method of determining positions by prosection. Actually, the surveyor does not regard the point as well established until the intersection is checked by a line from a third station. In practical work, of course, each station is not occupied separately for the determination of each point; the instrument is set up at a station, lines are drawn to all required points in view, and each line is appropriately marked; then a second station is occupied, and the operation repeated, and so on, the various intersections being marked as the work proceeds. A second method of establishing positions is that of 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 and 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; place the edge of the rule upon the plotted position of this station and swing the alidade (the rule always being kept on the plotted point) until the object is bisected by the telescope cross-hairs; draw this line, and its intersection with the first will give the required point, Vie 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 undetermined 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 maybe 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 equal to the length of the base line (reduced to 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 was measured, the scale of the chart would be determined, being equal to the distance on the chart between base stations divided by the length of the base line. 430. 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 telescope, it being evident that the closer the distance the fewer divisions will appear between them. The facility with which distances can be measured by this method makes it most important that all telescopes of theodolites, transits, and plane tables be fitted as telemeters, and that stadia rods be provided for all surveying work. Speaking approximately, it may be said that the number of divisions intercepted between the cross- hairs will vary directly as the distance of the stadia rod. This would be exactly true if we looked at the object through an empty tube, directly between the hairs. Since, however, the rays from the stadia are refracted by the object glass before they are intercepted by the wires, the statement, to be absolutely exact, must be slightly modified; but for practical surveying work it may be accepted as given. 422. There are two methods of installing the telemeter cross-hairs — the first, in which they are immovably secured in the telescope and always remain at the same distance apart, and the second, in which the distance of the cross hairs is made variable, being under the control of the observer. The former is generally regarded as the preferable method, and when it is employed it is evident that the subtended height of the stadia bears a constant ratio to the distance of the staff from the telescope. It proves most convenient in practice 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 SURVEYING. 135 When the cross-hairs are movable the ratio becomes variable, but the principle of measuring j^mains 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. 423. 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. The use of the telemeter and stadia for measuring distances is limited to the distance at which the scale divisions can be accurately read through the telescope. For fairly close work and with the 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 fixed length, as, for example, 10 feet, and of slight width and thickness; this is held at right angles to the line of sight from the observer, who notes the angle subtended by the total length; tables are prepared by which the distance corresponding to each angle is given. 427. The Sextant. — This instrument is of the greatest value in hydrographic surveying. It is fully described elsewhere in this work and its adjustment explained (Chap. YIII). 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 yarious 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 hori*)n. 428. The Level. — This is an instrument for the accurate measure of differences of elevation. It consists of a telescope, 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 a'titude 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 observa- 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 points, and, while holding it on the ground in a truly vertical posi- tion, move the target, under the direction of the observer at the telescope, to a point where it is exactly bisected by the horizontal cross-hair; the height of the target on the staff — that is, the height of the cross- hair above the level of the first point — is then accurately 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 number of shifts any difference may be measured. The work of the level may be performed equally well by a theodolite whose telescope is adjusted to the true horizontal. 430. Heliotrope and Heliograph. — 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 be distinguishable. The instruments vary widely in form of construction and, in the absence of those made for the purpose, substitutes may easily be devised. 431. Astronomical Transit Instruments. — 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 horizon,tal 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 (fig. 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 sides, and are pro- vided with verniers giving the angular distance from the middle arm. The pro- tractor being set for the right and left angles, it is so moved that the three arms pass through the respective stations, when th^ center marks the position of the ob- server. Center pieces of various 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 they were laid off will be on the ^'*^'- ''^• 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 part of its course along the beam. Upon each head a socket is constructed to carry a plain point, exchangeable for an ink or a 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 passes 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 Fig. 57. 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 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 be given any desired value. Being adjusted in this respect, if a distance is taken off a chart with the legs at one end of the instrument, then those at the other end will 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 HYDBOGRAPHIC 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 signals; certain other positions, known as inain triangulation 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 ea(!h 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 base near the end of the triangulation, 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 clote 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 points 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 jtiq 5g_ 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 about tides and currents which is to appear upon the chart. Observations are made to determine the magnetic variation 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 hydrographic 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. 43§. 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, the value of each side becomes twice as great as it was before; with the same triangulation, therefore, distances vary directly with the length of the base line; it may thus be seen that if an error exists in measurement which is only a small fraction 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 MARIT^E 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 facihtj' 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, whatever its nature, the distance traversed being appropriately marked after each fleet, while an observer, with a theodolite or transit, insures the measurement being made accurately along the line. 440. The most careful measurements are made by a steel tape 100 feet long, stretched along a series of battens which are supported by metal crutches and made exactly horizontal by a level. The tape is stretched to a uniform tension 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 ground a peg carrying in its top a tack; the exact end of the tape is marked by a score filed on the head of the tack at a point marked by a plumb bob from the tape, and this score becomes the origin for the next fleet. An assistant precedes the measuring party before each shift of the battens, and is accurately aligned by the theodolite to mark the true direction of the base line. The result of this method of measurement gives the horizontal distance between the points. It can be depended upon for the greatest degree of accuracy of any method, excepting that with a special base-measuring apparatus, which is seldom employed in marine surveys. 441. A second method of base measurement is with the surveyor's chain. This depends for accu- racy upon the surface traversed being plane and level, a condition that is well fulfilled on a sandy beach, where the chain is nearly as accurate as the tape and much more rapid. A surveyor's chain is usually 100 feet long; the exact value of its length 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 pins driven into the ground; the alignment is kept by the theodolite. 442. Where neither chain nor tape 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 l)e taken as giving a closer result. 444. A crude method of measuring a base is by means of the velocity of sound, though this would never be used where close results are expected. Fire a gun at one end" of the base and at the other note by the most accurate means available the time between seeing the flash and hearing the report. Repeat several times in each direction. The mean 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 positions of the two stations which are most widely separated may be deter- mined astronomically and plotted; the triangulation is then plotted upon anv 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 positions 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 wide variety. A vessel regularly fltted 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 be provided, if possible, before beginning any surveying work. Regular tripod signals, which are quickly erected and are visible, under favorable circumstances, for many miles, are almost invariably employed tomark 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- Of THE UNIVERSITY « ^'^ J 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 t^urmounted by a flag, suggest some of the secondary signals that may be employed; sometimes objects are found that are sufficiently distinct in themselves to be used as signals without further marking, as a 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. 44§. The Main Triaxgulation. — 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, such as mountain peaks, which would not otherwise be regarded as properly within the limits of the survey. Great care should be taken in observing all angles upon which the main triangulation is based; the best available instrument should be employed; angles taken with a theodolite or transit should be repeated, and observed with telescope direct and reversed, and the mean result taken; if the sextant is used, a 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 w-ell 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. The 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. . 451. 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 equal 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 3(K^ 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 w^ere taken, the resulting latitude would be SO^^ 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 ihe 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 ia used, the same end of the roof should always be the near one to the observer; in taking the sun, however, as the personal error may not be the same for approaching as for separating limbs, every series of observations should be made up of an equal number of sights taken under each condition. 453. With all of this in mind, we arrive at the general rule that astronomical determinations shall be based upon the mean of observations, under similar conditions, of todies 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 the 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 topography, and should be employed when available. Points on shore may also be plotted by sextant angles, using the three-point problem, or by any other reliable method. 457. 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 of which depend upon the scope of the survey. It is usual for one series of lines to extend in a direction normal to the general trend of the shore line. In most cases a second series runs perpendicular to the first, and in surveys of 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 Dy the time interval or patent-log distances. 45§. There are a number of methods for determining positions while sounding, which may be described briefly as follows: By two 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 teken 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. EuNNiNG 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 8URVEYIKG. 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 Cause 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 understand 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 ounces, or aVjout 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 the^ go. The atmospheric pressure at sea level throughout the heated areas will thus be diminished, while that over the circumjacent cooler areas will be correspondingly increased. As the result of this difference of pressure, there will be movement of the surface air away from the region of high 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 immediately 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 ronunaieiy 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 Distribution 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 isolaaric 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 at)out 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 rapidh' 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. Skasonal Variations of Pressure. — 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, in keeping with its slight contrast between winter and summer temperatures, similar variations of pressure do not exist. 467. The Prevailing Winds. — As a result of the distribution of 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 of southern latitudes. 46S. 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, tlie occurrence of the latter within the limits of the trade wind region being furthermore con- fined in point of time to the late summer and autumn months of the respective hemispheres, and in scene of action to the western portion of the several oceans. The South Atlantic Ocean alone, however, enjoys complete immunity from tropical cyclonic storms. 470. The Doldrums. — The equatorial girdle of low pressure occupies a position 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 i^atitudes. — 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 horse 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 become 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 a^ain 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 temj^erate 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 explanation 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 oljedience to these gradients, constantly diverted to the left by the effect of the earth's rotation, constitutes the steady westerly winds of the south temperate zone. 473. The Monsoon Winds. — The air over the land is warmer in summer and colder in winter than that over the adjacent oceans. During the former season the continents thus 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 wind, 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 northeast (winter) monsoon blows in the China Sea from October to April, the southwest (summer) monsoon from May to September. The former is marked by all the steadiness of the trades, often attaining the force of a moderate gale; the latter appears as a light breeze, unsteady in direction, and often sinking to a calm. Its prevalence is frequently interrupted by tropical cyclonic storms, locally known as typhoons, 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 6583—06 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 of high pressure, from the center of which the baric gradients radiate in all directions, giving rise to an outflowing system of winds, which by the effect of the earth' s rotation is converted into an outflowing spiral eddy or anticyclonic tohirl. 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 ^nd round this area by the west; similarly for the other hemisphere. CYCLONIC STORMS. 147 CHAPTER XIX. OYOLONIO STORMS. 476. Variations of the Atmospheric Pressure. — The distribution of the atmospheric pressure previously described (Chap. XVIII) 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 stationary, 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. m. 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 fr^uently 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 ca*e 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. 480. Cyclones and Cyclonic Circulations. — A central area of low barometer will thus be sur- rounded by a system of Avinds 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 148 CYCLONIC STORMS. motion. Where the barometric gradients are steep, these winds are apt to be strong; where they are gentle, the winds are apt to be weak; where they are absent, as is the case af the center or bottom of the depression, calms are apt to prevail. Around the center of the area of high pressure a similar system of wind will 1)9 found, but blowing in a contrary direction. Here the barometric gradients are directed radially outward, with the result that in place of the inflowing, we have an outflowing 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 shoiyn in the accompanying diagrams (fi^. 60), which exhibit the general character of cyclonic (around the low) and anticyclonic (around the high) circulations in the northern An icyclonic. NORTHERN HEMISPHEKE. Cyclonic. Anticyclonic. Cyclonic. SOUTHERN 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 which 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. 481. Features of 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 slow. 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-pr»s5ure 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 haying 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, with 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. 483. Tropical Cyclonic Storms. — The occurrence of tropical cyclonic storms is confined to the summer and autumn months of the respective hemispheres, and to the western part of the several oceans, the North Atlantic, the North Pacific, the South Pacific, and the Indian Ocean. They are unknown in the South Atlantic Ocean. The Arabian Sea and the Bay of Bengal are also visited by cyclonic storms, the season of their occurrence extending from May to" October. 484. Motion 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 Bfrmn^ jrade wind region, to follow a path which tends at once westward and away from the equator. This motion continues until the limits of the trades are reached, where the path ordinarily recurves, and the 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. 485. Bate OF Progress of the Storm Center. — Within the tropics (in the northern henaisphere) 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 A'elocity 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 cyclonic storm in either hemisphere and the cyclonic circulation of the wind about the storm center are" given in figures 61 and 62; that for the northern hemisphere applying to the West India hurricane; that for the southern hemisphere to the hurricanes of • iiii, 9° . , . , , . .i » i , i n in i a ]. . j the South Pacific Ocean. ui:. ; ..'^ -.i v.--. :' ^ ^.- .'v:-^:.:.*; ; ; ; i ; ; ; 4§6. Character of Tropical Cyclonic 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 srx 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. 4§§. To Fix the Distance op'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 hove-to in advance of a tropical cyclonic storm will experience a long heavy swell, a falling barometer with torrents of rain, and winds of steadily increasing force. The shifts of wind will depend upon the position of the vessel with respect to the path followed by the storm center. Immediately upon the path, the wind will hold steady in direction until the passage of the central calm, the "eye of the storm," after which the gale will renew itself, but from a direction opposite to that which it previ- 150 OYOLONIC STORMS. ously had. To the right of the path, or in the right-hand semicircle of the storm (the observer being supposed to face along the track), the wind, as the center advances and passes the vessel, will constantly shift to the right, the rate at which the successive shifts follow each other increasing with the prox- imity to the center; in this semicircle, then, in order that the wind shall draw aft with each shift, the vessel must be hove-to on the starboard tack; similarly, in the left-hand semicircle, the wind will con- stantlv shift to the left, and here the vessel must be hove-to on the port tack. These rules hold alike for both hemispheres and for cyclonic storms 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. Dangerous 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 becoming involved in the actual center itself, inasmuch as there is a distinct tendency on tlie part of the latter to move away from the equator. For these reasons the more remote semicircle has been called the dangerous; the less remote, i\\Qnavigable. 491. Maneuvering. — A vessel sus- pecting 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 hour, 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 from 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 v."ith 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 by 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 op 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 Ihble, Northern Hemisphere. If wind 1 Direction Direction shifts to- If wind shifts towards tlie If wind steady with falling If wind steady with rising 1 of wind. of center. wards the left. barometer. barometer. i right. North. ESE. a Run SSW. a Run SSW. ffi Run SSW. a NNE. NE. ENE. SE. SSE. South. 95 li" -: <^ Run SW. Run WSW. Run West. old CO if obli port ti Run SW. Run WSW. Run West. old course obliged to port tack. Run SW. Run WSW. Run West. old CO if obli starbo East. ESE. SSW. SW. ' wind irry sa oblige rboard Run WNW. Run NW. urse ged ick. Run WNW. Run NW. Run WNW. Run NW. §li SE. WSW. Run NNW. r„ Run NNW. ^g Run NNW. K) ^ -^ SSE. West. on star il as lor d to hea tack. Run North. tr^ Run North. SS o' Run North. f 5- ai South. WNW. Run NNE. ^ < am Run NNE. p p Run NNE. 8= ssw. SW. NW. NNW. Run NE. Run ENE. Run NE. Run ENE. 6^ Run NE. Run ENE. < H 1'^ WSW. North. I^g- Run East. 5 Run East. clo Run East. P i West. NNE. s-^^ Run ESE. '^o Run ESE. §g Run ESE. %^ WNW. NE. - a, g p Run SE. Run SE. S S Run SE. 00 NW. ENE. Run SSE. ^5^ Run SSE. ° fT Run SSE. <= g NNW. East. no 22. $2. o- Vt«r Run South. 3 if Run South. 3 k; Run South. 3 if a Courses given are for wind two points on starboard quarter, but it U 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 qbliged 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 1 of wind. of center. right. wards the left. barometer. barometer. 1 North. WSW. Run SSE. a . a Run SSE. a 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 course « as if obliged to h port tack. ENE. NW. Run SW. Run SW. re Run SW. East. NNW. Run WSW. 50 oq s 3 '^ s • wind c sail as lo d to he. tck. Run WSW. arse as k d to he ard tack Run WSW. ESE. SE. SSE. North. - NNE. NE. Run West. Run WNW. Run NW. Run West. Run WNW. Run NW. Run AVest. Run WNW. RunNW. South. ENE. Run NNW. 5 0' n por ngas ive-to. Run NNW. 5 5 Run NNW. is- SSW. East. Run North. ?:ra Run North. o 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^ O" 32™. 2 Corr. for +74° Long. (Tab. 11), + 10 L. M. T. of local transit, 22 42 Transit, 22« 0" 42"" Transit, 22"^ 0'^ 42" H. W.Lun. Int. (App. IV), 8 44 L. W. Lun. Int. (App. IV), 2 49 L. M. T., H. ^Y., { l^rfi Jf 9 26 p. m. L. M. T., L. W., ' { "^J, JJg 3^ ^^ ^^^ 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" 36"'. 6 Corr. for +122° Long. (Tab. 11),+ 22 L. M. T. of local transit, 6 12 59 H. W. Lun. Int. (App. IV), + 11 43 L.M.T..H.W., {MayVl'2.42p.m. Example: Find the time of low water at Singapore on the night of May 28, 1879. G. M. T. of Gr. transit, 2S^ b"" 55"'. 3 Corr. for —104° Long. (Tab. 11), — 13 L. M. T. of local transit, 28 5 42 L. W. Lun. Int. (App. IV), + 4 02 L-M.T.,L.W., " {MV28,V44p.m. 156 TIDES. Example: Find the time of morning high water and afternoon low water at Gibraltar on June 26, 1879. G. M. T. of Gr. upper transit, 25'^ 4" 40"'. 1 G. M. T. of Gr. upper transit, 26 5 27 .0 G. M. T. of Gr. lower transit, Corr.for + 5° Long. (Tab. 11), L. M. T. of local lower trans. , Transit, 2"/ 17'* 05" Transit, 25'' 17'' 05" H.W.Lun.Int. (App. IV), 135 L. W.Lun. Int. (App. IV) , 7 55 2)51 10 07 .1 25 17 04 + 01 25 17 05 L. M. T., H. W., j f ly*^. ,. , L. M. T., L. W., j f \,?^, ' ' (June 26, 6.40 a. m. ' ' I June 2b, 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 developed 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 by tidal observations made within the lagoon with which this inlet communicates, because the range of the tide within the lagoon is less than upon the outside coast. A partial obstruction, like a bridge, or a natural contraction of the channel section, while it may not reduce the total range of the tide or materially affect the time of high or low tides, will alter the relative heights above and below at intermediate stages, so that the hydrographer must be careful to see that no such obstruction intervenes between his field of work and the gauge. 511. 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 rejilace 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. 513. There are frequently remarkable facts in reference to tides and currents to be obtained from persons having local knowledge; these should be examined and recorded. The date and circumstances of the highest and lowest tides ever known form important items of information. 514. Planes of Reference. — The 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 vxiter is a plane whose depression below mean sea level corresponds with half the mean semi-diurnal range, while the depression of mean low-water springs corresponds with half the mean range of spring tide; mean lower low 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 Mark. — The plinth of a light-house, the water table of a substantial building, the base of a monument, and the like, are proper benches; and when these are not within reach, a mark TIDES. 157 may be made on a rock not likely to be moved or started by the frost, or, if no rock naturally exists in the neighborhood, a block of stone buried below the reach of frost and plowshare should be the resort. When a bench is made on shore, it should be marked by a circle of 2 or 3 inches diameter with a cross in the center, indicating the reference point. The levelings between this point and the gauge should be be run over twice and the details recorded. A bench made upon a wharf or other 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 nmst 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 acroi-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 l^elow 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 l)y 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 class-es of gauge are to be employed, as it furnishes a standard for comparison of absolute heights, and also serves to detect any defects in the mechanical details upon which all other gauges are to a greater or less extent dependent. 519. Where there is considerable swell, and where, from the situation of the gauge or the great range of the tide (making it inconvenient for the observer to see the figures in certain positions) the staff gauge can not be used, recourse must be 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 attached to a wire or cord which passes over pulleys and terminates in a counterpoise whose position on a vertical graduated scale shows the height of tide. 520. An Autumatic 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 the staff gauge, the readings of which should be noted by hand at appropriate points of the graphic re«ord. 158 OCEAN CURKENTS. CHAPTER XXI. OCEAN OUEEENTS. 521. An ocemi 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: Drift and Stream Currents. A Drift Current is one which arises from the effect of wind upon the surface water, impelling the particles to leeward. Such currents reach only to shallow 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 haa 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 localit}^ 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 anj^ 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; ( fc ) by comparison of the position of a vessel 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, resi)ectively, 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 ^ccuracy. 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. 52§. 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 CUERENTS. 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 foHowed and the set and drift of current at different points are not indicated, and m "the case of objects floating otherwise than in a completely submerged condition account must be taken of the fact that the drift is influenced by the wind. But even this general information is of great value in researches as to ocean currents, and navigators who desire to aid in the work of investi- gation may do so by throwing overboard, from time to time, sealed bottles containing a 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. At.Cape 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. 530. 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 fiftieth 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 w^estward of the region of the Equatorial Counter Current the North and the South Equatorial Currents unite. A large part of the combined 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 westw^ard, 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 Straits of 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, fiows 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 eastward, 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 jxinction 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 \yater, 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 mooa is near the equator ttie current presents a narrow front with very high velocity in the axis of maximum strength, while at periods of great northerly or 160 OCEAN CUKEENTS. southerly declination the front broadens, the current decreasing at the axis and increasing at the edges. These tidal effects are not, however, observed in the open sea. The velocity of the Gulf Stream varies with the seasons, following the variation in the intensity of the trade winds, to which it largely owes its origin. The drift of the current under average conditions mav 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, LI knots per hour. Off Fowey Rocks: Mean surface velocity in axis, ;15 knots; allowance in crossing, 2\ knots per hour. Off Cape' Hat teras: Mean surface velocity in axis, upward of 2 knots; allowance in crossing the stream, 1| knots per hour between the IOC-fathom curve and a point 40 miles outside that curve. 533.~ After passing beyond the longitude of the easternmost portions of North America, it is gen- erally regarded that the Gulf Stream, as such, ceases to exist; but by reason of the prevalence of westerly winds the direction of the set toward Europe is continued until the continental shores are approached, when the current divides, one branch going to the northeastward and entering the Arctic regions and the other running off toward the south and east in the direction of the African coast. These currents have received, respectively, the designations of the Easterlif, Northeast, 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 watch, 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 Eastern and Western continents. The central space thus inclosed, in which no well-marked currents are observed, and in the waters of which great quantities of the Sargasso or gulf weed are encountered, is known as the Sargasso Sea. 535. The Southeast Drift Current carries its waters to the northwest coast of Africa, whence they follow the general trend of the land from Cape Spartel to Cape Verde. From this 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. liennell's 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. 53§. 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 Southern Connecting Current and flows toward the African coast in about the latitude of Tristan d'Acunha. It then joins its waters with those of the general northerly current that sets out of the Antarctic region, forming a current which flows to the northward along the southwest African coast and eventually connects with the Southern Equatorial Current, thus completing the surface circulation of the South Atlantic. 540. There are two other currents whose effects are felt in the Atlantic, one originating in the Indian Ocean and flowing around the Cape of Good Hope, the other originating in the Pacific and flow- ing around Cape Horn. They will be 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 winds, the currents produced in the two hemispheres being denominated, respectively, the Northeim and the Southern Equatorial Currents. These are separated, as also in the case of the Atlantic, by an east- setting stream, about 800 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 Japan Stream, but which more frequently receives its Japanese name of iTwro jSmo, or "black stream." This current, the waters of which are dark in color and contain a variety of seaweed similar to "gulf weed," carries the warm tropical water at a rapid rate to the northward and eastward along the coasts of Asia and its offlying islands, presenting many analogies to the Gulf Stream of the Atlantic. The limits and volume of the Kuro Siwo vary according to the monsoon, being augmented during the season of southwesterly winds and diminished during the prevalence of those from northeast. The current sets to the north along the east coast of Formosa, and in about latitude 26° N. changes its course to northeast, arriving at the extreme southwestern point of Japan by a route to westward of the Meiaco- sima and Loo-choo islands. A branch makes off from the main stream to follow northward along the west coast of Japan, entering the Sea of Japan by the Korea Channel; but the principal current bends toward the cast, flows through Van Diemen Strait and the passages between 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 between Bungo and Kii channels, where its average drift ia between 2 and 3 knots per hour. Continuing beyond the southeastern extremity of Nipon, the direction OCEAK CURRENTS. 161 of the stream l:)ecomes somewhat more northerly, and its width increases, witli consequent loss of velocity. In the Kuro 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 Oya Siwo. 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 ) , when it begins to bend toward SS VV. , 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, which appear to be produced by the prevailing winds. During the dry season — January, February, and March — the currents generally set toward southeast; during the rainy season— from May to October — especially in July, August, and September, the currents set to northwest, particularly from Cosas Island and the Gulf of Nicoya 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 Bossel Current, 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 Current, sets toward south and west, arriving off the east coast of Australia, along which 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 Current, maintains the general easterlj^ 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 Yaldivia and Valparaiso, follows generally the direction of the coast lines of Chile and Peru (though at times setting directly toward the shore in such manner as to constitute a great danger to the navigator), and forms the important current which has been called variously the 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 WNW. and west; beyond the meridian of the Galapagos it widens rapidly, and the current is lost in the equatorial current, near 108° W. As often happens in similar 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. 548. Currents of the Indian Ocean. — In this ocean the currents to the north of the equator are very irregular; the periodical winds, the alternating breezes, and the changes of monsoon produce currents of a variable nature, their direction 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-movmg current vary with the longitude as well as with the season. Upon reaching about the meridian of Rodriguez Island, a branch makes off toward the south and west, flowing pa^t Mauritius, then to the south of Madagascar (on the meridian of which it is 480 miles broad) , and thereafter, rapidly diminishing its breadth, forming part of the Agulhas Cur- rent a little to the south of Port Natal. The main equatorial current continues westward until passing the north end of Madagascar, where, encountering the obstruction presented by the African continent, it divides, one branch following the coast in a northerly, the other in a southerly, direction. The former, in the season of the southwest monsoon, is merged into the general easterly and northeasterly drift that prevails throughout the ocean from the northern limit x)f the Equatorial Current on the south, as far as India and the adjacent Asiatic shores on the north; but during the northeast monsoon, when there exists in the northern regions of the Indian Ocean a westerly drift current analogous to the Northern Equatorial Currents produced in the Atlantic and Pacific by the northeast trades, there is formed an east-setting Equatorial Counter Current, which occupies a narrow area near the equator and is made up of the waters accumu- lated at the western 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 manj^ of the characteristics of the Gulf and Japan streams. This current skirts the east coast of South Africa and 6583—06 11 162 OCEAN CUKRENTS. attains considerable velocity over that part between Port Natal and Algoa Bay. During the summei' 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 tlie 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 coaal of Australia. 552. As in the other oceans, a general northerly current is observed to set into the Indian Ocean from the Antarctic regions. EXTEACTS FROM NAUTICAL ALMANAC. 163 APPENDIX I. EXTRACTS FROM THE AMERICAN EPHEMERIS AND NAUTICAL ALMA- NAC, FOR THE YEAR 1879, WHICH HAVE REFERENCE TO THE EXAMPLES FOR THAT YEAR GIVEN IN THIS WORK. [Extracts: Page I.] AT GREEN\VICH APPARENT NOON. THE SUN'S Apparent Right Ascension. Diff. for 1 hour. Apparent Declination. Difl. for 1 hour. Semi- diameter. Sidereal Time of the Semi- diameter passing the Meridian. Equation of Time, to be added to subtracted from Appar- ent Time. Diff. for 1 hour. JANUARY. Sun. Mon. Tues. 20 4 60. 17 10. 626 20 9 14.84 10. 595 20 13 28. 75 10.564 S. 20 21 9. -f31.54 20 8 20.4 32.49 S. 19 55 9. 1 4-33.43 16 17.58 69.72 16 17.48 69.61 16 17. 38 69.51 10 56. 68 11 14.74 11 32.05 0.769 0.T38 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 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. 4 30 43. 2 4 53 49. 1 5 16 49. 8 9 54. 1 9 22 35. 4 9 44 7.5 10 5 29.9 10 26 42. 3 10 47 44. 7 11 8 36. 4 11 29 17. 1 N. 11 49 46.4 -t-57.85 57.64 57.41 54.40 54.03 53.64 53.23 52.80 52.37 51.92 51.45 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 0.60 3 42. 46 3 24. 43 35. 02 19.60 4.54 10. 15 24. 46 38.36 51. 85 1 4.93 1 17.60 0.768 0.754 0.748 0.649 0.635 0.620 0.604 0.687 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 -f42.86 42.17 39.33 38.59 35.52 34.72 33.91 -1-33.06 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 25.18 30.40 45.58 47.90 51.32 50.68 49.47 47.69 0.229 0.206 0.109 0.084 0.014 0.039 0.062 0.086 Note. — Mean Time of the Semidiameter passing 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 FEOM NAUTICAL ALMANAC. [Extracts: Page I.J AT GREENWICH APPARENT NOON— Continued. THE sun's Apparent Right Ascension. h. m. 8. Diff. for 1 hour. Apparent Declination. DiflE. for 1 hour. Semi- diameter. Sidereal Time of the Semi- diameter passing the Meridian. Equation of Time, to be subtracted \ from j added 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 6 19 6 23 33.74 10.312 57.61 10.348 6.09 10.358 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 -1-14.64 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 -r 0.32 23 24 33. 1 - 3.78 23 22 49. 5 4.81 23 20 41. 3 - 5.84 15 47. 63 68.70 15 47. 30 68.81 15 47. 20 68.84 15 47. 00 68.90 15 46. 91 68.92 68.98 15 46.48 15 46. 43 68.98 15 46. 27 68.94 15 46. 24 68.93 15 46. 22 68.91 28.86 54.76 42.87 18.42 5.89 11.75 24.86 16.72 29.42 41.97 0.455 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 5 39. 82 9.964 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 N. 19 54 41.3 -19. 76 20.71 29.72 30.57 -31.41 15 46. 30 15 46. 33 15 46.94 15 47.03 15 47. 13 68.30 68.24 67.51 67.43 67.35 5 10.04 5 17.99 6 10.85 6 13. 15 6 14. 84 0.339 0.321 0.108 0.083 0.059 SEPTEMBER. Tobestibtract- ed from Ap- parent Time. Wed. Thur. 11 13 33. 93 11 17 9.68 8.993 8.988 4 59 24. 2 4 36 36. 2 -56.90 -57. 10 15 55. 81 15 56.06 64.12 64.10 3 1.29 3 22.03 0.862 0.867 DECEMBER. Mon. Tues. 18 18 1 24.12 5 50. 72 11. 108 11. 107 S. 23 27 17. 3 S. 23 26 54. 3 + 0.37 + 1.55 16 18. 13 16 18. 18 I 71.30 71.30 1 16.61 46.64 1.248 1.246 Note. — Mean Time of the Semidiameter passing 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 FEOM NAUTICAL ALMANAC. 165 [Extracts: Page II.J AT GREENWICH MEAN NOON. Day of the Week. Day of the Month. THE SUN'S Apparent Right Ascension. h. m. Diflf. for 1 hour. Apparent Declination. Diff. for 1 hour. Equation of Time, to be subtractedfrom added to Mean Time. Diflf. for 1 hour. Sidereal Time or Right As- cension of Mean Sun. JANUARY. Frid. Sat. Mon. Tues. 10 11 20 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. 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 11 14.60 0.738 11 31.91 0.706 19 18 32. 66 19 22 29. 22 19 57 58. 24 20 1 54.80 APRIL. Tues. 1 Wed. 2 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 6 10 25 29 54.27 9.098 32.68 9.102 26.22 9.146 5.87 9.157 9.91 9.236 51.77 9.252 34.02 9.269 43.19 9.321 27.08 9.338 11.41 9.366 56.19 9.375 41.42 9.394 27.11 9.414 34.67 9.494 22.79 9.515 N. 4 4 7 7 9 10 10 11 11 12 12 12 13 14 N.14 30 39. 4 + 57.86 53 45. 6 57.65 10 .20. 3 56.08 32 42. 8 55.77 44 7.4 53.65 53.24 5 30.1 26 42. 8 52.81 29 18.1 51.16 49 47. 6 50.98 10 5.4 50.48 30 11. 2 49.97 50 4.7 49.46 9 45.4 48.92 26 14.5 46.65 44 46.7 + 46.04 4 0.65 3 42. 50 1 56. 74 1 39.83 4.54 10. 15 24. 46 1 4.94 1 17.61 1 29. 83 1 41.61 1 52.93 2 3.80 2 42. 46 2 50. 89 0.758 0.754 0.709 0.698 0.620 0.604 0.587 0.536 0.518 0.500 0.481 0.462 0.442 0.361 0.340 37 41 1 5 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 3 4 3 7 3 11 3 15 31 35 39 19 23 27 31 0.01 9.723 53.65 9.747 47.89 9.771 42.71 9.7% 27.90 9.896 25.67 9.919 24.01 9.942 36.81 10. 166 40.75 10. 173 45.12 10. 190 49.91 10.207 N. 17 20 17 35 17 51 18 6 19 4 19 18 19 32 21 27 21 36 21 45 N.2] 54 3.5 56.3 31.6 48.9 53.8 37.6 1.8 5.9 37.4 46.5 33.0 + 40.06 39.33 38.59 37.84 34.72 33.91 33.09 24.28 23.34 22.40 + 21. 45 42.68 45.59 47.91 49.64 50.68 49.47 47.68 0.46 53.08 45.26 37.03 0.134 0.109 0.084 0.060 0.039 0.062 0.086 0.297 0.315 0.334 0.361 42.69 39.24 35.80 32.35 18.58 15.14 11.69 37.27 33.83 30.38 26.94 To be added to JUNE. sribtr acted from Mean Time. Sat. 7 Sun. 8 Wed. 11 Sat. 14 Sun. 15 Wed. 25 Thur. 26 Frid. 27 5 34.00 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.S88 6 19 26.86 10.382 6 23 35. 96 10.376 N.22 45 9.9 22 50 49. 3 23 5 23. 23 16 17. 4 23 19 6.4 23 24 33. 2 23 22 49. 7 N.23 20 41.6 + 14.64 13.64 10.62 7.55 + 6.52 -3.78 4.81 -5.84 1 28.85 1 17.77 42. 86 5.89 6.80 2 16. 70 2 29.40 2 41. 95 0.455 0.467 0.600 0.526 0.632 0.532 0.626 0.519 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 Note. — The Seniidiameter 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 north declinations are decreasing and south declinations increasing. Difl. for 1 hour. + 9 ■.8665. 166 EXTRACTS FROM NAUTICAL ALMANAC. [Extracts: Page II.] AT GREEN\A/'ICH MEAN NOON— Continued. Day of the Week. Day of the Month. THE SUN'S Apparent Right Ascension. h. m. s. Diff. for 1 hour. Apparent Decimation. Diff. for 1 hour. Equation of Time, to be siMr acted from Mean Time. Diff. for 1 hour. Sidereal Time or Right As- cension of Mean Sun. h. m. AUGUST. Tues. Wed. 27. 45 4 17.82 9.610 9.586 N. 17 1 29. 2 N. 16 45 8. 6 40. 52 41. 20 SEPTEMBEE. 5 47. 69 5 41.51 To he added to Mean Time. 0.246 0.270 8 54 39. 76 8 58 36. 31 Wed. Thur. 10 11 11 13 34.39 11 17 10.19, .996 .990 N. 4 59 21. 3 N. 4 36 32. 9 -56.91 -57.12 3 1.33 3 22.07 0.862 0.867 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 9.367 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 ■65.65 55.34 55.02 50.34 49.82 14 7.02 0.548 14 19.89 0.524 14 32. 18 0.500 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. 15 9 14.01 15 13 18.76 10.180 10.216 S. 17 41 18. 4 S.17 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 16 42 16 59 17 3 17 8 17 12 18 1 18 5 18 10 40.65 10.844 1.22 10.869 29.19 10.960 52.48 10.979 16.23 10.998 40.41 11.015 24.34 11. 104 50.85 11.103 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 10 5.66 9 41. 65 7 59. 91 7 33. 18 7 5.99 6 38. 37 1 16.58 46. 63 16. 71 0.987 1.013 1.104 1.123 1.142 1.159 1.248 1.246 1.244 16 47 16 51 17 7 17 11 17 15 17 19 18 2 18 6 18 10 46.31 42.87 29.10 25.66 22.22 18.78 40.92 37.48 34.03 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 north declinations are decreasing and south declinations increasing. Diff. for 1 hour. + 9«.8565 EXTRACTS FROM KAUTICAL 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. True LONGITUDE. Diflf. for 1 hour. LATITUDE. A k' o / // 1 It II II h. in. 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.] GREENWICH MEAN TIME. THE MOON S SEMIDIAMETER. Noon. Midnight. HORIZONTAL PARALLAX. Noon. Diff. for 1 hour. Midnight. Diff. for 1 hour. MERIDIAN PASSAGE. h. m. 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. 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 14 45. 6 14 43. 7 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 -0.05 53 56. 7 +0.17 54 3.6 0.41 54 16.5 0.67 54 35. 8 0.94 55 2.1 +1.24 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. L09 55 17.9 +1.39 21 3.8 1.71 21 44.3 L67 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 IVIAY. 28 29 25 26 27 16 44.6 16 38.5 15 47.0 15 59. 4 15 49. 8 15 58. 7 16 7.2 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 JUNE. 15 54. 3 16 3.0 16 11. 1 57 59. 1 58 31. 7 59 3.0 1.37 1.34 1.26 58 15.5 1.36 58 47. 6 1.30 59 17.5 1.17 4 40.1 5 27.0 6 15.6 14.9 15.9 7.3 8.3 1.94 1.98 2.08 5.7 6.7 7. 7 168 EXTRACTS FROM NAUTICAL ALMA]S^AC. [Extracts: Pages V-XII.] GREENWICH MEAN TIME. THE moon's right ASCENSION AND DECLINATION. Hour. Right Ascension, f^^'f^ Declination. Difl. for 1 m. Hour. Right Ascension. f^^\'^^; i Declination. • Difif. for 1 m. h. m. «• «■ o / // II h. m. s. s. O / Hi II 1 THURSDAY, APRIL 10. WEDNESDAY, MAY 28. 17 18 19 17 18 38.57 17 21 17.16 17 23 55. 54 2.6448 2.6414 2.6379 S. 26 19 38. 3 26 19 41.1 S. 26 19 33.0 - 0.138 + 0.044 + 0.225 6 7 8 10 19 4. 23 10 21 7. 78 10 23 11. 34 2.0591 2.0592 2.0593 N. 7 4 18.5 6 49 52. 4 N. 6 35 23. 4 -14.411 14.459 -14. 607 WEDNESDAY, APRIL 16. THURSDAY, JUNE 26. 4 5 6 22 12 47. 08 22 14 39. 29 22 16 31. 30 1.8718 1.8686 1.8653 S. 8 12 37. 4 7 59 36. 1 S. 7 46 33. 5 +13. 010 13. 032 +13.064 2 3 11 11 37 41. 96 11 39 46. 49 11 56 28.42 2.0743 2. 0707 2.0989 S. 2 35 36. 4 2 50 44. 4 S. 4 51 36. 5 -16.135 15. 133 -15.069 FRIDAY, APRIL 25. MONDAY, DECEMBER 8. 16 17 18 5 41 33. 19 5 43 48. 55 5 46 3. 93 2.2558 2.2562 2.2566 N. 26 5 43. 8 26 4 23. 5 N. 26 2 55. 2 - 1.272 1.405 - 1.637 2 3 4 12 23 13.52 12 25 23.37 12 27 33. 54 2. 1615 2.1668 2.1722 S. 8 9 24.4 8 23 44. 9 S. 8 38 3. 8 14.354 14. 328 14.302 TUESDAY, APRIL 29. 11 12 13 9 2 56. 23 9 5 4.49 9 7 12.66 2.1384 2.1369 2.1356 N. 15 27 3. 6 15 14 52. 7 N. 15 2 36. 3 -12. 136 12.227 -12.318 EXTEACTS FROM NAUTICAL ALMANAC. [Extracts: Pages relating to Planets.] GREENWICH MEAN TIME. 169 JTJFITER. ^^TEISTTTS. April. April. J3 1 •o >, si Q Apparent Right Ascension. Var. of R. A. fori Hour. Apparent Declination. Var. of Dec. fori Hour. Meridian Passage. B O "S Apparent Right Ascension. Var. of R.A. fori Hour. Apparent Declination. - Var. of Dec. fori Hour. Meridian Passage. Noon. Noon. Noon. Noon. Nomi. Noon. Noon. Noon. 16 16 17 18 h. m. s. 22 25 51.70 22 26 35.54 22 27 19.02 22 28 2.14 +1.834 1.819 1.804 +1.789 o / // -10 44 29.6 10 40 28.0 10 36 28.1 —10 32 30.0 II +10.10 10.03 9.96 +9.89 h. m. 20 50.0 20 46.8 20 43.6 20 40.3 24 25 26 h. m. 8. 4 19 14.43 4 24 19.28 4 29 24.88 + 12.686 12.718 + 12.748 o / // +22 40 33.2 22 55 4.9 +23 8 59.5 II +37.08 35.55 +34.00 h. TO. 2 10.7 2 11.9 2 13.0 Day of the Month. 1st. 11th. 21st. 31st. Day of the month. 1st. 6th. llth. 16th. 21st. 26th. Polar Semidiameter Horizontal Parallax // 16.4 1.6 II 16.7 1.6 II 17.1 1.6 II 17.5 1.6 Semidiameter Hor. Parallax II 6.0 6.2 6.1 6.3 II 6.2 6.4 II 6.3 6.5 II 6.4 6.7 n 6.6 6.8 September. m:a.rs. 5 § ■o 1 Apparent Right Ascension. Var. of R.A. fori Hour. Apparent Decimation. Var. of Dec. fori Hour. Meridian Passage. March. § o Q Apparent Right Ascension. Var. of R.A. fori Hour. Apparent Declination. Var. of Dec. fori Hour. Meridian Passage. Noon. Noon. Noon. Noon. 16 17 h. m. «. 22 32 5.11 22 31 38.03 «. -1.134 -1.120 O 1 It —10 44 20.5 -10 46 57.2 II -6.58 -6.47 h. m. 10 49.8 10 45.5 Noon. Noon. Noon. Noon. 17 18 19 h. ni. s. 20 5 56.83 20 9 1.27 20 12 5.45 s. +7.690 7.680 +7.669 O 1 II -21 13 58.1 21 5 40.4 -20 57 10.7 II +20.48 20.98 +21.48 h. m. 20 26.4 20 25.6 20 24.7 Day of Month. 1st. llth. 21st. 31st. Polar Semidiameter Horizontal Parallax II 23.6 2.2 II 23.5 2.2 II 23.2 2.2 II 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 EXTRACTS FROM NAUTICAL ALMANAC. [Extracts: Pages relating to Fixed Stars.] ' FIXED ST^RS. MEAN PLACES FOR 1879.0. (Jan. 0+^016, Washington.) star's Name. Magni- tude. Right Ascension. An. Variation. Declination. An. Varia- tion. cc Ursae Min. (Polaris) * . 2 1 1 3 1 1 1 1.2 A. TO. s. 1 14 24.861 1 33 12.133 4 28 58.716 6 15 38.457 6 39 48.935 13 18 49.216 14 10 8.551 16 21 59.432 +21^485 + 2.233 + 3.437 + 3.633 + 2.645 + 3.154 + 2.735 + 3.670 +88 39 49.92 -57 51 5.79 +16 15 53.35 +22 34 26.94 -16 33 4.30 -10 31 44.21 +19 48 48.59 -26 9 41.94 II +19.00 +18.40 + 7.59 - 1.48 - 4.68 -18.90 -18.87 - 8.34 cc Eridani (Achernar) (X Tauri (Aldebaran) ju Geminoruni N.orS. Corr. Eq. t. Corr. ± Si-h •n- h. m. s. G.A.T L.A.T.i Jh. m, 8.1 o---y-AE.orW. sec cosec cos sin siu i ti 2). OL, (10) s^h h. m. 8. G.A.T L.A.T., [A. m. s.' Long.2 \o"","-;i^E.orVf. sec cosec cos sin sin i <2 2). J72 FORMS FOR WORK, FORM FOB TIME SIGHT OF A STAR (SrM»EB LINE). h. m. s. o ' II h. m. s. R.A , W T or Obs. alt. Corr. h (4) I. C. dip ref. W. Corr. * C-W + Chro. t C. C. + / // (11) G.M. T. R. A. M. S. Red. (Tab. 9) + + .. / II G. S, T. R.A. * (12) H. A. from Gr. E 4- 1 II Dec. N. or S. (6)p . o r II A •- Li sec (») Lji sec P cosec cosec cos • (I") S2 cos 8l gj-ft sin «2-A sm h. TO. «. 2) li. m. 8. 2). Gr. H. A E.orW. Gr. H. A (M) H. A.i E.orW. sin Hi H. A.j sin i ^^ f A. TO. s. 1 • { h. TO. s. I (") Long.i i-";"-;"-V"iE.orW. Long.o j" V;--;;-iE.orW. FORM FOB TIME SIGHT OF A PLANET (SUMNER LINE). W T h. m. s. orW. Obs.; Corr. h (16) par. {*) I. C. dip ref. Corr. alt. O ' II * + R.A. H. D. G. M. T. Corr. R.A. h. m. s. s. ± h. Dec. H. D. G. M. T. Corr. Dec. («)p O ' 4- ' II ....N.orS. C-W + .. ... II Chro. t. ±.. .... ... C. C. + R.A. M.S. +.. s. ± h. TO. s. > II + ^^^^ GST > II R. A.* •• N.orS. (i2)H.A.fromGr ...E. ' 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 h. m. s. + Obs. alt. ^ Chro. t. C. C. ± (16) S. D. Aug. (4)I.C. (")G. M. T R. A. M. S. + Red. (Tab. 9) + G. S. T. R. A. C dip FOBMB FOR WOEK. 173 FORM FOR TIME SIUHT OF MOOX'S LOWER LIMB (SUMNER LINE). = ' " h. m. s. ° ' " (")R. A. (")Dec. N.orS. + M.D. + M. D. + + No. min. ± No. min. ±. s. M.D. + m. No. min. ± s. Corr. 4; h. VI. s. R. A. Corr. Dec. N.orS. (i2)H.A.fromGr E.orW. 1st corr. ± (•)p O / II Approx. alt p." Method. sec. tan . (2<)9>i" N.orS. ) Chro. error on G. M. T. W. T., P. M C-W + P.M. Chro. t. A.M.Chro.t. - Elap. time h. m. s. (28) Dee. H. D. at merid. , atU_ id. /~ (28)Eq. t. H. D. Long. Corr. Eq. t. Long. : Corr. : Dec. (31) Tab. 37 H. D. ±. L ±. 1st pt. ± . 2d pt. ± . Eq.eq.K alt. /"■ N.orS. H. D. (prev. 1 ^ noon) I ~' H. D. (foil. 1 ^ noon) / ~" DifF. 241' 4, . Difl. 1'' ± . DilT. for long. ± . N.orS. H. D. at merid. ± logA( + ).... logB( + ). log ( + ).... log (±). O r tan (zb) d i tan ( + ). log (±).... log (±). 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 RELATING TO THE FORMS. 1. It is not necessarj' to convert departure into difference of longitude for each 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 work 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 minus terms of the correction. 5. For time sights and IS called the tangent of the angle A, abbreviated tan A; -TJ — ? — > is called the cotangent of the angle A, abbreviated cot A; — ~ , > is called the secant of the angle A, abbreviated sec A; — - — TT — i — > is called the cosecant of the angle A, abbreviated cosec A; 1 — cosine A, is called the versed sine of A, abbreviated vers A. 1 — sine A, is called the vo-versed sine of A, abbreviated covers A. The following relations may be seen to exist between the various functions: 1 . a c —. — I- = 1 -r- — ^ = — = cosec A; sin A '• « ' \ cos A 1 tan A sin A cos A = 1 c -=^^=secA; a = l-i--r = - = cotA; a i = «=tanA. c Hence the cosecant is the reciprocal of the sine, the secant is the reciprocal of the cosine, the cotan- gent is the reciprocal of the tangent, and the tangent equals the sine divided by the cosine. The 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: sin B = — = cos A; tan B = — = cot A; sec B = — = cosec A. EULES AND PRINCIPLES OF MATHEMATICS. 188 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, 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 which a radius revolves from an initial position OB, successively passing the points A, B'', A^. In considering the angle made by this radius at any position, P^, P^, P^^^, P^^^^, with the Hnc , OB, its position of origin, the functions will depend * upon the ratios existing between the sides of a right triangle whose base, b, will always lie within BB/ and whose perpendicular, a, will always be parallel to AA/', while its hypotenuse, c (of a constant length equal to that of the radius), will depend upon the 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 O A^ as their negative directions, the sign of the hypotenuse being always positive, the sign of any function may be deter- mined by the signs of the sides of the triangle upon -^ which it depends. Fig. 67. For example, the sine of the angle P^^OB is -, and since a is positive the quantity has a positive value; its cosine is -, and as b is measured in a negative direction from O the cosine must therefore be negative. In the first quadrant, between 0° and 90°, all quantities being positive, all functions will also l)e positive. In the second quadrant, between 90° and 180°, sin A f = J is positive; cos A ( =- j has a nega- ative value because b is negative; tan Ay =t J is also negative because of b. The cosecant, secant, and cotangent have, as in all cases, the same signs as the sine, cosine, and tangent, respectively, being the reciprocals of those quantities. In the third quadrant, between 180° and 270°, sin A f =- j and cos A f =- J are both negative, because both a and b have negative values; tan A f =t ) is positive for the same reason. In the fourth quadrant, between 270° and 360°, sin A-f =- j is negative, cos A ( =- j is positive, and tan A ( =r j is also negative. From a consideration of the signs in the manner that has been indicated the following relations will appear: sin A = sin (180°-A) = -sin (18Q° + A) = — sin (360° -A). cos A = — cos (180°— A) = - cos (180° + A) = cos (360°— A). tan A = — tan (180°— A)=tan (180° + A) = — tan (360°— A). sin A = cos (90° — A) = — cos (90°+A) = -cos (270°— A) = cos (270° +A). Any similar relation may be deduced from the figure. It is of great importance to have careful regard for the signs of the functions in all trigonometrical solutions. 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 legs than the number of integral places in tlie natural number. Thus, the index of the logarithm of any number (integral or mixed) between 10 and 100 is 1; from 100 to 1000 it is 2; from 1000 to 10000 it is 3, etc. ; the method of finding the logarithms from this table will be evident from the rules that follow: To find the logarithm of any number less than 100, enter the first page of the table, and opposite the given number will be found the logarithm with its index prefixed. Thus, opposite 71 is 1.85126, which 18 its logarithm. To find the logarithm of any number between 100 and 1000, find the given number in the left-hand col- umn of the table of logarithms, and immediately under in the next column is a number, to which must be prefixed the number 2 as an index (because the number consists of three places of figures), and the required logarithm will be found. Thus, if the logarithm of 149 was required, this number being found in the left-hand column, against it, in the column marked at the top (or bottom) is found 17319, pre- fixing to which the index 2, we have the logarithm of 149, 2.17319. To find the logarithm of any number between 1000 and 10000, find the three left-hand figures of the given number in the left-hand column of the table of logarithms, opposite to which, in the column that is marked at the top (or bottom) with the fourth figure, is to be found the required logarithm, to which must be prefixed the index 3, because the number contains 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 by inspection in the small table in the margin, marked at the top 29; opposite to the fifth figure of the number, 7, in the left-hand column, is the corresponding correction, 20, in the right-hand column. Again, if the logarithm of 1495738 was required, the logarithm corresponding to 149 at the left, and 5 at the top, is, as in the last example, 17464; the difference between this and the next greater is 29; multiplying this by 738 (the given number excluding the first four figures) gives 21402; crossing off the three right-hand figures of this product (because the number 738 consists of three figures), we have the correction 21 to be added to 17464; and the index to be prefixed is 6, because the given number consists of 7 places of figures; therefore the required logarithm is 6.17485. This correction, 21, may be found as above, by means of the marginal table marked at the top 29, taking at the side 7.38 (or 7J nearly), to which corresponds 21 , as before. To find the logarithm of any mixed decimal number, find the logarithm of the number, as if it were an integer, by the preceding rules, to which prefix the index of the integral part of the given number. Thus, if the logarithm of the mixed decimal 149.5738 was required, find the logarithm of 1495738, with- out noticing the decimal point; this, in the last example, was found to be 17485; to this prefix the index 2, corresronding to the integral part 149; the logarithm sought will therefore be 2.17485. To find the logarithm of any decimal fraction less than unity, it must be observed that the index 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 following rule: Find the logarithm of a fraction as if it were a whole number; see how many ciphers precede the first figure of the decimal fraction, subtract that number from 9, and the remainder will be the index of the given fraction. Thus the logarithm of 0.0391 is 8.59218 — 10; the logarithm of 0.25 is 9.39794 — 10; the logarithm of 0.0000025 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 of the negative value of any index. Thus, if the number corresponding to the logarithm 1.52634 were required, find 52634 in the coVumn 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. RULES 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 number will be 3.745. If the index be 8. corresponding to a number less than unity, the number will be 0.03745. Again, if the number corresponding to the logarithm 3.57811 were required, find, against 378 and under 5, the logarithm 57807, the difference between this and the next greater logarithm, 57818, being 11, and the difference between 57807 and the given number, 57811, being 4; in the marginal table headed 11, find in the right hand column the 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 34-1=4 places, the number is 3785.4. If the given logarithm were 5.57811, since the index 5 requires that there shall be six places in the whole number, it is desirable to seek accuracy to the sixth figure. The logarithmic part being the same as in the example immediately preceding, it is found as before that the first four figures are 3785, the difference between the next lower and next greater logarithms is 11, and between the next lower logarithm and the given one is 4; divide 4 by 11 and the quotient is .36; drop the decimal point, annex and point off, and the number required is found to be 378536. It may be remarked that in using five-place logarithm tables it is not generally to be expected that results will be exact beyond the fifth figure. To show, at one view, the indices corresponding to mixed and decimal numbers, the following examples are given: Mixed number. Logarithms. 40943.0 Log. 4.61218 4094. 3 Log. 3. 61218 409. 43 Log. 2. 61218 40.943 Log. 1.61218 4.0943 Log. 0.61218 Decimal number. Logarithms. 0.40943 Log. 9.61218 — 10 0.040943 Log. 8.61218 — 10 0.0040943 Log. 7.61218 — 10 0.00040943 Log. 6.61218 — 10 0.000040943 Log. 5.61218—10 To perform multiplication by logarithms, add the logarithms of the two numbers to be multiplied and the sum will be the logarithm of their product. Example I. Multiply 25 by 35. 25 Log. 1. 39794 35 Log. 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. 7.91116 Example IV. Multiply 0.25 by 0.003. 0.25 Log. 9.39794 0.003 Log. 7.47712 Product, 0. 00075 Log. 6.87506 In the last example, the sum of the two logarithms is really 16.87506—20; this is the same as 6.87506— 10, or, remembering that the quantity is less than unity, simply 6.87506. To perform division by logarithms, from the logarithm of the dividend subtract the logarithm of the divisor; the remainder will be the logarithm of the quotient. Example I. Divide 875 by 25. 875 Log. 2. 94201 25 Log. 1 . 39794 Quotient, 35 Log. 1.54407 Example II. Divide 40.32 by 22.4. 40.32 Log. 1.60552 22. 4 Log. 1 . 35025 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 Locr. 8. 39794 Quotient, 1.8 Log. 0.25527 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; for this reason it is necessary to borrow 10 in the index before making the subtraction, that is, to regard the logarithm of .00075 as 16.87506 — 20; hence the quotient is less than unity. 186 RULES AND PRINCIPLES OB" MATHEMATICS. The arithmetical complement of a logarithm is the difference between that logarithm and the loga- rithm of unity (10.00000—10, or 0.00000). It is therefore the logarithm of unity divided by that number which is the reciprocal of the number; and, since the effect of dividing by any number is the game as that of multiplying by its reciprocal, it follows that, in performing division 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 subtractici the difference between only two quantities can be taken at a time, it is frequently a convenience to deai with the arithmetical complements rather than with the logarithms themselves. Example I. Divide 875 by 25. 875 Log. 2.94201 25 Log. 1.39794 Colog. 8.60206 Quotient, 35 Log. 1.54407 Example II. Divide 0.00075 by 0.025. 0.00075 Log. 6.87506 0.025 Log. 8.39794 Colog. 1.60206 Simplify the expression, Example III. 40.32 X .00815 22.4 X .0025 40.32 Log. 1.60552 .00815 Log. 7.91116 22.4 Log. 1.35025 Colog. 8. 64975 .0025 Log. 7.39794 Colog. 2.60206 Result, 5.868 Log. 0.76849 Quotient, 0.03 Log. 8.47712 To perform involution hf logarithms, multiply the logarithm of the given number by the index of the power to which the quantity is to be raised; the product will be the logarithm of the power sought. 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 -30, which In the last example, the full product of the multiplication of 9.39794—10 by 3 is 28.19382- is equivalent to 8.19382— 10. To perform evolution by logarithms divide the logarithm of the number by the index of the power; the quotient will be the logarithm of the root sought. If the number whose root is to be extracted is a decimal fraction less than unity, increase the index of its logarithm by adding a number of tens which shall be less by one than the index of the power before making the division. Example I. Required the square root of 324. 324 Log.2) 2.51055 Answer, 18 Log. 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— 30> which, divided by 3, gives 9.39794—10. To find the logarithm of any function of an angle, Table 44 must be employed. This table is so arranged that on every page there appear the logarithms of all the functions of a certain angle A, together with those of the angles 90°— A, 90° + A, and 180°— A; thus on each page may be found the logarithms of the functions of four different angles. The number of degrees in the respective angles are printed in bold-faced type, one in each corner of the page; the number of minutes corresponding appear in one column at the left of the jmge 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 invariable rule must be to take the name of the function from the top or the bottom of the page, according as the number of degrees of the given angle is found at the top or bottom; and to take the minutes from the right or left hand column, according as the 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. sin 149° 50' =9. 70115, the equality of the functions agreeing with trigonometrical deductions; (in this statement numerical values only are regarded, and not signs; the latter must, of course, be taken into account in all operations). Example II. Required the log. sine, cosecant, tangent, cotan- gent, secant, and cosine of 75° 42'. Log. sin 9. 98633 Log. cot 9. 40636 Log. cosec 10. 01367 Log. sec 10. 60730 Log. tan 10. 59364 Log. cos 9. 39270 Example I. 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 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, ° 57' 06^''. For 42° 57' Log. sin Log. cos Log. tan 9. 83338 9. 86448 9. 96890 d + 1 — 1 -f 3 For 42° 57' 06". 9. 83339 9. 86447 9. 96893 Required the log. of 175° 32' 36". Example II. secant, cosecant, and cotangent For 175° 32' d For 175° 32' 36" Log. sec Log. cosec Log. cot 10. 00132 11. 10858 11. 10726 — 1 +97 +98 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 any 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) by finding, 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 ^0 = 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 c? = 11; n = 29 X ^0 = 23; therefore, the angle is 155° 43' 23". Or, in adjacent "Diff." column find, abreast 11, 23 or 24 seconds. Example I. Find angles less than 90° corresponding to log. cot 10.33621, log. sec 10.11579, and log. cos 8.70542. Log. cot 10. 33621 24 45 Log. sec 10. 11579 40 00 Log. cos 8. 70542 87 05 4 116 15 22 28 Example II. Find angles in second quadrant corresponding to log. tan 10.15593, log. sin 8.87926, and log. cosec 10.04944. Log. tan 10. 15593 124 55 Log. sin 8. 87926 175 39 Log. cosec 10. 04944 116 49 19 69 3 42 25 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 1'' 44" 00^ corresponding in time to 2 X 13° 00', and in the A. M. column 10*" 16"" 00% which is the same subtracted from 12'^. These columns are of use in working the various formulae 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 d, the logarithmic difference for the respective columns, appears below. Example I. Given t=V 48°' 44% find log. cot J t. For I'' 48" 40", log. cot. i t 10. 61687 Diff. for 4% Col -B, - 28 For l^" 48"' 44», log. cot ^ t 10. 61659 Example II. Given log. sin I t 9.91394^ find the Hour A. M. corresponding. For 9.91389, 4''39n2» Diff. for 5, Col. C, - 5 For 9.91394. 4 39 07 EULES AND PRINCIPLES OF MATHEMATICS. 189 MISCELIiANEOUS USEFUL DATA. Earth's Polar radius=6,356,583.8 meters. Earth's Equatorial radius=6,378,206.4 meters. Earth's Compression = oqo 4gg - Earth's Eccentricity=0.0824846 Number of feet in one statute mile =5280 Number of feet in one nautical mile =6080. 27 Sine of l'''=0. 00000485 Sine of 1^=0.00029089 The Napierian base £=2.7182818 The modulus of common logarithms=0.4342945 French meter in English feet, 3.2808333 French meter in English statute miles, 0.000621369 French meter in nautical miles, 0.000539593 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 grain8=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.^ Length of pendulum which vibrates second at Greenwich, 39.1393 inches. log 8. 9163666. log 3. 7226339. log 3. 7839229. 6855749. 4637261. 4342945. 6377843. 5159842. 7933496. 7320663. log 4. log 6. logo, log 9. logo, log 6. log 6. Bar. 30.00 in.; ther. 62<* F. APPENDIX IV. MAEITIME 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 ihe 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. [Pag el91 o Place. Lat. N. Long. \V L(in. Int. Range. 1 H.W. L.W. Spg. Neap. C 9 •0 2 £ fl C3 Salisbury Island * E pt ...... > II 63 27 00 63 06 00 62 37 00 62 35 00 62 48 00 62 50 00 62 30 00 62 07 00 61 18 00 60 10 00 60 40 00 60 52 00 60 33 00 61 21 00 61 40 00 60 00 00 59 48 00 59 07 00 57 35 00 57 00 00 56 32 45 55 27 04 55 13 33 54 55 50 54 26 55 54 00 05 53 50 00 53 42 37 53 34 25 53 26 00 52 40 07 52 21 16 52 15 36 52 06 00 51 53 00 51 38 48 50 42 10 49 59 54 49 53 00 49 45 29 49 35 40 49 41 20 49 36 50 49 15 20 49 04 20 48 42 01 48 30 15 48 16 55 47 53 10 48 08 58 47 42 45 47 48 30 47 34 02 46 39 24 46 37 04 46 43 20 46 49 34 47 17 55 47 00 26 46 56 30 46 46 51 47 15 30 47 35 13 o / // 76 30 00 77 50 00 78 08 00 77 33 00 74 00 00 75 20 00 74 03 00 72 25 00 70 02 00 67 05 00 67 50 00 64 40 00 64 12 00 65 00 00 64 30 00 64 28 00 64 07 15 63 20 00 61 20 00 62 07 00 61 40 13 60 12 34 59 08 01 57 56 40 57 12 40 56 31 31 56 23 00 56 59 50 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- Nottingham Island : S. pt 8 58 2 46 13.5 6.1 Digges Island : W. extreme Cape Wostenholme Charles Island ■. E. pt 1 W. pt 1 1 Cape Weggs 1 Prince of Wales Sound: Center of ent . . . Cape of Hopes Advance Akpatok Island: E. pt Green Island: NE.pt .............. 1 Button Islands: N. pt Cape Chidleigh :::::::::::::: i::::::::::: i Resolution Island: S. pt., Hutton h'dPd E. pt., C. Resolution Black Head 1 "::: 1 1 1 Eclipse Harbor : E. side 8 00 7 00 1 48 48 5.0 5.2 2.0 2.1 Nachvack Bay: Islands off entrance Saddle Island Port Man vers : Entrance :;::::::::: i Nain : Church 7.00 5 30 48 11 43 6.5 6.9 3.0 3.2 Hopedale Harbor: Hill to E'd Ail ick Harbor: Cape Mokkivik Cape Harrison : N. extreme .::::::::::: i Indian Harbor: Obs 6 10 12 23 7.0 3.2 Outer Gannet Island: Summit Gready Harbor Cartwright Harbor: Caribou Castle Indian Tickle: Summit 6 27 15 6.0 2.8 Roundhill Island : Summit Occasional Harbor: E. summit of Twin I. Cape St. Lewis: SE. pt 6 38 6 30 26 18 5.0 3.5 2.3 1.6 Battle Islands: NE. extreme, SE. I Table Head j Belle Isle : Light-house .. 1 Cape Bauld : Light-house Bell Island: S. end ... Cape St. John : Gull Island light Tilt Cove, Union Copper Mine Funk Island: Summit :::::::::::::::::::::::::::: i Offer Wadham : Light-house ! 1 Toulinguet Islands: Light-house Seldom-come-by Harbor: Shiphill Cape Freels : Gull I 1 t 1 Greenspond Island Cape Bonavista: Light-house Catalina Harbor: Green I. light -house . . Bonaventure Head Hearts Content: Light-house 7 23 1 11 4.1 1.9 Baccalieu Island: Light-house 5 ^ Harbor Grace: Light-house on beach . . . Cape St. Francis: Light-house 7 15 1 03 3.3 L5 St. Johns Harbor: Chain Rock Battery.. Cape Race: Light-house 7 12 6 50 1 01 38 3.3 6.5 L5 3.0 Cape Pine: Light-house Trepassey Harbor : Shingle Neck Cape St. Mary : Light- house 6 50 8 20 38 2 08 6.6 7.2 3.1 3.3 Little Placentia Harbor: W. side Coopers Cove .... Burin Island : Light-house ... Laun : Gr. Laun R. C. Church 8 05 8 23 8 53 8 22 1 53 2 11 2 41 2 10 7.0 6.6 6.5 6.2 3.2 3.1 3.0 2.9 St. Pierre: U. S. Coast Survey Station... Brunet Island: Mercers Hd. light-house. Boar Islands: Burgeo I. light-house Page 192] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. EAST COAST OF NORTH AMERICA— Continued. pBfl ;5- Place. La Poile Bay : Gr. Espic Church Cape Ray : Light-house Codroy Island: S. side Boat Harbor Cape St. George: Red I., SE. pt Cow Head: NW. extreme Port Saunders: NE. point of entry Rich Point: Light-house Ferolle Point: Cove Point, NE. extreme Flower Cove: Capstan Pt Green Island: 150 fms. from NE. end . . Cape Norman : Light-house Chateau Bay: S. pt. Castle I Amour Point: Light-house Wood Island: S. pt Greenly Island : Light-house Bradore Bav : Obs. Spot, Jones Pt Old Fort Island: Center Great Mecatina Island : SE pt Mecatina Harbor: S. point of Dead Cove Little Mecatina I.: S. pt. C. McKinnon. St. Mary 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 Magdalen : Light-house. Cape Rosier: Light-house Cape Gasp^ : Light-house Anticosti Island: Heath Pt. light-house SW. pt. light-house . . Bonaventure Island : E. pt Leander Shoal Macquereau Point Chaleur Bay : Carlisle Dalhousie I Miscou Island: NE. pt., Point Birch ... Miramichi Bay: Portage I., N. pt Point Escumenac: Light-house North Point: Light-house Richmond Harbor: Royalty Pt East Point: Light-house Charlottetown: Flag-staff on fort Gt. Bird Rock : Light-house East Island: E. extreme Entry Island : Light-house Amherst Hbr.: N. side of entrance Deadman Rock: W. pt St. Paul Island: Light-house, NE. end. Light-house, SW. end. Cape North: Light-hotfse St. Anns Harbor: E. pt. entrance Sydney Harbor: Light-house Lat. K. 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 47 50 40 47 37 40 47 16 30 47 14 23 47 16 03 47 13 50 47 11 20 47 01 45 46 21 00 46 12 25 Long. W. 58 24 10 59 18 00 59 23 40 59 13 10 57 50 00 57 17 07 57 24 20 57 02 40 56 44 45 56 33 40 55 53 52 55 50 20 56 51 05 57 08 00 57 10 50 57 14 12 57 46 00 58 51 00 58 59 20 59 20 00 59 45 00 59 57 00 60 08 00 61 44 00 63 27 03 66 22 44 67 21 55 71 12 19 73 33 04 68 27 40 66 46 00 65 19 30 64 12 00 64 09 35 61 42 30 63 35 46 64 08 00 64 18 00 64 46 30 65 19 00 66 22 10 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. /(. 711. 8 50 8 50 "9*40' 1 25 1 43 1 48 6 07 1 52 1 46 1 33 1 25 1 20 1 25 4 20 5 15 8 17 11 07 30 35 25 10 L. W. Spg. Neap. h. m. 2 38 ft. 6.0 2 32 4.3 6 45 4.0 7 05 7 18 54 8.1 10.8 14.6 7 33 7 13 6 50 6 40 12.0 10.5 6.4 5.5 6 35 6 40 3.6 4.9 7 33 8 07 9 10 8 25 10 59 4.7 4.8 8.1 4.0 2.3 11 00 11 55 2 20 4 23 2.4 1.8 1.4 6.4 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 7.8 4.7 4.1 1.8 2.5 1.2 0.9 0.7 3.2 1.4 L6 8.7 3.1 APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. EAST COAST OF NORTH AMERICA— Continued. [Page 193 Place. Lat. N. Long. W. Lun. Int. H. W. L. W. Range. Neap. 5** 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 observatory 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, McNutta 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 Enrage : 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 Gannet Rock: Light-house, NE. pt Machias Island: Light-house Calais : Astronomical station Eastport: Cong. Church Quoddy Head: Light-house Machias: Town Hall Petit Manan Island: Light-house 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 Church Portland: Custom-house Portland Head light-house . . Cape Elizabeth: Light-house (west) Wood Island : Light-house Boon 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 45 11 05 44 54 15 44 48 55 44 43 01 44 22 03 44 14 29 43 58 08 44 48 23 44 25 29 44 06 06 43 47 03 43 45 53 43 42 26 43 54 55 43 54 29 44 18 52 43 39 28 43 37 23 43 33 51 43 27 24 43 07 17 59 40 25 59 59 26 61 03 00 61 36 00 59 46 08 62 42 10 61 52 00 61 29 10 61 01 47 60 55 41 61 08 14 61 32 40 61 52 45 63 35 22 63 33 30 63 54 00 64 06 00 64 17 35 64 18 00 64 37 30 64 47 15 65 15 45 65 37 11 66 00 52 66 09 21 66 12 40 66 23 38 65 47 20 65 00 45 64 57 00 63 48 30 64 46 55 65 32 00 66 03 20 66 27 40 66 49 00 67 02 52 66 54 10 66 44 00 66 47 00 67 06 13 67 16 50 66 59 14 66 57 04 67 27 22 67 51 51 68 11 58 68 07 44 68 46 59 69 00 19 69 06 52 68 51 28 69 18 59 69 45 32 69 49 00 69 57 44 69 46 37 70 15 18 70 12 30 70 12 11 70 19 46 70 28 37 h. m. 7 45 7 55 9 05 9 34 9 20 9 26 7 55 7 43 7 45 7 34 7 32 '7'39 8 17 9 35 10 00 10 29 10 49 11 07 27 11 21 11 07 11 04 11 09 11 00 11 02 'io'si' 11 36 11 09 11 02 23 11 35 11 09 10 45 12 13 2 54 11 06 11 12 h. m. ft. 1 35 1 47 2 47 5.0 5.0 3.5 3 13 3 00 3 10 1 47 1 36 1 38 3.9 2.8 3.1 5.0 6.5 1 46 5.2 1 30 "i'36 7.1 '7.'6" 2 05 3 23 3 41 8.5 12.8 16.0 4 36 4 41 5 27 20.8 27.5 33.0 7 27 50.5 56 58 26 08 00 30.0 23.9 24.5 23.3 24.9 5 21 *4"56' 5 40 5 05 22.5 'i8."6' 23.3 20.9 4 59 15.5 6 47 5 22 4 55 4 31 15.1 11.7 11.0 10.2 6 16 7.9 10 18 4 51 4.9 10.1 4 51 10.2 ft. 3.1 3.1 1.8 2.0 1.4 L6 3.1 4.0 4.1 3.2 4.4 "4.' 3 5.2 9.5 n.8 15.4 20.4 24.4 37.4 22.2 17.7 18.2 17.1 18.2 16.7 "i3.*2 17.1 15.2 11.3 11.0 8.6 8.1 7.5 5.8 3.6 7.3 7.5 6583—06- -13 Page 194] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. EAST COAST OF NORTH AMERICA— Continued. Place. Whale Back : Light-house Portsmouth : Navy-yard 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 : Li^ht-house (south ) Monomoy Pomt: 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 : Li^ht-house Cutty hunk : Light-house New Bedford : Baptist Church Sakonnet Point: Light-house Beaver Tail : Light-house Newport: Flagstaff, torpedo station Bristol Ferry : Light-house Providence: Unitarian Church Point Judith : Light-house Block Island: Light-house (SE) Watch Hill Point: Light-house Montauk Point: Light-house Stonington : Light-house New London : Groton Monument . . Little Gull Island: Light-house Gardners Island: Light-house, N. pt... Plum Island: Light-house, W. pt Say brook : Light-house, Lynde Pt New Haven : Yale College spire ( middle ) Bridgeport Harbor: Light- house Norwalk Island : Light-house Shinnecock Bay : Light-house Fire Island : Light-house Albany: Dudley Observatory New York : Navy-yard flagstaff City Hall Fort Wadsworth: Light-house Lat. N. Long. W. Lun Int. Range. H. W. L. W. Spg. Neap. O 1 II 43 03 32 O 1 II 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 69 57 01 69 59 39 70 05 57 69 36 33 69 57 57 70 45 29 70 36 01 70 50 08 70 57 01 70 55 36 71 13 30 71 24 00 71 19 40 71 15 39 71 24 19 71 28 55 71 33 08 71 51 32 71 51 27 71 54 49 72 04 47 72 06 26 72 08 44 72 12 43 72 20 37 72 55 45 73 10 49 73 25 11 72 30 16 73 13 08 73 44 56 73 58 51 74 00 24 74 03 15 h. m. h. m. ft. ft. 43 04 56 43 04 16 11 23 5 09 10.5 7.7 42 56 15 42 58 02 42 48 30 42 48 55 11 19 11 23 4 58 5 10 10.0 9.1 7.3 6.6 42 41 07 42 39 43 42 38 21 11 17 11 13 5 04 5 00 10.1 10.1 7.4 7.4 42 36 46 42 36 07 42 32 48 11 02 4 49 10.2 7.5 42 31 00 42 30 20 42 22 48 11 16 11 09 5 03 4 57 10.6 10.6 7.7 7.7 42 22 22 42 21 28 11 27 5 17 11.0 8.1 42 19 41 42 16 11 11 09 4 56 10.9 8.0 41 58 44 42 00 12 41 43 20 42 02 23 11 23 11 36 5 11 5 25 10.8 11.6 7.9 8.5 41 40 17 41 33 34 41 16 55 40 37 05 12 11 12 00 04 5 57 5 48 6 00 4.6 4.3 3.8 3.4 3.1 2.3 41 17 01 41 28 08 41 28 51 41 20 55 41 24 52 41 38 10 41 26 30 41 26 58 41 29 07 41 38 34 41 49 26 41 21 40 41 09 10 41 18 14 41 04 16 41 19 31 41 21 16 41 12 23 41 08 29 41 10 25 7 51 11 34 7 31 7 36 7 57 7 40 7 40 7 48 7 53 8 12 7 32 7 33 8 49 8 20 9 09 9 26 9 26 9 40 i 5i 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 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 1.7 1.2 2.2 2.6 3.1 2.6 2.8 2.6 3.6 3.4 2.3 2.2 2.1 1.5 2.1 1.9 2.0 1.7 41 16 17 41 18 28 41 09 24 41 02 56 40 51 03 40 37 57 42 39 50 40 42 02 40 42 44 10 29 11 08 11 09 11 03 7 48 7 19 5 13 8 44 4 11 4 54 5 04 4 56 1 38 1 20 46 2 49 4.3 7.0 8.4 8.2 3.0 2.2 2.8 5.3 2.8 4.9 5.9 5.7 2.0 1.4 1.8 3.4 40 36 20 7 41 i 38 5.4 3.5 APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. EAST COAST OF NORTH AMERICA— Continued. [Page 195 Place. Sandy Hook : Light-house ( rear) , Light-ship Navesink Highlands: N. Ught-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 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 Edenton: 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 Lat. N. Long. W. Lun. Int. Range. H.W. L.W. Spg. Neap. a I II 40 27 42 40 28 15 o / // 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 67 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 h. m. 7 30 h. m. 1 23 ft. 5.6 ft. 3.6 40 23 48 39 45 52 39 30 22 39 21 59 38 47 20 7 50 7 48 9 59 1 43 1 42 3 57 2.7 4.2 4.7 1.7 2.7 3.0 38 55 59 39 56 53 39 53 14 39 44 27 38 46 42 37 54 40 8 16 1 28 53 12 00 8 17 1 47 8 58 8 02 6 40 1 50 5.6 6.2 7.0 6.7 5.4 3.6 4.4 5.2 4.9 3.5 37 23 46 37 07 22 39 17 48 38 58 53 38 02 19 38 52 30 38 55 14 8 03 6 34 4 39 31 7 42 2 19 44 10 53 6 52 1 56 3.0 1.4 LO 1.7 3.5 2.0 LO 0.8 1.1 2.5 38 53 20 37 00 06 36 49 33 37 32 16 36 55 35 36 17 58 8 44 9 05 4 30 7 53 2 17 2 47 11 55 1 43 3.0 3.2 4.3 3.2 2.0 2.1 2.8 2.1 36 03 24 36 22 36 35 49 07 7 37 1 26 3.4 2.2 35 15 17 35 06 32 35 06 21 7 00 45 2.2 1.5 34 37 22 34 43 05 33 34 26 6 29 7 21 20 1 08 4.4 3.3 3.0 2.3 33 22 08 33 13 21 8 39 3 38 4.3 2.9 33 01 06 32 41 43 6 59 50 5.9 4.1 32 46 34 32 26 02 32 05 33 7 20 8 10 1 10 2 06 6.0 8.5 4.2 5.9 32 01 20 32 04 52 31 23 28 31 21 54 31 08 02 31 08 51 30 40 23 7 10 8 13 7 30 7 40 7 30 8 00 1 04 3 07 1 24 1 44 1 27 1 57 7.9 7.6 8.4 7.5 7.5 7.8 5.5 5.3 5.8 5.2 5.3 5.4 30 40 18 30 23 36 30 19 43 7 39 7 36 1 31 1 33 6.9 5.4 4.8 3.7 29 53 20 29 53 07 28 27 37 26 56 54 25 35 25 25 13 17 8 12 8 00 8 00 8 20 8 21 2 00 1 52 2 00 2 16 2 08 5.3 5.9 1.8 2.6 2.7 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 : Light-house Sand Key : Light-house Key West: Light-house Loggerhead Key : Light-house Sanibel Island : Light-house Gasparilla Island : Light-house Tampa Bay : Egmont Key light Cedar Keys: Ast. station, Depot Key Seahorse 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 : 17,400 feet Cofre de Perote Mount: 14,000 feet Alvarado : 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 26 97 46 55 98 04 55 97 49 55 97 22 00 97 13 00 97 13 35 99 06 39 96 24 39 96 20 22 96 07 57 96 05 30 97 15 55 97 07 30 95 44 48 95 11 14 95 08 00 95 05 12 Lun. Int. H. W. h. m. 8 22 8 24 8 40 9 20 9 44 12 17 42 11 32 42 2 00 [12 10] [11 10] '[iils] [11 25] [1 35" [12 00 [0 20 [0 23] [11 53] [11 15] [10 55] [10 54] [11 00] [11 50" [0 18^ [0 40 2 17 3 17 [4 18] [4 07] [4 35] [4 25] [155] [106] [2 49] L. W. 00 05 20 36 21 10 6 19 5 07 7 13 8 30 [5 35] [4 55] 'i4'20i [3 09] [6 50] [5 40] [5 45] [6 35] [5 33] [5 00] [4 42] [4 41] [4 47] [5 38] [6 33] [6 56] 8 41 9 36 [10 33] [10 23] [10 47] [10 35] [8 03] [7 19] [8 38] Range. Spg. Neap. ft. 2.6 1.9 1.5 1.6 1.4 2.3 1.4 1.8 3.1 2.6 [2.5] [2.1] [i'T] [1-5] [2.1] [2.0] [2.3] [2.1] [1.8] [1.6] [1.7] [L9] [2.1] [2.0] [2.2J [2.0] 1.7 0.9 [1.4] [1.6] [1.6] [1-6] [1.4] [1.3] [2.4] ft. 1.3 1.0 0.8 0.9 0.8 1.2 0.7 0.9 1.5 1.2 1.3 0.6 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: NE. pt Laguna de Terminos: Vigia tower, W. end Carmen I Paypoton Mount: Summit Lerma : Church , Campeche: Light-house Fort San Jos6 Point Palmas Sisal: Fort light Madagascar Reef : Center Progreso: Light-house Silan: Village Lagartos: Village 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: NW. Cay Alacran Reef: Perez Cay Contoy 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 Chinch orro Bank: Cayo Lobos light Half-Moon Cay : Light-house Mauger Cav, NW. end: Light-house Glover Reef: SW. Cay English Cay : Light-house St. Georges Cay: Center Sand-Fly Cays: Hut, 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: NW. extreme Seal Cays: S. Cay Omoa: Entrance Cape Triunfo: Bluff pt Cougrehoy 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, N W. pt. of GeorgeCay Bonacca Island: Summit, 1,200 feet Misteriosa Bank: S. Point Swan Islands: NW. pt. of W. I Lat. N. Long. V^^. Lun. Int. Range. 1 H. W. L. W. spg- Neap. O t II 18 34 00 o / // 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 91^30 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. A. 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 19 50 20 19 51 36 2 59 9 28 2.1 1.3 21 02 00 21 10 06 21 26 30 10 20 4 10 1.8 0.9 21 17 00 21 23 00 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 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. 8 Place. Great Rock Head : Bluff extreme Cape Camaron Brewers Lagoon: E. side of entrance Patook River: E. side of entrance Carataska Lagoon: E. side of entrance . Cape Gracias-d-Dios: Light-house Caxones Reef: Great Hobby Islet Gorda Bank: Gorda Cay Farrall Rock: Center Half-Moon Cay : Center Alargate Reef: E. pt Mosquito Cays: S. end ?. Rosalind Bank: NW. extreme Serranilla Bank : Beacon Cay Serrana Bank: Little Cay Quita Sueno Bank: S. extreme of reef.. Spit at NW. end... Roncador Cay: S. pt Old Providence: Isabel House St. Andrews Island: SW. cove, Entrance I Courtown Cays: Middle Cay Albuquerque Bank : Smith Cay Brangmans Bluff : Extreme Pearl Cays: Colombilla Cay Pearl Cays Lagoon: Mosquito Pt Cookra Hill: Summit Bluefields: Schooner Pt Little Corn Island : Gun Pt Great Corn Island : Wells N. of Quin Bluff Greytown : Light-house Mount Cartago: Peak, 11,100 feet Port Limon : Grape Cay light Carreta Poiiit: 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. . . L4t. N. 15 53 00 16 00 00 15 51 50 15 48 50 15 23 40 15 00 00 16 03 30 15 52 00 15 51 00 15 08 50 15 07 00 14 21 12 16 54 00 15 47 45 14 21 33 14 08 00 14 30 00 13 34 30 13 22 54 12 31 40 12 24 00 12 10 00 14 03 00 12 22 35 12 20 39 12 15 30 11 59 00 12 17 30 12 09 17 10 56 15 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 Long. W. 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 Lun. Int. H. W. 10 20 4 00 4 00 4 00 1 50 1 40 1 35 1 00 1 00 L. W. Range. Spg. Neap. h. m. 4 07 10 13 10 13 10 13 03 7 52 7 47 7 13 7 13 ft. 2.0 2.0 2.0 1.0 2.0 2.0 2.0 1.5 1.6 /t. LI 1.1 LI 0.5 1.1 1.1 1.1 0.8 0.9 WEST COAST OF NORTH AMERICA. Point Barrow: Highest lat. of U. S Icy Cape: Extreme Cape Lisburne: 849 feet Cape Krusenstern: Extreme Chamisso Island : Summit Cape Espenberg: Extreme Diomede Island : Fairway Rock . . . Cape Prince of Wales: W. pt , Port Clarence: Point Spencer King Island: N. pt Cape Nome: Extreme St. Michael: Fort , Stuart Island: W. pt Cape Romanzof : Extreme St. Lawrence Island : E. pt NW.pt St. Matthew Island: SE.pt Pinnacle Islet: Summit, 930 feet. . . Nunivak Island: Cape Etolin Hagenmeister Island 23 30 16 00 52 00 09 00 14 30 32 00 35 30 33 30 16 40 00 00 26 00 26 00 34 30 40 00 16 00 50 00 18 00 13 00 25 22 48 31 1 156 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 45 6 10 [2 05] [8 05] 4 40 5 33 1 50 1 10 0.6 2.0 [8 25] [120] [2.1] [4.5] 11 3.1 0.2 1.1 0. L6 APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. WEST COAST OF NORTH AlVTRBICA— Continued. [Page 199 1 Place. Lat. N. Long. W. Lun Int. Range. 1 H.W. L. W. Spg. Neap. i s i •8 « m e s « « n « M -w « 6 C3 V V fl « « M hi fl © fl > Cape Menchikof : Extreme O 1 II 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 O 1 II 157 58 30 160 34 54 169 39 50 Long. E. 173 12 24 177 30 00 179 12 06 Long. W. 176 52 00 174 15 18 170 17 52 166 31 44 162 38 00 162 18 00 160 38 39 160 31 14 159 56 06 159 23 05 159 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 h. m. h. m. ft. ft. Port MoUer St. George Island: S. side ^ Attu Island: Chichagof Harbor 3 35 3 30 9 48 9 43 5.7 5.2 2.9 2.7 Kiska Island : Kiska Harbor, Ast. sta . . . Amchitka Island : Constantine Harbor . . Adakh Island : Bay of Islands 3 25 9 38 5.0 2.6 Atka Island: Nazan Bay (church) Pribilof Island: St. Paul I., village Unalaska Island: C. S. station, Iliuliuk . Sannakh Reefs : S. edge 4 17 3 50 12 13 10 29 9 58 6 10 2.7 2.9 5.7 1.4 1.5 2.8 Sannakh Island : NE. end Unga Island 2 40 8 55 8.2 4.1 Popof Island : Humboldt I Nagai Island : Sanborn Harbor Koniushi Island : N W. harbor NE. harbor Simeonof Island : Simeonof Harbor Cape Strogonof : Extreme 2 20 8 33 7.5 3.8 Chignik Bay : Anchorage Ano wik Island : S. end 1 45 7 58 8.1 4.0 Chiachi Islands Light-House Rocks Chirikof Island Kodiak Island, St. Paul Harbor: Cove N W. of village 16 50 6 24 7 05 9.0 10.1 4.5 5.1 Port Etches Middleton Island Mount St. Elias: Summit Yakutat Bay : Port Mulgrave 34 6 41 9.5 5.0 Lituya Bay Sitka: Middle of parade ground 06 45 30 6 17 6 56 6 39 9.9 18.6 17.7 5.2 9.7 9.2 Juneau Wrangell: Ast. station North Island : N. pt Cape Knox : Extreme Port Kuper: Sansum I 00 6 12 11.5 6.1 Forsyth Point: Extreme St. James Cape: S. extreme Cumshewa Harbor: N. side of entrance . Skidegate Bay : Rock on bar 07 6 19 12.8 6.7 Rose Spit Point: Extreme Massett Harbor: Uttewas village Cape Edenshaw : Extreme Hecate Bay: Observatory Islet 12 15 45 6 08 7 20 10.0 12.4 5.8 7.1 Stamp Harbor: Observatory Islet Island Harbor: Observatory Islet Cape Beale: Light-house 12 20 6 15 9.9 5.7 Refuge Cove: Village on W. side Hesquiat Harbor: Boat Cove 12 05 5 56 10.3 5.9 Estevan Point: S. extreme Nootka Sound : Friendly Cove 12 05 5 55 9.8 5.6 Port Langford: Colwood Islet Esperanza Inlet: Observatory Rock Kyuquot Sound : Shingle Point 11 55 11 50 11 47 5 45 5 38 5 34 9.7 9.3 9.3 5.5 5.3 5.3 Nasparti Inlet: Head Beach Cook Cape: Solander I North Harbor: Observatory Eock. „ Page 200] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. •WEST COAST OF NORTH AMERICA— Continued. Place. Lat. N. Long. W. Lun. Int. H.W. L.W. Range. Neap. Koprino Harbor: Observatory Rock Hecate Cove: Kitten Islet Triangle Island: W. side Cape Scott: Summit Bull Harbor, Hope Island : N. pt. Indian I . Port Alexander: Islet in center Beaver Harbor: Shell Islet Cormorant I. : Yellow Bluff in Alert Bay. Baynes Sound: Beak Pt Nanoose Harbor: Entrance Rock Nanaimo: Light-house Benson's House Victoria: Light-house Esquimalt: Fisgard I. light Race Island : Light-house Sooke Inlet: Secretary I Port San Juan : Pinnacle Rock Port Harvey : Tide Pole Islet Port Neville : Robber' s Nob Knox Bay, Thurlow Island: Stream at head of 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 Pomt Arena: Light-house Point Reyes: Light-house San Francisco: Coast Survey ast. station . Presidio station Mare Island: Stone block, obs. station. . . Benicia: Church Farallon Islet: Light-house Santa Clara: Catholic Church Mount Hamilton: Obs. peak San Jose: Spire Pigeon Point: Light-house 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 15 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 12'S 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 24 122 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] 9.8 [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 6.2 5.6 5.0 5.3 7.1 6 19 11 25 10 35 10 45 6 42 5 37 5 49 7.7 3.2 9.4 7.8 7.3 6.0 5.8 5.7 5.7 5.3 4.7 4.1 5.1 5.1 4.6 6.6 5.6 4.5 St. 5.6 6.1 6.0 6.7 6.6 6.4 7.4 8.3 7.7 4.8 5.6 4.9 5.0 4.4 4.6 7.2 6.0 4.0 3.7 3.3 3.4 4.1 4.5 1.9 6.1 6.4 4.7 4.3 3.5* 3.4 3.3 3.3 3.1 3.0 APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. WEST COAST OF NORTH AMEBICA— Continued. [Page 201 1 Place. Lat. N. Long. W. Lun Int. Range. 1 H. W. L. W. Spg. Neap. £ g i i e .0 i 1 Santa Cruz: Warehouse flagstaff Monterey: C. S. azimuth station Point Pinos: Light-house Piedras Blancas: 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 35 110 41 47 111 01 43 111 06 53 111 21 03 111 27 14 111 58 04 112 05 39 112 19 56 112 47 36 112 51 59 h. TO. 10 54 10 43 h. TO. 4 27 4 24 ft. 5.2 4.8 ft. 3.3 3.1 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 Loma: 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 : ObeUsk San Miguel Island : Seal Pt 9 23 3 02 4.9 2.2 Santa Rosa Island: E. pt Santa Cruz Island : NE. pt 9 29 3 06 4.9 2.2 Anacapa Island: E. pt Santa Barbara Island : Summit San Nicolas Island: Summit 9 20 9 28 9 28 3 04 3 08 3 06 4.9 5.1 5.0 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 bay 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^t. 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 Bartolome: N. side of entrance Asuncion Island: Summit of island San Ignacio Point: Extreme 9 00 2 37 8.2 2.8 Abreojos Point: Extreme of rocky ledge. San Domingo Point: Edge of cliff San Juanico Point: Knoll 9 00 2 48 6.7 2.3 8 29 2 17 5.7 1.6 Alijos Rocks: South Rock 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 Tod OS Santos: Foot of hill, Lobos Pt San Lucas: Steep sand beach, NW. pt. of bay San Jos6 del Cabo: NE. side of entrance. Arena Point: Extreme 8 36 2 20 4.5 1.2 Arena de la Ventana: Extreme Pichilinque Bay: SE. pt. of San Juan, Nepomezeino I La Paz : Obs. spot, El Mogot« 9 40 3 34 5.4 1.3 Lupona Point: Extreme San Evaristo: 3 m. S. of S. Evaristo Hd. San Marcial Point: Extreme Salinas Bay: Beach, NE. pt. of bay Pulpito Point: Summit Muleje: Equipalito Pt San Marcos Island : S. sand spit Santa Maria Cove: Beach on NW. shore. San Carlos Point: Extreme Santa Teresa Bay: Beach on N. side 11 50 5 47 11.2 2.6 Page 202] APPENDIX IV. MAKITIME POSITIONS AND TIDAL DATA. WEST COAST OF NORTH AMEB.ICA— Continued. Place. Lat. N. Long. W. Lun. Int. Range. 1 H.W. L.W. Spg. Neap. i S a e V H « •2 S 2 a Las Animas : Low pt . ' II 28 47 40 28 49 11 28 56 39 29 13 52 29 33 08 29 57 27 30 25 16 31 02 57 31 46 10 31 00 54 30 16 05 29 54 12 29 16 12 28 45 55 28 45 28 28 03 22 27 50 28 26 58 59 26 41 09 26 16 35 25 33 56 25 23 06 25 11 42 24 38 52 23 10 40 22 30 26 21 32 30 21 30 45 20 45 50 20 36 26 20 25 00 19 34 48 19 17 15 18 42 57 18 59 41 18 20 55 10 17 00 19 13 25 19 03 15 17 58 21 17 40 15 17 37 50 17 31 28 17 16 13 16 49 10 16 19 37 15 39 09 15 40 41 15 44 58 15 52 17 16 09 49 14 17 44 13 55 15 13 34 20 13 28 49 13 20 00 13 17 09 12 27 54 11 14 45 11 03 10 10 36 46 9 43 45 8 10 13 8 04 30 7 43 32 7 24 20 O 1 II 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 h. m. h. m. /<. ft. 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 Firmin: Beach, N. of bight San Felipe Point: Peak, 1,000 feet Philips Point: Beacon Georges Island: NE. shore - Cape Tepoca: Hill, 300 feet Libertad Anchorage : Beach . ..... Patos Island : SE. end Tiburon Island: SE. end . Kino Point: 0.2 mile N. 88° W. of mound . San Pedro : N. side of bay 1 i Guaymas: Light-house ^ 11 30 5 26 5.0 1.2 Claris Island : NW. part Santa Barbara: NW. side of bay Agiabampo: SE. side of entrance Topolobampo : SE. end of Santa Maria I . . Navachista: W. side of creek 1 1 Playa Colorado: N. side of entrance Altata: N. side of entrance 1 10 07 9 08 3 59 2 51 5.8 3.8 1.4 0.9 Mazatlan : Light-house Palenita Village: Boca Tecapan San Bias : Custom-house 9 08 2 52 3.2 LO Maria Mad re Island: SE. extreme Mita Point: Extreme Penas Anchorage: Mouth of Rio Real . . . Cape Corrientes : Extreme Perula Bay : Smooth Rock 9 07 2 53 2.5 1.1 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 9 07 2 54 L9 1.3 8 50 2 38 2.0 0.9 Tequepa Harbor: Limekiln Acapulco: Light-house 1 Maldonado : El Recordo Pt Port Angeles: Light-house Sacrificios Point: Highest pt. of cape Port Guatulco: Cross Morro Ayuca : Summit of N. edge of cape . Salina Cruz : Light-house Champerico: Inshore end of iron wharf. . San Jos6 de Guatemala: Light-house Acajutla: Light-house 2 50 2 50 2 55 3 05 3 15 9 02 9 02 9 08 9 18 9 28 8.5 9.0 9.5 10.0 10.5 4.6 4.9 5.1 5.4 5.7 Libertad: Light-house La Union : Light-house Chicarene Point: Extreme Corinto: Light-house 2 55 3 00 2 50 2 45 9 08 9 12 9 02 8 68 10.5 10.0 9.5 9.0 5.7 5.4 5.1 4.9 San Juan del Sur: Signal station Salinas Bay: Salinas Islet Port Culebra: Extremity of Mala Pt Ballena Bay: N. EsteroToussa Parida Anchorage: S. pt. of Deer Id PortNuevo: Entrada Pt 3 15 9 28 10.5 5.7 Bahia Honda: W. end of Centinela I Coiba (Quibo) Island: Observation pt. . . 3 10 9 22 11.0 5.9 APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. WEST COAST OF NORTH AMERICA— Continued. [Page 203 Place. Cocos Island : Head of Chatham Bay Panama: NE. bastion, ast. station Taboga Island: Church Cape Mala: Extreme Malpelo Island: Summit Lat. N. 5 32 57 8 57 12 8 47 45 7 27 40 4 03 00 Long. W. 86 59 17 79 32 05 79 33 16 79 59 25 81 36 00 Lun. Int. H. W. h. VI. 3 00 3 00 3 10 L. W. h. TO. 9 14 9 13 9 22 Range. Spg. Neap. ft. 16.0 15.4 13.0 ft. 8.7 8.3 7.0 WEST INDIA ISLANDS. Memory Rock: Center Bahama Island: W. pt Abaco Island : Light-house Little Guana Cay : Light-house Walker Cay: Highest part Great Isaac Cay : Light-house Gun Cay: Light-house 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 Clarence Harbor: Light-house Eleuthera Island : Light-house Royal Island : Eastern Pass Nassau: Light-house Andros Island : Light-house Great Stirrup Cay : Light-house Little Stirrup Cay: W. end San Salvador (Cat I.): Light-house Concepcion Island : W. bay Watlings Island: Hunchinbroke Rock .. Rum Cay: Harbor Pt Castle Island: Light-house Fortune Island: S. end Crooked Island: Moss flagstaff Bird Island : Light-house Samana Cay : W. pt Plana Cay: NW. pt Mariguana Island : SE. pt Hogsty Reef: NW. Cay Inagua Island : Light-house Little Inagua Island: N W. pt W. CaicosCay: Hill, SE. end French Cay: W. pt Fort George Cay: Old magazine Caicos Island : Parsons Pt. , S. islet Turk Island : Light-house Square Handkerchief Bank: NE. breaker Silver Bank : E. extreme Navidad Bank : Center of E. side Cape Maysi : Light-house Port Baracoa: Light-house Port Cayo Moa: Carenero Pt Port Nipe: Roma Pt Lucrecia Point : Light-house Port Sam a: E. side of entrance Peak of Sama: Summit, 885 feet Port Naranjo: E. side of entrance Jibara: Fort San Fernando Port Padre: Guinchos Pt Port Nue vitas: Light-house 26 56 53 26 41 18 25 51 30 26 31 10 27 15 42 26 02 00 25 34 30 22 45 10 22 22 30 21 42 00 22 01 15 22 14 02 22 20 44 22 31 15 22 51 00 23 32 15 23 06 00 25 00 00 25 31 20 25 05 37 24 43 45 25 49 40 25 49 12 24 06 15 23 50 50 23 56 40 23 37 45 22 06 40 22 32 40 22 47 30 22 51 00 23 05 30 22 34 38 22 16 30 21 40 30 20 56 00 21 30 40 21 37 30 21 30 00 21 54 00 21 29 33 21 30 55 21 06 30 20 35 00 20 02 00 20 15 10 20 21 40 20 41 41 20 47 14 21 04 24 21 09 00 21 07 00 21 07 30 21 07 05 21 18 30 21 38 54 79 06 79 00 77 10 76 57 78 23 79 06 79 18 78 06 77 34 75 44 75 10 75 45 75 28 75 51 74 51 75 46 74 59 76 13 76 51 77 21 77 46 77 53 77 57 75 26 75 07 74 28 74 50 74 20 74 22 74 20 74 22 73 49 73 38 72 47 73 50 73 40 73 42 72 28 72 12 72 07 71 31 71 07 70 29 69 21 68 47 74 09 41 74 29 34 74 53 44 75 33 18 75 36 59 75 47 18 75 47 40 75 52 18 76 07 48 76 35 34 77 05 32 7 40 8 20 8 20 7 00 7 20 7 40 7 00 7 20 "7*56' 7 30 5 40 6 20 Too' 1 28 3.2 L7 2 08 3. 2 08 48 1 08 1 28 48 4.1 4.0 4.0 3.0 4.0 1 08 3. "i"38T*3.*5* 1 18 11 53 08 48 3.0 2.8 2.4 L5 2.1 2.1 2.1 L5 2.1 L5 L5 L4 2.2 L2 r Page 204] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. WEST INDIA ISLANDS— Continued. Place. Maternillos Point: Light-house Cay Verde: NW. end Cay Confites: S. pt Pared on 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 FeUpe 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 Antonio : Folly Pt. Light Port Maria: NW. wharf St. Ann Bay: Long wharf , Falmouth: Fort Montego Bay: Fort St. Lucia: Fort Savanna-la-Mar : Fort Kingston : Plum Pt. light Port Royal: Fort Charles, flagstaff . . . Morant 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. 40 02 08 45 11 14 29 10 56 30 12 34 14 10 01 54 09 21 08 03 51 44 55 00 35 30 57 45 01 58 50 13 57 31 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 48 51 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 04 77 37 33 77 39 23 78 09 11 80 27 51 80 29 26 81 07 20 81 43 18 82 21 30 82 21 17 84 57 28 83 31 18 83 09 13 81 07 18 80 26 32 77 43 30 75 52 12 75 09 27 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 69 19 23 69 16 00 70 41 27 71 39 03 71 47 20 72 11 42 72 49 45 73 23 07 72 42 52 73 18 34 72 39 05 72 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 59 68 27 34 Lun. Int. Range. H. W. h. m. L. W. h. m. Spg. ft. 7 20 1 08 2.8 30 18 2 18 1 56 2.2 1.3 8 30 2 18 1.5 4 47 11 00 2.0 8 20 7 50 2 30 2 00 2.2 2.6 [1.3] [LI] [1-2] [1.1] 9 00 2 48 3.0 6 50 39 5.5 [1.2] [2.5] [2.2] Neap. ft. 1.6 1.2 0.7 0.9 LI LI 1.8 L5 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 Culebi ita Island : Light-house Vieques (Crab) Island: Port Ferro light. St. Thomas: FortChristian,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, Pick- 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. 18 02 43 18 11 56 18 25 09 18 28 56 18 23 05 17 57 10 18 18 44 18 05 20 18 20 23 18 18 08 18 25 04 18 30 39 18 45 11 18 36 30 17 45 09 18 35 37 18 16 42 18 13 06 18 04 07 17 53 58 17 39 10 17 29 10 17 18 12 17 13 38 17 07 52 17 35 50 17 00 00 17 06 54 16 55 18 16 42 12 15 59 50 16 25 09 16 11 57 16 13 14 16 13 56 16 19 56 16 10 17 15 52 59 15 51 32 15 34 34 15 17 27 15 42 00 14 35 44 14 43 54 14 46 13 14 23 23 14 01 54 13 05 42 13 02 45 13 09 40 13 09 19 13 00 25 12 03 02 11 10 08 Long. W. 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 Lun. Int. H. W. h. tn. "7 '04 8 21 [7 31] [7 35] [7 11] 4 00 3 50 2 50 2 50 2 30 3 50 L. W. h. m. '"2'66' 2 20 [1 30] [1 40] [0 58] Range. Spg. ft. "2.' 6" 1.3 [1.0] [1.0] [1.1] [1.2] [1.5] [2.0] [1.3] 10 12 1.5 10 02 1.1 9 02 3.0 9 05 L6 8 42 10 02 1.5 2.1 Neap. ft. "i."6 0. 0.8 0.6 L5 0.8 0.8 1.1 Page 206] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. WEST INDIA ISIiANDS— Continued. 1 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 / 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 59 12 06 17 12 31 05 O 1 II 63 05 48 63 36 00 63 48 00 65 26 38 66 12 31 66 39 10 68 14 10 68 39 19 68 55 60 68 56 16 70 02 34 h. m. h. m. ft. ft. Pampatar, Margarita I. : San Carlos Castle . Tortugas Island: S. end of W. Tortugillo Islet Orchila Island : S. side Roques Islands: Pirate Cay Bonaive Island: Light-house Little Curasao Island: Light-house Curasao Island: Fort Nassau Light-house Oruba Island: Light-house NORTH AND EAST COASTS OF SOUTH AMERICA. c © V « « i 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 1.5 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 1.. Santa Marta: Light-house Rio de la Hacha: Light on church Cape La Vela: Sand beach inside cape .. Bahia Honda: E. pt., S. side Espada Point: Extreme Maracaibo : Zapara I. light 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 1.7 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 Vaaquez Puerto Santo Bay: Sand spit S. of Morro . Tres Puntas Cape: Extreme UnareBay: Obs. spot, 200 yds. S. of Morro Pena Point: Extreme Pato Island: E. pt Mocomoco Pt. : Extreme Port of Spain : King's Wharf light Chac^chacare Island: Rocks off SW. pt. . Galera Point: NE. extreme, Ught-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. Place. Demerara: Georgetown light-house Nickerie River: Light-house Paramaribo : Stone steps Maroni River: W. light-house Salut Islands: Light-house Enfant Perdu Islet: Light-house... Cayenne: Light-house Connetable Islet: Center .-. . Carimare Mount: Summit Orange Cape: Extreme .. May6 Mountain: Summit North Cape: Extreme ... Cape Magoari: Extreme Para: Custom-house Atalaia Point: Light- house Itacolomi Point: Light-house Maranhao Island : Landing place Santa Anna Island : Light-house Tutoya: Entrance Paranahiba River: Amar^ao Village Ceara: Light-house Ja^uaribe River: Pilot station Cai^ara: Village Cape St. Roque: Extreme Rio Grande do Norte: Light-house Natal: Cathedral Parahiba River: Light- house at entrance. Parahiba: Cathedral Olinda: Light-house Pernambuco: Picao light-house „ Cape St. Augustine: Light-house Tamandare : Village Maceio: Light-house San Francisco River: Light-house at en- trance Cotinguiba River: Light-house at en- trance Vaza Harris River: Semaphore at en- trance Real River: Light-house Conde: Village Garcia d' Avila: Tower Bahia: Santo Antonio light-house Itaparica: Fort on N. pt. Morro de Sao Paulo: Light-house Camamu: Village Contas: Church Ilheos: Church Olivenga: Center of village Una: Center of village Comandatuba: Center of village Santa Cruz: Church Porto Seguro : Matriz Church -Prado: River entrance Alcobaga: Center of village Caravellas : Center of village .- Abrolhos Island : Light-house Porto Alegre: Center of village Espiritu Santo Bay : Light-house Guarapiri Islets: E. islet Benevente: Village Itapemirim : Moscas Islet Sao Joao da Barra: Light-house Cape St. Thome: Extreme ^^ Macahe : Fort at entrance Lat. N. 49 20 58 30 49 30 44 50 16 50 02 40 56 20 49 30 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 Long. W. 58 11 30 57 00 30 55 08 48 54 00 30 52 34 53 52 21 11 52 20 26 51 55 36 51 50 36 51 27 46 50 54 46 49 56 46 48 23 30 48 30 01 47 20 54 44 25 56 44 18 45 43 37 30 42 18 02 41 40 35 38 28 25 37 44 55 36 02 52 35 15 52 35 11 55 35 12 43 34 49 30 34 53 04 34 50 36 34 51 57 34 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 Lun. Int. H. W. h. TO. 4 18 5 50 4 27 11 50 6 50 5 35 5 05 5 25 5 50 4 05 4 33 4 20 4 17 4 10 3 50 3 50 3 35 3 25 3 10 3 15 2 50 "2*46 2 20 L. W. h. m. 9 50 12 00 10 30 5 37 38 11 47 11 17 11 37 12 00 10 17 10 50 10 32 10 29 10 22 10 00 10 00 9 47 9 37 9 23 9 27 9 00 '8'52 30 Range. Spg. ft. 8.6 "9.'6" 6.0 11.0 16.5 13.1 11.7 8.2 8.0 7.0 8.5 7.8 7.6 6.0 6.3 6.4 6.0 6.4 7.5 4.0 "5.'6' 9.2 Neap. ft. 3.9 4.3 2.7 5.2 7.9 6.2 5.6 3.9 3.8 4.2 3.3 4.1 3.7 3.6 2.9 3.0 3.1 2.9 3.1 3.6 1.9 "2.4 4.4 Page 208] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. NORTH AND EAST COASTS OF SOUTH AMERICA— Continued. Place. Lat. S. Santa Anna Island : Summit Barra Sao Joao: Village Busios: 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 IJbatuba: 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 Concei^ao : Church Quemada Grande Island : Summit, 623 ft. Iguape: Quay Bom Abrigo Islet: Light-house Ilha do Mel: Light-house Paranagua: Quay Antonina: Quay Coral Islet: Center Itacolomi Islet: Center Sao Francisco : Center of town Itapacaroya: Church Cambria: Church Arvoredo Island : Light-house Anhatomirim : Light-house St. Catharine Island : Rapa Pt Naufragados light Nostra Senhora do Deserto : Quay Coral Island: Summit, 230 feet Cape St. Martha: Light-house Torres Point: Extreme Rio Grande do Sul: Light-house Castillos: Beuna Vista Hill, 184 feet Cape Santa Maria: Light-house 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 Belgrano: Anchor-Stock Hill Argentina: Fort 22 26 00 22 37 00 22 46 00 23 00 42 22 53 15 23 01 43 22 54 46 22 54 15 23 03 40 22 32 00 23 03 40 23 04 20 22 57 20 23 09 20 23 00 30 23 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. Lun. Int. 41 43 41 59 41 54 42 00 42 01 42 54 43 09 43 10 43 08 43 11 43 33 43 59 44 02 44 08 44 19 44 05 44 42 45 04 45 03 45 00 45 15 45 21 46 15 46 19 45 40 46 47 46 41 47 32 47 51 48 19 48 31 48 43 48 23 48 25 48 39 48 36 48 36 48 22 48 34 48 26 48 35 48 34 48 33 48 49 49 43 52 07 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 '2'56' 1 35 2 50 2 55 2 35 4 00 8 20 2 00 6 30 6 43 9 50 'ebb L. w. h. m. Range. ft. 8 42 4. 9 b'bo "i.2 7 47 9 00 9 05 8 47 10 12 2 08 8 12 00 12 15 3 35 '6'66 5.3 5.0 5.9 2.0 3.5 4.0 2.1 5.3 ih'.s Neap. 2.3 "2." 6 2.5 2.8 3.1 2.8 0.9 0.9 2.3 2.7 1.4 3.5 '8.'2 APPENDIX IV. [Page 209 MARITIME POSITIONS AND TIDAL DATA. NORTH AND EAST COASTS OF SOUTH AMERICA— Continued. o Place. Lat. S. Long. W. Lun. Int. Range. 1 H. W. L.W. Spg. Neap. i < 2 Labyrinth Head Summit ........ o / // 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 O 1 II 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 o'l 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 h. TO. h. m. ft. ft. Union Bay * Indian Head . San Bias Harbor: SW. end of Hog Islet. . San Bias Bay: Summit of Rubia Pt Rio Negro : Main Pt 10 50 4 38 14.7 7.7 Bermeia Head' E summit Port San Antonio: Point Villarino San Antonio Sierra: Summit 10 35 4 23 23.5 12.3 Port San Jos6: San Quiroga Pt Delgado Point: SE. cliff Cracker Bay Anchorage ..... Port Madryn: Anchorage off cave bluff . Chupat River: Entrance 7 05 52 is. 2 6.9 Port St. Elena: St. Elena pen 3 50 10 03 16.8 8.8 Leones Island : SE. summit Melo Port- W. pt Port Malaspina' S. pt . ... Cape Three Points: NE. pitch Port Desire : Largest ruin 00 6 12 18.3 9.6 Sea Bear Bay: "Wells Pt Port San Julian: Sholl Pt 10 35 9 20 9 00 8 40 8 18 4 20 4 19 4 23 3 08 2 47 2 28 2 06 10 33 10 32 29.5 39.6 40.0 45.6 38.7 9.9 7.8 15.4 20.7 20.9 23.9 20.2 5.2 6.0 Port Santa Cruz: Mount at entrance Coy Inlet: Height S. side of entrance Gallegos River: Observation mound Cape Virgins: SE. extreme Cape San Diego : Extreme Staten Island, Cape St. John: Light- 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 3 50 10 03 6.7 5.2 Wollaston Island : Middle Cove Barne veldt Islands: Center Cape Horn : South summit, 500 ft -. . . Hermite Island: St. Martin Cove 4 07 10 02 4.8 3.8 WEST COAST OF SOUTH AMERICA. 2 False Cape Horn : S. extreme 55 43 15 55 52 30 56 28 50 55 24 50 54 45 40 54 24 48 54 30 00 53 18 30 52 55 30 52 46 15 52 42 50 52 23 55 68 04 40 69 17 30 68 41 30 70 01 30 71 36 10 72 10 20 73 00 00 74 18 15 74 36 30 74 46 50 74 42 20 68 25 45 Ildef onso Island : Highest summit Diego Ramirez Island: Highest summit . York Minster Rock: Summit, 800 ft Cape Desolation: S. summit 3 50 10 03 5.0 3.9 Mount Skyring: Summit, 3,666 ft Noir Island: SE. extreme 2 20 1 50 8 33 8 03 4.8 4.7 3.7 3.7 Landfall Island: Summit of Cape Inman. Cape Deseado: Peaked summit . . Apostle Rocks: W. rocks Cape Pillar: N. cliff 32 8 19 8 20 8 24 8 35 6 45 2 07 2 08 2*12 2 25 4.0 39.4 39.0 30.0 39.0 3.1 20.6 20.4 15.7 20.4 Dungeness Point: Light-house Cape Espiritu Santo: NE. cliff 52 39 00 1 68 34 00 52 32 00 ; 68 45 20 52 17 54 68 57 10 Catharine Point: NE. extreme Cape Possession : Light-house Cape Orange : N. extreme 52 28 40 52 28 00 52 38 18 52 46 20 69 24 00 69 33 00 70 14 16 70 25 25 Delgada Point: Light-house 8 47 9 23 2 40 3 20 39.0 21.0 20.4 11.0 Cape Gregory : Light-house Cape San Vicente: W. extreme. 6583—06- Page 210] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. WEST COAST OF SOTJTH AMERICA— Continued, Piace. Elizabeth Island : NE. bluff Sandy Point: Light-house Cape St. Valentine: Summit, at extreme. Port Famine: Observatory Cape San Isidro: Extreme Cape Fro ward: Summit of bluff Mount Pond : Summit Port Gallant: Wigwam Pt Charles Island : White rock near N W. end Rupert Island : Summit Mussel Bay : Entrance Tilly Bay : Sarah I Borja Bay : Bluff on W. shore Cape Quad : Extreme Barcelo Bay : Entrance Swallow Bay : Shag I Cape Notch : Extreme Playa Parda Cove: Summit of Shelter I . . Pollard Cove: Entrance Port Angosto: Hay Pt ; . . St. Anne Island: Central summit Half Port Bay: Point Upright Port: Entrance Port Tamar : Mouat Islet Port Churruca: Summit of Blanca Pen . . Valentine Harbor: Observation mount . . Cape Parker: W. summit Mercy Harbor: Summit of Battle I Mayne Harbor: Observation spot Port Grappler: Observation spot Port Riofrio: Vitalia I Eden Harbor: Observation spot Halt Bay : Observation islet Westminster Hall Islet: E. summit Evangelistas Island: Light-house Cape Victory: Extreme Cape Isabel : W. extreme Cape Santiago : Summit Molyneux Sound: Romalo I Cape Tres Puntas: Summit, 2,000 ft Port Henry : Observation spot Mount Corso: SW. summit Rock of Dundee: Summit Santa Barbara Port: N. extreme obs. pt . Guaineco Islands: Speedwell Bay, hill, NE.pt Port Otway : Observation spot Cape Tres Montes: Extreme Cape Raper: Rock close to cape Christmas Cove: SE. extreme Hellyer Rocks: Middle Cape Taytao: W. extreme Socorro Island: S. extreme Mayne Mountain: Summit, 2,080 ft Port Low : Observation islet Huafo Island : S. extreme Port San Pedro: Cove on S. shore Cape Quilan: S W. extreme Corcovado Volcano: Summit, 7,510 ft... Minchinmadiva Volcano: S. summit, 8,000 feet Castro: E. end of town Lat. S. 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 Long. W. 70 37 51 70 54 24 70 34 27 70 58 31 70 55 03 71 17 15 71 55 30 71 59 41 72 04 45 72 10 42 72 19 30 72 27 10 72 34 15 72 32 25 72 38 00 72 47 30 72 47 55 73 00 30 73 12 05 73 21 30 73 15 30 73 17 45 73 16 15 73 44 28 73 59 33 74 17 45 74 13 30 74 38 14 74 04 00 74 17 39 74 23 27 74 25 10 74 20 55 74 23 10 75 06 00 74 55 00 75 13 20 75 27 45 74 51 30 75 22 00 75 13 20 75 34 00 75 40 30 75 28 20 75 10 00 75 18 20 75 25 30 75 37 55 75 31 30 75 12 00 75 06 00 75 08 45 74 07 45 73 59 35 74 42 00 73 41 50 74 22 00 72 44 40 72 30 30 73 45 20 Lun. Int. Range. H. W. h. m. 10 24 11 03 11 58 12 21 28 1 20 1 54 1 53 'i'si' "i'69 55 55 30 15 "o'io 00 12 20 12 10 01 L. w. h. m. 4 24 5 03 5 58 6 21 6 53 7 40 8 11 8 08 '7"44' '7'2i" 7 07 7 08 6 45 6 30 '6'25' 6 13 10 00 Spg. Neap. ft. 8.0 5.0 6.0 8.0 7.0 8.0 5.5 5.0 '4.' 5' To" 6.0 4.4 4.5 5.3 4.4 6.2 6.1 6 21 18. ft. 4.2 2.6 3.1 4.2 3.7 4.2 2.9 3.9 '3." 5 '3."i 4.6 3.4 3.5 4.1 "i'i 3.4 4.8 3.1 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: La Picuta San Carlos de Ancud: Light-house Condor Cove: Landing Eanu Cove: Anchorage Muilcalpue Cove: Landing place Milagro Cove: Landing place Laruehuapi Cove: Landing place Valdi via : 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 Chanaral 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 Lath's. Long. W. Lun Int. Range. H. W. L. W. Spg. Neap. O / It O 1 II h. m. h. m. ft. ft. 42 23 00 73 36 00 73 25 00 72 45 00 73 07 15 42 04 00 42 03 00 41 46 08 1 10 7 35 14.8 7.5 41 46 40 73 52 54 04 6 20 5.9 3.0 40 46 19 73 51 00 73 49 50 73 45 00 73 45 20 73 41 50 40 43 18 40 35 52 40 21 04 40 11 47 00 6 13 7.2 3.7 39 51 37 73 26 25 10 25 4 13 5.6 2.8 39 23 00 73 14 00 10 18 4 05 4.9 2.5 38 21 22 73 58 06 10 20 5 07 3.3 1.7 37 35 20 73 39 55 10 15 4 02 4.9 2.5 37 22 30 73 40 00 10 10 3 55 5.3 2.7 37 05 20 73 11 13 10 05 3 50 4.9 2.5 36 59 07 73 32 30 10 10 3 55 6.0 3.0 36 42 00 73 07 27 10 04 3 51 5.3 2.7 36 36 45 73 02 49 10 05 3 53 5.0 2.5 34 46 02 72 06 12 9 57 3 48 4.1 2.1 33 34 13 71 38 00 9 44 3 34 4.0 2.0 33 38 30 69 56 30 70 41 32 71 38 52 33 26 42 33 01 08 9 37 3 26 3.9 2.0 33 01 52 71 38 42 71 32 56 32 46 00 9 35 3 25 4.1 2.1 32 07 55 71 33 22 9 30 3 20 3.9 2.0 31 51 45 71 34 51 9 26 3 16 4.2 2.1 31 39 30 71 35 20 71 39 21 71 39 00 71 39 00 71 31 09 31 17 05 1 30 50 45 30 14 00 30 15 14 9 15 3 05 4.1 2.1 29 56 15 71 21 00 8 58 2 48 4.9 2.5 29 56 24 71 21 53 71 22 21 71 33 20 71 34 38 71 36 40 71 15 45 29 55 10 29 34 40 29 15 45 29 00 50 1 28 27 20 8 23 2 10 4.9 2.5 28 05 45 71 12 48 8 50 2 38 4.9 2.5 28 04 30 71 11 32 71 09 38 71 03 26 70 58 45 27 54 10 27 39 20 27 20 00 8 21 2 08 5.6 2.5 27 03 15 70 52 54 8 50 2 37 4.9 2.5 27 03 15 70 53 45 70 51 55 70 44 25 26 51 05 1 26 34 30 9 00 2 47 5.0 2.5 26 20 00 70 37 25 9 05 2 52 4.9 2.5 26 16 12 80 11 43 70 43 57 70 44 03 26 09 15 25 39 30 9 10 , 2 57 5.0 2.5 25 31 00 70 41 18 ^ 70 34 10 25 25 20 9 20 3 07 4.9 2.5 25 07 00 70 30 16 9 35 3 22 5.0 2.5 25 05 25 70 29 50 9 30 "3 17 4.9 2.5 24 34 30 70 36 29 70 33 00 70 32 28 70 25 18 24 15 00 23 53 00 23 38 50 9 05 2 52 4.7 2.4 23 33 05 70 26 55 Page 212] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. WEST COAST OF SOUTH AMERICA— Continued. Place. Moreno Mountain: Summit Constitution Cove: Shingle pt. of island. Mexillones Mount: Summit Port Cobija: Landing place Tocopilla: Extremity Point San Francisco Head : W. pitch Loa River: Mouth Lobos Point: Outward pitch Pabellon de Pica: Summit Patache Point: Extreme Iquique: Light-house Mexillon Bay : Landing place Pisagua: Pichalo Pt., extreme Gorda Point: W. low extreme Lobos Point: Summit Arica: Iron church Schama Mount: Highest summit Coles Point: Extreme Ilo: Mouth of rivulet Port Mollendo : Light-house Islay : Custom-house 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 Mesa de Dona Maria: Central summit. . . Carreta Mount: Summit San Gullan Island: N. summit Paraca Bay: N. extreme of W. pt Pisco: Light-house 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 Pescadores Islands: Summit of largest. . . Pelado Island: Summit Sup6 : W. end of village Huarmey : W. end of sandy beach Colina Redonda: Summit Samanco Bay : Cross Pt Chimbote: Village, N. part Chao Islet: Center Guanape Islands: Summit of highest Huanchaco Point: SW. extreme Malabrigo Bay : Rocks Pacasmayo: Light-house Eten Head : Light-house 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 Parinas Point: Extreme Cape Blanco: Under middle of high cliff. Tumbez: Malpelo Pt Lat. S. 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 f7 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 16 40 3 30 42 Long. W. 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 71 20 72 02 72 07 72 27 73 16 73 41 74 27 74 51 75 09 75 30 75 49 76 16 76 27 76 18 76 10 76 24 76 31 76 38 76 48 77 02 77 15 77 14 77 16 77 50 77 43 78 10 78 21 78 30 78 35 78 45 78 56 79 06 79 26 79 33 79 51 79 57 80 42 80 51 81 09 81 05 81 07 81 17 81 12 80 28 Lun. Int. Range. H. W. h. m. 9 35 9 44 8 55 9 00 8 35 "8*32 7 49 7 55 7 39 6 47 6 16 5 47 5 08 4 50 4 19 4 64' 3 20 L. W. Spg. Ngap. A. m. 3 22 3 31 2 42 2 22 "2*26" 1 37 1 43 1 27 35 04 12 00 11 21 11 03 10 32 ioii' 9 33 3.9 4.0 4.8 2 47 ! 4. 9 5.0 '5."6' 5.6 5.3 6.2 3.9 3.8 3.5 2.1 2.0 2.1 2.5 3.5 ft. 2.0 2.0 2.4 2.5 2.5 "2." 5 2.8 2.7 3.1 2.0 1.9 1.1 1.0 1.1 1.3 1.8 APPENDIX IV. [Page 213 MARITIME POSITIONS AND TIDAL DATA. WEST COAST OF SOUTH AMERICA— Continued. Place. Lat. S. Long.W. Lun. Int. Range. 1 H. W. L. W. Spg. Neap. 9 -d a i S 9 a Guayaquil River: Lighten Santa Clara I. Guayaquil, Concejo: S. pt. of city Puna* Mandinga Pt. light o / « 3 10 40 2 12 24 2 44 30 2 12 00 1 16 55 1 03 30 56 50 35 25 21 30 Lat. N. 50 10 40 00 1 03 30 1 36 00 1 49 36 2 37 10 2 58 10 3 49 27 4 17 06 5 28 46 6 41 19 6 49 45 8 12 30 8 28 50 8 54 30 8 56 32 8 39 00 / 1/ 80 25 29 79 52 19 79 53 "45 h. m 4 00 7 00 h. TO. 10 13 1 00 ft. 10.0 11.0 ft. 5.1 5.6 Point Santa Elena: Veintemilla light Plata Isle: E. pt 80 59 00 81 03 55 80 55 55 80 42 50 3 00 9 13 7.9 4.0 Cape San Lorenzo: Marlingspike Rock. . Manta Bay : Light-house 3 10 9 23 7.5 3.8 Caraques Bay: Punta Playa 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 Cape Pasado: Extreme 3 15 9 28 9.9 5.0 Point Galera: N. extreme Cape San Francisco: SW. extreme Esmeralda River: Light-house' Mangles Point: S. pt. of creek entrance. . Tumaco : S. pt. of El Morro I 3 35 9 48 13.2 7.1 Guascama Point: Extreme Gorgona Island : Watering Bay Buenaventura: Basan Pt 6 00 12 13 13.2 7.1 Chirambiri Point: N. extreme Cape Corrientes: SW. extreme 3 40 3 30 9 53 9 43 13.1 13.3 7.0 7.2 Cupica Bay: Entrance to Cupica River. . Cape Marzo: SE. extreme Isla del Rey : Extreme of Cocos Pt Darien Harbor : Graham Pt . . ..... 3 00 9 13 15.7 8.5 Flamenco Island : N. Pt Chepillo Island : Center .... 3 05 3 30 9 18 9 42 16.0 15.0 8.7 8.1 Point Cham6: Extreme ISLANDS IN THE ATT. ANTIC OCEAN. « -d 1 m H • 2 N < i N 2 « % Fseroe Islands, Strom Islet: Thorshaven Fort flagstaff 62 02 26 62 18 20 61 23 00 57 35 52 39 40 07 39 27 00 38 32 09 38 31 45 38 34 30 38 25 00 38 40 30 39 05 24 38 38 20 37 44 16 37 49 20 36 56 00 37 16 44 33 03 15 32 35 45 32 37 42 32 43 14 32 45 00 32 48 07 6 43 08 7 00 36 6 45 30 13 42 21 31 08 00 31 08 49 28 34 00 28 37 39 28 44 00 28 28 12 28 13 00 28 00 45 27 13 45 25 40 40 25 08 21 25 10 00 24 47 06 16 16 20 16 33 30 16 55 16 16 39 31 16 57 30 17 16 05 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 11 30 5 18 3.9 1.8 St. George Island : Light-house Graciosa Island : Santo Fort light Terceira Island : Monte del Brazil, near Anera 20 6 32 4.4 2.0 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 ........ 15 6 27 5.7 2.6 40 6 52 6.6 3.0 Madeira Island : Funchal light 35 6 47 6.6 3.0 Fora I. light-house Pico Ruivo, summit 6,056 ft Pargo (W.) Pt Page 214] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ISLANDS IN THE ATLANTIC OCEAN— Continued. Place. Lat. N. Salvage Islands: Light-house, Gran Sal- vage I Alegranza Island: Delgada Pt. light ... Lanzarote Island: Port Naos light Pechinguera Pt. light Lobos Island: Martino Pt. light Fuerta Ventura Island : Jandia Pt. light Gran Canaria: Isleta Pt. light Palmas light Teneriffe Island: Anga Pt. light Santa Cruz, Br. con- sulate Summitof peak, 12, 180 ft Gomera Island : Port Gomera Ferro Island : Port Hierro Palma Island : Light, NE. pt San Antonio Island: Bull Pt. light Summit, 7,400 ft.. St. Vincent Island : Porto Grande light St. Lucia Island : N. pt Raza Island: E. pt St. Nicholas Island: Light-house Sal Island: N. pt. light S. pt :..-. Boavista Island: NW. pt NE. pt Light-house Mayo Island: English Road St. Jago Island: Reta Pt. light Porto Praya, S. light . . Fogo Island : N. S. da Luz, village Brava Island : Light-house Ireland Island: Dock yard clock tower. Bastion C Hamilton Island : Gibbs Hill light St. Davids Island: Light-house St. Paul Rocks: Summit, 64 ft Rocas Reef: NW. sandy islet Fernando Noronha: The Pyramid Ascension Island : Fort Thornton St. Helena Island: Obs. Ladder Hill . . . Martin Vaz Rocks: Largest islet Trinidad Island: SE.pt Inaccessible Island : Center Tristan d'Acunha Islands: NW. pt Gough Island: Penguin Islet Port Egmont: Observation spot Mare Harbor: Observation spot Port Louis: Flagstaff, govt, house Port Stanley: Governor's house Cape Pembroke: Light-house South Georgia Island : N. cape Shag Rocks: Center Sandwich Islands: S. Thul6 Traverse I. volcano . 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 Long. W. 15 54 00 13 29 31 13 33 07 13 52 05 13 49 13 14 31 35 15 25 11 15 24 56 16 08.11 16 15 09 16 38 02 17 05 55 17 54 22 17 47 01 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 Lun. Int. H. W. 50 40 1 15 20 5 50 7 30 5 50 7 04 5 05 5 00 5 20 3 00 3 35 3 40 12 50 7 20 5 31 L. W. h. m. 7 00 6 50 7 27 6 30 12 00 1 20 12 00 52 11 18 11 13 11 30 9 10 9 48 9 53 5 40 1 08 11 27 Range. Spg. Neap. 8.5 9.3 7.8 3.3 4.4 4.8 4.0 10.0 6.0 2.0 2.8 3.5 4.0 5.2 10.7 4.3 /t. 3.9 4.3 3.6 4.0 1.5 2.0 2.2 2.6 4.6 2.7 0.9 1.3 1.6 1.8 2.4 5.6 2.2 APPENDIX IV. MARITIME POSITIONS AND 'xIDAL DATA. ISLANDS IN THE ATLANTIC OCEAN— Continued. [Page 215 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 Lnn. Int. H. W. h. m. L. W. Range. Spg. Neap. h. TO. 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.'s sta Lands End: Longships light-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 Aberyst with : 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: Ay re 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 50 44 15 50 46 35 50 48 03 50 53 45 50 42 07 50 39 42 50 34 30 50 31 10 50 13 18 50 20 02 50 10 49 50 08 30 49 57 40 50 02 44 50 04 10 49 53 33 50 33 00 51 04 00 51 12 05 51 27 24 51 27 48 51 36 50 51 37 52 51 41 00 51 43 15 52 24 20 52 45 00 53 18 30 53 18 54 53 25 15 53 24 02 53 26 38 53 24 04 53 55 03 54 03 14 54 24 56 54 30 50 54 33 00 54 38 10 55 28 10 55 32 55 Long. 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 20 38 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 3 36 00 4 51 20 4 38 10 4 41 00 1 10 11 24 11 09 10 35 11 10 11 31 35 11 05 6 29 5 25 5 20 4 45 4 15 5 45 5 00 7 00 6 45 5 45 5 40 5 41 5 40 7 25 7 24 10 00 11 08 11 00 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 13.2 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 8.7 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 "i3.'i 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-houBe 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 i North Ronaldsay : 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 Cot^aet Island : Light-house Tynemouth: Souter Point light-house North Shields: Light-house Sunderland : N. pier light Hartlepool : Light-house Flamborough : New light-house Humber River: Killingholme middle light. 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 : OrdYiance 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 Lat. N. 38 27 26 00 52 43 18 39 40 20 24 50 19 22 47 08 51 25 11 28 30 40 37 30 40 16 59 15 16 45 23 24 33 00 51 15 08 02 09 22 27 20 44 25 41 22 51 54 28 15 08 33 28 07 26 03 11 00 02 09 57 23 46 00 37 00 20 06 58 10 00 30 55 07 41 51 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 57 33 22 25 22 45 36 30 16 20 1 16 02 1 08 41 1 29 50 47 30 2 55 25 46 30 46 22 04 06 44 53 23 06 33 22 08 05 10 54 59 00 39 00 32 00 21 30 26 00 21 30 10 19 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. Range. H. W. h. m. 11 35 55 10 20 5 10 '5'35' '635 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. Spg. h. m. 5 23 ft. 7 08 4 08 11.2 4.0 11 22 'ii"47' "'6"22' 12.8 ii.'i* is." 4* 3 44 4 37 3 22 5.0 5.2 4 17 6.0 3 17 3 47 6.4 9.8 6 36 7 02 8 08 11.2 11.7 15.5 8 11 8 28 16.5 15.0 9 31 9 32 9 43 10 36 14.8 14.6 14.2 15.8 11 29 3 35 4 53 5 44 10 03 18.5 6.2 7.8 11.2 10 23 10.6 9 43 10.8 9 53 10.7 9 53 10 03 10.7 12.3 13 18.7 Neap. ft. 5.3 6.7 2.4 7.7 "4.' 8 '5.' 7 4.2 2.2 2.2 2.6 2.7 4.2 6.1 6.4 8.5 7.5 7.4 7.3 7.0 10.2 3.6 4.5 6.6 4.4 5.3 4.6 4.6 4.6 5.3 8.0 APPENDIX IV. MAEITIME POSITIONS AND TIDAL DATA. ATLANTIC COAST OF EUROPE— Continued. [Page 217 Place. Eeragh Island : Light-house Arran Island : Light-house Galway : Mutton I. light Golam Head: Tower Slyne Head: N. light-house Clifden Bay: Gortrumnagh Hill Tully Mountain: Ordnance survey station Inishboffin: Lyon Head light Inishturk Island: 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: Light-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 Lame: Farres Pt. light-house Belfast Bay : Light, east side Mew Islands : Light-house Donaghadee: Ijght-house South Rock: Light vessel Dundrum Bay: St. John Pt. light Carlingford Lough: Haulbowjine Rk. It. . Drogheda: Light-house Rockabill : Light-house Howth Peninsula: Bailey light Dublin : Observatory N. wall light Poolbeg: Light-house Kingstown : E. 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 Waterf ord : Hoop Pt. light Lat. N. 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 67 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 02 20 19 25 21 51 6 28 45 6 10 45 5 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 10 5 03 5 28 6 55 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 '5"65" L. W. Spg. 10 28 10 19 13.4 15.1 10 29 13.2 10 33 12.1 11 03 10.4 11 23 11.4 11 16 11.2 11 41 11.6 43 1 35 7.5 8.0 4 18 6.7 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 8.8 12.' 3" Neap. ft. 5.7 6.4 5.7 5.2 4.5 5.3 4.8 5.3 3.4 3.6 4.5 "6." 3 "7."4 9.2 6.8 7.5 7.6 6.4 6.9 5.1 2.9 5.1 '6.2 Page 218] APPENDIX IV. MAKITIME POSITIONS AND TIDAL DATA. ATLANTIC COAST OF ETTROPE— Continued. Place. Waterford: Cathedral 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-house Capel Island : Tower Ballycottin : Light-house Cork Harbor: Haulbowline Coal Wharf Queenstown : Roches Pt. light Kinsale: Light- house, S. pt Seven Heads: Tower Galley Head : Light on summit Stag Rocks: Largest Alderney Harbor: Old pier light St. Heliers: Light on Victoria Pier Vardo: Fortress Vadso: Light-house North Cape: Extreme Fruholm: Light-house Hammerfest: Light-house Tromso: Observatory Hekkingen : Light-house Andenes: Light-house Lodingen (Hjertholm): Light-house Lofoten Island: Skraaven I. light Glopen light Gryto: Light-house Stot: Light-house Traenen : Soe Islet light Bronnosund : Light-house Villa: Light-house Halten Island : Light-house Koppem Agdenes: Light-house Trondheim: Mumkholmen flagstaff Grip: Church Christiansund : Storvaden Freikallen Hestskjaer : Ligh t-house Stemshesten ^rstenen : Light-house Svinoen Islet Hjoerringa Mountain: Summit Hornelen Mountain: Summit Batalden Island : Store Kinnsund : Light-house Alden Helliso: Light-house Bergen: Cathedral Lorstakken Mountain: Summit Marstenen Islet: Light-house Furen Islet Ulsire: Light-house Hvidingso: Light-house Port Stavanger: Light-house Obristadbroekke: Light-house Synesvarde Mountain : Summit Kompas Mountain : Summit Lister: Light-house Lindesnes : Light-house Ry vingen Island : Light-house Christianssand : Odderoen light 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 70 22 00 70 04 00 71 11 00 71 06 00 70 40 15 69 39 12 69 36 05 69 19 30 68 24 40 68 09 20 67 53 15 67 23 15 66 56 35 66 25 50 65 28 40 64 32 55 64 10 25 63 48 25 63 38 45 63 27 04 63 13 11 63 07 01 63 03 04 63 05 00 62 58 49 62 48 20 62 19 38 62 11 12 61 51 21 61 38 40 61 33 35 61 19 16 60 45 05 60 23 37 60 21 39 60 07 50 59 57 44 59 18 20 59 03 10 58 58 30 58 39 25 58 36 56 58 25 51 58 06 25 57 58 55 57 58 00 58 07 50 Long. W. 7 06 24 7 10 15 7 33 05 54 54 32 39 35 08 50 34 51 10 59 00 18 20 15 14 31 58 42 51 57 10 13 27 12 00 06 44 Long. 31 07 29 45 25 40 23 59 23 40 18 57 17 50 16 08 16' 02 14 40 13 04 13 52 13 28 11 59 12 13 10 42 9 24 9 44 9 45 10 23 36 43 46 29 12 6 36 5 16 5 07 15 47 46 47 42 20 19 01 03 52 24 45 33 49 58 34 03 29 00 E. 30 00 00 00 00 00 15 00 30 40 30 30 50 50 30 10 50 45 20 30 05 35 04 55 32 10 25 59 11 38 45 14 55 15 35 00 30 35 20 20 35 08 49 20 •10 50 30 Lun. Int. Range. 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 10 15 9 43 4 16 L.W. h. m. Spg. Neap. ft. 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 31.2 9.0 8 40 7 48 6 55 5 23 5 04 4 48 3 55 3 40 8.3 7.8 7.0 6.9 4.1 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 8. 4 4. 1 5. 2. 9 2.1 0.8 10 15 1.1 0.5 APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ATLANTIC COAST OF EUROPE— Continued. [Page 219 Place. Okso: Light-house Hamberg: Mill Arendal Inlet: Inner Torungerne light. Jomfruland : Light-house Langotangen : Light-house Langesund : Church Frederiksvsern : Lookout tower Svenor: Light-house Foerder Islet: Light-house Fulehuk : Light-house Basto : Light-house Horten : Church Holmestrand: Church Drobak : Church Oscarsberg: Fort flagstaff Christiania: Observatory Strom tangen (Torgauten): Light-house Fredriksten : Fort clock tower Torbjornskjser: Light-house Koster : Light-house Stromstad: Steeple Nord Koster Islands: Light-house Wadero Island: Light-house Hollo Island: Light-house Paternoster Rocks: Light-house Gotten burg: 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 Ystad: Light-house Sandhammaren : Light-house Hano Island : Light-house Karlshamn : Light-house Karlskrona: Stumholm Tower Oland Island : Light on S. pt Gottland Island: Hoburg light, S. pt... Ostergarns light Faro Island : Holmadden light Sparo Vestervik : Granso light Haradsskar Islet : 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 Lat. N. / // 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 Long. E. 03 30 31 36 47 55 36 15 45 50 45 14 03 28 09 26 31 55 36 25 32 45 29 52 19 15 38 08 36 55 43 35 50 15 24 09 47 20 00 45 Lun. Int. Range. H. W. 11 10 11 00 11 02 11 13 11 28 11 53 11 54 12 14 12 29 12 51 12 51 12 27 12 41 12 49 12 59 12 49 13 09 13 49 14 n 14 50 14 52 15 36 16 24 18 11 18 59 19 22 16 40 16 59 16 11 17 52 18 03 17 37 18 41 19 24 18 49 18 22 18 26 18 24 18 09 18 22 17 08 17 33 17 02 17 04 17 01 h. m. 4 17 4 34 5 22 L. W. h. TO. Neap. 10 10 1.0 0.7 10 00 1.3 1.0 10 37 1.2 0.9 Page 220] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ATLANTIC COAST OF ETJBOPE— Continued. Place. Lat. N. Hudiksvalls: Court-house Gnarp: Church Sundsvall: Church Lungo: Light-house Skags Head : Light-house '. Hohnogadd : Light-house Umea: Bredekar Light Bjuroklubb: Light-house Pitea Rodkallen : Light-house Maloren: Light-house Tornea: Light-house Uleaborg: Karlo I. light Ulko Kalla Rock : Light-house Norrsher Islet: Kvarken light Kaske: Shelgrund I. light Bierneborg: Sebsher light Nuistad: Ensher light Abo: Observatory Aland Island : Shelsher light Ekkere light Logsher light Bogsher: Beacon Ute Islet: Light-house Gange: Gange I. light Rensher: Light-house Helsingfors: Observatory Soder 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 has tion Cathedral St. Petersburg: Observatory Pulkowa: Observatory Peterhof : Pier-head light Oranienbaum: Light-house Seskar Islet: Light-house Narva: Lights, 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 61 43 57 62 02 51 62 23 30 62 38 35 63 11 55 63 35 34 63 39 33 64 28 50 65 19 10 65 18 53 65 31 30 65 48 30 65 02 20 64 20 05 63 14 08 62 20 06 61 28 29 60 43 10 60 26 57 60 24 45 60 13 20 59 50 50 59 31 11 59 46 30 59 46 00 59 56 10 60 09 43 60 06 40 59 58 45 59 58 08 60 00 40 60 06 22 60 12 31 60 14 43 60 11 05 59 58 14 59 59 44 59 56 30 59 46 19 59 53 26 59 55 40 60 02 08 59 28 04 59 49 10 59 41 06 59 42 00 59 27 05 59 26 28 59 36 22 59 27 55 59 21 30 59 18 06 59 05 25 58 55 02 58 23 02 57 54 37 58 05 50 58 23 10 57 03 28 56 56 36 57 48 02 57 48 10 57 24 00 56 31 01 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 61 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. H. W. h. m. h. TO. Spg. Neap. ft. APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ATLANTIC COAST OF EUROPE— Continued. [Page 221 Place. 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 Oxhoit: Light-house Hela: Light-house Rixhoft: Light-house Leba: Church tower Stopelmunde: Church Jershoft: Light-house 1 Rugenwalde: St. Mary's Church Coslin: St. Mary's Church Funkenhagen : Light-house Col berg: St. Mary's Church Gross-Horst: Light-house Cammin : Cathedral tower WoUin: Church tower Stettin: N. Castle tower Swinemunde: Light-house Streckelsberg: Survey station near beacon Usedom: Church tower Lassau: Church tower Wolgast: Church tower Griefswald: St. Nicholas Church Griefswalder Oie : Light-house Granitz : Castle tower Bergen : Church tower Arkona: Light-house Stralsund : St. Mary's Church Darsserort: Light-house Wustrow: Church Ribnitz: Church tower Warnemunde: 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 Marienleuchte : 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 30 55 54 39 48 54 47 05 54 54 28 54 40 23 54 56 48 54 58 05 55 02 46 55 03 52 55 05 31 55 03 04 Long. E. 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 Lun. Int. Range. H. W. L. W. Neap. h. TO. ft. 20 6 33 5.2 3.0 Page 222] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ATLANTIC COAST OF EUROPE— Continued. Place. Keitum: Church Fohr: St. Nicholas Church Galgenberg: Survey station Husum : Church Tonning: Church Busum : Church Helgoland: Light-house Scharhorn: Beacon Neuwerk : Light-house Cuxhaven : Light-house Stade: Church steeple Steinkirchen : Church Altona: Observatory Hamburg: Observatory Berlin : Observatory Harburg: Light-house Hohe Weg: Light-house Lang warden: 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 Proeste : 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: Waldemar'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 7 54 09 41 45 35 41 22 03 13 58 59 53 12 25 11 58 03 12 17 16 12 32 40 12 03 07 12 07 36 12 38 24 12 41 26 12 34 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 L. W. 2 10 1 45 1 11 11 29 39 4 00 5 00 25 54 10 04 11 27 11 05 24 9 33 h. m. St. 7 47 7.8 8 23 7 57 7 24 5 17 10.8 11.0 11.7 8.1 6 51 "i6"i3 'ii"i2 10.1 6 38 7 07 6 23 6 17 5 15 4 53 6 36 3 21 8.5 '6."i' 10.1 10.4 9.5 13.2 8.0 7.3 0.6 Neap. St. 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 r APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ATLANTIC COAST OF E U HOPE— Continued. [Page 223 1 Place. Lat. N. Long. E. Lun .Int. Range. H. W. L. W. Spg. Neap. i M d a K a a a Tuno Island : Light-house o / // 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 / // 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 4 46 36 4 53 01 5 07 50 4 29 03 4 18 30 4 15 10 4 10 45 4 28 50 4 07 40 4 26 26 3 58 35 3 35 48 3 34 32 4 22 18 4 24 44 4 24 12 3 06 54 2 55 51 2 55 22 2 45 34 2 20 14 2 22 31 2 06 34 1 51 07 1 35 02 1 33 47 1 49 56 1 30 46 1 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 h. m. h. m. ft. ft. Sanisoe Island : Nordby Church tower . . Aarhus: Cathedral spire Hjelrn Islet: Light-house Forntts : Light-house Hals: Church tower Aalborg: St. Rudolph's Church ..." Cape Skaw, or Skagen: Old light-house . Hirtshals: Light-house 1 5 46 4 18 11 58 10 30 1.0 1.2 0.5 0.7 Haustholm : Light-house Boobjerg : Light-house Ringkiobins;: Church spire Loune: Church tower 2 35 8 47 2.1 1.2 Blaabjerg: Summit, 100 ft Guldager: Church 2 35 2 34 8 47 8 46 4.5 4.7 2.6 2.7 Fano Island : Nordby Church Mano Island: Church spire Niewe Diep: Time-ball station 7 17 1 05 3.9 2.0 Amsterdam : W. church tower Utrecht: Observatory Leyden : Observatory The Hague: Church tower 1 Scheveningen : Light-house : . . Brielle: Light-house 2 50 3 35 2 20 3 20 9 02 9 47 8 32 9 32 4.8 6.7 5.2 9.8 2.5 3.5 2.8 5.2 Rotterdam : Time-ball station Hellevoetsluis : Time- ball station Willemstadt: Light-house Goedereede: Light on church tower Flushing: Time-ball station Light, VVesthaven bastion Brussels: Observatory 44 6 56 14.7 7.8 Antwerp : Observatory 4 15 10 27 14.8 7.8 Notre Dame Cathedral Blankenberghe: Fort light-house Ostend : Light-house 05 02 6 17 6 32 12.5 16.1 6.7 8.4 Church tower Nieuport: Templars tower 10 6 22 15.7 8.4 Paris: Observatory Dunkerque: Tower 11 58 11 59 11 39 11 17 11 18 5 58 6 16 6 13 5 51 5 52 16.8 19.0 21.0 21.5 25.2 8.5 9.6 10.7 11.0 12.8 Gravelines: Light on N. breakwater Calais: Light on old fort Cape Gris Nez: Light-house Boulogne, C. Alprech: Light-house Abbeville: Tower Cayeux : Light-house Dieppe: W. jetty light 10 54 5 48 27.3 13.3 Ailly Point: Light-house St. Valery en Caux: Light on W. break- water 10 29 10 06 5 33 5 02 26.8 23.3 13.1 11.4 Fecamp: N. jetty light Cape La Heve: S. light Havre: S. jetty light 9 03 4 14 22.5 11.0 Honfleur: Hospital jetty light Caen : Church tower Port Corseulles: W. jetty light Point De Ver: Light-house Cape La Hougue: Light-house 8 13 8 14 2 45 2 37 18.5 17.0 8.2 7.5 Cape Barfleur: Light-house Cherbourg: Light, W. head of break- water Naval Observatory 7 30 1 44 17.6 7.8 Cape La Hague: Light-house Casquets Rocks: Light on N\V. rock 6 20 15 15. 5 6.9 Page 224] 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: Rochebourne light Cape Frehel : Light-house Heau de Brehat: Light-house Morlaix, He Noire: Light-house De Bas Islet: Light-house Abervrach : Light on Vrach Islet Ushant: 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 Paimboeuf: Steeple Nantes: Cathedral Noir Moutier Island : Light-house Le Pilier Island : Light-house D' Yell Island : Light-house La Chaume: Light-house Point de Grouin du Con: Light-house. . R4 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. Andre Bayonne: Cathedral Biarritz : Light-house St. Jean de Luz: St. Barbe Point light . Fuenterrabia: Light on Cape Higuera.. Port Pasages: Light at entrance San Sebastian: Monte Igueldo light Bilbao: Light on Galea Castle Castro Urdiales: Santa Ana Castle light Santona: Pescador Point light Santander: Cape Mayor light San Martin de la Arena: Light-house. . . San Vincent de la Barquera: End of new mole Rivadesella: Mount Somos light Gijon: Santa Catalina light Aviles: Light-house Rivadeo: Light-house Estaca Point: Light-house Lat. N. Long. W. Lun. Int. Range. H. W. L. W. 8pg. Neap. a 1 II 49 27 13 49 06 28 / II 2 31 31 2 48 49 1 48 25 1 26 39 1 36 46 1 49 20 1 58 41 2 19 08 3 05 11 3 52 33 4 01 38 4 34 34 5 03 26 4 29 36 4 34 28 4 52 03 4 45 25 4 32 50 4 22 30 3 57 15 3 30 35 3 21 31 3 13 38 3 06 09 2 50 07 2 55 08 2 45 28 2 38 05 2 31 25 2 25 48 2 11 50 2 02 09 1 32 59 2 13 16 2 21 37 2 22 56 1 47 45 1 27 49 1 33 40 1 08 57 1 10 40 57 50 1 24 37 1 15 16 1 10 24 1 04 27 34 42 1 28 43 1 33 16 1 39 53 1 47 30 1 56 05 2 01 40 3 .04 06 3 16 10 3 28 06 3 47 40 4 01 00 4 24 55 5 07 10 5 40 11 5 56 00 7 03 00 7 42 00 h. m. 6 12 h. m. 07 ft. 26.0 ft. 11.5 49 22 27 49 02 54 6 07 15 30.8 13.5 48 50 07 48 52 13 48 40 18 48 41 05 5 50 5 55 5 43 09 04 04 36.7 34.7 36.0 16.0 15.2 15.7 48 54 33 48 40 23 48 44 45 48 36 57 48 28 31 48 23 32 48 19 10 5 35 5 00 4 35 4 00 3 35 3 23 12 00 11 25 11 00 10 25 10 00 9 45 30.4 23.1 22.0 20.6 18.9 19.5 13.3 10.6 10.1 9.5 8.7 9.0 48 02 40 48 02 28 3 25 9 53 17.2 7.9 48 00 47 47 47 52 47 43 17 47 38 51 3 04 3 05 3 00 9 31 9 34 9 27 11.1 13.3 13.0 5.1 6.1 6.0 47 44 53 47 18 42 47 29 10 47 19 18 47 32 53 47 39 30 47 17 53 3 09 3 25 3 35 3 20 3 45 5 47 9 36 9 50 9 58 9 46 10 08 12 11 13.8 16.6 16.9 16.7 16.6 15.8 6.3 7.7 7.9 7.7 7.7 7.4 47 18 30 47 19 44 3 25 9 47 16.7 7.7 47 16 18 47 17 17 47 13 08 47 00 41 47 02 35 3 35 4 18 5 50 3 05 9 56 10 39 12 28 9 26 16.6 17.0 16.5 16.7 7.7 7.9 7.7 7.7 46 43 04 46 29 38 46 20 41 3 18 3 20 9 40 9 44 14.7 12.7 6.8 5.9 46 14 40 46 09 25 46 00 36 45 56 37 46 02 49 3 27 3 27 3 45 9 22 9 22 9 55 16.6 16.6 16.7 7.7 7.7 7.7 45 41 39 45 35 14 45 34 10 3 35 9 53 16.8 7.8 44 50 19 43 29 29 6 30 12 15.3 7.1 43 29 38 43 23 58 43 23 30 3 07 9 14 12.3 5.8 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 2 55 2 50 2 50 2 55 3 05 3 00 3 00 9 05 9 03 9 03 9 07 9 18 9 14 9 14 11.7 12.7 11.8 12.3 14.8 11.7 10.4 5.5 5.9 5.5 5.7 6.9 5.5 4.9 43 32 48 43 38 05 43 34 40 43 47 20 2 50 2 45 2 45 9 03 8 58 8 58 13.5 12.0 14.4 6.3 4.9 3.9 APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ATLANTIC COAST OF EUROPE— Continued. [Page 225 Place. Port Cedeira: Light-house Ferrol : Old naval observatory Priorino Chico light Coruna: Hercules Tower light Cape Finisterre: Light-house Vigo: Ores I. light J Oporto: Light, N. S. de Luz Cape Mondego : Light-house Berlanga Island : Light-house Peniche: Light-house Cape Roca : I^ight-house Lisbon : Royal Observatory Setubal : Light-house Cape St. A'incent: Light-house Lagos: Church Cape Sta. Maria: Light-house Ayamonte : Light-house Huelva: Plaza at head of mole San Lucar: Chipiona light Cadiz: Observatory of San Fernando San Sebastian light Cape Trafalgar: Light-house Tarifa: Light-house Algeciras: Verde I. light Gibraltar: Dockyard flagstaff Europa Pt. light Lat. N. Long. W. Lun. Int. Range. H. W. L.W. Spg. Neap. o / // 43 39 00 43 29 30 43 27 30 43 23 10 42 52 45 42 12 30 41 09 10 40 10 47 39 24 49 39 21 00 38 46 49 38 42 31 38 29 15 37 01 20 37 07 48 36 58 23 37 11 00 37 15 08 36 43 58 36 27 40 36 31 30 36 10 50 35 59 53 36 07 19 36 07 10 36 06 25 O 1 II 8 05 30 8 13 29 8 20 20 8 24 26 9 15 28 8 54 00 8 40 35 8 54 15 9 30 29 9 22 30 9 29 46 9 11 10 8 56 00 8 58 00 8 39 53 7 51 48 7 24 00 6 57 12 6 26 30 6 12 20 6 19 00 6 02 08 5 36 31 5 26 12 5 21 17 5 20 42 h. m. 2 43 2 44 h. in. 8 56 8 57 14.8 14.9 6.1 6.1 2 43 2 42 8 56 8 55 14.8 10.0 6.1 4.6 2 25 2 20 8 38 8 35 10.0 7.0 4.3 3.0 2 05 8 15 7.8 3.4 2 20 2 10 8 05 8 20 11.1 11.6 4.8 5.0 1 55 8 08 13.0 5.6 1 15 7 28 12.3 5.6 1 45 7 58 11.8 5.4 1 32 7 52 5.6 2.6 1 35 7 55 3.7 1.7 COASTS OF THE MEDITEBRANEAN, ADRIATIC, AND BLACK SEAS. Malaga: Light-house 36 42 39 Almeria: Light-house 36 50 12 Cape de Gata: Light-house ' 36 42 57 Mazarron : Light-house 37 33 28 Cartagena: Arsenal gate 37 35 50 Escombrera light 37 33 22 Porman : Light-house 37 34 38 Santa Pola Bay: Light-house 38 12 30 Alicante: N. mole light 38 20 12 Villajoyose: Light-house 38 30 00 Benidonne: Tower 38 30 57 Altea: Light-house 38 33 30 Calpe: Church tower 38 38 36 Morayva: Tower 38 40 51 Jarea: Cape San Antonio light 38 48 06 Denia: Mole-head light 38 51. 00 CapeCullera: Light-house I 39 12 15 Valencia: Light-house 39 28 05 Mole-end light | 39 27 50 Columbretes Islands: Light-house 39 53 57 Oropesa Cape: Light-house 40 04 53 Vinaroz: Mole-headlight 40 27 48 Port Alfaques: Bana light ; 40 33 30 Cape Tortosa: Light-house 40 43 10 Tarragona: E. mole light 41 06 00 Barcelona: E. mole-headlight 41 22 10 PalamosBay: Molino Pt. light 41 50 04 Cadaques: Clock tower 42 16 15 Cape Creux: Light-house 42 19 10 i Cape Bear: Light-house I 42 30 59 Port Vendres: Fort Fanal light I 42 31 18 4 24 38 2 27 50 2 11 12 1 15 12 59 09 57 58 50 20 30 12 28 48 11 42 10 06 04 02 Long. E. 02 52 09 17 12 02 07 30 Long. W. 13 37 19 48 18 50 Long. E. 41 19 08 56 28 48 39 45 53 55 1 14 42 2 10 52 3 08 28 3 17 10 3 18 55 3 07 30 3 06 50 15 5 00 8 35 11 30 2.9 1.5 1.5 0.8 6583—06- -15 Page 226] APPENDIX IV. MAEITIME POSITIONS AND TIDAL DATA. COASTS OF THE MEDITEBBANEAN, ADRIATIC, AND BLACK SEAS— Continued. 1 Place. Lat. N. Long E. Lun. Int. Range. 1 H. W. L. W, 8pg. Neap. S 2 i e t i V S e Port Nouvelle: S. jetty light O 1 II O 1 II 43 00 47 3 04 08 43 23 50 1 3 42 08 43 29 17 i 4 08 32 h. m. h. m. ft. ft. Cette: Light, St. Louis mole Aigues Mortes: Espignette Pt. light Planier Rock : Light-house 43 11 57 43 20 43 43 18 22 43 10 21 43 05 10 43 01 01 43 32 51 43 33 51 43 41 32 5 13 51 5 20 46 5 23 43 5 36 42 5 56 06 6 08 39 7 00 54 7 08 02 7 17 13 Marseille: Janet Cliff light 7 31 2 00 0.6 0.3 New observatory Ciotat: Berouard mole light Toulon : St. Mandrien light 8 22 2 24 0.6 0.2 Grand Riband Island : Light-house Cannes: Light-house Antibes: Garoupe light 1 Nice: Light-house Ville Tranche: Mole-head light 43 41 58 1 7 18 42 43 40 30 : 7 19 41 . .......... Cape Ferret light Port Ibiza: Light-house 38 54 10 39 06 34 1 27 25 2 57 20 2 37 00 4 18 20 8 51 08 8 13 29 8 10 00 8 23 56 9 08 35 9 20 21 9 29 40 Cabrera Island : Light-house 1 Pi (Majorca) : Light-house 39 33 00 t Port Mahon (Minorca): Light-house Cape Spartivento: Light- house 39 51 53 38 52 34 Cape Sandalo: Light on San Pietro I 39 08 44 Porte Conte: Cape Caccia light j 40 33 50 Port Torres: Light-house 40 50 25 Cape Testa: Light-house '41 14 36 Razzoli Island: Light-house 41 18 24 Caprera Island : Galera Pt 41 14 15 Cape Figari: Signal station 40 59 52 40 54 55 39 55 45 39 05 15 39 12 35 41 22 10 41 52 50 42 18 14 42 35 10 43 01 45 42 41 47 41 35 45 43 57 17 9 39 07 9 44 22 9 43 25 9 32 35 9 07 20 9 11 15 8 35 45 9 09 04 8 43 25 9 24 10 9 27 00 Cape Tavolara: Light-house Cape Bellavista: Light-house Cape Carbonera: Cavoli I. light Cagliari: Light on mole Bonifacio: Mount Pertusato light Ajaccio: Light-house Corti : Church tower Calvi : Light-house Cape Corso: Giraglia I. light Bastia: Light-house Porto Vecchio: Cbiape Pt. light Cape Melle: Light-house 9 22 05 8 10 22 Genoa: San Benigno light 44 24 15 8 54 19 Spezzia: Fort Santa Maria light 44 04 00 43 46 04 43 32 33 43 02 57 42 45 14 42 35 06 42 21 28 9 50 48 Florence : Observatory 11 15 22 10 17 25 9 51 07 10 24 38 10 05 50 10 03 54 10 18 39 10 55 24 11 46 50 12 28 40 13 35 15 12 57 17 14 14 44 14 15 38 14 11 40 14 51 40 13 12 00 15 39 11 15 13 42 13 21 16 13 22 04 12 29 50 Leghorn (Livorno): Light on S. end of curved breakwater Capraia Island : Cape Ferrajone light Elba Island, Porto Longone: Fort For- cado light Pianosa Island: Light on battery, W. side of fort Africa Rock : Light-house . ... Monte Christo Islet: Summit 42 20 15 Giglio Island. Cape Rosso: Light-house . Civita Vecchia: Light N. end of break- water 42 19 13 42 05 38 41 53 54 Rome : Observatory Gaeta: Orlando tower '. 41 12 27 Ponza Islet: Punto dellaGuardia light .. 40 52 38 Naples: Observatory 40 51 46 40 50 15 40 32 07 38 28 43 38 42 40 Light on elbow of mole 4 00 10 13 0.7 0.2 Capri Island: Carena Pt. light Lipari Island : Casa Bianca light Ustica Island : NPl point light Faro of Messina: Capo di Faro light .38 16 02 Milazzo: Light-house 38 16 10 Palermo: Observatory 38 06 44 Light on mole head 38 07 56 38 00 39 Trapani : Palumbo Rock light APPENDIX IV. [Page 227 MARITIME POSITIONS AND TIDAL DATA. COASTS OF THE MEDITERRANEAN, ADRIATIC, AND BLACK SEAS— Continued. Place. Maritimo Island: Light on SW. pt Marsala: W. mole light Girgenti: Port Empedoche light Gozo Island : Light on N W. pt Malta Island, Valetta Harbor: Light- house Linosa Island : Landing Cove Lampedusa Island: Carallo Bianco light. Cape Passaro: Light-house Syracuse: Maniace Castle light Augusta Port: Torre d' Avola light Catania: Sciari Biscari light Cape Taormina: Semaphore Messina: San Ranieri light Cape Peloro: Light-house Cape Spartivento: Light-house Cape Colonna: Light-house Cotrone: Mole-head light Taranto: Cape St. Yito light Gallipoli: St. Andrea light Cape Sta. Maria di Leuca: Light-house. . Cape Otranto: Light-house Port Otranto: Castle Brindisi : Light-house Bari: St. Catalolo light Viesti: Light on St. Croce Rock Manfredonia: Light-house Tremiti Islands: Caprara I. light Ancona: Monte Cappucini light Malamocco: Rocchetta Mole light Venice: Site of tower of St. Mark Lat. N. Grado: Church tower Monfalcone: Church tower Trieste: Observatory Nautical Academy. Theresa Mole light '. . Capo d'Istria: Light-house Isola: Light-house Pirano : Light-house Salvore Point: Light-house Citta Nuova: Light-house Parenzo: Cathedral tower Rovigno: St. Eufemia light Pola: N." cupola of observatory Promontore Point: Porer Rock light Nera Point: Light-house Fiume: Cathedral tower Porto Re : Light-house Veglia: Mole head Prestenizza Point: Light-house Chei-so : Kimen Point light Galiola Rock: Light-house Unie Island: Netak Point light Lussin Piccolo: Sta. Maria Church St. PietrodiNembo Island: Health office. Gruizza Rock: Light-house Zengg: Mole-head light Terstenik Rock: Light-house Carlobago: Light-house Zara: Church tower Blanche Point: Light-house Zara Vecchia: Church tower Port Tajer: Lestrice I. light Lucrietta Island: Light-house Sebenico : Mount Tartaro Rogosnizza Port : Mulo Rock light Zirona Grande Island: St. George Church tower Trani: Cathedral tower 37 57 13 37 47 10 37 16 55 36 04 10 35 54 00 35 51 50 35 29 37 36 41 03 37 03 04 37 12 39 37 29 35 37 50 25 38 11 33 38 16 02 37 55 29 39 01 29 39 04 38 40 24 41 40 02 48 39 47 43 40 06 23 40 09 06 40 39 36 41 08 19 41 53 17 41 37 39 42 08 14 43 37 14 45 20 30 45 25 58 45 41 06 45 48 33 45 38 51 45 38 54 45 33 00 45 32 34 45 31 54 45 29 24 45 19 16 45 13 45 45 05 00 44 51 49 44 45 30 44 57 24 45 19 36 45 16 18 45 01 30 45 07 12 44 57 36 44 43 36 44 37 20 44 31 49 44 27 42 44 24 42 44 59 24 44 40 06 44 31 30 44 07 05 44 09 06 43 56 16 43 51 15 43 37 36 43 45 08 43 31 00 43 27 00 43 31 02 Long. E. o / // 12 02 55 12 25 59 13 32 27 14 12 55 14 31 30 12 52 09 12 36 12 15 07 45 15 17 37 15 13 20 15 05 19 15 18 30 15 34 36 15 39 11 16 03 31 17 12 09 17 08 07 17 12 23 17 56 55 18 22 17 18 31 25 18 28 45 17 59 37 16 50 52 16 11 13 15 55 34 15 31 36 13 31 18 12 19 09 12 20 29 13 22 54 13 32 10 13 46 00 13 45 14 13 43 18 13 39 32 13 33 48 13 29 30 13 33 42 13 35 39 13 38 00 13 50 46 13 53 36 14 08 42 14 26 41 14 33 42 14 34 36 14 16 30 14 23 30 14 10 36 14 14 06 14 28 06 14 33 28 14 34 06 14 53 48 14 34 42 15 04 24 15 14 05 14 49 24 15 26 21 15 12 06 15 34 24 15 58 07 15 55 00 16 08 51 16 15 09 H.W. ft. m. 3 12 3 00 L. W. 9 25 9 13 3 30 10 15 9 20 9 00 8 15 8 10 6 10 9 43 4 45 3 50 3 25 2 35 Range. 0.7 0.9 1.8 3.3 2.0 3.4 1.2 2 25 1.1 20 1.0 Neap. 0.2 0.3 0.5 0.9 0.6 0.9 0.3 0.3 0.3 Page 228] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. COASTS OF THE MEDITERRANEAN, ADRIATIC, AND BLACK SEAS— Continued. Place. Lat. N. Port Spalato: Cathedral tower Solta I. , Port Oli vetto : St. Nicholas tower . Spalato Passage: Speo Pt. light Makarska: Church tower Porno Rock: Center St. Andrea Rock: Summit Lissa Island : Hoste Rock light Pakonjidol Rock: Light-house Lesina Island: Port Gelsa light St. Giorgio Pt. light Sabioncello Peninsula: Cape Gomena light Sorelle Rocks: Light-house Curzola Island: Porto Bema mole head.. Porto Valle Grande, church tower Lagostini Island: Glavat Rock light Lagosta Island : St. George Chapel Cazza Island: Light-house Pelagosa Rock : Light-house Meleda Island: Port Palazzo Ruin Olipa Rock : Light-house Pettini di Ragusa Rocks: Light-house... Bobara Rock : Summit Molonta Peninsula: Summit Ostro Point: Light-house Cattaro: Health office Budua: Mole-head light Katie Rock : St. Domenica Chapel Antivari : Pt. Valoviea light Dulcigno: W. windmill Cape Rodoni: Guard-house Cape Pali : Guard-house Durazzo: Light-house Cape Laghi : Ruin Skumbi River: Pyramid at mouth. Semeny River: Samana Pt. light . . Vojazza River: Pyramid at mouth Saseno Island: Light-house Avlona: Light-house Cape Linguelta: Extreme Mount Cica: Pyramid Port Palermo: Pyramid Cape Kiefali: Pyramid Fano Island: Pt. Kastri light Port Pagonia: Ruin Port Gomenitza: Well Dogana Port Parga: Madonna I Port St. Spiridione: Convent Corfu : Light-house Paxo Island: Madonna I. light Prevesa; Fort Nuovo minaret Port Drepano: Observation island Port Vliko: Custom-house Port Vathi: Lazaretto light Port Argostoli : St. Theodoro light Patras: Light-house Katakolo: Light-house Zante: Mole light Strovathi, or Strivali Island: Stamphani I. light.... i Proti Passage: Marathon Pt Navarin : Light-house Mothoni: Round tower Koroni Anchorage: Mole light Petalidi Bay: Petalidi Pt Candia Island, Port Suda: Light-house. . Megalo Kastron : Mole light 43 30 07 43 23 50 43 19 12 43 17 46 43 05 28 43 01 43 43 04 30 43 09 24 43 09 50 43 07 30 43 02 50 42 57 42 42 54 19 42 57 37 42 45 54 42 45 05 42 45 05 42 23 30 42 47 06 42 45 30 42 39 00 42 35 08 42 27 04 42 23 36 42 25 30 42 16 42 42 11 43 42 05 15 41 55 47 41 35 10 41 23 31 41 18 40 41 08 44 41 02 12 40 47 00 40 36 14 40 30 12 40 25 30 40 25 17 40 12 00 40 02 57 39 54 29 39 51 53 39 39 27 39 29 50 39 16 32 39 39 54 39 37 05 39 11 30 38 56 30 38 47 25 38 40 40 38 22 04 38 11 36 38 15 00 37 38 20 37 47 10 37 15 12 37 03 38 36 54 10 36 48 40 36 47 50 36 57 20 35 28 55 35 20 30 Long. E. 16 26 16 11 16 24 17 01 15 27 i.5 45 16 12 16 27 16 41 17 12 17 00 19 17 12 44 16 51 32 16 43 07 17 08 54 16 51 45 16 29 29 16 15 12 17 22 51 17 46 48 18 03 08 18 10 49 18 25 36 18 32 00 18 46 12 18 50 36 18 56 25 19 04 19 19 12 29 19 27 15 19 24 54 19 27 14 19 26 47 19 26 30 19 20 14 19 19 14 19 16 15 19 27 55 19 17 45 19 38 .33 19 47 53 19 54 55 19 26 06 20 07 12 20 17 09 20 24 55 19 43 09 19 56 30 20 12 34 20 45 40 20 44 16 20 42 44 20 43 37 20 29 30 21 43 50 21 18 55 20 55 26 21 01 14 21 34 .35 21 40 29 21 42 40 21 58 00 21 56 42 24 09 39 25 09 44 Lun. Int. H. W. L. W. h. m. ft. Range. Spg. Neap. 4 00 10 30 2. 4 ft- 0.7 3 40 9 53 1.0 0.3 APPENDIX IV. [Page 229 MARITIME POSITIONS AND TIDAL DATA. COASTS OF THE MEDITERRANEAN, ADRIATIC, AND BLACK SEAS— Continued. Place. Kandeliu8a Island : Light-house StampaU Island, ]Maltezaiia Port: Agios loanes 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 : Am j^no Pt Thermia Island: Ruins of Cythnus Jura Island: North pt Port St. Nikolo: Light-house St. Nikalao Island: Port Mandri Andros Island, Cape Fasse: Light-house. leraka: Acropolis Port Kheli : Light-house Poros Island : Light-house ^gina: Light-house Piraeus: Light-house Athens: Observatory Cape Colonna: Extreme Port Raphti: Statue I Petali Island : Trago I. peak Euripo Strait: Light-house Skiathos Island : Mount Stavros Salonika: S. bastion Port Baklar: Cape Xeros Lemnos Island : Kastro Castle Port Moudros: Sangrada Pt Strati Island : St. Strati Church Mityleni Island, PortSigri: Light-house. "Mitvleni: Light on Mity- leni Pt.... Port lero: Sidero Islet Psara Island: Fort Tchesm^: C. Kezil light Samos Island: Fonia Pt. light Port Isene: Tower Kos : Light-house Marmorice Harbor: Adassi Pt. light... Makry Harbor: Kasil I Rhodes Port: Arab's Tower light Port Lindo: Tower Dardanelles: Hellas Pt. light Gallipoli: Light-house 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 Varna Bay : Light-house Kusterjeh: Cape Kusterjeh light Danube River: Salina light Fidonisi Island : Light-house Odessa: Observatory Dnieper Bay: Fort Nikolaeo light Sebastopol : E. light-house Balaklava Bay : Hospital Kertch : Light-house Berdiansk: Breakwater light Saukhoum : Light-house Batoum: Light-house 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 39 10 48 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 36 55 00 36 48 00 36 39 33 36 26 00 36 05 53 40 02 30 40 24 27 41 01 20 41 01 02 41 00 35 41 00 16 41 21 15 Long. E. 41 42 43 44 45 45 46 46 44 44 45 46 42 41 52 04 27 52 10 00 10 20 09 47 16 00 28 36 34 27 36 55 29 50 21 03 45 00 58 00 39 30 26 59 25 26 24 28 25 13 00 24 23 15 24 40 30 25 23 00 25 14 21 25 14 08 24 56 14 24 32 23 24 23 35 24 44 32 24 19 44 24 04 12 24 42 30 23 05 40 23 08 53 23 25 45 23 25 30 23 38 10 23 43 55 24 02 15 24 03 00 24 16 42 23 36 45 23 27 07 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 27 18 25 28 18 00 29 06 13 28 16 24 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 27 35 54 27 58 35 28 39 14 29 41 14 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 Lun. Int. H. W. L. W. h. m. Range. Spg. Neap. Page 230] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. COASTS OF THE MEDITERRANEAN, ADRIATIC, AND BliACE SEAS— Continued. Place. Trebizond : Light-house Sinope: Light-house Bender ErekH: Light-house Marmora Island: Light off E. pt Artaki Bay: Zeitijn Adasi Islet Tenedos Island : Ponente Pt. light Port Ajano: Nikolo Rock Port Ali-Agha: W. pt. 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 Sutr (ancient Tyre) : Light-house Acre: Light-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. VV. 41 38 1 07 57 2 25 45 3 03 29 5 16 46 5 48 31 5 55 41 WEST COAST OF AFRICA. Lun. Int. H. W. L. W. h. m. i h. m. 9 40 9 40 9 45 9 55 10 00 3 35 3 33 2 46 1 55 1 30 Range. Spg. I Neap. ft. ft. 9 15 3 15 i 2.5 9 45 3 35 3 30 3 30 3 15 3 45 3 50 9 57 9 55 1.4 1.0 1.1 1.2 1.9 4.2 3.0 8 58 t 2. 6 8 07 3.3 7 40 : 8. 0.7 1.2 I 0.3 0.4 0.3 0.3 0.3 0.5 1.1 0.8 1.3 1.5 3.7 El Araish : S. pt. of entrance . . . Sah: 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. Lat. N. Long. W. Lun Int. Range. H.W. L.W. Spg. Neap. Cape Blanco, North : Extreme / // 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 4 59 15 4 22 10 4 24 47 4 52 18 4 45 00 4 47 45 4 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 / // 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 1 45 00 1 38 00 1 21 05 1 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 h. m. h. m. fl. ft. Mogador Harbor: English consulate Cape Ghir: Extreme 1 05 7 17 10.9 5.0 Cape Noun : Extreme 1 Cape J uby : Extreme 11 55 11 50 5 43 5 38 8.5 7.3 3.9 3.4 Cape Bojador: Extreme Penha Grande Ouro River entrance: Dumford Pt Pedra de Galha Cape Blanco, South : Extreme 11 35 5 23 5.5 2.5 Portendik: Village St. Louis: Light-house Almadie Point: Light-house Cape Verde : Light-house Port Dakar: Light-house Cape Manoel : Light-house 1 Goree Island: Fort 1 Bird Island : Flagstaff ! 1 Bathurst: Flagstaff 9 00 2 50 5.9 2.7 Carabane: Light-house Nunez River: Sand I Ponga River entrance: Observation pt . . Isles de Los: Light-house 7 30 1 20 11.4 5.2 iVIatacong Island : House Scarcies River: W. end of Yellaboi I Sierra Leone: Light on cape N. battery Sherbro Island: N. island Sherbro River: Manna Pt 7 40 1 30 11.6 5.3 5 50 12 00 10.4 4.8 Gallinas River: W. elbow of Kamasoun J . Cape Mount: W. peak Cape Mesurado: Light-house Monrovia: Light-house Marshall: Agent's house Grand Bassa: Agent's house 5 40 11 54 6.0 2.5 Cestos: Factory Sangwin River: Sangwin Pt Sinon : Bloobarra Pt 4 50 4 30 11 05 10 43 4.8 4.3 2.0 1.8 Cape Palmas: Light-house Tabou River: Tabou Pt Axim Bay : Ft. St. Anthony Cape Three Points: Light-house Dix Cove: Fort 4 00 10 13 4.7 i.9 Tacorady Bay: Tacorady Pt :::;::::::: i Chama Bay: Dutch Fort El Mina Bav: Ft. St. George Cape Coast Castle : Light-house 4 20 10 32 6.0 2.5 Accra: Light-house Volta River entrance: Dolbens Pt Lagos River: Light-house 4 20 4 50 10 33 11 05 4.2 3.3 1.8 1.3 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): To wnsend flagstaff ( Dunketo wn ).. Fernando Po Island: Light-house San Bento River: Joho Pt. (approx.) ... Princes Island: Diamond Rocks, center of largest ^ St. Thomas Island: Ft. San Sebastian licrht Anno Bon Island : Turtle Islet Cape Lopez : Light-house Mayumba Bay : Light-house 4 25 10 38 7.0 2.9 Page 232] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. WEST COAST OF AFRICA— Continued. 1 Place. Lat. S. Long. E. Lun. Int. Range. 1 H. W. L. W. Spg. Neap. 1 Loango Bay : Indian Pt. light / // I o / // 4 40 00 11 46 30 h. m. 4 13 h. m. 10 26 ft. 6.5 ft. 2.7 Black Point Bay: Sandy Pt 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 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 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. Mary 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 Bav : 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. Simons Bay : Light-house 34 10 45 CapeHangklip: Extreme -^4 2.^ 48 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 38 04 00 2 35 8 48 5.2 2.2 Quoin Pointf Extreme 34 46 45 Cape Agulhas : Light-house 34 49 45 34 23 47 34 11 10 34 04 35 34 06 15 34 12 30 34 01 41 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 33 57 43 33 50 27 33 36 09 .^.^ 9R 00 3 21 9 33 5.4 1.9 Bird Islands: Light-house Port Alfred: Signal staff Waterloo Bay: Maitland Signal Hill Madagas(!ar Reef: Center ; 33 23 10 Cove Rock: Center .. . ^^ 05 10 East London : Light-house 33 01 45 ^9 49 00 3 37 9 50 5.0 1.8 Cape Morgan: Extreme Hole-in-the-Wall '. ". 32 02 30 Rame Head" Extreme -^1 ^s l.^ • - Cape Hermes: Extreme 31 38 06 31 26 15 29 52 40 29 00 12 28 32 30 28 09 36 25 58 49 24 05 30 23 45 30 22 05 00 21 31 00 20 38 10 20 10 42 18 52 50 18 01 24 17 51 50 17 15 00 AVaterfall Bluff Port Natal (Durban): Light-house Dumford Point: Extreme Cape St. Lucia: Extreme 3 58 10 11 5.6 1.6 Cape Vidal: Extreme Delagoa Bay: Reuben Pt. light 5 10 11 22 11.9 3.4 Cape Corrientes: Small rock Innamban Bay: Barrow Hill light Cape St. Sebastian' Extreme 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 . 1 APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. EAST COAST OF AFRICA AND THE RED SEA— Continued [Page 233 -» 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 Mafaniale Island: Center Port Mokamba: Mokambo Pt o / // 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 26 18 50 26 45 48 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 O / 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 34 50 45 33 59 43 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 h. m. h. 111. ft. ft. Port Mozambique: St. George I. light... San Sebastian light . . Cape Cabeceira: Light-house 4 00 10 12 11.8 3.4 Port Conducia: Bar Pt Lurio Bay : Pando Pt Pemba Bay : N. pt. light ! i Querimba Islands: Ibo I. light 1 1 Numba Island : E. pt Cape Delgado : Light-house 3 59 10 11 11.3 3.3 Msimbati : Ras 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 Bagamoyo: French Mission Zanzibar: English consulate 4 05 10 17 14.5 6.0 Tanga Bay : Light-house Mombasa: Light-house Port Melinda: A^asco 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 11.7 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 1 Ras Hafun: E. extreme of Africa Cape Guardafui: E. pt 1 6 00 12 12 6.1 2.5 Kal Farun Islet: Center Abd-al-Kuri Island : NE. pt Socotra Island : Tamarida, mosque Ras Antareh: Extreme of rocky pt Mait Island : Center :::::: i 7 05 1 17 7.5 3.1 Port Berbera: Light-house 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 Bay Massaua Harbor: N. pt. of entrance Kh6r Nowarat: Shatireh Islet 45 6 57 4.0 1.7 Suakin : Light-house 2 io 8 22 1.7 0.7 Makaua Island : S. pt St. Johns Island: Peak 1 Daedalus Shoal: Light-house Kosair Anchorage: SW. angle of fort Brothers Island: Light-house 6 40 28 2.0 0.8 Safajah Island : N. summit Ashrafl Island: Light-house 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 1 Sherm Joobbah : Entrance i Sherm Wej : Light-house 1 Sherm Hassejv: Anchorage 1 Yembo: Anchorage Page 234] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. EAST COAST OF AFRICA AND THE RED SEA— Continued. Place. Sherm Rabigh : Anchorage Jiddah: Jezirah el Mifsaka I Lith: Agha Islet Jelalil: Anchorage Kunfidah : Islet Khor Nohud: Entrance Farisan I. Anchorage: Jebel Mandhakh. Gizau : Fort Loheiya: Hill Fort Kamardn Bay : Harbor Hodeida Road Jebel Zukur Island: N. pt Mokha: N. Fort Lat. N. Long. E. Lun Int. Range. H.W. L.W. Spg. Neap. o / // 22 43 50 21 28 00 20 09 00 19 55 30 19 07 40 18 15 50 16 50 15 16 53 00 15 42 00 15 20 30 14 47 00 14 03 53 13 19 43 o / n 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. m. ft. Jl. 3 30 9 42 2.0 0.8 . 1 15 7 27 2.9 1.2 11 45 5 33 4.5 1.9 ISLANDS OF THE INDIAN OCEAN. 32 Chitlac Islet: S. end Betrapar Islet: N. Island Kittan Islet: S. end Cardamiim 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 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 Mal^, or Kings Island : Flagstaff Pha-li-du Island: Northern end Moluk Island: Center Himmittee 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 Jetty Bird Island: Tree Chagos Archipelago, Peros Banhos: Dia- mond Islet Diego Garcia : N. end of Middle I Cargados Carajos : Establishment I . , flag- staff 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 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 55 00 59 00 25 00 26 30 01 30 25 45 44 00 10 15 41 00 57 00 16 00 10 30 07 00 14 30 Lat. S. 41 30 40 56 52 26 53 00 37 15 43 06 15 00 13 37 25 12 40 22 19 52 36 19 59 45 20 08 46 20 24 20 72 42 54 72 09 54 72 59 00 72 44 00 72 41 00 73 40 00 72 37 40 72 15 10 73 35 54 73 01 15 72 55 54* 73 12 54 72 41 54 73 20 00 72 53 00 72 57 24 73 28 00 73 30 24 73 24 54 73 34 24 72 48 00 73 03 00 73 35 54 73 13 00 73 06 54 53 41 03 53 23 38 55 27 10 55 27 23 55 12 19 71 43 47 72 23 50 59 46 40 63 25 38 57 39 14 57 32 35 57 29 26 57 47 14 10 20 11 27 20 4 22 1 30 1 50 20 48 4 00 6. 3 5 15 6 25 10 35 7 43 8 03 6 32 7 00 2.5 2.9 4.3 5.8 4.0 5.5 3.0 1.2 1.4 1.2 1.7 1.2 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. Eeunion Island: St. Denis light Bel- Air light O / 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 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 h. VI. h. m. ft. ft- St Paul light St. Pierre light Troinelin Island N end 11 50 5 38 3.5 0.6 Agalegas Island : N W. pt Alphonse Island: SE. part (Trees) Cape St Mary S extreme St. Augustine Bay: Nosi Vei I 5 40 1 11 52 9.8 2.9 Murderers Bay: Center of Murder I Cape St Vincent' Extreme 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 17 53 00 Coffin Island: Nosi Vac 1 17 29 00 Cape St Andrew Extreme ^ 16 12 10 Bovanna Bay Barabata Pt 16 07 00 15 46 30 15 43 45 15 11 42 Cape Tauzon Extreme Majunga ( Mojanga) : Light-house 4 15 11 28 10.9 3.2 Narendri Bay : Moormora Pt 14 40 18 Port Radama- Pt Blair i 13 ,59 00 47 24 36 47 58 21 Radama Islands: N. pt. Nossuvee I Baratoube Bay : Anibubuka Pt Nosi Be : Hellville jetty Minow Islands' N pt Cireat I 13 55 40 13 27 15 13 23 38 12 49 30 12 27 20 12 03 18 U 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 12 25 00 11 34 48 11 40 44 9 46 20 9 22 35 9 41 20 47 48 05 47 59 30 48 17 34 48 38 57 48 45 45 49 11 21 Cape San Sebastian* Extreme Pnrf T ,i \7t>i-r>nnl • N nf nf t>ntranr't> 49 17 25 49 35 56 49 45 06 49 54 00 49 56 25 Port Ladv Frances' Sunson Pt Port Looke' Pt Bathurst Port Leven" S. pt. Nosi Hau I Andrava Bay : Berry Head Vohemar' Flagstaff 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 Cape East' XJgoncy I Venangue B6 Bay Entrance Port Choiseul : Maran Seelzy Village 3 45 9 57 5. i j 1.5 St. Marys Island: Light on Madame I .. Port Tantang- Flagstaff Fenerive Point' Flagstaff Tamatave: Pt. Hastie 4 00 10 12 7.3 ; 2.1 Matatane' Village Santa Lucia: N. end of town, Obs. Rock. Point Ytapere' Extreme 1 Ytapere Bay: N. pt i Fort Dauphin : Flagstaff 4 15 10 27 4.7 ) 1.3 Europa Island' Center Bassas da India' E pt Mavotta Island : Zaoudzi 4 00 10 13 n.9 2.0 Johanna Island : Landing place, Pomoni Harbor Mohilla Island: Numa Choa Harbor Glorioso Islands' W. islet Comoro Island: Islet in Mauroni Bay . . . 4 45 10 58 10.0 1.7 Aldabra Island: West I., E. side entrance. i ' 1 Page 236] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ISLANDS OF THE INDIAN OCEAN— Continued. Place. Prince Edwards Islands: Marion I., Obs. spot, NE. side Penguin Islands: Center of SW. islet . .. Possession Island : N W. pt Twelve Islands: Summit NE. I Navire Bay Hog Island: Summit East Island: Center 46 49 30 46 36 00 46 22 00 46 01 00 46 28 18 46 10 40 46 26 00 Lun. Int. Long. E. Christmas Harbor 48 40 00 BlighsCape 48 26 45 Cape Bourbon 49 42 00 Mollov, Port Roval Sound: U. S. Tr. of Venus Obs., 1874 49 21 22 Cape Challenger 49 41 00 Balfour Rock. 49 29 00 Heard Island: Cape Laurens, NW. end.. 53 02 45 Sealing station ' 53 13 00 ~ • 53 02 50 38 42 51 37 50 00 I 12 06 22 10 25 19 McDonald Island, Summit St. Pauls Island: Ninepin Rock Amsterdam Island: Summit, 2,750 feet.. Keeling or Cocos Islands: Direction 1. . . Christmas Island : Flying Fish Cove 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 H. W. 14 10 40 10 50 5 20 7 10 L. W. 6 36 Range. Spg. ft. 4.6 4 28 3.0 4 38 3.3 1 32 5.1 1 00 4.5 Neap. ft. 1.3 0.9 1.0 1.5 1.3 SOUTH COAST OF ASIA. Aden: Telegraph station Sughra: Sheik's house Mokatein : Black ruin Howaiyuh: Sheik's house Banderburum: SE. house of town Makalleh Bay : Flagstaff Shahah Roads: Custom-house Sharmoh : Single house Kosair: High house Sihut: Center of town Ras Fartak: Extreme pt Damghot: Town Merbat: Town Kuria Maria Is., Hullaniyeh I. : NE. bluff Ras Sherbedat: Point Cape Isolette: Islet Masirah Island: Point Abu- Rasas Point Ras Ye 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 Musendom: N. end of island Great Quoin Islet : Center Sharjah: High tower with flagstaff Abu-Thabi : Fort flagstaff Al Beda' a Harbor : Nessah Pt . , N . extreme Ras Rakkin: NW. pt Bahrain Harbor: Portuguese fort Basrah : Custem-house flagstaff Kuweit Harbor: N. end of town Khdrig Islet: Fort flagstaff Abu Shahr: Residency flagstaff Shaikh Shu'aib Islet: E. end Kais Islet: NE. pt Lat. N. 12 47 16 13 22 00 13 24 50 13 28 45 14 20 10 14 31 15 14 43 50 14 49 00 14 54 40 15 12 00 15 38 00 16 30 00 16 59 00 17 32 45 17 53 15 19 00 25 20 10 00 20 31 30 22 32 40 23 38 00 23 52 00 23 51 30 24 21 50 25 21 00 26 24 13 26 30 00 25 21 34 24 29 02 25 17 24 26 10 55 26 13 56 30 32 00 29 22 56 29 15 25 28 59 07 26 47 40 26 33 37 Long. 44 59 45 40 46 26 46 39 48 56 49 07 49 35 49 57 50 16 51 10 52 14 52 48 54 43 56 03 56 20 57 51 58 38 58 58 59 48 58 30 58 08 57 26 56 46 56 22 56 32 56 31 55 24 54 22 51 33 51 13 50 32 47 51 48 00 7 49 8 20 50 50 21 11 50 50 35 53 23 36 54 02 21 9 45 9 15 9 30 1 41 2 07 2 38 3 32 3 03 3 20 5 15 11 30 05 7 12 30 6 17 1 13 6 40 4.9 7.0 9.6 8.9 6.0 6.4 8.3 2.6 2.0 2.8 2.9 4.4 4.1 4.8 X 1.5 '3." 8 APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. SOUTH COAST OF ASIA— Continued. [Page 237 Place. Lat. X. Biisiduh: Chapel 26 39 12 Haujam Islet: Ruined mosque 26 40 49 Kasm : Fort 26 57 27 Jashak Bav : Telegraph office ' 25 38 19 KubKalat: High peak, 1,680 feet : 25 29 45 ChahbarBay: Telegraph office Gwatar Bav : Islet Karachi: Manora light Observatory Mandavi : Light-house Beyt ( 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-^ Cam bay : 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 Yingorla 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 16 43 25 03 17 G wadar Bay : Telegraph office 25 07 19 Pasni: Telegraph office 25 15 52 Ormarah: Telegraph office 25 11 55 Sunmiyani : Jam's house 25 25 19 Cape Monze: Peak 24 50 03 47 37 49 50 50 00 29 20 14 00 14 00 38 00 06 00 41 20 02 21 47 00 35 54 17 00 05 20 12 19 20 10 53 45 42 08 58 00 59 30 33 26 05 12 21 24 29 25 51 10 53 20 49 00 25 00 17 28 38 15 52 17 51 10 45 00 42 00 15 10 58 00 30 00 53 20 30 47 04 00 29 55 47 10 17 20 8 59 00 6 55 40 5 55 30 6 01 25 6 10 10 6 25 00 7 45 00 8 33 30" 10 18 00 10 45 28 11 55 40 Long. E. 55 16 47 55 54 25 56 17 37 57 46 14 59 40 32 60 37 40 61 26 24 62 19 42 63 28 37 64 37 02 66 35 39 66 39 58 58 06 01 33 20 15 04 40 57 06 58 54 36 00 06 32 50 45 49 35 14 00 21 08 35 10 38 40 49 27 48 44 48 56 48 49 02 40 15 56 19 39 54 50 54 00 46 10 37 00 27 15 03 40 22 30 26 40 39 50 50 40 21 51 29 40 31 10 46 40 14 40 20 40 34 00 56 45 32 35 07 47 11 26 12 50 Lun. Int. Range. 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 H. w. h. m. 10 50 9 20 9 20 8 50 10 15 12 05 4 27 11 -26 10 34 10 34 10 50 11 21 11 33 18 1 52 1 37 1 55 2 02 8 10 8 37 L. W. /(. m. Spg. ft. 4 35 3 05 11.6 I 5.3 7.8 1 3.6 3 05 ^. 1 2 35 4 00 7.3 3.4 5 39 10. 8 ! 5. 2 11 18 29.8 I 15.1 5 08 12.0 ! 4.9 4 10 5.2 2.5 4 11 5.0 4 28 6. 5 3. 4 4 59 5 06 2.7 2.1 6 16 2.5 7 51 7 36 3.0 2.0 7 49 2.0 8 07 1.9 1 44 2.0 2 37 2.1 Page 238] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. SOUTH COAST OF ASIA— Continued. Place. Madras: Observatory Light-house Pulicat: Light-house Armeghon : Light-house Kistna: Light-house MasuHpatam: 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: NVV. peak Cape Negrais: Extrerag 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 . . . Lat. 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 09 57 17 11 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 Long. E. 80 14 51 80 17 00 80 19 12 80 12 30 80 59 00 81 11 00 82 15 05 83 17 42 84 07 30 84 52 06 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 Range. H.W. 8 41 8 42 8 48 9 21 1 25 1 02 'g'io' 3 05 9 50 9 40 4 26 3 07 2 12 10 50 10 40 11 50 5 50 7 20 10 18 L. W. Spg. h. m. 2 26 3.1 2 35 2 34 4.5 4.4 3 00 6.8 9 06 7 56 "3'28' 11.2 13.1 "*7.'6' 9 55 18.7 3 37 3 27 6.3 11 15 10 49 8 49 16.9 11.7 19.2 4 20 4 10 15.6 18.0 5 40 8.8 12 00 1 08 4 02 14.4 'i6."5' "7.'6' 9 40 6 00 3 14 7.1 12 13 n.5 Neap. 1.2 1.9 1.8 2.6 4.4 5.6 "3.'0 2.9 2.1 7.0 5.0 7.4 5.9 6.9 6.2 4.' 5 '3.' 2 3.1 4.9 APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. SOUTH COAST OF ASIA— Continued. [Page 239 Place. Nicobar Islands, Nancowry Harbor: Naval Pt Great Nicobar: W. pt. Galathea Bay . Acheen ( Acheh) Head: Pulo Bras light N. extreme Diamond Point: Light-house Point Baru or Datu : Extreme Point Bon or Djabon: P^xtreme Moeara-Kompehi : Fort Djambi: Flagstaff of fort Palembang: Residency flagstaff Lampong Bay: Telok Betong light Blimbing Bay Kroe: Village 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 Ayer Bangis : Fort flagstaff Natal: Fort flagstaff Nias Island : Lagoendi Bay Sitoli Lapan Siboga: FlagstaflE Singkel: Post-office Bangkaru Islands: Bay Simaloe Island: NW. pt Tampat Toe won; Flagstaff Analaboe Batve Toetong: Landing place Lat. N. o / // 8 02 10 6 46 20 5 45 00 5 34 40 5 15 58 Lat. S. 00 32 1 00 55 1 23 13 1 35 33 2 59 26 5 27 00 5 55 02 5 11 24 5 18 50 4 48 35 3 59 25 3 47 22 2 44 54 2 10 35 59 56 57 53 53 58 07 41 03 13 02 56 Lat. N. 11 41 33 11 34 47 1 17 36 1 24 16 1 44 24 2 16 47 2 02 32 2 51 30 3 14 59 4 08 14 4 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 40 5 50 5 35 5 29 L. W. Spg. Neap. h. m. 2 52 ft. 8.3 ft. 2.8 3 44 5 34 5.2 8.7 2.3 3.7 11 52 2.6 12 03 4.0 1.1 11 48 5.5 1.4 11 42 2.8 0.' 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 Lepaf : Light-house Pulo Jelaka: Light-house Billiton Island: Tandjong Pandanfiag staff Langkuas I. light Gaspar Island : Peak Lat. S. 6 44 30 6 08 46 5 12 17 3 13 05 3 00 48 2 34 18 2 23 20 2 04 03 1 38 26 1 29 00 3 19 10 2 56 52 2 52 05 2 44 40 2 32 12 2 24 30 105 11 48 105 26 58 106 27 33 106 13 02 106 27 22 106 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 52] [0 38] [8 21] [5. 6] 2.5 3.8 [10. 1] [9.3] [9 29] [6.6] 0.7 1.1 Page 240] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. EAST COAST OF ASIA— Continued. o Place. Lat. S. Lor^. E. Lun. Int. Range. 1 H. W. L. W. Spg. Neap. ii a V I a s Im .S Ceicer de Mer Island: SW. hill Natuna Islands: Murundum 1., SE. pt. . Low I 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 Canton Pulo: Light- house... a Chnm-Cflllfl.n Islet! Waterinc nlapp g ! Tourane Bay : Light-house a i Hnn-M(^! Summit j9 Nam-Dinh: Citadel tower '3 Hon Dau Island: Light-house 9 00 2 48 4.3 2.1 Hai-Fong: Observation pagoda Hai-Duong: Citadel tower i a 20 56 29 106 17 56 Ha-Noi: Citadel tower 21 01 57 21 29 00 18 09 00 105 48 40 109 06 00 109 .35 00 1 Pak-Hoi : Custom-house flagstaff Hainan Island : Ca.np Bnstinn extrpmR 5 00 11 12 14.0 6.6 rjflfllnncr Rfl.v. F, Rrnthpr 18 11 30 109 41 .30 APPENDIX IV. [Page 241 MARITIME POSITIONS AND TIDAL DATA. EAST COAST OF ASIA— Continued. 1 Place. Lat. N. Long. E. Lun. Int. Range. 1 H. W. L. w. Spg. Neap. i Hainan Island: Light-house O 1 II 20 01 15 15 46 30 16 36 00 16 40 07 16 49 55 20 42 03 21 22 30 21 24 15 21 31 00 21 34 00 21 28 00 22 11 40 22 11 24 23 06 35 22 02 00 21 48 50 22 16 52 22 16 23 22 03 40 22 15 45 22 27 06 22 24 06 22 30 42 22 32 54 22 18 30 22 48 14 22 48 07 22 56 24 23 14 00 23 20 43 23 15 43 23 32 30 23 47 15 24 09 49 24 23 16 24 25 44 24 49 13 24 52 12 24 59 36 25 02 18 25 12 00 25 16 30 25 26 10 25 58 10 25 59 00 26 08 26 26 09 29 26 22 37 26 30 00 26 36 06 26 42 30 26 51 25 26 58 52 27 09 20 27 09 42 27 19 18 27 26 18 27 37 36 28 05 07 28 43 45 29 22 45 29 34 20 29 51 53 29 57 08 29 59 21 30 04 30 O / 1/ 110 16 10 111 14 30 111 40 30 112 43 32 112 20 44 116 43 07 111 10 30 111 15 25 111 38 30 111 46 43 112 21 30 113 34- 00 113 33 25 113 16 30 113 47 00 113 56 20 114 09 31 114 10 02 114 19 25 114 22 07 114 36 45 114 39 12 114 50 00 115 01 00 115 06 54 115 47 56 116 04 26 116 29 44 116 47 00 116 40 22 117 17 04 117 42 00 117 36 48 118 13 30 118 10 00 118 30 11 118 41 00 118 58 00 119 27 07 119 10 36 119 35 00 119 45 00 119 56 07 119 59 02 119 27 16 119 37 35 120 24 06 120 29 40 120 10 00 h. m. h. m. ft. Tt- Paracel Islands: Triton I Observation bank Lincoln I Woody I Pratas Island : NE. part Ty-fung-kyoh Island : Center Tien-pak Harbor: Pauk Pyah Islet Song-yui Point: Extreme 11 50 5 37 8.2 3.8 Hui-lang-san Harbor: Mamechow Islet. Mandarins Cap: Summit, 200 ft" Macao : Fort Guia light 9 50 3 38 6.3 3,0 Fort San Francisco Canton : Dutch Folly light 2 00 8 00 5.1 2.4 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 Bay : Obs. spot Cupchi Point: Hill Breaker Point: Light-house 9 20 2 52 4.4 2.0 i Cape of Good Hope: Light-house Swatau : British consulate 2 50 9 00 7.5 3.5 Lamock Island: Light-house Brothers Islets: SE. Islet Tong-sang Harbor: Fall Peak 11 20 5 08 12.0 7.6 Chapel Island : Light-house Amoy : Taitan I. light Dodd Island: Light-house 05 6 13 15.5 9.9 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 1 1 JNIin River: Pagoda, Losing I 30 9 45 7 00 3 33 19.3 19.0 12.2 12.0 TemplePt Alligator Island : Summit Tung-yung Islands: Peak, N. end Coney Island: Summit . Double Peak Island : Highest peak Pih-seang Island : Town I 120 11 12 120 22 42 120 32 33 120 42 34 .... . Dangerous Rock : Summit Tae Islands: Summit Nam-quan Harbor: Bate I 120 25 50 120 32 42 120 27 14 121 06 36 121 12 09 121 30 04 9 50 3 38 17.2 10.9 Ping-fong Island: Summit Pih-quan Peak: Summit Port Namki : E. horn Pih-ki-shan Island: Summit Pe-shan Islands: Summit, SW. end Tung-chuh Island: Summit .." 121 55 21 122 13 16 121 43 15 Kweshau Islands: Patahecock. Nimrod Sound: Middle islet Tong-ting Islet: Summit 122 35 24 121 43 06 121 45 22 , 122 03 47 Chin-hai : Citadel Ning-po: Square I. light 1 00 7 12 8.8 4.6 Chusan Islands: Ting-hai Harbor 6583—06- -16 Page 242] APPENDIX IV. MAEITIME POSITIONS AND TIDAL DATA. EAST COAST OF ASIA— Continued. Place. Lat. N. Video Island : Summit West Volcano Island: Light-house Chapu : Battery Gutzlaff Island : Light-house Saddle Islands: N. Saddle light. . . West Barren Island: Summit Shanghai: Eng. consulate flagstaff Wusung: Light-house Shaweishan Island: Light-house.. 30 08 04 30 20 50 30 36 00 30 48 37 30 51 41 30 44 07 31 14 42 31 23 18 31 25 27 Pescadores Islands: Fisher L light ! 23 32 53 Second pt.on N.side j Makung Harbor.. 23 32 54 South Cape : Light-house Takau : Saracen Head Port Heongsan Tam-sui Harbor: White Fort Kelung Harbor: Light-house Soo (Sauo) Bay: Beach near village Botel Tobago Sima: S. extreme Tanjong Datu Sarawak River: Po Pt. light Sanlwak : Fort Cape Sirik: Light-house Tanjong Barram Bruni River: Light-house Labuan I., Victoria Hbr. : Light-house. Sandakhan Harbor: Light-house L'nsang: Anchorage Cape Kaniongan: E. pt. of Borneo Pamaroongl. : E. pt. delta River Koetei. Pulo Laut: S. pt. Koengit Islet Selatan Point: Extreme of Sita Pt Bandjermasin: Residency flagstaff Sampit Bay: Bandaran Pt Kottaringin Bay : Samadra I Succadana: Town Padang Tikar; Point Port Laykan: SW. pt. of Celebes Macassar: Fort light Palos Bay: Village at head Cape Rivers: NE. Cape, Slime Islet Gorontalo : Light-house Manado Bay: Light- house Bajuren Island : Summit Tagulanda Island: Peak Seao Island : Conical peak Sauguir Island : S. pt. Cape Palumbatu. . Taluat Island: Kabruang I., SE. pt Cape Flesko: Extreme Cape Talabo : E. end . . Wowoni Island: N. pt Bouton Island: N. pt . E. pt . Fort . . Cape Lassa: Extreme . Salavar Idand: N. pt . S. pt . 21 55 00 22 36 14 24 46 00 25 10 24 25 09 12 24 35 28 22 01 40 05 15 43 50 33 55 45 20 36 15 02 00 15 25 50 10 16 30 04 00 Lat. S. 45 00 4 05 42 10 40 18 55 16 00 54 00 14 00 40 00 5 36 00 5 08 09 57 00 Lat. N. 1 20 00 29 41 1 31 00 2 07 00 2 22 00 2 44 00 3 21 00 3 49 00 27 00 Lat. S. 46 00 3 58 00 4 23 30 15 00 29 15 35 00 47 00 5 5 5 5 6 26 00 Long. E. 122 45 48 121 51 25 121 03 00 122 10 12 122 40 17 123 08 27 121 28 55 121 29 36 122 14 12 119 28 05 119 30 12 120 51 00 120 15 54 120 55 00 121 25 00 121 44 28 121 49 20 121 39 45 109 39 07 110 30 30 109 20 40 111 21 20 113 58 57 115 03 00 115 16 05 118 07 20 119 16 00 118 56 00 117 37 00 116 01 40 114 42 18 114 34 56 113 08 00 111 24 00 109 58 00 109 16 00 119 26 00 119 23 55 119 47 30 120 43 30 123 03 08 124 50 00 125 22 00 125 24 30 125 26 00 125 39 00 127 02 30 124 26 00 123 27 00 123 00 00 123 04 00 123 16 00 122 36 41 120 29 00 120 30 00 120 28 30 Lun. Int. Range. h. m. 12 9 45 10 00 10 15 6 00 4 00 5 20 9 35 12 00 [7 45] 7 00 4 40 6 00 L. W. Spg. //. m. ft. 8 06 I 9. 1 3 32 4.0 3 47 4 03 12 13 8.0 3.0 5.8 10 12 11 35 9.0 14.1 3 23 5 50 5.5 5.2 [1 33] [7.0] 47 7.2 10 55 3.9 12 15 Neap. Jt. 1.7 3.4 1.3 2.5 3.9 6.1 2.4 2.2 3.1 2.9 4. 3 3. 1 APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. EAST COAST OF ASIA— Continued. [Page 243 Place. Anjer: Fourth pt. light Bantam : Flagstaff Batavia: Observatory Buitenzorg: Palace tower Boompjeo Island : Racket I. light . Cheribon: Light-house Tegal: Flagstaff Pekalongan: Light W. of entrance. Samarang: Light-house Rembang: Residency flagstaff Surabaya: Time-ball station Pasuruan : Light-house Madura Island: Light-house Soemenep flagstaff Besuki: Light-house Cape Sedano: NE. pt. of Java Banjuwangi : Fort Bantenan : S. pt. of Java Barung Island : S. pt Kambangan Island : Light-house . . Cape Anjoe: Extreme Karimon Djawa Island: Flagstaff Rawean Island : Sangkapura flagstaff Great Solombo Island: NW. pt Arentes Island: S. pt Bali Island: Billing light-house Peak, 11,326 ft Badong Bav, Kotta village. Lombok Island : Peak 12, 379 ft Ampenam light . . Sumbawa I. : Sumbawa village Tambora Volcano, sum- mit E. side 6i crater . . . Bima, flagstaff Postilion Islands: N. island Maria Reigersbergen I Ardassier Islands: S. id Brill Reef: Light-house Hegadis Island Token Bessi I.: Wangi-Wingi, NW. pt. Binongko, S. pt 1 Gunong Api : Volcano Lucipari Islands : N. islet Flores Island : Reo village Ende village Flores Head, extreme Komba Island: Peak, S. part Adenara Island : Summit, Mount Woka. Lombata Island: Mount Lamararap Pan tar Island: S. peak of saddle on S. pt Ornbay Island: Dololo anchorage Timor Island: Deli, custom-house Atapopa Koupang, Fort Concor- dia Rotti Island: W. pt Saru Island: Seba Bay, on NW. side.. Sandalwood Island : Nangamessie. Wetta Island : Ilwaki road Roma Island: W. pt 6 04 15 6 01 20 6 07 40 6 35 45 5 56 15 6 43 00 6 51 09 6 51 29 6 57 09 6 42 18 7 12 10 7 37 30 7 02 00 7 02 30 7 43 25 7 49 00 8 12 30 8 47 00 8 32 00 7 46 30 7 25 00 5 52 57 5 51 18 5 32 28 5 05 46 8 05 30 8 21 00 8 42 30 8 23 00 8 34 15 8 32 00 8 12 30 8 27 00 6 31 00 7 30 00 7 35 00 6 05 50 6 07 00 5 15 00 6 17 00 6 43 00 5 28 30 8 16 15 8 50 55 8 04 45 7 48 00 8 20 30 8 33 00 8 34 00 8 12 00 8 34 00 9 00 00 10 09 54 10 46 00 10 29 00 9 35 03 7 53 00 7 38 00 Lun. Int. Range. Long. E. 105 53 106 08 106 48 106 49 108 22 108 34 109 08 109 41 110 25 111 20 112 43 112 55 112 41 113 53 113 41 114 26 114 22 114 25 113 15 109 02 106 24 H. W. 110 25 29 112 39 10 114 23 42 114 35 00 115 03 48 115 28 00 115 08 47 116 27 30 116 04 09 117 20 33 117 57 00 118 43 55 118 43 00 117 56 00 117 22 00 118 56 50 122 40 00 123 32 00 123 59 00 126 43 30 127 30 00 120 29 55 121 38 40 122 52 00 123 31 00 123 15 00 123 22 00 124 06 00 124 23 00 125 33 57 124 52 00 123 33 57 122 52 00 121 46 00 120 14 30 126 22 00 127 19 00 h. m. 7 11 [11 58] [6 00] 12 07 11 44 10 00 8 33 10 50 7 50 L. W. Spg. Neap. h. m. ft. 58 2.4 [5 46] [3.0] [12 13] [4.0] 00 45 5 64 5 31 3 45 2 21 4 38 1 37 6 12 6 58 10 50 4 37 4.9 6.2 5.8 5.7 5.7 11 20 I 5 07 16.5 ft. 0. 1.7 2.3 8 2.6 5.2 1.8 3.0 2.0 2.0 2.0 2.9 5.6 Page 244] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. EAST COAST OF ASIA— Continued. Place. Moa Island: Buffalo Peak, 4,100 ft Sermalta Island : NE. pt Damma Island: Kulewatta Harbor, N.pt Nila Island: Center Mano or Bird Island: NW. extremity. Timor Laiit Island: Olilet, on E. coast. Vordate Island : S. pt Mulu Island: N. pt Arru Islands: S. island N. pt Great Ki Island: S. pt Tello Islands: S. island, summit Tehor Island: NE. pt Matabella Islands: Kukur Goram Islands: Goram Mosque Banda Island: Mole Bouro Island, Kajeli : Fort Defense . . . Ceram Island: Kawa Amboina Island : Light-house Xulla Islands, Taliabo Island: NW. pt. Mangola Island: E. pt . Besi Island: E. pt Oby Major Island : W. pt Popa Island: Outer Extremity Bay Mysole Island : Efbe Harbor Gebey Islands: NW. pt Gillolo Island: Cape Tabo: E. extreme Cape Salawag: NE. pt . Derrick Point: N. ex- treme Molucca Is. , Makkian I. : Fort Reeburgh Ternate Island: Residency Batian Island : Church Meiaco-Sima Is., Kumi I: N. Beach ... Broughton Bay : Land- ing place Port Haddington: Hamilton pt Tai-pin-san: Hirara, Karimata Anch Raleigh Rock: Summit, 270 ft Ti-ao-usu Island : Summit, 600 ft Hoa-pin-su Island : N. face Loo Choo Islands, Great Loo Choo: Nafa-Kiang Yori-.sima, 413 ft. . Yerabu-sima peak, 687 ft : Kakirouma: Sum- mit, 2,207 ft Iwo-sima: Volca- no, 541 ft Oho-sima: N. ex- treme Kikai-jima: Sum- nnit, 867 ft Lat. S. 8 12 00 8 14 00 7 03 00 6 44 00 5 32 50 7 55 00 7 04 GO 6 35 00 10 00 20 00 56 00 20 00 44 00 33 00 03 05 31 53 22 48 55 52 41 00 44 00 48 12 28 00 30 00 11 21 04 00 Lat.N. 02 02 11 00 1 26 00 2 12 00 24 00 47 13 Lat. S. 38 03 Lat. N. 24 26 00 24 21 30 24 25 00 24 48 18 25 55 00 25 58 30 25 47 07 26 12 25 27 02 00 27 21 00 27 44 00 27 53 00 28 31 40 28 18 00 Lun. Int. Long. E. Range. 128 01 129 00 128 28 129 29 130 17 131 23 131 55 131 40 134 24 134 40 132 54 131 58 131 47 131 50 131 25 129 53 127 06 128 07 128 10 122 20 126 21 126 01 127 18 129 55 130 12 129 17 30 128 52 00 128 37 00 128 03 30 127 21 00 127 22 39 127 28 21 122 56 00 124 17 40 124 06 40 125 17 57 124 35 00 123 40 00 123 30 31 127 40 10 128 25 24 128 33 10 128 59 00 128 14 30 129 42 30 129 59 00 h. m. L. W. h. m. Spg. ft. Neap. 7 57 7 32 9.0 4.2 6.6 3.1 2 20 8 32 7.5 5.5 5 00 11 10 3.9 2.9 7 27 1 14 4.9 2.1 6 30 15 5.8 2.5 APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. EAST COAST OF ASIA— Continued. [Page 245 Place. Barbae Island, Cape Melville: Light- house Paldwan Island, Cape Bovliluyan: S. extreme Victoria Peak, 5,680 ft. Port Rovalist: Tide Pole Pt. Light TaytayFort Port Barton : BubonPt. Kabuli I. : Summit, N. extreme Cuyo Island: Obs. 8pot^ Agutaya Islet: Summit of Mt. Aguade.. Quiniluban Islet: Summit Culion Island: Fort Busuanga Island: Mt. Tundalara Apo Islet : Summit Caluya Island : Summit Semerara Island: N. extremity Mindoro Island: Mangarin Pt., SE. ex- tremity Sablayan Pt.,Vantay. Monte Calavite Escarceo Pt Pt. Dumaly Ylin Island Lubang Island, Port Tulig _ ...... Luzon Island, Batangas: Ast. station... Balayan : Plaza Rizal Loro Peak : Summit, 3,985 feet Caballo I. : Light-house . Corregidor Island: Light- house Cavite: San^leyPt. light. Manila: Pasig light-house Manila: Cathedral Subig: Town CaponesIslet:Light-house Iba: Ast. station Port Masinloc: Bani Pt.'. Santa Cruz: Plaza Sual: Army Hospital Silaqui Islet: Summit Port San Fernando: Main street Candon : Ast. station Port Santiago: Remark- able tree S. of port / Vigan : Race track Salomague Island: Port Salomague flagstaff Currimao : Town Capa Bojeador: Light- house Mairaira Pt. : Semaphore Aparri : Plaza Port San Vicente: San Vicente Islet CapeEngano: Rona Islet / Camiguin I. : Summit Fuga island: W. summit. Dalupiri Island: Peak . . . Calayan Island : NE. pt Babayan Claro Island: AY. pt Lat. N. 7 49 25 8 20 25 9 22 30 9 43 43 10 50 00 10 29 19 11 26 25 10 51 26 11 09 09 11 25 47 11 53 53 12 02 09 12 39 46 11 54 28 12 06 45 12 20 03 12 50 15 13 28 40 13 31 35 13 06 05 12 17 15 13 49 30 13 45 22 13 56 17 14 12 20 14 21 48 14 22 27 14 29 50 14 35 49 14 35 31 14 52 36 14 55 33 15 19 30 15 34 48 15 45 43 16 04 06 16 27 15 16 37 15 17 11 43 17 16 55 17 33 56 17 47 17 18 01 09 18 31 08 18 39 02 18 21 43 18 28 32 18 32 02 18 50 26 18 52 54 19 03 03 19 22 00 19 30 00 Lun. Int. Long. E. Range. H.W. 117 00 00 117 09 35 118 17 30 118 43 03 119 31 10 119 05 36 119 29 55 121 00 25 120 56 26 120 45 38 120 00 48 120 12 56 120 27 18 121 30 24 121 20 10 121 03 33 120 44 42 120 22 33 120 59 17 121 29 20 121 01 53 120 09 58 121 02 56 120 43 37 120 38 10 120 36 40 120 33 48 120 54 40 120 57 19 120 58 06 120 13 52 120 00 15 119 57 11 119 54 16 119 54 00 120 06 01 119 56 10 120 18 25 120 26 14 120 25 07 120 22 51 120 25 04 120 28 44 120 35 35 120 50 53 121 37 27 122 04 14 122 05 49 121 48 26 121 15 42 121 11 28 121 32 00 121 52 00 h. m. [11 30] Spg. Neap. h. m. ft. [5 20] [6.5] [11 07] [10 22] 10 44 "i9'42i [10 20] [10 21] [9 40] 5 43 6 00 [4 50] [4.9] [3 56] [4.4] [4 10] ■[4'33i [4.6] [3." 8] [3 33] [3 44] [3 29] [2.4] [2.3] [2.6] -0 02 3.2 -0 12 5.0 2.7 Page 246] APPENDIX IV. maritimp: positions and tidal data. EAST COAST OF ASIA— Continued. Place. Burias Island: Marinduque I. Balingtang Islands Batan Island: Mount Irada Ibayat Island: Mount Santa Rosa Yami Island: Islet off SW. part Luzon Island, Port Dimasalasan: En- Poiiiio i.VpoVt'pomio! 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 Busainga : Summitof MountCatala. Maestro de Campo Island, Port Con- cepcion: Point Fernandez Ban ton Island : Ban ton Mountain Tablas Island : Tab las 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 L, SW. pt .. Panay Island, Iloilo: Fort San Jos^ Pan de Azucar Bat batan 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 Basianaiig Bay: N. pt. of Donauang I. PoUoc: Small hill back of town Lat. X. 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 Lun. Int. Long. E. 122 14 00 122 01 20 121 52 30 121 58 24 122 19 20 121 54 48 123 43 53 124 06 48 124 04 48 124 04 18 123 49 22 123 35 58 123 14 36 123 12 47 123 07 34 123 02 45 121 54 33 121 43 08 122 04 48 122 08 38 121 58 32 121 53 53 122 17 08 122 16 26 122 33 23 125 43 14 124 51 37 124 18 15 124 59 56 124 36 20 124 22 07 124 50 15 124 32 35 123 54 18 123 34 26 123 06 09 123 18 43 123 07 05 122 55 42 122 40 20 122 34 26 121 54 27 122 09 09 121 52 36 121 58 59 122 28 50 122 45 03 126 02 53 125 31 17 125 58 22 125 28 30 125 47 48 125 34 35 125 13 48 123 57 37 124 11 42 H. W. h. m. 6 08 [4 30] L. W. h. ni. 00 [10 20] 6 53 11 47 11 06 [11 40] 6 00 1 25 4 50 5 22 [6 15] -6'i3' Range. Spg. Neap. /<■ 5.2 [5.5] 1.5 1.1 2.8 2.0 4.2 1.9 [6.5] 5.1 APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. EAST COAST OF ASIA— Continued. [Page 247 6 »' -d s « H Cm M si S £ Place. Lat. N. Long. E. Lun Int. Range. ' 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 32 51 38 23 37 38 58 16 39 09 00 38 56 00 40 35 00 39 30 46 39 16 00 38 43 17 38 47 50 38 52 38 38 40 00 39 04 00 38 27 00 37 58 00 37 27 40 36 26 45 36 24 30 36 07 00 O / 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 21 27 120 55 00 117 42 48 117 11 44 118 31 00 122 00 00 121 18 03 121 35 59 121 08 26 121 15 54 121 51 59 122 11 30 123 10 34 124 34 40 124 34 30 126 36 27 126 28 00 126 24 00 126 01 09 h. m. h. m. ft. ft. Zamboanga: Fort... Sibuc-o 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] 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 1 Sibutu Island: Hill on E. coast Simonor Island: NW. pt 1 1 Bahaltolis Island: Sandakan Harbor... Bongao Island : S. pt 1 Keenapoussan Island : Center Bubuan Island: Lagoon entrance Cuad Basang Island : SW. pt 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 . Dalrymple Harbor, Tul- yan Islet Jolo light-house [9 38] [3 10] [5.0] Doc Can Islet: W. extreme Pangituran Island : S W. pt Basilan Island: La Isabela Wang-kia-tia Bay : Langwang temple . . Kyauchau Bay : Yunuisan light Staunton Island: Landing place, N. side. Shantung Promontory: Light-house , .. Weihaiwei: Light, S. side 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 flagstaff Miautao Island: Peak of N. Island Pei-ho: S. Taku Fort, S. Cavalier 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 Liao-ti-shan Promontory: SW. pt. light Port Arthur: Obs. spot 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 Wolmi 4 19 10 31 28.8 n.6 Marjori banks Harbor: Manzoc Islet Tas de foin Islet: Center Guerin Island: Summit, 969 ft Page 248] APPENDIX IV. MAEITIME POSITIONS AND TIDAL DATA. EAST COAST OF ASIA— Continued. Place. Kokoun-tan Islands: Camp Islet Barren Island : Center, 600 ft Sea Kock: Center, 160 ft Modeste Island: N. peak, 1,228 ft Ross Island : Peak, 1,920 ft Kuper Harbor: NE. extreraeof JoslingI 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 NoOsima: Summit Wilson I.. Yeboshi Sima: Light-house Yobuko Harbor: Bluff opposite Nicoya Hirado No Setb: 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: MountMatomi,6,252ft 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 TanabeBay : Fossil pt Oo-sima Hbr. : Kashinosaki light, E. pt Uragami Harbor: Village pt Ovvashi Bay: Hikimoto Mura Harbor: Osima Islet Lat. N. 35 48 08 35 21 00 34 42 00 34 42 30 34 06 00 34 17 20 34 01 23 33 57 00 33 59 00 33 29 40 34 39 00 34 33 00 34 48 00 35 07 15 34 18 55 33 44 30 33 52 10 33 53 50 33 41 30 33 32 30 33 23 31 32 36 45 32 13 12 32 03 00 32 43 21 32 36 05 31 35 39 31 20 00 31 12 00 31 12 43 30 59 30 30 51 00 30 50 00 30 47 00 30 17 00 30 05 00 29 59 00 29 54 00 29 52 00 29 38 00 29 08 00 28 47 30 33 57 46 33 58 53 33 59 11 33 23 19 34 22 37 34 35 58 34 37 27 34 38 05 34 39 20 34 41 18 34 39 45 34 35 12 34 07 42 33 57 34 33 41 14 33 28 15 33 33 37 34 06 10 34 13 52 Lun. Int. Long. E. Range. 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 51 h. m. 9 05 L. W. Spg. Neap. 7 35 8 56 9 23 7 54 6 40 T26 30 5 55 11 16 7 30 6 23 h. m. 2 52 10.5 1 23 2 44 7.0 6.7 3 10 6.4 1 41 8.4 1 00 "i'os' 10.5 "9.'5" 2 20 6.7 12 08 5 04 5.0 10.2 1 25 4.7 10 4.7 ft. 4.2 3.0 2.4 2.5 3.5 4.4 2.4 2.0 4.5 2.0 2.0 APPENDIX IV. [Page 249 MAEITIME POSITIONS AND TIDAL DATA. EAST COAST OF ASIA— Continued. o Place. Lat. N. Long. E. Lun. Int. Range. H. W. L.W. Spg. Neap. a h i * M "S s Matoya Harbor: Anori-saki light Omoi Saki : Light-house O 1 II 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 60 33 52 00 33 39 00 33 04 24 32 29 00 32 00 40 31 27 00 30 28 26 29 46 28 35 42 13 38 16 57 39 16 30 39 27 17 41 25 58 41 33 34 40 50 00 41 16 17 40 31 00 39 12 02 38 29 23 38 19 55 36 47 47 37 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 O / II 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 00 139 08 00 139 31 00 138 48 15 139 34 00 139 17 45 139 50 24 139 43 31 140 00 00 140 02 00 140 14 02 140 19 40 140 52 22 141 35 33 141 52 50 141 59 00 141 27 32 140 56 36 140 44 40 140 22 37 139 31 00 139 32 58 139 15 31 138 27 09 137 03 15 137 22 00 139 03 01 136 54 00 136 58 24 136 01 22 133 23 00 131 36 00 131 18 00 131 09 00 130 50 29 140 41 49 140 59 33 144 52 38 145 49 10 145 34 40 145 18 00 141 38 40 141 19 00 146 15 00 149 14 00 149 34 00 150 28 30 151 52 50 152 24 00 153 12 30 154 08 00 154 39 00 154 44 00 154 32 00 156 15 20 156 26 00 h. m. 5 52 h. m. 12 04 ft. 4.3 f;7 Shimizu Bay : Mound on pt 5 52 12 04 3.9 1.6 Mikomoto Island : Light-house Simoda Harbor: Center I Yokosuka Harbor: Eyi Yama pt Yokohama: English Hatoba hght Tokio: Naval Observatory 5 25 11 30 4.9 1.9 No Sima Saki : Light-house 5 04 11 17 3.7 1.4 Vries Island (0 Sima) Volcano: Sum- mit, 2,512 ft Kozu Shima \"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 . _ f 1 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 4 30 10 45 3.4 L3 Tatsupi Saki: N. side Bittern Rocks: SW. rock Tobi Shima: Takamori Yama Awa Sima: NE. extreme Sado Island: Ya Saki Fushiki Harbor: Light-house CapeRoigen: 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 2 30 8 42 0.6 0.4 11 41 5 28 1.1 0.5 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 3 40 3 32 3 41 3 48 3 33 4 50 10 00 9 45 9 53 10 00 9 46 11 05 3.0 3.5 3.0 3.1 2.1 3.7 1.2 1.5 1.4 1.4 0.5 1.8 Kunashir Island: St. Anthonys Peak. . . Iturup Island : NE. pt Urup Island : Cape Vanderlind Broughton Island : Summit Simusir Island: Prevost Peak \ 1 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 i i t j 1 1 Page 250] APPENDIX lY. MARITIME POSITIONS AND TIDAL DATA. EAST COAST OF ASIA— Continued. o Place. Lat. N. Long. E. Lun. Int. Range. 1 H. W. L. W. Spg. Neap. ci 2 9 ei ■c e Cape Clonard : Extreme 1 II O 1 II 36 05 45 i 129 33 30 36 36 00 129 20 00 37 09 30 1 131 55 00 37 30 00 i 130 53 00 39 19 12 1 127 32 48 42 14 30 ! 137 17 00 42 38 05 130 48 45 42 33 40 1 131 10 00 43 05 13 i 131 53 56 42 41 00 1 133 02 00 43 22 00 135 15 00 43 53 40 1 135 27 19 44 30 00 : 136 02 00 44 43 45 136 22 30 44 46 15 136 27 15 45 05 00 136 44 00 45 19 30 137 10 15 h. m. h. VI. ft. ft- Ping-hai Harbor Lian court Rocks: Summit, 410 ft Matu Sima: Peak, 4,000 ft Port Lazaref: S. 1| miles from the S. end of Bontenef I Wawoda Rock : Summit, 12 ft , Expedition Bay: Light-house Port Novogorod : Light-house Vladivostok: Cape Galdobin light Cape Povorotiiyi: Light-house 2 45 9 00 1.9 0.8 Port Olga: Light-house St. Vladimir Bay: Orekhera Pt Shelter Bay Svbillo Bay Pique Bay Bullock Bay Luke Point: Extreme Cape Disappointment: Extreme Cape Suffren: Extreme 45 41 30 47 20 00 48 59 30 51 28 00 45 53 10 46 01 20 54 24 30 53 08 05 55 11 00 56 25 28 56 22 30 59 19 45 51 02 00 52 52 37 53 04 30 54 56 00 54 32 24 56 10 00 58 26 00 59 55 00 62 14 30 60 18 00 63 12 00 64 16 00 64 25 55 64 24 30 64 46 00 6-1 50 00 137 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 Long. E. 178 40 00 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 Shan tar Island : N. pt Port Aian : Cape Vneshni St. Jona Island: Summit, 1,200 ft Okhotsk : Battery 10 7 30 ; 8,4 3.4 Cape Lopatka: Extreme 3 55 3 30 10 08 4. 6 9 45 5. 1 1.9 2.1 Petropavlovsk: Rakof light Cape Shipunski : Extreme Bering Island: Cape Khitroff t Mednoi, or Copper Island: SE. extreme. Cape Kamchatka: Extreme i 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 i 4.5 1.8 ! ............ Cape Tchoukotskoi: Extreme :::::::::::::::::::::::::: i Port Providence: Emma Harbor Cape Indian : Extreme 1 i. Arakam Island : Cape Kiguinin Anadir River: Mouth . . . . Cape Bering: Extreme \ Long. W. 65 00 30 ! 175 54 00 66 02 00 i 169 32 30 East Cape: Extreme.. ISLANDS OF THE PACIFIC. » e is, si ft i a Malpelo Island: Summit, 1,200 ft Cocos Island: Head of Chatham Bay. . . Redondo Rock: Summit, 85 ft 4 03 00 5 32 57 13 30 20 00 18 50 34 25 1 22 55 81 36 00 86 59 17 91 03 00 89 58 43 90 30 08 90 44 23 91 49 43 Towers Island : W. cliff Bindloe Island: S. summit . Abingdon Island: Summit, 1,950 ft Wenman Island: Summit, 550 ft j APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ISLANDS or THE PACIFIC— Continued. [Page 261 1 • Place. Lat. S. Long. \V. Lun. Int. Range. H. W. L. W. Spg. Neap. i M C 9 i -d « H « 1 « Albemarle Island: Iguana Cove Marlborough Island : Cape Hammond . . James Island: Sugarloaf, 1,200 ft Jervis Island : Summit O 1 II 59 00 31 00 15 20 25 00 36 30 33 25 50 30 1 19 op 1 25 00 44 15 Lat. N. 1 57 17 3 51 26 4 41 10 5 52 15 13 30 49 00 Lat. S. 2 40 54 2 35 00 1 50 00 1 29 14 1 23 42 1 17 14 36 00 Lat. N. 11 10 20 54 51 30 1 38 45 1 44 15 2 03 00 3 01 30 4 35 25 5 55 07 6 14 00 7 05 30 7 09 17 7 15 00 8 14 00 8 27 00 8 19 00 8 54 21 9 28 09 10 03 40 10 17 25 11 48 00 11 19 21 11 24 00 11 07 00 11 40 00 10 05 00 11 40 00 9 39 00 1 II 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. TO. 2 00 h. m. 8 13 ft. 6.2 ft. 3.1 2 45 8 58 5.2 2.6 Duncan Island: Center hill : : : i Indefatigable Island : NW. bay Barrington Island: W. summit, 900 ft.. Charles Island: Summit, 1,780 ft Fatu Huku or Hood Island : E. summit, 640 ft 2 00 8 13 6.2 3.1 2 10 8 23 6.0 3.0 Chatham Island: Mount Pitt, 800 ft Christmas Island: N. pt. of Cook Islet.. Fanning Island: Flagstaff, entrance to English Hbr 2 20 4 25 6 00 8 33 10 38 12 15 6.5 2.4 2.4 3.3 1.4 1.4 Washington Island Palmyra Island 5 25 11 40 1.5 0.9 Baker Islet: Center Howland Islands: Center island Arorai or Hurds Island : S. pt Tamana Island : Center 7 10 1 00 6.2 3.6 Onoatoa Island : Center Taputeuea or Drummond Island: SE. pt. Nukunau or Byron Island : SE. pt Peru or Francis Island: NW. pt Nonuti or Sydenham Island 1 1 Aranuka or Henderville Island: VV. pt. of W. island Apamama or Hoppers Island : Entrance islet 4 30 10 45 4.7 2.7 Maiana Island: S. pt Tarawa Island: NE. pt Apaiang Island: S. pt _ Maraki Island: N. pt -. Taritari Island: S. pt Ebon Atoll: Rube Pt 4 45 11 00 4.7 2.7 4 45 11 00 4.7 2.7 Jaluit or Bonham Islands: Jarbor Pier. Burrh Island: Port Rhin, N. pt. of en- trance 5 00 11 15 5.0 2.8 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 Ibbetsonlsland: NE. end, an- chorage Maloclab Islands: NW. end Karen Islet. Wotje or Romanzov Islands: Christmas Harbor Litkieh Island : NW. pt Ailuk Islands: Capeniur Islet Bigar Islet : Center Kongelab or Pescadores Islands: Center of group ... 4 50 11 00 6.2 3.6 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 1 Page 262] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ISLANDS OF THE PACIFIC— Continued. Place. Lat. N. • Long. E. Lun. Int. Range. 1 H. w.; L. W. spg- Neap. m IS § M e fl 2 H a 03 c M ? El « e 2 Greenwich Island: Northern islet Matelotas group: Easternmost of the S. islands / // 1 04 00 8 18 30 9 29 00 9 52 30 10 06 00 9 46 00 8 06 00 6 40 00 7 21 45 7 15 00 8 35 00 8 03 00 7 43 30 7 29 30 7 22 00 8 09 00 6 40 00 7 38 00 8 59 45 8 25 30 7 18 30 5 55 00 5 29 18 3 51 00 7 39 00 5 48 00 7 00 35 6 41 45 6 14 00 5 20 06 6 53 55 7 02 00 7 08 00 7 19 00 7 40 30 8 08 00 4 20 00 3 02 00 5 20 00 13 25 48 14 07 30 14 59 22 15 08 30 15 17 10 16 20 00 16 41 00 17 17 00 17 36 00 18 04 00 18 46 20 19 45 00 20 00 00 20 32 54 O / II 154 47 55 137 33 30 138 04 00 139 42 00 139 46 00 140 35 00 140 52 00 143 11 00 143 57 30 144 31 00 144 36 00 146 50 00 145 55 45 146 24 30 147 06 48 147 42 00 149 21 00 149 27 30 150 14 30 151 49 15 151 56 30 153 13 30 153 58 00 155 00 54 155 05 00 157 31 30 158 12 21 159 50 00 160 38 43 163 00 45 134 05 24 133 18 03 134 27 00 134 32 30 134 39 30 134 17 00 132 21 00 131 11 00 132 16 00 144 39 30 145 13 04 145 36 20 145 43 55 145 42 50 145 39 00 145 47 00 145 57 00 145 55 00 145 52 00 145 41 45 145 30 00 145 21 00 144 54 00 h. m. h. m. ft. ft. Yap Island : Light in Tomil Bay Eau Island : Center 7 15 1 00 3.4 1.9 XJluthi or Mackenzie Islands: Mogmog Islet Feys or Tromelin Island: E. extreme . . Sorol or Philip Island : Center Eauripik or Kama Islands: E. islet Oleai group: Raur Islet, N. pt Ifalik or Wilson Islets: N. end Faraulep Island : S. end W. Faiu Islet: Center Olimarao Islet: Center Toass Island: Center Satawal Island : Center Coquille or Pikelot Island: Center Suk or Polusuk Island: S. end Los Martires: Ollap Islet, N. pt Namonuito Islands: Magur Islet Hall Island: Namuine Islet Hogolu (Hogulu) Group: N. end of Tsis Islet Namoluk Islands: NW. islet Mortlock Islands: Lukanor, Port Cha- misso Nukuor or Monteverde Islands: E. pt. . Oraluk or Bordelaise Island : Center . . . Ngatik or Valientes Islands: E. extreme. Ponapi Island: Jamestown Harbor Mokil or Duperrey Islands: Aoura, NE.pt Pingelasp or MacAskill Islands: E. end of island 4 00 10 15 4.3 2.4 • ITalan or Strong Island : Chabrol Harbor . Angaur Island: SW.pt 6 00 12 15 3.5 2.0 Pililu Island: S. pt Earakong or Akamokan Island : Center. Korror Islands: Korror Harbor, Mal- akal pier Baubeltaub Island: Cape Artingal Kyangle Islets: Center of largest Warren Hastings Island: Center Nevil or Lord North Island: Center Sonserol Island : Approx Guam Island: Fort Sta. Cruz, San Luis d'Apra 7 20 1 20 2.6 1.5 Rota Island: Summit Tinian Island : Sunharon village Saipan Island: Magicienne Bay, land- ing Tanapag Hbr., Garapag. Anataxan Island: Center 7 00 50 2.0 1.1 Sarignan Island:* Center Guguan Island : Center Alamaguan Island: Center Pagan Island: SW.pt . .. Agrigan Island: SE. pt Asuncion Island: Crater, 2,600 ft Urracas Islands: Largest islet. Farralon de Pajaros: S. end APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ISLANDS OF THE PACIFIC— Continued. [Page 253 Place. Wake Island: Obs. spot Gaspar Rico Reef: N. clump of rocks. . Johnston or Cornwallis Islands: Flag- staff on W. island Clipperton Island : Center 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 . 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. Midway Islands: N. end Sand Islet . . . Ocean Island: Sand Islet Marcus Island: Center Bonin Is., Parry s 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 MotuMli Island : Summit, 130 ft Ua-Huka or Ua-Una Island'. N. pt ... Fetouhouhou Island: NE. pt Caroline Islands: Solar Eclipse Transit Pier : Vostok Island : Center Flint Island : S. extremity Lat. N. 19 15 00 14 41 00 16 44 48 10 17 00 19 46 14 20 03 00 19 28 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 Long. E. 166 31 30 168 54 28 Long. W. 169 32 24 109 13 00 155 05 31 155 48 00 155 55 00 156 00 15 156 35 04 156 26 00 156 35 00 157 18 32 157 39 07 157 48 44 157 51 34 157 51 54 159 30 47 159 40 08 161 58 17 164 40 47 166 17 57 168 00 52 170 39 20 171 44 00 173 57 00 175 46 00 177 21 30 178 27 45 Long. E. 154 00 00 142 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. \V. 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 Lun. Int. Range. H. W. h. TO. h. m. ft. 3 09 9 06 2.3 2 20 8 10 1.6 3 32 2 38 9 58 8 56 2.2 2.1 3 46 I'm 9 59 1.5 10 20 2.0 3 30 9 45 1.1 6 10 00 2.4 2 30 8 45 3.1 3 50 10 05 3.5 4 00 10 14 1.1 Neap. 1.3 0.9 1.2 1.1 0.8 1.1 0.6 1.4 1.9 2.1 0.7 Page 254] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ISLANDS OF THE PACIFIC— Continued. 6 Place. Lat. S. Long. W. Lun. Int. Range. 1 H. W. L.W. Spg. Neap. i H H a 8 8 » M 9 V H 8 ei 7 m a S e Maiden Island: Flagstaff, W. side Starbuck Island: Flagstaff, W. side Penrhyn or Tongarewa Island : NNW. pt. Jarvis Island : Center / II 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 O ' ' II 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 h. m. h. m. St. ft. 6 00 12 15 1.5 0.9 Reirson Island : Church Humphrey Island : N. pt Union or Tokelau Islands: Spot N. of Fakaofu or Bowditch Islet 1 6 00 12 13 2.4 1.4 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 Enderburv Island: W. pt 5 00 ii i5 4.6 2.7 Phoenix Island, N. pt Birneys Island : S. pt Gardners Island : Center . j McKean Island : Center Hulls Island: W. pt Mukulaelae or Mitchells Island: S. pt. . . Funafuti or Ellice Island: E. pt Nukufetau or De Peysters Island: S. pt . Vaitupu Island : S. end 1 1 Nui or Netherland Island: S. pt Nauomaga Island : Center I Niutao Island : Church Nanomea Island: Center 1 Ocean or Paanopa Island : Center ( appx ) . Pleasant Island : Center Indispensable Reefs: S. pt. of S. reef... Rennel Island : SE. extreme W.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 6 45 33 3.3 2.0 Stewart Islands: Largest islet Isabel Island: N. side of Cockatoo Islet. Gizo or Shark Island: N. point village. . Choiseul Island: Choiseul Bay en- trance 5 00 11 15 3.5 2.1 Treasury Islands: Observation Islet Bougainville Island: Hiisker Pt, Ge- zelle Harbor i 1 12 00 5 47 1 2.7 ' 1.6 Buka Island : Cape North Lord Howe Group: Center, small SW. islet i ! Center, small NE. islet ! ! NW. pt. of Ham- mond I 1 " i New Britain, Blanche Bay: Matupi I. N. pt 9 00 2 45 2.1 1.3 Duke of York Island: Makada Har- bor, Spit Pt , i APPENDIX IV. MAKITIME POSITIONS AND TIDAL DATA. ISLANDS OF THE PACIFIC— Continued. [Page 255 Place. New Ireland: Carteret Harbor, Cocoa- nut I Katharine Haven Holz Haven, E. side New Hanover Island: AVater Haven, creek mouth North Haven anchorage . . St. Matthias Island: SW. extreme Admiralty Island: Nares Harbor, obs. islet St. Andrew Island: Violet Islet, 60 ft . Jesus Maria Island: SE. pt Commerson Island: Center of largest islet Anchorite Island: N. pt Hermit or Loaf Island: Peme Islet . . . Purdy Island : Mole Islet Point d' LTrville : extreme Drei Cap Peninsula: Wass Islet Triton Bay: Fort Dubus, Dubus Haven Cape Walsche: Extreme Fly River: Free Islet, S. pt Port Moresby: N. end of Jane I Cape Rodney: P^xtreme South Cape: S. pt. Su Au I Hay ter Island : W. end Cape Cretin : Cretin Islets Trobriand Islands: NE. pt. Cape Denis Woodlark Islands: N. pt D'EntrecasteauxIs. : Ferguson I., SW. extreme Well Island, E. pt Normanbyl., obs. islet St. Aignan Island: Summit Renard Islands: W. pt Rossel Island: E. pt Adele Island : S. extreme Coringa Islands: Chilcott Islet Herald Cays: NE. Cay Tregosse Islands; S. islet Lhou Reef: Observation Cay Mellish Reef: Cay beacon Bampton Island Renard Island : Center Wreck Reef: Bird Islet Cato Island: Center 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 '. Lat. S. 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 Long. E. 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 68 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 Lun. Int. H. W. h. m. 2 50 L.W. 9 03 2 30 55 8 43 7 08 50 2 38 15 25 3 00 2 12 4 45 7 05 10 58 53 4 50 11 05 Range. Spg. Neap. ft. ft. 2.4 1.4 2.4 1.4 7.3 4.3 8.0 4.8 8.1 5.8 4.8 3.4 3.0 4.2 1.8 2.5 3.8 2.3 Page 266] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ISLANDS OF THE PACIFIC— Continued. 1 Place. Lat. S. Long. E. Lun. Int. Range. 1 H. W. L. W. Spg. Neap. i M « ■s •c fit s Torres or Ababa Island: Hayter Bay, Middle I O / /I 13 15 00 13 48 00 14 11 00 14 58 00 16 26 00 17 44 58 18 47 30 19 31 17 o / // 166 33 00 167 30 31 167 30 00 168 02 00 167 47 15 168 18 50 168 58 00 169 27 30 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- aee Aurora Island : Laka-rere Mallicollo 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 Eesolution, Mission . Erronaii, or Futuna Island: NW. pt Aneityum Island: Port Anatom, Sand Islet 19 31 20 170 11 15 20 15 17 169 44 45 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 11 55 00 12 30 10 18 38 -15 19 07 09 19 05 30 18 36 00 17 40 45 17 44 45 18 06 50 18 22 00 19 09 38 171 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 Walpole Island : S. pt ... Mitre Island: Center Rotumah Island: Epipigi Peak Kandavu Island: N. rock Astrolabe Reef light 6 15 00 4.2 2.5 Mt. Washington, N. peak N'galoa Harbor, outer beacon 6 40 25 4.0 2.4 Vatu Lele Island : S. pt Ovalau Island : Levuka light-house Viti Levu Island: Summit of Malolo Islet . Suva Harbor, low light 6 30 15 3.6 2.2 ^Nlbega or Mbengha Island: Swan Har- bor, Leaven Pt Matuku Island : N. side of Matuku en- trance a Moflla Island: Rocks off N. nt 18 .32 49 fl Xffan Island: Herald Bav. E. aide 1 17 59 32 « Wakava Island : Rocky Peak 17 37 11 17 27 14 17 15 21 16 42 01 16 57 53 16 49 19 16 08 00 16 46 00 15 44 45 17 03 00 17 25 33 17 17 20 17 10 00 17 25 26 Makongai Island: Dilliendreti Peak Goro Island : N W. pt Vanua Levu Island : Mount Dana Nandi, observation islet . . . . 5 Savu Savu Pt. ; ex- treme 6 00 12 13 4.3 2.6 NE. Pt Taoiuni Island: Somu-Somu town Thikorabia Island: E. hummock Naitamba Island : Center 1 Vatu Vara Island: N. end, summit Kanathea Island : S. pt Vanua Mbalavu Island: NW. pt Mango Island : Pier end 6 10 00 3.1 1.9 Thithia Island: Highest peak 1 17 44 12 17 39 33 Tuvutha Island: Peak. Naian Island: Summit, 580 ft . . 17 59 00 18 14 10 18 25 46 18 38 56 18 46 00 ..... Lakemba Island: Kendi Pt Oneata Island: Summit of Loa I Mothe Island: Summit Mamuka Island: Center, 260 feet 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 Sirnonoff 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. Nine or Savage 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. , Vincennea Pt . Huaheine Island: Light-house Ulietea Island : Regent Pt Tahoa Island: Center Bola-Bola Island: Otea- Van ua village.. Tubal 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 Gambier Island : Flagstaff Marutea or Lord Hood Island: Center. . Maria or Moerenhout Island: Center. . . Vahanga Island : W. pt , Morane or Cadmus Island: Center Tureia or Carysfort Island: E. pt 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. Pihaki 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. H. W. L. W. h. m. 6 35 'e'io" 6 40 6 25 7 00 6 00 3 10 12 00 12 10 20 '6"66' 28 13 45 12 13 9 23 5 48 6 00 1 50 8 03 Range. Spg. Neap. ft- ft. 3-. 5 '3."i' 2.1 "i."9 4.4 2.7 3.1 2.7 4.6 1.9 1.6 2.7 2.4 1.4 1.0 0.6 L4 0.8 2.4 1.4 6583—06- -17 Page 258] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ISLANDS OF THE PACIFIC— Continued. a* H Place. Hao or La Harpe Island: NW. pass Paraoa or Glocester Island : Center Ravahere Island: S. pt Reitoru or Bird Island: N. beach Hikueru or Melville Island, E. pt Tauere Island: NW. pt Puka-puka Island: E. pt Napuka Island : W. pt Angatau or Araktcheff Island: W. pt . . Tukume or Wolkonsky Island: NW. pt. Tuanske Island: 'N W. pt Nihiru Island (Tuanake): SW. pt Anaa Island: Islet in N. pass Tepoto Island : N. pt Haraiki or Crocker Island: SW. pt Makemo or Phillips Island: W. pass... Fakarana or Wittgenstein Island: SE. pass Taiaro or Kings I. : Middle of W. shore. Aratika Island: E. pt Toau or Elizabeth Island: Amyot Bay, Takapoto Island: S. pt Aheu Island : Lagoon Entrance Rangiroa Island: E. pt Makatea Island : W. pt Matahiva Island : W. pt 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 Easter Island : Cooks Bay, mission Rapa or Oparo Island: Tauna Islet Bass Islets (Morotiri): SE. islet, 344 ft Tubuai or Austral Is. , Vavitoa I. : Center Tubuai I.: Flag staff, N. side. . . Rurutu I. : N. pt . Rimitara I. : Cen- ter Hull Island : N W. pt Mangaia Island: Center Rarotonga Island : N W. pt Mauki or Parry Island : Center Mitiero Island : Center Vatiu or Atiu Island: Center Hervey Islets: Center Aitutaki Island: Center Vavau Island: Port Valdes, Sandy Pt. Kao Island : Summit, 5,000 ft Tofua Island: Summit, 2,800 ft Tongatabu Island: Light-house Minerva Reefs, N. Minerva: NE. side . S. Minerva: S. side of entrance Kermadec Is. , Raoul or Sunday I. : Den- ham B. flag staff Macauleyl.: Center Curtis I. : Center Conway Reef: Center Lat.S. Long. W. Lun. Int. Range. H.W. L.W. Spg. Neap. O 1 II 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 23 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. m. 8 55 2.4 . ft. 1.4 m 4 30 10 43 2.1 L3 4 00 40 10 10 15 6 53 6 25 3.3 2.8 2.4 2.0 1.7 1.4 3 00 9 13 2.4 1.4 6 00 12 15 2.7 1.7 6 20 10 3.8 2.3 6 20 7 50 10 1 35 3.8 5.5 2.3 3.3 6 00 12 13 3.3 2.7 APPENDIX IV. [Page 259 MARITIME POSITIONS AND TIDAL DATA. ISLANDS OF THE PACIFIC— Continued. «^ Place. Lun. Int. Range. 1 H. W. L. W. Spg. Neap. Loyalty Is., Uvea or Halgan I.: Uvea o r II 20 27 06 20 46 00 21 42 00 21 29 12 22 00 10 22 16 22 22 28 44 22 42 30 29 03 45 29 56 00 31 31 38 31 45 10 54 19 00 50 32 15 52 33 26 49 42 00 47 43 00 43 57 24 43 49 03 1 II 166 35 25 167 02 30 168 00 0(5 165 58 50 166 05 00 166 25 52 166 28 51 167 27 55 167 58 06 159 04 30 159 05 58 159 16 10 158 56 00 166 13 20 169 08 41 178 43 05 179 00 27 Long. W. 176 32 15 176 42 00 h. m. h. m. ft. ft. Lifu I. : Wreck Bay, NW. shore 6 30 18 4.2 2.5 Mare or Britannia I. : S. pt. Port Kanala' Observatory Port St. Vincent: Marceau I 5 40 8 25 11 52 2 13 3.3 3.1 2.0 1.9 Noumea : Light-house Balari Pass* Amed^e I. light 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 Lord Howe Island: S. end of middle 'beach 8 20 2 08 5.4 3.3 Balls Pyramid: Summit, 1,816 ft Macquarie Island :N. pt Auckland Is.: Port Ross, Terror Cove.. Campbell Island: S. harbor. Shoal Pt.. Antipodes Island: Summit, 600 ft Bounty Islands: Anchorage N. I., West 11 50 11 45 3 20 5 38 5 33 9 30 3.2 3.5 5.3 2.6 2.9 4.3 Chatham Island, Whare-Kauri Island: Port W^aitangi Pt Hanson Chatham Island, Whare-Kauri Island: Port Hutt, Gordon Pt ~ 5 22 23 2.5 2.1 AUSTRALIA. i s » S *^ ! * s E V *i c 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 16 30 130 37 00 130 27 00 129 37 00 129 20 42 129 48 14 128 10 00 126 57 00 126 12 00 125 38 45 125 39 00 124 55 00 125 12 00 125 00 00 124 42 00 125 07 00 125 01 00 124 32 11 124 14 00 124 04 00 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 1 Pearce Point: Extreme Cape Londonderry Extreme Cassini Island S pt .::::::::: i Cape Voltaire* Flat Hill Barker Islets: Center ... Mon tali vet Islands' W^ islet Maret Islets: N. islet . ... Colbert Islet' Center Prince Regent River: Mount Trafalgar . :::::::: i De Freycinet Islets: Beacon on summit. Red Islet' Center Cockell Islet- W pt Page 260] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ATTSTBAIilA — Continued. Place. MacLeay Islets: Rock off N. end Port Usborne: S. pt Fitz Roy River: Escape Pt Cape L'Eveque: Extreme Lacepede Island: NW. islet Cape Baskerville: Extreme Cape Latouche Tr^ville: Extreme Turtle Isles : Center of N. isle Cape Lambert: Extreme Legendre Island : NW. extreme Rosemary Island : \V. 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 Nuyta Point: Extreme West Cape Howe : Extreme Eclipse Islets: Summit of largest King George Sound: Commissariat house near Albany jetty Bald Isle: Center Hood Point: Doubtful Isles Recherche Archipcilago: 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 Melbourne: Observatory Lat. S. O > II 15 52 00 15 39 25 17 24 25 16 23 00 16 50 00 17 09 00 18 29 00 19 54 00 20 36 00 20 19 00 20 27 00 20 35 00 20 16 45 20 40 40 21 46 41 24 00 00 25 29 19 28 18 05 28 12 00 31 18 00 32 00 20 32 03 12 32 27 00 33 31 45 34 21 55 34 52 00 35 05 00 35 09 00 35 11 54 35 02 20 34 55 00 34 24 00 34 30 00 32 57 00 32 34 00 32 01 30 32 48 00 34 29 29 35 00 15 35 20 15 34 43 22 33 44 08 32 29 42 34 28 25 35 18 21 35 07 31 34 12 00 34 50 25 35 36 45 35 45 30 35 51 00 35 34 06 36 57 00 38 04 18 38 26 00 38 24 39 38 23 47 38 51 45 39 35 38 38 18 00 38 08 52 37 49 53 Long. E. 123 45 00 123 36 27 123 39 47 122 55 45 122 05 30 122 15 00 121 54 00 118 48 00 117 11 00 116 45 00 116 30 00 116 23 00- 115 22 00 115 27 45 114 10 08 113 21 00 112 57 09 113 35 33 114 14 30 115 30 00 115 30 12 115 44 23 115 44 00 115 00 15 115 08 00 116 01 00 116 38 00 117 40 00 117 53 45 117 54 04 118 27 00 119 34 00 121 58 00 124 39 00 125 30 00 132 33 00 134 13 40 135 24 56 135 56 09 1.36 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 39 143 57 03 144 37 00 144 21 47 144 58 35 Lun. Int. H. 'V. h. m. 11 30 [10 16] [10 53] 11 50 35 8 20 4 31 4 04 4 00 11 52 "6"26' 10 43 2 02 2 19 L. W. h. m. 5 10 [3 43] [4 40] 9 35 6 55 2 15 10 45 10 22 10 15 5 40 "6*35' 4 30 8 20 8 41 Range. Spg. 17.1 • • ■< • [2.*!] [2.6] 5.1 5.5 11.4 10.2 6.3 5.8 4.2 *2."7' 2.5 3.0 L9 Neap. 10.4 0.3 0.3 0.7 0.6 0.9 0.3 "6*2 2.1 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 Promontory: 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 Bate man Bay: Observation head UlladuUa: Inner end of pier Jervis Bay : Light-house Kiama Harbor: Outerextremeof S. head Wollongong: 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. Head light 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 Bo wen: Observation rock Percy Isles: Pine I. light Northumberland Isles: Summit of Prud- hoe I Cape Palmerston: N. extreme Cape Conway: SE. pt Port MoUe: 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 Lat. S. 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 15 21 32 00 20 32 20 20 18 50 20 15 30 20 00 50 19 57 30 19 41 50 19 19 20 19 11 25 18 45 30 18 09 30 17 40 40 17 09 45 16 04 20 15 45 00 15 29 45. 15 16 30 Long. E. Lun. Int. Range. H.W. L.W. Spg. Neap. O / 1, 144 52 51 h. m. h. m. ft- A 145 01 34 146 25 16 147 18 39 148 04 00 147 47 39 148 07 24 10 38 4 25 8.1 6.2 146 37 43 149 55 10 149 58 39 8 40 2 27 4.5 3.4 150 03 04 149 54 45 150 01 34 8 05 1 52 5.2 3.1 150 13 34 150 12 34 8 20 2 07 5.3 3.2 150 29 29 150 46 26 8 20 2 07 5.4 3.3 150 52 19 150 55 14 151 12 23 151 18 15 8 40 2 27 4.2 2.5 151 20 30 151 48 19 152 13 20 152 33 40 8 35 8 15 2 23 2 00 4.7 5.8 2.8 3.6 152 55 19 153 17 00 9 00 2 46 4.1 2.4 153 23 10 153 35 55 8 15 2 00 4.0 2.4 153 01 48 153 33 50 10 45 4 30 6.4* 3.9 153 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 10 05 3 53 9.0 5.4 148 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 30 146 17 30 145 23 15 8 55 2 43 7.5 4.5 Page 262] APPENDIX lY. MARITIME POSITIONS AND TIDAL DATA. AUSTRALIA— Continued. 1 Place. Lat. s. Long. E. Lun. Int. Range. 1 H.W. L.W. Spg. Neap. 'i a » 9 Of Murdock Point' Extreme ... o / // 14 37 15 14 10 00 14 07 45 14 00 30 13 24 45 12 51 00 11 58 15 11 55 00 11 46 30 11 36 30 10 41 30 10 37 45 10 22 00 10 46 00 10 36 05 17 36 40 17 35 10 17 06 50 1 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 19 142 32 24 142 39 20 142 21 19 142 10 50 141 53 49 140 37 06 139 45 56 139 38 36 h. m. h. TO. ft. ft. Cape Melville: NE. extreme Flinders Island : N. extreme of N. island . Claremont Point: Extreme Cape Sidmouth : Extreme 9 00 2 47 9.6 5.8 Cape Direction : NE. extreme Cape Grenville: Extreme _ Sir Charles Hardy Island: N. extreme of SE. isle Bird Island: NW. isle Hannibal Isles: E. isle Cape York : Sextant Rock 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 11 10 5 00 9.0 6.9 Leven River: W. entrance head Emu Bay : Blackman Pt Hunter Island: N. pt Cape Grim: Outer Doughboy Islet Albatross Islet: N. pt Arthur River: Entrance Pieman River: Rocks close to entrance. Macquarie Harbor: Entrance Islet Cape Sorrell : Light-house 7 20 1 07 2.7 2.1 Port Davey: Pollard Head Southwest Cape: Extreme pt Mewstone Rock: Center Cape Bruny : 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 ZEALAND. Three Kings Islands: NE. extreme of NE. island 34 06 20 34 25 07 34 31 00 35 00 20 35 01 44 35 17 00 172 08 49 173 03 34 173 00 54 173 32 39 173 45 48 174 06 06 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 ZEALAND— 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 White Island: Summit, 863 ft Cape Runaway : Extreme East Cape: Islet, 420 ft Tolaga Bay : Matu-heka Islet Mahia Peninsula: S. extreme of Port- land I Ahuriri Harbor: 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 Moly neux 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 Lat. S. Port William: Howell's House Paterson Inlet: Glory Cove Port Adventure: White Beach, S. end. Port Pegasus: Cove abreast Anchor- agel Codfish Island : N W. extreme Snares Islands: SW. islet. 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 49 166 27 44 Lun. Int. H. W. h. TO. 7 15 7 05 7 20 7 05 7 05 8 10 8 00 6 05 4 40 4 52 9 40 9 15 9 10 9 08 9 05 9 00 8 40 4 45 3 45 3 31 1 05 "ii'io 10 10 10 20 9 55 9 45 6 00 1 00 11 45 L.W. h. TO. 1 05 55 1 10 55 55 2 00 1 50 12 15 10 50 10 54 3 30 3 05 3 00 2 55 2 50 2 50 2 30 11 00 10 00 9 39 7 15 "b'ob 4 00 4 10 3 45 3 35 12 15 9 15 5 40 Range. Spg. Neap. Jt. 6.5 6.7 10.8 10.7 6.1 6.6 3.5 5.7 3.6 6.3 11.6 11.9 12.3 12.6 10.0 9.2 7.5 7.4 5,6 7.8 9.5 12.0 11.6 7.6 7.8 7.9 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 6.2 6.2 Page 264] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. THE ARCTIC REGIONS. Place. Cape Walsingham : Extreme Mile Island: N. pt Marble Island: E. end Cape Kendall : Extreme Iglooik Island: E. pt Victoria Harbor: N. shore Elizabeth Harbor: Entrance Magnetic Pole, 1831 Port Neill : N. pt. of entrance Port Bowen: N. cove Battv 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 (a) 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. Long. W. Lun. Int. Range. H.W. L.W. Spg. Neap. / H 66 00 00 O t II 69 28 00 77 50 00 91 06 00 87 15 00 81 31 00 91 30 33 92 10 56 96 47 00 89 00 54 88 54 48 91 08 00 90 12 00 73 10 00 64 45 00 61 18 00 63 38 00 64 45 00 70 20 00 110 48 15 179 57 00 Long. E. 150 30 00 104 01 00 59 10 00 53 01 50 65 40 00 58 45 00 44 17 00 42 30 00 40 33 30 36 51 30 38 08 30 35 37 00 39 48 54 20 00 00 17 23 00 11 40 30 11 07 00 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 53 40 18 53 23 00 52 54 00 51 45 48 51 10 48 50 43 36 48 57 00 50 20 48 49 44 00 48 51 00 48 26 00 48 30 42 48 10 30 47 52 00 47 46 48 h. TO. h. m. ft. ft. 64 04 00 62 33 00 63 42 00 4 00 10 15 12.0 5.1 69 21 00 70 09 17 6 50 40 8.0 4.2 70 38 14 70 05 00 73 09 13 73 13 39 ! 73 13 00 i 73 50 05 76 49 00 11 38 . 5 29 5.5 2.9 81 04 40 82 27 00 82 40 00 10 35 4 20 2.6 1.0 82 54 00 83 07 00 1 74 47 10 68 55 00 1 20 7 40 3.8 1.9 75 10 00 77 41 00 70 25 00 70 55 00 76 58 00 10 00 3 50 7.0 4.0 79 55 00 65 50 18 66 45 50 64 32 06 65 12 17 63 53 36 65 07 00 7 18 5 05 9 02 2 00 11 30 3 10 2.2 3.8 9.1 1.3 2.1 5.2 68 08 51 74 30 00 9 05 2 55 13.9 7.8 76 35 00 79 50 00 79 42 00 81 38 00 75 55 00 14 12 14 6 25 5 58 5.3 5.4 3.0 2.0 72 47 48 72 20 42 10 50 4 38 8.0 3.0 70 40 00 69 14 04 69 13 12 69 07 30 68 49 06 68 42 30 68 58 30 66 55 54 65 48 42 8 05 6 20 1 52 07 7.5 10.0 3.6 4.8 65 24 30 64 10 36 63 29 12 6 40 27 12.5 6.0 63 05 12 62 50 00 62 42 36 61 59 36 61 28 20 6 12 00 9.0 3.6 61 10 24 61 09 42 6 15 03 12.0 4.8 61 12 12 60 47 30 60 48 36 aCape Morris Jesup (the most northern known land), 83° 39' N., 30° 40' W. (approx.). APPENDIX IV. [Page 265 MARITIME POSITIONS AND TIDAL DATA. THE ARCTIC REGIONS— Continued. 1 Place. Lat. N. Long. W. Lun. Int. Range. 1 H. W. L. W. Spg. Neap. •0 d « 2 « « « u M Julianshaab: Village O 1 II 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 66 22 45 66 32 40 66 33 42 66 07 30 66 27 29 66 26 30 65 30 15 64 48 04 64 08 40 64 04 09 63 48 06 63 48 19 64 35 42 64 55 27 65 16 14 65 45 00 / // 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 h. m. 4 56 5 33 2 55 4 00 h. m. 11 09 11 46 9 10 10 13 ft. 7.0 8,6 9.4 7.5 ft. ' 2.8 3.4 3.8 3.0 Neunortalik: Village Frederiksthal : Village Cape Farewell : Staten Huk Aleuk Islands : Center Cape Tordenskjold: Extreme Cape Bille: Extreme Cape Juul: Extreme Cape Lowenorn : Extreme Dannesbrog Island: Beacon Ingolsfjeld Rignv Mount: Summit Pendulum Islands 11 05 11 10 4 53 4 58 6.7 3.7 3.9 2.1 Cape Philipp Broke Cape Bismark : Extreme Jan Mayen Island: Mt. Beerenberg, 6,870 ft Youngs Fore- land, or Cape Northeast Mary Muss Bay. . Lianganaes Point. 11 21 5 06 3.8 2.2 Rissnaes Point . ... Grimsey Norddranger: Tr. Station Skagataas Point . North Cape : Kalf atindr Straumness Point Fugle or Staabierg Huk : Point Snaef ells Yokul : Tr. Station Reykiavik: Observatory 5 10 11 25 14.5 8.4 Ingolfshofde • Tr Station Papey Island* Tr. Station Reythur Fjeld" Tr Station ' Page 266] INDEX TO APPENDIX IV. Page. Admiralty Islands 255 Adriatic Sea 226-228 Africa, east coast 232, 233 nort;h coast 230 west coast 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 Ceylon 237 Chile 209-212 China 240-242, 247 Sea 240 Entrance 240 Cochin China 240 Colombia, north coast . 198, 206 west coast 213 Connecticut 194 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 EUice Islands 254 Europe, Atlantic coast. 215-225 Falkland Islands 214 Fiji Islands 256, 257 Florida 195,196 Formosa Island 242 France, north and west coasts 223,224 France, south coast 225, 226 Galapagos Islands 250, 251 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 IMagdalen Islands 192 Maine 193 Malaysia 238,239 Maldi ve 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 PhiHppine Islands 245-247 Phojnix 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 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 Aboukir Bay 230 Abreojos Point 201 Abrolhos Island 207 Absecon Inlet 195 Acajutla 202 Acapulco 202 Accra 231 Acheen Head 239 Aconcagua Mountain 21 1 Acre 230 Adakh Island 199 Adalia 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 ^ina 229 Aero Island 222 ^rstenen 218 Africa Rock 226 Agalegas Island 235 Agdenes 218 Agiabampo 202 Agrigan Island 252 AguadillaBay 205 Aguja Point 212 Agulhas.Cape 232 Agutaya Islet 245 Aheu Island 258 Ahunui Island 257 Ahuriri 263 AiSima 249 Aian 250 Aignan, St., Island 255 Aigues Mortes 226 Ailinginae Islands 251 Ail lick Harbor 191 Ailly Point 223 Ailuk Islands 251 KBGiONS AND COASTS — Continued. Page. Tasmania 262 Texas 196 Tonga Islands 258 Trinidad 206 Tuamotu Archipelago. . 257, 258 Tunis 230 Turkey 228,229,230 Uruguay 208 PLACES. 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 Alargate Reef 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 Alcobaga 207 Aldabra Island 235 Alden 218 Alderney Harbor 218 Alegranza Island 214 Alegre, Porto 207 Alert's Winter Quarters . . . 264 Alessandro, San, Island ... 253 Aleuk Islands 265 Alexander, Port 232 Vancouver 200 Alexandretta 230 Alexandria 230 Alfaques, Port 225 Alfred, Port 232 Algeciras 225 Algier 230 Ali-Agha, Port 230 Alicante 225 Alijos Rocks 201 Alipee 237 Alligator Island . 241 Reef 196 Almadie Point 231 Almeria 225 Alphonse Island 235 Alta Vela 204 Altata 202 Altea 225 Altona 222 Alvarado 196 Amager Island 222 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 268] INDEX TO APPENDIX IV. Page. Antareh, Ras 233 Antibes 226 Anticosti Island 192 Antigua 205 Antipodes Island 259 Antivari 228 Antofagasta 211 Antonina 208 Antonio, Port 204 San, Cape, Ai^entina . 208 Cuba 204 Mt. and Island... 214 Port, Argentina.. 209 Chile.. 211 Sierra 209 Antwerp 223 Aoga Shima 249 Aor, Pulo 240 Aotea 263 Apaiang Island 251 Apalachicola 196 Apamama 251 Aparri . J 245 Apenrade 221 Apo Islet 245 Apostle Rocks 209 Arago Cape 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. California .... 201 Arenas Cay 197 Arendal Inlet 219 Arentes Island 243 Argentina 208 ArgostoH, Port 228 Arica 212 Arichat Harbor 193 Arkona 221 Armeghon 238 Arnheim, Cape 259 Amo Atoll 251 Arorai Island 251 Arran Island 217 Arrowsmith Islands 251 Arm 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 Athens 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 Bagamoyo 233 Bahaltolis 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 Baliibac Island 245 BalaklavaBay 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 221 Ballycottin 218 Balstrum 222 Balta Island 216 Baltic Port 220 Baltimore 195 Bampton Island 255 Banda Island 244 Banderburum .' 236 Bandjermasin 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. . . 251 Point 198 Bartholomew, St 205 Cape 209 Bartolom^, San 201 Barton, Port 245 Bani, Point 239 Barung Island 243 Bas, De, Island 224 Basdorf 221 Basianang Bay 246 Bdsidiih 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 Batoum 229 Batticaloa 237 Battle Islands 191 Batty Bay 264 BatveToetong 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 Beachy Head 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 BecduRaz 224 Beda'a,Al 236 Bedford, Cape 261 Bees, St 215 Beeves Rocks 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 Bermeja Head 209 Bermudas 214 BernalChico 196 Bernardo Islands 257 Berwick 216 Besuki 243 Betrapar Islet 234 Beverly 194 Beyt 237 Bhaunagar 237 Blanche Point 227 Biarritz 224 Bickerton Island 259 Bideford 215 Bidstone 215 Bierneborg 220 Bigar Islet 251 Bikini Islands 251 Bilbao 224 Bille,Cape 265 Billiton Island 239 Bindloe Island 250 Bintang Hill 238 Bintoean 239 Bird Island, Australia 262 Bahamas 203 Banda Sea 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 BlighsCape 236 BlimbingBay 239 Blinyu 239 Block Island 194 Bloody Foreland 217 Bluefields 198 Bluff Harbor 263 Boar Islands 191 Boavista Island 214 Page. BobaraRock 228 Bodie Island 195 Bogense 222 Bogsher 220 Bohol Island.... 246 Bojador, Cape 231 Bojeador, Cape 245 Bola-Bola Island 257 Bom 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 Bon ham Islands 251 Bonifacio 226 Bonin Islands 253 Boobjerg 223 Booby Island, Leeward Is. . 205 Queensland 262 Boompjeo Island 243 Boon Island 193 Borda, Cape 260 Bordeaux 224 Bordelaise Island 252 BorjaBay 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 Bou vets Island 215 Bovliluyan, Cape 245 Bowditch Islet 254 Bowen, Port, Australia 261 BaffinsBay 264 Bowling Green, Cape 261 Boyanna Bay 235 BradoreBay 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 BrillReef 243 Brindisi 227 Brisbane 261 Page 270] INDEX TO APPENDIX IV. Page. Bristol, England 215 Khode Island 194 Britannia Island 259 Broadhaven 217 Broken Bay 261 Bronnosund 218 Brothers Island, Red Sea . . 233 Islets, China 241 Broughton Bay 244 Head 248 Island....- 249 Rock 249 Brunet Island 191 BruniRiver 242 Brunswick, Georgia 1 95 Maine 193 Bruny, Cape 262 Island 262 Brussels 223 Brusterort 221 Bryer Island 193 Bubuan 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 Cabrutlslet 234 Cadaques 225 Cadiz 225 Cadmus Island 257 Caen 223 Cagayan Jolo Island 247 Cagayanes Islands 247 Cagliari 226 Caigara 207 Caicos Island 203 West, Cay 203 PLACES — continued . Pftge. Calaan, Point 246 Calais, France 223 Maine 193 Calavite, Monte 245 Calayan 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 Camamu 207 Camaron Cape 198 Camasusu Island 246 Cambay l 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 Carlingford Lough 217 Carlobago 227 Carlos, San, de Ancud 211 Point 201 Carmen Island 197 Caroline Islands, N. Pacific . 252 S.Pacific 253 Carousel Island 192 Carreta Mountain 212 Point 198 Carreto, Port 206 Carrizal, 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 Castlehaven 216 Castro 210 Urdiales 224 Cat Island 196 Catalina Harbor 191 Sta., Island 201 Catania 227 Catastrophe, Cape 260 Catbalogan 246 Catharine Point 209 St 215 Island 208 Cato Island 255 Catoche Cape 197 Cattaro 228 Cautanduanco Islands 246 Cavite 245 Caxones 198 Cayenne 207 Cayeux 223 Caymans 204 Cazza Island 228 Ceard 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 Chacachac^re Island 206 Chacopata 206 ChagosArch 234 Chagres 206 ChahbarBay 237 Chala Point 212 ChaleurBay 1 192 Challenger, Cape 236 ChamaBay 231 INDEX TO APPENDIX IV. [Page 271 Page. Cham-Callao Island 240 Cham^, Point 213 Chamisso Island 198 Champerico 202 Chanaral Bay , 211 Island 211 Chandeleur Islands ., 196 Chao Islet 212 Chapellsland 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 Chitlac Islet 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 Churruca, Port 210 Chusan Islands 241 PLACES — continued . Page. Claris Island 202 Cica. Mount 228 Cienfuegos 204 Ciotat 226 Cispata, Port 206 CittaNuova 227 Civita Vecchia 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 L 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 Confites Cay 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 Cornwallis Islands 253 Port 238 Coro, Velade 206 Coromandel Harbor 263 Coronation Island 215 Corregidor Island 245 Corrientes, Cape, Argentina . 208 Colombia 213 Mexico 202 S.Africa 232 Corsarios Bay 206 CorseuUes, Port 223 Corso, Cape 226 Mountain 210 Corti 226 Coruna 225 Corvo Island 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 Bay 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. Pagfe. Crooked Island 203 Crozet Islands 236 Cruz Cape 204 Sta., Brazil 207 California 201 Island 201 Islands, Philip- pines 247 S. Pacific ... 255 Leeward Islands . 205 Luzon 245 Port 209 Cuad Basang Island 247 Cuba 203,204 Culebra 202 Culebrita Island 205 Culion Island 245 Cullera, Cape 225 Culver Point 260 Cumana 206 Cumberland Island 261 Cumshewa Harbor 199 Cupchi Point 241 Cupica Bay 213 Curasao Island 206 Little 206 Currimao 245 Currituck Beach 195 Curtis Island 258 Port 261 Curzola Island 228 Cutty hunk Light 194 Cuvier, Cape 260 Island 263 Cuxhaven 222 Cuyo Island 245 Cyprus 230 Dsedalus Shoal 233 Dago Island 220 Dakar, Port 231 Dalcahue 211 Dale Point 259 Dalrymple Harbor 247 Port 262 Dalupiri Island 245 Damghot 236 Damma 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, St. , Island 214 DeKastri 250 De Peysters Island 254 Deadman Rock 192 PLACES — continued. Page. Deception Island 215 Deimaniyeh 236 Delagoa Bay 232 Delgada Point 209 Delgado,Cape 233 Point 209 Demerara 207 Denia 225 Deni8,St 235 Denison, Port 261 D' En trecasteaux Islands 2.55 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 DimasalasaUj Port 246 Dinding Channel 238 Dingle Bay 216 Diomede Island 198 Direction, Cape 262 — — Island 240 Disappointment, Cape, Sib. 250 — Washington 200 Discovery Harbor 264 Diseilsland 233 DiuHead 237 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 21 7 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 Drummond Island 251 Dublin 217 Ducie Island 257 Page. Duff Islands 255 Duke of Clarence Island . . . 254 York I., N. Britain. 254 S.Pac... 254 DulceGulf 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 Cape 199 Edenton 195 Edinburgh 216 Eeragh Island 217 Egedesmunde 264 Eggegrund Islet 219 Egmont Mountain 263 Port 214 Eimeo Island 257 Ekholm Islet 220 Elba Island 226 Elbing 221 Elena, St., Port 209 Sta., Point 213 Elephant Bay. 232 Eleuthera Island 203 Elias, St. , Mount 199 Elizabeth Bay 232 Cape 193 City. 195 Harbor 264 Island, Chile 210 TuamotuArch 257, 258 Port 232 INDEX TO APPENDIX IV. [Page 273 I'age. Elizabeth Reef 259 Ellice Islands 254 p:mdeii 222 P^mma, Great, Island 203 Emu Bay 262 Enanger 219 E^ndelave Island 222 Enderbury Island 254 Enderby Island 260 Endermo 249 Enfant Perdu Island 207 Engano, Cape 245 Engano Island 239 Engelholm 219 English Cay 197 Eniwetok Islands 251 Enrage Cape 193 Ensenada 201 Entry Island 192 Erromango Island 256 Erronan Island 256 Escarceo Point 245 Escarseo Point 206 Eschholtz Islands 251 Escudo de Veragua 198 Escumenac Point 192 Esdu Island 234 Esmeralda Islet 206 River 213 Espada Point, Colombia 206 Hayti 204 Espenberg, Cape 198 Esperanza Inlet 199 Espiritu Santo Bay 207 Cape 209 Esquimalt 200 Essington, Port 259 Estaca Point 224 Estangues Point 206 Estevan Point 199 Etches, Port 199 EtenHead 212 Eu,Pulo 240 Eureka 200 Euripo Strait 229 Europa Island 235 Eustatius, St 205 Evangelistas Island 210 Evaristo, San 201 Expedition Bay 250 Faero Islands 213 Fair Isle Skroo 216 Fairy, Port 260 Faiu, W., Islet 252 Fakaof u Islet 254 Fakarana Island 258 Falkenberg 219 Falkland Islands 214 Falmouth, England 215 — — Jamaica 204 False Cape Horn 209 Point 238 Falster Island 222 Falsterbo 219 Famagusta 230 Famine, Port 210 Fanad Point 217 Fanning Island 251 Fano Island, Adriatic 228 Denmark 223 6583—06 IS PLACES — continued . Page. Farallon Islet 200 Faraulep Island 252 Farewell, Cape, Greenland. 265 New Zealand 263 Farina, Cape 230 Farisan Island 234 Earn Island 216 Faro Island, Sweden 219 of Messina 226 Farquhar Islands 235 Farrall Rock 198 Farralon de Pajaros 252 Fartak, Ras 236 Fastnet Rock 216 Father Point 192 Fatsizio Island 249 Fatu Hiva Island 253 Huku Island, Galapagos 251 Marquesas . . 253 Fatuna Island 257 Fayal Channel 213 Island 213 Fecamp 223 Felipe, San, Cavs 204 — Point' 202 FeUx, St., Island, Chile ... 211 S. Pacific ... 258 Fenerive Point 235 Fermin Point 201 Fernandina 195 Fernando Noronha 214 Po Island 231 San, River 196 Port 245 Trinidad 206 Ferolle Point 192 Ferro Island 214 Ferrol 225 Fetouhouhou Island 253 Feys Island 252 Fidonisi Island 229 Figari Cape 226 Filzand Island 220 Finisterre, Cape 225 Firase Rocks 248 Fire Island 194 Firmin, San 202 Fischausen 221 Fish, Great, Bay 232 Little, Bay 232 Fiskernaes 264 Fitz Roy River 260 Fiume 227 Five Fathom Bank 195 Flamborough 216 Flamenco 211 Island 213 Flat Island 234 Flattery, Cape 200 Flensberg 221 Flesko, Cape 242 Flinders Island 262 Islands 261 River 1. 262 Flint Island 253 Florence 226 Flores Island, Azores 213 Indian Arch 243 Uruguay 208 Florida Island 254 FlowerCove 192 Page. Flushing 223 Fly River 255 Foerder Islet 219 Fogo Island 214 Fohr 222 Foreland, North 215 South 215 Form igas Islands .' 213 Shoal 204 Formosa Island 242 Fornses 223 Forsmark 219 Forsyth Point 199 Forth Mountain 217 Fortune Island 203 Foulwind, Cape 263 Four, Le, Rock 224 Fowey Rocks 195 Fowler Point 260 Francis Island 251 St., Cape, C. Colony. . . 232 Newf'dl'd . . 191 Francisco, San 200 Cape 213 Head 212 River 207 Sao 208 Frankland Island 261 Franklin Harbor 260 Franz Josef Land 264 Eraser River 200 Frayle Rock 204 Fravles Point 212 Frederick, Port 262 Frederik Hendrik, Cape. . . 262 Frederikshaab 264 Frederiksthal 265 Frederiksvaern 219 Fredriksten 219 FreelsCape 191 Frehel, Cape 224 Freikallen 218 Fremantle 260 French Cay 203 Frigate Shoal 253 Freycinet, De, Islets 259 Peninsula 262 Frio, Cape, Brazil 208 W.Africa 232 Port 208 Froward Cape 210 Fruholm 218 Frying Pan Shoals 195 Fuenterrabia 224 Fuerta Ventura Island 214 Fuerte Island 206 Fuga Island 245 Fugle Huk 265 Fulanga Island 257 Fulehuk 219 Funafuti Island 254 Funk Island 191 Funkenhagen 221 Furen Islet 218 Fushiki 249 Futuna Island 256 GaalongBay 240 Gabo Island 261 Gabriel Mountain 216 Gaeta 226 Page 274] INDEX TO APPENDIX IV. Page. Gafor Island 234 Galapagos Islands 250, 251 Galera Point, Ecuador 213 Trinidad 206 Galgenberg 222 GaliolaRock 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, Mull of 215 Galveston 196 Galway 217 Gambier Island 257 Gauge 220 Gannet, Outer, Island 191 Rock 193 Gap Rock 241 Garcia d' A Vila 207 Gardiner Island 253 Gardners I., Long 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 George, Fort, Cay 203 St., Cape, Florida 196 Newf'dl'd . . 192 Nova Scotia. 193 Island, Alaska . . . 199 Azores 213 Georges Island 202 St., Cay 197 Georgetown 195 Georgia, South, Island 214 Geronimo, San, Island 201 Geyser Reef 235 Gharib, Ras 233 Ghir,Cape 231 Gibdo Island 246 Gibraltar 225 Giglio Island 226 Gijon 224 Gilbert Islands 251 Gillolo Island 244 Ginger Cay 203 Girgenti 227 Gizau 234 Gizo Island 254 Glaa Island .• 216 Glasgow 216 Glashedy Island 217 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 GolamHead 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 Gorontalo 242 Goto Island 248 Gottenburg 219 Gottland Island 219 Gough Island 214 Gozier Islet 205 Gozo Island 227 Gracias d 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 Great Bird Rock 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 Griefswalder Oie 221 Grim, Cape 262 Grimsey Norddranger 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 (juanica 205 Guantanamo 204 Guarapiri Islets 207 Guaratiba Cape 208 Guardaf ui. 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 GwatarBay 237 Habana . .• 204 Habibas Island 230 Hacha, Rio de la 206 Haddington, Port 244 Haediclsland 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-yun-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 276 Page. Hanalei 253 HanfelahBay 233 Hangklip, Cape 232 Hannibal Isles 262 Hano Island 219 Ha-Noi 240 Hao Island 258 Haradsskar Islet 21 9 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 Haujam Islet 237 Haustholm 223 Haute Island 193 Havre 223 Capele 193 Hawaii 253 Hay ter Island 255 Heard Island 236 Hearts Content 191 Heau de Brehat 224 Heawandu Island 234 Hecate Bay 199 Cove 200 Hecla, Cape 264 Hed, Easal 236 Hee-tah-doo Island 234 Hegad is 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 HelvickHead 218 Henderson Island 257 Henderville Island 251 Henlopen Cape 195 Henry 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 Hesselo Island 222 Hessenstein 221 Hestskjaer 218 Heve, Capela 223 Hiaou Island 253 Hikueru Island 258 Hillswickness 216 Hilo 253 Himmittee Island 234 Hindwar 237 PLACES — continued. Page. Hiogo 248 HiradoNoSeto 248 Hirtshals 223 Hiva-Oa Island 253 Hjelm Islet 223 Hjertholm 218 Hjoerringa Mountain 218 Hoa-pin-su Island 244 Hobart Town 262 HodeidahRoad 234 Hog Island, Indian Ocean. . 235 Virginia.! 195 Islands 197 Hogland Island 220 Hogolu Islands 252 HogstyReef 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 Holyhead 215 Hon Dau Island 240 HondeklipBay 232 Honfleur 223 Hongkong 241 Hon-M^ 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 Howaiyuh 236 Howe, Cape, East 261 West 260 Lord, Island 257, 259 Islands 254 Sound 200 Howland Islands 251 Howth Peninsula 217 Huafo Island 210 H uaheine Island 257 Huanchaco Point 212 Huarmey 212 Huasco 211 Hudiksvalls 220 Huelva 225 Hiigeber^ 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 Hunterlsland, 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 262 Iglooik Island 264 Ignacio, San, Point 201 Iguape 208 IkiSima 248 Ildefonso Islands 209 Ilha Grande 208 Ilheos 207 Ilo 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 InishrahuU 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 IslaGrande 202 Island Harbor 199 Islav 212 Isle'of Man 215 Isola 227 Isolette, Cape 236 Istria, Cape d' 227 Page 276] INDEX TO APPENDIX IV. Page. Itacolomi Islet 208 Point 207 Itapacaroya Point 208 Itaparica 207 Itapemirim 207 Iturup Island 249 Ivigtuk 264 Iwo Shima 248 Iwo-sima 244 Jabwat Island 251 Jackson, Port 261 Jacksonville 195 Jacmel 204 Jacobshavn 264 Jaffa, Cape 260 Jago, St., Island 214 Jaguaribe Kiver 207 Jaluit Island 251 Jamaica 204 James Island 251 St., Cape, C. China... 240 Vancouver 1 . 199 Jan Mayen Island 265 JaraHead 211 Jarea 225 Jarvis Island 254 JashakBay 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 Bay 261 Cape 260 Island 251 Jesus Maria Island 255 Jibara 203 Jiddah 234 Jighinsk Island 264 Joao, San, da Barra 207 Johanna Island 235 John, St., Cape, Newf'dl'd. 191 Staten Island 209 Island 205 Johns, St., Island, Red Sea. 233 N. Brunswick ... 193 Newfoundland. . . 191 River. 195 Johnston Islands 253 Jolo Islands 247 Jomfruland 219 Jona, St., Island 250 Jos6, San, California 200 de Guatemala 202 delCabo 201 Port 209 Joseph 1 len ry , Cape 264 Juan P'ernandez Island 258 San 205 Cape 205 delSur 202 Point 197 Port, Peru 212 Vancouver I. 200 St., Bay 206 Juanico, San, Point 201 PLACES — continued . Page. Juby, 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 KabendaBav 232 Kabuli Island 245 KadoSima 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 Kaske 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 Keituin 222 Kelung 242 Kendall, Cape 264 Kent Island 261 Keppel Island 257 Kennadec Islands 258 Kertch 229 Ketoy Island 249 Page. Key West 196 Kharig Islet 236 Kharim-Kotan Island 249 Khaur Fakan Bay 236 Kheli 229 KhorNohud 234 Nowarat 233 Ki Islands 244 Kiama Harbor 261 Kidnappers Cape 263 Kiefali, Cape 228 Kiel 221 Kikai-jima ' 244 KilMney 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 Kinkwosan 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 200 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 218 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 2.38 Kroe 239 Kronberg 222 Kronstadt 220 INDEX TO APPENDIX IV. [Page 277 Page. Krusenstern Cape 198 KubKalat 237 Kuchino Shima 248 Kuchinotsu 248 Kuino 220 Kullen Point 219 Kumi Island 244 Kumpta 237 Kunashir Island 249 Kundapur 237 Kunfidah 234 Kuper Harbor 248 Port 199 Kuria Maria Islands 236 KuroSima 248 KusakakiJima 248 Kusrovie Rock 240 Kusterjeh 229 Kutpur 237 Kuweit 236 Kweshan Islands 241 Kyangle Islets 252 Kyauchau Bay 247 Kyuquot Sound 199 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 LampongBay 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 I^ngwarden 222 Lanzarote Island 214 Laruehuapi Cove 21 1 Lassa, Cape 242 Lassau 221 Latakiyah 230 Latouche Tr^ville, 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^preau Cape 193 Lerma 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 Leyte 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 Lisiansky Island 253 Lissa Island 228 List 221 Lister 218 Lith 234 Litkieh Island 251 Little Hope Island 193 LituyaBay 199 Liverpool 215 Port 235 River 259 Livorno 226 Lizard Point 215 Llico 211 Loa River 212 Page. Loango Bay 232 Lobito Point 232 Lobos Cay, Bahamas 203 Mexico 196 de Afuera Island 212 Tierra 212 Island, Canaries 214 Uruguay 208 Point, N. Chile 212 S.Chile 212 Lodingen 218 Lofoten Island 218 Loggerhead Key 196 Loheiyah 234 Loma Point 201 Lomas Point 212 Lombata Island 243 Lombok Island 243 London, East 232 Ix)ndonderry 217 Cape 259 Long Island, Bahamas 203 ■= United States 194 Loo Choo Islands 244 Look6, Port 235 Lookout Cape, N. Carolina. 195 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 LotsWifeRock 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 Island 239 Lucipari Islands 243 Lucrecia Point 203 Lucrietta Island 227 Liiis, San, Island 202 Luk6 Point 250 Lundy Island 215 Lunenburg 193 Lungo 220 Lupona Point 201 Page 278] INDEX TO APPENDIX IV. Page. LurioBay 233 Luasin Piccolo 227 Luzon Island 245, 246 Lyo Island 222 Maasin 246 Macah6 207 Macao 241 MacAskill Islands 262 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 Mahe 237 Mahia Peninsula 263 Mahon, Port 226 Maiana Island 251 Maiden Rocks 217 Mairaira Point 245 M^it Island 233 Maitea Island 257 Maitencillo Cove 211 Majamba Bay 235 Majorca 226 Majunga 235 Majuro Islands 251 MakallehBay 236 Makarska 228 Makatea Island 258 Makaua Island 233 Makemo Island 258 Makers Ledge, South 192 Makkian Island 244 Makongai Island 256 Makrv 229 Mala Point 203 Malabrigo Bay 212 Malacca 238 Malaga 225 Malaita Island 254 Malamocco 227 Malaepina, Port 209 PLACES — continued. Page. Maiden Island 254 Maldonado, Mexico 202 Uruguay 208 Male Island 234 MalembaBay 232 Malin Head 217 Mallicollo Island 256 Malmo 219 Malo, St 224 Maloclab Islands 251 Maloren 220 Malpelo Island, Galapagos. 250 Panama 203 Malta 227 Mamuka 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 MantaBay 213 Manua Island 257 Manukau Harbor 263 Manvers, Port 191 Manzanilla Bay 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 MargaretBay 193 Margate Head 232 Maria Island 257 Madre Island 202 Port 204 Sta. , Cape, Portugal 225 Uruguay ... 208 Cove 201 di Leuca, Cape. . . 227 Island, Azores... 213 Chile 211 S. Pacific ... 256 Port 247 Mariana Islands 252 Maricas Islands 208 Marie Galante 205 Page. Marienleuchte 221 Mariguana Island 203 Marinduque Island 246 Marion Island 236 Maripipi Island 246 Maritimo Island 227 Marjes Islets 206 Marjoribanks 247 Marks, St 196 Marlborough Island 251 Marmora Island 230 Marmorice 229 MaroReef 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 Marzo Cape 213 Mas-af uera Island 258 Masbate 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 255 Maternillos Point 204 Matinicus Rock 193 Matoya 249 Matthew Island 256 St., Island, Alaska 198 Burma 238 Siberia 250 Matthias, St., Island 255 Matu Sima 250 Matuku Island 256 MaugerCay 197 Maui Island 253 Mauki Island 258 Maunganui Harbor 262 INDEX TO APPENDIX IV. [Page 279 Page. 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 Mazemba River 232 Mbega Island 256 MchingaBay 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 MellishReef 255 Melmore Head 217 Melo, Port 209 Melville, Cape, Baldbac I.. 245 Queensland 262 Island, Australia 259 Barrows Strait. . . 264 Tuamotu Arch... 258 Memel 221 Memory Rock 203 Menali Island 238 Menchikof Cape 199 Mendocino Cape 200 Mendoza Island 241 Merbat 236 Mercy Harbor 210 Mergui 238 Mesa de Dona Maria 212 Messina 227 Mesurado, Cape 231 Meurka 233 Mew Islands 217 MewstoneRock 262 Mexican Boundary 201 Mexico, City of 196 MexillonBay 212 Mexillones Mountain 212 Mezen 264 Mugan Mwania 233 Miautao Island 247 Michael, St. , Fort 198 Island 213 Michaeloff Island 257 Middleton Island 199 Midway Islands 253 Miguel, San, Island 201 Islands 247 MikakeJima 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 Mindoro Island 245 Mine Head 218 Minerva Reefs 258 Minikoi Island 234 MinoSima 249 Minorca 226 Minots Ledge 194 Minow 235 MinsenerSand 222 Mintok 239 MiramichiBay 192 Misamis 247 Miscou Island 192 Mississippi River, mouth . . 196 City 196 Misteriosa Bank 197 MitaPoint 202 Mitchells Island 254 Mitho 240 Mitiero Island 258 Mitre Island 256 Mityleni Island 229 MizenHill 216 MoaCavo, Port 203 Island 244 Moalalsland 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 212 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 Montebello 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 MorecambeBay 215 Moreno Mountain 212 Moresby, Port 255 Moreton, Cape 261 Morgan, Cape 232 Morjovetz Island 264 Morlaix 224 Morotiri Islands 258 Morro Ayuca 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 Moudroa 229 Moukon rushi Island 249 Moulmein 238 River 238 Mount, Cape 231 Mourondava 235 Moville 217 Mozambique 233 Msimbati 233 Mugeres Island 197 Muilcalpue Cove 211 Mukulaelae Island 254 Muleje 201 Mulu Island 244 Mura Harbor 248 MuratHill 233 Murderers Bay 235 Murdock Point 262 Murundum Island 240 Mururoa Island 257 Muscat 236 Musendum, Ras 236 Mussel Bay 210 Mysole Island 244 Nachvack Bay 191 Nafa-Kiang 244 Nagai Island 199 Nagasaki 248 Naian Island 256 Nain 191 Nairn Cay 203 Naitamba Island 256 NakanoShima 248 Page 280] INDEX TO APPENDIX IV. Page. Nakkehooed 222 Nam-Dinh 240 Namki, Port 241 Namoluk Islands 252 Namonuito Islands 252 Nam-quan 241 Namu Island 251 Nanaimo 200 Nancowry Harbor 239 Nanka Island 239 Nanomea Island 254 Nanoose Harbor 200 Nantes 224 Nantucket Island 194 S.Shoal 194 Naples 226 Napuka Island 258 Nar Foree Island 234 Naranjo, Port 203 Narendri Bay 235 Nargen Island 220 Narva 220 Nasca Point 212 Nasparti Inlet 199 Nassau 203 Natal, Brazil 207 Port, Africa 232 Sumatra..^ 239 Natashquan Point 192 Natuna Islands 240 Naturaliste, Cape 260 Nauomaga Island 254 Navachista 202 Navalo, Port 224 Navarin 228 Cape 250 Navassa Island 204 Navesink Highlands 195 NavidadBank 203 Bay 202 Navire Bay 236 Naxos Island 229 Nazaire, St. , Port 224 Necker Island 253 Needles Rocks 215 Negapatam 237 Negrais, Cape 238 Negro, Rio 209 Negros Island 246 Neill, Port 264 Nelson 263 Cape 260 Port 259 Nemuro 249 Neptune Isles 260 Nera Point 227 Netherland Island 254 Neunortalik 265 Neuwerk 222 Nevil Island 252 Neville, Port 200 Nevis 205 New Bank 197 Bedford 194 Britain 254 Caledonia 259 Guinea 255 Hanover 255 Haven 194 Hebrides 256 Ireland 255 PLACES — continued. Page. New London 194 Orleans 196 Plymouth 263 South Orkneys 215 Shetland 215 Westminster 200 York 194 Newbern 195 Newburyport 194 Newcastle 261 Newfoundland 191,192 Newport, Ireland 217 Rhode Island 194 Newton Head, Great 218 Ngatik Islands 252 Ngau Island 256 Nias Island 239 Nice 226 Nicholas,' St',' island" "'...'. 214 Nicholson, Port 263 Nickerie River 207 Nicobar, Great, Island 239 Islands 238, 239 Nicolas Mole 204 San, Island 201 Nidingen Islet 219 Nieuport 223 Niewe Diep 223 Nihiru Island 258 Niigata 249 Nikalao, St. , Island 229 Nikolaevsk 250 Nikolaia, St., Cape 250 Nikolo, St., Port 229 Nila Island 244 Nile River 230 Nimrod Sound 241 Nine-pin Rock 241 Ning-po 241 Nipe, Port 203 Nitendi Island 255 Niua-fu 257 Niuchwang 247 Niutao Island 254 No Sima Saki 249 Noir Island 209 Noir Moutier Island 224 Nolloth, Port 232 Nome Cape 198 Nonuti Island 251 NootkaSound 199 Nord Koster Islands 219 Norderney 222 Norfolk 195 Island 259 Norman Cape 192 Norrkopings Inlopp 219 Norrsher Islet 220 Norrtelge 219 North Cape, Arctic Amer. . 264 Brazil 207 C.Breton 1 192 Iceland 265 New Zealand 262 Norway 218 Harbor 199 Island, Vancouver 199 Volcano Islands. . 253 Lord, Island 252 Standing Creek 197 Northumberland Cape 260 Northumberland Isles 261 Northwest Cape 260 Norwalk Island 194 Noshiaf Misaki 249 Saki 249 Nosi Be 235 Nostra Senhora do Deserto. 208 Notch Cape 210 Notsuke 249 Nottingham Island 191 Noumea 259 Noun, Ca,pe 231 Nouvelle, Port 226 Nova Zembia 264 Novogorod, Port 250 Nu'evitas, Port 203 Nuevo, Port 202 Nugget Point 263 Nui Island 254 Nuistad 220 Nuka-Hivi 253 Nukufetau Island 254 Nukunau Island 251 Nuku-nono 254 Nukuor Islands 252 Nukutavake Island 257 Nukutipipi Island 257 Numba Island 233 Nunez River 231 Nunivak Island 198 Nurse Channel Cay 203 Nuyts Point 260 Ny Sukkertop 264 Nyborg 222 Nykjobing 222 Oahu 253 Oataf u Island 254 Oban 216 Obi Islands 240 Obispo Shoal 197 Obristadbroekke 218 Observatipn Island 248 Oby Major Island 244 Occasional Harbor 191 Ocean Island, N. Pacific . . . 253 S.Pacific 254 Ockseu Island 241 Ocracoke 195 Oddensby 222 Odenskholm 220 Odessa 229 Odia Islands 251 Oeno Island 257 Offer Wadham 191 Oho-sima 244 Okayama, Port 248 Okhotsk 250 Oki Islands 249 Okishi Bay 249 Okso 219 Oland Island 219 Old Fort Island 192 Point Comfort 195 Providence 198 Oleai Islands 252 Oleron Island .' 224 Olga, Port 250 Olimarao Islet 252 Olinda 207 OlipaRock. 228 INDEX TO APPENDIX IV. [Page 281 Page. Oliutorski, Cape 250 Oliven^a 207 Omapui Island 247 Omenali Island 264 Omo Island 222 Omoa 197 Omoi Saki 249 One Fathom Bank 238 Oneata, Island 256 Onega 264 Ongea Levu Island 257 Ono Islands 257 Onoatoa Islands 251 06-Sima Harbor 248 Oparo Island 258 Opobo Kiver 231 Oporto 225 Oraluk Island 252 Oran 230 Orange Cape, Brazil 207 Magellan Strait.. 209 Oranienbaum 220 Orchila Island 206 Oregrund 219 Orfordness 216 Orizaba Mountain 196 Orkney Islands 216 Ormarah 237 Ormoc 246 Ornbay Island 243 OroNoSima 248 Oropesa Cape 225 Orskar Rock 219 Oruba Island 206 Osaka 248 Osaki Bay 248 Oscarsberg 219 OscuroHead 211 Osnabrug 257 Ostend 223 Osthammar 219 Ostro Point 228 Otago Harbor 263 Otranto, Cape and Port 227 Otway, Cape 260 Port 210 Oune-Kotan Island 249 Ouro River 231 Ovalau Island 256 Owashi Bay 248 Oxford 215 Oxhoft 221 Paanopa Island 254 Pabellon de Pica 212 Pacasmayo 212 Padang 239 Tikar 242 Padaran, Cape 240 Padre, Port 203 Pagan Island 252 Pagonia, Port 228 Paimboeuf 224 Paita 212 Paix, Port 204 Pajaros Islets 211 Pak Chan River 238 Pak-Hoi 240 Pakonjidol Rock 228 Palamos Bay 225 Palanog.... 246 PLACES — continued. Paldwan Island 245 Palembang 239 Palenita 202 Palermo 226 Port 228 Pali, Cape 228 Pallas Rocks 248 Palliser, Cape 263 Palm Islancis 261 Palma Island 214 PalmasBay 208 Cape 231 Point 197 Palmerston, Cape 261 Islands 257 Palmyra Island 251 Palompon 246 Palos Bay 242 Pamaroong Island 242 Pampatar Island 206 Pan de Azucar Island . . 211 Panama 203 Panay Island 246 Pangituran 247 Panjang Island 240 PankPiahRock 241 Pantar Island 243 Papey Island 265 Paposo Road 211 Para 207 ParacaBay 212 Paraeel Islands 241 Parahiba River and Port . . 207 Paramaribo 207 Paranagua 208 Paranahiba River 207 Paraoa Island 258 Parati 208 Paredon Grande Cay 204 Parenga-renga 262 Parenzo 227 Parga 228 Parida 202 Parinas Point ...^ 212 Paris 223 Parker Cape 210 Paros Island 229 Parry Island 258 Parrys Group 253 Pasado Cape 213 Pasages, Port 224 Pascagoula, East 196 Pasni 237 Passaro, Cape 227 Pasuruan 243 Patache Point 212 Patani, Cape 240 Paternoster Rocks 219 Paterson Inlet 263 Pato Island 206 Patook River 197 Patos Island 202 Patras 228 Patrick, St. , Head 262 Patterson, Port 259 Paul, St. , de Loando 232 Island, N. Amer. 192 Tuamotu ... 257 Reunion Island . . 235 Rocks 214 Pauls, St. , Island 236 Page. Paumben Pass 237 Paxo Island 228 Paypoton Mountain 197 Paz, La 201 Pearce Point. 259 Pearl and Hermes Reef 253 Cays 198 Pedra Blanca Rock 241 Branca 238 deGalha 231 Pedro Bank 204 San 202 Point 211 Port 210 Peel 260 Island 253 Pegasus, Port 263 Pei-ho 247 Pekalongan 243 Pelado Island 212 Pelagosa Rock 228 Peloro, Cape 227 Pemba Bay 233 Pembroke Cape 214 Pena Point 206 Penang, Pulo 238 Penas Anchorage 202 Pendulum Islands 265 Penguin Islands 236 Penha Grande 231 Peniche 225 Penmarch Rocks 224 Penrhyn Island 254 Pensacola 196 Pentland Skerries 216 Percy Isles 261 Perim Island, Africa 233 India 237 Pernambuco 207 Pernau 220 Peros Banhos Islands 234 Perth 260 Peru Island 251 PerulaBay 202 Pescadores Islands, Asia, E. coast 242 N. Pacific 251 Peru 212 Point 212 Pe-shan Islands 241 Petali Island 229 Petalidi Bay 228 Peter, St., Port 224 Peterhof 220 Petersburg, St 220 Petersdorf ' 221 Petit Manan Island 193 Petite Riviere 204 Terre 205 Petropavlovsk 250 Petropolis 208 Pha-li-du Island 234 Philadelphia 195 Philip Island 252 Philipp Broke, Cape 265 Philips Point 202 Phillip, Port 260 Phillips Island 258 Phoenix Island 254 Pi 226 Piafiosa Island 226 Page 282] INDEX TO APPENDIX IV. Page. Pichidanque 21 1 Pichilinque Bay 201 Pico Island 213 Pictou Harbor 193 Piedra Blanca 247 Piedras Blancas 201 Cay, Cuba, N. coast. . . 204 S. coast 204 Point 208 Pieman River 262 Pierre, St., Newf'dl'd 191 Reunion 1 235 Rock 240 Pietro di Nembo, St. , Island . 227 Pigeon Point 200 Pih-ki-shan Island 241 Pih-quan Peak 241 Pih-seang Island 241 Pikelot Island 252 Pilier, Le, Island 224 Pililu Island 252 Pillau 221 Pillar, Cape, Chile 209 Tasmania 262 Pinaki Island 257 Pine, Cape 191 Pines, Isle of 204 Pingelasp Islands 252 Ping-fong Island 241 Ping-hai Harbor 250 Pinnacle Islet 198 Pinos Point 201 Pique Bay 250 Piraeus 229 Pirano 227 Pisagua 212 Pisang 239 Pisco 212 Pitcairn Island 257 Pitea 220 Pitong Island 238 Placentia Harbor 191 Point 197 Pladda Island 216 Plana Cay 203 PlanierRock 226 Plata, Isle 213 La 208 Port 204 Platte Island 234 Playa Colorado 202 Maria, La ^. 201 PardaCove 210 Pleasant Island 254 Plettenburg Bay 232 Plum Island 194 Plymouth, England 215 U. S 194 PoileBay 192 Pola 227 Sta.,Bay 225 Polillo Island 246 Pollard Cove 210 Polloc 246 Polusuk Island 252 Porno Rock 228 Ponafidin Island 249 Ponapi Island 252 Pond Mountain 210 Pondicherri 237 Ponga River 231 PLACES — continued. Page. Ponza Islet 226 Poolbeg 217 Popa Island 244 Popof Island 199 Porcos Grande Islet 208 Porebander 237 Porman 225 Poro musir Island 249 Poros Island 229 Port au Prince 204 of Spain 206 Royal, Jamaica 204 S. Carolina 195 Said 230 Portendik 231 Porthcurnow 215 Portland, Bay 260 Cape 262 England 215 Maine 193 Porto Bello 206 R6 227 Rico 205 Santo 213 Seguro 207 Vecchio 226 Portsmouth, England 215 U. S 194 Possession, Cape 209 Island 236 Postilion Islands 243 Povorotny i, Cape 250 Prado 207 Pratas Island 241 Premeira Islands 233 Preservation Inlet 263 Prestenizza Point 227 Prevesa 228 Pribilof Island 199 Prince Edward Island 192 Edwards Islands 236 Prince of Wales Cape 198 Island 262 Sound 191 Regent River 259 Princes Island 231 Proeste 222 Progreso 197 Promontore Point 227 Proti Passage 228 Proven 264 Providence 194 Island 251 Port 250 Psara Island 229 Pucio Point 246 Puerto Cabello 206 Santo Bay 206 Puka-puka Island 258 Puka-ruha Island 257 Pulicat 238 Pulkowa 220 Pulpito Point 201 Puna 213 Purdy Island 255 Putziger Heisternest 221 Pyramid Point 241 Pyramidal Rocks 240 Quaco, Cape 193 Quad, Cape 210 Page. Quaebo River 231 Quebec 192 Queen Charlotte Island 257 Queenstown, Ireland 218 N. Zealand 263 Quelpart Island 248 Quemada Grande Island. . . 208 Quentin, San, Port 201 Querimba Islands 233 QueuleBay 211 Quilan, Cape 210 Quilca 212 Quillimane 232 River 232 Quilon 237 Quin Hon 240 Quiniluban Islet 245 Quintero Point 211 Quita Sueno Bank 198 Quoddy Head 193 Quoin Great, Island 236 Point 232 Race, Cape 191 Island 200 Rachado, Cape 238 Radakala Islands 251 Radama Islands 235 Port 235 Ragged Island 203 Ragusa Rocks, Pettini di . . 228 Rakkin, Ras 236 Raleigh Rock, China 241 Formosa 244 Ramas, Cape 237 Rame Head 232 Ramree Island 238 Rangiroa Island 258 Rangoon 238 River 238 Ranu Cove 211 Raoul Island 258 Rapa Island 258 Raper Cape 210 Raphti, Port 229 Rarotonga Island 258 Rasa Island 253 Rathlin Island 217 O'Birne Island 217 Ratnagherry 237 Ravahere Island 258 Ravn Storo 264 Ra wean Island 243 Ray Cape 192 Raza Island, Brazil 208 C.Verde Is 214 L. California 202 Razzoli Island 226 R6 Island 224 Real River 207 Reao Island 257 Recherche Archipelago 260 Recife Cape 232 Red Islet 259 Redang, Great, Harbor 240 Redfield Rocks 249 Redonda Islet 205 Redondo Rock 250 Refuge Cove 199 Reirson Island 254 Reitoru 258 INDEX TO APPENDIX IV. [Page 283 Page. Rembang 243 Remedies Bay 202 Renard Island 255 Islands 255 Rennel Island 254 Rensher 220 Repon, Pulo 240 Resolution Island 191 Reunion Island 235 Revel 220 Rey, Isladel 213 Reyes Head 211 Point 200 Reykianaes 265 Revkiavik 265 ReVthurFjeld 265 Rhio 238 Rhodes, Port 229 Rhvnns of Islay 216 Ribnitz 221 Rich Point 192 Richmond 195 Harbor 192 River 261 Riga 220 Rigny Mount 265 Rimitara Island 258 Ringkjobin 223 Rio Grande del Norte 196 do Norte 207 Sul 208 Janeiro 208 Riofrio, Port 210 Risiri Islet.. 249 Rissnaes Point 265 Rivadeo 224 Rivadesella 224 Rivers, Cape 242 Rixhoft 221 Roa Poua Island 253 Roatan 197 Roberts Point 200 Roca, Cape 225 Partida, Mexico, E. coast 196 W. coast 202 RocasReef 214 Rochefort 224 Rochelle 224 Rockabill 217 Rockall Islet 213 Rockingham Bay 261 Rockland 193 RoddBay 261 Rodkallen 220 Rodney, Cape 255 Rodom, Cape 228 Rodriguez Island 234 Rodsher Island 220 Roeskilde 222 Rogosnizza 227 Roigen, Cape 249 Rokuren Island 248 Roma Island 243 Romain Cape 195 Roman, San, Cape 206 Romanzof Cape 198 Romanzov Islands 251 Romblon Island 246 Rome 226 Ronaldsay, North 216 PLACES — continued. Page. Roncador Cay 198 Rongerik Islands 251 Roodewal Bay 232 Roque, St., Cape 207 Roques Islands 206 Rosa, Sta. , Island 201 Rosalia, Sta. , Bay 201 Rosalind Bank 198 Rosario Island 253 Rose Island 257 Spittoint 199 Rosemary Island 260 Rosier Cape 192 Ross Island 248 Rossel Island 255 Rostock 221 Rota Island 252 Rotterdam 223 Rotti Island 243 Rottnest Island 260 Rotumah Island 256 Round Island 247 Roundhill Island 191 Rovigno 227 RoxoCape 196 Royal Island 203 Royalist, Port 245 Ruad Island 230 Riigenwalde 221 Rum Cay 203 Runaway, Cape 263 Runo Island 220 Rupertlsland 210 Rurutu Island 258 Ry vingen Island 218 Saba 205 Sabine Pass 196 Sabioncello Peninsula 228 Sablayan Point 245 Sable Cape 193 Island 193 Sacatula River 202 Sacrificios Island 196 Point 202 Saddle Group 242 Island 191 Sado Island.. 249 Safajah Island 233 Safatu Island 240 Saida 230 Saigon 240 Saintes Islands 205 Saipan Island 252 Sakai 248 Sakhalin Island 250 Sakonnet Point 194 Sal Cay 204 Island 214 Sala y Gomez 258 SaladoBay 211 Salayar Island 242 SaldanhaBay 232 Salem 194 Sali 230 SalinaCruz 202 Salinas Bay, C. America 202 L. California .... 201 Point 204 Salisbury Island 191 Salomague Island 245 Page. Salonika 229 Salovetski 264 Saltee, Great 217 Salut Islands 207 Salvador, San 203 Salvage Islands 214 Salvore Point 227 Sama, Port and Peak 203 Samana 204 Cay 203 Samanco Bay 212 Samar Island 246 Samarang 243 Sambro Islands 193 Samoan Islands 257 Samos Island 229 Sampit Bay 242 Samso Island 222 Samsoe Island 223 Sand Island 196 Key 196 Sandakhan Bay 242 Sandalo, Cape 226 Sandalwood Island 243 SandflyCay 197 Sandhammaren 219 Sandwich Island 256 Islands 214 Sandy Cape 261 Hook 195 Point 210 Sanguin River 231 Sanibel Island 196 Sankaty Head 194 Sannakh Island 199 Santander 224 River 196 Santiago Cape 210 de Chile 211 Cuba 204 Port 245 Santona 224 Santos 208 Sapelo Island 195 Sarage Island 257 Saranguni Islands 246 Sarawak 242 River 242 Sariguan Island 252 Sarstoon River 197 Saru Island 243 Saseno Island 228 SatanoMisaki 248 Satawal Island 252 Saugor Island 238 Sauguir Island 242 Sauh, Pulo 238 Saukhoum 229 Saunders, Port 192 SauoBay 242 Savaii Island 257 Savanilla 206 Savannah 195 Savanna-la-Mar 204 Saybrook 194 Scalp Mountain 217 Scarries River 231 Scatary Island 193 Schama Mountain 212 Schank, Cape 261 Schanz Island 251 Page 284] INDEX TO APPENDIX IV. Page. Scharhom 222 Scheveningen 223 Schillighorn 222 Schleimunde 221 Schleswig 221 Schonbei^ 221 Scilly Islands, England 215 S. Pacific 257 Scott Cape 200 Scutari 229 Sea Bear Bay 209 Eock 248 Seal Cays 197 Island 193 Seao Island 242 Seattle 200 Sebaatian,San,Cape,M'g'sc'r 235 Spain 224 St., Cape, S. Africa... 232 Island 208 Sebastopol 229 Sebenico 227 Sedano, Cape 243 SedashigarBay 237 Seguin Island 193 Sein, I. de 224 Sejro Island 222 Selatan Point 242 Seldom-come-by Harbor 191 Semeny River 228 Semerara Island 245 Semiamoo Bay 200 Semione Island 240 Sentinel Island 248 Series Island 257 Sermalta Island 244 Sermelik Fjord 264 Sermo Island 229 Serrana Bank 198 Serranilla Bank 198 Seskar Islet 220 Setubal 225 SeuheliPar 234 Seven Heads 218 Seychelle Islands 234 Sfax 230 Shag Rocks 214 Shahah 236 Shahr, Abu 236 Shaikh Shu'aib Islet 236 Shaluitien Island 247 Shanghai 242 Shannon River 216 Shantar Islands 250 Shantung 247 Sharjah 236 Shark Island 254 Sharmoh 236 Shaweishan Island 242 Shelburne Harbor 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 ShimizuBay 249 Shimonoseki Strait 248 Shinnecock Bay 194 Ship Island 196 Shoal 196 Shipunski, Cape 250 ShirasuReef 248 Shoals, Isles of 194 Shoal water Cape .' 200 Island 239 SiaiTgao Island 246 Siassi 247 Siberaet Island 239 Siboga 239 Sibuco Bay . .- 247 Sibutu Island 247 Sibuyan Island 246 Sidmouth, 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 Siriya Saki 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 Skerryvore Rocks 216 Skiathos Island 229 SkidegateBay 199 Skoorgaarde 221 Skumbi River 228 Sky ring Mountain 209 SligoBay 217 Slyne Head 217 Smalls Rocks 215 Smerwick 216 Smith Island, Japan 249 Washington 200 Smyrna 230 Snaefells Yokul 265 Snares Islands 263 Page. Socorro Island, Chile 210 Mexico 202 Socotra Island 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 Spitzbergen 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 Page. Stewart Islands 254 Stirrup Cays 203 Stirsudden 220 Stockholm 219 Stonington 194 Stopelmiinde 221 Stora 230 Stornoway 216 Stot 218 Stralsund i21 Strati Island 229 Straumness Point 265 Streaker Bay 260 Streckelsberg 221 Strogonof Cape 199 Stromstad 219 Stromtangen 219 Strong Island 252 Strovathilsland 228 Stuartlsland 198 Suakin 233 Sual 245 Subig 245 Succadana 242 Suda,Port 228 Sueik 236 Suez 233 Suff ren, Cape 250 Sugar Loaf Point 261 Sughrah 236 Suk Island 252 Sulphur Island 253 Sumbawa Island 243 Sum burgh Head 216 Sunda Strait 239 Sunday Island 258 Sunderland 216 Sundsvall 220 Sunraiyani 237 Sup6 212 Sur 230 Surabaya 243 Surat 237 River 237 Surigao 246 Surop 220 Susaki 248 Suwanose 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 Tabasco River 197 PLACES — continued . Page. Tablas Island 246 Point 211 Table Bay 232 Head 191 Island 238 Taboga Island 203 Tabou River 231 Tacloban 246 Tacoma 200 Tacorady Bay 231 Tae Islands 241 Tagulanda Island 242 Tahiti 257 Tahoa Island 257 Tahuata Island 253 Taiaro Island 258 Tai-pin-san 244 Tajer, Port 227 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 Toewon 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 Taormina 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 Tchesm^ 229 Tchoukotskoi, Cape 250 Tegal 243 Page. Tehor Island 244 Tellicherri 237 Tello Islands 244 Tematangi Island 257 Tenasserim 238 Tenedos Island 230 Teneriffe Island 214 Tenez, Cape 230 Tepoca Cape 202 Tepoto Island 258 Tequepa 202 Terceira Island 213 Teresa, Sta., Bay 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. of Biaf ra 231 West Indies- 205 Thom6, 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 TobiShima: 249 Tobol Ali 239 Tocopilla 212 TodosSjmtos 201 To-dulsland 234 Tof ua Island 258 TokaraJima 248 Tokelau Islands 254 Token Bessi Island 243 Tokio 249 TolagaBay 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 286] INDEX TO APPENDIX IV. Page. Tordenskjold, 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 Totoyalsland 257 Toulinguet Islands 191 Toulon 226 TouraneBay 240 Towers Island 250 Townsend, Port 200 Trfenen 218 Trafalgar, Cape 225 TraleeBay 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 TromelinIsland,Carolinel8. 252 Indian Ocean 235 Tromso 218 Trondheim 218 Troon 215 Truxillo 197 Tsau-liang-hai 248 Tscheljuskin, Cape 264 Tsmano 235 Tsu Sima 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 217 Tumaco 213 Tumbez 212 Tung-chuh Island 241 Tung-yung Islands 241 Tuni-ang Island 241 Tunis 230 Tuno 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 Tutoya 207 Tutuila Island 257 Tuvutha Island 256 Tuxtla Volcano 196 Twelve Islands 236 TwofoldBay 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 UjiShima 248 Uleaborg 220 Ulietea Island 257 Ulko Kalla Rock 220 Ulladulla 261 Ulsire 218 Uluthi Islands 252 Umea 220 Una 207 Unalaska Island 199 UnareBay 206 Underut Islet 234 Underwood, Port 263 Unga Island 199 Unie Island 227 Union Bay 209 Islands 254 Portdela 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 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 VarellaCape 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 Veglia 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 Island 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 Wind ward Is. 205 Port, S. Pacific. . . 259 Vineyard Haven 194 INDEX TO APPENDIX IV. [Page 287 Page. Vingorla 237 Rocks 237 Virgin Gorda 205 Virgins, Cape 209 VitiLevu 256 Vizagapatam 238 Viziadrug 237 Vladimir, St., Bay 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 Vostoklsland 253 Vourlah 230 Vries 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 WalkerCay 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 Bay 232 Watlings Island 203 Wawoda Rock 250 Wedge Island 193 WeggsCape 191 Weichselmunde 221 Weihaiwei 247 Wellington 263 Wenman Island 250 Wessel, Cape 259 West Cape 263 Western, Port 261 Westminster Hall Islet 210 Wetta Island 243 Wexford 217 Whaingaroa Harbor 263 Whale Back 194 Whalefish Island 264 White 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 Wusiraado Point 248 Wustrow 221 Wusung 242 Xulla Islands 244 Yakuno Shima 248 YakutatBay 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 Yoko Shima 248 Yokohama 249 Yoko-shima 244 Yokosuka 249 York, Cape, Greenland 264' Queensland 262 Minster Rock 209 Youghal 218 Ystad 219 YtapereBay 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 . LUNAE DISTANCES. APPENDIX Y. LUNAR 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 vv^ith a close degree of accuracy by this method, it would be an invaluable aid to the navigator, eliminating all anxiety as to change of rate of the chronometer, and even rendering it possible to navigate a vessel without such an instrument. It is unfortunately the case, however, that the method does not afford results that may be regarded as reliable within small limits, since a very small error in the observed angle, which it may not be possible to avoid even though every care be taken, causes a large error in the deduced time. Navigators of the present day do not, there- fore, employ the method of lunar distances except under extraordinary circumstances, such as when an accident to the chronometer occurs, or, on a very long voyage, when there is reason to suspect the cor- rectness of the chronometer error as brought 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 bright fixed stars selected in the path of the moon. All the distances that can be observed on the same day are grouped together under that date, and the columns are read from left to right across both pages of the same opening. The letter W. or E. is affixed to the name of the sun, planet,- or star to indicate that it is on the west or east side of the moon. An observer on the surface of the earth having meas- ured a lunar distance, corrected it for instrumental error-s 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 w ill 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, and combining the results. Before taking the observation, the Nautical Almanac must be examined to see from what objects the distances are computed. If the star or planet selected for observation is not recognized from its position relatively to other bodies in the heavens, it can easily be identified from the distance given in the Almanac; for the observer may set the sextant to the distance computed roughly for the estimated time at the meridian of Greenwich, and direct his sight to the east or west of the moon, according as the object is marked E. or W. in the Nautical Almanac, and, having found the reflected image of the moon upon the horizon glass, sweep the instrument to the right or left, and the image will pass 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 examined; but in measuring small distances the use of the telescope is not of such great importance, and a sight tube may then be used,. taking care, however, that the eye and point of contact of the objects on the horizon glass be equally distant from the plane of the instrument. It is always conducive to accuracy to use a telescope, and, after a little practice, this is easily done. While one person is observing the distance of the objects, two others should observe the altitudes. The chronometer should be under the eye of a fourth person appointed to note the time; the observer who takes the angular distance gives previous notice to the others to be ready with their altitudes by the time he has finished his observation, which, being done, the time, altitudes, and distance should be carefully noted; if other sets of observations are taken it must be done within the space of fifteen minutes, and the mean of all the observations should be worked as a single one. When a ship is rolling considerably it is difficult to measure the distance of the objects, but when steady there is much less difficulty, especially in small distances, which are much more easily measured than large ones, and are not so liable to error from an ill adjustmentof the telescope; an observer would therefore do well to choose those times for observation when the distance of the objects is less than 70° or 80°. But it must be observed that neither of the objects, if possible, ought to be at a less altitude than 10°, on account of the uncertainty of the refraction near the horizon, for the horizontal refraction varies from 33' to 36' 40'' by an alteration of 40° in the thermometer; this alteration might cause an error of 2° in the longitude with an observer who uses the mean refraction. LUNAR DISTANCES. 289 111 measuring the distance of the moon from the sun we must bring the moon's round Hmb in contact with the nearer limb of the sun. In measuring the distance of the moon from a planet or fixed star the round limb must be brought in contact with the center of the star or planet, observing that, the seraidiameter of the planet being only a few seconds, the center of it can be estimated sufficiently near for all the purposes of this observation. In taking the altitude of the moon, the round limb, whether it be the upper or lower, must be brought to the horizon. In misty weather it is rather difficult to observe the altitude of the stars on account of their dimness. Sometimes they are «o dim that thev can not be seen through the telescope of a sextant, particularly if the mirrors are not well silvered. In this case the telescope must be laid aside and the altitude taken with a sight tube. It has been assumed that there were observers enough to measure tile altitudes when the distance was observed, but if that is not the case t>he altitudes may be estimated in a manner to be explained hereafter. The method here given is that of Professor Chauvenet, and involves the use of the tables in this Appendix. The object of these tables is to give the true correction of a^unar distance in all cases when, with the apparent distance of the moon from the sun, a planet, or star, the apparent altitudes of the two objects have also been obtained by observation. They enable us readily to take into amount: First, the parallax of the moon in the latitude of the observer, allowing for the spheroidal figure of the earth; second, the parallax of the sun or a planet; third, the true atmospheric refraction, allowing for the actual state of the air as shown by the barometer and thermometer; and, fourth, that effect of refraction which gives the apparent disks of the moon and sun an oval or elliptical figure. The longitude deduced from a lunar observation, when no attention is paid to the spheroidal figure of the earth, to the barometer and thermometer, or to the elliptical figure of the disks, may in certain cases be in error a whole degree. It is true these extreme cases are rare in practice, but cases are common in which from such neglect the error in the longitude is 10^, 15^, or 20^, and it i^ absolutely necessary to get rid of such errors and to leave no other inaccuracy in the result than that which unavoidably follows from the observations. The Observation. — The record of a complete observation embraces: 1. The latitude and approximate longitude of the place of observation. 2. The approximate local time. 3. The time of observation as shown by a chronometer, and the error of the chronometer, or its difference from mean Greenwich time. 4. The apparent distance of the moon's bright limb from a star or planet, or from the nearer Ihnb of the sun. 5. The apparent altitude of the moon's upper or lower limb-above the sea horizon. 6. The apparent altitude of the star, planet, or lower limb of the sun above the sea horizon. 7. The height of the barometer and thermometer. 8. The height of the eye above the level of the sea. 9. The index correction of the sextant. The index correction of the sextant may be supposed to be previously determined; but, since even in the best instruments it is not constant, Us determination should be considered a necessary part of the observation. The error of the chronometer alluded to is that which is obtained by applying the daily rate (multiplied by the proper number of days) to the error found before leaving port. The agreement or disagreement of the error thus found with that found by the lunar observation will be the test of the accuracy of the chronometer, subject, of course, to the accepted limits of accuracy of the observation itself. Prepakatiox of the Data. — Greenwich Date. — Correct the chronometer time for its error from Greenwich time and deduce the Greenwich date, i. e., the Greenwich day and hour (mean time), reck- oning the hours in succession from to 24, beginning at noon. NaiUical Almanac. — With the Greenwich date enter the Almanac and take out the moon's semi- diameter and horizontal parallax; if the sun is observed, take its semidiameter; in the case of a planet, take its horizontal parallax only. Apparent Altitude of the Moon. — To the altitude given by the sextant apply the index correction of the instrument and subtract the dip of the horizon (Table 14). « If the lower limb is observed, add the semidiameter and augmentation (Table 18) ; if the upper limb is observed, subtract the augmented semi- diameter. The result is the apparent altitude of the moon's center, denoted " C 's App. Alt." Apparent Altitude of the Sun, Planet, or Star. — To the observed altitude apply the index correction of the sextant, and subtract the dip (Table 14) ; and if the sun is used, add its semidiameter when the lower limb is observed, or subtract it when the upper limb is observed. The result is the apparent altitude required, denoted by "O's or >j<'s App. Alt." Apparent Distance. — First, when the sun is used, to the observed distance (corrected for index error when necessary) add the moon's augmented semidiameter and the sun's semidiameter; second, Avhen a planet or star is used, add the moon's augmented semidiameter if its nearer limb is observed, but subtract it if its farther limb is observed. The result is "App. Dist." Moon's Reduced Parallax and Refraction.— Enter Table 19 with the latitude of the place of observa- tion and the moon's horizontal parallax, and take out the correction, which add to the horizontal iferallax. Call the result the moon's reduced parallax, or " C 's Red. P." Enter Table I with the moon's apparent altitude, and take out the mean reduced refraction, and apply to this mean refraction the corrections given in Tables 21 and 22, adding or subtracting these cor- rections according to the directions in the tables. The result is the moon's reduced refraction, or "C 's Red. R." a The tables designated by their numbets in Arabic notation are to be found in Part 11. The tables contained in ihla Appendix, which are for excliislve use with lunar-distance observations, are denoted by Roman numbers. 6583—06 19 290 LUNAR DISTANCES. Subtract the "C's Red. R." from the "C's Red. P." and mark the result as "'C's Red. P. and R." Reduced Parallax and Refraction of Sun, Planet, or StarJ'— With, the apparent altitude of the sim, planet, or star, take from Table I the mean reduced refraction, which correct by Tables 21 and 22. If the 8U0 is observed, subtract its horizontal parallax (which may always be taken at 8'^5) from its reduced refraction, and mark the result as "0's Red. P. and R." If a planet is observed subtract its horizontal parallax, and mark the result as " >l<'s Red. P. and R." If a star is observed, its reduced refraction is at once the required " -Jf's Red. P. and R." Computation of the True Distance. — Take from Tables II, III, IV, and V respectively the four logarithms A, B, C, I), * and place these logarithms each at the head of a column, marking the columns A, B, C, and D; then put the — log of C 's Red. P. and R. (Table IX) in columns A and B. log of 0's or >f:'s Red. P. and R. (Table IX) in columns and D. log sin ([ 's App. Alt. (Table 44) in columns A and D. log sin 0'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 C 's Correction, which is to be marked + when the app. dist. is less than 90°, but — when the app. dist. is greater than 90°. The sum oif the four logs in Col. B is the log (Table IX) of the Second Part of C '« 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 0's or sjc's Correction, which is to be marked — when the app. dist. is less than 90°, but + when the app. dist. is greater than 90°. The sum of the four logs in Col. D is the log (Table IX) of the Second part of the Q' s or ':^' s Correc- tion, which is always to be marked +. Combine the first and second parts of the C's correction according to the signs prefixed; that is, take their swn if they have the same sign, but their difference if they have different signs, and prefix the sign of the greater to the result, which call " C's whole correction.'" In the same manner form the "0's or >|<'s whole correction.^ ^ First Correction of Distance. — Combine the ([_'s whole corr. and the 0's or >fc's vihole corr., according to their signs; the result is the First Correction of Distance, which is to be added to or subtracted from the apparent distance, according as its sign is + or — . * Second Correction of Distance. — Enter Table VI with the Apparent Distance and the First Correction of Distance, and take out the Second Correction of Distance, which is to be applied to the distance according to the directions in the side columns of the Table. Correction for the Elliptical Figure of the Moon^s Disk, or Contraction of the Moon's Semi-diameter. — Enter Table VII A with the C's App. Alt. and C's Red. P. and R., and take out the number. With this number and the C's whole correction enter Table VII B and take out the required contraction, which is to be added to the app. dist. when the farther limb is observed, but subtracted when the nearer limb is observed. Correction for the Elliptical Figure of the Sun's Disk, or Contraction of the Sun's Semi-diameter. — Enter Table VIII A with the 0's App. Alt. and 0's Red. P. and R., and take out the number. With this number and the 0's whole corr. enter Table VIII B and take out the required contraction, which is always to be subtracted from the distance (the 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 South, change the sign from + to — or from — to +. With the sun's or star's declination and the apparent distance, take from Table XI B the second part of N, giving it the same sign 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 Find the Greenwich Time. — Find in the Nautical Almanac the two distances between which the true distance falls. Take out the first of these, together with the Prop. Log following it, and the hours of Greenwich time over it. Find the difference between the distance taken from the Almanac and the true distance, and to the log of this difference (Table IX) add the Prop. Log from the Almanac; the sum is the log (Table IX) of an interval of time to be added to the hours of Greenwich time taken from the Almanac. The result is the approximate Greenwich time. To correct this Greenwich time, take the difference between the two Prop. Logs in the Almanac which stand against the two distances between which the true distance falls. With this difference and the interval of time just found enter Table X and take out the seconds, which are to be added to the approximate Greenwich time when the Prop. Logs are decreasing, but subtracted when the Prop. Logs are increasing. The result is the true Greenwich time. ' By comparing with this the local mean time the longitude will be found; or,- if testing the time shown by chronometer, the difference between the true Greenwich time and the time shown by the chronometer is the error of the chronometer as determined by 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 " ^'s Red. P. ; ud R.," this designation has been retained in order to give simplicity and uniformity at once to the rules and the tables. bNo interpolation is necessary iu taking out these logarithms. LUNAE DISTANCES. 291 Degree of Dependence. — If the error thus determined agrees with that deduced by means of the rate and original error, it may be accepted as a confirmation of the rate of the chronometer; if otherwise, more or less doubt is thrown upon the chronometer, according to the degree of accuracy of the lunar 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, 18" 8" 0% the observed distance of Q's andC 's nearer limbs was 43° 52^ 10^^; observed alt. C, 49° 32' 50^' observed alt. 0, 5° 27' IC; barometer, 29'". 1; thermometer, 75°; height of the eye above the sea, 20" I. C, O' OO''; required the longitude. L. M. T., Sept. 6, Long., D. R., G. M. T., approx., Obs. Alt. C, Dip, Table 14, C's Aug. S. D., C's App. Alt., C'sRed. R., Table I Bar. 29'M, Table 21, Ther. 75°, Table 22, C's Red. R., C's Red. P., C's Red. P. andR., 18'>08" + 2 00 20 08 49' ' 32' 50" — 4 23 + 15 01 49 43 28 r, V 16" - 3 - - 4 1 09 54 23 53 14 Preparation of the Data. C'sS. D., Aug. Table 18, C's Aug. S. D, Obs. Alt. 0, Dip, O'sS. D., . 0's App. Alt, 0'sRedR., Table I, Bar., Table 21, Ther., Table 22, — O's Red. R., O's Par., 0's Red. P. and R., •f 14' 50".0 11 .2 15 01 .2 5 + o 27/ 4 15 10" 23 55 5 38 42 > 8' 57" 16 28 8 13 8 8 05 C's Par., N. A., Aug., Table 19, 2 C's Red. P., 54' 19". 4 + 3 .6 54 23 .0 Obs. Dist. 01 |C, 43° 52' 10" C'sAug. S. D., + 15 01 0's S. D., + . 15 55 App. Dist., C's Dec, N. A., 0'8 Dec, N. A., 44 23 06 25° N. 6°N. log A, Table II, 0. 0021 log C 's Red. r. and R., 3. 5043 log sin C ' s App. Alt. , 9. 8825 log cot App. Dist. , 0. 0093 /log, Table IX, 3. 3982 \lst Part C 's corr. , +41' 42" B. log B, Table III, 9. 9951 log C 's Red. P. and R., 3. 5043 log sin O's App. Alt., 8. 9929 log cosec App. Dist., 0. 1552 /log, Table IX, 2. 6475 \2d Part C 's corr., - 7' 24" C ' s whole corr. , +34' 18" log N, Tabs. XI and IX, ( - ) 0. 845 log sin Lat, + 35° 30', ( + ) 9. 764 flog, Table IX, (-) 0.609 \Corr. for Compression, — 4" Computation of the True Distance. C. log C, Table IV, 9. 9949 log 0'8 Red. P. and R., 2. 6857 log sin O's App. Alt, 8. 9929 log cot App. Dist. , 0. 0093 /log. Table IX, 1. 6828 \lst Part ' s corr. , -0' 48" D. log D, Table V, 9. 9992 log O's Red. P. and R., 2. 6857 logsinC'sApp. Alt, 9.8825 log cosec App. Dist., 0. 1552 /log, Table IX, 2. 7226 \2d Part O's corr., +8' 48" O's whole corr., +8' 00" App. Dist., 1st Corr., 2d Corr., Table VI, Contraction of C 's\ S. D.,TableVII,| Contraction of 0's\ S. D., Table VIII, / Corr. for Comp. True Distance, 44' + 06" 18 16 20, 4 45 04 44 292 LUNAR DISTANCES. Extract from Nautical Almanac, September, 1855. GREENWICH MEAN TIME: LUNAR DISTANCES. ^5 star's name and position. Midnight. P. L. of Diff. XVi. p. L. of Diff. XVIIIh. P. L. Of Diff. XXIh. P. L. i of Diff. 6 Sun E. 48° W hh" 3422 47° 25^ W 3427 46° 3^ \r' 3433 44° W ZW' 3438 i Computation of Greenwich Mean Time. True Distance, Distance, N. A., at XVIIP, Difference, Approximate interv^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 2h 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^'. Preparation of the Data. L. M. T. , August 29, 9'' 40™ 00' Long, by D. E., +8 01 40 Approx. G. M. T., Obs. alt. C Dip, C'saug. S. D., (C's App. Alt., + C'sRedR.,TableI, Bar., Table 21, + Ther., Table 22, + (i:'sRedR., C'sRed. P., fii'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 (i:'sS.D.,Naut.Al., Aug., Table 18, + C's aug S. D., Obs. alt. >fc, Dip, >)<'s App. Alt, >)<'sRed.R.,TableI, Bar., Table 21, + Ther., Table 22, + ::+c's Red. R., *'sRedP., 16' 26". 3 2 .0 16 28 .3 52° 34' 4 40" 09 52 30 31' 13" 2 5 20 >|<'s Red. P. and R., 1 20 C's Par., N. A., Aug., Table 19, C Red p., Obs. Dist. -X- IC, C's aug., S. D., App. Dist., C'sDec, N. A., :^c's Dec, N. A., + 60' 11". 8 8 .3 60 20 .1 46° 30' 16 23" 28 46 13 55 4° N. 30° S. LUNAE DISTANCES. 293 A. log A, Table II, 0.0274 log C's Red. P. and R., 3.4919 log sin a 's App. Alt., 9.0632 logcot App. Dist., 9.9813 (log, Table IX, \lst Part C 's corr., B. 2.5638 + 6' 06^^ log B, Table III, 0.0001 log C's Red. P. and R., 3.4919 log sin >|<'s App. Alt., 9.8995 log cosec App. Dist, 0.1414 flog. Table IX, \2d Part (L's corr., C's whole corr., 3.5329 56^ 51^^ 50 45 log N, Tabs. XI and (— ) 1.230 IX, logsinLat, -55°, ( — ) 9.913 flog Table IX, l^Corr. for Comp., ( + ) + 1.143 14// Computation of the True Distance. C. log C, Table IV, 9.9999 log Jfc's Red. P. and R., 1.9031 log sin >f:'s App. Alt., 9.8995 logcot App. Dist., 9.9813 1.7838 flog. Table IX, \lst Part sjc's corr. D. log D, Table V, 0.0267 log >fc's Red. P. and R., 1.9031 log sin C 's App. Alt., 9.0632 log cosec App. Dist., 0.1414 riog. Table IX, \2d Part >l<'s corn, >|<'s whole corr., 1.1344 + 0^ 14^^ — 47 App. Dist, 46' 13^ 5y^ 1st corr., — 51 32 2dcorr., Table VI, — 22 Contraction of C's) , S.D., Table VII,i + 17 Corr. for Comp., + 14 True Distance, 45 22 32 Extract from Nautical Almanac, Augtisi, 1855. GREENWICH MEAN TIME: LUNAR DISTANCES. |a A Star's name and positi'on. Midnight. P. L. of Diff. XV h. P. L. of Difl. XVIII h. P. L. of Difl. XXI*. P. L. of Difl. 29 Fomalhaut W. 42° 11^ 34'^ 2535 43° 51^ 59^^ 2527 45° 32^ 35^' 2521 47° 13^ 19'^ 2516 Computation of Greenwich Mean Time. True Distance, Dist., N. A., at XV, Difference, Approx. interval. Add— Approx. G. M. T., Corr., Table X, TrueG. M. T., L. M. T., Long. , 45° 22'' 32'^ 43 51 59 1 30 33 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 NauticafAlmanac 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: X--J-, where x — change of altitude, in minutes, between first altitude and time of measuring the lunar distance, being positive or negative according as body is rising or falling; d = difference between first and second altitudes, in minutes; e = time, in seconds, between first altitude and lunar observations; and t = time in seconds, between first and second altitudes. The change of altitude thus deduced, applied with proper sign to the first altitude, gives the altitude at time of observing the lunar distance. Example: Suppose the distances and altitudes of the sun and moon were observed, as in the following table; it is required to find the altitudes at the time of measuring the mean distance. Times by chro- nometer. 2" 03" 2 04 2 05 20' 20 50 Mean, 2 04 30 Lunar dis- tance. 40° 00^ 00^^ 40 00 30 40 01 ^0 40 00 40 For C- Times by chro- nometer. 2'> 02 2 06 "00' 10 '•{ Obs. alt. (I'sL.L. 20° W 21 20 d, 34 Times by chro- nometer. 2^ 02° 2 07 30' 00 Obs. alt. Q's L. L. 40° 20' 39 12 Time of lunar obs. Time of 1st alt., 2'' 04" 2 02 30' 00 / 2 30 1 150* x = + ^^ ^.}^^ = + 2(/-4 = + 20' 24'' First altitude, 20° 46' 00" X, + 20 24 10 250^ ForQ. Time of lunar obs., Time of 1st alt., 30 270' 2'' 04" 2 02 "■{' 08 68' 30' 30 e, 68 X 120 270 First altitude, X, Required altitude. j 2 00 t 120' = — 30'. 2 = — 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 s^ec t; sin h = t^os (A — L) sind . sin 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 which has the same name or sign as the declination and is numericallv 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, 1" 58™ 46' 0's Dec, 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, L 74 55 20 13 23 58 3 50 ref. — par. -f- App. alt. 13 27 48 sin (-) 9.59991 cosec(— ) 0.34989 cos (+) 9.4152a sin (+) 9.36500 APPENDIX V: TABLE I. [Page 295 | Mean Reduced Refraction for Lunars. Barometer 30 inches. Fahrenheit's Thermometer 50°. Apparent al- Reduced re- DifF. to Apparent al- Reduced re- Apparent al- Reduced re- Apjmrent al- Reduced re- titude. fraction. 1'. titude. fraction. titude. fraction. titude. fraction. o / 5 / If 9 54.2 1.6 o / 10 5 24.1 O ' 15 3 41.7 o / 27 2 7.8 5 9 46.3 1.5 5 5 21.6 10 3 39.4 27 30 2 5.7 10 9 38.6 1.5 10 5 19.2 20 3 37.1 28 2 3, 7 15 9 31.0 1.5 15 5 16.8 30 3 34.9 28 30 2 1.7 20 9 23.7 1.4 20 5 14.4 40 3 32.7 29 1 59.8 25 9 16.5 1.4 25 5 12.1 50 3 30.6 29 30 1 58.0 5 30 9 9.5 1.4 10 30 5 9.8 16 3 28.5 30 1 56.2 35 9 2.7 1.3 35 5 7.5 10 3 26.5 30 30 1 54.5 40 8 56.0 1.3 40 5 5.3 20 3 24.5 31 1 52.8 45 8 49.5 1.3 45 5 3.1 30 3 22.6 31 30 1 51.2 50 8 43.1 1.2 50 5 0.9 40 3 20.7 32 1 49.7 55 8 36. 9 1.2 55- 4 58.8 50 3 18.8 32 30 1 48.2 6 8 30.9 1.2 11 4 56.7 17 3 16.9 33 1 46.7 5 8 24.9 1.2 5 4 54.6 10 3 15.1 33 30 1 45.3 10 8 19.1 1.1 10 4 52.5 20 3 13.4 34 1 44.0 15 8 13.4 1.1 15 4 50.5 30 3 11.6 34 30 1 42.7 20 8 7.8 1.1 20 4 48.5 40 3 9.9 35 1 41.4 25 8 2.4 1.1 25 4 46. 6 50 3 8.2 35 30 1 40.2 6 30 7 57.0 1.0 11 30 4 44.6 18 3 6.6 36 1 39.0 35 7 51.8 1.0 35 4 42.7 10 3 5.0 36 30 1 37.8 40 7 46.7 1.0 40 4 40,8 20 3 3.4 37 1 36.7 45 7 41.7 1.0 45 4 38.9 30 3 1.8 37 30 1 35.6 50 7 36.7 1.0 50 4 37.1 40 3 0.3 38 1 34.5 55 7 31.9 0.9 55 4 35.3 50 2 58.8 38 30 1 33.5 7 7 27.2 0.9 12 4 33.5 19 2 57.3 39 1 32.5 5 7 22.6 0.9 5 4 31.7 10 2 55.9 39 30 1 31.5 - 10 7 18.0 0.9 10 4 30.0 20 2 54.4 40 1 30.6 15 7 13.6 0.9 15 4 28.3 30 2 53.0 40 30 1 29.6 20 7 9.2 0.9 20 4 26.6 40 2 51.6 41 1 28.7 25 7 4.9 0.8 25 4 24.9 50 2 50.3 41 30 1 27.8 7 30 7 0.8 0.8 12 30 4 23.2 20 2 49.0 42 1 27.0 35 6 56.6 0.8 35 4 21.6 10 2 47.6 42 30 1 26.2 40 6 52.6 0.8 40 4 20.0 20 2 46.4 43 1 25.4 45 6 48.6 0.8 45 4 18.4 30 2 45.1 43 30 1 24.6 50 6 44.8 0.8 50 4 16.8 40 2 43.8 44 1 23.8 55 6 40.9 0.7 55 4 15.2 50 2 42.6 44 30 1 23.1 8 6 37.2 0.7 13 4 13.7 21 2 41.4 45 1 22.4 5 6 33.5 0.7 5 4 12.2 10 2 40.2 46 1 21.0 10 6 29.9 0.7 10 4 10.7 20 2 39.0 47 1 19.6 15 6 26.3 0.7 15 4 9.2 30 2 37.9 48 1 18.4 20 6 22.8 0.7 "JO 4 7.7 40 2 36.7 49 ' 1 17.2 25 6 19.4 0.7 25 4 6.3 50 2 35.6 50 1 16.0 8 30 6 16.0 0.7 13 30 4 4.8 22 2 34.5 51 1 15.0 35 6 12.7 0.6 35 4 3.4 10 2 33.4 52 1 13.9 40 6 9.5 0.6 40 4 2.0 20 2 32.4 53 1 13.0 45 6 6.3 0.6 45 4 0.6 30 2 31.3 54 1 12.0 50 6 3.1 0.6 50 3 59.3 40 2 30.3 55 1 11.1 55 6 0.0 0.6 55 3 57.9 50 2 29.2 56 1 10.3 9 5 57.0 0.6 14 3 56.6 23 2 28.2 57 1 9.5 5 5 54.0 0.6 5 3 55. 3 20 2 26.3 58 1 8.7 10 5 51.1 0.6 10 3 54.0 40 2 24.4 59 1 8.0 15 5 48.2 0.6 15 3 52.7 24 2 22.5 60 1 7.3 20 5 45. 3 0.6 20 8 51.4 20 2 20.7 62 1 6.0 25 5 42.5 0.5 25 3 50.1 40 2 18.9 64 1 4.9 9 30 5 39.8 0.5 14 30 3 48.9 25 2 17.2 (6 1 3.8 35 5 37.0 0.5 35 3 47.6 20 2 15.5 68 1 2.9 40 5 34.4 0.5 40 3 46. 4 40 2 1.3.9 70 1 2.0 45 5 31.7 0.5 45 3 45.2 26 2 12.3 73 1 1.0 50 5 29.2 0.5 50 3 44.0 20 2 10.8 76 1 0.1 55 5 26.6 0.5 55 3 42.8 40 2 9.3 80 59.2 10 5 24.1 15 3 41.7 27 2 7.8 90 58.3 Page 2961 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 41' 42' 43' 44' 45' 46' 4J' 48' 49' 50' 51' 5'2' 53' 54' 55' 5° 0^ 2 4 6 8 .0288 .0286 .0284 .0282 .0281 0295 0293 0291 0289 0287 0301 0299 0297 0296 0294 0308 0306 0304 0302 0300 0298 0296 0295 0293 0291 0315 0313 0311 0309 0307 0321 0319 0317 0315 0313 0328 0326 0324 0322 0320 0335 0333 0330 0328 0326 0324 0322 0320 0318 0316 0341 0339 0337 0335 0333 0331 0329 0327 0325 0323 0348 0346 0344 0341 0339 0337 0335 0333 0331 0329 0327 0325 0323 0321 0319 0355 0352 0350 0348 0346 '0361 0359 0357 0354 0352 0368 0366 0363 0361 0359 0356 0354 0352 0350 0348 0346 0344 0341 0339 0337 0335 0334 0332 0330 0328 0326 0324 0322 0320 0319 5 10 12 14 16 18 .0279 .0277 .0275 .0274 .0272 0285 0284 0282 0280 0278 0292 0290 0288 0286 0285 0305 0303 0301 0299 0297 0311 0309 0307 0306 0304 0302 0300 0298 0296 0295 0318 0316 0314 0312 0310 0344 0341 0339 0337 0335 0350 0348 0346 0344 0341 0339 0337 0335 0333 0331 5 20 22 24 26 28 5 30 32 34 36 38 .0270 .0269 .0267 .0265 .0264 0277 0275 0273 0272 0270 0283 0281 0280 0278 0276 0289 0288 0286 0284 0282 0296 0294 0292 0290 0289 0287 0285 0283 0282 0280 0279 0277 0275 0274 0272 0308 0306 0304 0303 0301 0314 0313 0311 0309 0307 0321 0319 0317 0315 0313 0333 0331 0329 0327 0325 0346 0344 '0342 0340 0338 0336 0334 .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 0281 0279 0277 0276 0274 0273 0271 0270 0268 0267 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 0311 0309 0308 0306 0304 0317 0315 0314 0312 0310 0323 0321 0320 0318 0316 0329 0327 0326 0324 0322 5 40 42 44 46 48 0296 0295 0293 0291 0290 0302 0301 0299 0297 0296 0308 0306 0305 0303 0301 0314 0312 0311 0309 0307 0320 0318 0316 0315 0313 0332 0330 0328 0326 0324 6 50 52 54 56 58 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 0288 0287 0285 0283 0282 0294 0292 0291 0289 0287 0300 0298 0296 0295 0293 0305 0304 0302 0300 0299 0311 0309 0308 0306 0304 0317 0315 0313 0312 0310 0323 0321 0319 0317 0316 6 2 4 6 8 0247 0245 0244 0243 0241 0252 0251 0249 0248 0247 0258 0256 0255 0254 0252 0263 0262 0261 0259 0258 0269 0268 0266 0265 0263 0275 0273 0272 0270 0269 0280 0279 0277 0276 0274 0286 0284 0283 0281 0280 0291 0290 0288 0287 0285 0284 0282 0281 0279 0278 0297 0295 0294 0292 0291 0303 0301 0299 0298 0296 0308 0307 0305 0303 0302 0300 0299 0297 0295 0294 0292 0291 0289 0288 0286 0314 0312 0310 0309 0307 6 10 12 . 14 16 18 6 20 22 24 26 28 0240 0239 0237 0236 0235 0246 0244 0243 0242 0240 0251 0250 0248 0247 0246 0256 0255 0254 0252 0251 0262 0261 0259 0258 0257 0267 0266 0265 0263 0262 0273 0271 0270 0269 0267 0266 0264 0263 0262 0260 0278 0277 0275 0274 0273 0289 0288 0286 0285 0283. 0295 0293 0292 0290 0289 0306 0304 0302 0301 0299 0297 0234 0233 0231- 0239 i 0245 0238 1 0243 0237 0242 0236 0241 0234 ! 0240 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 0270 0268 0267 0266 0264 0282 0280 0279 0277 0276 0287 0286 0284 0283 0281 0298 0296 0295 0293 0292 6 30 32 34 36 38 0233 0238 0232 0237 0231 0236 0230 ' 0235 0229 j 0234 0244 0242 0241 0240 0239 0249 0248 0246 0245 0244 0254 0253 0251 0250 0249 0259 0258 0257 0255 0254 0264 0263 0262 0260 0259 0275 0273 0272 0271 0269 0280 0278 0277 0276 0274 0285 0284 0282 0281 0279 0290 1 0295 0289 0294 0287 0292 0286 0291 0284 i 0290 6 40 42 44 46 48 0227 0226 0225 0224 0223 0232 0231 0230 0229 0228 0238 0236 0235 0234 0233 0243 0241 0240 0239 0238 0248 0246 0245 0244 0243 0253 0252 0250 0249 0248 0258 0257 0255 0254 0253 0252 0250 0249 0248 0247 0263 0262 0260 0259 0258 0268 0267 0265 0264 0263 0273 0272 0270 0269 0268 0278 0277 0275 0274 0273 0283 0288 0282 ' 0287 0280 0285 0279 ! 0284 0278 : 0283 0276 0281 0275 i 0280 0274 0279 0272 1 0277 0271 1 0276 6 50 52 54 56 58 0222 0221 0220 0219 0218 0227 0226 0225 0224 0223 0232 0231 0230 0229 0227 0237 0236 0235 0233 0232 0242 0241 0239 0238 0237 0247 0246 0244 0243 0242 0257 0255 0254 0253 0252 "0251 0262 0260 0259 0258 0257 0266 0265 0264 0263 0261 0271 0270 0269 0267 0266 7 0217 0222 0226 0231 .0236 0241 0246 0255 0260 0265 0270 1 0275 APPENDIX V: TABLE II. [Page 297 Log. A, f;)r computing the llrst Correction of the Lunar Distance. App. alt. of moon. 7° 0^ 3 6 9 12 Reduced parallax and refraction of moon. 1 44' 45' 46' 47' 48' ! 49' j 50' 61' 52' 58' 51' 55' 56' 57' .0222 .0220 .0218 .0217 .0215 0226 0225 0223 0222 0220 0231 0230 0228 0226 0225 0223 0222 0220 0219 0217 0236 0234 0233 0231 0230 0241 0239 0238 0236 0234 0246 0244 0242 0241 0239 0251 0249 0247 0245 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 7 30 33 36 39 42 .0214 .0213 .0211 .0210 .0208 0219 0217 0216 0214 0213 0228 0226 0225 0223 0222 0233 0231 0230 0228 0227 0237 0236 0234 0233 0231 0242 0240 0239 0237 0236 0247 0245 0243 0242 0240 0251 0250 0248 0246 0245 0243 0241 0240 0238 0237 0256 0254 0253 0251 0249 0248 0246 0244 0243 0241 0261 0259 0257 0255 0254 0252 0250 0249 0247 0246 0244 0242 0241 0239 0238 0236 0235 0233 0232 0231 0229 0228 0226 0225 0224 0265 0263 0262 0260 0258 .0207 .0206 .0204 .0203 .0202 0211 0210 0209 0207 0206 0205 0203 0202 0201 0200. 0216 0215 0213 0212 0210 0220 0219 0218 0216 0215 0225 0224 0222 0221 0219 0230 0228 0227 0225 0224 0222 0221 0219 0218 0217 0234 0232 0231 0229 0228 0227" 0225 0224 0222 0221 0239 0237 0235 0234 0232 0231 0229 0228 0227 0225 0257 0255 0253 0252 0250 02"48 0247 0245 0244 0242 7 45 48 51 54 57 8 3 6 9 12 .0200 .0199 .0198 .0196 .0195 0209 0208 0206 0205 0204 0213 0212 0211 0209 0208 0218 0216 0215 0214 0212 0211 0210 0208 0207 0206 0235 0234 0232 0231 0229 0240 0238 0237 0235 0234 0232 0231 0229 0228 0227 0225 0224 0222 0221 0220 "0219 0217 0216 0215 0214 0212 0211 0210 0209 0208 0249 0248 0246 .0194 .0193 .0192 0198 0197 0196 0195 0193 0203 0201 0200 0199 0198 0207 0206 0204 0203 0202 0215 0214 0213 0211 0210 0219 0218 0217 0215 0214 0224 0222 0221 0220 0218 0228 0227 0225 0224 0222 0241 0239 0238 0236 0235 0245 0243 0242 0240 0239 8 15 18 21 24 27 8 30 33 36 39 42 0192 0191 0190 0189 0188 0196 0195 0194 0193 0192 0201 0199 0198 0197 0196 0205 0203 0202 0201 0200 0209 0207 0206 0205 0204 0213 0212 0210 0209 0208 0217 0217 0214 0213 0212 0211 0209 0208 0207 0206 0221 0220 0218 0217 0216 0215 0213 0212 0211 0210 0233 0232 0231 0229 0228 0237 0236 0235 0233 0232 0187 0186 0184 0183 0182 0191 0190 0188 0187 0186 0195 0193 0192 0191 0190 0199 0197 0196 0195 0194 0203 0201 0200 0199 0198 0207 0205 0204 0203 0202 0223 0221 0220 0219 0217 0216 0215 0214 0212 0211 0226 0225 0224 0223 0221 0230 0229 0228 0226 0225 8 45 48 51 54 57 0181 0180 0179 0178 0177 0185 1 0189 0184 0188 0183 1 0187 0182 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 0220 0219 0218 0216 0215 0224 0223 0221 0220 0219 9 3 6 9 12 0176 0175 0174 0173 0172 0180 - 0184 0179 ' 0183 0178 ! 0182 0177 0181 0176 i 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 0213 0211 0210 0209 0218 0216 0215 0214 0213 9 15 18 21 24 27 0171 0170 0170 0175 0179 0174 0178 0173 0177 0172 0176 0171 0175 0182 0181 0180 0179 0179 0186 01-85 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 0207 0206 0205 0204 0212 0211 0209 0208 0207 9 30 33 36 39 42 9 45 48 51 54 57 10 0170 0174 0170 0173 0169 0172 0168 0171 0167 ! 0170 0178 0177 0176 0175 0174 0181 0180 0179 0178 0177 0185 0184 0183 0182 0181 "0180 0179 0178 0177 0176 0188 0187 -0186 0185 0184 0192 0191 0190 0189 0188 0195 0194 0193 0192 0191 0199 0198 0197 0196 0195 0203 0201 0200 0199 0198 0206 0205 0204 0203 0202 0166 0165 0164 0163 0163 0169 0169 0168 0167 0166 0173 0172 0171 0170 0169 0176 0176 0175 0174 0173 0183 0182 0182 0181 0180 0187 0186 0185 0184 0183 0J9O 0189 0188 0187 0186 0194 0193 0192 0191 0190 0197 0196 0195 0194 0193 0201 0200 0199 0198 0197 0203 0202 0201 0200 0162 J 0165 0169 0172 0175 0179 1 0182 0186 0189 0192 0196 0199 1 Page 298] 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 46' 47' 48' 49' 60' 61' 52' 63' 54' 66' 1 56' 57' 68' 10° 0^ 5 10 15 20 25 .0162 .0160 .0159 .0158 .0156 .0155 0165 0164 0162 0161 0160 0158 0169 0167 0166 0164 0163 0162 0172 0171 0169 0168 0166 0165 0175 0174 0172 0171 0170 0168 0179 0177 0176 0174 0173 0171 0182 0181 0179 0178 0176 0175 0186 0184 0182 0181 0179 0178 0189 0187 0186 0184 0183 0181 0192 0191 0189 0187 0186 0184 0196 0199 0194 0197 0192 0196 0191 0194 0189 j 0192 0188 1 0191 10 30 35 40 45 50 55 .0154 .0153 .0151 .0150 .0149 .0148 0157 0156 0155 0153 0152 0151 0160 0159 0158 0157 0155 0154 0164 0162 0161 0160 0158 0157 0167 0166 0164 0163 0162 0160 0170 0169 0167 0166 0165 0163 0173 0172 0171 0169 0168 0167 0177 0175 0174 0172 0171 0170 0180 0178 0177 0175 0174 0173 0183 0181 0180 0179 0177 0176 0186 0185 0183 0182 0180 0179 0189 0188 0186 0185 0183 0182 11 5 10 15 20 25 11 30 35 40 45 50 55 .0147 .0146 0150 0149 0148 0146 0145 0144 0153 0152 0151 0149 0148 0147 0156 0155 0154 0152 0151 0150 0159 0158 0157 0155 0154 0153 0162 0161 0160 0158 0157 0156 0165- 0164 0163 0161 0160 0159 0168 0167 0166 0164 0163 0162 0171 0170 0169 0167 0166 0165 0174 0173 0172 0170 0169 0168 0177 0176 0175 0173 0172 0171 0181 0179 0178 0176 0175 0174 0143 0142 0141 0140 0139 0138 0146 0145 0144 0143 0142 0141 0149 0148 0147 0146 0145 0144 0152 0151 0150 0149 0148 0146 0155 0154 0153 0151 0150 0149 0158 0157 0156 0154 0153 0152 0161 0160 0158 0157 0156 0155 0164 0162 0161 0160 0159 0158 0167 0165 0164 0163 0162 0161 0159 0158 0157 0156 0155 0154 0170 0168 0167 0166 0165 0163 0162" 0161 0160 0159 0158 0157 0172 ai7i 0170 0169 0167 0166 12 5 10 15 20 25 0137 0136 0135 0134 0133 0132 0140 0139 0138 0137 0136 0135 0143 0142 0141 0140 0139 0138 0145 0144 0143 0142 0141 0140 0139 0138 0137 0136 0136 0135 0148 0147 0146 0145 0144 0143 0151 0150 0149 0148 0147 0146 0154 0153 0152 0151 0150 0148 0157 0156 0154 0153 0152 0151 0165 0164 0163 0162 0160 0159 12 30 35 40 45 50 55 0131 0130 0129 0129 0128 0127 0134 0133 0132 0131 0130 0129 0137 0136 0135 0134 0133 0132 0142 0141 0140 0139 0138 0137 0145 0144 0143 0142 0141 0140 0147 0146 0145 0144 0143 0142 0150 0149 0148 0147 0146 0145 0153 0152 0151 0150 0149 0148 0155 0154 0153 0152 0151 0150 0158 0157 0156 0155 0154 0153 0158 0156 0155 13 5 10 15 20 25 0126 0125 0124 0123 0123 0122 0129 0128 0127 0126 0125 0124 0131 0130 0129 0129 0128 0127 0134 0133 0132 0131 0130 0129 0136 0135 0135 0134 0133 0132 0189 0138 0137 0136 0135 0134 0141 0141 0140 0139 0138 0137 0144 0143 0142 0141 0140 0139 0147 0146 0145 0144 0143 0142 0149 0148 0147 0146 0145 0144 0152 0151 0150 0149 0148 0147 0154 0153 0152 0151 0150 0149 13 30 35 40 45 50 55 0121 0120 0120 0124 0123 0122 0121 0120 0120 0126 0125 0124 0124 0123 0122 0129 0128 0127 0126 0125 0124 0131 0130 0129 0128 0128 0127 0133 0133 0132 0131 0130 0129 0136 0135 0134 0133 0132 0132 0138 0138 0137 0136 0135 0134 0141 0140 0139 0138 0137 0136 0143 0142 0142 0141 0140 0139 0146 0145 0144 0143 0142 0141 0148 0147 0146 0145 0145 0144 14 5 10 15 20 25 0119 0118 0117 0117 0116 0115 0121 0121 0120 0119 0118 0118 0124 0123 0122 0121 0121 0120 0126 0125 0124 0124' 0123 0122' 0128 0128 0127 0126 0125 0124 0131 0130 01,29 0128 0128 0127 0133 0132 0132 0131 0130 0129 0136 0135 0134 0133 0132 0131 0138 0137 0136 0135 0135 0134 0140 0139 0139 0138 0137 0136 0143 0142 0141 0140 0139 0138 14 30 35 40 45 50 55 0114 0114 0113 0112 0112 0111 0117 0116 0115- 0115 0114 0113 0119 0118 0118 0117 0116 0116 0121 0121 0120 0119 0118 0118 0124 0123 0122 0121 0121 0120 0126 0125 0124 0124 0123 0122 0128 0128 0127 0126 0125 0124 0131 0130 0129 0128 0127 0127 0133 0132 0131 0130 0130 0129 0135 0134 0134 0133 0132 0131 0137 0137 0136 0135 0134 0133 15 0110 0113 0115 0117 0119 1 0121 0124 0126 0128 0130 0133 1 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. 43' 49' 60' 61' 62' 68' 54' 66' 66' 57' 58' 59^ 15° 0^ 10 20 30 40 .0110 .0109 .0108 .0107 .0105 0113 0111 0110 0109 0107 0115 0113 0112 0111 0110 0117 0116 0114 0113 0112 0119 0118 0116 0115 0114 0121 0120 0119 0117 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 50 16 10 20 30 .0104 .0103 .0102 .0101 .0100 0106 0105 0104 0103 0102 0108 0107 0106 0105 0103 OHO 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 20 30 40 50 19 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 0108 0107 0106 0105 0104 10 20 30 40 50 0086 0085 0084 0083 0082 0087 0087 0086 0085 0084 0089 0088 0087 0087 0086 0091 0090 0089 0088 0087 0092 0092 0091 0090 0089 0094 0093 0092" 0091 0090 0096 0095 0094 0093 0092 0098 0097 0096 0095 0094 0099 0098 0097 0096 0095 0101 0100 0099 0098 0097 0103 0102 0101 0100 0099 20 10 20 30 40 0082 0081 0080 0079 0079 0083 0082 0082 0081 0080 0085 0084 0083 0082 0082 0086 0086 0085 0084 0083 t)088 0087 0086 0086 0085 0084 0083 0082 0082 0081 0080 0079 0079 0078 0077 0076 0076 0075 0074 0074 0090 0089 0088 0087 0086 0091 0090 0089 0089 0088 0093 0092 0091 0090 0089 0088 0088 0087 0086 0085 0094 1 0096 0093 1 0095 0093 0094 0092 0093 0091 0092 0098 0097 0096 0095 0094 50 21 10 20 30 40 50 22 10 20 30 40 50 23 10 0078 0077 0076 0076 0075 0079 0079 0078 0077 0076 0081 0080 0079 0079 0078 0082 0082 0081 0080 0079 0079 0078 0077 0076 0076 0075 0074 0074 0073 0072 0085 0085 0084 0083 0082 0087 0086 0085 0085 0084 0090 0089 0088 0087 0087 0091 0091 0090 0089 0088 0093 0092 0091 0090 0090 0074 0074 0073 0072 0072 0076 0075 0074 0074 0073 0077 0076 0076 0075 0074 0082 0081 0080 0079 0079 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 0071 0070 0070 0069 0068 0072 0072 0071 0070 0070 0074 0073 0072 0072 0071 0070 0070 0069 0069 0068 0078 0077 0076 0076 0075 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 20 30 40 50 24 10 20 30 40 50 0068 0067 0067 0066 0069 0069 0068 0067 0067 0072 0071 0071 0070 0069 0 0" 10" 2. 7782 2. 7789 2.7796 2. 7803 2. 7810 2. 7818 2. 7825 2. 7832 2. 7839 2.7846 10 10 2. 7853 2. 7860 2. 7868 2. 7875 2. 7882 2. 7889 2. 7896 2. 7903 2. 7910 2. 7917 10 20 2. 7924 2. 7931 2. 7938 2. 7945 2. 7952 2. 7959 2. 7966 2. 7973 2. 7980 2. 7987 10 30 2. 7993 2. 8000 2. 8007 2. 8014 2. 8021 2. 8028 2. 8035 2. 8041 2. 8048 2. 8055 10 40 2. 8062 2. 8069 2. 8075 2. 8082 2. 8089 2. 8096 2. 8102 2.8109 2.8116 2. 8122 10 50 2. 8129 2. 8136 2. 8142 2. 8149 2. 8156 2. 8162 2. 8169 2. 8176 2. 8182 2. 8189 11 2. 8195 2. 8202 2. 8209 2. 8215 2. 8222 2. 8228 ,2. 8235 2. 8241 2. 8248 2. 8254 11 10 2. 8261 2. 8267 2. 8274 2. 8280 2. 8287 2. 8293 2. 8299 2. 8306 2. 8312 2. 8319 11 20 2. 8325 2. 8331 2. 8338 2. 8344 2. 8351 2. 8357 2. 8363 2. 8370 2. 8376 2. 8382 11 30 2. 8388 2. 8395 2. 8401 2. 8407 2. 8414 2. 8420 2. 8426 2. 8432 2. 8439 2. 8445 11 40 2. 8451 2. 8457 2. 8463 2. 8470 2. 8476 2. 8482 2. 8488 2. 8494 2.8500 2. 8506 11 50 2.8513 2. 8519 2. 8525 2. 8531 2. 8537 2. 8543 2. 8549 2. 8555 2. 8561 2. 8567 12 2. 8573 2. 8579 2. 8585 2. 8591 2.8597 1 2.8603 2. 8609 2. 8615 2. 8621 2. 8627 12 10 2. 8633 2. 8639 2. 8645 2. 8651 2.8657 ' 2.8663 2. 8669 2. 8675 2. 8681 2. 8686 12 20 2. 8692 2. 8698 2. 8704 2. 8710 2. 8716 2. 8722 2. 8727 2. 8733 2. 8739 2. 8745 12 30 2. 8751 2. 8756 2. 8762 2. 8768 2. 8774 . 2. 8779 2. 8785 2. 8791 2. 8797 2. 8802 12 40 2. 8808 2. 8814 2. 8820 2.8825 2. 8831 •: 2. 8837 2. 8842 2. 8848 2. 8854 2. 8859 12 50 2. 8865 2. 8871 2. 8876 2. 8882 2.8887 ^ 2.8893 2. 8899 2. 8904 2. 8910 2. 8915 .0 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 i 2.9004 2.9009 2. 9015 2. 9020 2. 9025 13 20 2. 9031 2. 9036 2.9042 2. 9047 2.9053 i 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 i 2.9165 2. 9170 2. 9175 2.9180 2. 9186 13 50 2. 9191 2. 9196 2. 9201 2. 9206 2.9212 ! 2.9217 2. 9222 2. 9227 2. 9232 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 1 2. 9385 2. 9390 14 30 2. 9395 2. 9400 2. 9405 2. 9410 2. 9415 2. 9420 2. 9425 2. 9430 2. 9435 2. 9440 14 40 2. 9445 2. 9450 2. 9455 2. 9460 2. 9465 2. 9469 2. 9474 2. 9479 2. 9484 2. 9489 14 50 2. 9494 2. 9499 2. 9504 2. 9509 2. 9513 2. 9518 2. 9523 2. 9528 2. 9533 1 2. 9538 15 2. 9542 2. 9547 2. 9552 2. 9557 2. 9562 2. 9566 2. 9571 2. 9576 2. 9581 1 2. 9586 15 10 2. 9590 2. 9595 2.9600 2. 9605 2.9609 2. 9614 2. 9619 2. 9624 2. 9628 1 2. 9633 15 20 2. 9638 2. 9643 2. 9647 2. 9652 2. 9657 2. 9661 2. 9666 2. 9671 2. 9675 2. 9680 15 30 2. 9685 2. 9689 2. 9694 2. 9699 2. 9703 2. 9708 2.9713 2.9717 2. 9722 2. 9727 15 40 2. 9731 2. 9736 2. 9741 2. 9745 2. 9750 2. 9754 2. 9759 2. 9763 2. 9768 2. 9773 15 50 2. 9777 2. 9782 2. 9786 2. 9791 2. 9795 2. 9800 2. 9805 2.9809 2. 9814 2.9818 16 2. 9823 2. 9827 2. 9832 2. 9836 2.9841 2. 9845 2. 9850 2. 9854 2. 9859 2. 9863 16 10 2. 9868 2. 9872 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 3. 0187 3.0191 3. 0195 3. 0199 3.0204 3. 0208 17 30 3. 0212 3. 0216 3. 0220 3. 0224 3. 0228 3. 0233 3. 0237 3. 0241 3. 0245 3. 0249 17 40 3. 0253 3. 0257 3. 0261 3. 0265 3. 0269 3. 0273 3. 0278 3. 0282 3. 0286 3. 0290 17 50 3. 0294 3. 0298 3. 0302 3. 0306 3. 0310 3. 0314 3. 0318 3. 0322 3. 0326 3. 0366' 3. 0330 3. 0370 18 3. 0334 3. 0338 3. 0342 3. 0346 3. 0350 3. 0354 3. 0358 3. 0362 18 10 3. 0374 3. 0378 3. 0382 3. 0386 3. 0390 3. 0394 3. 0398 3. 0402 3. 0406 3. 0410 18 20 3. 0414 3. 0418 3. 0422 3. 0426 3. 0430 3. 0434 3. 0438 3. 0441 3. 0445 3. 0449 18 30 3. 0453 3. 0457 3. 0461 3. 0465 3. 0469 3. 0473 3. 0477 3. 0481 3. 0484 3. 0488 18 40 3. 0492 3. 0496 3.0500 3. 0504 3. 0508 3. 0512 3. 0515 3. 0519 3. 0523 3. 0527 18 50 3. 0531 3. 0535 3. 0538 3. 0542 3.0546 I 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: TABLE IX. [Page 315 Logarithms of Small Arcs in Space or Time. Arc. 0" 1" 2" 8" 4" 5" 6" 7" 8" 9" O ' O** 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 3.0917 3. 0920 3. 0924 3. 0927 3. 0931 20 40 3. 0934 3. 0938 3. 0941 3. 0945 3. 0948 3. 0952 3. 0955 3.0959 3. 0962 3. 0966 20 50 3. 0969 3. 0973 3. 0976 3. 0980 3. 0983 3. 0986 3. 0990 3. 0993 3. 0997 3.1000 21 3. 1004 3. 1007 3. 1011 3. 1014 3. 1017 3. 1021 3. 1024 3. 1028 3. 1031 3.1035 21 10 3. 1038 3. 1041 3.1045 3. 1048 3. 1052 3. 1055 3. 1059 3. 1062 3.1065 3.1069 21 20 3. 1072 3. 1075 3. 1079 3. 1082 3. 1086 3. 1089 3. 1092 3. 1096 3.1099 3. 1103 21 30 3. 1106 3. 1109 3. 1113 3.1116 3. 1119 3. 1123 3. 1126 3. 1129 3. 1133 3. 1136 21 40 3. 1139 3. 1143 3. 1146 3.1149 3. 1153 3. 1156 3.1159 3. 1163 3. 1166 3. 1169 21 50 3. 1173 3. 1176 3. 1179 3. 1183 3. 1186 3. 1189 3. 1193 3. 1196 3. 1199 3. 1202 3. 1235 22 3. 1206 3. 1209 3. 1212 3. 1216 3. 1219 3. 1222 3. 1225 3. 1229 3. 1232 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. 1.342 3. 1345 3. 1348 3. 1351 3. 1355 3. 1358 3. 1361 3.1364 22 50 3. 1367 3. 1370 3. 1374 3. 1377 3. 1380 3. 1383 3. 1386 3. 1389 3. 1392 3. 1396 23 3. 1399 3. 1402 3. 1405 3. 1408 3. 1411 3. 1414 3. 1418 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. 1514 3. 1517 3. 1520 23 40 3. 1523 3. 1526 3. 1529 3. 1532 3. 1535 3. 1538 3. 1541 3. 1544 3. 1547 3. 1550 23 50 3. 1553 3. 1556 3. 1559 3.1562 3.1565 3. 1569 3. 1572 3. 1575 3. 1578 3. 1581 24 3, 1584 3. 1587 3. 1590 3. 1593 3. 1596 3. 1599 3. 1602 3. 1605 3. 1608 3. 1611 24 10 3. 1614 3. 1617 3. 1620 3.1623 3.1626 3. 1629 3. 1632 3. 1635 3. 1638 3. 1641 24 20 3.1644 3. 1647 3. 1649 3.1652 3.1655 3. 1658 3. 1661 3. 1664 3. 1667 3. 1670 24 30 3. 1673 3. 1676 3. 1679 3. 1682 1 3. 1685 3. 1688 3. 1691 3. 1694 3. 1697 3.1700 24 40 3.1703 3. 1706 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 I 3.1744 3. 1746 3. 1749 3. 1752 3. 1755 3. 1784 3. 1758 25 3. 1761 3. 1764 3. 1767 3.1770 3.1772 3. 1775 3. 1778 3. 1781 3. 1787 25 10 3. 1790 3. 1793 3. 1796 3. 1798 3. 1801 3. 1804 3. 1807 3. 1810 3. 1813 3. 1816 25 20 3. 1818 3. 1821 3. 1824 3. 1827 3. 1830 3. 1833 3. 1836 3. 1838 3. 1841 3. 1844 25 30 3. 1847 3. 1850 3. 1853 3. 1855 3. 1858 3. 1861 3. 1864 3. 1867 3. 1870 3. 1872 25 40 3. 1875 3. 1878 3. 1881 3. 1884 3. 1886 3. 1889 3. 1892 3. 1895 3. 1898 3. 1901 25 50 3. 1903 3. 1906 3. 1909 3.1912 1 3.1915 3.1917 3. 1920 3. 1923 3. 1926 3. 1928 26 3. 1931 3. 1934 3. 1937 3. 1940 3. 1942 3. 1945 3. 1948 3. 1951 3. 1953 3. 1956 26 10 3. 1959 3. 1962 3. 1965 3. 1967 3. 1970 3. 1973 3. 1976 3. 1978 3. 1981 3. 1984 26 20 3. 1987 3. 1989 3. 1992 3. 1995 3. 1998 3. 2000 3. 2003 3.2006 3.2009 3. 2011 26 30 3. 2014 3. 2017 3. 2019 3. 2022 3. 2025 3. 2028 3. 2030 3. 2033 3. 2036 3. 2038 26 40 3.2041 3. 2044 3. 2047 3. 2049 3. 2052 3. 2055 3. 2057 3.2060 a. 2063 3. 2066 26 50 3. 2068 3. 2071 3. 2074 3. 2076 3. 2079 3. 2082 3. 2084 3. 2087 3.2090 3.2092 27 3. 2095 3. 2098 3.2101 3. 2103 3. 2106 3. 2109 3.2111 3. 2114 3.2117 3. 2119 27 10 3. 2122 3. 2125 3. 2127 3. 2130 3.2133 3. 2135 3. 2138 3. 2140 3. 2143 3. 2146 27 20 3. 2148 3. 2151 3. 2154 3. 2156 3. 2159 3. 2162 3.2164 3. 2167 3. 2170 3. 2172 27 30 3. 2175 3. 2177 3. 2180 3. 2183 3. 2185 3. 2188 3. 2191 3. 2193 3. 2196 3. 2198 27 40 3. 2201 3.2204 3. 2206 3. 2209 3. 2212 3. 2214 3. 2217 3. 2219 3. 2222 3. 2225 27 50 . 3. 2227 3. 2230 3. 2232 3. 2235 3. 2238 3. 2240 3. 2243 3. 2245 3. 2248 3. 2250 28 3. 2253 3. 2256 3. 2258 3. 2261 3. 2263 3. 2266 3. 2269 3. 2271 3. 2274 3. 2276 28 10 3. 2279 3. 2281 3. 2284 3. 2287 3. 2289 3. 2292 3. 2294 3.2297 3.2299 3. 2302 28 20 3. 2304 3. 2307 3. 2310 3. 2312 3. 2315 3.2317 3. 2320 3. 2322 3. 2325 3. 2327 28 30 3. 2330 3. 2333 3.2335 3. 2338 3. 2340 3. 2343 3. 2345 3. 2348 3. 2350 3.2353 28 40 3. 2355 F 3. 2358 3. 2360 3. 2363 3. 2365 3. 2368 3. 2370 3. 2373 3. 2375 3. 2378 28 50 3. 2380 3. 2383 3. 2385 3. 2388 3. 2390 3. 2.393 3. 2395 3. 2398 3.2400 3. 2403 29 3. 2405 3. 2408 3. 2410 3. 2413 3. 2415 3. 2418 3. 2420 3. 2423 3. 2425 3. 2428 29 10 3. 2430 3. 2433 3.2435 3. 2438 3. 2440 3. 2443 3. 2445 3.2448 3.2450 3. 24.53 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. 2541 3. 2543 3. 2545 3.2548 3.2550 Page 316] APPENDIX V: TABLE IX. Logarithms of Small Arcs in Space or Time. Arc. 0" 1" 2" 3" 4" 6" 6" 7" j 8" 9" 0^ 30" ft 0^ 3. 2553 3. 2555 3. 2558 3.2560 3. 2562 3. 2565 3. 2567 3. 2570 3. 2572 ' 3. 2574 30 10 3. 2577 3. 2579 3. 2582 3. 2584 3. 2586 3. 2589 3. 2591 3. 2594 3. 2596 3. 2598 30 20 3. 2601 3. 2603 3. 2605 3. 2608 3. 2610 3. 2613 3. 2615 3. 2617 3. 2620 3. 2622 30 30 3. 2625 3. 2627 3. 2629 3. 2632 3. 2634 3. 2636 3. 2639 3. 2641 3. 2643 3. 2646 30 40 3. 2648 3. 2651 3. 2653 3. 2655 3. 2658 3. 2660 3. 2662 3. 2665 3. 2667 3. 2669 . 30 50 3. 2672 3. 2674 3. 2676 3. 2679 3. 2681 3. 2683 3. 2686 3. 2688 3. 2690 3. 2693 31 3. 2695 3. 2697 3.2700 3. 2702 3. 2704 3. 2707 3. 2709 3. 2711 3. 2714 3. 2716 31 10 3. 2718 3. 2721 3. 2723 "3. 2725 3. 2728 3. 2730 3. 2732 3. 2735 3. 2737 3. 2739 31 20 3. 2742 3. 2744 3. 2746 3. 2749 3. 2751 3. 2753 3. 2755 3. 2758 3. 2760 3. 2762 . 31 30 3. 2765 3. 2767 3. 2769 3. 2772 3. 2774 3. 2776 3. 2778 3. 2781 3. 2783 ! 3. 2785 | 31 40 3. 2788 3. 2790 3. 2792 3. 2794 3. 2797 3. 2799 3. 2801 3. 2804 3. 2806 3. 2808 31 50 3. 2810 3. 2813 3. 2835 3.2815 3. 2838 3. 2817 3. 2840 3. 2819 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 3. 2862 3. 2865 3. 2867 3. 2869 3. 2871 3. 2874 3. 2876 32 20 3. 2878 3. 2880 3. 2882 3. 2885 3. 2887 3. 2889 3. 2891 3. 2894 3. 2896 3. 2898 32 30 3. 2900 3. 2903 3. 2905 3. 2907 3.2909 3. 2911 3. 2914 3. 2916 3. 2918 3. 2920 32 40 3. 2923 3. 2925 3. 2927 3. 2929 3. 2931 3. 2934 3. 2936 3. 2938 3. 2940 3. 2942 32 50 3. 2945 3. 2947 3. 2949 3. 2951 3. 2953 3. 2956 3. 2958 3.2960 3. 2962 3. 2964 33 3. 2967 3. 2969 3. 2971 3. 2973 3. 2975 3. 2978 3. 2980 3. 2982 3. 2984 3. 2986 33 10 3. 2989 3. 2991 3. 2993 3. 2995 3. 2997 3.2999 3. 3002 3. 3004 3. 3006 3. 3008 33 20 3. 3010 3. 3012 3. 3015 3. 3017 3. 3019 3. 3021 3. 3023 3. 3025 3. 3028 3. 3030 33 30 3. 3032 3. 3034 3. 3036 3. 3038 3. 3041 3. 3043 3. 3045 3. 3047 3. 3049 3. 3051 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 3. 3145 3. 3147 3. 3149 3. 3151 3. 3153 3. 3156 3. 3158 34 30 3. 3160 3. 3162 3. 3164 3. 3166 3. 3168 3. 3170 3. 3172 3. 3174 3. 3176 3. 3179 34 40 3. 3181 3.3183 3. 3185 3. 3187 3. 3189 3. 3191 3. 3193 3. 3195 3.3197 3. 3199 34 50 3. 3201 3. 3204 3. 3206 3. 3208 3. 3210 3. 3212 3. 3214 3. 3216 3. 3218 3. 3220 35 3. 3222 3. 3224 3. 3226 3. 3228 3. 3230 3. 3233 3. 3235 3. 3237 3. 3239 3. 3241 35 10 3. 3243 3. 3245 3. 3247 3. 3249 3. 3251 3. 3253 3. 3255 3. 3257 3. 3259 3. 3261 35 20 3. 3263 3. 3265 3. 3267 3. 3269 3. 3272 3. 3274 3. 3276 3. 3278 3. 3280 3. 3282 35 30 3. 3284 3. 3286 3. 3288 3. 3290 3. 3292 3. 3294 3. 3296 3. 3298 3. 3300 3. 3302 35 40 3.3304 3. 3306 3. 3308 3. 3310 3. 3312 3. 3314 3.3316 3. 3318 3. 3320 3. 3322 35 50 3. 3324 3. 3326 3. 3328 3. 3330 3. 3332 3. 3334 3. 3336 3. 3339 3. 3341 3. 3343 36 3. 3345 3. 3347 3.3349 3. 3351 3. 3353 3.3355 3. 3357 3. 3359 3.3361 .3.3363 | 36 10 3. 3365 3. 3367 3. 3369 3. 3371 3. 3373 3. 3375 3. 3377 3. 3379 3. 3381 3. 3383 36 20 3. 3385 3. 3387 3. 3389 3. 3391 3. 3393 3. 3395 3. 3397 3. 3398 3.3400 3. 3402 36 30 3. 3404 3. 3406 3. 3408 3. 3410 3. 3412 3. 3414 3. 3416 3. 3418 3. 3420 3. 3422 36 40 3. 3424 3. 3426 3. 3428 3. 3430 3. 3432 3. 3434 3. 3436 3. 3438 3. 3440 3. 3442 36 50 3. 3444 3. 3446 3.3448 3. 3450 3. 3452 3. 3454 3. 3456 3. 3458 3. 3460 3. 3462 37 3.3464 3. 3465 3. 3467 3. 3469 3. 3471 3. 3473 3. 3475 3. 3477 3. 3479 3. 3481 37 10 3. 3483 3.3485 3. 3487 3. 3489 3. 349i 3. 3493 3. 3495 3. 3497 3. 3499 3. 3501 37 20 3. 3502 3. 3504 3. 3506 3. 3508 3. 3510 3. 3512 3. 3514 3. 3516 3. 3518 3. 3520 37 30 3. 3522 3. 3524 3. 3526 3. 3528 3.3530 3. 3531 3. 3533 3. 3535 3. 3537 3. 3539 37 40 3. 3541 3. 3543 3. 3545 3. 3547 3. 3549 3. 3551 3. 3553 3. 3555 3. 3556 3. 3558 37 50 3. 3560 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. 3688 3. 3690 39 3. 3692 3. 3694 3. 3696 3. 3698 3. 3700 3. 3701 3. 3703 3. 3705 3. 3707 3. 3709 39 10 3. 3711 3.3713 3. 3714 3.3716 3. 3718 3. 3720 3. 3722 3. 3724 3. 3725 3. 3727 39 20 3. 3729 3. 3731 3.3733 3. 3735 3. 3736 3. 3738 3. 3740 3. 3742 3. 3744 3. 3746 39 30 3. 3747 3. 3749 3.3751 3. 3753 3. 3755 3. 3757 3. 3758 3. 3760 3. 3762 3. 3764 39 40 3.3766 3. 3768 3. 3769 3. 3771 3. 3773 3. 3775 3. 3777 3. 3779 3. 3780 3. 3782 39 50 3. 3784 3. 3786 3. 3788 3. 3789 3. 3791 3. 3793 3. 3795 3. 3797 3. 3798 I 3. 3800 1 APPENDIX V: TABLE IX. [Page 317 Logarithms of Small Arcs in Space or Time. Arc. 0" 1" 2" 3" 4" 5" 6" 7" 8" »" o / 0" 40" 0^ 3. 3802 3. 3804 3. 3806 3. 3808 3. 3809 1 3. 3811 3. 3813 3. 3815 3. 3817 3. 3818 40 10 3. 3820 3. 3822 3. 3824 3. 3826 3. 3827 3. 3829 3. 3831 3. 3833 3. 3835 3. 3836 40 20 3. 3838 3. 3840 3. 3842 3.3844 3. 3845 3. 3847 3. 3849 3. 3851 3. 3852 3. 3854 40 30 3. 3856 3. 3858 3. 3860 3. 3861 3. 3863 3. 3865 3. 3867 3. 3869 3. 3870 3. 3872 40 40 3. 3874 3. 3876 3. 3877 3. 3879 3. 3881 3. 3883 3. 3885 3. 3886 3. 3888 3. 3890 40 50 3. 3892 3. 3893 3. 3895 3. 3897 3. 3899 3.3916 3. 3901 3. 3902 3.3904 3. 3906 "3. 3923 3. 3908 3. 3925 41 3. 3909 3.3911 3. 3913 3. 3915 3. 3918 3. 3920 3. 3922 41 10 3. 3927 3. 3929 3. 3930 3. 3932 3. 3934 3.3936 3.3938 3. 3939 3. 3941 3. 3943 41 20 3. 3945 3. 3946 3. 3948 3. 3950 3. 3952 3.3953 3.3955 3. 3957 3. 3959 3. 3960 41 30 3. 3962 3. 3964 3. 3965 3. 3967 3. 3969 3. 3971 3. 3972 3. 3974 3. 3976 3. 3978 41 40 3. 3979 3. 3981 3. 3983 3. 3985 3. 3986 3. 3988 3. 3990 3. 3992 3. 3993 3. 3995 41 50 3. 3997 3. 3998 3. 4000 3.4002 3. 4004 3. 4005 3. 4007 3. 4009 3. 4011 3. 4012 42 3. 4014 3. 4016 3.4017 3. 4019 3. 4021 3. 4023 3. 4024 3. 4026 3. 4028 3. 4029 42 10 3. 4031 3. 4033 3. 4035 3. 4036 3. 4038 3. 4040 3. 4041 3. 4043 3. 4045 3.4047 42 20 3. 4048 3. 4050 3. 4052 3. 4053 3. 4055 3. 4057 3. 4059 3.4060 3. 4062 3. 4064 42 30 3. 4065 3. 4067 3. 4069 3. 4071 3. 4072 3. 4074 3. 4076 3. 4077 3. 4079 3. 4081 42 40 3. 4082 3. 4084 3. 4086 3. 4087 3. 4089 3. 4091 3. 4093 3. 4094 3. 4096 3. 4098 42 50 3. 4099 3.4101 3. 4103 3. 4104 3. 4106 3. 4108 3. 4109 3.4111 3.4113 3.4115 43 3.4116 3.4118 3. 4120 3.4121 3. 4123 3. 4125 3. 4126 3. 4128 3. 4130 3. 4131 43 10 3. 4133 3. 4135 3.4136 3. 4138 3. 4140 3. 4141 3. 4143 3. 4145 3. 4146 3. 4148 43 20 3. 4150 3. 4151 3. 4153 3.4155 3. 4156 3. 4158 3. 4160 3.4161 3. 4163 3. 4165 43 30 3. 4166 3. 4168 3.4170 3. 4171 3.4173 3.4175 3. 4176 3.4178 3. 4180 3. 4181 43 40 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. 4216 3. 4201 3. 4203 3. 4219 3. 4205 3. 4206 3. 4208 3. 4209 3. 4211 3.4213 3. 4214 44 3. 4218 3. 4221 3.4223 i 3.4224 3. 4226 3. 4228 3. 4229 3. 4231 44 10 3. 4232 3. 4234 3. 4236 3. 4237 3. 4239 3. 4241 3. 4242 3. 4244 3. 4246 3. 4247 44 20 3. 4249 3. 4250 3. 4252 3. 4254 3. 4255 3. 4257 3. 4259 3. 4260 3. 4262 3. 4263 44 30 3. 4265 3. 4267 3. 4268 3. 4270 3. 4272 3. 4273 3. 4275 3. 4276 3. 4278 3. 4280 44 40 3. 4281 3. 4283 3. 4285 3. 4286 3. 4288 3. 4289 3. 4291 3. 4293 3.4294 3. 4296 44 50 3. 4298 3. 4314 3. 4299 3. 4301 3. 4302 3. 4304 3. 4306 3.4307 3. 4309 3. 4310 3.4312 45 3. 4315 3.4317 3. 4318 3. 4320 3. 4322 3. 4323 3. 4325 3. 4326 3. 4328 45 10 3. 4330 3. 4331 3. 4333 3. 4334 3. 4336 3. 4338 3. 4339 3. 4341 3. 4342 3. 4344 45 20 3. 4346 3. 4347 3. 4349 3. 4350 3. 4352 3. 4354 3. 4355 3. 4357 3. 4358 3. 4360 45 30 3. 4362 3. 4363 3. 4365 3. 4366 3. 4368 3. 4370 3. 4371 3. 4373 3. 4374 3. 4376 45 40 3. 4378 3. 4379 3. 4381 3. 4382 3. 4384 3. 4385 3. 4387 3. 4389 3. 4390 3. 4392 45 50 3. 4393 3. 4395 3. 4396 3. 4398 3. 4400 3. 4401 3. 4403 3. 4404 3. 4406 3. 4408 46 3. 4409 3.4411 3.4412 3. 4414 3. 4415 3. 4417 3. 4419 3. 4420 3. 4422 3. 4423 46 10 3. 4425 3. 4426 3. 4428 3. 4429 3. 4431 3.4433 3. 4434 3. 4436 3.4437 3.4439 46 20 3.4440 3.4442 3.4444 3. 4445 3. 4447 3. 4448 3. 4450 3. 4451 3. 4453 3. 4454 46 30 3. 4456 3.4458 3. 4459 3. 4461 3. 4462 3. 4464 3. 4465 3.4467 3. 4468 3. 4470 46 40 3. 4472 3.4473 3. 4475 3.4476 3. 4478 3. 4479 3. 4481 3. 4482 3. 4484 3. 4486 46 50 3. 4487 3. 4489 3.4490 3.4492 3. 4493 3. 4495 3. 4496 3. 4498 3. 4499 3. 4501 47 3. 4502 3. 4504 3. 4506 3. 4507 3. 4509 3. 4510 3. 4512 3. 4513 3. 4515 3. 4516 47 10 3. 4518 3. 4519 3. 4521 3. 4522 3. 4524 3. 4526 3. 4527 3. 4529 3. 4530 3. 4532 47 20 3. 4533 3. 4535 3. 4536 3. 4538 3. 4539 3. 4541 3. 4542 3.4544 3. 4545 3. 4547 47 30 3. 4548 3. 4550 3. 4551 3. 4553 3. 4555 3. 4556 3. 4558 3. 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 1 47 50 3. 4579 3. 4580 3. 4582 3. 4583 3. 4585 3. 4586 3. 4588 3. 4589 3. 4604 3. 4591 3.4592 48 3. 4594 3. 4595 3. 4597 3. 4598 3. 4600 3. 4601 3. 4603 3.4606 3.4607 | 48 10 3. 4609 3.4610 3.4612 3. 4613 3. 4615 3. 4616 3.4618 3. 4619 3. 4621 3. 4622 48 20 3. 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. 4646 3. 4648 3. 4649 3.4651 3.4652 48 40 3. 4654 3. 4655 3. 4657 3. 4658 3. 4660 3. 4661 3. 4663 3. 4664 3. 4666 3. 466; 48 50 3. 4669 3. 4670 3. 4672 3. 4673 3. 4675 3. 4676 3. 4678 3. 4679 3. 4681 3. 4682 49 3. 4683 3. 4685 3. 4686 3. 4688 3. 4689 3. 4691 3. 4692 3. 4694 3. 4695 3. 4697 49 10 3. 4698 3.4700 3. 4701 3. 4703 3. 4704 3. 4706 3. 4707 3. 4709 3. 4710 3.4711 . 49 20 3. 4713 3. 4714 3. 4716 3.4717 3. 4719 3. 4720 3. 4722 3. 4723 3. 4725 3. 4726 49 30 3. 4728 3. 4729 3. 4730 3. 4732 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. Arc. 0" 1" 2" 3" 4" 5" 6" 7" ' S" 9" O 1 0" 50" II 3. 4771 3. 4773 3. 4774 3. 4776 3. 4777 3. 4778 3. 4780 3. 4781 3. 4783 3. 4784 50 10 3. 4786 3. 4787 3. 4789 3. 4790 3. 4791 3. 4793 3. 4794 3. 4796 3. 4797 3. 4799 50 20 3.4800 3. 4802 3. 4803 3. 4804 3. 4806 3. 4807 3. 4809 3. 4810 3. 4812 3. 4813 50 30 3. 4814 3. 4816 3.4817 3. 4819 3. 4820 3. 4822 3. 4823 3. 4824 3. 4826 3. 4827 50 40 3. 4829 3. 4830 3. 4832 3. 4833 3. 4834 3. 4836 3. 4837 3. 4839 3. 4840 3. 4842 50 50 3. 4843 3. 4844 3. 4846 3. 4847 3.4849 3. 4850 3. 4852 3. 4853 3. 4854 3. 4856 51 3. 4857 3. 4859 3. 4860 3. 4861 3. 4863 3. 4864 3. 4866 3. 4667 3. 4869 3. 4870 51 10 3. 4871 3. 4873 3. 4874 3. 4876 3. 4877 3. 4878 3. 4880 3. 4881 3. 4883 3. 4884 51 20 3. 4886 3. 4887 3. 4888 3. 4890 3. 4891 3. 4893 3. 4894 3. 4895 3. 4897 3. 4898 51 30 3. 4900 3. 4901 3. 4902 3. 4904 3. 4905 3. 4907 3. 4908 3. 4909 3. 4911 3. 4912 51 40 3. 4914 3. 4915 3. 4916 3. 4918 3. 4919 3. 4921 3. 4922 3. 4923 3. 4925 3. 4926 51 50 3. 4928 3.4929 3. 4930 3. 4932 3. 4933 3. 4935 3. 4936 3. 4937 3. 4939 3. 4940 52 3. 4942 3. 4943 3.4944 3. 4946 3. 4947 3. 4949 3. 4950 3. 4951 3.4953 3.4954 | 52 10 3. 4955 3. 4957 3. 4958 3. 4960 3. 4961 3. 4962 3. 4964 3. 4965 3. 4967 3. 4968 52 20 3. 4969 3. 4971 3. 4972 3. 4973 3. 4975 3. 4976 3. 4978 3. 4979 3. 4980 3. 4982 52 30 3. 4983 3. 4984 3. 4986 3. 4987 3. 4989 3. 4990 3. 4991 3. 4993 3. 4994 3. 4995 52 40 3. 4997 3. 4998 3. 5000 3. 5001 3. 5002 3. 5004 3. 5005 3. 5006 3. 5008 3. 5009 52 50 3.5011 3. 5012 3. 5013 3. 5015 3. 5016 3. 5030 3. 5017 3. 5031 3. 5019 3.5032 3. 5020 3. 5034 3. 5022 3. 5035 3. 5023 3. 5037 53 3. 5024 3. 5026 3. 5027 3. 5028 53 10 3. 5038 3. 5039 3. 5041 3. 5042 3. 5043 3. 5045 3. 5046 3. 5047 3. 5049 3. 5050 53 20 3. 5051 3. 5053 3. 5054 3. 5056 3. 5057 3. 5058 3. 5060 3. 5061 3. 5062 3. 5064 53 30 3. 5065 3. 5066 3. 5068 3. 5069 3. 5070 3. 5072 3. 5C73 3. 5075 3. 5076 3. 5077 53 40 3. 5079 3. 5080 3. 5081 3. 5083 3. 5084 3. 5085 8. 5087 3. 5088 3. 5089 3. 5091 53 50 3. 5092 3. 5093 3. 5095 3. 5096 3. 5097 3. 5099 3. 5100 3. 5101 3. 5103 3. 5104 54 5. 5105 3. 5107 3. 5108 3. 5109 3.5111 3. 5112 3.5113 3. 5115 5.5116 3.5117 54 10 3.5119 3.5120 3.5122 3. 5123 3. 5124 3. 5126 3.5127 3.5128 3. 5130 3. 5131 54 20 3. 5132 3. 5134 3. 5135- 3. 5136 3. 5138 3. 5139 3. 5140 3. 5141 3.5143 3. 5144 54 30 3. 5145 3. 5147 3. 5148 3. 5149 3. 5151 3. 5152 3. 5153 3. 5155 3. 5156 3. 5157 54 40 3. 5159 3. 5160 3.5161 3. 5163 3. 5164 3. 5165 3.5167 3. 5168 3. 5169 3. 5171 54 50 3. 5172 3.5173 3. 5175 3. 5176 3.5177 3. 5179 3. 5180 3. 5181 3. 5183 3.5184 55 3. 5185 3. 5186 3. 5188 3. 5189 3. 5190 3. 5192 3. 5193 3. 5194 3. 5196 3. 5197 55 10 3. 5198 3. 5200 3«5201 3. 5202 3. 5204 3. 5205 3. 5206 3. 5207 3. 5209 3. 5210 55 20 3. 5211 3. 5213 3.5214 3. 5215 3. 5217 3. 5218 3. 5219 3. 5221 3. 5222 3. 5223 55 30 3. 5224 3. 5226 3. 5227 3. 5228 3. 5230 3. 5231 3. 5232 3. 5234 3. 5235 3. 5236 55 40 3. 5237 3. 5239 3. 5240 3. 5241 3. 5243 3. 5244 3. 5245 3. 5247 3. 5248 3. 5249 55 50 3. 5250 3. 5252 3. 5253 3. 5254 3. 5256 3. 5257 3. 5258 3. 5260 3. 5261 3. 5262 56 3. 5263 3. 5265 3. 5266 3. 5267 3. 5269 3. 5270 3. 5271 3. 5272 3. 5274 3. 5275 56 10 3. 5276 3. 5278 3. 5279 3. 5280 3. 5281 3. 5283 3. 5284 3. 5285 3. 5287 3. 5288 56 20 3. 5289 3. 5290 3. 5292 3. 5293 3. 5294 3. 5296 3. 5297 3. 5298 3. 5299 3. 5301 56 30 3. 5302 3. 5303 3. 5305 3. 5306 3. 5307 3. 5308 3. 5310 3. 5311 3. 5312 3. 5314 56 40 3. 5315 3. 5316 3. 5317 3. 5319 3. 5320 3. 5321 3. 5322 3. 5324 3. 5325 3. 5326 56 50 3. 5328 3. 5329 3. 5330 3. 5331 3. 5333 3. 5334 3. 5335 3. 5336 3. 5338 3. 5339 57 3. 5340 3. 5342 3. 5343 3.5344 3. 5345 3. 5347 3. 5348 3. 5349 3. 5350 3. 5.352 57 10 3. 5353 3. 5354 3. 5355 3. 5357 3. 5358 3. 5359 3. 5361 3. 5362 3. 5363 3. 5.364 57 20 3. 5366 3. 5367 3. 5368 3. 5369 3. 5371 3. 5372 3. 5373 3. 5374 3. 5376 3. 5377 57 30 3. 5378 3. 5379 3. 5381 3. 5382 3. 5383 3. 5384 3. 5386 3. 5387 3. 5388 3. 5390 57 40 3. 5391 3. 5392 3. 5393 3. 5395 3. 5396 3. 5397 3. 5398 3. 5400 3. 5401 3. 5402 57 50 3. 5403 3. 5405 3. 5406 3. 5407 3. 5408 3. 5410 3.5411 3. 5412 3. 5413 3. 5415 58 3. 5416 3. 5417 3. 5418 3. 5420 3. 5421 3. 5422 3. 5423 3. 5425 3. 5426 3. 5427 58 10 3. 5428 3. 5429 3.5431 3. 5432 3. 5433 3. 5434 3. 5436 3. 5437 3. 5438 3. 5439 58 20 3. 5441 3. 5442 3. 5443 3.5444 3. 5446 3. 5447 3. 5448 3. 5449 3. 5451 3. 5452 58 30 3. 5453 3. 5454 3. 5456 3. 5457 3. 5458 3. 5459 3. 5460 3. 5462 3. 5463 3. 5464 58 40 3. 5465 3. 5467 3. 5468 3. 5469 3. 5470 3. 5472 3. 5473 3. 5474 3. 5475 3. 5477 58 50 3. 5478 3. 5479 3. 5480 3. 5481 3. 5483 3; 5484 3. 5485 3. 5486 3. 5488 3. 5489 59 3. 5490 3. 5491 3. 5492 3. 5494 3. 5495 3. 5496 3. 5497 3. 5499 3.5500 3. 5501 59 10 3. 5502 3. 5504 3. 5505 3. 5506 3. 5507 3. 5508 3. 5510 3. 5511 3. 5512 3. 5513 59 20 3. 5514 3. 5516 3. 5517 3. 5518 3. 5519 3. 5521 3. 5522 3. 5523 3. 5524 3. 5525 59 30 3. 5527 3. 5528 3. 5529 3. 5530 3. 5532 3. 5533 3. 5534 3. 5535 3. 5536 3. 5538 59 40 3. 5539 3. 5540 3. 5541 3. 5542 3. 5544 3. 5545 3. 5546 3. 5547 3. 5549 3. 5550 59 50 3. 5551 3. 5552 3. 5553 3. 5555 3. 5556 3. 5557 3. 5558 3. 5559 3. 5561 3. 5562 UNIVERSITY Of APPENDIX V: TABLE IX. [Page 319 Logarithms of Small Arcs in Space or Time. Arc. 1 0" 1" ! 2" i 8" 4" 5" 6" '- 8" 9" o / 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 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 3. 5751 2 40 3. 5752 3. 5753 3. 5754 3. 5755 3. 5756 3. 5758 3. 5759 3. 5760 3. 5761 3. 5762 2 50 3. 5763 3. 5765 3. 5766 3. 5767 3. 5768 3. 5769 3. 5770 3. 5771 3. 5773 3. 5774 1 3 3. 5775 3. 5776 3.5777 3. 5778 3. 5780 3. 5781 3. 5782 3. 5783 3. 5784 3. 5785 3 10 3. 5786 3. 5788 3. 5789 3. 5790 3. 5791 3. 5792 3. 5793 3. 5794 3. 5796 3. 5797 3 20 3. 5798 3. 5799 3. 5800 3. 5801 3. 5802 3. 5804 3. 5805 3.5806 3. 5807 3. 5808 3 30 3. 5809 3. 5810 3. 5812 3. 5813 3. 5814 3. 5815 3. 5816 3. 5817 3. 5818 3. 5819 3 40 3. 5821 3. 5822 3. 5823 3. 5824 3. 5825 3. 5826 3. 5827 3. 5829 3. 5830 3. 5831 3 50 3. 5832 3. 5833 3. 5834 3. 5835 3. 5837 3. 5838 3. 5839 3. 5840 3. 5841 3. 5842 1 4 3. 5843 3. 5844 3. 5846 3. 5847 3. 5848 3. 5849 3. 5850 3. 5851 3. 5852 3. 5853 4 10 3. 5855 3. 5856 3. 5857 3. 5858 3. 5859 3. 5860 3. 5861 3. 5862 3. 5864 3. 5865 4 20 3. 5866 3. 5867 3. 5868 3. 5869 3. 5870 3. 5871 3. 5873 3. 5874 3. 5875 3. 5876 4 30 3. 5877 3. 5878 3. 5879 3. 5880 3. 5882 3. 5883 3. 5884 3. 5885 3. 5886 3. 5887 4 40 3. 5888 3. 5889 3. 5891 3. 5892 3. 5893 3. 5894 3. 5895 3. 5896 3. 5897 3. 5898 4 50 3. 5899 3. 5901 3. 5902 3. 5903 3.5904 3. 5905 3. 5906 3. 5907 3. 5908 3. 5910 1 5 3.5911 .3.5912 1 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 3.59»T 3. 5928 3. 5930 3. 5931 3. 5932 5 20 3. 5933 3. 5934 3. 5935 3. 5936 3. 5937 3. 5938 3.5940 3. 5941 3. 5942 3. 5943 5 30 3. 5944 3. 5945 3. 5946 3. 5947 3. 5948 3. 5949 3. 5951 3. 5952 3. 5953 3. 5954 5 40 3. 5955 3. 5956 3. 5957 3. 5958 3. 5959 3.5960 3. 5962 3. 5963 3. 5964 3. 5965 5 50 3. 5966 3. 5967 3. 5968 3. 5969 3. 5970 3. 5971 3. 5973 3. 5974 3. 5975 3. 5976 1 6 3. 5977 3. 5978 3. 5979 3. 5980 3. 5981 3. 5982 3. 5984 3. 5985 3. 5986 3. 5987 6 10 3. 5988 3. 5989 3. 5990 3. 5991 3. 5992 3.5993 3. 5994 3. 5996 3. 5997 3. 5998 6 20 3. 5999 3. 6000 3. 6001 3.6002 3. 6003 3.6004 3.6005 3. 6006 3.6008 3.6009 *6 30 3.6010 3. 6011 3. 6012 3. 6013 3. 6014 3. 6015 3. 6016 3. 6017 3. 6018 3. 6020 6 40 3. 6021 3.6022 i 3.6023 3. 6024 3.6025 ! 3.6026 3. 6027 3. 6028 3. 6029 3.6030 6 50 3. 6031 3.6033 I 3.6034 3. 6035 3.6036 i 3.6037 3. 6038 3. 6039 3. 6040 3. 6041 1 7 3. 6042 3.6043 3.6044 3. 6046 3.6047 3.6048 3. 6049 3. 6050 3. 6051 3. 6052 7 10 3. 6053 3.6054 3.6055 3. 6056 3. 6057 3. 6058 3. 6060 3.6061 3.6062 3. 6063 7 20 3. 6064 3.6065 3.6066 3. 6067 3. 6068 3. 6069 3. 6070 3. 6071 3. 6072 3. 6073 7 30 3. 6075 3.6076 3.6077 3. 6078 3.6079 3.6080 3. 6081 3. 6082 3. 6083 3. 6084 7 40 3. 6085 3.6086 3.6087 3. 6088 3.6090 I 3.6091 3. 6092 3. 6093 3. 6094 3. 6095 7 50 3. 6096 3.6097 3.6098 3. 6099 3.6100 ! 3.6101 3. 6102 3. 6103 3. 6104 3. 6106 1 8 3. 6107 3.6108 3.6109 3.6110 3.6111 3.6112 3.6113 3. 6114 3.6115 3.6116 8 10 3. 6117 3.6118 3.6119 3. 6120 3. 6121 3. 6123 3. 6124 3. 6125 3. 6126 3. 6127 8 20 3. 6128 3.6129 3.6130 3.6131 3. 6132 3. 6133 3. 6134 3. 6135 3. 6136 3. 6137 8 30 3. 6138 3.6139 1 3.6141 3. 6142 3. 6143 3. 6144 3. 6145 3. 6146 3. 6147 3. 6148 8 40 3. 6149 3. 6150 3.6151 3. 6152 3. 6153 3. 6154 3. 6155 3. 6156 3. 6157 3. 6158 8 50 3. 6160 3. 6161 3.6162 3. 6163 3.6164 3. 6165 3. 6166 3. 6167 3. 6168 3. 6169 1 9 3. 6170 3. 6171 3.6172 3. 6173 3. 6174 3. 6175 3. 6176 3.6177 3.6178 3. 6179 9 10 3. 6180 3. 6182 1 3.6183 3. 6184 3.6185 3. 6186 3. 6187 3. 6188 3. 6189 3. 6190 9 20 3. 6191 3. 6192 1 3.6193 3. 6194 3. 6195 3. 6196 3. 6197 3.6198 3. 6199 3.6200 9 30 3. 6201 3. 6202 3.6203 3. 6204 3. 6206 3. 6207 3. 6208 3. 6209 3. 6210 3. 6211 9 40 3. 6212 3. 6213 3. 6214 3. 6215 3. 6216 3. 6217 3. 6218 3. 6219 3. 6220 3. 6221 9 50 3. 6222 3. 6223 3. 6224 3. 6225 1 3.6226 3.6227 3. 6228 3. 6229 3. 6230 3. 6231 Page 320J APPENDIX Y: TABLE IX. Logarithms of Small Arcs in Space or Time. Arc. 0" 1" 2" 1 3" 4" 5" 6" 7" 8" 9" o / " Ih 10"' 0' 3. 6232 3. 6234 3. 6235 3. 6236 3.6237 1 3.6238 3. 6239 3. 6240 3. 6241 3. 6242 10 10 3. 6243 3. 6244 3. 6245 3. 6246 3. 6247 3. 6248 3. 6249 3. 6250 3. 6251 3. 6252 10 20 3. 6253 3. 6254 3. 6255 3. 6256 3. 6257 3. 6258 3. 6259 3. 6260 3. 6261 3. 6262 10 30 3. 6263 3. 6264 3. 6265 3.6266 ' 3.6268 3. 6269 3. 6270 3. 6271 3. 6272 3. 6273 10 40 3. 6274 3. 6275 3. 6276 3.6277 3.6278 3. 6279 3. 6280 3. 6281 3. 6282 3. 6283 10 50 3. 6284 3. 6285 3. 6286 3. 6287 3. 6288 3. 6289 3.6290 3. 6291 3. 6292 3. 6293 3. 6303 1 11 3. 6294 3. 6295 3. 6296 3. 6297 3. 6298 3. 6299 3. 6300 3. 6301 3. 6302 11 10 3. 6304 3. 6305 3. 6306 3. 6307 3. 6308 3. 6309 3. 6310 3. 6311 3.6312 3. 6313 11 20 3. 6314 3. 6315 3.6316 3. 6317 3. 6318 3. 6320 3. 6321 3. 6322 3. 6323 3. 6324 11 30 3. 6325 3. 6326 3. 6327 3. 6328 3. 6329 3. 6330 3. 6331 3. 6332 3. 6383 3. 6334 11 40 3. 6335 3. 6336 3. 6337 3. 6338 3. 6339 3. 6340 3. 6341 3. 6342 3. 6343 3. 6344 11 50 3. 6345 3. 6346 3. 6347 3. 6348 3. 6349 3. 6350 3. 6351 3. 6352 3. 6353 3. 6354 1 12 3. 6355 3. 6356 3. 6357 3. 6358 3. 6359 3. 6360 3. 6361 3. 6362 3. 6363 3. 6364 12 10 3. 6365 3. 6366 3. 6367 3. 6368 3. 6369 3. 6370 3. 6371 3. 6372 3. 6373 3. 6374 12 20 3. 6375 3. 6376 3. 6377 3. 6378 3. 6379 3. 6380 3. 6381 3. 6382 3. 6383 3. 6384 12 30 3. 6385 3. 6386 3. 6387 3.6388 3.6389 3. 6390 3. 6391 3. 6392 3. 6393 3. 6394 12 40 3. 6395 3. 6396 3. 6397 3. 6398 3. 6399 3. 6400 3. 6401 3. 6402 3. 6403 3. 6404 12 50 3. 6405 3. 6406 3.6407 3. 6408 3. 6409 3. 6419 3.6410 3. 6411 3. 6421 3. 6412 3. 6422 3. 6413 3. 6423" 3. 6414 1 13 3. 6415 3. 6416 3.6417 3. 6418 3. 6420 3. 6424 13 10 3. 6425 3. 6426 3. 6427 3.6428 3.6429 3. 6430 3. 6431 3. 6432 3. 6433 3. 6434 13 20 3. 6435 3. 6436 3. 6437 3. 6437 3. 6438 3. 6439 3. 6440 3. 6441 3.6442 3. 6443 13 30 3. 6444 3. 6445 3. 6446 3. 6447 3.6448 3. 6449 3. 6450 3. 6451 3. 6452 3. 6453 13 40 3. 6454 3. 6455 3. 6456 3. 6457 3. 6458 3.6459 3. 6460 3. 6461 3. 6462 3. 6463 13 50 3. 6464 3. 6465 3. 6466 3.6467 3. 6468 3. 6469 3. 6470 3.6471 3. 6472 3. 6473 1 14 3. 6474 3. 6475 3. 6476 3. 6477 3. 6478 3. 6479 3. 6480 3. 6481 3.6482 3. 6483 14 10 3. 6484 3. 6485 3. 6486 3. 6487 3. 6488 3. 6488 3. 6489 3. 6490 3. 6491 3. 6492 14 20 3. 6493 3. e-494 3. 6495 3. 6496 3. 6497 3. 6498 3. 6499 3. 6500 3. 6501 3. 6502 14 30 3. 6503 3. 6504 3. 6505 3. 6506 3. 6507 3. 6508 3. 6509 3. 6510 3. 6511 3. 6512 14 40 3. 6513 3. 6514 3. 6515 3. 6516 3. 6517 3. 6518 3. 6519 3. 6520 3. 6521 3. 6521 14 50 3. 6522 3. 6523 3. 6524 3. 6525 3. 6526 3. 6527 3. 6528 3. 6529 3. 6530 3. 6531 1 15 3. 6532 3. 6533 3.6534 i 3.6535 3. 6536 3. 6537 3. 6538 3. 6539 3. 6540 3. 6541 15 10 3. 6542 3. 6543 3.6544 i 3.6545 3. 6546 3. 6547 3. 6548 3. 6549 3. 6549 3. 6550 15 20 3. 6551 3. 6552 3.6553 ! 3.6554 3. 6555 3. 6556 3. 6557 3. 6558 3. 6559 3. 6560 15 30 3. 6561 3. 6562 3. 6563 3. 6564 3. 6565 3. 6566 3. 6567 3. 6568 3. 6569 3. 6570 15 40 3. 6571 3. 6572 3. 6572 3. 6573 3. 6574 3. 6575 3. 6576 3. 6577 3. 6578 3. 6579 15 50 3. 6580 3. 6581 3. 6582 3. 6583 3. 6584 3. 6585 3. 6586 3. 6587 3.6588 3. 6589 1 16 3. 6590 3. 6591 3. 6592 3. 6593 3. 6593 3. 6594 3. 6595 3. 6596 3. 6597 3. 6598 16 10 3. 6599 3. 6600 3. 6601 3. 6602 3. 6603 3. 6604 3. 6605 3. 6606 3. 6607 3. 6608 16 20 3. 6609 3. 6610 3.6611 3.6611 3. 6612 3. 6613 3. 6614 3. 6615 3. 6616 3.6^7 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 3. 6670 3. 6671 3. 6672 3. 6673 3. 6674 17 30 3. 6675 3. 6675 3. 6676 3. 6677 3. 6678 3. 6679 3. 6680 3. 6681 3. 6682 3. 6683 17 40 3. 6684 3. 6685 3. 6686 3. 6687 3. 6688 3. 6689 3. 6689 3. 6690 3. 6691 3. 6692 17 50 3. 6693 3. 6694 3. 6695 3. 6696 3. 6697 3. 6698 3. 6707 3. 6699 3. 6700 3. 6701 3. 6702 1 18 3. 6702 3. 6703 3. 6704 3. 6705 3. 6706 3. 6708 3. 6709 3. 6710 3.6711 18 10 3. 6712 3. 6713 3. 6714 3. 6715 3. 6715 3. 6716 3. 6717 3. 67-18 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. 6750 3. 6751 3. 6752 3. 6753 3. 6754 3. 6755 3. 6756 3. 6757 1 19 3. 6758 3. 6759 3. 6760 3. 6761 3. 6761 3. 6762 3. 6763 3.6764 3. 6765 3. 6766 19 10 3. 6767 3. 6768 3. 6769 3. 6770 3. 6771 3. 6772 3. 6772 3. 6773 3. 6774 3. 6775 19 20 3. 6776 3. 6777 3. 6778 3. 6779 3. 6780 3. 6781 3. 6782 3. 6782 3. 6783 3. 6784 19 30 3.J6785 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" I" 2" 3" 4" 5" 6" 7" 8" 9" o / V 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 j 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. 6871 3. 6863 3. 6864 3. 6865 3. 6865 1 21 3. 6866 3. 6867 3. 6868 3. 6869 3. 6870 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. 6915 3. 6916 3. 6917 3. 6918 3. 6919 1 22 3. 6920 3. 6921 3. 6921 3. 6922 3. 6923 3. 6924 3. 6925 3. 6926 3. 6927 3. 6928 22 10 3. 6928 3. 6929 3. 6930 3. 6931 3. 6932 3. 6933 3. 6934 3. 6935 3. 6936 3. 6936 22 20 3. 6937 3. 6938 3. 6939 3. 6940 3. 6941 3. 6942 3. 6943 3. 6943 3. 6944 3. 6945 22 30 3. 6946 3. 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. 3962 3. 6963 22 50 3.6964 3. 6964 3. 6965 3. 6966 3. 6967 3. 6968 3. 6969 3. 6970 3. 6971 3. 6979 3. 6971 1 23 3. 6972 3. 6973 3. 6974 3. 6975 3. 6976 3. 6977 3. 6978 3. 6978 3. 6980 23 10 3. 6981 3. 6982 3. 6983 3. 6984 3. 6984 3. 6985 3. 6986 3. 6987 3. 6988 3. 6989 23 20 3. 6990 3. 6991 3. 6991 3. 6992 3. 6993 3. 6994 3. 6995 3. 6996 3. 6997 3. 6998 23 30 3. 6998 3. 6999 3. 7000 3. 7001 3.7002 3. 7003 3.7004 3. 7004 3. 7005 3.7006 23 40 3. 7007 3. 7008 3.7009 3. 7010 3. 7010 3. 7011 3. 7012 3. 7013 3. 7014 3. 7015 23 50 3. 7016 3. 7017 3. 7017 3. 7018 3. 7019 3. 7020 3. 7021 3. 7022 3. 7023 3. 7023 1 24 3. 7024 3. 7025 3. 7026 3. 7027 3. 7028 3. 7029 3. 7029 3. 7030 3. 703J 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. 7174 3. 7175 3. 7176 1 27 3. 7177 3. 7178 3. 7178 3. 7179 3. 7180 3. 7181 3. 7182 3.7183 3. 7183 3. 7184 27 10 3. 7185 3. 7186 3. 7187 3. 7188 3. 7188 3. 7189 3. 7190 3. 7191 3. 7192 3. 7192 27 20 3. 7193 3. 7194 3. 7195 3. 7196 3. 7197 3. 7197 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. 7271 3. 7271 3. 7272 3. 7273 3. 7274 3. 7275 1 29 3. 7275 3. 7276 3. 7277 3. 7278 3. 7279 3. 7279 3. 7280 3. 7281 3. 7282 3. 7283 29 10 3. 7284 3. 7284 3. 7285 3. 7286 3. 7287 3. 7288 3. 7288 3. 7289 3.7290 3. 7291 29 20 3. 7292 3. 7292 3. 7293 3. 7294 3. 7295 3. 7296 3. 7297 3. 7297 3. 7298 3. 7299 29 30 3. 7300 3. 7301 3. 7301 3. 7302 3. 7303 *3. 7304 3. 7305 3. 7305 3.7306 3. 7307 29 40 3. 7308 3.7309 3. 7309 3. 7310 3. 7311 3. 7312 3. 7313 3. 7313 3. 7314 3. 7315 29 50 3. 7316 3. 7317 3. 7317 3. 7318 3. 7319 3. 7320 3. 7321 3. 7322 3. 7322 3. 7323 6583— Oe Page 322] APPENDIX V: TABLE IX. Logarithms of Small Arcs in Space oi Time. Arc. • 0" 1" 2" 8" 4" o" 6" 7" 8" 9" O / 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. 7458 32 50 3. 7459 3. 7459 3. 7460 3. 7461 3. 7462 3. 7462 3. 7463 3.7464 3.7465 3. 7466 1 33 3. 7466 3. 7467 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. 7563 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. 7656 37 10 3. 7657 3. 7657 3. 7658 3. 7659 3. 7660 3. 7660 3. 7661 3. 7662 3. 7663 3. 7663 37 20 3.7664 ii.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 Space or Time. Arc. 0" 1" 2" 8" 4" 6" 6" V> 8" 9" 1 II 40 10 40 20 40 30 40 40 40 50 3. 7782 3. 7789 3. 7796 3. 7803 3. 7810 3. 7818 3. 7782 3. 7789 3. 7797 3. 7804 3. 7811 3. 7818 3. 7783 3. 7790 3. 7797 3. 7805 3. 7812 3. 7819 3.7784 3. 7791 3. 7798 3. 7805 3. 7813 3. 7820 3. 7784 3. 7792 3. 7799 3. 7806 3. 7813 3. 7820 3.7785 3. 7792 3.7800 3. 7807 3. 7814 3. 7821 3. 7786 3. 7793 3.7800 3. 7807 3. 7815 -8. 7822 3. 7787 3. 7794 3. 7801 3. 7808 3. 7815 3. 7823 3. 7787 3. 7795 3. 7802 3.7809 3. 7816 3. 7823 3.7788 3. 7795 3. 7802 3. 7810 3. 7817 3. 7824 1 41 41 10 41 20 41 30 41 40 41 50 3. 7825 3. 7832 3. 7839 3. 7846 3. 7853 3. 7860 3. 7825 3. 7833 3. 7840 3. 7847 3. 7854 X 7861 3. 7826 3. 7833 3. 7840 3. 7848 3. 7855 3. 7862 3. 7827 3.7834 3. 7841 3. 7848 3. 7855 3. 7863 3. 7828 3.7835 3.7842 3. 7849 3. 7856 3. 7863 3. 7828 3. 7835 3. 7843 3. 7850 3.7857 3. 7864 3.7829 3. 7836 3. 7843 3. 7850 3. 7858 3. 7865 3. 7830 3. 7837 3. 7844 3. 7851 3.7858 3.7865 3. 7830 3. 7838 3. 7845 3.7852 3.7859 3.7866 3. 7831 3. 7838 3. 7845 3. 7853 3.7860 3. 7867 1 42 42 10 42 20 42 30 42 40 42 50 3. 7868 3. 7875 3. 7882 3. 7889 3. 7896 3. 7903 3. 7868 3. 7875 3. 7882 3. 7889 3. 7897 3.7904 3. 7869 3. 7876 3. 7883 3. 7890 3. 7897 3.7904 3. 7870 3. 7877 3. 7884 3. 7891 3. 7898 3. 7905 3. 7870 3. 7877 3. 7885 3. 7892 3. 7899 3. 7906 3. 7871 3. 7878 3. 7885 3. 7892 3. 7899 3. 7906 3. 7872 3. 7879 ■3. 7886 3. 7893 3.7900 3. 7907 3. 7872 3. 7880 3. 7887 3. 7894 3. 7901 3. 7908 3. 7873 3.7880 3. 7887 3. 7894 3. 7901 3.7908 3. 7874 3. 7881 3. 7888 3. 7895 3.7902 3.7909 1 43 43 10 43 20 43 30 43 40 43 50 3. 7910 3. 7917 3. 7924 3. 7931 3. 7938 3. 7945 3. 7911 3. 7918 3. 7925 3. 7932 3. 7939 3. 7946 3. 7911 3. 7918 3. 7925 3. 7932 3. 7939 3. 7946 3. 7912 3. 7919 3. 7926 3. 7933 3. 7940 3. 7947 3. 7913 3. 7920 3. 7927 3. 7934 3. 7941 3. 7948 3. 7913 3. 7920 3. 7927 3.7934 3. 7941 3. 7948 3. 7914 3. 7921 3. 7928 3. 7935 3. 7942 3. 7949 3. 7915 3. 7922 3. 7929 3. 7936 3. 7943 3. 7950 3. 7916 3. 7923 3. 7930 3. 7937 3. 7943 3. 7950 3. 7916 3. 7923 3. 7930 3. 7937 3.7944 3. 7951 1 44 44 10 44 20 44 30 44 40 44 50 3. 7952 3. 7959 3. 7966 3. 7973 3. 7980 3. 7987 3. 7953 3. 7959 3. 7966 3. 7973 3. 7980 3. 7987 3. 7953 3. 7960 3. 7967 3. 7974 3. 7981 3. 7988 3. 7954 3. 7961 3. 7968 3. 7975 3. 7982 3. 7989 3. 7955 3. 7962 3. 7969 3. 7975 3. 7982 3. 7989 3. 7955 3. 7962 3. 7969 3. 7976 3. 7983 3. 7990 3. 7956 3. 7963 3. 7970 3. 7977 3. 7984 3. 7991 3. 7957 3. 7964 3. 7971 3. 7978 3. 7984 3. 7991 3. 7957 3. 7964 3. 7971 3. 7978 3.7985 3. 7992 3. 7958 3.7965 3. 7972 3. 7979 3. 7986 3. 7993 1 45 45 10 45 20 45 30 45 40 45 50 3. 7993 3.8000 3.8007 3. 8014 3. 8021 3. 8028 3. 7994 3. 8001 3. 8008 3. 8015 3. 8022 3. 8028 3. 7995 3.8002 3. 8009 3. 8015 3. 8022 3. 8029 3. 7995 3. 8002 3.8009 3. 8016 3. 8023 3. 8030 3. 7996 3.8003 3. 8010 3. 8017 3. 8024 3. 8030 3. 7997 3.8004 3. 8011 3. 8017 3. 8024 3. 8031 3. 7998 3.8004 3. 8011 3. 8018 3. 8025 3. 8032 3. 7998 3.8005 3. 8012 3. 8019 3. 8026 3. 8033 3. 7999 3.8006 3. 8013 3. 8020 3. 8026 3. 8033 3.8000 3.8006 3. 8013 3. 8020 3. 8027 3. 8034 3.8041 3.8048 3. 8054 3.8061 3.8068 3. 8075 1 46 46 10 46 20 46 30 46 40 46 50 3. 8035 3. 8041 3. 8048 3. 8055 3. 8062 3. 8069 3. 8035 3. 8042 3. 8049 3. 8056 3. 8062 3. 8069 3. 8036 3. 8043 3. 8050 3. 8056 3. 8063 3. 8070 3. 8036 3. 8043 3. 8050 3. 8057 3. 8064 3. 8071 3. 8037 3. 8044 3. 8051 3. 8058 3. 8065 3. 8071 3. 8038 3. 8045 3. 8052 3. 8058 3. 8065 3. 8072 3. 8039 3.8045 3. 8052 3. 8059 3. 8066 3. 8073 3. 8039 3. 8046 3. 8053 3. 8060 3.8067 3. 8073 3.8040 3. 8047 3. 8054 3.8060 3.8067 3. 8074 1 47 47 10 47 20 47 30 47 40 47 50 3. 8075 3. 8082 3. 8089 3. 8096 3. 8102 3. 8109 3. 8076 3. 8083 3. 8090 3. 8096 3. 8103 3. 8110 3. 8077 3. 8083 3. 8090 3. 8097 3. 8104 3.8110 3. 8077 3. 8084 3. 8091 3. 8098 3. 8104 3. 8111 3. 8078 3. 8085 3. 8092 3. 8098 3. 8105 3. 8112 3. 8079 3. 8085 3. 8092 3.8099 3. 8106 3.8112 3. 8079 3. 8086 3. 8093 3. 8099 3.8106 3. 8113 3. 8080 3. 8087 3. 8094 3.8100 3. 8107 3. 8114 3. 8081 3. 8088 3. 8094 3. 8101 3. 8108 3. 8114 3. 8081 3. 8088 3.8095 3. 8102 3. 8108 3. 8115 1 48 48 10 48 20 48 30 48 40 48 50 3.8116 3. 8122 3. 8129 3. 8136 3. 8142 3. 8149 3. 8116 3. 8123 3. 8130 3. 8136 3. 8143 3. 8150 3. 8117 3. 8124 3. 8130 3. 8137 3.8144 3. 8150 3.8118 3. 8124 3. 8131 3. 8138 3. 8144 3. 8151 3.8118 3. 8125 3. 8132 3. 8138 3. 8145 3. 8152 3.8119 3. 8126 3. 8132 3. 8139 3. 8146 3. 8152 3. 8120 3. 8126 3. 8133 3. 8140 3. 8146 3. 8153 3. 8120 3. 8127 3. 8134 3. 8140 3. 8147 3. 8154 3. 8121 3. 8128 3. 8134 3. 8141 3. 8148 3. 8154 3. 8122 3. 8128 3. 8135 3. 8142 3. 8148 3. 8155 1 49 49 10 49 20 49 30 49 40 49 50 3. 8156 3. 8162 3. 8169 3. 8176 3. 8182 3. 8189 3. 8156 3. 8163 3. 8170 3. 8176 3. 8183 3. 8190 3. 8157 3. 8164 3. 8170 3. 8177 3. 8184 3. 8190 3. 8158 3. 8164 3. 8171 3. 8178 3. 8184 3. 8191 3. 8158 3. 8165 3. 8172 3. 8178 3. 8185 3. 8191 3. 8159 3. 8166 3. 8172 3. 8179 3. 8185 3. 8192 3. 8160 3. 8166 3. 8173 3. 8180 3. 8186 3. 8193 3.8160 3. 8167 3. 8174 3. 8180 3. 8187 3. 8193 3. 8161 3. 8168 3. 8174 3. 8181 3. 8188 3. 8194 3. 8162 3. 8168 3. 8175 3. 8182 3. 8188 3. 8195 Page 324] APPENDIX V: TABLE IX. Logarithms of Small Arcs in Space or Time. Arc. 0" 1" 2" 3" 4" 6" 6" 7" 8" 9" / // 50 10 50 20 50 30 50 40 50 50 3. 8195 3. 8202 3. 8209 3. 8215 3. 8222 3. 8228 3. 8196 3. 8203 3. 8209 3. 8216 3. 8222 3. 8229 3. 8197 3. 8203 3. 8210 3. 8216 3. 8223 3.8230 3. 8197 3. 8204 3. 8211 3. 8217 3. 8224 3. 8230 3. 8198 3. 8205 3.8211 3. 8218 3. 8224 3. 8231 3. 8199 3. 8205 3. 8212 3. 8218 3. 8225 3. 8231 3. 8199 3. 8206 3. 8213 3. 8219 3. 8226 3. 8232 3.8200 3. 8207 3. 8213 3. 8220 3. 8226 3. 8233 3. 8201 3. 8207 3. 8214 3. 8220 3. 8227 3. 8233 3. 8201 3. 8208 3. 8214 3. 8221 3. 8228 3. 8234 1 51 51 10 51 20 51 30 51 40 51 50 3. 8235 3. 8241 3. 8248 3. 8254 3. 8261 3. 8267 3. 8235 3. 8242 3. 8248 3. 8255 3. 8261 3. 8268 3. 8236 3. 8243 3. 8249 3. 8256 3. 8262 3. 8269 3. 8237 3. 8243 3. 8250 3. 8256 3. 8263 3. 8269 3. 8237 3. 8244 3. 8250 3. 8257 3. 8263 3. 8270 3. 8238 3. 8245 3. 8251 3. 8258 3.8264 3. 8270 3. 8239 3. 8245 3. 8252 3. 8258 3. 8265 3. 8271 3. 8239 3. 8246 3. 8252 3. 8259 3. 8265 3. 8272 3. 8240 3. 8246 3. 8253 3. 8259 3. 8266 3. 8272 3. 8241 3. 8247 3. 8254 3. 8260 3. 8267 3. 8273 1 52 52 10 52 20 52 30 52 40 52 50 3. 8274 3. 8280 3. 8287 3. 8293 3.8299 3. 8306 3. 8274 3. 8281 3. 8287 3. 8294 3.8300 3. 8307 3. 8275 3. 8281 3. 8288 3. 8294 3. 8301 3. 8307 3. 8276 3. 8282 3. 8289 3. 8295 3. 8301 3. 8308 3. 8276 3. 8283 3. 8289 3. 8296 3. 8302 3. 8308 3. 8277 3. 8283 3. 8290 3.8296 3. 8303 3. 8309 3. 8278 3. 8284 3. 8290 3. 8297 3. 8303 ' 3. 8310 3. 8278 3. 8285 3. 8291 3. 8298 3. 8304 3. 8310 3. 8279 3. 8285 3. 8292 3. 8298 3. 8305 3. 8311 3. 8280 3. 8286 3. 8292 3. 8299 3. 8305 3. 8312 1 53 53 10 53 20 53 30 53 40 53 50 3. 8312 3. 8319 3. 8325 3. 8331 3. 8338 3. 8344 3. 8313 3. 8319 3. 8326 3. 8332 3. 8338 3. 8345 3. 8314 3. 8320 3. 8326 3. 8333 3. 8339 3. 8345 3. 8314 3. 8321 3. 8327 3. 8333 3. 8340 3. 8346 3. 8315 3. 8321 3. 8328 3. 8334 3. 8340 3. 8347 3. 8315 3. 8322 3. 8328 3. 8335 3. 8341 3. 8347 3. 8316 3. 8323 3. 8329 3. 8335 3. 8342 3. 8348 3. 8317 3. 8323 3. 8330 3. 8336 3. 8342 . 3. 8349 3. 8317 3. 8324 3. 8330 3. 8337 3. 8343 3. 8349 3. 8318 3. 8324 3. 8331 3. 8337 3. 8344 3. 8350 1 54 54 10 54 20 54 30 54 40 54 50 3. 8351 3. 8357 3. 8363 3. 8370 3. 8376 3. 8382 3. 8351 3. 8.358 3. 8364 3. 8370 3. 8377 3. 8383 3. 8389 3. 8395 3. 8402 3. 8408 3. 8414 3. 8420 3. 8352 3. 8358 3. 8365 3. 8371 3. 8377 3. 8383 3. 8352 3. 8359 3. 8365 3. 8371 3. 8378 3. 8384^ 3. 8353 3. 8359 3. 8366 3. 8372 3. 8378 3. 8385 3. 8354 3. 8360 3. 8366 3. 8373 3. 8379 3. 8385 3. 8354 3. 8361 3. 8367 3. 8373 3. 8380 3. 8386 3. 8355 3. 8361 3. 8368 3. 8374 3. 8380 3. 8387 3. 8356 3. 8362 3. 8368 3. 8375 3. 8381 3. 8387 3. 8356 3. 8363 3. 8369 3. 8375 3. 8382 3. 8388 1 55 55 10 55 20 55 30 55 40 55 50 3. 8388 3. 8395 3. 8401 3. 8407 3. 8414 3. 8420 3. 8390 3. 8396 3. 8402 3. 8409 3. 8415 3. 8421 3. 8390 3. 8397 3. 8403 3. 8409 3. 8415 3. 8422 3. 8391 3. 8397 3. 8404 3. 8410 3. 8416 3. 8422 3. 8392 "3. 8398 3. 8404 3. 8410 3. 841/ 3. 8428 3. 8392 3. 8399 3. 8405 3. 8411 3. 8417 3. 8424 3. 8393 3. 8399 3. 8405 3. 8412 3. 8418 3. 8424 3. 8394 3.8400 3. 8406 3. 8412 3. 8419 3. 8425 3. 8394 3.8400 3. 8407 3. 8413 3. 8419 3. 8425 1 56 56 10 56 20 56 30 56 40 56 50 3. 8426 3. 8432 3. 8439 3. 8445 3. 8451 3. 8457 3. 8427 3.8433 3. 8439 3.8445 3. 8452 3. 8458 3. 8427 3. 8434 3.8440 3.8446 3. 8452 3. 8458 3. 8428 3. 8434 3. 8440 3.8447 3. 8453 3. 8459 3. 8429 3. 8435 3. 8441 3. 8447 3. 8453 3. 8460 3. 8429 3. 8435 3. 8442 3. 8448 3. 8454 3. 8460 3. 8430 3. 8436 3. 8442 3. 8448 3. 8455 3. 8461 3. 8430 3. 8437 3.8443 3. 8449 3. 8455 3. 8462 3. 8431 3. 8437 3.8444 3. 8450 3. 8456 3. 8462 3. 8432 3. 8438 3.8444 3. 8450 3. 8457 3. 8463 1 57 57 10 57 20 57 30 57 40 57 50 3. 8463 3. 8470 3. 8476 3. 8482 3. 8488 3. 8494 3. 8464 3. 8470 3. 8476 3. 8483 3. 8489 3. 8495 3. 8465 3. 8471 3. 8477 3. 8483 3. 8489 3. 8495 3. 8465 3. 8471 3. 8478 3. 8484 3. 8490 3. 8496 3. 8466 3. 8472 3. 8478 3. 8484 3. 8491 3.8497 3. 8466 3. 8473 3. 8479 3. 8485 3. 8491 3. 8497 3. 8467 3. 8473 3. 8479 3. 8486 3. 8492 3. 8498 3.8468 3. 8474 3. 8480 3. 8486 3. 8492 3. 8499 3. 8468 3. 8474 3. 8481 3. 8487 3. 8493 3. 8499 3. 8469 3. 8475 3. 8481 3. 8487 3. 8494 3. 8500 1 58 58 10 58 20 58 30 58 40 58 50 3.8500 3.8506 3. 8513 3. 8519 3. 8525 3. 8531 3.8501 3. 8507 3. 8513 3. 8519 3. 8525 3. 8532 3. 8502 3. 8508 3. 8514 3. 8520 3. 8526 3. 8532 3. 8502 3. 8508 3. 8514 3. 8521 3. 8527 3. 8533 3. 8503 3. 8509 3. 8515 3. 8521 3. 8527 3. 8533 3. 8503 3. 8510 3. 8516 3. 8522 3. 8528 3. 8534 3. 8504 3. 8510 3. 8516 3. 8522 3. 8528 3. 8535 3. 8505 3. 8511 3. 8517 3. 8523 3. 8529 3. 8535 3. 8505 3. 8511 3. 8517 3. 8524 3. 8530 3. 8536 3. 8506 3. 8512 3. 8518 3. 8524 3. 8530 3. 8536 1 59 59 10 59 20 59 30 59 40 59 50 3. 8537 3. 8543 3. 8549 3. 8555 3. 8561 3. 8567 3.8538 3.8544 3. 8550 3. 8556 3. 8562 3. 8568 3. 8538 3. 8544 3. 8550 3. 8556 3. 8562 3. 8568 3. 8539 3. 8545 3. 8551 3. 8557 3. 8563 3. 8569 3. 8539 3. 8545 3. 8552 3. 8558 3. 8564 3. 8570 3. 8540 3. 8546 3. 8552 3. 8558 3. 8564 3.8570 3. 8541 3. 8547 3. 8553 3. 8559 3. 8565 3. 8571 3. 8541 3. 8547 3. 8553 3. 8559 3. 8565 3. 8572 3. 8542 3. 8548 3. 8554 3. 8560 3. 8566 3. 8572 3. 8542 3. 8549 3. 8555 3.8561 3. 8567 3. 8573 .... APPP:NDIX V: TABLE IX. [Page 325 Logarithms of Small Arcs in Space or Time. Arc. 1 0" 1" 2" 8" 4" 6" 6" 7" 8" 9" o / 2h Qm 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 30 3. 8591 3. 8592 3. 8593 3. 8593 3. 8594 3. 8594 3. 8595 3. 8596 3. 8596 3. 8597 40 3. 8597 3. 8598 3. 8599 3. 8599 3. 8600 3. 8600 3. 8601 3. 8602 3. 8602 3. 8603 50 3. 8603 3. 8604 3. 8605 3. 8605 3. 8606 3. 8606 3. 8607 3. 8608 3. 8608 3. 8609 2 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 2 3 3. 8681 3. 8681 3. 8682 3. 8682 3. 8683 3. 8684 3. 8684 3. 8685 3. 8685 3. 8686 3 10 3. 8686 3. 8687 3. 8688 3. 8688 3. 8689 3. 8689 3. 8690 3. 8691 3. 8691 3. 8692 3 20 3. 8692 3. 8693 3. 8693 3. 8694 3. 8695 3. 8695 3. 8696 3. 8696 3. 8697 3. 8698 3 30 3. 8698 3. 8699 3. 8699 3. 8700 3. 8701 3. 8701 3. 8702 3. 8702 3. 8703 3. 8703 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 i 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. 8754 3. 8749 3. 8749 3. 8750 2 5 3. 8751 3. 8751 3. 8752 3. 8752 3. 8753 3. 8754 3. 8755 3. 8755 3. 8756 5 10 3. 8756 3. 8757 3. 8758 3. 8758 3. 8759 3. 8759 3. 8760 3. 8760 3. 8761 3. 8762 5 20 3. 8762 3. 8763 3. 8763 3. 8764 3. 8764 3. 8765 3. 8766 3. 8766 3. 8767 3. 8767 5 30 3. 8768 3. 8769 3. 8769 3. 8770 3. 8770 3. 8771 3. 8771 3. 8772 3. 8773 3. 8773 5 40 3. 8774 3. 8774 3. 8775 3. 8775 3. 8776 3. 8777 3. 8777 3. 8778 3. 8778 3. 8779 5 50 3. 8779 3. 8780 3. 8781 3. 8781 3. 8782 3. 8782 3. 8783 3. 8783 3. 8784 3. 8785 2 6 3. 8785 3. 8786 3. 8786 3. 8787 3. 8788 3. 8788 3. 8789 3. 8789 3. 8790 3. 8790 6 10 3. 8791 3. 8792 3. 8792 3. 8793 3. 8793 3.8794 3. 8794 3. 8795 3. 8796 3. 8796 6 20 3. 8797 3. 8797 3. 8798 3. 8798 3. 8799 3. 8800 3.8800 3. 8801 3. 8801 3. 8802 6 30 3. 8802 3. 8803 3. 8804 3. 8804 3. 8805 3. 8805 3. 8806 3. 8806 3. 8807 3. 8808 6 40 3. 8808 3. 8809 3. 8809 3. 8810 3. 8810 3. 8811 3. 8812 3. 8812 3. 8813 3. 8813 6 50 3. 8814 3. 8814 3. 8815 3. 8816 3. 8816 3. 8817 3. 8817 3. 8818 3. 8818 3. 8819 2 7 3. 8820 3. 8820 3. 8821 3. 8821 3. 8822 3. 8822 3. 8823 3. 8824 3. 8824 3. 8825 7 10 3. 8825 3. 8826 3. 8826 3. 8827 3. 8828 3. 8828 3. 8829 3. 8829 3. 8830 3. 8830 7 20 3. 8831 3. 8832 3. 8832 3. 8833 3. 8833 3. 8834 3. 8834 3. 8835 3. 8835 3. 8836 7 30 3. 8837 3. 8837 3. 8838 3. 8838 3. 8839 3. 8839 3. 8840 3. 8841 3.8841 3. 8842 7 40 3. 8842 3. 8843 3. 8843 3. 8844 3. 8845 3. 8845 3. 8846 3. 8846 3. 8847 3. 8847 7 50 3. 8848 3. 8849 3. 8849 3. 8850 3. 8850 3. 8851 3. 8851 3. 8852 3. 8852 3. 8853 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 ?0 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 ?0 3. 8899 3. 8899 3. 8900 3.8900 3. 8901 3. 8901 3. 8902 3. 8903 3. 8903 3.8904 9 30 3.8904 3. 8905 3. 8905 3. 8906 3.8906 3. 8907 3. 8908 3. 8908 3.8909 3.8909 9 40 3. 8910 3. 8910 3. 8911 3. 8911 3. 8912 3. 8912 3. 8913 3. 8914 3. 8914 3. 8915 9 50 3. 8915 3. 8916 3. 8916 3. 8917 3. 8918 3. 8918 3.8919 3.8919 3. 8920 3.8920 Page 326] APPENDIX V: TABLE IX. Logarithms of Small Arcs in Space or Time. Arc. W 1" 2" 8" 4" 6" 6" 111 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 3. 8927 3. 8927 3. 8928 3. 8928 3. 8929 3.8929 3. 8930 3. 8930 3. 8931 3. 8932 10 5^0 3. 8932 3. 8938 8. 8933 3. 8934 8. 8934 3. 8985 3. 8935 3. 8936 3. 8987 3. 8937 10 80 3. 8938 3. 8938 8. 8939 3. 8939 3. 8940 3. 8940 3. 8941 3. 8941 3. 8942 3. 8943 10 40 3. 8943 3. 8944 8.8944 3. 8945 3. 8945 3. 8946 8. 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 8. 8963 3. 8964 3. 8964 8. 8965 11 20 3. 8965 3. 8966 3. 8966 3. 8967 8. 8967 3. 8968 8. 8969 3. 8969 3. 8970 3. 8970 11 30 3. 8971 3. 8971 8. 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. 8988 3. 8983 3. 8984 3.8985 3. 8985 3. 8986 8. 8986 8. 8987 2 12 3. 8987 8. 8988 3. 8988 3. 8989 3. 8989 3. 8990 3. 8991 3. 8991 3. 8992 3. 8992 12 10 3. 8993 8. 8998 3. 8994 8. 8994 3. 8995 3. 8995 3. 8996 3. 8997 3.8997 8. 8998 12 20 3. 8998 8. 8999 8. 8999 3.9000 3.9000 3. 9001 3.9001 3.9002 3. 9003 8. 9003 12 80 3.9004 3.9004 8. 9005 3.9005 3. 9006 3. 9006 3.9007 8. 9007 3. 9008 3. 9009 12 40 3.9009 3. 9010 3. 9010 3. 9011 3. 9011 3. 9012 3. 9012 3. 9013 8. 9013 3. 9014 12 50 3. 9015 3. 9015 3. 9016 3. 9016 3. 9017 3. 9017 3. 9018 8. 9018 8. 9019 3. 9019 2 13 3. 9020 3. 9021 3. 9021 8. 9022 3.9022 8. 9023 3. 9023 3. 9024 3. 9024 3.9025 13 10 3. 9025 3. 9026 3. 9027 3. 9027 3. 9028 8. 9028 3. 9029 3. 9029 3. 9030 8. 9080 13 20 3. 9031 3. 9031 3. 9032 3. 9033 3. 9033 3. 9034 3. 9084 3.9085 3. 9035 3. 9036 13 80 3. 9036 3. 9037 3. 9037 3. 9038 3. 9038 3. 9039 3. 9040 8. 9040 3. 9041 3.9041 13 40 3. 9042 8. 9042 8.9048 3. 9043 3. 9044 3. 9044 3. 9045 3. 9046 3. 9046 3. 9047 13 50 3.9047 8.9048 3.9048 3.9049 3. 9049 8. 9050 3. 9050 3. 9051 3. 9051 3. 9052 2 14 3.9053 3. 9058 3. 9054 3. 9054 3. 9055 3. 9055 3. 9056 8. 9056 3. 9057 3. 9057 14 10 3. 9058 3. 9058 3. 9059 3. 9060 3.9060 3. 9061 8. 9061 3. 9062 3. 9062 3. 9063 14 20 3. 9063 3.9064 3.9064 3. 9065 3.9066 3. 9066 8. 9067 3. 9067 3. 9068 3. 9068 14 30 3. 9069 3.9069 8. 9070 8. 9070 3.9071 3. 9071 8. 9072 3. 9078 3. 9073 3. 9074 14 40 3. 9074 8. 9075 8. 9075 8. 9076 3. 9076 3. 9077 3. 9077 8. 9078 8. 9078 3. 9079 14 50 3. 9079 3. 9080 3. 9081 3. 9081 3. 9082 3. 9082 3. 9088 8. 9088 8. 9084 3. 9084 2 15 3. 9085 3. 9085 3. 9086 3. 9086 3. 9087 3. 9088 3. 9088 8. 9089 3. 9089 3. 9090 15 10 3.9090 3. 9091 3. 9091 3. 9092 3.9092 3.9098 3. 9093 3. 9094 3. 9094 3. 9095 15 20 3.9096 3. 9096 8. 9097 8.9097 3. 9098 3. 9098 3. 9099 3. 9099 8. 9100 3. 9100 15 80 3. 9101 8. 9101 3. 9102 3. 9108 3. 9103 3. 9104 3. 9104 8. 9105 3. 9105 3. 9106 15 40 3. 9106 3. 9107 3. 9107 3. 9108 3. 9108 3. 9109 3.9109 8.9110 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. 9128 3. 9124 3. 9124 3. 9125 3. 9125 3. 9126 3. 9126 8. 9127 16 20 3. 9128 3. 9128 3. 9129 3. 9129 3. 9130 3. 9130 3. 9181 3. 9131 8. 9132 8. 9132 16 30 3. 9183 3. 9133 3. 9134 3. 9134 8. 9135 3.9135 3. 9186 3. 9137 3. 9137 3. 9138 16 40 3. 9138 3. 9139 3. 9139 8. 9140 8. 9140 3. 9141 3. 9141 3. 9142 8. 9142 3. 9143 16 50 3. 9143 3.9144 3.9144 3. 9145 3. 9146 3. 9146 3. 9147 3. 9147 3. 9148 3. 9148 2 17 3. 9149 8. 9149 8. 9150 3. 9150 3. 9151 3. 9151 3. 9152 3. 9152 3. 9153 3.9153 17 10 8. 9154 3. 9155 3. 9155 3. 9156 3. 9156 3. 9157 3. 9157 3. 9158 3. 9158 3. 9159 17 20 8. 9159 3. 9160 8. 9160 3. 9161 3. 9161 3. 9162 8. 9162 3. 9163 8. 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 8. 9171 8. 9171 8. 9172 3. 9172 3. 9173 3. 9173 3. 9174 3. 9175 17 50 3. 9175 8. 9176 3. 9176 3.9177 3.9177 3. 9178 3. 9178 3. 9179 8. 9179 8. 9180 2 18 3. 9180 8. 9181 8.9181 3. 9182 3. 9182 3. 9183 3. 9183 3. 9184 8. 9184 3. 9185 18 10 3. 9186 8. 9186 3. 9187 3. 9187 3. 9188 3. 9188 3. 9189 3. 9189 8. 9190 3. 9190 18 20 3. 9191 8. 9191 3. 9192 3. 9192 3. 9193 3. 9193 3. 9194 3. 9194 8. 9195 3. 9195 18 30 8. 9196 8. 9197 8. 9197 8. 9198 8. 9198 3. 9199 3. 9199 8.9200 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 8. 9207 3. 9207 3. 9208 8. 9209 3. 9209 3. 9210 8. 9210 8. 9211 3. 9211 2 19 3. 9212 3. 9212 3. 9213 3. 9213 3. 9214 8. 9214 3. 9215 3. 9215 3. 9216 3. 9216 19 10 3. 9217 3. 9217 8. 9218 3. 9218 3. 9219 8. 9219 8. 9220 3. 9221 8. 9221 3. 9222 19 20 3. 9222 3. 9228 8. 9223 3. 9224 3. 9224 8. 9225 8. 9225 3. 9226 3. 9226 3. 9227 19 30 3. 9227 3. 9228 3. 9228 3. 9229 3. 9229 8. 9280 3. 9280 3. 9231 3. 9231 8. 9232 19 40 8. 9232 3. 9283 8. 9233 3. 9234 3. 9235 3. 9235 3. 9236 3. 9236 3. 9237 8. 9237 19 50 3. 9238 3. 9288 8. 9239 3. 9239 3. 9240 3. 9240 3. 9241 3. 9241 3. 9242 3. 9242 APPENDIX V: TABLE IX. [Page 327 1 Logarithm 3 of Small Arcs in Space or Time. Arc. 0" 1" 2" 8" 4" 6" 6" 7" 8" 9" o / 2" 20°' II 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 3. 9276 3. 9277 3. 9277 3. 9278 3. 9278 21 10 3. 9279 3. 9279 3. 9280 3. 9280 3. 9281 3. 9281 3. 9282 3. 9282 3. 9283 3.9283 21 20 3. 9284 3. 9284 3. 9285 3. 9285 3. 9286 3. 9287 3. 9287 3. 9288 3. 9288 3. 9289 21 30 3. 9289 3. 9290 3. 9290 3. 9291 3. 9291 3. 9292 3. 9292 3. 9293 3.9293 3.9294 21 40 3.9294 3. 9295 3. 9295 3. 9296 3. 9296 3. 9297 3. 9297 3. 9298 3. 9298 3.9299 21 50 3. 9299 3. 9300 3.9300 3. 9301 3. 9301 3. 9302 3. 9302 3. 9303 3. 9303 3. 9308 3. 9304 3.9309 2 22 3. 9304 3. 9305 3. 9305 3. 9306 3. 9306 3. 9307 3. 9307 3. 9308 22 10 3. 9309 3. 9310 3. 9311 3. 9311 3. 9312 3. 9312 3. 9313 3. 9313 3. 9314 3. 9314 22 20 3. 9315 3. 9315 3. 9316 3. 9316 3. 9317 3. 9317 3. 9318 3. 9318 3.9319 3. 9319 22 30 3. 9320 3. 9320 3. 9321 3. 9321 3. 9322 3. 9322 3. 9323 3. 9323 3. 9324 3. 9324 22 40 3. 9325 3. 9325 3. 9326 3. 9326 3. 9327 3. 9327 3. 9328 3. 9328 3. 9329 3. 9329 22 50 3. 9330 3. 9330 3. 9331 3. 9331 3.' 9332 3. 9332 3. 9333 3. 9333 3. 9334 3. 9334 2 23 3. 9335 3. 9335 3. 9336 3. 9336 3. 9337 3. 9337 3. 9338 3. 9338 3. 9339 3. 9339 23 10 3. 9340 3. 9340 3. 9341 3. 9341 3. 9342 3. 9342 3. 9343 3. 9343 3. 9344 3.9344 23 20 3. 9345 3. 9345 3. 9346 3. 9346 3. 9347 3. 9348 3. 9348 3. 9349 3. 9349 3.9350 23 30 3. 9350 3. 9351 3.9351 3. 9352 3. 9352 3. 9353 3. 9353 3. 9354 3. 9354 3. 9355 23 40 3. 9355 3. 9356 3. 9356 3. 9357 3. 9357 3. 9358 3. 9358 3. 9359 3. 9359 3.9360 23 50 3. 9360 3. 9361 3. 9361 3. 9362 3. 9362 3. 9363 3. 9363 3. 9364 3. 9364 3. 9365 2 24 3. 9365 3. 9366 3. 9366 3. 9367 3. 9367 3. 9368 3. 9368 3. 9369 3. 9369 3. 9370 24 10 3. 9370 3. 9371 3. 9371 3. 9372 3. 9372 3. 9373 3. 9373 3. 9374 3. 9374 3. 9375 24 20 3. 9375 3. 9376 3. 9376 3. 9377 3. 9377 3. 9378 3. 9378 3. 9379 3. 9379 3. 9380 24 30 3. 9380 3. 9381 3. 9381 3. 9382 3. 9382 3. 9383 3. 9383 3. 9384 3. 9384 3. 9385 24 40 3. 9385 3. 9386 3. 9386 3. 9387 3. 9387 3. 9388 3. 9388 3. 9389 3. 9389 3.9390 24 50 3. 9390 3. 9391 3. 9391 3. 9392 3. 9392 3. 9393 3. 9393 3. 9394 3. 9394 3. 9395 2 25 3. 9395 3. 9396 3. 9396 3. 9397 3. 9397 3. 9398 3. 9398 3. 9399 3. 9399 3.9400 25 10 3.9400 3. 9401 3. 9401 3. 9402 3. 9402 3. 9403 3. 9403 3. 9404 3. 9404 3. 9405 25 20 3. 9405 3. 9406 3.9406 3. 9407 3. 9407 3. 9408 3. 9408 3. 9409 3. 9409 3. 9410 25 30 3. 9410 3.9411 3. 9411 3. 9412 3. 9412 3. 9413 3. 9413 3. 9414 3. 9414 3. 9415 25 40 3. 9415 3. 9416 3. 9416 3. 9417 3. 9417 3. 9418 3. 9418 3. 9419 3. 9419 3. 9420 25 50 3. 9420 3. 9421 3. 9421 3. 9422 3. 9422 3. 9423 3. 9423 3. 9424 3. 9424 3. 9425 2 26 3. 9425 3. 9426 3. 9426 3. 9427 3. 9427 3. 9428 3. 9428 3. 9429 3.9429 3. 9430 26 10 X 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" 8" 1 9" / 2'' 30" 3. 9542 3. 9543 3. 9543 8.9544 3.9544 3. 9545 3. 9545 3. 9546 3. 9546 1 3. 9547 30 10 3. 9547 3. 9548 3. 9548 3. 9549 3. 9549 3. 9550 3. 9550 3. 9551 3. 9551 3. 9552 30 20 3. 9552 3. 9553 3. 9553 3. 9554 3. 9554 3. 9554 3. 9555 3. 9555 3. 9556 3. 9556 30 30 3. 9557 3. 9557 3. 9558 3. 9558 3. 9559 3. 9559 3. 9560 3. 9560 3. 9561 3. 9561 30 40 3. 9562 3. 9562 3. 9563 3. 9563 3. 9564 3. 9564 3. 9565 3. 9565 3. 9566 3. 9566 30 50 3. 9566 3. 9567 3. 9567 3. 9568 3. 9568 3. 9569 3. 9569 3. 9570 3. 9570 3. 9571 2 31 3. 9571 3. 9572 3. 9572 3. 9573 3. 9573 3. 9574 3. 9574 3. 9575 3. 9575 3. 9576 31 10 3. 9576 3. 9577 3. 9577 3. 9578 3. 9578 3. 9578 3. 9579 3. 9579 3. 9580 3. 9580 31 20 3. 9581 3. 9581 3. 9582 3. 9582 3. 9583 3. 9583 3. 9584 3. 9584 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 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 j 3. 9609 32 20 3. 9609 3. 9610 3. 9610 3. 9611 3.9611 3. 9612 3. 9612 3. 9613 3. 9613 I 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. 9628 2 33 3. 9628 3. 9629 3. 9629 3. 9630 3. 9630 3. 9631 3. 9631 3. 9632 3.9632 3. 9633 33 10 3. 9633 3. 9634 3. 9634 3. 9634 3. 9635 3. 9635 3. 9636 3. 9636 3. 9637 3. 9637 33 20 3. 9638 3. 9638 3. 9639 3. 9639 3. 9640 3. 9640 3. 9641 3.9641 3. 9642 3. 9642 33 30 3. 9642 3. 9643 3.9643 3. 9644 3.9644 3.9645 3. 9645 3. 9646 3. 9646 3. 9647 33 40 3. 9647 3. 9648 3. 9648 3. 9649 3. 9649 3. 9650 3. 9650 3. 9651 3. 9651 3. 9652 33 50 3. 9652 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 3. 9678 3. 9679 3. 9679 3. 9680 34 50 3. 9680 3. 9681 3. 9681 3. 9682 3. 9682 3. 9682 3. 9683 3. 9683 3. 9684 ! 3. 9684 2 35 3. 9685 3. 9685 3. 9686 3. 9686 3. 9687 3. 9687 3. 9688 3. 9688 3. 9689 ! 3. 9689 35 10 3. 9689 3. 9690 3. 9690 3. 9691 3. 9691 3. 9692 3. 9692 3. 9693 3. 9693 3. 9694 35 20 3. 9694 3. 9695 3. 9695 3. 9696 3. 9696 3. 9696 3. 9697 3. 9697 3. 9698 3. 9698 35 30 3. 9699 3. 9699 3. 9700 3.9700 3. 9701 3. 9701 3. 9702 3. 9702 3. 9703 3. 9703 35 40 3. 9703 3. 9704 3. 9704 3. 9705 3. 9705 3. 9706 3. 9706 3. 9707 3. 9707 3. 9708 35 50 3. 9708 3. 9709 3. 9709 3. 9714 3.9710 3. 9710 3. 9710 3.9711 3.9711 3. 9716 3. 9712 3. 9716 3. 9712 2 36 3. 9713 3.9713 3. 9714 3. 9715 3. 9715 3. 9716 3. 9717 36 10 3.9717 3.9718 3.9718 3. 9719 3. 9719 3. 9720 3. 9720 3. 9721 3. 9721 3. 9722 36 20 3. 9722 3. 9722 3. 9723 3. 9723 3. 9724 3. 9724 3. 9725 3. 9725 3. 9726 ! 3. 9726 36 30 3. 9727 3. 9727 3. 9728 3.9728 3. 9729 3. 9729 3. 9729 3. 9730 3. 9730 3. 9731 36 40 3. 9731 3. 9732 3. 9732 3. 9733 3. 9733 3. 9734 3. 9734 3. 9735 3. 9735 3. 9735 36 50 3. 9736 3. 9736 3. 9737 3. 9737 3. 9738 3. 9738 3. 9739 3. 9739 3. 9740 3. 9740 2 37 3. 9741 3. 9741 3. 9741 3. 9742 3. 9742 3. 9743 3. 9743 3. 9744 3.9744 3. 9745 37 10 3. 9745 3. 9746 3. 9746 3. 9746 3. 9747 3. 9747 3. 9748 3. 9748 3. 9749 3. 9749 37 20 3. 9750 3. 9750 3. 9751 3. 9751 3. 9752 3. 9752 3. 9752 3. 9753 3. 9753 3. 9754 37 30 3. 9754 3. 9755 3. 9755 3. 9756 3. 9756 3. 9757 3. 9757 3. 9758 3. 9758 3. 9758 37 40 3. 9759 3. 9759 3. 9760 3. 9760 3. 9761 3. 9761 3. 9762 3. 9762 3. 9763 i 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" \» 2" 3" 4" 6" 6" 7" 8" 9" o / 2h 40" It 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 3. 9854 2 41 3, 9850 3. 9850 3. 9851 3. 9851 3. 9852 3. 9852 3.9852 3. 9853 3. 9853 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. 9879 3. 9875 3. 9876 3. 9876 2 42 3. 9877 3. 9877 3. 9878 3. 9878 3. 9878 3. 9879 3. 9880 3. 9880 3. 9881 42 10 3. 9881 3. 9882 3. 9882 3. 9882 3. 9883 3. 9883 3. 9884 3. 9884 3. 9885 3. 9885 42 20 3. 9886 3. 9886 3. 9886 3. 9887 3. 9887 3. 9888 3. 9888 3. 9889 3. 9889 3. 9890 42 30 3. 9890 3. 9890 3. 9891 3.9891 3.9892 3. 9892 3. 9893 3. 9893 3. 9894 3. 9894 42 40 3. 9894 3. 9895 3. 9895 3. 9896 3. 9896 3. 9897 3. 9897 3. 9898 3. 9898 3. 9898 42 50 3. 9899 3. 9899 3. 9900 3. 9900 3. 9901 3. 9901 3. 9902 3. 9902 3. 9903 3. 9907 3. 9903 2 43 3. 9903 3. 9904 3. 9904 3.9905 i 3.9905 3. 9906 3. 9906 3. 9906 3.9907 43 10 3. 9908 3. 9908 3. 9909 3.9909 .3.9910 3. 9910 3. 9910 3. 9911 3. 9911 3. 9912 43 20- 3. 9912 3. 9913 3. 9913 3.9914 3.9914 3. 9914 3. 9915 3. 9915 3. 9916 3. 9916 43 30 3. 9917 3. 9917 3. 9918 3.9918 3.9918 3. 9919 3. 9919 3. 9920 3. 9920 3. 9921 43 40 3. 9921 3. 9922 3. 9922 3.9922 3.9923 3. 9923 3. 9924 3. 9924 3. 9925 3. 9925 43 50 3. 9926 3. 9926 3. 9926 3.9927 1 3.9927 3. 9928 3. 9928 3.9929 3. 9929 3. 9930 2 44 3. 9930 3.9930 3. 9931 3.9931 i 3.9932 3. 9932 3. 9933 3. 9933 3. 9933 3. 9934 44 10 3. 9934 3. 9935 3. 9935 3.9936 ' 3.9936 3. 9937 3. 9937 3. 9937 3. 9938 3. 9938 44 20 3. 9939 3. 9939 3. 9940 3.9940 3.9941 3. 9941 3. 9941 3. 9942 3. 9942 3. 9943 44 30 3. 9943 3. 9944 3. 9944 3.9944 i 3.9945 3. 9945 3. 9946 3. 9946 3. 9947 3. 9947 44 40 3. 9948 3. 9948 3. 9948 3.9949 ; 3.9949 3. 9950 3. 9950 3. 9951 3. 9951 3. 9952 44 50 3. 9952 3. 9952 3. 9953 3.9953 1 3.9954 3. 9954 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 i 3.9967 3. 9967 3. 9968 3. 9968 3. 9969 3. 9969 45 30 3. 9969 3. 9970 3. 9970 3.9971 ! 3.9971 3. 9972 3. 9972 3. 9973 3. 9973 3.9973 45 40 3. 9974 3. 9974 3. 9975 3. 9975 3. 9976 3. 9976 3. 9976 3. 9977 3. 9977 3. 9978 45 50 3. 9978 3. 9979 3. 9979 3. 9980 3. 9980 3. 9980 3. 9981 3. 9981 3. 9982 3. 9982 2 46 3. 9983 3. 9983 3. 9983 3. 9984 3. 9984 3. 9985 3. 9985 3. 9986 3. 9986 3.9987 46 10 3. 9987 3. 9987 3. 9988 3. 9988 3. 9989 3. 9989 3. 9990 3. 9990 3. 9990 3. 9991 46 20 3. 9991 3. 9992 3. 9992 3. 9993 3. 9993 3. 9993 3. 9994 3. 9994 3. 9995 3. 9995 46 30 3. 9996 3. 9996 3. 9997 3. 9997 3. 9997 3. 9998 3. 9998 3. 9999 3. 9999 4.0000 46 40 4. 0000 4. 0000 4. 0001 4.0001 4. 0002 4.0002 4. 0003 4.0003 4. 0003 4.0004 46 50 4. 0004 4. 0005 4.0005 4. 0006 4. 0006 4. 0007 4.0007 4.0007 4.0008 4.0008 2 47 4. 0009 4. 0009 4. 0010 4. 0010 4. 0010 4.0011 4.0011 4.0012 4. 0012 4.0013 47 10 4. 0013 4. 0013 4. 0014 4. 0014 4.0015 4. 0015 4.0016 4. 0016 4. 0016 4.0017 47 20 4. 0017 4. 0018 4. 0018 4. 0019 4. 0019 4. 0019 4. 0020 4. 0020 4.0021 4.0021 47 30 4. 0022 4. 0022 4.0023 4. 0023 4. 0023 4. 0024 4. 0024 4. 0025 4. 0025 4.0026 47 40 4. 0026 4. 0026 4. 0027 4. 0027 4. 0028 4.0028 4. 0029 4.0029 4. 0029 4.0030 47 50 4. 0030 4. 0031 4. 0031 '4.0035 4. 0032 4. 0032 4. 0032 4. 0033 4. 0033 4. 0034 4. 0038 4.0034 2 48 4. 0035 4. 0035 4. 0036 4. 0036 4. 0037 4. 0037 4. 0038 4. 0038 48 10 4. 0039 4. 0039 4. 0040 4. 0040 4.0041 4. 0041 4. 0041 4.0042 4.0042 4.0043 48 20 4. 0043 4. 0044 4. 0044 4.0045 4. 0045 4. 0045 4. 0046 4. 0046 4. 0047 4. 0047 48 30 4. 0048 4. 0048 4. 0048 4. 0049 4. 0049 4. 0050 4. 0050 4. 0051 4. 0051 4.0051 48 40 4. 0052 4. 0052 4. 0053 4. 0053 4. 0054 4. 0054 4. 0054 4. 0055 4. 0055 4.0056 48 50 4. 0056 4. 0057 4. 0057 4. 0057 4. 0058 4. 0058 4. 0059 4. 0059 4. 0063 4.0060 4. 0064 4. 0060 2 49 4. 0060 4. 0061 4. 0061 4.0062 4. 0062 4. 0063 4. 0063 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" 5" 6" 7" 8" 9" O 1 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. 0215 4. 0219 4. 0223 4. 0227 4. 0231 4. 0235 4. 0215 4. 0219 4. 0223 4. 0228 4. 0232 4. 0236 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. 0239 4. 0243 4. 0247 4. 0251 4. 0256 4. 0260 4. 0240 4. 0244 4. 0248 4. 0252 4. 0256 4. 0260 4. 0240 4.0244 4. 0248 4. 0252 4. 0256 4. 0260 4. 0240 4. 0244 4. 0249 4. 0253 4. 0257 4. 0261 4. 0265 4. 0269 4. 0273 4. 0277 4. 0281 4. 0285 2 57 57 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 4. 0289 4. 0293 4. 0297 4. 0302 4. 0306 4. 0310 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. 0.320 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. | 2 4 8. 1 6 «. 1 1 1 2 8 8. 1 1 2 2 2 2 2 3 3 10 8. 1 1 2 2 3 3 3 3 3 12 8. 1 2 2 3 3 3 4 4 4 14 8. 1 2 2 3 4 4 4 4 4 16 8. 1 2 3 3 4 4 5 5 5 18 8. 1 2 3 4 5 5 5 6 6 20 8. 1 2 22 8. 1 3 24 8. 2 3 26 28 80 82 84 86 h. m. 10 20 h. m. 3 2 50 2 40 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 3 4 5 6 6 6 6 4 5 5 6 6 7 7 4 5 6 7 7 7 8 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 A. TO. 10 20 2 1 50 1 40 1 30 h. TO. 3 2 50 2 40 2 2 2 2 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. 1 38 8. 2 5 40 8. 3 5 7 9 10 42 8. 3 5 7 9 10 44 s. 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 60 8. 3 6 9 11 13 52 8. 3 6 54 56 58 60 62 64 66 68 70 8. 4 7 8. 4 7 8. 4 7 8. 4 7 8. 4 8 8. 4 8 8. 4 8 8. 4 8 8. 5 9 30 40 50 2 30 2 20 2 10 7 8 9 9 11 13 9 12 14 10 12 14 10 13 15 10 13 15 11 13 16 11 14 16 12 14 16 12 15 17 12 15 17 1 1 10 1 20 1 30 h. m. 10 20 2 1 50 1 40 1 30 h. TO. 3 2 50 2 40 10 11 12 12 11 12 12 12 12 12 13 13 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 1 19 19 1 20 20 21 21 21 19 21 21 22 Difference of the proportional logarithms in the Ephemeris. 1 72 8. 5 9 74 76 78 80 82 84 86 88 90 92 94 96 98 100 102 104 8. 5 9 13 16 19 21 22 23 23 8. . 5 9 13 16 19 2r 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 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. 13 8. 7 13 30 40 50 2 30 2 20 2 10 13 16 18 20 21 22 23 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 h. TO. 3 2 50 2 40 23 25 26 26 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. 1 106 108 110 112 114 116 118 120 122 124 126 128 180 182 184 136 188 8. 7 13 8. 7 13 8. 7 14 8. 7 14 8. 7 14 8. 8 14 8. 8 15 8. 8 15 s. 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 29 31 33 33 19 23 27 30 32 33 34 19 24 27 30 32 34 34 19 24 28 31 33 34 35 20 25 29 31 34 35 35 20 25 29 20 25 29 21 26 30 21 26 30 21 27 31 22 27 31 22 28 32 22 28 32 23 28 33 23 29 33 24 29 84 24 30 34 1 1 10 1 20 1 30 2 1 50 1 40 1 30 32 34 35 36 33 35 36 36 3.^ 35 37 37 34 36 38 38 34 37 38 39 35 37 39 39 35 38 39 40 36 38 40 40 37 39 41 41 37 40 41 42 38 40 42 42 38 41 42 43 The correction is to be added to the approximate Greenwich time when the proportional logarithms in the Ephemeris Me decreasing, and subtracted when they are increasing. Page 332] APPENDIX V: TABLE XI. For finding the value of N for Correcting Lunar Distances for the Compression of the Earth. Table XI A, giving 1st part of N. Table XI B, giving 2d part of N. Moon's declination. Other body' 3 declination. App. dist. App. 0° 8° 6° 9° 12° 16° 18° 21° 24° 27° 80° dist. 0° 8° 6° 9° II 12° 16° 18° 21° 24° II 27° II 80° // „ // // f/ II „ „ „ II „ o // 20 -0 3 6 10 13 16 19 22 25 28 31 20 +0 3 7 10 14 17 20 24 27 30 33 22 3 6 9 12 14 17 20 23 25 28 22 3 6 9 13 16 19 22 25 27 30 24 3 5 8 11 13 16 18 21 23 25 24 3 6 9 12 14 17 20 23 25 28 26 2 5 7 10 12 14 17 19 21 23 26 3 8 11 13 16 18 21 23 26 28 -0 2 2 4 4 7 6 9 8 11 10 13 12 15 14 17 16 19 21 28 -4-0 3 2 5 5 8 7 10 9 12 12 15 14 17 16 20 18 22 21 24 23 30 18 20 30 32 2 4 6 8 9 11 13 15 16 18 32 2 4 7 9 11 13 15 17 19 21 34 2 4 5 7 9 10 12 14 15 17 34 2 4 6 8 11 13 15 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 -0 2 3 3 5 4 6 6 8 7 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 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 y 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 48 2 2 3 3 5 5 6 6 8 8 9 9 11 11 12 13 14 13 15 15 50 -0 50 +0 52 2 3 4 5 5 6 7 8 9 52 2 3 4 6 7 9 10 12 13 14 54 2 3 3 4 5 6 7 7 8 54 3 4 6 7 9 10 11 13 14 56 2 2 3 4 5 5 6 7 8 56 3 4 6 7 8 10 11 12 14 58 60 -0 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 62 2 3 3 4 4 5 5 6 62 3 4 5 7 8 9 10 12 13 64 2 2 3 3 4 4 5 6 64 3 4 5 7 8 9 10 11 13 66 2 2 3 3 4 4 5 5 66 3 4 5 6 8 9 10 11 12 68 Y "Y 2 2 2 2 3 3 3 3 4 3 4 4 5 4 68 Y 3 3 4 4 5 5 6 6 8 7 9 9 10 10 11 11 12 12 70 -0 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 1 2 2 2 3 3 76 2 4 5 6 7 8 9 11 12 78 80 -0 "Y -"Y 1 1 1 1 2 1 2 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 82 1 1 1 1 1 2 82 2 4 5 6 7 8 9 10 11 84 1 1 1 1 1 1 84 2 4 5 6 7 8 9 10 11 86 1 1 1 1 86 2 4 5 6 ■7 8 9 10 11 88 -0 88 Y 2 2 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 90 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 1 96 2 4 5 6 7 8 9 10 11 98 _0 "Y 1 1 1 1 1 1 1 2 1 2 2 2- 98 Y 2 2 4 4 5 5 6 6 7 8 9 10 11 100 +0 100 +0 7 8 9 10 11 102 1 1 2 2 2 2 102 2 4 5 6 ■7 8 9 11 12 104 1 2 2 2 3 3 104 2 4 5 6 7 8 9 11 12 106 2 2 2 3 3 3 106 2 4 5 6 7 8 10 11 12 108 Y -^ 2 2 2 2 2 3 3 3 3 3 3 4 4 4 108 Y 2 3 4 4 5 5 6 6 7 7 9 9 10 10 11 11 12 12 110 +0 110 +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 Y 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 Y 2 2 3 3 4 4 5 5 5 6 6 7 7 8 8 9 9 10 128 2 2 3 3 4 5 6 6 7 8 9 9 10 11 12 12 13 13 14 15 130 i +0 130 +0 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'^e Dead reckoning. ) Adjustments, horizon mirror index mirror plane table sextant permanent theodolite or transit Afternoon sights Agulhas current Airy's method for great circle sailing. . Alidade, plane table Almanac, Nautical. (See Nautical Al- manac. ) Altitude and azimuth time azimuth azimuth circle, definition circum-meridian forms for definition ex-meridian forms for meridian, constant form for . . forms for latitude by observation of". reduction to forms. observed, how corrected of Polaris for latitude single, for chronometer error. latitude longitude ashore . . at sea. . . true, definition Altitudes, equal, forchro. error form longitude 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 tnown objects . horizon, for finding distance. . round of sextant and theodolite in hy- drography vertical terrestrial, to measure. 26 J°-45° on bow Anticyclonic regions, features of Apparent day, definition variation in length noon, definition tfane, conversion to mean . . . definition 246 245 417 244 248 414 399 550 194 416 235 366 363 217 334 220 334 333 329 330 334 294 340 316 339 346 349 294 321 347 352 224 357 166 415 151 139 415 458 139 146 481 273 273 273 292 273 Page. 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. 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 Bun, for compass error two, of object, with run be- tween Beaufort's scale for wind Art. Page. 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 74 79 160 64 14 70 70 71 138 112 74 135 139 159 152 29 161 11 111 65 17 64 116 109 109 128 112 112 110 110 31 58 110 23 23 21 154 21 21 21 22 23 22 138 137 136 43 43 46 42 112 44 42 31 43 27 333 834 INDEX TO PART 1. Subject. Art. Page. Bench mark definition . 516 156 Binnacles description . ... . 84 17 Bottom quality of, on chart 45 20 Boxing the compass ?7 16 Brazil current 538 160 Buoys - ^e>?, 47 C — W, definition 268 72 Cape Horn current 547 161 Celestial coordinates .. .. .... 234 65 equator, definition ... 215 63 horizon, definition ^13 63 latitude and longitude 238 65 definition 229 238 64 65 longitude and latitude definition 229 216 210 64 63 63 meridian, definition sphere or concave, definition. Celo-Navigation, definition 4 11 Chart {See also Projection). as record of piloting 166 49 employment in piloting 165 48 general features 36 18 189 57 for composite sailing. 197 59 ieobaric 465 46 143 21 measures of depth on Mercator, to construct 40 45 19 20 quality of bottom on standard meridians on 44 547 20 161 Chilean current Chronometer, advantage of more than one 265 268 72 72 C— W, definition care on shipboard 260 71 comparison 263 71 record 264 72 correction. {See Chro- nometer error. ) description 259 71 error, by equal alts 321 90 form . 176 single altitude . 316 88 time sight 316 88 signals . . . 314 87 transits 315 88 definition 261 71 differs from corr . 312 87 from rate 311 87 hack, use of 268 72 max. and min. ther- mometer 262 268 71 72 minus watch, definition. second difference 265 72 sigh t. ( See Time sight. ) temperature curve 266 72 transportation of 260 71 winding 262 71 Circle, declination, definition 216 216 217 373 63 63 63 114 hour, definition of altitude, definition equal altitude illumination 373 217 334 114 63 97 174 74 27 vertical, definition Circum-meridian altitude forms Civil time 277 70 Clouds, description and symbols Coefficients, constant 112 107 38 37 quadrantal semicircular 103 114 36 38 value and relation Collimation, line of, definition 414 132 Subject. Art. 268 56 263 264 434 198 184 199 196 200 210 333 Comparing watch, use of Comparison, barometer i chronometer, method . record . . . Compass, beam, description boxing I 27 compensation. {See Devia- | tion. ) , i declination definition deviation. (iSee Deviation. ) divisions on card dry error. (»5ee Error, compass.) local attraction Lord Kelvin Navy service, 7^-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 Siwo Labrador ocean, Atlantic cause of definition determination of drift, definition of Atlantic Indian Pacific 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 INDEX TO PART I. 335 Subject. Art. Current, ocean, stream, definition .. submarine Oya Siwo Peruvian Eennell'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 1 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 . . . Napier diagram for quadrantal, coefficients definition recompensation semicircular, coefficients — definition table theory of to apply find Diagram, time azimuth Difference, second. {See Second dif- ference. ) Dip of horizon, definition how applied none with artificial horizon variation in when land intervenes. Distance and bearing bv horizon angle 523 524 544 547 537 546 539 495 505 511 207 266 480 481 482 491 492 483 486 155 156 157 Page. 393 392 202 205 203 236 237 216 218 74 416 209 1 6 392 204 46 23 98 99 119 112 111 76 126 116 93 107 106 129 103 100 91 95 77 83 361 300 303 294 301 302 138 139 158 158 161 161 160 161 160 153 154 156 62 72 147 148 148 150 150 148 149 46 46 46 189 124 124 60 171 60 60 178 65 65 63 64 29 133 63 11 11 124 60 21 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 lunar. (*See Lunar distance.) of objects of known height. . polar, definition zenith. (*Sef Zenith distance. ) Distant object for compass error Diurnal inequality of tide type of tide Dividers, description proportional, description Doldrums Doubling angle on bow Drift current, definition currents, Atlantic Earth, definitions relating to Eccentricity, sextant Ecliptic, definition Elevated pole Ephemeris. (&e Nautical Almanac. ) Equal altitudes for chro. error form . . . longitude ashore . . at sea . Equation of time, definition in conversion of time . Equator, celestial, definition earth's Equatorial currents. {See Current. ) Equiangular spiral Equinoctial, definition Equinox, definition vernal. {See First point of Aries. ) Error, chro. (*See Chronometer.) compass, causes to apply find heeling. (&e Deviation.) index, sextant, description probable, of position, how shown sextant. (»S'ee Sextant.) Establishment, tidal, definitions Ex-meridian altitudes forms Extraordinary refraction near horizon. Extra-tropical cyclonic storms First point of Aries, definition hour angle is si- dereal time Flinders bar, definition to place Fogs and fog signals Forms for sights, etc notes on use recommended . Fractions, decimal Gauges, tide, description Geodesy, definition Geometry f ormulee derived fropi Geo-Navigation, definition Gimbals, compass chronometer Glasses, shade. {See Shade glasses. ) Globe, terrestrial, for comp. sailing. . . gt. circle sailing. Graduation, sextant, error Great oircle charts for comp. sailing. . . course sailing, advantages 139 219 90 503 503 7 435 470 144 523 533 6 248 225 214 321 347 352 275 288 215 215 226 73 77 82 249 410 497 334 301 493 226 276 105 127 163 411 518 412 4 28 259 200 193 248 189 197 6 186 336 INDEX TO PAET I. Subject. Great circle Bailing, Airy's method — computation definition graphic approx . . . methods terrestrial globe., time azimuth methods Greenwich adopted as prime meridian. time, to find Guinea current Gulf Stream, description extraordinary dip in Hack chronometer, use of Heading, magnetic, determination of. Heeling error. (/S'ee Deviation. ) Height, determination by barometer.. Heliograph, use in surveying Heliotrope, use in surveying Horizon angle, distance by artificial, description method of use no dip with should be tested . . . celestial, definition dip of, definition how applied none with artificial horizon variation in when land intervenes . mirror, adjustment description prismatic visible or sea, definition Horse latitudes Hour angle and declination time, 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 Siwo current ',\ Labrador current ' Lagging of tide Land and sea breezes Art. 194 190 183 192 188 193 191 342 280 535 532 301 268- 122 57 430 430 139 256 257 294 258 213 300 303 294 301 302 246 240 248 213 471 236 293 222 278 216 547 436 412 457 458 402 250 249 245 240 248 96 431 239 7 413 283 497 289 96 465 542 543 6 542 536 502 474 Page. 58 57 56 58 57 58 58 103 75 160 159 83 72 39 23 135 135 43 70 70 82 71 63 83 84 82 83 84 67 66 68 63 145 65 81 64 75 63 161 137 131 140 140 126 69 68 67 66 68 34 135 66 13 131 76 153 190 79 34 143 160 160 12 160 160 154 145 Subject. Art. Latitude, by meridian altitude forms .. Polaris reduction to meridian reduction to meridian, forms single altitude forms (f/ q/' method forms ...... celestial, definition definition difference of, definition horse Lead, arming . . . description line, marking of Level of bench mark surveying, use of description Lights, employment in piloting Line, base, description of of coUimation, definition position. ( See Sumner line. ) sight, definition Sumner. {See Sumner line.) Local attraction « . time, to find -. Log book chip ground patent electric registers revolutions as substitute . . Logarithms, explanation 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 329 340 334 339 339' 229 6 6 471 19 18 18 517 429 428 161 438 414 414 75 281 64 10 12 13 15 17 347 352 346 349 344 229 6 6 343 345 6 28 406 497 461 97 95 448 491 492 412 274 115 274 274 292 290 274 289 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 plane table Oya Si wo current Parallax, definition horizontal, in Nautical Al- manac how applied of planet or star Parallel of latitude, definition rulers, description sailing, description Passage, meridian, definition Pelorus, description Peruvian current Piloting, definition requisites 6583—06 22 288 287 38 40 179 333 329 330 334 216 6 271 342 342 343 44 342 345 39 175 178 6 254 473 294 401 406 394 212 93 282 305 283 283 285 209 239 6 1 7 499 396 415 255 242 418 644 304 305 306 294 173 271 35 547 130 131 Page. 79 i9 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 78 63 66 12 11 13 153 125 177 132 70 67 133 161 84 84 85 82 11 13 52 74 18 161 42 42 Subject. tidal. Plane of reference sailing table, adjustments description . to improvise use of Planet, correction of observed altitude, form for latitude sights . . . meridian altitude time sight identification of unknown . Planets, stars, and moon, use of . . Polar distance, definition Polaris, latitude by Pole, elevated star, latitude by Poles of earth Portable transit Position by angles between 3 objects.. 26J°-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. (*See Chronometer rate. ) Reciprocal bearings for compass error. Reckoning, dead. {See Dead reckon- ing. ) Record of astronomical work. chronometer comparisons . . piloting tidal Red sea, extraordinary dip in Reduction to meridian forms for Reference, planes of, tidal Refraction, correction for definition effect on dip Art. 514 169 417 416 420 418 294 402 401 219 340 214 340 6 431 151 146 142 138 145 134 144 143 133 166 407 458 410 465 479 466 476 342 217 602 43 38 42 37 435 418 9 432 433 151 255 498' 89 158 87 411 264 166 512 301 334 614 298 296 300 338 INDEX TO PART I. Subject 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 current 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 Semicircular deviation. (*SeeDeviation. ) Semidiameter, definition how applied measured of planet or star Semidiurnal type of tide 1 . . Sextant adjustments permanent angles for plotting soundings . choice of definition description eccentricity graduation errors mdex 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 289 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 Subject. Sidereal time, relation to mean | 287 S%ht, chronometer. ( See Time sight. ) equal alts. {See Equal altitudes. ) latitude. {See Latitude. ) line of, definition longitude. {See Longitude.) time. {See Time sight. ) Sights, afternoon employment of various morning -. noon „ Signals, surveying, description time, for chronometer error Silvering sextant mirrors Solar time. (*S'ee Apparent time. ) ! Solstice, definition 227 Sound, velocity of ' 314 Sounding machine, barometric corr < 24 depth recorder 23 description \ 20 tubes 21 414 399 408 394 396 447 314 254 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 Protractxjr, three armed. ) Storm center, motion of rate of progress to avoid fix bearing distance semicircles tables Storms, along transatlantic routes cyclonic. ( /SeeCyclonic storms. ) Stream current, definition Submarine ocean currents Sumner line, always recommended applications of choice of bodies description determination uses lines, intersection, computation graphically . when run in- tervenes.. Sun, correction of observed altitude 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 458 159 539 210 168 499 294 326 402 454 102 401 484 485 489 487 488 490 492 494 523 524 394 400 400 372 379 377 384 382 390 294 322 347 274 454 450 436 462 79 INDEX TO PART I. 339 Subject. Survey, to plot soundings in Surveying, hydrographic, definition. . . instruments marine, definition topographic, definition transit, description Symbols for clouds sea weather Table, plane. {See Plane table. ) tide time azimuth Telemeter, description substitute for use of Telescope, direct and reversed'. sextant, adjustment description zenith Temperature curve, chronometer Terrestrial object, true bearing of Tertiary meridian, definition determination of . . Theodolite, adjustments angles for plotting sound- ings description method of use Thermometer, 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. (^See Azimuth, time.) civil con version of. ( See Conversion. ) equation of. {See Equation of time. ) Art. 458 412 413 412 412 413 70 72 69 506 361 421 426 424 415 247 240 431 266 369 342 345 414 458 413 415 58 58 61 262 153 152 502 497 460 508 512 516 496 495 503 503 164 501 518 509 514 502 498 503 499 506 506 503 503 366 293 277 279 277 Page. 140 131 131 131 131 131 27 28 27 155 110 134 135 135 132 68 66 135 72 112 103 103 132 140 131 132 24 24 24 71 46 45 154 153 140 156 156 156 153 153 154 154 48 154 157 156 156 154 190 153 154 153 155 155 176 154 154 112 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. {See Sidereal time. ) signals for chronometer error . . . sight for chronometer error longitude ashore at sea forms for solar. {See Apparent time.) Topographic surveying, definition Topography in hydrographic survey . . Tracing paper to plot soundings 3 -point problem . Trade wind Transit, astronomical definition observations for chronometer error longitude portable surveying. (»S'ee 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 Art. prime Visible horizon, definition Watch, comparing, use of Weather symbols Wind, Beaufort's scale causes of definition doldrums effect of, on tides land and sea breezes monsoon normal pressure prevailing westerly " Roaring forties " storms. {See Cyclonic storms. Trade true direction and force Zenith, definition distance, definition how named telescope 280 281 506 331 314 316 346 349 412 456 160 433 469 431 271 315 344 431 331 172 170 448 449 503 483 486 21 402 74 77 82 476 478 477 51 241 413 139 217 217 213 268 69 67 464 463 470 501 474 473 465 467 472 472 469 68 212 221 329 431 i>^RT II. TABLES. 341 OOIvrTEISrTS of I>^RT II. Page. Explanation of the Tables 345 Table 1. Traverse Table, Quarter Points !I"I"I 352 2. Traverse Table, Degrees 368 8. 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 j. 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 28 B. 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. TABIiBS 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 Button's Logarithms; and if any difference was found, the numbers were calculated a third time by Taylor's Logarithms. The first table contains the difference of latitude and departure corresponding to distances not exceeding 300 miles, and for courses to every quarter point of the compass. Table 2 is of the same nature, but for courses consisting of whole degrees; it was originally of the same extent as Table 1, but has been extended to include distances up to 600 miles. The manner of using these tables is particularly explained under the different problems of Plane, Middle Latitude, and Mercator Sailing in Chapter V. The tables may be employed in the solution of any right triangle. TABLE 3: MERIDIONAL PARTS. This table contains the meridional parts, or increased latitudes, for every degree and minute to 80°, calculated by the following formula: w=^logtanr45° + ^^ -a(e^sinL + Je*sin»L + ie«sin5L+ ....), in which 10800'' the Equatorial radius a = ^ = 3437^74677 (log 3.5362739); M, the modulus of common logarithms = 0.4342945; ^=2.3025851 (log 0.3622157); C, the compression or meridional eccentricity of the earth according to Clarke (1880) = 293^65 "" 0-003407562 (log 7.5324437); e =^/2c~c' = 0.0824846 (log 8.9163666) ; ^ = 7915^7044558 (log 3.8984895) ; ae* = 23^38871 (log 1.3690072); iae* = 0^ 053042 (log 8. 7246192 ) ; la^= 0^000216523 (log 6.3355038). The results are tabulated to one decimal place, which is sufficient for the ordinary problems of from which navigation The practical application of this table is illustrated in Chapters II and V, in articles treating of the Mercator Chart and Mercator Sailing. TABLE -4: LENGTH OF DEGREES OF LATITUDE AND LONGITTTDE. This table gives the length of a degree in both latitude and longitude at each parallel of latitude on the earth's surface, in nautical and statute miles and in meters, based upon Clarke s value (1866) ot the earth's compression, gg^* In the case of latitude, the length relates to an arc of which the given degree is the center. TABLES 5 A, 5B: DISTANCE BY TWO BEARINGS. These tables have been calculated to facilitate the operation of finding the distance from an object by two bearings from a given distance run and course. In Table 5A the arguments are given mpomts, in Table 5B in degrees; the first column contains the multiplier of the distance run to give the distance of observed object at second bearing; the second, at time of passing abeam. The method is explained in article 143, Chapter IV. 345 346 EXPLANATION OF THE TABLES. TABLE 6: DISTANCE OF VISIBILITY OF OBJECTS. This table contains the distances, in nautical and statute miles, at which any object is visible at sea. It is calculated by the formulae: _ _ d = 1. 15 x/x, and d' = 1.32 ^^x, in which d is the distance in nautical miles, d^ the distance in statute miles, and x the height of the eye or the object in feet. To find the distance of visibility of an object, the distance given by the table corresponding to its height should be added to that corresponding to the height of the observer's eye. Example: Required the distance of visibility of an object 420 feet high, the observer being at an elevation of 15 feet. Diet, corresponding to 420 feet, 23.5 naut. miles. Dist. corresponding to 15 feet, 4.4 naut. miles. Dist. of visibilitv. 27.9 naut. miles. TABLE 7: CONVERSION OF ARC AND TIME. In the first column of each pair in this table are contained angular measures expressed in arc (degrees, minutes, or seconds), and in the second column the corresponding angles expressed in time (hours, minutes, or seconds). As will be seen from the headings of columns, the time corresponding to degrees (°) is given in hours and minutes; to minutes of arc (^), in minutes and seconds of time; and to seconds of arc (''''), in seconds and sixtieths of a second of time. The table will be especially convenient in dealing with longitude and hour angle. The method of its employment is best illustrated by examples. Example I. Required the time corresponding to 50° 31' 21^''. 50° 00' OO''' = "S^ 20" 00^ 31 00 = 2 04 21 = m 50 31 21 =3 22 05.4 Example II. Required the arc corresponding to &^ 33" 26^5. &" 32°' 00^ 1 24 00' 00" 21 00 37.5 6 33 26. 5 = 98 21 37. 5 TABLES 8 AND 9: SIDEREAL AND MEAN SOLAR TIMES. These tables give, respectively, the reductions necessary to convert intervals of sidereal time into those of mean solar time, and intervals of mean solar into those of sidereal time. The reduction for any interval is found by entering with the number of hours at the top and the number of minutes at the side, adding the reduction for seconds as given in the margin. The relations between mean solar and sidereal time intervals, and the methods of conversion of these times, are given in articles 289-291, Chapter IX. TABLE 10: SUN'S RISING AND SETTING. This table gives the local mean time of the sun's visible rising and setting — that is, of the appearance and disappearance of the sun's upper limb in the unobstructed horizon of a person whose eye is 15 feet above the level of the earth's surface, the atmospheric conditions being normal. The local apparent times of rising and setting were determined from the formula for a time sight, the altitude employed being — 0° 56' 08", made up of the following terms: Refraction, — 36' 29"; semi- diameter, — 16' 00"; dip, —3' 48"; and parallax, -[-9". To ascertain the time of rising or setting for any given date and place, enter the table with the latitude and declination, interpolating if the degrees are not even. In the line R will be found the time of rising; in the line S, the time of setting. Be careful to choose the page in which the latitude is of the correct name, and in which the "approximate date" corresponds, nearly or exactly, with the given date. This table is computed with the intention that, if accuracy is desired, it will be entered with the declination as an argument — not the date — as it is impossible to construct any table based upon dates whose application shall be general to all years. But as a given degree of declination will, in the majority of years, fall upon the date given in the table as the "approximate date," and as, when it does not do so, it can never be more than one day removed therefrom, it will answer, where a slight inaccuracy may be admitted, to enter the table with the date as an argument, thus avoiding the neces- sity of ascertaining the declination. Example: Find the local mean time of sunset at Rio de Janeiro, Brazil (lat. 22° 54' S., long. 43° 10' W.), on January 1, 1903 (dec. 23° 04' S.). Exact method. Lat. 22° \ Dec. 23° J Corr. for + 54' lat +02 Corr. for + 04' dec 00 Approximate method. :} gh 4gm Lat. 22°.. January 2 Corr. 'for + 54' lat +02 Corr. for 1 dav — 01 L. M. T. sunset 6 50 L. M. T. sunset 6 49 EXPLANATION OF THE TABLES. 847 TABLE 11: KEDUCTION FOB MOON'S TRANSIT. This table was calculated by proportioning the daily variation of the time of the moon's passing the .flieridian. The numbers taken from the table are to be added to the Greenwich time of moon's transit in west longitude, but subtracted in east longitude. TABLE 12: REDUCTIONS FOR NAUTICAL ALMANAC. This is a table of proportional parts for finding the variation of the sun' s right ascension or declination, or of the equation 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 sifle column ; also for finding the variation of the moon's declination or right ascension in any number of seconds of time, the motion in one minute being given at the top, and the numbers in the side column being taken for seconds. TABLE 13: CHANGE OF SUN'S RIGHT ASCENSION. This is a table that may be employed for finding the change of the sun's right ascension for any given number of hours, the hourly change, as taken from the Nautical Almanac, being given in the marginal columns. TABLE 14: DIP OF SEA HORIZON. This table contains the dip of the sea horizon, calculated by the formula: D = 58'^8v/F, in which F = height of the eye above the level of the sea in feet. It is explained in article 300, Chapter X. TABLE 15: DIP SHORT OF HORIZON. This table contains the dip for various distances and heights, calculated by the formula: D = ? (? + 0.56514 X h in which D represents the dip in miles or minutes, d, the distance of the land in sea miles, and h, the height of the eye of the observer in feet. TABLE 16: PARALLAX OF SUN. This table contains the sun's parallax in altitude calculated by the formula: par. = sin z X 8'^75, in which z = apparent zenith distance, the sun's horizontal parallax being 8'''. 75. It is explained in article 304, Chapter X. TABLE 17: PARALLAX OF PLANET. Parallax in altitude of a planet is found by entering at the top with the planet's horizontal parallax, and at the side with the altitude. TABLE 18: AUGMENTATION OF MOON'S SEMIDIAMETER. This table gives the augmentation of the moon's semidiameter calculated by the formula: x = c s^ sin h + ^* sin* V^ sin*< tan» h; in which * L = the latitude of the place; h = the true altitude; • p = the polar distance; and t = the hour angle of the star. Table A contains for the declination 88° 48', or p„ = 1° 12' =4320''', the^rs< correctim, ^ = —Po COS t — Jp'„ sin^ 1" cos t sin'^ t; Argument, the hour angle of the star, or 24'» — the hour angle. Table B contains the second correction, B = i p% sin 1" sin^ tta.nh+ \p\ sin» 1" sin* t tan* h; Arguments, the true altitude of the star and the hour angle, or 2'i^—the hour angle. This correction is always additive. Table C contains the third correction, C = Hp' -P\) sin V^ sin^ t tan h; Arguments, B and the declination of the star from 88° 47'' 20" to 88° 49' 20"'. Table D contains the fourth correction, — {p —Pa) COS i — J (p^ — p^o) sin'' 1" cos 3°, 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. 63 304.4 197.7 23 354.7 230.4 83 405.1 263.1 43 455. 4 295.7 04 255.0 165. 5 64 305.3 198.2 24 355.6 230.9 84 405.9 263.6 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 m 307.0 199.3 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 48 459.6 298.4 09 259.2 168.3 69 309.5 200.9 29 359.8 233.6 89 410.1 266.3 49 460.4 299.0 10 260.0 168.8 70 310.3 201.5 30 360.6 234.2 90 411.0 266.8 50 461.3 299.5 311 260.8 169.3 371 311.2 202.0 431 361.5 234.7 491 411.8 267.4 551 462.1 300.1 12 261.7 169.9 72 312.0 202.6 32 362.3 235.2 92 412.6 267.9 52 463.0 300.6 13 262.5 170.4 73 312.8 203.1 33 363.1 235.8 93 413. 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 16 265.0 172.1 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 78 317.0 205.8 38 367. 3 238.5 98 417.6 271.2 58 468.0 303.9 19 267.5 173.7 79 317.9 206.4 39 368.2 239.1 99 418.5 271.8 59 468.8 304.5 20 268.4 174. 2 174.8 80 381 318.7 206.9 40 369.0 239.6 5C0 419.3 272.3 60 469.7 305.0 321 269.2 319.5 207.5 441 369. 9 240.1 501 420.2 272.8 561 470.5 305.5 22 270.1 175.3 82 320.4 208.0 42 370.7 240.7 02 421.0 273.4 62 471.3 306.1 23 270.9 175.9 83 321.2 208.6 43 371. 5 241.2 03 421.9 273.9 63 472.2 306. 6 24 271.7 176.4 84 322.1 209.1 44 372. 4 241.8 04 422.7 274.5 64 473.0 307.2 25 272.6 177.0 85 322.9 209.6 45 373.2 242.3 05 423.5 275.0 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 30 331 276.8 179.7 90 327.1 212.4 212.9 50 451 377.4 378. 2 245.1 10 427.7 277.8 70 571 478.0 310.4 277.6 180.2 391 327.9 245. 6 511 428.5 278.3 478.9 311.0 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 59 385.0 250.0 19 435.3 282.6 79 485.6 315.3 40 285.2 185.1 400 335.5 217.8 60 385.8 250.5 20 436.1 283.2 80 486.4 487.2 315.9 341 286.0 185. 7 401 336. 3 218.4 461 386.6 251.0 521 436.9 283.7 581 316.4 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 70 394.2 255.9 30 444.5 288.6 90 591 494.8 495.7 321.3 351 294.4 191.1 411 223.8 471 395.0 256.5 531 445.3 289.2 321.9 52 295.2 191.7 12 345.5 224.4 72 395.8 257.0 32 446.1 289.7 92 496.5 322.4 53 296.1 192.2 13 346.4 224.9 73 396.7 257.6 33 447.0 290.3 93 497.3 322.9 54 296.9 192.8 14 347.2 225.4 74 397.5 258.1 34 447.8 290.8 94 498.1 323.5 55 297.7 193.3 15 348.1 226.0 75 398.3 258.7 35 448.7 291.4 95 499.0 324.1 56 298.6 193.9 16 348.9 226.5 76 399.2 259.2 36 449.5 291.9 96 499.8 324.6 57 299.4 194.4 17 349.7 227.1 77 400.0 259.8 37 450.3 292.5 97 500.6 325.1 58 300.2 194.9 18 350.6 227.6 78 400.9 260.3 38 451.2 293.0 98 501.5 325.7 59 301.1 195.5 19 351.4 228.2 79 401.7 260.9 39 452.0 293.6 99 502.3 326.2 60 301.9 196.0 20 352,2 228.7 80 402.6 261.4 40 Dist. 452.9 294.1 600 503.2 326.8 Dist. Dep. Lat. 1 Dist. Dep. Lat. Dist. Dep. Lat. Dep. Lat. Dist. Dep. Lat. 57° (123°, 237°, 303°). 1 6583—06- •28 Page 434] TABLE 2. Difference of Latitude and Departure for 34° (146°, 214°, 326° )• Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 0.8 0.6 61 50.6 34.1 121 100.3 67.7 181 150.1 101.2 241 199.8 134.8 2 1.7 1.1 62 51.4 34.7 22 101.1 68.2 82 150.9 101.8 42 200.6 135.3 3 2.5 1.7 63 52.2 35.2 23 102.0 68.8 83 151.7 102.3 43 201.5 135.9 4 3.3 2.2 64 53.1 35.8 24 102.8 69.3 84 152.5 102.9 44 202.3 136.4 5 4.1 2.8 65 53.9 36.3 25 103.6 69.9 85 153.4 103.5 45 203.1 137.0 6 5.0 3.4 66 54.7 36.9 26 104.5 70.5 86 154.2 104.0 46 203.9 137.6 7 5.8 3.9 67 55.5 37.5 27 105.3 71.0 87 155.0 104.6 47 204.8 138.1 8 6.6 4.5 68 56.4 38.0 28 106.1 71.6. 88 155.9 105.1 48 205.6 138.7 9 7.5 5.0 69 57.2 38.6 29 106.9 72.1 89 156.7 105.7 49 206.4 139.2 10 8.3 5.6 70 58.0 58.9 39.1 30 107.8 72.7 90 157.5 106.2 50 207.3 139.8 11 9.1 6.2 71 39.7 131 108.6 73.3 191 158.3 106.8 251 208.1 140.4 12 9.9 6.7 72 59.7 40.3 32 109.4 73.8 92 159.2 107.4 52 208.9 140.9 13 10.8 7.3 73 60.5 40.8 33 110.3 74.4 93 160.0 107.9 53 209.7 141.5 14 11.6 7.8 74 61.3 41.4 34 111.1 74.9 94 160.8 108.5 54 210.6 142.0 15 12.4 8.4 75 62.2 41.9 35 111.9 75.5 95 161.7 109.0 55 211.4 142.6 16 13.3 8.9 76 63.0 42.5 36 112.7 76.1 96 162.5 109.6 56 212.2 143.2 17 14.1 9.5 77 63.8 43.1 37 113.6 76.6 97 163.3 110.2 57 213.1 143.7 18 14.9 10.1 78 64.7 43.6 38 114.4 77.2 98 164.1 110.7 58 213.9 144.3 19 15.8 10.6 79 65.5 44.2 39 115.2 77.7 99 165.0 111.3 59 214.7 144.8 20 16.6 11.2 80 66.3 67.2 44.7 40 116.1 78.3 200 165.8 111.8 60 215.5 145.4 21 17.4 11.7 81 45.3 141 116.9 78.8 201 166.6 112.4 261 216.4 145.9 22 18.2 12.3 82 68.0 45.9 42 117. 7 79.4 02 167.5 113.0 62 217.2 146.5 23 19.1 12.9 83 68.8 46.4 43 118.6 80.0 03 168.3 113.5 63 218.0 147.1 24 19.9 13.4 84 69.6 47.0 44 119.4 80.5 04 169.1 114.1 64 218.9 147.6 25 20.7 14.0 85 70.5 47.5 45 120.2 81.1 05 170.0 114.6 65 219.7 148.2 26 21.6 14.5 86 71.3 48.1 46 121.0 81.6 06 170.8 115. 2 66 220.5 148.7 27 22.4 15.1 87 72.1 48.6 47 121.9 82.2 07 171.6 115.8 67 221.4 149.3 28 23.2 15.7 88 73.0 49.2 48 122.7 82.8 08 172.4 116.3 68 222.2 149.9 29 24.0 16.2 89 73.8 49.8 49 123.5 83.3 09 173.3 116.9 69 223.0 150.4 30 24.9 16.8 90 74.6 50.3 50 124.4 83.9 10 174.1 117.4 70 223.8 151.0 31 25.- 7 17.3 91 75.4 50.9 151 125.2 84.4 211 174.9 118.0 271 224.7 151.5 32 26.5 17.9 92 76.3 51.4 52 126.0 85.0 12 175.8 118.5 72 225.5 152.1 33 27.4 18.5 93 77.1 52.0 53 126.8 85.6 13 176.6 119.1 73 226.3 152.7 34 28.2 19.0 94 77.9 52.6 54 127.7 86.1 14 177.4 119.7 74 227.2 153.2 35 29.0 19.6 95 78.8 53.1 55 128.5 86.7 15 178.2 120.2 75 228.0 153.8 36 29.8 20.1 96 79.6 '53.7 56 129.3 87.2 16 179.1 120.8 76 228.8 154.3 37 30.7 20.7 97 80.4 54.2 57 130.2 87.8 17 179.9 121.3 77 229.6 154.9 38 31.5 21.2 98 81.2 54.8 58 131.0 88.4 18 180.7 121.9 78 230.5 155.5 39 32.3 21.8 99 82.1 55.4 59 131.8 88.9 19 181.6 122.5 79 231.3 156. 40 33.2 22.4 100 82.9 55.9 60 132.6 133.5 89.5 20 182.4 123.0 80 232.1 156.6 157.1 41 34.0 22.9 101 83.7 56.5 161 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 82 233.8 157.7 43 35.6 24.0 03 85.4 57.6 63 135.1 91.1 23 184.9 124.7 83 234.6 158.3 44 36.5 24.6 04 86.2 58.2 64 136.0 91.7 24 185.7 125. 3 84 235.4 158.8 45 37.3 25.2 05 87.0 58.7 65 136. 8 92.3 25 186.5 125.8 85 236.3 159.4 46 38.1 25.7 06 87.9 59.3 66 137.6 92.8 26 187.4 126.4 86 237.1 159.9 47 39.0 26.3 07 88.7 59.8 67 138.4 93.4 27 188.2 126.9 87 237.9 160.5 48 39.8 26.8 08 89.5 60.4 68 139.3 93.9 28 189.0 127.5 88 238.8 161.0 49 40.6 27.4 09 90.4 61.0 69 140.1 94.5 29 189.8 128.1 89 239.6 161.6 50 41.5 28.0 10 91.2 61.5 70 140.9 141.8 95.1 30 190.7 128.6 ^0 240.4 241.2 162.2 51 42.3 28.5 111 92.0 62.1 171 95.6 231 191.5 129.2 291 162.7 52 43.1 29.1 12 92.9 62.6 72 142.6 96.2 32 192.3 129.7 92 242.1 163.3 53 43.9 29.6 13 93.7 63.2 73 143.4 96.7 33 193.2 130.3 93 242.9 163.8 54 44.8 30.2 14 94.5 63.7 74 144.3 97.3 34 194.0 130.9 94 243.7 164.4 55 45.6 30.8 15 95.3 64.3 75 145.1 97.9 35 194.8 131.4 95 244.6 165.0 56 46.4 31.3 16 96.2 64.9 76 145.9 98.4 36 195.7 132.0 96 245.4 165.5 57 47.3 31.9 17 97.0 65.4 77 146.7 99.0 37 196.5 132.5 97 246.2 166.1 58 48.1 32.4 18 97.8 66.0 78 147.6 99.5 38 197.3 133.1 98 247.1 166.6 59 48.9 33.0 19 98.7 66.5 79 148.4 100.1 39 198.1 133.6 99 247.9 167.2 60 49.7 33.6 20 99.5 67.1 80 149.2 100.7 40 199.0 134.2 300 248.7 167.8 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. ^ )6° (1 24°, 236 °, 304° ). TABLE 2. [Page 435 Difference of Latitude and E -parture for 34° (146°, 214°, 326° ). Difit. 301 Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 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 45'J. 2 303.6 04 252. 170.0 64 301.8 203.5 24 351.5 237.1 84 401.3 270.6 44 451.0 .304. 2 05 252.9 170.6 65 302.6 204.1 25 352.3 237.7 85 402.1 271.2 45 451.8 304.8 06 253. 7 171.1 m 303.4 204.7 26 353.2 238.2 86 402. 9 271.8 46 452.6 305.3 07 254.5 171.7 67 304. 3 205.2 27 354. 238.8 87 403.8 272.3 47 453.5 305.9 08 255. 3 172.2 68 305.1 205. 8 28 354.8 239.3 88 404.6 272.8 48 454.3 306.4 09 256.2 172.8 69 305.9 206.3 29 355.7 239.9 89 405.4 273.4 49 455.2 307.0 10 311 257.0 257.8 173.3 70 306.7 206.9 30 356.5 357.3 240.4 90 406.2 274.0 50 456.0 307. 5 173.9 371 307.6 207.5 431 241.0 491 407.1 274.6 551 456.8 308.1 12 258.7 174.5 72 308.4 208.0 32 358.1 241.6 92 407.9 275.1 52 457.6 308.7 13 259.5 175. 73 309.2 208.6 33 359.0 242.1 93 408.7 275.7 53 458.4 309.2 14 260.3 175.6 74 310.1 209.1 34 359.8 242.7 94 409.5 276.2 54 459. 3 309.8 15 261.2 176.1 75 310.9 209.7 35 360.6 243.2 95 410.4 276.8 55 460.1 310.3 16 262.0 176.7 76 311.7 210.3 36 361.5 243.8 96 411.2 277.4 56 460.9 310.9 17 262.8 177.3 77 312.6 210.8 37 362.3 244.4 97 412.0 277.9 57 461.7 311.5 18 263.7 177.8 78 313.4 211.4 38 363.1 244.9 98 412.8 278.4 58 462.6 312.0 19 264. 5 178.4 79 314.2 211.9 39 364.0 245.5 99 413.7 279.0 59 463.4 312.6 20 265.3 178.9 80 315.0 212.5 40 364.8 365.6 246.0 500 501 414.5 279.6 60 464.2 313.1 321 266.1 179.5 381 315.9 213.0 441 246.6 415.3 280.1 561 465.1 313.7 22 267.0 180.1 82 316.7 213. 6 42 366.4 247.2 02 416.2 280.7 62 465.9 314.3 23 267.8 180.6 83 317.5 214.2 43 367.3 247.7 03 417.0 281.3 63 466.8 314.8 24 268.6 181.2 84 318.4 214.7 44 368.1 248.3 04 417.8 281.8 64 467.6 315.4 25 269.5 181.7 85 319.2 215.3 45 368.9 248.8 05 418. 6 282.4 65 468.4 315.9 26 270. 3 182.3 86 320.0 215.8 46 369.8 249.4 06 419.4 282.9 66 469.2 316.5 27 271.1 182.9 87 320. 8 216.4 47 370.6 250.0 07 420.3 283.5 67 470.1 317.1 28 271.9 183.4 88 321.7 217.0 48. 371.4 250.5 08 421.1 284.1 68 470.9 317.6 29 272.8 184.0 89 322. 5 217.5 49 372.2 251.1 09 421.9 284.6 69 471.7 318.2 30 273.6 274.4 184.5 90 323.3 218.1 50 373.1 373.9 251.6 252.2 10 422.8 285.2 70 472.6 318.7 331 185.1 391 324.2 218.6 451 511 423.6 285.8 571 473.4 319.3 32 275.2 185.6 92 325.0 219.2 52 374.7 252.8 12 424.4 286.3 72 474.2 319.9 33 276.1 186.2 93 325.8 219.8 53 375.6 253.3 13 425.3 286. 9 73 475.0 320.4 34 276.9 186.8 94 326.6 220.3 54 376.4 253.9 14 426.1 287.4 74 475.9 321.0 35 277.7 187.3 95 327.5 220.9 55 377. 2 254.4 15 426.9 288.0 75 476.7 321. 5 36 278.6 187.9 96 328.3 221.4 56 378.0 255.0 16 427.8 288.5 76 477.5 322.1 37 279.4 188.4 97 329.1 222.0 57 378.9 255.5 17 428.6 289.1 77 478.3 322.7 38 280.2 189.0 98 330. 222.6 58 379.7 256.1 18 429.4 289.6 78 479.2 323.2 39 281.0 189.6 99 330.8 223.1 59 380.5 256.7 19 430.3 290.2 79 480.0 323.8 40 281.9 190.1 400 331.6 223.7 60 381.3 257.2 20 •431. 1 290.8 80 480.8 324.3 324.9 341 282.7 190.7 401 332.4 224.2 461 382.2 257.8 521 431.9 291.3 581 481.6 42 283.5 191.2 02 333.3 224.8 62 383.0 258.3 22 432.8 291.9 82 482.5 325.4 43 284.4 191.8 03 334.1 225.4 63 383.8 258.9 23 433.6 292.5 83 483.3 326.0 44 285. 2 192.4 04 334.9 225.9 64 384.7 259.5 24 434.4 293.0 84 484.1 326.6 45 286.0 192.9 05 335.8 226.5 65 385.5 260.0 25 435.3 293.6 85 485.0 327.2 46 286. 9 193.5 06 336.6 227.0 66 386.3 260.6 26 436.1 294.1 86 485.8 327.7 47 287.7 194.0 07 337.4 227.6 67 387.2 261.1 27 436.9 294.7 87 486.6 328.2 48 288.5 194.6 08 338.3 228.1 68 388.0 261.7 28 437.8 295.3 88 487.5 328.8 49 289.3 195.2 09 339.1 228.7 69 388.8 262.3 29 438. 6 295.8 89 488.3 329.4 50 290.2 195.7 10 339.9 229.3 70 389.7 262.8 30 439.4 296.4 90 489.2 329. 9 330.5 351 291.0 196.3 411 340.7 229.8 471 390.5 263.4 531 440.3 296.9 591 490. 52 291.8 196.8 12 341.6 230. 4 72 391.3 263.9 32 441.1 297.4 92 490.8 331.0 53 292.7 197.4 13 342.4 230.9 73 392.1 264.5 33 441.9 298.0 93 491.6 331.6 54 293.5 198.0 14 343.2 231.5 74 393.0 265.0 34 442.7 298.6 94 492.5 332.2 55 294.3 198.5 15 344.1 232. 1 75 393.8 265.6 35 443.6 299.1 95 493.3 332.7 56 295. 1 199.1 16 344.9 232.6 76 394.6 266.2 36 444.4 299.7 96 494.1 333.3 57 296.0 199.6 17 345.7 233.2 77 395.5 266.7 37 445.3 300.2 97 494.9 333.8 58 296.8 200.2 18 346.5 233.7 78 396.3 267.3 38 446.1 300.8 98 495.8 334.4 59 297.6 200.7 19 347.4 234.3 79 397.1 267.9 39 446.9 301.4 99 496.6 334. 9 60 298.5 201.3 20 348.2 234.9 80 397.9 268.4 40 447.7 302.0 600 497.4 335.5 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 56° (124°, 236 °, 304° )• 1 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 66 54.1 37.9 26 103.2 72.3 86 153.4 106.7 46 201.5 141.1 7 5.7 4.0 67 54.9 38.4 27 104.0 72.8 87 153. 2 107.3 47 202.3 141.7 8 6.6 4.6 68 55.7 39.0 28 104.9 73.4 88 154. 107.8 48 203.1 142.2 9 7.4 5.2 69 56.5 39.6 29 105.7 74.0 89 154.8 108.4 49 204.0 142.8 10 8.2 5.7 70 57.3 40.2 30 106.5 74.6 90 155.6 109.0 50 204.8 143.4 11 9.0 6.3 71 58.2 40.7 131 107.3 75.1 191 156.5 109.6 251 205.6 144.0 12 9.8 6.9 72 59.0 41.3 32 108.1 75.7 92 157.3 110.1 52 206.4 144.5 13 10.6 7.5 73 59.8 41.9 33 108.9 76.3 93 158.1 110.7 53 207.2 145.1 14 11.5 8.0 74 60.6 42.4 34 109.8 76.9 94 158.9 111.3 54 208.1 145.7 15 12.3 8.6 75 61.4 43.0 35 110.6 77.4 95 159.7 111.8 55 208.9 146.3 16 13.1 9.2 76 62.3 43.6 36 111.4 78.0 96 160.6 112.4 56 209.7 146.8 17 13.9 9.8 77 63.1 44.2 37 112.2 78.6 97 161.4 113.0 57 210.5 147.4 18 14.7 10.3 78 63.9 44.7 38 113.0 79.2 98 162.2 113.6 58 211.3 148.0 19 15.6 10.9 79 64.7 45.3 39 113.9 79.7 99 163.0 114.1 59 212.2 148.6 20 16.4 11.5 .12.0 80 65.5 45.9 40 114.7 80.3 200 163.8 164.6 114.7 60 213.0 149.1 21 17.2 81 66.4 46.5 141 115.5 80.9 201 115.3 261 213.8 149.7 22 18.0 12.6 82 67.2 47.0 42 116.3 81.4 02 165.5 115.9 62 214.6 150.3 23 18.8 13.2 83 68.0 47.6 43 117.1 82.0 03 166.3 116.4 63 215.4 150.9 24 19.7 13.8 84 68.8 48.2 44 118.0 82.6 04 167.1 117.0 64 216.3 151.4 25 20.5 14.3 85 69.6 48.8 45 118.8 83.2 05 167.9 117.6 65 217.1 152.0 26 21.3 14.9 86 70.4 49.3 46 119.6 83.7 06 168.7 118.2 66 217.9 152.6 27 22.1 15.5 87 71.3 49.9 47 120.4 84.3 07 169.6 118.7 67 218.7 153.1 28 22.9 16.1 88 72.1 50.5 48 121.2 84.9 08 170.4 119.3 68 219.5 153.7 29 23.8 16.6 89 72.9 51.0 49 122.1 85.5 09 171.2 119.9 69 220.4 154. 3 30 24.6 17.2 90 73.7 51.6 50 122.9 86.0 10 172.0 172.8 120.5 70 221.2 154.9 31 25.4 17.8 91 74.5 52.2 151 123.7 86.6 211 121.0 271 222.0 155.4 32 26.2 18.4 92 75.4 52.8 52 124.5 87.2 12 173.7 121.6 72 222.8 156.0 33 27.0 18.9 93 76.2 53.3 53 125.3 87.8 13 174. 5 122.2 73 223.6 156.6 34 27.9 19.5 94 77.0 53.9 54 126.1 88.3 14 175.3 122.7 74 224.4 157.2 35 28.7 20.1 95 77.8 54.5 55 127.0 88.9 15 176.1 123.3 75 225.3 157.7 36 29.5 20.6 96 78.6 55.1 56 127.8 89.5 16 176.9 123.9 76 226.1 158.3 37 30.3 21.2 97 79.5 55.6 57 128.6 90.1 17 177.8 124.5 77 226.9 158.9 38 31.1 21.8 98 80.3 56.2 58 129.4 90.6 18 178.6 125.0 78 227.7 159.5 39 31.9 22.4 99 81.1 56.8 59 130.2 91.2 19 179.4 125.6 79 228.5 160.0 40 32.8 22.9 23.5 100 81.9 ^7.4 60 131.1 131.9 91.8 20 180.2 126.2 80 281 229.4 230.2 160.6 41 33.6 101 82.7 57.9 161 92.3 221 181.0 126.8 161.2 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 i 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 32 190.0 133.1 92 239.2 167.5 53 43.4 30.4 13 92.6 64.8 73 141.7 99.2 33 190.9 133.6 93 240.0 168.1 54 44.2 31.0 14 93.4 65.4 74 142.5 99.8 34 191.7 134.2 94 240.8 168.6 55 45.1 31.5 15 94.2 66.0 75 143.4 100.4 35 192.5 134.8 95 241.6 169.2 56 45.9 32.1 16 95.0 66.5 76 144.2 100.9 36 193.3 135.4 96 242.5 169.8 57 46.7 32.7 17 95.8 67.1 77 145.0 101.5 37 194.1 135.9 97 243.3 170.4 58 47.5 33.3 18 96.7 67.7 78 145. 8 102.1 38 195.0 136.5 98 244.1 170.9 59 48.3 33.8 19 97.5 68.3 79 146.6 102.7 39 195.8 137.1 99 244.9 171.5 60 49.1 34.4 20 98.3 68.8 80 147.4 103.2 40 196.6 137.7 300 245.7 172.1 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 55° (125°, 235 °, 305° )• TABLE 2. [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. 301 246.6 172.6 361 295.7 207.0 421 344.9 241.5 481 394.0 275.9 541 443.2 310.3 02 247.4 173. 2 62 296.5 207.6 22 345.7 242.0 82 394.8 276.4 42 444.0 310.9 03 248.2 173.8 63 297.4 208.2 23 346.5 242.6 83 395.7 277.0 43 444.8 311.4 04 249.0 174.3 64 298.2 208.8 24 347. 3 243.2 84 396.5 277.6 44 445.6 312.0 05 249.9 174.9 65 299.0 209.3 25 348.1 243.8 85 397.3 278.2 45 446.4 312.6 06 250.7 175.5 66 299.8 209.9 26 349.0 244.3 86 398.1 278.7 46 447.3 313.2 07 251.5 176.1 67 300.6 210.5 27 349.8 ,244.9 87 398.9 279.3 47 448.1 313.7 08 252.3 176.6 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 30 352.2 246.6 . 90 401.4 281.0 50 450.5 315.4 311 254.8 178.4 371 303.9 212.8 431 353.1 247.2 491 402.2 281.6 551 451.4 316.0 12 255.6 178.9 72 304.7 213.4 32 353.9 247.8 92 403.0 282.2 52 452.2 316.6 13 256.4 179.5 73 305.6 21.3. 9 33 354.7 248.3 93 403.9 282.8 53 453.0 317.2 14 257.2 180.1 74 306.4 214.5 34 355.5 248.9 94 404.7 283.3 54 453.8 317.7 15 258.0 180.7 75 307.2 215.1 35 356.3 249.5 95 405.5 283.9 55 454.6 318.3 16 258.9 181.2 76 308.0 215.6 36 357.2 250.1 96. 406.3 284.5 56 455.5 318.9 17 259.7 181.8 77 308.8 216.2 37 358.0 250.6 97 407.1 285.1 57 456.3 319.5 18 260.5 182.4 78 309.6 216.8 38 358.8 251.2 98 408.0 285.6 58 457.1 320.0 19 261.3 183.0 79 310.5 217.4 39 359.6 251.8 99 408.8 286.2 59 457.9 320.6 20 262.1 183.5 80 311.3 217.9 40 360.4 252.4 500 409.6 286.8 60 458.7 321.2 321 263.0 184.1 381 312.1 218.5 441 361.3 252.9 501 410.4 287.4 561 459.6 321.8 22 263.8 184.7 82 312.9 219.1 42 362.1 253.5 02 411.2 287.9 62 460.4 322.3 23 264.6 185.2 83 313. 7 219.7 43 362.9 254.1 03 412.1 288.5 63 461.2 322.9 24 265.4 185.8 84 314.6 220.2 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 1 291. 4 68 465.3 325.8 29 269.5 188.7 89 318.7 223.1 49 367.8 257.5 09 417.0 291.9 69 466.1 326.4 30 270.3 189.3 90 319.5 223.7 50 368.6 258.1 10 417.8 292.5 70 466.9 326.9 327.5 331 271.1 189.8 391 320.3 224.3 451 369.4 258.7 511 418.6 293.1 571 467.8 32 272.0 190.4 92 321.1 224.8 52 370.3 259.2 12 419.4 293.7 72 468.6 328.1 33 272.8 191.0 93 321.9 225.4 53 371.1 259.8 13 420.2 294.2 73 469.4 328.7 34 273.6 191.6 94 322.8 226.0 54 371.9 260.4 14 421.1 294.8 74 470.2 329.2 35 274.4 192.1 95 323. 6 226.5 55 372.7 261.0 15 421.9 295.4 75 471.0 329.8 36 275.2 192.7 96 324.4 227.1 56 373.5 261.5 16 422.7 296.0 76 471.9 330.4 37 276.1 193.3 97 325.2 227.7 57 374. 4 262.1 17 423.5 296.5 77 472.7 331.0 38 276.9 193.9 98 326.0 228.3 58 375.2 262.7 18 424.3 297.1 78 473.5 331.5 39 277.7 194.4 99 326.9 228.8 59 376.0 263.3 19 425.2 297.7 79 474.3 332.1 40 278.5 195.0 400 327.7 229.4 60 376.8 263.8 20 426.0 298.3 80 475. 1 332.7 341 279.3 195.6 401 328.5 230. 461 377.6 264.4 521 426.8 298.8 581 476.0 333.3 42 280.2 196.1 02 329.3 230. 6 62 378.5 265.0 22 427.6 299.4 82 476.8 333.8 43 281.0 196.7 03 330.1 231. 1 63 379.3 265.5 23 428.4 300.0 83 477.6 334.4 44 281.8 197.3 04 330.9 231.7 64 380.1 266.1 24 429.3 300.5 84 478.4 335.0 45 282.6 197.9 05 331.8 232. 3 65 380.9 266.7 25 430.1 301.1 85 479.2 335.6 46 283.4 198.4 06 332.6 232.9 66 381.7 267.3 26 430.9 301.7 86 480.1 336. 1 47 284.3 199.0 07 333.4 233.4 67 382.6 267.8 27 431.7 302.3 87 480.9 336.7 48 285.1 199.6 08 334.2 234.0 68 383.4 268.4 28 432.5 302.8 88 481.7 337.3 49 285.9 200.2 09 335.0 234.6 69 384.2 269.0 29 433.4 303.4 89 482.5 337.9 50 286.7 200.7 10 335.9 235.1 70 385.0 269.6 30 434. 2 304.0 90 483.3 338. 4 351 287.5 201.3 411 336.7 235.7 471 385.8 270.1 531 435.0 304.5 591 484.2 339.0 52 288.3 201.9 12 337.5 236.3 72 386.6 270.7 32 435.8 305.1 92 485.0 339.6 53 289.2 202.5 13 338.3 236.9 73 387.5 271.3 33 436.6 305.7 93 485.8 340.2 54 290.0 203.0 14 339.1 237.4 74 388.3 271.9 34 437.5 306.3 94 486.6 340.7 55 290.8 203.6 15 340.0 238.0 75 389.1 272.4 35 438.3 306.8 95 487.4 341.3 56 291.6 204.2 16 340.8 238.6 76 389.9 273.0 .36 439 1 307.4 96 488.3 341.9 57 292.4 204.7 17 341.6 239.2 77 390.7 273.6 37 439.9 308.0 97 489.1 342.5 58 293.3 205.3 18 342.4 239.7 78 391.6 274.2 38 440.7 308.6 98 489.9 343.0 59 294.1 205.9 19 343.2 240.3 79 392.4 274.7 39 441.5 309. 1 99 490.7 343.6 60 294.9 206.5 20 344.1 240.9 80 393.2 275.3 40 442.3 309.7 600 491.5 344.1 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 1 Dist. Dep. 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 71.7 82 147.2 107.0 42 195.8 142.2 3 2.4 1.8 63 51.0 37.0 23 99.5 72.3 83 148.1 107.6 43 196.6 142.8 4 3.2 2.4 64 51.8 37.6 24 100.3 72.9 84 148.9 108.2 44 197.4 143.4 5 4.0 2.9 65 52.6 38.2 25 101.1 73.5 85 149.7 108.7 45 198.2 144.0 6 4.9 3.5 66 53.4 38.8 26 101.9 74.1 86 150.5 109.3 46 199.0 144.6 7 5.7 4.1 67 54.2 39.4 27 102.7 74.6 87 151.3 109.9 47 199.8 145.2 8 6.5 4.7 68 55.0 40.0 28 103.6 75.2 88 152.1 110.5 48 200.6 145.8 9 7.3 5.3 69 55.8 40.6 29 104.4 75.8 89 152.9 111.1 49 201.4 146.4 10 8.1 5.9 70 56.6 41.1 30 105.2 106.0 76.4 90 153.7 154.5 111.7 50 202.3 146.9 11 8.9 6.5 71 57.4 41.7 131 77.0 191 112.3 251 203.1 147.5 12 9.7 7.1 72 58.2 42.3 32 106.8 77.6 92 155.3 112.9 52 203.9 148.1 13 10.5 7.6 73 59.1 42.9 33 107.6 78.2 93 156. 1 113.4 53 204.7 148.7 14 11.3 8.2 74 59.9 43.5 34 108.4 78.8 94 156.9 114. 54 205.5 149.3 15 12.1 8.8 75 60.7 44.1 35 109.2 79.4 95 157. 8 114.6 55 206.3 149.9 16 12.9 9.4 76 61.5 44.7 36 110.0 79.9 96 158.6 115.2 56 207.1 150.5 17 13.8 10.0 77 62.3 45.3 37 110.8 80.5 97 159.4 115.8 57 207.9 151.1 18 14.6 10.6 78 63.1 45.8 38 111.6 81.1 98 160.2 116.4 58 208.7 151.6 19 15.4 n.2 79 63.9 46.4 39 112.5 81.7 99 161.0 117.0 59 209.5 152.2 20 16.2 11.8 80 64.7 47.0 40 113.3 82.3 200 161.8 162.6 117.6 60 210. 3 152.8 21 17.0 12.3 81 65.5 47.6 141 114.1 82.9 201 118.1 261 211.2 153.4 22 17.8 12.9 82 66.3 48.2 42 114.9 83.5 02 163.4 118.7 62 212.0 154.0 23 18.6 13.5 83 67.1 48.8 43 115.7 84.1 03 164.2 119.3 63 212.8 154.6 24 19.4 14.1 84 68.0 49.4 44 116.5 84.6 04 165.0 119.9 64 213.6 155.2 25 20.2 14.7 85 68.8 50.0 45 117.3 85.2 05 165.8 120.5 05 214.4 155.8 26 21.0 15.3 86 69.6 50.5 46 118.1 85.8 06 166.7 121.1 66 215.2 156. 4 27 21.8 15.9 87 70.4 51.1 47 118. 9 86.4 07 167.5 121.7 67 216.0 156.9 28 22.7 16.5 88 71.2 51.7 48 119. 7 87.0 08 168.3 122.3 68 216.8 157.5 29 23.5 17.0 89 72.0 52.3 49 120.5 87.6 09 169.1 122.8 69 217.6 158.1 30 24.3 17.6 90 72.8 52.9 50 121.4 88.2 10 169.9 123.4 70 271 218.4 158.7 159.3 31 25.1 18.2 91 7S.6 53.5 151 122.2 88.8 211 170.7 124.0 219.2 32 25.9 18.8 92 74.4 54.1 52 123.0 89.3 12 171.5 124.6 72 220.1 159.9 33 26.7 19.4 93 75.2 54.7 53 123.8 89.9 13 172.3 125.2 73 220.9 160.5 34 27.5 20.0 94 76.0 55.3 54 124.6 90.5 14 173.1 125.8 74 221.7 161.1 35 28.3 20.6 95 76.9 55.8 55 125. 4 91.1 15 173.9 126.4 75 222.5 161.6 36 29.1 21.2 96 77.7 56.4 56 126.2 91.7 16 174.7 127.0 76 223.3 162.2 37 29.9 21.7 97 78.5 57.0 57 127.0 92.3 17 175. 6 127. 5 77 224.1 162.8 38 30.7 22.3 98 79.3 57.6 58 127.8 92.9 18 176.4 128.1 78 224.9 163.4 39 31.6 22.9 99 80.1 58.2 59 128.6 93.5 19 177.2 128.7 79 225.7 164.0 40 32.4 23.5 100 80.9 58.8 60 161 129.4 130.3 94.0 20 178.0 129.3 80 226.5 164.6 41 33.2 24.1 101 81.7 59.4 94.6 221 178.8 129.9 281 227.3 165.2 42 34.0 24.7 02 82.5 60.0 62 131.1 95.2 22 179.6 130.5 82 228.1 165. 8 43 34.8 25.3 03 83.3 60.5 63 131.9 95.8 23 180,4 131.1 83 229.0 166.3 44 35.6 25.9 04 84.1 61.1 64 132.7 96.4 24 181 2 131.7 84 229.8 166.9 45 36.4 26.5 05 84.9 61.7 65 133.5 97.0 25 182.0 132.3 85 230.6 167.5 46 37.2 27.0 06 85.8 62.3 66 134.3 97.6 26 182.8 132.8 86 231.4 168.1 47 38.0 27.6 07 86.6 62.9 67 135.1 98.2 27 183.6 133.4 87 232.2 168.7 48 38.8 28.2 08 87.4 63.5 68 135.9 98.7 28 184.5 134.0 88 233.0 169.3 49 39.6 28.8 09 88.2 64.1 69 136.7 99.3 29 185.3 134.6 89 233.8 169.9 50 40.5 29.4 10 89.0 64.7 70 137.5 138.3 99.9 30 186.1 135.2 90 234.6 170.5 51 41.3 30.0 111 89.8 65.2 171 100.5 231 186.9 135.8 291 235.4 171.0 52 42.1 30.6 12 90.6 65.8 72 139.2 101.1 32 187.7 136.4 92 236.2 171.6 53 42.9 31.2 13 91.4 66.4 73 140.0 101.7 33 188.5 137.0 93 237. 172.2 54 43.7 31.7 14 92.2 67.0 74 140.8 102.3 34 189.3 137.5 94 237.9 172.8 55 44.5 32.3 15 93.0 67.6 75 141.6 102.9 35 190.1 138.1 95 238.7 173.4 56 45.3 32.9 16 93.8 68.2 76 142.4 103.5 36 190.9 138.7 96 239.5 174.0 57 46.1 33.5 17 94.7 68.8 77 143.2 104.0 37 191.7 139. 3 97 240. 3 174.6 58 46.9 34.1 18 95.5 69.4 78 144.0 104.6 38 192.5 139.9 98 241.1 175.2 59 47.7 34.7 19 96.3 69.9 79 144.8 105.2 39 193.4 140.5 99 241.9 175.7 60 48.5 35.3 20 97.1 70.5 80 145.6 105.8 40 194.2 141.1 300 242.7 176.3 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 54° (126°, 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 0-t 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 89 395.6 287.4 49 444.2 322.7 10 311 250.8 182.2 70 299.3 217.5 30 347.9 252.8 90 396.4 288.0 50 445.0 323.3 251.6 182.8 371 300.2 218.1 431 348.7 253.3 491 397.3 288.6 551 445.8 323.8 12 252.4 183.4 72 301.0 218.7 32 349.5 253.9 92 398.1 289.2 52 446.6 324.4 13 253.2 184.0 73 301. 8 219.3 33 350.3 254.5 93 398.9 289.8 53 447.4 325.0 14 254.0 184.6 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. 221.6 37 353.6 256.9 97 402.1 292.1 57 450.7 327.4 18 257.3 186.9 78 305.8 222.2 38 354.4 257.5 98 402.9 292.7 58 451.5 328.0 19 258. 1 - 187.5 79 306.6 222.8 39 355.2 258.0 99 403.7 293.3 59 452.3 328.5 20 258.9 188.1 80 307.4 223.4 40 356.0 258.6 500 404.5 293.9 60 453.1 329.1 321 259.7 188.7 381 308.2 224.0 441 356.8 259.2 601 405.3 294.5 561 453.9 329.7 22 260.5 189.3 82 309.1 224.5 42 357.6 259.8 02 406.1 295.0 62 454.7 330.3 23 261. 3 189.9 83 309.9 225.1 43 358.4 260.4 03 407.0 295.6 63 455.5 330.9 24 262.1 190.5 84 310.7 225.7 44 359.2 261.0 04 407.8 296.2 64 456.3 331.5 25 262.9 191.0 85 311.5 226.3 45 360.0 261.6 05 408.6 296.8 65 457.1 332.1 26 263.7 191.6 86 312.3 226.9 46 360.8 262.2 06 409.4 297.4 66 457.9 332.7 27 264.6 192.2 87 313.1 227.5 47 361.6 262.8 07 410.2 298.0 67 458.7 333.3 28 265.4 192.8 88 313.9 228.1 48 362.4 263.3 08 411.0 298.6 68 459.5 333.8 29 266.2 193.4 89 314.7 228.7 49 363.3 263.9 09 411.8 299.2 69 460.3 334. 4 30 267.0 194.0 90 315.5 229.2 50 364.1 264.5 10 511 412.6 299.8 70 461.1 335.0 331 267.8 194.6 391 316.3 229.8 451 364.9 265.1 413.4 300.3 571 462.0 335.6 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 75 465.2 338.0 36 271.8 197.5 96 320.4 232.8 56 368.9 268.0 16 417.5 303.3 76 466.0 338. 5 37 272.6 198.1 97 321.2 233.4 57 369.7 268.6 17 418.3 303.9 77 466.8 339.1 38 273.5 198.7 98 322.0 233.9 58 370.5 269.2 18 419.1 304.4 78 467.6 339.7 39 274.3 199. 3 99 322.8 234.5 59 371.3 269.8 19 419.9 305.0 79 468.4 340.3 40 275.1 199.9 400 323.6 235.1 60 372. 2 270.4 20 420.7 305.6 80 469.3 340.9 341 275. 9 200.4 401 324.4 235.7 461 373.0 271. 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 ao8.6 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 50 283. 2. 205.7 10 331.7 241.0 70 380.2 276.3 30 428.8 311.5 90 477.3 346.8 351 284.0 206.3 411 332.5 241.6 471 381.1 276.9 531 429.6 312.1 591 478.2 347.4 52 284.8 206.9 12 333. 3 242.2 72 381.9 277.4 32 430.4 312.7 92 479.0 347.9 53 285. 6 207.5 13 334.1 242.8 73 382.7 278.0 33 431.2 313.3 93 479.8 348.5 54 286.4 208.1 14 334.9 243.4 74 383.5 278.6 34 432.0 313.9 94 480.6 349.1 55 287.2 208.7 15 335.8 243.9 75 384.3 279.2 35 432.9 314.4 95 481.4 349.7 56 288.0 209.3 16 336.6 244.5 76 385.1 279.8 36 433.7 315.0 96 482.2 350.3 57 288.8 209.8 17 337.4 245.1 77 385.9 280.4 37 434.5 315. 6 97 483.0 350.9 58 289.6 210.4 18 338.2 245.7 78 386.7 281.0 38 435.3 316.2 98 483.8 351.5 59 290.4 211.0 19 339.0 246.3 79 387.5 281.6 39 436.1 316.8 99 484.6 352.1 60 291.3 211.6 20 339.8 246.9 80 388.3 282.1 40 436.9 317.4 600 485.4 352.7 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 54° (1 26°, 234°, 306° )• Page 440] TABLE 2. Difference of Latitude and Departure for 37° (143°, 217 % 323° ). Dist. Lilt. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 0,8 0.6 61 48,7 36.7 121 96.6 72.8 181 144.6 108.9 241 192.5 145.0 2 1.6 1.2 62 49.5 37.3 22 97.4 73.4 82 145. 4 109.5 42 193.3 145. 6 3 2.4 1.8 63 50.3 37.9 23 98.2 74.0 83 146.2 110.1 43 194.1 146.2 4 3.2 2.4 64 51.1 38.5 24 99.0 74.6 84 146.9 110.7 44 194.9 146.8 5 4.0 3.0 65 51.9 39.1 25 99.8 75.2 85 147.7 111.3 45 195.7 147.4 6 4.8 3.6 66 52.7 39.7 26 100.6 75.8 86 148.5 111.9 46 196.5 148.0 7 5.6 4.2 67 53.5 40.3 27 101.4 76.4 87 149.3 112.5 47 197.3 148.6 8 6.4 4.8 68 54.3 40.9 28 102.2 77.0 88 150.1 113.1 48 198.1 149.3 9 7.2 5.4 69 55.1 41.5 29 103.0 77.6 89 150.9 113. 7 49 198.9 149.9 10 8.0 6.0 70 55.9 42.1 30 103.8 78.2 90 151.7 114.3 50 199.7 150.5 151.1 11 8.8 6.6 71 56.7 42,7 131 104.6 78.8 191 152.5 114.9 251 200.5 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. 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 39 111.0 8.3.7 99 158.9 119.8 59 f06.8 155.9 20 21 16.0 16.8 12.0 12.6 80 81 63.9 48.1 40 111.8 "112.6 84.3 200 159.7 120.4 60 207.6 156.5 64.7 48.7 141 84.9 201 160.5 121.0 261 208.4 157.1 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 09 166.9 125.8 69 214.8 161.9 30 24.0 18.1 90 71.9 54.2 54.8 50 151 119.8 90.3 10 167.7 126.4 70 215. 6 162.5 163.1 31 24.8 18.7 91 72.7 120.6 90.9 211 168.5 127.0 271 216.4 32 25.6 19.3 92 73.5 55.4 52 121.4 91.5 12 169.3 127.6 72 217.2 163.7 33 26.4 19.9 93 74.3 56.0 53 122.2 92.1 13 170.1 128.2 73 218.0 164.3 34 27.2 20.5 94 75.1 56.6 54 123.0 92.7 14 170.9 128.8 74 218.8 164.9 35 28.0 21.1 95 75.9 57.2 55 123.8 93.3 15 171.7 129.4 75 219.6 165.5 36 28.8 21.7 96 76.7 57.8 56 124.6 93.9 16 172.5 130.0 76 220.4 166.1 37 29.5 22.3 97 77.5 58.4 57 125.4 94.5 17 173.3 130.6 * 77 221.2 166.7 38 30.3 22.9 98 78.3 59.0 58 126.2 95.1 18 174.1 131.2 78 222.0 167.3 39 31.1 23.5 99 79.1 59.6 59 127.0 95.7 19 174.9 131.8 79 222.8 167.9 40 31.9 24.1 100 79.9 60.2 60 127.8 96.3 20 175.7 132.4 133. 80 223.6 168,5 169.1 41 32.7 24.7 101 80.7 60.8 161 128.6 96.9 221 176.5 281 224.4 42 33.5 25.3 02 81.5 61.4 62 129.4 97.5 22 177,3 133. 6 82 225.2 169.7 43 34.3 25.9 03 82.3 62.0 63 130.2 98.1 23 178.1 134. 2 83 226.0 170.3 44 35.1 26.5 04 83.1 62.6 64 131.0 98.7 24 178.9 134.8 84 226.8 170.9 45 35.9 27.1 05 83.9 63.2 65 131.8 99.3 25 179.7 135.4 85 227.6 171.5 46 36.7 27.7 06 84.7 63.8 66 132.6 99.9 26 180.5 136.0 86 228.4 172,1 47 37.5 28.3 07 85.5 64.4 67 133. 4 100.5 27 181.3 136.6 87 229.2 172.7 48 38.3 28.9 08 86.3 65,0 68 134. 2 101.1 28 182.1 137.2 88 230.0 173,3 49 39.1 29.5 09 87.1 65.6 69 135. 101.7 29 182.9 137.8 89 230.8 173.9 50 39.9 30.1 10 87.8 66.2 70 135.8 102.3 30 183.7 138.4 90 231.6 174.5 175. 1 51 40.7 30.7 111 88.6 66.8 171 136.6 102.9 231 184.5 139.0 291 232.4 52 41.5 31.3 12 89.4 67.4 72 137.4 103.5 32 185.3 139.6 92 233.2 175.7 53 42.3 31.9 13 90.2 68.0 73 138.2 104.1 33 186.1 140.2 93 234.0 176.3 54 43.1 32.5 14 91.0 68.6 74 139. 104.7 34 186.9 140.8 94 234.8 176.9 55 43.9 33.1 15 91.8 69.2 75 139.8 105.3 35 187.7 141.4 95 235.6 177.5 56 44.7 33.7 16 92.6 69.8 76 140.6 105.9 36 188.5 142.0 96 236.4 178.1 57 45.5 34.3 17 93.4 70.4 77 141.4 106.5 37 189.3 142.6 97 237.2 178.7 58 46.3 34.9 18 94.2 71.0 78 142.2 107.1 38 190.1 143.2 98 238.0 179.3 59 47.1 35.5 19 95.0 71.6 79 143.0 107.7 39 190.9 143. 8 99 238.8 179.9 60 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°, 23c ;°, 307= )• L»» TABLE 2. [Page 441 Difference of Latitude and Departure for 37° (143°, 21/ '°, 323' )• Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. : Dep. 301 240.4 181.1 361 288.3 217.3 421 336.2 253.4 481 384.1 289.5 541 432.0 325.6 02 241.2 181.7 62 289.1 217.9 22 337. 254.0 82^ 384.9 290.0 42 432.8 326.2 03 242.0 182.4 63 289.9 218.5 23 337.8 254.6 83 385.7 290.6 43 433.6 326.8 04 242.7 183.0 64 290.7 219.1 24 338.6 255.2 84 386.5 291.2 44 434.4 327. 3 05 243.5 183.6 65 291.5 219.7 25 339.4 255.8 85 387.3 291.8 45 435.2 327.9 06 244.3 184.2 66 292.3 220.3 26 340.2 256.4 86 388.1 292.4 46 436.0 328.5 07 245.1 184.8 67 293.1 220.9 27 341.0 257.0 87 388.9 293.0 47 436.8 329. 1 08 245.9 185.4 68 293.9 221.5 28 341.8 257.6 88 389.7 293.6 48 437.6 329.7 09 246.7 186.0 69 294.7 222.1 29 342.6 258.2 89 390.5 294.2 49 438.4 330.3 10 311 247.5 248.3 186.6 187.2 70 295.5 222.7 223.3 30 431 343.4 344.2 258.8 259. 4 90 491 391.3 294.8 50 439.2 330.9 331.5 371 296.3 392.1 295.4 551 440.0 12 249.1 187.8 72 297.1 223.9 32 345. 260.0 92 392.9 296.0 52 440.8 332.1 13 249.9 188.4 73 297.9 224.5 33 345.8 260.6 93 393.7 296.6 53 441.6 332.7 14 250.7 189.0 74 298.7 225.1 34 346.6 261. 2 94 394.5 297.2 54 442. 4 333. 3 1 15 251.5 189.6 75 299.5 225.7 35 347.4 261.8 95 395.3 297.8 55 443.2 333.9 16 252.3 190.2 76 300.3 226.3 36 348.2 262.4 96 396.1 298.5 56 444.0 334.6 17 253.1 190.8 77 301.1 226.9 37 349.0 263.0 97 396.9 299.1 57 444.8 235.2 18 253.9 191.4 78 301.8 227.5 38 349.8 263.6 98 397.7 399.7 58 445.6 335.8 19 254.7 192.0 79 302.6 228.1 39 350. 6 264.2 99 398.5 300.3 59 446.4 336. 4 20 321 255.5 256. 3 192.6 80 381 303.4 228.7 40 351.4 352.2 264.8 500 399.3 300.9 60 447.2 448.0 337.0 337.6 193.2 304.2 229.3 441 265.4 501 400.1 301.5 561 22 257.1 193.8 82 305.0 229.9 42 353.0 266.0 02 400.9 302.1 62 448.8 338.2 23 257.9 194.4 83 305.8 230.5 43 353.8 266.6 03 401.7 302.7 63 449.6 338.8 24 258.7 195.0 84 306.6 231.1 44 354.6 267.2 04 402.5 303.3 64 450.4 339.4 25 259.5 195.6 85 307.4 231.7 45 355.4 267.8 05 403.3 303.9 65 451.2 340.0 26 260.3 196.2 86 308.2 232.3 46 356.2 268.4 06 404.1 304.5 66 452.0 340.6 27 261.1 196.8 87 309. 232.9 47 357.0 269.0 07 404.9 305. 1 67 452.8 341.2 28 261.9 197.4 88 309.8 233.5 48 357.8 269.6 08 405.7 305.7 68 453.6 341.8 29 262.7 198.0 89 310.6 234.1 49 358.6 270.2 09 406.5 306.3 69 454.4 1 342.4 30 331 263.5 264.3 198.6 90 311.4 234.7 50 359.4 270.8 10 407.3 306.9 70 455.2 j 343.0 199.2 391 312.2 235. 3 451 360.1 271.4 511 408.1 307.5 571 456.0 343.6 32 265.1 199.8 92 313. 235.9 52 360.9 272.0 12 408.9 308.2 72 456. 8 i 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 1 345.5 35 267.5 201.6 95 315.4 237.7 55 363.3 273.8 15 411.3 310.0 75 459.2 346. 1 36 268.3 202.2 96 316.2 238.3 56 364.1 274.4 16 412.1 310.6 76 460.0 346.7 37 269.1 202.8 97 317.0 238.9 57 364.9 275.0 17 412.9 311.2 77 460.8 347.3 38 269. 9 203.4 98 317.8 239. 5 58 365.7 275.6 18 413.7 311.8 78 461.6 347.9 39 270.7 204.0 99 318.6 240.1 59 366.5 276.2 19 414.5 312.4 79 462.4 348.5 40 271. 5 204.6 400 319.4 240.7 60 367.3 276.8 20 415.3 416.1 313.0 313.6 80 581 463.2 464.0 349.1 341 272.3 205.2 401 320.2 241.3 461 368.1 277.4 521 349.7 42 273.1 205.8 02 321.0 241.9 62 368.9 278.0 22 416.9 314.2 82 464.8 350.3 43 273.9 206.4 03 321.8 242.5 63 369.7 278.6 23 417.7 314.8 83 465.6 350.9 44 274.7 207.0 (4 322.6 243.1 64 370.5 279.2 24 418.5 315.4 84 466.4 351.5 45 275.5 207. 6 05 323.4 243.7 65 371.3 279.8 25 419.3 316.0 85 467.2 352.1 46 276.3 208.2 06 324.2 244.3 66 372.1 280.4 26 420.1 316.6 86 468.0 352.7 47 277.1 208.8 07 325.0 244.9 67 372.9 281.0 27 420.9 317.2 87 468.8 353.3 48 277.9 209.4 08 325.8 245.5 68 373.7 281.6 28 421.7 317.8 88 469.6 353.9 49 278.7 210.0 09 326.6 246.1 69 374.5 282.3 29 422.5 318.4 89 470.4 354.5 50 279.5 210.6 10 327.4 246.7 70 375.3 282.9 30 423.3 319.0 90 471.2 355.1 351 280.3 211.2 411 328.2 247.3 471 376.1 283.5 531 424.1 319.6 591 472.0 355.7 52 281.1 211.8 12 329.0 247.9 72 376. 9 284.1 32 424.9 320.2 92 472.8 356.3 53 281.9 212.4 13 329.8 248.5 73 377.7 284.7 33 425.7 320.8 93 473.6 356. 9 54 282.7 213. 14 330.6 249.2 74 378.5 285.3 34 426.5 321.4 94 474.4 357. 5 55 283.5 213.6 15 331.4 249.8 75 379.3 285.9 35 427.3 322.0 95 475.2 358.1 56 284.3 214.2 16 332.2 250.4 76 380.1 286.5 36 428.1 322.6 96 476.0 358.7 57 285.1 214.8 17 333.0 251.0 77 380.9 287.1 37 428.9 323.2 97 476.8 359.3 58 285.9 215.4 18 333.8 251.6 78 381.7 287.7 38 429.7 323.8 98 477.6 359. 9 59 286.7 216.1 19 334.6 252.2 79 382.5 288.3 39 430.5 324.4 99 478.4 360.5 60 287.5 216.7 20 335.4 252.8 80 383.3 288.9 40 431.3 325.0 600 479.2 361.1 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. r )3° (1 27°, 233°, .307° )• 1 Page 442] TABLE 2. Difference of Latitude and Departure for 38° (142°, 218 °, 322° )• Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 0,8 0.6 61 48.1 37.6 121 95.3 74.5 181 142.6 111.4 241 189.9 148.4 2 1.6 1.2 62 48.9 38.2 22 96.1 75.1 82 143.4 112.1 42 190.7 149.0 8 2.4 1.8 63 49.6 38.8 23 96.9 75.7 83 144.2 112.7 43 191.5 149.6 4 3.2 2.5 64 50.4 39.4 24 97.7 76.3 84 145.0 113.3 44 192.3 150.2 5 3.9 3.1 65 51.2 40.0 25 98.5 77.0 85 145.8 113.9 45 193.1 150.8 6 4.7 3.7 66 52.0 40.6 26 99.3 77.6 86 146.6 114.5 46 193.9 151.5 7 5.5 4.3 67 52.8 41.2 27 100.1 78.2 87 147.4 115.1 47 194.6 152.1 8 6.3 4.9 68 53.6 41.9 28 100.9 78.8 88 148.1 115.7 48 195.4 152.7 9 7.1 5.5 69 54.4 42.5 29 101.7 79.4 89 148.9 116.4 49 196.2 153.3 10 7.9 6.2 70 55.2 43.1 30 102.4 80.0 90 149.7 117.0 50 197.0 153.9 11 8.7 6.8 71 55.9 43.7 131 103.2 80.7 191 150.5 117.6 251 197.8 154.5 12 9.5 7.4 72 56.7 44.3 32 104.0 81.3 92 151.3 118.2 52 198. 6 155.1 13 10.2 8.0 73 57.5 44.9 33 104.8 81.9 93 152.1 118.8 53 199.4 155.8 14 11.0 8.6 74 58.3 45.6 34 105.6 82.5 94 152.9 119.4 54 200.2 156.4 15 11.8 9.2 75 59.1 46.2 35 106.4 83.1 95 153.7 120.1 55 200.9 157.0 16 12.6 9.9 76 59.9 46.8 36 107.2 83.7 96 154.5 120.7 56 201.7 157.6 17 13.4 10.5 77 60.7 47.4 37 108.0 84.3 97 155.2 121. 3 57 202.5 158.2 18 14.2 11.1 78 61.5 48.0 38 108.7 85.0 98 156.0 121.9 58 203.3 158.8 19 15.0 11.7 79 62.3 48.6 39 109.5 85.6 99 156.8 122.5 59 204.1 159.5 20 15.8 ]2.3 12.9 80 63.0 49.3 40 110.3 86.2 200 201 157.6 123.1 60 204.9 205.7 160.1 21 16.5 81 63.8 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 68 211.2 165.0 29 22.9 17.9 89 70.1 54.8 49 117.4 91.7 09 164.7 128.7 69 212.0 165.6 30 23.6 18.5 90 70.9 55.4 50 118.2 92.3 10 165.5 129.3 70 212.8 166.2 31 24.4 19.1 91 71.7 56.0 151 119.0 93.0 211 166.3 129.9 271 213. 6 166.8 32 25.2 19.7 92 72.5 56.6 52 119.8 93.6 12 167.1 130.5 72 214.3 167.5 33 26.0 20.3 93 73.3 57.3 53 120.6 94.2 13 167.8 131.1 73 215.1 168.1 34 26.8 20.9 94 74.1 57.9 54 121.4 94.8 14 168.6 131.8 74 215.9 168.7 35 27.6 21.5 95 74.9 58.5 55 122.1 95.4 15 169.4 132.4 75 216.7 169.3 36 28.4 22.2 96 75.6 59.1 56 122.9 96.0 16 170.2 133.0 76 217.5 169.9 37 29.2 22.8 97 76.4 59.7 57 123.7 96.7 17 171.0 133.6 77 218.3 170.5 38 29.9 23.4 98 77.2 60.3 58 124.5 97.3 18 171.8 134.2 78 219.1 171.2 39 30.7 24.0 99 78.0 61.0 59 125.3 97.9 19 172.6 134.8 79 219.9 171.8 40 31.5 24.6 100 78.8 61.6 60 126.1 98.5 20 173.4 135.4 80 220. 6 172.4 41 32.3 25.2 101 79.6 62.2 161 126.9 99.1 221 174.2 136.1 281 221.4 173.0 42 33.1 25.9 02 80.4 62.8 62 127.7 99.7 22 174.9 136.7 82 222.2 173.6 43 33.9 26.5 03 81.2 63.4 63 128.4 100.4 23 175.7 137.3 83 223.0 174.2 44 34.7 27.1 04 82.0 64.0 64 129.2 101.0 24 176.5 137.9 84 223.8 174.8 45 35.5 27.7 05 82.7 64.6 65 130.0 101.6 25 177.3 138.5 85 224.6 175.5 46 36.2 28.3 06 83.5 65.3 66 130.8 102.2 26 178.1 139.1 86 225.4 176.1 47 37.0 28.9 07 • 84.3 65.9 67 131.6 102.8 27 178.9 139.8 87 226.2 176.7 48 37.8 29.6 08 85.1 66.5 68 132.4 103.4 28 179.7 140.4 88 226.9 177.3 49 38.6 30.2 09 85.9 67.1 69 133.2 104.0 29 180.5 141.0 89 227.7 177.9 50 39.4 30.8 10 86.7 67.7 70 134.0 104.7 30 181.2 182.0 141.6 90 291 228.5 178.5 51 40.2 31.4 111 87.5 68.3 171 134.7 105.3 231 142.2 229.3 179.2 52 41.0 32.0 12 88.3 69.0 72 135.5 105.9 32 182.8 142.8 92 230.1 179.8 53 41.8 32.6 13 89.0 69.6 73 136.3 106.5 33 183.6 143.4 93 230.9 180.4 54 42.6 33.2 14 89.8 70.2 74 137.1 107.1 34 184.4 144.1 94 231.7 181.0 55 43.3 33.9 15 90.6 70.8 75 137.9 107.7 35 185.2 144.7 95 232. 5 181.6 56 44.1 34.5 16 91.4 71.4 76 138.7 108.4 36 186.0 145.3 96 233.3 182.2 57 44.9 35.1 17 92.2 72.0 77 139.5 109.0 37 186.8 145.9 97 234.0 182.9 58 45.7 35.7 18 93.0 72.6 78 140.3 109.6 38 187.5 146.5 98 234. 8 183.5 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. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 52 ' (128°, 232°, 308°). TABLE 2. [Page 443 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. 301 237.2 185.3 361 284.5 222.3 421 331. 8 259.2 481 379.0 296.2 541 426.3 333.1 02 238.0 185.9 62 285.3 222.9 22 332.5 259.8 82 379.8 296.8 42 427.1 333. 7 03 238.8 186.6 63 286.0 223.5 23 333.3 260.4 83 380.6 297.4 43 427.9 334. 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 85 382.2 298.6 45 429.5 335.6 06 241.1 188.4 66 288.4 225.3 26 335.7 262.3 86 383.0 299.2 46 430.3 336.2 07 241.9 189.0 67 289.2 226.0 27 336. 5 262.9 87 383.8 299.8 47 431.0 336. 8 08 242.7 189.6 68 290.0 226.6 28 337.3 263.5 88 384.5 300.4 48 431.8 337.4 09 243.5 190.2 69 290.8 227.2 29 338.1 264.1 89 385.3 301.1 49 432.6 338.0 10 244.3 190.9 70 291.6 227.8 30 431 338.8 264.7 90 386.1 386.9 301.7 50 433.4 338.6 311 245.1 191.5 371 292.4 228.4 339.6 265.4 491 302.3 551 434.2 339.3 12 245.9 192.1 72 293.1 229.0 32 340.4 266.0 92 387.7 302.9 52 435.0 339. 9 13 246.6 192.7 73 293.9 229.6 33 341.2 266.6 93 388. 5 303.5 53 435. 8 340.5 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 37 344.4 269.1 97 391.6 306.0 57 438.9 343.0 18 250.6 195.8 78 297.9 232.7 38 345.2 269.7 98 392.4 306.6 58 439.7 343.6 19 251.4 196.4 79 298.7 233.3 39 345.9 270.3 99 393.2 307.2 59 440.5 344.2 20 252.2 197.0 80 299.4 234.0 40 346.7 270.9 500 501 394.0 307.8 60 441.3 344. 8 321 253.0 197.6 381 300.2 234.6 441 347. 5 271.5 394.8 308.4 561 442.1 345. 4 22 253.7 198.2 82 301.0 235.2 42 348.3 272.1 02 395.6 309.1 62 442.9 346.0 23 254.5 198.9 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 85 303.4 237.0 45 350.7 274.0 05 397.9 310.9 65 445.2 347.8 26 256.9 200.7 86 304.2 237.7 46 351.5 274.6 06 398.7 311.6 66 446.0 348.5 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 69 448.4 350. 3 30 331 260.0 260.8 203.2 90 307.3 240.1 50 354.6 277.1 10 401.9 314.0 70 449.2 450.0 350.9 203.8 391 308.1 240.7 451 355.4 277.7 511 402.7 314.6 571 351.6 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 33 262.4 205.0 93 309.7 242.0 53 357.0 278.9 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 14 405.0 316.4 74 452.3 353. 4 35 264.0 206.3 95 311.3 243.2 55 358. 5 280.1 15 405.8 317.1 75 453.1 354.0 36 264.8 206.9 96 312.1 243.8 56 359.3 280.7 16 406.6 317.7 76 453.9 354.6 37 265.6 207.5 97 312.8 244.4 57 360.1 281.4 17 407.4 318. 3 77 454.7 355.2 38 266.3 208.1 98 313.6 245.0 58 360.9 282.0 18 408.2 318.9 78 455.5 355. 8 39 267.1 208.7 99 314.4 245.7 59 361.7 282.6 19 409.0 319.5 79 456.3 356.4 40 267.9 209.3 400 315. 2 316.0 246.3 60 362.5 363.3 283.2 283.8 20 409.8 320.2 80 457.1 357.1 341 268.7 209.9 401 246.9 461 521 410.6 320.8 581 457.8 357.7 42 269.5 210.6 02 316.8 247.5 62 364.1 284.4 22 411.3 321.4 82 458.6 358.3 43 270.3 211.2 03 317.6 248.1 63 364.9 285. 1 23 412.1 322.0 83 459.4 358.9 44 271.1 211.8 04 318.4 248.7 64 365.6 285.7 24 412.9 322.6 84 460.2 359.5 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 46 272.7 213.0 06 319.9 250.0 66 367.2 286.9 26 414.5 323.8 86 461.8 360.8 47 273.4 213.6 07 320.7 250.6 67 368.0 287.5 27 415.3 324.5 87 462.6 361.4 48 274.2 214.3 08 321.5 251.2 68 368.8 288.1 28 416.1 325.1 88 463.3 362.0 49 275.0 214.9 09 322. 3 251.8 69 369.6 288.7 29 416.9 325.7 89 464.1 362.6 50 351 275.8 276.6 215.5 10 323.1 252.4 70 370.4 289.3 30 417.6 326.3 90 464.9 465.7 363.2 216.1 411 323.9 253.0 471 371.2 290.0 531 418.4 326.9 591 363.8 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. 255. 5 75 374.3 292.4 35 421.6 329.4 95 468.9 366. 3 56 280.5 219.2 16 327.8 256.1 76 375.1 293.1 36 422.4 330.0 96 469.7 366.9 57 281.3 219.8 17 328.6 256.7 77 375.9 293. 7 37 423.2 330.6 97 470.5 367.5 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 60 283.7 221.6 20 331.0 258.6 80 378.2 295.5 40 425.5 332.5 600 472.8 369.4 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 52° (128°, 232°, 308°). . ^ OF THE UNIVERSITY OF Page 444] TABLE 2. Difference of Latitrd^ and Departure for 39° (141°, 219°, 321° )• Dist. Lat. Dep. 0.6 Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 0.8 61 47.4 38.4 121 94.0 76.1 181 140.7 113.9 241 187.3 151.7 2 1.6 1.3 62 48.2 39.0 22 94.8 76.8 82 141.4 114.5 42 188.1 152.3 3 2.3 1.9 63 49.0 39.6 23 95.6 77.4 83 142.2 115. 2 43 188.8 152.9 4 3.1 2.5 64 49.7 40.3 24 96.4 78.0 84 143.0 115.8 44 189.6 153.6 5 3.9 3.1 65 50.5 40.9 25 97.1 78.7 85 143.8 116.4 45 190.4 154.2 6 4.7 3.8 66 51.3 41.5 26 97.9 79.3 86 144.5 117.1 46 191.2 154.8 7 5.4 4.4 67 52.1 42.2 27 98.7 79.9 87 145.3 117.7 47 192.0 155.4 8 6.2 5.0 68 52.8 42.8 28 99.5 80.6 88 146.1 118.3 48 192.7 156.1 9 7.0 5.7 69 53.6 43.4 29 100.3 81.2 89 146.9 118.9 49 193.5 156.7 10 7.8 6.3 70 54.4 44.1 30 101. 101.8 81.8 90 147.7 119.6 50 194.3 157.3 158.0 11 8.5 6.9 71 55.2 44.7 131 82.4 191 148.4 120.2 251 195.1 12 9.3 7.6 72 56.0 45.3 32 102.6 83.1 92 149.2 120.8 52 195.8 158.6 13 10.1 8.2 73 56.7 45.9 33 103.4 83.7 93 150.0 121.5 53 196.6 159.2 14 10.9 8.8 74 57.5 46.6 34 104.1 84.3 94 150.8 122.1 54 197.4 159.8 15 11.7 9.4 75 58.3 47.2 35 104. 9 85.0 95 151.5 122.7 55 198.2 160.5 16 12.4 10.1 76 59.1 47.8 36 105.7 85.6 96 152.3 123.3 56 198.9 161.1 17 13.2 10.7 77 59.8 48.5 37 106.5 86.2 97 153.1 124.0 57 199.7 161.7 18 14.0 11.3 78 60.6 49.1 38 107.2 86.8 98 153.9 124.6 58 200.5 162.4 19 14.8 12.0 79 61.4 49.7 39 108.0 87.5 99 154.7 125.2 59 201.3 163.0 20 15.5 12.6 80 62.2 50.3 40 108.8 88.1 200 155.4 125.9 60 202.1 163.6 21 16.3 13.2 81 62.9 51.0 141 109.6 88.7 201 156.2 126. 5 261 202.8 164.3 22 17.1 13.8 82 63.7 51.6 42 110.4 89.4 02 157.0 127.1 62 203.6 164.9 23 17.9 14.5 83 64.5 52.2 43 111.1 90.0 03 157.8 127.8 63 204.4 165.5 24 18.7 15.1 84 65.3 52.9 44 111.9 90.6 04 158.5 128.4 64 205.2 160. 1 25 19.4 15.7 85 66.1 53.5 45 112.7 91.3 05 159.3 129.0 65 205.9 166.8 26 20.2 16.4 86 66.8 54.1 46 113.5 91.9 06 160.1 129.6 66 206.7 167.4 27 21.0 17.0 87 67.6 54.8 47 114.2 92.5 07 160.9 130.3 67 207.5 168.0 28 21.8 17.6 88 68.4 55.4 48- 115.0 93.1 08 161.6 130.9 68 208.3 168.7 29 22.5 18.3 89 69.2 56.0 49 115.8 93.8 09 162.4 131.5 69 209.1 169.3 30 23.3 18.9 90 69.9 56.6 50 116.6 94.4 10 163.2 132.2 70 209.8 169.9 31 24.1 19.5 91 70.7 57.3 151 117.3 95.0 211 164.0 132.8 271 210.6 170.5 32 24.9 20.1 92 71.5 57.9 52 118.1 95.7 12 164.8 133.4 72 211.4 171.2 33 25.6 20.8 93 72.3 58.5 53 118.9 96.3 13 165.5 134.0 73 212.2 171.8 34 26.4 21.4 94 73.1 59.2 54 119.7 96.9 14 166.3 134.7 74 212.9 172.4 35 27.2 22.0 95 73.8 59.8 55 120.5 97.5 15 167.1 135.3 75 213.7 173.1 36 28.0 22.7 96 74.6 60.4 56 121.2 98.2 16 167.9 135.9 76 214.5 173.7 37 28.8 23.3 97 75.4 61.0 57 122.0 98.8 17 168.6 136.6 77 215.3 174.3 38 29.5 23.9 98 76.2 61.7 58 122.8 99.4 18 169.4 137.2 78 216.0 175.0 39 30.3 24.5 99 76.9 62.3 59 123.6 100.1 19 170.2 137.8 79 216.8 175. 6 40 31.1 25.2 100 77.7 62.9 60 124.3 125.1 100.7 20 171.0 138. 5 80 217.6 218.4 176.2 41 31.9 25.8 101 78.5 63.6 161 101.3 221 171.7 139.1 281 176.8 42 32.6 26.4 02 79.3 64.2 62 125.9 101.9 22 172.5 139.7 82 219.2 177. 5 43 33.4 27.1 03 80.0 64.8 63 126.7 102.6 23 173.3 140.3 83 219.9 178.1 44 34.2 27.7 04 80.8 65.4 64 127.5 103.2 24 174.1 141.0 84 220.7 178.7 45 35.0 28.3 05 81.6 66.1 65 128.2 103.8 25 174.9 141.6 85 221.5 179.4 46 35.7 28.9 06 82.4 66.7 66 129.0 104.5 26 175.6 142.2 86 222.3 180.0 , 47 36.5 29.6 07 83.2 67.3 67 129.8 105.1 27 176.4 142.9 87 223.0 180.6 48 37.3 30.2 08 83.9 68.0 68 130.6 105.7 28 177.2 143.5 88 223.8 181.2 49 38.1 30.8 09 84.7 68.6 69 131.3 106.4 29 178. 144.1 89 224.6 181.9 50 38.9 31.5 10 85.5 69.2 70 132.1 107.0 30 231 178.7 144.7 90 225.4 182.5 51 39.6 32.1 111 86.3 69.9 171 132.9 107.6 179.5 145.4 291 226.1 183. 1 52 40.4 32.7 12 87.0 70.5 72 133.7 108.2 32 180.3 146.0 92 226. 9 183.8 53 41.2 33.4 13 87.8 71.1 73 134.4 108.9 33 181.1 146.6 93 227.7 184.4 54 42.0 34.0 14 88.6 71.7 74 135.2 109.5 34 181.9 147.3 94 228.5 185.0 55 42.7 34.6 15 89.4 72.4 75 136.0 110.1 35 182.6 147.9 95 229.3 185.6 56 43.5 35.2 16 90.1 73.0 76 136.8 110.8 36 183.4 148.5 96 230.0 186. 3 57 44.3 35.9 17 90.9 73.6 77 137.6 111.4 37 184.2 149.1 97 230.8 186.9 58 45.1 36.5 18 91.7 74.3 78 138.3 112.0 38 185.0 149.8 98 231.6 187. 5 59 45.9 37.1 19 92.5 74.9 79 139.1 112.6 39 185.7 150.4 99 232.4 188.2 60 46.6 37.8 20 93.3 75.5 80 139.9 113.3 40 186.5 151.0 300 233.1 188.8 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 51° (129°, 231°, 309< ')• tablp: 2. [Page 445 Difference of Latitude and Departure for 39° (141°, 219°, 321° )• Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 233.9 189.4 361 280.6 227.1 421 327.2 264.9 481 373.8 302.6 541 420.4 340.4 02 234.7 190.0 62 281.3 227.8 22 328.0 265.5 82 374.6 303.3 42 421.2 341.0 03 235.5 190.6 63 282.1 228.4 23 328.7 266.2 83 375.4 303.9 43 422.0 341.7 04 236.3 191.3 64 282.9 229.0 24 329.5 266.8 84 376.1 304. 5 44 422.7 342.3 05 237.0 191.9 65 283.7 229.7 25 330.3 267.4 85 376.9 305.2 45 423.5 342.9 06 237.8 192.5 66 284.4 230.3 26 331.1 268.0 86 377.7 305.8 46 424.3 343.6 07 238.6 193.2 67 285. 2 230. 9 27 331.9 268.7 87 378.5 306.4 47 425.1 344.2 08 239. 4 193.8 68 286.0 231.5 28 332.6 269.3 88 379. 3 307.1 48 425.9 344.8 09 240.1 194.4 69 286.8 232.2 29 333.4 269.9 89 380.0 307.7 49 426.6 345.5 10 311 240.9 241.7 195.0 70 287.6 288.3 232.8 233.4 30 431 334.2 270.6 271.2 90 491 380.8 381.6 308.3 308. 9 50 551 427.4 346.1 195.7 371 335.0 428.2 346.7 12 242.5 196. 3 72 289.1 1234.1 32 335.7 271.8 92 382.4 309.6 52 429.0 347.4 13 243.3 196.9 73 289.9 1234.7 33 336.5 272.5 93 383.1 310.2 53 429.7 348.0 14 244.0 197.6 74 290.7 235.3 34 337.3 273.1 94 383.9 310. 8 54 430.5 348.6 15 244.8 198.2 75 291.4 236.0 35 338. 1 • 273.7 95 384.7 311.5 55 431.3 349.2 16 245.6 198.8 76 292.2 236.6 36 338. 8 274.3 96 385.5 312.1 56 432.1 349.9 17 246. 4 J 199. 5 77 293.0 237.2 37 339.6 275. 97 386.2 312.7 57 432.8 350.5 18 247.1 200.1 78 293.8 237.8 38 340.4 275.6 98 387.0 313.3 58 433.6 351.1 19 247.9 200.7 79 294.5 238.5 39 341.2 276.2 99 387.8 314.0 59 434.4 351.7 20 321 248.7 201.3 80 295.3 296.1 239.1 239.7 40 441 342.0 342.7 276.9 500 388.6 314.7 60 435.2 352.4 249.5 202.0 381 277.5 501 389.4 315.3 561 435.9 353.0 22 250.3 202.6 82 296.9 240.4 42 343.5 278.1 02 390.1 315.9 62 436.7 353.6 23 251.0 203.2 83 297.7 241.0 43 344.3 278.7 03 390.9 316.5 63 437.5 354.3 24 251.8 203.9 84 298.4 241.6 44 345.1 279.4 04 391. 7 317.1 64 438.3 354.9 25 252.6 204.5 85 299.2 242.2 45 345.8 280.0 05 392.5 317.8 65 439.1 355.5 26 253.4 205. 1 86 300.0 242.9 46 346. 6 280.6 06 393.2 318.4 66 439.8 356.2 27 254.1 205. 7 87 300.8 243.5 47 347.4 281.3 07 394.0 319.0 67 440. 6 356.8 28 254.9 206.4 88 301.5 244.1 48 348.2 281.9 08 394.8 319.6 68 441.4 357.4 29 255.7 207.0 89 302.3 244.8 49 349.0 282.5 09 395.6 320.3 69 442.2 358.1 30 331 256.5 207.6 208.3 90 303.1 245.4 50 349.7 283.2 10 396.3 320.9 70 443.0 "443. 7" 358.7 257.2 391 303.9 246.0 451 350. 5 283.8 511 397.1 321.6 571 359.3 32 258.0 208.9 92 304.7 246.7 52 351.3 284.4 12 397.9 322.2 72 444.5 359.9 33 258.8 209.5 93 305.4 247.3 53 352.1 285.0 13 398.7 322.8 73 445.3 360.6 34 259.6 210.2 94 306.2 247.9 54 352.8 285.7 14 399.4 323.4 74 446.1 361.2 35 260.4 210.8 95 307.0 248.5 55 353.6 286.3 15 400.2 324.1 75 446.9 361.8 36 261.1 211.4 96 307.8 249.2 56 354. 4 286.9 16 401.0 324.7 76 447.6 362.4 37 261.9 212.0 97 308.5 249.8 57 355.2 287.6 17 401.8 325. 3 77 448.4 363.1 38 262.7 212.7 98 309.3 250.4 58 355. 9 288.2 18 402. 5 325.9 78 449.2 363.7 39 263.5 213.3 99 310.1 251.1 59 356.7 288.8 19 403.3 326.6 79 450.0 364.3 40 341 264.2 265.0 213.9 400 310. 9 251.7 60 357.5 289.4 20 404.1 327.2 80 450.7 365.0 214.6 401 311.6 252.3 461 358.3 290.1 521 404.9 327. 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 88 457.0 370.0 49 271.2 219.6 09 317.9 257.3 69 364.5 295.1 29 411.1 332. 9 89 457.8 370.6 50 351 272.0 272.8 to to tol to PIP oo| to 10 411 318.6 258.0 70 365.3 295.7 30 411.9 333.5 90 591 458.5 371.3 319.4 258.6 471 366.0 296.4 531 412.6 334.1 459.3 371.9 52 273.6 221.5 12 320.2 259.2 72 366.8 297.0 32 413.4 334.8 92 460.1 5/2.5 53 274.3 222.1 13 321.0 259.9 7.J 367.6 297.6 33 414.2 335. 4 93 460.9 373. 2 54 275.1 222.7 14 321.8 260.5 74 368.4 298.3 34 415.0 336.1 94 461.6 373.8 55 275.9 223.4 15 322.5 261.1 75 369.2 298.9 35 415.8 336. 7 95 462.4 374.4 56 276.7 224.0 16 323.3 261.8 76 369. 9 299. 5 36 416.5 337.3 96 463.2 375.1 57 277.5 224.6 17 324.1 262.4 77 370.7 300.1 37 417.3 337. 9 97 464.0 375.7 58 278.2 225.3 18 324.9 263.0 78 371.5 300.8 38 418.1 338. 5 98 464.8 376.3 59 279.0 225. 9 19 325.6 263.6 79 372.3 301.4 39 418.9 339.1 99 465.5 376.9 60 279.8 226.5 20 326.4 264.3 80 373.0 302.0 40 419.6 339.8 600 466.3 377.6 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 5 1° (129°, 231°, 309° )• 1 Page 446] 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 1.3 62 47.5 39.9 22 93.5 78.4 82 139.4 117.0 42 185.4 155.6 3 2.3 1.9 63 48.3 40.5 23 94.2 79.1 83 140.2 117.6 43 186.1 156. 2 4 3.1 2.6 64 49.0 41.1 24 95.0 79.7 84 141.0 118.3 44 186.9 156. 8 5 3.8 3.2 65 49.8 41.8 25 95.8 80.3 85 141.7 118.9 45 187.7 157.5 6 4.6 3.9 66 50.6 42.4 26 96.5 81.0 86 142.5 119.6 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 45.0 30 99.6 83.6 90 145.5 122.1 50 191.5 160.7 11 8.4 7.1 71 54.4 45.6 131 100.4 84.2 191 146. 3 122.8 251 192.3 161.3 12 9.2 7.7 72 55.2 46.3 32 101.1 84.8 92 147.1 123.4 52 193.0 162.0 13 10.0 8.4 73 55.9 46.9 33 101.9 85.5 93 147.8 124.1 53 193.8 162.6 14 10.7 9.0 74 56.7 47.6 34 102.6 86.1 94 148.6 124.7 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 21 15.3 12.9 80 61.3 51.4 40 107.2 90.0 90.' 6 200 153.2 128.6 60 199.2 167.1 16.1 13.5 81 62.0 52.1 141 108.0 201 154.0 129.2 261 199.9 167.8 22 16.9 14.1 82 62.8 52.7 42 108.8 91.3 02 154.7 129.8 62 200.7 168.4 23 17.6 14.8 83 63.6 53.4 43 109.5 91.9 03 155.5 130.5 63 201.5 169.1 24 18.4 15.4 84 64.3 54.0 44 110.3 92.6 04 156.3 131.1 64 202.2 169.7 25 19.2 16.1 85 65.1 54.6 45 111.1 93.2 05 157.0 131.8 65 203.0 170.3 26 19.9 16.7 86 65.9 55.3 46 111.8 93.8 06 157.8 132.4 66 203.8 171.0 27 20.7 17.4 87 66.6 55.9 47 112.6 94.5 07 158.6 133.1 67 204.5 171.6 28 21.4 18.0 88 67.4 56.6 48 113.4 95.1 08 159.3 133.7 68 205.3 172.3 29 22.2 18.6 89 68.2 57.2 49 114.1 95.8 09 160.1 134.3 69 206.1 172.9 30 23.0 19.3 90 68.9 57.9 50 114.9 96.4 10 160.9 135.0 70 206.8 173.6 31 23.7 19.9 91 69.7 58.5 151 115.7 97.1 211 161.6 135.6 271 207.6 174.2 32 24.5 20.6 92 70.5 59.1 52 116.4 97.7 12 162.4 136.3 72 208.4 174.8 33 25.3 21.2 93 71.2 59.8 53 117.2 98.3 13 163.2 136.9 73 209.1 175.5 34 26.0 21.9 94 72.0 60.4 54 118.0 99. 14 163.9 137.6 74 209.9 176.1 35 26.8 22.5 95 72.8 61.1 55 118.7 99.6 15 164.7 138.2 75 210.7 176.8 36 27.6 23.1 96 73.5 61.7 56 119.5 100.3 16 165.5 138.8 76 211.4 177.4 37 28.3 23.8 97 74.3 62.4 57 120.3 100.9 17 166.2 139.5 77 212.2 178.1 38 29.1 24.4 98 75.1 63.0 58 121.0 101.6 18 167.0 140.1 78 213.0 178.7 39 29.9 25.1 99 75.8 63.6 59 121.8 102.2 19 167.8 140.8 79 213.7 179.3 40 41 30.6 25.7 100 76.6 64.3 60 122. 6 102.8 20 168.5 141.4 80 214.5 180.0 31.4 26.4 101 77.4 64.9 161 123.3 103.5 221 169. 3 142.1 281 215.3 180.6 '42 32.2 27.0 02 78.1 65.6 62 124.1 104.1 22 170.1 142.7 82 216.0 181.3 43 32.9 27.6 03 78.9 66.2 63 124.9 104.8 23 170.8 143.3 83 216.8 181.9 44 33.7 28.3 04 79.7 66.8 64 125.6 105.4 24 171.6 144.0 84 217.6 182.6 45 34.5 28.9 05 80.4 67.5 65 126.4 106.1 25 172.4 144.6 85 218.3 183.2 46 35.2 29.6 06 81.2 68.1 66 127.2 106.7 26 173.1 145.3 86 219.1 183.8 47 36.0 30.2 07 82.0 68.8 67 127.9 107.3 27 173.9 145.9 87 219.9 184.5 48 36.8 30.9 08 82.7 69.4 68 128.7 108.0 28 174.7 146.6 88 220.6 185.1 49 37.5 31.5 09 83.5 70.1 69 129.5 108.6 29 175.4 147.2 89 221.4 185.8 50 38.3 32.1 10 84.3 70.7 70 130.2 109.3 30 176.2 147.8 90 222.2 186.4 51 39.1 32.8 111 85.0 71.3 171 131.0 109.9 231 177.0 148.5 291 222.9 187.1 52 39.8 33.4 12 85.8 72.0 72 131.8 110.6 32 177.7 149.1 92 223.7 187.7 53 40.6 34.1 13 86.6 72.6 73 132.5 111.2 33 178.5 149.8 93 224. 5 188.3 54 41.4 34.7 14 87.3 73.3 74 133.3 111.8 34 179.3 150.4 94 225.2 189.0 55 42.1 35.4 15 88.1 73.9 75 134. 1 112.5 35 180.0 151.1 95 226.0 189.6 56 42.9 36.0 16 88.9 74.6 76 134. 8 113.1 36 180.8 151.7 96 226.7 190.3 57 43.7 36.6 17 89.6 75.2 77 135.6 113.8 37 181.6 152.3 97 227.5 190.9 58 44.4 37.3 18 90.4 75.8 78 136.4 114.4 38 182.3 153.0 98 228.3 191.6 59 45.2 37.9 19 91.2 76.5 79 137.1 115.1 39 183.1 153.6 99 229.0 192.2 60 46.0 38.6 20 91.9 77.1 80 137.9 115.7 40 183.9 154.3 300 229.8 192.8 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. J Dist. Dep. 1 Lat. Dist. Dep. Lat. 5 0° (130°, 230°, 310°) . TABLE 2. [Page 447 | Difference of Latitude and Departure for 40° (140°, 220 °, 320° ). Diet. Lat. Dep. Dlst. Lat. Dep. Dist. Lat. Dep. Dlst. Lat. Dep. Dist. Lat. Dep. 301 230.6 193.5 361 276. 5 232.1 421 322.5 270.6 481 368.5 309.2 541 414.4 347.7 02 231.3 194.1 62 277.3 232.7 22 323.3 271.3 82 369.2 309.8 42 415.2 348.4 03 232.1 194.8 63 278.1 233.3 23 324.0 271.9 83 370.0 310.5 43 416.0 349.0 04 232.9 195.4 64 278.8 234.0 24 324.8 272.6 84 370.8 311.1 44 416.7 349.7 05 233.6 196.1 65 279.6 234.6 25 325. 6 273. 2 85 371.5 311.7 45 417.5 350. 3 06 234.4 196.7 66 280.4 235.3 26 326.3 273.8 86 372.3 312.4 46 418.3 351.0 07 235.2 197.3 67 281.1 235.9 27 327.1 274.5 87 373.1 313.0 47 419.0 351.6 08 235.9 198.0 68 281.9 236.6 28 327.9 275.1 88 373.8 313.6 48 419.8 352.2 09 236.7 198.6 69 282.7 237.2 29 328.6 275.8 89 374.6 314.3 49 420.6 352.9 10 237.5 199.3 70 283.4 237.8 30 329.4 276.4 90 375.4 314.9 50 421.3 353.5 311 238.2 199.9 371 284.2 238.5 431 330.2 277.1 491 376.1 315. 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 93 377.7 316.9 53 423.6 355.5 14 240.5 201.8 74 286.5 240.4 34 332.5 279.0 94 378.4 317.5 54 424.4 356.1 15 241.3 202.5 75 287.3 241.0 35 333. 2 279.6 95 379.2 318.2 55 425.2 356.8 16 242.1 203.1 76 288.0 241.7 36 334.0 280.3 96 380.0 318.8 56 425.9 357.4 17 242.8 203.8 77 288.8 242.3 37 334.8 280.9 97 380.7 319.5 57 426.7 358.0 18 243.6 204.4 78 289.6 243.0 38 335.5 281.6 98 381.5 320.1 58 427.5 358.7 19 244.4 205.1 79 290.3 243.6 39 336.3 282.2 99 382.3 320.8 59 428.2 359.3 20 245. 1 205.7 80 291.1 244. 3 40 337.1 282. 8 500 383.0 321.4 60 429.0 360.0 360.6 321 245.9 206.3 381 291.9 244.9 441 337.8 283.5 501 383.8 322.0 561 429.8 22 246.7 207.0 82 292.6 245.6 42 338.6 284.1 02 384.6 322.7 62 430.5 361.2 23 247.4 207.6 83 293.4 246.2 43 339.4 284.8 03 385.3 323. 3 63 431.3 361.9 24 248.2 208.3 84 294.2 246.8 44 340.1 285.4 04 386.1 324.0 64 432.1 362.5 25 249.0 208.9 85 294.9 247.5 45 340.9 286.0 05 386.8 324.6 65 432.8 363.2 26 249.7 209.6 86 295.7 248.1 46 341.7 286.7 06 387.6 325.2 66 433.6 363. 8 27 250.5 210.2 87 296.5 248.8 47 342.4 287.3 07 388.4 325.9 67 434. 3 364.5 28 251. -3 210.8 88 297.2 249.4 48 343.2 288. 08 389.2 326.5 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 30 252.8 253. 6 212.1 90 298.8 250.7 50 344.7 289.3 10 390.7 327.8 70 436.6 366.4 331 212.8 391 299.5 251.3 451 345.5 289.9 511 391. 5 328.4 571 437.4 367.0 32 254.3 213.4 92 300.3 252.0 52 346.3 290.5 12 392.2 329.1 72 438.2 367.7 33 255.1 214.1 93 301.1 252.6 53 347. 291.2 13 393.0 329.7 73 438.9 368.3 34 255.9 214.7 94 301.8 253.3 54 347.8 291.8 14 393.8 330.4 74 439.7 369.0 35 256.6 215.3 95 302.6 253.9 55 348.6 292.5 15 394.5 331.0 75 440.5 369.6 36 257.4 216.0 96 303.4 254.6 56 349.3 293.1 16 395.3 331.6 76 441.2 370.2 37 258.2 216.6 97 304.1 255.2 57 350.1 293.8 17 396.1 332.3 77 442.0 370.9 38 258.9 217.3 98 304.9 255.8 58 350.8 294.4 18 396. 8 332.9 78 442.8 371.5 39 259.7 217.9 99 305.7 256.5 59 351.6 295.0 19 397.6 333.6 79 443.5 372.2 40 260.5 261.2 218.6 400 306.4 257.1 60 352.4 295.7 20 398.3 399. L 334.2 80 444.3 372.8 341 219.2 401 307.2 257.8 461 353.1 296.3 521 334.9 581 445.1 373.5 42 262.0 219.8 02 308.0 258.4 62 353.9 297.0 22 399.9 335.5 82 445.8 374.1 43 262.8 220.5 03 308.7 259.1 63 354.7 297.6 23 400.6 336.1 83 446.6 374.8 44 263.5 221.1 04 309.5 259.7 64 355. 4 298.3 24 401. 4 336.8 84 447.4 375.4 45 264.3 221.8 05 310.2 260.3 65 356.2 298.9 25 402.2 337.4 85 448.1 376.0 46 265.1 222.4 06 311.0 261.0 66 357.0 299.5 26 402.9 338.1 86 448.9 376.7 47 265.8 223.1 07 311.8 261.6 67 357.7 300.2 27 403.7 338.7 87 449.7 377.3 48 266.6 223.7 08 312.5 262.3 68 358.5 300.8 28 404.5 339.4 88 450.4 378.0 49 267.4 224.3 09 313.3 262.9 69 359.3 301.5 29 405.2 340.0 89 451.2 378.6 50 268.1 225.0 10 314.1 263.6 70 360.0 302.1 30 406.0 340.6 90 452.0 379.2 351 268.9 225.6 411 314.8 264.2 471 360.8 302. 8 531 406.8 341.3 591 452.7 379.9 52 269.6 226.3 12 315.6 264.8 72 361.6 303.4 32 407.5 341.9 92 453.5 380.5 53 270.4 226. 9 13 316.4 265.5 73 362.3 304.0 33 408.3 342.6 93 454.3 381.2 54 271.2 227.6 14 317.1 266.1 74 363.1 304.7 34 409.1 343.2 94 455.0 381.8 55 271.9 228.2 15 317.9 266.8 75 363.9 305.3 35 409.8 343.9 95 455.8 382.4 56 272.7 228.8 16 318.7 267.4 76 364.6 306.0 36 410.6 344.5 96 456.6 383.1 57 273.5 229.5 17 319.4 268.1 77 365.4 306.6 37 411.4 345.2 97 457.3 383. 7 58 274.2 230.1 18 320.2 268.7 78 366.2 307.3 38 412.1 345.8 98 458.1 384. 4 59 275. 230.8 19 321.0 269.3 79 366.9 307. 9 39 412.9 346.4 99 458.9 385.0 60 275.8 231.4 20 321.7 270.0 80 367.7 308.5 40 413.7 347.1 600 459.6 385.7 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. ^ 50° (1 30°, 230°, 310° )• Page 448] TABLE 2. Difference of Latitude and Departure for 41° (139°, 221°, 319° )• Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 0.8 0.7 61 46.0 40.0 121 91.3 79.4 181 136.6 118.7 241 181.9 158.1 2 1.5 1.3 62 46.8 40.7 22 92.1 80.0 82 137.4 119.4 42 182.6 158.8 3 2.3 2.0 63 47.5 41.3 23 92.8 80.7 83 138.1 120.1 43 183.4 159.4 4 3.0 2.6 64 48.3 42.0 24 93.6 81.4 84 138.9 120.7 44 184.1 160.1 5 3.8 3.3 65 49.1 42.6 25 94.3 82.0 85 139.6 121.4 45 184.9 160.7 6 4.5 3.9 66 49.8 43.3 26 95.1 82.7 86 140.4 122.0 46 185.7 161.4 7 5.3 4.6 67 50.6 44.0 27 95.8 83.3 87 141.1 122.7 47 186.4 162.0 8 6.0 5.2 68 51.3 44.6 28 96.6 84.0 88 141.9 123.3 48 187.2 162.7 9 6.8 5.9 69 52.1 45.3 29 97.4 84.6 89 142.6 124.0 49 187.9 163.4 10 7.5 6.6 70 52.8 45.9 30 98.1 85.3 90 191 143.4 144.1 124.7 50 251 188.7 189.4 164.0 11 8.3 7.2 71 53.6 46.6 131 98.9 .85.9 125.3 164.7 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 r02. 6 89.2 96 147.9 128.6 66 193.2 168.0 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 61.1 52.5 40 105.7 91.8 200 150.9 131.2 60 196.2 170.6 21 15.8 13.8 81 53.1 141 106.4 92.5 201 151.7 131. 9 261 197.0 171.2 22 16.6 14.4 82 61.9 53.8 42 107.2 93.2 02 152.5 132.5 62 197.7 171.9 23 17.4 15.1 83 62.6 54.5 43 107.9 93.8 03 153.2 133.2 63 198.5 172.5 24 18.1 15.7 84 63.4 55.1 44 108.7 94.5 04 154.0 133.8 64 199.2 173.2 25 18.9 16.4 85 64.2 55.8 45 109.4 95.1 05 154.7 134.5 65 200.0 173.9 . 26 19.6 17.1 86 64.9 56.4 46 110.2 95.8 06 155.5 135.1 66 200.8 174.5 27 20.4 17.7 87 65.7 57.1 47 110.9 96.4 07 156.2 135. 8 67 201.5 175.2 28 21.1 18.4 88 66.4 57.7 48 111.7 97.1 08 157.0 136.5 68 202.3 175.8 29 21.9 19.0 89 67.2 58.4 49 112.5 97.8 09 157.7 137.1 69 203.0 176.5 30 22.6 23.4 19.7 90 67.9 59.0 50 113.2 98.4 10 158.5 137.8 138. 4 70 203.8 177.1 31 20.3 91 68.7 59.7 151 114.0 99.1 211 159.2 271 204.5 177.8 32 24.2 21.0 92 69.4 60.4 52 114.7 99.7 12 160.0 139.1 72 205.3 178.4 33 24.9 21.6 93 70.2 61.0 53 115. 5 100.4 13 . 160. 8 139.7 73 206.0 179.1 34 25.7 22.3 94 70.-9 61.7 54 116.2 101.0 14 161.5 140.4 74 206.8 179.8 35 26.4 23.0 95 71.7 62.3 55 117.0 101.7 15 162. 3 141.1 75 207.5 180.4 36 27.2 23.6 96 72.5 63.0 56 117. 7 102.3 16 163.0 141.7 76 208.3 181.1 37 27.9 24.3 97 73.2 63.6 57 118.5 103. 17 163.8 142.4 77 209.1 181.7 38 28.7 24.9 98 74.0 64.3 58 119.2 103.7 18 164.5 143.0 78 209.8 182.4 39 29.4 25.6 99 74.7 64.9 59 120.0 104.3 19 165.3 143.7 79 210.6 183.0 40 30.2 30.9 26.2 100 75.5 65.6 66.3 60 161 120.8 121.5 105.0 105.6 20 221 166.0 144.3 80 211.3 183.7 184.4 41 26.9 101 76.2 166.8 145.0 281 212.1 42 31.7 27.6 02 77.0 66.9 62 122.3 106.3 22 167.5 145.6 82 212.8 185.0 43 32.5 28.2 03 77.7 67.6 63 123.0 106.9 23 168.3 146.3 83 213.6 185.7 44 33.2 28.9 04 78.5 68.2 64 123. 8 107.6 24 169.1 147.0 84 214.3 186.3 45 34.0 29.5 05 79.2 68.9 65 124.5 108.2 25 169.8 147.6 85 215.1 187.0 46 34.7 30.2 06 80.0 69.5 66 125.3 108.9 26 170.6 148.3 86 215.8 187.6 47 35.5 30.8 07 80.8 70.2 67 126.0 109.6 27 171.3 148.9 87 216.6 188.3 48 36.2 31.5 08 81.5 70.9 68 126.8 110.2 28 172.1 149. 6 88 217.4 188.9 49 37.0 32.1 09 82.3 71.5 69 127.5 110.9 29 172.8 150.2 89 218.1 189.6 50 37.7 32.8 10 83.0 72.2 70 128.3 111.5 112. 2 30 231 173.6 150.9 90 218.9 190.3 190.9 51 38.5 33.5 111 83.8 72.8 171 129.1 174.3 151.5 291 219.6 52 39.2 34.1 12 84.5 73.5 72 129.8 112.8 32 175.1 152.2 92 220.4 191.6 53 40.0 34.8 13 85.3 74.1 73 130.6 113.5 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. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 227.2 197.5 361 272.5 236.9 421 317.7 276.2 481 363.0 315.6 541 408.3 354.9 02 227.9 198.1 62 273.2 237.5 22 318.5 276.9 82 363.8 316.2 42 409.0 355.6 03 228.7 198.8 63 274.0 238.2 23 319.2 277.5 83 364.5 316.9 43 409.8 356.2 04 229.4 199.4 64 274.7 238.8 24 320.0 278.2 84 365.3 317.5 44 410.6 356.9 05 230.2 200.1 65 275.5 239.5 25 320.8 278.8 85 366.0 318.2 45 411.3 357.5 06 230.9 200.8 66 276.2 240.1 26 321.5 279.5 86 366.8 318.8 46 412.1 358.2 07 231.7 201.4 67 277.0 240.8 27 322.3 280.1 87 367.5 319.5 47 412.8 358. 8 08 232.5 202.1 68 277.7 241.4 28 323.0 280.8 88 368.3 320.1 48 413.6 359.5 09 233.2 202.7 69 278.5 242.1 29 323.8 281.5 89 369.0 320.8 49 414.3 360.2 10 234.0 203.4 70 279.2 242.7 30 324. 5 282.1 90 369.8 321. 5 50 415.1 360.8 311 234.7 204.0 371 280.0 243.4 431 325.3 282.8 491 370.6 322.1 551 415.8 361.5 12 235.5 204.7 72 280.8 244.1 32 326.0 283.4 92 371.3 322.8 52 416.6 362.1 13 236.2 205.4 73 281.5 244.7 33 326.8 284.1 93 372.1 323.4 53 417.3 362.8 14 237.0 206.0 74 282.3 245.4 34 327.5 284.7 94 372.8 324.1 54 418.1 363.4 15 237.7 206.7 75 283.0 246.0 35 328.3 285.4 95 373.6 324.7 55 418.9 364.1 16 238.5 207.3 76 283.8 246.7 36 329.1 286.0 96 374.3 325.4 56 419.6 364.8 17 239.2 208.0 77 284.5 247.3 37 329.8 286.7 97 375.1 326.0 57 420.4 365.4 18 240.0 208.6 78 285.3 248.0 38 330.6 287.4 98 375.8 326.7 58 421.1 366.1 19 240.8 209.3 79 286.0 248.7 39 331.3 288.0 99 376.6 327.4 59 421.9 366.7 20 241.5 209.9 80 286.8 249.3 250.0 40 332.1 288.7 500 377.3 328.0 60 422.6 367.4 321 242.3 210.6 381 287.5 441 332.8 289.3 501 378.1 328.7 561 423.4 368.0 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 65 426.4 370.7 26 246.0 213.9 86 291.3 253.2 46 336.6 292.6 06 381.9 332.0 66 427.2 371.3 27 246.8 214.5 87 292.1 253.9 47 337.4 293.3 07 382.6 332.6 67 427.9 372.0 28 247.5 215.2 88 292.8 254.6 48 338.1 293.9 08 383.4 333.3 68 428.7 372.6 29 248.3 215.9 89 293.6 255.2 49 338.9 294.6 09 384.1 333.9 69 429.4 373.3 30 249.1 216.5 90 294.3 255.9 50 339.6 295.2 10 384.9 334.6 70 430.2 374.0 331 249.8 217.2 391 295.1 256.5 451 340.4 295.9 511 385.7 335.2 571 430.9 374.6 32 250.6 217.8 92 295.8 257.2 52 341.1 296.5 12 386.4 335.9 72 431.7 375.3 33 251.3 218.5 93 296.6 257.8 53 341.9 297.2 13 387.2 336.5 73 432.4 375.9 34 252.1 219.1 94 297.4 258.5 54 342.6 297.9 14 387.9 337.2 74 433.2 376.6 35 252.8 219.8 95 298.1 259.2 55 343.4 298.5 15 388.7 337.9 75 434.0 377.2 36 253.6 220.4 96 298.9 259.8 56 344.1 299.2 16 389. 4 338.5 76 434.7 377.9 37 254. 3 221.1 97 299.6 260.5 57 344.9 299.8 17 390.2 339.2 77 435.5 378.5 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 40 256.6 223.1 400 301.9 262.4 60 347.2 301.8 20 392.4 341.1 80 437.7 380.5 341 257.4 223.7 401 302.6 263.1 461 347.9 302.5 521 393.2 341.8 581 438.5 381.2 42 258.1 224.4 02 303.4 263.7 62 348.7 303.1 22 394.0 342.5 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 88 443.8 386.8 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 70 471 354.7 308.4 30 400.0 347.7 90 445.3 387.1 351 230.3 411 310.2 269.6 355.5 309.0 531 400.7 348.4 591 446.0 387.7 52 265.7 230.9 . 12 310. 9 270.3 72 356.2 309.7 32 401.5 349.0 92 446.8 388.4 53 266.4 231.6 13 311.7 271.0 73 357.0 310.3 33 402.2 349.7 93 447.5 389.1 54 267.2 232.3 14 312.5 271.6 74 357.7 311.0 34 403.0 350.3 94 448.3 389.7 55 267.9 232.9 15 313.2 272.3 75 358.5 311.6 35 403.8 351.0 95 449.1 390.4 56 268.7 233.6 16 314.0 272.9 76 359.2 312.3 36 404.5 351.6 96 449.8 391.0 57 269.4 234.2 17 314.7 273.6 77 360.0 312.9 37 405.3 352.3 97 450.6 391.7 58 270.2 234.9 18 315.5 274.2 78 360.8 313.6 38 406.0 352.9 98 451.3 392.3 59 270.9 235.5 19 316.2 274.9 79 361.5 314.3 39 406.8 353.6 99 452.1 393.0 60 271.7 236.2 20 317.0 275.6 80 362.3 314.9 40 407. 5 354.3 600 452.8 393.6 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 49° (131°, 229°, 311° ). 1 6583—06 29 Page 450] TABLE 2. 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. 1 0.7 0.7 61 45.3 40.8 121 89.9 81.0 181 134.5 121.1 241 179.1 161.3 2 1.5 1.3 62 46.1 41.5 22 90.7 81.6 82 135.3 121.8 42 179.8 161.9 3 2.2 2.0 63 46.8 42.2 23 91.4 82.3 83 136.0 122.5 43 180.6 162.6 4 3.0 2.7 64 47.6 42.8 24 92.1 83.0 84 136.7 123.1 44 181.3 163.3 5 3.7 3.3 65 48.3 43.5 25 92.9 83.6 85 137.5 123.8 45 182.1 163.9 6 4.5 4.0 66 49.0 44.2 26 93.6 84.3 86 138.2 124.5 46 182.8 164.6 7 5.2 4.7 67 49.8 44.8 27 94.4 85.0 87 139.0 125. 1 47 183.6 165.3 8 5.9 5.4 68 50.5 45.5 28 95.1 85.6 88 139.7 125.8 48 184.3 165.9 9 6.7 6.0 69 51.3 46.2 29 95.9 86.3 89 140.5 126.5 49 185.0 166.6 10 7.4 6.7 70 52.0 46.8 30 96.6 87.0 90 141.2 127.1 50 185.8 167.3 168.0 11 8.2 7.4 71 52.8 47.5 131 97.4 87.7 191 141.9 127.8 251 186.5 12 8.9 8.0 72 53.5 48.2 32 98.1 88.3 92 142.7 128.5 52 187.3 168.6 13 9.7 8.7 73 54.2 48.8 33 98.8 89.0 93 143.4 129.1 53 188.0 169.3 14 10.4 9.4 74 55.0 49.5 34 99.6 89.7 94 144.2 129.8 54 188.8 170.0 15 11.1 10.0 75 55.7 50.2 35 100.3 90.3 95 144.9 130.5 55 189.5 170.6 16 11.9 10.7 76 56.5 50.9 36 101.1 91.0 96 145.7 131.1 56 190.2 171.3 17 12.6 11.4 77 57.2 51.5 37 101.8 91.7 97 146.4 131.8 57 191.0 172.0 18 13.4 12.0 78 58.0 52.2 38 102.6 92.3 98 147.1 132.5 58 191.7 172.6 19 14.1 12.7 79 58.7 52.9 39 103.3 93.0 99 147.9 133.2 59 192.5 173.3 20 14.9 13.4 80 59.5 53.5 40 104.0 93.7 200 148.6 133. 8 60 193.2 174.0 21 15.6 14.1 81 60.2 54.2 141 104.8 94.3 201 149.4 134.5 261 194.0 174.6 22 16.3 14.7 82 60.9 54.9 42 105.5 95.0 02 150.1 135.2 62 194.7 175.3 23 17.1 15.4 83 61.7 55.5 43 106.3 95.7 03 150.9 135.8 63 195.4 176.0 24 17.8 16.1 84 62.4 56.2 44 107.0 96.4 04 151.6 136.5 64 196.2 176.7 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 60.2 50 111.5 112.2 100.4 10 156.1 140.5 70 200.6 180.7 23.0 20.7 91 67.6 60.9 151 101.0 211 156.8 141.2 271 201.4 181.3 32 23.8 21.4 92 68.4 61.6 52 113.0 101.7 12 157.5 141.9 72 202.1 182.0 33 24.5 22.1 93 69.1 62.2 53 113.7 102.4 13 158.3 142.5 73 202. 9 182.7 34 25.3 22.8 94 69.9 62.9 54 114.4 103.0 14 159.0 143.2 74 203.6 183.3 35 26.0 23.4 95 70.6 63.6 55 115. 2 103.7 15 159.8 143.9 75 204.4 184.0 36 26.8 24.1 96 71.3 64.2 56 115.9 104.4 16 160.5 144. 5 76 205.1 184.7 37 27.5 24.8 97 72.1 64.9 57 116.7 105.1 17 161.3 145. 2 77 205.9 185.3 38 28.2 25.4 98 72.8 65.6 58 117.4 105. 7 18 162.0 145.9 78 206.6 186.0 39 29.0 26.1 99 73.6 66.2 59 118.2 106.4 19 162.7 146. 5 79 207.3 186.7 40 29.7 30.5 26.8 100 101 74.3 75.1 66.9 60 118.9 107.1 20 163. 5 147.2 80 281 208.1 187.4 41 27.4 67.6 161 119.6 107.7 221 164.2 147.9 208.8 188.0 42 31.2 28.1 02 75.8 68.3 62 120.4 108.4 22 165.0 148.5 82 209.6 188.7 43 32.0 28.8 03 76.5 68.9 63 121.1 109.1 23 165.7 149.2 83 210.3 189.4 44 32.7 29.4 04 77.3 69.6 64 121.9 109.7 24 166.5 149.9 84 211.1 190.0 45 33.4 30.1 05 78.0 70.3 65 122.6 110.4 25 167.2 150.6 85 211.8 190.7 46 34.2 30.8 06 78.8 70.9 66 123.4 111.1 26 168.0 151.2 86 212.5 191.4 47 34.9 31.4 07 79.5 71.6 67 124.1 111.7 27 168.7 151.9 87 213.3 192.0 48 35.7 32.1 08 80.3 72.3 68 124.8 112.4 28 169.4 152.6 88 214.0 192.7 49 36.4 32.8 09 81.0 72.9 69 125.6 113.1 29 170.2 153.2 89 214.8 193.4 50 37.2 33.5 10 81.7 73.0 70 126.3 113.8 30 170.9 153.9 90 215.5 194.0 51 37.9 34.1 111 82.5 74.3 171 127.1 114.4 231 171.7 154.6 291 216.3 194.7 52 38.6 34.8 12 83.2 74.9 72 127.8 115.1 32 172.4 155.2 92 217.0 195.4 53 39.4 35.5 13 84.0 75.6 73 128.6 115.8 33 173.2 155.9 93 217.7 196.1 54 40.1 36.1 14 84.7 76.3 74 129.3 116.4 34 173.9 156.6 94 218.5 196.7 55 40.9 36.8 15 85.5 77.0 75 130.1 117.1 35 174.6 157.2 95 219.2 197.4 56 41.6 37.5 16 86.2 77.6 76 130.8 117.8 36 175.4 157. 9 96 220.0 198.1 57 42.4 38.1 17 86.9 78.3 77 131.5 118.4 37 176.1 158.6 97 220.7 198.7 58 43.1 38.8 18 87.7 79.0 78 132.3 119.1 38 176.9 159.3 98 221.5 199.4 59 43.8 39.5 19 88.4 79.6 79 133.0 119.8 39 177.6 159.9 99 222.2 200.1 60 44.6 40.1 20 89.2 80.3 80 133.8 120.4 40 178.4 160.6 300 222.9 200.7 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 4 [8° (K J2°, 228° ,312). 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 23 314.4 283.0 83 358.9 323.2 43 403.5 363.3 04 225.9 203.4 64 270.5 243.6 24 315.1 283.7 84 359.7 323.9 44 404.3 364.0 05 226.6 204.1 65 271.2 244.2 25 315.8 284.4 85 360.4 324.6 45 405.0 364.7 06 227.4 204.8 66 272.0 244.9 26 316.6 285.1 86 361.2 325.2 46 405.8 365.4 07 228.1 205.4 67 272.7 245.6 27 317. 3 285.7 87 361.9 325.9 47 406.5 366.0 08 228.9 206.1 68 273.5 246.2 48 318.1 286.4 88 362.7 326.6 48 407.2 366.7 09 229.6 206.8 69 274.2 246.9 29 318.8 287.1 89 363. 4 327.2 49 408.0 367.4 10 230.4 207.4 70 275.0 247.6 30 319.6 287.7 90 364.1 327.9 50 408.7 368.0 311 231.1 208.1 371 275.7 248.3 431 320.3 288.4 491 364.9 328.6 551 409.5 368.7 12 231.9 208.8 72 276.5 248.9 32 321.0 289.1 92 365.6 329.2 52 410.2 369.4 13 232.6 209.4 73 277.2 249.6 33 321.8 289.7 93 366. 4 329.9 53 411.0 370.0 14 233.3 210.1 74 277.9 250.3 34 322.5 290.4 94 367.1 330.6 54 411.7 370.7 15 234.1 210.8 75 278.7 250.9 35 323.3 291.1 95 367.9 331.3 55 412.4 371.4 16 234.8 211.5 76 279.4 251.6 36 324.0 291.7 96 368.6 331.9 56 413.2 372.0 17 235.6 212.1 77 280.2 252.3 37 324.8 292.4 97 369.3 332.6 57 413.9 372.7 18 236.3 212.8 78 280.9 252.9 38 325.5 293.1 98 370.1 333.3 58 414.7 373.4 19 237.1 213.5 79 281.7 253.6 39 326.2 293.8 99 370.8 333.9 59 415.4 374.1 20 237.8 214.1 80 282.4 254.3 40 327.0 294.4 500 371.6 334. 6 60 416.2 374.7 321 238. 6 214.8 381 283.1 254.9 441 327.7 295.1 501 372.3 335.3 561 416.9 375.4 22 239.3 215.5 82 283. 9 255.6 42 328.5 295.8 02 373.1 335.9 62 417.6 376.1 23 240.0 216.1 83 284.6 256.3 43 329.2 296.4 03 373.8 336.6 63 418.4 376.7 24 240.8 216.8 84 285.4 257.0 44 330.0 297.1 04 374.5 337.2 64 419.1 377.4 25 241.5 217.5 85 286.1 257.6 45 330.7 297.8 05 375.3 337.9 65 419.9 378.1 26 242.3 218.1 86 286.9 258.3 46 331.4 298.4 06 376.0 338.6 66 420.6 378.7 27 243.0 218.8 87 287.6 259.0 47 332.2 299.1 07 376.8 339.3 67 421.4 379.4 28 243.8 219.5 88 288.3 259.6 48 332.9 299.8 08 377.5 339.9 68 422.1 380.1 29 244.5 220.1 89 289.1 260.3 49 333.7 300.4 09 378.3 340.6 69 422.8 380.7 30 331 245.2 220.8 90 289.8 261.0 50 334.4 301.1 10 379.0 341.3 70 423.6 424.3 381.4 246.0 221.5 391 290.6 261.6 451 335.2 301.8 511 379.7 341.9 571 382.1 32 246.7 222.2 92 291.3 262.3 52 335.9 302.5 12 380.5 342.6 72 425.1 382.8 33 247.5 222.8 93 292.1 263.0 53 336.6 303.1 13 381.2 343.3 73 425.8 383.4 34 248.2 223.5 94 292.8 263.6 54 337.4 303.8 14 382.0 343.9 74 426.6 384.1 35 249.0 224.2 95 293. 5 264.3 55 338.1 304.5 15 382.7 ^44.6 75 427.3 384.8 36 249.7 224.8 96 294.3 265.0 56 338.9 305.1 16 383.5 345.3 76 428.0 385.4 37 250.4 225.5 97 295.0 265.7 57 339.6 305. 8 17 384.2 346.0 77 428.8 386.1 3S 251.2 226.2 98 295.8 266.3 58 340.4 306.5 18 384.9 346.6 78 429.5 386.8 39 251.9 226.8 99 296.5 267.0 59 341.1 307.1 19 385.7 347.3 79 430.3 387.4 40 252.7 227.5 400 297.3 267.7 60 341.8 307.8 20 386.4 348.0 80 431.0 388.1 341 253.4 228.2 401 298.0 268.3 461 342.6 308.5 521 387.2 348.6 581 431.8 388.8 42 254.2 228.8 02 298.7 269.0 62 343.3 309.1 . 22 387.9 349.3 82 432.5 389. 4 ti 43 254.9 229.5 03 299.5 269.7 63 344.1 309.8 23 388.7 350.0 83 433.2 390.1 44 255.6 230.2 04 300.2 270.3 64 344.8 310.5 24 389.4 350.6 84 434.0 390.8 45 256.4 230.9 05 301.0 271.0 65 345.6 311.2 25 390.1 351.3 85 434.7 391.4 46 257.1 231.5 06 301.7 271.7 66 346.3 311.8 26 390.9 352.0 86 435.5 392.1 47 257.9 232.2 07 302.5 272.3 67 347.0 312.5 27 391.6 352.6 87 436.2 392.8 48 258.6 232.9 08 303.2 273.0 68 347.8 313.2 28 392.4 353.3 88 437.0 393.4 49 259.4 233.5 09 303.9 273.7 69 348.5 313.8 29 393.1 354.0 89 437.7 394.1 50 260.1 234.2 10 304. 7 274.3 70 349.3 314.5 30 393.9 354.6 90 438.4 394.8 351 260.8 234.9 411 305.4 275.0 471 350.0 315.2 531 394.6 355.3 591 439.2 395.4 52 261.6 235.5 12 306.2 275.7 72 350.8 315.8 32 395.3 356.0 92 440.0 396.1 53 262.3 236.2 13 306.9 276.4 73 351.5 316.5 33 396.1 356.6 93 440.7 396.8 54 263.1 236.9 14 307.7 277.0 74 352.3 317.2 34 396.8 357.3 94 441.4 397.5 55 263.8 237.5 15 308.4 277.7 75 353.0 317.8 35 397.6 358.0 95 442.2 398.1 56 264.6 238.2 16 309.1 278.4 76 353.7 318.5 36 398.3 358.6 96 442.9 398.8 57 265.3 238.9 17 309.9 279.0 77 354.5 319.2 37 399.1 359.3 97 443.7 399.5 58 266.0 239.6 18 310.6 279.7 78 355.2 319.9 38 399.8 360.0 98 444.4 400.1 59 266.8 240.2 19 311.4 280.4 79 356.0 320.5 39 400.6 360.6 99 445.2 400.8 60 267.5 240.9 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 89.2 83.2 82 133.1 124.1 42 177.0 165.0 3 2.2 2.0 63 46.1 43.0 23 90.0 83.9 83 133.8 124.8 43 177.7 165.7 4 2.9 2.7 64 46.8 43.6 24 90.7 84.6 84 134.6 125.5 44 178.5 166.4 5 3.7 3.4 65 47.5 44.3 25 91.4 85.2 85 135.3 126.2 45 179.2 167.1 6 4.4 4.1 66 48.3 45.0 26 92.2 85.9 86 136.0 126.9 46 179.9 167.8 7 5.1 4.8 67 49.0 45.7 27 92.9 86.6 87 136.8 127.5 47 180.6 168.5 8 5.9 5.5 68 49.7 46.4 28 93.6 87.3 88 137.5 128.2 48 181.4 169.1 9 6.6 6.1 69 50.5 47.1 29 94.3 88.0 89 138.2 128.9 49 182.1 169.8 10 7.3 6.8 70 51.2 47.7 30 95.1 95.8 88.7 90 139.0 139.7 129.6 50 182.8 170.5 11 8.0 7.5 71 51.9 48.4 131 89.3 191 130.3 251 183.6 171.2 12 8.8 8.2 72 52.7 49.1 32 96.5 90.0 92 140.4 130.9 52 184.3 171.9 13 9.5 8.9 73 53.4 49.8 33 97.3 90.7 93 141.2 131.6 53 185.0 172.5 14 10.2 9.5 74 54.1 50.5 34 98.0 91.4 94 141-. 9 132.3 54 185.8 173.2 15 11.0 10.2 75 54.9 51.1 35 98.7 92.1 95 142.6 133.0 55 186.5 173.9 16 11.7 10.9 76 55.6 51.8 36 99.5 92.8 96 143.3 133.7 56 187.2 174.6 17 12.4 11.6 77 56.3 52.5 37 100.2 93.4 97 144.1 134.4 57 188.0 175.3 18 13.2 12.3 78 57.0 53.2 38 100.9 94.1 98 144.8 135.0 58 188.7 176.0 19 13.9 13.0 79 57.8 53.9 39 101.7 94.8 99 145.5 135.7 59 189.4 176.6 20 21 14.6 13.6 80 58.5 54.6 40 102.4 103.1 95.5 96.2 200 146.3 136.4 60 261 190.2 177.3 15.4 14.3 81 59.2 55.2 141 201 147.0 137.1 190.9 178. 22 16.1 15.0 82 60.0 55.9 42 103.9 96.8 02 147.7 137.8 62 191.6 178.7 23 16.8 15.7 83 60.7 56.6 43 104.6 97.5 03 148.5 138.4 63 192.3 179.4 24 17.6 16.4 84 61.4 57.3 44 105.3 98.2 04 149.2 139.1 64 193.1 180.0 25 18.3 17.0 85 62.2 58.0 45 106.0 98.9 05 149.9 139.8 65 193.8 180.7 26 19.0 17.7 86 62.9 58.7 46 106.8 99.6 06 150.7 140.5 66 194.5 181.4 27 19.7 18.4 87 63.6 59.3 47 107.5 100.3 07 151.4 141.2 67 195.3 182.1 28 20.5 19.1 88 64.4 60.0 48 108.2 100.9 08 152.1 141.9 68 196.0 182.8 29 21.2 19.8 89 65.1 60.7 49 109.0 101.6 09 152.9 142.5 69 196.7 183.5 30 31 21.9 20.5 90 65.8 61.4 50 109.7 102.3 10 153.6 143.2 70 197.5 184.1 22.7 21.1 91 66.6 62.1 151 110.4 103.0 211 154.3 143.9 271 198.2 184.8 32 23.4 21.8 92 67.3 62.7 52 111.2 103.7 12 155.0 144.6 72 198.9 185.5 33 24.1 22.5 93 68.0 63.4 53 111.9 104.3 13 155.8 145.3 73 199.7 186.2 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 60 117.0 109.1 20 160.9 150.0 80 281 204.8 205.5' 191.0 41 30.0 28.0 101 73.9 68.9 161 117.7 109.8 221 161.6 150.7 191.6 42 30.7 28.6 02 74.6 69.6 62 118.5 110.5 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 70 124.3 115.9 30 168.2 156.9 157.5 90 212.1 197.8 51 37.3 34.8 111 81.2 75.7 171 125. 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° (1 33°, 227 °, 313° ). TABLE 2. [Page 453 Difference of Latitude and Departure for 43° (137°, 223 °, 317° ). Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 220.1 205.3 361 264.0 246.2 421 307.9 287.1 481 351.8 328.1 541 395.7 369.0 02 220 9 206.0 62 264.8 246.9 22 308.6 287.8 82 352.5 328.7 42 396.4 369.7 03 221.6 206.7 63 265.5 247.6 23 309.4 288.5 83 353. 2 329.4 43 397.1 370.3 04 222.3 207.3 64 266.2 248.3 24 310.1 289.2 84 354.0 330.1 44 397.9 371.0 05 223.1 208.0 65 267.0 248.9 25 310.8 289.9 85 354.7 330.8 45 398.6 371.7 06 223.8 208.7 66 267.7 249.6 26 311.6 290.5 86 355.4 331.4 46 399.3 372.4 07 224.5 209.4 67 268.4 250.3 27 312.3 291.2 87 356.2 332.1 47 400.1 373.1 08 225.3 210.1 68 269.1 251.0 28 313.0 291.9 88 356.9 332.8 48 400.8 373.7 09 226.0 210.7 69 269.9 251.7 29 313.8 292.6 89 357.7 333.5 49 401.5 374.4 10 311 226.7 211.4 70 270.6 252.3 30 314.5 293.3 ^0 358.4 334.2 50 402.2 375.1 227.5 212.1 371 271.3 253.0 431 315.2 293.9 491 359.1 334,9 551 403.0 375,8 12 228.2 212.8 72 272.1 253.7 32 316.0 294.6 92 359. 8 335,5 52 403.7 376.5 13 228.9 213.5 73 272.8 254.4 33 316.7 295.3 93 360.6 336,2 53 404.4 377.1 14 229.7 214.2 74 273.5 255.1 34 317.4 296.0 94 361.3 336.9 54 405.2 377.8 15 230.4 214.8 75 274.3 255.8 35 318.1 296. 7 95 362.0 337.6 55 405.9 378.5 16 231.1 215.5 76 275.0 256.4 36 318.9 297.4 96 362.8 338.3 56 406.6 379.2 17 231.8 216.2 77 275.7 257.1 37 319.6 298.0 97 363.5 338.9 57 407.4 379.9 18 232.6 216.9 78 276.5 257.8 38 320.3 298.7 98 364.2 339.6 58 408.1 380,6 19 233.3 217.6 79 277.2 258.5 39 321.1 299.4 99 364.9 340.3 59 408.8 381,2 20 234.0 218.2 80 381 277.9 259.2 40 321.8 300.1 500 365.7 341.0 60 409.6 381,9 321 234. 8 218.9 278.7 259.8 441 322.5 300.8 501 366.4 341.7 561 410.3 382.6 22 235.5 219.6 82 279.4 260.5 42 323.3 301.4 02 367.1 342.4 62 411.0 383.3 23 236.2 220.3 83 280.1 261.2 43 324.0 302.1 03 367.'8 343.0 63 411,8 384.0 24 237.0 221.0 84 280.8 261.9 44 324.7 302.8 04 368.6 343.7 64 412,5 384.6 25 237.7 221.7 85 281.6 262.6 45 325.5 303.5 05 369.3 344.4 65 413.2 385.3 26 238.4 222.3 86 282.3 263.3 46 326.2 304.2 06 370.0 345.1 66 414.0 386.0 27 239.2 223.0 87 283.0 263.9 47 326.9 304.9 07 370.8 345,8 67 414.7 386.7 28 239.9 223.7 88 283.7 264.6 48 327.7 305.5 08 371.5 346,5 68 415.4 387.4 29 240.6 224.4 89 284.5 265.3 49 328.4 306.2 09 372.3 347.1 69 416.2 388. 1 30 241.4 225.1 90 285.2 266.0 50 329.1 306. 9 10 373.0 347.8 70 416.9 388.7 331 242.1 225.7 391 286.0 266.7 451 329.9 307.6 511 373.8 348.5 571 417.6 389.4 32 242.8 226.4 92 286.7 267.3 52 330.6 308.3 12 374.5 349.2 72 418.3 390.1 33 243. 5 227.1 93 287.4 268.0 53 331.3 309.0 13 375.2 349.9 73 419.1 390.8 34 244.3 227.8 94 288.2 268.7 54 332.1 309.6 14 376.0 350.5 74 419.8 391.5 35 245.0 228.5 95 288.9 269.4 55 332.8 310.3 15 376.6 351.2 75 420.5 392.2 36 245.7 229.2 96 289.6 270.1 56 333.5 311.0 16 377.4 351.9 76 421.3 392.8 37 246.5 229.8 97 290.4 270.8 57 334.3 311.7 17 378.2 352.6 77 422.0 393,5 38 247.2 230. 5 98 291.1 271.4 58 335.0 312.4 18 378.9 353.3 78 422.7 394.2 39 247.9 231.2 99 291.8 272.1 59 335.7 313.0 19 379.6 354.0 79 423,5 394.9 40 248.7 231.9 400 292.6 272.8 60 336.5 313.7 20 380.3 354.6 80 424,2 395.6 341 249.4 232.6 401 293.3 273.5 461 337.2 314.4 521 381.1 355.3 581 424,9 396.2 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 30 387,6 361.5 90 431.5 402.4 351 256.7 239.4 411 300.6 280.3 471 344.5 321.2 531 388.4 362.1 591 432.3 403.1 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 57 261.1 243.5 17 305.0 284.4 77 348.9 325.3 37 392.8 366.2 97 436.7 407.2 58 261.8 244.2 18 305.7 285.1 78 349.6 326.0 38 393.5 366.9 98 437.4 407.8 59 262.6 244.8 19 306. 4 285.8 79 350.3 326.7 39 394.2 367.6 99 438.1 408.5 60 263.3 245.5 20 307.2 286.4 80 351.1 327.4 40 394.9 368.3 600 438.8 409.2 Dist. Dep. Lat, Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. ^ 17° (1 33°, 227 °, 313° ). 1 '•S* 1 Page 454] TABLE 2. » Difference of Latitude and Departure for 44° (136°, 224°, 316' ). Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 0.7 0.7 61 43.9 42.4 121 87.0 84.1 181 130.2 125.7 241 173.4 167.4 2 1.4 1.4 62 44.6 43.1 22 87.8 84.7 82 130.9 126.4 42 174.1 168.1 3 2.2 2.1 63 45.3 43.8 23 88.5 85.4 83 131.6 127.1 43 174.8 168.8 4 2.9 2.8 64 46.0 44.5 24 89.2 86.1 84 132.4 127.8 44 175.5 169.5 5 3.6 3.5 65 46.8 45.2 25 89.9 86.8 85 133.1 128.5 45 176.2 170.2 6 4.3 4.2 66 47.5 45.8 26 90.6 87.5 86 133.8 129.2 46 177.0 170.9 7 5.0 4.9 67 48.2 46.5 27 91.4 88.2 87 134.5 129.9 47 177.7 171.6 8 5.8 5.6 68 48.9 47.2 28 92.1 88.9 88 135.2 130.6 48 178.4 172.3 9 6.5 6.3 69 49.6 47.9 29 92.8 89.6 89 136.0 131.3 49 179.1 173.0 10 7.2 6.9 70 50.4 48.6 49.3 30 93.5 90.3 90 136.7 137.4 132.0 50 179.8 173.7 11 7.9 7.6 71 51.1 131 94.2 91.0 191 132.7 251 180.6 174.4 12 8.6 8.3 72 51.8 50.0 32 95.0 91.7 92 138.1 133.4 52 181.3 175.1 13 9.4 9.0 73 52.5 50.7 33 95.7 92.4 93 138.8 134.1 53 182.0 175.7 14 10.1 9.7 74 53.2 51.4 34 96.4 93.1 94 139.6 134.8 54 182.7 176.4 15 10.8 10.4 75 54.0 52.1 35 97.1 93.8 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 81 57.5 55.6 40 100.7 97.3 200 143.9 138.9 60 187.0 180.6 21 15.1 14.6 58.3 56.3 141 101.4 97.9 201 144.6 139.6 261 187.7 181.3 22 15.8 15.3 82 59.0 57.0 42 102.1 98.6 02 145.3 140.3 62 188.5 182.0 23 16.5 16.0 83 59.7 57.7 43 102.9 99.3 03 146.0 141.0 63 189.2 182.7 24 17.3 16.7 84 60.4 58.4 44 103.6 100.0 04 146.7 141.7 64 189.9 183.4 25 18.0 17.4 85 61.1 59.0 45 104.3 100.7 05 147.5 142.4 65 190.6 184.1 26 18.7 18.1 86 61.9 59.7 46 105.0 101.4 06 148.2 143.1 66 191.3 184.8 27 19.4 18.8 87 62.6 60.4 47 105.7 102.1 07 148.9 143.8 67 192.1 186.5 28 20.1 19.5 88 63.3 61.1 48 106.5 102.8 08 149.6 144.5 68 192.8 186.2 29 20.9 20.1 89 64.0 61.8 49 107.2 103.5 09 150.3 145.2 69 193.5 186.9 30 31 21.6 22.3 20.8 90 64.7 62.5 50 107.9 104.2 10 151.1 151.8 145. 9 70 194.2 187.6 21.5 91 65.5 63.2 151 108.6 104.9 211 146.6 271 194.9 188.3 32 23.0 22.2 92 66.2 63.9 52 109.3 105.6 12 152.5 147.3 72 195.7 188.9 33 23.7 22.9 93 66.9 64.6 53 110.1 106.3 13 153.2 148.0 73 196.4 189.6 34 24.5 23.6 94 67.6 65.3 54 110.8 107.0 14 153.9 148.7 74 197.1 190.3 35 25.2 24.3 95 68.3 66.0 55 111.5 107.7 15 154.7 149.4 75 197.8 191.0 36 25.9 25.0 96 69.1 66.7 56 112.2 108.4 16 155.4 150.0 76 198.5 191.7 37 26.6 25.7 97 69.8 67.4 57 112.9 109.1 17 156.1 150.7 77 199.3 192.4 38 27.3 26.4 98 70.5 68.1 58 113.7 109.8 18 156.8 151.4 78 200.0 193.1 39 28.1 27.1 99 71.2 68.8 59 114.4 110.5 19 157.5 152.1 79 200.7 193.8 40 28.8 27.8 100 71.9 69.5 60 115.1 111.1 20 158.3 152.8 80 201.4 202. 1 194.5 41 29.5 28.5 101 72.7 70.2 161 115.8 111.8 221 159.0 153.5 281 195.2 42 30.2 29.2 02 73.4 70.9 62 116.5 112.5 22 159.7 154. 2 82 202.9 195.9 43 30.9 29.9 03 74.1 71.5 63 117.3 113.2 23 160.4 154.9 83 203.6 196.6 44 31.7 30.6 04 74.8 72.2 64 118.0 113.9 24 161.1 155.6 84 204.3 197.3 45 32.4 31.3 05 75.5 72.9 65 118.7 114.6 25 161.9 156.3 85 205.0 198.0 46 33.1 32.0 06 76.3 73.6 66 119.4 115.3 26 162.6 157.0 86 205.7 198.7 47 33.8 32.6 07 77.0 74.3 67 120.1 116.0 27 163.3 157.7 87 206.5 199.4 48 34.5 33.3 08 77.7 75.0 68 120.8 116.7 28 164.0 158.4 88 207.2 200.1 49 35.2 34.0 09 78.4 75.7 69 121.6 117.4 29 164.7 159.1 89 207.9 200.8 50 36.0 34.7 10 79.1 76.4 70 122.3 118.1 30 165.4 159.8 90 208.6 201.5 51 36.7 35.4 111 79.8 77.1 171 123.0 118.8 231 166.2 160.5 291 209.3 202.1 52 37.4 36.1 12 80.6 77.8 72 123.7 119.5 32 166.9 161.2 92 210.0 202.8 53 38.1 36.8 13 81.3 78.5 73 124.4 120.2 33 167.6 161.9 93 210.8 203.5 54 38.8 37.5 14 82.0 79.2 74 125.2 120.9 34 168.3 162.6 94 211.5 204.2 55 39.6 38.2 15 82.7 79.9 75 125.9 121.6 35 169.0 163.2 95 212.2 204.9 56 40.3 38.9 16 83.4 80.6 76 126.6 122.3 36 169.8 163.9 96 212.9 205.6 57 41.0 39.6 17 84.2 81.3 77 127.3 123.0 37 170.5 164.6 97 213.6 206.3 58 41.7 40.3 18 84.9 82.0 78 128.0 123.6 38 171.2 165.3 98 214.4 207.0 59 42.4 41.0 19 85.6 82.7 79" 128.8 124.3 39 171.9 166.0 99 215.1 207.7 60 43.2 41.7 20 86.3 83.4 80 129.5 125.0 40 172.6 166.7 300 215.8 208.4 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. I 16° (1 34°, 226°, 314° )• TABLE 2. [Page 455 Difference of Latitude and Departure for 44° (136°, 224°, 316<= ). Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 216.5 209.1 361 259.7 250.8 421 302.8 292.5 481 346.0 334.1 541 389.2 375.8 02 217.2 209.8 62 260.4 251.5 22 303.6 293.2 82 346.7 334.8 42 389.9 376.5 03 218.0 210.5 63 261.1 252.2 23 304.3 293.8 83 347.4 335.5 43 390.6 377.2 04 218.7 211.2 64 261.8 252.9 24 305.0 294.5 84 348.2 336.2 44 391.3 377.9 05 219. 4 211.9 65 262.6 253.6 25 305.7 295.2 85 348.9 336.9 45 392.0 378.6 06 220.1 212.6 66 263.3 254.3 26 306.4 295.9 86 349. 6 337.6 46 392.8 379.3 07 220.8 213.3 67 264.0 254.9 27 307.2 296.6 87 350.3 338.3 47 393.5 380.0 08 221.6 214.0 68 264.7 255.6 28 307.9 297.3 88 351.0 339.0 48 394.2 380.7 09 222.3 214.7 69 265.4 256.3 29 308.6 298.0 89 351.7 339.7 49 394.9 381.4 10 223.0 223.7 215.4 216.0 70 266.2 257.0 30 431 309.3 310.0 298.7 90 491 352.5 340.4 50 395.6 382.1 311 371 266.9 257.7 299.4 353.2 341.1 551 396.4 382.7 12 224.4 216.7 72 267.6 258.4 32 310.8 300.1 92 353.9 341.8 52 397.1 383.4 13 225.2 217.4 73 268.3 259.1 33 311. 5 300.8 93 354.6 342.5 53 397.8 384.1 14 225.9 218.1 74 269.0 259.8 34 312.2 301.5 94 355.3 343.2 54 398.5 384.8 15 226.6 218.8 75 269.8 260.5 35 312.9 302.2 95 356.1 343.9 55 399.2 385.5 16 227.3 219.5 76 270.5 261.2 36 313.6 302.9 96 356.8 344.6 56 400.0 386.2 17 228.0 220.2 77 271.2 261.9 37 314.4 303. 6 97 357.5 345.2 57 400.7 386.9 18 228.8 220.9 78 271.9 262.6 38 315.1 304.3 98 358.2 345.9 58 401.4 387.6 19 229.5 221.6 79 272.6 263.3 39 315.8 305.0 99 358.9 346. 6 59 402.1 388.3 20 230.2 222.3 80 273.4 264.0 40 316.5 305.7 500 359.7 347.3 60 402.8 389.0 321 230.9 223. 381 274.1 264.7 441 317.2 306.4 501 360.4 348.0 561 403.6 389.7 22 231.6 223.7 82 274.8 265.4 42 318.0 307.0 02 361.1 348.7 62 404.3 390.4 23 232. 3 224.4 83 275.5 266.1 43 318.7 307.7 03 361.8 349.4 63 405.0 391.1 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 86 277.7 268.1 46 320.8 309.8 06 364.0 351.5 66 407.2 393.2 27 235.2 227.2 87 278.4 268.8 47 321.5 310.5 07 364.7 352.2 67 407.9 393.9 28 235.9 227.9 88 279.1 269.5 48 322.3 311.2 08 365.4 352.9 68 408.6 394.6 29 236.7 228.6 89 279.8 270.2 49 323.0 311.9 09 366.1 353.6 69 409.3 395.3 30 237. 4 229.2 90 280.5 270.9 50 323.7 312.6 10 366.9 354.3 70 410.0 396.0 331 238.1 229.9 391 281.3 271.6 451 324.4 313.3 511 367.6 355.0 571 410.7 396.7 32 238.8 230.6 92 282.0 272.3 52 325.2 314.0 12 368.3 355.7 72 411.5 397.3 33 239.5 231.3 93 282.7 273.0 53 325.9 314.7 13 369.0 356.4 73 412.2 398.0 34 240.3 232.0 94 283.4 273.7 54 326.6 315.4 14 369.7 357.1 74 412.9 398.7 35 241.0 232.7 95 284.1 274.4 55 327.3 316.1 15 370.5 357.8 75 413.6 399.4 36 241.7 233.4 96 284.9 275.1 56 328.0 316.8 16 371.2 358.4 76 414.3 400.1 37 242.4 234.1 97 285.6 275.8 57 328.7 317.5 17 371.9 359.1 77 415.1 400.8 38 243.1 234.8 98 286.3 276.5 58 329.5 318.2 18 372.6 359.8 78 415.8 401.5 39 243.9 235.5 99 287.0 277.2 59 330.2 318.9 19 373.3 360.5 79 416.5 402.2 40 341 244.6 236. 2 400 287.7 277.9 60 330.9 319.6 20 374.1 361.2 80 417.2 402.9 245.3 236.9 401 288.5 278.6 461 331.6 320.2 521 374.8 361.9 581 417.9 403.6 42 246.0 237.6 02 289.2 279.3 62 332.3 320.9 22 375.5 362.6 82 418.7 404.3 43 246.7 238.3 03 289.9 280.0 63 333.1 321.6 23 376.2 363.3 83 419.4 405.0 44 247.5 239.0 04 290.6 280.7 64 333.8 322.3 24 376.9 364.0 84 420.1 405.7 45 248.2 239.7 05 291.3 281.3 65 334.5 323.0 25 377.7 364.7 85 420.8 406.4 46 248.9 240.4 06 292.1 282.0 66 335.2 323.7 26 378.4 365.4 86 421.5 407.1 47 249.6 241.1 07 292.8 282.7 67 335.9 324.4 27 379.1 366.1 87 422.3 407.8 48 250.3 241.7 08 293.5 283.4 68 336.7 325.1 28 379.8 366.8 88 423.0 408.5 49 251.1 242.4 09 294.2 284.1 69 337.4 325.8 29 380.5 367.5 89 423.7 409.1 50 251.8 243.1 10 294.9 284.8 70 338.1 326.5 30 381.2 368.2 90 424.4 409.9 351 252.5 243.8 411 295.7 285.5 471 338.8 327.2 531 382.0 368.9 591 425.1 410.5 52 253.2 244.5 12 296.4 286.2 72 339.5 327.9 32 382.7 369.6 92 425.9 411.2 53 253.9 245.2 13 297.1 286.9 73 340.3 328.6 33 383.4 370.3 93 426.6 411.9 54 254.6 245.9 14 297.8 287.6 74 341.0 329.3 34 384.1 371.0 94 427.3 412.6 55 255.4 246.6 15 298.5 288.3 75 341.7 330.0 35 384.8 371.7 95 428.0 413.3 56 256.1 247.3 16 299.2 289.0 76 342.4 330.7 36 385.6 372.4 96 428.7 414.0 57 256.8 248.0 17 300.0 289.7 77 343.1 331.4 37 386.3 373.1 97 429.5 414.7 58 257.5 248.7 18 300.7 290.4 78 343.8 332.1 38 387.0 373.7 98 430.2 415.4 59 258.2 249.4 19 301.4 291.1 79 344.6 332.7 39 387.7 374.4 99 430.9 416.1 60 259.0 250.1 20 302.1 291.8 80 345.3 333.4 40 388.4 375.1 600 431.6 416.8 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 4 6° (IJ J4°, 226°, 314° ). 1 Page 456J TABLE 2. Difference of Latitude and Departure for 45° (135°, 22S °, 315° )• Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 0.7 0.7 61 43.1 43.1 121 85.6 85.6 181 128.0 128.0 241 170.4 170.4 2 1.4 1.4 62 43.8 43.8 22 86.3 86.3 82 128.7 128.7 42 171.1 171.1 3 2.1 2.1 63 44.5 44.5 23 87.0 87.0 83 129.4 129.4 43 171.8 171.8 4 2.8 2.8 64 45.3 45.3 24 87.7 87.7 84 130.1 130.1 44 172.5 172.5 5 3.5 3.5 65 46.0 46.0 25 88.4 88.4 85 130.8 130.8 45 173.2 173.2 6 4.2 4.2 66 46.7 46.7 26 89.1 89.1 86 131.5 131.5 46 173.9 173.9 7 4.9 4.9 67 47.4 47.4 27 89.8 89.8 87 132.2 132.2 47 174.7 174.7 8 5.7 5.7 68 48.1 48.1 28 90.5 90.5 88 132.9 132.9 48 175.4 175.4 9 6.4 6.4 69 48.8 48.8 29 91.2 91.2 89 133.6 133.6 49 176.1 176. 1 10 7.1 7.1 70 49.5 49.5 30 91.9 91.9 90 191 134.4 134.4 135.1 50 251 176. 8 176.8 11 7.8 7.8 71 50.2 50.2 131 92.6 92.6 135.1 177.5 177.5 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 14.8 14.1 80 56.6 56.6 40 99.0 99.0 200 141.4 142.1 141.4 142. 1 60 183.8 184.6 183.8 21 14.8 81 57.3 57.3 141 99.7 99.7 201 261 184.6 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 05 145.0 145.0 65 187.4 187.4 26 18.4 18.4 86 60.8 60.8 46 103.2 103.2 06 145.7 145.7 66 188.1 188.1 27 19.1 19.1 87 61.5 61.5 47 103.9 103.9 07 146.4 146.4 67 188.8 188.8 28 19.8 19.8 88 62.2 62.2 48 104.7 104.7 08 147.1 147.1 68 189.5 189.5 29 20.5 20.5 89 62.9 62.9 49 105.4 105.4 09 147.8 147.8 69 190.2 190.2 30 21.2 21.2 90 63.6 64.3 63.6 50 106.1 106.1 10 148.5 148.5 70 190.9 190.9 31 21.9 21.9 91 64.3 151 106.8 106.8 211 149.2 149.2 271 191.6 191.6 32 22.6 22.6 92 65.1 65.1 52 107.5 107.5 12 149.9 149.9 72 192.3 192.3 33 23.3 23.3 93 65.8 65.8 53 108.2 108.2 13 150.6 150.6 73 193.0 193.0 34 24.0 24.0 94 66.5 66.5 54 108.9 108.9 14 151.3 151.3 74 193.7 193.7 35 24.7 24.7 95 67.2 67.2 55 109.6 109.6 15 152.0 152.0 75 194.5 -194. 5 36 25.5 25.5 96 67.9 67.9 56 110.3 110.3 16 152.7 152.7 76 195.2 195.2 37 26.2 26.2 97 68.6 68.6 57 111.0 111.0 17 153.4 153.4 77 195.9 195.9 38 26.9 26.9 98 69.3 69.3 58 111.7 111.7 18 154.1 154.1 78 196.6 196.6 39 27.6 27.6 99 70.0 70.0 59 112. 4 112.4 19 154.9 154.9 79 197.3 197.3 40 28.3 28.3 100 70.7 70.7 60 113.1 113.1 20 155.6 155.6 80 198.0 198.0 41 29.0 29.0 101 71.4 71.4 161 113.8 113.8 221 156.3 156.3 281 198.7 198.7 42 29.7 29.7 02 72.1 72.1 62 114.6 114.6 22 157.0 157.0 82 199.4 199.4 43 30.4 30.4 03 72.8 72.8 63 115.3 115.3 23 157.7 157.7 83 200.1 200.1 44 31.1 31.1 04 73.5 73.5 64 116.0 116.0 24 158.4 158.4 84 200.8 200.8 45 31.8 31.8 05 74.2 74.2 65 116.7 116.7 25 159. 1 159.1 85 201.5 201. 5 46 32.5 32.5 06 75.0 75.0 66 117.4 117.4 26 159.8 159.8 86 202.2 202.2 47 33.2 33.2 07 75.7 75.7 67 118.1 118.1 27 160.5 160.5 87 202.9 202.9 48 33.9 33.9 08 76.4 76.4 68 118.8 118.8 28 161.2 161.2 88 203.6 203.6 49 34.6 34.6 09 77.1 77.1 69 119.5 119.5 29 161.9 161.9 89 204.4 204.4 50 35.4 35.4 10 77.8 77.8 70 120.2 120.2 30 162.6 162.6 90 205.1 205.1 51 36.1 36.1 HI 78.5 78.5 171 120.9 120.9 231 163.3 163.3 291 205.8 205.8 52 36.8 36.8 12 79.2 79.2 72 121.6 121.6 32 164.0 164.0 92 206.5 206.5 53 37.5 37.5 13 79.9 79.9 73 122.3 122.3 33 164.8 164.8 93 207.2 207.2 54 ' 38.2 38.2 14 80.6 80.6 74 123.0 123.0 34 165.5 165.5 94 207.9 207. f 55 38.9 38.9 15 81.3 81.3 75 123.7 123.7 35 166.2 166.2 95 208.6 208.0 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. i, 15° (1 35°, 225 °, 315° )• TABLE 2. [Page 457 Difference of Latitude and Departure for 45° (135°, 225°, 315' ')• Dist. Lat. Dep. Dist. 361 Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 212.8 212.8 255.3 255.3 421 297.7 297.7 481 340.1 340.1 541 382.5 382.5 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 88 345.1 345.1 48 387.5 387.5 09 218.5 218.5 69 260.9 260.9 29 303.4 303.4 89 345.8 345.8 49 388.2 388.2 10 219.2 219.2 70 261.6 261.6 30 304.1 304.1 90 346.5 346.5 50 388.9 388.9 311 219.9 219.9 371 262.3 262.3 431 304.8 304.8 491 347.2 347.2 551 389.6 389. 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 79 268.0 268.0 39 310.4 310.4 99 352.8 352.8 59 395.3 395.3 20 226.3 226.3 80 268.7 268.7 40 311.1 311.1 500 353.5 353.5 60 396.0 396.0 321 227.0 227.0 381 269.4 269.4 441 311.8 311.8 501 354.3 354.3 561 396.7 396.7 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 64 398.8 398.8 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 30 331 233.3 233.3 90 275.8 275.8 50 318.2 318.2 10 360.6 360.6 70 403.0 403.0 234.1 234.1 391 276.5 276.5 451 318.9 318.9 511 361.3 361.3 571 403.8 403.8 32 234.8 234.8 92 277.2 277.2 52 319.6 319.6 12 362.0 362.0 72 404.5 404.5 33 235. 5 235.5 93 277.9 277.9 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 19 367.0 367.0 79 409.4 409.4 40 240.4 240.4 400 282.8 282.8 60 325.3 325.3 20 367.7 367.7 80 410.1 410.1 341 241.1 241.1 401 283.6 283.6 461 326.0 326.0 521 368.4 368.4 581 410.8 410.8 42 241.8 241.8 02 284.3 284.3 62 326.7 326.7 22 369.1 369.1 82 411.5 411.5 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 25 371.2 371.2 85 413.7 413.7 46 244.7 244.7 06 287.1 287.1 66 329.5 329.5 26 371.9 371.9 86 414.4 414.4 47 245.4 245.4 07 287.8 287.8 67 330.2 330.2 27 372.6 372.6 87 415.1 415.1 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 50 351 247.5 248.2 247.5 10 289.9 289.9 70 332.3 332.3 30 374.8 374.8 90 417.2 417.2 248.2 411 290.6 290.6 471 333.1 333.1 531 375.5 375.5 591 417.9 417.9 52 248.9 248.9 12 291.3 291.3 72 333.8 333.8 32 376.2 376. 2 92 418.6 418.6 53 249.6 249.6 13 292.0 292.0 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 39 381.1 381.1 99 423.6 423.6 60 254.6 254.6 20 297.0 297.0 80 339.4 339.4 40 381.8 381.8 600 424.3 424.3 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 45° (135°, 225°, 315 '). 1 Page 458] TABLE 3. Meridional Parts, or Increased Latitudes. • Comp 1 • 293.465 M. 0° 1° 2° 8° 4° 6° 6° 7° 8° 9° M. 0.0 59.6 119.2 178.9 238.6 298.3 358.2 418.2 478.3 538.6 1 1.0 60.6 20.2 79.9 39.6 99.3 59.2 19.2 79.3 39.6 1 2 2.0 61.6 21.2 80.8 40.6 300.3 60.2 20.2 80.3 40.6 2 3 3.0 62.6 22.2 81.8 41.6 01.3 61.2 21.2 81.3 41.6 3 4 4.0 63.6 23.2 82.8 42.5 02.3 62.2 22.2 82.3 42.6 4 5 5.0 64.6 124.2 183.8 243.5 303.3 363.2 423.2 483.3 543.6 5 6 6.0 65.6 25.2 84.8 ' 44.5 04.3 64.2 24.2 84.3 44.6 6 7 7.0 66.6 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 14.9 74.5 134.1 193.8 253.5 313.3 373.2 433.2 493.4 553.7 15 16 15.9 75.5 35.1 94.8 54.5 14.3 74.2 34.2 94.4 54.7 16 17 16.9 76.5 36.1 95.8 55.5 15.3 75.2 35.2 95.4 55.7 17 18 17.9 77.5 37.1 96.8 56.5 16.3 76.2 36.2 96.4 56.7 18 19 18.9 78.5 38.1 97.8 57.5 17.3 77.2 37.2 97.4 57.7 19 20 19.9 79.5 139.1 198.8 258.5 318.3 378.2 438.2 498.4 558.7 20 21 20.9 80.5 40.1 99.7 59.5 19.3 79.2 39.2 99.4 59.7 21 22 21.9 81.5 41.1 200.7 60.5 20.3 80.2 40.2 500.4 60.7 22 23 22.8 82.4 42.1 01.7 61.5 21.3 81.2 41.2 01.4 61.7 23 24 23.8 83.4 43.1 02.7 62.5 22.3 82.2 42.2 02.4 62.7 24 25 24.8 84.4 144.1 203.7 263.5 323.3 383.2 443.2 503.4 563.7 25 26 25.8 85.4 45.1 04.7 64.5 24.3 84.2 44.2 04.4 64.7 26 27 26.8 86.4 46.0 05.7 65.5 25.3 85.2 45.2 05.4 65.7 27 28 27.8 87.4 47.0 06.7 66.5 26.3 86.2 46.2 06.4 66.8 28 29 28.8 88.4 48.0 07.7 67.4 27.3 87.2 47.2 07.4 67.8 29 30 29.8 89.4 149.0 208.7 268.4 328.3 388.2 448.2 508.4 568.8 30 31 30.8 90.4 50.0 09.7 69.4 29.3 89.2 49.2 09.4 69.8 31 32 31.8 91.4 51.0 10.7 70.4 30.3 90.2 50.2 10.4 70.8 32 33 32.8 92.4 52.0 11.7 71.4 31.3 91.2 51.2 11.4 71.8 33 34 33.8 93.4 53.0 12.7 72.4 32.3 92.2 52.2 12.4 72.8 34 35 34.8 94.4 154.0 213.7 273.4 333.3 393.2 453.2 513.4 573.8 35 36 35.8 95.4 55.0 14.7 74.4 34.3 94.2 54.3 14.5 74.8 36 37 36.7 96.4 56.0 15.7 75.4 35.3 95.2 55.3 15.5 75.8 37 38 37.7 97.3 57.0 16.7 76.4 36.2 96.2 56.3 16.5 76.8 38 39 38.7 98.3 58.0 17.7 77.4 37.2 97.2 57.3 17.5 77.8 39 40 39.7 99.3 159.0 218.7 278.4 338.2 398.2 458.3 518.5 578.8 40 41 40.7 100.3 60.0 19.7 79.4 39.2 99.2 59.3 19.5 79.9 41 42 41.7 01.3 61.0 20.6 80.4 40.2 400.2 60.3 20.5 80.9 42 43 42.7 02.3 62.0 21.6 81.4 41.2 01.2 61.3 21.5 81.9 43 44 43.7 03.3 63.0 22.6 82.4 42.2 02.2 62.3 22.5 82.9 44 45 44.7 104.3 164.0 223.6 283.4 343.2 403.2 463.3 523.5 583.9 45 46 45.7 05.3 65.0 24.6 84.4 44.2 04.2 64.3 24.5 84.9 46 47 46.7 06.3 66.0 25.6 85.4 45.2 05.2 65.3 25.5 85.9 47 48 47.7 07.3 67.0 26.6 86.4 46.2 06.2 66.3 26.5 86.9 48 49 48.7 08.3 68.0 27.6 87.4 47.2 07.2 67.3 27.5 87.9 49 50 49.7 109.3 168.9 228.6 288.4 348.2 408.2 468.3 528.5 588.9 50 51 50.7 10.3 69.9 29.6 89.4 49.2 09.2 69.3 29.5 89.9 51 52 51.6 11.3 70.9 30.6 90.4 50.2 10.2 70.3 30.5 90.9 52 53 52.6 12.3 71.9 31.6 91.4 51.2 11.2 71.3 31.5 91.9 53 54 53.6 13.2 72.9 32.6 92.4 52.2 12.2 72.3 32.5 93.0 54 55 54.6 114.2 173.9 233.6 293.4 353.2 413.2 473.3 533.5 594.0 55 56 55.6 15.2 74.9 34.6 94.4 54.2 14.2 74.3 34.6 95.0 56 57 56.6 16.2 75.9 35.6 95.4 55.2 15.2 75.3 35.6 96.0 57 58 57.6 17.2 76.9 36.6 96.3 56.2 16.2 76.3 36.6 97.0 58 59 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° 6° 6° 7° 8° 9° M. TABLE 3. [Page 459 | Meridional Parts, or Increased Latitudes. Comp 1 * 293.466 M. 10° 11° 12° 18° 14° 16° 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 1 600.0 60.6 21.5 82.5 43.9 05.4 67.3 29.5 92.0 54.9 1 2 01.0 61.7 22.5 83.6 44.9 06.5 68.3 30.5 93.1 56.0 2 3 02.0 62.7 23.5 84.6 45.9 07.5 69.4 31.6 94.1 57.0 3 4 03.0 63.7 24.5 85.6 46.9 08.5 70.4 32.6 95.2 58.1 4 5 604.1 664.7 725.5 786.6 847.9 909.6 971.4 1033. 7 1096.2 1159. 1 5 6 05.1 65.7 26.6 87.6 49.0 10.6 72.5 34.7 97.3 60.2 6 7 06.1 66.7 27.6 88.7 50-0 11.6 73.5 35.7 98.3 61.2 7 8 07.1 67.7 28.6 89.7 51.0 12.6 74.6 36.8 99.4 62.3 8 9 08.1 68.7 29.6 90.7 52.0 13.7 75.6 37.8 1100.4 63.3 9 10 609.1 669.8 730.6 791.7 853.1 914.7 976.6 1038. 9 1101. 4 1164.4 10 11 10.1 70.8 31.6 92.7 54.1 15.7 77.7 39.9 02.5 65.4 11 12 11.1 71.8 32.7 93.8 55.1 16.8 78.7 40.9 03.5 66.5 12 13 12.1 72.8 33.7 94.8 56.1 17.8 79.7 42.0 04.6 67.5 13 14 13.1 73.8 34.7 95.8 57.2 18.8 80.8 43.0 05.6 68.6 14 15 614.1 674.8 735.7 796.8 858.2 919.8 981.8 1044.1 1106.7 1169. 7 15 16 15.2 75.8 36.7 97.8 59.2 20.9 82.8 45.1 07.7 70.7 16 17 16.2 76.8 37.7 98.9 60.2 21.9 83.9 46.1 08.8 71.8 17 18 17.2 77.9 38.8 99.9 61.3 22.9 84.9 47.2 09.8 72.8 18 19 18.2 78.9 39.8 800.9 62.3 24.0 85.9 48.2 10.9 73.9 19 20 619.2 679.9 740.8 801.9 863.3 925.0 987.0 1049.3 1111.9 1174. 9 20 21 20.2 80.9 41.8 02.9 64.3 26.0 88.0 50.3 13.0 76.0 21 22 21.2 81.9 42.8 04.0 65.4 27.1 89.0 51.3 14.0 77.0 22 23 22.2 82.9 43.8 05.0 66.4 28.1 90.1 52.4 15.0 78.1 23 24 23.2 83.9 44.9 06.0 67.4 29.1 91.1 53.4 16.1 79.1 24 25 624.2 684.9 745.9 807.0 868.5 930.1 992.1 1054. 5 1117. 1 1180. 2 25 26 25.3 86.0 46.9 08.1 69.5 31.2 93.2 55.5 18.2 81.2 26 27 26.3 87.0 47.9 09.1 70.5 32.2 94.2 56.6 19.2 82.3 27 28 27.3 88.0 48.9 10.1 71.5 33.2 95.3 57.6 20.3 83.3 28 29 28.3 89.0 49.9 11.1 72.6 34.3 96.3 58.6 21.3 84.4 29 30 629.3 690.0 751.0 812.1 873.6 935.3 997.3 1059. 7 1122. 4 1185.5 30 31 30.3 91.0 52.0 .13.2 74.6 36.3 98.4 60.7 23.4 86.5 31 32 31.3 92.0 53.0 14.2 75.6 37.4 99.4 61.8 24.5 87.6 32 33 32.3 93.1 54.0 15.2 76.7 38.4 1000.4 62.8 25.5 88.6 33 34 33.3 94.1 55.0 16.2 77.7 39.4 01.5 63.9 26.6 89.7 34 35 634.3 695.1 756.0 817.3 878.7 940.5 1002.5 1064.9 1127. 6 1190.7 35 36 35.4 96.1 57.1 18.3 79.7 41.5 03.6 65.9 28.7 91.8 36 37 36.4 97.1 58.1 19.3 80.8 42.5 04.6 67.0 29.7 92.8 37 38 37.4 98.1 59.1 20.3 81.8 43.6 05.6 68.0 30.8 93.9 38 39 38.4 99.1 60.1 21.3 82.8 44.6 06.7 69.1 31.8 95.0 39 40 639.4 700.2 761.1 822.4 883.8 945.6 1007.7 1070. 1 1132. 9 1196. 40 41 40.4 01.2 62.2 23.4 84.9 46.7 08.7 71.2 33. 9 97.1 41 42 41.4 02.2 63.2 24.4 85.9 47.7 09.8 72.2 35.0 98.1 42 43 42.4 03.2 64.2 25.4 86.9 48.7 10.8 73.2 36.0 99.2 43 44 43.4 04.2 65.2 26.5 88.0 49.7 11.8 74.3 37.1 1200.2 44 45 644.5 705.2 766.2 827.5 889.0 950.8 1012. 9 1075. 3 1138. 1 1201.3 45 46 45.5 06.2 67.3 28.5 90.0 51.8 13.9 76.4 39.2 02.3 46 47 46.5 07.3 68.3 29.5 91.0 52.8 15.0 77.4 40.2 03.4 47 48 47.5 08.3 69.3 30.5 92.1 53.9 16.0 78.5 41.3 04.5 48 49 48.5 09.3 70.3 31.6 93.1 54.9 17.0 79.5 42.3 05.5 49 50 649.5 710.3 771.3 832.6 894.1 955.9 1018. 1 1080. 5 1143. 4 1206.6 50 51 50.5 11.3 72.3 33.6 95.2 57.0 19.1 81.6 44.4 07.6 51 52 51.5 12.3 73.4 34.6 96.2 58.0 20.2 82.6 45.5 08.7 52 53 52.5 13.4 74.4 35.7 97.2 59.0 21.2 83.7 46.5 09.7 53 54 53.6 14.4 75.4 36.7 98.2 60.1 22.2 84.7 47.6 10.8 54 55 654.6 715.4 776.4 837.7 899.3 961.1 1023. 3 1085. 8 1148. 6 1211.8 55 56 55.6 16.4 77.4 38.7 900.3 62.1 24.3 86.8 49.7 12.9 56 57 56.6 17.4 78.5 39.8 01.3 63.2 25.3 87.9 50.7 14.0 57 58 57.6 18.4 79.5 40.8 02.3 64.2 26.4 88.9 51.8 15.0 58 59 58.6 19.4 80.5 41.8 03.4 65.2 27.4 89.9 52.8 16.1 69 M. 10° 11° 12° 18° 14° 15° 16° 17° 18° 19° M. Pag •e 460] TABLE 3. Meridional Parts, or Increased Latitudes. Comp 1 293.465 M. 20° 21° 22° 28° 24° 25° 26° 27° 28° 29° M. 1217. 1 1280. 8 1344.9 1409. 5 1474. 5 1540. 1 1606. 2 1672. 9 1740. 2 1808. 1 1 .18.2 81.9 46.0 10.6 75.6 41.2 07.3 74.0 41.3 09.2 1 2 19.3 82.9 47.1 11.6 76.7 42.3 08.4 75.1 42.4 10.4 2 3 20.3 84.0 48.1 12.7 77.8 43.4 09.5 76.2 43.6 11.5 3 4 21.4 85.1 49.2 13.8 78.9 44.5 10.6 77.4 44.7 12.6 4 5 1222. 4 1286. 1 1350. 3 1414. 9 1480. 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 90.8 58.2 26.3 16 17 35.1 98.9 63.2 27.9 93.1 58.8 25.0 91.9 59.4 27.5 17 18 36.2 1300.0 64.2 29.0 94.2 59.9 26.2 93.0 60.5 28.6 18 19 37.3 01.1 65.3 30.0 95.2 61.0 27.3 94.1 61.6 29.7 19 20 1238. 3 1302. 1 1366. 4 1431. 1 1496. 3 1562. 1 1628. 4 1695. 3 1762. 7 1830. 9 20 21 39.4 03.2 67.5 32.2 97.4 63.2 29.5 96.4 63.9 32.0 21 22 40.4 04.3 68.5 33.3 98.5 64.3 30.6 97.5 65.0 33.2 22 23 41.5 05.3 69.6 34.4 99.6 65.4 31.7 98.6 66.1 34.3 23 24 42.6 06.4 70.7 35.4 1500.7 66.5 32.8 99.7 67.3 35.4 24 25 1243. 6 1307. 5 1371. 8 1436. 5 1501. 8 1567. 6 1633. 9 1700.9 1768. 4 1836. 6 25 26 44.7 08.5 72.8 37.6 02.9 68.7 35.0 02.0 69.5 37.7 26 27 45.7 09.6 73.9 38.7 04.0 69.8 36.1 03.1 70.7 38.9 27 28 46.8 10.7 75.0 39.8 05.1 70.9 37.3 04.2 71.8 40.0 28 29 47.9 11.7 76.1 40.9 06.2 72.0 38.4 05.3 72.9 41.2 29 30 1248. 9 1312. 8 1377. 1 1442.0 1507. 3 1573. 1 1639. 5 1706.5 1774. 1 1842.3 30 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. 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 1786.4 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 55 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 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° 25° 26° 27° 28° 29° M. TABLE 3. [Page 461 | Meridional Parts, or Increased Latitudes. Comp. 1 293.465 • M. 30° 81° 82° 88° 34° 86° 86° 87° 88° 89° M, 1876. 7 1946. 2016. 2086. 8 2158. 4 2230. 9 2304.2 2378. 5 2453.8 2530. 2 1 77.8 47.1 17.2 88.0 59.6 32.1 05.5 79.8 55.1 31.5 1 2 79.0 48.3 18.3 89.2 60.8 33.3 06.7 81.0 56.4 32.8 2 3 80.1 49.4 19.5 90.3 62.0 34.5 07.9 82.3 57.6 34.0 3 4 81.3 50.6 20.7 91.5 63.2 35.7 09.2 83.5 58.9 35.3 4 5 1882. 4 1951. 8 2021.9 2092. 7 2164.4 2236. 9 2310. 4 2384. 8 2460. 2 2536. 6 5 6 83.6 52.9 23.0 93.9 65.6 38.2 11.6 86.0 61.4 37.9 6 7 84.7 54.1 24.2 95.1 66.8 39.4 12.9 87.3 62.7 39.2 7 8 85.9 55.3 25.4 96.3 68.0 40.6 14.1 88.5 64.0 40.5 8 9 87.0 56.4 26.6 97.5 69.2 41.8 15.3 89:8 65.2 41.7 9 10 1888. 2 1957. 6 2027. 7 2098. 7 2170. 4 2243. 2316. 5 2391. 2466. 5 2543. 10 11 89.3 58.7 28.9 99.8 71.6 44.2 17.8 92.3 67.8 44.3 11 12 90.5 59.9 30.1 2101. 72.8 45.5 19.0 93.5 69.0 45.6 12 13 91.6 61.1 31.3 02.2 74.0 46.7 20.3 94.8 70.3 46.9 13 14 92.8 62.2 32.4 03.4 75.2 47.9 21.5 96.0 71.6 48.2 14 15 1893. 9 1963. 4 2033. 6 2104. 6 2176.4 2249. 1 2322. 7 2397. 3 2472. 8 2549. 5 15 16 95.1 64.6 34.8 05.8 77.6 50.3 24.0 98.5 74.1 50.7 16 17 96.2 65.7 36.0 07.0 78.8 51.6 25.2 99.8 75.4 52.0 17 18 97.4 66.9 37.1 08.2 80.0 52.8 26.4 2401.0 76.6 53.3 18 19 98.5 68.1 38.3 09.4 81.2 54.0 27.7 02.3 77.9 54.6 19 20 1899. 7 1969. 2 2039. 5 2110. 6 2182. 5 2255. 2 2328. 9 2403.5 2479. 2 2555. 9 20 21 1900.8 70.4 40.7 11.8 83.7 56.4 30.1 04.8 80.4 57.2 21 22 02.0 71.5 41.8 12.9 84.9 57.7 31.4 06.0 81.7 58.5 22 23 03.1 72.7 43.0 14.1 86.1 58.9 32.6 07.3 83.0 59.8 23 24 04.3 73.9 44.2 15.3 87,3 60.1 33.8 08.5 84.3 61.0 24 25 1905. 5 1975. 2045. 4 2116.5 2188. 5 2261. 3 2335. 1 2409. 8 2485. 5 2562. 3 25 26 06.6 76.2 46.6 17.7 89.7 62.5 36.3 11.1 86.8 63.6 26 27 07.8 77.4 47.7 18.9 90.9 63.8 37.6 12.3 88.1 64.9 27 28 08.9 78.5 48.9 20.1 92.1 65.0 38.8 13.6 89,3 66.2 28 29 10.1 79.7 50.1 21.3 93.3 66.2 40.0 14.8 90.6 67.5 29 30 1911.2 1980. 9 2051. 3 2122. 5 2194. 5 2267. 4 2341. 3 2416. 1 2491. 9 2568. 8 30 31 12.4 82.0 52.5 23.7 95.7 68.7 42.5 17.3 93.2 70.1 31 32 13.5 83.2 53.6 24.9 96.9 69.9 43.7 18.6 94.4 71.4 32 33 14.7 84.4 54.8 26.1 98.1 71.1 45.0 19.8 95.7 72.7 33 34 15.8 85.5 56.0 27.3 99.4 72.3 46.2 21.1 97.0 73.9 34 35 1917. 1986. 7 2057. 2 2128. 5 2200. 6 2273. 5 2347. 5 2422. 3 2498. 3 2575. 2 35 36 18.2 87.9 58.4 29.6 01.8 74.8 48.7 23.6 99.5 76.5 36 37 19.3 89.1 59.5 30.8 03.0 76.0 49.9 24.9 2500.8 77.8 37 38 20.5 90.2 60.7 32.0 04.2 77.2 51.2 26.1 02.1 79.1 38 39 21.6 •91.4 61.9 33.2 05.4 78.4 52.4 27.4 03.4 80.4 39 40 1922. 8 1992. 6 2063. 1 2134. 4 2206. 6 2279. 7 2353.7 2428. 6 2504. 6 2581. 7 40 41 23.9 93.7 64.3 35.6 07.8 80.9 54.9 29.9 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.?" 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 2074. 9 45.2 17.5 90.7 64.8 40.0 16.1 93.4 49 50 1934. 4 2004. 3 2146. 4 2218. 7 2291. 9 2366. 1 2441.2 2517. 4 2594. 7 50 51 35.5 05.4 76.1 47.6 19.9 93.2 67.3 42.5 18.7 96.0 51 52 36.7 06.6 77.3 48.8 21.1 94.4 68.6 43.7 20.0 97.3 52 53 37.8 07.8 78.5 50.0 22.4 95.6 69.8 45.0 21.2 98.5 53 54 39.0 08.9 79.7 51.2 23.6 96.9 71.1 46.3 2447.5 22.5 99.8 54 55 1940. 2 2010. 1 2080. 8 2152. 4 2224. 8 2298. 1 2372. 3 2523. 8 2601.1 55 56 41.3 11.3 82.0 53.6 26.0 99.3 73.6 48.8 25.1 02.4 56 57 42.5 12.5 83.2 54.8 27.2 2300.5 74.8 50.1 26.4 03.7 57 58 43.6 13.6 . 84.4 56.0 28.4 01.8 76.1 51.3 27.6 05.0 58 59 44.8 14.8 85.6 57.2 29.6 03.0 77.3 52.3 28.9 06.3 59 M. 30° 81° 82° 88° 84° 86° 86° 87° 88° 89° M. Page 462] TABLE 3. Meridional Parts, or Increased Latitudes. Comp 1 293.465 M. 40° 41° 42° 48° 44° 45° 46° 47° 48° 49° M. 2607. 6 2686. 2 2766. 2847. 1 2929.5 3013. 4 3098.7 3185. 6 3274. 1 3364. 4 1 08.9 87.6 67.4 48.5 30.9 14.8 3100. 1 87.1 75.6 65.9 1 2 10.2 88.9 68.7 49.9 32.3 16.2 01.6 88.5 77.1 67.4 2 3 11.5 90.2 70.1 51.2 33.7 17.6 03.0 90.0 78.6 69.0 3 4 12.8 91.5 71.4 52.6 35.1 19.0 04.4 91.4 80.1 70.5 4 5 2614. 1 2692. 8 2772. 8 2853. 9 2936. 5 3020. 4 3105. 9 3192. 9 3281. 6 3372. 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 95.8 84.6 75.1 7 8 18.1 96.8 76.8 58.0 40.6 24.7 10.2 97.3 86.1 76.6 8 9 19.4 98.1 78.1 59.4 42.0 26.1 11.6 98.8 87.6 78.1 9 10 2620. 7 2699. 5 2779. 5 2860. 8 2943. 4 3027. 5 3113. 1 3200.2 3289. 3379. 6 10 11 22.0 2700. 8 80.8 62.1 44.8 28.9 14.5 01.7 90.5 81.2 11 12 23.3 02.1 82.2 63.5 46.2 30.3 16.0 03.2 92.0 82.7 12 13 24.6 03.4 83.5 64.9 47.6 31.7 17.4 04.6 93.5 84.2 13 14 25.9 04.8 84.8 66.2 49.0 33.2 18.8 06.1 95.0 85.7 14 15 2627. 2 2706. 1 2786. 2 2867. 6 2950. 4 3034. 6 3120. 3 3207. 6 3296. 5 3387. 3 15 16 28.5 07.4 87.5 69.0 51.8 36.0 21.7 09.0 98.0 88.8 16 17 29.8 08.7 88.9 70.3 53.2 37.4 23.2 10.5 99.5 90.3 17 18 31.1 10.1 90.2 71.7 54.5 38.8 24.6 12.0 3301. 91.8 18 19 20 32.4 11.4 91.6 73.1 55.9 40.2 26.0 13.4 02.5 93.4 19 2633. 7 2712. 7 2792. 9 2874. 4 2957. 3 3041. 7 3127. 5 3214. 9 3304. 3394. 9 20 21 35.0 14.0 94.3 75.8 58.7 43.1 28.9 16.4 05.5 96.4 21 22 36.3 15.4 95.6 77.2 60.1 44.5 30.4 17.9 07.0 98.0 22 23 37.6 16.7 97.0 78.6 61.5 45.9 31.8 19.3 08.5 99.5 23 24 38.9 18.0 98.3 79.9 62.9 47.3 33.3 20.8 10.0 3401.0 24 25 2640. 2 2719. 3 2799. 7 2881. 3 2964. 3 3048. 7 3134. 7 3222. 3 3311.5 3402. 6 25 26 41.6 20.7 2801. 82.7 65.7 50.2 36.2 23.7 13.0 04.1 26 27 42.9 22.0 02.4 84.0 67.1 51.6 37.6 25.2 14.5 05.6 27 28 44.2 23.3 03.7 85.4 68.5 53.0 39.0 26.7 16.0 07.2 28 29 45.5 24.7 05.1 86.8 69.9 54.4 40.5 28.2 17.5 08.7 29 30 2646. 8 2726. 2806. 4 2888. 2 2971. 3 3055. 9 3141. 9 3229. 6 3319. 3410. 2 30 31 48.1 27.3 07.8 89.5 72.7 57.3 43.4 31.1 20.5 11.8 31 32 49.4 28.6 09.1 90.9 74.1 58.7 44.8 32.6 22.1 13.3 32 33 50.7 30.0 10.5 92.3 75.5 60.1 46.3 34.1 23.6 14.8 33 34 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 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 ^7.9 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 13.0 96.5 81.5 68.1 56.3 46.2 38.0 48 49 71.7 51.3 32.2 14.3 97.9 82.9 69.5 57.8 47.7 39.5 49 50 2673. 1 2752. 7 2833. 5 2915. 7 2999. 3 3084. 4 3171.0 3259. 3 3349. 2 3441. 50 51 74.4 54.0 34.9 17.1 3000. 7 85.8 72.5 60.7 50.8 42.6 51 52 75.7 55.3 36.2 18.5 02.1 87.2 73.9 62.2 52.3 44.1 52 53 77.0 56.7 37.6 19.9 03.5 88.7 75.4 63.7 53.8 45.7 53 54 78.3 58.0 39.0 21.2 04.9 90.1 76.8 65.2 55.3 47.2 54 55 2679. 6 2759. 3 2840. 3 2922. 6 3006.3 3091. 5 3178. 3 3266. 7 3356. 8 3448. 8 55 56 81.0 60.7 41.7 24.0 07.7 93.0 79.7 68.2 58.3 50.3 56 57 82.3 62.0 43.0 25.4 09.2 94.4 81.2 69.7 59.9 51.9 57 58 83.6 63.4 44.4 26.8 10.6 95.8 82.7 71.; 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° 43° 44° 46° 46° 47° 48° 49° M. TABLE 3. [Page 463 | Meridional Parts, or Increased Latitudes. ^°°^P- 293.465 M. 60° 61° 62° 68° 64° 55° 66° 57° 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. S 74.6 78.5 84.9 94.2 06.6 22.1 17 18 84.5 79.2 76.0 75.0 76.3 80.2 86.7 96.1 08.5 24.1 18 19 86.1 80.8 77.6 76.7 78.1 82.0 88.5 97.9 10.4 26.1 19 20 3487. 7 3582. 4 3679. 3 3778. 3 3879. 8 3983. 7 4090. 3 4199. 8 4312. 3 4428. 20 21 89.2 84.0 80.9 80.0 81.5 85.5 92.1 4201. 6 14.2 30.0 21 22 90.8 85.6 82.5 81.7 83.2 87.2 93.9 03.5 16.1 31.9 22 23 92.4 87.2 84.2 83.3 84.9 89.0 '95.7 05.3 18.0 33.9 23 24 93.9 88.8 85.8 85.0 86.6 90.7 97.5 07.2 19.9 35.8 24 25 3495. 5 3590. 4 3687. 4 3786. 7 3888. 3 3992. 5 4099. 3 4209. 4321. 8 4437. 8 25 26 97.1 92.0 89.1 88.4 90.0 94.3 4101. 1 10.9 23.7 39.8 26 27 98.6 93.6 90.7 90.0 91.8 96.0 02.9 12.8 25.6 41.7 27 28 3500. 2 95.2 92.3 91.7 93.5 97.8 04.8 14.6 27.5 43.7 28 29 01.8 96.8 94.0 93.4 95.2 99.5 06.6 16.5 29.4 45.7 29 30 3503. 3 3598. 4 3695. 6 3795. 1 3896. 9 4001.3 4108. 4 4218. 3 4331. 3 4447. 6 30 31 04.9 3600. 97.3 96.8 98.6 03.1 10.2 20.2 33.2 49.6 31 32 06.5 01.6 98.9 98.4 3900. 4 04.8 12.0 22.0 35.2 51.6 32 33 08.0 03.2 3700. 5 3800. 1 02.1 06.6 13.8 23.9 37.1 53.5 33 34 09.6 04.8 02.2 01.8 03.8 08.3 15.6 25.8 39.0 55.5 34 35 3511. 2 3606. 4 3703. 8 3803. 5 3905. 5 4010. 1 4117.4 4227. 6 4340. 9 4457. 5 35 36 12.7 08.0 05.5 05.1 07.2 11.9 19.2 29.5 42.8 59.4 36 37 14.3 09.6 07.1 06.8 09.0 13.6 21.0 31.3 44.7 61.4 37 38 15.9 11.2 08.7 08.5 10.7 15.4 22.9 33.2 46.6 63.4 38 39 17.5 12.8 10.4 10.2 12.4 17.2 24.7 35.1 48.6 65.4 39 40 3519. 3614. 5 3712. 3811.9 3914. 1 4018. 9 4126. 5 4236. 9 4350. 5 4467. 3 40 41 20.6 16.1 13.7 13.6 15.9 20.7 28.3 38.8 52.4 69.3 41 42 22.2 17.7 15.3 15.2 17.6 22.5 30.1 40.7 54.3 71.3 42 43 23.7 19.3 17.0 17.0 19.3 24.3 31.9 42.5 56.2 73.3 43 44 25.3 20.9 18.6 18.6 21.0 26.0 33.8 44.4 58.2 75.3 44 45 3526. 9 3622. 5 3720. 3 3820. 3 3922. 8 4027. 8 4135. 6 4246. 3 4360. 1 4477.2 45 46 28.5 24.1 21.9 22.0 24.5 29.6 37.4 48.1 62.0 79.2 46 47 30.1 25.7 23.6 23.7 26.2 31.4 39.2 50.0 63.9 81.2 47 48 31.6 27.3 25.2 25.4 28.0 33.1 41.0 51.9 65.9 83.2 48 49 33.2 29.0 26.9 27.1 29.7 34.9 42.9 53.8 67.8 85.2 49 50 3534.-8 3630. 6 3728. 5 3828. 7 3931. 4 4036. 7 4144. 7 4255. 6 4369. 7 4487. 2 50 51 36.4 32.2 30.2 30.4 33.2 38.5 46.5 57.5 71.7 89.1 51 52 37.9 33.8 31.8 32.1 34.9 40.2 48.3 59.4 73.6 91.1 52 53 39.5 35.4 33.5 33.8 36.6 42.0 50.2 61.3 75.5 93.1 53 54 41.1 37.0 35.1 35.5 38.4 43.8 52.0 63.1 77.4 95.1 54 55 3542. 7 3638. 6 3736. 8 3837. 2 3940. 1 4045. 6 4153. 8 4265.0 4379. 4 4497.1 55 56 44.3 40.3 38.4 38.9 41.8 47.4 55.7 66.9 81.3 99.1 56 57 45.9 41.9 40.1 40.6 43.6 49.1 57.5 68.8 83.2 4501. 1 57 58 47.4 43.5 41.7 42.3 45.3 50.9 59.3 70.7 85.2 03.1 58 59 49.0 45.1 43.4 45.0 47.0 52.7 61.1 72.5 87.1 05.1 59 M. 50° 61° 62° 68° 64° 56° 56° 67° 58° 69° M. 1 Page 464] TABLE 3. Meridional Parts, or Increased Latitudes. Comp 1 293.465 M. 60° 61° 62° 68° 64° 66° 66° 67° . 68° 69° M. 4507.1 4628.7 4754. 3 4884. 1 5018. 4 5157. 6 5302. 1 5452. 4 5609.1 5772. 7 1 09.1 30.8 56.4 86.3 20.6 59.9 04.6 55.0 11.8 75.5 1 2 11.1 32.9 58.6 88.5 22.9 62.3 07.0 57.6 14.4 78.3 2 3 13.1 34.9 60.7 90.7 25.2 64.7 09.5 60.1 17.1 81.1 3 4 15.1 37.0 62.8 92.9 27.5 67.0 11.9 62.7 19.8 83.8 4 5 4517. 1 4639. 4764. 9 4895. 1 5029. 8 5169. 4 5314. 4 5465. 2 5622. 4 5786. 6 5 6 19.1 41.1 67.1 97.3 32.1 71.8 16.9 67.8 25.1 89.4 6 7 21.1 43.2 69.2 99.5 34.3 74.2 19.3 70.4 27.8 92.2 7 8 23.1 45.2 71.3 4901. 7 36.6 76.5 21.8 72.9 30.5 95.1 8 9 25.1 47.3 73.5 03.9 38.9 78.9 24.3 75.5 33.2 97.9 9 10 4527. 1 4649.4 4775. 6 4906. 1 5041. 2 5181.3 5326. 7 5477. 1 5635. 9 5800. 7 10 11 29.1 51.5 77.8 08.3 43.5 83.7 29.2 80.7 38.5 03.5 11 12 31.1 53.5 79.9 10.5 45.8 86.0 31.7 83.2 41.2 06.3 12 13 33.1 55.6 82.0 12.8 48.1 88.4 34.2 85.8 43.9 09.1 13 14 35.1 57.7 84.2 15.0 50.4 90.8 36.6 88.4 46.6 11.9 14 , 15 4537. 1 4659. 7 4786. 3 4917. 2 5052. 7 5193. 2 5339. 1 5491.0 5649.3 5814. 7 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. 1 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 06.1 31.0 59.9 93.4 31.7 75.2 24.4 79.9 42.1 11.9 49 50 4608. 2 4733. 1 4862. 1 4995. 6 5134. 5277. 6 5427. 5582. 5 5744.9 5914. 8 50 51 10.2 35.2 64.3 97.9 36.4 80.1 29.5 85.2 47.7 17.7 51 52 12.3 37.3 66.5 5000. 2 38.7 82.5 32.0 87.8 50.4 20.6 52 53 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. 60° 61° 62° 63° 64° 65° 66° 67° 68° 69° M. TABLE 3. [Page 465 | Meridional Parts, or Increased Latitudes. Comp. 1 * 293.465 M. 70° 71° 72° 78° 74° 76° 76° 77° 78° 7»° M. 5943. 9 6123. 5 6312. 5 6512.0 6723. 2 6947. 7 7187. 3 7444.4 7721. 6 8022. 7 1 46.8 26.6 15.8 15.4 26.8 51.6 91.5 48.8 26.4 27.9 1 2 49.7 29.7 19.0 18.9 30.5 55.4 95.6 53.3 31.3 33.2 2 3 52.7 32.8 22.3 22.3 34.1 59.3 99.7 57.7 36.1 38.5 3 4 55.6 35.8 25.5 25.7 37.7 63.2 7203. 9 62.2 40.9 43.7 4 5 5958. 5 6138. 9 6328. 8 6529. 1 6741.4 6967. 1 7208. 7466. 7 7745. 8 8049.0 5 6 61.5 42.0 32.0 32.6 45.0 70.9 12.2 71.1 50.6 54.3 6 7 64.4 45.1 35.3 36.0 48.7 74.8 16.4 75.6 55.5 59.6 7 8 67.3 48.2 38.5 39.5 52.3 78.7 20.5 80.1 60.3 64.9 8 9 70.3 51.3 41.8 42.9 56.0 82.6 24.7 84.6 65.2 70.2 9 10 5973. 2 6154. 4 6345. 6546. 4 6759. 7 6986. 5 7228. 9 7489. 1 7770. 1 8075. 5 10 11 76.2 57.5 48.3 49.8 63.3 90.4 33.1 93.6 74.9 80.8 11 12 79.1 60.6 51.6 53.3 67.0 94.3 37.3 98.1 79.8 86.1 12 13 82.1 63.7 54.8 56.7 70.7 98.3 41.5 7502. 6 84.7 91.5 13 14 85.0 66.8 58.1 60.2 74.3 7002.2 45.7 07.1 89.6 96.8 14 15 5988. 6169. 9 6361. 4 6563.7 6778. 7006. 1 7249. 9 7511. 7 7794. 5 8102. 2 15 16 90.9 73.0 64.7 67.1 81.7 10.0 54.1 16.2 99.4 07.5 16 17 93.9 76.1 67.9 70.6 85.4 14.0 58.3 20.7 7804. 3 12.9 17 18 96.9 79.2 71.2 74.1 89.1 17.9 62.5 25.3 09.3 18.3 18 19 99.8 82.3 74.5 77.6 92.8 21.8 66.7 29.8 14.2 23.7 19 20 6002. 8 6185. 5 6377. 8 6581. 6796. 5 7025. 8 7270. 9 7534. 4 7819. 1 8129. 1 20 21 05.8 88.6 81.1 84.5 6800. 2 29.7 75.2 38.9 24.1 34.5 21 22 08.7 91.7 84.4 88.0 03.9 33.7 79.4 43.5 29.0 39.9 22 23 11.7 94.8 87.7 91.5 07.6 37.7 83.7 48.1 34.0 45.3 23 24 14.7 98.0 91.0 95.0 11.3 41.6 87.9 52.7 39.0 50.8 24 25 6017. 7 6201.1 6394. 3 6598. 5 6815. 7045.6 7292. 2 7557. 3 7844. 8156. 2 25 26 20.7 04.2 97.6 6602. 18.8 49.6 96.4 61.8 48.9 61.6 26 27 23.6 07.4 6400.9 05.5 22.5 53.5 7300.7 66.4 53.9 67.1 27 28 26.6 10.5 04.3 09.0 26.2 57.5 05.0 71.0 58.9 72.6 28 29 29.6 13.7 07.6 12.5 30.0 61.5 09.2 75.7 63.9 78.0 29 30 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 06.5 34 35 6047. 6 6232. 6 6427. 6 6633. 7 6852.4 7085. 5 7335.0 7603. 4 7894. 1 8211. 1 35 36 50.6 35.8 30.9 37.2 56.2 89.5 39.3 08.1 99.2 16.6 36 37 53.6 38.9 34.2 40.8 60.0 93.5 43.6 12.8 7904. 2 22.1 37 38 56.6 42.1 37.6 44.3 63.7 97.6 47.9 17.4 09.3 27.7 38 39 59.7 45.3 40.9 47.9 67.5 7101.6 52.3 22.1 14.4 33.3 39 40 6062.7 6248. 4 6444.3 6651.4 6871. 3 7105. 6 7356. 6 7626. 8 7919. 4 8238. 8 40 41 65.7 51.6 47.6 55.0 75.1 09.7 60.9 31.4 24.5 44.4 41 42 68.7 54.8 51.0 58.5 78.9 13.7 65.3 36.1 29.6 50.0 42 43 71.7 58.0 54.4 62.1 82.6 17.8 69.6 40.8 34.7 55.6 43 44 74.8 61.2 57.7 65.7 86.4 21.8 74.0 45.5 39.9 61.2 44 45 45 6077.8 6264. 4 6461.1 6669. 2 6890. 2 7125. 9 7378. 3 7650.2 7945. 8266. 8 46 80.8 67.6 64.5 72.8 94.0 29.9 82.7 55.0 50.1 72.4 46 47 83.9 70.8 67.8 76.4 97.8 34.0 87.1 59.7 55.2 78.1 47 48 86.9 74.0 71.2 80.0 6901. 7 38.1 91.4 64.4 60.4 83.7 48 49 89.9 77.2 74.6 83.5 05.5 42.2 95.8 69.1 65.5 89.3 49 50 6093.0 6280. 4 6478.0 6687. 1 6909. 3 7146. 2 7400.2 7673. 9 7970. 7 8295.0 50 51 96.0 83.6 81.4 90.7 13.1 50.3 04.6 78.6 75.9 8300.7 51 52 99.1 86.8 84.8 94.3 16.9 54.4 09.0 83.4 81.0 06.4 52 53 6102. 1 90.0 88.2 97.9 20.8 58.5 13.4 88.1 86.2 12.0 53 54 05.2 6108. 2 93.2 91.6 6701. 5 24.6 62.6 17.8 . 92.9 91.4 17.7 54 55 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° 73° 74° 76° 76° 77° 78° 79° M. 6583— Oe Page 466] TABLE 4. 1 Length of a Degree in Latitude and Longitude. Degree of Long. Degree of Lat. Lat. Lat. Naut. miles. statute miles. Meters. Naut. miles. Statute miles. Meters. o 60. 068 69. 172 Ill 321 59. 661 68. 704 110 567 o 1 0.059 9.162 1 304 .661 .704 568 1 2 0.031 9.130 1 253 .662 -705 569 2 3 59. 986 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 .820 753 24 25 54. 473 62.729 100 952 59. 769 68.829 110 768 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. Length of a Degree in Latitude and Longitude. [Page 467 Degree of Long. 1 Degree of Lat. 1 Lat. Naut. miles. Statute miles. Meters. Naut. miles. Statute miles. Meters. o 45 42. 546 48. 995 78 849 59. 965 69. 054 Ill 131 o 45 46 1.801 8.136 7 466 .976 .066 151 46 47 1.041 7.261 6 058 .987 .079 170 47 48 0.268 6.372 4 628 .997 .091 190 48 49 39. 484 5.469 3 174 60. 008 .103 210 49 50 38. 688 44.552 71 698 60. 019 69. 115 111 229 50 51 7.880 3.621 200 .029 .127 249 51 52 7.060 2.676 68 680 .039 .139 268 52 53 6.229 1.719 7 140 .050 .151 287 53 54 5.386 0.749 5 578 .060 .163 306 54 55 34. 532 39. 766 63 996 60. 070 69. 175 111 325 55 56 3. 668 8.771 2 395 .080 .086 343 56 57 2.794 7.764 774 .090 .197 362 57 58 1.909 6.745 59 135 .100 .209 380 58 59 1.015 5.716 7 478 .109 .220 397 59 60 30. 110 34.674 55 802 60. 118 69. 230 111 415 60 61 29. 197 3.623 4 110 .128 .241 432 61 62 8.275 2.560 2 400 .137 .251 448 62 63 7.344 1.488 675 .145 .261 464 63 64 6.404 0.406 48 934 .154 .271 480 64 66 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 2J^ 2K . i »y* »% 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 1.53 3f 1.14 0.76 1.47 0.99 1.94 1.30 2.64 1.77 4 1.00 0.71 1.27 0.90 1.62 1.15 2.12 1.50 2.85 2.01 4i 0.90 0.66 1.12 0.83 1.40 1.04 1.77 1.31 2.29 1.69 3.05 2.26 ^ 0.81 0.63 1.00 0.77 1.23 0.95 1.53 1.18 1.91 1.48 2.45 1.90 3.25 2.51 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 5i 0.64 0.55 0.77 0.66 0.92 0.79 1.09 0.94 1.30 1.11 1.56 1.34 1.88 1.62 5J 0.60 0.53 0.72 0.63 0.85 0.75 1.00 0.88 1.18 1.04 1.39 1.23 1.66 1.46 5f 0.57 0.52 0.68 0.61 0.79 0.72 0.93 0.84 1.08 0.98 1.26 1.14 1.48 1.34 6 0.54 0.50 0.64 0.59 0.74 0.69 0.86 0.80 1.00 0.92 1.16 1.07 1.35 1.24 6i 0.52 0.49 0.60 0.57 0.70 0.66 0.81 0.76 0.93 0.88 1.07 1.01 1.23 1.16 6^ 0.50 0.47 0.58 0.55 0.67 0.64 0.77 0.73 0.88 0.84 1.00 0.96 1.14 1.09 6| 0.48 0.46 0.55 0.54 0.64 0.62 0.73 0.71 0.83 0.80 0.94 0.91 1.06 1.03 7 0.46 0.45 0.53 0.52 0.61 0.60 0.69 0.68 0.79 0.77 0.89 0.87 1.00 0.98 7i 0.45 0.44 0.51 0.51 0.59 0.58 0.67 0.66 0.75 0.74 0.84 0.83 0.94 0.93 7^ 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 71 0.42 0.42 0.48 0.48 0.55 0.55 0.62 0.62 0.69 0.69 0.77 0.77 0.86 0.86 8 0.41 0.41 0.47 0.47 0.53 0.53 0.60 0.60 0.67 0.67 0.74 0.74 0.82 0.82 8i 0.41 0.41 0.46 0.46 0.52 0.52 0.58 0.58 0.65 0.65 0.72 0.72 0.79 0.79 8* 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 8| 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 9J 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 0.65 0.59 lOi 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 0.57 101 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 IH 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 13i 0.48 0.24 0.51 0.26 0.55 0.28 0.58 0.30 0.61 0.32 0.64 0.33 0.-67 0.35 13J 0.50 0.23 0.53 0.25 0.57 0.27 0.60 0.28 0.63 0.30 0.66 0.31 0.69 0.32 13f 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 1 1 points. »H \ * 1 *K 4M 1 ^K 1 6 5Ji 1 4f 3.44 2.76 5 2.76 2.30 3.62 3.01 H 2.31 1.98 2.91 2.50 3.80 3.26 H 1.99 1.76 2.44 2.15 3.05 2.69 3.96 3.49 5| 1.75 1.59 2.10 1.90 2.55 2.31 3.18 2.88 4.12 3.72 6 1.57 1.45 1.85 1.71 2.20 2.03 2.66 2.46 3.31 3.05 4.26 3.94 6i 1.42 1.34 1.65 1.56 1.94 1.82 2.29 2.16 2.77 2.61 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 61 1.21 1.17 1.38 1.33 1.57 1.52 1.81 1.75 2.10 2.04 2.47 2.39 2.95 2.87 7 1.13 1.11 1.27 1.25 1.44 1.41 1.64 1.61 1.88 1.84 2.17 2.13 2.55 2.50 7i 1.06 1.05 1.19 1.17 1.33 1.32 1.50 1.49 1.70 1.69 1.94 1.92 2.24 2.22 7i 1.00 1.00 1.11 1.11 1.24 1.24 1.39 1.38 1.56 1.55 1.76 1.76 2.01 2.00 7f 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 81 0.81 0.80 0.88 0.87 0.96 0.95 1.04 1.03 1.14 1.12 1.24 1.22 1.35 1.34 9 0.78 0.77 0.85 0.83 0.92 0.90 1.00 0.98 1.08 1.06 1.18 1.15 1.28 1.25 9i 0.76 0.74 0.82 0.80 0.89 0.86 0.96 0.93 1.04 1.01 1.12 1.09 1.21 1.18 9i 0.74 0.71 0.80 0.77 0.86 0.83 0.93 0.89 1.00 0.96 1.08 1.03 1.16 1.11 9f 0.73 0.68 0.78 0.74 0.84 0.79 0.90 0.85 0.97 0.91 1.04 0.97 1.11 1.04 10 0.71 0.66 0.77 0.71 0.82 0.76 0.88 0.81 0.94 0.87 1.00 0.92 1.07 0.99 lOi 0.70 0.63 0.75 0.68 0.80 0.72 0.86 0.77 0.91 0.82 0.97 0.88 1.03 0.93 10^ 0.69 0.61 0.74 0.65 0.79 0.69 0.84 0.74 0.89 0.78 0.94 0.83 1.00 0.88 101 0.68 0.59 0.73 0.63 0.77 0.66 0.82 0.70 0.87 0.75 0.92 0.79 0.97 0.83 11 0.68 0.56 0.72 0.60 0.76 0.64 0.81 0.67 0.85 0.71 0.90 0.75 0.95 0.79 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 O.'&O 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 m 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 €.71 0.43 0.74 0.44 0.77 0.46 0.80 0.48 0.83 0.50 0.86 0.51 13 0.69 0.38 0.72 0.40 0.75 0.42 0.78 0.43 0.80 0.45 0.83 0.46 0.86 0.48 13i 0.70 0.36 0.73 0.37 0.76 0.39 0.78 0.40 0.81 0.41 0.83 0.43 0.86 0.44 ISi 0.71 0.34 0.74 0.35 0.76 0.36 0.79 0.37 0.81 0.38 0.84 0.39 0.86 0.41 13| 0.73 0.31 0.75 0.32 0.77 0.33 0.80 0.34 0.82 0.35 0.84 0.36 0.86 0.37 14 0.74 0.28 0.77 0.29 0.79 0.30 0.81 0.31 0.83 0.32 0.85 0.32 0.87 0.33 6^ 6-K 6 6Ji QVa m ' 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 71 8 2.06 2.06 2.36 2.36 2.74 2.74 3.24 3.24 3.94 3.93 4.97 4.97 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 8i 81 9 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 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 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 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 9J 91 10 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 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 1.14 1.05 1.22 1.13 1.31 1 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 j 1.13 1.33 1.20 1.42 1.29 1.53 1.38 1.65 1.49 m lOf 11 1.06 0.94 1.13 0.99 ].20 1.05 1.27 1.12 1.35 1.19 1.44 1.27 1.55 1.36 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 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 Hi lU 111 12 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 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 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 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 12J 12| 13 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 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 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 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 13J 131 14 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 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 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 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 6A. Distance of an Object by Two Bearings. Difference between Difference between the course and first bearing, in points. the course andsecond bearing, in points. 75i 7M ^V* 8 8K s% 8K 9 8i 6.07 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 6.12 4.97 ^ 2.31 2.21 2.60 2.49 2.96 2.84 3.44 3.30 4.11 3.93 5.10 4.88 9| 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 lOi: 1.78 1.61 1.93 1.75 2.12 1.92 2.34 2.11 2.61 2.36 2.95 2.67 3.41 3.08 4.04 3.65 lOJ 1.66 1.46 1.79 1.58 1.94 1.71 2.12 1.87 2.34 2.06 2.60 2.29 2.94 2.59 3.38 2.98 10| 1.56 1.34 1.67 1.43 1.80 1.64 1.96 1.67 2.12 1.82 2.33 2.00 2.68 2.22 2.91 2.60 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 1.65 2.10 1.69 2.29 1.84 llj 1.34 1.03 1.41 1.09 1.49 1.16 1.68 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 1.06 1.49 1.10 1.67 1.17 1.67 1.24 1.78 1.32 1.91 1.41 12 1.23 0.87 1.29 0.91 1.36 0.96 1.41 1.00 1.49 1.05 1.67 1.11 1.66 1.17 1.77 1.25 12i 1.19 0.80 1.24 0.83 1.29 0.87 1.35 0.91 1.41 0.96 1.48 1.00 1.56 1.05 1.65 1.11 m 1.15 0.73 1.20 0.76 1.24 0.79 1.29 0.82 1.36 0.86 1.41 0.89 1.47 0.93 1.56 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 0.66 1.20 0.67 1.24 0.69 1.29 0.72 1.34 0.74 1.39 0.77 13i 1.07 0.55 1.10 0.57 1.13 0.58 1.17 0.60 1.20 0.62 1.24 0.64 1.28 0.66 1.32 0.68 m 1.05 0.50 1.08 0.51 1.10 0.62 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 0.60 1.19 0.61 1.22 0.62 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 9K 9M 9K 10 lOK lOJ^ >0H " 1 • lOir 4.97 4.50 m 3.99 3.52 4.91 4.33 10| 3.34 2.87 3.94 3.38 4.83 4.14 11 2.88 2.39 3.30 2.74 3.87 3.22 4.74 3.94 m 2.53 2.04 2.84 2.28 3.24 2.61 3.80 3.05 4.63 3.72 m 2.27 1.75 2.50 1.93 2.79 2.16 3.18 2.46 3.72 2.88 4.62 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 1.66 2.41 1.71 2.68 1.90 3.04 2.15 3.53 2.50 4.26 3.01 12i 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 12^ 1.62 1.03 1.72 1.09 1.83 1.16 1.96 1.24 2.11 1.34 2.30 1.46 2.66 1.62 2.86 1.82 12| 1.53 0.91 1.61 0.96 1.69 1.01 1.80 1.07 1.92 1.14 2.06 1.23 2.24 1.34 2.47 1.47 13 1.44 0.80 1.51 0.84 1.58 0.88 1.66 0.92 1.76 0.98 1.87 1.04 2.01 1.11 2.17 1.21 131^ 1.37 0.71 1.42 0.73 1.48 0.76 1.66 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 0.76 1.67 0.79 1.76 0.83 13| 1.25 0.54 1.29 0.55 1.33 0.57 1.38 0.69 1.42 0.61 1.48 0.63 1.64 0.66 1.62 0.69 14 1.21 0.46 1.24 0.47 1.27 0.49 1.31 0.60 1.35 0.52 1.39 0.53 1.44 0.55 1.50 0.57 llJi 1 il'A 1 llJi - 1 125^ 1 12J^ 1 12% 1 n 1 m 4.12 2.77 m 3.31 2.101 3.96 2.51 12| 2.77 1.65 3.18 1.90 3.80 2.26 13 2.38 1.32 2.66 1.48 3.05 1.69 3.62 2.01 13^ 2.10 1.08 2.29 1.18 2.66 1.31 2.91 1.60 3.44 1.77 m 1.88 0.89 2.02 0.95 2.20 1.04 2.44 1.15 2.76 1.30 3.25 1.53 131 1.70 0.73 1.81 0.77 1.94 0.83 2.10 0.90 2.31 0.99 2.61 1.12 3.06 1.31 14 1.56 0.60 1.64 0.63 1.73 0.66 1.86 0.71 1.99 0.76 2.19 0.84 2.46 0.94 2.85 1.09 TABLE 5B. [Page 471 | Distance of an Object by Two Bearings. Difference between DifiEerence between the course and first bearing. the course and second bearing. 20° 22° 24° 26° 28° 80° 32° 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 1.86 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 1.26 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 1.16 0.91 1.33 1.05 1.65 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 0.63 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 0.86 0.78 0.96 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 0.76 0.90 0.84 70 0. 45 1 0. 42 0.50 0.47 0.57 0.53 0.63 0.59 0.70 0.66 0.78 0.73 0.86 0.81 72 0. 43 ' 0. 41 0.49 0.47 0.55 0.52 0.61 0.58 0.68 0.64 0.75 0.71 0.82 0.78 74 0. 42 i 0. 41 0.48 0.46 0.53 0.51 0.59 0.57 0.65 0.63 0.72 0.69 0.79 0.76 76 0. 41 1 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 0.69 0.66 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 0.56 0.66 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 0.69 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 0.68 0.62 0.62 92 0.36 0.36 0.40 0.40 0.44 0.44 0.48 0.48 0.62 0.62 0.67 0.67 0.61 0.61 94 0.36 0.35 0.39 0.39 0.43 0.43 0.47 0.47 0.61 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 0.69 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 0.67 100 0.35 0.34 0.38 0.38 0.42 0.41 0.46 0.45 0.49 0.49 0.63 0,52 0.67 0.66 102 0.35 0.34 0.38 0.37 0.42 0.41 0.45 0.44 0.49 0.48 0.53 0.51 0.66 0.55 104 0.34 0.33 0.38 0.37 0.41 0.40 0.45 0.43 0.48 0.47 0.62 0.50 0.66 0.54 106 0.34 0.33 0.38 0.36 0.41 0.39 0.45 0.43 0.48 0.46 0.62 0.50 0.66 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 0.65 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 0.60 0.41 0.53 0.43 128 0.36 0.28 0.39 0.31 0.42 0.33 0.45 0.36 0.48 0.38 0.50 0.40 0.63 0.42 130 0.36 0.28 0.39 0.30 0.42 0.32 0.45 0.36 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 0.62 0.37 0.64 0.39 136 0.38 0.26 0.41 0.28 0.44 0.30 0.47 0.32 0.49 0.34 0.62 0.36 0.65 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 0.61 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 0.62 0.31 0.56 0.32 0.67 0.34 146 0.42 0.24 0.45 0.25 0.48 0.27 0.51 0.28 0.63 0.30 0.56 0.31 0.68 0.32 148 0.43 23 0.46 0.25 0.49 0.26 0.52 0.27 0.64 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 0.65 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 0.26 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 26 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 Page 472] TABLE 5B. Distance of an Object by Two Bearings. Difference Difference between the course and first bearing. between the course 1 1 ind second 84° 36° 88° 40° 1 42° 44° 1 46° 1 bearing. 44° 3.22 2.24 46 2.69 1.93 3.39 2.43 48 2.31 1.72 2.83 2.10 3.55 2.63 50 2.03 1.55 2.43 1.86 2.96 2.27 3.70 2.84 52 1.81 1.43 2.13 1.68 2.54 2.01 3.09 2.44 3.85 3.04 54 1.63 1.32 1.90 1.54 2.23 1.81 2.66 2.15 3.22 2.60 4.00 3.24 56 1.49 1.24 1.72 1.42 1.99 1.65 2.33 1.93 2.77 2.29 3.34 2.77 4.14 3.43 58 1.37 1.17 1.57 1.33 1.80 1.53 2.08 1.76 2.43 2.06 2.87 2.44 3.46 2.93 60 1.28 1.10 1.45 1.25 1.64 1.42 1.88 1.63 2.17 1.88 2.52 2.18 2.97 2.57 62 1.19 1.05 1.34 1.18 1.51 1.34 1.72 1.52 1.96 1.73 2.25 1.98 2.61 2.30 64 1.12 1.01 1.25 1.13 1.40 1.26 1.58 1.42 1.79 1.61 2.03 1.83 2.33 2.09 66 1.06 0.96 1.18 1.07 1.31 1.20 1.47 1.34 1.65 1.51 1.85 1.69 2.10 1.92 68 1.00 0.93 1.11 1.03 1.23 1.14 1.37 1.27 1.53 1.42 1.71 1.58 1.92 1.78 70 0.95 0.89 1.05 0.99 1.16 1.09 1.29 1.21 1.43 1.34 1.58 1.49 1.77 1.66 72 0.91 0.86 1.00 0.95 1.10 1.05 1.21 1.15 1.34 1.27 1.48 1.41 1.64 1.56 74 0.87 0.84 0.95 0.92 1.05 1.01 1.15 1.10 1.26 1.21 1.39 1.34 1.53 1.47 76. 0.84 0.81 0.91 0.89 1.00 0.97 1.09 1.06 1.20 1.16 1.31 1.27 1.44 1.40 78 0.80 0.79 0.88 0.86 0.96 0.94 1.04 1.02 1.14 1.11 1.24 1.22 1.36 1.33 80 0.78 0.77 0.85 0.83 0.92 0.91 1.00 0.98 1.09 1.07 1.18 1.16 1.28 1.27 82 0.75 0.75 0.82 0.81 0.89 0.88 0.96 0.95 1.04 1.03 1.13 1.12 1.22 1.21 84 0.73 0.73 0.79 0.79 0.86 0.85 0.93 0.92 1.00 0.99 1.08 1.07 1.17 1.16 86 0.71 0.71 0.77 0.77 0.83 0.83 0.89 0.89 0.96 0.96 1.04 1.04 1. 12 1.12 88 0.69 0.69 0.75 0.75 0.80 0.80 0.86 0.86 0.93 0.93 1.00 1.00 1.08 1.07 90 0.67 0.67 0.73 0.73 0.78 0.78 0.84 0.84 0.90 0.90 0.97 0.97 1.04 1.04 92 0.66 0.66 0.71 0.71 0.76 0.76 0.82 0.82 0.87 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 0.57 0.63 0.60 0.66 0.64 0.70 0.68 0.74 0.72 0.79 0.76 0.83 0.80 108 0.58 0.55 0.62 0.59 0.66 0.62 0.69 0.66 0.73 0.70 0.77 0.74 0.81 0.77 110 0.58 0.54 0.61 0.57 0.65 0.61 0.68 0.64 0.72 0.68 0.76 0.71 0.80 0.75 112 0.57 0.53 0.61 0.56 0.64 0.59 0.68 0.63 0.71 0.66 0.75 0.69 0.79 0.73 114 0.57 0.52 0.60 0.55 0.63 0.58 0.67 0.61 0.70 0.64 0.74 0.68 0.78 0.71 116 0.56 0.51 0.60 0.54 0.63 0.57 0.66 0.60 0.70 0.63 0.73 0.66 0.77 0.69 118 0.56 0.50 0.59 0.52 0.63 0.55 0.66 0.58 0.69 0.61 0.72 0.64 0.76 0.67 120 0.56 0.49 0.59 0.51 0.62 0.54 0.65 0.57 0.68 0.59 0.72 0.62 0.75 0.65 122 0.56 0.47 0.59 0.50 0.62 0.53 0.65 0.55 0.68 0.58 0.71 0.60 0.74 0.63 124 0.56 0.46 0.59 0.49 0.62 0.51 0.65 0.54 0.68 0.56 0.71 0.58 0.74 0.61 126 0.56 0.45 0.59 0.48 0.62 0.50 0.64 0.52 0.67 0.54 0.70 0.57 0.73 0.59 128 0.56 0.44 0.59 0.46 0.62 0.49 0.64 0.51 0.67 0.53 0.70 0.55 0.73 0.57 130 0.56 0.43 0.59 0.45 0.62 0.47 0.64 0.49 0.67 0.51 0.70 0.53 0.72 0.55 132 0.56 0.42 0.59 0.44 0.62 0.46 0.64 0.48 0.67 0.50 0.70 0.52 0.72 0.54 134 0.57 0.41 0.59 0.43 0.62 0.45 0.64 0.46 0.67 0.48 0.69 0.50 0.72 0.52 136 0.57 0.40 0.60 0.41 0.62 0.43 0.65 0.45 0.67 0.47 0.70 0.48 0.72 0.50 138 0.58 0.39 0.60 0.40 0.63 0.42 0.65 0.43 0.67 0.45 0.70 0.47 0.72 0.48 140 0.58 0.37 0.61 0.39 0.63 0.40 0.65 0.42 0.68 0.43 0.70 0.45 0.72 0.46 142 0.59 0.36 0.61 0.38 0.63 0.39 0.66 0.41 0.68 0.42 0.70 0.43 0.72 0.45 144 0.60 0.35 0.62 0.36 0.64 0.38 0.66 0.39 0.68 0.40 0.71 0.41 0.73 0.43 146 0.60 0.3,4 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 between the course Difference between the course and first bearing. and second bearing. 48° 50° 62° 64° 56° 58° 60° 58° 4.28 3.63 60 3.57 3.10 4.41 3.82 62 3.07 2.71 3.68 3.25 4.54 4.01 64 2.70 2.42 3.17 2.85 3.79 3.41 4.66 4.19 66 2.40 2.20 2.78 2.54 3.26 2.98 3.89 3.55 4.77 4.36 68 2.17 2.01 2.48 2.30 2.86 2.65 3.34 3.10 3.99 3.71 4.88 4.53 70 1.98 1.86 2.24 2.10 2.55 2.39 2.94 2.76 3.43 3.22 4.08 3.83 4.99 4.69 72 1.83 1.74 2.04 1.94 2.30 2.19 2.62 2.49 3.01 2.86 3.51 3.33 4.17 3.96 74 1.70 1.63 1.88 1.81 2.10 2.02 2.37 2.27 2.68 2.58 3.08 2.96 3.58 3.44 76 1.58 1.54 1.75 1.70 1.94 1.88 2.16 2.10 2.42 2.35 2.74 2.66 3.14 3.05 78 1.49 1.45 1.63 1.60 1.80 1.76 1.99 1.95 2.21 2.16 2.48 2.43 2.80 2.74 80 1.40 1.38 1.53 1.51 1.68 1.65 1.85 1.82 2.04 2.01 2.26 2.23 2.53 2.49 82 1.33 1.32 1.45 1.43 1.58 1.56 1.72 1.71 1.89 1.87 2.08 2.06 2.31 2.29 84 1.26 1.26 1.37 1.36 1.49 1.48 1.62 1.61 1.77 1.76 1.93 1.92 2.13 2.12 86 1.21 1.20 1.30 1.30 1.41 1.41 1.53 1.52 1.66 1.65 1.81 1.80 1.98 1.97 88 1.16 1.16 1.24 1.24 1.34 1.34 1.45 1.45 1.56 1.56 1.70 1.70 1.84 1.84 90 1.11 1.11 1.19 1.19 1.28 1.28 1.38 1.38 1.48 1.48 1.60 1.60 1.73 1.73 92 1.07 1.07 1.14 1.14 1.23 1.23 1.31 1.31 1.41 1.41 1.52 1.52 1.63 1.63 94 1.03 1.03 1.10 1.10 1.18 1.17 1.26 1.26 1.35 1.34 1.44 1.44 1.55 1.54 96 1.00 0.99 1.06 1.06 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 l.]5 1.13 1.22 1.19 1.29 1.27 104 0.90 0.87 0.95 0.92 1.00 0.97 1.06 1.02 1.12 1.08 1.18 1.14 1.25 1.21 106 0.88 0.84 0.92 0.89 0.97 0.94 1.03 0.99 1.09 1.04 1.14 1.10 1.20 1.16 108 0.86 0.82 0.90 0.86 0.95 0.90 1.00 0.95 1.05 1.00 1.11 1.05 1.17 1.11 110 0.84 0.79 0.88 0.83 0.93 0.87 0.98 0.92 1.02 0.96 1.08 1.01 1.13 1.06 112 0.83 0.77 0.87 0.80 0.91 0.84 0.95 0.88 1.00 0.93 1.05 0.97 1.10 1.02 114 0.81 0.74 0.85 0.78 0.89 0.82 0.93 0.85 0.98 0.89 1.02 0.93 1.07 0.98 116 0.80 0.72 0.84 0.75 0.88 0.79 0.92 0.82 0.96 0.85 1.00 0.90 1.04 0.94 118 0.79 0.70 0.83 0.73 0.86 0.76 0.90 0.79 0.94 0.83 0.98 0.86 1.02 0.90 120 0.78 0.68 0.82 0.71 0.85 0.74 0.89 0.77 0.91 0.80 0.96 0.83 1.00 0.87 122 0.77 0.66 0.81 0.68 0.84 0.71 0.87 0.74 0.90 0.77 0.95 0.80 0.98 0.83 124 0.77 0.63 0.80 0.66 0.83 0.69 0.86 0.71 0.90 0.74 0.93 0.77 0.96 0.80 126 0.76 0.61 0.79 0.64 0.82 0.66 0.85 0.69 0.88 0.71 0.91 0.74 0.95 0.77 128 0.75 0.59 0.78 0.62 0.81 0.64 0.84 0.66 0.87 0.69 0.90 0.71 0.93 0.74 130 0.75 0.57 0.78 0.60 0.81 0.62 0.83 0.64 0.86 0.66 0.89 0.68 0.92 0.71 132 0.75 0.56 0.77 0.57 0.80 0.59 0.83 0.61 0.85 0.64 0.88 0.66 0.91 0.68 134 0.74 0.54 0.77 0.55 0.80 0.57 0.82 0.59 0.85 0.61 0.87 '0.63 0.90 0.65 136 0.74 0.52 0.77 0.53 0.80 0.55 0.82 0.57 0.84 0.58 0.87 0.60 0.89 0.62 138 0.74 0.50 0.77 0.51 0.79 0. 53 0.81 0.54 0.84 0.56 0.86 0.58 0.89 0.59 140 0.74 0.48 0.77 0.49 0.79 0.51 0.81 0.52 0.83 0.54 0.86 0.55 0.88 0.57 142 0.74 0.46 0.77 0.47 0.79 0.49 0.81 0.50 0.83 0.51 0.85 0.52 0.87 0.54 144 0.75 0.44 0.77 0.45 0.79 0.46 0.81 0.48 0.83 0.49 0.85 0.50 0.87 0.51 146 0.75 0.42 0.77 0.43 0.79 0.44 0.81 0.45 0.83 0.46 0.85 0.47 0.87 0.49 148 0.76 0.40 0.77 0.41 0.79 0.42 0.81 0.43 0.83 0.44 0.85 0.45 0.87 0.46 150 0.76 0.38 0.78 0.39 0.80 0.40 0.81 0.'41 0.83 0.42 0.85 0.42 0.87 0.43 152 0.77 0.36 0.78 0.37 0.80 0.38 0.82 0.38 0.83 0.39 0.85 0.40 0.87 0.41 154 0.77 0.34 0.79 0.35 0.81 0.35 0.82 0.36 0.84 0.37 0.85 0.37 0.87 0.38 156 0.78 0.32 0.80 0.32 0.81 0.33 0.83 0.34 0.84 0.34 0.86 0.35 0.87 0.35 158 0.79 0.30 0.81 0.30 0.82 0.31 0.83 0.31 0.85 0.32 0.86 0.32 0.87 0.33 160 0.80 0.27 0.82 0.28 0.83 0.28 0.84 0.29 0.85 0.29 0.86 0.30 0.88 0.30 Page 474] TABLE 6B. Distance of an Object by Two Bearings. Difference Difference between the course and first bearing. between the course and second bearing. 62° 64° 66° 68° 70° 72° 74» 76° 72° 5.08 4.84 74 4.25 4.08 5.18 4.98 76 3.65 3.54 4.32 4.19 5.26 5.10 78 3.20 3.13 3.72 3.63 4.39 4.30 5.34 5.22 80 2.86 2.81 3.26 3.21 3.78 3.72 4.46 4.39 5.41 5.33 82 2.58 2.56 2.91 2.88 3.31 3.28 3.83 3.80 4.52 4.48 5.48 5.42 84 2.36 2.34 2.63 2.61 2.96 2.94 3.36 3.35 3.88 3.86 4.57 4.55 5.54 5.51 86 2.17 2.17 2.40 2.39 2.67 2.66 3.00 2.99 3.41 3.40 3.93 3.92 4.62 4.61 5.59 5.57 88 2.01 2.01 2.21 2.21 2.44 2.44 2.71 2.71 3.04 3.04 3.45 3.45 3.97 3.97 4.67 4.66 90 1.88 1.88 2.05 2.05 2.25 2.25 2.48 2.48 2.75 2.75 3.08 3.08 3.49 3.49 4.01 4.01 92 1.77 1.76 1.91 1.91 2.08 2.08 2.28 2.28 2.51 2.51 2.78 2.78 3.11 3.11 3.52 3.52 94 1.67 1.66 1.80 1.79 1.95 1.94 2.12 2.11 2.31 2.30 2.54 2.53 2.81 2.80 3.14 3.13 96 1.58 1.57 1.70 1.69 1.83 1.82 1.97 1.96 2.14 2.13 2.34 2.33 2.57 2.55 2.84 2.82 98 1.50 1.49 1.61 1.59 1.72 1.71 1.85 1.84 2.00 1.98 2.17 2.15 2.36 2.34 2.59 2.56 100 1.43 1.41 1.53 1.51 1.63 1.61 1.75 1.72 1.88 1.85 2.03 2.00 2.19 2.16 2.39 2.35 102 1.37 1.34 1.46 1.43 1.55 1.52 1.66 1.62 1.77 1.73 1.90 1.86 2.05 2.00 2.21 2.16 104 1.32 1.28 1.40 1.36 1.48 1.44 1.58 1.53 1.68 1.63 1.79 1.74 1.92 1.87 2.07 2.01 106 1.27 1.22 1.34 1.29 1.42 1.37 1.51 1.45 1.60 1. 54 1.70 1.63 1.81 1.74 1.94 1.87 108 1.23 1.17 1.29 1.23 1.37 1.30 1.44 1.37 1.53 1.45 1.62 1.54 1.72 1.63 1.83 1.74 110 1.19 1.12 1.25 1.17 1.32 1.24 1.39 1.30 1.46 1.37 1.54 1.45 1.64 1.54 1.74 1.63 112 1.15 1.07 1.21 1.12 1.27 1.18 1.33 1.24 1.40 1.30 1.48 1.37 1.56 1.45 1..65 1.53 114 1.12 1.02 1.17 1.07 1.23 1.12 1.29 1.18 1.35 1.24 1.42 1.30 1.50 1.37 1.58 1.44 116 1.09 0.98 1.14 1.03 1.19 1.07 1.25 1.12 1.31 1.17 1.37 1.23 1.44 1.29 1.51 1.36 118 1.07 0.94 1.11 0.98 1.16 1.02 1.21 1.07 1.26 1.12 1.32 1.17 1.38 1.22 1.45 1.28 120 1.04 0.90 1.08 0.94 1.13 0.98 1.18 1.02 1.23 1.06 1.28 1.11 1.34 1.16 1.40 1.21 122 1.02 0.86 1.06 0.90 1.10 0.93 1.15 0.97 1.19 1.01 1.24 1.05 1.29 1.10 1.35 1.14 124 1.00 0.83 1.04 0.86 1.08 0.89 1.12 0.93 1.16 0.96 1.21 1.00 1.25 1.04 1.31 1.08 126 0.98 0.79 1.02 0.82 1.05 0.85 1.09 0.88 1.13 0.92 1.18 0.95 1.22 0.99 1.27 1.02 128 0.97 0.76 1.00 0.79 1.03 0.82 1.07 0.84 1.11 0.87 1.15 0.90 1.19 0.94 1.23 0.97 130 0.95 0.73 0.98 0.75 1.02 0.78 1.05 0.80 1.09 0.83 1.12 0.86 1.16 0.89 1.20 0.92 132 0.94 0.70 0.97 0.72 1.00 0.74 1.03 0.77 1.06 0.79 1.10 0.82 1.13 0.84 1.17 0.87 134 0.93 0.67 0.96 0.69 0.99 0.71 1.01 0.73 1.04 0.75 1.08 0.77 1.11 0.80 1.14 0.82 136 0.92 0.64 0.95 0.66 0.97 0.68 1.00 0.69 1.03 0.71 1.06 0.74 1.09 0.76 1.12 0.78 138 0.91 0.61 0.94 0.63 0.96 0.64 0.99 0.66 1.01 0.68 1.04 0.70 1.07 0.72 1.10 0.74 140 0.90 0.58 0.93 0.60 0.95 0.61 0.97 0.63 1.00 0.64 1.03 0.66 1.05 0.68 1.08 0.70 142 0.90 0.55 0.92 0.57 0.94 0.58 0.96 0.59 0.99 0.61 1.01 0.62 1.04 0.64 1.06 0.65 144 0.89 0.52 0.91 0.54 0.93 0.55 0.96 0.56 0.98 0.57 1.00 0.59 1.02 0.60 1.05 0.62 146 0.89 0.50 0.91 0.51 0.93 0.52 0.95 0.53 0.97 0.54 0.99 0.55 1.01 0.57 1.03 0.58 148 0.89 0.47 0.90 0.48 0.92 0.49 0.94 0.50 0.96 0.51 0.98 0.52 1.00 0.53 1.02 0.54 150 0.88 0.44 0.90 0.45 0.92 0.46 0.94 0.47 0.95 0.48 0.97 0.49 0.99 0.50 1.01 0.50 152 0.88 0.41 0.90 0.42 0.92 0.43 0.93 0.44 0.95 0.45 0.97 0.45 0.98 0.46 1.00 0.47 154 0.88 0.39 0.90 0.39 0.91 0.40 0.93 0.41 0.94 0.41 0.96 0.42 0.98 0.43 0.99 0.43 156 0.89 0.36 0.90 0.37 0.91 0.37 0.93 0.38 0.94 0.38 0.96 0.39 0.97 0.39 0.99 0.40 158 0.89 0.33 0.90 0.34 0.91 0.34 0.93 0.35 0.94 0.35 0.95 0.36 0.97 0.36 0.98 0.37 160 0.89 0.30 0.90 0.31 0.91 0.31 0.93 0.32 0.94 0.32 0.95 0.33 0.96 0.33 0.98 0.33 TABLE 5B. [Page 475 Distance of an Object by Two Bearings. Difference between t>li6 course Difference between the course and first bearing. and second bearing. 78° 80° 82° 84° 86° 88° 90° 1 92° 1 88° 5.63 5.63 90 4.70 4.70 5.67 5.67 92 4.04 4.04 4.74 4.73 5.70 5.70 94 3.55 3.54 4.07 4.06 4.76 4.75 5.73 5.71 96 3.17 3.15 3.57 3.55 4.09 4.07 4.78 4.76 5.74 5.71 98 2.86 2.83 3.19 3.16 S.bd 3.56 4.1] 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° 1 98° 1 100° 102° 1 104° 1 106° 108° 1 104° 5.74 5.57 106 4.80 4.61 5.78 5.51 108 4.12 3.92 4.78 4.55 5.70 5.42 110 3.62 3.40 4.11 3.86 4.76 4.48 5.67 5.33 112 3.23 2.99 3.61 3.35 4.09 3.80 4.74 4.40 5.63 5.22 114 2.92 2.66 3.22 2.94 3.59 3.28 4.07 3.72 4.70 4.30 5.59 5.10 116 2.66 2.39 2.91 2.61 3.20 2.88 3.57 3.21 4.04 3.63 4.67 4.19 5.54 4.98 118 2.45 2.17 2.65 2.34 2.90 2.56 3.19 2.81 3.55 3.13 4.01 3.54 4.62 4.08 5.48 4.84 120 2.28 1.97 2.45 2.12 2.64 2.29 2.88 2.49 3.17 2.74 3.52 3.05 3.97 3.44 4.57 3.96 122 2.12 1.80 2.27 1.92 2.43 2.06 2.63 2.23 2.86 2.43 3.14 2.66 3.49 2.96 3.93 3.33 124 2.00 1.65 2.12 1.76 2.26 1.87 2.42 2.01 2.61 2.16 2.84 2.35 3.11 2.58 3.45 2.86 126 1.88 1.52 1.99 1.61 2.11 1.71 2.25 1.82 2.40 1.95 2.59 2.10 2.81 2.27 3.08 2.49 128 1.78 1.41 1.88 1.48 1.98 1.56 2.10 1.65 2.23 1.76 2.39 1.88 2.57 2.02 2.78 2.19 130 1.70 1.30 1.78 1.36 1.87 1.43 1.97 1.51 2.08 1.60 2.21 1.70 2.36 1.81 2.54 1.94 132 1.62 1.20 1.69 1.26 1.77 1.32 1.86 1.38 1.96 1.45 2.07 1.54 2.19 1.63 2.34 1.74 134 1.55 1.12 1.62 1.16 1.68 1.21 1.76 1.27 1.85 1.33 1.94 1.40 2.05 1.47| 2.17 1.56 136 1.49 1.04 1.55 1.07 1.61 1.12 1.68 1.16 1.75 1.22 1.83 1.27 1.92 1.34 2.03 1.41 138 1.44 0.96 1.49 0.99 1.54 1.03 1.60 1.07 1.66 1.11 1.74 1.16 1.81 1.21 1.90 1.27 140 1.39 0.89 1.43 0.92 1.48 0.95 1.53 0.98 1.59 1.02 1.65 1.06 1.72 1.10 1.79 1.15 142 1.34 0.83 1.38 0.85 1.43 0.88 1.47 0.91 1.52 0.94 1.58 0.97 1.64 1.01 1.70 1.05 144 1.30 0.77 1.34 0.79 1.38 0.81 1.42 0.83 1.46 0.86 1.51 0.89 1.56 0.92 1.62 0.95 146 1.27 0.71 1.30 0.73 1.33 0.75 1.37 0.77 1.41 0.79 1.45 0.81 1.50 0.84 1.54 0.86 148 1.23 0.65 1.26 0.67 1.29 0.69 1.33 0.70 1.36 0.72 1.40 0.74 1.44 0.76 1.48 0.78 150 1.20 0.60 1.23 0.61 1.26 0.63 1.29 0.64 1.32 0.66 1.35 0.67 1.38 0.69 1.42 0.71 152 1.18 0.55 1.20 0.56 1.22 0.57 1.25 0.59 1.28 0.60 1.31 0.61 1.34 0.63 1.37 0.64 154 1.15 0.50 1.17 0.51 1.19 0.52 1.22 0.53 1.24 0.54 1.27 0.56 1.29 0.57 1.32 0.58 156 1.13 0.46 1.15 0.47 1.17 0.47 1.19 0.48 1.21 0.49 1.23 0.50 1.25 0.51 1.28 0.52 158 1.11 0.42 1.13 0.42 1.14 0.43 1.16 0.44 1.18 0.44 1.20 0.45 1.22 0.46 1.24 0.47 160 1.09 0.37 1.11 0.38 1.12 0.38 1.14 0.39 1.15 0.39 1.17 0.40 1.19 0.41 1.21 0.41 Page 476] TABLE 5B. Distance of an Object by Two Bearings. Difference Difference between the course and first bearing. between the course and second bearing. 110° 112° 114° 116° 118° 120° 122° 120° 5.41 4.69 122 4.52 3.83 5.34 4.53 124 3.88 3.22 4.46 3.70 5.26 4.36 126 3.41 2.76 3.83 3.10 4.39 3.55 5.18 4.19 128 3.04 2.40 3.36 2.65 3.78 2.98 4.32 3.41 5.08 4.01 130 2.75 2.10 3.00 2.30 3.31 2.54 3.72 2.85 4.25 3.25 4.99 3.82 132 2.51 1.86 2.71 2.01 2.96 2.20 3.26 2.42 3.65 2.71 4.17 3.10 4.88 3.63 134 2.31 1.66 2.48 1.78 2.67 1.92 2.91 2.09 3.20 2.30 3.58 2.57 4.08 2.93 136 2.14 1.49 2.28 1.58 2.44 1.69 2.63 1.83 2.86 1.98 3.14 2.18 3.51 2.44 138 2.00 1.34 2.12 1.42 2.25 1.50 2.40 1.61 2.58 1.73 2.80 1.88 3.08 2.06 140 1.88 1.21 1.97 1.27 2.08 1.34 2.21 1.42 2.36 1.52 2.53 1.63 2.74 1.76 142 1.77 1.09 1.85 1.14 1.95 1.20 2.05 1.26 2.17 1.34 2.31 1.42 2.48 1.53 144 1.68 0.99 1.75 1.03 1.83 1.07 1.91 1.13 2.01 1.18 2.13 1.25 2.26 1.33 146 1.60 0.89 1.66 0.93 1.72 0.96 1.80 1.01 1.88 1.05 1.98 1.10 2.08 1.17 148 1.53 0.81 1.58 0.84 1.63 0.87 1.70 0.90 1.77 0.94 1.84 0.98 1.93 1.03 150 1.46 0.73 1.51 0.75 1.55 0.78 1.61 0.80 1.67 0.83 1.73 0.87 1.81 0.90 152 1.40 0.66 1.44 0.68 1.48 0.70 1.53 0.72 1.58 0.74 1.63 0.77 1.70 0.80 154 1.35 0.59 1.39 0.61 1.42 0.62 1.46 0.64 1.50 0.66 1.55 0.68 1.60 0.70 156 1.31 0.53 1.33 0.54 1.37 0.56 1.40 0.57 1.43 0.58 1.47 0.60 1.52 0.62 158 1.26 0.47 1.29 0.48 1.32 0.49 1.34 0.50 1.37 0.51 1.41 0.53 1.44 0.54 160 1.23 0.42 1.25 0.43 1.27 0.43 1.29 0.44 1.32 0.45 1.35 0.46 1.38 0.47 124° 1 126° 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 3.63 2.27 4.28 2.63 144 2.42 1.42 2.62 1.54 2.86 1.68 3.17 1.86 3.57 2.10 4.14 2.43 146 2.21 1.24 2.37 1.32 2.55 1.43 2.78 1.55 3.07 1.72 3.46 1.93 4.00 2.24 148 2.04 1.08 2.16 1.14 2.30 1.22 2.48 1.31 2.70 1.43 2.97 1.58 3.34 1.77 150 1.89 0.95 1.99 0.99 2.10 1.05 2.24 1.12 2.40 1.20 2.61 1.30 2.87 1.44 152 1.77 0.83 1.85 0.87 1.94 0.91 2.04 0.96 2.17 1.02 2.33 1.09 2.52 1.18 154 1.66 0.73 1.72 0.76 1.80 0.79 1.88 0.83 1.98 0.87 2.10 0.92 2.25 0.99 156 1.56 0.64 1.62 0.66 1.68 0.68 1.75 0.71 1.83 0.74 1.92 0.78 2.03 0.83 158 1.48 0.56 1.53 0.57 1.58 0.59 1.63 0.61 1.70 0.64 1.77 0.66 1.85 0.69 160 1.41 0.48 1.45 0.49 1.49 0.51 1.53 0.52 1.58 0.54 1.64 0.56 1.71 0.58 138° 1 140° 142° 144° 146° 148° 160° 1 148° 3.85 2.04 150 3.22 1.61 3.70 1.85 152 2.77 1.30 3.09 1.45 3.55 1.66 154 2.43 1.06 2.66 1.16 2.96 1.30 3.38 1.48 156 2.17 0.88 2.33 0.95 2.54 1.04 2.83 1.15 3.22 1.31 158 1.96 0.73 2.08 0.78 2.23 0.84 2.43 0.91 2.69 1.01 3.05 1.14 160 1.79 0.61 1.88 0.64 1.99 0.68 2.13 0.73 2.31 0.79 2.55 0.87 2.88 0.98 TABLE 6. Distance of Visibility of Objects at Sea. [Page 477 Height, Nautical Statute Height, Nautical Statute Height, Nautical Statute feet. miles. miles. feet. miles. miles. feet. miles. miles. 1 1.1 1.3 100 11.5 13.2 760 31.6 36.4 2 1.7 1.9 105 11.7 13.5 780 32.0 36.9 3 2.0 2.3 110 12.0 13.8 800 32.4 37.3 4 2.3 2.6 115 12.3 14.1 820 32.8 37.8 5 2.5 2.9 120 12.6 14.5 840 33.2 38.3 6 2.8 3.2 125 12.9 14.8 860 33.6 38.7 7 2.9 3.5 130 13.1 15.1 880 34.0 39.2 8 3.1 3.7 135 13.3 15.3 900 34.4 39.6 9 3.5 4.0 140 13.6 15.6 920 34.7 40.0 10 3.6 4.2 145 13.8 15.9 940 35.2 40.5 11 3,8 4.4 150 14.1 16.2 960 35.5 40.9 12 4.0 4.6 160 14.5 16.7 980 35.9 41.3 13 4.2 4.8 170 14.9 17.2 1,000 36.2 41.7 14 4.3 4.9 180 15.4 17.7 1,100 38.0 43.8 15 4.4 5.1 190 15.8 18.2 1,200 39.6 45.6 16 4.6 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 96.0 110.6 I 80 10.3 11.8 700 30.3 34.9 8,000 102.6 118.1 85 10.6 12.2 720 30.7 36.4 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. ^ II s. ^ II S. s^ II S- bV II S. in II S. in 1 4 61 4 4 121 8 4 181 12 4 241 16 4 301 20 4 2 8 62 4 8 122 8 8 182 12 8 242 16 8 302 20 8 3 12 63 4 12 123 8 12 183 12 12 243 16 12 303 20 12 4 16 64 4 16 124 8 16 184 12 16 244 16 16 304 20 16 5 20 65 4 20 125 8 20 185 12 20 245 16 20 305 20 20 6 24 m 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 10 8 212 14 8 272 18 8 332 22 8 33 2 12 93 6 12 153 10 12 213 14 12 273 18 12 333 22 12 34 2 16 94 6 16 154 10 16 214 14 16 274 18 16 334 22 16 35 2 20 95 6 20 155 10 20 215 14 20 275 18 20 335 22 20 36 2 24 96 6 24 156 10 24 216 14 24 276 18 24 336 22 24 37 2 28 97 6 28 157 10 28 217 14 28 277 18 28 337 22 28 38 2 32 98 6 32 158 10 32 218 14 32 278 18 32 338 22 32 39 2 36 99 6 36 159 10 36 219 14 36 279 18 36 339 22 36 40 2 40 100 6 40 160 10 40 220 14 40 280 18 40 340 22 40 41 2 44 101 6 44 161 10 44 221 14 44 281 18 44 341 22 44 42 2 48 102 6 48 162 10 48 222 14 48 282 18 48 342 22 48 43 2 52 103 6 52 163 10 52 223 14 52 283 18 52 343 22 52 44 2 56 104 6 56 164 10 56 224 14 56 284 18 56 344 22 56 45 3 105 7 165 11 225 15 285 19 345 23 46 3 4 106 7 4 166 11 4 226 15 4 286 19 4 346 23 4 47 3 8 107 7 8 167 11 8 227 15 8 287 19 8 347 23 8 48 3 12 108 7 12 168 11 12 228 15 12 288 19 12 348 23 12 49 3 16 109 7 16 169 11 16 229 15 16 289 19 16 349 23 16 50 3 20 110 7 20 170 11 20 230 15 20 290 19 20 350 23 20 51 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 sliould be remembered that the fractions are sixtieths; thus, the value in time ol 42" is not 2>.48, but 2>|§>«2>.8. TABLE 8. [Page 479 Sidereal into Mean Solar Time. 1 To be subtracted from a sidereal time interval. 1 1 Oh Ih 2" 81" 4h 6" fth Jt For seconds.! m. 1 2 3 4 m. 8. 0.000 0. 164 0. 328 0. 491 0. 655 m. 8. 9.830 9.993 10. 157 10. 321 10. 485 TO. 8. 19.659 19. 823 19.987 20. 151 20. 314 TO. 8. 29. 489 29. 653 29. 816 29. 980 30. 144 TO. 8. 39. 318 39. 482 39. 646 39. 810 39.974 TO. 8. 49. 148 49. 312 49. 475 49. 639 49. 803 TO. 8. 58. 977 59. 141 59. 305 59. 469 59. 633 TO. 8. 1 8.807 1 8.971 1 9.135 1 9.298 1 9.462 8. 1 2 3 4 8. 0.003 .005 .008 .011 5 6 7 8 9 0. 819 0. 983 1. 147 1.311 1.474 10.649 10. 813 10. 976 11. 140 11.304 11.468 11. 632 11. 795 11.959 12. 123 20. 478 20. 642 20. 806 20. 970 21. 134 30. 308 30. 472 30. 635 30. 799 30. 963 40. 137 40. 301 40. 465 40. 629 40. 793 49. 967 50. 131 50. 295 50. 458 50. 622 59. 796 59. 960 1 0.124 1 0.288 1 0:452 1 9.626 1 9.790 1 9.954 1 10.118 1 10.281 5 6 7 8 9 .014 .016 .019 .022 .025 10 11 12 13 14 1.638 1. 802 1.966 2. 130 2. 294 21. 297 21. 461 21. 625 21. 789 21. 953 31. 127 31. 291 31. 455 31. 618 31. 782 40. 956 41. 120 41. 284 41. 448 41.612 50. 786 50. 950 51. 114 51. 278 51. 441 1 0.616 1 0.779 1 0.943 1 1. 107 1 1. 271 1 10.445 1 10.609 1 10.773 1 10.937 1 11.100 10 11 12 13 14 .027 .030 .033 .035 .038 15 16 17 18 19 2. 457 2. 621 2. 785 2. 949 3. 113 12.287 12. 451 12. 615 12. 778 12. 942 22. 117 22. 280 22. 444 22. 608 22. 772 31. 946 32. 110 32. 274 32. 438 32. 601 41. 776 41. 939 42. 103 42. 267 42. 431 51. 605 51. 769 51. 933 52. 097 52. 260 1 1.435 1 1.599 1 1. 762 1 1. 926 1 2.090 1 11.264 1 11.428 1 11.592 1 11.756 1 11.920 15 16 17 18 19 .041 .044 .046 .049 .052 20 21 22 23 24 3.277 3.440 3. 604 3. 768 3. 932 13. 106 13. 270 13.434 13. 598 13. 761 22. 936 23. 099 23. 263 23. 427 23. 591 32. 765 32. 929 33. 093 33. 257 33. 420 42. 595 42. 759 42. 922 43. 086 43. 250 52. 424 52. 588 52. 752 52. 916 53. 080 1 2.254 1 2.418 1 2.582 1 2. 745 1 2.909 1 12.083 1 12.247 1 12.411 1 12.575 1 12.739 20 21 22 23 24 .055 .057 .060 .063 .066 25 26 27 28 29 4. 096 4. 259 4. 423 4. 587 4. 751 13.925 14. 089 14.253 14.417 14.581 23. 755 23. 919 24. 082 24. 246 24. 410 33. 584 33. 748 33. 912 34. 076 34. 240 43. 414 43. 578 43. 742 43. 905 44. 069 53. 243 53. 407 53. 571 53. 735 53. 899 1 3. 073 1 3.237 1 3. 401 1 3.564 1 3.728 1 12.903 1 13.066 1 13.230 1 13.394 1 13.558 25 26 27 28 29 .068 .071 .074 .076 .079 30 31 32 33 34 4. 915 5. 079 5. 242 5. 406 5. 570 14. 744 14. 908 15.072 15. 236 15. 400 24. 574 24. 7.38 24. 902 25. 065 25. 229 34. 403 34. 567 34. 731 34. 895 35. 059 44. 233 44. 397 44. 561 44. 724 44. 888 54. 063 54. 226 54. 390 54. 554 54. 718 1 3.892 1 4.056 1 4.220 1 4.384 1 4.547 1 13.722 1 13.886 1 14.049 1 14.213 1 14.377 30 31 32 33 34 .082 .085 .087 .090 .093 35 36 37 38 39 40 41 42 43 44 5. 734 5. 898 6. 062 6. 225 6. 389 6. 553 6. 717 6. 881 7.045 7. 208 - 15.563 15. 727 15. 891 16. 055 16.219 25. 393 25. 557 25. 721 25. 885 26. 048 35. 223 35. 386 35. 550 35. 714 35. 878 45. 052 45. 216 45. 380 45. 544 45. 707 54. 882 55. 046 55. 209 55. 373 55. 537 1 4.711 1 4.875 1 5.039 1 5.203 1 5.367 1 14.541 1 14.705 1 14.868 1 15.032 1 15. 196 35 36 37 38 39 .096 .098 .101 .104 .106 16.383 16. 546 16. 710 16.874 17.038 26. 212 26. 376 26. 540 26. 704 26. 867 36. 042 36. 206 36. 369 36. 533 36. 697 45. 871 46. 035 46. 199 46. 363 46. 527 55. 701 55. 865 56. 028 56. 192 56. 356 1 5.530 1 5.694 1 5.858 1 6.022 1 6.186 1 15.360 1 15.524 1 15.688 1 15.851 1 16.015 40 41 42 43 44 .109 .112 .115 .117 .120 45 46 47 48 49 50 51 52 53 54 7. 372 7. 536 7.700 7.864 8.027 17.202 17.366 17.529 17.693 17. 857 27. 031 27. 195 27. 359 27. 523 27. 687 36. 861 37. 025 37. 188 37. 352 37. 516 46. 690 46. 854 47. 018 47. 182 47. 346 56. 520 56. 684 56. 848 57. Oil 57. 175 1 6.350 1 6.513 1 6.677 1 6.841 1 7.005 1 16.179 1 16.343 1 16.507 1 16.671 1 16.834 45 46 47 48 49 .123 .126 .128 .131 .134 8. 191 8. 355 8. 519 8. 683 8. 847 18. 021 18. 185 18.349 18.512 18.676 27. 850 28.014 28. 178 28. 342 28. 506 37. 680 37. 844 38. 008 38. 171 38. 335 47. 510 47. 673 47. 837 48. 001 48. 165 57. 339 57. 503 57. 667 57. 831 57. 994 1 7. 169 1 7. 332 1 7. 496 1 7.660 1 7. 824 1 16.998 1 17. 162 1 17.326 1 17.490 1 17.654 50 51 52 53 54 .137 .139 .142 .145 .147 55 56 57 58 59 9. 010 9. 174 9. 338 9. 502 9. 666 18.840 19. 004 19. 168 19. 331 19. 495 28. 670 28. 833 28. 997 29. 161 29. 325 38. 499 38. 663 38. 827 38. 991 39. 154 48. 329 48. 492 48. 656 48. 820 48. 984 58. 158 58. 322 58. 486 58. 650 58. 814 1 7. 988 1 8.152 1 8.315 1 8.479 1 8.643 1 17.817 1 17.981 1 18.145 1 18.309 1 18.473 55 56 57 58 59 .150 .153 .156 .158 0.161 Page 480] TABLE 8. Sidereal into Mean Solar Time. 1 To be subtracted from a sidereal time interval. Sh 9* lOh llh 12" igk 14h ISk For seconds. 1 m. m. s. TO. S. TO. 8. TO. «. TO. s. TO s. TO. S. TO. S. 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. 794 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 58. 610 2 8.440 2 18.269 2 28. 099 4 .011 6 1 19.456 1 29. 285 1 39. 115 1 48.944 58. 774 2 8.603 2 18.433 2 28. 263 5 .014 6 1 19.619 1 29.449 1 39.279 1 49. 108 1 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 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 59. 265 2 9.095 2 18.924 2 28. 754 8 .022 9 1 20. Ill 1 29. 940 1 39. 770 1 49.600 59. 429 2 9.259 2 19.088 2 28. 918 9 .025 10 1 20.275 1 30. 104 1 39.934 1 49. 763 59. 593 2 9.423 2 19.252 2 29. 082 10 .027 11 1 20. 439 1 30. 268 1 40. 098 1 49.927 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 59. 921 2 9.750 2 19.580 2 29. 409 12 .033 13 1 20. 766 1 30. 596 1 40. 425 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 50.419 2 0.248 2 10. 078 2 19. 907 2 29. 737 14 .038 15 T 21. 094 1 30.923 1 40. 753 1 50.583 2 0.412 2 10. 242 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 17 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 1 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. 238 2 1.067 2 10. 897 2 20. 727 2 30.556 19 .052 20 1 21.913 1 31. 743 1 41. 572 1 51.402 2 1.231 2 11. 061 2 20. 890 2 30. 720 20 .055 21 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 22.404 1 32.234 1 42. 064 1 51. 893 2 1.723 2 11.552 2 21. 382 2 31.211 28 .063 24 25 1 22. 568 1 32. 398 1 42.227 1 52.057 2 1.887 2 11. 716 2 21.546 2 31. 375 24 .066 1 22. 732 1 32.562 1 42. 391 1 52.221 2 2.050 2 11. 880 2 21. 709 2 31. 539 25 .068 26 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 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 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 1 23.387 1 33.217 1 43. 047 1 52.876 2 2.706 2 12. 535 2 22. 365 2 32. 194 29 .079 30 1 23.551 1 33. 381 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 2 22. 856 2 32. 686 32 .087 33 1 24.043 1 33.872 1 43. 702 1 53. 531 2 3.361 2 13. 191 2 23. 020 2 32. 850 83 .090 34 35 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 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 88 .104 39 1 25.026 1 34.855 1 44.685 1 54.514 2 4.344 2 14. 173 2 24.003 2 33. 833 39 .106 40 1 25. 190 1 35.019 1 44.849 1 54. 678 2 4.508 2 14. 337 2 24. 167 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 2 24. 658 2 .34.488 48 .117 44 1 25.845 1 35.674 1 45. 504 1 55. 333 2 5.163 2 14. 993 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 2 36. 454 54 .147 65 1 27.647 1 37.476 1 47. 306 1 57. 136 2 6.965 2 16. 795 2 26. 624 55 .150 56 1 27.811 1 37. 640 1 47.470 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. Sidereal into Mean Solar Time. [Page 481 01 •a To be subtracted from a sidereal time inteirval. 16k 17h ISh lOi" 201' 21h 22b 281" For seconds.! TO. 1 2 3 4 5 6 7 8 9 TO. S. 2 37. 273 2 37. 437 2 37. 601 2 37. 764 2 37. 928 m. 8. 2 47. 102 2 47. 266 2 47. 430 2 47. 594 2 47. 758 TO. 8. 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 TO. 8. 3 16.591 3 16. 755 3 16.919 3 17.083 3 17.246 TO. 8. 3 26.421 3 26.585 3 26. 748 3 26. 912 3 27.076 TO. 8. 3 36. 250 3 36. 414 3 36.578 3 36. 742 3 36.906 TO. 8. 3 46. 080 3 46. 244 3 46. 407 3 46. 571 3 46. 735 8. 1 2 3 4 8. 0.003 .005 .008 .011 2 38. 092 2 38. 256 2 38. 420 2 38. 584 2 38. 747 2 47. 922 2 48. 085 2 48. 249 2 48. 413 2 48. 577 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 10 11 12 13 14 .014 .016 .019 .022 .025 .027 .030 .033 .035 .038 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 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 10.857 3 11. 021 3 11. 185 3 11.349 3 11.513 3 11. 676 3 11.840 3 12.004 3 12. 168 3 12.332 3 20. 687 3 20. 851 3 21.014 3 21. 178 3 21. 342 3 21.506 3 21. 670 3 21. 834 3 21. 997 3 22. 161 3 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 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 .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 35 36 37 38 39 .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 40 41 42 43 44 .109 .112 .115 .117 .120 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 3 53. 452 3 53. 616 3 53. 780 3 53. 943 3 54. 107 45 46 47 48 49 50 51 52 53 54 .123 .126 .128 .131 .134 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 14.953 3 15. 117 3 15.281 3 15.444 3 15.608 3 15. 772 3 15.936 3 16. 100 3 16.264 3 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 .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 66. 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 6583—06- -31 Page 482] TABLE 9. Mean Solar into Sidereal Time. s To be added to a mean time interval. 1 Oh Ih 2h Ch 4h oh 6h 7h 1 For seconds J m. 1 2 3 4 TO. 0.000 0.164 0.329 0.493 0. 657 TO. «. 9.856 10.021 10. 185 10.349 10.514 TO. «. 19. 713 19.877 20.041 20. 206 20. 370 m. s. 29. 569 29. 734 29. 898 30. 062 30. 227 7)1. S. 39. 426 39. 590 39. 754 39. 919 40. 083 40. 247 40. 412 40. 576 40. 740 40. 904 VI. S. 49. 282 49. 447 49.611 49. 775 49. 939 TO. «. 59. 139 59. 303 59. 467 59. 632 59. 796 TO. 8.995 9.160 9.324 9.488 9.652 8. 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 to. 432 50. 597 50. 761 59. 960 1 0. 124 1 0. 289 1 0.453 1 0.617 9.817 9.981 10. 145 10. 310 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 31. 705 31. 869 41. 069 41.233 41. 397 41. 561 41.726 41.890 42. 054 42. 219 42. 383 42. 547 50. 925 51. 089 51.254 51.418 51.582 0.782 0.946 1.110 1.274 1.439 10. 638 10. 802 10. 967 11. 131 11.295 10 11 12 13 14 15 16 17 18 19 .027 .030 .033 .036 .038 .041 .044 .047 .049 .052 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 51. 746 51. 911 52. 075 52. 239 52. 404 1.603 1.767 1.932 2.096 2.260 11. 459 11.624 11. 788 11.952 12.117 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 3.285 3.450 3.614 3.778 3.943 4.107 4.271 4.435 4.600 4.764 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. 812 42.711 42. 876 43. 040 43. 204 43. 368 52. 568 52. 732 52. 896 53. 061 53. 225 2.424 2.589 2.753 2.917 3.081 12. 281 12.445 12. 609 12. 774 12. 938 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 .055 .057 .060 .063 .066 .068 .071 .074 .077 .079 .082 .085 .088 .090 .093 .096 .099 .101 .104 .107 13.963 14. 128 14. 292 14.456 14.620 23. 820 23.984 24. 148 24. 313 24. 477 33. 676 33. 841 34. 005 34. 169 34. 333 43. 533 43. 697 43. 861 44. 026 44. 190 53. 389 53. 554 53. 718 53. 882 54. 046 3.246 3.410 3.574 3.739 3.903 -y 13. 102 13. 266 13. 431 13. 595 13. 759 13. 924 14. 088 14. 252 14. 416 14. 581 4.928 5.093 5.257 5.421 5.585 14. 785 14.949 15. 113 15. 278 15.442 24. 641 24. 805 24. 970 25. 134 25. 298 34. 498 34. 662 34.826 34. 990 35. 155 44. 354 44.518 44. 683 44. 847 45.011 54.211 54. 375 54. 539 54. 703 54. 868 4.067 4.231 4.396 4.560 4.724 35 36 37 38 39 5.750 5.914 6.078 6.242 6.407 15.606 15.770 15.935 16. 099 16.263 25. 463 25. 627 25. 791 25. 955 26.120 35. 319 35. 483 35. 648 36.812 35. 976 45. 176 45. 340 45. 504 45. 668 45. 833 55. 032 55. 196 55. 361 55. 525 55. 689 4.888 5.053 5.217 5.381 5.546 14. 745 14. 909 15. 073 15. 238 15. 402 40 41 42 43 44 6.571 6.735 6.900 7.064 7.228 16.427 16.592 16. 756 16. 920 17.085 26. 284 26. 448 26. 612 26. 777 26. 941 36. 140 36. 305 36. 469 36. 633 36. 798 45. 997 46. 161 46. 325 46. 490 46. 654 55. 853 56.018 56. 182 56. 346 56. 510 -j- 5.710 5.874 6.038 6.203 6.367 6.531 6.695 6.860 7.024 7.188 15. 566 15. 731 15. 895 16. 059 16. 223 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 .110 .112 .115 .118 .120 .123 .126 .129 .131 .134 .137 .140 .142 .145 .148 45 46 47 48 49 50 51 52 53 54 7. 392 7.557 7.721 7.885 8.049 8.214 8.378 8.542 8.707 8.871 17.249 17.413 17.577 17. 742 17.906 18.070 18.234 18. 399 18.563 18. 727 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 -J 16. 388 16. 552 16. 716 16. 881 17.045 17. 209 17. 373 17.538 17. 702 17.866 27. 927 28. 091 28. 255 28.420 28. 584 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 48. 461 48. 625 48. 790 48. 954 49. 118 i 57. 496 57. 660 57. 825 57. 989 58. 153 7.353 7.517 7.681 7.845 8.010 55 56 57 58 59 9.035 9.199 9.364 9.528 9.692 18.892 19. 056 19. 220 19. 384 19. 549 i 28. 748 28.912 29. 077 29. 241 29. 405 58.317 58. 482 58. 646 58. 810 58. 975 8.174 8.338 8.502 8.667 8.831 18.030 18.195 18. 359 18. 523 18. 688 55 56 57 58 59 .151 .153 .156 .159 0.162 TABLE 9. [Page 483 Mean Solar into Sidereal Time. To be added to a mean time interval. 1 8" 9" 10" . 11'' 12h ISk 14h ISfc For seconds J m. 1 2 3 4 VI. s. 1 18.852 1 19.016 1 19. 180 1 19.345 1 19.509 m. B. 1 28.708 1 28.873 1 29.037 1 29.201 1 29.365 1 29.530 1 29.694 1 29.858 1 30.022 1 30.187 7/1. 8. 1 38.565 1 38. 729 1 38.893 1 39.058 1 39.222 1 39.386 1 39. 550- 1 39.715 1 39. 879 1 40.043 m. 8. 1 48.421 1 48.585 1 48.750 1 48.914 1 49.078 1 49.243 1 49.407 1 49.571 1 49.735 1 49.900 m. s. 1 58.278 1 58.442 1 58.606 1 58. 771 1 58.935 1 59.099 1 59.263 1 59. 428 1 59. 592 1 59. 756 m. 8. 2 8.134 2 8. 298 2 8.463 2 8.627 2 8.791 m. s. 2 17.991 2 18.155 2 18.319 2 18.483 2 18.648 m. 8. 2 27.847 2 28.011 2 28. 176 2 28. 340 2 28.504 «. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 s. 0.003 .005 .008 .011 .014 .016 .019 .022 .025 .027 .030 .033 .036 .038 5 6 7 8 9 1 19.673 1 19.837 1 20.002 1 20. 166 1 20.330 2 8.956 2 9.120 2 9. 284 2 9. 448 2 9.613 2 18.812 2 18.976 2 19. 141 2 19.305 2 19.469 2 28.668 2 28. 833 2 28. 997 2 29. 161 2 29. 326 10 11 12 13 14 1 20.495 1 20.659 1 20.823 1 20.987 1 21. 152 1 30.351 1 30.515 1 30.680 1 30.844 1 31.008 1 40.207 1 40.372 1 40.536 1 40. 700 1 40. 865 1 50.064 1 50.228 1 50.393 1 50.557 1 50. 721 1 59.920 2 0.085 2 0.249 2 0.413 2 0.578 2 9.777 2 9. 941 2 10. 105 2 10.270 2 10.434 2 19.633 2 19. 798 2 19.962 2 20. 126 2 20. 290 2 29.490 2 29. 654 2 29. 818 2 29. 983 2 30. 147 15 16 17 18 19 1 21. 316 1 21.480 1 21.644 1 21.809 1 21.973 1 31. 172 1 31.337 1 31.501 1 31.665 1 31.829 1 41.029 1 41. 193 1 41.357 1 41.522 1 41.686 1 50. 885 1 51.050 1 51.214 1 51.378 1 51.542 2 0.742 2 0.906 2 1. 070 2 1. 235 2 1.399 2 10.598 2 10. 763 2 10.927 2 11.091 2 11.255 2 20.455 2 20. 619 2 20. 783 2 20. 948 2 21.112 2 30. 311 2 30.476 2 30. 640 2 30. 804 2 30. 968 15 16 17 18 19 20 21 22 23 24 .041 .044 .047 .049 .052 .055 .057 .060 .063 .066 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 1 22. 137 1 22.302 1 22.466 1 22.630 1 22. 794 1 31.994 1 32. 158 1 32. 322 1 32.487 1 32.651 1 41. 850 1 42.015 1 42. 179 1 42.343 1 42. 507 1 51. 707 1 51.871 1 52.035 1 52.200 1 52. 364 2 1.563 2 1.727 2 1. 892 2 2.056 2 2.220 2 11.420 2 11.584 2 11. 748 2 11.912 2 12. 077 2 21.276 2 21. 440 2 21. 605 2 21. 769 2 21.933 2 31. 133 2 31. 297 2 31.461 2 31.625 2 31. 790 1 22.959 1 23. 123 1 23.287 1 23.451 1 23. 616 1 32.815 1 32.979 1 33. 144 1 33.308 1 33.472 1 42.672 1 42.836 1 43.000 1 43. 164 1 43. 329 1 43.493 1 43.657 1 43.822 1 43.986 1 44. 150 1 52.528 1 52.692 1 52.857 1 53.021 1 53. 185 2 2.385- 2 2.549 2 2.713 2 2.877 2 3.042 2 12. 241 2 12.405 2 12.570 2 12. 734 2 12. 898 2 22.098 2 22. 262 2 22.426 2 22. 590 2 22. 755 2 31. 954 2 32. 118 2 32. 283 2 32. 447 2 32.611 25 26 27 28 29 .068 .071 .074 .077 .079 1 23.780 1 23.944 1 24. 109 1 24. 273 1 24.437 1 33.637 1 33. 801 1 33. 965 1 34. 129 1 34. 294 1 53. 349 1 53.514 1 53.678 1 53.842 1 54.007 2 3.206 2 3.370 2 3.534 2 3.699 2 3.863 2 13.062 2 13.227 2 13.391 2 13.555 2 13. 720 2 22. 919 2 23. 083 2 23. 247 2 23.412 2 23. 576 2 32. 775 2 32.940 2 33. 104 2 33. 268 2 33.432 30 31 32 33 34 .082 .085 .088 .090 .093 35 36 37 38 39 40 41 42 43 44 1 24.601 1 24.766 1 24.930 1 25.094 1 25.259 1 34.458 1 34.622 1 34. 786 1 34.951 1 35. 115 1 44.314 1 44.479 1 44.643 1 44.807 1 44.971 1 54. 171 1 54.335 1 54.499 1 54.664 1 54. 828 2 4.027 2 4.192 2 4.356 2 4.520 2 4.684 2 13.884 2 14.048 2 14. 212 2 14. 377 2 14. 541 2 23. 740 2 23. 905 2 24. 069 2 24. 233 2 24. 397 2 33. 597 2 33. 761 2 33. 925 2 34. 090 2 34. 254 2 34.418 2 34. 582 2 34. 747 2 34.911 2 35. 075 2 35. 239 2 35. 404 2 35. 568 2 35. 732 2 35. 897 35 36 37 38 39 .096 .099 .101 .104 .107 1 25.423 1 25.587 1 25. 751 1 25.916 1 26.080 1 35.279 1 35.444 1 35.608 1 35. 772 1 35.936 1 45. 136 1 45.300 1 45.464 1 45.629 1 45. 793 1 54. 992 1 55. 156 1 55.321 1 55.485 1 55. 649 2 4.849 2 5.013 2 5.177 2 5.342 2 5.506 2 14. 705 2 14. 869 2 15. 034 2 15. 198 2 15. 362 2 24. 562 2 24. 726 2 24. 890 2 25.054 2 25. 219 40 41 42 43 44 .110 .112 .115 .118 .120 45 46 47 48 49 1 26.244 1 26. 408 1 26.573 1 26. 737 1 26.901 1 36. 101 1 36.265 1 36.429 1 36.593 1 36. 758 1 36.922 1 37.086 1 37.251 1 37.415 1 37. 579 1 45. 957 1 46. 121 1 46.286 1 46.450 1 46.614 1 55. 814 1 55.978 1 56. 142 1 56. 306 1 56. 471 2 5.670 2 5.834 2 5.999 2 6.163 2 6.327 2 15.527 2 15.691 2 15. 855 2 16.019 2 16. 184 2 25. 383 2 25. 547 2 25. 712 2 25. 876 2 26. 040 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 .123 .126 .129 .131 .134 50 51 52 53 54 1 27.066 1 27. 230 1 27.394 1 27.558 1 27. 723 1 46. 778 1 46.943 1 47. 107 1 47. 271 1 47. 436 1 56.635 1 56. 799 1 56.964 1 57. 128 1 57.292 2 6.491 2 6.656 2 6.820 2 6.984 2 7. 149 2 16.348 2 16.512 2 16.676 2 16. 841 2 17.005 2 26. 204 2 26. 369 2 26. 533 2 26. 697 2 26. 861 2 36. 061 2 36. 225 2 36. 389 2 36.554 2 36. 718 2 36. 882 2 37. 047 2 37. 211 2 37. 375 2 37.539 .137 .140 .142 .145 .148 55 56 57 58 59 1 27. 887 1 28. 051 1 28.215 1 28.380 1 28.544 1 37. 743 1 37.908 1 38.072 1 38.236 1 38.400 1 47. 600 1 47. 764 1 47.928 1 48.093 1 48.257 1 57.456 1 57.621 1 57. 785 1 57.949 1 58. 113 2 7.313 2 7.477 2 7.641 2 7. 806 2 7.970 2 17. 169 2 17.334 2 17.498 2 17.662 2 17.826 2 27.026 2 27. 190 2 27. 354 2 27.519 2 27. 683 .151 .153 .156 .159 0,162 Page 484] TABLE 9. Mean Solar into Sidereal time. i To be added to a mean time interval. 16i> l?!- ISfc lOk SOI- 21'' 22h 23i> For seconds. m. 1 2 3 4 m. s. 2 37. 704 2 37. 868 2 38. 032 2 38. 196 2 38. 361 m. «. 2 47. 560 2 47. 724 2 47. 889 2 48. 053 2 48. 217 TO. «. 2 57. 417 2 57. 581 2 57. 745 2 57. 909 2 58. 074 in. s. 3 7. 273 3 7. 437 3 7. 602 3 7. 766 3 7. 930 TO. 8. 3 17. 129 3 17.294 3 17.458 3 17.622 3 17.787 TO. 8. 3 26. 986 3 27. 150 3 27. 315 3 27. 479 3 27. 643 TO. 8. 3 36. 842 3 37. 007 3 37. 171 3 37. 335 3 37.500 TO. .«. 3 46. 699 3 46. 863 3 47.027 3 47. 192 3 47. 356 s. 1 2 3 4 s. 0.003 .005 .008 .011 5 6 7 8 9 2 38.525 2 38. 689 2 38. 854 2 39. 018 2 39. 182 2 48. 381 2 48. 546 2 48. 710 2 48. 874 2 49. 039 2 58. 238 2 58. 402 2 58. 566 2 58. 731 2 58. 895 3 8.094 3 8.259 3 8.423 3 8.587 3 8.751 3 8.916 3 9.080 3 9.244 3 9. 409 3 9.573 3 17.951 3 18. 115 3 18.279 3 18.444 3 18. 608 3 27. 807 3 27. 972 3 28. 136 3 28. 300 3 28. 464 3 37. 664 3 37. 828 3 37. 992 3 38. 157 3 38. 321 3 47.520 3 47. 685 3 47. 849 3 48.013 3 48. 177 5 6 7 8 9 .014 .016 .019 .022 .025 10 11 12 13 14 2 39. 346 2 39. 511 2 39. 675 2 39. 839 2 40. 003 2 49. 203 2 49. 367 2 49. 531 2 4e. 696 2 49. 860 2 59. 059 2 59. 224 2 59. 388 2 59. 552 2 59. 716 3 18. 772 3 18.937 3 19. 101 3 19.265 3 19.429 3 28. 629 3 28. 793 3 28. 957 3 29. 122 3 29. 286 3 38. 485 3 38. 649 3 38. 814 3 38. 978 3 39. 142 3 39. 307 3 39.471 3 39. 635 3 39. 799 3 39. 964 3 48. 342 3 48.506 3 48. 670 3 48. 834 3 48. 999 10 11 12 13 14 .027 .030 .033 .036 .038 -15 16 17 18 19 2 40. 168 2 40. 332 2 40. 496 2 40. 661 2 40. 825 2 50. 024 2 50. 188 2 50. 353 2 50. 517 2 50. 681 2 59. 881 3 0.045 3 0.209 3 0.373 3 0.538 3 9.737 3 9.901 3 10.066 3 10.230 3 10.394 3 19.594 3 19.758 3 19.922 3 20. 086 3 20.251 3 29. 450 3 29. 614 3 29. 779 3 29. 943 3 30. 107 3 49. 163 3 49. 327 3 49. 492 3 49. 656 3 49. 820 15 16 17 18 19 .041 .044 .047 .049 .052 20 21 22 23 24 2 40. 989 2 41. 153 2 41.318 2 41. 482 2 41. 646 2 50. 846 2 51. 010 2 51. 174 2 51. 338 2 51. 503 3 0.702 3 0.866 3 1. 031 3 1. 195 3 1. 359 3 10.559 3 10.723 3 10.887 3 11.051 3 11.21^ 3 20. 415 3 20. 579 3 20. 744 3 20. 908 3 21.072 3 30. 271 3 30. 436 3 30. 600 3 30. 764 3 30. 929 3 40. 128 3 40. 292 3 40. 456 3 40. 621 3 40. 785 3 40. 949 3 41. 114 3 41. 278 3 41.442 3 41. 606 3 49. 984 3 50. 149 3 50. 313 3 50. 477 3 50. 642 3 50. 806 3 50. 970 3 51. 134 3 51. 299 3 51.463 20 21 22 23 24 25 26 27 28 29 .055 .057 .060 .063 .066 .068 .071 .074 .077 .079 25 26 27 28 29 2 41.810 2 41. 975 2 42. 139 2 42. 303 2 42.468 2 51. 667 2 51. 831 2 51. 995 2 52. 160 2 52. 324 3 1. 523 3 1. 688 3 1. 852 3 2.016 3 2.181 3 11.380 3 11. 544 3 11.708' 3 11. 873 3 12.037 3 21. 236 3 21.401 3 21.565 3 21. 729 3 21. 893 3 31.093 3 31.257 3 31.421 3 31. 586 3 31. 750 30 31 32 33 34 2 42. 632 2 42. 796 2 42. 960 2 43. 125 2 43. 289 2 52. 488 2 52. 653 2 52. 817 2 52.981 2 53.145 3 2.345 3 2. 509 3 2.673 3 2.838 3 3.002 3 12.201 3 12.366 3 12.530 3 12.694 3 12.858 3 22.058 3 22. 222 3 22.386 3 22.551 3 22. 715 3 31.914 3 32. 078 3 32.243 3 32.407 3 32.571 3 41.771 3 41.935 3 42. 099 3 42. 264 3 42. 428 3 51. 627 3 51. 791 3 51. 956 3 52. 120 3 52. 284 30 31 32 33 34 .082 .085 .088 .090 .093 35 36 37 38 39 2 43.453 2 43. 617 2 43. 782 2 43. 946 2 44. 110 2 53. 310 2 53. 474 2 53. 638 2 53. 803 2 53. 967 3 3.166 3 3.330 3 3.495 3 3.659 3 3.823 3 13.023 3 13. 187 3 13,351 3 13.515 3 13.680 3 22. 879 3 23. 043 3 23.208 3 23.372 3 23. 536 3 32. 736 3 32.900 3 33.064 3 33.228 3 33. 393 3 42. 592 3 42. 756 3 42.921 3 43. 085 3 43. 249 3 52. 449 3 52. 613 3 52. 777 3 52.941 3 53. 106 35 36 37 38 39 .096 .099 .101 .104 .107 40 41 42 43 44 2 44. 275 2 44. 439 2 44. 603 2 44. 767 2 44. 932 2 54. 131 2 54. 295 2 54. 460 2 54. 624 2 54. 788 3 3.988 3 4.152 3 4.316 3 4. 480 3 4.645 3 13.844 3 14.008 3 14. 173 3 14.337 3 14.501 3 23. 700 3 23. 865 3 24. 029 3 24. 193 3 24. 358 3 33.557 3 33. 721 3 33. 886 3 34. 050 3 34. 214 3 43. 413 3 43.578 3 43. 742 3 43. 906 3 44. 071 3 53. 270 3 53.434 3 58. 598 3 53. 763 3 53. 927 40 41 42 43 44 .110 .112 .115 .118 .120 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 2 45. 096 2 45. 260 2 45. 425 2 45. 589 2 45. 753 2 54. 952 2 55.117 2 55. 281 2 55. 445 2 55. 610 3 4. 809 3 4.973 3 5.137 3 5.302 3 5.466 3 14.665 3 14.830 3 14.994 3 15. 158 3 15.322 3 24.522 3 24. 686 3 24. 850 3 25.015 3 25. 179 3 34. 378 3 34.543 3 34. 707 3 34. 871 3 35. 035 3 44.235 3 44. 399 3 44. 563 3 44. 728 3 44. 892 3 54. 091 3 54. 256 3 54. 420 3 54. 584 3 54. 748 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 .123 .126 .129 .131 .134 .137 .140 .142 .145 .148 2 45. 917 2 46. 082 2 46. 246 2 46. 410 2 46. 574 2 55. 774 2 55. 938 2 56. 102 2 56. 267 2 56. 431 3 5.630 3 5.795 3 5.959 3 6.123 3 6.287 3 15.487 3 15.651 3 15.815 3 15.980 3 16. 144 3 25. 343 3 25.508 3 25. 672 3 25. 836 3 26.000 3 35. 200 3 35. 364 3 .35. 528 3 35. 693 3 35. 857 3 45. 056 3 45. 220 3 45. 385 3 45. 549 3 45. 713 3 54. 913 3 55. 077 3 55. 241 3 55. 405 3 55.570 2 46. 739 2 46. 903 2 47. 067 2 47. 232 2 47. 396 2 56. 595 2 56. 759 2 56. 924 2 57.088 2 57. 252 3 6.452 3 6.616 3 6.780 3 6.944 3 7. 109 3 16.308 3 16.472 3 16.637 3 16.801 3 16.965 3 26. 165 3 26. 329 3 26.493 3 26.657 3 26.822 3 36.021 3 .36. 185 3 36. 350 3 36. 514 3 36.678 3 45. 878 3 46. 042 .3 46. 206 3 .46. 370 3 46.5.35 3 55. 734 3 55. 898 3 56.063 3 56. 227 3 56. 391 .151 .153 .156 .159 0. 162 TABLE 10. Mean Time of Sun's A^isible Rising and Setting. [Page 485 ® H S ^ XI ■p (N on IM a (V g" a «M 1-5 -S a 5 -s Hi o •xojddv ifi ^ V- CC Oi pJcBrtcopiaJtfcc«a2|P:5aJrtM03cceHa2daJpicBejao«c«cJcert JiCOiCOlOOlOrHiOrH ■^rH-*i--('*rtTrrtTiio)'T:>c^co(Nc<5c^eoc^eOM|eococ^coc^e'5c^eoc^-*c^-* »0^iCCDiOCOii^50iC!0 i/5^ii5^iOeO»C^U2^ 'ii^«OiO:0»O^iC^ia<0iO<0 iC O lO O lO O is O T)< .-( •.)< Ti rf i-i ■^ ,-1 T)i r-l Tj< ,-( ^ lO to irt O iC CD >0 «£> iC to iC to iC to IC to lO to iC to g'-^C^KNCOiHiCOStOODOO iOOiOOiOOT)<0-^0 .^lOtOiCtOiCtOiOtOiOtO ^ictoictoictoictoicto I OS M CO lO to t ^iCtO»OtOiOtOiOtOvOtO •xoaddv ^"^ .^12; ^ iC <^ lO ?0 iC ^ i^ ^ iC «0 uO CO iC CO lO to lO i;0 lO «D QOOCDCMuJ-^OJCOrHXOiOQO^^OCi-^iCiMI^OOl CCfNCOC^COfNMC^COC^fNCOC^CCC^COMCCfMCOlNCO lOcOiCcOiCCOiCCOiOCD lOcOiOtCiCCOiCcOiCcOiOcO ooiiOi-icocorHicait^ i0 00-^O(M!MOC00ai0 lOCOiCCOiOCOiOtOiC^ ooocca>'MrHO(Nas'^ ■^O'^O'* r-l -^tH CO rH iCCOiftcDiCCOiOCOiOCO t^Q0«0O't!rHCCCCi-l(N(N?ilN(NCCC^CO(NOOC^CO lOCOiOCOiCCOiOiOiftCOiiCtDiOCOjAOiCcOiCCOiOcO r*COOOO'^OSCOTH»-'^a>i'NpQi-iaicocoiOcocoooo COrHCOr-tCOf-ICOrHCOf-tC0 5Jo5CS'N(NC0OrH»H ^iC^iCcOiiOcOiOcOii?5cO iCcoiOcOiOcOiCiCOiCco ocaas'«*cocor>.ioa>'^oc5^ t^ CO 00 iC Tt* O ^iCCO»OCO"DCOiOCOiCcO lO^iCCOiCcOiOcOiOCO S£'«i'(NCOCO*l'^'HiCQ^ ^iCCOiCCOiOcOiCcOiCCO Oicpaat^oOoot^OicoO lOCOiOCOiCcOiCCOiCCO ^lOCOTfCOCO'^iNiO'N^ ^^JiOCOiCcOiCCDiOcOiCCO -^iCCOiC'^'^'<7*COiCCOcO ^iCcOvCcOiOcoiOcOiOcO rHOOr^OlQOOOOit^O iCCOiCcOiCCOiCCOiCcO COr-(C^C^r-tCOO'^ai>C t^t^cOOOiOO-^i-l'NCN'-'CO 3i-H00i-lCOiNCOiNCOC^ 5 CO »C CO iC CO iC CO iC CO COIN lOcO OOCjj)t>-t^iX>OiiOO-<1COiOcOiOcOiCCOiOCO COoso ■^THTPrH-^iH-'J^rH'^i-tCOC^ iCcOiOCOi^cOiCiCOiOCOiCCO c^CO-^iC-^iOiO'^CO'^cp'cOI-^C^ODi-IOOOaiOiO ^lOCOiOcOiOCOiCCOiOcOuCCOiCCOiCCOiOCTiCCO ai iH 00 iC COiO N t^C^I CO ift CO coco CO Tf iC CO lO CD I ^ lO ic ic Tf S COiCcOiO CO CO r-^ 00 CO »o CO »0 CO lOtO c^ l~* iC CO iC CO iCiC CO iCI> Tt< OO CO 00 CO 05 (N OS *-' o ^lOcOiCCOiCCOiOcOiCCOiiOcOiCCOiOcOiCcOiOCO lO COiC C^<7>iN COiC CO 00 CO 00 '^ iC CO lOCO (^t~-ict^icr^cDcococpi>iCGC'^oOTf05coasc^o! rfjiOCOiCcOiCCOiCCOiCColiCCOiOCOiCCOLCcOiOCO^ 5C0»0 COu ■I IN OCO 05 CO • -^ ^- »0 CO 5 CO lO COiO CO iC CO '^ t^ CO iCi cOiO CO 5S iCCO OS-^OOTfOpiOt^cOCOCOCOt^ »oocooo^cor^t^i>*t :ii5oiJt'<5»ooicoioO|iCo»ooiooiooiCi-i ^lOcOiCcOiCCOiCcOiCCO jiOcOiCCOiOCOiCcOiOcO SOOiCOOvCO'^as'^olcOfHCOi— liNiNiNN'^^CO lO T-H lO iC cOiO cOiC CO iCCO^ CO ! 5 COiO CO iC lO OS »f? '7* CO i-t '^ .-< -^ r-1 X* iC CO tO O coco lOcO r* OS t^ Oi t^ 0i r-- 00 r^ 00 00 i>- oo r* Oi co i^ co o ic o & lO O ^ O iC O iC O lO O iC O lO O lO O lO t-( lO i-( ^lOCOiCCOiOCO^cOiCCO iCCOiCCOiCcOiOCOiCCO iC COiC c oooiooot^oi>i-'lt;rr-icor-ico'Nic. CO t^ CO r-1 lO I— 1 lO T— < lO I— I CO iC CO >0 CO »0 CO Oi-iO»-HOrHOiHOi-l cOcDCDCDCDcOCOCOcOCO !s^3ss to to to CO CO CO CD ) to to to to cooc^o»c^ t to to to iC to u HOT^eO>-ICCi-l!cO.-l£J' _ _ i Oi-lOi-lOrHO ^tototototototototototoototototototototo C^^C^rt|c>|,^(M,-IMrtCMrHMrHC^rJC^£J^C^^lNpHC|JrHC2 0.-I0 to to to Or-(Oi-i > to to to to . .-10.-IO to to to to t-.&T-i Or-(C to to to to to t ,rt^„TtirtiTj<,-iC0i-^C0rH«li-IC5i--iCgwMi-HM^CC-HC0rH sSS3SoSo?^o;=i|o;-io;-io;^orHOri P^tOtOtOtOtOtOtOtOtOtOtOtOtOtOtOtOtOtOtOtO Olio to to to i-Orl to to to 0T-10.-I to to to to rtajaSaoPHCcOScdpHCB 05ai05co05a2P5!M?ia3 PScoOit»33aQrtcc05od O 1-1 IM «l to to to to 1-iOr^O-H to to to to to OiH to to tt^^O t^ 00 Cs tD Page 486] TABLE 10. Mean Time of Sun's Visible Rising and Setting. S .a 5 o .2 T-H IN a> .Q 3 ^|zi •xojddv •xojddv T)H t~ Tj< r- T)< t~ Tf t- T)( t~ ■.!< t~ iOCOCO:pOGOaDT-l»OCC CTtooiostoc^icoinooo TIii-ICOlHCOC» ^ l*» -^ !:-• SCOOOtOO'^J' r-l CO i-H T)i i-H ,C* »0 CO lO CD lO o«2;oco 0000cOQ'*(Nrt'^O5CO iOCOlOCO»OCOlOCO"^CO t^oi'»}'i-i(M".t*Qcor^t2? mioiooiooiOO'^o ■*cOTtit>--.jOaocoQrHM i^cOiCCOiCCOiCCOiCCD r-(.-(0>cor^»oior^coai >CCOiCCO»OCOiOCOiCCO OiiOcot^-giosc^iMC»Tj< > iC lO lO lO ■^CO-^CO-^CO-^lt^TlIt^ ■*i-ii-cooic^i-toc^oi-^r-co S'*cocoT*(^ iOr*"*^'^t OOiCCOCOiOOOCOOi— ii-*iOCOGOiCcOI^Tf!j>C^i-l lOCOiOCOiOCOiOCOiCCO »QOcocot^iC:aicoo(M'M;ocoosici>cocoQO'^a> ^lOCOiOcOiO C^ 'MCOC^CO CO lO CO »/^ CD (>J CO r-f CO i-( CO i-( iOCO>CCDiOCOiCcO»OCO ^iOCO»C COiC t-COO^"n"OlcOi-tC^COOfOiCOt^t^ CO lO CO tO CO C^COMCOlMCOrHCO lOCOiCCOiCCOiCCOiCCO ^CoS^04(M rfjiOcO tOcOiC ■^a>COCCt^cO0DiCOi'^»-HC^cOO'fC^COCOiC^iOiHC005l:^GO<35COO & CO M CO C^ CO ^ lO CO lO coo C^COC^WiN -^ lO CO iC CO C^CMC^iMC^COtNCOtNCO iCcOOcOiCCOiOCOiCCO C^COC^COT-ICOi-HCOrH-^ lOCOiOCOiOCOiOCOiOCO i-l-^OlCOOOODCDOTt^r-l r-tTP0rf0Tj*0>500 lOcOiOcOiCCOiCCOiCCO OC^COCOWiCOt^ODOO 1-HTfrH'^rH'^rH'^O"^ lOCOiCCOOCOtOCOiOCO SCO CJ to CO '^ COC^ CO tN CO rf^iO COiO COiO ■^co - - _ C^COfTJ CO(N CO O CO O CO lO'MCOrWt-'OOQOiOir^OCO.-l _. I ) ?5 Ci-HOCMTj.CM -NeOCMCOCMCOCMCOCMCO OCDiOCOOcOOCDOCO CMCOCMCOrHCOi-l'^t-('<*« OCOOCDICCOOCDOCD i-HOiOQOirH _ _ . . . COCMCOCCCMCCC^COC^ICO lOcOOcDOCOiOCOiOCD OOCMt^COCO-^-^iOCOCOCMOOi-iai JCMCOCMCOCMCOCMCOC-'^c S*COt^t^t^r*Q0cDt30iOO5 ^ iC CO lO CD O rl '^ i-H -^ i-l CD lO CD lO CD e Q CO Oi CO Oi S5 lO iH -^ rH TJ4 ^ iC CO O CO o r- QO i^ 00 00 CO O CO O CD OOtJ^OCOt-hCMCMCMCO Tt•C^^Tt^CMTt^CM'^CMTrCM OcDOcDiCCDiOcDOcD i-HCOi-H-^OiCOSOoOco OCMOOCOt^'^CDiOOcO CO CO CM CO CM CO CM CO CMCC O^OOCOOCOOCOOCO h»r>.coGOiCQC'^aicoo COCMCOCMCOCMCOCMCOCO OCOiCCOOCOiOcDOCD l^OOt^OlCOOiOOOf-tTfrH- 5 COO CD Tj< rH "Tf" C4 Tt* C^ O COO COO CO ' CM CO CO •CS'^t^CM ) COOCD CM CO 1-1 '^ rf CMrPCM O COOCD »CMOCMOCMCOi-ICDr ftO rHO i-l O ^OcDO COO rH O rH O r-t j COO COO CO I 3t^oaoo5Qoasa>ooai Sr-IO.-C^.-l'^rHTj^rH 5CDOCDOCOOCOOCD S^ ^ ^ Tf Tf< O rH O I— ( O ^O COO COO OCOO CO CO r-tO.-lOr-t CO O CD O CO St- Tt< t>. -^ CO OtHO T-(0 rfjO COO COO ■»*< CPTt-CMI^THt* ^01-l DCDOCO O i-( O »-1 o O CDO CD O CO 5000CD"^CO SOCOOCDOCD ,OOOt^Ot-i-*COi-iOCM ■rtiCM-^ O CO O CM-^CM COOCO Tj*CM TjiCM O CD O CO O i-i O OCOO OOCDOJ iHOtH COOCO ■^i-iTpCM OCOO CD iCCOiC t^ CO t^ CO 00 C^ 00 f-l lO r-t lO 1— I »d— t CO lO CO iC CO iC CO 3CO00'*00'*t~-«»'t^-* 5 .-I CO 1-1 CO O CO H O *-1 O I— t O rH ) CO CO CO CO CO CO SCO "-I CO "-I CO Oi-(Oi-(0 .C> CO CO CO CO CO ^COi-ICOrHiCO^COi-(CO^COi-lCOCS S*i-i^05T(icoi>COOOCO ■ CO 00 ot^«^asTj(N05c^a> CO 00 >noo Moom 00 CO 00 CO 00 i-l-^Tfi-ltaQOOOOQtp COOOCOOOCOOOC^OOClOl r*»Hc^cot^THco»ooo!o>-ooo O'^rHCO.-l 00 CO 00 CO 00 C<>Mfr)COr-ICOO^SlO cooocooocoooeooocooo ' t~ Tfl t- T}< O •.}< t- glCCO tOtC cot- CO 8 00 lO coo ■^O-^r-l 00 CO 00 CO 00 eOCDCOO^OCO«D^COO C^C^CMlMCJCOi-ICOrH-!!' lOC^t-lO-^OOi-lr-l g'inr~coOTC_-- ■*O'^O'3>i-IC0i-IC0i-i oo-*iq 1--M.HO0-*! C^ C^COrHCO i> T)i r- •.* t^ inooi-i(Nt«oe3Qooio S"oacot~iOicoDc^i-ia>co '5'0'VO-*0'*i-.'* «0 t» CO O O M ■^ iH Co i~^ CO T— I CO C^ CO 04 r*t-i/5oc^coaiio^oo e 2J CO o lO 00 1 fc O >C O iC iC L ^lO O iC O ** t (NCOOiOt~00>CONCO CTiira«OOOCO.-lQOf-aO lOO>0 0'*0-<3j'r~cot- COOOOiOlNOtOtOQCO lOO^O'^.HeoiHcoiN cooocooocoooeooocooo 0(Ntoi>oc^iOgoo>eo OiOiCiO"SO'>Seoooeooocooo t~«o-j03!Q05iO-5ioooiO ■*t~T)(r.eot-eoooeooo toQO(NCOI> S' t^ Q »0 C^ CO .c* lO to iO :o lO COf-l lO o^ t- tC O O L^ i^ «>iOO-*tO t^Oi»Oi-(COCOT-*:OaOOO lOrHCOCOOtOt— OS-^IM sSoiooS ^lOtOiOtOiOtOiCtOiOtO Si-ir-OiOD c eO»0>H1^0»0>tDrHT)ICOiC4tOO>QOt^'-lT)o> rf*iOtO»OtO»O^U0^iCtD eoiNoimiooiTH-^t-OJ OJeO-HCOr-ieOiH'>S<0'^ rH to t- as CO CO CM C^ (M 05 t^Tft-T). Til I> Tf C- <0000 0"CCOO»«0 0>05tOCOiM«0 ii:)toiotoiotoictoiCto,-^t^Tj-^t ;o50oOi:it~co>0"»'Tj to ic to ic to SOSOODi-l t-C i-l -* rH T)H rt ' rf* lO to lO to iC t i-iTj ^ CO C^ CO 04 CO to O to lO to isoOT*, RO< cool coo* .^ iC to iC to iC OIOi-lrHOCOOOTtl[-tO Ol'J104-j<04T»>rH-*iHTJ' lOtOiCtOiOtOiCtO^tO ;(Ni-l0401i-ICOO'*00>0 SCO CO CO CO CO ^lO tOlO to>c CO coco 04 CO to »^ to lO to Jt-OStOOiiCOTjIrHC SCO 04 CO Ol CO riS>OtOiOtOiO CO CO CO to »o to iC to > toioto Oi O t-* CO »0 iO lO O lis O lO o ■* r- •<}< t- T)> t^ 01t>-050t~COT(ltOr-<00 iOOt) T)t I- •* J> ^ to to Tf 00 OJ © 3 lO to lO to iC t^ o> 04 1- •* lo r» OJ inoiOOic ~ - 1 04 >-< o oj go -^ P rH iC rH »C O lO >>otomtoioto gooi i!5i-i § to-* COO) iaoioo lO tOtC tOiC gggss t-totor^icojTfQoit-i C4C0 04C004COOJ^04t)I lOtOiCtOiOtOiCtOiOtO ^coosTjioototot^ooa r-<-* — — — 5 to lis to > U5 to lO to lO to sssss iO coo CO o COiCCOiCCO 'NcoTHTt*o»2astDoot^|r>'aicooTt*<-iw(N^^|Oioa>t; iCCD»CCOiOcOiCcOO?0 d Tf (N -<** (N -^ O CO iC CO lO CO UO COiCCOiC CO O COiO CO i-tC0t-OG05>01 ^iCCOiOCDiOCOOCOiOCO jCOCOCOOOCOCOCOCOOOCOj lOCOOCOiOcOOOOCOi CO 05 CO COiCCO CO 00 cocoes CO lO coo cOiOCO lt>-OCOf-lOCOCO'csos s; o 1— to i-H o ^O CO O coo CO O CO O CO S*aooccocoOQOcor>-co OrHOr- lOr-iOrHOrH rfJOCOOcOOcoOcOOCO OOCOt^COt^-'^COOOO ocoocoocoocooco 5§C0CO 5 coo CO t^CSCOCOO"^ CO CO CO CO CO CO O CO O coo CO >coco(Nr-o CO o5 65 CO 66 o CO o coo ocO" COOCO 0> 0005 0000"^ QO-^t*OcOOOCOO^ Tf CS ■<*< (N -^ CS O COOCOO CO ,: (OOCOOCO t>.<:Ot^cOI>>t>COt*co^- Ot-iOi— tOi— lOi— 'Oi-H ocoocoocoocooco 30 GOO coo d ^ O ^H O rl O i-l >0 coo CO oco O CO o o o OCO'-HOJiH (NOC^OCJ CO O CO OcO ^^ ."^izi pc; CO CO x> CO CO CStNCO-MCOifNCOCSCOejCOi-HCOf^CO — " — T-i O t-H O i-H O 1-1 O i-( COcOcOCOCOCOCOCO CO CO to to to to to , p^aioicadixpiinfica pixai'^pixfiaioicB fiicBPiaifimfiiaatiixi .-tCO^COr-ICO^-^^-^ )t-lOrt ^ to to to Or-lOrHOi-l to to to to to to SS83S CO coco CO CO rf QOQO r-lOr-jOi-* CO CO CO CO CO p^odtfoQPjaBtfcQKaQ ^^^ir^'l^ V WXlT'XXT'X XTXTT' Page 488] - TABLE 10. Mean Time of Sun's Visible Rising and Setting. 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ScDCOCDcOiCCDii liOcOiCCOOcOiCcOiCCO 3 Ci CTSO CO t-( r-coco-.r- iOOOQO:ii--l kc cOiO cDiC coco CO iC CO lO CD >i-H Oi (M OOCO 5 COiO CO iCcO ^'^'^LcN!f:;?59<2!::l?5002sc^r^co iC CO Id CO I UOCOiOcOiCC » (N O i-i --H Q C^ :OrHO»-HOr-( a CD CO CO CO CD CO lO T-l lO 1— I I lO coo CO I >ot>co HU5.-I0 >iOcOiC 00 C^ Ol rH ^ ' r-(OrHiO 61 -^ OJ '^ C^ " 3 <0 O CD »0 CD L I i'^ C^ -^ CO'- iiC CO O CO iC ! : CO CO CO CO CO 5 CO lO CO O CO : O pH O i-H O rH ; CD CO CO CD CO CO O COiO CD 'o CO iCOOCOOa-Mi-tQiM ascooDor^co CD iC CO iC CD 1-HiOCSl CO iC CO lO CD CDiO CD 'rJOi-'C^aiccooococoicr* CO -^ CO CO iC CO lO CO iC :gSSSS2 a CO CD CD CD CD CO iC-lOr^ lO CO O CO a ^ 1 O f-H (M Oi CO : O rH O i-H O 1-1 a CO CO CO CD lO CO ldl-HC!-l iC CO O CO gOOi-iOiCO r-i O I— I iC 1— I ; !0 CD CD CO iC CD t>. ■* cpcO iC r-liO 1-4 lO COOCO rf coco 10 T— I O O CD O CO iC CO O CO OGOCOOKN O CO »c CD lO CDO CO lO CD u :Tfi:^cOcol> SCOOCOOCO Tt< OOCO o "J'fN-^CO CDiC CD CO t^ rf< GO CO O i-( r SCOiO COOCO COTfCO ICCOOCO CO CO CO CO CO CO O CO O CD i-lOCOCCiCCOCOOQOCOOS Tji CO ■<** CO CO lO CO iC CO o CO CO CO CO CO CD lO CD O CD C0 20 -J — CO CO CO CO iC CO lO coo -^rCDcDOOOCOOlfNrH "" 'SCOCOCOC0tJ< ; CO o CO o CD CDOOr^COOOOJOOfN ■* IM TI< cq TT ■* C>l '^ QO^'(/i»5r/3ct5co pt^ UQ cd cc Ph' cb 05 od pj co D:^' cc p^* oq (ij cc frj x p^' 02 CO CO CO CO ioocooO^DQOt©QOcooO'^loOepaot^Qpr»ooi^oor^»r^cot>-oot>-oot . -tp QO ^X) 00 -XJ ^ iC ■^ lO -^ lO 5 iC lO lO iO iC iC lOkCiCiOiCiOiOiCidO c»00a>0pCT>00<3i00O50DOs'aDOit^ai iC to iC ^ iC CO I^QCDQ^OOOOCOO iOtOiOcOiC?0>0'^iCtO iC^iC^iC«OiCtOiC«0 ^iC^i^COvCO»0^iO^ r-.(NCcO COO(NO(Nt-^r-(i-(rH(M iCco»OcDiOOiCcO»£5co tOCOiCCOiCCOiCCOiOCO iC^DiCcDvCcOiCCOiftcO QC^OCOOlCOOlTt^OO"^ litiCDiCCOiftCOiCCOiOO g'coaiifto^i00'^0"<9*o ^lOcoiocOiCcoiccoiceo giCt-^-^-HTf^McofMcoeo ^lOcOiOCOiOCOiCcOiCCO , ■^^COi-fCOlNC^C^'NCO «-HCO'— '■^OiCOiiCOSCO C^CO(M-^i-iiCOiOOcO<3^CO0>t JGOt^OOt^Ol COr-JCOi-HCOi-HCOr-lCOi-H lOCOiOCOiO'OlCCOiCCO >'^COTt"«#CO"^CO>/?(NCO »C*lCCOiCcOiOCOiCCOiOCO ICOcOCOt^i^t^C^OOfHOa ' i-H Tf rH Tf — I •<*< fH .^iCCOiO^iOcOiOCOiCcO ooaosooOrHt^c^r^co Tt^i-HCOfNCOC^COC^COCN iCcOiOOiCcOiCcOiCcO S*C005(NOiC'10i-ti-iOiM ^lOCO^OCOiOCOiOCOi^CO SCslrHfH^OfNOiCOOD-^ "^OCOiOCO»CcOiCcOlOcO g'MOt^^cDCOiC'^COiC COCCCOCOCOCOCOCOCOCO »^i/T)COiCcO»CcOiOcO»OcO T-(coi-(r^oaooia>opai TfiFHTPrHTPrHCOrHCO^ lOCOlCCOliiCOiOCOiCcD OOOI>OCO.-lCDC4»CCO COr4COC^CO(NCO(NCOC^ iCcOiCCOiCCOiCCOLOCD gocoi^t^r-oocooocooi COit^COtHCO^HCOi— (CQtH iCCOiOcOiCCOiCcOiOCO COOlO'-*'^r-(CO(NCOCO CO(NCO(NCOC^CO(NC0Csi iOCOiOCOiCCOiCCOiOCO 'f'^COiOCNvCf-l'.OOt^ CO(NCO(NCO(NCOiMC004 iCCOiCcOiCcOiCCOiCO cO-^iCTj^'-j'iO-^cocoi:^ COC^COtMCOC^COC^COiM lOCOiCCOiOcOiCcOiCcO COC^CO-COOQC^Oit-iOOrHOiC^OQCOt^'^CD»OiOcO CO (N CO W CO (N CO CO CO CO iCCOiCCOiCCOiOCOiCcO Ncoc^coc^coc^Scico lOCOiOCOiOCOiCcOiCcO r-iCcocoiOt^Tj^Qocooi COC^CO(NCOiM0O(MCOcooooot>-o> iOCOiC<©iCCOtCtOiOcO •*'^coiO'-JcooQca><3st>-oco^'fcO'W'^(Nco|ot^asa>t^oiOfM'»j*'^ COCOCOCOCOCOCOCOCOCO lOcOiC'-OiCiCOiCCOuOco! tOCOiCcOvO':OiOOiCCO •NCOrHCOOSO^OO'-Hr^C^UCCO'^in COCOCOCO(NCOC0'^(MTt*|!N^W'^ lOcOiOcOiCcOiCCOiOCO (^ 1:0 'H QO Oi OS 61 -^ CO "* rH ■'f lOOiOCDiCcOiCtOiCcO oOl-lcoco■^'^^^^c01-HQO i-HlOi—(»Cr-iiCi— llOr-(lO iCcoiocoi/5cOiOco»i:>co S*r^cococOiO»ococpcoGO COCOCOCOCOCOCOCOCOCO ^i£5cOiO'^i^COiiiCDiCCO g';OiCnOcOCOt^(MdOO COCOCOCOCOCOCOCOCOTji rf*iOcOiOCO»CCOiOCO>OCO «-HOiOaOOOr)cOCO>OiC :ococo'nOSrHI>CO lOcOiCcOiCcOiCcOiCCO 05C0t^C0COiCTt*cOC0G0 (N-^!M"^COTt<(NTj1C0Tr urjcoiOcOiOcOiOcOiOcD i—iasOi-'Goco«OTt S*COa'(NOO(NOi'^r*CO COCOCOTt*COTjct> •8^Bp •xojddv ^^ ;(Nr-IO(MOO'rt<|>cOiQOD :co'^cOTjCcO Tt<00C0OOC000iCC0t^ r-HlOr-lOi-lOOOOO iC-^COCOrHOOOiOC lOcOiCcOiOCOiCOL cocooo iccoior* oOCOip-f oooo< iC C^ lO I> li ai(Nr-.TPiccpcOQOi- 500 COOQCOC iC t^ iC t^ ■' lOi-^coco HlC 1— llO'-H - ■^ l>» Tf l>» f-'»-Haicot^iOiCr^coci'— I'-woicor^co'Coocoo C0iOi-4iOi-l iC CO »0 O lO lO i-H iC F-< lO CO lO cOiC CO r-iOOOOOOOOt-i SCO t^»c sOO-^COCO-^GOCOOlOrH aiCCOlOCDlOCDlCCO>OCD «t^(N050i-( iccoio coin c OOOOOOOi-tiOi-i COCOMOOr aiOiOCOI>rHaaaii--CO ;C0'^(NTj<(MT*-i-to>o»'Mr^"*thto:i-— 't^-s* rHiOrliOr-l lO CO lO CO lO JCOCDOODOOQCOCOCO-^ siOcDiCCOiOCOincO»OcO rHiOOiftOOOOOO iCcDiOcOiCt^iOt^iCt^ ^'OOtJ^cOCC^COCOOOCO SrHTPrH'^.— (^rHiOi— tiO .lOCOiOCOiftCOvOcOiOCO pjcQpl^COp^OCplHCCOtHX lOOOOO OOOOiC«-(iCt-"**^l> P4ccO:2(/:5pdccp" ^ t» cO'^cor^c r^ ,_( ^ Tf 1-1 r* c ■^ CO CO CO CO CO ^ t-. ■^ t^ ^ t>B CO— '0"^r>-r*'*o — '■iTTCOCOCOCOCO - TJ< t^ -^ t- ^ l> coco D5 CO 05 CO pi X 05 OQ of «5 Page 490] TABLE 10. Mean Time of Sun's Visible Rising and Setting. 1 a "s 53 o Oh a s § 'M a h P o ■ TS QQ a el +j 3 ■-C rt h-1 01 42 Fl -w ;-( o c ^ o1 .^.^ ^ •xojddv •ajBp xojdd V .^?5 aj» pHtBPdaJP^HaJWcotft/! ;m.Nire(MlONT)<Oi lOiCiOiCiCiiSiOiCiOiO S*c^corHooi-iQooooooiaiOsa>a> ■>*O-fl'O-<»"O-*O'WO,-*O-*O'»OiClO Tf r-< TJ« tH CC t-( CO f-l CO tH CO tH CO rH CO i-( CO i-l CO iH ,«i iCt to iC CO iC CO iO CO iC CO lO CO >0 CO to CO iO CD iC CO ;0Q»Ol^cOC0C0iOt^tC00N*00"^'^C00SC^OC^f-l :eOrHCOr-ieOi-ICOi-ICOi-liCOi-ieOriCOr-ICOC^C01N iiOCOiOCOtOCOiCCOiCCOjiOCDiCCOiOCOtOCOiOCO g'lOO-^OCO-HlNfMC^CO i-iCOO-^O^iOCQCOOOt^ COC^COC4COC^COCCCOO>iOO-*"-ICON c^cQC^ie^c^coiMcocMco lOCOtOCOiCCOtCCOiOCO t^coco-^iniCTjicoc coc^icO(Mco(Mcoi^eo coiocoiocoiocoicto ■^t^COOgOJOi-li-IOlM •ciio 1-1 iM O CO CO -^ I ■^coiO t^ * CO»C CO 1— 1 lO rH iC X'^tOiOTj^r^coCiF i-(tPi-iiOt-»iOOiCOvO a>ocoOGOt-(r>-i-it^(N iOcO-^'«C0I:>-CCQ0'Mas COrHCOr-IC^fHCOr-lWi-t TH(MOC0a)'<*<00iOl^^l':DI>-iC00-t<^(MOi-iiH t^OO^OS'^OCOiHlNOJ OJCOOJCOrHCOi-tCOi-HCO ooo'^cn-nceocO'Tj-iMo (NCO(MCOr-U3 '^ oo^-t^osiOi-'ccicoc; 0!P OiOO OOCCCNi-HiCOOGOiOO S2 t^OiOit^THiOCO ICOiOf-tt^OiOlcOi-l'^'" lOOiC COiO CO oooo Ot--iC OOOOIOOIC1-110.-I r-tCOOiOCOlNCOlCOOO ■c>-l■*r-l•<»•(^^■»c^^•>J>c'^t^'«**t^'<*t* •^CSi-IC^IOO'^iOt^COO iOOiCiH-*i-lTJir-l-cfit^ioocq-*oot- "^(NCOCMCOCOCOCOC^CO T)it~--^r»-^i>'^t^'^r» COrHCOiCOSCOlOOlTHCO coeocococ-. ^ 05 C* t^ ^ tO -^ CO CO i-H GO OJ O CO C^ -^ >0 f-t t^ Oi o S 000© 0000 00 lOi-llOi-ltOiHiOiH-^CM S*co"j''<»'coc^aoo>or~co OOOOOOiOi-HOrl S'(NG0QOQ0C0»0»OC000 S'oscor^iCTjco iO>-itOi-liOi-liO(N'0>iM C^-*CM-*(N'*01COCO coc^eoiOOoQt^i-iTfio ■vfj-^c^-j'Scocococo OOOCO(NeMCOGOi-ICOiJJ eococ-iTKC^i'^.-iiOi-iirt »-HCS00C^iC>Oi-IG00QCM T»jiiMio--iio Qt-Ht^iOCOOSOiCOiCt^ ■^t-^-^t^-^t^-^oo-^oo r^'^ic^ioot^coc^cct^Tji i-liOr-liOOOOO>OrH --9't^'^OO'^OOCOOO OCJiOCOOCM'*t~05CO ^OOOOfHiCr-f^C^ -»JC CMTfO^-On-liOi-lOpO -^t^-^r-Tjir^-^GO^oo i-nArHiOiHOOOOrH ■*t~TtH--T)<00-a<00-*00 iMOGOincoocouscoc rHOOO ■*G0 ■*00 Oi-liO -* GO CO 00 CO GO COOGOiClijiOCOCOOCO ■*00CO0OCOO0TO00eO00 i0I>-0>C0C0C>t^C0OC0 lOr-ITyiC^I'^CNCOCOCO'Ct* CO 00 CO 00 CO 00 CO 00 CO 00 i^iOi-»ooeo '^C^'irCOCOCOC^-'rC^lO CO GO CO 00 CO 00 CO 00 coco c^piosiNcoioeooioiM S5!S icococo55coe6fJTi< iOCOlMQGOCOT) lo i-H 3 eo ■* cco-*co»-ioi^'^cot-* as^coiCt-HOit^cocoGC.oocJcooor^coi-HOitOiQ eocoeococO'^co'^cO'^'HiOi-iiOr-iiooooo " ~ CO 'X cox •^ (N -^ CMCOCO eo»coxco» S'fMCOOsaiiOCOi-ir^r^rH COtOOiOi-^COOXiCCO cococ^coc4TiTjit~Tjit»''90'N 1-1'VCM ^ " coxcox - iC iC. . _ CO C-( CO CO CO ■^ coxcoxcox aaCOCOOSTj-t^iCiCt^cO C0T(>C0-frH>OOOU5i-( COXCOXCOXCOOaCMCT* X a. —11^ MCO CO lO CO lO COXCOXCOOiCOOlCOOl ,«"r-coT)'ooeocoi^cor-ilxiO-^oa>'*ira»0'* eCMC0C0'*C0TlOO>0OiO-H •■*l— •*C-->1-JOO'coo>cooscoo» P^oDMccOHC/QOiccPcScrQb^aiKKC^fKOHCoOHcnWxOHcnPdccOHCOPJaipHCC f_) T-l CO CO -^ '-ST' CO t-» 00 OS ;^ CO '^r lO iC vO lO s « TABLE 10. Mean Time of Sun's Visible Rising and Setting. [Page 491 S ^ 1 B II .a CO t^ 00 o P:h°6PhCCP^gqP^c»Pjcq P4a3(4cc(:>ixi: :OiC«Oi0^iC«OOOu^cOU5 Sr-lgOO^St^rHlOW^ ■^oecOeorHMi-ico :oin^^OLOcOLC^u2 _.^ - — -_i.A— ...— . ..^^:^.. i r-IOJi-(lMiHe^rHOI.-l6)i-l55 ^iC^lOidOiCiOiCiOiO jiCiCiOiOiOiOidO'SiC ^lOCOiOCOiO^OiCCOiC OC^OiMi-HC^i-HINi-IC^r-lC^ ooMO»i-ii-ioc^Oicot~in*.oO'*ooeco>wrtQ gOoOiHto?^iow*'*c<; lOCOiOCOOCOOCOCScO iO>dCiO:OiCCDU0!^tO (NOC^OiiCcO'*iTfcoicc^coi-*i:^oooas r*(Nt>'CCi©'^iCkCTr''-(ooo ■^TpiCCOiOCCiOCCiCCO iCiCiOTfi:OCCI>>CC3DC^.OO»-TtTt<00CC;a0(NOli--lQi--l^OrH0i ^10101010101010101010 lOiOiOiOiOiOtOiO^iO Tj*iOTPTjirrTrTji'^-^'»r ^lO^iOiOiOiOiOiOiOiO lOt^iOi^'^iOt^iOQOTf lOiOiOiOiOiOiOiOiOiO lo ^ lb ■^ lb cc iOiOiOiOiOiOiOiO»OiO GOCOOiCOanNQrHi-HrH "^"^Tr''^TjOiOiO C^t^COO-^tf-iOiOTfiT'COt^OO lOCCOCOiOCOiOCOiOCO^OCO lOiOiOiOiOiOiOiO^iOOiO C^O>COOCCCI>TPX'»OiO';OiO lOCOiOCOiOCOiOCCiOCOiOCO lOiOiOiOiOiOiO^iOiOiOiO lOTriOTPiocoiocoiocciooo iOiOiO»OiOiOiOiOiOiO»OiO »c^ocoai"^aiTtoccio : ■^ lO -^ ^ '^ ■^ JiOiOiOiOtOiOiOiOiCO lOiOiOiOiOiOiOiOiOiO scO'-icoQ'^o-^aiioas :'^iOTPLO'tOiOiOiOiOiOiO»0 ^asTrOlC'OOCOC>(Nli-HC^.-'^(3» " — — — "^-^jio-^io-^iOTrio-^ocoioco .lOLOtCiOiOiOiC^LOOiOiO OOOOOiOOiiOOS'^O"^ iOiOiO»0»OiOiOiOiC>0 ; Tt< lO -^ lO •'T* a lO vO »0 »0 lO ^ lO O lO o lO ■^ lO Tt« lO lO »0 iO O lO asi>GOt^oo UOiOiOiOiOiOiOiOiOiO GO 00c " Tj< Tj< lb '^ S lO lO lO lO >'^C^iO(NiO{NiOi-tiO»-l : -mo TfiOTf » lO lO lO lO tO lO ■^ lO Tl» lO tO lO lO lO lO 5 t-H toQr ■' lO "^ *b ' 5 lO lO lO u iGOOicxjoQasGoaiaoait lOiOiOiOiOiOiOiOiOu TjiOi-tiO'-''*^-^'^C^Tf(NC0 ■< lO ^ lO ■^ MO lO lO lO lO -^ lO >0 >0 lO iO lO 5'^iO'V*0'«J*iO'^iO'^ SiOiOiO^iOiOiOiOiO i.iOCOXJOOCOCO'^O^NcOtM s-^iO-^iOTjiio-^iOTrio AiOiO'OiOiOvOiOiOiOiO t^fNr»^t^«-Ht-*'— •GOi-HQO'— (Xioaioo5Oi0s^ " lO ^ lb "■ 5 lO >0 »0 u rr lO lOiO )OiOOOQQOi-HGOt-lOO lO lO lO lO \0 "^ »o ■^ lO tO lO lO lO lO 5 lO lO tO lO lO O : -Tf lO -^ lO ■^ * lO lO »0 lO lO lO -^ lO Tf< lO lO lO lO lO lO fio ''if lO'■ ^ lO 'O lO t 5iOiOiOiO»0»OiOiO ;Tr lO lO lO lO lO lO lO OsQOQQO ■^ lO lO *o >0 lO lO lO lO lO lO iO »t^iot^TT'MOiC^aiC^OsiMas!NOS(N > TP lO "^ *0 Tf lO JiOiOiOvOiOiOiOiO ^ lO - «^ lO ■^ lO ■^ lO lO tO lO lO lO o iGOiO00iOGO»OG0>OcO4O:00iOG0iO00»OG0iO00iO - . - - - - - - - " - -J, - - - - - — - - 3 lO lO lO :Vib-rTiib^»b'^iO'^»o 1 aiO^iOiOiOOtOiOiO-C ^ to -^ lO ■^ «b 5 lO lO lO lO »0 lO JGOiOGOtOOO'^OO'^ jTi'iO-^iO'ViO'^iO SiOiOiOiOiOiOiO^ oO'^cO'g'oO'^cO'^00'^ •rrib'Vib'^iO^iO'TiO lO^tOiOiOiOiO^tOiO i^iO'^iOTriO'^iO^iO jiOiO'OiOiOiOiOiOiOiOi 5 rococo r« lO-^ lO 5 »OiO lO 00 to 00 CO 00 <^ -^r lO ^ »c ^ »o lO lO lO »0 lO o OOtpOOtpXCOOOO! ■^iO^»b'^iOTr»0; iOiOiO^iOiOiO^ I 300-X>Q0':DQ0tO00tp00cD S^TtO-^iOtfiO'^iO'^ib ^lOlOlOlOiOlOlOl0^lO OicwP^aiQ^aQpHCQtf 02 tfdrtoQtf c»PiQQW<»pcfiP5xP^coaic»Ciico oi oi oi co afi co od ^ oJ c/i O! cc o ""o^^r^ o* CO ''^r^ *^2b ^25^ t* 00 a> ^5 y— a co ^ I lO «g r* g g o^ Page 492] TABLE 10. Mean Time of Sun's Visible Rising and Setting. 13 as &d ea x » 4) H 3 ^ ■fr O •? ^ a 3 .^^ •xojddv ^co c^ c3 (M CJ C^ p.(N'} 00 t^ .-H in M M IC rt t^ 00 P CO 'M CO lO i-l t~ 00 CO -^ CO ■^ CO "^ CO Tj^ CO Tf CO "^ CO ■^ CO "^ CO ^ co^ C4O-*00C0Cp00-«iO5 SCC^OC-IC^IQ-^OOCOCOOO-^OC^ c^ocoOjCOOcomcoiftcoiO'^iO COiCCOiCCOlOCOiOcOiO COiCCO-'tcO'^CO'^CO"^ iMpiOOOt^iOOCOCJO CO^CO^CO'^COtPCOtj* •ajBp •xojddv .'^^ TT ■^ -^ -^ -^ Tf i-t f-( T-t ri ; CO .— ' 00 O 05 CO » :OiC to iC O iC i-4r-(NiClcO'^iCcC':p^coo?^cc .-li-(rHf-li-t,-Hr-(OiMO TP'rt*'£>(MGOQ001Wt^ "^in^C000i-Oi or* to iC CO to .-HtD«nO'^««DWt>-0 0>OsOt-C^C ..(OCC^iCKM 0C40'3Dr-0>000 cO»CCOiC jo6io cou^co !NOlM< iC cOiC c U-Ht-C^COCC"^»OCOCOi-l cO»CCOiCcOiOCO>OCOiC i-H^C-ixO-^^iOC^t^T-t (NOC^O COiC COiO c^oc^oc^o CO lO CO iC CO lO t^OOi^ COiCCOiO Ot^MCOCO^ (NOC^OCMO COiOcOiC COiO SOiOOOif-iOOC^t^-COCO lOCOOC^OC^OCSOCI ^lOiOcO'OcOiOcOiOcOiC ; 00 !M CO 1-t o> o c . ^ - JOOSrHOn iiOCCi^CCiCCOOC^OlN ^iCiO>CiO»OiOcOiOCOiC ) CO I^- 'TK CO U^ lO c ■CCOOC^Oii-HOOr-lOO oc^oc^o(N<:5csi^(N ioc^oc^oc4 COiOcOiOCOiCCOiOCOiC iCOiOCOiOcOiOcOiOCOvO gr^-rft^COOOC^IOXMQ— I iCCOiOCOiOCOiOCOOOO ^iCiCtOiOiOiOiOiCCOiO gcococpior^ior^-^coco iOC»OiOCOiOCO»OCt-^i^c• CC CO COiC COiO 8Or-i0iC^00C0r-'^l>-iCC0c0»0r-"^00C00i-cof-cocor^ic iCCOiOOOiOCCiOCOiCOO giCOO'^Oa-'^QCOOC^r-i^OJ^OOOCOOS'^OO COiOCOiCCOOCOOCCOOOOCOOCOOC^OiM lOiCiOiCifOiOcOiOCOiO COiOCOiCcOiCcOiOCOiC > CO lO CO iC CO lO TjH ic CO -^ r>- CO CO lO COiOCOiC CO »0 CO lO CI Oi CO X '^ b- CO iC COiC COiO t^-^QOCOOKMOf-HiHO 0(NOC^ cOiCCOiO OCJ rHC0Q0C0a0»C01"^O'^rHC0f-(C0(MiM |ioccir5coiocoiccoiccoKccoocoocoocooco 'lOiOiCidCiCiOiOiOiC iO»CCOiOCOiOCOiCcOiC gCOCCCOCl'^C^'^tHiOr-l ^iCiOiOiOiCtO'CiOxOtC OOOOGOt^OSt^OiCOOCD iCOcpOCOOil^O>l>C^ ^- _- iC^iO-^iCCOiCCOiOC^ lOCCUScOiCCOiOCCOCO lO "CIO lO iCiO iC lO iC >iO lO lO lO tOiO lO lO lO CD iC (Ni— iCOOTj lO coocooco lOiC OtOcOiC j£^t>.^t>.C^t^C^50(NcO pCS^OiOidCiOiOiOutiiCiO COCOCOiOCOiO'^iO'^iO lOiOiCiOiCiCiCiCiCC ^■^TfCOiCCOiCCOiCiM iCidOiOiCiCiiCiOiOiO fiOO>OOSiHOSi-HOat-lOO SiiOTriCTriCM'iCTfiCTp tH0Oi-IQ0C0cO lOiCiCvCiCiOiCiOiCO coc^cOt-(cOr-^^-t-^^*o iCiOutiiOiCiOiOiOiOiO •^CO'^iC'<* 00 r* 00 r* 00 1^ oo t^ oo t^ oo t* oo t^ oo t^ lO iC lO >C lO iC iCidC lO lO iC iCiC vC iCiO »0 Id lO f^COP^GQCiCOOicOCCHCO C£3cop:5coa3ccp:Hccp^a}CiHXp^czJpHa5pE^c/;p£HC^ r-l CM CO '^ CO CO CO CO Q:J:/^*PehODP^:>dP^gcPhOD CO l> 00 OS O CO CO CO CO "!?< TABLE 10. Mean Time of Sun's Visible Rising and Setting. [Page 493 2^^ 1 n •D O ^ i X3 •■a ■e S o 0) ^ s 2 09 5! 5? S rtcortasrtcOpSWOScB ajOQpJOipjGQP^GOpjGQ S^ CO Ol O (N t~ lO 'f (32 i-( Mt^!O'^OO"*!P00M O OT O CC 1-1 CJ rH IM rH (N C^ .H IN tH CO iH « O CO O ojostfcnp^cApiccpijcoaictipjcccijcaajcopjcn »OOC3-*«Or-ltOlO.-l eOr-l'*r-l^rHlOOiOO H«O>n C0lHC0r-IC0O'*O'*l0 t^-^t-'*t»'*t»Tj-*-.Ot~COOrH S:iO"^iOCO»OCOiOCOOCO gvOM't~(Na>05C/5'^cor^r-io>oo ■^TJ^Tj^Tf^'^'n^'^'^CO ScoT-(ooo>ot-*(NiOii:)CO eoiOco-^'^'^'^-v*-^ s;^J"5-fCO«5^aOO»Ot~ BcoiocoiOco>oco'J'- C^iOCOiCCOiOCOiOCOiO Ol'J<(N'HiCt>OS-*COO OC^rHC^i-lrHrHrHCJr-1 lO ^ tQ lO i?5 lO 8tO in rH iH 50 to O r) •* 0> r~ «5 O ■* CO N lO r-t to lO O "O iH •* iH -"J" 64 CO 5l C^ CO 04 ■* i-( t» O O O 30 CO 00 CO 00 CO 00 CO 00 CO oo co oo eo oo eo oo co o> ri Sr»QH-*oooicoco iOiCO'*oeoi-ieo C^eOt^COOOCOOOCOODCO Ql^t-OteOC^iOr-ctO c5c^c^c^coi-i-eoo)oot^eoc3t» ■-cot-cot-eot~coooco TJKNOOI^COCOOOOOCOCO >«oocmoooo»-*-^o» locoocoincom'j"* .T»^lOiH0000iHtOCO OCOr-IC^Mr-IMrHCOO Qoeooocooocooocoooco COOCOr-llOCOOeOO(NrH• -^ t* -^ t* -^ t^ -^ r* CO OQiniraootoocjoQ ■■1COt~COt~COl>CO00CO t~C^Q0lC0t0t0C00»OC0>C0iOt~i-l lOeOO'MOlMOOIOlMi-l'-li-lrHt-IOC^OC^O l(Mf~50f1i-Ht>.t~NC-*'9<-*lOCO t~eor-cot»eot~cot~co C^tO-^COt^rHQ00C0>C KDC-'^t>**^t>-'^t^-^ coiO !t^'^t*COt>COt~»COt^CO t^T-taaoo(Nto»ccot^o ■^■^'^COlOCOiOCOU^CO tO'^tO'^CD'^tO'^tOTf >r-co-*50.-cococO'^ >CIO(MOCarHi-ir-li-l ^lOTfcOt^rHOliOC^tO lOCOt^OOt^CO'S't'-* TT'^-t+i^'^'^-^'COvOCO iOCO»CCOO!NO!N0(N0 ^tOiOtOiOtOiOtOiOtOiO gOOiHOOiHOOCOt-'^iO rHi-IC^rHCMOC50IMO ^tOiCtOiOtOiOtOiOtOiO i£iOiotO"rtioocoa5i-ioo SrHrHi-lrHi-li-lTHr-lC^rt ^toiotototointoiotoio t~i-ii-it^>ocoo»oO'^eo rHr-liMOlMONiOCOlO t-»'^t^Tjit*»'^i>cot*co Ot-'*-*t^OT COt^OQt^lcO-*t^iHO<^-*'->l'000 CJlOOfNtO'^ - ^- ■^I'COiOCOlOCOiOCOSC^ tO'^tO-^tO-^tOi^t*'^ T)i-»ftO(Na3 05i-lf»'^-^l i5itO'tJ>tO'*tD-c-^OT^c^pM90|lO^;tOlnoo3|g;^^l^g|«cOlOto^;;^^ rf*tOiOtOiOtOiOtOiOtOiOtOu^tOiCtO>OtOiOtOiC Ol o to in c^ o c^ t tOiOtOi MiO to-* COlO COiOCO^ to "»*< to ■<*' to g'dCOOMF-I^HfNOCOOsH'OOiOr^tOtOCOiOas'^ OC^i-II^iHC^i-HNi-li-l i-li-lr-li-li-lrHi-li-li-li-H ^ to o to in to lO to lo to lO to lO to in o lO to in to in Stot^t^t^ootoosinos-^ rf^toiotointointointoin g-^C^-^i-tiOOtOOtpOl OCOOCOOCOOCOOCJ rf|tointointointointoin OCOiHC^IC^iHCOO-^OS rtC^i-IC-OCOOCOOCO^ tointointoiOtointo^ O404cooinoi:^r*oo OlrHOlOOl to in to in to OO^O lOtOiO t^Oi00t^Oltp7HinO4CO toint H rH iH rH iH 04 r ) coin to in to u r^ oac 04C toin t loogit^otD >04004 1-104 5 into in to in JOOOO»0>0)0100>00 )TH0Qi-'r^O4r^O4tO STt^incoincoincoincoj^C'tOCoocoocooco .cjininininioininininin to intointoin tomtom |com'3iin^:»'iSi3!in tomt S'm^lC'^tO'^tOTt-04CC04QOiH m-^m'^m'^mis^mTjimTtim'^m'^m'^m-^ ^mmmmmmmmmmmmmmmmmmmm coScOOco m tom tom l0 1^ m-^ m mmmm m oooocn •n'O'^ O CO m to m tom ^moi'^coco'^oitoi-i li-l04iH0) 5 tom torn to 64i-(04tOi-tl^i-10DOC > CO o CO o CO o CO ; sm tomtom tom t i-IOiiHOOOIOOOJt^COtO oeoo to m torn to cooco mtom •xojddv Q jgCOO^COOiCOOOCOCOCOOO S'qmqcoqccocoooo to ic o lO «^ -^iC -^ iC 'T' UOTT ■^ O TJ^ lis ■^ lO -^ iC lO lO OMQCOOWOCOQCO S tO lO iC 5 lOiO iC 5 lO lO lO i» lO 5 lO lO lO iC lO tft) ^ ) -^ L3 >*< lO -^ C p5a2P^aQpdc»P£5c»(i^cc!p5a2p:HaiQ3c»p4a2pH"aQ a:3c»oiMa5aQoico»3c»jP£ic/if4coei4COP:5ccC4GO tH C^ CO Th ^C r^VX^Xs ;rTXVT^~s Page 494] TABLE 10. Mean Time of Sun's Visible Rising and Setting. S 3 ^ rp. a ,^!zi •xojddv A •xojddv J!, OiHfNCO-^ lOOt^OOCi Or-{C^C*5Tt< iOCOt^QOOS WccrtccajaartcortcoWcDPtHccanaQrtaJaHCK'rtcceHaipiHCcWM^ §dlHOr-lO>-10T-lOrt Oi-HOr-IOi-IOrHOi-l ss OCOiOC^lOiNiOC^ C^ lO (N lO C^ CD -M ^ COtOcOOOOcD^CDCO T**THCOrHM.HCOi-i«i-H0:>i-l?0»-HC0r Ot-IO)-HOt-(OiHOi-( Oi-I0.-I0>-I0i-(0^ p!HCBp:^GOp:5cCp^a5pc^OQa5«^ CO-HCOi-HCOi— ICOiHCOi-HCOrH :0 -O O '.O O CO --0 c; -^ -^ OrHOrHOr-iOi-HOiH iCC^iO'MiOC^IiCt-HiO'' THOiHOiHOiHOi-i zO CO O CO ^ O CD CO ^ O ':OC^CO(NCOrHI>r-(I-TH 0?-lOrHOi-lOi-lOTH COOOtOtOOCOCDCD^ Jcp-^'-OCOcOCOCOCOi— CO :OrHOi-*Or-IOrHOrH *CDCDcDCOcoir-cor>.c^i:^iNr^(M! OrHOrHO t-1 CO CO ^ ^ '^ ^ OrHOi-H COCO O CO Or-iOi-lOrHOr-lOT-l cDCOCOOcOcOCOcocOcO O»H0r-t0rH0r-l0r-(Or-l t0:0^c0cDC0'"-0C0c0^OO r^t-ir^i-ir*ot^ot>«ot^o OrHOi-IOi-tO^Oi-lOt-t co^cocoOi i-lr-lr-t,-lrHrHrHOTHO COCOCDCOCOCOCOCOCOCO COcDCOCOCDCOcOCOCDcOcOCO coocoocooicooi'^ai-^cc ^.-ti-HrHrHOrHOi-IOi-HO COcOcOcOcOcOcOCDcOCDcOcO T^CTiiCasiOGOiCQOcOOOCDt^ rHOrHOi-iOi-lOr-(Or-lO CDCOCOCOCOCOCOCOCOCOCOCO -^OicoGor-oor^t— cot— ooco r-iOrHOfHOrHOi-fOiHO COcOCO'-OCOCOCOcDcOCOcOco r^GOGOccoir^Oicoocoouo i-IOrHOT-IOTHO(NOC^O COcDCOcOCOCOcOcDcOCDCOCO ;Oir^0^i-iCOrHiO(NiO SOGOi-Ht^-f-tcOC^cOiMiC :i-lrH.-HrHTHi-(THiHiHr-( scococococococDcococo j'OOOi-lt^'— IcO'MCOCOiO :,-li-|?H<-li-li-ir-*THT-l»-l >cocOcOcocOcDcococOco i O CO 1-4 tXM r- CO : iH rH rH rH tH T-( rH aCOCOCOcOCOCOCO CO to CO CO CO ; O GO iH !>• (M t^ :0 ; rH r-f i-l tH r-l tH iH a CO CD CO CO CO CO CO CO'Tt^iO CD CO CO ; O CO tH I>(M CD CO :rHi— IrHT-HrHr-lT— I icOcOCOCOCOcOCO COCO CD (NTf CO-t -t CO CO CO CO CO COCO CO CO CO CD CO '^ Tt* Tt< lO CO CO CO CO CD CD CO »C(N CO»H CO CO CO CO '^ Tj< Tf CO iC (M i-t iH tH 1-1 rH i-l CD CO CO CO CD CO COC^C-rH CD X) COCO lO 'rt< lO CO CD C^COCOu :rHi-liHr-lr-trHi-(r ScocDcococDcDcDc i O 00 C^ C^ CO CO Tj< »COCOCDCOCOCOCO CO CO CO a O 00 .-I CO -!MO:irHOOiiMOO :0t-10T a CO CO CO C HOt-IO > CD CD CO :Oi-IOr a COCO CO C Dr^ocp 5 COCO CO )ODtHCOCOiCtcOcO(M SOOOOOOOOO scococococococococo CO CO I>(M CO 1-1 C CO CO CO CD CO CO c CD -'HOiQOOSrHr^(NCO (NOiMOtMO(MOCOcOTHiC»OCOcO'(MCOi-IOa (MOiNOC^OiMOC^O COCDCDCOCOCOCOCOCOCO -- . . oa O O 00 1-1 r^ CO CO -"f lO S^OOlOCOiOCOiCOOiCCOiO cDcocOCOCOiCcOiCCOiCCOiO COtNl^rHXCSOSGOr J r^ o CO 00 oi t^ iH c C^COC^iC'^COcOiM^-i-H (NO(NOiMOC^OC CD CO .-lOi-lOi-IO CD CO CO CD CD CO CO(N CTiQ COCO CD CO (MCOCOiHiOOcOCOQOlN- ^COCOcOcDcDCDiOCOiC OOOiOCOi-fcOfNiC'^'^irjCO O1iOC0iOC0»OC0iOC0iOC0iO cOiCCOiCiCOiOCDiCCOiCCOiO Oil^OCOOliCCOCOiCC^COO (MiCCOiCCOiOCOiCCOiCCOin CD»CCDiCcOiOcOiCCOiCCOi/3 OJiCi-tfiNc^-^i-iicasi-oo CNiOCOiCCCiOCO»CCO'<:fCOTfi COiOCOiCCOiOCDiOCOOCOiO (Mi-lCOOSvOCOCOCO00iO .TjHCOCDTt*r^fM tNOCO-^COTPCO'^CO'tCO''^ cOOCOiOCOiOCOiOCOiOcOvO ^J -^ccMic— I thOiho^o co cd co co cd co COaiOOt^lOCOrH-^COCOiOrHcOOS iH iC i-( lO CD iC CD »0 COiO CO lO CO lO CD lO CO iC GOt--OcOiMTj Oi Ol l-^ O lO kO lO ■^(MCDOOOOiOr* COiOCOiO co-^ . , _ _ O lO O lO O uti COiO CD lO CO lO cOiHOOCT>OOCo ■• -■ -- co»o T-HiCCOCOiCC^t^OcOCO CDiO p^ccp4a3p^ccp:^cdo^a5 pin'ocp^cQCi^cop^cdp^aQ CcjccoioDCESccp^aQp^cc aiGOp^coo:^ccp:^aip4aQc4a:i »cc^i>.ooiGOi— ir>-coidoco OcOC^Tj^-rffMCOOOQCOOcO C^CO(NCO!NCO(MCOC5 i-H to r-l to rH t i^tocotocoootocotoeo Scoocoo(XiOooogo® OrH0rHO.-H0-H05 ^tOCOtOtOCOtOtOtOCDtO r-IOi-HOr-iOiHO'-IO ^(OtOtOtOOtOtOtOCOtO THOrHOr-IOi-(Oi-(0 ^(^OitOtOOtOtOtOtOtOCO S'iOOO»f^GOiOt^tOt>-tOtO C^tOr^iOC^iCOOiOOO-^* T-lOi^Oi-tOrHOiHO rHOr-tOTHOr-IOi-IO ^•ootototoototototo to^OtOtOOtOtOtOtOtO s §§ C4aQP4ccP>4CC0Ha}^oQ COiHWi-IMi-IMr-IWC^ Oi-IOrHOr-lOrHOrH tocotototocotototoo iSSSSSS t-H c^ 05 3* iS CO CO CO CO CO coc^coc^coc^eoiNcoc^ Or-tOr-tOrHOi-lO»-l (O ^ c© CO CO CO CO ^ ^ O C0 CO <0 CO CO cococOcocO COCDcOcO^O CO CO CO CO CO S»ccoiO»ooj<3>«» ^a a>04 1^00 ^ X 000 oooor*or*ot^ot>- 000000000 OOOOOOOOi-HO 1-1 O 1-t O rH O rH O t-H O CO CO CO CO CO cOCOCOcOcO cOcOcOcOCOcOCOCOCO^ cOCOCOCDCOCDCDCOCOcO ^00*-iCOCt^cO00i^GOiCCsiC r-lOi-lOr-lOT-lO»-10 ^cocococococo'^cococo rHOr-lOC^O(MOC^C5 ^cococococococococo*-o S^'^'M-^'NCOCOIO'^S* C^OC^OC^O(NO(NO ^cocococococotocococo Ph (/} Cl^ OQ Ph OD C^ X tf CO COC^COC4{NClC^!NWC^ OF-iOT-(Ot-iOiHO»-< CO CO CO CO CO CO CO CO CO CO cococOcOcococOcocOcO Tj^cp'^iC'^iC'^iCiOiO rHOFHOw-lOf-HOi-HO COcOCDcOCOCOcOCOcOCO i-(Oi-l3iHO»HOrHO cocococococococococo r^cooocooocococ^^^ rHO»-HOr-tOi-HOrlO COCOCOcOCOCO'^COcOCO Oi^aiCOOCOOfNrHC^ rHOr-10 OC^OtMOC^OC^iO COCO^COCOCOCOCOCDiO OS -^ O '(f O CO 1-1 CO rH M (MM(N rHco^eoo-^o T-10C^»0(M0C^0C^0 !NO(NOC^OCMO(NO cOcOCOCOi^cOcOCOCOcO COCOCOCOCOCD^COCOCO NCOC^S^COfMCO'-i-^i-l'iCQiCOiCOaiCOGOt^t* C^O(NOCSOcNOC^OC^O(NiOC>I^C^»/5iM^ ^Ocoi^cOcDCOCOcOcOCO cOCOcOiOCOiCCOiOCOiO TfOl'GOOOQOI>a>COOCpiHiO i-t'^(MCOCOCO'*(N^i-l C^OC^O(NOC^iCC^iC!coa>ioQ'^i-Hco r- ocorHicc^-^co'g'S'coUo^g'^^SQt-^ooco e^c4oC^OC^OOCOiOCOiCCOiO CDiCcOiOCOiCCOiOCOiC COiCcOiOCOiOCOtCCOiO oi oiosoaoi— l^*'^^co^^^lC co sInOC^OC^OG^O^iO ?4Scoii5cOLOCOiCiC6iC COiibCOiScSibcOiOCOiS CO'^CO^'^TTTj^'t'Tji^ 1^ CO CO CO CO CO CD CO CO CO lO CD iC CO lO CO iC CO iC CO »C CO iC cO UO cO iC CO iC CO ift CO iC CO iC CO lO CO iC CD lO )So 3'^"*COiCC4COi-il>0 SiOCOiOCOiOCOiOCOiLft OOOiClOOOt^^COtNiC gi>r-(oooooasa5Gooi> 010C^OC<»tOC^iOCOiO ^COCDCOCDCOiCCCiOCOiC THr*iMCOC0»C'«f'^iCC0 COiCCOiOCOiOCOiOCOiC cOiCcO^OCDiOCOiOcOiC COiOCOiOOOiScO'^"'**'^ CDiCCOiCcOiCcOiOCOiC .-icDfN»OCOTt00<3Si-IODC^t>"COCO C^OCOkOCOiCCOiCCOO ^CDCOCDiO'DiCcOiOCOiO Tt^'Xi-OQOO COiO'^'^'^'^'V'9<^'^|^"^'^''I^'^"^CO COidCOiCCOiOcOiOCOiOCOiOCOiCcOvOCOiCCOiO ScoScoiOcOifsSSSS CO ic CO lO « xn CO lo -^ '^ t^cOiOCDiOcOtCCOiCcOi^' CDidCDiCCDiOCOiCCDiO rHt^C^CO-^iOiCCOt^lN OOf-iaiOii-lOOiMCO'^iO ■^■^"^■^■^tP'^^^tT* TfTt<-^CCiOCOiOCOiOCO CO iC CO lO CO iC CO i^ CO lO CO iC CD lO CO »C CO ifi CO v/5 gc^ti^w^^^tocot^c^ QO-— losooa^i-ii^coco CO lO CO lO CO lO CO lO CO iC CO lO CO iC -^ -^ "^ Tt* -"^ Tji ^ CO iC CO lO CD iC CO O CO iC CO iC CO id CO iC CO iC CO iC gco»0'^"^'^cor*rHasQ COiOCOiOCOlOCOiOCOiO rf-COiOCO^XiiCCOiitjCDtn _^COiC coiocoicco^-^'OCOiCcOiO CO-^iCCOCOi-HQOOSOaO ■^'^■^•^'^TP'«*C^GOOQOsirHr-COCD'^'^COCOI>i-i ^•^■^•^^Tj^TfTjtiOCOiidCOiCCOiOCOiCCOiCCO COiCCOiCCOiCCOiCcOiCCOiCCOiCCOiCcO'OCOiO t^C^OOf-IOSOSr-tGOCOCO ■^'^COCOr^r-lOiOSi-lOO ■^ T}< -^ Tf ■^ CO lO CO iC CO 10 cO u5 CO lO CO lO C^ O (N •XJiCCOiOcOiCCOiOcOiO COidCOiCCOiCcOiCt^iO OS 0> 1-t CO C^ CO -^ iC CO CO t^ 1-w Oi Oi I— ' 00 CO CO iC ^ Tj^cOiOCOidCOiOCOiOCO lOCOiOlNOC^OlNOOJ CD lO CD lO.CO iCcOiCcOiC COiOCOtOI>Ot^iCt^»0 iHcocoiCiococp'-'Coai tOCO»OCOOCO»OCOiC(N CDiCCD»0«0kOc0iCC0iO COCOiOr-(l>!3S0500^CO iCCOiCCOiCC^IiCtNOiM COiCcOiCCDiCCDiOt^iO gQQMCO'a**^^C^OOO ?S0C40COiOC^C0C0t-H tI^CO-^COiCCOiBCOlCCO COiOCDidCDiOcOiCCDiC SOsCOi-^C^iNO'^OSCOI:^ ^COiCCOiCCDiOcOiCcOiO C^lOClCOiHi— ICOOiiCt^ '^COTt'COiCCO'CtMiOC^ COiO'OiCCOiCCOidCOiO S05 0i-Haicor*'<*'iccoco COTt<'*COTj.i-lOi00rHCDCO'*iCC^ CD»CcO»OCDiOcOiCCOiC ga>t^t^05io^HTj-t^^ioc^coTt«o (NiCc CO »o t^ iO t* id t^ ic t> ic r* ic i> iC t^ lO iC C^OrHOr-* iC t^ lO t> iC i^icoco(NOiOoor*o OrHrHrH I> Id t>iC fti-HOr-lO c^idr*oi>io COrHO^COI>»*idt>CO idc^< coidt i-IOr-*Of-l id i>- Id t^ Id Soc^oo i-H 1-H O C>- id t> Id Tt* Id t^ CO OS O 1-lOr-tOpHO t> idi>idr^id OacOrH-^-<* * -(O rHOrHOrHOO 5l>»dt^idl:^idC*id 1-tOl-HO i>iot^»d COOOH>i-t'^ r-< O •-* id CJ »0 r* id i> - -^ ? t^ CO Id id C;J CO < >oo 5t>idt>- 0000 td t^id t>iO (N-^idc^t^ooit;::'"'^ ^^-y,-lTjir-l'^fOldO cotdcoidcoidcoidcoid S ?1 g3 S c5 (N S ■^co c Id OiJ coidc SCO t-iid^co : Id o id O id > "T t^ "«*< t^ ■'J' y* c^ CO 3; \q CO CO CO. CO CO Ot>-C0idC0(N0i0S(N<0 rHidriidr-lidiH^C^Tf oSo^ C^ ■^Id 1-H 00a CCHCoQCKCfiP^cdP^cdtfaQ Page 496] TABLE 10. Mean Time of Sun's Visible Rising and Setting. S -s 9 '3 ^ .3 "i^ •xojddv pjaQp:HCOp^cOp:^OD0^co Q^oQp^adp^cQp^cfipi^aD pc^aQp^oQPcHcdP^c/^pc^aQ gOi-HOrHOTHOrHOr-l Oi-lOi-iOt- t^ 0> t^ Oi !>• Cl oooooooooo .-lOi-HOf-lOrHOrHO rHO.-lOrHOC40(MiO O^oqPhgqPhOQP^cqPhod Oi-lOTHOrHOi-iOr-* oooooooooo rHOrHOr-lOi-lOi-lO i-lCsi-H00(NGOC^I>COhJ*^^<^'OiOOioi>-'^t^ccaoc^csc^Oi— (t-HO i-l!N(NC^COi-(COQ-^as oot^oocor*Oi?ooic CO ^ CO "^ CO ^ CO "^ 'W' ^ S-50 0r*CTiCOGOCT>t>0';Di-(iCC^'<**COCO^rHiOO COiOCO-^CO-^ CO "V^"^ >*<'**"* •^'OQ0iCO'* CO'^CO'^COTfOO-^'^'^ rHCOC^C^COTH'^O'^OOS r>-05aoaoocOiHiot^aiCOQ"Tt*C^C0'^rH TfCO-^CCiOCOiOCOiCCO ■^c^tDor*ooas«OrHT}f iCCOiCOOiCC^>CnMO(N gOt^f-n'OtNiCCOCO-^tN S'Tf^OCO-tOf-HOOOCiOS "^'*S<"^'^'^M'"^'^*fCO S*Q0Oa>OlQt^(N?DC0iC TTTpTfCOiOCOiOOOiCCO ^tOi0^tOOiC«3iCOiC g'C^r-COiCiO'*:DC^GCr-( iOCOiOCOiOCO»OCOiOCO oicict^iOi>icr*io jr^c^cocOTj^-^co-^TH ^OCSOOrHCCCO'^iCOilr^-OOOOC^tO'^COt^O S CO iC CO iJf; CO ^ CO lO CO iScOt0 040C^O(N06i O C^ i-l rH ^ rH i-H i-H rH T COiC^DiCOiC'^iCCDiO OiCCDiCt*iOI>iCr*iO t^iOX>iOt^iCt^iOt^^ lOCOOrHOOOaiCOtHtDCOlOiCCOIVrHCiOSi-t^ iCCOiOCOiOCOOCNOC^O'MOC0':0lC-^l-*C^05OrHQCC0iOlCC000i-' lOfMOC^O'NOC^OfMOCSIrHTHr-li-lrHrHrHrH S'lOcOt^'MaiOOOOC^t^- ^lOOCOGOrHOOxNr* iOCO»OCO»OCOO(NO(N OtNOCMOiMr-li-lrHi-l ^ CO lO ?o iC ^ lO !>■ iC t>- lO r^ iC t> lO t* lO C-- iC !>• lO ■'j'cDc^aiOT-n^Tt*^ i-HrHi-irHrHlNOiMO >(MCi0OO00'M(DiCTT'I>r >C^O»OTti^-^r*rHOai'M<^ 0C40(N0C^0(N'-ti-l--Hi-*i-trHrHr-lCS0CiH (MOiMOCOiOCOiCCOiC cir^C^i3SOtHCOCOcCiiCeO I>r-IO^'M'£l»C5COQQr-l ^ i> ic t^ lO t> lO i> lO i> lO r* ic r* ic f* ic c^ lO i> ic iC^ooio woe ^'OIXNiC^COt^iHOlOO C^CO'^J'COt^THOOOCOiO (NOC^OtNOCOiCCOtrs e'*CO■ Tjt t^ 'i^ t» ^ C^ tJ* t^ ^ S'OCOiMOiCGOOOvQrHtN (NO(NO(MiO(NiOCOtC '<*jTt< t^T}Ht^-.#t^TjiO0-^O0"<*» tO ■* 1> T}l t~Tjl| OlMOIMrHrH-Hi-HC^O ■*coici«iom>5iiMOiN > CQ O CM O 0 oOTjj- ■>)< t- T)< t~ ■* r- ■* 00 ■* 00 ■* 00 ■* 00 -^ 00 CO 00 CO 00 CO 00 CO 00 CO 00 CO rH O iC C*^ OS 00 CO -^ 00 O CM vC t^ Q CO in 00 Oi -^ -^ O t^ t^ O -^ CO CM lO rH <£> ■^CI-^CM-^T-llOt-HiOr-l OOOOrHiOi-t-^CM-^ COCOCOCO-^CMiOi-lOO t» -^ 1> -^ I> -^ t^ -^ t^ -^ 00 -^ 00 -^ CO CO 00 CO 00 CO 00 CO 00 CO 00 CO 00 CO Oa CO OOC^-^I^^OrH^OlOT-H i-HTjIi-H^rHiOOOO SScotfaipiHcopiHaiWw JCOiCrHrHO^OCM- ;05t^t0O'*'C0CM>0i-l«3 iOOiOi-("3"'-<'^CMC^jC^CMCOCMTjir-liOOOO 00 CO 00 CO 00 CO X CO 00 CO 00 CO 00 CO 00 CO 00 CO 05 CM oicceHaaaiaJWcrJpiHCC OicopiHcntfoQaHCiopiJcQ TABLE 10. Mean Time of Sun's Visible Rising and Setting. [Page 497 > m »4 a eu rrl 3 -K OQ JH -^A O a Z/J ■■t3 •X o J d d V ;^mA^(A(a;i,^;^ui (^!£(iiai;AmAdi(£tmm'Xit^mfid!i;iriifiai QJoapjoipi^cnpjaipjccPfjoQ lOOiOOOOOOOiO O lO O >S rH lO i-l lO rH 25 lOOiSOOiOOiO Oiooiraoiooici-i'"* gs giOQt»05CCt-0«5 iCOiOOiSOI'O'"* fi<5J TPOOQOootoo-^fq'N'^o iM-^CJCOC^eOWKlCOMeOM r-IQ0C<3«lfflT)-itoo5 iHT)li-( Tt* r-4 ^ T— i ^ tH CO lC ^ lO CC tC CO UB i-H eo c-i M 6> CO eOiO CO tA ^ lO COC^>CQt~00 (NCOfNCOCMOl a>cOTHiqc30-aio»ioi> OJCOOCMINrHMQ^OD 3lO COlO ^ to 00 00 too-* 1-1 CO i-H CO ca CO to vO to 4C COlC 1-1 CO CO 1-1 ■* OS -«OitlO'*i-l'J'rHTl< >iCtOi/3tOiOtOiCtOiC g>o S-^OiCOOtOtOt>.lC tOtC^iCiCLCiO^iC 05-*OcOi-ir-isqQ-ai3i »0»CtOiOtOiCtO^CtOvC gg lOQOCD^GOiCOlCOrHlN Tj< go <0 !>• 00 lO rH CQ rH CO rH CO :d lO o ic ?0 »C OiCOi-HC^ MO rl CO C^ CO C4 CO O lO O lO ?0 lO cooiio coco ^ OOiOOJCO^iN rH CO rH COIN CO ^ lO i^O lO <:D iO C^ r-ICOO>lOCO fH-^rHCOTHCO CO CO CO u5 oi CO rH CO rH CO r-( CO 1:010 CO iC^iC SiCO'^fHCOC^C^COQ iCOiOOtOOLOOiO iCiOCO^COiOCOiCCOiO OOCOOiC<-HTt<2?COCO(N lOUDOiCOiOOiOOiO iCiCCDiOCOiCCO^CDiC ait^QcOi-HiCtJ"^COC0 iCiOOOOiOOiOOiC iCiCcOiOcOiC^vOCOiC ■»**aoici>i>-cooo;go COiOCOtCCOiOCOiOCOiO Si-HiCOcOOSt^t^OOCO iCOiOOTfO-^O-l* CDiCCOiCcOiCcOiOcOiO SiMiOt-l^Qt^asoOOD COiOCOiOcOiCcOiOcDiC T-t TJ« rl ^ 1-1 CO COiO CO vO COiC iCQ0?OCOI>»O r-( CO i-H CO rH CO CO lC CO ^ CO lO OCOrHfNCOrHTfOlOOQCOt^ CO lO COiO CO ^ I-H TT r-( CO iH CO CO UO CO LO COlO COO-^C^COCOC^Tt*OiCO SCOiOcOiO rH -^r-l-^r COiOCOiO CDi^ asr>-OcOrHT*-(Nt^T SOiOOiOOiOOiCO SCOvCCOiOCOOcOiCcO gS ■^OCOt^C^QOMCOrH OiCOiOOiCOiOO COlCCOlOCDlOCOiOCO CTiCCOt^rHCOC^^CO-^ iOlQOlCOOO^OiA iCiCCOiOcDificOiOCOiO osoooQOr-ir^c^cocoic iOiOOiOO»00»00^ iCtOCDiOCOiCCOvOCOiO OSOiOOirHOOiMI>-C^CO COCO^NiOrH^Or^Oi OiCOlOOiOOiOOti< COiCcOiOCOOcOiCcOiC CO-^-^COlOCJCOrHt^rH OtOOiOOiOOiOOiO tOiOCOiOCOiCCOiOcO.iC CO^'^iCiC'^CpCOCOfM OiOOiOOiOOiCOiO COlCCOiCCOiOCOiOcOiO USOOOOiCOiCiSiO lOCOCOCO'-OvOcOiOcOiC ;r*iCQO'^cocoo>coc^ riOOiCO^OiCOiOO jiOCDiOCOiCCOiOCOiCcC giC i> ic 00 Tj< a> ■" SOiCOQCO lOOOO COiOcOiOcOiOCDCOCO •xoiddv Q*^ 6583—06- ?COQ0iOO5^Ol'ft0»CpOCOOiOO»0 SOiCOOOOOOO >COlCCOCOCOCOCDCOCD gs OOOt^Ot~iHtDi-ltO 000000000 tototototototototo ST-Hi-lrt-JOI^OOJO OOOOOOOOiO tOtOtOtOtOtOtOtOtOirt geji-icqi-ii-ic^rtcq© 000000000 totototototototototo SCOi-ieOiHCJCJC^'Ni-l 000000000 totototototototototo cot^'^to'jiiOio-^toTf OiOOiCOiOOiQOiO tOLOtOiAtOiOtO^tOiO cooOT»ioo5it^intototo O^OiQOiAOlCOiO toiOtoiotoictoiCtoLC MOiTtiai*^Q0if5co>f?t^ OiOOiCOiOOiOOiO tOiOtOU^tOiAtOvCtOiA gcocot^otoi-iioc^'^coeo OT)ii-c*r to lC to O t 00Q0>0>O00i-lt~(Nt0C^iO OlSOrfrt-ilrH'^r-lTjirt'* tOiCtOiCtOiCtOiOtOiOtOiC t^O»OOi-IO)Q005i-IOOi-lt» OiOOiOOlOrHTJIiHTJIrHi^ tOiCtOiCtOiOtOiOtOiOtOiitl SCOt^C^OOCa^rHOOOCTi lOOi/^OiOOiOiHiOi-l-^ tOiOtOtCtOOtOiOtOiCtOiC to>5r»'j'cC'*QOCo^cjoc^ oiaoico»oOiOOiCi-(»c toictoictoictoiotoiotova tpt^totot^tooOtOooi^ioa'^ OOOiCOL^OiOOinOvC tOiOtOiCtOuJtOiOtOiOtOiO coiHcoo3'0'*CT>'Oa> oooooooiooira tototototototo^to^ i-(iOi-iT) to CO to to to to OiHOi-lOi-IOi-IOi-< totototototototototo gS j«tO CO CO CO S1-< ^ 't-< "^ w^ CO CO CO CO CO CO -^ ,-( CO rH CO rH CO rH CO rH OrHOrHOrHOrHOrH cocococococococococo pc?GGpHCOQ:^cop:ja)p:jcG ^^^:^ '^^ pjGQQJcnOjaipiJaQPf^oQ coocooeoo^O's'O totototototototototo SOT 1HO to to to COrHCOi-ICO^CO^HCOi^ OrHOr-IOilOiHOi-l totototototototototo no to to to OJCOOnCOpHCap^GOpiJU] o-a» W5 C^ "^ COQCOi-fl>-Tf*"^l>.-l iCQ0l-'^05-«*'X)COTHOc^i'MO'^30 0^oO"^oTjl COOICOC-«P C0rHrJUtiai'*^OJ!cOOiOQOtOcDOO^OC MC^C^C^C4CSCOC^COC^ COr-ICOrHCOi-HCOi— t^rH gOOtOOiiCOCOC^C^COO i-tCOi-HCOG^COC^CCC^CO -*i-ico(Mincoco'^!N oiopooa>toi-iio .COC^COr-4COrHCOrH'^rH i/5t-HOOOOO>CH>i-HO C4CO(NCOiM(N(N'MCOC^ ^C0-»:*'"^C0iCC^i:Oi-it^O00aidG0Ot>f-H5O S5 r-< -^ i-H ■<»< 1-1 '^ rH ^ — ' ' ' '* f-lCOrHCO O »C CD iC C^CO{MCOC^CO CO iC CD lO ^ lO CO^'l^-^COcOfNt^^C S'c^coccco .-H •CCO»CCOiOCD»/i gT-JOQiMaOCOt^McDTfiiC ^co id cOiO »C CO iC S i-HiCihS rfj CD iC CD iC C^ Q C^ C CO iC CD u aOC0OC^r-l(Nr-lr-(CaC ^ CO iC CO iC « ^lC^H 5iO CD»C lOiCcD"* 1-H ''J^ r-t ■<*< COiC COO CD iC CO >0 CO iC OSOOOSi-»00(Nr*CO<:D i-C^fNOOiMCOC^COC^CO COiOcDiCCO»OcOidcOiC '«*'iCiO"^«OC0t^C^00i-t -iOC0CD»0 ""'*■"' W COIN CO iN CO C^ CO C^l CO CDiCiCOiCcOiOcOtCCDiO coQcooi'^aiicooict^ CDiCCDiOCOiOCDiiScDiO gOi »C Oi iC rf*COO CDiO 2S2 CDiO CD iCCDiC |i-tiMC^tNCcOI>iC00'rfOcO>0 00COCO!M'^COCDiOCO»OCOiO ^cOC^COC^iOCOiOCO'^ cOiOcOiCcDiCcOif^cDiC Tj<'^'*Jiot>-ior*icc -SoO OO ^ CO CD CO CO OOO CD CO CD OO coco CD t^-^i^-cot^cot^cor^co OOOOOOOOOO COCDCDcOCDcOCDCDCOCD gggggggggg COCOCOCOCOCOCOCOCOCD g^ C> "5* 35 OOOO jg CO CO a5 CO OOO CO CO CO §3g CO coco SOr-fOrlOi-lOi-lOi-l •cjcocococococococococo OOOOOOOOO CDCOCDCDcOcOcDcOCOCD aiOaO<7sOaOr-tOOi-icO OiC»— liOi— tiQi— I'O'— (lO COiCCOiOcDiCicDiCCOiC aocodocOoO^OS2?Osc^ OOOOOOOOOO CDCDCDcOCDCOcOCOCDCO F-tt^C^r^(Nt^fMCDCOcp CDiCCOvCCOiCCOiOCDiO ^0-h0i-h0Q0O 0.-H0^0f-l0r-t0 COCOCOCDCOCDCDCDCOCO SCDcOcDCDtCr^»Ot*iO OOOOOOOOO COcDcDcocDcDcOcOCDCO OOOOOOOOOO CDcDCDCDcOCDCDcDcOCO Or-lOt-HOt-lOr-tO—l cDcOcOcoCOCOCOcOcOCO -ICO-NCOC^COfNCOfMCOC^COW o "S~^~X s "§" ~T"S" ^ ^ Or^Oi-lOrHOf-HOi-H CO ^ CD CO CD CD CD CO CO CO a^astfcoPiHaiMoQpHCO ^xxir OOOOOOOOOO cOcDCOCDCO'OCDCOcDCO lO g? »o 00 lO 00 >c CO lo 00 OOOOOOOOOO cOcDcOcOcocOcOcOCOcO COC^CO(M- 00 OS ^D^ CO CO CO CO ^ S •§ ■* r2 1 3 I TABLE 10. Mean Time of Sun's Visible Rising and Setting. [Page 499 ■J ^«3 •xojddv ^!zi •xojddv P'^ ogigg^;^ §!5;S?g"SSSSS SS f 00 tc cfl c^ 50 00 o •<}• -^ o5 05 lO (N CO -^ c^ -^ t* -^ r* -^a* c* TT t* -^ t* -^ t> -^ t^ T3* g'OOOCOiOtO(N005COiO (NCOiMCOlMCOCOC^COIN ^-^iHt^ooOiOcoojr^oi S^'^i-ICOCvlCOlMCOC^C^l S*OT;g"C^0O«O'-IM O-*i-l-VrtC0i-IC0C^C0 iiOOOt^tOOCOCOOtOt^ feO^O-'J'iH'^i-l'^t-lCO t^ji.HcoiO'^oioeoiO C001'10000>5i-"^i-iCO t~r)<00CO0OC0O0CO00CO OiOOOiCOlOr-l'^ t-'^i>'^«cococoooco QHCfiO^cfiCiHccoJcnpHcc CO^O-^t^tOiCOO-^OJ COCO'*(N'^i-iiOOOiO oocooocowcooocowci :DCOCO?DOOaOOi— tr-M ' — 1-liClO 00 CO 00 00 CJCOCO 00 CO 00 cooococ tOO>NCOCT>«5t^O»iOi-l *' — f-4-^ T-H 00 CO 00 CO i-(coc^ 00 CO 00 CO CM IMC TOOOCOC ■^OioD'-Oi— (cMiociOiic C<»C^CMCMCOCSCOt-(COt-i i~-^t»-*t~-5ft~-cococo .«5C0 — O>'*tO00COi-< 00 CO 00 ■*T-icOC cooococ O5'»**c-ii-nor*ai-^coo i-ico600005-1'-^'C»3l-JiT)i00OC0t0t-C0 ^t^T}-«'J>-*l>CO t-coooc cooirM"~oOTjOrHCMT}*0000>^»-Hf-llCt^OaCO __ ._ ..I — 'c< fj C4 CM CO c^i CO .-I CO i-H OTTi-H'^i-ICOr-ICOCMCO sss SCO t>. to OS CO CJ 1-1 lO iC to iC lO o to tOTjitO^tO'^t*^ SOii^:oococoOiOt>. ■^O-^rH'^i-l'^i-lCO 5 rH rt t- ;0 CO CTi OiO CO 00 CO o-q>i-ieo 00 CO 00 CO Soos'cocRop'^-gioo ■vOOtOtCtOO*^ t»'0 O lO lO t~ rC I> ^t I> -^ t- ■* t^ ■>!< t» Tf t» -1^ t>. -^ t» •<* t» CO « i-iciOOiO 3tOU5tO lO ^ "^ to ■'I* 8-*CMi-n0 050DtOOCO I00i00-*0'<»ir-f* tOO?OOt^QtOCMCO'<5*i— I -^ ^~OiOOiOO lo toio toio tOtO to tf. coco tCiOtO tO tOtO to tO S CO r-l -i^H r-t ^ .^tOOtOiOtO to CO ■'i< Tji CM to r-< tO to lO to tO ISZI tO'^';0'"*t**^t^^t^^ CM3'-«-liO •OOiOOtOOiOiOOiO tOiOtOiOtOiOtO-^l^-^ COOtOt^Oi'^COrHtOt^ f-^-*rHeOtHCOCMCOCJCM Oia''*OOOtCCMi-lt-.tO COCMCOCMeOi-l''S>r-l'^0' OOtOr-lTt'Tfi-lt^OOO'* O'*i-l'*i-l'Vi-lC0CMC0 COCMtOQOCt^rt-^'*!-! 00OStDt^CMiC-*C0tOT-l 'ij'OiOOiOOiOOiOO tOtOtOtOtOtCtOiOtoiO ■<*0 CMCOC^CMCOCMCOCMCOiH J— iiOtJi-^OOOOC^-* S»OtOCO-1'iO.-lOOOO r-IU5Tl.-itOT)jii-(T)<.-icooicoc^co g'tOi-iocoo>ao>-ii-»c0 feCOCMCOCMCOCMCOCMCOlM rfjtOiOtOtOtOiOtOtOtOtO g'OOi-i05M(>-'*tOiQiQ COCOCOCMCOCMCOCMCOCM .^tOiCtOiOtOiOtOiOtOtO g*t~.TfioOCOmCM.-I^CMQ CMCOCMC061COCOCOCOCO ^tOiOtOtOtOiOtOiOtOtO -*Tl■■<* I>'*t»-tl-*t»'!>'t~'^ O«CMt^C0i0i0-S-C^ tOiOtOiOtOiOtOtCtOtO tDC00DC^CnOT-(05CMt~ eOCMCOCMCOCMTfrirrTH tOtOtOtOtOiOtOlO'OiO CO o <5 CO CM to ■^ -"f r- CM 05 o» cm t^ -ai ni t^ cm o o> ^f— tiOOiOOtCOiOO 'OiOOtOO'OO'OiH^ to lO to lO to lO to lO to lO to -^ t^ Tj^t^Tji t^TiH t^-^ SiOTjit^CMOlOiHOO'COtptO^OOCMQi; i"*rH"^f— l-^r-ilOO tOOlOOlCOOt ; to to to lO to lO to lO to tO to to to to t^ - COOO-^t^tOtOl^iOOOCO COCMCOCMCOCMCOCMCOCM tOtOtOtOtOtOtOtOtOtO S'-^OOtOt^tOtOt^tOOOTJ* CMCOCMCOCMCOCMCOCMCO ^tOtOtOtOtOiOtOiOtOtC 0>C0OCM-Hi-IC0O'^CTi CMCOCOCOCOCOCOCOCOCM to to to to to to totc to to ;i— irMcMCMcoi-i-»ro-^aa :eM'>a-itOi-nO JS to to to to t~oooocoo> rH tO c-t to I— I -^ to tO to tO to tO tOOOtOt-^t^tOOCtOCTi-^ CMCOCMCOCMCOCMCOCMCO tOtOtOtOtOtOtOtOtOtO C^COCOCO'^CM-*rHiOO CMtJ'CM'3'CM'^CM-^CM-* tOtOtOiOtOtOtOtCtOiO ocM>-ioeoo>-*r-toiO ■*CM-^CM-»r-(-9i-l to tO to to to to to to to to iOt>-totoogt005cOi-HCM CO CM M C5 CO 04 ■» CM tOtOtOtOtOiOtOtO CMOl'^t^t^ 00 CO Q 1-1 CM Oi -^ T}1 »— I IC r— tO O to to tO to to to lO to otoo tOtOiO CM O -* 00 to t^ 00 ■^ CM ■» 1-1 tr r-l T)> to to to to to tO to tOQCO lOtCiO -^COCMOICOi-l-^OtOC b CO CO CO CO CO CO CO CM CO CM CO CM ■'f CM TC 5 to tO to lO to to to tO to tO to tO to tO to toast^oooDt^aitD^Hto ""'5CMCOCMCOCMCOCOCO ttOiOtOtOtOtOtOtO OSOOOSOOOI^'-lt^'-ttOCMtOCO'^'^COtOCOtDC^ r1 ■^ rH T)< CM tOtOtOtOtOtOtOtOtOtO CM "^ CM "V CM TT CM tOtOtOtOtOtOtOtO g" COtO -tp tO tH to 1— t tO jjtoiO toto ^ ■^ ^ ^ to ^ i-H iQ r^ to tH lO to tO to tO to tO tocotocotocMt^c^r^i-t .-MiOi— 'tOr-itOt— ttOi— ItO tOtOtOtCtOiOtOtOtOtO SSgS8 ^ CD CC to "^O 1-1 OS .H Oi C^ OS tl »0 r-l lO r— ( IQ «£i iC CO iC <:0 iC c^ccMQOcooocor--coco r-Hi0^^iOr-(iCi-HiCr-liC ,^iCC0iCCOiCcOi.0^iC osooiOioaii-tao "^ CO iC co»0 CO CO lO lO CO »c 4C) r^ »^ t— ( iC lit O lO "^ lO )-^GO^OOCCiOOMOOCC *cOcOcocococ0^cocOcO 0000000000 ■tf COcOCOcOCOcOcO^OCOcO oocooicooicotj'Coas'M 0000000000 tO-OtOCOCOCOcOCDcOcO OC^O^OMOi-^r-^^ — ■*- O f— I O t— I o (O CO CO CO 'X) r-iO coco I— ( ^ 1— I c to CO coc r^ t^GOiOO" (N'^CCCJ-^'-iCOOt^ COCOCOCOCOCOW '* «0 tO CO »0 CO iO CO iO«OU3 l^ rH 00 O OS OS (M -^ C^ Tf (N CC CO CO iC CO J5 CO lO CO W5CO« iC cOiO 1-1 1^ (N r^ CO CO Tt* iCcpiO COTft>.rfr^COXCOa>'N CO lO CO iC CO lO CO iCcOiO ^ O i-H O r-l O r-l CO CO CO CO CO CO CO COCOiC ■o 00 ic 00 lO 00 ic 30 ic X' I -p go 0000000000 cOCOcOcOcOcocOcOcOCD 8SS to toto )toootcoo|-oootooctor;32GS 00 to to to to to 0000 to to to to to to to ooS to to to g'CMMCMCMOICMCMCOCJCO OrHOrHOrlOrtOr-l .c* totototototototototo tfoQSHOQpiJaJtfcoOSoi ""^h"" CM CO "ri'" i?b CMCOCJCOCMCOrHCO^CO Or-l0rH0iHOr-(0'-l totototototototototo ojcopdaspdcopHaQaicc Tjt -V to f^ CO r- 'OO'HCOr^'^^^ iOr-fO > to to to to to to to to |S3SS8S8S8£ jcOcOCOCOcOcOcOCOCOtO tf cc a; CO Qtj (^ Oh* cc Cei OQ tf'coC^oQp^ccpciaQp^GQ Page 500] TABLE 10. Mean Time of Sun's Visible Rising and Setting. -C^I:^ltO!M<;D05«DCCCpCC«:OW<:p 00'30COt^'*l>Tt<^-" §ss i:^(or^0 kO »C»C»/5>OiCiOOidCiCiO ^Mi-l'^'-^'^'-H'^O"^OOO»0aiC00i«0C>':0G0k0Q0r*t^00t^00':000OlQ0(O0^ S;iOO^OiOOiOOiOO'^0»Ou:3u^iOiOiCiCiO'iOtO»OiCiOiC»CiO»0»OOiO ^vCtOtC*^iC'^»OtOiOtO jiO ':0»C^»C»dCiOiCvO iClif5tft»0>CiC»OiO>dO jiO iC»OUtnOiO>ftiOtOiCtOiC giOOiOOiOOiOOiOO ^iCtOiO^iOOiCtOvOCO g*ioco»cc:Ni?oi-*a>r>-air*co LfSSiCiCiOiOiOiOiOiO iCtOiOiOiO>OiC»Cift>iO r>-OQOOooa>a>a>a>oo iCtOiLOCOiOiOiO^OiO 00Q0Q0t^01^-0i«t^(M ^uT'tOiO'tOiCcOiCOiOXi iO«OiOtOcO<:D*XiiC:OiokoiCOiOOiCtOLOOiO :OiCOiCtO»C«Out)50iOtOiO * -^ 'Tf '«+< CO lO CO C^ ift CO lO CO '^ -. , J. <:OiOtO»OtOiCCOiCOOcbvO lOrH i-(02J ^ )coo5C0GC-j*r^Tf^-iC'^; -U^QC^OOCOOiC^OC^ 5iOtOiO'^iCtOiOOiCtO«0:0?0'X>i:0'^i:00':OiCtOiC^iO':OiOcOiC^iC tOiCtOiOtOtOtOiOtOiCCOiO S't^iCCO'^ai'^OiCOQCO r-'iM.-'i-IC^OCOO'^O 'rtCCT)-^OCOO'Mi-(i-l(Ni-H ^lO^OiOtOiOtOiC^OtOtO <©OtO'OcD'^';0^:OiC OiO^iCtOiO^Oir^OiOUoiOOiCySii^OiOOiCOiO e;oocoas»oOlCQ'^l-^co■^^'^^coc^■-+<7sl«ai»coor-('»f giOOiCOOOOOOOOOOOOOOOOiCOiCOiCOiCOiCOiCrHiC.-l»OiHiOi-HiCi-HOrHi5 _(*iC*^uSOtOO^Oon>oOf ___ ^-^- -. -:=:- --,- -OOi-liC'M'^COCO-t*'N»Cr-«tOO«oaa ;»OOOOc500000jOOOOOOOSOiOJOOOiCOOi--(»Cr-4iCT-iiOrH»Or-(»Oi-HiOi-lif3i-(Tf* iiO'0 00:OCO;OCOCO^i?0^<0'^';0:OOtOtOiC'^iC^iC':0»C':OiCOiCi OiOtOi^^OiCOiC^iO^OiO ^coiO'M'Oi-ir'-oaooi |a>oiooo*-it^cCi-HiCT-li5.-tTj< ^CO(:D'-0:000^':0^^ -^tDOO'0:0':0*,OCOiO ;0iCO»0*^iCOiC^iC OiCOiC^iOOiO^iOOiO sX'^r^c^ocOiC'^-^ iCcoy^'Mt-r-i^iOoajasOQOrHr^iMcocoic-^- kCCOOC-ICOi-iO^OOOiT . ._ . - , . . . .-, . O op rH r^ CM CO CO iC -^ '^ -_ . . _. >0 00 00 0|OOOOOOOOOiCli-Hii5i-i»r:)i-(iOT-(»OiHtOrHiC.-(iCi-H»Ci-iiCC^'^OcOtC<^iO'0>o!tOiC^iCtOiCXiiCtOiOcOiO r-«OiQO0iMQpC^I:^C0c0»O>Ct0-^^-C000C*iooco^--^^iOio '■£> CO t^ c^ cc OOOOOOOOOO ooooo ^O'CiO';0'0<0:0:0;0C0 tOOCOcOCOCO':OOOiCitOiCOiC^iC':OiCOiO!tOiOCOiOOiO':0»CCOiO<©0 •xoidd V ^^ S*^aicoQO'^t^ic:oto«oU-*cooDC-ia>'— (OOfMOi OOOOOOOOOO OOOOOOr-iOi-HiC ^COiX>--OtOCO^!©tOCOOtOO^Ot0^i:D';0':DiO S'Cox'to^t^ic OrHOOOOOOOO ^cO^'Xi«0'X>'XiOtO:00 S'tMO'-t'Oliil^QOcO'tOcOiC Oi-tOOOOOOOO ^cOtOtOtO^OCOOtOO'^ X ■^ Ol CO O 1— I 1-1 Q CO Ol -^ CO lO t^ CO lO 00 '^ O^ CO O O O O I-H O rH O f-i iC i-i iC iH »C rH lO I-H iC rH lO COOcOCOCOCOcOCOcOiC COuOCOiCOiCOiOcOifl ^ C^ OQ Tj; t--. lO CO cOiOcOiOcOiOcOiCCOiO CDiCcOiO^iCcOiOCOiCCOiO o>-+I^>Cai'q*O'*<0^vCt-- t^COCO-^OCOi-Hi-tcOO "^OOCOt^OQiO!: Oi-hOOOOOOOO rHOi-HOi-HOi-HiCf-HiOj-HiOr-iiOCaiOC^tCCi^ (NtPCJt:OC0COcO00iCaiC0i-H(M c^-rrc^-^c^'^c-i'^c^'^co'':}* cOiCOiCCOiCCOiCCOiCCOiO J lO Oi CO 1-H '^ooicco OrHOOOOOOOOOOrHOrHiOrH'C'-HiS ^tocococococococototocococo^ocoiccoiccoic t^iOaOCOOC^C^QCOOOiiQr^«OiCGOCOO(M(NOCOOO i-HiOrHtO(NiC(N>OC^'^jC1-^c^t^'ft»CCOcOtM OOOOOOOOOO ^'COCOCOCOCOCOCOCOCOCO 3T}.cO»Ot^COa5'MOO!NOO'*CO -. - ,_ .. _-.HrHOC^QO'^t>-'^»Ot^COa5--_ -, -_ :0000000000 OOi-HOrHiOT-nOi-HiOi-HiOi-HiCNiCfN'^iM'^ ^tOCOCOCOCOCOcOCOCOCO cOcOCOCOCCiOCOiCCOiOCOiOcOtOcOiOcOiCcOiO COt(til>-COOVi-Hi-HOCOOQiOO (N-^c^-^c^-^co-^cocococo tOiCCOiCCDtCCOiCOt^COiO xoooo^cocoiC»cco!coT-Hoooioooc^cocO'^'OC^r*oaioOf-Ht^co»ciOco OOrMi3i--UtlrHU5rHiO'rHiCr-(TtCC0iOC0iOc0iC COvCCOiOCOiCCOiCCOiCcOiO p^cop:iccp!jiXp5MQ3coteoQp4copc;a)O^Q005c/ia2aQp:3coa3^ftHQ'2CEHCC O ^^^ r-! C^ CO -^ -"^^ CD 1-* 00 05 g> 1 1 a o ^ -5 O S i ^ 4 1 3 "* .S TABLE 10. Mean Time of Sun's Visible Rising and Setting. [Page 501 •xojdd V o a ?3 ?5 s s § s piccp^ccpdcoaJMa^ccWodoiaicijaJoaaJijcc KaiojaJaSaJojaJWcc ai as oj ai PS cb ptj oc 05 m CO CO M S S ■^ lO ■^ lO -rp lO '^ iQ Tji iC T lO Tf< lO "^ lO T Ui ■^ iC ^ O lO iC lO »C irt iCiC 1^ iC lO iCiC lO lO lO lO lO iC 1^ Goi»oor*t^t--t^r*t>-t > iC iC »c iC lO lO ^ iO iOi040»OiOiCiC^»j0^l^iCvCiO*OiOU5iOiOiO ICiO^iOiOOiCiCOiC ■f iC CO »C' CO i^D ;^"t0 iC CO coco to CO iC iC >C lO iC OiCOiOOiOOiOOiC co*o<^iOcoiccoio«oif; CO 0>*^ 0>"* OS SQOiCOO lO «OiO oto»ooiOtoio aoa50ioiasoDOcooi'*'-HtO'Nto-COtO-^CO (0>0:OiOtOiOtOiCtOiC gTHi-lr-tOC^O»COO:»COOO -^J'-OiCtDiCtOvOtCOtOiC ■^t^icr^iOtocoiot^ic tOiCitOiCtOiOtOutitOiO gCOQCOOi'^^GOiOOOCO j^(OiO<^iC<:0>0!OiOCD>C r^i-x>ot^»coO'^o>cooco ;OiCcDiO:ou^tDut)toiC lOiCiCTPtOCOt^COGOiM 00-rf<0iC«O(MO«-HT-(O THCNJJrHCOO'^anO': >iCO»«oooi>-r-aocoa>cooiioO'^t-^coc^!NcO'-iTt*QiOCT>toc ■tOi^tOiOtOiOtOu^itOiC GOf-HCiOOOi-'ai(NOO ^TfrHTj4(N-^C^COCCDOiCrH;^ C^COCO(N-^,-(iCOtOOS l>.GOOOt^OtOT-tiO(NCO * ^ ''l^ C^ Tj< Ol ^ ^i:OiO';OiO?DiCtOiC)tOiO CM-^cSTpCSJ-^CM-^tMCO :OiCtOiCtOif3«OiOcOvO SOOOi-lt^lNtOCOTj4'rt«CO ^tOiCtOiOtOiCtOiCcOiC (NrfC^'^fN'^C^COCOCO tOiC^OiC^OOtOiO^iO •xojdd V sMt-CO'^-^iOiOCOt^lN !00>-IOlOOOii-(t^CO«0 H <>» '^ C^ -*< (N "* ^tOiO«OiCtO>OCOiCtOiO C^Tt4c>»TtCOCOCOCOCOCO '.OiCtOiOtDiO<£)iCtOiO S*-^COiOut>?OCO00C^OO'MOilcOCO'^cO'XiiOt^COOi»COC^ ^iC:OiG(OiOCDiC«OiC rH<:OC^iCCO"^iCC050r-l COCOCOCOCOCOCOCOCOCO COiC^OlO^iO^OiC^OiC ^Tt'ifiCOt^C-IGOOOCi COCOCOCOCOCOCOCOTj-C^^COrf< SCOj^TTtMrrC^-^C^ S:OiO(0»CtOiCtOiC r-»I— COtD'^'Tt^COCOt^'-H t^C^00r-lOOi---^ tT-iOoococ5i-i (OiC^iO > O lO CO iC to lO ■^ 00 to CO liCr-liOr-l SCOiCcOiC cOiO co»c CO lO cOiC cOiC COt^OOiOOCOC^O'^CO iCrHiOiHpi-lOr-tOO COiCCOiCt^iOI^-iOt^iO »c^O"*aiict^i>coa>'^ ico-^cocococococococo icOiCCOiCcOiOCOiOcOiC ■^CO'^CO'VGSI'^C^tPC^ -XnOcOvCOiOCOtO'C'iO - »C Oi CO .-H 1-H SasiOCOt^COlOl'^'-lr-ICOOicp^-QO-^ T-nA^iCrHJiCrHOi-lOOOOOO coiccoocoic 'co»cr^ior*iOi>ioi^ic COCOCOCOCOCOCOCO'^CO ^COiCcOiOcOiCcOiC<0»0 to»o CO iC CO iC CO lO (MO'^OOcOcOGO^c: COiOcOvOCOiCcOii^t T^Oifti00t-iCiOC0(NO OrHOOOOi-lOt-HO Siccor>-»coicooi-ic^aa COCOCOCOCOCO'^CO'^CN ^COiOCOiOCOiOCOiCtOiC COiOCOiO 00C0O»-l0105h^l>C0i0OC0i-li-tC0ai'»CC000-^O'-HC00it0c0 '^C^>OC^iOr-iOi-(iOr-liOi-io^-ioi>Tt*c^'^ ) iC CO lO CO iC CO iC :cocococO'^cO"^c^Trc^ ^COiCCOOcOiOCOiCCOiO lOiHiO COiC CO (N,-l0iC0I^cp>CiC0iMT-HQC0t^C0'5'01C^ rHOOOOOOjOOrlOrHiOi-iiC—iU^ c*t-»»-Haiait-(t*coiCicco S:cCCOCO^0 COCOOOiOOCOcOr-dOOi ■^•H'^T-tiLCrHiOrHiOO COvOcOiOcOiOcOiCcOiO S8 CtHCOPjaSPScOCdoJOScC 03 CO OS en Oh 03 Oh CQPS CO Oh OS Oh CIS OS CC 05 us Oh . T)> !n ?5 e5 ?! N CO ■^ irj M M m « OHCOPSccOHCcMasOSa} m 05 -"T Page 502] TABLE 10. Mean Time of Sun's Visible Rising and Setting. CO - B i N a r-H ^ xojddv g f^aiA^Ci'^ficDCiia: iHjQQP^cooJtnp^aQpjco pct^'OH^P^cnC^cdp^cc s s 0CHC/^p:4GQ0JGOp^cQP:^oQ • OOI>QOt^C30cOOO!cOGCOQOcOCOcOai'«Os lOiOiOiCiCOiCiOiOL t^(Nt^rHt-.rHI>.-.aOr |ooc5cooaiO- OS CD O lO > i-H CO •—( CO iN CO J CD lO CD iC CO iC i-t-^COCC^iMiCi-ICOO goOOsOsOlOOO'-it^fNcD i-HCOr-lCO!M'MICO ^CDiCOiCcDiCcDiO«OiC SCOt^-^cDiCiftcD^t^CO C^COlMCOC^CO-MCOfNCO ^CDiOCOiCcDiOCDiOcDiC c^ioeo-T*. C-^.»iOGOcDr^i--cD I-lCOI-l'^0I-ICO^-tCOr^CO cOiOOiOCDiOCDiOCOO O-^rHCOfMiMCOi-HiOO i:nco!Mcoimco(Nco)C^C^iMCO(NCOO COOCOiCCO»CcDiOCOiiS rOtNCO'NCO(MCOi-l-<*-*r-cO»C < CO !M CO (M CO C4 I CD ii5 CD lO CD iC CD lO CD »0 CO >0 C •xojddv Si-Hr-HNQ-^OiiCt^CDCD COCOCOCOCOlNCO-MCOC^ ^ CO liD CD iC CO lO CD lO CO iC GOiCOSCOi-tC^Wr^'^ai COC^COCJ CDiOcDiO ■^ (N '^ C^ ^^ r-l CD iC CO lO CD ift gCDOOr^l^OlcDO"***-HCO COC^CO»cr^-^ *jcoc^'^iCrHcxioOi-)io lOOOOOO CO iC t^ iC t^ lO ^ ^ SO OJ O 1/5 -£• I^ -J >ooooooo • iC t^ iCl^ iC t* lO O 05 (N « lO T)< 00 T 1-H lO T— ( lO 1— ( lO c^ Tj< t^ -(j4 r^ -^ ■^lOt^r-lrfOO CO CO eo 55 Scooior)>r-c^o>Oi-too lOi— (lOi— liOrHiOr-lOO COtOiO'^QOINOOJCOt^ OOOOOOi-llOi-liO H (N Ol -^ I-- CO -^ iC ) Tt* r^ o »o o? CO r-t c 5lr~iai> OOOi-l lO t- »/5 r* lO SBS S3S rHTfOJtOCO OrllCrHin Sr-(0 i-H O 1— t ^ t^ "^ t* ^ Jt^vOOCOCOQCOt^ ;aocorH,-c*cor-iOQ»• CO l^ to ■* 05 C<1 i-( lO rH lO tH U^ I> ■* I> Tf t- ■<}< TjiaotoiOoscoc^oiOt~ rH lO 1"* iC S rH iC (M iC IN •* OS ■* eq r-i in CO 00 iQ rH C CJ-^C^tJicO- t^ -^ t^ -^ t^ ' 5 i-liO O) -* IN ■* C f t^ Tj< t~- Tf t- ■<* 1 3 iC 00 1-1 5 CO CO CO ■*C4 ■^IM C-10SiOtOQOCOrH050to|oDC^(NODtOTjir-^OtO»C O) ■* C^ Tt> CO CO t^ '-^ I> Tt* I^ -^ )iOC^iOi-t i-IO"5WQOCO CO -^ CO coco CO t^ ■* I> Tjl t~ -^ to to O i-H >C l> c ■^ OJ lO C^ lC 1-1 < C~ TJi t^ ■* W<}< c COCO' rHiot^Oicol-'i^aioo-^cooioo- 5M'*CO'*c5 - T}< t^ ■'^ t^ T^ t- -^ t^ -^jH r-- oo •^00-* OOi-(iO a0"« -^ I> ■^ OS-^CJ 1-1 O t^OSTfcOO CO CO CO CO TP CO I> ■'I* t* "^ t* "^ O-M-^OOOOiCC^iHtOtO ^ •tj" t» -* 1 -HrHtptOrHrHt^tOCOOl 5 O !< t~ TJ< S 05C0'«<00O(Mt01>C0O oOiH»o(Nioc^'iCC^C JCOOOC lOOCOiOt^lMQ I C^ •* CO CO T)< M I 00 CO 00 CO 00 CO iQ tOOQ C0 1-103; to ^ CO ^ CO CO T}4 t^ ^ t^ Tj< So)-*c --i^coopc 5CO COCOC •iCOiOO tOi-l gcNCOlNCOCO . t^ -^ £> Tjl t>. (MiOOiOOin CO CO C^ COO) ^ t** ^ t~" ^ 00COi-IO»iO>QO5-HC0t^ COCOlMOOt^COdOO iniHoooorHS C^TfoO'^OO'^OOCO 00 CO 00 CO I'^CO ) CO 00 ■*coco CO GO CO T)<(NiOrH 00 CO 00 CO THtOif51NO>COCO-^OCO (NC^tOOO Tjl 6l -^ f-l ot)o ^^ pHCAPiHcdC4cQtf ccpHoi Oh as (< c^ tf si (4 ca Cij cc to l^ ao 05 ^^^ •^ ^ ^ -^ ia t^ocomoooi- O O rH 10 i-l rr c 00 Tf 00 CO 00 CO G SCO CO )C0 00 o-*co coTTca CO 00 CO iOi-(00 00 CO 05 CO T)m'^Oio-»toooico O00i0r-1"^1N-*0-- ' - CO"<1<00C000C000C00C piaiKaJpiaJpH'MttJaj aJcortaJpHoartaaWco rH O 1* t^ to iC 00 co^ -■ — CO 00 ■OOOU3 ooeoc:>2 to t^ 00 ~02 TABLE 10. Mean Time of Sun's Visible Rising and Setting. [Page 503 a 03 +^ H ■ © P ie; ft a CO ^ a d^ a •9JBp ■xojddv •8;bP •xojddv p:^ GC Bh' OS p4 OQ P^ !»' Ph' CQ p^oQP^cQpijaQpjaQfi^aQ .c* lO lO O iCO CO r-l-.** CO Tj< O ^ O MO CO rt CO iH lOtOiCCOiOSOiOCO^CO 0C£>eoc0'<OQDC^COOO'**'iOCOt^ iC '^ iC ? t>- GO as CO T-t ■'I' c T-Haso>o(>'C^^'^'^cDc^c 5 COiCOiO ?o i-H (N iH (N i-H C^ vO CD lO CO iC "^O 00 r^ i> d »ft O M* COiO COiO COiC CO S*C*lOi-H(5JOWQ0»Cc0c0 S'THl3>prHOS(Nt>-C0CO»A g*OOOOSQQOTHt^(NiCCO tJ< iC M CD i-t f^ Q Oi 00 Q iCcOcOOiC^iHOfNOi-^ liJidCiOiOcOiCcOiOco l>. lA 00 CO O iH i-H O (N O CSJ iH M iH CO iC CO iC CO lO o -tj^cOCOt^-W^OOOiC^t^eOCOiCiOcOCOt^ COiOOOiOCOiCCOOlr*t^0*i0Oe0^CJTjJ 5 COiO COiC COu i-H C^ i-H CM i-i (N iC CO iCCOiOcO ;woiTj^coiooocoocMw 5 CO lO CO iC CO L C^^r-i^T-i^y-Ar-i^r-i^Z ) o a> c^ t>- ■*»< >cou:) cDioco lO ?0 lO COiO CO CMOtM lOcOiO CO lO ^i" CO lO CM 1> CO lO CO iC CO lO CO g'O000lOiQQOI:^i-(iOCMN*'^C0iC»-HC0O00a>0S Tf^-^CO'^COiOCOutJCOiOCOiOCOlOCOiCCOiCClO QOOCOi-fi^CM-^^tOiO CMOC^IOCMOCMOC^IO lOCOiCCOiCcOiCcOiCCO S'OaDOiaiOQQI>r-(cOC00(3iOt^i-i SCOiOOiOCO CO CO ''i^ -^ CO CO lO CO lO CO iC CO lOCMOi-tO 3 tOxCcOiOCO l> rH CO CM lO ■* iC COiO cOiO CO CMiCi-HCOOOOOOit^OtOCM JOCMOCMO > COiC COiO CO iH O i-t r-i r^ rH lO coo COiC CO SOOOOlOlOOOt^'-'cOCM OCO'«*- inopOOO^t^QCOCMiCCO ■^■^COrJ*00>OWiOCOtO COiOCCiOCOiCCOiCCOLO CMiScMiOCMOCMOCMO ^ lO iCiC vO O lO u5 iC iC lO iC iC lO iC iCiO O iCin iC iC lO iC O lO CO iC CO lO CO ■^"^COid— tCOO^-dClOOO CMOCMOCMOCMOi-*OrHr4 lOCO^OcOiCCOiOCOiOCOiOCO S*OCOdasGOOr^rHcOCMUOCO"^"g*CO»OC^COi-'t^ OOOOaOiOOOt^^cOC^l '^'^MTj^COiiCCOiOCOiOCOiOCOiOCOiOCOiCWiO COiOCMiOCMOCMOCMO ^lOiCiOOiOiCiOiCidOiCi^iOOi^iOOiOiOiO iCiCiOiCiOcDiCcOiOco g'Oooooioooir-ocO'-HiCCMiocO'rt^-^coiocMcorHr^OQOasOiooor^rH coMiCcoTtCiCiOiCiCiCiCidO iCiCOiCi/^iOiCCOiOCO iOcOiCCD»OCOvCCOiOCOiCCO iCcoT*t-ico(NiccO'^'^coiccmcd -fJ^'^Tt^Tf^CO'^COOCOiOCOiOCOiOCOiC'COiCCOiOCOiOCOiCCOiCCMiCCMO CMOCMOCMOCMOCMOCJO ^lOiCiOiCiOiCOiOvOiCiiCiOOiOiCiOiOiddC iC»OiCiOiCiOiCiCiC)'-0 iCCOiOcOiCcOiCCOiOCOiOCO S*i-ia>QOiOoaii-*oOr-( ■^Tj^^TfTpiCCCiOCOiO t^CMt^COCO-^iCiOTt^cO COCOCMI>CMXi-iOiOQ ai*H00rHI:>.CMCOCOiOTPiC»O COiOCOOCOiOCOiCCOO COiCCOiCCOiCCOtOCOO CMOCMOCMOCMOCMOcio iCiOiOiOiOiCiOvCiO iCiCiCiOiO»OiC»C»OCO lOCOiOCOiOcOiOCOiftCOiOCO T^Tj CO GO CM OS 1—1 o o JrHgiCMO0CMi>COr--^ CO >0 CO »C CO lO CO lO CO lO CO O coo CM O CM O CM O CM O iC lO lO iC lO >OiC lO lO iC iC CO »0 CO lO CO >0 CO iC CO lO CO aicoQOcoQO'^r^TtC0 coio6QiOcoScoiccoL6jcou^c^iaco»ocou5coio coiccoocoocoo?Jo ?ic5 iCiOiddfDiCiCiCiC»C iC lOiOiOiOtOiCiO^iO lOiOiOCOiCCDiOcoAcOiCCO ocoaicoa3-^oo-^t-ir:!'t^cocococoi--»ooo-^GoH*'a>cocicMQCMi-ii-ii-(rHCM '<*- ^ O iC lO lO lO iC iC lO uO iC •f^^^TfiOCOtOCOiC COCOCJcOCMCOCMI^CMr^ ■«r ui Tji ic -^ »^ ■^ lO ^ ic Ti< »o -^ »o Tj< iO Ti< lO -^ ic lO iC >0 »0 »^ iCidO iC lO iC lO iC lO iC idO lO iCiO 0-^»0'^»OiC»C»Crf»OTj-iot S*OscOOl coOi TJI iC -^ »0 '«?< ^lOiOiOOiOidCOiCiC S '«J< lO '<*' O -^ L p:HGCp4cGpHi/io:^cop:;aD O i-H CM CO oa^ooocooocoootooocp vOiCiOu3iO»OiOiCidC p^odp^copi^aiOiCQpHQO ^TX-- CO I> 00 o> c-^cot^cpr^cob-cot^co lOiOiCiCiOidOiOiCiO tOcOcOcOcocOcOc ? CO 00 CO 00 CO GO CD 00 « PhoqP5cqo5cqo3cqcihco O f-l CM CO tP ift t* UO t>- 1/5 iC lOiO lO lO lO iC lO iC iC *C ii5 I CO CO CO CO 1 Tf tC -^ »C I lO lO iC kO aOC^OOCOGOCOGOCO lO iOiO 00 CO 00 CO Tjt lO TJ" lO iJs CO !>■ 00 0> ^S~^ Page 604] TABLE 10. Mean Time of Sun's Visible Rising and Setting. ^ •:3 <4; CO a 1 P4 ?5 S ■xoaddy a M H 1 n » 0) M (M .Q t»- S 8 a a D 11 o OJ o P OJ P a •aij'Bp •xojddv q'' pHccWcortoaPiSafiiHaa Pn cc Ph aj Pi co Oh co PS ui ' IN M (N 61 aiC^HCOCOr-dCO^t^t^C OiOOiOOiCiOiOiCO ,cju^<0iC?Di^«DiOC0»O«DNOC0''ft0'^e0'^tDTj<«0 S PHoa'pHrfirtaQPiccPHai pHaiPHCcPHaJPSccPSaJ -.^U Oii^ySOCOcOOOr^Oi OTPO-^O-VOOOOCOrHCOTHCCr-lC^lt-HC^C^ TT*COTft^<^I:>-TtTt4t>Hf>I>T^t>Tt«t>Tt1I>-<^t^ ; oo cc c^ y^ Tf< *r CD c^QC ooocc^cott'c ■(CC!aii-iOCOTt<'Xli-fQCO^r-t-i>CO'^eC>rH^GC(MlOiO iCCOCCO«OCCOC0|O'Vu:>-^»0T}*i0'Vu:Srrj'^i0'^O'ViC'^u:5C0OjC0OC0OCCOC^r-((Nr-( sgOCOOOOOcpO-^fHC^ICC OiCoOr^COCi-rff-HWCC QXiQOOOiCOCOCOOO QpOOi-C'OCCCCOcOt^O S=i-HC^oc^Occocooco,ocoiOcoiccou5Tj'0'X>iHicco trHOi-HOi-lTHrHi-lTH — '*'TfMiCr-(<£)OOOaiait^O--Or-(iCCCCO'#(N<:o' iHrHi-Hi-Hi-Hr-lfHf— ' lO CO iC CO lO CO lO t ) tOiOCO iCCOiCCOiCcOiCcOiCcO JCOTt* cO-«*^ »i— n>-oooasoiooot-^r-( SiC-^iOcOiCcOiCcOiCO CO IN iC CO -^ -^ CO iC CO lO CO »C CO iC cOiMIr* COiO CO OOOOSOlOOi— it^lMiOCO i-l rH Or ' lO CO lO C Jf-HOiM SCOiC CO iCCOiOCD '*iOC^COtHODaiOiCOi-( ; CO iC -. 5coiccoiccoicco a> iH 00 (N t^ CO CD iC CO >C CD lO CD lO COiOCO It^iHOC ScOiOCO iHi-iOiM lO CD lO CD 00(NcocO»OiCCOcC(Mr^ 5C^O 3CDiO cOiO CD iC C^O(N cOiOCO C^ O (N iH rH r-t tH to CO O CD lO CD iC CDiC CD MC-^CD SCOiOCO CO t^ (N 00 iCCD iCCD aOO-^r-'^t^iC^DcOiCt^- :C^O!MOC^OMOCOiOcO COiC iCcO lOcDiCCO »ocoaicoa>'^oo-^t^iCi :cOOC^OC^OiMO(NO siOCOiOcOiOcOiCCOlC^O t^cocot^icooTtcog?riO(MrHrH(NO'Maico C^O!tiCO OiN CD lOCD »o co»o C OlOTTj^^lt^COcO COiC 5cDiC CD lO COiOcO )CDiO CDiC CO tC 0 ^cD lo cdlo r^-'t^ot) cOiOCO Oi"«j-^t :N Od O C^ iC CD iC CO lO CO iC 0!N0 CDiO CD !> lO i~i ^ '-^ "^ C^ :coocoocoocoocoo iiOcOutiCOiCCDiCCDiCCD COC^COcOtNCOC^'^r-l'Tt^OtOOCD .COOCOOCOOCO :iC CO iC CO iC CD »C OCOO -^lOCD saiTtCOO 3 »C CD »C CO 'O5i^oooooocii>asr^o laiOlOiaiOOOOOOOrHOOrHl-^T-ir^iMCD'MCDC^ :c»locoiCco< aiOiOiCiCiCcDiCCOiOCO 50COO SCDiCCD cOCOiC COOCO lOcOiC COiO"^'^'*'^»dCOiOCOcOC^cDT-ft^,-(t>- ^O^iOOSlOCr. OOa>0 010 0irH'0^i-400rHOOC^r-(Nr-COr-COCDCOCO'*flO*+'lOlC >Tt<00'^00'^00COC ■cDt^CDt^cDlr^cot^ 50COO iCDiOcD COOCO lO CD iC OCOO ■^liSCD COOCOO lO CDiC CO COOCOOCOOCOOCOO iCcOvOCDiCCDiOCDiOCO OOCOai(MCiC^Oi!MOl'NOr-l ■^ lO ■Tf< lO rP iC ^ lO OiC lO iC iCi li^ O'^ OTf<0-t<< lO Tj* lO tJ< < CiCiO iiOcOtCcOiCcDi '^O'^O'^OCOOCOO lOCDiOCOuTtiCOiOcDi^CO »Ct^iO00iC00»OQ0iC00 ^ tO Tf U I -^ 00 '^ QO '^ 00 iOOCOODCOOOcDOOcpoOcO j»CiC»C»ddCiOidOiC 00 CD op t^ CO t^ 00 1>- 00 r^ CO t^ 00 1^ 00 r^ 00 r^ 00 r* lO lO lO iCiO iCiCidC lO lO lO iC iC >0 iCiO lO iC lO PScotfcoOHCoP^oof^M CI ?^ P^cQP^cnpHaiP^HaiPiHai Th JT" CO ^"^Tq CO CO CO CO CO iOiC»OiOiCiCidCOO oor^oot^t^t^t^t^t^t^ r^ 00 CI ^^^ TABLE 10. Mean Time of Sun's Visible Rising and Setting. 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CO »o coio OJ O CO iC CO CD lO CD -^ CC 'f cO(N00i ) iC COiC CO » ■Tf CD TJ< CD Tf C ^OlCiC^IIr^'^iCCDCOcOOO H(C. TTcO'^CC-^CD'^cOTfCD ,■ 3 CO ic toe 5ir5 coicc ■«COTjTl4t* > (N QC Oi i-H t>. '< >C0SCMOCMC JaicMoocot^iCcpcoTfr* eoa>i-iOQCMoO'o c sc5i— it-i05cor^ic »ot^c^OiO(Nr^'^iO Tj< iC CO iC CO lO ■^ CD ri* CO ** CO S'C0aiCMOrHr-4OiNaSTf r-*rHi-i(NT-l(Mi-ICSOCM ^iCCOiOCOiCcOiCCDiCCD 00»CCDCD»O0DCCaS(N<— 0lCiCOOCOO ^CD'^COTt^cO'^CO'^CO ffl CO rH rH CM O -^ CNOCOOCOOCO CD lO CD lO CO O CD )iCcOt^ >coi5co i CO ^ CO CMTj^rHlOOiCOGOr-r*05 rHCMrH(N0C^10CM0CM iOCD»C)CD»C '^iCCOiCcO 00 a»t^ iC cDiC p iC rH -^ CM CO CO CM rH CM rH CM rH CM CO iC CO 1^5 CO lO CO "^CJiCMrHQCO lO CO lO "^ »o -^ . •^ CO rf< CD -^ CO 1 CM coOlCao^- socoOcoioco 5 iC CO iC> CO '^ CO JiOrHCp ■iCMrH^ SCOiOCO iC CO lO CO i/ti CO TjOCO'-^l'*C^lOCOTf*Tj» — . — . ^» ., — ■*■ —H CM rH CM rH CM rH OJ ^colOcOlCcDiCco MO'^iO'H'CDcor-cor^ ffcoocooco .C* iC CO lO CO iC ocoocoo iO lO CO iC CO cooco o co< lO CD iC CO tC C ^rH ICM rH CM OCO liCCOiC rH OC CM r- CM CD CO I rH CM rH CM rH CM rH I CD lO CO iC CO iC CD , > -^ CO CO t^ CM QO > »C CD lO CD lO CD ga>cooicocccooOTt*r^ coocooc ^iC CO lO CDl O CO O CO o CDiC CO iC CD « t^ iC CD iC CO CD CO c :oocooco ,0 CD iC COiO ocooco CO »0 CDiC CD iC COiC COiC CO >ocoocoocoo,co< ;cOiOCDvCcOiOCD >^C sCOOCOOCMQCMrHCMr ft Tt4 O -"J^ O "^ rf^iO CDiC CO iC -O m CO lO CD iC CO lO CO tO COiO CD lO CD IrHMO 'iCCDiC CMOCOOCOOiCOO^ O'^O'TfOCOOCO CDiOcOtCCDiOCOO COiCCO 00 ift t^ lO 1-* CO S&Oooocoo lACOiACO^CO ft -rr lO "^ iC -^ L ,^ kC lO iC lO iC L • r^ t^cor^oo Cti CO 05 c« d CO Ci5 cc p:5 CG D3 co Ct5 x Sh' co rt x od co r*oo t^ 00 1^ ■^ lO 'J' lO Tf lO »0 iC lO ^ Sr^ cocoQO TT 40 ■^ iC iC lC ifl lO iC rH CM CO ^ ■""u6"*^^CO !>• ^"^ ^ > 00 CO CO CO QO CD 05 CO Ci lO ^ lO Ci lO 04 lO -*** lO ■^ o "^ <5 lO tO iC CO kC CO Qicooic»tfc»tfcdaH*QoM^^^^*^^^^^ SSS SioS^cS Page 506] TABLE 10. Mean Time of Sun's Visible Eising and Setting. ^ -a 'O OD 3 fi n "1 ^ V rd a a (-) d CB ■xojddv Ufa Pl5 OQ pi CC p4 03 p4 CO e4 CO OHQQPJosaiaQPiH'KP^co Oi-tOrHOrtOi-tO-H ; -H* c^ fj^ :oiHO a CO O ^ M ■* C4 Tf (N '»< CI 3 CO to Ot-( o. CO CO CO c Oi-iOrHOi-IOrHOi-l cocococotoococo^to CScDOScoOnocPicESHaa tfcctfaQOHOJOHCKaJco'pScc CO^COi-tCCr-(COrHO0i-(ICCr-IMi-l«li-tCOiHCCi-ICOi-t O 1-1 O i-i O iH O i-H O i-H 0>HOi-lO-HOi-IOi-IOr-( cocococococococococo cocDcoco^cococo?o?o^co - HOrHOrHOrHOr-l OrHOi-H Oi-lOr-IOrH SCOCOCOOcOtOOCO IcO co^^^^^tOCOCO 3iOCO J CO CO iCCOiCCO 1-^ CO Oi-hOt CO CO CO ? ^3 coco CO "fee- CO CO^ ' rHOiHOrHOrHOrH CO ^ O <0 CO CO to to to to MCOCOKICOCOCCCOCOCOCOCO Oi-HOi-IOi-lOrtOtHOrH tococctotoococococococo CjiCCOiOMiOCOiOlMinc^iO ; CO to Tf CO Tj< O -^ >|-tOl-HOT-( > to CO O to CD •xoiddy * to to to ' 5 to to to U5 to »i 0.-tOf to to to t if:)rt*iCi'^»C»CiCiO"^»OI'^iC'^tO'*tOC*5tOCOtO 0rH0rH0i-l0.-10i-l,0^0rH0r-l0rH0.-t totototototototototo cotototototototototo Oi-lOi-tOi--Or-COr-(Or-( totototototototototototo iCiOiOidCtO"<#tOTft^ Or-lOr-tOrHOrHOrl to to to to to to to to to to • iCt— lOt^'Ct^tOt^-tO HOrH )-OtO OrHOr to to to t s 00 to 00 to 00 to I-- tot > to to to t lOrHC > to to t : r) to 00 to 00 r* t :Or-iOr » to to to t lOr-tC > to to t toto^t^-icr-icoo-^oo -'rfr^'^Ot^COOOCCOOrMOO'MOii-tCii-iOSi— lOr-lO , -^ .^ .— — 'Or-f Oi-lOrHOrHOC^O(N totototototototototototo -^oo'^aicooiccioooo totototototototototototo >t*to )rHO ) to to 00iC00iC05'rtoo>ico"^o :CT>r^ooi>oot^ooQOi^oo * to to to t (Oi-l< ' to to t ^ost^osooooooccoir^oi J Ci to O iC O >: 50t0— (iCi-i-t*iM"^^ (MOCSO(NOC^O(N totototototototototo i—^Q'^Oicasioaitoxto tOtOtOtOtOtOiOtO^OtOiOtO COfNDOD0(Na3^-^i-i»C oiOQtDa>t^Qor*aoooi^oo tOtOtOtOiOtOiCtOiCtOiCtO CO CO < ^totototototototototo tOTHtOfMiCC^-^COCCrt* ri'^(Mi0r-(OOl^O0Ca>0D0C0it^Ot0i-li0'-<»0'M OC^lOC^OCNIOOJOC^.OCJOC^lOC^OtNOC^iCC^IiCC^iOCOiCCOOCOiOCO C0t0t0t0t0t0:0t0t0t0 tOtOtOtOtOtOtOtOtOtO vOtOiOtOiCtOtOtOiOtOiOtO tOiHtOC^iOCO-3"^CO>Q C^uO^tOrHt^QOOOiO totototototototototo tOtOtOtOtOtOtOtO»OtO piooooaiciaiaoot^r >C^tOCOiC^'?fiCiCOtO c^to ;,-^r-lrHi-lOr-lO(NOC^O!NOC^OC10C^O(N OC^OCMOC^IidMOCO rf^totototototototototototototototototototo totototototoictoioto >ao as oi 00 o e^^OOOOOiaiOQpf-Ht^'MtOCOiCCO-^'^COiCC^tO g^,HT-n-HOfNOC^O'MOC^OCtOCMOC^Oi-ltO'MiCCO'^-^COiO(MtO lOCOiOCOiOCOiOCCiOCOiOCO iOtOtCtO»OtOiOtO»/5tOiOtO i-ir^QOO<5sOiODOt^i-H tOC^iOCO'^'^COiC(MtOi-U^ O !N O C^l »0 !N lO CO iC CO lO CO iC CO iC CO tC CO lO CO lO CO tOtOtOtOiOtOiOtOiCtD iCtOiCtOiCtOiOtOiCtOiCtO ^tOtOtOtOtOtOtOtOtOtOtOtOtOtOtOtOtOtOtOtO tOtOiCtOvCtOiOtOiCtO ;ooooiosooor^r >(MiOCO-3'TttDOi^OCOC^ OrHOiHOTHOtMOtN (itf tOtOtDtOtOtOtOtOtOtO g'l^iC^t^-3<00COpiHi-t O i-H O rH O iH O C^ O C^ ^ to to to to to to to to to to S'tO'^^iCCOb*i-(0000 Or-tOiHOr-lOiHOC^ .CjtiStOtOtOtOtOtOtOtOtO S* -^i C^ tM CO r-( iC a> to t- CC to O M< 1-H (M CO O »C Oi r- ^cOtOtDtOtOtOiCtO»CtO iCitOiOtOiCtOiOtOiOtO totototototototototo STfCOtCrHtOOh-OiOi tOtOtOtOtOtOtOtOiCtO co-^fNtcotooaoor^as tOtOtOtOtOtOiOtOiOtO iHCOQ"^aitOr^t^tO(35 tOtOtOtOiOtOiOtOiOtO ^oO'^t^toidt^-'t'O:) tOtDiOtOOtOiOtOiOtO COtHt^COiCiCCOtOiNOO »OtOiCtOiOtOiOtO»OtO S8 ooooasi>.i-(iOcocO'^(Nto< 3 OS CO i-( iC CO >OiOOut)r-liOr-IU3iHUOT-|iOi-|-^iHTt<.QO0OlOi00r-(tOC^ tOCOiCiCOiOCO'«tCO'^"^Tti'^ iCtOiOtOiOtOiCtO^tOiOtO GCOtOT-HOC^'^-^COtC iOCOOtOiCtO»CtD t^OiiCi-iCOCOiHiOOit^ Xlr-iC0CNCO(NCOCJC^C^ iCtO»CtOiOtO»OtOiOtO t^oi>ni-(cocOf-i:^t>a> C^lN(NCOC^C0C^C0rHCOr-(CO lOtOiiitOiOtOiCtOiOtOiOtO Oj OQ pe; CO f^ OD pc^ GC f^ CO p:;copjG0pc^cop^copc^GOp:^co 00 O) o TABLE 10. Mean Time of Sun's Visible Rising and Setting. [Page 507 a "3 •9%Vp - . •xojddv o°° ^ ^ o S ?3 ?5 s a p4aQ94aQCiHcn04i£04aQ rtoQaiooWaQP^aJP^oQ OrHO.-IOr-lOr-lOi-l s ^ CO rH CO ^^ CO ^-< CO lH CO W Oi-(OTHOr-iOi-fOi-( S; S 5S K; CO CO CO CO SS 9 P^oDPSadP^odtf oqWx OHodrt^P^odrtaoflticc CO Oa>i-<00r-(00rHC0C^r*iNt^C0 OrHOrHOr-lOrHOrH |Of-(NGOtNGCCOCOCOt>-CO g*OCOOcOaacOO"»J*X'^GO>Ot^iCt^i:Ocp<:OOl:^ ioi>iooO"^oicoa>coo lOC^iOC^iOWiOCNiCCO SSc^tOc^ioc^oSioS S^Scotocoitocoioco ^ in o lO o ic ?D lO CO urs o lO to ic (^j o -^o ic co icco -pt>-cpoQicoO'^(?i'^ocoQcoi-t(Mc^rHC^oco Q3!^'5<»^t:::5©t:£: iCC^i?Sc^iOC^iOC^iOCOi0 55iCCOinCOiOCOiOCOiOCOT*<00-^COTt'CO-^ »ocoio^io;oic^ic>cou5«oioto»n?ointoicco lOcoi^fSin^ooino iOr-lif5r-tiO(NiO?4iOC^ t^COtOCO^'^O-^i^iO -^^tC^r^COoQC^GOiNOO iCC^iOC^iCC5iO(NiO(N iO<£nO'£>iOtOiOtDiOtO iCCOiOCOiCCOiftCOiOCO iO»iC«Ou^OiOtDiO«0 S'cCOiCOOvOOiOt-'-^C^ CO C^ C^ CO 1-H ''J^ p lO Q S iZ5 'M iC CO lO CO iC CO lO CO lO CO lO CO lO 00 lO CO lO CO ^i0«0»0i:0i0tC!»CC0i0O uOcOiCOO'XiiOcOiOtO -^lOr-(Tt*C^'^COCOCOC^"<**!'-GOG03004t^0^rHiOC^-^COCO'^ giOCOiOCOiQCOiOCOOCO iCCOiOCO'^CO-^CO'^CO '«:}— (t^ iAcO»OCOiOCO»OCO»OCO ^iCCO»C'^iO^-LC:OiOtO iceoiCcoiZScO'^coTiico ^-r»coaQ<:ooi^OO^rH ^COtTCO'^CO'^'^'^"^ a>r>-cor^r>-ooi:-ai-^o iC--t^!Mcocooi^^»g iOtoin^iceoiO<©ioouo?oio«oiOOicoinaiGOoooi Tp-^-^Tt^'^CO'^OS'^ gOOnco Tjl'^CO'^COiOCOiOCO^ Tt< -^ ''i^ -^ lO -^ '^ '^ "^ -^ Tj< -^ CO -I' CO i5 CO lO c intOiO!dOtOiCtOvntOiOO»OOiOCOi0^iC«0 S'?Hr^OG00505GOOI^TH lOCOiOCO'^CO'*-^'*'* ■£i050Qpt^C o iwro-*o-a-Gooor^aiiCQ -^TPCC-^CO-^CO-^COiC ^iO';ciO!0»ccoioovo, CO S*l>Oi:Oi-<-^fMCOCOC^»C COiOCO»OCOiOCOlCCOiC *cO'^'MiCi— (r^aioooo< 5 -^ 5iC COiC 3 tCiCcO CCiO C^ lO C^ iOcOiCCOiCI> See OODOOOst^i-liCC^ C^O(NO iCi t>- u^ t^ S(M COMiC^COiOi-t^-OOi SC^OiMOtNO . iC C^ iC t- iC t* H X Oi O t^ 1-1 lO CO ^oas.-^ao(Nr»GOi/:asTt'oco'N i CO-^COTi^cO'^J^COiOCOiC iCiCOiCcOiCCOiCCOiCCC . ■♦COOtOCOcOt^COiOOS COiOCOiCCSiCC4iC(NiO iCcOiCCOiOCOiC<:OiOcD -^i-nNcootoxr^cooi C^OCMOC^OiHOtHO -<:ocorH-iiCt-iCt^iOt^ GOoocoo'^c^f-iTfasco ,-lO.«ii-l.-(r-ir-l.-HOr-t ocomcor-aiiO.-(Tf*coiM-3'otooDcc:oo-^'M COiOC^iCC^ii:)(NO!MO iCCOiOcOtOOi01>iLCI> CSIOiHO C^T**OI^r-0:'iC(NC^'^ OrHOtNOCM Di-trfCOcOiOi— ICOOSQO ■JOCIOtMOC^Oi-iO t^oicrJco-**f-«coas05 i-ir-lr-ti-l,-(iHrHi-iO^ ?^'^Pt:r'^^'^'-''*co'ciOI> lOlNOiHOr Mr* iC t^ iC (>• ii i^QA 0C-10(N ; O CO C^l -^ Tt* 5 |> iC I> uO t* (Mr-osoi r*»HiC"^(Ncoasaii-*'M covoi-'t^asasr*cJiccc^coiO "Oi-i OiMOC" OC^iOlNiOCOLOCOiCTO -^rHcO'Tfi-tr^xOLO'M OC^OC^OC^iOCO'CCO iCr-ior>-oi>Tfc^o6lo M> iC t- lO l> OtNiOCO i CO coic r-(GOaiOCOM i-H r-i O C^ O 6l iC t* lO t* lO t* 1 t^ Ci O CO C^ CO iC 3(NOC1ir3CO lOCCiO c»5 "^ t^'^ t* rHI>giOit^C^'^"'t-0^ ^o^^oo^oc^ lO t^ lO t~- lO t^ C^HOCOiOOSl t~ tC t~ -^C t~ tOfMCCiOQGCt^^ . . iOcciociOiScc-i;f*T)i'>r ■'JHiCOOStDC^C^tOOO'-ICOiC soot^i^^-^-^^oot^^ cotociQ'^ii'O^asiOTj* «l-*-^-*'CO-*-U<-*rJi ^ iO t^ ic t^ lO t^ -^ t^ "<3< t^ Tji r^ Tj* t^ -^^i t>. Tj< c^ Tf t^ GOOSiCCO^t^t^rHCOiO cc-*eo>ocoicc^oc^o COU5CJO(NOi-IOr tOOOrHt^tOMi-lt^tOCO COOINOi-liHr-lrHOIN -1< CO ■^00 Tf 00 Tjl 00 ■* CO ooocoioccofMior^^ 1-ii-ii-ii-ioc^oc-iioco TjHo0'^00's*<00rt-i :0(SiSc^iric^iAccidccJTfici5'>*"3>Ti<'*cort'o5io c^kCcooi-'i'coan^ CCliOIMiCINOi-iO ■^t^T^WTj^cO-^OO 'ot^-^c^o^t^cocot^o i-lrHOCmCC^iOCO-*'"}' -*oOTfCi5-<}mN»O g*(NrHa)cototocca50coitotoccooici5tot^c^i-i lOCO-^CC'^CO"rtiCC'^'<1iiCO-^00»OC<»iOC^lCC^O iCOi-c-i^tooii-ycot CJOC^OiHOrHi-iC TfloOTCOO'^OO'^OO'' i-ico»coic>>cccc-itoai OMtC(N-^cCTfTrcO'* •^OOCOOOCiSOOCCOOCOOO i>»ccooooiccoot^ic c^oicr^<35coc*jo i-IOr-I.HOr-lOC iQ CO 1-1 l~ t^ rt cococMcocq-s-c^-flii-iic S-^JiCOOtOt^OCO-^OlOO CqcOtNCOi-t-i^i-l-^OTji OiOto-^c^ir^ooi-i'^to I^iCdiOI^>Oi-iO— lO 1'C~-*I>TfH>- C^I-^OOl^-'ti-lOtOiCO 6)iOi-iia.-iOt-ioOr-i ■^[-■.jH>'^ODt)IOO-<<<00 iOiCOOtOg'lMOCOOi-l'*'*i-itOO>»OOC3>t^ O i-H lO (M lO (MiCiCC^ lOrlTfcNCOCJCOCO COOOCOX'COOOCOOO iCC^OtOtOi— lr-(lOtOO OiOOiOiOOiCO'*OOTtii-(C004 coxco»oi<3»ccioi (^oQ^i^aiPjaQPi^aQpHaQ to r^ 08 05 lO iC lO iC TABLE 11. [Page 509 For reducing the Time of the Moon's passage over the Meridian of Greenwich to theTime of ita pass- age over any other Meridian. The numbers taken from this Table are to be added to the Time at Greenwich in West Longitude, subtracted in East Longitude. Longi- tude. Dally variation of the moon's passing the meridian. Longi- tude. 40" 42m 44m« 46m 48-" 60"- 62m 54m ee^ 68m 60m 62m 64m 66"' o 5 10 15 20 25 30 m. 1 1 2 2 3 3 m. 1 1 2 2 3 3 m. 1 1 2 2 3 4 TO. 1 1 3 2 3 4 TO. 1 1 2 3 3 4 TO. 1 1 2 3 3 4 TO. 1 1 2 3 4 4 m. 1 1 2 3 4 4 TO. 1 2 2 3 4 5 TO. 1 2 2 3 4 5 m. 1 2 2 3 4 5 TO. 1 2 3 3 4 5 m. 1 2 3 4 4 5 TO. 1 2 3 4 5 5 o 5 10 15 20 25 30 35 40 45 50 55 4 4 5 6 6 4 5 5 6 6 4 5 5 6 7 4 5 6 6 7 5 5 6 7 7 5 6 6 7 8 5 6 6 7 8 5 6 7 7 8 5 6 7 8 9 6 6 7 8 9 6 7 7 8 9 6 7 8 9 9 6 7 8 9 10 6 7 8 9 10 35 40 45 50 55 60 65 70 75 80 7 7 8 8 9 7 8 8 9 9 7 8 9 9 10 8 8 9 10 10 8 9 9 10 11 8 9 10 10 11 9 9 10 11 12 9 10 10 11 12 9 10 11 12 12 10 10 11 12 13 10 11 12 12 13 10 11 12 13 14 11 12 12 13 14 11 12 13 14 15 60 65 70 75 80 85 90 95 100 105 9 10 11 11 12 10 10 11 12 12 10 11 12 12 13 11 11 12 13 13 14 15 15 16 17 11 12 13 13 14 12 12 13 14 15 12 13 14 14 15 13 13 14 15 16 13 14 15 16 16 14 14 15 16 17 14 15 16 17 17 15 15 16 17 18 15 16 17 18 19 16 16 17 18 19 85 90 95 100 105 110 115 120 125 130 12 13 13 14 14 13 13 14 15 15 13 14 15 15 16 15 15 16 17 17 15 16 17 17 18 16 17 17 18 19 16 17 18 19 19 17 18 19 19 20 18 19 19 20 21 18 19 20 21 22 19 20 21 22 22 20 20 21 22 23 20 21 22 23 24 110 115 120 125 130 135 140 145 150 155 15 16 16 17 , 17 16 16 17 17 18 16 17 18 18 19 17 18 19 19 20 20 21 22 22 23 18 19 19 20 21 21 22 23 23 24 19 19 20 21 22 19 20 21 22 22 20 21 22 22 23 21 22 23 23 24 22 23 23 24 25 22 23 24 25 26 23 24 25 26 27 24 25 26 27 28 25 26 27 27 28 135 140 145 150 155 160 165 170 175 180 18 18 19 19 20 19 19 20 20 21 20 20 21 21 22 22 23 24 24 25 23 24 25 25 26 24 25 25 26 27 25 26 26 27 28 26 27 27 28 29 27 27 28 29 30 28 28 29 30 31 28 29 30 31 32 29 30 31 32 33 160 165 170 175 180 40°> 42m 44m 46m 48m 60m 62m 54m 56m 58m 60m 62m 64- 66m Page 510] TABLE 12. For finding the Variation of the Sun' s Right Ascension or Declination or of the Equation of Time, in 1 any number of minutes of time, the Horary Motion being given 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. Horary motion. 1" 2" 8" 4" 6" 6" 7" 8" 9" 10" 11" 12" 13" 14" 16" 16" 17" 18" 19" 1 1 2 1 1 1 1 1 2 3 1 1 1 1 1 1 1 3 4 1 1 1 1 1 1 1 4 5 6 1 1 1 1 1 2 1 2 1 2 2 5 2 2 2 6 7 2 2 2 2 2 2 2 7 8 2 2 2 2 2 2 2 3 8 9 2 2 2 2 2 2 2 3 3 3 9 10 11 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 10 3 3 3 3 3 11 12 2 2 2 2 2 3 3 3 3 3 4 4 12 13 1 2 2 2 2 2 3 3 3 3 3 4 4 4 13 14 2 2 2 2 3 3 3 3 4 4 4 4 4 14 15 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 5 5 15 16 5 5 5 16 17 2 2 2 3 3 3 3 4 4 4 5 5 5 5 17 18 2 2 2 2 3 3 3 4 4 4 5 5 5 5 6 18 19 2 2 2 3 3 3 3 4 4 4 5 5 5 6 6 19 20 2 2 2 2 2 2 3 3 3 3 3 4 4 4 4 5 5 5 6 6 6 20 21 4 4 5 5 5 6 6 6 7 21 22 2 2 3 3 3 4 4 4 5 5 6 6 6 7 7 22 23 2 2 2 3 3 3 4 4 5 5 5 6 6 7 7 7 23 24 2 2 2 3 3 4 4 4 5 5 6 6 6 7 7 8 24 25 26 2 2 2 2 3 3 3 3 3 3 4 4 4 4 5 5 5 5 5 6 6 6 6 7 7 7 7 8 8 25 26 7 8 8 27 2 2 3 3 4 4 5 5 5 6 6 7 7 8 8 9 27 28 2 2 3 3 4 4 5 5 6 6 7 7 7 8 8 9 28 29 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 29 30 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 8 8 8 8 9 9 10 30 31 9 9 10 31 32 2 2 3 3 4 4 5 5 6 6 7 7 8 9 9 10 10 32 33 2 2 3 3 4 4 5 6 6 7 7 8 8 9 9 10 10 33 34 2 2 3 3 4 5 5 6 6 7 7 8 9 9 10 10 11 34 35 2 2 2 2 3 3 4 4 4 4 5 5 5 5 6 6 6 7 7 7 8 8 8 8 9 9 9 10 10 11 11 35 36 10 11 11 36 37 2 2 3 4 4 5 6 6 7 7 8 9 9 10 10 11 12 37 38 2 3 3 4 4 5 6 6 7 8 8 9 10 10 11 11 12 38 39 2 3 3 4 5 5 6 7 7 8 8 9 10 10 11 12 12 39 40 2 2 3 3 3 3 4 4 5 5 5 5 6 6 7 7 7 8 8 8 9 9 9 10 10 10 11 11 11 12 13 13 40 41 12 12 41 42 2 3 4 4 5 6 6 7 8 8 9 10 11 11 12 13 13 42 43 2 3 4 4 5 6 6 7 8 9 9 10 11 11 12 13 14 43 44 2 3 4 4 5 6 7 7 8 9 10 10 11 12 12 13 14 44 45 2 2 2 3 3 4 4 5 5 5 5 6 6 7 7 8 8 8 8 9 9 10 10 11 11 11 12 13 14 14 45 46 2 12 12 13 14 15 46 47 2 2 3 4 5 5 6 7 8 9 9 10 11 12 13 13 14 16 47 48 2 2 3 4 5 6 6 7 8 9 10 10 11 12 13 14 14 15 48 49 2 2 3 4 5 6 7 7 8 9 10 11 11 12 13 14 15 16 49 50 2 3 3 4 4 5 5 6 6 7 7 8 8 8 9 9 9 10 10 11 11 12 12 13 13 13 14 14 15 16 16 50 51 2 3 3 14 15 51 52 2 3 3 4 5 6 7 8 9 10 10 11 12 13 14 15 16 16 52 53 2 3 4 4 5 6 7 8 9 10 11 11 12 13 14 15 16 17 53 54 2 3 4 5 5 6 7 8 9 10 11 12 13 14 14 15 16 17 54 55 56 2 2 3 3 4 4 5 5 6 6 6 7 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 15 16 17 17 55 14 15 16 17 18 56 57 2 3 4 5 6 7 8 9 10 10 11 12 13 14 15 16 17 18 57 58 2 3 4 5 6 7 8 9 10 11 12 13 14 15 15 16 17 18 58 59 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 59 60 2 3 4 6 6 / 8 9 10 11 12 13 14 15 16 17 18 19 60 TABLE 12 , [Page 511 For finding the Variation of the Sun's Elight Ascension or Declination, or of the Equation of Time, in I any number of minutes of time , the Horary Motion being given it the top o ndmg : the page in seconds, and the number of minutes of time in the side colu mn. Also for fi the Variation of the Moon's Declination or Right Ascension in seconds of time, the motion in one minute beiner eiven 1 at the top, and the n ambers in the side column being taken for seconds. M. Horary motion. 1 M. 20" 21" 22" 28" 24" 25" 26" 27" 28" 29" 80" 81" 82" 88" 84" 85" 86" 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 3 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 8 4 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 4 5 2 2 2 2 2 2 2 2 2 3 2 2 2 2 3 3 3 3 3 3 3 5 6 2 2 3 3 3 3 3 3 3 3 3 4 4 6 7 2 2 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 7 8 3 3 3 3 3 3 3 4 4 4 4 4 4 4 5 5 5 8 9 3 3 3 3 4 4 4 4 4 4 5 5 5 5 5 5 5 9 10 3 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 6 6 6 6 10 11 4 4 5 5 5 5 6 6 6 6 6 6 7 11 12 4 4 4 5 5 5 5 5 6 6 6 6 6 7 7 7 7 12 13 4 5 5 5 5 5 6 6 6 6 7 7 7 7 7 8 8 13 14 5 5 5 5 6 6 6 6 7 7 7 7 7 8 8 8 8 14 15 5 5 6 6 6 6 7 7 7 7 8 8 8 8 9 9 9 15 16 5 6 6 6 6 7 7 7 .7 8 8 8 9 9 9 9 10 16 17 6 6 6 7 7 7 7 8 8 8 9 9 9 9 10 10 10 17 18 6 6 7 7 7 8 8 8 8 9 9 9 10 10 10 11 11 18 19 6 7 7 7 8 8 8 9 9 9 10 10 10 10 11 11 11 19 20 7 7 7 7 8 8 8 8 8 8 9 9 9 10 10 10 11 11 11 12 12 20 21 7 9 9 9 10 10 11 11 11 12 12 12 13 21 22 7 8 8 8 9 9 10 10 10 11 11 11 12 12 12 13 13 22 23 8 8 8 9 9 10 10 10 11 11 12 12 12 13 13 13 14 23 24 8 8 9 9 10 10 10 11 11 12 12 12 13 13 14 14 14 24 25 8 9 9 10 10 10 11 11 12 12 13 13 13 14 14 15 15 25 26 9 9 10 10 10 11 11 12 12 13 13 13 14 14 15 15 16 26 27 9 9 10 10 11 11 12 12 13 13 14 14 14 15 15 16 16 27 28 9 10 10 11 11 12 12 13 13 14 14 14 15 15 16 16 17 28 29 10 10 11 11 12 12 13 13 14 14 15 15 15 16 16 17 17 29 30 10 11 11 12 12 12 13 13 14 14 15 15 16 16 17 17 18 18 30 31 10 11 11 12 13 13 14 14 15 16 16 17 17 18 18 19 81 32 11 11 12 12 13 13 14 14 15 15 16 17 17 18 18 19 19 82 33 11 12 12 13 13 14 14 15 15 16 17 17 18 18 19 19 20 33 34 11 12 12 13 14 14 15 15 16 16 17 18 18 19 19 20 20 34 35 12 12 13 13 13 14 15 15 16 16 17 18 18 19 19 20 20 21 85 36 12 13 14 14 15 16 16 17 17 18 19 19 20 20 21 22 36 37 12 13 14 14 15 15 16 17 17 18 19 19 20 20 21 22 22 37 38 13 13 14 15 15 16 16 17 18 18 19 20 20 21 22 22 23 38 39 13 14 14 15 16 16 17 18 18 19 20 20 21 21 22 23 23 39 40 13 14 15 15 15 16 16 16 17 17 18 19 19 20 21 21 22 23 23 24 40 41 14 14 17 18 18 19 20 2f 21 22 23 23 24 25 41 42 14 15 15 16 17 18 18 19 20 20 21 22 22 23 24 25 25 42 43 14 15 16 16 17 18 19 19 20 21 22 22 23 24 24 25 26 43 44 15 15 16 17 18 18 19 20 21 21 22 23 23 24 25 26 26 44 45 15 16 16 17 17 17 18 18 19 20 20 21 22 23 23 24 25 26 26 27 28 45 46 46 15 18 19 20 21 21 22 23 24 25 25 26 2V 47 16 16 17 18 19 20 20 21 22 23 24 24 25 26 27 27 28 47 48 16 17 18 18 19 20 21 22 22 23 24 25 26 26 27 28 29 48 49 16 17' 18 19 20 20 21 22 23 24 25 25 26 27 28 29 29 49 50 17 18 18 19 19 20 20 20 21 21 22 22 23 28 23 24 25 26 27 28 28 29 30 50 51 17 18 24 25 26 26 27 28 29 30 31 51 52 17 18 19 20 21 22 23 28 24 25 26 27 28 29 29 30 31 52 53 18 19 19 20 21 22 23 24 25 26 27 27 28 29 30 31 32 53 54 18 19 20 21 22 28 23 24 25 26 27 28 29 30 31 32 32 54 55 18 19 20 21 22 23 24 25 26 27 28 28 29 30 31 32 83 55 56 19 20 21 21 22 23 24 25 26 27 28 29 30 31 32 33 34 56 57 19 20 21 22 28 24 25 26 27 28 29 29 30 31 32 33 34 57 58 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 36 58 59 90 21 22 23 24 25 26 27 28 29 30 80 31 32 33 84 35 59 60 20 21 22 23 24 25 26 27 28 29- 30 31 32 33 34 35 36 60 Page 512] TABLE 12. For finding the Variation of the Sun's Eight Ascension or Declination, or of the Equation of Time, in any number of minutes of time, the Horary Motion being given at the top of the page in seconds, and the number of minutes of time in the side column. Also for finding the Variation of the Moon's Declination or Right Ascension in seconds of time, the motion in one minute being given at the top, and the numbers in the side column being taken for seconds. M. Horary motion. 1 M. 37" 88" 89" 40" 41" 42" 48" 44" 45" 46" 47" 48" 49" 60" 51" 62" 63" 1 2 3 4 5 1 1 2 2 3 1 1 2 3 3 1 1 2 3 3 1 1 2 3 3 1 1 2 3 3 1 1 2 3 4 1 1 2 3 4 1 1 2 3 4 1 2 2 3 4 1 2 2 3 4 1 2 2 3 4 1 2 2 3 4 1 2 2 3 4 1 2 3 3 4 1 2 3 3 4 1 2 3 3 4 1 2 3 4 4 1 2 3 4 5 6 7 8 9 10 4 4 5 6 6 7 7 8 9 9 4 4 5 6 6 7 8 8 9 10 4 5 5 6 7 7 8 8 9 10 10 11 12 12 13 14 14 15 16 16 4 5 5 6 7 7 8 9 9 10 11 11 12 13 13 14 15 15 16 17 4 5 5 6 7 8 8 9 10 10 11 12 12 13 14 4 5 6 6 7 8 8 9 10 11 4 5 6 6 7 4 5 6 7 7 5 5 6 7 8 5 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 6 7 8 9 10 11 12 13 14 15 8 9 9 10 11 8 9 10 10 11 8 9 10 11 11 8 9 10 11 12 9 9 10 11 12 9 10 10 11 12 13 14 14 15 16 9 10 11 11 12 9 10 11 12 13 9 10 11 12 13 10 10 11 12 13 10 11 11 12 13 11 12 13 14 15 16 17 18 19 20 10 10 11 12 12 10 11 11 12 13 13 14 15 15 16 16 17 18 18 19 20 20 21 22 22 23 23 24 25 25 26 27 27 28 29 29 30 30 31 32 32 33 34 34 35 35 36 37 37 38 11 12 13 13 14 11 12 13 14 14 15 16 16 17 18 19 19 20 21 22 12 12 13 14 15 12 13 14 14 15 12 13 14 15 15 13 13 14 15 16 13 14 15 16 16 13 14 15 16 17 14 14 15 16 17 14 15 16 16 17 14 15 16 17 18 16 17 18 19 20 21 22 23 24 25 13 14 14 15 15 14 15 16 16 17 15 15 16 17 18 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 26 27 28 29 30 16 17 17 18 19 19 20 20 21 22 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 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 17 18 19 19 20 21 21 22 23 23 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 18 18 19 20 21 18 19 20 20 21 19 20 21 21 22 20 20 21 22 23 20 21 21 22 23 20 21 22 23 24 21 22 22 23 24 21 22 23 24 25 22 23 23 24 25 22 23 24 25 26 23 23 24 25 26 23 24 25 26 27 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 21 22 23 23 24 25 25 26 27 27 28 29 29 30 31 31 32 33 33 34 22 22 23 24 25 25 26 27 27 28 29 29 30 31 32 32 33 34 34 35 22 23 24 24 25 26 27 27 28 29 29 30 31 32 32 33 34 34 35 36 37 37 38 39 39 40 41 42 42 43 23 23 24 25 26 23 24 25 26 26 24 25 25 26 27 24 25 26 27 27 25 26 26 27 28 25 26 27 28 29 26 27 28 28 29 26 27 28 29 30 27 28 29 29 30 27 28 29 30 31 31 32 33 34 35 26 27 28 29 29 27 28 29 29 30 28 28 29 30 31 28 29 30 31 31 29 30 30 31 32 29 30 31 32 33 30 31 32 33 33 31 31 32 33 34 31 32 33 34 35 32 33 34 34 35 36 37 38 39 40 30 31 32 32 33 34 34 35 36 37 31 32 32 33 34 35 35 36 37 38 31 32 33 34 35 35 36 37 38 38 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 36 36 37 38 39 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 37 38 38 39 40 38 38 39 40 41 38 39 40 41 42 39 40 41 42 43 40 41 42 42 43 41 42 42 •43 44 46 47 48 49 50 35 36 36 37 38 38 39 40 40 41 36 36 37 38 39 39 40 41 41 42 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 1 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, 1 and the number of minutes of time in the side column. A-lso for finding the Variation of the | Moon's Declination or Right Ascension in seconds of time, he motion in one minute being given | at the top, and the numbers in the side column being ta.ken for seconds M Horary motion. 1 M. 54" 65" 66" 67" 68" 59" 1 60" 1 61" 1 62" 63" 64" 1 66" 66" 67" 68" 69" 70" 1 1 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 2 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 6 5 5 5 5 5 5 5 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 9 9 9 10 10 10 10 10 10 11 11 11 11 11 11 12 12 10 11 10 10 10 10 11 11 11 11 11 12 12 12 12 12 12 13 13 11 12 U 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 15 16 16 16 17 17 17 17 18 18 18 18 19 16 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 19 20 20 20 21 21 21 22 22 22 23 23 23 20 21 19 19 20 20 20 21 21 21 22 22 22 23 23 23 24 24 25 21 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 24 25 25 25 26 26 27 27 28 28 28 29 29 25 26 23 24 24 25 25 26 26 26 27 27 28 28 29 29 29 30 30 26 27 24 25 25 26 26 27 27 27 28 28 29 29 30 bO 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 27 28 28 29 29 30 30 31 31 32 32 33 33 34 34 35 35 30 31 28 28 29 29 30 30 31 32 32 33 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 32 32 33 33 34 34 35 36 36 37 37 38 39 39 40 40 41 35 36 32 33 34 34 35 35 36 37 37 38 38 39 40 40 41 41 42 36 37 33 34 35 35 36 36 37 38 38 39 39 40 41 41 42 43 43 37 38 34 35 35 36 37 37 38 39 39 40 41 41 42 42 43 44 44 38 39 35 36 36 37 38 38 39 40 40 41 42 42 43 44 44 45 46 39 40 36 37 38 37 38 38 39 39 39 40 41 41 42 41 42 42 43 43 43 44 45 45 46 47 40 41 37 40 40 44 44 45 46 46 47 48 41 42 38 39 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 41 42 43 43 44 45 45 46 47 48 48 49 50 51 51 44 45 41 41 42 42 43 43 44 44 44 44 45 45 46 47 47 48 49 50 50 51 52 53 45 46 41 46 47 48 48 49 50 51 51 52 53 54 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 49 50 51 52 53 53 54 55 56 57 58 58 50 48 49 50 51 52 53 54 54 55 56 57 58 59 60 51 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 56 57 58 59 60 61 61 62 63 64 65 55 55 56 57 58 59 60 61 62 63 63 64 56 57 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 6V 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 6583—06 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" 78" 74" 76" 76" 77" 78" 79" 80" 81" 82" 88" 84" 86" 86" 87" 1 2 3 4 5 1 2 4 5 6 1 2 4 5 6 7 8 10 11 12 1 2 4 5 6 7 9 10 11 12 13 15 16 17 18 19 21 22 23 24 26 27 28 29 30 32 33 34 35 37 38 39 40 41 43 44 45 46 47 49 50 51 52 54 55 56 57 58 60 61 62 63 64 66 67 68 69 71 72 73 1 2 4 5 6 7 9 10 11 12 14 15 16 17 19 20 21 22 23 25 1 3 4 5 6 1 3 4 5 6 1 3 4 5 6 1 3 4 6 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 8 9 10 11 13 14 15 16 18 19 20 21 23 24 25 8 9 10 11 13 14 15 16 18 19 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 16 17 18 19 20 13 14 15 17 18 19 20 21 22 24 13 14 16 17 18 19 20 22 23 24 25 26 28 29 30 31 32 34 35 36 37 38 40 41 42 43 44 46 47 48 49 50 52 53 54 55 56 58 59 60 61 62 64 65 66 67 68 70 71 72 14 15 17 18 19 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 26 27 28 29 30 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 21 22 23 24 25 25 26 27 28 30 26 27 28 30 31 32 33 35 36 37 38 39 41 42 43 44 46 47 48 49 51 52 53 54 56 57 58 59 60 62 63 64 65 67 68 69 70 72 73 74 26 28 29 30 31 27 28 29 30 32 27 28 30 31 32 27 29 30 31 33 28 29 30 32 33 28 29 31 32 33 28 30 31 32 34 29 30 31 33 34 29 30 32 33 35 29 31 32 34 35 30 31 33 34 35 30 32 33 34 36 30 32 33 34 36 38 39 41 42 44 26 27 28 29 30 31 32 33 34 36 33 34 35 36 38 33 34 35 37 38 33 34 35 1 35 36 36 37 38 39 1 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 43 44 46 47 48 36 38 39 41 42 43 45 46 48 49 37. 38 40 41 43 44 45 47 48 50 37 39 40 42 43 31 32 33 34 35 36 37 38 39 40 37 38 39 40 41 43 44 45 46 47 49 50 51 52 53 39 40 41 43 44 45 46 48 49 50 51 53 54 55 56 58 59 60 61 63 64 65 66 68 69 70 71 73 74 75 39 41 42 43 44 46 47 48 49 51 52 53 54 56 57 40 41 42 44 45 40 42 43 44 46 41 42 43 45 46 41 43 44 45 47 42 43 45 46 47 42 44 45 46 48 44 46 47 49 50 45 46 48 49 51 31 32 33 34 35 36 37 38 39 40 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 41 42 43 44 45 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 46 47 48 49 50 54 56 57 58 59 60 62 63 64 65 "66 67 69 70 71 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 63 64 66 67 68 64 65 66 68 69 64 66 67 69 70 65 67 68 69 71 66 67 69 70 72 67 68 70 71 73 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 65 66 67 68 70 65 67 68 69 71 69 70 72 73 74 70 71 72 74 75 71 72 73 75 76 71 73 74 76 77 72 74 75 77 78 73 75 76 77 79 74 75 77 78 80 51 52 53 54 55 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 86 80 82 83 85 86 81 83 84 86 87 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 column. Also for finding the Variation of the Moon's Declination or Right Ascension, in seconds of time, the motion in one minute being given at the top and the numbers in the side column being taken for seconds. M. Horary motion. / M. 88" 89" 90" 91" 92" 98" 94" 96" 96" 97" 98" 99" 100" 101" 102" 108" 104" 1 2 3 4 5 1 3 4 6 7 1 3 4 6 7 2 3 5 6 8 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 47 48 50 51 53 54 56 57 59 60 2 3 5 6 8 9 11 12 14 15 17 18 20 21 23 24 26 27 29 30 2 3 5 6 8 9 11 12 14 15 17 18 20 21 23 25 26 28 29 31 2 3 5 6 8 2 3 5 6 8 2 3 5 6 8 2 3 5 6 8 2 3 5 6 8 2 3 5 7 8 2 3 5 7 8 2 3 5 7 8 2 3 5 7 8 2 3 5 7 9 2 3 5 7 9 2 3 6 7 9 1 2 3 4 5 6 7 8 9 10 9 10 12 13 15 16 18 19 21 22 9 10 12 13 15 16 18 19 21 22 9 11 12 14 16 9 11 13 14 16 10 11 13 14 16 10 11 13 14 16 10 11 13 15 16 10 11 13 16 16 10 12 13 16 17 10 12 13 16 17 10 12 13 15 17 10 12 14 15 17 10 12 14 16 17 10 12 14 16 17 6 7 8 9 10 11 12 13 14 15 17 19 20 22 23 17 19 20 22 24 17 19 21 22 24 18 19 21 22 24 18 19 21 23 24 18 20 21 23 25 18 20 21 23 26 18 20 22 23 25 27 28 30 32 33 19 20 22 24 25 19 20 22 24 26 19 21 22 24 26 19 21 23 24 26 11 12 13 14 16 16 17 18 19 20 21 22 23 24 25 23 25 26 28 29 31 32 34 35 37 24 25 27 28 30 31 33 34 36 37 39 40 42 43 45 46 47 49 50 52 25 26 28 29 31 25 27 28 30 31 25 27 29 30 32 26 27 29 30 32 26 27 29 31 32 26 28 29 31 33 26 28 30 31 33 27 29 30 32 34 27 29 31 32 34 27 29 31 33 34 28 29 31 33 35 16 17 18 19 20 32 33 35 36 38 32 34 36 37 38 33 34 36 37 39 33 34 36 38 39 33 35 36 38 40 34 35 37 38 40 34 36 37 39 40 34 36 38 39 41 35 36 38 40 41 35 37 38 40 42 35 37 39 40 42 44 45 47 49 51 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 31 32 33 34 35 38 40 41 43 44 45 47 48 50 51 39 41 42 44 46 47 49 50 52 53 55 56 58 59 61 40 41 43 44 46 48 49 51 52 54 40 42 43 45 47 48 50 51 53 54 41 42 44 45 47 49 50 52 53 55 41 43 44 46 48 42 43 45 46 48 42 44 46 47 49 42 44 46 47 49 43 45 46 48 50 43 46 47 48 60 44 46 48 49 51 45 46 48 50 52 53 56 57 58 60 45 47 49 50 52 26 27 28 29 30 49 51 52 54 55 50 51 63 54 56 50 52 63 65 67 61 62 54 56 57 51 63 64 56 68 62 63 56 67 68 62 54 56 57 59 53 54 66 58 60 54 55 57 69 61 31 32 33 34 36 36 37 38 39 40 53 54 56 57 59 53 55 56 58 59 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 69 60 62 64 66 69 61 63 64 66 60 62 63 65 67 61 62 64 66 67 61 63 65 66 68 62 64 66 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 62 63 65 66 68 62 64 65 67 68 63 64 66 67 69 64 65 67 68 70 71 73 74 76 78 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 76 69 71 72 74 76 70 71 73 75 77 70 72 74 76 77 71 73 75 76 78 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 67 69 70 72 73 75 76 78 79 81 68 70 71 73 74 76 77 79 80 82 83 85 86 88 89 69 71 72 74 75 77 78 80 81 83 84 86 87 89 90 70 71 73 74 76 77 79 80 82 83 85 86 88 90 91 71 72 74 75 77 72 74 75 77 78 73 74 76 78 79 74 75 77 78 80 74 76 78 79 81 76 77 78 80 82 76 78 79 81 83 77 78 80 82 83 77 79 81 82 84 78 80 82 83 85 79 81 82 84 86 80 81 83 ■85 87 88 90 92 94 95 97 99 101 102 104 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 78 80 81 83 84 86 87 89 90 92 79 81 82 84 85 80 81 83 85 86 81 82 84 86 87 82 83 86 86 88 82 84 86 87 89 83 86 87 88 90 84 86 87 89 91 86 87 88 90 92 86 88 89 91 93 87 88 90 92 94 88 89 91 93 94 56 57 58 59 60 82 84 85 87 88 87 88 90 91 93 88 89 91 92 94 89 90 92 93 95 90 91 93 94 96 91 92 94 95 97 91 93 96 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 Page 516] TABLE 12. For finding the Variation of the Sun's Eight Ascension or Declination, or of the Equation of Time, in any number of minutes of time, the Horary Motion being given at the top of the page in seconds, an^ the number of minutes of time in the side column. Also for finding the Variatior of the Moon's Declination or Right Ascension, in seconds of time, the motion in one minute being given at the top and the numbers in the side column being taken for seconds. M. Horary motion. M. 106" 106" 107" 108" 109" 110" 111" 112" 118" 114" 115" 116" 117" 118" 1 2 3 4 5 2 4 5 7 9 2 4 5 7 9 2 4 5 7 9 2 4 5 7 9 2 4 5 7 9 2 4 6 7 9 2 4 6 7 9 2 4 6 7 9 2 4 6 8 9 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 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 28 30 32 33 35 19 21 23 25 27 20 21 23 25 27 20 22 23 25 27 20 22 24 25 27 20 22 24 26 28 20 22 24 26 28 21 22 24 26 28 21 23 24 26 28 21 23 25 27 29 21 23 25 27 29 21 23 25 27 29 21 23 25 27 29 22 24 26 28 30 11 12 13 14 15 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 54 56 58 60 61 55 57 58 60 62 55 57 59 61 62 56 58 59 61 63 56 58 60 62 64- 57 59 61 62 64 57 59 61 63 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 31 32 33 34 35 36 37 38 39 40 63 65 67 68 70 64 65 67 69 71 64 66 68 70 71 65 67 68 70 72 65 67 69 71 73 66 68 70 72 73 67 68 70 72 74 67 69 71 73 75 68 70 72 73 75 68 70 72 74 76 69 71 73 75 77 70 72 73 75 77 70 72 74 76 78 71 73 75 77 79 36 37 38 39 40 41 42 43 44 45 72 74 75 77. 79 72 74 76 78 80 73 75 77 78 80 74 76 77 79 81 74 76 78 80 82 75 77 79 81 83 76 78 80 81 83 77 78 80 82 84 77 79 81 83 85 78 80 82 84 86 79 81 82 84 86 79 81 83 85 87 80 82 84 86 88 81 83 85 87 89 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 81 82 84 86 88 89 91 93 95 96 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 90 92 94 95 97 91 93 95 96 98 92 94 95 97 99 93 94 96 98 100 94 95 97 99 101 94 96 98 100 102 95 97 99 101 103 96 98 100 102 104 97 99 101 103 105 98 100 102 104 105 99 101 102 104 106 99 101 103 105 107 100 102 104 106 108 51 52 53 54 55 56 57 58 59 60 98 100 102 103 105 99 101 102 104 106 100 102 103 105 107 101 103 104 106 108 102 104 105 107 109 103 105 106 108 110 104 105 107 109 111 105 106 108 110 112 105 107 109 111 113 106 108 110 112 114 107 109 111 113 115 108 110 112 114 116 109 111 113 115 117 110 112 114 116 118 56 57 58 59 60 TABLE 12. [Page 517 For finding the Variation of the Sun's Eight Ascension or Declination, or of the Equation of Time, in any number of minutes of time, the Horary Motion being given at the top of the page in seconds, and the number of minutes of time in the side column. Also for finding the Variation of the Moon's Declination or Right Ascension in seconds of time, the motion in one minute being given at the top, and the numbers in the side column being taken for seconds. Horary motion. 1 M. M. 119" 120" 121" 122" 128" 124" 126" 126" 127" 128" 129" 180" 181" 182" 1 2 3 4 5 6 7 8 9 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 TO 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 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 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 32 34 36 38 40 32 34 36 38 40 32 34 36 38 40 33 35 37 39 41 33 35 37 39 41 33 35 37 39 41 33 35 38 40 42 34 36 38 40 42 34 36 38 40 42 34 36 38 41 43 34 37 39 41 43 35 37 39 41 43 35 37 39 41 44 35 37 40 42 44 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 42 44 46 48 50 42 44 46 48 50 42 44 46 48 50 43 45 47 49 51 43 45 47 49 51 43 45 48 50 52 44 46 48 50 52 44 46 48 50 53 44 47 49 51 53 45 47 49 51 53 45 47 49 52 54 46 48 50 52 54 46 48 50 52 55 46 48 51 53 55 21 22 23 24 25 52 54 56 58 60 61 63 65 67 69 52 54 56 58 60 52 54 56 58 61 53 55 57 59 61 53 55 57 59 62 54 56 58 60 62 54 56 58 60 63 55 57 59 61 63 55 57 59 61 64 55 58 60 62 64 56 58 60 62 65 56 59 61 63 65 57 59 61 63 66 57 59 62 64 66 26 27 28 29 30 31 32 33 34 35 62 64 66 68 70 63 65 67 69 71 63 65 67 69 71 64 66 68 70 72 64 66 68 70 72 65 67 69 71 73 65 67 69 71 74 66 68 70 72 74 66 68 70 73 75 67 69 71 73 75 67 69 72 74 76 68 70 72 74 76 68 70 73 75 77 36 37 38 39 40 71 73 75 77 79 72 74 76 78 80 73 75 77 79 81 73 75 77 79 81 74 76 78 80 82 74 76 79 81 83 75 77 79 81 83 76 78 80 82 84 76 78 80 83 85 77 79 81 83 85 77 80 82 84 86 78 80 82 85 87 79 81 83 85 87 79 81 84 86 88 36 37 38 39 40 41 42 43 44 45 81 83 85 87 89 82 84 86 88 90 83 85 87 89 91 83 85 87 89 92 84 86 88 90 92 85 87 89 91 93 85 88 90 92 94 86 88 90 92 95 87 89 91 93 95 87 90 92 94 96 88 90 92 95 97 89 91 93 95 98 90 92 94 96 98 90 92 95 97 99 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 91 93 95 97 99 92 94 96 98 100 93 95 97 99 101 94 96 98 100 102 94 96 98 100 103 95 97 99 101 103 96 98 100 102 104 97 99 101 103 105 97 99 102 104 106 98 100 102 105 107 99 101 103 105 108 100 102 104 106 108 100 103 105 107 109 101 103 106 108 110 46 47 48 49 50 101 103 105 107 109 102 104 106 108 110 103 105 107 109 111 104 106 108 110 112 114 116 118 120 122 105 107 109 111 113 105 107 110 112 114 106 108 110 113 115 107 109 111 113 116 108 110 112 114 116 109 111 113 115 117 110 112 114 116 118 111 113 115 117 119 111 114 116 118 120 112 114 117 119 121 51 52 53 54 55 56 57 58 59 60 111 113 115 117 119 112 114 116 118 120 113 115 117 119 121 115 117 119 121 123 116 118 120 122 124 117 119 121 123 125 118 120 122 124 126 119 121 123 125 127 119 122 124 126 128 120 123 125 127 129 121 124 126 128 130 122 124 127 129 131 123 125 128 130 132 56 57 58 59 60 Page 518] TABLE 12. For finding the Variation of the Sun's Eight Ascension or Declination, or of the Equation of Time, in any number of minutes of time, the Horary Motion being given at the top of the page in seconds, and the number of minutes of time in the side column. Also for finding the Variation of the Moon's Declination or Right Ascension in seconds of time, the motion in one minute being given at the top, and the numbers in the side column being taken for seconds. M. Horary motion. M. 188" 184" 185" 186" 187" 188" 139" 140" 141" 142" 148" 144" 146" 146" 1 2 3 4 5 2 4 7 9 11 2 4 7 9 11 2 5 7 9 11 2 5 7 9 11 2 5 7 9 11 2 5 7 9 12 2 5 7 9 12 2 5 7 9 12 2 5 7 9 12 2 5 7 9 12 2 5 7 10 12 2 5 7 10 12 2 5 7 10 12 2 5 7 10 12 1 2 3 4 5 6 7 8 9 10 13 16 18 20 22 13 16 18 20 22 14 16 1^ 20 23 14 16 18 20 23 14 16 18 21 23 14 16 18 21 23 14 16 19 21 23 14 16 19 21 23 14 16 19 21 24 14 17 19 21 24 14 17 19 21 24 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 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 21 22 23 24 25 26 27 28 29 30 47 49 51 53 55 58 60 62 64 67 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 58 60 63 65 67 59 61 63 65 68 59 61 63 66 68 59 62 64 66 69 60 62 64 67 69 60 63 65 67 70 61 63 65 68 70 61 63 66 68 71 62 64 66 69 71 62 64 67 69 72 62 05 67 70 72 63 65 68 70 73 63 66 68 71 73 26 27 28 29 30 31 32 33 34 35 69 71 73 75 78 69 71 74 76 78 70 72 74 77 79 70 73 75 77 79 71 73 75 78 80 71 74 76 78 81 72 74 76 79 81 72 75 77 79 82 73 75 78 80 82 73 76 78 80 83 74 76 79 81 83 74 77 79 82 84 75 77 80 82 85 75 78 80 83 85 31 32 33 34 35 36 37 38 39 40 80 82 84 86 89 80 83 85 87 89 81 83 86 88 90 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 60 124 126 129 131 133 125 127 130 132 134 126 128 131 133 135 127 129 131 134 136 128 130 132 135 137 129 131 133 136 138 130 132 134 137 139 131 133 135 138 140 132 134 136 139 141 133 135 137 140 142 133 136 138 141 143 134 137 139 142 144 135 138 140 143 145 136 139 141 144 146 56 57 58 59 60 ' ^ 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 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. 1 M. 147" 148" 149" 160" 161" 162" 168" 164" 166" 166" 167" 168" 169" 160" 1 2 3 4 5 2 5 7 10 12 2 5 7 10 12 2 5 7 10 12 3 5 8 10 13 3 5 8 10 13 3 5 8 10 13 3 5 8 10 13 3 5 8 10 13 3 5 8 10 13 3 I 10 13 3 5 8 10 13 3 5 8 11 13 3 5 8 11 13 3 5 8 11 13 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 15 17 20 22 25 15 17 20 22 25 15 17 20 22 25 15 18 20 23 25 15 18 20 23 25 15 18 20 23 25 15 18 20 23 26 15 18 21 23 26 16 18 21 23 26 16 18 21 23 26 16 18 .21 24 26 16 18 21 24 26 16 19 21 24 27 16 19 21 24 27 6 7 8 9 10 27 29 32 34 37 27 30 32 35 37 27 30 32 35 37 28 30 33 35 38 28 30 33 35 38 28 30 33 35 38 28 31 33 36 38 28 31 33 36 39 28 31 34 36 39 29 31 34 36 39 29 31 34 37 39 29 32 34 37 40 29 32 34 37 40 29 32 35 37 40 11 12 13 14 15 16 17 18 19 20 39 42 44 47 49 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 64 66 69 71 74 64 67 69 72 74 65 67 70 72 75 ■65 68 70 73 75 65 68 70 73 76 66 68 71 73 76 66 69 71 74 77 67 69 72 74 77 67 70 72 76 78 68 70 73 75 78 68 71 73 76 79 68 71 74 76 79 69 72 74 77 80 69 72 75 77 80 26 27 28 29 30 31 32 33 34 35 76 78 81 83 86 76 79 81 84 86 77 79 82 84 87 78 80 83 85 88 78 81 83 86 88 79 81 84 86 89 79 82 84 87 89 80 82 85 87 90 80 83 85 88 90 81 83 86 88 91 81 84 86 89 92 82 84 87 90 92 82 85 87 90 93 83 85 88 91 93 31 32 33 34 35 36 37 38 39 40 88 91 93 96 98 89 91 94 96 99 89 92 94 97 99 90 93 95 98 100 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 41 42 43 44 45 100 103 105 108 110 101 104 106 109 111 102 104 107 109 112 103 105 108 110 113 103 106 108 111 113 104 106 109 111 114 105 107 110 112 115 105 108 110 113 116 106 109 111 114 116 107 109 112 114 117 107 110 113 115 118 108 111 113 116 119 109 111 114 117 119 109 112 115 117 120 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 113 115 118 120 123 113 116 118 121 123 114 117 119 122 124 115 118 120 123 125 116 118 121 123 126 117 119 122 124 127 117 120 122 125 128 118 121 123 126 128 119 121 124 127 129 120 122 125 127 130 120 123 126 128 131 121 124 126 129 132 122 125 127 130 133 123 125 128 131 133 46 47 48 49 50 125 127 130 132 135 137 140 142 145 147 126 128 131 133 136 138 141 143 146 148 127 129 132 134 137 139 142 144 147 149 128 130 133 135 138 128 131 133 136 138 129 132 134 137 139 130 133 135 138 140 131 133 136 139 141 132 134 137 140 142 133 135 138 140 143 133 136 139 141 144 134 137 140 142 145 135 138 140 143 146 136 139 141 144 147 51 52 53 54 55 56 57 58 59 60 140 143 145 148 150 141 ]43 146 148 151 142 144 147 149 152 143 145 148 150 153 144 146 149 151 154 145 147 150 152 155 146 148 151 153 156 147 149 152 154 157 147 150 153 155 158 148 151 154 156 159 149 152 155 157 160 56 57 58 59 60 Page 520] TABLE 13. For finding the Sun's change of Right Ascension for any given number of hours. Hourly Number of hours. Hourly tion. 1 2 3 4 5 6 7 8 9 10 H 12 tion. «. ». s. s. s. s. s. s. s. s. «. 8. s. s. 8.50 8.5 17.0 25.5 34.0 42.5 51.0 59.5 68.0 76.5 85.0 93.5 102.0 8.50 8.55 8.6 17.1 25.7 34.2 42.8 51.3 59.9 68.4 77.0 85.5 94.1 102.6 8.55 8.60 8.6 17.2 25.8 34.4 43.0 51.6 60.2 68.8 77.4 86.0 94.6 103.2 8.60 8.65 8.7 17.3 26.0 34.6 43.3 51.9 60.6 69.2 77.9 86.5 95.2 103.8 8.65 8.70 8.7 17.4 26.1 34.8 43.5 52.2 60.9 69.6 78.3 87.0 95.7 104.4 105.0 8.70 8.75 8.8 17.5 26.3 35.0 43.8 52.5 61.3 70.0 78.8 87.5 96.3 8.75 8.80 8.8 17.6 26.4 35.2 44.0 52.8 61.6 70.4 79.2 88.0 96.8 105.6 8.80 8.85 8.9 17.7 26.6 35.4 44.3 53.1 62.0 70.8 79.7 88.5 97.4 106.2 8.85 8.90 8.9 17.8 26.7 35.6 44.5 53.4 62.3 71.2 80.1 89.0 97.9 106.8 8.90 8.95 9.0 9.0 17.9 26.9 27.0 35.8 44.8 53.7 54.0 62.7 71.6 80.6 89.5 90.0 98.5 107.4 108.0 8.95 9.00 18.0 36.0 45.0 63.0 72.0 81.0 99.0 9.00 9.05 9.1 18.1 27.2 36.2 45.3 54.3 63.4 72.4 81.5 90.5 99.6 108.6 9.05 9.10 9.1 18.2 27.3 36.4 45.5 54.6 63.7 72.8 81.9 91.0 100.1 109. 2 9.10 9.15 9.2 18.3 27.5 36.6 45.8 54.9 64.1 73.2 82.4 91.5 100.7 109.8 9.15 9.20 9.2 18.4 27.6 36.8 46.0 55.2 64.4 73.6 82.8 92.0 101.2 110.4 9.20 9.25 9.3 18.5 27.8 37.0 46.3 55.5 64.8 74.0 83.3 92.5 101.8 111.0 9.25 9.30 9.3 18.6 27.9 37.2 46.5 55.8 65.1 74.4 83.7 93.0 102.3 111.6 9.30 9.35 9.4 18.7 28.1 37.4 46.8 56.1 65.5 74.8 84.2 93.5 102.9 112.2 9.35 9.40 9.4 18.8 28.2 37.6 47.0 56.4 65.8 75.2 84.6 94.0 103.4 112.8 9.40 9.45 9.5 18.9 28.4 37.8 47.3 56.7 66.2 75.6 85.1 94.5 104.0 113.4 9.45 9.50 9.5 19.0 28.5 38.0 47.5 57.0 66.5 76.0 85.5 95.0 104.5 114.0 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 38.8 48.5 48.8 58.2 67.9 68.3 77.6 87.3 97.0 106.7 116.4 117.0 9.70 9.75 9.8 19.5 29.3 39.0 58.5 78.0 87.8 97.5 107.3 9.75 9.80 9.8 19.6 29.4 39.2 49.0 58.8 68.6 78.4 88.2 98.0 107.8 117.6 9.80 9.85 9.9 19.7 29.6 39.4 49.3 59.1 69.0 78.8 88.7 98.5 108.4 118.2 9.85 9.90 9.9 19.8 29.7 39.6 49.5 59.4 69.3 79.2 89.1 99.0 108.9 118.8 9.90 9.95 10.0 10.0 19.9 29.9 39.8 49.8 50.0 59.7 60.0 69.7 79.6 89.6 99.5 109.5 119.4 9.95 10.00 20.0 30.0 40.0 70.0 80.0 90.0 100.0 110.0 120.0 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 20.4 30.6 40.8 51.0 51.3 61.2 71.4 71.8 81.6 82.0 91.8 92.3 102.0 112.2 122.4 10.20 ^ 10.25 10.3 20.5 30.8 41.0 61.5 102.5 112.8 123.0 10.25 10.30 10.3 20.6 30.9 41.2 51.5 61.8 72.1 82.4 92.7 103.0 113.3 123.6 10.30 10.35 10.4 20.7 31.1 41.4 51.8 62.1 72.5 82.8 93.2 103.5 113.9 124.2 10.35 10.40 10.4 20.8 31.2 41.6 52.0 62.4 72.8 83.2 93.6 104.0 114.4 124.8 10.40 10.45 10.5 20.9 31.4 31.5 41.8 42.0 52.3 62.7 73.2 83.6 94.1 104.5 105.0 115.0 115.5 125.4 10.45 10.50 10.5 21.0 52.5 63.0 73.5 84.0 94.5 126.0 10.50 10.55 10.6 21.1 31.7 42.2 52.8 63.3 73.9 84.4 95.0 105.5 116.1 126.6 10.55 10.60 10.6 21.2 31.8 42.4 53.0 63.6 74.2 84.8 95.4 106.0 116.6 127.2 10.60 10.65 10.7 21.3 32.0 42.6 53.3 63.9 74.6 85.2 95.9 106.5 117.2 127.8 10.65 10.70 10.7 21.4 32.1 42.8 53.5 64.2 74.9 75.3 85.6 96.3 107.0 117.7 118.3 128.4 10.70 10.75 10.8 21.5 32.3 43.0 53.8 64.5 86.0 96.8 107.5 129.0 10.75 10.80 10.8 21.6 32.4 43.2 54.0 64.8 75.6 86.4 97.2 108.0 118.8 129.6 10.80 10.85 10.9 21.7 32.6 43.4 54.3 65.1 76.0 86.8 97.7 108.5 119.4 130.2 10.85 10.90 10.9 21.8 32.7 43.6 54.5 65.4 76.3 87.2 98.1 109.0 119.9 130.8 10.90 10.95 11.0 21.9 22.0 32.9 33.0 43.8 44.0 54.8 55.0 65.7 76.7 87.6 88.0 98.6 99.0 109.5 110.0 120.5 121.0 131.4 10.95 11.00 11.0 66.0 77.0 132.0 11.00 11.05 11.1 22.1 33.2 44.2 55.3 66.3 77.4 88.4 99.5 110.5 121.6 132.6 11.05 11.10 11.1 22.2 33.3 44.4 55.5 66.6 77.7 88.8 99.9 111.0 122.1 133.2 11.10 11.15 11.2 22.3 33.5 44.6 55.8 66.9 78.1 89.2 100.4 111.5 122.7 133.8 11.15 11.20 11.2 22.4 33.6 44.8 56.0 67.2 78.4 89.6 100.8 112.0 123.2 134.4 135.0 11.20 11.25 11.3 22.5 33.8 45.0 56.3 67.5 78.8 90.0 101.3 112.5 123.8 11.25 11.30 11.3 22.6 33.9 45.2 56.5 67.8 79.1 90.4 101.7 113.0 124.3 135.6 11.30 11.35 11.4 22.7 34.1 45.4 56.8 68.1 79.5 90.8 102.2 113.5 124.9 136.2 11.35 11.40 11.4 22.8 34.2 45.6 57.0 68.4 79.8 91.2 102.6 114.0 125.4 136.8 11.40 11.45 11.5 22.9 34.4 45.8 57.3 68.7 80.2 91.6 103.1 114.5 126.0 137.4 11.45 TABLE 13. [Page 521 | For finding the Sun's change of Right Ascension for any given number of hours. Hourly Number of hours. Hourly tion. 13 14 16 161 17 18 19 20 21 22 28 24 varia- tion. 8.' 50 110. 5 119. 127.5 136.0 144.5 153.0 161. 5 170. 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 8.65 112.5 121.1 129.8 138.4 147.1 156.7 164.4 173.0 181.7 190.3 199.0 207.6 8.65 8.70 113.1 121.8 130.5 139.2 147.9 148.8 156.6 165.3 166.3 174.0 182.7 191.4 200.1 201.3 208.8 8.70 8.75 113.8 122.5 131.3 140.0 157.5 175.0 183.8 192.5 210.0 8.75 8.80 114.4 123.2 132.0 140.8 149.6 158.4 167.2 176.0 184.8 193.6 202.4 211.2 8.80 8.85 115.1 123.9 132.8 141.6 150.5 159.3 168.2 177.0 185.9 194.7 203.6 212.4 8.85 8.90 115.7 124.6 133.5 142.4 151.3 160.2 169.1 178.0 186.9 195.8 204.7 213.6 8.90 8.95 116.4 "117. 125.3 134.3 143.2 152.2 161.1 170.1 179.0 180.0 188.0 196.9 205.9 207.0 214.8 8.95 9.00 126.0 135. 144.0 153.0 162.0 171.0 189.0 198.0 216.0 9.00 9.05 117.7 126.7 135.8 144.8 153.9 162.9 172.0 181.0 190.1 199.1 208.2 217.2 9.05 9.10 118.3 127.4 136.5 145.6 154.7 163.8 172.9 182.0 191.1 200.2 209.3 218.4 9.10 9.15 119.0 128.1 137.3 146.4 155.6 164.7 173.9 183.0 192.2 201.3 210.5 219.6 9.15 9.20 119.6 128.8 138.0 147.2 156.4 157.3 165.6 174.8 184.0 193.2 194.3 202.4 211.6 212.8 220.8 9.20 9.25 120.3 129.5 138. 8 148.0 166.5 175.8 185.0 203.5 222.0 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 9.35 121.6 130.9 140.3 149.6 159.0 168.3 177.7 187.0 196.4 205.7 215.1 224.4 9.35 9.40 122.2 131.6 141.0 150.4 159.8 169.2 178.6 188.0 197.4 206.8 216.2 225.6 9.40 9.45 122.9 132.3 141.8 151.2 152.0 160.7 170.1 179.6 189.0 198.5 199.5 207.9 217.4 226.8 9.45 9.50 123.5 133.0 142.5 161.5 171.0 180.5 190.0 209.0 218.5 228.0 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 9.70 126.1 135.8 136.5 145.5 155.2 156.0 164.9 174.6 184.3 194.0 203.7 204.8 213.4 223.1 232.8 9.70 9.75 126.8 146.3 165.8 175.5 185.3 195.0 214.5 224.3 234. 9.75 9.80 127.4 137.2 147.0 156.8 166.6 176.4 186.2 196.0 205.8 215.6 225.4 235.2 9.80 9.85 128.1 137.9 147.8 157.6 167.5 177.3 187.2 197.0 206.9 216.7 226.6 236.4 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 9.95 129.4 139.3 149.3 150.0 159.2 160.0 169.2 179.1 189.1 199.0 209.0 218.9 228.9 238.8 9.95 10.00 130.0 140.0 170.0 180.0 190.0 200.0 210.0 220.0 230.0 240.0 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 10.20 132.6 133.3 142.8 153.0 163.2 173.4 174.3 183.6 193.8 204.0 205.0 214.2 224.4 225.5 234.6 244.8 10.20 10.25 143.5 153.8 164.0 184.5 194.8 215.3 235.8 246.0 10.25 10.30 133.9 144.2 154.5 164.8 175.1 185.4 195.7 206.0 216.3 226.6 236.9 247.2 10.30 10.35 134.6 144.9 155.3 165.6 176.0 186.3 196.7 207.0 217.4 227.7 238.1 248.4 10.35 10.40 135.2 145.6 156.0 166.4 176.8 187.2 197.6 208.0 218.4 228.8 239.2 249.6 10.40 10.45 135.9 146.3 156.8 167.2 177.7 188.1 198.6 209.0 219.5 229.9 240.4 250.8 10.45 10.50 136.5 147.0 157.5 168.0 178.5 189.0 199.5 210.0 220.5 231.0 241.5 252.0 10.50 10.55 137.2 147.7 158.3 168.8 179.4 189.9 200.5 211.0 221.6 232.1 242.7 253.2 10.55 10.60 137.8 148.4 159.0 169.6 180.2 190.8 201.4 212.0 222.6 233.2 243.8 254.4 10.60 10.65 138.5 149.1 ]59.8 170.4 181.1 191.7 202.4 213.0 223.7 234.3 245.0 255.6 10.66 10.70 139.1 149.8 160.5 171.2 181.9 182.8 192.6 203.3 214.0 224.7 235.4 246.1 247.3 256.8 10.70 10.75 139.8 150.5 161.3 172.0 193.5 204.3 215.0 225.8 236.5 258.0 10.75 10.80 140.4 151.2 162.0 172.8 183.6 194.4 205.2 216.0 226.8 237.6 248.4 259.2 10.80 10.85 141.1 151.9 162.8 173.6 184.5 195.3 206.2 217.0 227.9 238.7 249.6 260.4 10.85 10.90 141.7 152.6 163.5 174.4 185.3 196.2 207.1 218.0 228.9 239.8 250. 7 261.6 10.90 10.95 142.4 153.3 164.3 175.2 186.2 197.1 208.1 219.0 230.0 240.9 251.9 262.8 10.95 11.00 143.0 154.0 165.0 176.0 187.0 198.0 209.0 220.0 231.0 242.0 253.0 264.0 11.00 11.05 143.7 154.7 165.8 176.8 187.9 198.9 210.0 221.0 232.1 243.1 254.2 265.2 11.05 11.10 144.3 155.4 166.5 177.6 188.7 199.8 210.9 222.0 233.1 244.2 255.3 266.4 11-10 11.15 145.0 156.1 167.3 178.4 189.6 200.7 211.9 223.0 234.2 245.3 256.5 267.6 11.15 11.20 145.6 156.8 168.0 179.2 190.4 191.3 201.6 212.8 224.0 235.2 246.4 257.6 268.8 270.0 11.20 11.25 11.25 146.3 157.5 168.8 180.0 202.5 213.8 225.0 236.3 247.5 258.8 11.30 146.9 158.2 169.5 180.8 192.1 203.4 214.7 226.0 237.3 248.6 259.9 271.2 11.30 11.35 147.6 158.9 170.3 181.6 193.0 204.3 215.7 227.0 238. 4 249.7 261.1 272.4 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. G 240.5 251.9 263. 4 1 274. 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. / 11 1 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 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 TABLE 15. Dip of the Sea at different Distances from the Observer. Dist. of Land in Sea Miles. Height of the Eye above the Sea in Feet. 1 5 10 16 20 25 30 86 40 \ / 11 1 23 1 34 1 45 57 / 68 79 / 91 ^ 6 12 17 23 28 34 40 45 \ 4 8 12 15 19 23 27 30 1 3 6 9 12 15 17 20 23 li 3 5 7 10 12 14 16 19 li 3 4 6 8 10 12 14 16 2 2 4 5 7 8 9 11 12 .2^ 2 3 4 6 7 8 9 10 3 2 3 4 5 6 7 8 9 3i 2 3 4 5 6 6 7 8 4 5 2 2 3 4 4 5 4 5 5 6 6 7 6 7 7 3 6 2 3 4 4 5 5 6 6 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. 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 IT. Parallax in Altitude of a Planet. [Page 523 •8pn;mv ° =Sg^S^^^^ggS§SS,^g?2^gSggSggg O o K 1 ^^S?S^&5^^S5i^gS^S^^SS=^^'°'^^^^® ee §S?5^S?5?^?1SS^S2S^S°^**-'^'«^=^<^^® 1 c5c5S^?q5^§S2^SI5;^?H^IS'^°°'^'^"^'***^'^'~"^ 01 &j^^§5?j?5§ssi::s;2;s?3^^<=^*-^^'«^«<^'^® St at C<)C^-t^coic-*ececc<»rHO ClMrHT-li— li— Ii-Ht— iT-HfHi—lr-lrH e< r-lT-lpQ0t^CDiOiO-*eCC-coicin)-*ec(MT-ir-toosooi>-*■<*< eoec(Nr-it-io t-.|:^<:OkO-*eOCq(MrH0005aOt^l>COlOlOTjoot^t>.i;D«oio-<**-*Tt O»O50000t^t^l>-<©:O«DlClO'*'^'* CO eC C<|(MC.|:^i:0«Oi010lOiC'*-*-*05eCe<5C<>N(MC ft 70° 60° 60° 40° 30° 20° 10° 0° 10° 20° 80° 40° 60° 60° 70° o 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 36 31 27 25 22 21 21 25 36 31 26 23 20 17 16 16 II 18 14 10 6 2 - 2 - 7 -16 18 13 9 4 - 6 -14 -26 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 II 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 o 14 16 18 20 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 53 48 43 40 39 39 43 56 - 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 10 20 30 40 50 60 70 18 10 20 30 40 50 60 70 99 95 93 95 102 91 87 85 86 92 103 81 76 74 74 78 87 105 68 63 60 59 61 66 79 108 68 63 60 58 59 63 74 100 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 20 10 20 30 40 50 60 70 100 95 93 94 100 92 87 85 85 90 100 82 76 74 73 76 83 100 36 31 25 21 17 13 10 6 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 24 26 10 20 30 40 50 60 70 10 20 30 40 50 60 70 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 22 24 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 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 10 20 30 40 50 60 70 26 1 a 4 a 70° 60° 60° 40° 30° 20° 10° 0° 10° 20° 80° 40° 60° 60° 70° < § c "3 ft Latitude of same name as declination. Latitude of different name from declination. TABLE 26. [Page 541 | Variation of Altitude in one minute from meridian passage Lati- tude. Declination of the same name as the latitude; upper transit; reduction kddltlre. Lati- tude. 0° 1° 2° 8° 4° 6° 6° JO 8° 9° 10° 11° o II II 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 28.1 27.8 22,2 18.5 15.8 4 5 22.4 28.0 27.7 22.1 18.4 5 6 18.7 22.4 28.0 27.6 22.0 6 7 16.0 18.6 22.3 27.9 27.4 7 8 14.0 16.0 18.6 22.3 27.8 8 9 12.4 13.9 15.9 18.5 22.2 27,7 9 10 11.1 12.4 13.9 15.8 18.5 22,1 27.6 10 11 10.1 11.1 12.3 13.8 15.8 18,4 22.0 27.4 11 12 9.2 10.1 11.1 12.3 13.8 15.7 18.3 21.9 27.3 12 13 8.5 9.2 10.0 11.0 12.2 13.7 15.6 18.2 21.7 27.1 13 14 7.9 8.5 9.2 10.0 10.9 12.1 13.6 15.5 18.0 21.6 26.9 14 15 7.3 7.8 8.4 9.1 9.9 10.9 12.1 13.5 15.4 17.9 21,4 26,7 15 16 6.8 7,3 7.8 8.4 9.1 9.8 10.8 12.0 13.4 15.3 17.8 21.3 16 17 6.4 6.8 7.2 7,8 8.3 9.0 9.8 10.7 11.9 13.3 15.2 17.6 17 18 6.0 6.4 6.8 7,2 7.7 8.3 8.9 9.7 10.6 11.8 13.2 15.0 18 19 5.7 6.0 6.3 6.7 7.2 7.6 8.2 8,9 9.6 10.6 11.7 13.1 19 20 20 5.4 5.7 6.0 6.3 6.7 7.1 7.6 8,1 8.8 9,5 10.5 11.6 21 5.1 5.4 5.6 5.9 6.3 6.6 7.0 7,5 8.1 8,7 9,5 10.4 21 22 4.9 5.1 5.3 5.6 5.9 6.2 6.6 7,0 7,5 8,0 8.6 9.4 22 23 4.6 4.8 5.0 5.3 5.5 5.8 6.1 6,5 6.9 7.4 7,9 8.6 23 24 4.4 4.6 4.8 5.0 5.2 5.5 5.8 6,1 6.4 6.8 6.4 7,3 7.8 24 25 4.2 4.4 4.6 4.7 5.0 5.2 5.4 5.7 6.0 6,8 7.2 25 26 4.0 4.2 4.3 4.5 4.7 4.9 5,1 5.4 5.7 6.0 6.3 6.7 26 27 3.9 4.0 4.1 4.3 4.5 4.7 4.9 5.1 5.3 5.6 5.9 6.2 27 28 3.7 3.8 4.0 4.1 4.3 4.4 4.6 4.8 5.0 5.3 5.5 5.8 28 29 3.5 3.7 3.8 3.9 4.1 4.2 4.4 4.6 4.7 5.0 5.2 5.5 29 30 3.4 3.5 3.6 3.7 3,9 4.0 4.2 4.3 4.5 4,7 4.9 5.1 30 31 3.3 3.4 3.5 3.6 3.7 3.8 4.0 4.1 4.3 4,4 4.6 4.8 31 32 3.1 3.2 3.3 3.4 3.5 3.7 3.8 3.9 4.1 4,2 4.4 4.6 32 33 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.9 4,0 4.2 4.3 33 34 2.9 3.0 3.1 3.2 3.2r 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 2.3 2.4 2.4 2.5 2,6 2.6 2.7 2.7 2.8 2.9 3.0 3.0 40 41 2.3 2.3 2,4 2.4 2,5 2.5 2.6 2.6 2.7 2.8 2.8 2.9 41 42 2.2 2.2 2.3 2.3 2.4 2.4 2.5 2.5 2.6 2.6 2.7 2.8 42 43 2.1 2.1 2.2 2.2 2.3 2.3 2.4 2.4 2.5 2.5 2.6 2.7 43 44 2.0 2.1 2.1 2.1 2.2 2.2 2.3 2.3 2.4 2.4 2.5 2.5 44 45 2.0 2.0 2.0 2.1 2.1 2.2 2.2 2.2 2.3 2.3 2.4 2.4 45 46 1.9 1.9 2.0 2.0 2.0 2.1 2.1 2.2 2.2 2.2 2,3 2.3 46 47 1.8 1.9 1.9 1.9 2.0 2.0 2.0 2.1 2.1 2.1 2,2 2.2 47 48 1.8 1.8 1.8 1.9 1.9 1.9 2.0 2.0 2.0 2.1 2,1 2.1 48 49 1.7 1.7 1.8 1.8 1.8 1.8 1.9 1.9 1.9 2.0 2.0 2.1 49 50 1.6 1.7 1.7 1.7 1.8 1.8 1.8 1.8 1.9 1.9 1.9 2.0 50 51 1.6 1.6 1.6 1.7 1.7 1.7 1.7 1.8 1.8 1.8 1.9 1.9 51 52 1.5 1.6 1.6 1.6 1.6 1.6 1.7 1.7 1.7 1.8 1.8 1.8 52 53 1.5 1.5 1.5 1.5 1.6 1.6 1.6 1.6 1.7 1.7 1.7 1.7 53 54 1.4 1.4 1.5 1.5 1.5 1.5 1.5 1.6 1.6 1.6 1,6 1.7 54 55 55 1.4 1.4 1.4 1.4 1.5 1.5 1.5 1.5 1.5 1.6 1,6 1.6 56 1.3 1.3 1.4 1.4 1.4 1.4 1.4 1.4 1.5 1.5 1,5 1.5 56 57 1.3 1.3 1.3 1.3 1.3 1.4 1.4 1.4 1.4 1,4 1.4 1.5 57 58 1.2 1.2 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1,4 1.4 1.4 58 59 1.2 1.2 1.2 1.2 1.2 1.3 1.3 1,3 1.3 1,3 1.3 1.3 59 60 1.1 1.1 1.2 1.2 1.2 1.2 1.2 1,2 1.2 1,2 1.3 1.3 60 0° 1° go 3° 4° 6° 6° 7° 8° 9° 10° 11° De clinatioi 1 of the same nan le as the latitude; upper trai [isit; redu ction add lUve. Page 542] TABLE 26. Variation of Altitude in one minute from meridian passage. Declination of the same name as the latitude; npper transit reduction addltlTe. Lati- tude. Lati- tude. 12° 18° 14° 16° 16° 17° 18° 19° 20° 21° 22° 23° 24° o // // II II II II II II II // „ II II o 9.2 8.5 7.9 7.3 6.8 6.4 6.0 5.7 5.4 5.1 4.9 4.6 4.4 1 10.1 9.2 8.5 7.8 7.3 6.8 6.4 6,0 5.7 5.4 5.1 4.8 4.6 1 2 11.1 10.0 9.2 8.4 7.8 7.2 6.8 6.3 6.0 5.6 5.3 5.0 4.8 2 3 12.3 11.0 10.0 9.1 8.4 7.8 7.2 6.7 6.3 5.9 5.6 5.3 5.0 3 4 13.8 12.2 10.9 9.9 9.1 8.3 7.7 7.2 6.7 6.3 5.9 5.5 5.2 4 5 15.7 13.7 12.1 10.9 9.8 9.0 8.3 7.6 7.1 6.6 6.2 6.8 5.5 5 6 18.3 15.6 13.6 12.1 10.8 9.8 8.9 8.2 7.6 7.0 6.6 6.1 5.8 6 7 21.9 18.2 15.5 13.5 12.0 10.7 9.7 8.9 8.1 7.5 7.0 6.5 6.1 7 8 27.3 21.7 18.0 15.4 13.4 11.9 10.6 9.6 8.8 8.1 7.5 6.9 6.4 8 9 27.1 21.6 17.9 15.3 13.3 11.8 10.6 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 11.1 12.4 14.1 16.3 19.5 24.2 24 25 7.7 8.3 9.0 9.9 10.9 12.2 13.9 16.1 19.2 23.8 25 26 7.1 7.6 8.2 8.9 9.8 10.8 12.1 13.7 15.9 18.9 23.5 26 27 6.6 7.0 7.5 8.1 8.8 9.6 10.6 11.9- 13.5 15.6 18.6 23.1 27 28 6.2 6.5 7.0 7.4 8.0 8.7 9.5 10.5 11.7 13.3 15.4 18.3 22.7 28 29 5.7 6.1 6.4 6.9 7.3 7.9 8.6 9.4 10.3 11.5 13.1 15.1 18.0 29 30 5.4 5.7 6.0 6.4 6.8 7.2 7.8 8.4 9.2 10.1 11.3 12.8 14.9 30 31 5.1 5.3 5.6 5.9 6.3 6.7 7.1 7.7 8.3 9.0 10.0 11.1 12.6 31 32 4.8 5.0 5.2 5.5 5.8 6.2 6.5 7.0 7.5 8.1 8.9 9.8 10.9 32 33 4.5 4.7 4.9 5.1 5.4 5.7 6.1 6.4 6.9 7.4 8.0 8.7 9.6 33 34 4.3 4.4 4.6 4.8 5.1 5.3 5.6 5.9 6.3 6.8 7.3 7.8 8.6 34 35 4.0 4.2 4.4 4.5 4.7 5.0 5.2 5.5 5.8 6.2 6.6 7.1 7.7 35 36 3.8 4.0 4.1 4.3 4.5 4.7 4.9 5.1 5.4 5.7 6.1 6.5 7.0 36 37 3.6 3.8 3.9 4.0 4.2 4.4 4.6 4.8 5.0 5.3 5.6 6.0 6.4 37 38 3.4 3.6 3.7 3.8 4.0 4.1 4.3 4.5 4.7 4.9 5.2 5.5 5.8 38 39 3.3 3.4 3.5 3.6 3.8 3.9 4.0 4.2 4.4 4.6 4.8 5.1 5.4 39 40 3.1 3.2 3.3 3.4 3.6 3.7 3.8 4.0 4.1 4.3 4.5 4.7 5.0 40 41 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.9 4.0 4.2 4.4 4.6 41 42 2.9 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.7 3.8 4.0 4.1 4.3 42 43 2.7 2.8 2.9 3.0 3.0 3.1 3.2 3.3 3.5 3.6 3.7 3.9 4.0 43 44 2.6 2.7 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.8 44 45 2.5 2.6 2.6 2.7 2.8 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 45 46 2.4 2.4 2.5 2.6 2.6 2.7 2.8 2.8 2.9 3.0 3.1 3.2 3.3 46 47 2.3 2.3 2.4 2.4 2.5 2.6 2.6 2.7 2.8 2.9 2.9 3.0 3.1 47 48 2.2 2.2 2.3 2.3 2.4 2.4 2.5 2.6 2.6 2.7 2.8 2.9 3.0 48 49 2.1 2.1 2.2 2.2 2.3 2.3 2.4 2.4 2.5 2.6 2.6 2.7 2.8 49 50 2.0 2.0 2.1 2.1 2.2 2.2 2.3 2.3 2.4 2.4 2.5 2.6 2.6 50 51 1.9 2.0 2.0 2.0 2.1 2.1 2.2 2.2 2.3 2.3 2.4 2.4 2.5 51 52 1.8 1.9 1.9 1.9 2.0 2.0 ■2.1 2.1 2.1 2.2 2.2 2.3 2.4 52 53 1.8 1.8 1.8 1.9 1.9 1.9 2.0 2.0 2.0 2.1 2.1 2.2 2.2 53 54 1.7 1.7 1.7 1.8 1.8 1.8 1.9 1.9 1.9 2.0 2.0 2.1 2.1 54 55 55 1.6 1.6 1.7 1.7 1.7 1.8 1.8 1.8 1.9 1.9 1.9 2.0 2.0 56 1.5 1.6 1.6 1.6 1.6 1.7 1.7 1.7 1.8 1.8 1.8 1.9 1.9 56 57 1.5 1.5 1.5 1.5 1.6 1.6 1.6 1.6 1.7 1.7 1.7 1.8 1.8 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° 13° 14° 16° 16° 17° 18° 19° 20° 21° 22° 23° 24° De 3linatior I of the f iame na neas th B latitud e; nppei transit; reducti on add/1 lye. TABLE 26. [Page 543 | Variation of Altitude in one minute from meridian passage. Lati- tude. Declination of the same name as the latitude; upper transit ; reduction additlre. Lati- tude. 26° 26° 27° 28° 29° 80° 81° 82° 88° 84° 86° 86° 87° // // II II II II „ II II // II II 4.2 4.0 3.9 3.7 3.5 3.4 3.3 3.1 3.0 2.9 2.8 2.7 2.6 1 4.4 4.2 4.0 3.8 3.7 3.5 3.4 3.2 3.1 3.0 2.9 2.8 2.7 1 2 4.6 4.3 4.1 4.0 3.8 3.6 3.5 3.3 3.2 3.1 3.0 2.8 2.7 2 3 4.7 4.5 4.3 4.1 3.9 3.7 3.6 3.4 3.3 3.2 3.0 2.9 2.8 3 4 5.0 4.7 4.5 4.3 4.1 3.9 3.7 3.5 3.4 3.3 3.1 3.0 2.9 4 5 5.2 4.9 4.7 4.4 4.2 4.0 3.8 3.7 3.5 3.3 3.2 3.1 3.0 5 6 5.4 5.1 4.9 4.6 4.4 4.2 4.0 3.8 3.6 3.5 3.3 3.2 3.0 6 7 5.7 5.4 5.1 4.8 4.6 4.3 4.1 3.9 3.7 3.6 3.4 3.3 3.1 7 8 6.0 5.7 5.3 5.0 4.8 4.5 4.3 4.1 3.9 3.7 3.5 3.4 3.2 8 9 6.4 6.0 5.6 5.3 5.0 4.7 4.4 4.2 4.0 3.8 3.6 3.5 3.3 9 10 6.8 6.3 5.9 5.5 5.2 4.9 4.6 4.4 4.2 3.9 3.8 3.6 3.4 10 11 7.2 6.7 6.2 5.8 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 9.1 8.2 7.6 7.0 6.4 6.0 5.6 5.2 4.9 4.6 4.4 4.1 3.9 14 15 9.9 8.9 8.1 7.4 6.9 6.4 5.9 5.5 5.2 4.8 4.5 4.3 4.0 15 16 10.9 9.8 8.8 8.0 7.3 6.8 6.3 5.8 5.4 5.1 4.8 4.5 4.2 16 17 12.2 10.8 9.6 8.7 7.9 7.2 6.7 6.2 5.7 5.3 5.0 4.7 4.4 17 18 13.9 12.1 10.6 9.5 8.6 7.8 7.1 6.6 6.1 5.6 5.2 4.9 4.6 18 19 16.1 13.7 11.9 10.5 9.4 8.4 7.7 7.0 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 26 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 30 22.3 20.6 16.3 13.5 11.4 9.9 29 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 6.1 6.5 7.1 7.7 8.5 9.4 10.6 12.2 14.5 17.9 39 40 5.3 5.6 6.0 6.4 6.9 7.5 8.2 9.2 10.4 11.9 14.1 17.4 40 41 4.9 5.2 5.5 5.8 6.2 6.7 7.3 8.0 8.9 10.1 11.6 13.8 17.0 41 42 4.5 4.8 5.0 5.3 5.7 6.1 6.6 7.1 7.8 8.7 9.8 11.3 13.4 42 43 4.2 4.4 4.6 4.9 5.2 5.5 5.9 6.4 6.9 7.6 8.5 9.5 11.0 43 44 3.9 4.1 4.3 4.5 4.8 5.1 5.4 5.8 6.2 6.7 7.4 8.2 9.3 44 45 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 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 2.9 3.0 3.1 3.2 3.3 3.4 3.6 3.7 3.9 4.1 4.4 4.6 5.0 49 50 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.5 3.6 3.8 4.0 4.2 4.5 50 51 2.6 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.4 3.5 3.7 3.9 4.1 51 52 2.4 2.5 2.6 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.4 3.6 3.7 '52 53 2.3 2.3 2.4 2.5 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.3 3.4 53 54 2.2 2.2 2.3 2.3 2.4 2.5 2.5 2.6 2.7 2.8 2.9 3.0 3.2 54 55 2.0 2.1 2.1 2.2 2.3 2.3 2.4 2.4 2.5 2.6 2.7 2.8 2.9 55 56 1.9 2.0 2.0 2.1 2.1 2.2 2.2 2.3 2.4 2.4 2.5 2.6 2.7 56 57 1.8 1.9 1.9 2.0 2.0 2.0 2.1 2.2 2.2 2.3 2.3 2.4 2.5 57 58 1.7 1.8 1.8 1.8 1.9 1.9 2.0 2.0 2.1 2.1 2.2 2.3 2.3 58 59 1.6 1.7 1.7 1.7 1.8 1.8 1.9 1.9 1.9 2.0 2.0 2.1 2.2 59 60 1.6 1.6 1.6 1.6 1.7 1.7 1.7 1.8 1.8 1.9 1.9 2.0 2.0 60 25° 26° 27° 28° 29° 80° 31° 32° 88° 84° 86°I 86° 87° Dec lination of the iame nai ne as th e latitud e; uppei • transit reducti on «ddl tlTe. Page 544] TABLE 26. Variation of Altitude in one minute from meridian passage. Declination of the same name as the latitude; upper transit ; reduction addltire. Lati- tude. Lati- tude. 88° 89° 40° 41° 42° 48° 44° 45° 46° 47° 48° 49° 60° o 2.5 II 2.4 II 2.3 II 2.3 2.2 2.1 2.0 2.0 1.9 1.8 1.8 1.7 1.7 o 1 2.6 2.5 2.4 2.3 2.2 2.2 2.1 2.0 1.9 1.9 1.8 1.7 1.7 1 2 2.6 2.5 2.4 2.4 2.3 2.2 2.1 2.0 2.0 1.9 1.8 1.8 1.7 2 3 2.7 2.6 2.5 2.4 2.3 2.2 2.2 2.1 2.0 1.9 1.9 1.8 1.7 3 4 2.8 2.7 2.6 2.5 2.4 2.3 2.2 2.1 2.0 2.0 1.9 ].8 1.8 4 5 2.8 2.7 2.6 2.5 2.4 2.3 2.2 2.2 2.1 2.0 1.9 1.9 1.8 5 6 2.9 2.8 2.7 2.6 2.5 2.4 2.3 2.2 2.1 2.0 2.0 1,9 1.8 6 7 3.0 2.9 2.7 2.6 2.5 2.4 2.3 2.2 2.2 2.1 2.0 1.9 1.8 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 14 15 3.8 3.6 3.4 3.3 3.1 3.0 2.8 2.7 2.6 2.4 2.3 2.2 2.1 15 16 4.0 3.8 3.6 3.4 3.2 3.0 2.9 2.8 2.6 2.5 2.4 2.3 2.2 16 17 4.1 3.9 3.7 3.5 3.3 3.1 3.0 2.8 2.7 2.6 2.4 2.3 2.2 17 18 4.3 4.1 3.8 3.6 3.4 3.2 3.1 2.9 2.8 2.6 2.5 2.4 2.3 18 19 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 2.4 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 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 5.8 5.4 5.0 4.6 4.3 4.0 3.8 3.5 3.3 3.1 3.0 2.8 2.6 24 25 6.2 5.7 5.3 4.9 4.5 4.2 3.9 3.7 3.5 3.3 3.1 2.9 2.7 25 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 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 35 17.9 14.1 11.6 9.8 8.5 7.4 6.6 5.9 5.3 4.8 4.4 4.0 35 36 17.4 13.8 11.3 9.5 8.2 7.2 6.4 5.7 5.1 4.6 4.2 36 37 17.0 13.4 11.0 9.3 8.0 7.0 6.2 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 6.3 5.1 5.6 39 40 40 15.5 12.2 10.0 8.4 7.2 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 7.6 10.6 13.1 49 50 4.8 5.1 5.6 6.1 6.7 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 3.3 3.5 3.7 3.9 4.1 4.4 4.8 5.2 5.8 6.5 7.4 8.7 10.6 54 55 3.0 3.2 3.3 3.5 3.7 4.0 4.3 4.6 5.0 5.5 6.2 7.1 8.3 55 56 2.8 2.9 3.1 3.2 3.4 3.6 3.8 4.1 4.4 4.8 5.3 5.9 6.8 56 57 2.6 2.7 2.8 2.9 3.1 3.2 3.4 3.6 3.9 4.2 4.6 5.0 5.6 57 58 2.4 2.5 2.6 2.7 2.8 2.9 3.1 3.3 3.5 3.7 4.0 4.4 4.8 58 59 2.2 2.3 2.4 2.5 2.6 2.7 2.8 3.0 3.1 3.3 3.6 3.8 4.2 59 60 2.1 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 3.0 3.2 3.4 3.6 60 38° 39° 40° 41° 42° 43° 44° 45° 46° 47° 48° 49° 60° Dec lination of the 8 ame nan ne as th( J latitud e; upper transit; reducti on additive. TABLE 26. [Page 545 Variation of Altitude in one minute from meridian passage. Lati- tude. Declination of the same name as the latitude; upper transit; reduction additire. Lati- tude. 61° 52° 63° 64° 56° 66° 67° 1] 68° 50° 60° 61° 62° 68° 1 2 3 4 // 1.6 1.6 1.6 1.7 1.7 It 1.5 1.6 1.6 1.6 1.6 1.5 1.5 1.5 1.5 1.6 II 1.4 1.4 1.5 1.5 1.5 II 1.4 1.4 1.4 1.4 1.5 II 1.3 1.3 1.4 1.4 1.4 II 1.3 1.3 1.3 1.3 1.3 II 1.2 1.2 1.3 1.3 1.3 II 1.2 1.2 1.2 1.2 1.2 II 1.1 1.2 1.2 1.2 1.2 n 1.1 1.1 1.1 1.1 1.1 II 1.0 1.1 1.1 1.1 1.1 II 1.0 1.0 1.0 1.0 1.0 o 1 2 3 4 5 6 7 8 9 1.7 1.7 1.8 1.8 1.8 1.7 1.7 1.7 1.7 1.8 1.6 1.6 1.6 1.7 1.7 1.5 1.5 1.6 1.6 1.6 1.5 1.5 1.5 1.5 1.6 1.4 1.4 1.4 1.5 1.5 1.4 1.4 1.4 1.4 1.4 1.3 1.3 1.3 1.4 1.4 1.3 1.3 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.3 1.1 1.2 1.2 1.2 1.2 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 5 6 7 8 9 10 11 12 13 14 1.9 1.9 1.9 2.0 2.0 1.8 1.8 1.8 1.9 1.9 1.7 1.7 1.8 1.8 1.8 1.6 1.7 1.7 1.7 1.7 1.6 1.6 1.6 1.6 1.7 1.5 1.5 1.6 1.6 1.6 1.4 1.5 1.5 1.5 1.5 1.4 1.4 1.4 1.4 1.5 1.3 1.3 1.4 1.4 1.4 1.3 1.3 1.3 1.3 1.3 1.2 1.2 1.2 1.3 1.3 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.3 1.3 1.3 1.1 1.1 1.1 1.1 1.2 10 11 12 13 14 15 16 17 18 19 2.0 2.1 2.1 2.2 2.2 1.9 2.0 2.0 2.1 2.1 1.9 1.9 1.9 2.0 2.0 1.8 1.8 1.8 1.9 1.9 1.7 1.7 1.8 1.8 1.8 1.6 1.6 1.7 1.7 1.7 1.5 1.6 1.6 1.6 1.6 1.5 1.5 1.5 1.5 1.6 1.4 1.4 1.5 1.5 1.5 1.3 1.4 1.4 1.4 1.4 1.3 1.3 1.3 1.3 1.4 1.2 1.2 1.2 1.2 1.2 15 16 17 18 19 20 21 22 23 24 2.3 2.3 2.4 2.4 2.5 2.1 2.2 2.2 2.3 2.4 2.0 2.1 2.1 2.2 2.2 1.9 2.0 2.0 2.1 2.1 1.9 1.9 1.9 2.0 2.0 1.8 1.8 1.8 1.9 1.9 1.7 1.7 1.7 1.8 1.8 1.6 1.6 1.6 1.7 1.7 1.5 1.5 1.6 1.6 1.6 1.4 1.5 1.5 1.6 1.5 1.4 1.4 1.4 1.4 1.5 1.3 1.3 1.3 1.4 1.4 1.4 1.4 1.4 1.5 1.5 1.2 1.2 1.3 1.3 1.3 20 21 22 23 24 25 26 27 28 29 2.6 2.6 2.7 2.8 2.9 2.4 2.5 2.6 2.6 2.7 2.3 2.3 2.4 2.5 2.5 2.2 2.2 2.3 2.3 2.4 2.0 2.1 2.1 2.2 2.3 1.9 2.0 2.0 2.1 2.1 1.8 1.9 1.9 2.0 2.0 1.7 1.8 1.8 1.8 1.9 1.6 1.7 1.7 1.7 1.8 1.6 1.6 1.6 1.6 1.7 1.5 1.5 1.5 1.5 1.6 1.3 1.3 1.4 1.4 1.4 25 26 27 28 29 30 31 32 33 34 3.0 3.1 3.2 3.4 3.5 3.7 3.9 4.1 4.3 4.6 2.8 2.9 3.0 3.1 3.2 2.6 2.7 2,8 2.9 3.0 2.5 2.5 2.6 2.7 2.8 2.3 2.4 2.4' 2.5 2.6 2.2 2.2 2.3 2.4 2.4 2.0 2.1 2.2 2.2 2.3 1.9 2.0 2.0 2.1 2.1 1.8 1.9 1.9 1.9 2.0 1.7 1.7 1.8 1.8 1.9 1.6 1.6 1.7 1.7 1.7 1.5 1.5 1.6 1.6 1.6 1.4 1.4 1.5 1.5 1.5 30 31 32 33 34 35 36 37 38 39 3.4 3.6 3.7 3.9 4.2 3.1 3.3 3.4 3.6 3.8 2.9 3.0 3.2 3.3 3.5 2.7 2.8 2.9 3.0 3.2 2.5 2.6 2.7 2.8 2.9 2.3 2.4 2.5 2.6 2.7 2.2 2.3 2.3 2.4 2.5 2.0 2.1 2.2 2.2 2.3 1.9 2.0 2.0 2.1 2.1 1.8 1.8 1.9 1.9 2.0 1.7 1.7 1.7 1.8 1.8 1.6 1.6 1.6 1.7 1.7 35 36 37 38 39 40 41 42 43 44 5.0 5.4 5.9 6.5 7.3 4.5 4.8 5.2 5.7 6.3 4.0 4.3 4.6 5.0 5.4 3.7 3.9 4.1 4.4 4.8 3.3 3.5 3.7 4.0 4.3 3.1 3.2 3.4 3.6 3.8 2.8 2.9 3.1 3.2 3.4 2.6 2.7 2.8 2.9 3.1 2.4 2.5 2.6 2.7 2.8 2.2 2.3 2.4 2.5 2.6 2.0 2.1 2.2 2.3 2.3 1.9 1.9 2.0 2.1 2.2 1.8 1.8 1.9 1.9 2.0 40 41 42 43 44 45 46 47 48 49 8.4 9.9 12.1 7.0 8.0 9.5 11.6 6.0 6.7 7.7 9.1 11.1 5.2 5.8 6.5 7.4 8.7 4.6 5.0 5.5 6.2 7.1 4.1 4.4 4.8 5.3 5.9 3.6 3.9 4.2 4.6 5.0 3.3 3.5 3.7 4.0 4.4 4.8 5.4 6.1 7.2 8.8 3.0 3.1 3.3 3.6 3.8 4.2 4.6 5.1 5.9 6.8 2.7 2.8 3.0 3.2 3.4 2.4 2.6 2.7 2.8 3.0 2.2 2.3 2.4 2.6 2.7 2.0 2.1 2.2 2.3 2.4 45 46 47 48 49 50 51 52 53 54 10.6 8.3 10.2 6.8 7.9 9.7 5.6 6.4 7.6 9.2 3.6 4.0 4.3 4.9 5.5 3.2 3.5 3.8 4.1 4.6 2.9 3.0 3.3 3.6 3.9 2.6 2.7 2.9 3.1 3.4 50 51 52 53 54 55 56 57 58 59 60 10.2 7.9 6.4 5.4 4.6 4.0 9.7 7.6 6.1 5.1 4.3 9.2 7.2 5.9 4.9 8.8 6.8 5.5 8.3 6.5 7.9 8.3 6.5 7.9 5.3 6.1 7.4 4.3 5.0 5.8 7.0 3.7 4.1 4.7 5.4 6.6 55 56 57 58 59 60 61° 62° 63° 54° 56° 66° 57° 58° 59° 1 60° 61° 62° 68° Declination of the same name as the latitude; upper transit; reduction additive. | '6583—06 35 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° 2° 3° 4° 5° 6° 7° 8° 9° 10° 11° O 1 2 3 4 u 28.1 It 28.1 22.4 28.1 22.4 18.7 II 28.1 22.4 18.7 16.0 H 28.1 22.4 18.7 16.0 14.0 II 22.4 18.7 16.0 14.0 12.5 II 18.7 16.0 14.0 12.5 11.2 II 16.0 14.0 12.5 11.2 10.2 II 14.0 12.4 11.2 10.2 9.3 II 12.4 11.2 10.2 9.3 8.6 8.0 7.5 7.0 6.6 6.2 u 11.1 10.1 9.3 8.6 8.0 7.4 7.0 6.6 6.2 5.9 II 10.1 9.3 8.6 8.0 7.4 o 1 2 3 4 5 6 7 8 9 22.4 18.7 16.0 14.0 12.4 18.7 16.0 14.0 12.4 11.2 16.0 14.0 12.4 11.2 10.2 14.0 12.5 11.2 10.2 9.3 12.5 11.2 10.2 9.3 8.6 11.2 10.2 9.3 8.6 8.0 10.2 9.3 8.6 8.0 7.5 9.3 8.6 8.0 7.5 7.0 8.6 8.0 7.5 7.0 6.6 7.0 6.6 6.2 5.9 5.6 5.3 5.1 4.8 4.6 4.4 5 6 7 8 9 10 11 12 13 14 11.1 10.1 9.2 8.5 7.9 10.1 9.3 8.5 7.9 7.4 9.3 8.6 7.9 7.4 6.9 8.6 8.0 7.4 6.9 6.5 8.0 7.4 7.0 6.5 6.2 7.4 7.0 6.5 6.2 5.8 7.0 6.6 6.2 5.8 5.5 6.6 6.2 6.9 5.6 5.3 6.2 5.9 5.6 5.3 5.0 5.9 5.6 5.3 5.0 4.8 5.6 5.3 5.0 4.8 4.6 10 11 12 13 14 15 16 17 18 19 7.3 6.8 6.4 6.0 5.7 6.9 6.5 6.1 5.7 5.4 6.5 6.1 5.8 5.5 5.2 6.1 5.8 5.5 5.2 4.9 5.8 5.5 5.2 5.0 4.7 5.5 5.2 5.0 4.8 4.5 5.3 5.0 4.8 4.6 4.4 5.0 4.8 4.6 4.4 4.2 4.8 4.6 4.4 4.2 4.0 4.6 4.4 4.2 4.1 3.9 4.4 4.2 4.1 3.9 3.8 4.2 4.1 3.9 3.8 3.6 15 16 17 18 19 20 21 22 23 24 5.4 5.1 4.9 4.6 4.4 5.1 4.9 4.7 4.4 4.2 4.9 4.7 4.5 4.3 4.1 4.7 4.5 4.3 4.1 3.9 4.5 4.3 4.1 4.0 3.8 4.3 4.2 4.0 3.8 3.7 4.2 4.0 3.9 3.7 3.6 4.0 3.9 3.7 3.6 3.5 3.3 3.2 3.1 3.0 2.9 3.9 3.7 8.6 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 20 21 22 23 24 25 26 27 28 29 4.2 4.0 3.9 3.7 3.5 4.1 3.9 3.7 3.6 3.4 3.9 3.8 3.6 3.5 3.3 3.8 3.6 3.5 3.4 3.2 3.7 3.5 3.4 3.3 3.1 3.5 3.4 3.3 3.2 3.1 3.0 2.9 2.8 2.7 2.6 3.4 3.3 3.2 3.1 3.0 3.2 3.1 3.0 2.9 2.8 3.1 3.0 2.9 2.8 2.8 3.1 3.0 2.9 2.8 2.7 3.0 2.9 2.8 2.7 2.6 25 26 27 28 29 30 31 32 33 34 3.4 3.3 3.2 3.0 2.9 3.3 3.2 3.1 2.9 2.8 3.2 3.1 3.0 2.9 2.8 3.1 3.0 2.9 2.8 2.7 3.0 2.9 2.8 2.7 2.6 2.9 2.8 2.7 2.6 2.5 2.4 2.4 2.3 2.2 2.1 2.8 2.7 2.6 2.5 2.5 2.7 2.6 2.6 2.5 2.4 2.7 2.6 2.5 2.4 2.4 2.6 2.5 2.5 2.4 2.3 2.5 2.5 2.4 2.3 2.3 30 31 32 33 34 35 36 37 38 39 2.8 2.7 2.6 2.5 2.4 2.7 2.6 2.5 2.5 2.4 2.7 2.6 2.5 2.4 2.3 2.6 2.5 2.4 2.4 2.3 2.5 2.5 2.4 2.3 2.2 2.5 2.4 2.3 2.3 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 2.2 2.1 2.0 2.0 1.9 1.9 1.8 1.7 2.2 2.2 2.1 2.1 2.0 1.9 1.9 1.8 1.8 1.7 2.2 2.1 2.1 2.0 2.0 35 36 37 38 39 40 41 42 43 44 2.3 2.3 2.2 2.1 2.0 2.0 1.9 1.8 1.8 1.7 1.6 1.6 1.5 1.5 1.4 2.3 2.2 2.1 2.1 2.0 2.2 2.2 2.1 2.0 2.0 2.2 2.1 2.1 2.0 1.9 2.2 2.1 2.0 2.0 1.9 2.1 2.1 2.0 1.9 1.9 2.1 2.0 2.0 1.9 1.8 2.0 2.0 1.9 1.9 1.8 2.0 1.9 1.9 1.8 1.8 1.9 1.8 1.8 1.7 1.7 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 1.9 1.9 1.8 1.7 1.7 1.9 1.8 1.8 1.7 1.7 1.9 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 1.8 1.7 1.7 1.6 1.6 1.7 1.7 1.6 1.6 1.5 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 45 46 47 48 49 50 51 52 53 54 1.6 1.6 1.5 1.5 1.4 1.6 1.6 1.5 1.4 1.4 1.6 1.5 1.5 1.4 1.4 1.6 1.5 1.5 1.4 1.4 1.5 1.5 1.4 1.4 1.3 1.5 1.5 1.4 1.4 1.3 1.5 1.5 1.4 1.4 1.3 1.5 1.4 1.4 1.3 1.3 1.3 1.2 1.2 1.1 1.1 1.0 1.5 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 55 56 57 58 59 60 1.4 1.3 1.3 1.2 1.2 1.1 1.4 1.3 1.3 1.2 1.2 1.1 1.3 1.3 1.3 1.2 1.2 1.1 1.3 1.3 1.2 1.2 1.2 1.1 1.3 1.3 1.2 1.2 1.1 1.1 1.3 1.3 1.2 1.2 1.1 1.1 1.3 1.2 1.2 1.2 1.1 1.1 1.3 1.2 1.2 1.1 1.1 1.1 1.2 1.2 1.2 1.1 1.1 1 1.2 1.2 1.1 1.1 1.1 1.0 1.2 1.2 1.1 1.1 1.1 1.0 55 56 57 58 59 60 0° 1° 2° 8° 4° 6° 6° 7° 8° 9° 10° 11° Declination of a different name from the latitude; upper transit; reduction addltlye. 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° 28° 24° o II II II II II • II II II II II II II o 9.2 8.5 7.9 7.3 6.8 6.4 6.0 5.7 5.4 5.1 4.9 4.6 4.4 1 8.5 7.9 7.4 6.9 6.5 6.1 5.7 5.4 5.1 4.9 4.7 4.4 4.2 1 2 7.9 7.4 6.9 6.5 6.1 5.8 5.5 5.2 4.9 4.7 4.5 4.3 4.1 2 3 7.4 6.9 6.5 6.1 5.8 5.5 5.2 4.9 4.7 4.5 4.3 4.1 3.9. 3 4 7.0 6.5 6.2 5.8 5.5 5.2 5.0 4.7 4.5 4.3 4.1 4.0 3.8 4 5 6.5 6.2 '5.8 5.5 5.2 5.0 4.8 4.5 4.3 4.2 4.0 3.8 3.7 5 6 6.2 5.8 5.5 5.3 5.0 4.8 4.6 4.4 4.2 4.0 3.9 .S.7 3.6 6 7 5.9 5.6 5.3 5.0 4.8 4.6 4.4 4.2 4.0 3.9 3.7 3.6 3.5 7 8 5.6 5.3 5.0 4.8 4.6 4.4 4.2 4.0 3.9 3.7 3.6 3.5 3.4 8 9 5.3 5.0 4.8 4.6 4.4 4.2 4.1 3.9 3.8 3.6 3.5 3.4 3.3 9 10 5.0 4.8 4.6 4.4 4.2 4.1 3.9 3.8 3.6 3.5 3.4 3.3 3.2 10 11 4.8 4.6 4.4 4.2 4.1 3.9 3.8 3.6 3.5 3.4 3.3 3.2 3.1 11 12 4.6 4.4 4.3 4.1 3.9 3.8 3.7 3.5 3.4 3.3 3.2 3.1 3.0 12 13 4.4 4.3 4.1 3.9 3.8 3.7 3.5 3.4 3.3 3.2 3.1 3.0 2.9 13 14 4.2 4.1 3.9 3.8 3.7 3.5 3.4 3.3 3.2 3.1 3.0 2.9 2.8 14 15 4.1 3.9 3.8 3.7 3.5 3.4 3.3 3.2 3.1 3.0 2.9 2.8 2.8 15 16 3.9 3.8 3.7 3.5 3.4 3.3 3.2 3.1 3.0 2.9 2.8 2.8 2.7 16 17 3.8 3.7 3.5 3.4 3.3 3.2 3.1 3.0 2.9 2.8 2.8 2.7 2.6 17 18 3.7 3.5 3.4 3.3 3.2 3.1 3.0 2.9 2.9 2.8 2.7 2.6 2.5 18 19 3.5 3.4 3.3 3.2 3.1 3.0 2.9 2.9 2.8 2.7 2.6 2.6 2.5 19 20 3.4 3.3 3.2 3.1 3.0 2.9 2.9 2.8 2.7 2.6 2.6 2.5 2.4 20 21 3.3 3.2 3.1 3.0 2.9 2.8 2.8 2.7 2.6 2.6 2.5 2.4 2.4 21 22 3.2 3.1 3.0 2.9 2.8 2.8 2.7 2.6 2.6 2.5 2.4 2.4 2.3 22 23 3.1 3.0 2.9 2.8 2.8 2.7 2.6 2.6 2.5 2.4 2.4 2.3 2.3 23 24 3.0 2.9 2.8 2.8 2.7 2.6 2.5 2.5 2.4 2.4 2.3 2.3 2.2 24 25 2.9 2.8 2.7 2.7 2.6 2.5 2.5 2.4 2.4 2.3 2.3 2.2 2.2 25 26 2.8 2.7 2.7 2.6 2.5 2.5 2.4 2.4 2.3 2.3 2.2 2.1 2.1 26 27 2.7 2.7 2.6 2.5 2.5 2.4 2.4 2.3 2.2 2.2 2.1 2.1 2.1 27 28 2.6 2.6 2.5 2.5 2.4 2.3 2.3 2.2 2.2 2.1 2.1 2.1 2.0 28 29 2.6 2.5 2.4 2.4 2.3 2.3 2.2 2.2 2.1 2.1 2.0 2.0 2.0 29 30 2.5 2.4 2.4 2.3 2.3 2.2 2.2 2.1 2.1 2.0 2.0 2.0 1.9 30 31 2.4 2.4 2.3 2.3 2.2 2.2 2.1 2.1 2.0 2.0 2.0 1.9 1.9 31 32 2.3 2.3 2.2 2.2 2.2 2.1 2.1 2.0 2.0 1.9 1.9 1.9 1.8 32 33 2.3 2.2 2.2 2.1 2.1 2.1 2.0 2.0 1.9 1.9 1.9 1.8 1.8 33 34 2.2 2.2 2.1 2.1 2.0 2.0 2.0 1.9 1.9 1.9 1.8 1.8 1.8 34 35 2.2 2.1 2.1 2.0 2.0 2.0 1.9 1.9 1.8 1.8 1.8 1.7 1.7 35 36 2.1 2.1 2.0 2.0 1.9 1.9 1.9 1.8 1.8 1.8 1.7 1.7 1.7 36 37 2.0 2.0 2.0 1.9 1.9 1.9 1.8 1.8 1.8 1.7 1.7 1.7 1.6 37 38 2.0 1.9 1.9 1.9 1.8 1.8 1.8 1.8 1.7 1.7 1.7 1.6 1.6 38 39 1.9 1.9 1.9 1:8 1.8 1.8 1.7 1.7 1.7 1.6 1.6 1.6 1.6 39 40 1.9 1.8 1.8 1.8 1.7 1.7 1.7 1.7 1.6 1.6 1.6 1.6 1.5 40 41 1.8 1.8 1.8 1.7 1.7 1.7 1.6 1.6 1.6 1.6 1.5 1.5 1.5 41 42 1.8 1.7 1.7 1.7 1.7 1.6 1.6 1.6 1.6 1.5 1.5 1.5 1.5 42 43 1.7 1.7 1.7 1.6 1.6 1.6 1.6 1.5 1.5 1.5 1.5 1.4 1.4 43 44 1.7 1.6 1.6 1.6 1.6 1.5 1.5 1.5 1.5 1.5 1.4 1.4 1.4 44 45 1.6 1.6 1.6 1.5 1.5 1.5 1.5 1.5 1.4 1.4 1.4 1.4 1.4 45" 46 1.6 1.6 1.5 1.5 1.5 1.5 1.4 1.4 1.4 1.4 1.4 1.3 1.3 46 47 1.5 1.5 1.5 1.5 1.4 1.4 1.4 1.4 1.4 1.3 1.3 1.3 1.3 47 48 1.5 1.5 1.4 1.4 1.4 1.4 1.4 1.4 1.3 1.3 1.3 1.3 1.3 48 49 1.4 1.4 1.4 1.4 1.4 1.3 1.3 1.3 1.3 1.3 1.3 1.2 1.2 49 50 1.4 1.4 1.4 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.2 1.2 1.2 50 51 1.4 1.3 1.3 1.3 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.2 1.2 51 52 1.3 1.3 1.3 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.2 1.1 1.1 52 53 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.1 1.1 1.1 53 54 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.1 1.1 1.1 1.1 1.1 1.1 54 55 1.2 1.2 1.2 1.2 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 55 56 1.2 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.0 1.0 1.0 56 57 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.0 1.0 1.0 1.0 1.0 1.0 57 58 1.1 1.1 1.1 1.1 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 58 59 1.1 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.9 0.9 59 60 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.9 0.9 0.9 0.9 0.9 0.9 60 12° 18° 14° 16° 16° 17° 18° 19° 20° 21° 22° 28° 24° Dec! ination of a dlff« rent nai ne from the latit ude; up per tran sit; redu ction ad ditire. Page 548] TABLE 26. Variation of Altitude in one minute from meridian passage. Declination of a different name from the latitude; upper transit; reduction additive. tude. Lati- tude. 26° 26° 27° 28° 29° 30° 31° 82° 83° 34° 35° 36° 37° o II // II II II II II n II II II II II o 4.2 4.0 3.9 3.7 3.5 3.4 3.3 3.1 3.0 2.9 2.8 2.7 2.6 1 4.1 3.9 3.7 3.6 3.4 3.3 3.2 3.1 2.9 2.8 2.7 2.6 2.6 1 2 3.9 3.8 3.6 3.5 3.3 3.2 3.1 3.0 2.9 2.8 2.7 2.6 2.5 2 3 3.8 3.6 3.5 3.4 3.2 3.1 3.0 2.9 2.8 2.7 2.6 2.5 2.4 3 4 3.7 3.6 3.5 3.4 3.4 3.3 3.2 3.0 2.9 2.8 2.7 2.6 2.6 2.5 2.4 4 5 3.3 3.2 3.1 3.0 2.9 2.8 2.7 2.6 2.5 2.4 2.3 5 6 3.4 3.3 3.2 3.1 3.0 2.9 2.8 2.7 2.6 2.5 2.4 2.4 2.3 6 7 3.3 3.2 3.1 3.0 2.9 2.8 2.7 2.6 2.5 2.5 2.4 2.3 2.2 7 8 3.2 3.1 3.0 2.9 2.8 2.7 2.7 2.6 2.5 2.4 2.3 2.3 2.2 8 9 10 3.1 3.0 2.9 2.9 2.8 2.7 2.6 2.5 2.4 2.4 2.3 2.2 2.2 9 3.1 3.0 2.9 2.8 2.7 2.6 2.5 2.5 2.4 2.3 2.2 2.2 2.1 10 11 3.0 2.9 2.8 2.7 2.6 2.5 2.5 2.4 2.3 2.3 2.2 2.1 2.1 11 12 2.9 2.8 2.7 2.6 2.6 2.5 2.4 2.3 2.3 2.2 2.2 2.1 2.0 12 13 2.8 2.7 2.7 2.6 2.5 2.4 2.4 2.3 2.2 2.2 2.1 2.1 2.0 13 14 2.7 2.7 2.6 2.5 2.4 2.4 2.3 2.3 2.2 2.1 2.1 2.0 2.0 14 15 2.7 2.6 2.5 2.5 2.4 2.3 2.3 2.2 2.1 2.1 2.0 2.0 1.9 15 16 2.6 2.5 2.5 2.4 2.3 2.3 2.2 2.2 2.1 2.0 2.0 1.9 1.9 16 17 2.5 2.5 2.4 2.3 2.3 2.2 2.2 2.1 2.1 2.0 2.0 1.9 1.9 17 18 2.5 2.4 2.4 2.3 2.2 2.2 2.1 2.1 2.0 2.0 1.9 1.9 1.8 18 19 20 2.4 2.4 2.3 2.2 2.2 2.1 2.1 2.0 2.0 1.9 1.9 1.8 1.8 19 2.4 2.3 2.3 2.2 2.1 2.1 2.0 2.0 1.9 1.9 1.9 1.8 1.8 20 21 2.3 2.3 2.2 2.1 2.1 2.0 2.0 2.0 1.9 1.9 1.8 1.8 1.7 21 22 2.3 2.2 2.2 2.1 2.1 2.0 2.0 1.9 1.9 1.8 1.8 1.7 1.7 22 23. 2.2 2.2 2.1 2.1 2.0 2.0 1.9 1.9 1.8 1.8 1.8 1.7 1.7 23 24 2.2 2.1 2.1 2.0 2.0 1.9 1.9 1.8 1.8 1.8 1.7 1.7 1.6 24 25 2.1 2.1 2.0 2.0 1.9 1.9 1.8 1.8 1.8 1.7 1.7 1.6 1.6 25 26 2.1 2.0 2.0 1.9 1.9 1.9 1.8 1.8 1.7 1.7 1.7 1.6 1.6 26 27 2.0 2.0 1.9 1.9 1.9 1.8 1.8 1.7 1.7 1.7 1.6 1.6 1.6 27 28 2.0 1.9 1.9 1.9 1.8 1.8 1.7 1.7 1.7 1.6. 1.6 1.6 1.5 28 29 1.9 1.9 1.9 1.8 1.8 1.7 "1.7 1.7 1.6 1.6 1.6 1.5 1.5 29 30 1.9 1.8 1.8 1.8 1.7 1.7 1.7 1.6 1.6 1.6 1.5 1.5 1.5 30 31 1.8 1.8 1.8 1.7 1.7 1.7 1.6 1.6 1.6 1.5 1.5 1.5 1.5 31 32 1.8 1.8 1.7 1.7 1.7 1.6 1.6 1.6 1.5 1.5 1.5 1.5 1.4 32 33 1.8 1.7 1.7 1.7 1.6 1.6 1.6 1.5 1.5 1.5 1.5 1.4 1.4 33 34 1.7 1.7 1.7 1.6 1.6 1.6 1.5 1.5 1.5 1.5 1.4 1.4 1.4 34 35 1.7 1.7 1.6 1.6 1.6 1.5 1.5 1.5 1.5 1.4 1.4 1.4 1.4 35 36 1.6 1.6 1.6 1.6 1.5 1.5 1.5 1.5 1.4 1.4 1.4 1.4 1.3 36 37 1.6 1.6 1.6 1.5 1.5 1.5 1.5 1.4 1.4 1.4 1.4 1.3 1.3 37 38 1.6 1.5 1.5 1.5 1.5 1.5 1.4 1.4 1.4 1.4 1.3 1.3 1.3 38 39 1.5 1.5 1.5 1.5 1.4 1.4 1.4 1.4 1.4 1.3 1.3 1.3 1.3 39 40 1.5 1.5 1.5 1.4 1.4 1.4 1.4 1.3 1.3 1.3 1.3 1.3 1.2 40 41 1.5 1.4 1.4 1.4 1.4 1.4 1.3 1.3 1.3 1.3 1.3 1.2 1.2 41 42 1.4 1.4 1.4 1.4 1.4 1.3 1.3 1.3 1.3 1.2 1.2 1.2 1.2 42 43 1.4 1..4 1.4 1.3 1.3 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.2 43 44 1.4 1.4 1.3 1.3 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.2 1.2 44 45 1.3 1.3 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.2 1.2 1.1 1.1 45 46 1.3 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.2 1.2 1.1 1.1 1.1 46 47 1.3 1.3 1.2 1.2 1.2 1.2 1.2 1.2 1.1 1.1 1.1 1.1 1.1 47 48 1.2 1.2 1.2 1.2 1.2 1.2 1.1 1.1 1.1 1.1 1.1 1.1 48 49 1.2 1.2 1.2 1.2 1.2 1.1 1.1 1.1 1.1 1.1 1.1 49 50 1.2 1.2 1.2 1.1 1.1 1.1 1.1 1.1 1.1 1.1 50 51 1.2 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.0 51 52 1.1 1.1 1.1 1.1 1.1 1.1 1.0 1.0 52 53 1.1 1.1 1.1 1.1 1.0 1.0 1.0 53 54 1.1 1.0 1.0 1.0 1.0 1.0 54 55 1.0 1.0 1.0 1.0 1.0 55 56 1.0 1.0 1.0 1.0 56 57 1.0 1.0 1.0 57 58 59 60 1.0 0.9 0.9 58 59 60 0.8 0.8 0.8 26° 26° 27° 28° 29° 80° 81° 82° 83° 84° 85° 36° 87° Decl ination of the sj ime nam e as the latltudt i; lower transit; reductic >n subtri ictlre. TABLE 26. [Page 549 | Variation of Altitude in one minute from meridian passt^e. Lati- tude. Declination of a different name from the latitude; upper transit; reduction additive. Lati- tude. 38° 39° 40° 41° 42° 43° 44° 46° 46° 47° 48° 49° 60° o II // II II II II 11 II II II II II II 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 2.3 2.2 2.1 2.1 2.0 1.9 1.9 1.8 1.8 1.7 1.6 1.6 1.5 5 6 2.2 2.2 2.1 2.0 2.0 1.9 1.8 1.8 1.7 1.7 1.6 1.6 1.5 6 7 2.2 2.1 2.0 2.0 1.9 1.9 1.8 1.8 1.7 1.6 1.6 1.5 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 •i.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 1.6 1.5 1.5 1.4 1.4 1.4 1.3 1.3 1.3 1.2 22 23 1.6 1.6 1.6 1.5 1.5 1.4 1.4 1.4 1.3 1.3 1.3 1.3 1.2 23 24 1.6 1.6 1.5 1.5 1.5 1.4 1.4 1.4 1.3 1.3 1.3 1.2 1.2 24 25 1.6 1.5 1.5 1.5 1.4 1.4 1.4 1.3 1.3 1.3 1.2 1.2 1.2 25 26 1.6 1.5 1.5 1.5 1.4 1.4 1.4 1.3 1.3 1.3 1.2 1.2 1.2 26 27 1.5 1.5 1.5 1.4 1.4 1.4 1.3 1.3 1.3 1.2 1.2 1.2 1.2 27 28 1.5 1.5 1.4 1.4 1.4 1.3 1.3 1.3 1.3 1.2 1.2 1.2 1.1 28 29 1.5 1.4 1.4 1.4 1.4 1.3 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 45 46 47 48 1.1 1.1 1.1 0.9 0.9 0.9 6.9 0.9 0.9 49 0.9 0.9 0.9 0.8 49 50 51 52 53 54 0.9 0.9 0.9 0.8 0.8 0.9 0.9 0.8 0.8 0.8 0.9 0.8 0.8 0.8 0.8 0.8 0.8 0.7 0.7 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 50 51 52 53 54 0.9 0.9 0.8 0.8 0.9 0.9 0.8 0.9 0.9 0.9 55 56 57 58 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 0.7 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° 39° 40° 41° 42° 48° 44° 4»° 4«° 47° 48° 49° 60° Dec] ination of the St ime nam e as the latitude ; lowerl ransit; ] reductio Q snbtra ctiye. Pag e560] TABLE 26. Variation of Altitude in one minute from meridian passage. Declination of a different name from the latitude; upper transit; reduction addltire. Lati- tude. Lati- tude. 61° 52° 58° 54° 56° 66° 67° 58° 69° 60° 61° 62° 63° o It II II II II II II „ II II II II II o 1.6 1.5 1.5 1.4 1.4 1.3 1.3 1.2 1.2 1.1 1.1 1.0 1.0 1 1.6 1.5 1.5 1.4 1.4 1.3 1.3 1.2 1.2 1.1 1.1 1.0 1.0 1 2 1.5 1.5 1.4 1.4 1.3 1.3 1.3 1.2 1.2 1.1 1.1 1.0 1.0 2 3 1.5 1.5 1.4 1.4 1.3 1.3 1.2 1.2 1.1 1.1 1.1 1.0 1.0 3 4 1.5 1.5 1.4 1.4 1.3 1.3 1.2 1.2 1.1 1.1 1.1 1.0 1.0 4 5 1.5 1.4 1.4 1.3 1.3 1.3 1.2 1.2 1.1 1.1 1.0 1.0 1.0 5 6 1.5 1.4 1.4 1.3 1.3 1.2 1.2 1.2 1.1 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 L2 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 30" 1.1 1.1 1.0 1.0 1.0 29 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 0.9 0.8 0.8 0.8 0.9 0.9 0.8 0.9 0.9 0.9 45 • 0.9 0.9 0.8 0.8 0.8 0.8 0.8 0.8 0.7 0.7 0.7 0.7 0.7 45 46 0.9 0.9 0.8 0.8 0.8 0.8 0.8 0.8 0.7 0.7 0.7 0.7 0.7 46 47 0.9 0.8 0.8 0.8 0.8 0.8 0.8 0.7 0.7 0.7 0.7 0.7 0.6 47 48 0.8 0.8 0.8 0.8 0.8 0.8 0.7 0.7 0.7 0.7 0.7 0.7 0.6 48 49 0.8 0.8 0.8 0.8 0.8 0.7 0.7 0.7 0.7 0.7 0.7 0.6 0.6 49 50 0.8 0.8 0.8 0.8 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.6 0.6 50 51 0.8 0.8 0.8 0.8 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.6 0.6 51 52 0.8 0.8 0.8 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.6 0.6 0.6 52 53 0.8 0.8 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.6 0.6 0.6 0.6 53 54 0.8 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.6 0.6 0.6 0.6 0.6 54 55 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.6 0.6 0.6 0.6 0.6 55 56 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.6 0.6 0.6 0.6 0.6 0.6 56 57 0.7 0.7 0.7 0.7 0.7 0.7 0.6 0.6 0.6 0.6 0.6 0.6 0.6 57 - 58 0.7 0.7 0.7 0.7 0.7 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 58 59 0.7 0.7 0.7 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.5 59 60 0.7 0.7 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.5 60 61° 52° 58° 54° 55° 66° 57° 58° 59° 60° 61° 62° 63° D eclinatic n of the same ne ime as tl le latitu de; lowe r transit ; redact ion subt ractlre. TABLE 27. [Page 551 Reduction to be applied to Altitudes near the Meridian. Var. Imin. (Table Time from meridian passage. 1 Var. m. 8. m. 8. m. 8. m. 8. TO. 8. m. 8. TO. 8. m. s. TO. 8. TO. 8. TO. 8. TO. 8. TO. 8. (Table 26.) 30 1 1 30 2 2 80 3 8 80 4 4 30 5 5 30 6 6 80 26.) II / // f II / II 1 II / // t n 1 II / // / II / II 1 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 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 41 2 5 2 31 3 3 31 5.0 6.0 1 6 13 24 37 54 1 13 1 36 2 1 2 30 3 1 3 36 4 13 6.0 7.0 2 7 16 28 44 1 3 1 26 1 52 2 22 2 55 3 32 4 12 4 56 7.0 8.0 2 8 18 32 50 1 12 1 38 2 8 2 42 3 20 4 2 4 48 5 38 8.0 9.0 2 9 20 36 56 1 21 1 50 2 24 3 2 3 45 4 32 5 24 6 20 9.0 10.0 2 10 22 40 44 1 2 1 30 2 3 2 15 2 40 3 23 4 10 5 2 6 7 2 10.0 11.0 3 11 25 1 9 1 39 2 56 3 43 4 35 5 32 6 36 7 45 11.0 12.0 3 12 27 48 1 15 1 48 2 27 3 12 4 3 5 6 3 7 12 8 27 12.0 13.0 3 13 29 52 1 21 1 57 2 39 3 28 4 23 5 25 6 33 7 48 9 9 13.0 14.0 3 14 31 56 1 27 2 6 2 51 3 44 4 43 5 50 7 4 8 24 9 51 14.0 15.0 4 15 34 1 1 34 2 15 3 4 4 5 3 6 15 7 34 9 10 34 15.0 16.0 4 16 36 1 4 1 40 2 24 3 16 4 16 5 24 6 40 8 4 9 36 11 16 16.0 17.0 4 17 38 1 8 1 46 2 33 3 28 4 32 5 44 7 5 8 34 10 12 11 58 17.0 18.0 4 18 40 1 12 1 52 2 42 3 40 4 48 6 4 7 30 9 4 10 48 12 40 18.0 19.0 5 19 43 1 16 1 59 2 51 3 53 5 4 6 25 7 55 9 35 ,11 24 13 23 19.0 20.0 5 20 45 1 20 2 5 3 4 5 5 20 6 45 8 20 10 5 12 14 5 20.0 21.0 5 21 47 1 24 2 11 3 9 4 17 5 36 7 5 8 45 10 35 12 36 14 47 21.0 22.0 5 22 49 1 28 2 17 3 18 4 30 5 52 7 25 9 10 11 5 13 12 15 29 22.0 23.0 6 23 52 1 32 2 24 3 27 4 42 6 8 7 46 9 35 11 36 13 48 16 12 23.0 24.0 6 24 54 1 36 2 30 3 36 4 54 6 24 8 6 10 12 6 14 24 16 54 24.0 25.0 6 25 56 1 40 2 36 3 45 5 6 6 40 8 26 10 25 12 36 15 25.0 26.0 6 26 58 1 44 2 42 3 54 5 18 6 56 8 46 10 50 13 6 26.0 27.0 7 27 1 1 1 48 2 49 4 3 5 30 7 12 9 7 11 15 27.0 28.0 7 28 1 3 1 52 2 55 4 12 5 43 7 28 9 27 11 40 28.0 Page 552] TABLE 27. Eeduction to be applied to Altitudes near the Meridian, Var. 1 min. (Table 26.) Time from meridian passage. Var. Imin. (Table 26.) m. s. 7 m. s. 7 30 TO. «. 8 TO. S. 8 30 TO. s. 9 TO. S. 9 30 TO. S. 10 TO. S. 10 30 m. 8. 11 TO. S. 11 30 TO. S. 12 TO. S. 12 30 TO. H. 18 0.1 0.2 0.3 0.4 / // 5 10 15 20 6 11 17 23 1 ir 6 13 19 26 1 II 7 14 22 29 1 II 8 16 24 32 9 18 27 36 / II 10 20 30 40 1 II 11 22 33 44 12 24 36 48 1 II 13 26 40 53 » II 14 29 43 58 16 31 47 1 2 / II 17 34 51 1 8 fi 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 24 29 34 39 44 28 34 39 45 51 32 38 45 51 57 36 43 51 58 1 5 40 49 57 1 5 1 13 45 54 1 3 1 12 1 21 50 1 1 10 1 20 1 30 55 1 6 1 17 1 28 1 39 1 1 13 1 25 1 37 1 49 1 6 1 19 1 33 1 46 1 59 1 12 1 26 1 41 1 55 2 10 1 18 1 34 1 49 2 5 2 21 1 24 1 41 1 58 2 15 2 32 0.5 0.6 0.7 0.8 0.9 1.0 2.0 3.0 4.0 5.0 49 1 38 2 27 3 16 4 5 56 1 52 2 49 3 45 4 41 1 4 2 8 3 12 4 16 5 20 1 12 2 24 3 37 4 49 6 1 1 21 2 42 4 3 5 24 6 45 1 30 3 4 30 6 1 7 31 1 40 3 20 5 6 40 8 20 1 50 3 40 5 31 7 21 9 11 2 1 4 2 6 3 8 4 10 5 2 12 4 24 6 37 8 49 11 1 2 24 4 48 7 12 9 36 12 2 36 5 12 7 49 10 25 13 1 2 49 5 38 8 27 11 16 14 5 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 4 54 5 43 6 32 7 21 8 10 5 37 6 34 7 30 8 26 9 22 6 24 7 28 8 32 9 36 10 40 7 14 8 26 9 38 10 50 12 2 13 15 14 27 15 39 16 51 18 14 8 6 9 27 10 48 12 9 13 30 14 51 16 12 17 33 18 54 20 15 9 1 10 32 12 2 13 32 15 2 16 33 18 3 19 33 21 3 22 34 10 11 40 13 20 15 16 40 11 1 12 52 14 42 16 32 18 22 12 6 14 7 16 8 18 9 20 10 13 13 15 26 17 38 19 50 22 2 14 24 16 48 19 12 21 36 24 26 24 28 48 15 37 18 14 20 50 23 26 26 2 16 54 19 43 22 32 25 21 28 10 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 11.0 12.0 13.0 14.0 15.0 8 59 9 48 10 37 11 26 12 15 10 19 11 15 12 11 13 7 14 4 11 44 12 48 13 52 14 56 16 18 20 20 21 40 23 20 25 20 13 22 3 23 53 25 43 27 34 22 11 24 12 26 13 28 14 24 15 26 27 28 39 28 39 16.0 17.0 18.0 19.0 20.0 13 4 13 53 14 42 15 31 16 20 15 15 56 16 52 17 49 18 45 17 4 18 8 19 12 20 16 19 16 20 28 21 40 21 36 22 57 24 18 24 4 25 34 26 40 16.0 17.0 18.0 19.0 20.0 21.0 17 9 21.0 TABLE 27. [Page 553 Reduction to be applied to Altitudes near the Meridian Var. 1 min. (Table Time from meridian passage. 1 Var. 1 min. (Table m.. s. m. 8. m. 8. m. 8. m. 8. m. s. TO. 8. TO. 8. TO. 8. TO. 8. TO. 8. TO. 8. TO. 8. 26.) 13 30 14 14 30 15 15 80 16 16 30 17 17 30 IS 18 30 19 19 80 26.) ii 1 It / // ' II ' // ' // / // / II ' // 1 II e II / // / II 1 II // 0.1 018 20 21 22 24 26 27 029 31 32 34 36 38 0.1 0.2 36 39 42 45 48 51 54 58 1 1 1 5 1 8 112 116 0.2 0.3 55 59 1 3 1 7 112 117 122 127 132 137 143 148 154 0.3 0.4 113 1 18 124 130 136 142 149 156 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 4 314 3 25 3 37 3 48 0.6 0.7 2 8 217 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 5 419 4 34 4 49 5 4 0.8 0.9 244 2 56 3 9 3 22 3 36 3 50 4 5 4 20 4 36 4 52 5 8 5 25 5 42 0.9 1.0 3 2 3 16 3 30 3 45 4 4 16 4 32 4 49 5 6 5 24 5 42 6 1 6 20 1.0 2.0 6 4 6 32 7 7 30 8 8 32 9 4 9 38 1012 10 48 1124 1^ 2 12 40 2.0 3.0 9 7 9 48 10 30 11 15 12 1 12 48 13 38 14 27 1519 1612 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. Time from meridian passage. Var. Imiu. 1 min. 1 (Table m. s. m. 8. m. 8. m. 8. m. 8. TO. 8. TO. 8. TO. 8. TO. 8. m. s. TO. 8. TO. 8. TO. 8. (Table 26.) 20 20 30 21 21 30 22 22 30 23 23 30 24 24 30 25 25 30 26 26.) II 1 11 ' // / II ' // 1 II ' II 1 II 1 II / II ' II f II / II / // II 0.1 40 42 044 46 48 51 53 55 •0 58 1 1 2 1 6 1 8 0.1 0.2 1 20 124 128 132 137 141 146 150 155 2 2 5 210 2 15 0.2 0.3 2 2 6 2 12 2 19 2 25 2 32 2 39 2 46 2 53 3 3 7 3 15 3 23 0.3 0,4 2 40 2 48 2 56 3 5 314 3 22 3 32 3 41 3 50 4 410 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 4 517 5 31 5 46 6 615 6 30 6 46 0.6 0.7 4 40 454 5 9 5 24 5 39 5 54 610 6 27 6 43 7 717 7 35 7 53 0.7 0.8 5 20 5 36 5 53 610 6 27 6 45 7 3 7 22 7 41 8 8 20 8 40 9 1 0.8 0.9 6 618 6 37 6 56 716 7 36 7 56 817 8 38 9 9 22 9 45 10 8 0.9 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 1.0 2.0 13 20 14 14 42 15 24 16 8 16 52 17 38 18 24 1912 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— 1st correction. Argument, the star's hour angle (or 241"— the star's hour angle).] Oh -1 12 00.0 11 59.9 11 59.8 11 59.6 11 59.3 -1 11 58.9 11 58.6 11 68.0 11 57.4 11 56.7 10 11 12 13 14 15 16 17 18 19 1165. 1155. 1154. 1153. 1152. 1150. 1149. 1148. 1146. 1145. 20 21 22 23 24 25 26 27 28 29 -1 -1 1143. 1141. 1140. 1138. 1136. 1134. 1132. 1130. 1127, 1125, 3a 31 32 33 34 35 36 37 38 39 — 1 -1 1123, 1120, 1118, 11 15. 11 12. 1109. 1106, 1103, 1100, 10 57, 40 41 42 43 44 45 46 47 48 49 — 1 — 1 10 64 10 51, 10 47, 10 44, 10 40, 10 37, 10 33, 10 29, 10 26, 10 21, 60 51 52 63 64 66 56 57 68 69 60 10 17. 10 13. 10 09. 10 06. 10 00. 09 56. 09 51. 09 47. 09 42. 09 37. 09 32. li" -1 09 32. 09 27. 09 22. 09 17. 09 12. -1 09 07, 09 02, 08 66, 08 51, 08 46, -1 08 40. 08 34. 08 28. 08 22. 08 16. -1 08 10. 08 04. 07 68. 07 52. 07 46. -1 07 39. 07 33. 07 26. 07 19. 07 13. -1 07 06. 06 69. 06 52. 06 45. 06 38. llh -1 06 31. 06 24. 0616 06 09. 06 01. -1 05 64. 05 46. 05 38. 05 31. 06 23. -1 06 16, 05 07. 04 69. 04 51. 04 42. -1 04 34. 04 26. 04 17. 04 09. 04 00. -1 03 62, 03 43, 03 34. 03 25. 03 16. -1 03 07. 02 58. 02 49. 02 40. 02 30. -1 02 21. 4.9 5.0 5.0 5.2 5.3 5.3 5.4 6.4 5.5 5.6 5.8 6.8 5.9 5.9 6.0 6.1 6.2 6.2 6.3 6.4 6.5; 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, 7.7 7.8 7.8 8.0 8.0 8.0 8.2 8.2 8.3 8.4 8.4 8.5 8.6 8.7 8.7 8.8 8.9 9.0 9.0 9.0 9.2 9.2 9.4 9.4 IC -1 02 21. 02 11. 02 02. 0152. 0143. -1 01 33. 0123. 0113. 0103, 00 53, -1 00 43. 00 33. 00 23. 0012. 00 02. -0 69 62. 59 41. 69 31. 59 20. 59 09. -0 58 58, 58 48, 68 37, 68 26 58 15, -0 58 04, 57 52. 67 41, 57 30, 67 18, -0 67 07. 66 56. 56 44. 66 32. 56 21. -0 56 09. 65 67. 65 46. 66 33. 55 21. -0 65 09, 54 57, 54 45. 64 32. 64 20. -0 64 08, 53 55, 63 43, 53 30. 53 18. -0 63 05, 62 52, 52 39, 52 26 52 13, -0 52 00, 6147, 5134, 5121, 5108. -0 60 64. 9.5 9.5 9.6 9.7 9.7 9.8 9.9 10.0 10.0 10.1 10.2 10.2 10.3 10.3 10.5 10.5 10.6 10.6 10.7 10.8 10.9 10.9 10.9 11.1 11.1 11.2 11.2 11.3 11.4 -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 12.5 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 41.1 50 28.1 60 14. 50 01.: -0 49 47. 49 33. 49 20. 49 06. 48 52. 13.3 13.4 -0 48 38. 48 24. 48 10. 47 56. 47 42. -0 47 28. 47 14. 47 00. 46 46. 46 31. -0 46 17. 46 02, 46 48, 45 33, 45 18, -0 45 04, 44 49, 44 34, 44 19, 44 04, -0 43 60. 43 36. 43 20. 43 05. 42 49. -0 42 34. 42 19. 42 04. 4148. 4133. -0 41 18. 4102. 40 47. 40 31. 40 16. -0 40 00. 39 44. 39 28. 39 13. 38 67. Oh -0 38 41. 38 25. 38 09. 37 63. 37 37. -0 37 21. 37 05. 36 48. 36 32. 36 16. -0 36 00. 13.5 13.6 13.7 13.7 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 14.6 14.6 14.6 14.7 14.8 14.8 14.8 9 "•' ^14.9 ^'-^ ''■' ''•' 9 ^^-^ 7 15.2 ' 15.2 5 15.3 ^ 15.3 9 15.3 0-15.4 7 15.5 ' 15.5 15.6 16.6 15.7 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 16.3 4h -0 36 36 35 35 34 -0 34 34 34 33 33 00.0 43.7 27.3 10.9 64.5 38.1 21.6 05.0 48.4 31.7 -0 33 32 32 32 32 -0 31 31 31 31 30 15.0 58.2 41.4 24.6 07.8 60.9 34.0 27.1 10.1 53.0 -0 30 30 30 29 29 -0 29 28 28 28 27 36.0 18.9 01.7 44.6 17.3 00.1 42.8 26.5 08.2 50.8 -0 27 27 26 26 26 -0 26 25 25 25 24 33.4 16.0 58.6 41.0 23.5 05.9 48.3 30.7 13.1 55.4 8h -0 24 24 24 23 23 -0 23 22 22 22 21 -0 21 21 21 20 20 -0 20 19 19 19 18 -0 18 37.7 20.0 02.2 44.4 26.6 08.8 50.9 33,0 16.1 67.2 39.2 21.2 03.2 45.2 27.1 09.0 60.9 32.8 14.6 56.4 38.2 16.3 16.4 16.4 16.4 16.4 16.5 16.6 16.6 16.7 16.7 16.8 16.8 16.8 16.8 16.9 16.9 16.9 17.0 17.1 17.0 17.1 17.2 17.2 17.2 17.2 17.3 17.3 17.3 17.4 17.4 17.4 17.5 17.5 17.5 17.6 17.6 17.6 17.6 17.7 17.7 17.7 17.8 17.8 17.8 17.8 17.9 17.9 17.9 17.9 18.0 18.0 18.0 18.0 18.1 18.1 18.1 18.1 18.2 18.2 18.2 6>> -0 18 38.2 18 20.0 18 01.8 17 43.5 17 26.2 -0 17 06.9 16 48.6 16 30.3 16 11.9 16 63.5 -0 15 35.1 16 16.7 14 58.3 14 39.9 14 21.5 -0 14 03.0 13 44.5 13 26.0 13 07.5 12 48.9 -0 12 30.3 12 11.7 11 53.1 11 34.6 11 15.9 -0 10 57.2 10 38.6 10 20.0 10 01.4 09 42.7 -0 09 24.0 09 05.3 08 46.6 08 27.9 08 09.1 -0 07 50.4 07 31.7 07 12.9 06 64.1 06 35.3 7h -0 06 16.6 06 67.8 05 39.0 06 20.2 06 01.4 -0 04 42.6 04 23.8 04 05.0 03 46.2 03 27.4 -0 03 08.6 02 49.7 02 30.9 02 12.0 01 63.2 -0 01 34.4 01 16.5 00 56.7 00 37.8 00 18.9 -0 00 00.0 18.2 18.2 18.3 18.3 18.3 18.3 18.3 18.4 18.4 18.4- 18.4 18.4 18.4 18.4 18.6 18.5 18.6 18.5 18.6 18.6- 18.6 18.6 18.6 18.6 18.7, 18.6 18.6 18.6 18.7 18.7- 18.7 18.7 18.7 18.7 18.7 18.7 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 68 57 56 66 54 53 52 61 60 49 48 47 46 46 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 26 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 6 4 3 2 1 eh Change the sign to -t- when the argument is found at the bottom. TABLE 28B. [Page 566 For finding the Latitude of a place by Altitudes of Polaris. [B=the 2d correction. This correction is always additive.] star's Star's altitude. 1 Star's angle. 10° 16° 16° 17° 18° 19° 20° 21° 22° 28° hour angle. h. m. II II II // II II II II II // A. m. 00 0.0 0-0.0 0.0 .0 0.0.0 0.0 0.0.0 0.0 0.0 0.0 0.0 12 00 10 0.0" 0.0\ 0.0 1 0.0 1 0.0 1 0.0 1 0.0 -? 0.0 -? 0.0-° 0.0 •? 11 50 20 o.ii 0-1 a 0.1:1 o.i;; 0.1 -; 0.1-; 0.1 2 0.1 \ 0.1 "2 0.1 -9 0.3 "o 0.6-5 0.9 -; 1.3-' 40 30 0.2 , 0.2 , 0.2 2 0.2 2 0.2-2 0.2-3 0.3-0 0.3-2 0.3-' 0.6 -, 0.9 -, 1.6 -J 2.1-5 2.7- 3.2 •« 30 40 0.3'i 0.3-2 0.4-5 0.4-, 0.4-3 0.5 3 0.5-3 0.5 -, 20 50 0.4' 0.5-3 0.6 -, 0.6 -, 0.7-3 0.8-3 0.8 -, 0.8 •; 10 1 00 0.5'; 0.8- 0.9- 3 0.{ h 1.0- 1.4- 1-1 1-5-5 00 10 0.7-2 1.1- 1.2 - 1.5 1.3- 1-4 • 1-7- 2.2-5 2.8-5 3.4-5 4.0- 10 50 20 0.9-2 1.4-4 1.5 -" 1.6 -; 1.7-4 1-8-6 1.9 -J 2-0-5 2.5-5 3-1 1 3.7- 40 30 1.1 •- 1.7 -J 2.3-^ 2.6-, 2.9-^ 3.3-, 3.6-^ 4.0 -'^ 1.8- 2.2 -J 3.0 -* 1-8-5 2.0-4 2.1-5 2.3-5 2.4-5 2.9-5 3.5-5 4-1- 30 40 2.3-, 2.8 -J 2-4 1 2.6-5 3.1 1 4.2-^ 4.9 -fi 5.5 -J 6-1-6 6.7- 7.4-^ 2.8-5 3.3- 20 50 2.9-5 3.8-; 10 2 00 3- 2' 3.4- 3.9- 4-5-6 5.1- 5.8 -' 6.4- 7.1-; 00 10 3.5 -J 4.0 -J 5.0-^ 3.7-fi 4.3- 4.8-5 5.9-' 6.5- 7.0- 7.6-', 3.9-6 4.8-1 5.4- 6.1 •; 6.8-, 7-5-8 8.3-* 8.9-^ 9-6 -« 10.4-^ 5.0 -; 5.7-; 6-4-1 7.2- 7-9-8 8.7-^ 9.4-; 5.3 -J 6.0 ■« 6.3-5 7.1-5 9 50 20 4.5-f 5.1-' 5.7-6 40 30 6.8-; 30 40 7-5-8 7.9-5 8.7-5 20 50 5.5-^ 6.0-^ 6.3 -fi 6.9- 8-3 -« 10 3 00 9.1 -* 9.5-' 00 10 4.3-; 6.6 -J 7.5 -fi 8.1 -' 8.6-' 8.0 •« 8.4-; 9.1-; 9-8-1 9.9-^ 10.4 -J 8 50 20 4.7-^ 7.1 -J 8.6-' 10.2 -; 10.9-^ 10. 7 -J 11.3-5 12.1-5 40 30 5.0 -J 7.6 -J 9.2-; 11.5 -! 30 40 5.3, 8.1-5 8- 7-5 9.2 -J 9.2-' 9.8 •« 9.9-; 10.4"! 11.1 -; 11.0 -! 11. 6 -■; 12.2 •« 12.9-5 20 50 5.7-^ 8.6-5 10.5-^ 11.7 -! 12.3 -; 13.0-^ 13. 7-; 10 4 00 6.0-^ 9.1-^ 9.7-^ 10.4-^ 11.0-^ 11.7-^ 12.3-" 13.0 -J 13.0-^ 13.7 -^ 14.4-^ 00 10 6.3-; 9.6 ■;; 10.2-^ 10.9 •" 11.6-° 12.2-^ 13.6 -; 14-3 -« 15.0-^ 7 50 20 6.6-^ 10.0 -^ 10.7 , 11.3 •; 12.1 , 12.8-^ 13.6 -, 14.3 •: 14.9-^ 15-7 -! ^ 40 30 6.8-^ 10.4 •, 11.1 -J 11.7-1 12.5 -^ 13.3 -^ 14.0-^ 14.8 -f 15.6-1 16.3 -5 30 40 7.0 •; 10.8 -J 11.4! 12.1 -J 13.0-^ 13.8-^ 14.5 -^ 15.3-5 16.1 •! 16.9 -5 20 50 7.3-^ 11.1-^ 11. 8 -J 12.5 -J 13.4-^ 14.2 -J 15.0 -, 15.8 -^ 16.6-^ 17.5 -! 10 5 00 10 7.5-^ -776 -1 11.4-^ 11.6-^ 12.1 "^ 12.4-^ 12.9 •* 13.2-^ 13.7-^ 14.0-^ 14.5-^ 14.8-^ 15.4-^ 16.2-'' 16.5-^ 17.1-^ 17.4-^ 17.9-'' 18.3-^ 00 6 50 15.7-^ 20 7.8 -f 11.7 -l 12.6-^ 13.4-2 14.2-^ 15.1-0 16.0-^ 16.8-^ 17.7-^ 18.6-^ 40 30 7.9 -f, 11.9 •; 12. 7 -^ 13.6-^ 14.4 •„ 15.3 -„ 16.2-2 17.1 l 18.0 -f 18.9 t 30 40 7.9-^ 12.0 -j 12.9 •, 13.7 -^ 14.6-2 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 -i 16.5-^ 17.3-0 18.2-^ 19.1 -| 10 6 00 7.9-" 12.2 -^ 13.0 •" 13.9-^ 14.7-0 15.6-0 16.5-0 17.3-0 18.3-^ 19.2-1 6 00 TABI .E 28C. [ C=the 3d ( jorrection. 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" 30" 40" 60" 0" 10" 20" tt // II II II // II II II II // II II II 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 .0 0.0 0.0 10 +0.2 +0.1 +0.1 + 0.0 0.0 -0.0 -0.1 -0.1 -0.2 - -0.2 -0 .3 —0.4 -0.4 20 0.4 0.3 0.2 0.1 0.0 0.1 0.2 0.3 0.4 0.5 .6 O.V 0.8 30 0.6 0.5 0.3 0.1 0.0 0.1 0.3 0.5 0.6 0.7 .8 1.1 1.2 40 0.8 0.6 0.4 0.2 0.0 0.2 0.4 0.6 0.8 1.0 1 .2 1.5 1.6 50 +1.0 +0.7 +0.5 + 0.2 0.0 -0.2 -0.5 -0.9 -1.0 -1.2 — 1 .5 — l.V -2.1 Note,— Below 16° B is nearly proportional to the altitude. Page 556] TABLE 28B. For finding the Latitude of a place by Altitudes of Polaris. [B=the 2d correction. This correction is always additive.] Star's liour angle. Star's altitude. h. m. 00 10 20 30 40 50 1 00 10 20 30 40 50 2 00 0.0 0.0 0.1 0.3 0.6 1.0 1.4 1.8 2.3 2.9 3.6 4.3 5.0 5.8 , 6.6 • 7.5 • 8.3 • 9.2 ■: 10.0 •* 10.9 -J 11.8 ■: 12.6 * 13.5 • 14.3 * 15.1 * 15.9 16.6 17.2 17.8 18.3 18.8 19.2 19.5 19.8 20.0 20.1 20.2 20.1 20.5 20.7 20.9 21.0 21.1 30° 31° 0.0 0.0 0.2 0.5 0.8 1.3 1.8 21.4 22.4 23.2 24.0 24.6 25.3 25.8 26.2 26.6 26.9 27.0 27.1 0.0 0.0 0.2 0.5 0.8 1.3 1.9 2.5 3.3 4.1 5.0 6.0 7.0 8.2 9.3 10.4 11.6 12.9 14.1 15.4 16.6 17.8 19.0 20.1 21.2 22.3 23.2 24.1 24.9 25.7 26.4 27.0 27.4 27.8 28.0 28.2 28.3 S9'> 0.0 0.0 0.2 0.5 0.9 1.4 1.9 2.6 3.4 4.3 5.3 6.2 7.3 8.5 9.6 10.8 12.0 13.3 14.6 16.0 17.3 18.5 19.7 20.9 22.0 23.1 24.1 25.1 25.9 26.7 27.4 28.0 28.5 28.8 29.1 29.3 29.4 Star's hour angle. h. m. 12 00 11 50 40 30 20 10 00 10 50 40 30 20 10 00 9 50 40 30 20 10 00^ 8 50 40 30 20 10 00 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., B=the 2d correction.] 88° 47' 80" 10 20 30 40 50 0.0 +0.2 0.4 0.6 0.8 +1.0 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 50" 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 0.0 10" 0.0 -0.0 0.1 0.1 0.2 -0.2 20" 0.0 -0.1 0.2 0.3 0.4 -0.5 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 88^ 49' 0" 0.0 -0.3 0.6 0.8 1.2 -1.5 10" 20" 0.0 -0.4 0.7 1.1 1.5 -1.7 0.0 -0.4 0.8 1.2 1.6 -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 TABLE 28C. [C = the 3d correction. Hor. Arg., the star's declination. Vert. Arg., B = the 2d correction.] 10 20 30 40 50 20" 0.0 +0.2 0.4 0.6 0.-8 +1.0 88° 47' 30" 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 0.0 10" 0.0 -0.0 0.1 0.1 0.2 -0.2 20' 0.0 -0.1 0.2 0.3 0.4 -0.5 30" 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 iO" 0.0 -0.2 0.5 0.7 1.0 -1.2 88° 49' 0.0 -0.3 0.6 0.8 1.2 -1.5 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 angle. star's altitude. 1 Star's hour angle. 44° 45° 46° 47° 48° 49° 50° 51° 52° h. m. /' // „ II „ „ II II II h. in. 00 0.0 1 0.0 , 0.0 1 0.0 , 0.0 1 0.0 1 0.0 , 0.0 1 0.0 1 12 00 10 0.1 • 0.1 "2 0.1 \ 0.1 2 0.1 \ 0.1 'o 0.1 0.1 -3 0.4 -l 1.0- 1.7 •• 2- 611 ^•7 0.1 '3 11 50 20 0.3 4 0.3 \ 0.3 -5 0.3 -5 0.4 \ 0.4 'l 0.4 % 0.4 \ 40 30 0.7 • 0.7 -^ 0.8 i 0.8 7 0.9 % 0.9 -7 0.9 -l 1.6 9 2-5i-i 1.0 \ 30 40 1.3 •' 1.4 •; 1-4 8 1.5 -g 1.5 Z 2-3i1 3.4 • 1.6 •' 2.4i- 3.5 •; 1.8i'o 20 50 1 00 2.0 9 2.9; 4.0 • 5-1 13 9.3;-" 10.9^' 2-1 9 3.0; 4-1 12 6.6 -^ 9.6 •; 11.3 2 *> 12^-'^ 2.3 9 3-2;! 2.8 • 3.9 • 10 00 10 20 30 40 50 2 00 4-2;-3 5.5 • 6- 9" 8.3;-^ 10.0 •; 4 4 5 7'-' 7-i;-: 8.7 10- 4 is 12.2^-^ 4.5 5-9i5 7.4!'fi 9.0 • 10.7J-; 12.6: 14.5 2.0 4-7 •; 7.6 • 9.3,8 11.1 • 13. 0„^ 4.9 • 6.3,1 7.9- 9.6-^9 11-52:0 13. 5''" 5.o!-J 6.6!-^ 8.2 • 10-0-9 11-92 13.9^° 6.8}:; .18 10. 3 20 12. 3 22 14. 5 2.2 16-7 23 19-0 25 21-5 24 23. 9 \\ 26-4 25 28. 9 ^-^ 10 50 40 30 20 10 00 10 12.61.7 13-0 1.9 13. 5 1:9 14.0 2.0 15.0 2*1 15.62J 16.1 2.3 9 50 20 14.3t, 14. 9 1.9 15- 4 1.9 16.0 2.0 16. 5 2 1 17.1 2.2 17.7 2.3 18.4 2.3 40 30 16- 2 1.9 16. 8 1.9 17.3 2.1 18.0 2.0 18.62-, ly. Ooo 20. 2 3 20. 7 2 4 30 40 18-1 1.8 18.7 2.0 19.4 2.0 20. 21 20. 7 22 Z\* Ooo 22. 3 2 3 23. 1 2 4 20 50 19. 9 20 20. 7 1.9 21-4 2.0 22.12:1 22. 9 22 23. 7 2.3 24.624 25. 5 24 10 3 00 21. 9 f: 22.6„„ 23. 4„" 24.2„„ 25. 1 „ „ 26.0,^ 27. ,' 27.9„' 00 3175 Y^ 34-0 25 36.5^-; 10 23.7 •, 24.62.0 25.4 2.1 26.4 2.1 27. 3 "■; Zo, «^ 2 2 zy. 2 A 30.42 4 8 50 20 25.6^, 26.61.9 27-5 2.0 28. 5 20 29. 5 2', 30. 5 2 2 31. 7 2 2 oZ, 2 4 40 30 27. b,. 28. 5 1 9 29. 5 1 9 30. 5 2 1 31.621 OiU. '00 00, y ^ 35. 2 2 3 30 40 29.3, « 30. 4 lis 31. 4 1:9 32.61:9 33. 7 2.0 34. 9 21 36.2 21 37. 5 2.3 38. 9 \\ 20 50 31-iifi 32. 2 , 7 33. 3 19 34. 5 1.9 35. 7 2.0 37.0 2.0 Ou. I oy. 021 41. 2 43: 4 2-^ 10 4 00 32. 7 33.9," 35. 2 , ^ 36.4,' 37. 7 , „ 39. „ „ 40. 4 „\ 41. 9 „■, 00 10 34.3|-J 35. 6 lie 36. 9 1:6 38.2 • 39. 5 18 41.0 1.8 42. 5 1.8 44.0 1.9 45-5 2; 47.5 f; 49.4 -^ 51. 1 ;•! 52.7 • 54. ^-^ 7 50 20 35. 9 1 4 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 1:3 38. 613 40.0 1.4 41- 4 1.4 42.81.6 44. 4 1.5 46.0 1.6 47. 7 1.6 30 40 38. 610 39. 9 12 41. 4 1.2 42-81.3 44. 4 1.3 45. 9 1.4 47.61.4 !H-^i-5 20 50 39.8 41.1 1.1 42-61.1 44.1 1.2 45. 7 1.2 47- 3 1.3 49.0 1.3 50.81.3 10 5 00 40.7 ■„ 42. 2 „ 43. 7 „ 45. 3 'I 46. 9 , „ 48. 6, V 50. 3 , ^ 52. 1 , , 00 10 41.6 -g 43.1 -g 44.6 8 46.3 \ 47.9'° 49.7 8 51.5 9 53. 2 10 55.2 1-2 6 50 20 42.4 ■, 43.9 6 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 4 44.5 4 46.1 • 47.7 • 49.4 -5 51.2 "5 53.1 5 54.9 -6 56.9 'l 30 40 43.3 'o 44.9 2 46.5 \ 48.1 3 49.9 \ 51.7 2 53.6 55.5 \ 57.5 \ 20 50 43.6 i 45.1 '0 46.7 \ 48.4 1 50.1 1 51.9 \ 53.9 1 55.7 \ 57.8 'l 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 001 •rection. Hor. Arg., the star's decli nation. Vert. Arg., B=t he 2d correc jtion.] B. 88° 47' 88° 48' 88° 49' 20" 30" 40" 60" 0" 10" 20" 30" 40" 60" 0" 10" 20" // // „ II It // II II II II „ // II II 30 +0.6 +0.5 fO.3 +0.1 0.0 -0.1 — 0.8 -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 ).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 fO.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 of Polaris. [B=the 2d correction. This correction Is always additive.] star's hour angle. Star's altitude. 1 Star's hour angle. 63° 64° 65° 56° 57° 58° 69° 60° h. m. 00 o"oo.i aoo.i o'oo.i aoo.2 1 II 0.0 0.2 / II O.O02 O.O02 O.Ooo 0-6 0.7 h. m. 12 00 10 nb-' n Jo-4 l04 ^•^.3 0.2 0.3 0.2o4 0.60.7 2:2?-: 3.5;-^ 11 50 20 30 40 50 0.50.5 {•0 0.8 2' 8'-" 7 ^ 1-2 0.5 0.5 1 1 •3 5 0.6 I0.8 0^' "j.3 0.5 0.6 2:J- 3.1-; 0.5 0.7 3.2;j ?1- 2:2;° 3-4 15 40 30 20 10 1 00 4.0 1.4 1.6 1.8 1.9 1 ^•2l4 5.6,, 7-3i8 11.1 -J 4 3 1.5 1.7 2.0 2.0 7 q 4-5 4.7 1.6 1.9 2.0 2.3 4.9 ! 5.0 .8 .0 .2 .4 00 10 20 30 40 5.4 7.0 8.8 10.7 5 7 9 11 8 5 5 5 6.1 ■' 7-9 • 11. 9 ^J 6.3 8.2 10.2 12.5 6.61; 8.4 • 10.624 13.02 5 15. 5, « 6.8^ 8.82 11.0^ 13.4' 11-5 25 14.0^-J 10 50 40 30 20 50 12.8~; 13.32 3 15.6^-^ 13 8 OQ 14.32 5 16.8^-^ 14. 8 :•: 16. Oj-" 16. 7 '-^ 10 2 00 15.0 2.3 9.4 16 1 2.5 ?7 17.4 2.7 9 S 18. l'-^ 18.8^-* 2.9 21.7qi 19.6^-^ 00 10 17.3 18. 2 6 18 6 oi9.3;:8 20.1 20.830 22.63-2 29. 1 \\ 32.434 3.5.8 -J 39.2;^ 42.6,, 46.03:3 52: 6 ^-J 55.7^-; 9 50 20 30 19.7 2.5 22. 2 2.6 20.52:6 21 24 3 2.7 0^7 22. 1 2 8 24.9: /^. y 2 9 25. 8 3 23. 8 q 26.8 • 24.83 27.93- 40 30 40 24. 8 2.6 25.7 2.7 26 7 2.8 27.7 2.9 28. 8 3 29.93 31.1 32 20 50 27.4 2.7 28.4 2.7 i>9 5 2.8 30.62.9 31. 8 3.0 33.O32 04. Q Q 10 3 00 30.1 2.5 ?6 31-12.7 32 3 2.8 >8 33.53^ 34-831 037.93-0 36.2: 37.63 3 9 00 10 32.6 33.827 35 1 36.5 29 39.4,: 40.93 8 50 20 35. 2 2-6 36.5 2.7 37 -2.8 39.42:8 40.9 2.9 42.53- 44. 2 3 2 40 30 37.82.5 39. 2 2 6 40 7 ' 2.6 42.228 43.82.9 45.630 47.431 30 40 40.324 41.82.5 43 "^2.6 45.O27 46.7 2.9 48.629 50. 530 20 50 !f-^2:3 f^' - 2.4 45 9 2.5 47.72; 49.62.6 51.528 53. 5 2 9 10 4 00 45.0^^ 46-^3 48 4 2 4 50.3 52.2 54.3„2 56.9 2-5 56. 4 _ 58.8„-; 00 10 047.22a 49.0.;, 50 °2.3 052.8-3 54.8:' 59. 2 ;-, 1 1.628 1 4.4 • 7 50 20 49.3 2.0 51.12:0 53 I0I 55.1 22 57.22:3 59.42-4 1 1.92 4 40 30 51. 3 1.8 53.1 1.9 55 2ic, 57. 3 1.9 oy. ^91 1 1.8 2"i 1 4.3 2-J 1 6.9^-^ 30 40 53.1 1.5 55.0 1.6 5Y ll7 59.2i8 1 l-^LS 1 3. 9 2 1 6.5;-J 1 9.22'-? 20 50 ^!-?l.5 56. 6 1.5 58 «15 \ i-2 6 1 3.4,] 1 5. 9 5:; 1 8.5^:^ 1 11. 3, 8 10 5 00 56.1, „ ^^•ll3 1 ^3 1 2.6,3 1 5.0^^ 1 ^-41:2 1 ^-Si 110-3 5 113-1 c 00 10 57.3o:- 59.4i:o 1 1 ^n 1 9.01:2 111.8- 114.7- 6 50 20 58. z Q Q 1 0.4o8 1 2 '08 1 5.O09 1 7.609 1 10.2io 1 13.1 09 114.0j.-8 1 16. 1 9 1 17.0°8 40 30 59.0:^ } ]-lol 1 3 9 0.7 1 5.9 : 1 8.5^: 111. 2 J: 30 40 50 59.6n„ 59. 9 J-^ 1 1.800 1 2.lJ-^ 1 4 1 4 9 ^0.3 "02 1 6.604 1 7.o;-^ 1 7.l"-^ 1 9.2o4 1 9.60' 1 11.8o4 112. 2 02 1 12.4" 1 14.804 1 15.2o2 1 15. 4 "-^ 1 17. 8n? 1 l«.2j- 1 18. 4" 20 10 6 00 1 0.0°-^ 1 2.3°-^ 1 4 7°- 1 9.7°-^ 6 00 TABL E 28C. [C = t] le 3d correction. Hor. Arg., the star's c leclination. Vert. Arg., B = the 2d corr action.] B. 88° 47' 88° 48' 88° 49' 1 20" 80" 40" 50" 0" 10" 20" 80" 40" 60" 0" 10" 20" „ „ II „ II // II „ „ II II „ II II 30 +0.6 + 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 560] TABLE 28D. For finding the Latitude of a place by Altitudes of Polaris. [D=the ■tth correction. (D has the same sign as A when the Dec. <88°48', the opposite sign when the Dec. >88° 48'.)] . [Vertical Argument, A = the 1st correction. Horizontal Argument, the star's declination.] A. Declination, 88° 47' 88° 48' Proportional parts. 1 20" 25" 30" 85" 40" 46" 60" 56" 0" 6" 10" 16" 20" 26" 1" 2" 8" 4" 2 4 6 8 0.0 1.1 2.2 3.3 4.4 n 0.0 1.0 1.9 2.9 3.9 0.0 0.8 1.7 2.5 3.3 0.0 0.7 1.4 2.1 2.8 n 0.0 0.6 1.1 1.7 2.2 0.0 0.4 0.8 1.2 1.7 0.0 0.2 0.6 0.8 1.1 1.4 1.7 1.9 2.2 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 II 0.0 0.1 0.3 0.4 0.6 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 // 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 II 0.0 0.1 0.3 0.4 0.6 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 0.0 0.2 0.6 0.8 1.1 1.4 1.7 1.9 2.2 2.5 2.8 3.0 3.3 II 0.0 0.4 0.8 1.2 1.7 II 0.0 0.6 1.1 1.7 2.2 II 0.0 0.7 1.4 2.1 2.8 0.0 0.0 0.1 0.1 0.1 II 0.0 0.0 0.1 0.2 0.2 0.3 0.3 0.4 0.4 II 0.0 0.1 0.2 0.2 0.3 0.4 0.5 0.6 0.7 II 0.0 0.1 0.2 0.3 0.4 10 12 14 16 5.6 6.7 7.8 8.9 4.9 5.8 6.8 7.8 4.2 5.0 5.8 6.7 7.5 8.3 9.2 10.0 3.4 4.2 4.9 5.5 2.8 3.3 3.9 4.4 2.1 2.5 2.9 3.3 2.1 2.5 2.9 3.3 3.8 4.2 4.6 5.0 2.8 3.3 3.9 4.4 3.4 4.1 4.9 5.5 0.1 0.2 0.2 0.2 0.6 0.6 0.8 0.9 18 20 22 24 10.0 11.1 12.2 13.3 8.8 9.7 10.7 11.7 6.2 6.9 7.7 8.3 5.0 5.5 6.1 6.7 3.8 4.2 4.6 5.0 5.0 5.5 6.1 6.7 6.2 6.9 7.7 8.3 0.2 0.3 0.3 0.3 0.4 0.4 0.4 0.4 0.5 0.6 0.6 0.7 0.7 0.8 0.8 0.9 0.9 1.0 1.1 1.1 1.2 1.2 1.3 1.3 1.4 1.4 1.5 1.6 1.6 1.7 1.7 1.8 1.8 1.9 1.9 2.0 0.7 0.8 0.9 1.0 1.1 1.1 1.3 1.3 1.4 1.5 1.6 1.7 1.0 1.1 1.3 1.4 26 28 30 32 14.4 15.6 16.7 17.8 12.7 13.6 14.6 15.6 10.8 11.7 12.5 13.3 9.0 9.7 10.4 11.1 7.2 7.8 8.3 8.9 5.4 5.8 6.2 6.7 3.6 3.9 4.2 4.4 4.7 5.0 5.3 5.6 5.4 5.8 6.2 6.7 7.1 7.5 7.9 8.3 7.2 7.8 8.3 8.9 9.4 10.0 10.6 11.1 9.0 9.7 10.4 11.1 1.4 1.5 1.7 1.8 1.9 2.0 2.1 2.2 34 36 38 40 42 44 46 48 50 52 54 56 18.9 20.0 21.1 22.2 16.6 17.5 18.4 19.4 14.2 15.0 15.8 16.7 11.8 12.5 13.2 13.9 14.6 15.3 16.0 16.7 9.4 10.0 10.6 11.1 11.7 12.2 12.8 13.3 7.1 7.5 7.9 8.3 8.8 9.2 9.6 10.0 11.8 12.5 13.2 13.9 0.5 0.5 0.5 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.8 23.3 24.4 25.6 26.7 27.8 28.9 30.0 31.1 20.4 21.4 22.3 23.3 17.6 18.3 19.2 20.0 5.8 6.1 6.4 6.7 6.9 7.2 7.5 7.8 8.8 9.2 9.6 10.0 11.7 12.2 12.8 13.3 14.6 15.3 16.0 16.7 1.7 1.8 1.9 2.0 2.3 2.4 2.6 2.6 24.3 25.3 26.2 27.2 28.2 29.2 30.1 31.1 32.1 33.0 34.0 35.0 20.8 21.7 22.5 23.3 17.3 18.0 18.8 19.4 13.9 14.4 15.0 15.6 10.4 10.8 11.2 11.7 10.4 10.8 11.2 11.7 13.9 14.4 15.0 15.6 17.3 18.0 18.8 19.4 2.1 2.2 2.2 2.3 2.8 2.9 3.0 3.1 58 60 62 64 66 68 70 72 / // 20 40 1 00 1 20 1 40 2 00 32.2 33.3 34.4 35.6 24.2 25.0 25.8 26.7 20.1 20.8 21.5 22.2 16.1 16.7 17.2 17.8 12.1 12.5 12.9 13.3 8.0 8.3 8.6 8.9 4.0 4.2 4.3 4.4 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 4.0 4.2 4.3 4.4 4.6 4.7 4.9 5.0 8.0 8.3 8.6 8.9 9.2 9.4 9.7 10.0 12.1 12.5 12.9 13.3 13.8 14.2 14.6 15.0 16.1 16.7 17.2 17.8 20.1 20.8 21.5 22.2 0.8 0.8 0.9 0.9 0.9 0.9 1.0 1.0 2.4 2.5 2.6 2.7 2.8 2.8 2.9 3.0 3.2 3.3 3.4 3.6 36.7 37.8 38.9 40.0 27.5 28.3 29.2 30.0 22.9 23.6 24.3 25.0 18.3 18.9 19.4 20.0 13.8 14.2 14.6 15.0 9.2 9.4 9.7 10.0 4.6 4.7 4.9 5.0 18.3 18.9 19.4 20.0 22.9 23.6 24.3 25.0 3.7 3.8 3.9 4.0 Proportional parts. 1 // 0.2 0.4 0.6 0.7 0.9 1.1 0.2 0.3 0.5 0.7 0.8 1.0 0.1 0.3 0.4 0.5 0.7 0.8 0.1 0.2 0.4 0.5 0.6 0.7 II 0.1 0.2 0.3 0.4 0.5 0.6 II 0.1 0.1 0.2 0.2 0.3 0.4 II 0.0 0.0 0.1 0.1 0.2 0.2 II 0.0 0.0 0.1 0.1 0.1 0.1 II 0.0 0.0 0.0 0.0 0.0 0.0 II 0.0 0.0 0.1 0.1 0.1 0.1 II 0.0 0.0 0.1 0.1 0.2 0.2 II 0.1 0.1 0.2 0.2 0.3 0.4 II 0.1 0.2 0.3 0.4 0.5 0.6 0.1 0.2 0.4 0.5 0.6 0.7 TABLE 28D. [Page 661 1 For finding the Latitude of a place by Altitudes of Polaris. 1 [D- the 4th correction. (D has the same sign as A when the Dec. <88° 48', the opposite sign when the Dec. >88° 48'.)] 1 [Vertical Argument A =the 1st correction. Horizontal Argument, the star's declination.] i A. Declination, 88° 48' 88° 4»' Proportional parts. 1 80" 86" 40" 46" 50" 66" 0" 5" 10" 16" 20" 1" 2" 8" 4" // II II ,/ II „ // II II II II n II II II 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2 0.8 1.0 1.1 1.2 1.4 1.6 1.7 1.8 1.9 2.1 2.2 0.0 0.1 0.1 0.1 4 1.7 1.9 2.2 2.5 2.8 3.1 3.3 3.6 3.9 4.2 4.4 0.1 0.1 0,1 0.2 6 2.5 2.9 3.3 3.8 4.2 4.6 5.0 5.3 5.8 6.2 6.7 0.1 0.2 0.2 0.3 8 3.3 3.9 4.4 5.0 5.6 6.1 6.7 7.2 7.8 8.3 8.9 0.1 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 6.7 7.8 8.9 10.0 11.1 12.2 13.3 14.4 16.2 15.6 16.7 17.8 0.2 0.4 0.5 0.7 0.7 0.9 18 7.5 8.8 10.0 11.2 12.5 13.8 15.0 17.5 18.8 20.0 0.2 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 23.3 25.0 26.7 0.3 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 0.4 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 30 12.5 14.6 16.7 18.8 20.8 22.9 25.0 27.1 29.2 31.2 33.3 0.4 0.8 1.2 1.6 32 34 13.3 14.2 15.6 17.8 20.0 22.2 24.4 26.7 28.9 31.1 33.3 35.5 0.4 0.9 1.3 1.8 1.9 16.6 18.9 21.2 23.6 26.0 28.4 30.7 33.1 35.4 37.8 0.5 0.9 1.4 36 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 38 15.8 18.4 21.1 23.8 26.4 29.0 31.6 34.2 37.0 39.6 42.2 0.5 1.1 1.6 2.2 40 42 16.7 19.4 22.2 25.0 27.8 30.6 33.3 36.1 38.9 41.7 44.4 0.6 1.1 1.7 2.2 17.6 20.4 23.3 26.2 29.2 32.1 35.0 37.9 40.8 43.8 46.7 0.6 1.2 1.8 2.4 44 18.3 21.4 24.4 27.5 30.6 33.7 36.8 39.8 42.8 45.9 48.9 0.6 1.2 1.8 2.4 46 19.2 22.3 25.6 28.8 32.0 35.1 38.3 41.5 44.8 47.9 51.1 0.6 1.3 1.9 2.6 48 50 20.0 23.3 24.3 26.7 30.0 33.3 36.7 40.0 43.3 46.7 50.0 53.3 0.7 1.3 2.0 2.7 20.8 27.8 31.2 34.7 38.2 41.7 45.1 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 3.0 56 58 23.3 27.2 31.1 35.0 38.9 42.8 46.7 50.5 54.4 58.3 62.2 0.8 1.6 2L3 3.1 24.2 28.2 32.2 36.2 40.3 44.3 48.3 52.3 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 3.3 62 25.8 30.1 34.4 38.8 43.0 47.3 51.7 56.0 60.3 64.6 68.9 0.9 1.7 2.6 3.4 64 26.7 31.1 32.1 35.6 40.0 44.4 48.9 53.3 57.8 62.2 66.7 71.1 0.9 1.8 1.8 2.7 2.7 8.6 66 27.5 36.7 41.2 45.8 50.4 55.0 59.6 64.2 68.8 73.3 0.9 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 t It 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. // „ II II II II „ II „ II „ 20 0.1 0.1 0.1 0.2 0.2 0.3 0.? 0.3 0.3 0.3 0.4 040 0.2 0.3 0.4 0.4 0.5 0.5 0.6 0.6 0.6 0.7 0.7 100 0.4 0.5 0.6 0.6 0.7 0.8 0.8 0.9 0.9 1.0 1.1 120 0.5 0.7 0.7 0.8 0.9 1.1 1.1 1.2 1.3 1.4 1.5 140 0.6 0.8 0.9 1.0 1.1 1.3 1.4 1.5 1.6 1.7 1.8 200 0.8 1.0 1.1 1.2 1.4 1.6 1.7 1.8 1.9 2.1 2.2 6583—06- -36 Page 562] TABLE 29. Conversion Tables for Nautical and Statute Miles. Naviical miles into statute miles. Statute miles into nautical 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 Xautical 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 English. Meters. Feet. Yards. Statute miles. Nautical miles. 1 2 3 4 3.280 833 3 6.561 666 7 9.842 500 13.123 333 3 1.093 611 1 2.187 222 2 3, 280 833 3 4.374 444 4 0.000 621 369 .001 242 738 .001 864 106 .002 485 475 0.000 539 593 .001 079 185 .001 618 778 .002 158 370 5 6 7 8 9 16.404 166 7 19.685 000 22.965 833 3 26.246 666 7 29.527 500 5.468 055 6 6.561 666 7 7.655 277 8 8.748 888 9 9.842 500 . 003 106 844 .003 728 213 .004 349 582 .004 970 950 .005 592 319 .002 697 963 .003 237 556 .003 777 148 .004 316 741 .004 856 333 English to metric. No. Feet to meters. Yards to meters. Statute miles to meters. Nautical miles to meters. 1 2 3 4 0.304 800 6 0.609 601 2 0.914 401 8 1.219 202 4 0.914 401 8 1.828 803 7 2.743 205 5 3.657 607 3 1, 609. 35 3, 218. 70 4, 828. 05 6,437.40 1, 853. 25 3, 706. 50 5, 559. 75 7,413.00 5 6 I 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.] Equivaient temperatures — Fahr., Cent. Mau Ro=| c°=| (po- -32°). ' C o=JRO==|(F°- -32°). Fo. c°. R°. F°. 51 C°. R°. 1 -17.2 -13.8 +10.6 + 8.4 2 16.7 13.3 52 11.1 8.9 Equivalent temperatures— Centigrade and Fahrenheit. 3 16.1 12.9 53 11.7 9.3 4 15.6 12.4 54 12.2 9.8 F°= g C°+32°. 5 15. 12. 55 12. 8 10. 2 6 7 14.4 13.9 11.6 11.1 56 57 13.3 13.9 10.7 11.1 C°. F°. C°. r°. c°. F°. c°. F°. c°. F°. 8 13.3 10.7 58 14.4 11.6 -10 14.0 32.0 10 50. 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 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 1 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— Maumur and Fahrenheit. 28 29 30 2.2 1.7 1.1 1.8 1.3 0.9 78 79 80 25.6 26.1 26.7 20.4 20.9 21.3 F°=| R°+32°. R°. F°. R°. F°. R°. F°. R°. F°. 31 32 — 0.6 0.0 -0.4 0.0 81 82 27.2 27.8 21.8 22.2 33 34 + 0.6 1.1 + 0.4 0.9 83 84 28.3 28.9 22.7 23.1 —10 - 9 9.5 11.8 1 32.0 34.2 10 11 54.5 56.8 20 21 77.0 79.2 35 1.7 1.3 85 29.4 23.6 - 8 14.0 2 36.5 12 59.0 22 81.5 36 2.2 1.8 86 30.0 24.0 — 7 16.2 3 38.8 13 61.2 23 83.8 37 2.8 2.2 87 30.6 24.4 — 6 18.5 4 41.0 14 63.5 24 86.0 38 3.3 2.7 88 31.1 24.9 — 5 20.8 5 43.2 15 65.8 25 88.2 39 3.9 3.1 89 31.7 25.3 — 4 23.0 6 45.5 16 68.0 26 90.5 40 4.4 3.6 90 32.2 25.8 — 3 25.2 7 47.8 17 70.2 27 92.8 41 5.0 4.0 91 32.8 26.2 — 2 27.5 8 50.0 18 72.5 28 95.0 42 5.6 4.4 92 33.3 26.7 — 1 29.8 9 52.2 19 74.8 29 97.2 43 44 6.1 6.7 4.9 5.3 93 94 33.9 34.4 27.1 27.6 45 7.2 5.8 95 35.0 28.0 46 7.8 6.2 96 35.6 28.4 47 8.3 6.7 97 36.1 28.9 48 8.9 7.1 98 36.7 29.3 49 9.4 7.6 99 37.2 29.8 50 +10.0 + 8.0 100 +37.8 + 30.2 TABLE 32. 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goKjuiod 'aoi;oaiip anix «o totoco?o^o»( coco o5 ooooo ooooo f-lrHOOiO ft^i-lt^tO ^ OOOCOOi CD CO t^ lO lO CO C^ t^ C^ GO O i-HlOCOI^ NrHrti-liHi-lr-IOOO rHrHlMM o o>-*eoc^ ^ lOC4iOi-H O 00t1 '^ o lOiO "^ -^ "^ ooooo ■*0>mi-IQQ to "^ ^ ■^ CQ ooooo ■Hi-lrHO ooooo ojc^oom rH i-tt-OTt< T-lrHiHOO OiO-*-^ iHiHOOO i-lOiO'*-^ i-HiHOOO OlO-*05CO thoooo O -^C^THrH OOOOO i-(0(NO O -^INi-lr-l ^ -"JllOr-dO O OTrHi-HO _ ^Q0lQO) ■^ -^ COCO W OOOOO c^ Olio coo ■* CO CO CO CO ooooo COO lO-fl" ooooo ooooo TJH ^ Tf rji CO ooooo iO(MOOCtO -^ '^■^COCO ooooo rHOlt^lOeO ^ CO CO CO CO ooooo CO CO cocoes ooooo c^oa>oDt~- cocooio (M IM r-l 1-1 tH r-l oooooo aSiOCONi-H ooooo t^iOCOC^i-H OiXt^tOiO lOC coeocococo c^c^(NC^(N inc CO CO CO CO (N ooooo 1-H O X t^-^ cocoe^CJiN OOOOO OOiOCOr-lO OOt^tOlO-* coeocococo C^CJIMC^O) ooooo OOOOO O'^C^OOO " CO CO CO e^ OOOOO Tf c^ O OO t- COCOCOIMC^ OOOOO rjooot^io coeoc^c^cM ooooo OJ(MlMCJC5 ooooo ooooo COC^rHOOl ooooo -lO-^ca ooooo ■^cocococl cjc^nS ooooo ooooo cococo?ie^ ooooo oa>ooi>-t^ C^ tH rH r-t iH ooooo incOINOO OOOOO C0COO)(M(N ooooo rHCOtOTfeq tO-*C^O OOOOO >(M 00 lO CO i-l O CO iHC^ to _. -, , . _ io-<*eoco(NMme GO t^ '^ ooooo osoor^ toiO ooooo t^ toio-^co ooooo lO-^ cocoes ooooo iOeot~GOO> t^ to -(t CO '^^ ooooo ■O'* COIN .-I OOOOC^ tOiO ooooo t^ to lO T)< ■.*' ooooo tOlO TjH Tf CO ooooo ■W<})(NlMiNiM ooooo OOOO t^ too O) iHiH— (iHrH OOOOOO oot^t>to>oio iH iH rH rH rH i-t oooooo Ji-lOOOOt^toiOiOTjH*^ OOOOO OOOOOO OOO t^ to OOOOO OOOOO C-t~- 0.0 -t^tOtCi ooooo . to tOiOiO ooooo ooooo lO ■.jl ^ CO CO ooooo COCO-IO ooooo iHi-hOOO tH i-H rH i-H iH ooooo r-l00010> ooooo GO t^CO lO-^ ooooo t^ tOiOrJi CO ooooo to to -^ CO CO ooooo »0 -ifT* CO CO (N ooooo ■^COC^diH ooooo COfNCO 1-HO ooooo Oi Oa O^CO 00 ooooo lOtot^oooi OlMTjitOOO tOiO^T)icO(M OOOOOO •^ -^ CO CO (N i-H OOOOOO CO CO C^ (N 1-t T-l OOOOOO COlM N t^ 3> -*eOINr-IO ooscooe^ t^OOOOl -^ ira i^ •>!< i-i lO o>o»oooot~ occt>.c loc^i^ect-cjoir-ioigto i-iiocoi-iioN'f^tH03Ti< tOiOiOift-^p^-^-^-rt^cOCO n>Mi-io>5 to to to to lO OOOOXMiC 05OT(ie<5>-( r* t>-toto to OTtlSSaS to »o »C iC o ■*©MCOi-( ■>J< Oi-HOO) T) •^»00tO OOOOOr-l i-IOO>00 00 053 00 "5 to TOOSS 1-11(5 l>t>- tOtOiC 0000 CO c< IM CO rj< r-l T}< OiOOC^t^ to CO I— I L r-l CO iC C4 O) O 0> ■^ i-H •* 00t- iHrHlO to 00 CO CO-*i-l-*iM t>tO tOOiO COtOlNO-^ to li^ »0 i£3 -tj^ OOi-llNiO0000(MOlM i-KNOOrHCOO-^C^O r-IOJ00I>tOiOlC-0<-OMo-*co Tjf'^coeoco i-iC4tOiH00 tOlAlQtOOO .H-^rr-ltO tHt-(COtpOi OtJ<0),HiO ■0'«'C0lN ^ ^ CO CO CO CO to »/5 »C to 00 »-* ■*C0C^QO0 oooooiMinoo Ttl'^COCOCO COCOCOMC^lIN tUCOiHOS CO CO CO CO c^ m 1-j rC t» iM to ■WeOlNNr-1 C^iHOOi Oli-IOOiC CO CO CO CO OJ ■*C0C0OH r-l fH OOOOOIMlO T-IOOlO-* eoeococjca COIMIMrH (NINC^OllM ■*-ttOoS tOOOrHrH to eOCOlNCllN oot^tot^oiiH'Ooo'^oo OiO-WCOC^iNi-IOOiO COOJOlCJiMINCNCJC^iH to lO 00 -511-1 C0C0C0.i-( ■*C0 04C"00ocot- COOCOlHl"— -* ' eolMOJOit .. OiiCOO"^ COO>iOr*COl> lO lib lO iij< -^ 00000 lO ^ -1^ "^ 00000 rH 00 to ■* 01 lO ^ ^ ^ ^ 00000 00 to-^ OIO 00000 8t^COOOO»OCOiHOiQO lOlCiOTjlri<-<1*TrCOCO 1-1000000000 OiHMCO'fiOtOt^OOas OfHC^CO-^ iMTftoO-^ OIIMi- 10 ■* Til -a< CO pl>-*THO0 cooie5iiMiH in^iojoos ^ ■^ -# ■^ CO 00000 eor-iooot- ^ ^ ^ CO CO 00000 1* CO 55 CO CO 00000 CO CO CO CO CO 00000 C0O)O4^rH lOO iO -^ -11 00000 CO CO CO CO CO 00000 to -# 04000 CO CO CO CO 04 00000 -* 04000 t~ CO CO CO 01 04 00000 COCOM04c5 00000 tOlO'*04iH O0QC~>«'^ COCOCOCOCO 0504 0104 04 00000 ©00^0 >atoc-co0> oe^-jitooo «55 5 ■^-w CO CO 05 OlTjic cococ lO 1-1 1^ ■^ rH 00 iH t-^rHOlt^ r-lOO lO lO lO "rl* tP -^ 000000 HCOCOCOCO 000000 00 t^ to lO -<)< CO 04 04 04 04 01 04 00000© t- to Tj< 05 04 iH 010)04 04 04 01 ©00000 804^64048 00000© N04S04§r-t oo©©oo C0 04 1-I00100 04 04O4 04.HrH 00000© oo4-*toaoO [Page 567 .\ Page 568] TABLE 34. For finding the distance of an object by an angle, measured from an elevated position, between the object and the horizon beyond. Dist., yards. Height of the Eye Above the Level of the Sea, in Feet. Dist., yards. 20 30 40 50 60 70 80 90 lOO llO ISO 100 200 300 400 500 / 3 44 1 50 1 12 52 41 1 5 37 2 46 1 49 1 21 1 03 ; 7 29 3 43 2 26 1 48 1 25 / 9 21 4 39 3 04 2 16 1 48 o / 11 11 5 35 3 41 2 44 2 10 o / 13 00 6 31 4 19 3 12 2 32 o / 14 47 7 27 4 56 3 40 2 54 o / 16 34 8 23 5 33 4 08 3 17 o / 18 16 9 18 6 11 4 36 3 39 o / 19 58 10 13 6 48 & 04 4 01 o / 21 37 11 08 7 25 5 32 4 24 100 200 300 400 500 600 700 800 900 1,000 34 28 24 21 18 52 44 38 33 29 1 10 1 01 51 45 40 1 29 1 15 1 05 57 50 1 47 1 31 1 18 1 09 1 01 2 05 1 46 1 32 1 22 1 12 1 05 59 53 49 45 2 24 2 01 1 46 1 33 1 23 1 15 1 08 1 02 57 52 2 42 2 18 2 00 1 45 1 34 3 01 2 34 2 13 1 57 1 45 3 20 2 50 2 27 2 10 1 56 3 38 3 05 2 41 2 22 2 07 600 700 800 900 1,000 1,100 1,200 1,300 1,400 1,500 16 15 13 12 11 26 23 21 19 18 35 32 29 27 24 45 41 37 34 31 55 50 45 41 38 1 24 1 17 1 10 1 04 59 1 34 1 26 1 18 1 12 1 07 1 02 58 54 50 47 1 44 1 35 1 27 1 20 1 14 1 54 1 44 1 35 1 27 1 21 1,100 1,200 1,300 1,400 1,500 1,600 1,700 1,800 1,900 2,000 10 16 15 14 13 12 22 21 19 18 17 29 27 25 23 22 35 33 31 29 27 42 39 36 34 32 48 45 42 39 37 55 51 48 45 42 1 08 1 04 1 00 56 53 1 15 1 10 1 06 1 02 58 1,600 1,700 1,800 1,900 2,000 2,100 2,200 2,300 2,400 2,500 11 10 16 15 14 13 12 20 19 18 17 16 25 24 22 21 20 30 28 27 25 24 35 33 31 29 28 40 38 36 34 32 45 42 40 38 36 50 47 45 42 40 55 52 49 47 44 2,100 2,200 2,300 2,400 2,500 2,600 2,700 2,800 2,900 3,000 11 11 10 15 14 14 13 12 19 18 17 16 15 , 23 22 20 19 19 26 25 24 23 22 30 29 28 26 25 34 33 31 30 28 38 36 35 33 32 42 40 38 37 35 2,600 2,700 2,800 2,900 3,000 3,100 3,200 3,300 3,400 3,500 12 11 10 15 14 13 13 12 18 17 16 15 15 21 20 19 18 17 24 23 22 21 20 27 26 25 24 23 30 29 28 27 26 34 32 31 30 29 3,100 3,200 3,300 3,400 3,500 3,600 3,700 3,800 3,900 4,000 12 11 11 10 14 13 13 12 12 17 16 15 15 14 19 19 18 17 16 22 21 20 20 19 25 24 23 22 21 27 26 25 25 24 3,600 3,700 3,800 3,900 4,000 4,100 4,200 4,300 4,400 4,500 11 11 10 14 13 13 12 12 16 15 15 14 14 18 17 17 16 16 20 20 19 18 18 23 22 21 21 20 4,100 4,200 4,300 4,400 4,500 4,600 4,700 4,800 4,900 5,000 11 11 10 13 13 12 12 U 15 15 14 14 13 17 17 16 15 15 19 19 18 17 17 4,600 4,700 4,800 4,900 5,000 '^ ssVyj_Oh i^^e^ TABLE 35. [Page 569 Speed in knots per hour developed by a vessel traversing a measured nautical mile in anv eiven 1 number of minutes and seconds. ' " 1 Number of minutes. 1 2 3 4 5 6 7 8 9 10 11 12 Sec. Knots. Knots. Knots. Knots. Knots. Knots. Knots. Knots. Knots. Knots. Knots. Knots. U 60. 000 30. 000 20. 000 15. 000 12.000 10. 000 8.571 7.500 6.666 6.000 5.455 5.000 1 59. 016 29. 752 19. 890 14. 938 11. 960 9.972 8.551 7.484 6.654 5.990 5.446 4.993 1 2 58. 065 29. 508 19. 780 14. 876 11,920 9,944 8.530 7.468 6.642 5.980 5.438 4.986 2 'A 57. 143 29. 268 19. 672 14. 815 11.880 9 917 8 510 7.453 6.629 5.970 5.429 4.979 3 4 5 56. 250 55.'385 29. 032 19.565 19. 460 14.754 14. 694 11.841 11.803 9.890 9."863 8 490 8, 470 7.438 7.422 6. 617 6.605 5.960 5.950 5.421 4.972 4 28. 800 5. 413 4.965 5 6 54. 545 28. 571 19. 355 14.634 11.764 9.836 8.450 7.407 6. 593 5.940 5.405 4.958 6 7 53.731 28.346 19. 251 14. 575 11. 726 9. 809 8.430 7.392 6.581 5.930 5.397 4.951 7 8 52. 941 28. 125 19. 149 14. 516 11. 688 9.783 8.411 7.377 6.569 5.921 5.389 4.945 8 9 10 52. 174 27. 907 19.048 14. 458 11.650 11. 613 9.756 9. 729 8.392 8.372 7.362 6.557 6.545 5.911 5.381 4.938 9 51. 429 27. 692 18. 947 14. 400 7.346 5.902 5.373 4. 9.32 10 11 50. 704 27. 481 18. 848 14. 342 11. 575 9.703 8.353 7.331 6.533 5.892 5.365 4. 924 11 12 50. 000 27. 273 18. 750 14. 286 11. 538 9.677 8.334 7.317 6.521 5.882 5.357 4.918 12 13 49. 315 27. 068 18. 652 14. 229 11. 501 9.651 8.315 7.302 6.509 5.872 5.349 4.911 13 14 48. 649 26. 866 18. 556 14. 173 11.465 9.625 8.295 8.276 7.287 6.498 5.863 5.341 4.904 14 15 48. 000 26. 667 18. 461 14. 118 11. 428 9.600 7.272 6.486 5.853 5.333 4.897 15 16 47. 368 26. 471 18. 367 14. 063 11. 392 9.574 8.257 7.258 6.474 5.844 5.325 4.891 16 17 46. 753 26. 277 18. 274 14. 008 11.356 9.549 8.238 7.243 6.463 5. 834 5.317 4.884 17 18 46. 154 26. 087 18. 182 13. 953 11.321 9.524 8.219 7.229 6.451 5.825 5.309 4.878 18 19 20 45. 570 45.000 25. 899 18. 090 13. 900 11. 285 11. 250 9.499 8.200 8.181 7.214 6.440 5.815 5.301 4.871 19 25. 714 18. 000 13. 846 9.473 7.200 6.428 5.806 5.294 4.865 20 21 44.444 25. 532 17. 910 13. 793 11.214 9.448 8.163 7.185 6.417 5.797 5.286 4.858 21 22 43. 902 25. 352 17. 822 13. 740 11. 180 9.424 8.144 7.171 6.405 5.787 5.278 4.851 22 23 43. 373 25. 175 17. 734 13. 688 11. 146 9.399 8.126 7.157 6.394 5.778 5.270 4.845 23 24 42. 857 25.000 17.647 13. 636 13.584 11.111 11. 077 9.375 9.350 8.108 7.142 6.383 5.769 5.263 4.838 24 25 42. 353 24. 828 17. 560 8.090 7.128 6.371 5.760 5. 255 4.832 25 26 41. 860 24.658 17. 475 13. 533 11. 043 9.326 8.071 7.114 6.360 5.750 5.247 4.825 26 27 41. 379 24. 490 17. 391 13. 483 11. 009 9.302 8.053 7.100 6.349 5.741 5.240 4.819 27 28 40. 909 24. 324 17. 307 13. 433 10. 975 9.278 8.035 7.086 6.338 5.732 5.232 4.812 28 29 40. 449 24. 161 24. 000 17. 225 17. 143 13. 383 10. 942 9.254 8.017 7.072 6.327 6.315 5.723 5.714 5.224 4.806 29 30 30 40. 000 13. 333 10. 909 9.230 8.000 7.059 5.217 4.800 31 39. 560 23.841 17.061 13. 284 10. 876 9.207 7.982 7.045 6.304 5. 705 5.210 4.793 31 32 39. 130 23. 684 16. 981 13. 235 10. 843 9.183 7.964 7. 031 6.293 5.696 5.202 4.787 32 33 38. 710 23. 529 16. 901 13. 186 10.810 9.160 7.947 7.017 6.282 5.687 5.195 4.780 33 34 35 38.298 23. 377 16. 822 13. 138 10. 778 9.137 7.929 7.004 6.271 5.678 5.187 4.774 34 35 37. 895 23. 226 16.744 13. 091 10. 746 9.113 7.912 6.990 6.260 5.669 5.179 4.768 36 37. 500 28.077 16. 667 13. 043 10. 714 9.090 7.895 6.977 6.250 5.660 5.172 4.761 36 37 37. 113 22. 930 16. 590 12. 996 10. 682 9.068 7.877 6.963 6.239 5.651 5.164 4.755 37 38 36. 735 22. 785 16. 514 12. 950 10. 651 9.045 7.860 6.950 6.228 5.642 5.157 4.749 38 39 40 36. 364 22.642 16. 438 16. 363 12. 903 10. 619 9.022 7.843 6.936 6.217 5.633 5.150 4.743 39 36. 000 22. 500 12. 857 10. 588 9.000 7.826 6.923 6.207 5.625 5.143 4.737 40 41 35. 644 22. 360 16. 289 12.811 10. 557 8.977 7.809 6.909 6.196 5.616 5.135 4.731 41 42 35. 294 22. 222 16.216 12.766 10. 526 8. 955 7.792 6.896 6.185 5.607 5.128 4.724 42 43 34. 951 22, 086 16. 143 12. 721 -10. 495 8. 933 7. 775 6.883 6.174 5.598 5.121 4.718 43 44 34. 615 21. 951 16. 071 12. 676 10. 465 8.911 7.758 6.870 6.164 5.590 5.114 4.712 44 45 34. 286 21. 818 16. 000 12. 631 10.434 8.889 7.741 6.857 6.153 5.581 5.106 4.706 45 46 33. 962 21. 687 15. 929 12. 587 10. 404 8.867 7.725 6.844 6. 143 5.572 5.099 4.700 46 47 33. 645 21.557 15. 859 12. 543 10. 375 8. 845 7.708 6.831 6.132 5.564 5.091 4.693 47 48 33. 333 21. 429 15. 789 12.500 10. 345 8.823 7.692 6.818 6.122 5.555 5.084 4.687 48 49 50 33. 028 21. 302 15. 721 12. 456 12.413 10. 315 8.801 7. 675 7.659 6.805 6.792 6.112 6.101 5.547 5.077 4.681 49 50 32. 727 21. 176 15. 652 10. 286 8.780 5.538 5.070 4.675 51 32. 432 21. 053 15. 584 12. 371 10. 256 8.759 7.643 6.779 6.091 5.530 5.063 4.669 51 52 32. 143 20. 930 15. 517 12. 329 10. 227 8.737 7.627 6.766 6.081 5.521 5.056 4.663 52 53 31. 858 20. 809 15. 450 12. 287 10. 198 8.716 7.611 6.754 6.071 5.513 5.049 4.657 53 54 31.579 20. 690 15. 384 12. 245 12. 203 10. 169 10. 140 8.695 7.595 6.741 6.060 5.504 5.042 4.651 54 55 31. 304 20. 571 15.319 8.675 7.579 6.739 6.050 5.496 5. 035 4.645 55 56 31. 034 20. 455 15. 254 12. 162 10. 112 8.654 7.563 6.716 6.040 5.487 5.028 4.639 56 57 30. 769 20. 339 15. 190 12. 121 10. 084 8.633 7.547 6.704 6.030 5.479 5.020 4.633 5/ 58 30. 508 20. 225 15. 126 12. 080 10. 055 8.612 7.531 6.691 6.020 5.471 5.013 4.627 58 59 30. 252 20. 112 15. 062 12.040 10. 027 8.591 7.515 6. 679 6.010 5.463 5.006 4.621 59 Sec. 1 2 3 4 *» 6 7 8 9 10 11 12 Sec. Page 570] TABLE 36. Reduction of Local Mean Time to Standard Meridian Time, and the reverse. [If local meridian is east of standard meridian, subtract from local mean time, or add to standard meridian time. If local meridian is west of standard meridian, add to local mean time, or subtract from standard meridian time.] Difference of longitude be- Reduction to be applied to local mean time. Difference of longitude be- Reduction to be applied to local mean time. tween local meridian and standard meridian. tween local meridian and standard meridian. O / O 1 Minutes. o / o / Minutes. - 00 to 07 7 23 to 7 37 30 08 to 22 1 7 38 to 7 52 31 23 to 37 2 7 53 to 8 07 32 38 to 52 3 8 08 to 8 22 33 53 to 1 07 4 8 23 to 8 37 34 1 08 to 1 22 6 8 38 to 8 52 35 1 23 to 1 37 6 8 53 to 9 07 36 1 38 to 1 52 7 9 08 to 9 22 37 1 53 to 2 07 8 . 9 23 to 9 37 38 2 08 to 2 22 9 9 38 to 9 62 39 2 23 to 2 37 10 9 63 to 10 07 40 2 38 to 2 52 11 10 08 to 10 22 41 2 53 to 3 07 12 10 23 to 10 37 42 3 08 to 3 22 13 10 38 to 10 52 43 3 23 to 3 37 14 10 53 to 11 07 44 3 38 to 3 52 15 11 08 to 11 22 46 3 53 to 4 07 16 11 23 to 11 37 46 4 08 to 4 22 17 11 38 to 11 52 47 4 23 to 4 37 18 11 63 to 12 07 48 4 38 to 4 52 19 12 08 to 12 22 49 4 53 to 5 07 20 12 23 to 12 37 50 5 08 to 5 22 21 12 38 to 12 52 51 5 23 to 5 37 22 12 53 to 13 07 52 5 38 to 5 62 23 13 08 to 13 22 63 5 63 to 6 07 24 13 23 to 13 37 54 6 08 to 6 22 25 13 38 to 13 52 56 6 23 to 6 37 26 13 53 to 14 07 56 6 38 to 6 52 27 14 08 to 14 22 57 6 63 to 7 07 28 14 23 to 14 37 58 7 08 to 7 22 29 14 38 to 14 52 59 TABLE 37. [Page 671 | Log. A and Log. B. [For Computing the Equation of Equal Altitudes. For Noon, A-; for Midnight, A+; for Noon or Midnight, B+. 1 Argument=Elapsed Time.] 13 Ok " 1 - " ! •' 1 . 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 5 .4059 .4059 9. 4059 .4074 .4031 .4113 .3952 .4177 .3817 .4266 .3620 .4383 .3348 9. 4059 9. 4074 9. 4030 9.4113 9. 3950 9. 4178 9. 3814 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 .4076 .4026 .4117 .3943 .4183 .3803 .4275 .3600 9. 3596 .4393 9. 4396 .3221 9. 3316 9. 4059 9. 4076 9. 4025 9. 4118 9. 3941 9. 4184 9. 3800 9. 4277 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 .4284 .3580 .4405 .3294 9. 4060 9. 4058 9. 4079 9. 4020 9. 4122 9. 3931 9. 4191 9. 3786 9. 4286 9. 3576 9. 4407 9. 3289 16 .4060 .4058 .4079 .4019 .4123 .3929 .4193 .3783 .4288 .3572 .4409 .3283 17 .4060 .4057 .4080 .4018 .4124 .3927 .4194 .3780 .4289 .3568 .4411 .3278 18 .4061 .4057 .4080 .4017 .4125 .3925 .4195 .3777 .4291 .3564 .4414 .3272 19 20 .4061 9. 4061 .4057 9. 4057 .4081 .4016 .4126 .3923 .4197 .3774 .4293 .3559 .4416 .3266 9. 4081 9. 4015 9. 4127 9. 3921 9. 4198 9. 3771 9. 4295 9. 3555 9.4418 9. 3261 21 .4061 .4056 .4082 .4014 .4128 .3919 .4199 .3768 .4297 .3551 .4420 .3255 22 .4061 .4056 .4083 .4013 .4129 .3917 .4201 .3765 .4299 .3547 .4423 .3249 23 .4061 .4056 .4083 .4012 .4130 .3915 .4202 .3762 .4300 . 3542 .4425 .3244 24 25 .4061 .4055 .4084 .4010 .4131 .3913 .4204 9. 4205 .3759 .4302 .3538 .4427 .3238 9. 4062 9. 4055 9. 4084 9.4009 9. 4132 9. 3911 9. 3756 9. 4304 9. 3534 9.4430 9. 3232 26 .4062 . 4055 .4085 .4008 .4133 .3909 .4207 .3752 .4306 .3530 .4432 .3226 27 .4062 .4054 .4086 .4007 .4134 .3907 .4208 .3749 .4308 .3525 .4434 .3220 28 .4062 .4054 .4086 .4006 .4135 .3905 .4209 .3746 .4310 .3521 .4437 .3214 29 .4062 .4054 .4087 .4004 9. 4003 .4136 .3903 .4211 .3743 .4312 .3516 .4439 .3208 30 9. 4062 9. 4053 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 .3998 9. 3997 .4141 .3892 9. 3889 .4218 9. 4220 .3727 .4321 .3494 .4451 .3178 9. 3172 35 9.4064 9. 4051 9. 4091 9. 4142 9. 3723 9. 4323 9. 3490 9. 4453 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 40 .4065 . 4049 . 4093 .3991 .4147 .3880 .4226 .3710 .4331 .3471 .4463 .3148 9.4065 9.4048 9.4094 9. 3990 9. 4148 9. 3878 9. 4227 9. 3707 9. 4333 9. 3467 9.4465 9. 3142 41 .4065 . 4048 . 4095 .3988 .4149 .3875 .4229 .3703 .4335 .3462 .4468 .3135 42 .4065 . 4047 . 4095 .3987 .4150 .3873 .4231 .3700 .4337 .3457 .4470 .3129 43 .4066 . 4047 . 4096 .3985 .4151 .3871 .4232 .3696 .4339 .3453 .4473 .3123 44 .4066 .4046 .4097 .3984 .4152 .3868 .4234 9. 4235 .3693 .4341 .3448 .4475 .3116 45 9. 4066 9. 4045 9. 4097 9. 3982 9. 4154 9. 3866 9. 3690 9. 4343 9. 3443 9.4477 9.3110 46 .4067 .4045 .4098 .3981 .4155 .3863 . 4237 .3686 .4345 .3438 .4480 .3103 47 .4067 .4044 .4099 .3979 .4156 .3861 .4238 .3683 .4347 .3433 .4482 .3097 48 .4067 .4043 .4100 .3978 .4157 .3859 .4240 .3679 .4349 .3429 .4485 .3091 49 50 .4068 .4043 .4100 .3976 9. 3975 .4158 .3856 .4242 9. 4243 .3675 9. 3672 .4351 9. 4a53 .3424 .4487 .3084 9. 4068 9. 4042 9. 4101 9. 4159 9. 3854 9. 3419 9.4490 9. 3078 51 .4068 .4041 .4102 .3973 .4161 .3851 .4245 .3668 .4355 .3414 .4492 .3071 52 .4069 .4041 .4103 .3972 .4162 .3849 .4246 .3665 .4357 .3409 .4494 .3064 53 .4069 .4040 .4103 .3970 .4163 .3846 .4248 .3661 .4359 .3404 .4497 .3058 54 .4069 .4039 .4104 .3969 9. 3967 .4164 .3843 .4250 .3657 .4361 .3399 .4500 .3051 55 9. 4070 9. 4038 9. 4105 9.4165 9. 3841 9. 4251 9.3654 9. 4363 9.3394 9.4503 9.3044 56 .4070 .4038 .4106 .3965 .4167 .3838 .4253 .3650 .4366 .3389 .4505 .3038 57 .4071 .4037 .4107 .3964 .4168 .3836 .4255 .3646 .4368 .3384 .4508 .3031 58 .4071 .4036 .4107 .3962 .4169 .3833 .4256 .3643 .4370 . 3379 .4510 .3024 59 .4071 .4035 9. 4034 .4108 9. 4109 .3960 9. 3959 .4170 9. 4172 . 3830 .4258 .3639 .4372 .3374 .4513 .3017 60 9. 4072 9. 3828 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+. i Argument=Elapsed Time.] 3*^ 6 h 7 h i! h Oi- lOh llh 1 Log. A. Log. B. Log. A. Log. B. Log. A. Log. B. Log. A. Log. B. 9. 0943 Log. A. Log. B. Log. A. Log. B. m. 9. 4515 9. 3010 9. 4685 9. 2530 9.4884 9. 1874 9. 5115' 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 , 4893- .1848 .5123 .0906 .5389 .9447 5691 .6701 a .4523 .2989 .4694 . 2502 . 4895- .1835 .5127 .0887 .5393 .9416 ,5696 .6632 4 .4526 9. 4528 .. 2982 .4697 9. 4701 .2492 9. 2483 .4899 9. 4902 .1822 9. 1809 .5132 9. 5136 .0867 9. 0848 .5398 9. 5403 .9384 8. 9352 .5701 .6560 6^6488 9. 2975 a 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 .4539 .2947 .4713 .2444 9. 2434 .4917 .1756 .5153 .0769 .5422 9.5427 .9221 .5728 .6183 10 9. 4542 9. 2940 9. 4716 9. 4921 9. 1742 9. 5157 9. 0749 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 15 .4552 9. 4555 .2911 .4729 . 2395 .4935 .1687 .5174 9.5178 . 0667 .5446 .9048 .5756 .5764 9. 2903 9. 4732 9. 2385 9. 4939 9. 1673 9. 0646 9. 5451 8. 9013 9.57ol 8. 5674 16 .4558 .2896 .4735 .2375 .4943 .1659 .5182 .0625 .5456 .8977 . 5767 . 5583 17 .4561 .2888 .4738 .2365 .4946 .1645 .5186 .0604 .5461 .8940 .5772 .5488 18 .4563 .2881 .4742 .2355 .4950 .1630 .5191 .0583 . 5466 .8903 .5778 .5392 -19 .4566 .2873 .4745 .2344 .4954 .1616 9. 1602 . 5195 .0561 9. 0540 .5470 9. 5475 .8866 .5783 .5293 20 9.4569 9. 2866 9. 4748 9. 2334 9. 4958 9.5199 8. 8829 9. 5789 8.5192 21 .4572 .2858 .4751 .2324 .4961 .1587 .5204 .0518 .5480 .8791 .5794 .5088 22 .4574 .2850 .4755 .2313 .4965 .1573 .5208 . 0496 .5485 .8752 .5800 .4981 23 .4577 .2843 .4758 .2303 .4969 .1558 .5212 .0474 .5490 .8713 .5806 .4871 24 .4580 .2835 .4761 .2292 .4973 .1543 .5217 .0452 . 5495 .8674 .5811 .4758 25 9. 4583 9. 2827 9.4764 9. 2282 9. 4977 9. 1528 9. 5221 9. 0429 9. 5500 8. 8634 9. 5817 8. 4641 26 .4585 .2819 .4768 .2271 .4980 .1513 .5225 .0406 .5505 .8594 .5822 .4521 27 .4588 .2812 .4771 .2261 .4984 .1498 .5230 .0383 .5510 .8553 .5828 .4397 28 .4591 .2804 .4774 .2250 .4988 .1483 .5234 .0360 .5515 .8512 .5834 .4270 29 30 .4594 .2796 9. 2788 .4778 9. 4781 .2239 .4992 9. 4996 .1468 .5238 .0337 .5520 .8470 .5839 . 4138 9. 4597 9. 2228 9. 1453 9. 5243 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 35 .4608 . 2756 .4794 .2184 9. 2173 .5011 .1390 5261 .0218 .5545 .8253 .5868 9. 5874 .3403 9. 4611 9. 2747 9. 4798 9. 5015 9. 1375 9. 5265 9. 0194 9. 5550 8. 8208 8. 3239 36 .4614 .2739 .4801 .2162 .5019 .1359 .5269 .0169 .5555 .8162 .5879 .3067 37 .4617 .2731 .4804 .2151 .5023 .1343 .5274 .0144 .5560 .8115 .5885 .2888 38 .4620 .2723 .4808 .2140 .5027 .1327 .5278 .0119 .5565 .8068 .5891 .2701 39 .4622 .2714 .4811 .2128 .5031 .1310 .5283 9.5287 .0094 .5570 .8020 .5897 .2505 8. 2299 40 9. 4625 9.2706 9.4815 9.2117 9. 5035 9.1294 9. 0069 9. 5576 8. 7972 9. 5902 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 9. 4640 .2672 9.2664 .4828 9. 4832 .2070 9. 2059 .5050 9.5054 .1228 9. 1211 .5305 .9965 . 5596 .7772 .5926 .1354 9. 5310 8. 9938 9. 5601 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 .4652 .2629 .4846 .2011 .5070 9. 5074 .1142 .5328 9. 5333 .9830 ..5622 .7505 .5955 7. 9756 50 9. 4655 9. 2620 9.4849 9. 1999 9. 1125 8. 9802 9. 5627 8. 7449 9. 5961 7. 9348 51 .4658 .2611 .4853 .1987 .5078 .1107 .5337 .9774 . 5632 .7392 .5967 .8897 52 .4661 .2602 .4856 .1974 .5082 .1089 .5342 .9745 .5638 .7335 .5973 .8391 53 .4664 . 2593 .4860 .1962 .5086 .1072 .5347 .9717 . 5643 .7276 .5979 .7817 54 55 .4667 9. 4670 .2584 .4863 .1950 9. 1937 .5091 .1054 .5351 .9688 .5648 .7217 .5985 .7154 9. 2575 9. 4867 9. 5095 9. 1036 9. 5356 8. 9659 9. 5654 8. 7156 9. 5991 7. 6368 56 .4673 .2566 .4870 .1925 .5099 .1017 .5361 .9630 .5659 .7094 .5997 .5405 57 .4676 .2557 .4874 .1912 .5103 .0999 .5365 .9600 .5664 .7032 .6003 .4162 58 .4679 .2548 .4877 .1900 .5107 .0981 .5370 .9570 .5669 .6968 .6009 .2407 59 60 .4682 .2539 .4881 .1887 .5111 .0962 9. 0943 .5375 .9540 .5675 9. 5680 .6903 .6015 6. 9591 9. 4685 9. 2530 9. 4884 9. 1874 9. 5115 9. 5379 8. 9509 8. 6837 9. 6021 Inf. 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 Midnight. B — . 1 Argument = Elapsed Time. | 3*" 12h 181' 1 14h ISh lefc 17>> 1 Log. A. Log. B. Log. A. Log. B. Log. A. Log. B. Log. A. Log. B. L<«. A. Log.B. Log. A. Log.B. m. 9. 6021 Inf. 9.6406 8. 7563 9. 6841 9.0971 9. 7333 9. 3162 9. 7895 9.4884 9. 8539 9. 6383 1 .6027 6. 9603 .6412 .7641 .6848 .1014 .7342 .3194 .7905 .4911 .8550 .6407 2 .6033 7. 2431 .6419 .7718 .6856 .1057 .7351 .3225 .7915 .4937 .8562 .6431 3 .6039 .4198 .6426 .7794 .6864 .1099 .7360 .3256 .7925 .4963 .8573 .6455 4 .6045 .5453 .6433 .7868 .6872 .1141 .7369 .3287 .7935 .4990 .8585 .6478 5 9. 6051 7.6428 9.6440 8. 7942 9. 6879 9. 1183 9. 7378 9. 3319 9. 7945 9. 5016 9. 8597 9. 6502 6 .6057 .7226 .6447 .8015 .6887 .1224 .7386 .3350 .7955 .5042 .8608 .6526 7 .6063 .7902 .6454 .8087 .6895 .1265 .7395 .3380 .7965 .5068 .8620 .6550 8 .6069 .8488 .6461 .8158 .6903 .1306 .7404 . 3411 .7975 .5094 .8632 .6573 9 10 .6075 .9005 .6467 .8227 .6911 .1347 .7413 .3442 9. 3472 .7986 9. 7996 .5120 .8644 .6597 9. 6082 7. 9469 9. 6474 8. 8296 9. 6919 9. 1387 9. 7422 9. 5146 9. 8655 9. 6621 n .6088 .9889 .6481 .8364 .6926 .1428 .7431 .3503 .8006 .5171 .8667 .6644 12 .6094 8. 0273 .6488 .8432 .6934 .1468 .7440 .3533 .8016 .5197 .8679 .6668 13 .6100 .0627 .6495 .8498 .6942 .1507 .7449 .3563 .8027 .5223 .8691 .6691 14 15 .6106 9. 6112 .0955 8. 1260 .6502 . 8564 8. 8628 .6950 9. 6958 .1547 .7458 .3593 .8037 .5248 .8703 . 6715 9. 6509 9. 1586 9. 7467 9. 3623 9. 8047 9. 5274 9. 8715 9. 6738 16 .6119 .1547 .6516 .8692 .6966 .1625 .7476 . 3653 .8058 .5300 .8727 .6762 17 .6125 .1816 .6523 .8756 .6974 .1664 .7485 .3683 .8068 .5325 .8739 .6785 18 .6131 .2071 .6530 .8818 .6982 .1703 .7494 .3713 .8078 .5351 .8751 .6809 19 .6137 .2312 .6538 .8880 8. 8941 .6990 .1741 .7503 9. 7512 .3742 .8089 .5376 .8763 .6832 20 9.6144 8. 2541 9. 6545 9. 6998 9. 1779 9. 3772 9. 8099 9. 5401 9. 8775 9. 6856 21 .6150 .2759 .6552 .9002 .7006 .1817 .7522 .3801 .8110 .5427 .8787 .6879 22 .6156 .2967 .6559 .9062 .7014 .1855 .7531 .3831 .8120 .5452 .8799 .6903 23 .6163 .3166 .6566 .9121 .7022 .1893 .7540 .3860 .8131 .5477 .8812 .6926 24 25 .6169 .3357 .6573 9. 6580 .9180 8. 9238 .7030 9. 7038" .1930 .7549 .3889 .8141 .5502 .8824 .6949 9. 6175 8. 3540 9. 1967 9. 7558 9. 3918 9. 8152 9. 5528 9. 8836 9. 6973 26 .6182 .3717 .6588 .9295 .7047 .2004 .7568 .3947 .8162 .5553 .8848 .6996 27 .6188 .3887 .6595 .9352 .7055 .2041 .7577 .3976 .8173 .5578 .8861 .7019 28 .6194 .4051 .6602 .9408 .7063 .2078 .7586 . 4005 .8184 .5603 .8873 .7043 29 .6201 .4210 .6609 .9464 .7071 .2114 9. 2150 .7595 .4033 .8194 .5628 .8885 .7066 30 9. 6207 8. 4363 9. 6616 8. 9519 9. 7079 9. 7605 9. 4062 9. 8205 9. 5653 9. 8898 9. 7089 31 .6214 .4512 .6624 .9573 .7088 .2186 .7614 .4090 .8216 .5677 .8910 .7112 32 .6220 .4657 .6631 .9627 .7096 .2222 .7624 .4119 .8227 .5702 .8923 .7136 33 .6226 .4796 .6638 .9681 .7104 .2258 .7633 .4147 .8237 .5727 .8935 .7159 34 35" .6233 .4932 .6645 .9734 8. 9787 .7112 .2293 .7642 .4175 .8248 .5752 .8948 .7182 9. 6239 8. 5064 9. 6653 9. 7121 9.2329 9. 7652 9. 4204 9. 8259 9. 5777 9. 8961 9.7205 36 .6246 .5192 .6660 .9839 .7129 .2364 .7661 .4232 .8270 .5801 .8973 .7228 37 .6252 .5318 .6667 .9891 .7137 .2399 .7671 .4260 .8281 .5826 .8986 .7251 38 .6259 .5440 .6675 .9942 .7146 .2434 .7680 .4288 .8292 .5850 .8999 .7275 39 40 .6265 .5559 .6682 .9993 9. 0043 .7154 .2468 .7690 .4316 .8303 .5875 .9011 .7298 9. 6272 8. 5675 9. 6690 9. 7162 9. 2503 9. 7699 9.4343 9. 8314 9.5900 9. 9024 9. 7321 41 .6279 .5788 .6697 .0093 .7171 .2537 .7709 .4371 . 8325 .5924 .9037 .7344 42 .6285 .5899 .6704 .0142 .7179 .2571 .7718 .4399 .8336 .5948 .9050 .7367 43 .6292 .6008 .6712 .0191 .7187 .2605 .7728 .4426 .8347 .5973 .9063 .7390 44 45 .6298 .6114 .6719 .0240 .7196 9.7204 .2639 .7738 9. 7747 .4454 .8358 .5997 .9075 . 7413 9. 6305 8. 6218 9. 6727 9. 0288 9. 2673 9.4481 9. 8369 9.6022 9.9088 9. 7436 46 .6311 .6320 .6734 .0336 .7213 .2706 . 7757 .4509 .8380 .6046 .9101 .7459 47 .6318 .6419 .6742 .0384 .7221 .2740 .7767 .4536 .8391 .6070 .9114 .7482 48 .6325 .6517 .6749 .0431 .7230 .2773 .7776 .4563 .8402 .6094 .9127 . 7505 49 50 .6331 .6613 .6757 9.6764 .0478 .7238 .2806 .7786 .4590 .8414 .6119 .9140 .7529 9. 6338 8. 6707 9. 0524 9. 7247 9. 2839 9. 7796 9.4617 9. 8425 9. 6143 9.9154 9. 7552 51 .6345 .6799 .6772 .0570 .7256 .2872 .7806 .4644 .8436 .6167 .9167 .7575 52 .6351 .6890 .6779 .0616 .7264 - . 2905 .7815 .4671 .8447 .6191 .9180 .7598 53 .6358 .6979 .6787 .0662 .7273 .2937 .7825 .4698 .8459 .6215 .9193 .7621 54 55 .6365 9. 6372 .7067 8.7153 .6795 .0707 .7281 .2970 .7835 .4725 .8470 .6239 .9206 .7644 9. 6802 9. 0752 9. 7290 9.3002 9.7845 9. 4752 9. 8481 9. 6263 9. 9220 9.7667 56 .6378 .7237 .6810 .0796 .7299 .3034 .7855 .4778 .8493 .6287 .9233 .7690 57 .6385 .7321 .6818 .0840 .7307 .3066 .7865 .4805 .8504 .6311 .9246 .7713 58 .6392 .7402 .6825 .0884 .7316 .3098 .7875 .4831 .8516 .6335 .9260 .7736 59 .6399 . 7483 .6833 .0928 .7324 .3130 .7885 .4858 .8527 .6359 .9273 .7759 60 9.6406 8. 7563 9. 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 Altitudes. For Noon, A — ; for Midnight, A +; for Noon or Midnight, B — . | Argument = Elapsed Time.] ISh 19" aoh 21h 22h 23i> 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. w. 9. 9287 9. 7782 0. 0172 9. 9167 0. 1249 0. 0625 0. 2623 0. 2279 0.4623 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 .7873 .0237 .9260 .1330 .0727 .2729 .2401 .4680 .4540 .8000 .7967 9. 9355 9. 7896 0. 0253 9. 9284 0.1351 0. 0753 0. 2756 0. 2431 0. 4720 0. 4582 0. 8081 0. 8049 6 .9368 .7919 .0270 .9307 .1371 .0779 .2783 .2462 .4761 .4625 .8163 .8133 7 .9382 .7942 .0286 .9331 .1392 .0805 .2810 .2493 .4801 .4668 .8247 .8218 8 .9396 .7965 .0303 .9355 .1412 .0830 .2838 .2524 .4842 .4711 .8333- .8305 9 10 .9410 .7988 .0319 .9378 9. 9402 .1433 .0856 .2865 .2556 0. 2587 .4884 .4755 .8420 .8393 9. 9424 9. 8011 0. 0336 0. 1454 0.0882 0. 2893 0. 4926 0. 4799 0. 8508 0.8483 11 .9437 .8034 .0353 .9426 .1475 .0909 .2921 .2619 .4968 .4844 .8599 .8574 12 .9451 .8057 .0370 .9449 .1496 .0935 .2949 .2650 .5010 .4889 .8691 .8667 13 .9465 .8080 .0386 .9473 .1517 .0961 .2977 .2682 .5053 .4934 .8786 .8763 14 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 .9550 .8218 .0489 .9616 .1645 .1119 . 3150 0. 3179 .2876 .5319 .5213 .9396 .9378 20 9.9564 9. 8241 0. 0506 9. 9640 0. 1667 0. 1146 0.2909 0. 5365 0. 5261 0. 9506 0. 9489 21 .9579 .8264 .0523 .9664 .1689 .1173 .3208 .2942 .5411 .5309 .9618 .9603 22 .9593 .8287 .0541 .9687 .1711 .1200 .3238 .2975 .5458 .5358 .9734 .9719 23 .9607 .8310 .0558 .9711 .1733 .1226 .3268 .3008 .5505 .5407 .9853 .9839 24 25 .9622 .8333 . 0576 . 9735 .1755 .1253 .3298 .3041 .5553 .5457 .9975 .9961 1. 0087 9. 9636 9. 8356 0. 0593 9. 9760 0. 1777 0. 1280 0. 3328 0. 3075 0. 5601 0. 5507 LOlOO 26 .9651 .8379 .0611 .9784 .1799 .1308 .3359 .3109 .5649 .5557 .0228 .0216 27 .9665 .8402 .0628 .9808 .1821 .1335 .3389 .3143 .5698 .5608 .0361 .0350 28 .9680 .8425 .0646 .9832 .1844 .1362 .3420 .3177 .5748 .5660 .0497 .0487 29 .9695 .8448 .0664 .9856 .1867 .1389 .3451 .3211 0. 3245 .5798 .5712 .0638 .0628 30 9. 9709 9.8471 0. 0682 9. 9880 0. 1889 0. 1417 0.3482 0. 5848 0.5764 1. 0783 1. 0774 31 .9724 .8494 .0700 .9904 .1912 .1444 .3514 .3280 .5899 .5817 .0934 .0925 32 .9739 .8517 .0718 .9929 .1935 .1472 .3545 .3315 . 5951 .5871 .1089 .1081 33 .9754 .8540 .0736 .9953 .1958 .1499 .3577 .3350 .6003 .5925 .1250 .1242 34 .9769 .8563 .0754 .9977 .1981 .1527 0. 1555 .3609 0.3641 .3385 0.3420 .6056 .5979 .1416 .1409 35 9.9784 9. 8586 0. 0772 0.0002 0.2004 0. 6110 0.6034 1. 1590 1. 1583 36 .9798 .8609 .0790 .0026 .2028 .1582 .3674 .3456 .6164 .6090 .1770 .1764 37 .9813 .8632 .0809 .0051 .2051 .1610 .3706 .3491 .6218 .6147 .1958 .1952 38 .9829 .8655 .0827 .0075 .2075 .1638 .3739 .3527 .6273 .6204 .2154 .2149 39 .9844 .8678 . 0845 .0100 .2098 .1667 .3772 .3563 .6329 .6261 .2359 .2354 40 9. 9859 9. 8701 0.0864 0. 0124 0. 2122 0. 1695 0. 3805 0. 3599 0. 6386 0. 6319 1. 2573 1. 2569 41 .9874 .8724 .0883 .0149 .2146 .1723 .3839 .3636 .6443 .6378 .2799 .2795 42 .9889 .8748 .0901 .0173 .2170 .1751 .3873 .3673 . 6501 .6438 .3037 .3033 43 .9904 .8771 .0920 .0198 .2194 .1780 .3907 .3710 .6560 .6498 .3288 .3285 44 45 .9920 9. 9935 .8794 .0939 0. 0958 .0223 .2218 .1808 .3941 .3747 0.3784 .6619 . 6559 .3554 .3552 9. 8817 0. 0248 0. 2243 0. 1837 0. 3975 0. 6679 0. 6621 1. 3837 1. 3835 46 .9951 .8840 .0976 .0272 .2267 .1866 .4010 .3822 .6740 .6684 .4140 .4138 47 .9966 .8863 .0995 .0297 .2292 .1895 .4045 .3859 .6802 .6747 .4465 .4463 48 .9982 .8887 .1015 .0322 .2316 .1924 .4080 .-3897 .6865 .6811 .4815 .4814 49 .9998 .8910 .1034 .0347 .2341 .1953 .4115 .3936 0. 3974 .6928 0. 6993 .6876 .5196 .5195 50 '0. 0013 9. 8933 0. 1053 0. 0372 0.2366 0. 1982 0. 4151 0. 6942 1. 5613 1.5612 51 .0029 .8956 .1072 .0397 .2391 .2011 .4187 .4013 .7058 .7008 .6074 .6073 52 .0044 .8980 .1092 .0422 .2416 .2040 .4223 .4052 .7124 .7076 .6588 .6587 53 .0060 .9003 .1111 .0447 .2442 .2070 .4260 .4091 .7191 .7144 .7171 .7171 54 .0076 .9026 .1131 .0473 .2467 0. 2493 .2099 .4297 .4130 0.4170 .7259 .7214 .7844 .7843 55 0. 0092 9. 9050 0. 1150 0. 0498 0.2129 0. 4334 0. 7328 0. 7284 1. 8638 1. 8638 56 .0108 .9073 .1170 .0523 .2518 . 2159 .4371 .4210 . 7398 .7355 .9610 .9610 57 .0124 .9096 .1190 ' . 0548 .2544 .2189 .4408 .4250 .7469 .7428 2. 0863 2. 0863 58 .0140 .9120 .1209 .0574 .2570 .2219 .4446 .4291 .7541 .7501 .2627 .2627 59 .0156 .9143 .1229 .0599 .2596 0. 2623 .2249 .4485 .4331 .7615 .7576 2.5640 2.5640 60 0. 0172 9. 9167 0. 1249 0. 0625 0. 2279 0. 4523 0. 4372 0. 7689 0.7652 Inf. Inf. TABLE 38. [Page 575 Error in Longitude due to one minute Error of Latitude. 2 ad. i . P-I Latitude. i . nag at 6 0° 6° 10° 15° 20° 25° 30° 85° 40° 45° 50° 56° 60° 66° 70° 76° o 10 20 30 40 50 60 10 20 30 40 50 60 15 20 30 40 50 60 o 110 / .4 .4 .4 .5 .7 .9 1 4 4 5 6 9 / .4 .5 .6 .8 1.2 / .5 .6 .7 1.0 .5 .7 .9 1.3 / .6 .8 1.1 1 .7 1.0 1.5 .8 1.2 2.3 1 1.0 1.6 1 L3 2.6 .9 1.6 t L8 1.2 2.7 1 2.9 L8 3.0 t / / o 110 o 10 20 30 40 50 60 105 .3 .3 .3 .4 .4 .6 3 3 4 5 6 9 .3 .4 .5 .6 .8 1 3 4 6 7 2 .4 .5 .7 1.0 .4 .6 .8 1.3 .5 .7 1.1 .6 .9 1.5 .8 1.2 2.4 105 10 20 30 40 50 60 100 .2 .2 .2 .2 .3 .3 2 2 3 3 4 6 .2 .3 .3 .4 .6 .9 3 3 4 6 8 .3 .4 .5 .7 1.2 .4 .5 .6 .9 .4 .5 .8 1.3 .5 .7 1.1 2.1 .6 .9 L5 .8 LI 2.4 1.1 L6 1.6 2.7 2.9 100 15 20 30 40 50 60 15 20 30 40 50 60 95 '.2 1 1 2 2 3 3 .1 .2 .2 .3 ,4 .6 2 2 3 4 6 9 .2 .3 .4 .5 .8 .3 .3 .5 .7 1.1 .3 .4 .6 .9 .4 .5 .8 1.3 .5 .6 LO 2.1 .6 .8 L5 .8 LI 2.5 LI L6 1.7 2.8 3.0 95 15 20 30 40 50 60 20 30 40 50 60 70 90 .0 .0 .0 .0 .0 .0 1 1 1 2 2 .1 .1 .2 .2 .3 .6 1 1 2 3 4 5 1 .1 .2 .3 .5 .9 .2 .3 .5 .8 .2 .4 .6 1.1 .3 .5 .9 .4 .7 1.3 .6 1.0 2.2 .7 1.5 1.1 2.7 1.6 3.0 90 20 30 40 50 60 70 20 30 40 50 60 70 20 30 40 50 60 70 85 .1* .1* .1* .1* .2* .3* 1* .0 .0 .0 .1 .1 .2 1 1 2 3 6 .0 .1 .2 .3 .5 1.1 .1 .2 .3 .5 .9 .1 .2 .4 .7 .2 .4 .6 1.1 .3 .5 .9 .3 .7 L3 .5 LO 2.3 .7 L5 1.0 2.7 L6 3.1 85 20 30 40 50 60 70 80 " '.2* .2* .2* .3* .4* .6* 2* 2* 2* 2* 2* 3* .1* .1* .1* .1* .0 .0 1* 1 1 2 .1* .0 .1 .2 .3 .6 .0 .1 .2 .3 .5 1.2 .0 .1 .3 .5 .9 .0 .2 .4 .7 .1 .3 .6 1.1 .1 .4 .9 .2 .6 L3 .4 .9 2.4 .5 L5 .9 2.8 1.5 3.1 80 20 30 40 50 60 70 20 30 40 50 60 70 75 .3* .3* .4* .4* .6* 1.2* 3* 3* 3* 3* 4* 6* .2* .2* .2* .2* .2* .3* 2* 2* 1* 1* 1* .2* .1* .1* .0 .1 .2 .1* .1* .0 .1 .3 .6 .1* .0 .1 .3 .5 L2 .1* .1 .2 .5 .9 .1* .1 .4 .7 •.2t .0 .2 .4 .9 .0 .2 .5 1.1 .2* .0 .3 .7 .0 .4 .8 .1 .6 1.3 .2 .9 2.5 .3 1.5 .6 3.0 1.2 75 20 30 40 50 60 70 20 30 40 50 60 70 70 .4* .4* .5* .6* .9* 1 4* 4* .4* 5* 6* 2* .3* .3* .3* .3* .4* .6* 3* 3* 3* 2* 3* 3* .3* .2* .2* .2* .1* .1* .3* .2* .1* .0 .1 .2 .2* .1* .0 .1 .2 .6 .2* .1* .1 .3 .5 1.2 .2* .1 .5 LI .2* .2 .8 .2* .6 1.3 60° .2* .8 2.6 .2* L5 .2* 3.1 VO 20 30 40 50 60 70 3 m Sg 0° 5° 10° 15° 20° 25° 80° 85° 40° 46° 50° 55° 66° 70° 75° "3 2 59 28 8 31 52 84177 181 15823 84282 182 15718 00105 99895 1 60 28 32 84358 181 15642 84464 182 15536 00106 99894 M. M. Hour p. M. Hour A. M. Cosine. DiS.l'. Secant. Cotangent. Diff. 1'. Tangent. Cosecant. Sine es'* 86° Page 612] TABLE U. 4° Log. Sines, Tangents, and Secants 175° M. Hour A. M. Hour p. M. Sine. Diff . 1'. Cosecant. Tangent. Difif. 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 32 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 85717 176 14283 00112 99888 53 8 26 56 33 4 85780 175 14220 85893 176 14107 00113 99887 52 9 10 26 48 11 26 40 33 12 85955 173 14045 86069 174 13931 00114 99886 51 50 33 20 8. 86128 173 11. 13872 8. 86243 174 11. 13757 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 18 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 15 11 26 34 8. 86987 169 11. 13013 8. 87106 171 11. 12894 10. 00120 9. 99880 45 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 34 32 87661 168 12339 87785 168 12215 00123 99877 41 11 25 20 34 40 8. 87829 166 11.12171 8. 87953 167 11. 12047 10. 00124 9. 99876 40 21 25 12 34 48 87995 166 12005 88120 167 11880 00125 99875 39 22 25 4 34 56 88161 165 11839 88287 166 11713 00126 99874 38 23 24 56 35 4 88326 164 11674 88453 165 11547 00127 99873 37 24 24 48 35 12 88490 164 11510 88618 165 11382 00128 99872 36 25 11 24 40 35 20 8. 88654 163 11. 11346 8. 887b3 165 11. 11217 10. 00129 9. 99871 35 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 30 11 24 36 8. 89464 161 11. 10536 8. 89598 162 11. 10402 10. 00134 9. 99866 31 23 52 36 8 89625 159 10375 89760 160 10240 00135 99865 29 32 23 44 36 16 89784 159 10216 89920 160 10080 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 "il. 09740" 90240 159 09760 00138 99862 9. 99861 26 25 11 23 20 36 40 8. 90260 157 8. 90399 158 11. 09601 10. 00139 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 166 08971 00143 99857 21 40 11 22 40 *0 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 08350 00147 99853 17 44 45 22 8 37 52 91655 152 08345 91803 154 08197 00148 99852 16 11 22 38 8. 91807 152 11.08193 8. 91957 153 11. 08043 10.00149 9. 99851 15 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 11.07439 8. 92716 150 11. 07284 10. 00155 9. 99845 10 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 06835 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 06391 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 99836 1 60 20 40 94030 144 05970 94195 145 05805 00166 99834 M. Hour p. M. Hour A. M. Cosine. Diflf. 1'. Secant. Cotangent. Diff.l'. Tangent. Cosecant. Sine. M. 94° 86° 6° TABLE U. Log. Sines, Tangents, and Secants. A B B [Page 613 5 6 7 8 10 11 12 13 14 Hour A. M. Ho\ir p. M 11 20 00 19 52 19 44 19 36 19 28 11 19 20 19 12 19 04 18 56 18 48 11 18 40 18 32 18 24 18 16 18 08 11 18 00 17 52 17 44 17 36 17 28 11 17 20 17 12 17 04 16 56 16 48 40 00 40 08 40 16 40 24 40 32 40 40 40 48 40 56 41 04 41 12 41 20 41 28 41 36 41 44 41 52 30 ■31 32 33 ^4 35 36 37 38 39 40 41 42 43 44 45 46 47 48 J9 50 51 52 53 55 56 57 58 59 60 11 16 40 16 32 16 24 16 16 16 08 11 16 00 15 52 15 44 15 36 15 28 42 00 42 08 42 16 42 24 42 32 42 40 42 48 42 56 43 04 43 12 Sine. 8. 94030 94174 94317 94461 94603 8. 94746 94887 95029 95170 95310 Difl. Cosecant. Tangent. Diff. Cotangent. Secant 8. 95450 95589 95728 95867 96005 8. 96143 96280 96417 96553 96689 11. 05970 05826 05683 05539 05397 11. 05254 05113 04971 04830 04690 43 20 43 28 43 36 43 44 43 52 11 15 20 15 12 15 04 14 56 14 48 11 14 40 14 32 14 24 14 16 14 08 11 14 00 13 52 13 44 13 36 13 28 44 00 44 08 44 16 44 24 44 32 44 40 44 48 44 56 45 04 45 12 45 20 45 28 45 36 45 44 45 52 46 00 46 08 46 16 46 24 46 32 8. 96825 96960 97095 97229 97363 8. 97496 97629 97762 97894 98026 8. 98157 98288 98419 98549 98679 8. 98808 98937 99066 99194 99322 8. 99450 99577 99704 99830 99956 n 13 20 46 40 13 12 46 48 13 04 46 56 12 56 47 04 12 48 47 12 11 12 40 47 20 12 32 47 28 12 24 47 36 12 16 47 44 12 08 47 52 12 00 48 00 Hour p. M. Hour A. M, 9. 00082 00207 00332 00456 00581^ 9.00704 00828 00951 01074 01196 9. 01318 01440 01561 01682 01803 01923 Cosine. 55 57 59 61 JM 66 68 70 72 JA 77 79 81 83 86 88 90 92 94 96 11. 04550 04411 04272 04133 03995 11.03857 03720 03583 03447 03311 94195 94340 94485 94630 94773 94917 95060 95202 95344 95486 95627 95767 95908 96047 96187 11. 05805 2 05660 4 05515 05370 05227 11.03175 03040 02905 02771 02637 11. 02504 02371 02238 02106 01974 11. 01843 01712 01581 01451 01321 11 99 101 103 105 107 110 112 114 116 118 121 123 125 127 129 132 Diff. 01192 01063 00934 00806 00678 11 00550 0042 00296 00170 00044 10, 99918 99793 99668 99544 99419 96325 96464 96602 96739 96877 11. 05083 04940 04798 04656 04514 11. 04373 04233 04092 03953 03813 10. 00166 00167 00168 00169 00170 10. «)6l71 00172 00173 00175 00176 10.00177 00178 00179 00180 00181 . 97013 97150 97285 97421 97556 , 97691 97825 97959 98092 98225 , 98358 98490 98622 98753 8. 99015 99145 99275 99405 99534 8. 99662 99791 99919 9. 00046 00174 10, 99296 99172 99049 98926 98804 10, 98682 98560 98439 98318 98197 98077 9. 00301 00427 00553 00679 00805 11.03675 03536 03398 03261 03123 11. 02987 02850 02715 02579 02444 11.02309 02175 02041 01908 01775 11.01642 01510 01378 01247 01116 Diff. Cosine. 9. 99834 99833 99832 99831 998 30 9. 99829 99828 99827 99825 99824 9.99823 99822 10. 00183 00184 00185 00186 00187 10. 00188 00190 00191 00192 00193 10. 00194 00196 00197 00198 00199 77 \ 11. 00985 00855 00725 00595 00466 89 ! 11 91 93 95 97 9. 00930 01055 01179 01303 01427 9. 01550 01673 01796 01918 02040 02162 100 102 104 106 108 111 113 115 117 120 122 124 126 128 131 133 10, 00338 00209 00081 99954 99826 10 99699 99573 99447 99321 99195 10, 99070 98945 98821 98697 98573 10. 98450 98327 98204 98082 97960 97838 10. 00200 00202 00203 00204 00205 10. 00207 00208 00209 00210 00212 10. 00213 00214 00215 00217 00218 10. 00219 00220 00222 00223 J)0224 10. 00225 00227 00228 00229 00231 10. 00232 00233 00235 00236 00237 00239 99821 99820 99819 9.99817 99816 99815 99814 99813 M. 9. 99812 99810 99809 99808 99807 9. 99806 99804 99803 99802 99801 9.99800 99798 99797 99796 99795 9. 99793 99792 99791 99790 99788 21 9. 99787 99786 99785 99783 99782 9. 99781 99780 99778 99777 99776 9. 99775 99773 99772 99771 997 69 99768 99767 99765 99764 99763 99761 96° Cotangent. Diff. Tangent. Cosecant. Diff. Sine. M 3 Seconds of time 1 Prop, parts of cols, ■{I 1' js 3" 4" 5- 6> 7' 16 17 33 3S 49 50 66 66 1 82 83 1 99 100 1 115 116 1 Page 614] TABLE 44. Log. Sines, Tangents, and Secants. 6° A - A B B C c 173° M. Hour A. M. Hour p. M. Sine. Diflf. Cosecant. Tangent. Diff. Cotangent. Secant. Diff. Cosine. M. 60 11 12 00 48 00 9. 01923 10. 98077 9. 02162 10. 97838 10. 00289 9. 99761 1 11 52 48 08 02043 2 97957 02283 2 97717 00240 99760 59 2 11 44 48 16 02163 4 97837 02404 4 97596 00241 99759 58 8 11 36 48 24 02283 .6 97717 02525 6 97475 00243 99757 57 4 5 11 28 48 32 02402 7 9 97598 02645 8 97355 10.97234 00244 10. 00245 99756 56 55 11 11 20 48 40 9. 02520 10. 97480 9. 02766 9 9. 99755 6 11 12 48 48 02639 11 97361 02885 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 99751 52 9 10 10 48 49 12 0'49 20 02992 17 97008 03242 17 96758 00251 99749 51 11 10 40 9. 08109 19 10. 96891 9. 03861 19 10. 96639 10. 00252 9. 99748 50 11 10 82 49 28 03226 20 96774 03479 21 96521 00258 99747 49 12 10 24 49 36 03342 22 96658 03597 23 96403 00255 99745 48 18 10 16 49 44 03458 24 96542 03714 24 96286 00256 99744 47 14 10 08 49 52 03574 26 96426 03832 26 96168 00258 99742 46 15 11 10 00 50 00 9. 08690 28 10? 96310 9. 08948 28 10. 96052 10. 00259 9. 99741 45 16 9 52 50 08 08805 80 96195 04065 30 95935 00260 99740 44 17 9 44 50 16 08920 31 96080 04181 32 95819 00262 99738 48 18 9 86 50 24 04034 83 95966 04297 34 95708 00268 99737 42 19 9 28 50 32 04149 85 95851 04413 36 95587 00264 99736 41 40 20 11 9 20 50 40 9. 04262 37 10. 95738 9. 04528 38 10. 95472 10. 00266 9. 99784 21 9 12 50 48 04876 39 95624 04643 39 95357 00267 99788 89 22 9 04 50 56 04490 41 95510 04758 41 95242 00269 99731 38 28 8 56 51 04 04603 43 95397 04873 43 95127 00270 99780 37 24 . 8 48 51 12 04715 44 95285 04987 45 47 95013 10. 94899 00272 99728 36 35 25 11 8 40 51 20 9. 04828 46 10. 95172 9. 05101 10. 00278 9. 99727 26 8 82 51 28 04940 48 95060 05214 49 94786 00274 99726 34 27 8 24 51 86 05052 50 94948 05328 51 94672 00276 99724 33 28 8 16 51 44 05164 52 94836 05441 58 94559 00277 99723 32 29 8 08 51 52 05275 54 94725 05553 54 94447 00279 99721 9. 99720 81 80 80 11 8 00 52 00 9. 05886 56 10. 94614 9. 05666 56 10. 94884 10. 00280 31 7 52 52 08 05497 57 94508 05778 58 94222 00282 99718 29 82 7 44 52 16 05607 59 94393 05890 60 94110 00288 99717 28 88 7 86 52 24 05717 61 94283 06002 62 93998 00284 99716 27 84 7 28 52 32 05827 1 68 94173 06113 64 93887 10. 93776 00286 10. 00287 99714 26 85 11 7 20 52 40 9. 05937 65 10. 94063 9. 06224 66 9. 99713 25 86 7 12 52 48 06046 67 93954 06335 68 93665 00289 99711 24 87 7 04 52 56 06155 69 93845 06445 69 93555 00290 99710 28 88 6 56 53 04 06264 70 98786 06556 71 9.3444 00292 99708 22 39 6 48 53 12 53 20 06372 9. 06481 72 93628 06666 73 93834 00293 10. 00295 99707 9. 99705 21 20 40 11 6 40 74 10. 93519 9. 06775 75 10. 98225 41 6 82 53 28 06589 76 93411 06885 77 98115 00296 99704 19 42 6 24 58 36 06696 78 93804 06994 79 93006 00298 99702 18 48 6 16 58 44 06804 80 93196 07103 81 92897 00299 99701 17 44 6 08 53 52 06911 81 98089 07211 83 84 92789 00301 99699 16 15 45 U 6 00 54 00 9. 07018 83 10. 92982 9. 07320 10. 92680 10. 00302 9. 99698 46 5 52 54 08 07124 85 92876 07428 86 92572 00804 99696 14 47 5 44 54 16 07231 87 92769 07536 88 92464 00305 99695 18 48 5 36 54 24 07837 89 92663 07648 90 92357 00807 99693 12 49 50 5 28 11 5 20 54 32 07442 91 92558 07751 92 92249 10. 92142 00808 99692 9. 99690 11 10 54 40 9. 07548 93 10. 92452 9. 07858 94 10. 00810 51 5 12 54 48 07653 94 92347 07964 96 92036 00811 99689 9 52 5 04 54 56 07758 96 92242 08071 98 91929 00313 99687 8 58 4 56 55 04 07863 98 92137 08177 99 91823 00314 99686 1 54 4 48 55 12 07968 100 92032 08288 101 91717 00316 99684 6 5 155 11 4 40 55 20 9. 08072 102 10. 91928 9. 08889 103 10. 91611 10. 00317 9. 99688 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 00820 99680 8 58 4 16 55 44 08383 107 91617 08705 109 91295 00822 99678 2 59 4 08 55 52 08486 109 91514 08810 HI 91190 00828 99677 1 60 4 00 56 00 08589 111 91411 08914 113 91086 00825 99675 M. M. Hour p. M. Hour A. M. Cosine. Diflf. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. Sine. i!: A A B B C C 88° Seconds of time iB 2« 3« 4s 6' 6» 7" (A. Prop, parts of cols. < B Ic 14 14 28 28 42 42 1 56 56 1 69 70 1 83 84 1 97 98 1 TABLE 4-t. [Page 615 - Log. Sines, Tangents, and Secants. JO A A B B C C 172° M. Hour A. M. Hour p. M. Sine. Diff. Cosecant. Tangent. Difl. Cotangent. Secant. Diff. Cosine. M. 60 11 4 56 9. 08589 10. 91411 9. 08914 jlO. 91086 10. 00325 9.99675 1 3 52 56 8 08692 2 91308 09019 2 1 90981 00326 1 99674 59 2 3 44 56 16. 08795 3 91205 09123 3 90877 00328 99672 58 3 3 36 56 24 08897 5 91103 09227 5 \ 90773 00330 99670 57 4 3 28 56 32 08999 6 91001 09330 7 90670 00331 t 99669 9. '99667 56 55 5 11 3 20 56 40 9. 09101 8 10. 90899 9. 09434 8 110.90566 10. 00333 6 3 12 56 48 09202 10 90798 09537 10 90463 00334 ; 99666 54 7 3 4 56 56 09304 11 90696 09640 11 90360 00336 99664 53 8 2 56 57 4 09405 13 90595 09742 13 90258 00337 99663 52 9 2 48 57 12 57 20 09506 14 16 90494 09845 15 16 90155 00339 I 99661 51 10 11 2 40 9. 09606 10. 90394 9. 09947 10. 90053 10. 00341 9. 99659 50 11 2 32 57 28 09707 18 90293 10049 18 1 89951 00342 99658 49 12 2 24 57 36 09807 19 90193 10150 20 1 89850 00344 99656 48 13 2 16 57 44 09907 21 90093 10252 21 89748 00345 99655 47 14 15 2 8 57 52 10006 22 89994 10353 23 89647 00347 99653 46 11 2 58 9. 10106 24 10. 89894 9. 10454 24 10.89546 10. 00349 9. 99651 45 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 I 99648 43 18 1 36 58 24 10402 29 89598 10756 29 , 89244 00353 1 i 99647 42 19 1 28 58 32 10501 30 i 89499 32 110.89401 10856 31 , 89144 00355 99645 41 20 11 1 20 58 40 9. 10599 9. 10956 33 10.89044 10. 00357 9. 99643 40 21 1 12 " 58 48 10697 34 ! 89303 11056 34 88944 00358 1 99642 39 22 1 4 58 56 10795 35 89205 11155 36 ' 88845 00360 1 99640 38 23 56 59 4 10893 37 89107 11254 37 ; 88746 00362 1 i 99638 37 24 48 59 12 10990 38 89010 11353 39 ! 88647 00363 1 i 99637 36 35 25 11 40 59 20 9. 11087 40 110.88913 9. 11452 41 ilO. 88548 10. 00365 1 19.99635 26 32 59 28 11184 42 i 88816 11551 42 88449 00367 1 1 99633 34 27 24 59 36 11281 43 1 88719 11649 44 88351 00368 1 99632 33 28 16 59 44 11377 45 88623 11747 46 : 88253 00370 1 99630 32 29 30 8 59 52 11474 46 88526 11845 47 i 88155 00371 99629 31 30 11 10 9. 11570 48 110.88430 9. 11943 j 49 ilO. 88057 10:00373 9. 99627 31 10 59 52 8 11666 50 ! 88334 12040 51 87960 00375 99625 29 32 59 44 16 11761 51 i 88239 12138 52 87862 00376 99624 28 33 59 36 24 11857 53 ' 88143 12235 ! 54 87765 00378 1 i 99622 27 34 59 28 32 11952 54 88048 12332 55 i 87668 00380 1 i 99620 26 35 10 59 20 1 40 9. 12047 56 10. 87953 9. 12428 57 \Q. 87572 10. 00382 1 [9.99618 25 36 59 12 48 12142 58 87858 12525 59 • 87475 00383 1 i 99617 24 37 59 4 56 12236 59 87764 12621 60 , 87379 00385 1 ! 9^615 23 38 58 56 1 4 12331 61 87669 12717 62 , 87283 00387 1 99613 22 39 40' 58 48 1 12 12425 62 87575 12813 64 j 87187 00388 1 1 99612 21 10 58 40 1 1 20 9. 12519 64 10. 87481 9.12909 65 10.87091 10. 00390 1 9.99610 20 41 58 32 1 28 12612 66 87388 13004 67 86996 00392 1 99608 19 42 58 24 1 36 12706 67 87294 13099 68 ^ 86901 00393 1 i 99607 18 43 58 16 1 44 12799 69 87201 13194 70 86806 00395 1 99605 17 44 45 58 8 1 52 12892 70 87108 13289 72 86711 00397 1 99603 16 10 58 12 9. 12985 72 10. 87015 9. 13384 73 10. 86616 10. 00399 1 19.99601 15 46 57 52 2 8 13078 74 86922 13478 75 86522 00400 1 i 99600 14 47 57 44 2 16 13171 75 86829 13573 77 86427 00402 1 1 99598 13 48 57 36 2 24 13263 77 86737 13667 78 86333 00404 99596 12 49 57 28 2 32 13355 78 86645 13761 80 86239 00405 99595 11 50 10 57 20 1 2 40 9.13447 80 10. 86553 9. 13854 81 10. 86146 10. 00407 9. 99593 10 51 57 12 2 48 13539 82 86461 13948 83 86052 00409 99591 9 52 .57 4 2 56 13630 83 86370 14041 85 85959 00411 99589 8 53 56 56 3 4 13722 85 86278 14134 86 85866 0O412 99588 V 54 55 56 48 10 56 40 3 12 13813 ■87 88 86187 14227 88 85773 00414 2 99586 6 5 1 3 20 9. 13904 10. 86096 9. 14320 90 10. 85680 10. 00416 2 9. 99584 56 56 32 3 28 13994 90 86006 14412 91 85588 00418 2 99582 4 57 56 24 3 36 14085 91 85915 14504 93 85496 00419 2 99581 3 58 56 16 3 44 14175 93 85825 14597 95 a5403 00421 2 99579 2 59 56 8 3 52 14266 95 85734 14688 96 ' 85312 1 00423 2 99577 1 60 56 4 14356 96 85644 14780 9§ 85220 00425 2 99575 M. Hour p. M. Hour A. M. Cosine. DiflE. Secant. 1 Cotangent. Diff. Tangent. Cosecant. Diff. Sine. M. .V A A B B C C 82° 1 f jeconds of tl 1» 2' i 8» 4" 5« I e- 1 '• fA 12 24 i 36 48 60 72 84 ] °rop. parts o fcols.-^B 12 24 37 ' 1 49 1 61 73 1 1 86 1 Page 616] TABLE 44. Log. Sines, Tangents, and Secants. 8° A A B B C C 171° M. Hour A. M. Hour p. M. Sine. Diff. Cosecant. Tangent. Diff. Cotangent. Secant. Diff. Cosine. M. 10 66 14 9. 14356 10. 85644 9. 14780 10. 85220 10. 00425 9. 99575 60 1 55 52 4 8 14445 1 85555 14872 1 85128 00426 99574 59 2 55 44 4 16 14535 3 85465 14963 3 85037 00428 99572 58 3 55 36 4 24 14624 4 85376 15054 4 84946 00430 99570 57 4 55 28 4 32 14714 6 85286 15145 6 84855 00432 99568 56 5 10 55 20 1 4 40 9. 14803 7 10. 85197 9. 15236 7 10. 84764 10. 00434 9. 99566 55 6 55 12 4 48 14891 8 85109 15327 9 84673 00435 99565 54 7 55 4 4 56 14980 10 85020 15417 10 84583 00437 99563 53 8 54 56 5 4 15069 11 84931 15508 12 84492 00439 99561 52 9 54 48 5 12 15157 13 84843 15598 13 84402 00441 99559 9. 99557 51 50 10 10 54 40 1 5 20 9. 15245 14 10. 84755 9. 15688 14 10. 84312 10. 00443 11 54 32 5 28 15333 16 84667 15777 16 84223 00444 99556 49 12 54 24 5 36 15421 17 84579 15867 17 84133 00446 99554 48 13 54 16 5 44 15508 18 84492 15956 19 84044 00448 99552 47 14 54 8 5 52 15596 20 84404 16046 20 83954 00450 99550 46 15 10 54 1 6 9. 15683 21 10. 84317 9. 16135 22 10. 83865 10. 00452 9. 99548 45 16 53 52 6 8 15770 23 84230 16224 23 83776 00454 99546 44 17 53 44 6 16 15857 24 84143 16312 25 83688 00455 99545 43 18 53 36 6 24 15944 25 84056 16401 26 83599 00457 99543 42 19 53 28 6 32 16030 27 83970 16489 27 83511 00459 99541 41 40 20 10 53 20 1 6 40 9. 16116 28 10. 83884 9. 16577 29 10. 83423 10. 00461 9. 99539 21 53 12 6 48 16203 30 83797 16665 30 83335 00463 99537 39 22 53 4 6 56 16289 31- 83711 16753 32 83247 00465 99535 38 23 52 56 7 4 16374 32 83626 16841 33 83159 00467 99533 37 24 52 48 7 12 16460 34 83540 16928 35 83072 00468 99532 36 25 10 52 40 1 7 20 9. 16545 35 10. 83455 9. 17016 36 10. 82984 10. 00470 9. 995.30 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 52 8 7 52 16886 41 42 83114 17363 42 82637 00478 99522 9. 99520 31 30 30 10 52 18 9. 16970 10. 83030 9. 17450 43 10. 82550 10. 00480 31 51 52 8 8 17055 44 82945 17536 45 82464 00482 99518 29 32 51 44 8 16 17139 45 82861 17622 46 1 82378 00483 99517 28 33 51 36 8 24 17223 47 82777 17708 48 1 82292 00485 99515 27 34 51 28 8 32 17307 48 82693 17794 49 82206 10. 82120 00487 99513 9.99511 26 25 35 10 51 20 1 8 40 9. 17391 49 10. "82609 9.17880 50 10. 00489 36 51 12 8 48 17474 51 82526 17965 52 i 82035 00491 99509 24 37 51 4 8 56 17558 52 82442 18051 53 i 81949 00493 99507 23 38 50 56 9 4 17641 54 82359 18136 55 81864 00495 99505 22 39 50 48 9 12 17724 55 56 82276 10. 82193 18221 56 81779 00497 99503 21 40 10 50 40 1 9 20 9. 17807 9. 18306 58 10. 81694 10. 00499 9. 99501 20 41 50 32 • 9 28 17890 58 82110 18391 59 81609 00501 99499 19 42 50 24 9 36 17973 59 82027 18475 61 81525 00503 99497 18 43 50 16 9 44 18055 61 81945 18560 62 81440 00505 99495 17 44 50 8 9 52 18137 62 81863 18644 63 65 81356 10. 81272 00506 99494 16 15 45 10 50 1 10 9. 18220 63 10. 81780 9. 18728 10. 00508 9. 99492 46 49 52 10 8 18302 65 81698 18812 66 81188 00510 99490 14 47 49 44 10 16 18383 66 81617 18896 68 81104 00512 99488 13 48 49 36 10 24 18465 68 81535 18979 69 81021 00514 2 99486 12 49 49 28 10 32 18547 69 81453 10. 81372 19063 9. 19146 71 72 80937 00516 2 99484 9. 99482 11 10 50 10 49 20 1 10 40 9. 18628 71 10. 80854 10. 00518 2 51 49 12 10 48 18709 72 81291 19229 74 80771 00520 2 99480 9 52 49 4 10 56 18790 73 81210 19312 75 80688 00522 2 99478 8 53 48 56 11 4 18871 75 81129 19395 76 80605 00524 2 99476 7 54 55 48 48 11 12 18952 76 81048 19478 78 80522 00526 2 99474 6 5 10 48 40 1 11 20 9. 19033 78 10. 80967 9. 19561 79 10. 80439 10. 00528 2 9. 99472 56 48 32 11 28 19113 79 80887 19643 81 80357 00530 2 99470 4 57 48 24 11 36 19193 80 80807 19725 82 80275 00532 2 99468 3 58 48 16 11 44 19273 82 80727 19807 84 80193 00534 2 99466 2 59 48 8 11 52 19353 83 80647 19889 85 80111 00536 2 99464 1 60 48 12 19433 85 80567 19971 87 80029 00538 2 99462 M. M. Hour p. M. Hour A. M. Cosine. DifE. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. Sine. 98° A A B B . C C 81° Seconds of time 1' Os 3» i' 5" 6» 1' Prop, parts of cols. 10 44 40 1 15 20 31 10. 78618 9. 21971 32 10. 78029 10. 00589 9.99411 ?ei 44 32 15 28 21458 88 78542 23049 34 77951 00591 99409 34 ?! 44 24 15 36 21534 84 78466 22127 35 77873 00593 99407 83 ?S 44 16 15 44 21610 85 78390 22205 86 77795 00596 99404 32 29 44 8 15 52 21685 37 78315 22283 38 77717 00598 99402 81 80 10 44 1 16 9. 21761 88 10. 78239 9. 22361 89 10. 77639 10. 00600 9. 99400 80 81 43 52 16 8 21886 89 78164 22438 40 77562 00602 99898 29 8'^ 43 44 16 16 21912 40 78088 22516 41 77484 00604 99396 28 88 43 36 16 24 21987 42 78013 22598 48 77407 00606 99894 2V 34 43 28 16 32 22062 48 77938 22670 44 77330 00608 99892 26 25 35 10 43 20 1 16 40 9. 22137 44 10. 77863 9. 22747 45 10. 77258 10. 00610 9. 99890 36 48 12 16 48 22211 45 77789 22824 47 77176 00612 99888 24 87 43 4 16 56 22286 47 77714 22901 48 77099 00615 99385 23 88 42 56 17 4 22361 48 77639 22977 49 77023 00617 99383 22 39 42 48 17 12 22435 49 77565 28054 50 52 76946 00619 99381 21 20 40 10 42 40 1 17 20 9. 22509 50 10. 77491 9. 28130 10. 76870 10. 00621 9. 99379 41 42 32 17 28 22588 52 77417 23206 53 76794 00628 99377 19 42 42 24 17 86 22657 53 77843 23283 54 76717 00625 99375 18 43 42 16 17 44 22731 54 77269 23859 56 76641 00628 2 99372 17 44 45 42 8 17 52 22805 55 77195 23435 57 76565 00630 2 99370 16 15 10 42 1 18 9. 22878 57 10. 77122 9. 23510 58 10. 76490 10. 00632 2 9. 99368 46 41 52 18 8 22952 58 77048 23586 60 76414 00684 2 99366 14 47 41 44 18 16 28025 59 76975 23661 61 76839 00636 2 99364 13 48 41 36 18 24 28098 60 76902 28787 62 76263 00688 2 99862 12 49 41 28 18 32 23171 62 76829 28812 63 76188 00641 2 99359 11 10 50 10 41 20 1 18 40 9. 23244 63 10. 76756 9. 28887 65 10. 76113 10. 00648 2 9. 99857 51 41 12 18 48 23317 64 76683 28962 66 76038 00645 2 99355 9 52 41 4 18 56 23390 65 76610 24037 67 75963 00647 2 99358 8 53 40 56 19 4 23462 67 76538 24112 69 75888 00649 2 99351 1 54 55 40 48 10 40 40 19 12 23585 68 76465 24186 70 75814 00652 2 99348 6 5 1 19 20 9. 28607 69 10. 76393 9. 24261 71 10. 75789 10. 00654 2 9. 99846 56 40 32 19 28 23679 71 76321- 24335 78 75665 00656 2 99844 4 57 40 24 19 36 23752 72 76248 24410 74 75590 00658 2 99342 3 58 40 16 19 44 23823 78 76177 24484 75 75516 00660 2 99840 2 59 40 8 19 52 23895 74 76105 24558 76 75442 00663 2 9938/ 1 60 40 20 23967 76 76083 24632 78 75368 00665 2 993;^ M. Hour p. M. Hour A. M. Cosine. Diff. Secant. Cotangent.] Diff. Tangent. Cosecant. Diff. Sine. M. 99° A A B, B C C 80° 1 Seconds of lime . Prop, parts of cols. 19 28 19 29 1 1 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. 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 75961 24706 1 75294 00667 99333 59 2 39 44 20 16 24110 2 75890 24779 2 75221 00669 99331 58 3 39 36 20 24 24181 3 75819 24853 4 75147 00672 99328 57 4 5 39 28 20 32 24253 5 6 75747 24926 5 75074 00674 99326 56 55 10 39 20 1 20 40 9. 24324 10. 75676 9. 25000 6 10. 75000 10. 00676 9. 99324 6 39 12 20 48 24395 7 75605 25073 7 74927 00678 99322 54 7 39 4 20 56 24466 8 i 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 10 38 40 21 12 24607 10 , 75393 25292 11 74708 00685 99315 51 1 21 20 9. 24677 11 10. 75323 9.25365 ! 12 10. 74635 10. 00687 9. 99313 50 11 38 32 21 28 24748 13 75252 25437 13 74563 00690 99310 49 12 38 24 21 36 24818 14 75182 25510 14 74490 00692 99308 48 13 38 16 21 44 24888 15 75112 25582 15 74418 00694 99306 47 14 38 8 21 52 24958 16 75042 25655 1 16 74345 00696 10. 00699 99304 46 15 10 38 1 22 9. 25028 17 10. 74972. 9.25727 I 18 10. 74273 9. 99301 45 16 37 52 22 8 25098 18 74902 25799 j 19 74201 00701 99299 44 17 37 44 22 16 25168 19 74832 25871 20 74129 00703 99297 43 18 37 36 22 24 25237 20 74763 25943 21 74057 00706 99294 42 19 20 37 28 22 32 25307 22 74693 26015 22 73985 00708 99292 41 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 36 48 23 12 25652 27 74348 26372 : 28 73628 00719 99281 36 35 25 10 36 40 1 23 20 9. 25721 28 10. 74279 9.26443 ' 29 10. 73557 10. 00722 9. 99278 26 36 32 23 28 25790 30 74210 26514 : 31 73486 00724 99276 34 27 36 24 23 36 25858 31 74142 26585 32 73415 00726 99274 33 28 36 16 23 44 25927 32 74073 26655 33 73345 00729 99271 32 29 30 36 8 10 36 23 52 25995 33 74005 26726 34 35 73274 00731 99269 31 30 1 24 9. 26063 34 10. 73937 9. 26797 10. 73203 10. 00733 9. 99267 31 35 52 24 8 26131 35 73869 26867 36 73133 00736 99264 29 32 35 44 24 16 26199 36 73801 26937 38 73063 00738 99262 28 33 35 36 24 24 26267 38 73733 27008 39 72992 00740 99260 27 34 35 28 24 32 26335 39 73665 27078 40 72922 00743 99257 26 25 35 10 35 20 1 24 40 9. 26403 40 10. 73597 9. 27148 41 10. 72852 10. 00745 9. 99255 36 35 12 24 48 26470 41 73530 27218 42 72782 00748 99252 24 37 35 4 24 56 26538 42 73462 27288 44 72712 00750 99250 23 38 34 56 25 4 26605 43 73395 27357 45 72643 00752 99248 22 39 34 48 25 12 26672 44 73328 27427 46 47 72573 00755 10. 00757 2 99245 21 20 40 10 34 40 1 25 20 9. 26739 45 10. 73261 9. 27496 10. 72504 2 9. 99243 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 2 99233 16 15 45 10 34 1 26 9. 27073 51 10. 72927 9. 27842 53 10. 72158 10. 00769 9. 99231 46 33 52 26 8 27140 52 72860 27911 54 72089 00771 2 99229 14 47 33 44 26 16 27206 53 72794 27980 55 72020 00774 2 99226 13 48 33 36 26 24 27273 55 72727 28049 56 71951 00776 2 99224 12 49 33 28 26 32 27339 56 72661 28117 58 71883 00779 2 99221 11 10 50 10 33 20 1 26 40 9. 27405 57 10. 72595 9. 28186 59 10. 71814 10. 00781 2 9. 99219 51 33 12 26 48 27471 58 72529 28254 60 71746 00783 2 99217 9 52 33 4 26 56 27537 59 72463 28323 61 71677 00786 2 99214 8 53 32 56 27 4 27602 60 72398 28391 62 71609 00788 2 99212 7 54 32 48 27 12 27668 61 72332 28459 63 65 71541 00791 2 99209 6 5 55 10 32 40 1 27 20 9. 27734 63 10. 72266 9. 28527 10. 71473 10. 00793 2 9. 99207 56 32 32 27 28 27799 64 72201 28595 66 71405 00796 2 99204 4 57 32 24 27 36 27864 65 72136 28662 67 71338 00798 2 99202 3 58 32 16* 27 44 27930 66 72070 28730 68 71270 00800 2 99200 2 59 32 8 27 52 27995 67 72005 28798 69 71202 00803 2 99197 1 60 32 28 28060 68 71940 28865 71 71135 00805 2 99195 M. Hour P.M. Hour A. M. Cosine. Diff. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. Sine. M. 100° A A B B C C 79° Seconds of time : 1' 2» 3« 1 f 5* 6» 7» fA 9 Prop, parts of cols.<^B 9 Ic 17 18 1 26 26 1 34 35 1 43 44 1 51 53 2 60 62 2 TABLE 44. [Page 619 Log. Sine?, Tangents, and Secants. 11° A A B B C C 168° M. Hour A. M. Hour p. M. Sine. Difl. Cosecant. Tangent. Diff. Cotangent. Secant. Difl. Cosine. M. 60 10 32 1 28 9. 28060 10. 71940 9. 28865 10. 71135 10. 00805 9.99195 1 31 52 28 8 28125 1 71875 28933 1 71067 00808 99192 59 2 31 44 28 16 28190 2 71810 29000 2 71000 00810 99190 58 3 31 36 28 24 28254 3 71746 29067 3 70933 00813 99187 57 4 31 28 28 32 28319 4 7168] 29134 4 70866 00815 99185 56 55 5 10 31 20 1 28 40 9. 28384 5 10. 71616 9. 29201 5 10. 70799 10. 00818 9. 99182 6 31 12 28 48 28448 6 71552 29268 6 70732 00820 99180 54 / 31 4 28 56 28512 7 71488 29335 8 70665 00823 99177 53 8 30 56 29 4 28577 8 71423 29402 9 70598 00825 99175 52 9 30 48 29 12 28641 9 71359 29468 10 70532 00828 99172 51 50 10 10 30 40 1 29 20 9. 28705 10 10. 71295 9. 29535 11 10. 70465 10.00830 9. 99170 11 30 32 29 28 28769 11 71231 29601 12 70399 00833 99167 49 12 30 24 29 36 28833 12 71167 29668 13 70332 00835 99165 48 13 30 16 29 44 28896 13 71104 29734 14 70266 00838 99162 47 14 30 8 29 52 28960 14 71040 29800 15 70200 00840 99160 46 45 15 10 30 1 30 9. 29024 16 10. 70976 9. 29866 16 10. 70134 10. 00843 9. 99157 16 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 41 40 20 10 29 20 1 30 40 9. 29340 21 10. 70660 9. 30195 22 10. 69805 10. 00855 9. 99145 21 29 12 30 48 29403 22 70597 30261 23 69739 00858 99142 39 22 29 4 30 56 ' 29466 23 - 70534 30326 24 69674 00860 99140 38 23 28 56 31 4 29529 24 70471 30391 25 69609 00863 99137 37 24 28 48 31 12 29591 25 70409 30457 26 69543 00865 99135 36 35 25 10 28 40 1 31 20 9. 29654 26 10. 70346 9. 30522 27 10. 69478 10. 00868 9. 99132 26 28 32 31 28 29716 27 70284 30587 28 69413 00870 99130 34 27 28 24 31 36 29779 28 70221 30652 29 69348 00873 99127 33 28 28 16 31 44 29841 29 70159 30717 30 69283 00876 99124 32 29 28 8 31 52 29903 30 70097 30782 31 69218 00878 99122 31 30 10 28 1 32 9. 29966 31 10. 70034 9. 30846 32 10..69154 10. 00881 9. 99119 30 31 27 52 32 8 30028 32 69972 30911 33 69089 00883 99117 29 32 27 44 32 16 30090 33 69910 30975 35 69025 00886 99114 28 33 27 36 32 24 30151 34 69849 31040 36 68960 00888 99112 27 34 35^ 27 28 32 32 30213 35 69787 31104 37 68896 00891 99109 26 10 27 20 1 32 40 9. 30275 36 10. 69725 9.31168 38 10. 68832 10. 00894 2 9. 99106 25 36 27 12 32 48 30336 37 69664 31233 39 68767 00896 2 99104 24 37 27 4 32 56 30398 38 69602 31297 40 68703 00899 2 99101 23 38 26 56 33 4 30459 39 69541 31361 41 68639 00901 2 99099 22 39 40 26 48 33 12 30521 40 69479 31425 42 68575 00904 2 99096 21 20 10 26 40 1 33 20 9. 30582 41 10. 69418 9. 31489 43 10. 68511 10. 00907 2 9. 99093 41 26 32 33 28 30643 42 69357 31552 44 68448 00909 2 99091 19 42 26 24 33 36 30704 43 69296 31616 45 68384 00912 2 99088 18 43 26 16 33 44 30765 45 69235 31679 46 68321 00914 2 99086 17 44 26 8 33 52 30826 46 47 69174 31743 47 68257 00917 2 99083 16 45 10 26 1 34 9. 30887 10. 69113 9.31806 J 49 10. 68194 10. 00920 2 9. 99080 15 46 25 52 34 8 30947 48 69053 31870 50 68130 00922 2 99078 14 47 25 44 34 16 31008 49 68992 31933 51 68067 00925 2 99075 13 48 25 36 34 24 31068 50 68932 31996 52 68004 00928 2 99072 12 49 25 28 34 32 31129 51 68871 32059 53 67941 00930 2 99070 11 50 10 25 20 1 34 40 9. 31189 52 10.68811 9. 32122 54 10. 67878 10. 00933 2 9.99067 10 51 25 12 34 48 31250 53 68750 32185 55 67815 00936 2 99064 9 52 25 4 34 56 31310 54 68690 32248 56 67752 00938 2 99062 8 53 24 56 35 4 31370 55 68630 32311 57 67689 (X)941 2 99059 / 54 24 48 35 12 31430 56 68570 32373 58 67627 00944 2 99056 6 55 10 24 40 1 35 20 9. 31490 57 10. 68510 9. 32436 59 10. 67564 10. 00946 2 9. 99054 5 56 24 32 35 28 31549 58 68451 32498 60 67502 00949 2 99051 4 57 24 24 35 36 31609 59 68391 32561 61 67439 00952 2 99048 3 58 24 16 35 44 31669 60 68331 32623 63 67377 00954 2 9904(5 2 59 24 8 35 52 31728 61 68272 32685 64 67315 00957 3 951043 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" i' 3' 4" 5» 6» f A 1 8 Prop, parts of cols. ^B 8 16 16 1 23 24 1 31 32 1 39 40 2 47 54 49 57 2 2 Page 620] TABLE 44. Log. Sines, Tangents, and Secants. 12° A A B B C C 167° M. Hour A. M. Hour p. M. Sine. Diff. Cosecant. Tangent. Dlfl. Cotangent. Secant. Diff. Cosine. M. 10 24 1 36 9. 31788 10. 68212 9. 32747 10. 67253 10. 00960 9. 99040 60 1 23 52 36 8 31847 1 68153 32810 1 67190 00962 99038 59 2 23 44 36 16 '31907 2 68093 32872 2 67128 00965 99035 58 3 23 36 36 24 31966 3 68034 32933 3 67067 00968 99032 57 4 23 28 36 32 32025 4 67975 32995 9. 33057 4 67005 00970 99030 56 55 5 10 23 20 1 36 40 9. 32084 5 10. 67916 5 j 10. 66943 10. 00973 9. 99027 6 23 12 36 48 32143 6 67857 33119 6 66881 00976 99024 54 7 23 4 36 56 32202 7 67798 33180 7 ; 66820 00978 99022 53 8 22 56 37 4 32261 8 67739 33242 8 1 66758 00981 99019 52 9 22 48 37 12 32319 9 67681 33303 9 I 66697 00984 99016 51 10 10 22 40 1 37 20 9.32378 1 10 10. 67622 9. 33365 10 10.66635 10. 00987 9. 99013 50 11 22 32 37 28 32437 10 67563 33426 11 i 66574 00989 99011 49 12 22 24 37 36 32495 i 11 67505 33487 12 1 66513 00992 99008 48 13 22 16 37 44 32553 12 67447 33548 13 ' 66452 00995 99005 47 14 22 8 37 52 32612 13 67388 33609 14 66391 00998 99002 46 15 10 22 1 38 9. 32670 i 14 ilO. 67330 | 9. 33670 15 10.66330 10. 01000 9. 99000 45 16 21 52 38 8 32728 15 67272 33731 16 66269 01003 98997 44 17 21 44 38 16 32786 16 67214 • 33792 17 66208 01006 98994 43 18 21 36 38 24 32844 17 67156 33853 18 . 66147 01009 98991 42 19 20 21 28 38 32 32902 18 67098 33913 19 66087 01011 98989 41 10 21 20 1 38 40 9. 32960 19 10.67040 9. 33974 20 10.66026 10. 01014 9. 98986 40 21 21 12 38 48 33018 20 j 66982 34034 21 i 65966 01017 98983 39 22 21 4 38 56 33075 21 i 66925 34095 22 1 65905 01020 98980 38 23 20 56 39 4 33133 22 66867 34155 23 ; 65845 01022 98978 37 24 20 48 39 12 33190 23 66810 34215 24 1 65785 01025 98975 36 35 25 10 20 40 1 39 20 9. 33248 24 10. 66752 9. 34276 25 10.65724 10. 01028 1 19.98972 26 20 32 39 28 33305 25 66695 34336 26 1 65664 01031 98969 34 27 20 24 39 36 33362 26 66638 34396 27 65604 01033 98967 33 28 20 16 39 44 33420 I 27 66580 34456 28 65544 01036 98964 32 29 20 8 39 52 33477 j 28 66523 34516 29 1 65484 01039 98961 31 30 10 20 1 40 9.33534 -29 10. 66466 9. 34576 30 10.65424 10. 01042 9. 98958 30 31 19 52 40 8 33591 29 66409 34635 31 i 65365 01045 1 98955 29 32 19 44 40 16 33647 ! 30 66353 34695 32 65305 01047 98953 28 33 19 36 40 24 33704 31 66296 34755 33 1 65245 01050 2 98950 27 34 35 19 28 40 32 33761 32 66239 34814 34 ! 65186 01053 2 98947 26 10 19 20 1 40 40 9. 33818 33 10. 66182 9. 34874 35 {10.65126 10. 01056 2 9. 98944 25 36 19 12 40 48 33874 34 66126 34933 36 ^ 65067 01059 2 1 98941 24 37 19 4 40 56 33931 35 66069 34992 37 65008 01062 2 i 98938 23 38 18 56 41 4 33987 ' 36 66013 35051 38 64949 01064 2 1 98936 22 39 18 48 41 12 34043 \ 37 65957 35111 39 64889 01067 2 98933 21 40 10 18 40 1 41 20 9. 34100 38 10. 65900 9. 35170 40 10.64830 10. 01070 2 9.98930 20 41 18 32 41 28 34156 39 65844 35229 41 64771 01073 2 98927 19 42 18 24 41 36 34212 40 65788 35288 42 64712 01076 2 : 98924 18 43 18 16 41 44 34268 41 65732 35347 43 64653 01079 2 . 98921 17 44 18 8 41 52 34324 42 65676 35405 44 45 64595 01081 2 1 98919 16 15 45 10 18 1 42 9. 34380 43 10. 65620 9. 35464 10. 64536 10. 01084 2 i 9. 98916 46 17 52 42 8 34436 44 65564 35523 46 64477 01087 2 1 98913 14 47 17 44 42 16 34491 45 65509 35581 47 64419 01090 2 1 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 1 64302 01096 2 i 98904 11 50 10 17 20 1 42 40 9.34658 i 48 10. 65342 9. 35757 50 ,10.64243 10. 01099 2 19.98901 10 51 17 12 42 48 34713 48 65287 35815 51 i 64185 01102 2 98898 9 52 17 4 42 56 34769 49 65231 36873 52 I 64127 01104 2 98896 8 53 16 56 43 4 34824 ! 50 65176 35931 53 i 64069 01107 2 98893 7 54 16 48 43 12 34879 51 65121 35989 54 1 64011 OHIO 3 98890 6 5 55 10 16 40 1 43 20 9. 34934 52 10. 65066 9. 36047 55 10.63953 10.01113 3 ! 9. 98887 56 16 32 43 28 34989 53 j 65011 36105 56 63895 01116 3 98884 4 57 16 24 43 36 35044 i 54 \ 64956 36163 57 63837 01119 3 98881 3 58 16 16 43 44 35099 55 64901 36221 58 1 63779 01122 3 98878 2 59 16 8 43 52 35154 56 64846 36279 59 63721 01125 3 98875 1 60 16 44 35209 57 64791 36336 60 63664 01128 3 98872 M. M. Hour p. M. Hour A. M. Cosine. Diff. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. Sine. 102 A A B B C C 77° 1 Seconds of time Prop, parts of col8. Prop, parts of cols.-{B ic 7 7 13 14 1 20 21 1 26 28 2 33 35 2 39 42 2 46 49 3 •WMM Page 622] TABLE 44. Log. Sines, Tar gents, and Secants. 14° A A B B C C 165° M. Hour A.M. Hour p. M. Sine. Difl. Cosecant. Tangent. Diff. Cotangent. Secant. Difl. Cosine. M. 10 8 1 52 9. 38368 10. 61632 9. 39677 10. 60323 10. 01310 9. 98690 60 1 7 52 52 8 38418 1 61582 39731 1 60269 01313 98687 59 2 7 44 52 16 38469 2 61531 39785 2 60215 01316 98684 58 3 7 36 52 24 38519 2 61481 39838 3 60162 01319 98081 57 4 7 28 52 32 38570 3 61430 39892 3 60108 01322 98678 56 55 5 10 7 20 1 52 40 38620 4 10. 61380 9. 39945 4 10. 60055 10. 01325 9. 98675 6 7 12 52 48 38670 5 61330 39999 5 60001 01329 98671 54 7 7 4 52 56 38721 6 61279 40052 6 599-^8 01332 98668 58 8 6 56 53 4 38771 7 61229 40106 7 59894 01335 98665 52 9 10 6 48 53 12 38821 7 8 61179 40159 8 59841 01338 98662 9. 986.59 51 50 10 6 40 1 53 20 9. 38871 10. 61129 9.40212 9 10. 59788 10. 01341 11 6 32 53 28 38921 9 61079 40266 10 59734 01344 98656 49 12 6 24 53 36 38971 10 61029 40319 10 59681 01348 98652 48 13 6 16 53 44 39021 11 60979 40372 11 59628 01351 98649 47 14 6 8 53 52 39071 11 60939 40425 12 13 59575 01354 -^ . 98646 9. 98643 46 45" 15 10 6 1 54 9. 39121 12 10. 60879 9. 40478 10. 59522 10. 01357 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 5 28 54 32 39319 15 60681 10. 60631 40689 9. 40742 17 17 59311 01370 — J- 98630 9. 98627 41 '40 20 10 5 20 1 54 40 9. 39369 16 10. 59258 10. 01373 21 5 12 54 48 39418 17 60582 40795 18 59205 01377 98623 39 22 5 4 54 56 39467 18 60533 40847 19 59153 01380 98620 38 23 4 56 55 4 39517 19 60483 40900 20 59100 01383 98617 37 24 4 48 55 12 39566 20 60434 40952 21 59048 10. 58995" 01386 10. 01390 98614 36 35 25 10 4 40 1 55 20 S. 39615 20 10. 60385 9. 41005 22 9. 98610 26 4 32 55 28 39664 21 60336 41057 23 58943 01393 98607 34 27 4 24 55 36 39713 ! 22 60287 41109 23 58891 01396 98604 33 28 4 16 55 44 39762 23 60238 41161 24 58839 01399 2 98601 32 29 30 4 8 55 52 39811 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 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 29 59945 41474 30 58526 01419 2 98581 26 35 10 3 20 1 56 40 9. 40103 10. 59897 9. 41526 30 10. 58474 01422 2 9. 98578 25 36 3 12 56 48 40152 29 59848 41578 31 58422 01426 2 98574 24 37 3 4 56 56 40200 30 59800 41629 32 58371 01429 2 98571 23 38 2 56 57 4 40249 31 59751 41681 33 58319 01432 2 98568 22 39 40 2 48 57 12 40297 32 59703 41733 34 35 58267 01435 2 98565 21 20 10 2 40 1 57 20 9. 40346 33 10. 59654 9. 41784 10. 58216 10. 01439 2 9. 98561 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 35 59510 41939 37 58061 01449 2 98551 17 44 2 8 57 52 40538 36 59462 41990 38 58010 01452 10. 01455 2 985^8 16 45 10 2 1 58 9. 40586 37 10. 59414 9. 42041 39 10. 57959 2 9. 98545 15 46 1 52 58 8 40634 37 59366 42093 40 57907 01459 3 98541 14 47 1 44 58 16 40682 38 59318 42144 41 57856 01462 3 98538 13 48 1 36 58 24 40730 39 59270 42195 42 57805 01465 3 98535 12 49 1 28 58 32 40778 40 41 59222 42246 43 57754 01469 3 98531 9. 98528 11 10 50 10 1 20 1 58 40 9. 40825 10. 59175 9. 42297 43 10. 57703 10. 01472 3 51 1 12 58 48 40873 42 59127 42348 44 57652 01475 3 98525 9 52 1 4 58 56 40921 42 59079 42399 45 57601 01479 3 98521 8 53 56 59 4 40968 43 59032 42450 46 57550 01482 3 98518 7 54 48 59 12 41016 9. 41063 44 45 58984 42501 47 57499 01485 3 98515 6 55 10 40 1 59 20 10. 58937 9. 42552 48 10. 57448 10. 01489 3 9. 98511 5 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. Difl. Tangent. Cosecant. Diff. Sine. M. 104° A A B B C C 75° Seconds of time 1' 2« 3» '4' a» 0. n Prop, parts of cols.'jB ic 6 7 12 13 1 18 20 1 24 31 26 33 2 2 37 39 2 43 46 3 TABLE 44. [Page 623 Log. Sines, Tangents, and Secants. 15° A A B B C C 164° M. Hour A.M. Hour p. M. Sine. Diff. Cosecant. Tangent. Difl. j Cotangent. Secant. Diflf. Cosine. M. 10 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 58606 42906 2 57094 "■ 01512 98488 58 3 59 36 24 41441 2 58559 42957 2 57043 01516 98484 i 57 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 1 55 6 59 12 48 41582 5 58418 43108 5 56892 01526 98474 .54 / 69 4 56 41628 5 58372 43158 6 56842 01529 98471 53 8 58 56 1 4 41675 6 58325 43208 7 ! 56792 01533 98467 52 9 10 58 48 1 12 41722 7 58278 43258 7 i 56742 01536 98464 9. 98460 51 50 9 58 40 2 1 20 9. 41768 8 10. 58232 9. 43308 8 110.56692 10. 01540 11 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 1 56542 01550 98450 47 14 58 8 1 52 41954 11 58046 43508 11 i 56492 01553 98447 9. 98443 46 45 15 9 58 2 2 9. 42001 11 10. 57999 9. 43558 12 110.56442 10. 01557 16 57 52 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 i 56293 01567 98433 42 19 20 57 28 9 57 20 2 32 42186 14 57814 43756 16 56244 01571 98429 41 2 2 40 9. 42232 15 10. 57768 9. 43806 16 10.56194 10. 01574 9. 98426 40 21 57 12 2 48 42278 16 57722 43855 17 56145 01578 98422 39 22 57 4 2 56 42324 17 57676 43905 18 56095 01581 1 ' 98419 38 23 56 56 3 4 42370 17 57630 43954 19 56046 01585 98415 37 24 56 48 3 12 42416 18 1 57584 44004 20 55996 01588 98412 36 25 9 56 40 2 3 20 9. 42461 19 '10.57539 9. 44053 20 ilO. 55947 10. 01591 9. 98409 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 22 55849 01598 2 98402 33 28 56 16 3 44 42599 21 57401 44201 23 55799 01602 2 98398 32 29 56 8 3 52 42644 22 57356 44250 24 55750 01605 2 98395 31 30 9 56 2 4 9. 42690 23 10. 57310 9. 44299 25 10. 55701 10. 01609 2 9. 98391 30 31 55 52 4 8 42735 24 57265 44348 25 j 55652 01612 2 98388 29 32 55 44 4 16 42781 24 57219 44397 26 55603 01616 2 98384 28 33 55 36 4 24 42826 25 57174 44446 27 55554 01619 2 98381 27 34 55 28 4 32 42872 26 57128 44495 28 55505 01623 2 98377 26 25 35 9 55 20 2 4 40 9. 42917 27 10. 57083 9. 44544 29 10. 55456 10. 01627 2 9. 98373 36 55 12 4 48 42962 27 57038 44592 29 i 55408 01630 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 t31 55310 01637 2 98363 22 39 54 48 5 12 43098 30 56902 44738 32 55262 01641 2 98359 21 40 9 54 40 2 5 20 9. 43143 30 10. 56857 9. 44787 33 10. 55213 10. 01644 2 9. 98356 20 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 33 34 56677 44981 36 37 55019 01658 3 98342 16 15 45 9 54 2 6 9. 43367 10. 56633 9. 45029 10. 54971 10. 01662 3 9. 98338 46 53 52 6 8 43412 35 56588 45078 38 54922 01666 3 98334 14 47 53 44 6 16 43457 36 56543 45126 38 54874 01669 3 98331 13 48 53 36 6 24 43^02 36 56498 45174 39 54826 01673 3 98327 12 49 53 28 6 32 2 6 40 43546 37 56454 45222 40 54778 10. 54729 01676 3 98324 11 10 50 9 53 20 9. 43591 38 10. 56409 9. 45271 41 10. 01680 3 9. 98320 51 53 12 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 41 56231 45463 9.45511 44 45 54537 01694 3 98306 6 9. 43813 42 10. 56187 10. 54489 10. 01698 3 9. 98302 5 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 54346 01709 3 98291 2 59 52 8 7 52 43990 45 56010 45702 48 54298 01712 3 98288 1 60 52 8 44034 46 55966 45750 49 54250 01716 4 98284 M. Hour p. M. Hour A. M. Cosine. Diff. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. Sine. M. 105° A A B B C C 74° 1 Seconds of time 1« 2s 3- 4s 6» «s 7«J Prop, parte of cols. I B 6 6 11 12 1 17 18 1 23 25 2 28 31 2 34 37 3 40 43 3 Page 624] TABLE 44. Log. Sines, Tangents, and Secants. 16° A A B B C C 168° 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. 54250 10.01716 9. 98284 60 1 51 52 8 8 44078 1 55922 45797 1 54203 01719 98281 59 2 51 44 8 16 44122 1 55878 45845 2 54155 01723 98277 58 3 51 36 8 24 44166 2 55834 45892 2 54108 01727 98273 57 4 51 28 8 32 44210 3 55790 45940 3 54060 01730 98270 56 55 5 9 51 20 2 8 40 9. 44253 4 10. 55747 9. 45987 4 10. 54013 10. 01734 9. 98266 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 50 48 9 12 44428 6 7 55572 46177 7 53823 01749 -Y 98251 51 50 10 9 50 40 2 9 20 9. 44472 10. 55528 9.46224 i 8 10. 53776 10.01752 9. 98248 11 50 32 9 28 44516 8 55484 46271 9 53729 01756 98244 49 12 50 24 9 36 44559 9 55441 46319 9 53681 01760 98240 48 13 50 16 9 44 44602 9 55398 46366 10 53634 01763 98237 47 14 50 8 9 52 44646 10 55354 46413 11 53587 01767 98233 46 15 9 50 2 10 9. 44689 11 10. 55311 9.46460 12 10.53540 10. 01771 9. 98229 45 16 49 52 10 8 44733 11 55267 46507 12 53493 01774 98226 44 17 49 44 10 16 44776 12 55224 46554 13 53446 01778 98222 43 18 49 36 10 24 44819 13 55181 46601 14 53399 01782 98218 42 19 20 49 28 10 32 44862 14 .55138 46648 15 53352 01785 98215 41 9 49 20 2 10 40 9. 44905 14 10. 55095 9. 46694 15 10. 53306 10. 01789 9. 98211 40 21 49 12 10 48 44948 15 55052 46741 16 53259 01793 98207 39 22 49 4 10 56 44992 16 55008 46788 17 53212 01796 98204 38 23 48 56 11 4 45035 16 54965 46835 18 53165 01800 98200 37 24 48 48 11 12 46077 17 54923 46881 . 19 53119 01804 98196 36 35 25 9 48 40 2 11 20 9. 45120 18 10. 54880 9. 46928 19 10. 53072 10. 01808 2 9. 98192 26 48 32 11 28 45163 18 54837 46975 20 1 53025 01811 2 98189 34 27 48 24 11 36 45206 19 54794 47021 21 ! 5-2979 01815 2 98185 33 28 48 16 11 44 45249 20 54751 47068 22 52932 01819 2 98181 32 29 48 8 11 52 45292 21 54708 47114 : 22 : 52886 01823 2 98177 31 30 30 9 48 2 12 9. 45334 21 10. 54666 9.47160 ! 23 10.52840 10. 01826 2 9. 98174 31 47 52 12 8 45377 22 54623 47207 24 ' 52793 01830 2 98170 29 32 47 44 12 16 45419 23 54581 47253 25 52747 01834 2 98166 28 33 47 36 12 24 45462 23 54538 47299 26 52701 01838 2 98162 27 34 47 28 12 32 45504 24 54496 47346 26 52654 01841 2 98159 26 35 9 47 20 2 12 40 9. 45547 25 10. 54453 9.47392 ! 27 10. 52608 10. 01845 2 9. 98155 25 36 47 12 12 48 45589 26 54411 47438 28 52562 01849 2 98151 24 37 47 4 12 56 45632 26 54368 47484 29 52516 01853 2 98147 23 38 46 56 13 4 45674 27 54326 47530 29 52470 01856 2 98144 22 39 46 48 13 12 45716 28 54284 47576 30 52424 01860 2 2 98140 9. 98136 21 20 40 9 46 40 2 13 20 9. 45758 28 10. 54242 9. 47622 31 10. 52378 10. 01864 41 46 32 13 28 45801 29 54199 47668 32 52332 01868 3 98132 19 42 46 24 13 36 45843 30 54157 47714 32 52286 01871 3 98129 18 43 46 16 13 44 45885 31 54115 47760 33 52240 01875 3 98125 17 44 46 8 13 52 45927 31 54073 47806 34 52194 01879 3 98121 9.98117 16 15 45 9 46 2 14 9. 45969 32 10. 54031 9. 47852 35 10. 52148 10. 01883 3 46 45 52 14 8 46011 33 53989 47897 36 52103 01887 3 98113 14 47 45 44 14 16 46053 33 53947 47943 36 52057 01890 3 98110 13 48 45 36 14 24 46095 34 53906 47989 37 52011 01894 3 98106 12 49 45 28 14 32 46136 35 53864 48035 38 51965 01898 3 98102 11 10 50 9 45 20 2 14 40 9. 46178 36 10. 53822 9. 48080 39 10. 51920 10. 01902 3 9. 98098 51 45 12 14 48 46220 36 53780 48126 39 51874 01906 3 98094 9 52 45 4 14 56 46262 37 53738 48171 40 51829 01910 3 98090 8 53 44 56 15 4 46303 38 53697 48217 41 51783 01913 3 98087 7 54 55 44 48 15 12 46345 38 53655 48262 42 51738 01917 3 98083 6 5 9 44 40 2 15 20 9. 46386 39 10. 53614 9. 48307 43 10. 51693 10. 01921 3 9. 98079 56 44 32 15 28 46428 40 53572 48353 43 51647 01925 3 98075 4 57 44 24 15 36 46469 41 53531 48398 44 51602 01929 4 98071 3 58 44 16 15 44 46511 41 53489 48443 45 51557 01933 4 98067 2 59 44 8 15 52 46552 42 53448 48489 46 51511 01937 4 98063 1 60 44 16 46594 43 53406 48534 46 51466 01940 4 98060 M. Hour p. M. Hour A. M. Cosine. Diff. Secant. Cotangent Diff. Tangent. Cosecant. Diff, Sine. M. 106° A A B B C C 73° Seconds of time Prop, parte of cols. ■< B (C TABLE 44. Log. Sines, Tangents, and Secants. [Page 625 17° A A B B C - C 162° M. Hour A.M. Hour p. M. Sine. Dia. Cosecant. Tangent. Diff. Cotangent. Secant. Diff. Cosine. M. 9 44 2 16 9. 46594 10. 53406 9. 48534 10. 51466 10. 01940 9.98060 60 i 43 52 16 8 46635 1 53365 48579 1 51421 01944 98056 59 2 43 44 16 16 i6676 1 53324 48624 1 51376 01948 98052 58 3 43 36 16 24 46717 2 53283 48669 2 51331 01952 98048 57 4 43 28 16 32 46758 3 53242 48714 3 51286 01956 98044 56 55 b 9 43 20 2 16 40 9. 46800 3 10. 53200 9. 48759 4 10. 51241 10. 01960 9. 98040 6 43 12 16 48 46841 4 53159 48804 4 51196 01964 98036 54 / 43 4 16 56 46882 5 53118 48849 5 51151 01968 98032 53 8 42 56 17 4 46923 5 53077 48894 6 51106 01971 98029 52 9 10 42 48 17 12 46964 6 53036 48939 7 51061 01975 98025 51 9 42 40 2 17 20 9. 47005 7 10. 52995 9. 48984 7 10. 51016 10. 01979 9. 98021 50 11 42 32 17 28 47045 7 52955 49029 8 50971 01983 98017 49 12 42 24 17 36 47086 8 52914 49073 \ 9 50927 01987 98013 48 13 42 16 17 44 47127 9 52873 49118 10 50882 01991 98009 47 14 42 8 17 52 47168 9 52832 49163 10 50837 01995 98005 46 15 9 42 2 18 9. 47209 10 10. 52791 9. 49207 11 10. 50793 10. 01999 9. 98001 45 10 41 52 18 8 47249 11 52751 49252 12 .50748 02003 97997 44 17 41 44 18 16 47290 11 52710 49296 12 50704 02007 97993 43 18 41 36 18 24 47330 12 52670 49341 13 50659 02011 97989 42 19 41 28 18 32 47371 13 52629 49385 14 50615 02014 97986 41 40 20 9 41 20 2 18 40 9.47411 13 10. 52589 9. 49430 15 10. 50570 10. 02018 9. 97982 2-1 41 12 18 48 47452 14 52548 49474 15 50526 02022 97978 39 22 41 4 18 56 47492 15 52508 49519 16 50481 02026 97974 38 23 40 56 19 4 47533 15 52467 49563 17 50437 02030 2 97970 37 24 25 40 48 19 12 47573 16 52427 49607 18 50393 02034 2 97966 36 35 9 40 40 2 19 20 9.47613 17 10. 52387 9. 49652 18 10. 50348 10. 02038 2 9. 97962 26 40 32 19 28 47654 17 52346 49696 19 50304 02042 2 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 30 40 8 19 52 47774 19 52226 49828 21 50172 02054 2 97946 31 30 9 40 2 20 9. 47814 20 10. 52186 9. 49872 22 10.50128 10. 02058 2 9. 97942 31 39 52 20 8 47854 21 52146 49916 23 50084 02062 2 97938 29 32 39 44 20 16 47894 21 52106 49960 24 50040 02066 2 97934 28 33 39 36 20 24 47934 22 52066 50004 24 49996 02070 2 97930 27 34 39 28 20 32 47974 23 23 52026 10. 51986 50048 9. 50092 25 26 49952 10. 49908 02074 2 97926 26 25 35 9 39 20 2 20 40 9. 48014 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 1 49820 02086 2 97914 23 38 38 56 21 4 48133 25 51867 50223 28 49777 02090 3 97910 22 39 38 48 21 12 48173 26 51827 50267 29 49733 02094 3 3 97906 21 20 40 9 38 40 2 21 20 9. 48213 27 10. 51787 9.50311 29 10. 49689 10. 02098 9. 97902 41 38 32 21 28 48252 27 51748 50355 30 49645 02102 3 97898 19 42 38 24 21 36 48292 28 51708 50398 31 49602 02106 3 97894 18 43 38 16 21 44 48332 29 51668 50442 32 49558 02110 3 97890 17 44 38 8 21 52 48371 29 30 51629 10. 51589 50485 32 49515 02114 3^ 97886 9. 97882 16 15 45 9 38 2 22 9. 48411 9. 50529 33 10. 49471 10.02118 3 46 37 52 22 8 48450 31 51550 50572 34 49428 02122 3 97878 14 47 37 44 22 16 48490 31 51510 50616 35 49384 02126 3 97874 13 48 37 36 22 24 48529 32 51471 50659 35 49341 02130 3 97870 12 49 37 28 22 32 48568 33 33 51432 10. 51393 50703 9. 50746 36 49297 . 02134 3 97866 11 10 50 9 37 20 2 22 40 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 53 36 56 23 4 48725 35 51275 50876 39 49124 02151 4 97849 / 54 36 48 23 12 48764 36 51236 50919 40 4908r 02155 4 97845 6 5 55 9 36 40 2 23 20 9. 48803 37 10.51197 9. 50962 40 10. 49038 10. 02159 4 9. 97841 56 36 32 23 28 48842 37 . 51158 51005 41 48995 02163 4 97837 4 57 36 24 23 36 48881 38 51119 51048 42 48952 02167 4 97833 3 58 36 16 23 44 48920 39 51080 51092 43 48908 02171 4 97829 2 59 36 8 23 52 48959 39 51041 51135 43 48865 02175 4 97825 1 60 36 24 48998 40 51002 51178 44 48822 02179 4 97821 M. M. Hour p. M. Hour A. M. Cosine. Diff. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. Sine. 107° A A B B C C 72^ Seconds of time 1« 2' •i' 4" 6» 6< 7" Prop, parts of cols. ^B 1 ^"^ 5 6 10 11 1 15 17 1 20 22 2 25 28 2 30 33 3 35 39 3 65 3—06- -40 Page 626] TABLE 44. Log. Sines, Tangents, and Secants. 18° A A B B C C 161° M. Hour A.M. Hour p. M. Sine. Did. Cosecant. Tangent. DifT. Cotangent. Secant. Diff. Cosine. M. 9 36 2 24 9.48998 10. 51002 9.51178 10. 48822 10. 02179 9. 97821 60 1 35 52 24 8 49037 1 50963 51221 1 48779 02183 97817 59 2 36 44 24 16 49076 1 50924 51264 1 48736 02188 97812 58 3 35 36 24 24 49115 2 50885 51306 2 48694 02192 97808 57 4 5 35 28 24 32 49153 3 50847 51349 3 3 48651 10. 48608 02196 10. 02200 97804 56 55 9 35 20 2 24 40 9. 49192 3 10. 50808 9. 51392 9. 97800 6 35 12 24 48 49231 4 ' 50769 51435 4 48565 02204 97796 54 1 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 34 32 25 28 49424 7 50576 51&48 8 48352 02225 97775 49 12 34 24 25 36 49462 8 50538 51691 8 48309 02229 97771 48 13 34 16 25 44 49500 8 50500 51734 9 48266 02233 97767 47 14 34 8 25 52 49539 9 50461 51776 10 48224 02237 97763 46 15 9 34 2 26 9. 49577 9 10.50423 9. 51819 10 10. 48181 10. 02241 9. 97759 45 16 33 52 26 8 49615 10 50385 51861 11 48139 02246 97754 44 17 33 44 26 16 49654 11 50346 51903 12 48097 02250 97750 43 18 33 36 26 24 49692 11 50308 51946 13 48054 02254 97746 42 19 20 33 28 26 32 49730 12 50270 51988 13 48012 02258 97742 9. 97738 41 40 9 33 20 2 26 40 9.49768 13 10. 50232 9. 52031 14 10. 47969 10. 02262 21 33 12 26 48 49806 13 50194 52073 15 47927 02266 97734 39 22 33 4 26 56 49844 14 50156 52115 15 47885 02271 2 97729 38 23 32 56 27 4 49882 14 50118 52157 16 47843 02275 2 97725 37 24 25 32 48 27 12 49920 15 50080 52200 9. 52242 17 17 47800 02279 2 97721 36 35 9 32 40 2 27 20 9. 49958 16 10.50042 10. 47758 10. 02283 2 9.97717 26 32 32 27 28 49996 16 50004 52284 18 47716 02287 2 97713 34 27 32 24 27 36 50034 17 49966 52326 19 47674 02292 2 97708 33 28 32 16 27 44 50072 18 49928 52368 20 47632 02296 2 97704 32 29 32 8 27 52 50110 18 49890 52410 9. 52452 20 47590 02300 2 97700 31 30 9 32 2 28 9. 50148 19 10. 49852 21 10. 47548 10. 02304 2 9. 97696 30 31 31 52 28 8 50185 20 49815 52494 22 47506 02309 2 97691 29 32 31 44 28 16 50223 20 49777 52536 22 47464 02313 2 97687 28 33 31 36 28 24 50261 21 49739 52578 23 47422 02317 2 97683 27 34 31 28 28 32 50298 21 49702 52620 24 47380 02321 10. 02326 2 2 97679 26 25 35 9 31 20 2 28 40 9. 50336 22 ilO. 49664 9. 52661 24 10.47339 9. 97674 36 31 12 28 48 50374 23 49626 52703 25 47297 02330 3 97670 24 37 31 4 28 56 50411 23 49589 52745 26 47255 02334 3 97666 23 38 30 56 29 4 50449 24 49551 52787 27 47213 02338 3 97662 22 39 30 48 29 12 50486 25 49514 52829 27 47171 02343 3 97657 21 20 40 9 30 40 2 29 20 9. 50523 25 10.49477 9. 52870 28 10. 47130 10. 02347 3 9. 97653 41 30 32 29 28 50561 26 49439 52912 29 47088 02351 3 97649 19 42 30 24 29 36 50598 26 49402 52953 29 47047 02355 3 97645 18 43 30 16 29 44 50635 27 49365 52995 30 47005 02360 3 97640 17 44 45 30 8 29 52 50673 28 49327 53037 31 46963 02364 3 97636 16 15 9 30 2 30 9. 50710 28 10.49290 9. 53078 31 10. 46922 10. 02368 3 9. 97632 46 29 52 30 8 50747 29 49253 53120 32 46880 02372 3 97628 14 47 29 44 30 16 50784 30 49216 53161 33 46839 02377 3 97623 13 48 29 36 30 24 50821 30 49179 53202 34 46798 02381 3 97619 12 49 29 28 30 32 .50858 31 49142 53244 34 46756 02385 3 97615 11 10 50 9 29 20 2 30 40 9. 50896 31 10.49104 9. 53285 35 10. 46715 10.02390 4 9. 97610 51 29 12 30 48 50933 32 49067 53327 36 46673 02394 4 97606 9 52 29 4 30 56 50970 33 49030 53368 36 46632 02398 4 97602 8 53 28 56 31 4 r^.007 33 48993 53409 37 46591 02403 4 97597 t 54 28 48 31 12 51'043 34 48957 53450 38 46550 02407 4 97593 6 55 9 28 40 2 31 20 9. 51080 35 10. 48920 9. 53492 38 10. 46508 10.02411 4 9. 97589 5 56 28 32 31 28 51117 35 48883 53533 39 46467 02416 4 97584 4 57 28 24 31 36 51154 36 48846 53574 40 46426 02420 4 97580 3 58 28 16 31 44 51191 37 48809 53615 41 46385 02424 4 97576 2 59 28 8 31 52 51227 37 48773 53656 41 46344 02429 4 97571 1 60 28 32 51264 38 48736 53697 42 46303 02433 4 97567 M. M. Hour p. M. Hour A. M. Cosine. Diff. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. Sine. 108= A A B B C C 71° Seconds of time 1» 2s gs 4» 6' 6' 7' Prop, parts of cols. f. Cosine. Diff. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. Sine. M. 110° A A B B C C 69° Seconds of time 1' 2" 3' 4« o' 6' J' Prop, parts of cols, i B lo 4 5 1 1^ 1 13 14 17 19 2 21 25 24 29 3 4 30 34 4 TABLE 44. Log. Sines, Tangents, and Secants. [Page 629 21° A A B B C C 158° M. Hour A.M. Hour P.M. Sine. Di«f. Cosecant. Tangent. Diff. Cotangent. Secant. Difl. Cosine. M. 9 12 2 48 9. 55433 10. 44667 9. 58418 10. 41582 10. 02985 9. 97016 60 i 11 52 48 8 65466 1 44634 58465 1 41545 02990 97010 69 'I 11 44 48 16 55499 1 44601 58493 1 41507 02995 97005 68 8 11 36 48 24 55532 2 44468 58531 2 41469 02999 97001 67 4 6 11 28 48 32 55564 2 44436 58669 2 41431 03004 96996 56 55 9 11 20 2 48 40 9. 56597 3 10. 44403 9. 58606 3 10. 41394 10. 03009 9. 96991 6 11 12 48 48 56630 3 44370 58644 4 41366 03014 96986 64 7 11 4 48 56 55663 4 44337 68681 4 41319 03019 96981 53 8 10 56 49 4 55696 4 44306 58719 5 41281 03024 96976 62 9 10 10 48 49 12 66728 5 44272 58767 6 41243 03029 96971 51 9 10 40 2 49 20 9. 55761 5 10. 44239 9. 68794 6 10. 41206 10. 03034 9. 96966 60 11 10 32 49 28 55793 6 44207 58832 7 41168 03038 96962 49 12 10 24 49 36 55826 6 44174 58869 7 41131 03043 96957 48 13 10 16 49 44 55858 7 44142 58907 8 41093 03048 96952 47 14 15 10 8 49 52 56891 7 8 44109 68944 "9. 58981 9 41056 03053 96947 46 46 9 10 2 50 9. 65923 10. 44077 9 10.41019 10. 03058 9. 96942 16 9 52 50 8 65966 9 44044 69019 10 40981 03063 96937 44 17 9 44 50 16 55988 9 44012 59056 10 40944 03068 96932 43 18 9 36 50 24 56021 10 43979 59094 11 40906 03073 96927 42 19 20 9 28 50 32 66063 10 43947 59131 12 40869 03078 2 96922 41 40 9 9 20 2 50 40 9. 56085 11 10. 43915 9. 59168 12 10. 40832 10. 03083 2 9.96917 21 9 12 50 48 56118 11 43882 59206 13 40795 03088 2 96912 39 22 9 4 50 56 56150 12 43860 69243 14 40757 03093 2 96907 38 23 8 56 61 4 56182 12 43818 69280 14 40720 03097 2 96903 37 24 25 8 48 51 12 56216 13 43785 59317 15 40683 03102 10. 03107 2 2 96898 9. 96893 36 35 9 8 40 2 61 20 9. 56247 13 10. 43763 9. 59364 16 10. 40646 26 8 32 51 28 56279 14 43721 69391 16 40609 03112 2 96888 34 27 8 24 51 36 56311 14 43689 59429 17 40571 03117 2 96883 33 28 8 16 61 44 56343 15 43657 59466 17 40534 03122 2 96878 32 29 8 8 51 52 56376 16 43625 59503 18 40497 03127 2 96873 31 30 30 9 8 2 52 9. 56408 16 10. 43592 9. 59540 19 10. 40460 10. 03132 2 9. 96868 31 7 52 52 8 66440 17 43560 69577 19 40423 03137 3 96863 29 32 7 44 52 16 56472 17 43628 59614 20 40386 03142 3 96858 28 33 7 36 52 24 66604 18 43496 59651 20 40349 03147 3 96853 27 34 7 28 52 32 2 52 40 56536 18 43464 69688 21 40312 03152 3 96848 26 25 35 9 7 20 9. 66668 19 10. 43432 9. 69726 22 10. 40275 10. 03157 3 9. 96843 36 7 12 52 48 66599 19 43401 59762 22 40238 03162 3 96838 24 37 7 4 52 56 56631 20 43369 69799 23 40201 03167 3 96833 23 38 6 66 53 4 66663 20 43337 59836 23 40165 03172 3 96828 22 39 6 48 53 12 56695 21 43305 69872 24 40128 03177^ 3 96823 21 20 40 9 6 40 2 53 20 9. 56727 21 10. 43273 9. 59909 26 10. 40091 10. 03182 3 9. 96818 41 6 32 63 28 56759 22 43241 69946 25 40054 03187 3 96813 19 42 6 24 63 36 56790 22 43210 69983 26 40017 031^2 3 96808 18 43 6 16 53 44 56822 23 43178 60019 27 39981 03197 4 96803 17 44 6 8 53 52 56854 24 24 43146 60056 9.60093 27 28 39944 03202 4 96798 16 16 46 9 6 2 54 9. 56886 10. 43114 10. 39907 10. 03207 4 9. 96793 46 5 52 64 8 66917 25 43083 60130 28 39870 03212 4 96788 14 47 5 44 64 16 56949 25 43061 60166 29 39834 03217 4 96783 13 48 6 36 54 24 56980 26 43020 60203 30 39797 03222 4 96778 12 49 6 28 54 32 57012 26 42988 60240 30 39760 03228 4 96772 11 50 9 5 20 2 54 40 9. 57044 27 10. 42956 9. 60276 31 10. 39724 10. 03233 4 9. 96767 10 61 5 12 54 48 57075 27 42925 60313 31 39687 03238 4 96762 9 52 5 4 64 56 57107 28 42893 60349 32 39661 03243 4 96757 8 53 4 56 66 4 57138 28 42862 60386 33 39614 03248 4 96752 7 54 4 48 55 12 57169 29 42831 60422 33 39578 03253 4 96747 6 65 9 4 40 2 55 20 9. 67201 29 10. 42799 9. 60459 34 10. 39541 10. 03268 5 9. 96742 6 56 4 32 56 28 67232 30 42768 60496 35 39605 03263 5 96737 4 67 4 24 56 36 57264 30 42736 60632 35 39468 03268 5 96732 3 68 4 16 65 44 57295 31 42706 60568 36 39432 ! 03273 6 96727 2 69 4 8 55 62 57326 32 42674 60605 36 39395 03278 6 96722 1 60 4 56 57358 32 42642 60641 37 39369 03283 5 96717 M. Hour P.M. Hour A. M. Cosine. Diff. Secant. Cotangent. Diff. Tangent. Cosecant. Difl. Sine. M. 1 111° A A B B C C 68°1 Second of time 1- 2> 3> 4" 6» 6- 7» 1 Prop, parts of cols.-{B 4 5 1 8 9 1 12 14 2 16 19 2 20 23 3 24 28 4 28 32 4 Page 630] TABLE 44. Log. Sines, Tangents, and Secants. 22« A A B B C C 157° M. Hour &.. M. Hour P. M. Sine. Diff. Cosecant. Tangent. Diff. Cotangent. Secant. Diff. Cosine. M. 60 9 4 2 56 9. 57358 10. 42642 9. 60641 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 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 39214 03304 96696 56 5 9 3 20 2 56 40 9. 57514 3 10. 42486 9. 60823 3 10. 39177 10. 03309 9. 96691 55 6 3 12 56 48 57545 3 42455 60859 4 39141 03314 96686 54 7 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 10 2 48 57 12 57638 5 42362 60967 5 39033 03330 96670 51 50 9 2 40 2 57 20 9. 57669 5 10. 42331 9. 61004 6 10. 38996 10. 03335 9. 96665 11 2 32 57 28 57700 6 42300 61040 t 38960 03340 96660 49 12 2 24 57 36 57731 6 42269 61076 7 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 42207 61148 8 38852 03355 96645 46 45^ 9 2 2 58 9. 57824 8 10. 42176 9.61184 9 10. 38816 10. 03360 9. 96640 16 1 52 58 8 57855 8 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 1 42084 61292 11 38708 03376 2 96624 42 19 20 1 28 58 32 57947 9. 57978 10 42053 61328 11 38672 03381 2 2 96619 9. 96614 41 40 9 1 20 2 58 40 10 10. 42022 9. 61364 12 10. 38636 10. 03386 21 1 12 58 48 58008 11 41992 61400 13 38600 03392 2 96608 39 22 1 4 58 56 58039 11 41961 61436 13 38564 03397 2 96603 38 23 56 59 4 58070 12 41930 61472 14 38528 03402 2 96598 37 24 . 48 59 12 58101 12 1 41899 61508 14 38492 03407 2 96593 36 25 9 40 2 59 20 9.58131 13 [10.41869 9. 61544 15 10. 38456 10. 03412 2 9. 96588 35 26 32 59 28 58162 13 1 41838 61579 15 38421 03418 2 96582 34 27 24 59 36 58192 14 1 41808 61615 16 38385 03423 2 96577 33 28 16 59 44 58223 14 i 41777 61651 17 38349 03428 2 96572 32 29 30 8 59 52 58253 15 41747 61687 17 38313 03433 3 96567 31 30 9 3 9. 58284 15 10. 41716 9. 61722 18 10. 38278 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 ! 41594 61865 20 38135 03459 3 96541 26 35 8 59 20 3 40 9. 58436 18 10.41564 9. 61901 21 10. 38099 10. 03465 3 9. 96535 25 36 59 12 48 58467 18 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 1 41473 62008 23 37992 03480 3 96520 22 39 58 48 1 12 58557 20 ! 41443 62043 23 37957 03486 3 96514 21 20 40 8 58 40 3 1 20 9. 58588 20 10. 41412 9. 62079 24 10. 37921 10. 03491 3 9. 96509 41 58 32 1 28 58618 21 41382 62114 24 37886 03496 4 96504 19 42 58 24 1»86 58648 21 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 37779 03512 4 96488 16 15 45 8 58 3 2 9. 58739 23 10. 41261 9. 62256 27 10. 37744 10. 03517 4 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 37426 03565 5 96435 6 5 55 8 56 40 3 3 20 9. 59039 2» 10. 40961 9. 62609 33 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 40812 62785 36 37215 03597 5 96403 M. Hour p. M. Hour A. M. Cosine. Diff. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. Sine. M. 112° A A B B C C 07° Seconds of time 1» 2' 3« 4« 5» 6" 7» Prop, parts of cols. { B Ic 4 4 1 8 9 1 11 13 2 15 18 3 19 22 3 23 27 4 27 31 6 TABLE 44. • [Page 631 Log. Sines, Tangents, and Secants. 28° A A B B C C 156° M. Hour A. M. Hour p. M. Sine. Difl. Cosecant. Tangent. Diff. Cotangent. Secant. Difl. Cosine. M. 8 56 3 4 9. 59188 10. 40812 9. 62785 10. 37215 10. 03597 9. 96403 60 1 55 52 4 8 59218 40782 62820 1 37180 03603 96397 59 2 55 44 4 16 59247 1 40753 62855 1 37145 03608 96392 58 3 55 36 4 24 59277 1 40723 62890 2 37110 03613 96387 57 4 5 55 28 4 32 59307 2 40693 62926 2 37074 03619 96381 56 55 8 55 20 3 4 40 9. 59336 2 10. 40664 9.62961 1 3 10. 37039 10. 03624 9. 96376 6 55 12 4 48 59366 3 40634 62996 i 3 37004 03630 96370 54 7 55 4 4 56 59396 3 40604 63031 4 36969 03635 96365 53 8 54 56 5 4 59425 4 40575 63066 ; 5 36934 03640 96360 52 9 54 48 5 12 59455 4 40545 63101 I 5 36899 03646 96354 51 10 8 54 40 3 5 20 9. 59484 5 10. 40516 9.63135 j 6 !10. 36865 10. 03651 9. 96349 50 11 54 32 5 28 59514 5 40486 63170 6 ! 36830 03657 96343 49 12 54 24 5 36 59543 6 40457 63205 7 36795 03662 96338 48 13 54 16 5 44 59573 6 40427 63240 1 7 36760 03667 96333 47 14 15 54 8 8 54 6' 5 52 59602 7 7 40398 63275 j 8 1 36725 03673 96.327 46 45 3 6 9. 59632 10. 40368 9.63310 ! 9 !l0. 36690 10. 03678 9. 96322 16 53 52 6 8 59661 8 40339 63345 ' 9 : 36655 03684 96316 44 17 53 44 6 16 59690 8 40310 63379 10 ; 36621 03689 2 96311 43 18 53 36 6 24 59720 9 40280 63414 10 ; 36586 03695 2 96305 42 19 20 53 28 6 32 59749 9 40251 63449 11 9. 63484 j 12 36551 03700 2 96300 41 40 8 53 20 3 6 40 9. 59778 10 10. 40222 10. 36516 10. 03706 2 9. 96294 21 53 12 6 48 59808 10 40192 63519 I 12 36481 03711 2 96289 39 22 53 4 6 56 59837 11 40163 63553 13 36447 03716 2 96284 38 2-. 52 56 7 4 59866 11 40134 63588 13 36412 03722 2 96278 37 24 25 52 48 8 52 "40 7 12 59895 12 40105 63623 1 14 36377 03727 2 96273 36 3 7 20 9. 59924 12 10. 40076 9. 63657 14 10. 36343 10. 03733 2 9. 96267 35 26 52 32 7 28 59954 13 40046 63692 15 36308 03738 2 96262 34 27 52 24 7 36 59983 13 40017 63726 1 16 36274 03744 2 96256 33 28 52 16 7 44 60012 14 39988 63761 ! 16 i 36239 03749 3 96251 32 29 30 52 8 7 52 60041 14 15 39959 63796 i 17 i 36204 03755 3 96245 31 8 52 3 8 9. 60070 10. 39930 9. 63830 17 110.36170 10. 03760 3 9. 96240 30 31 51 52 8 8 60099 15 39901 63865 18 1 36135 03766 3 96234 29 32 51 44 8 16 60128 15 39872 63899 18 : 36101 03771 3 96229 28 33 51 36 8 24 60157 16 39843 63934 19 36066 03777 3 1 96223 27 34 35 51 28 8 32 60186 16 39814 63968 20 36032 03782 10. 03788 3 3 96218 26 8 51 20 3 8 40 9. 60215 17 10. 39785 9. 64003 20 10. 35997 9. 96212 25 36 51 12 8 48 60244 17 39756 64037 21 35963 03793 3 96207 24 37 51 4 8 56 60273 18 39727 • 64072 21 35928 03799 3 96201 23 38 50 56 9 4 60302 18 39698 64106 22 35894 03804 3 96196 22 39 50 '48 9 12 60331 19 39669 64140 22 35860 03810 4 96190 21 40 8 50 40 3 9 20 9. 60359 19 10. 39641 9. 64175 23 10. 35825 10. 03815 4 9. 96185 20 41 50 32 9 28 60388 20 39612 64209 24 35791 03821 4 96179 19 42 50 24 9 36 60417 20 39583 64243 24 35757 03826 4 96174 18 43 50 16 9 44 60446 21 39554 64278 25 35722 03832 4 96168 17 44 50 8 9 52 60474 21 39526 64312 25 35688 03838 4 96162 16 45 8 50 3 10 9. 60503 22 10. 39497 9. 64346 26 10. 35654 10. 03843 4 9. 96157 15 46 49 52 10 8 60532 22 39468 64381 26 35619 03849 4 96151 14 47 49 44 10 16 60561 23 39439 64415 27 35585 03854 4 96146 13 48 49 36 10 24 60589 23 39411 64449 28 35551 03860 4 96140 12 49 49 28 10 32 60618 24 39382 64483 28 35517 03865 4 96135 11 10 50 8 49 20 3 10 40 9. 60646 24 10. 39354 9. 64517 29 10. 35483 10. 03871 5 9. 96129 51 49 12 10 48 60675 25 39325 64552 29 35448 03877 5 96123 9 52 49 4 10 56 60704 25 39296 64586 30 35414 03882 5 96118 8 53 48 56 11 4 60732 26 39268 64620 31 35380 03888 5 96112 7 54 48 48 11 12 60761 26 27 39239 10. 39211 64654 31 35346 10. 35312 03893 5 96107 6 55 8 48 40 3 11 20 9. 60789 9. 64688 32 10. 03899 5 9. 96101 5 56 48 32 11 28 60818 27 39182 64722 32 35278 03905 5 96095 4 57 48 24 11 36 60846 28 39154 64756 33 35244 03910 5 96090 3 58 48 16 11 44 60875 28 39125 64790 33 35210 03916 5 96084 2 59 48 8 11 52 60903 29 39097 64824 34 35176 03921 5 96079 1 60 48 12 60931 29 39069 64858 35 35142 039.27 6 96073 M. Hour p. M. Hour A. M. Cosine. Diff. Secant. Cotangent. Diff. Tangent. iCosecant. Diff. Sine. M. 113° A A B B C C 66° 1 Seconds of time , Prop, parts of cols, •{t 7 11 9 I 13 1 I 2 Page 632] TABLE 44. ] -,og. Sines, Tangents, and Secants. 24° A A B B C C 1 55° M. 60 M. Hour A. M. Hour P. M. Sine. Dili. Cosecant. Tangent. Diff. Cotangent. Secant. Diff. Cosine. 8.48 3 12 9. 60931 10. 39069 9. 64858 10. 35142 10. 03927 9. 96073 1 47 52 12 8 60960 39040 64892 1 35108 03933 96067 59 2 47 44 12 16 60988 1 39012 64926 1 35074 03938 96062 58 3 47 36 12 24 61016 1 38984 64960 2 35040 03944 96056 57 4 47 28 12 32 61045 2 38955 64994 2 3 35006 03950 96050 56 55 5 8 47 20 3 12 40 9. 61073 2 10. 38927 9. 65028 10. 34972 10. 03955 9. 96045 6 47 12 12 48 61101 3 38899 65062 3 34938 03961 1 96039 54 7 47 4 12 56 61129 3 38871 65096 4 34904 03966 1 96034 53 8 46 56 13 4 61158 4 38842 65130 4 34870 03972 1 96028 52 9 46 48 13 12 61186 4 38814 65164 5 34836 03978 1 96022 51 50 10 8 46 40 3 13 20 9. 61214 5 10. 38786 9. 65197 6 10. 34803 10. 03983 1 9.96017 11 46 32 13 28 61242 5 38758 65231 6 34769 03989 1 96011 49 12 46 24 13 36 61270 6 38730 65265 7 34735 03995 1 96005 48 13 46 16 13 44 61298 6 38702 65299 7 34701 04000 1 96000 47 14 46 8 13 52 61326 6 38674 65333 8 346()7 04006 1 95994 46 45 15 8 46 3 14 9. 61354 7 10. 38646 9. 65366 8 10. 34634 10.04012 1 9. 95988 16 45 52 14 8 61382 7 38618 65400 9 34600 04018 2 95982 44 17 45 44 14 16 61411 8 38589 65434 9 34566 04023 2 95977 43 18 45 36 14 24 61438 8 38562 65467 10 34533 04029 2 95971 42 19 45 28 14 32 61466 9 38534 65501 11 34499 04035 2 95965 41 40 20 8 45 20 3 14 40 9. 61494 9 10. 38506 9. 65535 11 10. 34465 10. 04040 2 9. 95960 21 45 12 14 48 61522 10 38478 65568 12 34432 04046 2 95954 39 22 45 4 14 56 61550 10 38450 65602 12 34398 04052 2 95948 38 23 44 56 15 4 61578 11 38422 65636 13 34364 04058 2 95942 37 24 44 48 15 12 61606 11 38394 65669 13 34.331 04063 2 95937 36 35 25 8 44 40 3 15 20 9. 61634 12 10. 38366 9. 65703 14 10. 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 44 8 15 52 61745 13 38255 65837 16 34163 04092 3 95908 31 30 8 44 3 16 9.61773 14 10. 38227 9. 65870 17 10. 34130 10. 04098 3 9. 95902 30 31 43 52 16 8 61800 14 38200 65904 17 34096 04103 3 95897 29 32 43 44 16 16 61828 15 38172 65937 18 34063 04109 3 95891 28 33 43 36 16 24 61856 15 38144 65971 18 34029 04115 3 95885 27 34 43 28 16 32 61883 16 38117 66004 19 33996 04121 3 95879 26 25 35 8 43 20 3 16 40 9. 61911 16 10. 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 18 10. 37951 9. 66204 22 10. 33796 10. 04156 4 9. 95844 41 42 32 17 28 62076 19 37924 66238 23 33762 04161 4 95839 19 42 42 24 17 36 62104 19 37896 66271 23 33729 04167 4 95833 18 43 42 16 17 44 62131 20 37869 66304 24 33696 04173 4 95827 17 44 42 8 17 52 62159 20 37841 66337 25 33663 04179 4 95821 16 45 8 42 3 18 9. 62186 21 10. 37814 9. 66371 25 10. 33629 10. 04185 4 9. 95815 15 46 41 52 18 8 62214 21 37786 66404 26 33596 04190 4 95810 14 47 41 44 18 16 62241 22 37759 66437 26 33563 04196 5 95804 13 48 41 36 18 24 62268 22 37732 66470 27 33530 04202 5 95798 12 49 41 28 18 32 62296 23 37704 66503 27 33497 04208 5 5 95792 11 50 8 41 20 3 18 40 9. 62323 23 10. 37677 9. 66537 28 10. 33463 10. 04214 9. 95786 10 51 41 12 18 48 62350 24 37650 66570 28 33430 04220 5 95780 9 52 41 4 18 56 62377 24 37623 66603 29 33397 04225 5 95775 8 53 40 56 19 4 62405 24 37595 66636 30 33364 04231 5 95769 7 54 40 48 19 12 62432 25 37568 66669 30 33331 04237 5 95763 6 55 8 40 40 3 19 20 9. 62459 25 10. 37541 9. 66702 31 10. 33298 10. 04243 5 9. 95757 5 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 Q 58 40 16 19 44 62541 27 37459 66801 32 33199 04261 6 95739 2 59 40 8 19 52 62568 27 37432 66834 33 33166 04267 6 95733 1 60 40 20 62595 28 37405 66867 33 33133 04272 6 95728 M. M. Hour p. M. Hour A. M Cosine. Diff. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. Sine. 114° A A B B C C 65'= Seconds of time 1" 2i 3. 4> 5' G» T Prop, parts of cols.-^B Ic 3 4 1 7 f 10 13 2 14 17 3 17 21 4 21 25 4 24 29 6 TABLE U. Page 633 Log. Sines, Tangents, and Secants. 25° A A B B C C 164° M. Hour A. M. Hour p. M. Sine. Diflf. Cosecant. Tangent. Diflf. Cotangent. Secant. Diff. Cosine. M. 8 40 3 20 9. 62595 10. 37405 9. 66867 10. 33183 10. 04372 9. 96728 60 1 89 52 20 8 62622 87878 66900 1 33100 04278 95722 59 2 39 44 20 16 62649 1 87351 66933 1 33067 04284 95716 58 8 39 86 20 24 62676 1 37824 66966 2 33034 04290 95710 57 4 39 28 20 82 62708 2 87297 66999 2 33001 04296 96704 56 55 5 8 39 20 8 20 40 9. 62730 2 10. 37270 9. 67032 8 10. 32968 10. 04802 9. 95698 6 39 12 20 48 62757 3 37243 67065 8 32985 04808 95692 54 7 39 4 20 56 62784 3 37216 67098 4 82902 04814 95686 53 8 38 56 21 4 62811 4 37189 67131 4 32869 - 04820 95680 52 9 10 38 48 21 12 62838 4 37162 67163 5 32837 04826 96674 51 8 88 40 8 21 20 9. 62866 4 10. 87135 9. 67196 5 10. 32804 10. 04382 •9. 96668 50 11 38 32 21 28 62892 5 37108 67229 6 82771 04387 95663 49 12 38 24 21 36 62918 5 37082 67262 7 i 32738 04343 95657 48 13 38 16 21 44 62945 6 37055 67295 7 82705 04349 96651 47 14 15 88 8 21 52 62972 6 87028 67827 8 8 82678 04.355 95646 46 45 8 38 3 22 9. 62999 7 10. 37001 9. 67860 10. 32640 10. 04361 2 9. 95639 16 87 52 22 8 63026 7 86974 67393 9 1 32607 04867 2 96638 44 17 37 44 22 16 63052 8 86948 67426 9 82574 04873 2 96627 43 18 37 36 22 24 63079 8 36921 67458 10 32542 04879 2 95621 42 19 37 28 22 32 63106 , 8 36894 67491 10 32509 04386 2 96615 41 40 20 8 37 20 8 22 40 9. 681.38 9 10. 36867 9. 67524 11 10. 82476 10. 04391 2 9. 96609 21 37 12 22 48 63159 9 86841 67556 11 32444 04397 2 96608 39 22 37 4 22 56 68186 10 36814 67589 12 32411 04403 2 95597 38 23 36 56 28 4 63213 10 36787 67622 12 32378 04409 2 95691 37 24 25 36 48 23 12 68239 11 86761 67654 13 32346 04415 2 3 95585 86 35 8 36 40 8 23 20 9. 68266 11 10. 36734 9. 67687 14 10. 82313 10. 04421 9. 96679 26 36 32 23 28 68292 11 36708 67719 14 32281 04427 3 95678 34 27 86 24 28 36 68819 12 36681 67752 15 82248 04488 8 96667 33 28 36 16 23 44 63345 12 86655 67785 15 32215 04489 3 95561 82 29 86 8 23 52 63872 18 13 36628 67817 16 32188 04445 3 95565 31 30 8 86 3 24 9. 63398 10. 36602 9. 67850 16 10. 32150 10. 04451 8 9. 95649 30 81 35 52 24 8 63425 14 86575 67882 17 32118 04457 3 95543 29 32 85 44 24 16 63451 14 86549 67915 17 32085 04463 8 95537 28 33 35 36 24 24 63478 15 36522 67947 18 32053 04469 8 95531 27 84 85 28 24 32 68504 15 36496 67980 18 19 32020 04475 8 96525 26 85 8 35 20 8 24 40 9. 68581 15 10. 36469 9. 68012 10. 31988 10. 04481 4 9. 96619 26 86 85 12 24 48 68557 16 36443 68044 20 31956 04487 4 95518 24 37 35 4 24 56 68588 16 36417 68077 20 81923 04493 4 96607 28 38 84 56 25 4 63610 17 36390 68109 21 81891 04500 4 96500 22 89 84 48 25 12 68636 17 86364 68142 21 81858 04506 4 96494 9. 96488 21 20 40 8 84 40 3 25 20 9. 63662 18 10. 36338 9. 68174 22 10. 31826 10. 04612 4 41 34 32 25 28 63689 18 36311 68206 22 31794 04518 4 96482 19 42 84 24 25 36 63715 19 36285 68239 23 81761 04624 4 96476 18 43 84 16 25 44 68741 19 36259 68271 23 81729 04630 4 95470 17 44 45 84 8 8 34 25 52 68767 19 86233 68808 24 81697 04686 4 95464 16 3 26 9. 63794 20 10. 36206 9. 68336 24 10. 81664 10. 04542 5 9. 96468 15 46 88 52 26 8 63820 20 86180 68868 25 81632 04548 5 96452 14 47 83 44 26 16 63846 21 86154 68400 25 31600 04564 5 96446 13 48 33 86 26 24 68872 21 86128 . 68432 26 81568 04660 5 96440 12 49 33 28 26 82 63898 22 86102 68465 27 81585 04666 5 96434 11 50 8 33 20 3 26 40 9. 63924 22 10. 86076 9.68497 ! 27 10. 31503 10. 04678 5 9. 95427 10 51 33 12 26 48 63950 28 86050 68529 1 28 31471 04579 6 95421 9 52 83 4 26 56 68976 23 86024 68561 28 31439 04586 5 95415 8 58 32 56 27 4 64002 23 85998 68593 ! 29 31407 04691 5 95409 7 54 32 48 27 12 64028 24 85972 68626 i 29 31374 04597 6 95403 6 6 55 8 32 40 3 27 20 9. 64054 24 10. 35946 9. 68658 30 10. 31342 10. 04603 6 9. 95397 56 32 82 27 28 64080 25 35920 68690 80 31810 04609 6 95891 4 57 82 24 27 86 64106 25 35894 68722 31 81278 04616 6 96384 3 58 82 16 27 44 64182 26 35868 68754 31 81246 04622 6 96878 2 59 32 8 27 52 64158 26 35842 68786 32 31214 04628 6 95872 1 60 M. 32 28 64184 26 35816 68818 38 31182 04634 6 96366 Hour p. M. Hour A. M. Cosine. Diflf. Secant. Cotangent. Diflf. Tangent. Cosecant. Diff. Sine. M. 115° A A B B C C 64° 1 Secondsof time 1' 2. 3. ]«. 6> 6" 7« (A 3 Prop, parts of cols. < B 4 ic 1 7 8 2 10 12 2 13 16 3 17 20 4 20 24 5 23 28 5 Page 634] TABLE U. Log. Sines, Tangents, and Secants. 26° A A B B C C 153° M. Hour A. M. Hour p. M. Sine. Diff. Cosecant. Tangent. Difif. 1 Cotangent. Secant. DiflE. Cosine. M. 60 8 32 3 28 9.64184 10.35816 9. 68818 10.31182 10. 04634 9. 95366 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 3 31 36 28 24 64262 1 35738 68914 2 31086 04652 95348 57 4 31 28 28 32 3 28 40 64288 2 35712 10. 35687 68946 2 31054 04659 95341 56 55 5 8 31 20 9. 64313 2 9. 68978 3 10.31022 10. 04665 9. 95335 6 31 12 28 48 64339 3 35661 69010 3 30990 04671 95329 54 7 31 4 28 56 64365 3 35635 69042 4 I 30958 04677 95323 53 8 30 56 29 4 64391 3 35609 69074 4 30926 04683 95317 52 9 30 48 29 12 3 29 20 64417 4 35583 10. 35558 69106 5 30894 10. 30862 04690 95310 9. 95304 51 50 10 8 30 40 9.64442 4 9. 69138 5 10. 04696 11 30 32 29 28 64468 5 35532 69170 6 30830 04702 95298 49 12 30 24 29 36 64494 5 35506 69202 6 ' 30798 04708 95292 48 13 30 16 29 44 64519 5 35481 69234 7 i 30766 04714 95286 47 14 15 30 8 29 52 64545 9. 64571 6 35455 69266 7 I 30734 04721 95279 46 8 30 3 30 6 10. 35429 9. 69298 8 10. 30702 10. 04727 2 9. 95273 45 16 29 52 30 8 64596 7 35404 69329 8 30671 04733 2 95267 44 17 29 44 30 16 64622 7 35378 69361 9 30639 04739 2 95261 43 18 29 36 30 24 64647 8 35353 69393 9 30607 04746 2 95254 42 19 29 28 30 32 64673 8 35327 69425 10 : .30575 04752 2 95248 41 20 8 29 20 3 30 40 9. 64698 8 10. 35302 9. 69457 11 10.30543 10. 04758 2 9. 95242 40 21 29 12 30 48 64724 9 35276 69488 11 1 30512 04764 2 95236 39 22 29 4 30 56 64749 9 35251 69520 12 30480 04771 2 95229 38 23 28 56 31 4 64775 10 35225 69552 12 i 30448 04777 2 95223 37 24 25 28 48 31 12 64800 10 35200 69584 13 1 30416 04783 10. 04789 3 95217 36 35 8 28 40 3 31 20 9. 64826 11 10. 35174 9. 69615 13 10. 30385 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 13 35073 69742 15 30258 04815 3 95185 31 8 28 3 32 9. 64953 10. 35047 9. 69774 16 ilO. 30226 10. 04821 3 9. 95179 30 31 27 52 32 8 64978 13 35022 69805 16 1 30195 04827 3 95173 29 32 27 44 32 16 65003 14 34997 69837 17 i 30163 04833 3 95167 28 33 27 36 32 24 65029 ^4 34971 69868 17 ' 30132 04840 3 95160 27 34 35 27 28 8 27 20 32 32 65054 14 15 34946 10. 34921 69900 18 i 30100 04846 4 4 95154 26 25 3 32 40 9. 65079 9. 69932 18 110.30068 10. 04852 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 i 29974 04871 4 95129 22 39 26 48 33 12 65180 16 34820 70058 21 29942 04878 4 95122 2.1 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 15 45 8 26 3 34 9. 65331 19 10. 34669 9. 70247 24 10. 29753 10. 04916 5 9. 95084 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 6 95071 13 48 25 36 34 24 65406 20 34594 70341 25 [ 29659 04935 5 95065 12 49 50' 25 28 34 32 65431 21 34569 70372 26 ' 29628 04941 5 95059 11 8 25 20 3 34 40 9. 65456 21 10. 34544 9. 70404 26 10.29596 10. 04948 5 9. 95052 10 51 25 12 34 48 65481 22 34519 70435 27 29565 04954 5 95046 9 52 25 4 34 56 65506- 22 34494 70466 27 29534 04961 5 950.39 8 53 24 56 35 4 65531 22 34469 70498 28 29502 04967 6 95033 7 54 24 48 35 12 65556 23 34444 70529 28 29471 04973 6 95027 6 55 8 24 40 3 35 20 9. 65580 23 10. 34420 9. 70560 29 10. 29440 10. 04980 6 9. 95020 5 56 24 32 35 2^ . 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 94995 1 60 M. 24 36 65705 25 34295 70717 32 29283 05012 6 94988 M. Hour p. M. Hour A. M. Cosine. Diff. Secant. Cotangent. Difl. Tangent. Cosecant. Diff. Sine. 116° A A B B C C 63° Seconds of time ]» 2» 3' 4» 6» i C' 7 = (A Prop, parts of cols. < B (c 3 4 1 6 8 2 10 12 2 13 16 3 16 19 20 24 4 5 22 28 6 r^ TABLE 44. Log. Sines, Tangents, and Secants. [Page 635 27° A A B B C C 152° M. Hour A.M. Hour P.M. Sine. Dltf. Cosecant. Tangent. Diff. Cotangent. Secant. Diff. Cosine. M. 60 8 24 3 86 9. 65705 10. 84295 9. 70717i 10. 29288 10. 05012 9. 94988 1 23 52 36 8 65729 84271 70748 1 29252 05018 94982 59 2 23 44 36 16 65754 1 34246 70779 1 29221 05025 94975 58 3 23 36 36 24 65779 1. ;W221 70810 2 29190 05031 94969 57 4 5^ 23 28 8 23 20 36 32 65804 2 34196 70841 2 29159 05038 94962 56 55 3 36 40 9. 65828 2 10. 34172 9. 70878 3 10. 29127 10.05044 9. 94956 6 23 12 36 48 65858 2 34147 70904 3 29096 05051 94949 54 7 23 4 36 56 65878 3 84122 70985 4 29065 05057 94943 53 8 22 56 37 4 65902 3 84098 70966 4 29034 05064 94936 52 9 22 48 37 12 65927 4 84078 70997 5 29008 05070 94930 51 50 10 8 22 40 3 37 20 9. 65952 4 10. 84048 9. 71028 5 10. 28972 10. 05077 9. 94923 11 22 32 37 28 65976 4 84024 71059 6 28941 05083 94917 49 12 22 24 87 36 66001 5 88999 71090 6 28910 05089 94911 48 13 22 16 37 44 66025 5 88975 71121 i 28879 05096 94904 47 14 22 8 37 52 66050 6 33950 71153 7 28847 10. 28816 05102 10.05109 2 2 94898 9. 94891 46 45 15 8 22 8 88 9. 66075 6 10. 38925 9. 71184 8 16 21 52 88 8 66099 6 33901 71215 8 28785 05115 2 94885 44 17 21 44 88 16 66124 < 38876 71246 9 28754 05122 2 94878 43 18 21 36 88 24 66148 / 88852 71277 9 28723 05129 2 94871 42 19 21 28 88 82 66173 8 83827 71308 10 28692 05135 2 94865 41 40 20 8 21 20 8 38 40 9. 66197 8 10. 83803 9. 71339 10 10. 28661 10. 05142 2 9. 94858 21 21 12 88 48 66221 8 38779 71370 11 28680 05148 2 94852 39 22 21 4 38 56 66246 9 83754 71401 11 28599 05155 2 94845 38 23 20 56 89 4 66270 9 33730 71481 12 28569 05161 3 94839 37 24 25 20 48 89 12 3 89 20 66295 10 33705 71462 12 28538 05168 3 94882 86 8-20 40 9. 66819 10 10. 33681 9. 71498 18 10. 28507 10. 05174 3 9. 94826 35 26 20 32 39 28 66343 11 83657 71524 18 28476 05181 3 94819 .84 27 20 24 39 36 66868 11 38632 71555 14 28445 05187 8 94818 33 28 20 16 39 44 66892 11 83608 71586 14 28414 05194 3 94806 32 29 20 8 89 52 66416 12 88584 71617 15 28383 05201 3 94799 31 30 30 8 20 8 40 9. 66441 12 10.83559 9. 71648 15 10. 28352 10. 05207 3 9. 94798 31 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 83 19 86 40 24 66513 13 1 83487 71740 17 28260 05227 4 94778 27 34 19 28 40 32 66587 14 33468 71771 17 28229 05238 4 94767 26 25 35 8 19 20 3 40 40 9. 66562 14 10. 33488 9. 71802 18 10. 28198 10. 05240 4 9. 94760 36 19 12 40 48 66586 15 83414 71888 19 28167 05247 4 94753 24 37 19 4 40 56 66610 15 88890 71868 19 28137 05253 4 94747 28 38 18 56 41 4 66634 15 83866 71894 20 28106 05260 4 94740 22 39 18 48 41 12 66658 16 33342 71925 20 21 28075 05266 4 94734 21 40 8 18 40 3 41 20 9. 66682 16 10. 38318 9. 71955 10. 28045 10. 05273 4 9. 94727 20 41 18 32 41 28 66706 17 88294 71986 21 28014 05280 4 94720 19 42 18 24 41 36 66781 17 83269 72017 22 27988 05286 5 94714 18 48 18 16 41 44 66755 17 33245 72048 22 27952 05293 5 94707 17 44 45 18 8 41 52 66779 18 18 38221 10. 33197 72Q78 23 28 27922 05300 5 94700 9. 94694 16 15 8 18 3 42 9. 66803 9. 72109 10. 27891 10. 05306 5 46 17 52 42 8 66827 19 33173 72140 24 27860 05313 5 94687 14 47 17 44 42 16 66851 19 88149 72170 24 27830 05820 5 94680 18 48 17 36 42 24 66875 19 83125 72201 25 27799 05826 5 94674 12 49 50 17 28 42 32 66899 20 33101 10. 33078 72281 25 26 27769 05333 5 94667 11 10 8 17 20 8 42 40 9. 66922 20 9. 72262 10. 27738 10. 05340 5 9. 94660 51 17 12 42 48 66946 21 88054 72298 26 27707 05846 6 94654 9 52 17 4 42 56 66970 21 88080 72323 27 27677 05353 6 94647 8 53 16 56 43 4 66994 21 83006 72854 27 27646 05860 6 94640 7 54 55 16 48 43 12 67018 22 82982 72884 28 28 27616 05866 6 6 94634 6 8 16 40 3 43 20 9. 67042 22 10. 82958 9. 72415 10. 27585 10. 05373 9. 94627 5 56 16 32 48 28 67066 23 32984 72445 29 27555 05380 6 94620 4 57 16 24 48 86 67090 23 32910 72476 29 27524 05386 6 94614 3 58 16 16 48 44 67113 1 23 32887 72506 80 27494 05393 6 94607 2 59 16 8 43 52 67137 1 24 32863 72587 80 27463 05400 6 94600 1 60 16 44 67161 j 24 32839 72567 81 27438 05407 7 94598 M. Hour p. M. Hour A.M. Cosine. Diflf. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. Sine. JI. 1 117° A A B B C C zi Seconds of time Prop, parts of cols. < B C 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. Diff. Cosecant. Tangent. Diff. Cotangent. Secant. Diff. Cosine. M. 60 8 16 3 44 9. 67161 10. 32839 9. 72567 10. 27433 10. 05407 9. 94593 1 15 52 44 8 67185 32815 72598 1 27402 05413 94587 59 2 15 44 44 16 67208 1 32792 72628 1 27372 05420 94580 58 3 15 36 44 24 67232 1 32768 72659 2 27341 05427 94573 57 4 15 28 44 32 67256 2 32744 72689 2 27311 05433 94567 56 55 5 8 15 20 3 44 40 9. 67280 2 10. 32720 9. 72720 3 10. 27280 10. 05440 9. 94560 6 15 12 44 48 67303 2 32697 72750 3 27250 05447 94553 54 7 15 4 44 56 67327 3 32673 72780 4 27220 05454 94546 53 8 14 56 45 4 67350 3 32650 72811 4 27189 05460 94540 52 9 14 48 45 12 67374 3 32626 72841 5 5 27159 10. 27128 05467 94533 9. 94526 51 50 10 8 14 40 3 45 20 9. 67398 4 10. 32602 9. 72872 10. 05474 11 14 32 45 28 67421 4 32579 72902 6 27098 05481 94519 49 12 14 24 45 36 67445 5 32555 72932 6 27068 05487 94513 48 13 14 16 45 44 67468 5 32532 72963 7 27037 05494 94506 47 14 14 8 45 52 67492 5 32508 72993 7 8 27007 05501 2 94499 46 45 15 8 14 3 46 9. 67515 6 10. 32485 9. 73023 10. 26977 10. 05508 2 9. 94492 16 13 52 46 8 67539 6 32461 73054 8 26946 05515 2 94485 44 17 13 44 46 16 67562 7 32438 73084 9 26916 05521 2 94479 43 18 13 36 46 24 67586 7 32414 73114 9 26886 05528 2 94472 42 19 13 28 46 32 67609 7 32391 73144 10 26856 05535 2 94465 41 40 20 8 13 20 3 46 40 9. 67633 8 10. 32367 9. 73175 10 10. 26825 10. 05542 2 9. 94458 21 13 12 46 48 67656 8 32344 73205 11 26795 05549 2 94451 39 22 13 4 46 56 67680 9 32320 73235 11 26765 05555 3 94445 38 23 12 56 47 4 67703 9 32297 V3265 12 26735 05562 3 94438 37 24 12 48 47 12 67726 9 10 32274 73295 12 26705 05569 3 94431 36 35 25 8 12 40 3 47 20 9. 67750 10. 32250 9. 73326 13 10. 26674 10. 05576 3 9. 94424 26 12 32 47 28 67773 10 32227 73356 13 26644 05583 3 94417 34 27 12 24 47 36 67796 10 32204 73386 14 26614 05590 3 94410 33 28 12 16 47 44 67820 11 32180 73416 14 26584 05596 3 - 94404 32 29 12 8 47 52 67843 11 32157 73446 15 26554 05603 3 94397 31 30 8 12 3 48 9. 67866 12 10. 32134 9. 73476 15 10. 26524 10. 05610 3 9. 94390 30 31 11 52 48 8 67890 12 32110 73507 16 26493 05617 4 94383 29 32 11 44 48 16 67913 12 32087 73537 16 26463 05624 4 94376 28 33 11 36 48 24 67936 13 32064 73567 17 26433 05631 4 94369 27 34 11 28 48 32 67959 13 32041 73597 17 26403 05638 10. 05645 4 4 94362 9. 94355 26 25 35 8 11 20 3 48 40 9. 67982 14 10. 32018 9. 73627 18 10. 26373 36 11 12 48 48 68006 14 31994 73657 18 26343 05651 4 94349 24 37 11 4 48 56 68029 14 31971 73687 19 26313 05658 4 94342 23 38 10 56 49 4 68052 15 31948 73717 19 26283 05665 4 94335 22 39 10 48 49 12 68075 15 31925 73747 20 26253 05672 4 94328 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 5 94307 18 43 10 16 49 44 68167 17 31833 73867 22 26133 05700 5 94300 17 44 10 8 49 52 68190 17 31810 73897 9. 73927 22 23 26103 10. 26073 05707 10. 05714 5 5 94293 9. 94286 16 15 45 8 10 3 50 9. 68213 17 10. 31787 46 9 52 50 8 68237 18 31763 73957 23 26043 05721 5 94279 14 47 9 44 50 16 68260 18 31740 73987 24 26013 05727 5 94273 13 48 9 36 50 24 68283 19 31717 74017 24 25983 05734 5 94266 12 49 9 28 50 32 68305 19 31695 74047 25 25953 05741 6 94259 11 10 50 8 9 20 3 50 40 9. 68328 19 10.31672 9. 74077 25 10. 25923 10. 05748 6 9. 94252 51 9 12 50 48 68351 20 31649 74107 26 25893 05755 6 94245 9 52 9 4 50 56 68374 20 31626 74137 26 25863 05762 6 94238 8 53 8 56 51 4 68397 21 31603 74166 27 25834 05769 6 94231 7 54 8 48 51 12 68420 9. 68443 21 21 31580 74196 27 25804. 05776 6 6 94224 9.94217 6 5 55 8 8 40 3 51 20 10. 31557 9. 74226 28 10. 25774 10. 05783 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 :5 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. Hour p. M. Hour A. M. Cosine. Diff. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. Sine. M 118° A A B B C C 61° Seconds of time 1" 2- 3» 4. o* C' 7' Prop, parts of cols. a 3' 4« 5» 6» 7' Prop, parts of cols.-fB Ic 3 4 1 6 7 2 8 11 3 11 15 4 14 18 4 17 22 5 20 26 6 Page 638] TABLE 44. Log. Sines, Tangents, and Secants. 80° A A B B C C 149° M. Hour A. M. Hour p. M. Sine. Difl. Cosecant. Tangent. Diff. Cotangent. Secant. Diff. Cosine. M. 8 4 9. 69897 10. 30103 9. 76144 10. 23856 10. 06247 9. 93753 60 1 7 59 52 8 69919 30081 76173 23827 06254 93746 59 2 59 44 16 69941 1 30059 76202 1 23798 06262 93738 58 3 59 36 24 69963 1 30037 76231 1 23769 06269 93731 57 4 59 28 32 69984 1 30016 76261 2 23739 06276 93724 56 55 5 7 59 20 4 40 9. 70006 2 10. 29994 9. 76290 2 10. 23710 10. 06283 9. 93717 6 59 12 48 70028 2 29972 76319 3 23681 06291 93709 54 7 59 4 56 70050 3 29950 76348 3 23652 • 06298 93702 53 8 58 56 1 4 70072 3 29928 76377 4 23623 06305 93695 52 9 58 48 1 12 70093 3 29907 76406 4 23594 06313 93687 51 50 10 7 58 40 4 1 20 9. 70115 4 10. 29885 9. 76435 6 10. 23565 10. 06320 9. 93680 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 93665 48 13 58 16 1 44 70180 5 29820 76522 6 23478 06342 2 93658 47 14 58 8 1 52 70202 5 29798 76551 7 23449 06350 2 93650 46 45 15 7 58 4 2 9. 70224 5 10. 29776 9. 76580 7 10. 23420 10. 06357 2 9. 93643 16 57 52 2 8 70245 6 29755 76609 8 23391 06364 2 93636 44 17 57 44 2 16 70267 6 29733 76639 8 23361 06372 2 93628 43 18 57 36 2 ^4 70288 6 29712 76668 9 23332 06379 2 93621 42 19 57 28 2 32 70310 7 7 29690 76697 9 23303 06386 2 93614 41 40 20 7 57 20 4 2 40 9. 70332 10. 29668 9. 76725 10 10. 23275 10. 06394 2 9. 93606 21 57 12 2 48 70353 8 29647 76754 10 23246 06401 3 93599 39 22 57 4 2 56 70375 8 29625 76783 11 23217 06409 3 93591 38 23 56 56 3 4 70396 8 29604 76812 11 23188 06416 3 93584 37 24 56 48 3 12 70418 9 29582 76841 12 23159 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 31 30 7 56 4 4 9. 70547 11 10. 29453 9. 77015 14 10. 22985 10. 06468 4 9. 93532 30 31 55 52 4 8 70568 11 29432 77044 15 22956 06475 4 93525 29 32 55 44 4 16 70590 11 29410 77073 15 22927 06483 4 93517 28 33 55 36 4 24 70611 12 29389 77101 16 22899 06490 4 93510 27 34 55 28 4 32 70633 9. 70a54 12 13 29367 77130 16 22870 06498 .4 4 93502 26 35 7 55 20 4 4 40 10. 29346 9.77159 17 10. 22841 10. 06505 9. 93495 25 36 55 12 4 48 70675 13 29325 77188 17 22812 06513 4 93487 24 37 55 4 4 56 70697 13 29303 77217 18 22783 06520 5 93480 23 38 54 56 5 4 70718 14 29282 77246 18 22754 06528 5 93472 22 39 40 54 48 5 12 70739 14 14 29261 10. 29239 77274 19 19 22726 06535 5 93465 21 20 7 54 40 4 5 20 9. 70761 9. 77303 10. 22697 10.06543 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 77418 21 22582 10. 22553 06573 5 93427 9. 93420 16 15 45 7 54 4 6 9. 70867 10. 29133 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 53 28 6 32 70952 9.70973" 18 18 29048 77562 24 24" 22438 06610 6 6 93390 9. 93382 11 10 50 7 53 20 4 6 40 10. 29027 9. 77591 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 52 48 7 12 71058 19 28942 77706 26 22294 06648 10. 06656 7 93352 6 5 55 7 52 40 4 7 20 9. 71079 20 10. 28921 9. 77734 26 10. 22266 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 1 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. M. Hour P. M Hour A. M. Cosine. Diff. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. Sine. 120= A A B B C C 59° 1 Seconds of time 1' 2» 3» 4a 6» 6» 7« Prop, parts of cols. \l 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. Diff. Cosecant. Tangent. Diff. Cotangent. Secant. Diff. Cosine. M. 7 52 4 8 9. 71184 10. 28816 9. 77877 10. 22123 10. 06693 9. 93307 60 1 51 52 8 8 71205 28795 77906 22094 06701 93299 59 2 51 44 8 16 71226 1 28774 77935 1 22065 06709 93291 58 3 51 36 8 24 71247 1 28753 77963 1 22037 06716 93284 57 4 5 51 28 8 32 71268 9. 71289 1 2 28732 77992 2 22008 06724 93276 56 7 51 20 4 8 40 10. 28711 9. 78020 2 10. 21980 10. 06731 9. 93269 55 6 51 12 8 48 71310 2 28690 78049 3 21951 06739 93261 54 7 51 4 8 56 71331 2 28669 78077 3 21923 06747 93253 53 8 50 56 9 4 71352 3 28648 78106 4 21894 06754 93246 52 9 50 48 9 12 71373 3 28627 78135 4 21865 06762 93238 51 10 7 50 40 4 9 20 9. 71393 3 10. 28607 9. 78163 5 10. 21837 10. 06770 9. 93230 50 11 50 32 9 28 71414 4 28586 78192 5 21808 06777 93223 49 12 50 24 9 36 71435 4 28565 78220 6 21780 06785 2 93215 48 13 50 16 9 44 71456 4 28544 78249 6 21751 06793 2 93207 47 14 50 8 9 52 71477 5 28523 78277 7 21723 06800 2 93200 46 45 15 7 50 4 10 9. 71498 5 10. 28502 9. 78306 7 10. 21694 10. 06808 2 9. 93192 16 49 52 10 8 71519 5 28481 78334 8 21666 06816 2 93184 44 17 49 44 10 16 71539 6 28461 78363 8 21637 06823 2 93177 43 18 49 36 10 24 71560 6 28440 78391 9 21609 06831 2 93169 42 19 49 28 10 32 71581 7 28419 78419 9 21581 06839 2 93161 41 40 20 7 49 20 4 10 40 9. 71602 7 10. 28398 9. 78448 9 10. 21552 10. 06846 3 9. 93154 21 49 12 10 48 71622 7 28378 78476 10 21524 06854 3 93146 39 22 49 4 10 56 71643 8 28357 78505 10 21495 06862 3 93138 38 23 48 56 11 4 71664 8 28336 78533 11 21467 06869 3 93131 37 24 25 48 48 11 12 71685 8 28315 78562 11 21438 06877 3 93123 36 7 48 40 4 11 20 9. 71705 9 10. 28295 9. 78590 12 10.21410 10. 06885 3 9. 93115 35 26 48 32 11 28 71726 9 28274 78618 12 21382 06892 3 93108 34 27 48 24 11 36 71747 9 28253 78647 13 21353 06900 3 93100 33 28 48 16 11 44 71767 10 28233 78675 13 21325 06908 4 93092 32 29 48 8 11 52 4 12 71788 10 28212 78704 14 21296 06916 4 93084 31 30 30 7 48 9. 71809 10 10. 28191 9. 78732 14 10.21268 10. 06923 4 9. 93077 31 47 52 12 8 71829 11 28171 78760 15 ! 21240 06931 4 93069 29 32 47 44 12 16 71850 11 28150 78789 15-1 21211 06939 4 93061 28 33 47 36 12 24 71870 11 28130 78817 16 i 21183 06947 4 93053 27 34 35 47 28 12 32 71891 12 28109 78845 16 21155 06954 4 93046 26 25 7 47 20 4 12 40 9. 71911 12 10. 28089 9. 78874 17 10.21126 10. 06962 5 9. 93038 36 47 12 12 48 71932 12 28068 78902 17 1 21098 06970 5 93030 24 37 47 4 12 56 71952 13 28048 78930 17 21070 06978 5 93022 23 38 46 56 13 4 71973 13 28027 78959 18 21041 06986 5 93014 22 39 46 48 13 12 71994 13 28006 78987 18 21013 06993 5 5 93007 9. 92999 21 20 40 7 46 40 4 13 20 9. 72014 14 10. 27986 9. 79015 19 10.20985 10. 07001 41 46 32 13 28 72034 14 27966 79043 19 1 20957 07009 5 92991 19 42 46 24 13 36 72055 14 27945 79072 20 ! 20928 07017 92983 18 43 46 16 13 44 72075 15 27925 79100 20 ; 20900 07024 6 92976 17 44 46 8 13 52 72096 15 27904 79128 21 : 20872 07032 6 92968 16 45 7 46 4 14 9. 72116 15 10. 27884 9. 79156 21 10.20844 10. 07040 6 9. 92960 15 46 45 52 14 8 72137 16 27863 79185 22 20815 07048 6 92952 14 47 45 44 14 16 72157 16 27843 79213 22 20787 07056 6 92944 13 48 45 36 14 24 72177 16 27823 79241 23 20759 07064 6 92936 12 49 45 28 14 32 72198 17 27802 79269 23 20731 07071' 6 92929 11 50 7 45 20 4 14 40 9. 72218 17 10. 27782 9. 79297 24 10. 20703 j 10. 07079 6 9. 92921 10 51 45 12 14 48 72238 18 27762 79326 24 20674 07087 7 92913 9 52 45 4 14 56 72259 18 27741 79354 25 20646 07095 7 92905 8 53 44 56 15 4 72279 18 27721 79382 25 20618 07103 / . 92897 7 54 44 48 15 12 72299 19 27701 79410 26 20590 07111 7 92889 9. 92881 6 5 55 7 44 40 4 15 20 9. 72320 19 10. 27680 9. 79438 26 10. 20562 10.07119 7 56 44 32 15 28 72340 19 27660 79466 26 20534 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 1 92858 2 59 44 8 15 52 72401 20 27599 79551 28 20449 07150 8 92850 1 60 44 16 72421 21 27579 79579 28 20421 07458 8 92842 M. M. Hour P. M. Hour A.M. Cosine. Diff. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. Sine. 121° A A B B C C 68° 1 Seconds of time 1» 2> 3' 4« 5" G» 7 " fA Prop, parts of cols. B |c 3 4 1 5 7 2 8 11 3 10 13 14 18 4 5 15 21 6 18 26 7 Page 640] TABLE 44. Log. Sines, Tangents, and Secants. - 32° A A B B C C 147° M. Hour A. M. Hour p. M. Sine. DifE. Cosecant. Tangent. DifE. Cotangent. Secant. DifE. Cosine. M. 60 7 44 4 16 9. 72421 10. 27579 9. 79579 10. 20421 10. 07158 9. 92842 1 43 52 16 8 72441 27559 79607 20393 07166 92834 59 2 43 44 16 16 72461 1 27539 79635 1 20365 07174 92826 58 3 43 36 16 24 72482 1 27518 79663 1 20337 07182 92818 57 4 43 28 16 32 72502 1 27498 79691 2 20309 07190 92810 56 55 5 7 43 20 4 16 40 9. 72522 2 10. 27478 9. 79719 2 10. 20281 10. 07197 9. 92803 6 43 12 16 48 72542 - 2 27458 79747 3 20253 07205 92795 54 7 43 4 16 56 72562 2 27438 79776 3 20224 07213 92787 53 8 42 56 17 4 72582 3 27418 79804 . 4 20196 07221 92779 52 9 10 42 48 17 12 72602 3 27398 79832 4 20168 07229 J- 92771 9. 92763 51 50 7 42 40 4 17 20 9. 72622 3 10. 27378 9. 79860 5 10. 20140 10. 07237 11 42 32 17 28 72643 4 27357 79888 5 20112 07245 1 92755 49 12 42 24 17 36 72663 4 27337 79916 6 20084 07253 2 92747 48 13 42 16 17 44 72683 4 27317 79944 6 20056 07261 2 92739 47 14 15 42 8 7 42 17 52 72703 5 27297 79972 7 20028 07269 2 2 92731 9. 92723 46 45 4 18 9. 72723 5 10. 27277 9. 80000 7 10. 20000 10. 07277 16 41 52 18 8 72743 5 27257 80028 7 19972 07285 2 92715 44 17 41 44 18 16 72763 6 27237 80056 8 19944 07293 2 92707 43 18 41 36 18 24 72783 6 27217 80084 8 19916 07301 2 92699 42 19 41 28 18 32 72803 6 27197 80112 9 19888 07309 3 92691 41 20 7 41 20 4 18 40 9. 72823 7 10.27177 9. 80140 9 10. 19860 10. 07317 3 9. 92683 40 21 41 12 18 48 72843 7 27157 80168 10 19832 07325 3 92675 39 22 41 4 18 56 72863 7 27137 80195 10 19805 07333 3 92667 38 23 40 56 19 4 72883 8 27117 80223 11 19777 07341 3 92659 37 24 40 48 19 12 72902 8 27098 80251 11 19749 07349 3 92651 36 35 25 7 40 40 4 19 20 9. 72922 8 10. 27078 9. 80279 12 10. 19721 10. 07357 3 9. 92643 26 40 32 19 28 72942 9 27058 80307 12 19693 07365 3 92635 34 27 40 24 19 36 72962 9 27038 80335 13 19665 07373 4 92627 33 28 40 16 . 19 44 72982 9 27018 80363 13 19637 07381 4 92619 32 29 30 40 8 19 52 73002 10 ; 26998 80391 13 14 19609 07389 4 92611 31 7 40 4 20 9. 73022 10 10. 26978 9. 80419 10. 19581 10. 07.397 4 9. 92603 30 31 39 52 20 8 73041 10 26959 80447 14 19553 07405 4 92595 29 32 39 44 20 16 73061 11 • 26939 80474 15 19526 07413 4 92587 28 33 39 36 20 24 73081 11 26919 80502 15 19498 07421 4 92579 27 34 ■35 39 28 20 32 73101 11 12 26899 10. 26879 80530 16 19470 07429 5 92571 26 25 7 39 20 4 20 40 9. 73121 9. 80558 16 10. 19442 10. 07437 5 9. 92563 36 39 12 20 48 73140 12 ! 26860 80586 17 19414 07445 5 92555 24 37 39 4 20 56 73160 12 t 26840 80614 17 19.386 07454 5 92546 23 38 38 56 21 4 73180 13 1 26820 80642 18 19358 07462 5 92538 22 39 38 48 21 12 73200 13 j 26800 13 ilO. 26781 80669 18 19331 07470 5 "5 92530 21 40 7 38 40 4 21 20 9. 73219 9. 80697 19 10. 19303 10. 07478 9. 92522 20 41 38 32 21 28 73239 14 1 26761 80725 19 19275 07486 6 92514 19 42 38 24 21 36 73259 14 26741 80753 20 19247 07494 6 92506 18 43 38 16 21 44 73278 14 26722 80781 20 19219 07502 6 92498 17 44 38 8 21 52 73298 15 26702 80808 20 19192 07510 6 92490 16 45 7 38 4 22 9. 73318 15 10. 26682 9. 80836 21 10. 19164 10. 07518 6 9. 92482 15 46 37 52 22 8 73337 15 26663 80864 21 19136 07527 6 92473 14 47 37 44 22 16 73357 16 26643 80892 22 19108 07535 6 92465 13 48 37 36 22 24 73377 16 26623 80919 22 19081 07543 6 92457 12 49 37 28 22 32 73396 16 26604 10. 26584 80947 23 23 19053 07551 7 92449 11 10 50 7 37 20 4 22 40 9. 73416 17 9. 80975 10. 19025 10. 07559 7 9. 92441 51 37 12 22 48 73435 17 26565 81003 24 18997 07567 7 92433 9 52 37 4 22 56 73455 17 26545 81030 24 18970 07575 7 92425 8 53 36 56 23 4 73474 18 26526 81058 25 18942 07584 7 92416 7 54 36 48 23 12 73494 18 26506 81086 25 18914 07592 7 92408 6 55 7 36 40 4 23 20 9. 73513 18 10. 26487 9.81113 26 10. 18887 10. 07600 7 9. 92400 5 56 36 32 23 28 73533 19 26467 81141 26 18859 07608 8 92392 4 57 36 24 23 36 73552 19 26448 81169 26 18831 07616 8 92384 3 58 36 16 23 44 73572 19 26428 81196 27 18804 07624 8 92376 2 59 36 8 23 52 73591 20 26409 81224 27 18776 07633 8 92367 1 60 M. 36 24 73611 20 26389 81252 28 18748 07641 8 92359 M. Hour p. M. Hour A. M. Cosine. DifE. Secant. Cotangent. DifE. Tangent. Cosecant. Diflf. Sine. 122° A A B B C C 67° Seconds of time 1' 2' 3» 4« 6» 6» 7 ' Prop, parts of cols. .^B Ic 2 3 1 6 7 2 7 10 3 10 14 4 12 17 5 15 21 6 17 24 7 TABLE 44. [Page 641 - Log. Bines, Tangents, and Secants. 83° A A B B C C 146° M. Hour A.M. Hour p. M. Sine. Diff. Cosecant. Tangent. Diff. Cotangent. Secant. Diff. Cosine. M.I 7 36 4 24 9. 73611 10. 26389 9. 81252 10. 18748 10. 07641 9. 92359 60 1 35 52 24 8 73630 26370 81279 18721 07649 92351 59 2 35 44 24 16 73650 1 26350 81307 1 18693 07657 92343 58 3 35 36 24 24 73669 1 26381 81335 1 18665 07665 92335 57 4 5 35 28 24 32 73689 1 26311 81362 2 18638 07674 92326 56 7 35 20 4 24 40 9. 73708 2 10. 26292 9. 81390 2 10. 18610 10. 07682 9. 92318 55 6 35 12 24 48 73727 2 26273 81418 3 18582 07690 92310 54 7 35 4 24 56 73747 2 26253 81445 3 18555 07698 92302 53 8 34 56 25 4 73766 3 26234 81473 4 18527 07707 92293 52 9 34 48 25 12 73785 3 26215 81500 4 18500 07715 92285 51 10 7 34 40 4 25 20 9. 73805 3 10. 26195 9. 81528 5 10. 18472 10. 07723 9. 92277 50 11 34 32 25 28 73824 3 26176 81556 5 18444 07731 2 92269 49 12 34 24 25 36 73843 4 26157 81583 5 18417 07740 2 92260 48 13 34 16 25 44 73863 4 26137 81611 6 18389 07748 2 92252 47 14 34 8 25 52 73882 4 26118 81638 6 18362 07756 2 92244 46 45 15 7 34 4 26 9. 73901 5 10. 26099 9. 81666 7 10. 18334 10. 07765 2 9. 92235 16 33 52 26 8 73921 5 26079 81693 7 18307 07773 2 92227 44 17 33 44 26 16 73940 5 26060 81721 8 18279 07781 2 92219 43 18 33 36 26 24 73959 6 26041 81748 8 18252 07789 3 92211 42 19 33 28 26 32 73978 6 26022 81776 9 18224 07798 3 92202 41 20 7 33 20 4 26 40 9. 73997 6 10. 26003 9. 81803 9 10. 18197 10. 07806 3 9. 92194 40 21 33 12 26 48 74017 7 25983 81831 10 18169 07814 3 92186 39 22 33 4 26 56 74036 7 25964 81858 10 18142 07823 3 92177 38 23 32 56 27 4 74055 7 25945 81886 11 18114 • 07831 3 92169 37 24 32 48 27 12 74074 8 25926 81913 11 18087 07839 3 92161 36 35 25 7 32 40 4 27 20 9. 74093 8 10. 25907 9. 81941 11 10. 18059 10. 07848 3 9. 92152 26 32 32 27 28 74113 8 25887 81968 12 18032 07856 4 92144 34 27 32 24 27 36 74132 9 25868 81996 12 18004 07864 4 92136 33 28 32 16 27 44 74151 9 25849 82023 13 17977 07873 4 92127 32 29 32 8 27 52 74170 9 25830 82051 13 17949 07881 4 92119 31 30 7 32 4 28 9. 74189 10 10. 25811 9. 82078 14 10. 17922 10. 07889 4 9.92111 30 31 31 52 28 8 74208 10 25792 82106 14 17894 07898 4 92102 29 32 31 44 28 16 74227 10 25773 82133 15 17867 07906 4 92094 28 33 31 36 28 24 74246 10 25754 82161 15 17839 07914 5 92086 27 34 31 28 28 32 74265 11 25735 82188 16 17812 07923 5 92077 26 35 7 31 20 4 28 40 9. 74284 11 10. 25716 9. 82215 16 10. 17785 10. 07931 5 9. 92069 25 36 31 12 28 48 74303 11 25697 82243 16 17757 07940 5 92060 24 37 31 4 28 56 74322 12 25678 82270 17 17730 07948 5 92052 23 38 30 56 29 4 74341 12 25659 82298 17 17702 07956 5 92044 22 39 30 48 29 12 74360 12 25640 82325 18 17675 07965 5 92035 21 20 40 7 30 40 4 29 20 9. 74379 13 10. 25621 9. 82352 18 10. 17648 10. 07973 6 9. 92027 41 30 32 29 28 74398 13 25602 82380 19 17620 07982 6 92018 19 42 30 24 29 36 74417 13 25583 82407 19 17593 07990 6 92010 18 43 30 16 29 44 74436 14 25564 82435 20 17565 07998 6 92002 17 44 30 8 29 52 74455 14 25545 82462 20 17538 ,08007 6 91993 16 15 45 7 30 4 30 9. 74474 14 10. 25526 9. 82489 21 10. 17511 10. 08015 6 9. 91985 46 29 52 30 8 74493 15 25507 82517 21 17483 08024 6 91976 14 47 29 44 30 16 74512 15 25488 82544 22 17456 08032 7 91968 13 48 29 36 30 24 74531 15 25469 82571 22 17429 08041 7 91959 12 49 29 28 30 32 74549 16 25451 82599 22 17401 08049 7 91951 11 10 50 7 29 20 4 30 40 9. 74568 16 10. 25432 9. 82626 23 10. 17374 10. 08058 y 9. 91942 51 29 12 30 48 74587 16 25413 82653 23 17347 08066 7 91934 9 52 29 4 30 56 74606 17 25394 82681 24 17319 08075 7 91925 8 53 28 56 31 4 74625 17 25375 82708 24 17292 08083 7 91917 7 54 55 28 48 31 12 74644 17 25356 82735 25 17265 08092 8 91908 6 5 7 28 40 4 31 20 9. 74662 17 10. 25338 9. 82762 25 10.17238 10. 08100 8 9. 91900 56 28 32 31 28 74681 18 25319 82790 26 17210 08109 8 91891 4 57 28 24 31 36 74700 18 25300 82817 26 17183 08117 8 91883 3 58 28 16 31 44 74719 18 25281 82844 27 17156 08126 8 91874 2 59 28 8 31 52 74737 19 25263 82871 27 17129 08134 8 91866 1 60 28 32 74756 19 25244 82899 27 17101 08143 8 91857 M. Hour P. M. Hour A. M. Cosine. Diff. Secant Cotangent. Diff. Tangent. Cosecant. Diff. Sine. M. 123° A B B C C 66° 1 Seconds of time 1" 2- 8» 4» 6» 6« 7- Prop, parts of cols. -jB 2 3 1 5 7 7 10 2 3 10 14 4 12 17 5 14 21 6 17 24 7 6583—06- -41 Page 642] TABLE 44. Log. Sines, Tangents, and Secants. 84° A A B B C C 145° M. Hour A. M. Hour p. M. Sine. Di£E. Cosecant Tangent. Diff. Cotangent. Secant. Diff. Cosine. M. 60 7 28 4 32 9. 74756 10. 25244 9. 82899 10. 17101 10.08143 9. 91857 1 27 52 32 8 74775 25225 82926 17074 08151 91849 59 2 27 44 32 16 74794 1 25206 82953 1 17047 08160 91840 58 3 27 36 32 24 74812 1 25188 82980 1 17020 08168 91832 57 4 5 27 28 32 32 74831 1 25169 83008 2 16992 08177 1 91823 56 7 27 20 4 32 40 9. 74850 2 10. 25150 9. 83035 2 10. 16965 10. 08185 1 9.91815 55 6 27 12 32 48 74868 2 25132 83062 3 16938 08194 1 91806 54 7 27 4 32 56 74887 2 25113 83089 3 16911 08202 1 91798. 53 8 26 56 33 4 74906 2 25094 83117 4 16883 08211 1 91789 52 9 26 48 33 12 74924 3 25076 83144 4 16856 08219 1 91781 51 50 10 7 26 40 4 33 20 9. 74943 3 10. 25057 9. 83171 5 10. 16829 10. 08228 1 9. 91772 11 26 32 33 28 74961 3 25039 83198 5 16802 08237 2 91763 49 12 26 24 33 36 74980 4 25020 83225 5 16775 08245 2 91755 48 13 26 16 33 44 74999 4 25001 83252 6 16748 08254 2 91746 47 14 26 8 33 52 75017 4 5 24983 83280 6 16720 08262 2 2 91738 46 45 15 7 26 4 34 9. 75036 10. 24964 9. 83307 7 10. 16693 10. 08271 9. 91729 16 25 52 34 8 75054 5 24946 83334 7 16666 08280 2 91720 44 17 25 44 34 16 75073 5 24927 83361 .8 16639 08288 2 91712 43 18 25 36 34 24 75091 6 24909 83388 8 16612 08297 3 91703 42 19 20 25 28 34 32 75110 6 6 24890 83415 9 16585 10. 16558 08305 10. 08314 3 3 91695 41 40 7 25 20 4 34 40 9. 75128 10. 24872 9.83442 9 9. 91686 21 25 12 34 48 75147 6 24853 83470 9 16530 08323 3 91677 39 22 25 4 34 56 75165 7 24835 83497 10 16503 08331 3 91669 38 23 24 56 35 4 75184 / 24816 83524 10 16476 08340 3 91660 37 24 24 48 35 12 75202 r-r 1 24798 83551 11 16449 08349 3 91651 36 25 7 24 40 4 35 20 9. 75221 8 10. 24779 9. 83578 11 10. 16422 10. 08357 4 9. 91643 35 26 24 32 35 28 75239 8 24761 83605 12 16395 08366 4 91634 34 27 24 24 35 36 75258 8 24742 83632 12 16368 08375 4 91625 33 28 24 16 35 44 75276 9 24724 83659 13 16341 08383 4 91617 32 29 24 8 35 52 75294 9 24706 83686 13 16314 08392 4 91608 31 30 7 24 4 36 9. 75313 9 10. 24687 9. 83713 14 10. 16287 10. 08401 4 9. 91599 30 31 23 52 36 8 75331 9 24669 83740 14 16260 08409 4 91591 29 32 23 44 36 16 75350 10 24650 83768 14 16232 08418 5 91582 28 33 23 36 36 24 75368 10 24632 83795 15 16205 08427 5 91573 27 34 23 28 36 32 75386 10 11 24614 83822 15 16 16178 08435 5 91565 9. 91556 26 25 35 7 23 20 4 36 40 9. 75405 10. 24595 9. 83849 10. 16151 10. 08444 5 36 23 12 36 48 75423 11 24577 83876 16 16124 08453 5 91547 24 37 23 4 36 56 75441 11 24559 83903 17 16097 08462 5 91538 23 38 22 56 37 4 75459 12 24541 83930 17 16070 08470 5 91530 22 39 40 22 48 37 12 75478 12 12 24522 83957 18 16043 08479 6 91521 9.91512 21 20 7 22 40 4 37 20 9. 75496 10. 24504 9. 83984 18 10. 16016 10. 08488 6 41 22 32 37 28 75514 13 24486 84011 18 15989 08496 6 91504 19 42 22 24 37 36 75533 13 24467 84038 19 15962 08505 6 91495 18 43 22 16 37 44 75551 13 24449 84065 19 15935 - 08514 6 91486 17 44 22 8 37 52 75569 13 24431 84092 20 15908 08523 6 91477 16 45 7 22 4 38 9. 75587 14 10.24413 9.84119 20 10. 15881 10. 08531 7 9. 91469 15 46 21 52 38 8 75605 14 24395 84146 21 15854 08540 7 91460 14 47 21 44 38 16 75624 14 24376 84173 21 15827 08549 7 91451 13 48 21 36 38 24 75642 15 24358 84200 22 15800 08558 7 91442 12 49 50 21 28 38 32 75660 15 15 24340 84227 22 15773 08567 7 91433 11 10 7 21 20 4 38 40 9. 75678 10. 24322 9. 84254 23 10. 15746 10. 08575 7 9. 91425 51 21 12 38 48 75696 16 24304 84280 23 15720 08584 7 91416 9 52 21 4 38 56 75714 16 24286 84307 23 15693 08593 8 91407 8 53 20 56 39 4 75733 16 24267 84334 24 15666 08602 8 91398 7 54 20 48 39 12 75751 17 17 24249 10. 24231 84361 9. 84388 24 25 15639 10. 15612 08611 8 91389 9. 91381 6 5 55 7 20 40 4 39 20 9. 75769 10. 08619 8 56 20 32 39 28 75787 17 24213 84415 25 15585 08628 8 91372 4 57 20 24 39 36 75805 17 24195 84442 26 15558 08637 8 91363 3 58 20 16 39 44 75823 18 24177 84469 26 15531 08646 8 91354 2 59 20 8 39 52 75841 18 24159 84496 27 15504 08655 9 91345 1 60 20 40 75859 18 24141 84523 27 15477 08664 9 91336 M. M. Hour p. M. Hour A.M. Cosine. Diff. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. Sine. 124° A A B B C C 6a Seconds of time 1« 2" 3» 4' 5» 6» 7« (A 2 Prop, parts of cols. -^B 3 Ic 1 1 5 7 2 7 10 3 9 14 4 11 17 5 14 20 7 16 24 8 TABLE 44. [Page 643 Log. Sines, Tangents, and Secants. 35" A A B B C C 144° M. Hour A. M. Hour p. M. Sine. Diff. Cosecant. Tangent. Difl. Cotangent. Secant. Diff.' Cosine. 1 M. 7 20 4 40 9. 75859 10. 24141 9.84523 10. 15477 10. 08664 9. 91336 60 1 19 52 40 8 75877 24123 84550 15450 08672 91328 59 2 19 44 40 16 75895 1 24105 84576 1 15424 08681 91319 58 3 19 36 40 24 75913 1 24087 84603 1 15397 08690 91310 57 4 5 19 28 7 19 20 40 32 75931 9. 75949 1 1 24069 84630 2 "2" 15370 10. 15343 08699 10. 08708 91301 56 4 40 40 10. 24051 9. 84657 9. 91292 55 6 19 12 40 48 75967 2 24033 84684 3 15316 08717 91283 54 7 19 4 40 56 75985 2 24015 84711 3 15289 08726 91274 53 8 18 56 41 4 76003 2 23997 84738 4 15262 08734 91266 52 9 10 18 48 41 12 76021 3 23979 84764 4 15236 08743 91257 51 50 7 18 40 4 41 20 9. 76039 3 10. 23961 9. 84791 4 10. 15209 10. 08752 2 9. 91248 11 18 32 41 28 76057 3 23943 84818 5 15182 08761 2 91239 49 12 18 24 41 36 76075 4 23925 84845 5 15155 08770 2 91230 48 13 18 16 41 44 76093 ' 4 23907 84872 6 15128 08779 2 91221 47 14 15 18 8 41 52 76111 4 23889 84899 6 15101 08788 2 91212 46 7 18 4 42 9. 76129 4 10. 23871 9. 84925 7 10. 15075 10. 08797 2 9. 91203 45 16 17 52 42 8 76146 5 23854 -84952 7 15048 08806 2 91194 44 17 17 44 42 16 76164 5 23836 84979 8 15021 08815 3 91185 43 18 17 36 42 24 76182 5 23818 85006 8 14994 08824 3 91176 42 19 17 28 42 32 76200 6 23800 85033 9. 85059 8 9 14967 10. 14941 08833 3 91167 41 40 20 7 17 20 4 42 40 9. 76218 - 6 10. 23782 10. 08842 3 9.91158 21 17 12 42 48 76236 6 23764 85086 9 14914 08851 3 91149 39 22 17 4 42 56 76253 6 23747 85113 10 14887 08859 3 91141 38 23 16 56 43 4 76271 7 23729 85140 10 14860 08868 3 91132 37 24 25 16 48 43 12 76289 t 23711 85166 11 14834 08877 10. 08886 4 4 91123 9.91114 36 35 7 16 40 4 43 20 9. 76307 10. 23693 9. 85193 11 IQ. 14807 26 16 32 43 28 76324 8 23676 85220 12 14780 . 08895 4 .91105 34 27 16 24 43 36 76342 8 23658 85247 12 14753 08904 4 91096 33 28 16 16 43 44 76360 8 23640 • 85273 12 14727 08913 4 91087 32 29 30 16 8 43 52 76378 9 9 23622 10. 23605 85300 "9. 85327 13 14700 08922 4 91078 31 7 16 4 44 9. 76395 13 10. 14673 10. 08931 5 9. 91069 30 31 15 52 44 8 76413 9 23587 85354 14 14646 08940 5 91060 29 32 15 44 44 16 76431 9 23569 85380 14 14620 08949 5 91051 28 33 15 36 44 24 76448 10 23552 85407 15 14593 08958 5 91042 27 34 35 15 28 7 15 20 44 32 76466 10 2.3534 85434 15 16 14566 10. 14540 08967 5 91033 26 4 44 40 9. 76484 10 10. 23516 9. 85460 10. 08977 5 9. 91023 25 36 15 12 44 48 76501 11 23499 85487 16 14513 08986 5 91014 24 37 15 4 44 56 76519 11 23481 85514 16 14486 08995 6 91005 23 38 14 56 45 4 76537 11 23463 85540 17 14460 09004 6 90996 22 39 14 48 45 12 76554 12 23446 85567 17 14433 09013 6 90987 21 40 7 14 40 4 45 20 9. 76572 12 10. 23428 9. 85594 18 10. 14406 10. 09022 6 9. 90978 20 41 14 32 45 28 76590 12 23410 85620 18 14380 09031 6 90969 19 42 14 24 45 36 76607 12 23393 85647 19 14353 09040 6 90960 18 43 14 16 45 44 76625 13 23375 85674 19 14326 09049 6 90951 17 44 45 14 8 45 52 76642 13 23358 85700 20 14300 09058 7 90942 16 7 14 4 46 9.76660 13 10. 23340 9. 85727 20 10. 14273 10. 09067 7 9. 90933 15 46 13 52 46 8 76677 14 23323 85754 20 14246 09076 7 90924 14 47 13 44 46 16 76695 14 23305 85780 21 14220 09085 7 90915 13 48 13 36 46 24 76712 14 23288 85807 21 14193 09094 7 90906 12 49 13 28 46 32 76730 14 23270 85834 22 14166 09104 7 90896 11 50 7 13 20 4 46 40 9. 76747 15 10. 23253 9. 85860 22 10.14140 10.09113 8 9. 90887 10 51 13 12 46 48 76765 15 23235 85887 23 14113 09122 8 90878 9 52 13 4 46 56 76782 15 23218 85913 23 14087 09131 8 90869 8 53 12 56 47 4 76800 16 23200 85940 24 14060 09140 8 90860 7 54 55 12 48 47 12 76817 16 23183 85967 9. 85993 24 24 14033 09149 8 8 90851 9. 90842 6 5 7 12 40 4 47 20 9. 76835 16 10. 23165 10. 14007 10. 09158 56 12 32 47 28 76852 17 23148 86020 25 13980 09168 8 90832 4 57 12 24 47 36 76870 17 23130 86046 25 13954 09177 9 90823 3 58 12 16 47 44 76887 17 23113 86073 26 13927 09186 9 90814 2 59 12 8 47 52 76904 17 23096 86100 26 13900 09195 9 90805 1 60 12 48 76922 18 23078 86126 27 13874 09204 9 90796 M. M. Hour P. M. Hour A. M. Cosine. Difl. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. Sine. 125' A A B B C C 64° 1 Seconds of time 1» 2« 8' 4' 5» 6- 7' fA Prop, parts of cols. B ic 2 3 1 4 7 7 10 2 3 9 13 5 11 17 6 13 20 7 16 23 8 Page 644] TABLE 44. Log. Sines, Tangents, and Secants. 86° A A B B C C 148° 1 M. Hour A. M. Hour p. M. Sine. Diff. Cosecant. Tangent. Diff. Cotangent. Secant. Diff. Cosine. M. 7 12 4 48 9. 76922 10. 23078 9. 86126 10. 13874 10. 09204 9. 90796 60 1 11 52 48 8 76939 23061 86153 13847 09213 90787 59 2 11 44 48 16 76957 1 23043 86179 1 13821 09223 90777 58 3 11 36 48 24 76974 1 23026 86206 1 13794 09232 90768 57 4 11 28 48 32 76991 1 23009 86232 2 13768 09241 90759 56 55 5 7 11 20 4 48 40 9. 77009 1 10. 22991 9. 86259 2 10. 13741 10. 09250 9. 90750 6 11 12 48 48 77026 2 22974 86285 3 13715 09259 1 90741 54 7 11 4 48 56 77043 2 22957 86312 3 13688 09269 90731 53 8 10 56 49 4 77061 2 22939 86338 4 13662 09278 90722 52 9 10 10 48 49 12 77078 3 22922 10. 22905 86365 4 4 13635 09287 90713 51 50 7 10 40 4 49 20 9. 77095 3 9. 86392 10. 13608 10. 09296 2 9. 90704 11 10 32 49 28 77112 3 22888 86418 5 13582 09306 2 90694 49 12 10 24 49 36 77130 3 22870 86445 5 13555 09315 2 90685 48 13 10 16 49 44 77147 4 22853 86471 6 ■13529 09324 2 90676 47 14 10 8 49 52 77164 4 22836 86498 6 13502 09333 2 2 90667 9. 90657 46 45 15 7 10 4 50 9. 77181 4 10. 22819 9. 86524 7 10. 13476 10. 09343 16 9 52 50 8 77199 5 22801 86551 7 13449 09352 2 90648 44 17 9 44 50 16 77216 5 22784 86577 7 13423 09361 3 90639 43 18 9 36 50 24 77233 5 22767 86603 8 13397 09370 3 90630 42 19 9 28 50 32 77250 5 22750 86630 8 13370 09380 3 90620 41 40 20 7 9 20 4 50 40 9. 77268 6 10. 22732 9. 86656 9 10. 13344 10. 09389 3 9. 90611 21 9 12 50 48 77285 6 22715 86683 9 13317 09398 3 90602 39 22 9 4 50 56 77302 6 22698 86709 10 13291 09408 3 90592 38 23 8 56 51 4 77319 7 22681 86736 10 13264 09417 4 90583 37 24 25 8 48 51 12 77336 7 22664 86762 11 13238 09426 4 90574 36 35 7 8 40 4 51 20 9. 77353 7 10. 22647 9. 86789 11 10. 13211 10. 09435 4 9. 90565 26 8 32 51 28 77370 7 22630 86815 11 13185 09445 4 90555 34 27 8 24 51 36 77387 8 22613 86842 12 13158 09454 4 90546 33 28 8 16 51 44 77405 8 22595 86868 12 13132 09463 4 90537 32 29 8 8 51 52 77422 8 22578 86894 13 13106 09473 6 90527 31 30 7 8 4 52 9. 77439 9 10. 22561 9, 86921 13 10. 13079 10. 09482 5 9. 90518 30 31 7 52 52 8 77456 9 22544 86947 14 13053 09491 5 90509 29 32 7 44 52 16 77473 9 22527 86974 14 13026 09501 5 90499 28 33 7 36 52 24 77490 9 22510 87000 15 13000 09510 5 90490 27 34 7 28 52 32 77507 10 22493 87027 15 15 12973 10. 12947 09520 5 90480 26 25 35 7 7 20 4 52 40 9. 77524 10 10. 22476 9. 87053 10. 09529 5 9. 90471 36 7 12 52 48 77541 10 22459 87079 16 12921 09538 6 90462 24 37 7 4 52 56 77558 11 22442 87106 16 12894 09548 6 90452 23 38 6 56 53 4 77575 11 22425 87132 17 12868 09557 6 90443 22 39 6 48 53 12 77592 11 22408 87158 17 12842 09566 6 90434 21 20 40 7 6 40 4 53 20 9. 77609 11 10. 22391 9. 87185 18 10. 12815 10. 09576 6 9. 90424 41 6 32 53 28 77626 12 22374 87211 18 12789 09585 6 90415 19 42 6 24 53 36 77643 12 22357 87238 18 12762 09595 7 90405 18 43 6 16 53 44 77660 12 22340 87264 19 12736 09604 7 90396 17 44 6 8 53 52 77677 13 22323 87290 19 12710 09614 7 90386 9. 90377 16 15 45 7 6 4 54 9. 77694 13 10. 22306 9. 87317 20 10. 12683 10. 09623 7 46 5 52 54 8 77711 13 22289 87343 20 12657 09632 7 90368 14 47 5 44 54 16 77728 13 22272 87369 21 12631 09642 7 90358 13 48 5 36 54 24 77744 14 22256 87396 21 12604 09651 7 90349 12 49 50 5 28 54 32 77761 14 22239 87422 22 12578 09661 8 90339 11 10 7 5 20 4 54 40 9. 77778 14 10. 22222 9. 87448 22 10. 12552 10. 09670 8 9. 90330 51 5 12 54 48 77795 15 22205 87475 22 12525 , 09680 8 90320 9 52 5 4 54 56 77812 15 22188 87501 23 12499 09689 8 90311 8 53 4 56 55 4 77829 15 22171 87527 23 12473 09699 8 90301 7 54 4 48 55 12 77846 15 22154 87554 24 12446 09708 8 90292 9. 90282 6 5 55 7 4 40 4 55 20 9. 77862 16 10. 22138 9. 87580 24 10. 12420 10.09718 9 56 4 32 55 28 77879 16 22121 87606 25 12394 09727 9 90273 4 57 4 24 55 36 77896 16 22104 87633 25 12367 09737 9 90263 3 58 4 16 55 44 77913 16 22087 87659 26 12341 09746 9 90254 2 59 4 8 55 52 77930 17 22070 87685 26 12315 09756 9 90244 1 60 4 56 77946 17 22054 87711 26 12289 09765 9 Diff. 90235 M. Hour p. M. Hour A. M. Cosine. Diff. Secant. Cotangent. Diff. Tangent. Cosecant. Sine. M. 126° A A B B C C 53° 1» 2» 8» 4» 6> 6» Ja Prop, parts of cols. {? 2 3 1 4 7 2 6 10 4 9 13 5 11 17 6 13 20 7 16 23 8 TABLE 44. [Page 645 Log. Sines, Tangents, and Secants. 87° A A B B C C 142° M. Hour A.M. Hour p. M. Sine. Difl. Cosecant. Tangent. Diif. Cotangent. Secant. Diff. Cosine. M. 7 4 4 56 9. 77946 10. 22054 9. 87711 10. 12289 10. 09765 9. 90235 60 1 3 52 56 8 77963 22037 87738 12262 09775 90225 59 2 3 44 56 16 77980 1 22020 87764 1 12236 09784 90216 58 3 3 36 56 24 77997 1 22003 87790 1 12210 09794 90206 57 4 5 3 28 7 3 20 56 32 78013 1 21987 87817 2 12183 09803 1 1 90197 56 55 4 56 40 9. 78030 1 10. 21970 9. 87843 2 10. 12157 10. 09813 1 9.90187 6 8 12 56 48 78047 2 21953 87869 3 12131 09822 1 90178 54 7 8 4 56 56 78063 2 21937 87895 3 12105 09832 1 90168 53 8 2 56 57 4 78080 2 21920 87922 3 12078 09841 1 90159 52 9 2 48 57 12 78097 2 21903 87948 4 12052 09851 1 90149 51 10 7 2 40 4 57 20 9. 78113 3 10. 21887 9. 87974 4 10. 12026 10. 09861 2 9. 90139 50 11 2 32 57 28 78130 3 21870 88000 5 12000 09870 2 90130 49 12 2 24 57 36 78147 3 21853 88027 5 11973 09880 2 90120 48 13 2 16 57 44 78163 4 21837 88053 6 11947 09889 2 90111 47 14 2 8 57 52 78180, 4 21820 88079 6 7 11921 09899 2 90101 46 45 15 7 2 4 58 9. 78197 4 10. 21803 9. 88105 10. 11895 10. 09909 2 9. 90091 16 1 52 58 8 78213 4 21787 88131 7 11869 09918 3 90082 44 17 1 44 58 16 78230 5 21770 88158 7 11842 09928 3 90072 43 18 1 36 58 24 78246 5 21754 88184 8 11816 09937 3 90063 42 19 20 1 28 7 1 20 58 32 78263 5 21737 88210 8 11790 09947 3 90053 41 4 58 40 9. 78280 5 10. 21720 9. 88236 9 10. 11764 10. 09957 3 9. 90043 40 21 1 12 58 48 78296 6 21704 88262 9 11738 09966 3 90034 39 22 1 4 58 56 78313 6 21687 88289 10 11711 09976 4 90024 38 23 56 59 4 78329 6 21671 88315 10 11685 09986 4 90014 37 24 48 59 12 78346 7 21654 88341 10 11659 09995 4 90005 36 35 25 7 40 4 59 20 9. 78362 7 10. 21638 9. 88367 11 10. 11633 10. 10005 4 9. 89995 26 32 69 28 78379 7 21621 88393 11 11607 10015 4 89985 34 27 24 59 36 78395 7 21605 88420 12 11580 10024 4 89976 33 28 16 59 44 78412 8 21588 88446 12 11554 10034 5 89966 32 29 8 59 52 78428 8 21572 88472 13 11528 10044 5 89956 31 30 30 7 5 9. 78445 8 10. 21555 9. 88498 13 10. 11502 10. 10053 5 9. 89947 31 6 59 52 8 78461 9 21539 88524 14 11476 10063 5 89937 29 32 59 44 16 78478 9 21522 88550 14 11450 10073 5 89927 28 33 59 36 24 78494 9 ^ 21506 88577 14 11423 10082 5 89918 27 34 35 59 28 6 59 20 32 78510 9 21490 88603 15 15 11397 10092 5 6 89908 26 25 5 40 9. 78527 10 10. 21473 9. 88629 10. 11371 10. 10102 9. 89898 36 59 12 48 78543 10 21457 88655 16 11345 10112 6 89888 24 37 59 4 56 78560 10 21440 88681 16 11319 10121 6 89879 23 38 58 56 1 4 78576 10 21424 88707 17 11293 10131 6 89869 22 39 58 48 1 12 78592 11 21408 88733 17 11267 10141 6 89859 21 40 6 58 40 5 1 20 9. 78609 11 10. 21391 9. 88759 17 10. 11241 10. 10151 6 9. 89849 20 41 58 32 1 28 78625 11 21375 88786 18 11214 10160 < 89840 19 42 58 24 1 36 78642 12 21358 88812 18 11188 10170 7 89830 18 43 58 16 1 44 78658 12 21342 88838 19 11162 10180 7 89820 17 44 58 8 1 52 78674 12 21326 88864 19 11136 10190 / 89810 9. 89801 16 15 45 6 58 5 2 9. 78691 12 10. 21309 9. 88890 20 10. 11110 10. 101^j9 7 46 57 52 2 8 78707 13 21293 88916 20 11084 10209 7 89791 14 47 57 44 2 16 78723 13 21277 88942 20 11058 10219 8 89781 13 48 57 36 2 24 78739 13 21261 88968 21 11032 10229 8 89771 12 49 57 28 2 32 78756 13 21244 88994 21 11006 10. 10980 10239 10. 10248 8 8 89761 11 10 50 6 57 20 5 2 40 9. 78772 14 10. 21228 9. 89020 22 9. 89752 51 57 12 2 48 78788 14 21212 89046 22 10954 10258 8 89742 9 52 57 4 2 56 78805 14 21195 89073 23 10927 10268 8 89732 8 53 56 56 3 4 78821 15 21179 89099 23 10901 10278 9 89722 7 54 56 48 3 12 78837 15 21163 89125 24 10875 • 10288 9 9 89712 9. 89702 6 5 55 6 56 40 5 3 20 9. 78853 15 10. 21147 9. 8915] 24 10. 10849 10. 10298 56 56 32 3 28 78869 15 21131 89177 24 10823 10307 9 89693 4 57 56 24 3 36 78886 16 21114 89203 25 10797 10317 9 89683 3 58 56 16 3 44 78902 16 21098 89229 25 10771 10327 9 89673 2 59 56 8 3 52 78918 16 21082 89255 26 10745 10337 10 89663 1 60 56 4 78934 16 21066 89281 26 10719 10347 10 89653 M. M. Hour p. M. Hour A. M. Cosine. Diff. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. Sine. 127° A A B B C C 52° 1 Seconds of time 1- 2» 3* 4> o* e* 7. Prop, parts of cols.-JB 2 3 1 4 7 2 6 10 4 8 13 6 10 16 6 12 20 7 14 23 8 Page 646] TABLE U. Log. Sines, Tan ^ents, and Secants. 88° A A B B C C 141° M. Hour A. M. Hour P. M. Sine. Diff. ! Cosecant. Tangent. Diff. Cotangent. Secant. Diff. Cosine. M. 6 66 5 4 9. 78934 10.21066 9. 89281 10. 10719 10. 10347 9. 89663 60 1 55 52 4 8 78960 21050 89307 10693 10357 89643 69 2 55 44 4 16 78967 21033 89333 1 10667 10367 89633 58 3 55 36 4 24 78983 21017 89359 1 10641 10376 1 89624 67 4 55 28 4 32 78999 21001 89386 2 2 10615 10386 1 1 89614 9. 89604 56 56 5 6 55 20 6 4 40 9. 79016 10. 20985 9. 89411 10. 10589 10. 10396 6 56 12 4 48 79031 20969 89437 3 10563 10406 1 89594 54 7 55 4 4 66 79047 2 20953 89463 3 10637 10416 1 89584 63 8 54 56 5 4 79063 2 20937 89489 3 10611 10426 1 89674 52 9 54 48 5 12 79079 2 20921 89515 9. 89541 4 4 10485 10. 10469 10436 2 89564 9. 89664 51 60 10 6 54 40 5 5 20 9. 79095 3 10. 20905 10. 10446 2 11 54 32 6 28 79111 3 20889 89567 6 10433 10456 2 89544 49 12 54 24 5 36 79128 3 20872 89593 6 10407 10466 2 89534 48 13 54 16 5 44 79144 3 20866 89619 6 10381 10476 2 89624 47 14 16 54 8 6 52 79160 4 4 20840 89646 6 10365 10486 2 3 89514 46 46 6 64 6 6 9. 79176 10. 20824 9. 89671 6 10. 10329 10. 10496 9. 89504 16 53 52 6 8 79192 4 20808 89697 7 10303 10506 3 89495 44 17 53 44 6 16 79208 5 20792 89723 / 10277 10516 3 89485 43 18 53 36 6 24 79224 6 20776 89749 8 10251 10626 3 89475 42 19 63 28 6 32 79240 5 20760 89775 8 10225 10535 3 89465 41 40 20 6 53 20 6 6 40 9. 79256 5 10. 20744 9. 89801 9 10. 10199 10. 10546 3 9. 89466 21 53 12 6 48 79272 6 20728 89827 9 10173 10656 4 89445 39 22 53 4 6 66 79288 6 20712 89853 10 10147 10665 4 89435 38 23 52 56 7 4 79304 6 20696 89879 10 10121 10576 4 89425 37 24 52 48 7 12 79319 6 20681 89906 10 10096 10585 4 89416 36 25 6 52 40 5 7 20 9. 79335 7 10. 20666 9. 89931 11 10, 10069 10. 10595 4 9. 89405 36 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 6 89385 33 28 52 16 7 44 79383 7 20617 90009 12 09991 10626 5 89375 32 29 52 8 7 52 79399 8 20601 90035 13 09966 10636 6 89364 31 30 6 52 6 8 9. 79415 8 10. 20585 9.90061 13 10. 09939 10. 10646 6 9. 89354 30 31 51 52 8 8 79431 8 20569 90086 13 09914 10656 5 89344 29 32 51 44 8 16 79447 8 20653 90112 14 09888 10666 5 89334 28 33 61 36 8 24 79463 9 20637 90138 14 09862 10676 6 89324 27 34 51 28 8 32 79478 9 20622 90164 15 09836 10686 6 89314 26 35 6 51 20 6 8 40 9. 79494 9 10. 20606 9. 90190 15 10. 09810 10. 10696 6 9. 89304 25 36 51 12 8 48 79610 10 20490 90216 16 09784 10706 6 89294 24 37 51 4 8 66 79526 10 20474 90242 16 09758 10716 6 89284 23 38 50 56 9 4 79542 10 20458 90268 16 09732 10726 6 89274 22 39 40 50 48 9 12 79568 10 20442 90294 17 09706 10736 7 " 7 89264 9. 89264 21 20 6 50 40 6 9 20 9. 79673 11 10. 20427 9. 90320 17 10. 09680 10. 10746 41 50 32 9 28 79589 11 20411 90346 18 09654 10756 7 89244 19 42 50 24 9 36 79605 11 20396 90371 18 09629 10767 7 89233 18 43 60 16 9 44 79621 11 20379 90397 19 09603 10777 7 89223 17 44 50 8 9 62 79636 12 20364 90423 19 09677 10787 7 89213 9. 89203 16 15 45 6 60 5 10 9. 79662 12 10. 20348 9. 90449 19 10. 09651 10. 10797 8 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 20286 90553 21 09447 10838 8 89162 11 60 6 49 20 5 10 40 9. 79731 13 10. 20269 9. 90578 22 10. 09422 10. 10848 8 9. 89162 10 51 49 12 10 48 79746 14 20254 90604 22 09396 10858 9 89142 9 52 49 4 10 66 79762 14 20238 90630 22 09370 10868 9 89132 8 53 48 56 11 4 79778 14 20222 90666 23 09344 10878 9 89122 7 54 55 48 48 6 48 40 n 12 79793 14 16 20207 90682 23 09318 10888 9 89112 6 5 5 11 20 9. 79809 10. 20191 9. 90708 24 10. 09292 10. 10899 9 9. 89101 56 48 32 11 28 79826 16 20175 90734 24 09266 10909 9 89091 4 57 48 24 11 36 79840 15 20160 90769 26 09241 10919 10 89081 3 58 48 16 11 44 79856 15 20144 90785 25 09215 10929 10 89071 2 59 48 8 11 62 79872 16 20128 90811 26 09189 10940 10 89060 1 60 48 12 79887 16 20113 90837 26 09163 10950 10 89050 M. Hour p. M. Hour A. M. Cosine. Diff. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. Sine. M. 128° A A B B C C 51° Seconds of time 1» 1 2' 3» 4' 6» 6« T (A Prop, parts of cols.-^B Ic 2 4 3 1 6 1 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. Diff. Cosecant. Tangent. Difif. Cotangent. Secant. Diff. Cosine. M. 60 6 48 5 12 9. 79887 10. 20113 9. 90837 10. 09163 10. 10950 9. 890S0 1 47 52 12 8 79903 20097 90863 09137 10960 89040 59 2 47 44 12 16 79918 1 20082 90889 1 09111 10970 89030 58 •6 47 36 1 12 24 79934 1 20066 90914 1 09086 10980 1 89020 57 4 47 28 1 12 32 79950 1 20050 90940 2 09060 10. 09034 10991 1 1 89009 9. 88999 56 55 5 6 47 20 5 12 40 9. 79965 1 10. 20035 9. 90966 2 10. 11001 6 47 12 12 48 . 79981 2 20019 90992 3 09008 11011 1 88989 54 / 47 4 12 56 79996 2 20004 91018 3 08982 11022 1 88978 53 8 46 56 13 4 80012 2 19988 91043 3 08957 11032 1 88968 52 y 46 48 13 12 80027 2 19973 91069 4 08931 10. 08905 11042 2 88958 51 10 6 46 40 5 13 20 9. 80043 3 10. 19957 9. 91095 4 10. 11052 2 9. 88948 50 11 46 32 13 28 80058 3 19942 91121 5 08879 11063 2 88937 49 V2 46 24 13 36 80074 3 19926 91147 5 08853 11073 2 88927 48 18 46 16 13 44 80089 3 19911 91172 6 08828 11083 2 88917 47 14 46 8 13 52 80105 4 19895 91198 6 08802 11094 2 88906 46 45 15 6 46 5 14 9. 80120 4 10. 19880 9. 91224 6 10. 08776 10. 11104 3 9. 88896 16 45 52 14 8 80136 4 19864 91250 i 08750 11114 3 88886 44 17 45 44 14 16 80151 4 19849 91276 7 08724 11125 3 88875 43 18 45 36 14 24 80166 5 19834 91301 8 08699 11135 3 88865 42 19 45 28 14 32 80182 5 19818 91327 8 08673 11145 3 88855 41 20 6 45 20 5 14 40 9. 80197 5 10. 19803 9. 91353 9 10. 08647 10.11156 3 9.88844 40 21 45 12 14 48 80213 5 19787 91379 9 08621 11166 4 88834 39 22 45 4 14 56 80228 6 19772 91404 9 08596 11176 4 88824 38 23 44 56 15 4 80244 6 19756 91430 10 08570 11187 4 88813 37 24 44 48 15 12 80259 6 19741 91456 10 08544 11197 4 4 88803 9. 88793 36 35 25 6 44 40 5 15 20 9. 80274 6 10. 19726 9. 91482 11 10. 08518 10. 11207 26 44 32 15 28 80290 7 19710 91507 11 08493 11218 5 88782 .34 27 44 24 15 36 80305 7 19695 91533 12 08467 11228 5 88772 33 28 44 16 15 44 80320 7 19680 91559 12 08441 11239 5 88761 32 29 30 44 8 15 52 80336 7 19664 91585 12 13 08415 11249 5 88751 31 6 44 5 16 9. 80351 8 10. 19649 9..91610 10. 08390 10. 11259 5 9. 88741 30 31 43 52 16 8 80366 8 19634 91636 13 08364 11270 5 88730 29 32 43 44 16 16 80382 8 19618 91662 14 08338 11280 6 88720 28 33 43 36 16 24 80397 8 19603 91688 14 08312 11291 6 88709 27 34 43 28 16 32 80412 9 19588 91713 15 08287 11301 6 88699 9. 88688 26 25 35 6 43 20 5 16 40 9. 80428 9 10. 19572 9. 91739 15 10. 08261 10. 11312 6 36 43 12 16 48 80443 9 19557 91765 15 08235 11322 6 88678 24 37 43 4 16 56 80458 9 19542 91791 16 08209 11332 6 88668 23 38 42 56 17 4 80473 10 19527 91816 16 08184 11343 7 88657 22 39 42 48 17 12 80489 10 19511 91842 17 08158 11353 7 88647 21 40 6 42 40 5 17 20 9. 80504 10 10. 19496 9. 91868 17 10.08132 10. 11364 7 9. 88636 20 41 42 32 17 28 80519 10 19481 91893 18 08107 11374 7 88626 19 42 42 24 17 36 80534 11 19466 91919 18 08081 11385 7 88615 18 43 42 16 17 44 80550 11 19450 91945 18 08055 11395 7 8S605 17 44 45 42 8 6 42 17 52 5 18 80565 9. 80580 11 12 19435 91971 19 19 08029 11406 8 88594 16 10. 19420 9. 91996 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 92048 20 07952 11437 8 88563 13 48 41 36 18 24 80625 12 19375 92073 21 07927 11448 8 88552 12 49 50 41 28 18 32 80641 13 19359 92099 21 . 07901 11458 9 9 88542 9. 88531 11 10 6 41 20 5 18 40 9. 80656 13 10. 19344 9. 92125 21 10. 07875 10. 11469 51 41 12 18 48 80671 13 19329 92150 22 07850 11479 9 88521 9 52 41 4 18 56 80686 13 19314 92176 22 07824 11490 9 88510 8 53 40 56 19 4 80701 14 19299 92202 23 07798 11501 9 88499 7 54 40 48 19 12 80716 14 19284 92227 23 07773 11511 9 88489 6 5 55 6 40 40 5 19 20 9. 80731 14 10. 19269 9. 92253 24 10. 07747 10. 11522 10 9. 88478 56 40 32 19 28 80746 14 19254 92279 24 07721 11532 10 88468 4 57 40 24 19 36 80762 15 19238 92304 24 07696 11543 10 88457 3 58 40 16 19 44 80777 15 19223 92330 25 07670 11553 10 88447 2 59 40 8 19 52 80792 15 19208 92356 25 07644 11564 10 88436 1 60 40 20 80807 15 19193 92381 26 07619 11575 10 88425 M. M. Hour P. M. Hour A. M. Cosine. Diff. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. Sine. 129<=' A A B B C C 50° j Seconds of time !• 2" 3» 4» 6' 6> 7" Prop, parts of cols.^B 2 3 1 4 6 3 6 10 4 8 13 5 10 16 7 12 19 8 13 23 9 Page 648J TABLE U. Log. Sines, Tangents, and Secants. 40° M. A A B B C C 139° Hour A.M. Hour p. M. Sine. Diff. Cosecant. Tangent. Diff. Cotangent. Secant. Diff. Cosine. M. 6 40 5 20 9. 80807 10. 19193 9. 92381 10. 07619 10. 11575 9. 88425 60 1 39 52 20 8 80822 19178 92407 07593 11585 88415 59 2 39 44 20 16 80837 19163 92433 1 07567 11596 88404 58 3 39 36 20 24 80852 1 19148 92458 1 07542 11606 88394 57 4 39 28 20 32 80867 1 19133 92484 2 2 07516 10. 07490 11617 10. 11628 88383 56 5 6 39 20 5 20 40 9. 80882 1 10. 19118 9. 92510 9. 88372 55 ^ 39 12 20 48 80897 1 19103 92535 3 07465 11638 88362 54 7 39 4 20 56 80912 2 19088 92561 3 07439 11649 88351 53 8 38 56 21 4 80927 2 19073 92587 3 07413 11660 88340 52 9 38 48 21 12 80942 2 19058 92612 4 07388 10.07362 11670 10. 11681 2 88330 51 50 10 6 38 40 5 21 20 9. 80957 2 10. 19043 9. 92638 4 2 9. 88319 11 38 32 21 28 80972 3 19028 92663 5 07337 11692 2 88308 49 12 38 24 21 36 80987 3 19013 92689 5 07311 11702 2 88298 48 13 38 16 21 44 81002 3 18998 92715 6 07285 11713 2 88287 47 14 15 38 8 21 52 81017 3 18983 92740 6 07260 11724 10. 11734 3 3 88276 46 45 6 38 5 22 9. 81032 4 10. 18968 9. 92766 6 10. 07234 9. 88266 16 37 52 22 8 81047 4 18953 92792 7 07208 11745 3 88255 44 17 37 44 22 16 81061 4 18939 92817 7 07183 11756 3 88244 43 18 37 36 22 24 81076 4 18924 92843 8 07157 11766 3 88234 42 19 20 37 28 22 32 81091 5 18909 92868 8 07132 11777 3 88223 41 6 37 20 5 22 40 9. 81106 5 10. 18894 9. 92894 9 10. 07106 10. 11788 4 9.88212 40 21 37 12 22 48 81121 5 18879 92920 9 07080 11799 4 88201 39 22 37 4 22 56 81136 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 25 6 36 40 5 23 20 9.81180 6 10. 18820 9. 93022 11 10. 06978 10. 11842 4 9. 88158 35 26 36 32 23 28 81195 6 18805 93048 11 06952 11852 5 88148 34 27 36 24 23 36 81210 7 18790 93073 12 06927 11863 5 88137 33 28 36 16 23 44 81225 7 18775 93099 12 06901 • 11874 5 88126 32 29 36 8 23 52 81240 7 18760 93124 12 06876 11885 5 88115 31 30 30 6 36 5 24 9. 81254 7 10. 18746 9. 93150 13 10. 06850 10. 11895 5 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 06748 :l1939 6 6 88061 26 25 35 6 35 20 5 24 40 9. 81328 9 10. 18672 9. 93278 15 10. 06722 10. 11949 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 11993 t 88007 21 40 6 34 40 5 25 20 9. 81402 10 10. 18598 9. 93406 17 10. 06594 10. 12004 7 9. 87996 20 41 34 32 25 28 81417 10 18583 93431 17 06669 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 11 18539 93508 19 06492 12047 8 87953 16 6 34 5 26 9. 81475 11 10. 18525 9. 93533 19 10. 06467 10. 12058 8 9. 87942 15 46 33 52 26 8 81490 11 18510 93559 20 06441 12069 8 87931 14 47 33 44 26 16 81505 12 18495 93584 20 06416 12080 8 87920 13 48 33 36 26 24 81519 12 18481 93610 20 06390 12091 9 87909 12 49 50 33 28 26 32 81534 12 18466 93636 21 06364 12102 9 87898 11 10 6 33 20 5 26 40 9. 81549 12 10. 18451 9. 93661 21 10. 06339 10. 12113 9 9. 87887 51 33 12 26 48 81563 13 18437 93687 22 06313 12123 9 87877 9 52 33 4 26 56 81578 13 18422 93712 22 06288 12134 9 87866 8 53 32 56 27 4 81592 13 18408 93738 23 06262 12145 10 87855 t 54 32 48 27 12 81607 13 18393 93763 23 06237 12156 10 10 87844 9. 87833 6 ' 5 55 6 32 40 5 27 20 9. 81622 14 10. 18378 9. 93789 23 10.06211 10. 12167 56 32 32 27 28 81636 14 18364 93814 24 06186 12178 10 87822 4 57 32 24 27 36 81651 14 18349 - 93840 24 06160 12189 10 87811 3 58 32 16 27 44 81665 14 18335 93865 25 06135 12200 10 87800 2 59 32 8 27 52 81680 15 18320 93891 25 06109 12211 11 87789 1 60 32 28 81694 15 18306 93916 26 06084 12222 11 87778 M. M. Hour p. M. Hour A. M. Cosine. Diff. Secant. Cotangent. Ditf. Tangent. Cosecant. Diff. Sine. 180' ) A A B B C C 49° Seconds of time 1» 2» 3s 48 5> 6» 1 ;» 1 (A Prop, parts of cols.-^B 2 3 1 4 6 3 6 : 7 10 13 4 5 9 1 11 13 16 19 22 7 8 9 TABLE 44. [Page 649 Log. Sines, Tangents, and Secants. 41° A A B B C C 188° M. Hour A. M. Hour p. M. Sine. Diff. Cosecant. Tangent. Diff. Cotangent. Secant. Diff. Cosine. M. 6 32 5 28 9. 81694 10. 18306 9. 93916 10. 06084 10. 12222 9. 87778 60 1 31 52 28 8 81709 18291 93942 06058 12233 87767 59 2 31 44 28 16 81723 18277 93967 1 06033 12244 87756 58 3 31 36 28 24 81738 1 18262 93993 1 06007 12255 87745 57 4 5 31 28 28 32 81752 1 18248 94018 2 05982 12266 87734 56 6 31 20 5 28 40 9. 81767 1 10. 18233 9. 94044 2 10. 05956 10. 12277 9. 87723 55 6 31 12 28 48 81781 1 18219 94069 3 05931 12288 87712 54 7 31 4 28 56 81796 2 18204 94095 3 05905 12299 87701 53 8 30 56 29 4 81810 2 18190 94120 3 05880 12310 87690 52 9 10 30 48 29 12 81825 2 18175 10. 18161 94146 4 05854 12321 2 87679 51 6 30 40 5 29 20 9. 81839 2 9. 94171 4 10. 05829 10. 12332 2 9. 87668 50 11 30 32 29 28 81854 3 18146 94197 5 05803 12343 2 87657 49 12 30 24 29 36 81868 3 18132 94222 5 05778 12354 2 87646 48 13 30 16 29 44 81882 3 18118 94248 6 05752 12365 2 87635 47 14 30 8 29 52 81897 3 18103 94273 6 05727 12376 3 87624 46 15 6 30 5 30 9. 81911 4 10. 18089 9. 94299 6 10. 05701 10. 12387 3 9.87613 45 16 29 52 30 8 81926 4 18074 94324 7 05676 12399 3 87601 44 17 29 44 30 16 81940 4 18060 94350 7 05650 12410 3 87590 43 18 29 36 30 24 81955 4 18045 94375 8 05625 12421 3 87579 42 19 29 28 30 32 81969 5 18031 94401 8 05599 12432 4 87568 41 20 6 29 20 5 30 40 9. 81983 5 10. 18017 9. 94426 8 10. 05574 10. 12443 4 9. 87557 40 21 29 12 30 48 81998 5 18002 94452 9 05548 12454 4 87546 39 22 29 4 30 56 82012 5 17988 94477 9 05523 12465 4 87535 38 23 28 56 31 4 82026 5 17974 94503 10 05497 12476 4 87524 37 24 25 28 48 31 12 82041 6 17959 94528 10 05472 12487 4 87513 36 35 6 28 40 5 31 20 9. 82055 6 10. 17945 9. 94554 11 10. 05446 10. 12499 5 9. 87501 26 28 32 31 28 82069 6 17931 94579 11 05421 12510 5 87490 34 27 28 24 31 36 82084 6 17916 94604 11 05396 12521 5 87479 33 28 28 16 31 44 82098 7 17902 94630 12 05370 12532 5 87468 32 29 28 8 31 52 82112 7 17888 94655 12 05345 12543 5 87457 31 30 30 6 28 5 32 9. 82126 7 10. 17874 9. 94681 13 10. 05319 10. 12554 6 9. 87446 31 27 52 32 8 82141 7 17859 94706 13 05294 12566 6 87434 29 32 27 44 32 16 82155 8 17845 94732 14 05268 12577 6 87423 28 33 27 36 32 24 82169 8 17831 94757 14 05243 12588 6 87412 27 34 35 27 28 32 32 82184 8 17816 94783 14 05217 12599 6 87401 26 6 27 20 5 32 40 9. 82198 8 10. 17802 9. 94808 15 10. 05192 10. 12610 7 9. 87390 25 36 27 12 32 48 82212 9 17788 94834 15 05166 12622 7 87378 24 37 27 4 32 56 82226 9 17774 94859 16 05141 12633 7 87367 23 38 26 56 33 4 82240 9 17760 94884 16 05116 12644 7 87356 22 39 40 26 48 33 12 82255 9 17745 94910 17 05090 12655 7 87345 21 20 6 26 40 5 33 20 9. 82269 10 10. 17731 9. 94935 17 10. 05065 10. 12666 7 9. 87334 41 26 32 33 28 82283 10 17717 94961 17 05039 12678 8 87322 19 42 26 24 33 36 82297 10 17703 94986 18 05014 12689 8 87311 18 43 26 16 33 44 82311 10 17689 95012 18 04988 12700 8 87300 17 44 45" 26 8 33 52 82326 10 17674 95037 19 04963 12712 8 87288 16 15 6 26 5 34 9. 82340 11 10. 17660 9. 95062 19 10. 04938 10. 12723 8 9. 87277 48 25 52 34 8 82354 11 17646 95088 20 04912 12734 9 87266 14 47 25 44 34 16 82368 11 17632 95113 20 04887 12745 9 87255 13 48 25 36 34 24 82382 11 17618 95139 20 04861 12757 9 87243 12 49 25 28 34 32 82396 12 17604 95164 21 04836 12768 9 87232 11 10 50 6 25 20 5 34 40 9. 82410 12 10. 17590 9. 95190 21 10. 04810 10. 12779 9 9. 87221 51 25 12 34 48 82424 12 17576 95215 22 04785 12791 10 87209 9 52 25 4 34 56 82439 12 17561 95240 22 04760 12802 10 87198 8 53 24 56 35 4 82453 13 17547 95266 22 04734 12813 10 87187 7 54 55 24 48 35 12 82467 13 17533 95291 23 04709 12825 10 10 87175 6 6 24 40 5 35 20 9. 82481 13 10. 17519 9. 95317 23 10. 04683 10. 12836 9. 87164 5 56 24 32 35 28 82495 13 17505 95342 24 04658 12847 10 87153 4 57 24 24 35 36 82509 14 17491 95368 24 04632 12859 11 87141 3 58 24 16 35 44 82523 14 17477 95393 25 04607 12870 11 87130 2 59 24 8 35 52 82537 14 17463 95418 25 04582 12881 11 87119 1 ao M. 24 36 82551 14 17449 95444 25 04556 12893 11 87107 M. Hour p. M. Hour A.M. Cosine. Diff. Secant. Cotangent. Difl. Tangent. Cosecant. Difl. Sine. 131° A A B B C C 48° 1 Seconds of time 1' 2* 3» 4- »• e* J* fA 2 4 Prop, parts of cols.^B 3 6 Ic 2 3 5 10 4 7 13 6 9 16 7 11 19 8 12 22 10 Page 650] TABLE 44. Log. Sines, Tangents, and Secants. 42° A A B B C C 137° M. Hour A. M. Hour p. M. Sine. Difi. Cosecant. Tangent. Dift. Cotangent Secant. Difl. Cosine. M. 6 24 5 36 9. 82551 10. 17449 9. 95444 10. 04556 10. 12893 9. 87107 60 1 23 52 36 8 82565 17435 95469 04531 12904 87096 59 2 23 44 36 16 82579 17421 95495 1 04505 12915 87085 58 •6 23 36 36 24 82593 1 17407 95520 1 04480 12927 87073 57 4 5 23 28 36 32 82607 1 17393 95545 2 04455 12938 87062 56 6 23 20 5 36 40 9. 82621 1 10. 17379 9. 95571 2 10. 04429 10. 12950 9. 87050 55 6 23 12 36 48 82635 1 17365 95596 3 04404 . 12961 87039 54 7 23 4 36 56 82649 2 17351 95622 3 04378 12972 87028 53 8 22 56 37 4 82663 2 17337 95647 3 04353 12984 2 87016 52 9 22 48 37 12 82677 2 17323 95672 4 04328 12995 2 87005 51 10 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 o 04252 13030 2 86970 48 13 22 16 37 44 82733 3 17267 95774 04226 13041 3 86959 47 14 15 22 8 37 52 82747 3 17253 95799 6 04201 13053 3 86947 46 6 22 5 38 9. 82761 3 10. 17239 9. 95825 6 10. 04175 10. 13064 3 9. 86936 45 16 21 52 38 8 82775 4 17225 95850 7 04150 13076 3 86924 44 17 21 44 38 16 82788 4 17212 95875 7 04125 13087 3 86913 43 18 21 36 38 24 82802 4 17198 95901 8 04099 13098 3 86902 42 19 21 28 38 32 82816 4 17184 95926 8 04074 13110 4 86890 41 20 6 21 20 6 38 40 9. 82830 5 10. 17170 9. 95952 8 10. 04048 10. 13121 4 9. 86879 40 21 21 12 38 48 82844 5 17156 95977 9 04023 13133 4 86867 39 22 21 4 38 56 82858 5 17142 96002 9 03998 13145 4 86855 38 28 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 86832 36 35 25 6 20 40 5 39 20 9. 82899 6 10. 17101 9. 96078 10. 13179 5 9. 86821 26 20 32 39 28 82913 6 17087 96104 11 03896 13191 5 86809 34 27 20 24 39 36 82927 6 17073 96129 11 03871 13202 5 86798 33 28 20 16 39 44 82941 6 17059 96155 12 03845 13214 5 86786 32 29 30 20 8 39 52 82955 7 7 17045 10. 17032 96180 12 03820 13225 6 86775 31 30 6 20 5 40 9. 82968 9. 96205 13 10. 03795 10. 13237 6 9. 86763 31 19 52 40 8 82982 7 17018 96231 13 03769 13248 6 86752 29 32 19 44 40 16 82996 7 17004 96256 14 03744 13260 6 86740 28 33 19 36 40 24 83010 8 16990 96281 14 03719 13272 6 86728 27 34 19 28 40 32 83023 8 16977 96307 14 03693 13283 7 86717 26 35 6 19 20 5 40 40 9. 83037 8 10. 16963 9. 96332 15 10. 03668 10. 13295 7 9. 86705 25 36 19 12 40 48 83051 8 16949 96357 15 03643 13306 7 86694 24 37 19 4 40 56 83065 8 16935 96383 16 03617 13318 7 86682 23 38 18 56 41 4 83078 9 16922 96408 16 03592 13330 7 86670 22 39 40 18 48 41 12 83092 9 16908 96433 16 03567 10. 03541 13341 8 8 86659 21 20 6 18 40 5 41 20 9. 83106 9 10. 16894 9. 96459 17 10. 13353 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 96535 18 03465 13388 8 86612 17 44 45 18 8 41 52 83161 10 16839 96560 19 19 03440 13400 8 86600 9. 86589 16 15 6 18 5 42 9. 83174 10 10. 16826 9. 96586 10. 03414 10. 13411 9 46 17 52 42 8 83188 11 16812 96611 19 03389 13423 9 86577 14 47 17 44 42 16 83202 11 16798 96636 20 03364 13435 9 86565 13 48 17 36 42 24 83215 11 16785 96662 20 03338 13446 9 86554 12 49 17 28 42 32 83229 11 16771 96687 21 03313 13458 9 86542 11 10 50 6 17 20' 5 42 40 9. 83242 11 10. 16758 9. 96712 21 10. 03288 10. 13470 10 9. 86530 51 17 12 42 48 83256 12 16744 96738 22 03262 13482 10 86518 9 52 17 4 42 56 83270 12 16730 96763 22 03237 13493 10 86507 8 53 16 56 43 4 83283 12 16717 96788 22 03212 13505 10 86495 7 54 55 16 48 6 16 40 43 12 83297 12 13 16703 10. 16690 96814 9. 96839" 23 03186 13517 10 11 86483 6 5 5 43 20 9. 83310 23 10. 03161 10. 13528 9. 86472 56 16 32 43 28 83324 13 16676 96864 24 03136 13540 11 86460 4 57 16 24 43 36 83338 13 16662 96890 24 03110 13552 11 86448 3 58 16 16 43 44 83351 13 16649 96915 25 03085 13564 11 86436 2 59 16 8 43 52 83365 14 16635 96940 25 03060 13575 11 86425 1 60 16 44 83378 14 16622 96966 25 03034 13587 12 86413 M. Hour P.M. Hour A. M. Cosine. Diff. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. Sine. M. 132 3 A A B B c C 470 Seconds of time V 2" 3' 4> 6» 9 16 7 6» 1' (A Prop, parts of cols. < B (c ■z 3 1 3 6 3 5 10 4 7 13 6 10 19 9 12 22 10 TABLE 44. [Page 651 Log. Sines, Tangents, and Secants. 43° A A B B C C 186° M. Hour A. M. Hour p. M. Sine. Diff. Cosecant. Tangent. Diff. Cotangent. Secant. Diff. Cosine. M. 6 16 5 44 9. 83378 10. 16622 9. 96966 10. 03034 10. 13587 9.86413 60 1 15 52 44 8 83392 16608 96991 08009 13599 86401 59 2 15 44 44 16 83405 16595 97016 1 02984 18611 86389 58 3 15 86 44 24 83419 1 16581 97042 1 02958 13623 86877 57 4 15 28 44 32 83482 1 16568 97067 2 02933 13634 86366 56 5 6 15 20 5 44 40 9. 83446 1 10. 16554 9. 97092 2 10. 02908 10. 18646 9. 86354 55 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 8 14 56 45 4 83486 2 16514 97168 3 02832 13682 2 86318 52 9 14 48 45 12 83500 2 16500 97193 4 02807 13694 2 86306 51 10 6 14 40 5 45 20 9. 88518 2 10. 16487 9. 97219 4 10. 02781 10. 13705 2 9. 86295 50 11 14 32 45 28 83527 2 16478 97244 5 02756 13717 2 86283 49 12 14 24 45 36 88540 3 16460 97269 5 02731 13729 2 86271 48 U 14 16 45 44 83554 3 16446 97295 02705 18741 3 86259 47 14 15 14 8 45 52 83567 3 16433 97320 6 02680 13758 10. 13765 3 3 86247 9. 86235 46 45 6 14 5 46 9. 83581 3 10. 16419 9. 97345 6 10. 02655 16 13 52 46 8 83594 4 16406 97371 7 02629 13777 3 86223 44 17 13 44 46 16 83608 4 16392 97396 7 02604 13789 3 86211 43 18 13 36 46 24 83621 4 16379 97421 8 02579 18800 4 86200 42 19 13 28 46 32 83634 4 16366 97447 8 02553 13812 4 86188 41 20 6 13 20 5 46 40 9. 83648 4 10. 16352 9. 97472 8 10. 02528 10. 13824 4 9. 86176 40 21 13 12 46 48 83661 5 16839 97497 9 02503 13836 4 86164 89 22 13 4 46 56 83674 5 16826 97523 9 02477 13848 4 86152 88 28 12 56 47 4 83688 5 16312 97548 10 02452 13860 5 86140 87 24 12 48 47 12 83701 5 16299 97573 10 02427 13872 5 86128 36 25 6 12 40 5 47 20 9. 83715 6 10. 16285 9. 97598 11 10. 02402 10. 13884 5 9. 86116 85 26 12 32 47 28 88728 6 16272 97624 11 02876 13896 5 86104 84 27 12 24 47 86 88741 6 16259 97649 11 02351 13908 5 86092 33 28 12 16 47 44 83755 6 16245 97674 12 02326 13920 6 86080 82 29 12 8 47 52 83768 6 16232 97700 12 02800 13982 6 6 86068 31 30 .SO 6 12 5 48 9. 83781 7 10. 16219 9. 97725 13 10. 02275 10. 13944 9. 86056 81 11 52 48 8 88795 7 16205 97750 13 02250 13956 6 86044 29 82 11 44 48 16 83808 7 16192 97776 13 02224 13968 6 86032 28 88 11 36 48 24 83821 7 16179 97801 14 02199 13980 7 86020 27 84 11 28 48 32 83834 8 16166 97826 14 02174 13992 7 86008 26 85 6 11 20 5 48 40 9. 83848 8 10. 16152 9. 97851 15 10. 02149 10. 14004 7 9. 85996 25 86 11 12 48 48 83861 8 16139 • 97877 15 02123 14016 7 85984 24 87 11 4 48 56 83874 8 16126 97902 16 02098 14028 7 85972 23 88 10 56 49 4 83887 8 16113 97927 16 02073 14040 8 85960 22 39 40 10 48 49 12 83901 9 16099 97953 16 02047 14052 8 85948 21 6 10 40 5 49 20 9. 88914 9 10. 16086 9. 97978 17 10. 02022 10. 14064 8 9. 85936 20 41 10 32 49 28 83927 9 16073 98003 17 01997 14076 8 85924 19 42 10 24 49 36 83940 9 16060 98029 18 01971 14088 8 85912 18 48 10 16 49 44 83954 10 16046 98054 18 01946 14100 9 85900 17 44 10 8 49 52 83967 10 16083 98079 19 01921 14112 9 85888 16 45 6 10 5 50 9. 83980 10 10. 16020 9. 98104 19 10. 01896 10. 14124 9 9. 85876 15 46 9 52 50 8 83993 10 16007 98130 19 01870 14136 9 85864 14 47 9 44 50 16 84006 10 15994 98155 20 01845 14149 9 85851 13 48 9 36 50 24 84020 11 15980 98180 20 01820 14161 10 85839 12 49 9 28 50 32 84033 11 15967 98206 21 21 01794 14173 10 85827 11 50 6 9 ?0 5 50 40 9. 84046 11 10. 15954 9. 98231 10. 01769 10. 14185 10 9. 85815 10 51 9 12 50 48 84059 11 15941 98256 22 01744 14197 10 85803 9 52 9 4 50 56 84072 12 15928 98281 22 01719 14209 10 85791 8 58 8 56 51 4 84085 12 15915 98307 22 01693 14221 11 85779 7 54 8 48 51 12 84098 12 15902 98332 28 01668 14234 11 85766 6 55 6 8 40 5 51 20 9. 84112 12 10. 15888 9. 98357 28 10. 01643 10. 14246 11 9. 85754 5 56 8 32 51 28 84125 12 15875 98383 24 01617 14258 11 85742 4 57 8 24 51 36 84138 13 15862 98408 24 01592 14270 11 85730 3 58 8 16 51 44 84151 13 15849 98438 24 01567 14282 12 85718 2 59 8 8 51 52 84164 13 15836 98458 25 01542 14294 12 85706 1 60 M. 8 52 84177 13 15823 98484 25 01516 14307 12 85693 M. Hour p. M. Hour A.M. Cosine. Diff. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. Sine. 183^ A A B B C C 46° 1 Secondsof time 1» 2» 3' 4» 5' 6» 7' Prop, parts of cols.-|B 2 3 2 3 5 7 6 9 13 3 i 5 j 6 8 16 8 10 19 9 12 22 U Page 652] TABLE 44. — Log. Sines, Tangents, and Secants. 44° A A B B C C 135° M. Hour A. M. Hour p. M. Sine. DifE. Cosecant. Tangent. DifE. Cotangent. Secant. Diff. Cosine. M. 6 8 5 52 9. 84177 10. 15823 9. 98484 10. 01516 10. 14307 9. 85693 60 1 7 52 52 8 84190 15810 98509 01491 14319 85681 59 2 7 44 52 16 84203 15797 98534 1 01466 14331 85669 58 3 7 36 52 24 84216 1 15784 98560 1 01440 14343 85657 57 4 5 7 28 52 32 84229 1 1 15771 10. 15758 98585 2 01415 14355 85645 56 6 7 20 5 52 40 9. 84242 9. 98610 2 10. 01390 10. 14368 9. 85632 55 6 7 12 52 48 84255 1 15745 98635 3 01365 14380 85620 54 7 7 4 52 56 84269 2 15731 98661 3 01339 14.392 85608 53 8 6 56 53 4 84282 2 15718 98686 3 01314 14404 2 85596 52 9 6 48 53 12 84295 2 15705 98711 4 01289 14417 2 85583 9. 85571 51 50 10 6 6 40 5 53 20 9. 84308 2 10. 15692 9. 98737 4 10. 01263 10. 14429 2 11 6 32 53 28 84321 2 15679 98762 5 01238 14441 2 85559 49 12 6 24 53 36 84334 3 15666 98787 5 01213 14453 2 85547 48 13 6 16 53 44 84347 3 15653 98812 5 01188 14466 3 85534 47 14 6 8 53 52 84360 3 15640 98838 6 01162 14478 3 85522 46 15 6 6 5 54 9. 84373 3 10. 15627 9. 98863 6 10. 01137 10. 14490 3 9. 85510 45 16 5 52 54 8 84385 3 15615 98888* 7 01112 14503 3 85497 44 17 5 44 54 16 84398 4 15602 98913 7 01087 14515 4 85485 43 18 5 36 54 24 84411 4 15589 98939 8 01061 14527 4 85473 42 19 20 5 28 54 32 84424 4 15576 98964 8 01036 14540 4 85460 41 40 6 5 20 5 54 40 9. 84437 4 10. 15563 9. 98989 8 10.01011 10. 14552 4 9. 85448 21 5 12 54 48 84450 5 15550 99015 9 00985 14564 4 85436 39 22 5 4 54 56 84463 5 15537 99040 9 00960 14577 5 85423 38 23 4 56 55 4 84476 5 15524 99065 10 00935 14589 5 85411 37 24 4 48 55 12 84489 5 15511 99090 10 00910 14601 5 85399 36 25 6 4 40 5 55 20 9. 84502 5 10. 15498 9.99116 11 10. 00884 10. 14614 5 9. 85386 35 26 4 32 55 28 84515 6 15485 99141 11 00859 14626 5 85374 34 27 4 24 55 36 84528 6 15472 99166 11 00834 14639 6 85361 33 28 4 16 55 44 84540 6 15460 99191 12 00809 14651 6 85349 32 29 4 8 55 52 84553 6 15447 99217 12 00783 14663 6 85337 31 30 6 4 5 56 9. 84566 6 10. 15434 9. 99242 13 10. 00758 10. 14676 6 9. 85324 30 31 3 52 56 8 84579 7 15421 99267 13 00733 14688 6 85312 29 32 3 44 56 16 84592 7 15408 99293 13 00707 14701 7 85299 28 33 3 36 56 24 84605 7 15395 99318 14 00682 14713 7 85287 27 34 3 28 56 32 84618 7 15382 99343 14 00657 14726 7 85274 26 25 35 6 3 20 5 56 40 9. 84630 8 10. 15370 9. 99368 15 10. 00632 10. 14738 7 9. 85262 36 3 12 56 48 84643 8 15357 99394 15 00606 14750 7 85250 24 37 •3 4 56 56 84656 8 15344 99419 16 00581 14763 8 85237 23 38 2 56 57 4 84669 8 15331 99444 16 00556 14775 8 85225 22 39 2 48 57 12 84682 8 15318 99469 16 00531 14788 8 85212 21 20 40 6 2 40 5 57 20 9. 84694 9 10. 15306 9. 99495 17 10. 00505 10. 14800 8 9. 85200 41 2 32 57 28 84707 9 15293 99520 17 00480 14813 8 85187 19 42 2 24 .57 36 • 84720 9 15280 99545 18 00455 14825 9 85175 18 43 2 16 57 44 84733 9 15267 99570 18 00430 14838 9 85162 17 44 2 8 57 52 84745 9 15255 99596 19 00404 14850 9 85150 16 15 45 6 2 5 58 9. 84758 10 10. 15242 9. 99621 19 10. 00379 10. 14863 9 9. 85137 46 1 52 58 8 84771 10 15229 99646 19 00354 14875 10 85125 14 47 1 44 58 16 84784 10 15216 99672 20 00328 14888 10 8.5112 13 48 1 36 58 24 84796 10 15204 99697 20 00303 14900 10 85100 12 49 1 28 58 32 84809 11 15191 99722 21 00278- 14913 10 85087 11 10 50 6 1 20 5 58 40 9. 84822 11 10. 15178 9. 99747 21 10. 00253 10. 14926 10 9. 85074 51 1 12 58 48 84835 11 15165 99773 21 00227 14938 11 85062 9 52 1 4 58 56 84847 11 15153 99798 22 00202 14951 11 85049 8 53 56 59 4 84860 11 15140 99823 22 00177 14963 11 85037 7 54 48 59 12 84873 12 15127 99848 23 00152 14976 11 85024 9. 85012 6 5 55 6 40 5 59 20 9. 84885 12 10. 15115 9. 99874 23 10. 00126 10. 14988 11 56 32 59 28 84898 12 15102 99899 24 00101 15001 12 84999 4 57 24 59 36 84911 12 15089 99924 24 00076 15014 12 84986 3 58 16 59 44 84923 12 15077 99949 24 00051 15026 12 84974 2 59 8 59 52 84936 13 15064 99975 25 00025 15039 12 84961 1 60 6 84949 13 15051 10.00000 25 00000 15051 12 84949 M. M. Hour p. M. Hour A. M. Cosine. Dift. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. Sine. 134° A A B B C C 45° Seconds of time 1" 2» 3» 4' b' 6» 7' fA Prop, parts of cols.-{B 2 3 2 3 6 5 9 5 6 13 6 8 16 8 10 'I 11 22 11 >f THE RETURN TO the circulation desk of any university of California Library or to the MORTHERH REGIONAL UBRABY FACILITY BIdg. 400, Richmond Field Station University of California Richmond, CA 94804-4698 2-month loans may be renewea y , ^^Xt may' be recharged by bringing booKs BeS'and recharges may be made 4 days prior to due date DUE AS STAMPED BELOW DECliJ94 20,000 (4/94) YD 1567 ^ ^ r^T