THE LIBRARY OF THE UNIVERSITY OF CALIFORNIA LOS ANGELES GIFT OF Bift U.C. Librait We keep on sale the largest stock of FINE SHOES in the city. Making to Measure, for Ladies, Gents, and Children, a specialty. Sea-faring men and their families will receive special attention. Any orders they may favor us with will be promptly and carefully filled. Kast's Fashionable Nos. 2, 4 and 6 DUPONT ST. SAN FRANCISCO CAL. Corner of Market and Dupont Streets. PIONEER SHIRT .FACTORY, No. 233 Kearny Street. FOR THE BEST FITTING SHIRT GO TO 233 KEARNY STREET, BET. BUSH AND SUTTER. A FINE ASSORTMEMT OF SHIRTS MADE TO ORDER, A SPECIALTY. Special Attention given to Afasters and Officers of Ships, W.W. MONTAGUE & CO. IMPORTERS OF Metals, Stoves . RANGES | CABOOSES, SHEET AND BOLT COPPER, SHEET IRON, WIRE, Rivets,Lead,Tin Plate RUBBER HOSE, SIIDEI ILIEOIKTS, IETO- MANUFACTURERS OF COPPER, SHEET IRON I TIN WARE PROMPT ATTENTION GIVEN TO SHIP WORK OF ALL KINDS. 1 10, 1 12, 1 14, 1 1 6 & 1 1 8 Battery Street SAN FRANCISCO. / it T. LUNDY, Importer and Jobber of AMERICAN AND FOREIGN Clocks, Jewelry AND OPTICAL GOODS, 9 CORNER OF MARKET SAN FRANCISCO. SILBERSTEIN'S SHIRT FACTORY Nos. 950 and 952 Market Street, UNDER THE BALDWIN, (Formerly of 506 Kearny Street,) SAN FRANCISCO, CAL. IMPORTER OF Meris Fine Furnishing Goods, HOSIERY, ETC., ETC. SPECIALTY SHIRTS TO ORDER. Sea Captains and Officers will do well to inspect our goods before purchasing else were their outfits. W. S. RAY. W. R. ANDERSON. db CO. 12 and 14 Market St. 9 and 11 Sacramento St. SAN FRANCISCO, CAL. Manufacture and keep constantly on hand, , SHIPS' STOVES Nos. 0, 1, 2, 3, 4, 5, 6 and 7. SUITABLE FOR VESSELS OF FROM 20 TO 2000 TONS. MISSISSIPPI STOVES (Sheet Iron) FOR S TEA MS II //V>' Also Manufacture and keep an assortment of the following on hand: Sidelights, Lanterns, Binnacle Lamps, Ships' Water Closets Tin, Copper, Sheet Iron Ware, Store Linings of all kinds, Extra Castings and Brick for all kinds of Ships' Stoves, Extra Basing and all Repairs for Water Closets, also Head Pumps; Red, Greeii and Round Fresual Glasses for all styles Sidelights and Lanterns. REPAIRS EXECUTED IN THE BEST POSSIBLE MANNER AT REASONABLE RATKS. Pottery; Antioch, Cal, Foundry; 228 Main St., S, F. Special Attention to Masters and Officers of Ships. UNIFORM CAPS MADE TO ORDER. SAN FRANCISCO. BRANCH, 910 MARKET STREET, ABOVE STOCKTON. THE FINEST GOODS ! THE LARGEST STOCK ! THE LOWEST PRICES ! Merchant Tailor, 203 MONTGOMERY ST., AND 103 THIRD ST., SAN FRANCISCO THE BEST FIT, LOWEST PRICES AND FINEST GOODS IN THE WORLD. The Great Artist and Cutter, FROM NEW YORK. 303 MONTGOMERY ST., AND 103 THIRD ST., SAN FRANCISCO LORENTZ FOARD, Dealer in New and Second-Hand SHIP MATERIAL The Highest Cash Price paid for Copper, Metal, Zinc* Lead, Sails, Rope, Etc. 3 I 5 STEUART STREET, NEAR MARKET, SAN FRANCISCO. All kinds of Blocks and Flags, old and new, always on hand. SAILS RENTED OUT BY THE DAY, WEEK OR MONTH IMPORTANT NOTICE TO OWNERS AND MASTERS OF VESSELS. METALINE BUSHING FOR BLOCKS. CAN BE RUN AT QUICK SPEED WITHOUT OIL. A new improvement in the Bushing of Blocks, which acting as its own lubricator, overcomes all friction, at the same lime allowing a heavier strain and workng easier than any other Hushing ever introduced in the market. For all places where a heavy strain and quick hoisting is required, it far excels all other kinds of Bushing. It is Admirably Adapted for Wheel Blocks on Account of its Durability. WE ALSO HAVE ALL KINDS OF BLOCKS AND LlGNUM-vriVK WoRK FOR SlUp'sUsE And we would be pleased to receive a call from you. Our Goods can be found at No. 18 Market St. , San Francisco, Cal. BAGNALL & LOUD, BOSTON, MASS. JOSEPH CHESSMAN, AGENT. Established in 1852. (FROM LONDON.) 418 BATTERY STREET, Between Washington and Merchant. SAN FRANCISCO, CALIFORNIA A LARGE ASSORTMENT OF CHARTS PUBLISHED BY The U. S. Hydrographic Office The British Admiralty The U. S. Coast Survey Messrs. Inray & Sons, Etc., Etc. SAILING DIRECTIONS, McNEVIN'S PRACTICAL NAVIGATION, SHIPPING LAWS, WORKS ON NAVIGATION, LOG BOOKS AND SLATES MARINEOPERA GLASSES TELIES COPIES, Sextants, Octants, and Quadrants, MESSRS. JOHN BLISS & GO'S PATENT TAFFRAIL LOG AND M C NEVIN'S LEE WAY INDICATOR. AGENT FOR MASSEY'S AND WALKER'S PATENT LOGS AN ASSORTMENT OF Chronometers by approved makers for sale or to hire. CHRONOMETERS REPAIRED, CLEANED AND RATED BY TRANSIT OBSERVATIONS. Watches of all descriptions Carefully Cleaned and li* 1 paired. ANDERSON & RANDOLPH, MANUFACTURING Jewelers and Silversmiths 101 & 103 MONTGOMERY ST. CORNER OF SUTTER, E CO tf W w HH H hJ H- I U t I O SAN FRANCISCO, CAL. n w z H en O a H > D O H o i i ^ i n THE LARGEST STOCK IN THE CITY OF Gold and Silver Watches, Diamonds, Jewelry and Silverware AT MANUFACTURERS' PRICES. SPECIAL ATTENTION PAID TO THE REPAIRING AND REGULATING OF FINE WATCHES, ETC. PLAZA STORES OF C. P. Yan Schaack & Co Nos. 706 TO 716 KEARNY STREET, OPPOISTE THE PLAZA, SAN FRANCISCO, CAL. Importers, Wholesale and Retail Dealers in FURNISHING GOODS, oiiOTimsro, HATS, CAPS, ETC., ETC. Captains and Officers of Ships would do well to call before making their purchases. SLOP-CHESTS FITTED UP ON REASONABLE TERMS. EXCELLENT OILSKINS, ETC., ETC. DR. SPINNEY & CO. No. ii KEARNY STREET, TREAT ALL CHRONIC AND SPECIAL DISEASES. YOUNG MEN Who may be suffering from the effect of youthful follies or indiscretion, will do well to avail themselves of this, the greatest boon ever laid at the alter of suffering humanity. DR. SPINNEY will guarantee to forfeit $5 f r every case of seminal weakness, or private disease of any kind or character which he undertakes and fails to cure. MIDDLE-AGED MEN. There are men of the age of thirty to sixty years who are troubled with too frequent evacuation of the bladder, often accompanied by a slight smarting sensation and a weakening of the system in a manner the patient cannot account for. On examining the urinary deposits a ropy sediment will often be found, and sometimes small particles of albumen will appear, or the color be of a thin and milkish hue, again changing to a dark and torpid appearance. There are many men who die of this difficulty, ignorant of the cause, which is the second stage of seminal weakness. Dr. S. & Co. will guarantee a perfect cure in all such cases, and a healthy restoration of the genito-urinary organs. Medicine Chests fitted up on reasonable terms. OFFICE HOURS: 10 to 4 and 6 to 8. Sundays from 10 to u a. m. Consultation free. Thorough examination and advice, $5. Call or address. DR. SPINNEY & CO. No. 1 1 Kearny Street, San Francisco THIS H A M M A M FINEST BATH HOUSE IN THE WORLD. Improved Turkish, Imperial Russian, Medicated AND Electric BATHS S ALL KINDS. NO CHARGE FOR MEDICAL SERVICES. Single Baths, $ 1.50 Ten Tickets, 10.00 A. M. LORYEA, M. D. PROPRIETOR. SAN FRANCISCO, CALIFORNIA. A. L. BANCROFT & CO. PRINTERS AND PUBLISHERS. Manufacturing and Publishing of Books for Authors. In addition to a large number of law-books, school-books, and pam- phlets that we have published during the last year or so, the following are among those which were published more particularly for authors, for which we will be pleased to receive orders: A La California. Sketches of Life in the Golden State. By Col. Albert S. Evans. 379 pages. 8vo. Cloth. Almond-Eyed. A Story of the Day. By Atwell Whitney. With 17 full- page illustrations. 170 pages, izmo. Paper. 1878. 50 cts. Behind the Arras. By C. M. Neville. 251 pages. 8vo. Paper. 1877. $1.00. Birthday Ode to Her Most Gracious Majesty Queen Victoria of England. By Mrs. Theresa Corlett. 8 pages. 8vo. 1877. 50 cts. Caxton's Book. A Collection of Essays, Poems, Tales and Sketches. By the late W. H. Rhodes. Edited by Daniel O'Connell. 300 pages. Large i2mo. Cloth. $3.00. Checkered Life; in the Old and New World. By Rev. J. L. Ver Mehr. 476 pages. Svo. Cloth. 1877. $3.00. Fidelite. By Edna Verne. 125 pages. . i2mo. Paper. 1877. 50 cts. Ho! for Elf-Land. By Alice Kingsbury. 136 pages. Small square 410. 9 full-page illustrations. 1877. $1.50. Journal of Army Life. By R. Glisan. 511 pages. Svo. Illustrated. $3.00. Madame Jane Junk and Joe. By Oraquill. 539 pages. Large i2mo. Cloth. $3.00. Semi-Tropical California. By Major Ben. C. Truman. 204 pages. 8vo. Cloth. Si. 50. Silver Shimmer. By William Darwin Crabb. 92 pages. i6mo. Cloth, $1.00. Paper, 50 cts. The New Penelope, and other Stories and Poems. By Frances Fuller Victor. 349 pages. Small Svo. Cloth. 1877. $2.00. The Coal Mines of the Western Coast of the United States. By W. A. Goodyear. 153 pages. Large i2mo. 1877. $2.50. The Log of an Ancient Mariner. Being the Life and Adventures of Captain Edgar Wakeman. 378 pages. Svo. Cloth. Illustrated. 1878. $3.00. The Poison Fountain, or Anti-Parental Education. By Zach. Montgomery. 189 pages. Svo. Cloth. 1878. $1.50. [JUST PUBLISHED.] A Guide to Practical Navigation. Containing the rules and methods of solving problems in the most practical manner; the simplest and most complete method of find- ing a ship's position at sea, as well as a thoroughly approved method of finding the latitude and longitude at the same instant of time by double altitudes. By Capt. E. McNevin. 348 pages. Svo. Cloth. 1878. $4.00. Any of the above sent by mail, post paid, on receipt of advertised price. [IN PRESS.] History of San Francisco, and Incidentally of California. By John S. Hittell. Svo. Cloth. $5.00. Apache-Land. By Chas. D. Poston. i2mo. Cloth. 150 pages. $2.00. A. L. BANCROFT & CO. 721 Market Street, San Francisco, Cal. A GUIDE TO THE RULES AND METHODS OF SOLVING PROBLEMS IN THE MOST PRACTICAL MAN- NER J THE SIMPLEST AND MOST COMPLETE METHOD FOR FINDING A SHIP'S POSITION AT SEA, AS WELL AS A THOROUGHLY APPROVED METHOD OF FINDING THE LATITUDE AND LONGITUDE AT THE SAME INSTANT OF TIME. BY DOUBLE ALTITUDES. BY CAPTAIN E. McNEVIK SAN FRANCISCO: A. L. BANCROFT & COMPANY, PRINTERS, 721 MABKKT STREET. 1878. Copyright, 18/7, T>y CAPTAIN E. McNEVIX. THE RIGHT OF TRANSLATION RESERVED BY THE AUTHOR. .55 S" PREFACE. THIS treatise Las been written, not for scientists but for seamen; to enable the navigator to find at any time quickly and accurately, his position at sea. By carefully studying the rules, and solving the problems herein given, he will assuredly be able to do so. The problems are solved in the simplest manner, and are only such as an experience of twenty years in the mercantile service has shown me to be necessary. This book is therefore not encumbered with matter and tables sel- dom or never used, at least by those in command of merchant vessels; all extra methods of determining latitude and longitude, either difficult in themselves or of doubtful accuracy, (such as lunar and stellar observations) being wholly omitted. This book, it is hoped will enable a seaman of ordinary education to instruct himself in all that is really necessary for him to know, while at the same time it will aid rather than repel (as many works have done) those de- sirous of subsequently attaining in this fine science a higher degree of skill than is needed for ordinary navigation. To polar-star observations for finding latitude, (of which some ex- amples are given) I do not attach much importance, as the pole star is too dim for observation, demanding, (what is seldom to be had,) a well defined horizon, and is besides, available only in the Northern hemisphere. As to lunars, aside from the expense of the requisite tables, and the fact that they would not be understood by more than one out of twenty, they are rendered still less necessary since the perfecting of chronometers. In my long career I have met but few men who could take, accurately, distances by lunar observations; though every master, when questioned as to his ability in this re- spect, can do so to perfection. There are a number of lunar tables published, but to those wanting such I would recommend Thomp- son's as being both simple and accurate. I have given Napier's logarithmic tables of natural numbers, being indispensable for accuracy in nautical calculations. These tables, Captain Thorn, in his treatise, not only omits, but repudiates, telling us, forsooth, that they " are never used at sea ! " He might almost 565323 PREFACE. as well have said that the compass had been rendered obsolete by some ' ' method " of his for finding the north. I mention this that no one may be led astray by statements so absurd. Moreover, we should never rely (as does this author) upon the crude approxima- tions of inspection. The necessary rules, however, for working by this method, are given for those who wish to employ them. For finding latitude by stellar altitudes (which circumstances not infrequently render desirable at sea) I have referred to the American Ephemeris for the declination of the fixed stars instead of to the English tables; and have also followed the star-notation of the for- mer. I have used a portion of the latter only in the problems foi exercise in this work. I would call the student's special attention to the system of finding simultaneously latitude and longitude by double altitude; a system not to be found in any American work that I have seen, and one upon which too much stress can scarcely be laid. In this work I would also call attention to a leeway indicator, (of .which a diagram is given) and which I have long used with great satisfaction at sea. This it is believed will be found highly useful to the mariner. In conclusion I would say, that as I have had in the preparation of this work only the needs and interests of sea-faring men in view, I trust that it will fulfill its mission and be thought worthy of their patronage. EDMUND McNEVIX. CONTENTS. PREFACE :t DEFINITIONS 5 TABLE OF ANGLES 9 MULTIPLICATION BY LOGARITHMS 10 DIVISION BY LOGARITHMS 11 REDUCTION 12 COMPOUND ADDITION 13 COMPOUND SUBTRACTION 1& LATITUDES 14 TRAVERSE SAILING 18 PARALLEL SAILING ... 19 MIDDLE LATITUDE SAILING 20 MERCATOR'S SAILING 30* DEVIATION OF THE COMPASS 39 VARIATION OF THE COMPASS 41 LEEWAY 4& DAY'S WORK 49 TIME . 55 AMPLITUDE 58 CORRECTION OF THE COMPASS BY AN AZIMUTH 62 LATITUDE BY MEUIDIAN ALTITUDE OF SUN 65 LATITUDE BY REDUCTION TO THE MERIDIAN 68 LATITUDE BY STAR'S MERIDIAN ALTITUDE 71 LONGITUDE BY CHRONOMETER 73 RULES FOR FINDING THE LONGITUDE 75 EXAMINATION PAPERS AS WORKED OUT FOR THE BOARD OF TRADE ... 81 LATITUDE AND LONGITUDE BY DOUBLE ALTITUDES 94 LATITUDE BY POLE STAR 104 To FIND THE TIME OF A STAR'S PASSING THE MERIDIAN, ALSO, ITS APPROXIMATE ALTITUDE 106 FINDING THE TIME AT A GIVEN MERIDIAN 108 To FIND THE ERROR OF A WATCH OR CHRONOMETER BY EQUAL ALTI- TUDES OF THE SUN Ill EQUATIONS OF EQUAL ALTITUDES 112. To FIND THE SHIP'S POSITION FROM TWO BEARINGS OF THE SAMI: OBJECT 115. TABLE FOR SAME 117. EXPLANATION OF THE TABLES 118 TABLES . ..... 127. CONTENTS. CONTENTS OF THE TABLES. PAGE I. LOGARITHMS OF NUMBERS 127 II. LOGARITHMIC SINES, TANGENTS, SECANTS, ETC 143 III. DIFFERENCE OF LATITUDE AND DEPARTURE FOR POINTS . . . 188 IV. DIFFERENCE OF 'LATITUDE AND DEPARTURE FOR DEGREES. . 204 V. MERIDIONAL PARTS 249 VI. REFRACTION 257 VII. DIP OF THE HORIZON 257 VIII. SUN'S PARALLAX 257 IX. To REDUCE THE EQUATION OF TIME TO ANY TIME UNDER THE MERIDIAN OF GREENWICH 258 X. To OBTAIN THE PROPORTIONAL PART OF THE RATE OF A CHRONOMETER FROM NOON, TO ANT GIVEN HOUR AT GREENWICH 258 XI. TURNING DEGREES INTO TIME, AND VICE VERSA 259 XII. To REDUCE THE SUN'S DECLINATION AT ANY MERIDIAN. . . . 26Q XIII. CORRECTION FOR APPARENT ALTITUDE OF SUN OR STAR . . . 262 XIV. NATURAL SINES AND COSINES 265 XV. FOR FINDING THE DISTANCE OF TERRESTRIAL OBJECTS AT SEA 274 XVI. LOGS A AND B FOR COMPUTING THE EQUATION OF EQUAL ALTITUDES 276 XVII. LoG-RisiNfl% FOR LATITUDE BY REDUCTION TO THE MERIDIAN. 277 XVIII. LOGARITHMS FOR FINDING THE APPARENT TIME OR HORARY ANGLE 285 XIX. LATITUDE BY ALTITUDE OF POLE STAR 294 XX. AMPLITUDE 295 XXI. NAUTICAL ALMANAC FOR 1878 ' 298 XXII. LATITUDES AND LONGITUDES OF THE PRINCIPAL PORTS, HAR- BORS, CAPES, ETC., IN THE WORLD 322 DEFINITIONS. 1. The Equator is a circle passing round the Earth, equally dis- tant from the poles, dividing the globe into the northern and south- ern hemispheres. 2. The Poles are the extremities of the earth's axis. 3. A Meridian is a great circle passing through both poles, cross- ing the equator at right angles, and dividing the globe into two parts, called eastern and western hemispheres. 4. The Ecliptic is the apparent annual path of the sun in the heavens. 5. The Tropics are that portion of the earth between 23i N, and 23i S. G. Latitude is the number of degrees N. or S. of the equator. 7. Parallels of Latitude are circles parallel to the equator. 8. Longitude is the number of degrees E. or AV. of Greenwich. 9. The Visible Horizon is the circle that bounds the observer's view at sea. 10. The Sensible Horizon is the circle that passes through the eye of an observer whose poles are in the zenith and Nadir. 11. The Rational Horizon is the circle parallel to the sensible horizon, whose plane passes through the center of the earth. 12. The True Course of a ship is the compass. course corrected for deviation, lee-way and variation. 13. A Magnetic Course is a compass course corrected for lee-way and deviation. 14. A Compass Course is the course steered by a compass. 15. Variation of the compass is the angle between the true north and the magnetic north. 1G. Deviation of the compass is the angle between the magnetic north and the compass north. 17. The Error of the compass is the sum of the deviation and variation. 18. Lee-way is the angle between the ship's course by compass and her path through the water. DEFINITIONS. 19. The Meridian Altitude of a celestial object is tlie highest alti- tude it attains, or its altitude when on the observer's meridian. 20. Azimuth is the angular distance of a body from the meridian, measured on the horizon. 21. Amplitude is the complement of azimuth, or the true bearing of an object, east or west, on the horizon. 22. Declination is the number of degrees any celestial "object is north or south of the equator; similar to latitude. 23. Polar Distance is the number of degrees an object is from the elevated pole. 24. Eight Ascension is the distance of a celestial object from the first point of Aries, measured in time eastward on the equinoctial. 25. The Dip or Depression of the horizon is the angle contained between the sensible and the visible horizon. 26. Refraction, is the difference between the real and the apparent place of a heavenly body, produced by the passage of the rays of light through the atmosphere. 27. Parallax is the difference between an altitude of a celestial body observed at the center of the earth and on the surface of the earth. Semi-diameter is half the angle under which the heavenly bodies appear to an observer on the earth. 28. An Observed Altitude is the height of the sun, moon, planet or star above the horizon, as measured by a quadrant or sextant. 29. The Apparent Altitude is the observed altitude corrected for index error and dip. 30. The True Altitude is the apparent altitude corrected for re- fraction and parallax. 31. Zenith Distance is the distance of a heavenly body from the zenith, or point of the heavens over our heads. 32. Vertical Circles are great circles passing through the zenith and Nadir; perpendicular to the horizon. 33. The Prime Yertical is a great circle passing through the zenith and Nadir, cutting the horizon in the east and west points. 34. Civil Time begins and ends at midnight; the first 12 hours called A. M. ; the last 12 hours called p. M. 35. Astronomical Time is the time between two successive tran- sits of the sun's mean center over the same meridian, which always begins at noon, and is reckoned through the 24 hours to noon again. 36. Mean Time is the hour angle of the mean sun westward of the meridian. 37. Apparent Time is the interval hetween the sun's departure from and his return to the same meridian; or time shown by the sun .according to his altitude, reckoned westward of the meridian. 38. Equation of Time is the difference between mean time and apparent time. DEFINITIONS. 39. The Hour Angle of a celestial object is an arc of the equator contained between the meridian of the place and that of the object. 40. The Complement of an arc or angle is what that arc or angle is short of being 90. 41. The Supplement of an arc or angle is what that arc or angle requires to make it 180. 42. The Co-latitude is the difference between a given latitude and 90. Polar distance is a celestial object's distance from the north pole. 43. The difference of latitude of two places is the portion of the meridian included between their parallels. 44. The difference of latitude of a ship is the distance she makes from any point, north or south. 45. The difference of longitude of two places is the portion of the equator included between their meridians. EIGHT- ANGLED TRIANGLE. 46. The course steered is the angle between the meridian and the ship's head; the course made good is the angle between the mer- idian and the ship's real track on the ocean. 47. The course is reckoned from the meridian accordingly, north or south towards the east or west, if less than eight points, or 90. 48. The course is measured in points of 11 15' each. 49. The rhumb line is the ship's track when crossing all the me- ridians at the same angle. 50. The distance between two places, or the distance sailed by the ship on a certain course, is measured in nautical miles of 60 to the degree of latitude, each containing 6082 feet. 51. Three such miles make a league. 52. The departure is the distance sailed clue east or west, or the distance from the ship's first meridian, and is always equal to the difference of latitude in miles. It is also called easting or westing, and is always expressed in miles. When a ship sails due east or west she makes no difference of latitude. 53. The difference of latitude is the space contained between two parallels of latitude, and is counted on the meridian. When a ship sails north or south she makes no departure. 54. Taking a departure means taking the bearing of any object by compass, or its angle with the meridian, and estimating- its dis- tance from the ship on leaving the land. GIVEN THE TRUE COURSE, TO FIND THE MAGNETIC COURSE. Easterly variation allow to the left hand. Easterly deviation allow in the same way. Westerly variation allow'to the rigljt hand. Westerly deviation allow in the same way. ALLOW LEEWAY GIVEN THE MAGNETIC COURSE, TO FIND THE TRUE COURSE. Easterly variation allow to the right hand. Easterly deviation allow in the same way- Westerly variation allow to the left hand. Westerly deviation allow in the same way. FROM THE WIND. PRACTICAL NAVIGATION. A TABLE OF THE ANGLES Which every point and quarter point of the compass makes with the meridian. NORTH. POINTS. O ' " POINTS. SOUTH. D. M. 8. 01 2 48 45 01 o$ 5 37 30 o{ of 8 2G 15 Of NbE NbW 11 15 00 SbE SbW 11 14 03 45 11 4 1G 52 30 if 19 41 15 If NNE NNW 22 30 00 2 SSE SSW 21 25 18 45 2i 24 28 07 30 2| 2| 30 56 15 n NEbN NWbN 3 33 45 00 3 SEbS SWb S 31 36 33 45 31 si 39 22 30 8| 42 11 15 sf NE NW 4 45 00 00 4 SE SW 41 47 48 45 41 50 37 30 44 4 53 26 15 4| NEbE NWbW 5 5G 15 00 5 SEbE SWbW 51 59 03 45 51 61 52 30 5 64 41 15 5f ENE WNW G 67 30 00 6 ESE WSW Gl 70 18 45 61 6^ 73 07 30 6* Gj 75 56 15 6f EbN WbN 7 78 45 00 7 EbS WbS 71 81 33 45 71 7* 84 22 30 7rV 87 11 15 7} EAST WEST 8 90 00 00 8 EAST WEST PRACTICAL NAVIGATION. MULTIPLICATION BY LOGAEITHMS. Place the numbers one under the other, the same manner as if they were to be multiplied by common multiplication. Give to each number its own index, which will always be one less than the figures in the whole number. Next, in Table I (logarithms of numbers), find the log. corres- ponding to each number, and place as in the worked example oppo- site; then add the logarithms andindexes together, and the index now obtained will show how many figures. are wanted in the answer, which is always one more than the index. 4 Rule for getting Five, or more Figures in tlie Answer. Find the Logarithm next less to the given log. which will point out the first four figures of your answer three on the left side, and the other at the head of the column you find the next less in; then take the next less log. found from yours, to which annex as many ciphers as there are figures wanted more than four, divide this by the difference, which is found in the column on the right hand side, and the quotient will be the remaining figures required; and if you want to turn the remainder into a decimal, annex a cipher and divide again by the same difference as before. Rule for taking out a Logarithm for a number consisting of Five, or more figures. Take out a log. for the first four figures and set it out to one side; then multiply the figures that there are more than four in your num- ber, by the difference on the right hand side of Table I. Cut off from the product to the right hand as many as you had over four in your number, and what remains being added to the logarithm DIYISIOX BY LOGARITHMS. 11 taken out for the first four figures, makes the logarithm required for the whole number. When the first of the figures pointed off is five, or exceeds five, add one to the figures you are going to apply to the log. of the first four figures. Multiply 7235 by 822, by Common Logarithms. 7 ' 91487 Add in Multiplication. Ans. 5947164 = 6.774310 774298 nearest less log. Diff. 73) 12000 (164 73 470 438 320 292 28 Remainder. Multiply 7890 by 987, by Common Logarithms. Multiply 4789 by 976, by Common Logarithms. Multiply 5648 by 765, by Common Logarithms. Multiply 6979 by 878, by Common Logarithms. Multiply 7898 by 549, by Common Logarithms. Multiply 348.25 by 71.25, by Common Logarithms. Multiply 7298 by 3.475, by Common Logarithms. Multiply 3650.0 by 208.0, by Common Logarithms. Multiply 65703 by 475, by Common Logarithms. Ans. 7787428 Ans. 4674064 Ans. 4320720 Ans. 6127549 Aus. 4336000 Ans. 24812.8* Ans. 25360.58* Aus. 759200 Ans. 31208920 NOTE. A decimal is got by annexing a cipher and dividing again. ' Bead explanation of Table I carefully. DIVISION BY LOGARITHMS. Place the number and their indexes as in multiplication, and get out the Logarithms, which are subtracted iu division. "When dividing for the figures wanted more than four, remember you do not use more than one cipher at a time, viz : Suppose the dif- ference between the logs is 15, and you annex three ciphers which make 15,000; now, if this is to be divided by say, 160)15,000(0 is the first figure because it will not go in 150, that is, taking one of the ciphers only at a time; and should it not go with another cipher taken in, as it may sometimes occur, then the second figures will also be 0. And again, should the logs, when looking for the next less, agree exactly, then, where they agree, it gives you the first four, and any more wanted will be ciphers annexed to make the required number; for example the index is 8 and the first four got out is 7799, then the proper answer is 779900000. 12 PRACTICAL NAVIGATION. Divide 8756403 by 228 by Common Logarithms. Log. of 1st 4 figures. Ans. Divide Divide Divide Divide Divide Divide Divide Divide Divide 8756403 = 6.942326- 228 = 2.357935 38405.3 = 4.584391 584331 -942306- 20 942326 33 left over four. 50 ditf. 20. 150 113) 600 (5.3 565 113) 350 (3 339 11 Remainder, 5678465 by 8789786 by 4785895 by 34650 by 3876000 by 8247877 by 248.603 by 425, 540, 487, 185, .12, 789, 3910, 8.50078 by 890.1, 84361912 by .0341, by Common Logarithms, by Common Logarithms, by Common Logarithms, by Common Logarithms, by Common Logarithms, by Common Logarithms, by Common Logarithms., by Common Logarithms, by Common Logarithms. Ans. Ans. Ans. Ans. Ans. Ans. Ans. Ans. 13361. 16277. 9827. 187.297. 32300074. 10453. .06358. .009550. Ans. 2473960227. REDUCTION. To reduce Degrees, Minutes and Seconds of Arc, to Minutes or Seconds of Arc. Multiply the degrees by 60, and to the product add the minutes. This sura is the whole of the minutes. Again multiply this sum by 60, and to the product add the sec- onds. This last sum is the whole of the seconds. Ex. 1. Reduce to minutes. 12 27' x 60 Ans. 747 miles. Ex. 2. Reduce to seconds. 35 00' 2G" x 60 2100 x CO Ans. 126026" To reduce Seconds or Minutes of Arc, to Degrees, Minutes and Seconds. Divide the seconds by 60, and the remainder, if there be any, will be the odd seconds. Again divide the preceding quotient by 60, and the remainder will be the odd minutes. And the last quotient will be the degrees, minutes and seconds. Ex. 1. Reduce 046 minutes degrees and minutes. 60)946' 15 46' COMPOUND SUBTRACTION. to 13 Ex. 2. Reduce 5674 seconds to degrees, miuutes and seconds. 60)5674" 60)94' 34" Ans. 1 34' 34" COMPOUND ADDITION. To add Degrees, Minutes and Seconds of Arc. Place degrees under degrees, minutes under minutes, and seconds under seconds. Add the seconds together, and if their sum be GO or upwards, re- duce it to minutes and seconds. Place the seconds that remain under the other seconds, and add the minutes to the other minutes. If the sum of the minutes equal 60, or more, reduce it to degrees and minutes. Place the minutes that remain under the other minutes, and add the degrees to the other degrees. Ex. 1. together. Add 49 38' and 22 58' 49 38' 22 58 Ans. 72 36' Ex. 2. Add 105 3 18" and 158 02' 10". 105 32' 18" 158 02 10 Ans. 263 34' 28" COMPOUND SUBTRACTION. To take the Difference between Degrees, Minutes and Seconds of Arc. Place the quantities as in addition. Begin at the seconds of the lesser quantity, and subtract them from those of the greater. If the seconds of the lesser quantity be more than those of the greater, add GO to those of the greater, and subtract those of the lesser from the sum. In the same manner subtract the minutes of the lesser quantity from those of the greater. If GO has been added to the minutes of the lesser quantity before subtracting them, proceed in the following manner with the degrees: 15' 40" from Ex. 1. Subtract 4 8 22' 26'. 8 22' 26" 4 15 40 Ans. 4 06' 4G" Ex. 2. Subtract 30 28' 54" from 80 40' 20". 80 40' 20" 30 2854 Ans. 50 11' 26" 14 PRACTICAL NAVIGATION. LATITUDES. To find the Difference of Latitude between Two Places whose Latitude is given. "When both latitudes are of the same name, that is, when they are both north or both south, take their difference by subtracting one from the other, for the difference of latitude. "When the latitudes are of different names, that is, when one is north and the other south, take their sum by adding both latitudes together for the difference of latitude. To name the different latitudes, consider whether the place bound to is north or south of the ship's place, and mark the differ- ent latitude north or south accordingly. Ex. 1. Given Point Bonita in lati- tude 37 49' N. and Cape Mendocino in latitude 40" 26' N. Required the dif- ference of latitude. Latitude Point Bonita . . . 37 Latitude Cape Mendocino. 40 49' N. 26 N. Difference of latitude =2 37' x60 157 miles. Ex. 2. Given Point Bonita in lati- tude 37 49' N. and Callao in latitude 12 04' S. Required the difference of latitude. Latitude Point Bonita 37 49' N. Latitude Callao 12 04 S. Difference of latitude = 49 53' S. x 60 2993 miles. Given the Latitude Left and Difference of Latitude, to find the Lati- tude In. When the latitude left and the difference of latitude are of the same name, add them together, their sum is the latitude in, and of the same name as the latitude left. "When the latitude left and difference of latitude are of different names, subtract the lesser from the greater, and their difference is the latitude in, of the same name as the greater. Ex. 1. Given the latitude left 19 06' X, and difference of latitude 2 24' N. Required the latitude in. Latitude left... 19 06' N. Difference lat.. 2 24 N. Latitude iu 21 30' N. Ex. 2. Given the latitude left 8 04' N. and difference of latitude C 05' S. Required the latitude in. Latitude left... 8 04' N. Difference lat... 6 05 S. Latitude in 1 59' N. Having the Latitude In, and Latitude Left, to find the Middle Latitude. Add the latitudes together and divide the sum by 2, and the re- sult is the middle latitude. "When the latitudes are of different names, add the half of the greater latitude to the half of the less latitude, and take their half sum for the middle latitude. If one latitude be great and the other small, take the half of the greater latitude for the middle latitude. MERIDIONAL DIFFERENCE OF LATITUDE. 15 Ex. 1. Given latitude left 19; O.V X. and latitude in G' 04' N. Required the middle latitude. Latitude left.. 19 05' N. Latitude in... 6 04 N. 2)25 09 Ans. 12 J 34'mid. lat. Ex. 2. Given latitude left 32 19' S. and latitude in 57' -4 !S. Required the middle latitude. Latitude left... 3'2'M9' S. Latitude in . . . 57 24 S. 2)89 43 Ans. 44 51'niid. lat. Ex. 3. Latitude of A. 40 43' N. Half of A. 20 21' Latitude of B. 34 22' S. Half of 13. 17 11' 2)37 32' Middle latitude, 18 46' To take out of the tables the Meridional Parts for a Given Latitude. Look for the number of degrees of latitude at the top of the table, and for the number of the minutes of latitude in the column marked miles. Then look down the column of figures under the degrees, until it meets the line of figures opposite the minutes. Take out the number at the point of meeting, which will be the meridional parts for the given latitude. Ex. 1. Find the meridional parts of 36 58' Ans. 2390. Ex. 2. Find the meridional parts of 28" 10' Ans. 17<>2. Ex. 3. Find the meridional parts of 46 J 48' Ans. 3185. Ex. 4. Find the meridional parts of 38 59' Ans. 2544. Given (he Latitude Left and Latitude In, to find the Meridional Dif- ference of Latitude. Take out the meridional parts for both latitudes. "When both latitudes are of the same name, take the difference of the meridional parts for the meridional difference of latitude. "When the latitudes are of different names, take the sum of the meridional parts for the meridional difference of latitude. Ex. 2. Given latitude left 4 28' N. and latitude in 2" 58' S. Required the meridional difference of latitude. Lat. left 4 28' N. mer. parts 268. Lat. in 2 58 S. mer. parts 178. Fx. 1. Given latitude left 39 44' N. and latitude in 46 J 24' N. Required the meridional difference of latitude. Lat, left 39 44' N. mer. parts 2C02. Lat. in 46 24 N. mer. parts 3150. 6 40 Mer. diff. lat. 548 mis. x60 400 miles. 7 26 Mcr. diff. lat. 446 mis. x60 446 miles. Given the latitude left in, as follows; required the meridional difference of latitude: No. Lat. left Lat. in Ans. No. Lat. left Lat. in Ans. 1 28 40' X 30 31' N 127 4 2 48' s 2 52' x 340 2 19 46' S 26 30' s 440 5 4 28' N 2 58' S 446 3 22 50' X 26 22* S 3049 C 65 27' s 1 08' S 5175 16 PRACTICAL NAVIGATION. Given (he Longitude of Two Places, to find their Difference of Longi- tude. When both longitudes are of the same name, that is, both east or west, take their difference for the difference of longitude. "When the longitudes are of different names, that is, one east and the other west, take their sum for the difference of longitude. When the difference of longitude exceeds 180 take it from 3GO and the remainder will be the difference of longitude. Ex. 1. Given Nemen's Island in longitude 179 07' E. and Drummond's Island in longitude 174' J 53' E. Re- quired their difference in longitude. Longitude Nemen's Is. 179 07' E. Longitude Drum. Is... 174 53 E. Difference longitude. .. 4 14' E. x60 254 miles. Ex. 2. Given Vonio Island in long- itude 177 14' E. and the Eddystone in longitude 4 16' W. Required their difference in longitude. Longitude Vonio Is. . . 177 14' E. Longitude Eddystone. 4 16 W. 181 30 360 00 Difference longitude. 178^30' x60 10710 miles. Given the longitudes of two places, A and B, as follows; required their difference in longitude. No. Longitude. Ans. No. Longitude. Ans. A B A B 1 2 3 128 32' W 66 a 24' E 46 28' W 138 23' E 7837'w 52 3 46' E 93 05' 145 01' 99 14' 4 5 6 11342'E 3 10' E 16' W 99 26' W 4 05' E 32' E 146 52' 055' 048' Given the Longitude Left and Difference of Longitude, to find the Longitude In. When the longitude left and difference of longitude are of the same name, take their sum for the longitude in, and it is of the same name as the longitude left. When the sum exceeds 180, take it from 360, and the remainder will be the longitude in, of contrary name to the longitude left. AVhen the longitude left and difference of longitude are of con- trary names, take their difference, which will be the longitude in, and of the same name as the greater. Ex. 1. Given longitude left 44 16' W., and difference of longitude 1 20' W. Required the longitude in. Longitude left 44 16" W. Difference of longitude 1 20 W. Longitude in 45' 36' W. Ex. 2. Given longitude left 165 18' W., and difference of longitude 7 46' W. Required the longitude in. Longitude left 175 18' W. Difference longitude. 7 46 W. 183 04 W. 360 00 Longitude in 170 56' E. MERIDIONAL DIFFERENCE OF LATITUDE. 17 Given longitude left and difference of longitude, as follows; re- quired tlie longitude in. No. Long, left Diff. long Ans. No. Long, left Diff. long Ans. 1 2 3 3 40' w 12 42' E 59 J 16' W 2 10' E 6 y 20' w 3 53' E 1 30' w 6 22' E 55 23' w 4 5 6 182 00' E 1422'E 1020'w 53 20' E 5 00' E 035'\v 124 40' w 19 22' E 10 U 55' w Given the Course and Distance to take out of Table III, for the Differ- ence of Latitude and Departure. If the course does not exceed 4 points or 45, look for it at the head or top of the page; but if it exceed 4 points or 45, look for it at the bottom of the page. Find the distance in one of the columns marked "Dist.," and take out of the two adjoining columns, to the right hand, the num- bers in the same line with it. Observe whether the course is found at the top or bottom of the page, and mark the numbers taken out according as they are marked at the part of the page the course is found in. Given course 2f points, distance 28 miles; to find difference of latitude and departure. (Table III.) Ans. Difference latitude 24.0; departure 14.4. Given course 34, distance 253 miles; to find difference latitude aud departure. Ans. Difference latitude 209.7; departure 141.5. Given the Difference of Latitude and Departure, to find the Course and Distance in Table IV. Look in Table IV, until the difference latitude and departure, or numbers near to them are found together; take out the course and distance corresponding thereto. Given difference latitude 55.4, departure 35.9; to find the course and distance. Ans. Course 33; distance 66 miles. Given difference latitude 71.0, departure 123.0; to find the course and distance. Ans. Course 60; distance 142 miles. PBAO. NAV. 2 18 PRACTICAL NAVIGATION. TRAVERSE SAILING. Traverse sailing is the finding of a single course or distance, such that it would have brought a ship to the same place that several courses and distances have done. Form a table similar to the one annexed to the first example. The fii*st column contains the several courses, the second contains the distance run on each course, the third and fourth are headed N. (for north) and S. (for south), and the fifth and sixth are headed E. (for east) and W. (for west). Find by inspection, the difference of latitude and departure for every course and distance. Proceed in the following manner: If the course does not exceed 4 points, or 45, look for it at the top of the page; but if it exceeds 4 points, or 45, look for it at the bottom of the page. (Table III.) Find the distance in one of the columns (of Table III) marked "Dist.," and take out of the adjoining columns, to the right hand, the numbers in the same line with it. Observe whether the course is found at the top or bottom of the page, and mark the numbers taken out according as they are marked at the part of the page the course is found in. Set the difference .of latitude under N. or S., according as the course is towards the north or south, and the departure xinder E. or W. , according as the course is towards the east or west. Then add the sums up carefully of the columns N., S.,E. and W. Take the difference between the sums of N. and S., which will be the difference of latitude made good, of the same name as the greater. Then as before, take the difference between the sums of E. and W., which will be the departure made good, and to be named the same as the greater. "With the difference of latitude and departure made good, find the course and distance. Look in Table IV, until the difference latitude and departure, or numbers near to them, are found together; take out the course and distance corresponding thereto. 1. A ship sails E. S. E. 14 miles, and then W. N. W. 28 miles; required the course and distance made good. Course. Dist, Diff. Lat. N. S. Den. E. W. SCE NGW 14 28 10.7 5.4 12.9 '25.9 (i 5.4 it ii ii 12.9 5.3 13.0 Difference latitude 5.3, depart- \uc 13.0, give Table iu IV. Course GS'. Distance 14'. PARALLEL SAILING. 19 2. A ship sails N. W. 30 miles, N. N. E. 21 miles, and S. E. 17 miles; required the course and distance made good. Course. Dist. Diff. Lat. Dcp. N. S. E. W. N 4 W N -2 K S 4E 30 21 17 21.2 19.4 12.0 8.0 12.0 21.2 40.6 12.0 12.0 20.0 21.2 20.0 " 28.6 1.2 Difference latitude 28.6 N., departure L 2 W., gives the course N. 2 W. Distance 29 miles. PARALLEL SAILING. To log. secant of the latitude add the log. of the departure, their sum less 10 from the index is the log. of the difference of longi- tude. 1. In latitude G6 40' north. The departure made good was 387 miles. Re- quired the difference of longitude by Parallel Sailing. Secant Latitude 66 40' = 10.402217 Table II. Log Departure 387 = 2.587711 Table I. Difference of longitude 977.1 2.989928 Table I. 2. In latitude 36 17' south. The departure made good was 187 miles. Re- quired the .difference of longitude by parallel sailing. Ans. 232.0 miles. 3. In latitude 63 39' N. The departure made good \vas 8.25 miles. Re- quired the difference of longitude by parallel sailing. Ans. 18'.59. 4. In latitude 53 52'. The departure made good was C.75 miles. Required the difference of longitude by parallel sailing. Ans. 11'. 44* 5. In latitude 54 12' N. The departure made good was 596 miles. Re- quired the difference of longitude by parallel sailing. Ans. 1019'. 6. In latitude 69 11' S. The departure made good was 64.75 miles. Re- quired the difference of longitude by parallel sailing. Ans. 182'. 2. 7. In latitude 43 35' S. The departure made good was 99 miles. Required the difference of longitude by parallel sailing. Ans. 136'. 7. 8. In latitude 66 40' S. The departure made good was 387 miles. Required the difference of longitude by parallel sailing. Ans. 977'. 1. 20 PRACTICAL NAVIGATION. MIDDLE LATITUDE. SAILING. Middle latitude is half the sura of the two latitudes when they are of the same name, or half their difference if of contrary names. Find the difference of latitude by subtracting if they are both north or both south, or adding, if one north and the other south. Then reduce this difference of degrees to miles by multiply ing the degrees by sixty (60) and call it proper difference of latitude. Find the difference of longitude thus: if both east or both west, subtract them; if one is east and the other west, add them, and if their sum exceeds 180 subtract the sum from 360, and the re- mainder will be the difference of longitude. Reduce this difference of degrees to miles in the same way as the latitude and call it difference of longitude. The course must be named the same as the longitude left, when the sum of the longitudes has to be taken from 3GO. In working, proceed as per example. NOTE. The tables for -working out all prjblems by Midlle Latitude, Bailing, are Tables I and II. TO FIND THE DEPARTURE. Find the logarithm of the difference of longitude, Table I of this book, call the index one less than the number of figures in the difference of longitude; find the first thi'ee figures in the left hand column, and opposite to them, and under the fourth figure at head of the column will be the required log., to which prefix the index, and this will give the log. required; and to find the log. co-sine of middle latitude, enter Table II, and with the degrees at the top or bottom of the page, and miles in the column of miles, will be found the log. wanted, the sum of these logs. Subtracting the radius will give the log. of the departure. The index of radius is always 10. TO FIND THE COURSE. Find the log. of the difference of latitude by the same rule as the above, also the log. of the departure; add the log. of departure to the radius, and subtract the log. of the difference of latitude, and this will give, the log. -tangent of the course. To find the tangent look in the column marked tangent at the top or bottom of the page, run up this column until the log. nearest to the given one is found, which will be the tangent of the course in degrees, the miles will be found in column of miles. Having found the course, name it north or south, and east or west, according as you have to make northing or southing, easting or westing, to arrive at the place hound to. MIDDLE LATITUDE SAILING. 21 TO FIND THE DISTANCE. A.ddthe log. of the difference of latitude to the log.-secant of the course, and subtract the radius, the difference will give the log. of the distance in Table I, if the index be 3, the answer will require 4 figures. Look in the column of logs, and find the nearest log., hav- ing done so, you will find the first three figures in the left hand col- umn, and the fourth figure at the top over the column where the log. is found. CASE 1. Ex. 1. Required the course and distance from A. to B. by calculation of mid- dle latitude, sailing principle. The latitude of A. is 51 01' N., and longitude is 122 27' W.; the latitude of B. is 4 22' S., and longitude is 144 W. A. lat.. 51 01' N. B. lat.. 4 22 S. Dif. lat.. 55 23 60 Dif. lat. miles. 3323 51 01' 4 22 2)46 39 23 19' Mid. lat. |Long..l22 27' W. 'Long.. 144 30 W. 22 03 60 1323 Dif. Ion. mis. TO FIND THE DEPABTUBE. Radius 10.000000 TO FIND THE COUBSE. Dif. lat. 33'23 3.521530 TO FIND THE DISTANCE. Rditis Ifl.OOOfOO Dif Ion" 1323 3 121560 Radius 10 000000 Dif. lat 3323 3 5V15;"0 Mid lat. 23 19' Cos 9.962999 Departure 1215 3084559 Course 20 05' . . Sec 10 02745 13.084559 10.000000 3.084559 3.6*158.1 13.548775 10.1'OOOCO Dep. 1215... , 3.034559 C'rsesS.2005 W' tan. 9.5J3029 Distance 3538 3.C48775 Ex. 2. Required the course and distance from A. to B. by calculation on middle latitude, sailing principle. The latitude of A. is 31 01' S. and its longitude 162 10' W. ; the latitude of B. is 38 55' S. and its longitude 152 00' E. Lat. of A.. 31 01' S. Lat. of B..38 55 S. 31 01' 33 55 Long.. 162 10' W. Long.. 152 00 E. Dif. lat 7 54 2)69 56 314 10 00 34 58' Alid lat Dif. lat. miles... 474 TO FIND THE DEPARTURE. Radius 10 000000 TO FIND THE COUBSE. Dif lat 474 2.C75778 45 50 Dif. Ion. 60 2750 Dif. Ion. mis. TO FIND THE DISTANCE. Radius 10.000COO Dif long 2~50 3.439333 Radius 10.000000 Dif. lat. 474 2.C.75778 Hid lat. 34 D 58' Cos.. 9.9135il Dep. 2254 3.362^14 Course 78 07'.... tec. 10.086302 13.352874 10000000 13.352874 2.075778 13.303(40 10.000000 Dep. 2254... . 3.352874 C'rse 8. 78 07' W. tan. 10 C77096 Distance 2302... . 3.3C:ObO 22 PRACTICAL NAVIGATION. Ex. 3. Required the course and distance from a place in the latitude of 36 53' S. and longitude of 20 0' E., to another place in the latitude of 32 38' S. and longitude of 8 54' W. Ans. N. 79 46' W. ; distance, 1447 miles; departure, 1424'. Ex. 4. Required the course and distance from a place in the latitude of 37 55' N. and longitude of 54 23' W., to another place in the latitude of 32 38' N. and longitude of 17 05' W. Ans. Course S. 80 03' E.; distance, 1854 miles; departure, 1827'. CASE II. The Latitude, Course, and Distance being given, to find the Departure, Latitude and Longitude. Ex. 1. A ship from latitude 29 47' N. and longitude 24 36' W., sails S. S. W. 3 W. 960 miles. Required the departure, difference of latitude and longitude. (From compass card, S. S. W. f W. is 30 56'.) TO FIND THE DIFFERENCE OP LATITUDE. As radius 10.000000 Is to distance 9GO 2.982271 So is co-siiie of course 30 56' 9 933369 12.915640 10.000000 Istodif. of lat. 60)823 2.915640 13 43' TO FIND THE LATITUDE IN. Dif. of lat. 823'. . 13 43' 8. Latitude left 29 47 N. Latitude in 16 04 N. Lat. left... 29 47' N. Lat. in.... 16 04 N. Sum of lat 2) 45 51 Mid. lat... 22 55' TO FIND THE DEPARTURE. As radius 10.000000 Is t J distance 900 2.-./82271 So is sine of course 30 56' 9.710997 12693268 10.000000 To the departure 493' .... 2.693268 TO FIND THE DIFFERENCE OF LONGITUDE As co-sine of mid. lat. 22 55' 9.964294 Is to the departure 493 2.693268 Sois radius 10.000000 12.693268 9.964294 To dif . of long. 60)536 2.728974 8 56" Lin. left 24 36' W Dif. long. 8 6 W Long, in 33 32' W Ex. 2. A ship from latitude 2 5' N., longitude 22 30' W., sails W. S. W. 256 leagues; required her present latitude and longitude. Ans. Latitude 2 49' S.; longitude 34 20' W. Ex. 3. A ship from latitude 34 35' N. and longitude 45 16' W.; course S. 83 36 E.; distance 101 miles. Required the latitude and longitude in. Ans. Latitude in 34 24' N.; longitude in 43 15' "W. Ex. 4. A ship from San Francisco in latitude 37 48' N; longitude 122 27' W., sails S. W. 200 miles. Required the latitude and longitude in. Ans. Latitude in 35 27' N.; longitude in 125 23' W. MIDDLE LATITUDE SAILING. 23 CASE III. Both Latitude and Departure from the Meridian being given, to find the Course, Distance and Difference of Longitude. Ex. 1. A ship in latitude 56 50' N., and longitude 20 KX W., sails south-east- erly until she makes '210 miles departure, and her latitude in is 49 15' N. Re- quired the course, distance and longitude in. Latitude left 56 50' N. Latitude in.. .49 15 N. Dif. of latitude .... 7 35 60 455 miles. 56 50' 49 15 Sum. 2)106 05 TO FIND THE COCESE. TO FIXD THE DISTANCE. Dif. latitude 455 2.638011 j Course 24 47' sine. . . 9.022409 Radius lO.oudOOO Dep. 210 2322219 Dtp. 210 2.3J2219 Kadius 10.000000 12.322219 2.658011 Courses. 24 47' E. tan. 9.G6420 12.322219 9.(i224 9 Distance 501 2.C998K) 53 0? Middle latitude. TO FIND THE DIF. OF LONG. Mtd. lat. 53 02 cos. . . 9.7791 r 8 Hep. 210 2.322-19 Kadius 10.0000CO Dif long. 60)349 12.322219 9.77i>128 2.543091 5 49' Long sailed from .. 20 10' W. Dif. long 5 49 E. Longitude in 14 21' W. Ex. 2. A ship in latitude 4 57' N.; longitude 30 10' E., sails south-westerly until her departure is 740 miles, and her latitude in 2 S. Required her course, distance and longitude in. Latitude left 4 57' N. 4 57' N. Latitude in 2 S. Dif. of latitude 6 57' 60 Difference latitude, 417 miles. 2)2 57 1 28' Middle latitude. TO FIND THE COCnSE. Dif.1at417 2.G50130 Radius 10.DOOOOO Departure 740 2.869.'3J 12.8f.9232 2.620136 C'rse S. 60 06' W. tan. 10.249096 TO FIND THE DISTANCE. Course 00 36' sin 9.940125 Departure 740 2.869232 Kadius 10.000000 12.869232 0.940130 Distance 849.... 2.9l>'.'107 TO FIND THE DIF. OF LONGITUDE. Mid. lat. 1 28' cos... 9.999358 Dep. 740 2.809232 Kadius 10 OOOi CO 19.80U2U 9.SI99858 Dif . long. 60) 740 2 .801)374 12 20' W. Long, sailed from . . 80 10' E. Dif . longitude 12 20 W. Longitude in 17 50' E. Ex. 3. A ship in latitude 4957'N., and longitude 15 1C' W., sails south- westerly until her departure is 789 miles, and latitude in is 39 20' N. Re- quired course, distance, longitude in. Ans. Course S. 51 05' W.; distance 1014 miles; longitude in, 33 45' W. 24 PKACTICAL NAVIGATION. CASE IV. Both Latitudes and Course given, to find the Departure, Distance and Difference of Longitude. Ex. 1. A ship from latitude 49 57' N. and longitude 30 00' W., sails S. W. J S. and after sailing several days finds by observation that her latitude is 45 31' N. Required distance sailed and longitude in. Turn the given course into degrees by Compass Table, find tJie departure, distance, and then the difference of longitude. Latitude left 49 57' N. Latitude in.. , . 45 31 N. 4 26 60 2GG miles. 49 57' N. 45 31 N. 2)95 28 47 44' Middle latitude. TO FIND THE DEPARTURE. Radius 10.000COO TO FIND THE DISTANCE. Course 39 Cos ... 9.890503 TO FIND THE DIF. OF LONGITrDE. Mid. lat. 47 44' Cos.. 9.827745 Departure 215 4 . . " :t33->.M Dil'. lat. 260. . 2 4488 Dif. lat. 266 . . . 2 424882 . .tan. 9.9083C9 Radius . .. 10.000000 Radius . lo 0> '1)000 Dep 215 4 ... Distance 342.3.... Dif. Ion. 60)320 5 20' Dif. Ion 12.333251 10.000000 12.424882 9.890503 12.333251 9.827745 . . . 2 333251 . .. 2.534379 2.505506 5 20 7 W. 30 00 W. Long. in... 35= 20' "W. Ex. 2. A ship from latitude 42 25' N, and longitude 15 6' W., sails N. E. by E. for two days and then finds by observation that she is in latitude 46 20' N. ; required the distance she has made and the longitude in. Ans. Departure, 351.7; distance, 423 miles; longitude in 6 54' W. Ex. 3. A ship from Cape Flattery in latitude 48 23' N., longitude 124 22' W., sails until she is in latitude 40 10' N, ; her course is S. W. ^ W. ; find longitude in and distance made. Ans. Longitude in, 138" 21' W. ; distance, 777 miles. Ex. 4. A ship from Cape Mendocino in latitude 40 29' N., longitude 124 29' W., sails S. W. by W. until she is in latitude 34 18' N.j required distance and longitude in. Ans. Distance, 668; longitude in, 136 08' W. MIDDLE LATITUDE SAILING. 25 CASE V. Both . Latitudes and Distance given, to find the Course and Differ- ence of Longitude. Ex. 1. A ship sails from latitude G 50' N., south-easterly 800 miles, when she arrives in latitude 5 00' S. Required her course and difference of longitude. Latitude left G 50' N. Half 3 25 Latitude in 5 00 S. Half 2 30 11 50' x 60 710 miles. TO FIKD THE COURSE. As the distance 800 2.903000 Is to radius 10.000000 So is dif . of lat. 710 2.8ol258 12.8ol2o8 2.903060 To co-sine of course S. 27 2G' E 9.94S1G3 2)5 55 2 J 57' Middle latitude. TO FIND THE DIFFERENCE OFLOXGITUEE. As co-sine mid. lat. 2 3 57' 9.999424 Is to taug. of course 27 26' 9.71.VJ42 So is dif. lat. 710 2.8ol258 13JMMOO 9.G091-J4 Difference of longitude 3CU 2.56707 S Ex. 2. A ship from latitude 5G 30' N. 1ms sailed south-easterly 257 miles, when she arrives in latitude 54 47' N. Required the course and difference of longitude. Ans. Course S. GG 22' E. ; difference of longitude 417 miles. Ex. 3. A ship sails from the latitude of 3 20' N. and longitude 29 37' W., 960 miles south-westerly, and then by observation finds that her latitude is 10 C 40' S. Required the course and longitude in. Ans. Course S. 29 03' \V. ; longitude in 37 24' W. Ex. 4. A ship sails from Santa Clara in latitude 3 14' S. north-westerly 300 miles, until it is found by observation that she is on the equator. Required the course and difference of longitude. Ans. Course N. 49 43' W.; difference of longitude 3 49' W. CASE VI. One Latitude, Course and Departure given, to find the Distance and Difference of Latitude and Difference of Longitude. Ex. 1. A ship sails E. S. E. from latitude 50 10' S. and longitude 30 W E. until her dcpariure is 957 miles; required distance sailed, and latitude and long- itude in. (Prom Compass Table the course E. S. E. is C7 30'.) FIRST: TO FIND THE DIF. OF LATITUDE. AH sine of course GT J 30' 9.965fl5 Is t > departure 937 2.980912 8ECO Lat. Dif. Lat. \D : TO FIKD LAT. IN. left 5010'S. of lat 6 36 S. Lat. left... Lat. in.... Sum Miiiulelat. . 50 10' S. . 66 46 S. bo id co-siue of course 07 30' To dif. of latitude, 60)390.4. . . . 6= 3G' 9.582840 12.563752 9.9G5615 in. .. . . . 5C 4G' S. .2) 106 56' . 53 28' 2.598137 THIRD: TO FIND THE DISTANCE. As sine of courso G7 3 30' 9.96."G15 Is to the 'departure 957' 2.080912 So is radius 10.000000 To the distance 103C. 12.980912 9.9G5(.15 3.015297 FOURTH: TO FIKD DIFFERENCE or LONGITUDE. As co-sine mid. lat. 53 28' 9774720 Is to the departure 957' 2.9801H2 So is radius 10.000000 To dif . of lo.n, 60)1608 3.20G183 26 4S' E. Longitude left 3000'E. Difference of longitude 2G 48 E. Longitude in 5648'E. 26 PRACTICAL NAVIGATION. Ex. 2. A ship sails S. S. W. from latitude 51 15'N., and longitude 9 50" W., until her departure is 250 miles. Required the distance sailed and the latitude and longitude in. Ans. Latitude in, 41 12 N.; longitude in, 15 51' W. ; distance, G53.3 Ex. 3. A ship from latitude 38 40' S., and longitude, 1 15' W., sails N. E. E. until her departure is 250 miles. Required the latitude and longitude in. Ans. Latitude in, 35 14' S.; longitude in, 3 57' E. ; distance, 324 miles. Ex. 4. A ship from latitude 30 15' S., longitude, 178 10' E., sails on a course N. 4 points E. until her departure is 150 miles. Required the distance sailed aud longitude and latitude in. Ans. Distance sailed, 212 miles: latitude in, 27 45' S., and longitude, 178 3 58' W. CASE VII. One Latitude, Distance, and Departure given, to find the Course, Dif- ference of Latitude, and Difference of Longitude. Ex. 1. A ship from latitude 49 30' N. aud longitude 25 00' W., sails south- easterly G45 miles until her departure is 500 miles. Required the course steered, and her latitude and longitude in. FIKST: TO FIND THE CODBSE. As di Stan- e 645 miles 2.809560 Is to radius . lOOOOnOO SECOND: TO FIND DIF. OF LATITUDE. As radius lO.OOuOOO Is to distance Gi5 2.8uy?(iO THIBD: LAT. ix AND MID. LAT. Lat. left. 49 30' N. So is departure 500 2 GH8970 bo is co-siue of c'rse 59 D 49' 9.800J8J Oil', of lat G 43 S. 12.C98970 'A8095oO 12.G10142 10.000000 Lat. in... 42 42 N. Sum.. i!)9'2 12 Hid lat iG C To Bine of c'rse S. 50 49' E. 9.889410 C 48' S. FOTJETH: TO FIND DIFFEBENCE OF LONGITUDE. As co-sine mid. lat. 40 00 9.8J0985 Is to departure 50u miles 2. 98970 So is radius 10.000000 12.698970 9.840985 To difference of longitude 60) 721 2.857985 12 01' E. FIFTH: TO FIND THE LONGITUDE IN. Longitude left 15=00' W. Difference of longitude 1201 E. Longitude in 12 C9' W. Ex. 2. A ship from latitude 54 N. and longitude 33 20' "W., sails 350 miles between north and cast, until she has made 220 miles of departure. Required the course, and latitude and longitude in. Ans. Course, N. 38 57' E. ; latitude hi, 58 32' N.; and longitude, 26 44' W. Ex. 3. A ship from latitude 23 50' N.; longitude 23 30' W., sails between the south and west, 375 miles, until her departure is 200 miles. Required the course, latitude and longitude in. Ans. Course, S. 32 14' W.; latitude in, 18 33' K; longitude iu, 27 05' W. MIDDLE LATITUDE SAILING. 27 CASE VIII. One Latitude, Departure, and Difference of Longitude given, to find Ike other Latitude, Course and Distance. Ex. 1. A ship from latitude 37 00' N., sails south-westerly xintil she has made 483 miles of departure, and 565 miles difference of longitude. Required her present latitude, course steered, and distance run. TO FISD THE MIDDLE LATITUDE. Asdif. of longitude 505 2.752048 I.s to radius ID 000000 Bo is departure 483 2.G83U47 12.CS3947 2.752018 Toco-sine inid. lat. 31 15' 9.931899 TO FIND THE COUBSE. As difference of latitude C9J' 2.818S49 1-itoru.dius li).0ii!0p So is departure 483 2.G3. 1 'J47 Middle latitude 31 15' Double middle latitude C2 30 Latitude left . 37 00 X. Latitude in.., .. 25 CON. 2.838849 To tang, course 34 59'. 9.845038 Diff. of latitude 11 30' =690 TO FDfD THE DISTANCE. As radiu 10.000COO Id to difference latitude 090 2.83*849 So is B.C. course 34 &D' 10.U8G547 12.925396 10.000000 To the distance 842. .. . . .2.9253U6 Ex. 2. A ship sails from latitude 49 30' N., south-easterly until her departure is 1G7 miles, and difference of longiturc is 252 miles. Required present latitude, course steered, and distance. Ans. Latitude in, 47 30' N. ; course, S. 54 18' E. ; distance, 205 miles. Ex. 3. A chip sails horn latitude 50 10' S., between the south and cast until her departure is ICO miles, and her difference of longi.ude 253 miles. Required her present latitude, course and distance. Ans. Latitude in, 51 1C' S.; course, E, S. E.; distance, 175.2 miles. GENEHAL RULES TABLES III AND IV. Solutions of the different cases by Inspection. If seeking a course which is under 45 it will be found at the top of the pages, but if it is over 45 it will be found at the bottom of the pages. If the departure, or difference of latitude, or distance, are too great to be found in the tables, divide them by 10 or by 100, and then multiply the quantities found (not the course or middle latitude) by the same number you used in dividing. To find the difference of longitude, use either of these two methods. (In look- ing in the table use the nearest number and nearest angle.) With the middle latitude as a course, and the departure in the latitude column, the difference of longitude will be found in the distance column. Or with the co-middle latitude (00 lat.) as a course, and with the difference of latitude in its own column, or the departure in its own column, will be found the difference of longitude in the distance column. CASE 1. Look for the middle latitude 23 as if it were a course. 28 PEACTICAL NAVIGATION. and for 132.3 (one-tenth the difference of longitude) in the distance column, opposite to which in the difference of latitude column -will be found 121.5 which being multiplied by 10, gives 1215 the depart- ure. "With 12.15 (one hundredth the departure) in the departure column and 33.23 (one hundredth of the difference of latitude) in the latitude column, will be found at the top of the page 20 the course; and 35.00 in the distance column, which being multiplied by 100, gives 3500 the distance. This can be also solved by taking the co-middle latitude (90 23') G7 as a course and the difference of longitude in the distance column will be found the departure in the departure column. Then proceed as before. CASE 2. Look for the course 31 at the top of the page, and 96.0 (one-tenth the distance) in its column opposite to the distance, in their columns will be the difference of latitude 822 and the de- parture 494. Then with the middle latitude 23 as a course, and the departure 49.4 (one-tenth) in the difference of latitude column, will be found 54.0 in the distance column; this multiplied by 10, gives the difference of longitude, 540. CASE 3. Look in the departure and latitude columns until they are found nearly to agree, 45.3 and 21.1; the course is found at the top of the page, it is 25. The distance, 50, is opposite in its col- umn; this multiplied by 10, gives the correct distance, 500. With the middle latitude 53 as a course, and one-tenth the departure in the latitude column, 35 is found in the distance column; this multi- plied by 10, gives 350, the difference of Jongitude. CASE 4. With the course 39, and one-tenth the difference of lati- tude, 2G.G in its column, in the departure column will be found 21.4, and in the distance column 34; these multiplied by 10, give the de- parture 214 and the distance 340. Then with the middle latitude, 48 as a course, and with 21.4 in the latitude column, 32 will be found in the distance column ; this multiplied by 10, gives 320 for difference of longitude. CASE 5. With one-tenth the distance, 80, and one-tenth the dif- ference of latitude, 71, in their columns at the top of the page, the course 27 will be found. Then with the middle latitude 1 (nearly) as a course, and the departure 36.3 in the latitude column, the dif- ference of longitude, 36.3, (one-tenth) will be opposite in the dis- tance column. CASE 6. Find the course 67, and one-tenth the departure, 95.7 in its column, these will be in the latitude and distance columns, 104 and 40.6, but as this course is 67 30', take half the sum columns of 67 and those of 68; this will give the correct difference of lati- MIDDLE LATITUDE SAILING. 29 tucle 39G, (39. G multiplied by 10) and the correct distance 1035, (103.5 x 10), then with the middle latitude as course, and depart- ure in latitude column, the difference of longitude 1590 will be found in the distance column. CASE 7. "With one-tenth the distance and departure, 64.5; 50, agreeing in their columns, the course, 51, will be found, and at the same time the difference of latitude 408 (40.8 x 10) in its column. Then with the middle latitude 46 as a course, and the departure 50 (one-tenth) in the latitude column, one-tenth of the difference of longitude will be found in the distance column 720, (72 x 10). CASE 8. "With one-tenth the difference of longitude, 56.5 in the distance column, and one-tenth the departure, 48.3 in the latitude column agreeing, will be found the middle latitude 31, at the top of the page. Then with the difference of latitude in its column, and the departure in its columns will be found the course, 35, at the top of the page, and the distance 850 in the distance column. LOGAEITHMIC SINES, TANGENTS AND SECANTS. This table contains the logarithmic, or, the artificial sines, tan- gents and secants, to each degree and minute of the quadrant, with their complements or co-sines, co-tangents and co-secants, to six places of figures, besides the index; but it may be observed, as of the last table, that five places being generally sufficient in the com- mon practice of navigation, when the sixth is omitted, and it is five or above, the preceding or fifth figure is to be increased by a unit. To find the Logarithmic Sine, Co-sine, etc., of any given Arc in Degrees and Minutes. If the given degrees be under 45, they are to be taken from the top, and the minutes from the left side column; opposite to which, in that column with the name of the logarithm at top, will be found the required logarithm. But if the degrees be more than 45, they will be found at the bottom of the page, and the minutes in the right-side column; like- wise the name of the logarithm is to be taken from the bottom of the page. "When the given degrees exceed 90, they are to be subtracted from 180 degrees, and the logarithm of the remainder taken out as be- fore, or the logarithmic sine, tangent, etc., of an arc more than 90 is the logarithmic co-sine, co-tangent, etc., of its excess above 90. 30 PRACTICAL NAVIGATION. To find the Arc in Degrees and Minutes nearest corresponding to a given Logarithmic Sine, Co-sine, etc. Look in the column marked at the top or bottom with the name of the given logarithm, and, when the nearest to it is found, the corresponding degrees and minutes will be those required; observ- ing, that when the name is at the top of the column, the degrees are to be taken from the top, and the minutes from the left-side col- umn; but, if the name be at the bottom, the corresponding degrees will be there likewise, and the minutes in the right-side column. MERCATOR'S SAILING. CASE 1. To find the Course and Distance by Mercator's Sailing. To this sailing apply the same rules as in middle latitude sail- ing, for finding difference of latitude and difference of longitude. To get the meridional difference of latitude enter Table V, with degrees sought at top of column, and miles in the left-hand side marked miles, and opposite miles and under degrees will be found the meridional number required. Having taken out the meridional parts for both latitudes, add or subtract them in the same manner as adding or subtracting to find the true" difference of latitude, and the sum or difference will give the meridional difference of latitude. Then proceed as per ex- ample. NOTE. Tables required for working Mercator's Sailing. Tables I, II, and V. The Latitudes and Longitudes of Tico Places given-, to find the Course and Distance between them. Ex. 1. Required the course and distance from Buena Vista to Rio Janeiro. Latitude Buena Vista 15 U 57' N. Latitude Rio Janeiro 22 54 S. Longitude 22 53' W. Longitude 43 16 W. Lat. Buena Vista 15 57' N. Lat. Ilio Janeiro 22 54 S. Diff. Latitude 38 51 CO In miles 2331 Meridional parts. . 970 Meridional parts. . 1412 Mcr. Diff. Lat. . . . 2382 Long. Bucna Vista 22o3'W Long, liio Janeiro 43 1C W Diff. Lon; 2023 60 In miles. 1223 TO FIND THE COURSE. As mer. diff. lat. 2382 3.376942 Is to radius. 10.000000 So is diff. long. 1223 3.087426 13.087426 3.376 1 J42 To tang, course S 27 11' W 9.7104S4 TO FIND THE DISTANCE. As radius 10.000CCO Is to prop. diff. lat. 2331 . .. 3.367542 So is secant course 27 11'. . 10.050830 13.418372 10.000000 To distance 2620. MEBCATOR 3 SAILING. 31 Ex. 2. Required the course and distance from A. to B. Lat. of A 50 30' S. Lat. of B 4S 20 S. 2 10 x 60 In miles 130 Meridional part 3521 i Longitude ... 147 50' W. Meridional part 3322 Mer. dif. of lat 199 TO FIND THE COURSE. As mer. dif. of lat, 199 2.298853 Is to radius 10.000000 So is dif. of long. 4392 3. 642662 13.642662 2.298853 Longitude. . . 138 58 E. 286 48 360 90 73 12 x 60 In miles 4392 TO FIND THE DISTANCE. As radius 10.000000 Is to prop. dif. of lat. 130. . . 2. 1 13043 So is secant of course. 87 24' 11.34329S 13.457241 10.000000 To tang, of course N 87 24' W 1 1. 343809 To the distance 2866 3.457241 Ex. 3. Required the course (in degrees and miles) and distance from A. to B. Latitude of A .... 55 22' N Longitude .... 7" 24' \V. Latitude of B 49 40 N Longitude 53 54 W. Aiis. CourseS. 78 35' W.j distance 172S. Ex. 4. Required the course (in degrees and miles) and distance from A. to B. Latitude of A 44 44' N Longitude 63 36' W. Latitude of B 33 07 S Longitude.... 17 58 E. Ans. CourseS. 43" 44' E.; distance 64G4. Ex. 5. Required the course (in degrees and miles) and distance from C to D. Latitude of C 54 32' S Longitude 36 J 12' W. Latitude of D .... 38 54 S Longitude.... 143 40 E. Ans. Course N. 82 42' E.; distance 7382. CASE II. One Latitude, Course and Distance given, to find the difference of Lat- ilu.de and difference of Longitude. Ex. 1. A ship from latitude 52 06' N. and longitude 35 06' W., sails N. W. by W. (56 15') 229 miles. Required the latitude and longitude in. TO FIND THE DIFFERENCE OF LAT. As radius 10.000000 Is to distance 229 2. 359835 So is co-siue of course 56 15' 9.744739 12. 104574 10.000000 To dif. of lat. 60)127.2 2.104574 2 07 TO FIND THE DIFFERENCE OF LONG. As radius 10.000000 Is to mer. dif. of lat. 212 2.32;>36 So is tang, of course 56 15' 10.175107 12.501443 10.000000 To dif. of long. 60)317.3. ... 2.501443 5 ' 17' TO FIND THE LATITUDE IN. Lat. left 52 l 06' N. . . .Mer. pts. 3675 Dif. of lat 2 7 N. Lat. in... 54 13' N....Mcr. pts. 3S87 Mer dif of lat. 212 TO FIND THE LONGITUDE IN. Longitude left 35 06' W. Dif. of long.. 5 17 W. Longitude in . . , . 40 J 23' W. 32 PRACTICAL NAVIGATION. Ex. 2. A ship from latitude 42 30' N. and longitude 58 51 W., sails S. W. by S. 591 miles. Required the latitude and longitude in. Ans. Latitude 34 19' N. ; longitude 65 51' W. CASE III. Both Latitudes and Departure given, to find the Course, Distance and Difference of Longitude. A ship from latitude 9 10' N. and longitude 19 32' W., sails in the S. E. quar- ter until she has made 415 miles of departure, and is by observation in latitude 2 19' S. Required her course, steered, distance run, and longitude in. NOTE. Find first proper difference of latitude, meridional difference of latitude, course, dis- tance, difference of longitude and longitude in. Latitude left 9 10' N Mer. parts 552. Latitude in 2 19 S Mer. parts 139. 11 29' X 60 In miles G89 Mer. dif. of lat. 691. TO FIND THE COUESE. As dif. of lat. 689 2.838219 Is to radius 10.000000 So is departure 415 2.618048 12.618048 2.838219 To tan", of course S. 31 04' E 9.779829 TO FIND THE DISTANCE. As sine of course 31 04' 9.712679 Is to departure 415 2.C18048 So radius 10.000000 12.618048 9.712679 To the distance 804. 2 . . 2. 905369 TO FIND THE DIFFERENCE OF LONG. As radius 10.000000 Is to mer. clif. of lat. 691 .... 2.839478 So is tang, of course 31 04'.. 9.779818 12.619296 10.000000 To dif. of long. 60)416.2 E. 2.619296 6 56' E. TO FIND THE LONGITUDE IN. Longitude left 19 32' W. Dif. of longitude 416' 656 E. Longitude in 12 3G' W. Ex. 2. A ship from latitude 49 57' N. and longitude 15 16' W., sails south- westerly until her departure is 789 miles, and is in by observation, latitude 39 20' N. Required her course, distance and longitude in. Ans. Course S. 51 05' W. ; longitude in 33 50' W.; distance 1014 miles. Ex. 3. A ship from latitude 49 57' N. and longitude 5 11' W., sails between the sou tli and west until she arrives in latitude 38 27' N., and finds she has made 440 miles of departure. Required the course she has steered, distance run and longitude the ship is in. Ans. Course S. 32 3 31' W.; distance 818.5 miles; longitude in 15 27' W, MERCATOR'S SAILING. 33 CASE IV. Both Latitudes and Course given, to find the distance and Difference of Longitude. Ex. 1. A ship from latitude 49 57' N. and longitude 30 00' W., sails S. W. * S. for several days, and then finds by observation that she is in latitude 45 31' N. Required the distance she has made and her present longitude. NOTE. First find proper difference of latitude, meridional difference of latitude, distance, difference of longitude and longitude in. Latitude left 49 57' N . Latitude in . . . 45 31 N . In miles 4 26' 60 266 TO FIND THE DISTANCE. As co-sine of course 39 22' . . 9. 888237 Is to dif. of lat. 266 2.424882 So is radius 10.000000 12.424882 9.888237 To the distance 344. 1 2.536645 Mer. parts 3470. Mer. parts 3074. 396 TO FIND DIFFERENCE OF LONGITUDE. As radius 10.000000 Is to mer. dif. of lat. 396 2.597695 So is tang, of course 39 22'. . 9. 914044 12.511739 10.000000 To dif. of long. 60)324.9. . . . 2.511739 5 24' Longitude left 30 00' W. Difference of longitude 5 24 W. Longitude in 35 U 24' W. Ex. 2. A ship from latitude 42 40' N. and longitude 16 20' W., sails N. E., and then finds by observation that she is in latitude 50 50' N. Required the distance sailed, and present longitude. Ans. Distance, 693 miles; longitude in, 4 23' W. Ex. 3. A ship from latitude 30 IV N. and longitude 5 10' E., sails S. by E., and then finds by sun's observation that she is in latitude 42 25' S. Required the distance sailed and longitude in. Ans. Distance, 1440 miles; longitude in, 20 48' E. Ex. 4. A ship from latitude 42 25' N. and longitude 15 06' W., sails N. E. 'by E., and finds by observation that she is in latitude 46 20' N. Required the distance sailed, and longitude in. Ans. Distance, 423 miles; longitude in, 6 54' W. PKAC. NAV. 3 PRACTICAL NAVIGATION. CASE V. Both Latitudes and Distance given, to find the Course and Difference of Longitude. Ex. 1. A ship from latitude 50 30' N. has sailed south-easterly 300 miles, when she arrives at latitude 45 40' N. Required her course steered, and differ- ence of longitude. NOTE. First find proper difference of latitude, meridional difference of latitude, course, and difference of longitude. Latitude left 50 & 30' N. Latitude in 45 40 N. 4 50' x 60 In miles.. 290 Meridional parts 3521 Meridional parts 3087 Mer. diff. of lat.. 434 TO FIND THE COURSE. As the distance, 300 2.477121 Is to radius 10.000000 . So is dif. of lat., 290 1.462398 12.462398 2.477121 To co-sine of course 14 50'. . 9.985277 TO FIND DIFFERENCE OF LONGITUDE. As co-sine of course, 14 50' . 9.985280 Is to mer. dif. of lat., 434. .. 2.637490 So is sine course, 14 50' 9.408254 12.045744 9.985280 To dif. of long., 114.9 2.060464 Ex. 2. A ship from latitude 36 20' N., and longitude 22 30' W., sails S. by W. 960 miles and finds her latitude is 10 40' S. Required the course and longi- tude in. Ans. 4 S. 28 57' W., and longitude in, 30 17' W. Ex. 3. A ship from latitude 56 30' N. has sailed south-easterly 257 miles, when she arrives at latitude 54 47' N. Required the course steered, and differ- ence of longitude. Ans. Course, S. 66 22' E.; difference of longitude, 418.2. MEECATOR 8 SAILING. 35 r CASE VI. One Latitude, Course, and Departure given, to find the Distance, Difference of Latitude and Difference of Longitude. Ex. 1. A ship from latitude 50 10' S., and longitude 30 00' E., sails E. S. E., until her departure is 957 miles. Required the distance sailed and her present latitude and longitude. NOTE. First find the difference of latitude, latitude in, and meridional difference of latitude, the distance and difference of longitude. TO FIND DIFFERENCE OF LATITUDE. As sine of course 67 30' .... 9.9(55615 Is to departure 957' 2.980912 So is co-sine of course 67 30' 9.582840 12.563752 9.965615 To dif. of lat. 60)396.4 6 3 36' S. Lat. left.. Dif. of lat. Lat. in. . 2.598137 50 10' S. 6 36 S. 56 46' S. TO FIND THE DISTANCE. As sine of course 67 30' 9.965615 Is to departure 957' 2.980912 So is radius 10.000000 12.980912 9.965615 To the distance 1036 3.015297 Mer. dif. of lat.. 3490 Mer. dif. of lat.. 4157 Mer. dif. of lat.. 667 TO FIND DIFFERENCE OF LONGITUDE. Longitude left: 30 00' E. Difference of longitude 26 50 E. Longitude in 56 50' E. As co-sine of course 67 30'. . 9.582840 Is to mer. dif. of lat. 667 2.824126 So is sine of course 67 30'. . . 9.965615 12.789741 9.582840 To dif. of long. 60)1610 3.206901 26 50' Ex. 2. A ship from latitude 51 15' N., and longitude 9 50' W., sails S. S. W. until her departure is 250 miles. Required the distance sailed, and latitude and longitude in. Ans. Latitude in, 41 11' N.; longitude in, 15 53' W., and distance 653.3 miles. Ex. 3. A ship from latitude 40 20' S., and longitude 20 40' E., sails N. N. E. until her departure is 500 miles. Required the distance sailed, and latitude and longitude in. Ans. Latitude in, 28 13' S.; distance, 1307 miles; longitude in, 30 24' E. 36 PRACTICAL NAVIGATION. CASE VII. On Latitude, Distance, and Departure given, to find the course, Differ- ence of Latitude, and Difference of Longitude. Ex. 1. A ship from latitude 54 N. and longitude 33 20' W., sails 350 miles "between north and east, until she has made 220 miles of departure. Required the course steered, and her present latitude and longitude. NOTE. First find the course, difference of latitude, latitude in and meridional difference of latitude, difference of longitude and longitude in. TO FIND THE COURSE. As the distance 350 2.544068 Is to radius 10.000000 So is departure 220. 2.342423 12.342423 2.544068 To sine course 38 57' 9.798355 TO FIND DIFFERENCE OF LATITUDE. As radius 10.000000 Is to distance 350 2. 544088 So is co-sine course 38 57'. . 9.890809 12.434877 10.000000 To difference latitude 272. 2 . 2. 434877 Lat. left 54 00' N. Mer. parts. . 3865 Dif, lat. 4 32 N. Lat. in 58 32' N. Mer. parts.. 4355 Mer. dif. lat. 490 Long, left 38 20' W. Dif. long. 6 36 E. Long, in 26 44' W. TO FIND DIFFERENCE OF LONGITUDE. As co-sine course 38 57 9. 890809 Is to mer. dif. lat. 490 2.690196 So is sine course 38 57' ..... 9. 798403 12.488597 9.890809 To dif. long. 396. 1 2. 597790 Ex. 2. A ship in latitude 49 30' N. and longitude 25 W., sails south-easterly 215 miles, making 167 miles departure. Required the course steered, and lati- tude and longitude in. Ans. Course, 50 58'; latitude in 47 15' N. ; longitude in 20 50' W. Ex. 3. A ship in latitude 49 30' N. and longitude 25" 00' W., sails south-east- erly 645 miles, making 500 miles departure. Required the course steered, and latitude and longitude in. Ans. Course, S. 50 49' E.; latitude in. 42 42' N.; longitude in, 12 57' W. MERCATOR'S SAILING. 37 CASE VIII. One Latitude, Course and Difference of Longitude given, to find the Distance and Difference of Latitude. NOTE. This case cannot be solved by middle latitude sailing. Ex. 1. A ship from latitude 34 29' N., sails S. 41 W., until the difference of longitude is 680 miles. Required latitude in and distance sailed. NOTE.- First find meridional difference of latitude, then latitude in, and difference of lati- tude in miles, then the distance. TO FIND MEE. DIF. OF LATITUDE. As radius 10.000000 Is to dif . long. 680 2.832509 So is co-tang, course 41 10.060837 12.893346 10.000000 To mer. dif. lat. 782.3 2.893346 Lat. left 34 29' N. Mer. parts 2207 Mer. dif. lat 782 Lat. in.. 23 06 N. Mer. parts 1425 Dif. lat. 11 23 60 In miles 683 TO FIND THE DISTANCE. As co-sine course 41 9.877780 Is to dif. lat. 683 2.834421 So is radius.. . 10.000000 12.834421 9.877780 To the distance 905'.. . 2.956641 Ex. 2. A ship from latitude 50 40' S., sails N. 50 00' E., until her difference of longitude is 550 miles. Required the latitude in and distance sailed. Ans. Latitude in, 45 32' S. ; difference of latitude in miles 308; distance 479. 2 miles. 38 PBACTICAL NAVIGATION. MERCATOR'S SAILING. Solutions of the Cases by Inspection. CASE I. Find the course from the tables by using the meridional difference of latitude, and difference of longitude, as difference of latitude and departure. Thus, with 23.8 in the latitude column, and 12.23 in the departure, 27 as a course will be found at the top of the page. With 27 as a course and the proper difference of lat- itude 23.31 (one hundredth) gives in the distance column 26, which multiplied by 100, gives 2600 as distance. CASE II. With the course three points at the top of the page and opposite the distance 59.1 (one-tenth) will be found the difference of latitude 49.1, which multiplied by 10, gives 491. Then with the same course and the meridional difference of latitude 628 in the lat- itude column, will be found the corresponding difference of longi- tude 42.0, which multiplied by 10, gives as difference of longitude 420. CASE III. With the proper difference of latitude 68.9 (one-tenth) and departure 41.5 (one-tenth) in their proper columns, find the course 31 at the top of the page, and the distance 800 in the dis- tance column. Then, with this course 31, and the meridional dif- ference of latitude in the latitude column, the difference of long- itude will be found in the departure column 41.4, multiplied by 10, gives 414. CASE IV. Find the course S. W. J S. among the points or de- grees, and the proper difference of latitude 26.6, adjoining to which will be the distance 340 and departure 21.4 in their respective col- umns. Then, in the same table, find the meridional difference of latitude 396 in the latitude column, stands 321, in the departure col- umn, which is the difference of longitude. CASE. V. Look in table IV until 30.0, one-tenth the distance, is found opposite 29.0, one-tenth the difference of latitude, in their columns. The course 15 is found at the top of the page, and the departure 78 (78x10) in the departure column. W T ith 43.4, one- tenth the meridional difference of latitude in the latitude column, and the course 15, the difference of longitude 116 (11.6x10) will be found in the departure column. CASE VI. Find the course 6 points at the bottom of the page, and the departure 96.7 (one-tenth) in its column, corresponding in their columns will be found the distance 1040 (104.0x10), and the difference of latitude 398 (39.8x10.) With the same course and the meridional difference of latitude 66.7 (one-tenth) in the latitude column, opposite in the departure column will be found the differ- ence of longitude 1608 (160.8x10). DEVIATION OF THE COMPASS. 39 CASE VII. Look in the tables until the distance 35.0 (one-tenth) and the departure 22.0 (one-tenth) are found in their columns to nearly agree (if not to agree), opposite to them in the latitude col- umn \vill be found the difference of latitude 2720 (27. 20x10) and the course 39 at the top of the page. With this course and one- tenth the meridional difference of latitude 49.0 in the latitude column, 39. G will be found adjoining in the departure column, this multi- plied by 10, will give 396, the difference of longitude. CASE VIII. With the course 41 at the top of the page, and the difference of longitude 68.0 (one-tenth) in the departure column, the meridional difference of latitude 785 will be found in the latitude column. Then with the difference of latitude 683 in its column, the distance 910 will be found in the distance column. DEVIATION OF THE COMPASS. Deviation of the compass is caused by the attraction of the iron in and on board the ship, such as her equipment, or cargo, etc. It depends, both for its amount and direction, on the position of the ship's head; it is named easterly when the north end of the needle is drawn, by the attraction of the ship's iron, to the right of the cor- rect magnetic north, westerly when the north end of the needle is drawn to the left of the correct magnetic north. Method for finding the Deviation. Every ship ought to be provided with a good Azimuth Compass, which should be placed on the mid-ship line of the poop, or quarter deck, and as far as possible from all iron, and in such a position as to allow the bearings to be clearly observed. This is called the Standard Compass, and by it all bearings should be taken, and the Binnacle Compass frequently compared with it. When the ship is ready to proceed on a voyage, the deviation of the Standard Com- pass is to be ascertained by one of the following methods: First method. By the known correct magnetic bearing of a dis- tant object. Select an object, the correct magnetic bearing of which is known, and at not less than six or seven miles distant, if the ship be lying in a roadstead; but if in a dock a less distance will suffice, and swinging the ship's head very evenly, take the bearing of the object by the Standard Compass as the ship's head comes up to each point in succession, and the difference between the known and observed bearing will be the amount of deviation on each point of compass. (See table 1 for finding the deviation.) 40 PRACTICAL NAVIGATION. The second method is fully explained in Table I (deviation card) with this difference only, that the correct magnetic bearing not hav- ing been given, it has to be found by taking the mean of the bear- ings of the distant object; this method of determining the devia- tion is sufficiently correct for practical purposes, but bear in mind that there is no such thing as an accurate "flying" bearing, and therefore it is preferable to swing the ship for adjustment while in a dock, or at anchor in a tide-way; and now to determine when the deviation is easterly or westerly. Kule : when the correct magnetic bearing of the distant object is to the right of the reading by com- pass on board, the deviation is east, and when to the left the devia- tion is west. Thus, the rule is precisely the same as that for finding the varia- tion of the compass from an Azimuth, or Amplitude, substituting correct magnetic for true bearing. The rule for applying the devi- ation is the same as that for applying the variation, ^that is, easterly to the right-hand and westerly to the left-hand. "When the deviation is to be added to the compass course to find the correct magnetic course made good, if the sum exceeds 90 de- grees take it from 180 degrees, and the remainder will be named N. if previously S., but S. if previously N. ; see example worked out- Course by Standard Compass N. N. E. or N 22 30' E. Deviation by Standard Compass 20 20 E. Correct magnetic course made good N 42 50' E. or N. E. J N. Course by Standard Compass E. by N. or N. 78 45' E. Deviation by Standard Compass 13 50 E. N. 92 35 E. 180 00 Correct magnetic course made good S 87 25' E. or E. J S. When the deviation is subtractive, and it exceeds the course, sub- tract the course from the deviation, and name the remainder East if the course is West; but West when the course is East. Course by Standard Compass S. W. by S. or S . . 33 45' W. Deviation of Standard Compass 14 00 W. Correct magnetic course made good 19 45' W. or S. by W. f W. Course by Standard Compass N. by W. or N. 11 15' W. Deviation by Standard Compass 14 00 E. N. IFIF E. or N. J E. VARIATION. 41 VARIATION. Next in order comes variation. "We will say but little on the sub- ject, as it is well understood by most seamen. Variation is the angle which the direction of the horizontal magnetic needle, when un- affected by deviaton, makes with the geographical meridian, and is named easterly when the magnetic north is to the right of the true north, and westerly when the magnetic north is to the left of the true north; and to know how to apply it, suppose yourself placed at the centre of the compass and looking directly forward to the point you are to allow the variation from, then, if the variation, is easterly, allow it to the right-hand of the course steered; but, if westerly, to the left-hand. Precisely the same as deviation. To fmd the True Course made good, with the Deviation on the Course steered, and the Variation proper to the locality. If the deviation and variation are of the same name, take their sum; but, if one is east and the other west, take their difference and give the remainder the name of the greater quantity. Apply this sum or difference to the course steered, easterly to the right-hand, westerly to the left. (See example.) Ex.1. Course steered W. S. W. or S. 67 30' W. Deviation 15 (X, W. Correction 31 30 W. Var. per chart. . 16 30 W. True course S. 36 00' W. Correction (sum) 31 J 30' W. Ex. 2. Course steered N. E. or N 45 00' E. Deviation 22 00' E. Correction 2 40 E. Var. per chart. . 18 00 W. True course N. 47 40' E. Correction (dif. ) . 4 00 E. The True Course given to find the Compass Course to steer, knowing the Variation and Deviation. The variation and deviation must be used separately; first, apply the variation to the true course to ascertain the correct magnetic course, and then find (from the deviation table) what compass course will make that correct magnetic. The only exception to this method is when the variation and de- viation are numerically the same, but have different names, in which case the one cancels the other, and the compass .course is the true course. In shaping the course to steer, having given the true course, deviation and variation, apply them in the opposite way to which they were applied in finding the true course from the com- pass, that is easterly to the left, and westerly to the right. Suppose the true course to be S. 40' W., with a correction of de- viation 5 00' E. and the variation 20 00' W. Subtract the east- 42 PRACTICAL NAVIGATION. erly deviation from westerly variation and the net result will be 15 00' W. to apply to tlie right hand, that will give the magnetic course to steer S. 55 00' W. or S. "VV. by W. First. A true course is the angle between the geographical mer- idian and the ship's real track on the surface of the sphere. Know- ing the true course, it may be converted into a magnetic course by the application of the variation, viz: easterly variation to the left, westerly variation to right of the true course. Second. A true bearing is the angle which the direction of an ob- ject makes with the geographical meridian. Knowing the true bear- ing, it may be converted into a magnetic bearing by the application of the variation, viz: easterly variation to the left, westerly variation to the right of the true bearing. Third. A magnetic course is the angle which a ship's track makes with the magnetic meridian, as a magnetic bearing is the angle be- tween the magnetic meridian and the direction of an object; such an angle can only be shown by a compass unaffected with deviation; but as the compasses of all iron ships have more or less deviation, and as any course steered, or bearing taken by any such compass is in a certain sense magnetic, it has been found necessary to distinguish these when corrected for deviation, as coriect magnetic course or bearings. Fourth. A compass course is the angle which the ship's track makes with the direction of the magnetic needle of the compass; such a course is affected with deviation and variation; applying the former, it becomes the correct magnetic course; applying both, it be- comes the true course. Fifth. A compass bearing is similarly the angle contained between the direction of the object and the direction of the magnetic needle of the compass; like the compass course, it is affected with devia- tion and variation; but the deviation to be applied in this case, is that clue to the Azimuth of the ship's head, not that on the point of bearing; when this correction is made it becomes the correct mag- netic, and the further application of the variation turns it into a true bearing; easterly deviation and variation to the right, westerly deviation and variation to the left. Sixth. In " cross- bearings," both bearing's must be corrected for the deviation dug to the direction of the ship's head at the instant of making the observation. The correction or error of the compass obtained by means of an Amplitude or Azimuth of the Sun, or any celestial object, is the variation and deviation combined on the course or direction of the ship's head at. the moment of making the observation; therefore, knowing the variation of the compass at any place, the deviation can readily be eliminated by one of the follow- ing rules: LEEWAY. 43 First. If the correction is greater than the variation, subtract the variation from the correction, and the remainder, which is the devia- tion, will be the same name as the correction. Correction and varia- tion of the same names both east or both west: Ex.2. Correction.. . 30 00' E. Ex. 1. Correction 39 00' W. Variation.. . 28 00 W. Deviation 11 00' W. Variation 22 00 E. Deviation 8 00' E. Second. If the correction is less than variation, subtract the cor- rection from the variation, and the remainder, which is the deviation, will be east when the correction is west, but west when the correction is east. Ex. 1. Correction 17 00' W. Variation.. . 30 00 W. Deviation.. . 13 00' E. Ex.2. Correction 10 00' E. Variation 25 00' E. Deviation.. . 15 00' W. Correction and variation of different names, one east and the other west. Add together the correction and variation, their sum, which is the deviation, will be the same now as the correction. Ex.3. Correction 10 00' W. Variation.. 5 00 E. Deviation.. . 15 00' W. Ex.4. Correction 16 00' E. Variation 13 00 W. Deviation 29 00' E. Third. If the variation is 00 00' the correction is the deviation. Fourth. If the correction is 00 00' the deviation is of the same amount as the variation, but of an opposite name; that is, east when the deviation is west, but west when the variation is east. NOTE. For correcting courses for deviation, see table 3, for deviation of Standard Compass, N. III. LEEWAY. When a ship is close-hauled and the wind blowing fresh, that part of the wind which acts upon the hull and rigging together with a considerable part of the force exerted on the sails, tend to drive her immediately from the direction of the wind, or as it is called to lee- ward; but as the bow of a ship exposes less surface to the water than the side, the resistance will be less in the first case than in the second; the velocity, therefore, in the direction of the head, will in most cases, be greater than the velocity in the direction of her side, and the ship's real course will be between the two directions. Now the angle contained between the line of the ship's apparent course, and the line she really describes through the water is termed the leeway. The quantity of leeway to be allowed will depend upon a variety of circumstances, such as the mould or build of a ship, the draught or the trim of the ship, the quantity of sail she may be under, her PKACTICAL NAVIGATION. speed through the water, and the sails being 1 properly set and trimmed to the wind, etc. No general rule can, be laid down that will deter- mine the quantity of leeway at all times. The most accurate method is to draw a semicircle on the taffrail with its diameter at right angles with the ship's keel, and apply as directed by the following plate: The semicircle A. consists of a small piece of polished brass upon which the points of the compass are correctly laid off; this semicircle is attached to the taffrail of the sliip. On the face of this semicircle or dial plate, we have a suitable pointer C., one end of which turns on the pin B., and to the other end we attach the line running to the log. It wil be seen by the above sketch, the manner in which the log line is fastened to the pointer, \\hen the 1 'g is to be drawn in, the line is slipped into the crutch and is held tight against the knot, as in sketch D., and the quantity of leeway is equivalent to the number of points indicated from the center line of the dial plate, which is to be applied to the ship's course as per rule. The leeway being determined it is to be allowed from the wind; that is, to the right of the course steered, when the wind is on the port side, and to the left when the wind is on the starboard side. How to apply the Variation, Deviation and Leeway. First. The calculator should suppose himself to be placed at the centre of the compass card, and looking outward in the direction of the ship's head; for example, suppose a ship is on the starboard tack with her head at north by compass, and the variation to be 2 points easterly, the deviation 2 points westerly and 1 point leeway; now 2 points east of north will give the course N.N.E., because easterly variation is always applied to the right hand; 2 points west- erly deviation gives the course north again, because westerly devia- tion is always applied to the left hand, and 1 point leeway with the wind on the starboard side will give the corrected course N. by "W. , because the wind throws the ship to the left hand, (1 point). Second. Suppose a ship's head S.E. by compass variation 1^ points east, deviation 1^ points east and 2 points leeway, the wind being from the N.E. Now 1J points easterly variation gives S.S. E.-rrE.; 1J points easterly deviation gives S. by E.^E., and 2 points leeway with the wind from the eastward gives the course S.f-W. Third. Suppose a ship's head by compass to be N.N.W., the va- riation to be 2 points west, the deviation 1^ points east, and leeway f point, the wind being from the S.W., 2 points westerly variation gives N.W. ; 1J points easterly deviation gives N.N.W.^W., and f point leeway, wind from S.W. gives the course N. by W.^W. Easterly variation and easterly deviation go together; that is, to the right-hand; westerly variation and westerly deviation go together; that is, to the left-hand, and leeway from the wind. VAKIATION, DEVIATION AND LEEWAY. The following examples, where the courses steered, and the vari- ation, deviation and leeway to be allowed on each, are given, from thence to find the true courses, will serve to exercise the learner in the foregoing rules. If any corrected course exceed 8 points or 90, it must be sub- tracted from 16 points or 180, and the name changed from north to south, or vice versa. Ex. 1. Ship' head N. ; variation, 2 points E. ; deviation, 2 points W. ; leeway 1 point starboard tack. Ex. 2. Ship's head S.E.; variation, 1^ point E.; deviation, 1J point E. and 2 points leeway; wind from N.E. Ex. 3. Ship's head N.N.W.; variation, 2 points \V. ; deviation, 1 point E.; leeway, f point; wind from S.W. These examples are marked out in degrees, instead of points, as it is more correct, so when points are given turn them into degrees and then apply deviation, variation and leeway, as per rules. Ex 1. Given a ship's head, N. 85 15' W. ; variation, 16 W. ; deviation, 19 41' E. ; leeway, 22 30'; wind being from S. S. W. Ship's head N. 85 15' W. Variation . . . .-.- . . 15 W. 101 15' 180 Deviation. S. 78 45' W. 19 41 E. 98 26' 80 N. 81 34' W. Leeway 22 30 True course N. 59 04' W. . Ex. 2. Ship's head S. 78 45' E. Variation 17 K. S. Gl 45' E. Deviation.. 22 30 W. S. 84 15 E. W'dW.S.W. 1'w'y. 5 45 True course . . . . S. 90 00' E. = East. PKACTICAL NAVIGATION. COURSES STEEBED AND CORRECTIONS GIVEN. To FIND CORRECTED COURSE. Courses steered. Wind. Variation. Deviation. Leeway. Corrected course. N. 30 45' E. N. 45 W. N. 45 E. S. 2230'W. South. N. 1130'W. N. W. N. E. S. E. West. E. by N. W. N. W. 11 15' W. 22 30' W. 1941'W. 16 W. 22 30' W. 16 45' E. 20 30' W. 18 E. 11 15' W. 22 30' W. 11 15' W. 22 30' E. 11 15' 2230' 33 45' 33 45' 22 30' 33 45' N. 13 15' E. N. 72 90' W. N. 19 41' W. S. 4945'E. S. 1115'E. N. 61 30' E. NO. 1. TABLE FOB FINDING DEVIATION. Form of registering the observations for determining the deviation of the Standard Compass by means of a known Correct Magnetic Bearing of a distant object. Read the rules on deviation carefully. Ship's Head by 1 Standard Compass. Bearing of Distant Object from Standard Compass on Board. Correct Magnetic Bearing of the Distant Object. Deviation of Standard Compass. North. N. 76 00' W. N. 60 30' W. 15 30' E. N. by E. N. 78 25 W. 17 55 E. N. N. E. N. 80 50 W. " " 20 20 E. N. E. by N. N. 81 10 W. it a 20 40 E. N. E. ' N. 81 30 W. < it 21 00 E. N. E. by E. N. 79 37 W. i ti 19 07 E. . E. N. E. N. 77 45 W. ( it 17 15 E. E. by N. N. 74 02 W. i ii 13 32 E. East. N. 70 20 W. t ti 9 50 E. E. by S. N. 66 00 W. < <( 5 30 E. E. S. E. N. 61 40 W. ' " 1 10 E. S. E. by E. N. 57 35 W. tt 2 25 W. S. E. ' N. 53 36 W. a it 7 00 W. S. E. by S. N. 50 37 W. 9 52 W. S. S. E. N. 47 45 W. 12 45 W. S. by E. N. 46 22 W. o 14 07 W. South. N. 45 00 W. < < 15 30 W. S. by W. N. 44 40 W. t < 15 50 W. S. S. W. N. 44 20 W. i < 16 10 W. S. W. by S. N. 44 53 W. ' ' 15 35 W. S. W. ' N. 45 30 W. 1 15 00 W. S. W. by W. N. 46 30 W. < < 14 00 W. W. S. W. N. 47 30 W. ' ' 13 00 W. W. by S. N. 49 00 W. ' ' 11 30 W. West. N. 50 30 W. ( 10 00 W. W. by N. N. 52 50 W. < ( 7 40 W. W. N. W. N. 55 10 W. < < 5 20 W. N. W. by W. N. 58 20 W. < 2 10 W. N. W. ' N. 61 31 W. ( 1 00 W. N. W. by N. N. 65 15 W. it t 4 45 W. N. N. W. N. 69 00 W. it f 8 30 W. N. by W. N. 70 30 W. " ' 12 00 W. Name the deviation east, when the correct magnetic bearing stands to right of that taken on board, and west when to the left. Look at compass in this table. DEVIATION OF THE COMPASS. 47 NO. 2. TABLE FOR FINDING DEVIATION. To determine the deviation at sea by the bearing of a distant object, its cor- rect magnetic bearing being unknown, take the bearing of a distant object by compass, on 32 points, and divide the sum of the bearings by 32, the result will be the correct magnetic bearing, approximately. Then the difference between the correct magnetic and compass bearing on each point, will be the deviation. Name the deviation East, when the correct magnetic is greater than bearing from ship. Name the deviation West, when correct magnetic is less than bear- ing from ship. Remember that easterly deviation goes to the right hand and westerly to the left hand. Look at compass in this table. Ship's.Head by Standard Compass. Bearing of Distant Object by Standard Compass. Correct Magnetic Bearing. Deviation of Standard Compass. North. N. 59 50' W. N. 63 00 W. 3 10' W. N. by E. N. 65 35 W. 2 35 E. N. N. E. N. 71 10 W. 8 10 E. N. E. by N. N. 76 10 W. 13 10 E. N. E. ' N. 79 50 W. 16 50 E. N. E. by E. N. 82 30 W. 19 30 E. E. N. E. N. 83 30 W. 20 30 E. E. by N. N. 84 05 W. 21 05 E. East. N. 83 20 W. 20 20 E. E. by S. N. 82 15 W. 19 15 E. E. S. E. N. 81 05 W. 18 05 E. S. E. by E. N. 79 30 W. 16 30 E. S. E. ' N. 77 40 W. 14 40 E. S. E. by S. N. 75 05 W. 12 05 E. S. S. E. N. 72 40 W. 9 40 E. S. by E. N. 69 00 W. 6 00 E. South. N. 66 10 W. 3 10 E. S. by W. N. 63 05 W. 00 05 E. S. S. W. N. 60 00 W. 3 00 W. S. W. by S. N. 56 30 W. 6 30 W. ' S. W. ' N. 53 20 W. 9 40 W. S. W. by W. N. 50 00 W. 13 00 W. W. S. W. N. 46 50 W. 16 10 W. W. by S. N. 43 45 W. 19 15 W. West. N. 41 50 W. 21 10 W. W. by N. N. 39 40 W. 23 20 W. W. N. W. N. 39 00 W. 24 00 W. N. W. by W. N. 39 25 W. 23 35 W. N. W. N. 41 00 W. 22 00 W. N. W. by N. N. 44 00 W. 19 00 W. N. N. W. N. 48 10 W. 14 50 W. N. by W. N. 53 45 W. 9 15 W. 32)2009 45'(62 48' Call the magnetic bearing 63 as there is 48' over. 48 PEACTICAL NAVIGATION. NO. 3. DEVIATION TABLE FOB STANDARD COMPASS. Ship's Head (or Course) by Standard Compass. Deviation of the Standard Compass Correct Magnetic Course made good by Steering as in the First Column. North. 15 30' E. N. 15 30' E. or N. by E. | E. nearly. N. by. E. 18 20 E. N. 29 35 E. N. N. E. | E. N. N. E. 20 20 E. N. 42 50 E. X. E. i N. N. E. by N. 21 15 E. N. 55 00 E. N. E. $ E. N. E. ' 21 00 E. N. 66 00 E. N. E. by E. 5 E. N. E. by E. 19 45 E. N. 76 00 E. E. by N. i N. E. N. E. 17 15 E. N. 84 45 E. E. \. N. E. by N. 13 50 E. S. 87 25 E. E. iS. East. 9 50 E. S. 80 10 E. E. JS. E. by S. 5 30 E. S. 73 15 E. E. by S. 4 S. E. S. E. 1 10 E. S. 66 20 E. S. E. by E. 1 E. S. E. by E. 3 10 W. S. 59 25 E. S. E. by E. 4 E, S. E. ' 7 00 W. S. 52 00 E. S. E. | E. S. E. by S. 10 15 W. S. 44 00 E. S. E. 1 S. S. S. E. 12 45 VV. S. 35 15 E. S. E. 1 S. S. by E. 14 30 W. S. 25 45 E. S. S. E. i E. South. 15 30 W. S. 15 30 E. S. bvE.f E. S. by W. 16 15 W. S. 5 00 E. S. ^E. S. S. W. 16 10 W. S. 6 20 W. S. g W. S. W. by S. 15 40 W. S. 18 05 W. S. by W. W. S. W. 15 00 W. S. 30 00 W. S. S. W. W. S. W. by W. 14 20 W. S. 41 55 W. S. W. i S. W. S. W. 13 00 W. S. 54 30 W. S. W. | W. W. by S. 11 30 W. S. 67 15 W. W. S. W. West. 10 00 W. S. 80 00 W. W. I S. W. by N. 7 50 W. N. 86 35 W. W. N. W. N. W. 5 20 W. N. 72 50 W. W. by N. 4 N. N. W. by W. 2 20 W. N. 58 35 W. N. W. by W. 1 W. N. W. ' 1 00 E. N. 44 00 W. N. W. N. N. W. by N. 4 40 E. N. 29 05 W. N. N. W. W. N. N. W. 8 30 E. N. 14 00 W. N. by W. i W. N. by W. 12 15 E. N. 1 00 E. N.JrE. METHOD OF WORKING DEAD RECKONING. 49 METHOD OF WOBKING DEAD BECKONING, OK WHAT IS COMMONLY CALLED DAY'S WOKK. To Correct the Courses for Variation, Deviation and Leeway. "When the variation is westerly allow it to the left hand of the course steered. When variation is easterly allow it to the right hand of the course steered. When the deviation is westerly allow it to the left hand of the course steered. When deviation is easterly allow it to the right hand of the course steered. If an azimuth be observed, the correction will be the variation and deviation combined on the azimuth due the ship's head on that course. To Correct the Course for Leeway. When on the starboard tack allow the leeway to the left hand of the compass course. When on the port tack allow it to the right hand of the compass course. First Course on Leaving the Land. Take the bearing of an object, whose position, or latitude and longitude are known, and estimate its distance off shore as a dis- tance, the opposite point to which is taken as a course, and being cor- rected for variation and deviation due the ship's head on that course. This is entered in the traverse table along with the other courses. If there is a current, the set and drift of which is known, allow the variation only on its set, and enter it in. the traverse table as a course and distance. Each course is to be corrected for variation, deviation and leeway, and entered in the traverse table, and set against each the distance run on that course. Traverse Table. Make a table which divide into six columns, in the first of these set down the several courses, and opposite to them in the second column enter the distance run on each course. The third and fourth columns are to be marked north and south, and are to contain the difference of latitude. The fifth and sixth are to be marked east and west, and to con- tain the departures. Find the difference of latitude and departure corresponding to each course and distance in Table III; set these down in their proper columns; if the difference of latitude is north, it must be placed in the north column; and if south in the south column; if the depart- ure is easterly place it in the east column, and if westerly place it in the west column. 4 50 PRACTICAL NAVIGATION. "When the course is due north, south, east or west, set down the distance in its respective column. Sum up the columns of northing, southing, easting and westing, of each column separately, then if the northing be less than the southing, subtract it from the southing, and the remainder will be the whole difference of latitude made good, and of the same name as the greater; in the same manner the difference between the sums of the east and west column is the whole departure made, and of the same name as the greater. Then the whole difference of latitude and departure will give the direct course and distance in Table IV. To find the course and distance, with the difference of latitude and departure made good, enter Table IV; seek in the columns until they are found to agree; opposite to which will be found the distance in its column. If the departure be greater than the difference of latitude, the course will be found at the bottom of the table, but if the depart- ure be less than the difference of latitude, the course will be found at the top of the table. To find Latitude in. If the latitude of the place from which the departure has been taken and the difference of latitude made be both north or both south, their sum will be the latitude of the same name; but if the difference of latitude is of a contrary name to the latitude left, their difference will be the latitude in, and of the same name as the greater. To find the Difference of Longitude. Add together the latitude left and latitude in, and take half their sum for the middle latitude; then, with the middle latitude as a course, enter Table IV and seek for the departure made good in the latitude column, and in the distance column opposite, will be found the difference of longitude made, which divided by 60; if over 60, will give the degrees and minutes to be named east or west, accord- ing to the departure. To find the Longitude in. If the longitude left and difference of longitude made be both east or west, their sum will be the longitude in and of the same name; but if the difference of longitude be of contrary name to the longitude left, their difference will be the longitude in and of the same name as the greater; but when their sum exceeds 180 degrees the ship has crossed the opposite meridian to that of Greenwich, in that case subtract it from 360 degrees, and the remainder will be the longitude in of a different name. In example No. 1, the courses are METHOD OF WORKING DEAD RECKOXIXG. 51 given in points, the learner however, will derive greater advantage by turning the points into degrees, and practicing that system only, as it will facilitate the application of the variation and deviation which is generally given in degrees. Ex. 1. A ship from a port in latitude 38 42' N., and longitude 51 32' W., bound to another port in latitude 43 D 27' N. and longitude 65 19' W. , sails the following courses: S.W. f W. 54 miles, S.W. by S. 38 miles, S. by E. A E. 37 miles, S.E. by E.^E. 40 miles, N. by E. E. 50 miles, S. by E.J E. 31 miles. He- quired the course, the distance and latitude and longitude in, also the course and distance to the port bound to by Mercator sailing. Course. Distance. Diff. of Lat. Departure. N.W.f W. S.W. by S. S. byE.JE. S.E. bvE.iE. N. by'E.m S. byE.^E. 54 38 37 40 50 31 N. 47.8 S. 32.2 31.6 35.4 18.9 30.1 E. 10.7 35.3 14.5 07.5 W. 43.4 21.1 '148.2 47.8 C8.0 64.5 64.5 Course S. 2 00' E. = 100 . 4 3.5 Distance 101 miles. The difference of latitude 100.4 miles and the departure 3.5, being looked for till they are found opposite each other in their respective columns in Table IV, gives the course S. 2 00' E., and the distance 101 miles. To Find the Latitude and Longitude. Latitude left 38 42' N. Difference of latitude . . 1 40 S. Latitude in 37 02' N. Sum 2)75 44 Middle latitude . . .37 52' Longitude left 51 32' W. Difference of longitude 05 E. Longitude in . . ... 51 27' W. The middle latitude as a course, and the de- parture in a latitude column, will give the difference of longitude in a distance column, 5 miles. The course to the port bound to, will be found to be N. 58 09' W., and the distance 729.6. Work it out as per rule in case I, example 1, page 30. CORRECT THE FOLLOWING COURSES FOR LEEWA Y AND VARIATION. GIVEN. Courses steered. Winds. Leeway. Variation. Courses correct'd E.N.E. N.W. N.E.iE. W. by S. N.W'. bvN. South. N.W. s.s.w. K. by N. West. N.W. by N. N.E. byN. E.S.E. W.S.W. SE. N. by E. N.N'.W. 1 14 i 2 H *j 1 H W. 2" W. li E. 1 \V. li W. <>,' E. 1 E. W.S.W. W. bvN.AN. S. bv'w. v\V. N.W, byN. S.S.W. S. F, b\- K.JE. W. i N. TO FIND ANSWER 52 PKACTICAL NAVIGATION. Ex. 2. April 11, 1876, Steamship "City of Panama," W. B. Seabury, Com- mander, from San Francisco, toward Victoria, at noon took our departure from Point Bonita in latitude 37 49' N., and longitude 122 31 W.; bearing by com- pass E. S. , distant 3 miles. HOURS. KNOTS. 10THS. COURSES. WINDS. LEEWAY. DEVIATION. 1 8 5 W. *N. N . W. 2 8 5 " 3 G 5 " 4 6 5 " 5 G 5 " G 6 5 (i 7 6 5 N. W. byN. 4N. " 8 6 " 9 6 5 " 10 6 5 " 11 6 5 it 12 6 5 N.W. byN. K 1 7 5 " 2 7 5 " 3 7 5 " 4 6 5 N. by W. 4 W. " 5 6 5 " 6 6 5 " 7 6 5 < 8 7 5 N. by W. | W. 1 9 7 5 1 10 8 5 < 11 8 5 < 12 9 5 ' COURSES. DISTANCE. N. s. E. W. N. 74 W. 43 04.2 42.8 N. 2| W. 33 29.1 ' 15.6 N. 3 W. 28 23.3 ' 15.6 N. 14 W. 26 24.9 < 07.5 N. If W. 41 38.6 ' 13.8 Dif. of lat.... 60)120.1 2 l 00' N. Latitude left 39 49' N. Difference of latitude 2 00 N. Departure. 95.3 Longitude left 122 31' W. Difference of longitude ... 2 03 W. Longitude in : 124 34' W. Latitude in 39 49' N. Sum 2)77 38 Middle latitude 38 49 True course, N. 38 00' W. ; distance, 153 miles. The middle latitude 38 49' (call it 39 00' as you have 49' over) as a course in Table IV, and the departure 95' in a latitude column, gives the difference of longitude 123 miles in a distance column, which divide by 60 gives 2 03' W., to be added to the longitude because the ship has been going to the westward. METHOD OF WORKING DEAD BECKONING. 53 Ex.3. o COURSES. x 8 s WINDS. I VIAT'N. REMARKS, ETC. W 8 * H fl 1 N. W. | N. 3 5 S. W. i S. | 25 W. A Point of Land. 2 " 3 5 II In Latitude . . 55 57' N 3 ii 3 5 In Longitude 16 04' W. 4 " 3 5 Bearing by Compass S. J W. 5 W. S. W. 5 5 N. W. by N. 1 11W. Head South. Deviat'n 14 W. 6 " 5 5 M 7 II 4 5 ii Distance 22 miles. 8 " 4 5 " 9 W.byN.^N. 5 5 S. W. 4 W. lj 28 W. 10 " 6 5 " Variation 25 E. 11 " 6 5 " 12 " 7 5 II 1 N. E. | E. 7 5 N. W. by N. | 20 E. 2 " 7 5 M 3 ' 7 " 4 7 " 5 N. N. E. 7 5 N. W. by W. 1 11 E. 6 " 6 5 " 7 " 6 5 " 8 " 6 6 ' 9 N. E. 4 E. 6 5 S. E. by E. 1 20 E. A Current set Correct Mag- 10 " 6 7 11 netic S. 22 E. 26 miles from 11 6 9 " the time the departure was 12 5 9 taken to the end of the day. BEARING OF LAND. FIBST COUBSE. THIRD COURSE. FIFTH COUBSE. S. i W. = S. 3 W. N. W. f N. Leeway W. by N. 4 N. N. N. E. Leeway 1 OPI | point to the right hand makes it into Leeway 1| point to the right hand point to the right hand makes it into >osite = N. 3 E. Dev. 14 W. ) , , i o p N.N.W. 4\V. makes it into N. N. E. by N. Var. 25 E.) "" Li Cj ' = N. 28 W. W. by W. i W. = N. 34 E. Cor. b'r'g, N. 14 E. Dev. 25 W. ) f.o Var. 25 E. J ~ N. 59 VV. Kr-ffi^v+a-w. Dev. 11 E) , nf>vn< Var. 25 EJ + -^ - c " Cor'd 1st.) -vr 90 TV Course. ) -^' V I . '-> Cor'd 3rd ; Course. ; Cor'd 5th 1 -M- i-^o -p Course. J ' N. 62 W. CUEBENT. SECOND COUESE. FOUBTH COURSE. SIXTH COUESE. S. S. E. = S. 22 E. W. S. W. Leeway N. E. f E. Leeway N. E. i E. Leewav Variation 25 E. 1 point to the left Vi*nii r l mnlrpQ it intr* f point to the right hand makes it into J point to the left hand makes it into Cor. Cur., S. 3 W. 11(1111 L llltlK( > lltJ.lJ.vU S. W. byW. N. E. byE. JE. N. E. i N. = S.56W. = N. 62 J E. = N. 42 E. Var. 25 E) , , , v Dev.llWJ +i * L" Var. 25 E) 4 ,- ( , F Dev. 20 E J + c " Dev. 20 E) , 4 rop- Var. 25 E/ + 4o L - Cor'd ) -KT 107 o -p Course.} IN> 1U/ * exceeds 90 Subtract ) i QAO from J 18U Cor'd 2nd) Q 7n \V Course. } - ' u Cor'd 4th) Q 700 17 Course, f ' s J ^- Cor'd 6th) -vr 070 77 Course, f JN - 87 * Ans. True course, N. 66 Q E. ; distance, 38 miles; difference of latitude, 15.2 departure, 34.6; latitude in, 56 12' N.; longitude in, 15 02' W. PRACTICAL NAVIGATION. Ex. 4. i COURSES. i B "\VlXD. 1 ri i KEMABKS. f, o w E W M H H Hi n 1 S.E.iS. 4 5 NE by EiE 8 14 W. Noon. A Point of Land. 2 i ( 4 5 1 1 mlatifmlp J 0' S 3 <( 4 5 <( JilLlt IHIU t<3 \J O. in longitude 1380'E 4 5 5 Bear'gbyCoiup NAY. byAV. 5 S.E. byS. 7 5 S. W. 10 18 W. Ship's he'd at 1st c'rse, per log. 6 " 6 5 " Distance 22 miles. 7 " 6 5 " 8 " 6 5 " 9 N.W.JN. 5 5 SWbyWiW 8 3E. 10 " 5 5 '" Var. 1 1 E. (to the right hand) 11 " 4 5 " 12 4 5 " 1 W. by S. 5 5 South. 11 14 E. 2 " 4 5 " 3 5 5 " 4 " 4 5 a 5 W.byN.N. 3 5 N.iE. 13 13 E. 6 " 3 5 " A Curr'nt set | N. by W. 1 W. 7 8 ii 2 2 5 5 M by Comp'ss \ (corr't magn'c) 20 miles from the time the de- 9 S.fE. 4 5 E4S. 12 3 W. parture was taken to the end 10 " G 5 " of the day. 11 " 7 5 t< 12 7 5 THCE COUBSES. DlST. DIF. LATITUDE. DEPAETUHE. Latitude left 29 02' S. Dif. of Latitude... + 16 S. N. S. E. W. Lat. in at Noon. . . 29 18' S. Sr;O Tf 99 - 1 1 -Q 1 Q-O OU Hi. N. 9 W. 2C2Q 20 11 tj 19-8 lo U .< 31 Sum of Latitude... 58 20' S. 37 E. 19 15-2 11-4 S. 51 E. 27 17-0 21-0 " Middle Latitude. . . 29 10' N. 17 W. 20 19-1 a 5-8 X. Go W. 20 8-5 " 18-1 Longitude left 168 2' E. N. G2 W. 12 5-6 " 10-6 *Dif. of Longitude + 10 E. S. 12 W. 26 25-4 5-4 Long, in at Xoon.l68 12' E. 53-0 68-9 51-3 43-0 True Course. Dist. 53-0 43-0 *The middle latitude 29 as a course, and the departure 8' - 3 in a latitude S. 27 E. 18' D.Lat 15-9 8-3 Dep. column, give the difference of longi- tude 10' (nearly) in a dist'ce col 'inn. TIME. 55 TIME. Time is measured by the motions of the heavenly bodies. Its divisions are years, mouths, days, hours, minutes and seconds. The day is the interval between two successive transits of the sun, moon, or a star over the same meridian. The solar, or apparent day, is the interval between the sun's de- parture from, and its return to the same meridian. This day is divided into 24 hours, each hour into 60 minutes, and each minute into 60 seconds. The length of the day is subject to continual changes, owing to the obliquity of the plane of the sun's path to the equinoctial, and to the eccentricity of the earth's orbit. Astrono- mers, so as to have a uniform measure of time, use, what is named, a mean solar day, the length of this day is equal to the average of all the apparent solar days in a year; in other words, it is the day that would be shown by the stin if it moved uniformly in its path, the ecliptic. As only apparent time can be obtained from observations, a cor- rection must be applied to this in order to reduce it to mean time, this correction is called the equation of time. When it is required to reduce apparent time to mean time, the equation of time must be taken from the first page of the Nautical Almanac for the given month and opposite the given day. This equation must be applied as directed at the head of its col- umn. To find the corrected equation of time take it out of its col- umn opposite the required day, also take out the hourly difference for the same day, and multiply it by the number of hours and dec- imals of an hour that are given as a part of that day, add this cor- rection for hourly difference if the equation of time is increasing, or subtract if decreasing. Suppose the apparent time is three hours P.M., March 5, 1878, at the meridian of Greenwich, that is, the sun has passed this meridian three hours, it is required to find the corresponding mean time. March 5, 1878, equation of time, N. Aim. llm: 40.95s. Hourly, dif. 0.573 Correction for 3 nours, decreasing (sub. ) 1.71 3 To be added to app. time + llm: 39.24s. 1.719 Apparent time 3h: 00m: OO.OOs. Mean time 3h: llm: 39.24s. When it is required to change mean into apparent time find the equation of time from the second page of the almanac for that month. Find the correction the same way as above, and apply the equation of time as directed at the head of the column. 56 PEACTICAL NAVIGATION. March 5, 1878, mean time at the meridian of Greenwich 3hr. P.M. Required the apparent time. March 5, 1878, equation of time, N. Aim. llm: 41.06s. Hourly dif. 0.573 Correction for 3 hours decreasing (sub. ) - 1.71s. 3 To be subtracted from mean time llm: 39.35s. 1.719 Mean time.. .. 3h: 00m: OO.OOs. Apparent time 2h: 48m: 20.25s. There are three ways of reckoning time, called civil, astronomical and nautical, the last is now obsolete. The civil day begins at midnight and ends the following midnight; it is divided into two parts, each of twelve hours; the first part is called A.M., meaning ante-meridian or before noon; the latter part is called P.M., meaning post-meridian or afternoon. The astronomical day begins at noon and ends the following noon; that is, it begins 12 hours alter the civil day, it is reckoned through the whole 24 hours from noon to noon. Thus from noon to mid**' night the day of the month and the hours of the day are the same for both methods, but from midnight to noon the civil day is 12 hours ahead of the astronomical day. So to turn A.M. civil time into astronomical time add 12 hours to it, and call it the day be- fore, civil date, for example: 10 o'clock A.M., June 5, civil time, is June 4, 22, astronomical time, and 23 hours June 4, astronomical day, is 12 o'clock A.M. June 5, civil time. All the computations of the Nautical Almanac are made for as- tronomical time at the meridian of Greenwich, it is therefore neces- sary,, in taking quantities out of the almanac to reduce the ship's time to Greenwich time. One complete revolution of a heavenly body, over three hundred and sixty degrees of longitude takes place in 24 hours. This is at the rate of 15 in one hour of time, there- fore at any place situated eastward of the meridian of Greenwich it . will be noon before it is noon at the meridian of Greenwich, and at any place situated to the westward of Greenwich it will be noon after it is noon at the meridian of Greenwich. All the reduction of time must be made at the rate of 15 to an hour. The rule for ap- plying longitude in time is this: Reduce the given longitude by multiplying by 4 and dividing by 6, Table XI, into time, and add it to the astTonomical time of the given place, if the longitude iu is west, and subtract it from the astronomical time if the longitude in is east, the sum or the remainder is the corresponding Greenwich time. If the longitude in is west, and the sum of the longitude in time, and the time at the given meridian is more than 24 hours, sub- tract 24 hours from it and call the remainder the time past noon of TIME. 57 the day that follows. If the longitude in is east aud the longitude in time is more than time at the given meridian, add 24 hours to the latter, and subtract the longitude in time, the remainder must be called the time past noon of the day before. "What will be the Greenwich time when it is 5 hours P.M. in longi- tude 50 W. Time at the given meridian 5h: 00m: P.M. Longitude in time. . . . +3h: 20m: w. Corresponding time at meridian Green .. 8h: 20m. Required the time at Greenwich when it is 7h:30m:l5s: P.M., in longitude 100 30' Time at the given meridian 7h: 30m: los: P.M. Longitude in time . . . - 6h : 42m : OOs : E. Corresponding time at mer. Green... Oh: 48m: 15s. Required the astronomical time at Greenwich corresponding to 7h:50m:25s: A.M., civil time; 145 16' "W. longitude; May 5. May 5. Time at the given meridian 7h: 50m: 25s: civil time. 12h: May 4 19h: 50m: 25s: astron. time. Longitude in time^^ +9h: 41m: 04s: W. 29h: 31m: 29s: 24h: 00m: OOs: May 5. Astronomical time at Greenwich. 5h: 31m: 29s: February 18; longitude 116 37' E.; time at ship, llh:37m:14s: M. civil time; required the astronomical time. , Feb. 18. Time at the given meridian llh: 37m: 14s: civil time. 12h: Feb. 17 23h: 37m: 14s: astron. time. Longitude in time . . - 7h : 46m : 28s : E. Feb. 17. Greenwich astronomical time.. 15h: 50m: 46s: May 17; in longitude 125 25' E.; astronomical time at ship, 3h: 10m; required the astronomical time at Greenwich. May 17. Time at ship.. 3h: 10.00m: P.M. 24h: May 16 27h: 10m: Longitude in time - 8h: 21m: 40s: E. May 16. Greenwich astron. time.. ISh: 48m: 20s: 58 PRACTICAL NAVIGATION. AMPLITUDE. To find the Correction and Deviation of the Compass by an Amplitude. (Table II, secant and sine for amplitude.) First. To the apparent astronomical time at ship apply the longi- tude in time; adding west, and subtracting east longitude for the apparent astronomical time at Greenwich. (NOTE. Turn the degrees into time by multiplying the degrees by 4, and dividing by 60. Or by Table XI. ) Ex. 35 25' x 4 60)141 40' 2h:21m:40s: Second. P.M. time is astronomical; A.M. is civil time, and re- quires 12 hours added to make it astronomical time of the day before, (therefore add 12 hours when the time is A.M. and call it a day back) then apply the longitude; when west, add; when east, subtract. Ex. June 20th, A. M. at ship time 9h :35m : 12h: 21h:35m: Third. In adding west longitude the time may exceed 24 hours, when it is so take 24 hours from it, and call the day one more. (NOTE. Read carefully the rules on time.) Fourth. In subtracting east, the longitude (in time) may exceed the time at ship; then borrow 24 hours to the time at ship, and sub- tract as before, but call the day one less, as you have borrowed a day by adding the 24 hours to the ship's time. This case only hap- pens when it is P.M. at ship. For example: January 20, 6h:40m: P.M., and longitude in time 10h:40m: east, you require 24h: to the 6h: making 30h:40m: and take 10h:40m: from that, leaves 20h: on January 19. Again January 20, 6h:40m: A.M., you will always add 12h: to A.M., making 18h:40m: on January 19; the longitude 10h:40m: west added on to 18h:40m: makes 29h: and 29m: then take 24h: from the 29h: and you have 5h: and 20m: on January 20. Fifth. To the apparent astronomical time at Greenwich, correct the sun's declination^ taken from first page of the month in -the Nau- tical Almanac, by the hourly difference in adjoining column; multi- ply the hourly difference by Greenwich time, turning the minutes AMPLITUDE. 59 into tenths of an Lour by dividing them by G, and if any over, annex a cipher, and divide by 6 again for a second decimal. For example: Should the time be 10h:33m: then 6 into 33=5 times and 3 over; to the 3 over annex a cipher, and you have 6 into 30, 5 times, mak- ing the time to multiply the hourly difference by 10h:55m. Ex. Suppose the declination to be.. 22 58' 57" Hours difference .. P2" 83 - 2 15 Time.. . 10 55 Correct declination 22 56' 42" 6415 6415 12830 60)1353565 It will be seen by the above example that there are four decimals, viz: Two in the hourly difference, and two in the longitude in time; therefore, cut off four from the right hand of the product, and you have left 135', and after dividing by 60 there will be a correction of 2' 15" to apply to the declination, and as the declination is decreas- ing subtract the correction, but if the declination is increasing add the correction and you have the correct declination. This rule is to be observed in all cases except in a meridian altitude. Sixth. To the secant (Table 2) of the latitude add the sine (Table 2) of the reduced declination. Their sum less 10 of the index is the log. sine (Table 2) of the true amplitude; to be reckoned from the west when P.M. at ship, and east when A.M.; toward the north when the decimation is north, or south when the declination is south. Seventh. Under the true amplitude place the sun's bearing by compass, and take notice how you put it down, because it is given in points, and you must turn it into degrees, counting from the east or west, toward the north or south. If in the example the bearing is given TV. by S. that would be 1 point from west toward the south. Turn 1 point into degrees and it will be "W. 11 15' S. ; or suppose the bearing was given S.S.E., in this case it would be 6 points from east, and turned into degrees would be E. 67 30' S. After getting the bearing by compass into proper form, proceed to find the correc- tion of the compass in the following manner. Eighth. If the true amplitude and sun's bearing from ship are both north or both south, subtract the less from the greater for the correction of the compass. Ninth. If the true amplitude and sun's bearing are one north and the other south, add them for the correction. 60 PRACTICAL NAVIGATION. Tenth. If the true amplitude is reckoned from the east, and the sun's bearing by compass from the west, or vice versa, add them together and take the sum from 180, the remainder will be the correction of the compass. Eleventh. Name this correction east, when the sun's true amplitude is on the right-hand of the sun's bearing from ship, and west when it is on the left-hand. Twelfth. The correction of the compass is deviation and variation combined. Thirteenth. To find the deviation underneath the correction of the compass, place the variation for that locality from the chart. Then if one is east and the other west, add them together, and the sum is the deviation; but if they are of like names, that is, both east or both west, subtract them for the deviation. Fourteenth. To know if the deviation is east or west, draw the compass and lay off the variation to the left of north if westerly, but to the right of north if easterly; lay off the correction in the same manner; then if the correction is on the right-hand of the variation, the deviation is easterly, but if to the left, it is westerly deviation. \ NOTE. The deviation thus found must only be applied to that point of the compass the ship's head was at when the observation was made. Observe carefully how the examples are worked out, and you will seldom make a mistake. Ex. 1. 1878, April 28th, at 6h:56m: P.M., apparent time at ship in latitude 43 40' S., and longitude 6 30' E. The sun's bearing setting was W.S. Required the true amplitude, the correction and deviation of the compass. Variation per chart 22 W. H. M. Apr. 28, App. T. ship 6 56 P.M. Longitude 6 30' E. -0 26 Greene-time, Apr. 28 6 30 Sun's Dec. Apr. 28, 1411'56"N. Hourly diff. 47"'l Cor. for 6h: 30m: .+ 56 Green'b- time 6 '5 Sun'sCor. declinat'n 1417'02"N. Latitude of ship 4340'. . Sec. . 10 -140640 Sun'sCor. Decl.14 17. .Sine. 9'392199 23555 282G6 60)30,6,215 5-6 TrueAmpl.W. 1957'N.Sine 9 '532839 Sun's bearingW. 2 49S. (Setting) Cor. of Compass 2246'E. Yar. per Chart 22 00 W. Deviation. . . 4446'E. for the point of the compass her head was at when the ' observation was made. AMPLITUDE. Gl Ex. 2. 1878, January 1st, 9h:12m: A.M., apparent time at ship in latitude 62 10' S., longitude 138 3 00'W. The sun's bearing rising was S. W. Required the true amplitude, the correction and deviation of the compass. Variation per chart 45 W. H. M. Jan. 1, App. T. ship 9 12 A.M. A.M. at ship. . . + 12 Dec. 31, Ast. time 21 12 Longitude 138 C 00'W. 9 12 Sum 3024 Less, 24h 24 Sun's Dec. Jan. 1st, 2300'02"S. Hourly diff. 12"-64 Cor. for 6h. 40m... - 1 21 6 4 Sun's Cor. Decl. . . 225S'41"S. 5056 7584 60)8,0,896 Gr'h time. Jan. 1st, 6 24 Latitude 62 10' Secant 10'330775 Declination... .22 59 Sine.. 9'591580 Sun's true amplitude E 56 45' S'. . . .Sine. . 9 '922355 Sun's bearing by Corn. W. 84 22 S. Sum 141 07' From.. ..180 00 Cor. of the compass 38 53' W. Variation per chart 45 00 W. Deviation 6 07' E. for the point her head was at. Ex. 3. 1878, May 31st, 7h:10m: P.M., apparent time at ship, in latitude 40 26' N., longitude 68 15' W., the sun's bearing setting was W.fN. Re- quired the true amplitude, the correction and deviation of the compass. Varia- tion per chart, 8 J W. Ans. True amplitude W . 29 30' N. ; correction, 21 04' E. ; deviation, 29 C 04' E. Ex. 4. 1878, September 5th, 6h:20: A.M., apparent time at ship, in latitude 46 05' 1ST. , longitude 3745'E., the sun's bearing rising was E.fS. Required the correction and deviation of the compass. Variation per chart, 4 W. Ans. 14 24' West. Ex. 5. 1878, September 23d, 5h:43m: A.M., apparent time at ship, in latitude 53 57' N., longitude 17 15' E., the sun's bearing rising was E. Required the correction and deviation of the compass. Variation per chart, 11 W. Ans. 110'E. Ex. 6. 1878, October 15th, 6h:39m: P.M., apparent time at ship, in latitude 5804'N., longitude 173 30' E., the sun's bearing setting was W.JN. Re- quired the correction and deviation of the compass. Vai'irtion per chart 10 E. Ans. True amplitude W. 16 U 14' S. ; correction, 19 03' W. ; deviation, 29 03' W. Ex. 7. 1878, May 29th, 6h:33m: A.M., apparent time at ship, in latitude 00', longitude 126 45' W., the sun's bearing rising E.^S. Required the correction and deviation of the compass. Variation of the chart, 5 E. Ans. 32 17' W. Ex. 8. 1878, June 21st, 9h:40m: P.M., apparent time at ship, in latitude 62 29' N., longitude 60 45'W., the sun's bearing setting was N.N.E.^E. Re- quired the correction and deviation of the compass. Variation per chart, 53 W. Ans. 540'W. NOTE. When the latitude is 0' 0" the declination is the sun's true amplitude, reckoned from the east when the observation is made in the morning; west if made in the afternoon; north or south according to the declination. When the BUU'B declination is O 1 0' 0" the nun's true amplitude is east when the observation is made in the moruiug; -west if made in the afternoon. 62 PRACTICAL NAVIGATION. CORRECTION AND DEVIATION OF THE COMPASS BY AN AZIMUTH. (Use Table II. for working out Azimuth.) First. To the mean time at ship add the longitude if west, and subtract it if east, in the same manner as shown in working ampli- tude, for finding the mean time at Greenwich; be sure and always date it. Second. To the observed altitude apply the index error first (if any); next the dip (Table VII.), always to be subtracted; then the refraction (Table VI.), also subtracted. Sun's pai-allax (Table VIII.) that add always. Sun's semi-diameter for the day of the month, from the Nautical Almanac, always to be added to the sun's lower limb, and subtracted from the upper limb, that will give the sun's true altitude. Third. Take the sun's declination from page 2d of the month, niid correct it by the hourly difference as before shown in amplitude, and find the polar distance as follows: if the declination and the latitude are of the same name, take the declination from 90; but if of contrary names add the declination to 90. Then add together the sun's true altitude, the latitude and the polar distance, divide this sum by 2 and call it the half sum, then take the difference between the half sum and the polar distance and call it the re- mainder. Fourth. Now add together the Secant (Table II.) of the true altitude. Secant (Table II.) of the latitude. Co-sine (Table II.) of the half sum. Co-sine (Table II.) of the remainder. To the nearest mile only. Fifth. Half the sum of these four logarithms will give the sine (Table II.) of half the true azimuth, which double and call it north in south latitude, and south in north latitude; east when the time is A.M.; west when the time is P.M. Sixth. Subtract the true bearing and bearing by compass when they have the same name for the correbtion. Seventh. If one bearing is north and the other south, take the true azimuth (that is, the true bearing) from 180, and change the north or south name only. Then the difference is the correction; AZIMUTH. except one bearing is east and the other west, when the sum of the two bearings is the correction. NOTE. Bo careful when taking the true bearing from 180, you do not change the east or west i;auie, only the north and south. Eighth. The correction will be easterly when the true bearing is on the right-hand of the bearing by compass; westerly when on the left. Ninth. If the correction and variation are of the same name, sub- tract them for the deviation. But if they are of different names, add them for the deviation. Tenth. To know if the deviation is easterly or westerly, draw the compass and lay off the variation to the left of north if westerly, but to the right of north if easterly; lay off the correction in the same manner; then if the correction is on the right-hand of the variation, the deviation is easterly, but if to the left-hand, it is westerly deviation. NOTE. Bear in mind that azimuths reckon from north and south points of the compass, not the same as amplitudes. When the latitude is in au azimuth, assume a name for it, taking care to use the name when naming the true azimuth. Name the true azimuth opposite to the name you have assumed, and proceed without any latitude. Ex. 1. 1878, June 4th, 61i: 8m: P.M., mean time at ship, in latitude 47 30' N., longitude 16 J 00' W. The sun's bearing by compass was W.^N. Altitude of sun's lower limb 33 44' 40". Index error - 2' 20". Eye 19 feet. Required the true azimuth, correction and deviation of the compass. Variation per chart, 4 W. H. M. , ff June 4, M.T.S. 6 8 P.M. Obs. alt 33 44 40 Sun's dec. .. Long'del6 = 0' 1 4 W. Index error.. - 2 20 Correction .. 27 33 N. Hourly diff. .... 17-37 2 5 M.T.G.. 7-2 M.T.G.June4 7 12 33 42 20 Sun'sRed.dec.22 29 38 Dip - 4 11 90 00 00 33 38 09 Polar dist. .. 67 30 22 60) 12,5,064 Kef -124 33 36 45 Palx 7 33 36 52 S. Semd 15 47 True alt 33 52 39 Secant . 0-080831 Latitude .... 47 30 00 Secant . 0-170317 Polar diet. . . 67 30 22 ^ i_ -\] Sum 1485301 o'wv- Half-sum. ... 74 26 30M Co-sine. 9'428263 Kemainder.. 656 8M Co-sine. 9-996812 *> l 4 W'> 2)19-676223 2 ) -.-Sine.... 9-838111 Sun's true azimuth S 87 04W. . 18000 \ Taking the true azimuth from 180, do not 777.7 ( chanye the West. Sun s true bearing N 92 56 W. \ Sun's bearing by compass N 8711W. Correction 5 45 W. being variation and deviation combined. Variation per chart 4 00 \V. Deviation of the compass 1 45\V. for Vie point her head was at. 64 PEACTICAL NAVIGATION. Ex. 2. 1878, July 2d, 8h:17m: P.M., mean time at ship in latitude 61 KX N., longitude 51 15' W. The sun's bearing by compass was N.JE. Altitude of the sun's lower limb 5 35' 15". Eye 19 feet. Required the true azimuth, cor- rection and deviation of the compass. Variation per chart, 56 W. H. M. July 2, M.T.S. .. 8 17P.M. Longitude " " W. M. T.G.July 2, 11 42 5 Si' 5l" Secant 0- Sun's dec. 23 2' 54%. H. D. Il'l9 " " " Secant 0. - 2 11 11-7 True alt. Latitude. Polar dist Sum Half-sum Remaind'rO 05 42 Co-sine 9- 66 59 17 Co-sine D-- 23 43 N. 90 60)10,0,923 19-912477 o , 2M1" 64 43. Sine... 9-95G238 2 ( 8. " " W. Taking from 180 do not change 1 180 thewestname 1 ( N.50 34W. ) Sun's bearing by compass N. 5 37 E. \ Add-when one E. and, the other W. ~~^~^~' ) Correction (being variation and de- viation) 56 11W. Variation per chart 66 OOW. Deviation of the compass 11 W. for the point her head was at. Ex. 3. 1878, August 20th, 9h : 40m : A. M. , mean time at ship in latitude 38 30 S. , longitude 95 15' E., the sun's bearing by compass was N.E. by E. Altitude sun's lower limb 25 30' 00". Eye 20 feet. Required the true azimuth, correc- tion and deviation of the compass. Variation per chart, 16 W. Ans. True azimuth N. 46 22' E. ; correction, 9 53' W. ; deviation, 6 07' E. NOTE. When the correction and variation per chart are contrary names, add them for the deviation. Ex. 4. 1878, November llth, 4h:52m: P.M., mean time at ship in latitude 32 30' 45" N., longitude 45 30' W., the sun's bearing by compass was W.^N. Altitude sun's lower limb 15 55' 30". Index error + 1' 40". Eye 20 feet. Re- quired the true azimuth, correction and deviation of the compass. Variation per chart, 14 W. Ans. True azimuth S. 56 J 12' W.; correction, 39 26' W.; deviation, 25 26' W. Ex. 5. 1878, December 15th, 8h:51m: A.M., mean time at ship in latitude 48 56' N., longitude 59 17' 30" W., the sun's bearing by compass was S. Alti- tude sun's lower limb 12 16' 30". Index error - 3' 10". Eye 20 feet. Required the true azimuth, correction and deviation of the compass. Variation per chart, 31 W. Ans. True azimuth S. 29 52' E.; correction 29 5? W.; Deviation, 1 OS' E. Ex. 6. 1878, June 17th, 3h: 40m: P.M., meantime at ship in latitude 29 30' N., longitude 125 45' E., the sun's bearing by compass was N. W.^N. Altitude sun's lower limb 11 30' 20". Index error + 1' 29". Eye 20 feet. Required the true azimuth, correction and deviation of the compass. Variation per chart, 2 W. Ans. True azimuth S. 110 26' W.; correction, 30 12' W.; deviation, 28 12' W. Ex.7. 1878, December 10th, 9h: 10m: A.M., mean time at ship in latitude 60 10' N., longitude 169 10' 30" E., the sun's bearing by compass was S.E. by S. Altitude sun's lower limb 4" 20' 30". Index error + 1' 20". Eye 20 feet. Required the true azimuth, correction and deviation of the compass. Variation per chart, 12 E. Ans. True azimuth S. 23 26' E.; correction, 10 19' E.; deviation, 1 41' W. NOTE. The deviation found is for that point of the compass the ship's head was at \vhen the observation was made. LATITUDE BY MERIDIAN ALTITUDE OF SUN. 65 LATITUDE BY THE MERIDIAN ALTITUDE OF THE SUN. First. Reduce the ship's longitude into time by multiplying the degrees by 4 and dividing by 60. Second. In page one of the month, Nautical Almanac (in this book) find the sun's declination for that day, and the hourly difference from the column of difference on the right; multiply this hourly difference by the hours and tenths of an hour of the longitude in time; point off from the right, the number of figures equal to the number of decimals on the hourly difference and longitude in time, the remaining figures will be seconds, which divide by 60 when it exceeds 60, and you have the correction, to be added to the declina- tion when the declination is increasing, but subtracted when de- creasing and in west longitude only. When the longitude is east, you must reverse the way of applying the correction; that is, when the declination is increasing subtract the correction, and when de- creasing add the correction. NOTE. See Table XII. for reducing the sun's declination at any meridian. Third. To the observed altitude apply the index error of the sextant (if any) according to the sign + add, or - subtract. Fourth. From Table VII. get the dip for the height of the eye, which is always subtracted. Fifth. From Table XIII. get the correction for apparent altitude, this, also, always subtracted, (this correction is the refraction and parallax,) or take out the refraction from Table VI. which subtract, and the sun's parallax, Table VIII. which is always to be added. Sixth. From page two of the month, Nautical Almanac (this book), get the sun's semi-diameter for that day, and add it to the altitude of the sun's lower limb, but subtract it if the upper limb is observed. This is called the true altitude of the sun's centre. Seventh. Take the true altitude from 90, which will give the sun's zenith distance, and give it the opposite name to the bearing of the sun; that is, if the sun bears north the zenith distance will be south, and if south call it north. Eighth. To find the latitude, add the zenith distance and declina- tion together when they are of the same name, but if one is north and the other south, subtract the less from the greater and call the latitude the same name as the greater. 5 66 PRACTICAL NAVIGATION. Ex. 1. 1878, August 10th, in longitude 124 30' W. the observed meridian alti- tude of the sun's lower limb was 37 10' 30", bearing north, the index error + 2' 40". Height of the eye 20 feet; required the latitude. Longitude 124 30' W. x 4 60)498 00 Long, in time 8h : 18m : Sun's dec. Aug. 10 1532'46"N. - 6 5 Cor. dec 1526'41"N. Hourly diff. 43". 95 8.3 13185 35160 60)36,4,785 6'04"785 Cor. 6'5"for 8h: 18m: To be subtracted because Declination decreasing, and longitude west. Obs. alt.... Index error. 37 10' 30" N. + 2 40 Cor. obs. alt 37 13 10 Dip Table VII - 4 17 App. Alt 37 08 53 Cor. Table XIII.. .-19 True alt 37 07 44 Sun's semid + 15 49 Sun's true alt 37 23 33 90 00 00 Zenith distance 52 36 27 S. Sun's cor. dec. . . 15 26 41 N. Subtract when contrary name*. Latitude in 37 J 09' 46" S. Called after the greater. Ex. 2. 1878, January 14th, in longitude 51 00' W. the observed meridian alti- tude of the sun's lower limb was 78 14' 10", bearing south, index error - 5' 50". Eye 18 feet; required the latitude. Ans. Sun's cor. dec. 21 15' 10" S.; latitude 9 35' 34" S. Ex. 3. 1878, September 23d, in longitude 159 00' W. the observed meridian altitude of the sun's lower limb was 70 54' 20", bearing north, index error - 3' 45". Eye 21 feet; required the latitude. Ans. Sun's cor. dec. 17' 35" S.; latitude 19 15' 41" S. Ex. 4. 1878, May 20th, in longitude 5 43' W. the observed meridian altitude of the sun's upper limb was 54 23' 10", bearing south, index error + 2' 10" Eye 20 feet; required the latitude. Ans. Sun's cor. dec. 20 01' 00" N.; latitude 55 56' 23" N. Ex. 5. 1878, January 20th, in longitude 5 20' W. the observed meridian alti- tude of the sun's lower limb was 22 10' 30", bearing south; index error - 3' 10". Eye 20 feet; required the latitude. Ans. Sun's cor. dec. 20 04' 59" S.; latitude 47 37' 53" N. Ex. 6. 1878, March 20th, in longitude 139 20' W. the observed meridian alti- tude of the sun's upper limb was 31 19' 40", bearing south, index error 4- 4' 15". Eye 20 feet; required the latitude. Ans. Cor. dec. 3' 38" N.; latitude 59 01' 31" N. LATITUDE BY MERIDIAN ALTITUDE OF SUN. 67 Ex. 7. 1878, November 16th, in longitude 171 00' E., the observed meridian altitude of the sun's lower limb was 71 "'43' 10", bearing South, index error - 1 20". Height of the eye 24 feet; required the latitude. Long 171 00' E. 4 60)684 00 Long, in time llh: 24m: Sun's dec. Nov. 16. 18 47' 29" S. - 7 6 Cor. Dec 18 40' 23" S. Obs. Altitude. 71 43' 10" S. - 1 20 - 4 4 71 37 08 - 16 + 16 13 Hr. dif 37".38 11 . 4 14952 3738 0*700 37 00 6.0)42.6.132 7' 06." 132 To be subtracted be- cause declination in- creasing, and longi- tude Eabt. 90 00 00 ~ 7r ~" " N. " " " S. Latitude in 00 33' 28" S. Ex. 8. 1878, March 31st, in longitude 155 45' E., the observed meridian alti- tude of the sun's lower limb was 68 55' 10", bearing south, index error -5' 40". Eye 19 feet; required the latitude. Ans. Sun's cor. dec., 4 3' 3" N. ; latitude, 25 02' 01" N. Ex. 9. 1878, September 23rd, in longitude 168 00' E., the observed meridian altitude of the sun's upper limb was 56 12' 20", bearing north, index error +3' 38". Eye 20 feet; required the latitude. Ans. Sun's cor. dec., 3' 40" N.; latitude, 34 01' 12" S. Ex. 10. 1878, March 20th, in longitude 45 30' E., the observed meridian alti- tude of the sun's lower limb was 63 5' 10", bearing north, index error - 4' 20". Eye 22 feet; required the latitude. Ans. Sun's cor. dec., 8' 30" S. ; latitude, 26 56' 30" S. Ex. 11. 1878, July 15th, in longitude 151 22' E., the observed meridian alti- tude of the sun's lower limb was 34 30' 20", bearing north, index error +4' 30". Eye 20 feet; required the latitude. Ans. Sun's cor. dec., 21 35' 34" N.; latitude, 33 39' 22" S. Ex. 12. 1878. June 10th, in longitude 130 55' E., the observed meridian alti- tude of the sun's upper limb was 55 25' 40", bearing north, index error -2' 57". Eye 20 feet; required the latitude. Ans. Sun's cor. dec., 23 0' 27" N.; latitude, 11 57' 28" S. G8 PRACTICAL NAVIGATION. TO FIND THE LATITUDE BY SEDUCTION TO THE MERIDIAN. NOTE. Tables required: log rising Table XVII; log co-sine Table II; log co-sine Table II; log natural number Table I; log natural sine Table XIV; natural co-sine Table XIV. First. Correct the watch, for what it is slow or fast for apparent time, and then apply the ship's run, viz: The difference of longitude made (in time) to the apparent time. If the time thus made is east, add, and if west, subtract; remember going east your time is behind, going west, your time will be too fast for the place you have got to. This will give the hour, angle, or time from noon. If the observation was made in the afternoon that is P.M. Second. Find the apparent time at Greenwich by turning the longitude into time by the usual method, viz: Multiplying by 4 and dividing by 6; if the longitude in time is west, add it to the hour angle (or apparent time at ship); and if east, subtract it. Third. If the time is A.M. add 12 hours to the time shown by watch, and change the date (as per rule) then apply the rate of the watch; if slow, add; if fast, subtract; next the ship's run if east, add; if west, subtract. This will give the apparent time at ship, which is to be subtracted from 24 hours, for the hour angle (or time from noon.) Fourth. To the apparent time at ship apply the longitude (in time), add if west, subtract if east; should the sum exceed 24 hours subtract 24 hours from the sum, and the remainder will be the Greenwich apparent time of the same name as date at ship. Fifth. Correct the sun's declination for the Greenwich time (as per rule), from page one of the month, Nautical Almanac, by the hourly difference. Sixth. Find the sun's true altitude by applying the index error, dip. correction from Table XIII and sun's semi-diameter. Seventh. Add together the log rising of the hour angle (Table XVII), log co-sine of the latitude, and co-sine of the sun's corrected declination (Table II). The sum of these logs (less tens in their index) will be the log of a natural number (Table I), to be added to the natural sine of the sun's true altitude (Table XIV), which gives the natural co-sine (Table XIV) of the sun's meridian zenith distance, of the opposite name to the bearing of the sun. Eighth. The zenith distance and the sun's corrected declination will give the latitude. If of the same name add them; if one north and the other south, subtract the less from the greater, and call the latitude after the greater. LATITUDE BY REDUCTION TO THE MERIDIAN. 69 Ex. 1. 1878, June 20th, P.M. at ship, in latitude by account 27 30' S., longi- tude 75 30' \V. The observed altitude of the sun's lower limb north of the ob- server was 38 20' 00"' Eye 16 feet. Time by watch Oh:29m:01s: P.M., which had been found fast for apparent time at ship lm:12s. The difference of longi- tude made since to the East was 9 miles; required the latitude by the reduction to the meridian. June 20th.. .. Fast Dif. Ion. 9'= Hour angle . . Long. 75 J 30' App. Gr'n'h) H. M. S. 29 01 P.M. 1 12 Sun's dec. . (Jr. 5h:3Um. 23 27' 10" K. 6 Hr. dif . 1".13 5.5 Obs. alt. . Dip . 38 20' 00" . 3 50 Cor 27 49 36 E. Cor. dec 23 27' 75 30' W. 4 10" N. 565 565 38 1C 10 1 5 Semid True alt. . 28 25 5 02 00 W. 6.215 38 15 05 15 46 60)302 00 5 30 25 . 3830'G1" KVi- no Time from noon .............. 28m: 25s: Latitude by account .......... 27 Sum's corrected declination... 23 Log rising 30' S ..................... Log cosine 27 N .................... Log cosine 2.88519 9.94793 9.96256 Natural number 625 Log. Hun's true altitude... ...38 31 Nat. sine... 62274 2.79568 Meridian zenith distance 51 bun's declination 23 01 S. Nat. cosine. 27 N. .G2899 Latitude 27 34' S. Ex. 2. 1878, October 28th, A.M. at ship, in latitude by account 25 40' N., longitude 45 35' W. The observed altitude of the sun's lower limb south of the observer was 50 53' 20". Eye 20 feet. Time by watch llh:23m:30s: A.M., which was slow to apparent time at ship 19m:OOs., and the difference of longi- tude made since to the east was 40 miles; required the latitude by the reduction to the meridian. Oct. 28 .11 23 30A.M. Sun's dec. . . 13 10' 44" 8. Hr. dif.50"25 Obs. alt.. . 50 53' 20" 12 Cor 2 21 Ap. T. G. 2.8 Dip . 4 17 Oct. 27 .23 23 30 Cor. dec... . 13 13' 05" S. 40200 50 49 03 Slow 19 00 1005 i Cor 41 Oct. 27 .23 42 30 60)140.700 50 48 22 Semid 16 9 Ap. time at 23 45 10 24 00 QO True alt.. . 51 04' 31" ship 27th ) > a o on w 23 4.) 10 Hr. angle. 14 50 G. T. Oct. 27.26 47 30 24 App. Gr'n'h) ._ time Oct. 28 } 2 Time from noon 14m: 50s Log rising 2.32093 Latitude by arcount 25 40' N Cosine 9.15488 Sun's decliuatioii 13 13 8 Cosine 9.98834 Natural number , Sun's true altitude 61 5 Nat. Sine , ... l 184 Log. .. 77806 2.26415 Meridian zenith distance 38 45' N. Nnt. Cosine : 77990 Hun's declination 13 13 S. Latitude 25 3U' N. 70 PRACTICAL NAVIGATION. Ex. 3. 1878, January 1st, A.M. at ship in latitude by account 6 0' N., longi- tude 87 45' west. The observed altitude of the sun's lower limb was 60 20' 10" south of the observer. Eye 16 feet. Time by watch llh:38m:20s: A. M., which was slow for apparent time at ship lm:20s; the difference of longitude made since to the west was 2 miles; required the latitude by reduction to the meridian. Ans. 63'N. Ex. 4. 1878, March 6th, P.M. at ship in latitude by account 42 2' S., longitude 166 0' west. The observed altitude of the sun's lower limb north of the observer was 52 U 48' 30". Index error + 1 ' 20". Eye at 20 feet. Time by watch Oh :25m : 30s: PM., which was fast for apparent time at ship 1m: 40s. The difference of longitude made since to the east was 38 miles; required the latitude by reduction to the meridian. Ans. 41 55' S. Ex. 5. 1878, October 20th, A.M. at ship in latitude by account 23 32' N., longitude 135 50' east. The observed altitude of the sun's lower limb south of the observer was 55 20' 10". Index error + 1' 10" . Eye 20 feet. Time by watch Oh:20m:OOs: which was fast 48m:OOs: for apparent time at ship. The difference of longitude made since to the west was 25 miles; required the latitude by the reduction to the meridian. An. 23 26' N. Ex. 6. 1878, September 24th, A.M. at ship in latitude by account 36 GO'S., longitude 159 30' east. The observed altitude of the sun's lower limb north of the observer was 53 45' 35". Eye at 20 feet. Time by watch 10h:20m:30s: A.M., which had been found to be slow lh:20:10s: of apparent time at ship. The difference of longitude made to the east was 25 miles after the error on ap- parent time at ship was determined. Index error- 1' 20"; required the latitude by the reduction to the meridian. Ans. 36 11' S. LATITUDE BY THE MERIDIAN ALTITUDE OF A STAR. 71 TO FIND THE LATITUDE BY THE MERIDIAN ALTITUDE OF A STAR. First. Correct the observed altitude for index error (when any). Second. Dip of the horizon (Table VII). Third. Correction for apparent altitude (Table XIII). NOTE. Re careful in taking out the correction from this table not to take out the sun's correction, in place of the star's correction. Fourth. Take the star's true altitude from 90 for the zenith dis- tance, and call it of contrary name to the bearing of the star when observed. Fifth. To the zenith distance apply the star's declination, found in the (Table of Fixed Stars) pages (242 to 245) of the American Ephemeris and Nautical Almanac for 1878. NOTE. The sign -f* (placed before the declination) stands for north declination. The sign * stands for south declination. Sixth. If the declination and zenith distance are of same name, add them for the latitude; when of contrary names, subtract them, and call the latitude of the same name as the greater. Ex. 1. January 1st, 1878, the meridian altitude of the star, a Virginis (Spica) was 31 27' 40" bearing south, index error +5' 20". Eye at 20 feet. Required the latitude in. Observed altitude 31 27' 40" S. Index error . . . . . . + 5 20 31 33 00 Dip. Table VII - 4 17 31 28 43 Correction Table XIII.... - 133 Star's true altitude 31 27 10 90 00 00 Zenith distance 58 32 50 N. Star's declination 10 31 25+S. Latitude 48 01' 25" N. Ex. 2. January 1st, 1878, the meridian altitude of the star, a Aurigoe (Capella) was 87 J 30' 40" bearing north. Eye 20 feet. Required the latitude in. Ans. Latitude, 43 18' 38" N. 72 PEACTICAL NAVIGATION. N Ex. 3. January 1st, 1878, the meridian altitude of the star, a Geminor (Castor) was 70 50' 30" bearing south, index error - 3' 10" to subtract. Eye 20 feet. Re- quired the latitude in. Ans. 51 26' 12" N. Ex. 4. January 1st, 1878, the meridian altitude of the star, b Orionis (JRigel) was 50 31' 50" bearing north, index error-f2' 10" to add. Eye 18 feet. Re- quired the latitude in. Ans. 47 51' 39" S. Ex. 5. January 1st, 1878, the meridian altitude of the star, 6 Geminor (Pollux) was 33 30' 20" bearing north. Eye 18 feet. Required the latitude in. Ans. 28 16' 01" S. Ex. 6. January 1st, 1878, the meridian altitude of the star, a Argus (Conopus) was 30 10' 15" bearing south, index error --3' 15" to subtract. Eye 16 feet. Required the latitude in. Ans. 7 20' 42" N. Ex. 7. January 1st, 1878, the meridian altitude of the star, a Aquilae (Altair) was 67 42' 30" bearing south, index error - 3' 40" to subtract. Eye at 20 feet. Reqnired the latitude in. Ans. 30 58' 42" N. LONGITUDE BY CHRONOMETER. 73 TO FIND THE LONGITUDE BY CHEONOMETEE. Rules for finding the Accumulated Rate, and whether the Chronometer is Losing or Gaining, etc. First. Take the given time by the chronometer, and apply the error giveii on the last date. Second. If fast the error is to be subtracted, if slow the error is to be added; then you have the chronometer regulated up to the time the last error was given. Third. Get the difference between the two errors and their dates; when both errors are slow or both fast, subtract; one slow and the other fast add them together, then bring this difference into seconds (if in minutes and seconds) by multiplying by 60, then the difference in seconds between the two errors is to be divided by the number of days between the given errors, and to what remains annex a cipher, and divide again for the tenths or decimal part of the daily rate. Fourth. Next, the number of days from the date of the last error and date of the chronometer is to be multiplied by the daily rate, (taking in the hours of the chronometer time as a decimal of a day by annexing a cipher to the hours, and dividing by 24), after cutting off the decimals, you have the accumulated rate from the last error given to the time shown by chronometer, which is to be added to the chronometer time when losing and subtracted when gaining. Fifth. To know when gaining or losing, use the following rules: ( When the chronometer is slow at 1st date, and at 2d date still slower. LOSING. < When the chronometer is fast at 1st date, and at 2d date not so fast. ( When the chronometer is fast at 1st date, and at 2d date is slow. ( When the chronometer is fast at 1st date, and at 2d date still faster. GAINING, -j When the chronometer is slow at 1st date, and at 2d date not so slow. ( When the chronometer is slow at 1st date, and at 2d date is fast. Ex. 1. Suppose the first date to he July 1st, and the second date September 20th. Interval or elapsed time 81 days. H. M. s. July 1st, slow 1 03 20 Sept. 20th, slow. . . 1 5 13.4 Slow and more slow, losing. Difference lost 1 53.4 60 Days elapsed 81)113. 4(ls.4 daily rate losing. 81 32.4 32.4 74 PKACTICAL NAVIGATION. Ex. 2. H. M. S. H. M. s. January 28th 3 27 18 Slow, January 1st 1 25 55 j January 1st, slow. . 1 25 55 Slow, January llth.' 1 25 20 j M. T. G., Jan. 1st. 4 53 13 As 10 days is to =35:27.2 Gain in 27d:5h - 1 35.2 Days from Jan. 1 to Jan. 28th. 27. 2 M. T. G., Jan. 28th 4 51 37.8 70 245 70 1.0)95/2.0 6.0)9.5.2 Gain in 27.2 days 1.35.2 Ex. 3. M. s. } July 1st, fast 10.4 > *Fast and then slow, losing. Sept. 20th, slow.... 1 43 ) Difference lost. . . 1 53.4=ls.4 losing daily. * Fast and slow, the sum is the difference. Ex. 4. M. s. ) July 1st, fast 3 20 > Fast and more fast, gaming. Sept. 20th, fast 5 13.4 ) Difference gained. 1 53. 4= Is. 4 gaming daily Ex. 5. M. s. } July 1st, slow 5 13.5 > Slow and less slow, gaining. Sept. 20th, slow 3 20 ) Difference gained . 1 53. 4 = 1 s. 4 gaining daily. Ex. 6. M. s. ) ' July 1st, slow 1 43 > *Slow and fast, gaining. Sept. 20th, fast 10.4 ) Difference gained. 1 53. 4= Is. 4 gaining daily. * Slow and fast, the sum is the difference. RULES FOB FINDING THE LONGITUDE. 75 KULES FOR FINDING THE LONGITUDE. First. After finding the mean time at Greenwich take out the declination from page two of the month. Nautical Almanac (this book) (or from the American Almanac, 1878) and correct it by the hourly difference found on page one of the month; multiply this hourly difference by the mean time at Greenwich, after divid- ing the minutes by G, same as in azimuth; this will give the cor- rection to be added to the declination when increasing, and sub- tract when decreasing. If correcting back from the following day, which may be done (when the hours of Greenwich time exceed 15); then by taking the mean time at Greenwich from 24 hours, you can get the next day's declination, and correct it back for what it wants (in time) of being noon of the next day, in which case you must sub- tract the correction when increasing, and add it when decreasing; this method has to be done on account of the difference for an hour in the Almanac being different in quantity Second. Take out the equation of time from page two in the Al- manac also, and correct it in the same manner as the declination; but when applying it to the apparent time at ship, always go by the rule at top of page one of the month in the Nautical Almanac. Third. If the declination and latitude are both north or both south, the declination is to be taken from 90 for the polar distance; but if one is north and the other south, the declination must be added to 90 for the polar distance. Fourth. Correct the sun's altitude in the same way as for the meridian altitude, first for index error (if any,) next the dip of the horizon (Table VII,) then the correction from (Table XIII), and sun's semi-diameter from the Nautical Almanac. Fifth. Add together the true altitude, the latitude, and polar dis- tance, divide this sum by 2, and call it the half sum, then take the true altitude from this half sum and call it ths remainder. NOTE. If the polar distance exceeds 90, take the secant of the corrected declination, in place of the co-secant of the polar distance. Sixth. Add together. * Secant of the latitude. Co-secant of the polar distance. Co-sine of the half sum. Sine of the remainder. H To seconds. Seventh. The sum of these four logs, rejecting 10 in their index, being added together will give the apparent time at ship in (Table XVIII), when a P.M. sight, and of the same date as the question; but if the sight be A.M., the time thus found is to be taken from 24 hours for the apparent time at ship, which date one day back of the date at the head of the question. 76 PKACTICAL NAVIGATION. Eighth. To the apparent time at ship apply the equation of time (according to the rule found at the top of page one, Nautical Al- manac), and this will give the mean time a, u ship. Ninth. If the mean lime at Greenwich is of the same date as mean time at ship, subtract the less from the greater, and that will be the longitude in time; but should either of the two times be of different dates, add 24 hours to whichever^ is the greatest date before sub- tracting, then turn the time into degrees by Td*ble XI, and name the longitude east, if Greenwich time is least ; and west, if Green- wich time is best. Tenth. Should the longitude in time exceed 12 hours, take it from 24 hours, before turning it into degrees; do not forget to change its name. Ex. 1. H. M. s. Mean time at ship. March 5th 20 14 36 Mean time at Greenwich, March 5th. 7 13 36 13 01 00 24 00 00 Longitude in time . . 10 59 00= 164 45' 00" W. . Eleventh. To find the logs, for seconds, take the difference be- tween the logs, for the given minutes, and the next higher number of minutes; multiply this difference by given number of seconds, and divide by GO; add the' quotient to the log. found for degrees and minutes, in the case of sine and secant; subtract it in the case of co-sine and co-secant. (See explanation of Table II.) Twelfth. To reduce the latitude to the time of observation. Remem- ber the latitude must always be reduced to the time of observation, and the usual method of doing this at sea, is to find the difference of latitude the ship has made in the interval between the time the sights were taken and the correct latitude obtained by observation at noon. With the course and distance sailed from time of sights enter (Table III) and find the difference of latitude in the latitude column, this difference is to be applied according to the course the ship has been steering; viz: "When the sights are taken in the after- noon, and in north latitude, and sailing north, add the difference of latitude; when sailing south, subtract the difference of latitude. Thus you will have the correct latitude of the ship at the time of sights. To apply this rule in south latitude simply substitute south for north. Thirteenth. To reduce the longitude by chronometer at time of sights to noon. Take the latitude in as a course, and the departure made in the interval, in the latitude column, the difference of longitude is found in the distance column. Apply this as follows: Observation taken in the morning, in west longitude. | g*|ifo| ^^' subtract. Observation taken in the afternoon, in west longitude. |^|l} u f ^J*' J^rf*"" 5 *' To or from the longitude by chronometer, will give the longitude in at noon. By substituting east for west, the same rule may be applied in east longitude. RULES FOR FINDING THE LONGITUDE. 77 Fourteenth. When the latitude arid declination is 0' 0"t take the true altitude from 90, and the zenith distance turned into time is the apparent time at ship if P.M., or taken from 24 hours for the apparent time if A.M. sights. Ex. 1. 1878, January 28th, P.M., at ship in latitude 32 44' 34" N. The ob- served altitude of the sun's lower limb was 22 3' 20"; index error+1' 02". Eye 20 feet Time by chronometer, 2Sd:3h:27m: 18s., which was slow for mean noon at Greenwich, lh: 25m: 55s., January 1st.; and on January llth was elow for mean noon at Greenwich lh: 25m: 20s. Required the longitude by chronom- eter. H H. 8. H. M. 8. Sun's dec .. 18 9' V S. H. dif . 3U".76 January Slow Jan 28th.... llth... 3 1 27 18 25 20 Slow Jan. Ift.. blow Jan. llth . 1 2:> Co .. 1 25 20 Cor 4k: for ] 52iu. J - 313 . 4.8G 4 52 38 Gain 10 days... .. = 35 Cor dec.. ... 18 f. 50 S. 3 18< JO a K M T G Jan 28 .| 51 38 Jan. llth to 28th. 17.2 Pol dis... . . 108 fi' RC" 6 0)193" 1850 7.0 '- S.13 245 35 6.0)6.0.?0 Accumulated rate, i.0.2 Observed altitude. 22 Index error 4- , 3 , 2Q 1 02 Equation of time . . . Cor. for 4h:52m Cor. equat'n of time. Secant = 0.075149-'' Co-sec. = 0.022038 Co-sine = 9.167739 Sine...= 9. 934430 \ M. S. 13 14.02" + 2.25 Hr. dif. 464 X Cor Dif 4.86 2784 3712 1850 22 Dip. for 2t)feet... - 22 Correction (table 13) - 4 4 2 22 17 05 12 13 16.27 075103 + 46 ,075149 021999 + 39 .2".-25E(.4 .... 85 Seconds. Cor Dif. 34 324 243 6.0)275.4 45.54 42 21 Sun's semidiameter + True altitude 22 Latitude 32 57 16 14 44 05 53 16 09 34 5tf . Polar distance 108 Sum 163 04 32 18 39 19 10 Seconds. 66 Cor Dif 252 210 6.0)235.2 Sum 81 \ 022038 168008 \ - 269 Remainder 59 H. App. time at ship ) January 28th. \ ' Equation of time. + Bf. 7 13 s. 32 16 i 9 19936 r> ' . ... 39.12 'U 67739 934424 . + 12 649 Seconds. 19 Cor Meantime atshipj q January 28th. j Mean time at j . Green'li Jan. 28. f 20 51 48 38 7C4 8491 6.0)10131 \934436 It ... 268.51 Lon 1000,4' XT Ans. Latitude of B 18 34' N. Longitude 72 53' E. Difference of latitude 348 Meridian difference latitude 362 Difference of longitude 1663 Course N. 77 43' E. Distance 1636 miles. EXAMINATION PAPERS. 85 Ex. 5. 1878, May 29th, 6h:30m: A.M., apparent time at ship, in latitude 29" 46' N., longitude 15' 40" E. The sun's magnetic amplitude was E.fS. Re- quired the true amplitu.de, and error of the compass, and supposing the variation to be 19" W., required the deviation of the compass for that position of the ship's head. C Sun's corrected declination 21 36' 45" N. True amplitude '. E. 25 7' N. Aus> ] Compass correction 3333'W. [ Deviation of the compass 14 33'W. Ex. G. 1878, August 25th, A.M., at ship in latitude 9 50' 15" S., the observed altitude of the sun's lower limb was 32 15' 20", index error-f 3' 40". Eye at 20 feet. Time by chronometer, 24d: 18h:58m:20s., which was slow for mean noon at Greenwich 2h:7m:33s. May llth, and on June 10th was slow for mean noon at Greenwich 2h : 5m : 48s. Required the longitude by chronometer. C Mean time at Greenwich, August 24th 20h:59m:43s. Polar distance 100 46' 30" Ans. < Sum of four logarithms 9.313965 Mean time at ship, August 24th 20h:26m: Ols. I Longitude 8 25' 30" W. Ex. 7. 1878, April 15th, 7h:21m: A.M., mean time at ship, in latitude 24 44' N., longitude 91 00' W., the sun's magnetic azimuth was E.fN., observed alti- tude of the sun's lower limb was 22 10' 40". Eye at 20 feet. Index error 0' 00". Required the true azimuth, correction, and deviation of the compass. Variation per chart, 9 east. Ans. - ' Mean timejat Greenwich, April 15th Hi : 25m. Polar distance 80 09' 24" Sum of four logarithms 19. 705025 True azimuth S. 90 48' E. Compass correction 7 38' E. Deviation of the compass 1 22' W. Ex. 8. 1878, January 1st, A.M., apparent time at ship, latitude by account 6 10' N., longitude 8745'W.,the observed altitude of the sun 'slower limb bear- ing south was GO 20' 10". Eye at 16 feet. Index error 0' 00". Time by watch, lib: 38m: 20s: A.M., which was found to be slow 1m: 20s. for apparent time at ship. The difference of longitude made since to the west was 2 miles. Required the latitude by reduction to the meridian. Ans. f Hour angle 20m : 28s. Sun's corrected declination 22 58' 53" S. I Sun's true altitude 60 32' 10" [Latitude 6 3' 0" N. Ex. 9. 1878, the observed meridian altitude of the star B. Geminor was 33 30' 20", bearing north. Index crror+0' 0". Eye at 18 feet. Required the latitude. . j Star's declination 28 19' 10" N. Ans< 1 Latitude. . . . 28 16' 10" S. 86 PRACTICAL NAVIGATION. Ex. 1. No. 3. HOUBS. 1 1 COTIESES. KNOTS. 1 WINDS. LEEWAY. DEVIAT'N. KEMABES, ETC. 1 w.s.w. 6 N.W. byN. i 17W. A point. 2 6 " In latitude 48 25' N 3 II 6 (< In longitude 57 19' W. 4 5 E.JN. 6 8 9 N.fE. i 174E. Bearing by Comp. , W.fN. Head N.W. Dev .54 E. 6 " 9 7 " Distance 19 miles. 7 " 9 7 " Variation, 20 W. 8 " 9 "7 (i 9 E.S.E.!S. 9 9 S.byW.4W. i 14 E. 10 " 9 7 " 11 " 9 7 " 12 " 9 7 tf ' 1 N.E. 10 8 X.W. byN. H 17 E. 2 " 10 8 " 3 " 10 7 " 4 a 10 7 " 5 N.E.4E. 7 5 N.E. by E. 1 20 E. 6 " 7 5 7 ti 7 it 8 i< 7 " A current set by compass 9 W.18. 6 S.fW. i 14W. N. 22 W. (corr't magnetic) 10 v 4 it 26 miles from the time the 11 (i 3 " departure was taken to the 12 3 , end of the day. Ans. corrected N. 84 E. ..N. 42 W. ( Bearin Current " 1st course '* 2d " " 3d ' " 4th " " 5th " " 6th " " Difference of latitude.. 27'. True course N. 76 E. I Latitude in 48 52' N. .S. 22 W Distance 24 miles S. 84 E. .S. 82 E. .N. 56 E. .N. 42 E. .S. 59 W. Departure 38 39 43 29 16 110'. 2 Distance 113 miles Longitude in 54 31' W. Ex. 2. 1878, December 1st, in longitude 11445'E. The observed .meridian altitude of the sun's upper limb was 69 26' 40" bearing S. ; index error - 5' 43". Height of eye 21 feet. Required the latitude. Sun's corrected declination 21 47' 50" S. Latitude . . 47' 49" S. Ans. Re- Ex. 3. In latitude 69 11' S. the departure made good was 64.75 miles. quired the difference of longitude by parallel sailing. Ans. Difference of longitude 182.2 Ex. 4. Required the course and distance from A to B by calculation on Mer- cator's principle. ( Latitude of A 17 36' N. Longitude 146 5' E. Latitude of B 23 46' N. Longitude 121 55' W. A J Difference of latitude , 370 ' I Meridian difference latitude 396 Difference of longitude 5520 I Course . . . N. 85 J 54' E. Distance 5175 miles EXAMINATION PAPERS. 87 Ex. 5. 1878, October 21st, 5h:23m: A.M. apparent time at ship in latitude 47 51' S., longitude 30 17' E. The sun's magnetic amplitude was S.E.JE. Required true amplitude and error of the compass, and supposing the variation to be 32 W., required the deviation of the compass for that position of the ship's head. C Sun's corrected declination 10 37' 39" S. I True amplitude E. 15 58' S. s< I Compass correction 23 13' W. [_ Deviation of the compass 5 47' E. Ex. 6. 1878, December 28th, A.M. at ship in latitude 50 Q 55' N., the observed altitude of the sun's lower limb was 10 58' 30", index error - 1' 20". Eye at 20 feet. Time by chronometer 27d:20h:10m:54s:, which was slow for mean noon noon at Greenwich 2h:35m:53s: October 3d, and on October 21st Avas slow for mean noon at Greenwich 2h :34m: 50s: Required the longitude by chrono- meter. f Mean time at Greenwich December 27th 22h:41m:46s: j Polar distance 113 17' 25" Ans. -I Sum of four logarithms 8.835525 I Mean time at ship December 27th 22h:00m:27s: I Longitude 10 19' 45" W. Ex. 7. 1878, November 4th, 2h:46m: P.M. mean time at ship in latitude 53 55' 15" N., longitude 163 49' 30" E., the sun's magnetic azimuth was S.W.fS. Ob- served altitude of the sun's lower limb 11 13' 10". Eye at 18 feet. Index error 1' 20". Required the true azimuth, correction and deviation of the compass. Variation of the compass 8 E. Mean time at Greenwich November 3d 15h:50m:42s: Polar distance 105 19' 54" Sum of four logarithms 19.126310 True azimuth S. 42 54' W. Compass correction 6 20' E. ^ Deviation of the compass 1 40' W. Ans. - Ex. 8. 1878, June 21st, P.M. apparent time at ship, latitude by account 8 10' N., longitude 100 33' E., the observed altitude of the sun's lower limb bearing N. was 73 45' 30". Eye at 12 feet. Index error - 0' 00". Time by watch llh: 54m: 10s P.M., which was found to be slow 26m:46s for apparent time at ship. The difference of longitude made to the west was 20 miles. Required the latitude by reduction to the meridian. "] Hour angle 19m:36s: Ans. 1 Sun ' s corrected declination 23 27' 30" N. j Sun's true altitude 73" 57' 43" ) Latitude 8 07' 30" N. Ex. 9. 1878, the observed meridian altitude of thu star A. Aquiloa was 67 3 42 30", bearing S. Index error 3' 10". Eye 20 feet. Required the latitude. A j Star's declination 8 32' 45" N. AnSl I Latitude 30 58' 42" N. 88 PEACTICAL NAVIGATION. Ex. 1. No. 4. HotTES. | 1 COURSES. W w M O WINDS. LEEWAY. DEVIAT'N HEMAKKS, ETC, 1 S.byW.fSV. 3 9 West. J 1 326' w A point. 2 " 3 8 " In latitude 49 3' S 3 4 3 " In longitude 166 12' E. 4 5 South 4 5 3 W.byS. s 520' E. Bearing by comp. SWby WW Head S. by E. Deviat'n 8 U E. 6 " fi 7 " Distance 21 miles. 7 " 5 4 " Variation 20 E. 8 " G G " 9 N. by E. 8 3 East, i 5' E. 10 " 8 9 " 11 " 8 9 " 12 " 8 9 " 1 W.byN.^N. 9 9 s.s.w.nv. ii 26 W. 2 " 10 3 . " 3 ' 10 4 " 4 " 10 4 " 5 W.byN. 10 4 North. i 2230'w 6 " 10 4 " 7 " 10 3 " 8 9 W.N.W. 9 9 9 9 S. W.byS. i 23 W. A current set by compass N.39 3 E. (correct magnetic )S 10 " 9 9 " miles from the time the de- 11 " 10 1 " parture was taken to the end 12 10 1 of the day. f Bearing corrected S. 87 E. Current " N. 59 E. 1st course " S. 25 W. 2nd " " S. 17 W. 3rd " " N. 25 E. Ans. { 4th " " N. G5 W. 5th " " N. 84 W. 6th " " N.62W. D ifference of latitude . . 38'. 6 True courses N .65 W. I Latitude in 48 24' S. - Distance 16 miles. 23 35 41 41 40 84'. 1 Distance 93 miles. Longitude in. . . . 164 4' E. Ex. 2. 1878, November IGth, in longitude 17114'E., the observed meridian alti- tude of the sun's lower limb was 71 43' 20", bearing south. Index error - 1' 30". Height of the eye 24 feet. Required the latitude. \ Sun's corrected declination 18 40' 22" S. Ans. 1 Latitude 33' 27" S. Ex. 3. In latitude 68 49' N. the departure made good was 677 miles, the difference of longitude by parallel sailing. Ans. Difference of longitude Required 1873 Ex.4. Required the course and distance from A. to B., by calculation on Mercator's principle. f Latitude of A 4 22' S. Longitude 18 21' E. I Latitude of B 68 20' S. Longitude 142 15' E Difference of latitude 3S38 Meridian difference latitude 5423 Difference of longitude 7434 Course S. 53 53' E. Distance 651 1 miles. Ans. EXAMINATION PAPERS. 89 Ex. 5. 1878, March 21st, 9li: 10m: A.M., apparent time at ship, in latitude 10 10' N., longitude 118 10' E. The sun's magnetic amplitude was E.N. Re- quired the true amplitude, and error of the compass, and supposing the variation to be 2" E., required the deviation of the compass for that position of the ship's head. r Sun's corrected declination 7' 36" N. j True amplitude E. 8' N. Ans> ^ Compass correction 2 41' E. Deviation of the compass 41' E. Ex. 6. 1878, March 21st, A.M., at ship in latitude 0' 0" S., the observed altitude of the sun's lower limb \?a3 36 15' 10". Index error-j-2' 38". Eye at 20 feet. Time by chronometer, 20d: 13h:21ui:50s., which was fast for mean noon at Greenwich 7m: 03.7s: January llth, and January 20th was fast for mean noon at Greenwich Gm : 25s. Required the longitude by chronometer. f Mean time at Greenwich, March 20th 13h:19m:41s. I Polar distance 89 52' 30" Ans. -I Sum of four logarithms 9.307006 Mean time at ship, March 20th 20h:33m: 20s. I Longitude 108 24' 45" E. Ex. 7. 1878, March 30th, 3h: 40m: 46s: P.M., meaji time at ship, in latitude 28 30' 15" S., longitude 174 20' W., the sun's magnetic azimuth was N. 80 52' 50" W., observed altitude of the sun's lower limb was 28 23' 40". Eye at 18 feet. Index error+5' 10". Required the true azimuth, correction, and de- viation of the compass. Variation per chart, 12 10' east. f Mean time at Greenwich, March 30th 15h: 18m: 6s. Polar distance 94 4' 37" Ans -I ^ um ^ * our lo aritnms 19.485071 I True azimuth N. 67 06' W. Compass correction 13 46' 50" E. * Deviation of the compass 1 36' 50" E. Ex. 8. 1878, November 16th, P.M., apparent time at ship, latitude by account 1 20' 30" S., longitude 171 00' E., the observed altitude of the sun's lower limb bearing south was 71 43' 20". Eye at 24 feet. Index error 1' 30". Time by watch on the 16th, 10h:31m:8s: P.M., which was fast lOh: 10m: 12s. for apparent time at ship. The difference of longitude made since to the east was 10 miles. Required the latitude by reduction to the meridian. (Hour angle 21m : 36s. Sun's corrected declination 18 40' 37" S. Sun's true altitude 71" 53' 05" Latitude 1 22' 00" S. Ex. 9. 1878, the observed meridian altitude of the star A. Spica \vas 31 27' 40", bearing north. Index error+5' 20". Eye at 20 feet. Required the latitude. A j Star's declination 10 31' 25" S. Ans< I Latitude 48 J 01' 25" N. 90 Ex. 1. PRACTICAL NAVIGATION. No. 5. Hotms. COUESES. KNOTS. 8 H l-t WINDS. LEEWAY. DEVIAT'N. EEMAEKS, ETC. 1 S.W.fS. 5 5 S.E. 1 G 30' W A point. 2 5 5 '< In latitude 34 28' S. 3 (1 5 11 In longitude 18 28' E. 4 5 N.byKfE. 6 6 5 E. by S. 1* 1230' E Bearing byComp., S.E.-|E. HeadS.E. Dev. 4 30' E. 6 " 7 5 (3 Distance 10 miles. 7 " 7 " Variation, 24 W. 8 a 7 " 9 KJS. 7 N.byE.JE. 1 15 E. 10 " 4 5 11 " 4 5 " 12 " 4 " 1 N.E.JN. 6 5 S.E.JS. 1 13 E. 2 " 6 5 " 3 " G " 4 " 6 " 5 SAY. IS. G 5 S.E.4E. i 345'W 6 " G 5 " 7 (i -6 5 it 8 " G 5 " A current set by compass 9 S.E.JE. 9 9 S.W. byW. i 725 / E. S. 46 E. (corr t magnetic) 10 " 9 8 " 10 miles from the time the 11 " 9 7 " departure was taken to the 12 9 G end of the day. f Bearing corrected N. 70 W. Ans. Current 1st course 2d ' 3d 4th ' 5th ' 6th ' Difference of latitude.. 10'.2 True course .......... S. 78 E. I Latitude in .......... 34 38' S. S. 70 E. S. 17 W Distance 22 miles ... N. 6 W. < 28 ....S. 82 E. ' 20 . ...N. 20 E. ' 25 ....S. 20 W. ' 26 . ...S. 70 E. ' 39 Departure 4G'.8 Distance 48 miles Longitude in 19 25' E. Ex. 2. 1878, June 10th, in longitude 30 30' W. The observed meridian alti- tude of the sun's lower limb was 78 19' 40" bearing N.; index error -4' 30". Height of eye 20 feet. Required the latitude. Sun's corrected declination . . . 23 2' 28" N. Ans. Latitude 11 28' 58" N. Re- Ex. 3. In latitude 48 28' N., the departure made good was 187 miles, quired the difference of longitude by parallel sailing. Ans. Difference of longitude 282' Ex. 4. Required the course and distance from A to B by calculation on Mer- cator's principle. Latitude of A 30 00' N. Longitude 30 00' E. Latitude of B 60 00' S. Longitude 150 00' W. A j Difference of latitude 5400 /ins. 4 Meridian diff cre nce latitude 6415 Difference of longitude 10800 I Course . . . S. 59 17' E. Distance 10571 miles EXAMINATION PAPERS. 91 Ex. 5. 1878, January 1st, 6h:40m: A.M. apparent time at ship in latitude 30 10' S., longitude 100 10' W. The sun's magnetic amplitude was E.fS. Required true amplitude and error of the compass, and supposing the variation to be 12 E., required the deviation of the compass for that position of the ship's head. f Sun's corrected declination 22 59' 45" S. J True amplitude E. 26 52' S. ns ' I Compass correction 18 26' E. (_ Deviation of the compass 6 26' E. Ex. 6. 1878, March 29th, P.M. at ship in latitude 33 8' 15" K, the observed altitude of the sun's lower limb was 27 U 58' 15", index error 2' 45" to subtract. Eye at 20 feet. Time by chronometer 28d:17h:16m:28s:, which was slow for mean noon noon at Greenwich lh:32m:17s: November 30, 1877, and on Decem- ber 30th, 1877, was slow for mean noon at Greenwich lh:28m:56s: Required the longitude by chronometer. , f Mean time at Greenwich March 28th 18h:35m:29s: Polar distance 86 38' 48" Ans. - Sum of four logarithms 9.375588 Mean time at ship March 29th 3h: 58m: 13s: Longitude.. ..140 41' 00" E. Ex. 7. 1878, April llth, 2h:7m:25s: P.M. mean time at ship in latitude 55 27' 45" S., longitude 52 OG' E., the sun's magnetic azimuth was N.JE. Observed altitude of the sun's lower limb 20 56' 45". Eye at 20 feet. Index error 3''40". Required the true azimuth, correction and deviation of the compass. Variation of the compass 36 W. (" Mean time at Greenwich April 10th 22h:39m:01s: Polar distance 98 21' 16" Sum of four logarithms 18.919596 True azimuth N. 33 30' W. Compass correction 39 07' W. ^ Deviation of the compass 3 07' W. Ans. Ex. 8. 1878, March 20th, P.M. apparent time at ship, latitude by accoimt44 30' N., longitude 119 00' W., the observed altitude of the sun's lower limb bearing S. was 45 2' 50". Eye at 22 feet. Index error- 7' 55". Time by watch Oh:29m:58s: P.M., which was found to be fast 3m: 30s: for apparent time at ship. The difference of longitude made to the east was 24 miles. Required the latitude by reduction to the meridian. * Hour angle 28m:04s: . i Sun's corrected declination 2' 46" N. Sun's true altitude 45 5' 39" Latitude.. . 44 31' 00" N. Ex. 9. 1878, January 1st, the observed meridian altitude of the star A. Regulus was 84' J 47' 20" bearing N. Index error +4' 20". Eye 11 feet. Required the lat- itude. Ans \ Star ' s declination 12 33' 40" N. Latitude.. 7 22' 11"N. 92 PRACTICAL NAVIGATION. Ex. 1. No. 6. HOURS. COUBSES. KNOTS. n | WINDS. LEE.WAT. DEVIAT'N REMABKS, ETC. 1 NEbyNiN. 4 8 S.E. byE. li 12 E. A point. 2 " 4 9 " In latitude 30 15' S. 3 ci 4 8 it In longitude 40 20' W. 4 5 N.N.W.JW. 5 5 5 5 W. by S. 2 730'W. Bearing by compass S. S. E. Head N.W. Dev. 4 30' W. 6 " 5 3 " Distance 10 miles. 7 " 5 3 " Variation 10 E. 8 " 5 3 " 9 N.E.JE. 4 S.E4E. 2* 1215' E 10 a 3 " 11 " 3 " 12 " 3 <( 1 N.JW. 4 9 W. by N. 2| 2 E. 2 " 5 8 " 3 " 6 8 " 4 " 7 5 " 5 N.fE. 7 1 E. by N. 2i 13 W. 6 " 6 3 " 7 " 6 3 " 8 " 6 3 " A current set by compass N. 9 N.E. 5 4 N.W. by N. 1 7 E. 25 W. (correct magnetic) 48 10 " 4 8 it miles from the time the de- 11 a 4 9 " parture was taken to the end 12 4 9 u of the day. Aus. f Bearing corr Current 1st course 2nd " 3rd " 4th " 5th " 6th " Difference of True courses ected N. 17W. - Distan ii ce 20 miles. 21.4 ' 13 ' 25 ' 26 ' 20 ' 30'. 1 156 miles. N. 15 W. N. 39 E. N. 3 W. N.42 E. N. 37 E. N. 20 W. N. 73 E. latitude.. 152'. 8 Departure. ..N. 11E. Distance.. Latitude in 27 42' S. Longitude in 39 46' W. Ex. 2. 1878, January 14th, in longitude 51 54' W., the observed meridian alti- tude of the sitn's upper limb Avas 78 35' 00", bearing south. Index error +5' 55". Height of the eye 18 feet. Required the latitude. \ Sun's corrected declination 21 15' 08" S. Ans. I Latitude 9 35' 32" S. Ex. 3. In latitude 66 40' S. the departure made good was 387 miles, the difference of longitude by parallel sailing. Ans. Difference of longitude Required 977.1 Ex.4. Required the course and distance from A. to B., by calculation on Mercator's principle. f Latitude of A 52 30' S. Longitude 167 30' E. Latitude of B 12 20' N. Longitude 92 32' W. Difference of latitude , 3890 Meridian difference latitude 4460 Difference of longitude 5998 Course. . . N. 53 22' E. Distance 6519 miles. Ans. EXAMINATION PAPERS. 93 Ex. 5. 1878, September 6th, 6h: 40m: A.M. apparent time at ship in latitude 38" 40' N., longitude 25 45' E. The sun's magnetic amplitude was E. by N. Required the true amplitude and error of the compass and supposing the varia- tion to be 8 \V., required the deviation of the compass for that position of the ship's head. r Sun's corrected declination 6 30' 46" N. I True amplitude. . . .E. 8 21' N. A YIQ J | Compass correction 2 54' E. (_ Deviation of the compass 10 54' E. Ex. 6. 1878, August 20th, P.M. at ship in latitude 36 41' 20" N., the ob- served altitude of the sun's lower limb was 23 27' 30", index error -3' 10". Eye at 19 feet. Time by chronometer 19d: 18h:10m:20s., which was slow for mean noon at Greenwich 24m: 46s: June 12th, and on June 20th, was slow for mean noon at Greenwich 25m : 30s. Required the longitude by chronometer. f Mean time at Greenwich, August 19th 18h:41m:24s: Polar distance 77 30' 10" Ans. -I Sum of four logarithms 9.514859 Mean time at ship, August 20th 4h: 42m : 24s: I Longitude . . 150 15' 0" E. Ex. 7. 1878, June 4th, 6h: 8m: P.M. mean time at ship, in latitude 47 30' N., longitude 16 20' W., the sun's magnetic azimuth was W.JN. Observed alti- tude of the sun's lower limb Avas 33 44' 40". Eye at 19 feet. Index error -2' 20". Required the true azimuth, correction and deviation of the compass. Variation per chart, 32 J W. f Mean time at Greenwich, June 4th 7h: 13m: 20s: Polar distance 67 30' 22" Sum of four logarithms 19.676223 True azimuth S. 87 04' W. Compass correction . 5 45' W. Deviation of the compass 26 15' E. Ans. Ex. 8. 1878, November 23d, P.M. apparent time at ship, latitude by account 50 30' N., longitude 38 30' W., the observed altitude of the sun's lower limb bearing S. was 18 49' 14". Eye at 20 feet. Index error - 4' 19". Time by watch Oh: 26m: 12s: P.M., which was found to be slow 2m: 20s: for apparent time at ship. The difference of longitude made since to the west was 18 miles. Re- quired the latitude by reduction to the meridian. r Hour angle 27m : 20s : Sun's corrected declination 20 25' 11" S. Ans> | Sun's true altitude 18 54' 13" Latitude 50 D 26' 00" N. Ex. 9. 1878, the observed meridian altitude of the star A Taurus was 50 17' 20" bearingS. Index error + 3' 10". Eye 20 feet. Required the latitude. . ( Star's declination 16 15' 54" N. ' < Latitude . . .56 00' 20" N. 94: PKACTICAL NAVIGATION. TO FIND THE LATITUDE AND LONGITUDE BY TWO OB- SERVED ALTITUDES, THE RESULT OF EACH COMPU- TATION BEING AT THE TIME AND PLACE WHERE THE GREATER ALTITUDE WAS TAKEN. The system of double altitudes herein introduced lias not heretofore been pub- lished in any American work, and its great advantage is that both latitude and longitude are thereby obtained simultaneously. First. Be careful to note the times by the same chronometer at each observation, and apply its error to the time shown when the greater altitude was taken, to obtain the mean time at Greenwich. Second. Take out the sun's declination on the given day from page two of the month of the nautical almanac, and correct it for Greenwich mean time by the hourly difference; the correction thus obtained is to be added when declination is increasing, but sub- tracted if decreasing. Third. Then ascertain the angle between the ship's course and sun's bearing at the time of taking the least altitude, with which, and the ship's run between the observations, find the correction for change of position, and apply the same, if any, to the least altitude. Fourth. If the less altitude be observed in the forenoon, add the correction thus found; if the angle is less than eight points, but if more, then subtract it. Fifth. If the less altitude is taken in the afternoon, then subtract the correction, if the angle is less than eight points; but if greater, then add it. Sixth. Should the angle between the ship's course and sun's bearing be equal to eight points or 90 degrees, then there is no correction to apply, because the lesser altitude is neither raised nor depressed. Seventh. In sailing directly towards or from the sun, apply the correction for the change of position in the following manner, viz: Eighth. When the lesser altitude is observed in the forenoon and sailing towards the sun, add the correction to the lesser altitude; but when sailing from the sun then subtract the correction from the lesser altitude. DOUBLE ALTITUDE. 95 Ninth. When the less altitude is taken in the afternoon and sailing but toward the sun, subtract the correction from the least altitude; when sailing from the sun, then add the correction to the least alti- tude. Tenth. Correct each of the altitudes for index error, if any; dip of the horizon, (Table VII, Kefraction Table VI, Parallax Table VIII), and sun's semi-diameter, Page 1 Nautical Almanac,) to be added to the sun's lower limb, but subtracted from the sun's upper limb to obtain the true altitude. Then proceed to find the latitude and lon- gitude of the ship when the greater altitude was observed, by the following rules : Eleventh. Add together the true altitudes and take half their sum; subtract the less altitude from the greater, and take half their difference. Twelfth. Find the interval between the times of observing the two altitudes, which call elapsed time; take half of the elapsed time and reduce it to degrees, by Table XI. Thirteenth. Add together the co-secant (Table II) of half the elapsed time, reduced as before, and the secant of the declination; their sum will be the co-secant of arc first. Fourteenth. Add together the co-secant of arc first, the co-sine of half the sum of the altitudes and the sine of half their difference; the sum of these logarithms will be the sine of arc second. Fifteenth. Add together the secant of arc first, the sine of half the sum of the altitudes, and the co-sine of half their difference, and the secant of arc second; their sum will be the co-sine of arc third. Sixteenth. Add together the secant of arc first, already found, and the sine of the declination; their sum will be the co-sine of arc fourth, when the latitude and declination are of the same name; but when they are of contrary names take the supplement for arc fourth, that is from 180. Seventeenth. Take the sum or difference of arcs third and fourth, for arc fifth. (See rule 20.) Eighteenth. Add together the secants of arc second (already found) and arc fifth, their sum will be the co-secant of the latitude when the greater altitude was observed, and the nearer it is taken to noon, the better. Having obtained the true latitude of the ship when the greater altitude was observed, proceed in the following manner to ascertain the longitude at the same instant. 96 PBACTICAL NAVIGATION. Nineteenth. To the co-secant of arc second add the co-nine of the latitude just found, their sum will give the co-secant of an arc in de- grees and minutes, which, converted into time by Table XI, produces arc A ; the difference between it and the half elapsed time will give the apparent time at ship when the greater altitude is taken in "the afternoon; but, should the greater altitude be observed in the fore- noon, then subtract it from 24 hours to obtain the apparent time past the preceding noon, to which apply the corrected equation for the mean time at ship; the difference between it and the mean time at Greenwich by the chronometer will be the longitude in time when the greater altitude was observed, which being converted into de- grees and minutes by Table XI, will produce the east longitude of the ship, if the time at ship be greater than Greenwich, but west, if less. Twentieth. When the sum of arcs third and fourth is equal to, or greater than 90, their difference is always arc fifth; bxit when their sum is less than 90, which will rarely happen, it may be doubtful whether their sum or difference ought to be taken for arc fifth, but the computation is soon made on both suppositions, for the secant of arc fifth is the last logarithm which is taken from the table, and the other parts of the calculation are therefore not affected by the change; one of the results must certainly be the required latitude, and the latitude by account will generally be sufficient to determine which of them ought to be taken. It may be useful to remark, the preceding not only applies to cases when the latitude and declination are of the same name, and very nearly alike in amount, in which case it becomes doubtful whether the sum or difference of arcs third and fourth shduld be taken to obtain arc fifth; hence it follows, such instances only occur between the tropics where the latitude by double altitudes is rarely observed, but should this method of ascertaining the ship's position be prac- ticed when the sun is vertical, or nearly so, then it becomes abso- lutely requisite to work the arcs very rigidly to the nearest second, on account of the difference of the sines answering to small arcs^ and co-sines of large ones varying so considerably; hence it is deemed advisable not to practice this method when the sun is within 5 of being vertical. DOUBLE ALTITUDE. 97 Ex. 1. April 13th, 1878, P.M., ship time at both observations in latitude by account 9 50' S., and longitude 10 24' W. Suppose the following true altitudes and times by chronometer were taken, to find the true latitude and longitude of the ship, the chronometer being 12m: 36s. slow of Greenwich time. H. M. S. Time by chron. at greater alt. 1 13 30 Chronometer slow + 12 36 Mean time at Green. April 13. 1 26 06 1st true alt. . 67 58 2nd true alt. 42 20 Sum 110 18. .Half sum. 55 09' Difference . . 25 38. .Half dif . . 12 49' Sun's dec. Apr. 13th. 9 06 13 N. Hr. dif. 54.30 + 1 16 1.4 Cor. dec 9 07 29 N. 21720 5430 6,0)76. "020 rie* H. M. S. Timebychr. Istobs. 1 13 30 2d " 3 24 20 Elapsed time 2)2 10 50 Half elapsed time . . 1 5 25. . 16 21' 15" Half el ap. time 16 21 15 Sun's dec 90729 1st arc 16 08 00 Half eum 550900 Half difference 12 49 00 2darc 27 08 00 ..Co-secant.. 0.550515 ..Secant 0.0055-21 Sine 9.200666 ..Co-secant.. 0.556036 Secant .. . . Co-sine 9.75GU03 Sine . . Sine 9.34W24 Co-sine . . 3d arc 20 36 00 Sine 9.659023 Secant .. ...Co sine.. 0.017449. . . .Secant .... 0.017449 9.914158 9.989042 0.050C36 80 29 9.218115 180 00 4th arc 99 31 00 Co-sine.. 99 31 5th arc 78 55 00 Marc 27 08 00.. ..Secant 0.716164 ..Secant 0.05063S.... Co-secant.. 0.340975 Latitudein ... 9 51 00 8. .Co-sec 0.7C6800... .Co-sine 9.993550 Co-secant.. C.334525....Arc A 27 34' H. M. S. Arc A in time 1 50 16 Half elapsed time 1 05 25 Apparent time at ship 44 51 Equation time + 31 Mean time at ship 45 22 Greenwich mean time. . . . 1 26 06 Longitude in time 40 44=10 11' 98 PRACTICAL NAVIGATION. Ex. 2. April 11, 1878, A.M. ship time at both observations, in latitude by account 43 J 10' N., and longitude G ' 32' W., when a chronometer showed 9h: 5S:n:36s. A.M. being 10m: 42s. slow of Greenwich mean time, the altitude of the sun's lower limb 39 J 45' 50", and at llh:4Sm:34s. A.M. By the same chronom- eter, the altitude of the sun's lower limb was 48 J 15' 25", the sun bearing at least altitude S. E.|E., and the ship's course between the observations Avas N.E.^N, The distance run being 14 miles; the height of the eye 18 feet, and index error 2' 10" to subtract. Required the true latitude and longitude of the ship, at the time of taking the greater altitude. H. M. S. , Apr. 11, time by chr. at greater alt . 11 48 34 A.M. Sun's dec. Apr. llth 8 22 29 N. 120000 Cor. for G. T.. 0000 Astronomical time, April 10th .... 23 48 34 Dec. for April llth 8 22 29 Chronometer slow -f 10 42 Taken out for the 11 as it wants Mean time at Greemvich Apr. 10th 23 59 16 & minute from noon of tUat date. Sun's bearing Avhen least altitude Avas taken S. E. E = S 4 points E. Ship's course between the observation N. E. N = S 12 points E. Angle between the ship's course and sun's bearing 8 .... points. Distance run 14 miles, with angle at 8 points, heuce, no correction for change of position. First observed altitude 39 45 50 Second observed altitude 48 15 23 Index error 2 10 Index error 2 10 39 43 40 48 13 15 Dip, Table VH , 04 04 Dip 04 C4 39 39 36 48 09 1 1 Refraction, Table VI 108 Refraction 51 39 38 28 48 08 20 Semi-diameter + 1550 Semi-diameter -f 1553 True altitude... .. 39 f,4 27 Sun's second true altitude... ..482419 o / // & M. s. First true alt. . . 39 54 27 Time by chr. at 1st alt. 9 5* ?6 A.M. Second true alt. 48 24 19 Time by chr. at 2nd alt. 11 43 31 A.M. Sum 83 1846 Half sum. 44 09' 23" Elapsed time 1 4'J 54 Half elapsed time 54 69=13 44' 45" Difference 829 r,2-Half dif. 4 14' 56" "' - Half elapsed time.. 13 44 45 Co-secant. O.C23997 Sun's declination... 8 22 29. ...Secant .. . 0.004666 Sine. .. 9.162885 Firstarc 133500 Co-secant. 0.6286H3... Secant... 0.019351... . Secant. 0.012351 Half sum 440023 Co-sine. . 9.855833 Sine 9.842946 Half difference 4 14 56 Sine 8 . 8(59863 Co-sine .. 9 . 998804 Second arc 13 04 00 Sine 9.354364 Secant... 0.011393 Third arc 42 48 CO Co-sine.. 9.865494 Fourtharc 812300 ... Co-sine. 9.1752*5 Fifth arc 38 35 00. ...Secant . .. 0.106959.... Second arc 13 04 00 Secant. .. 0.011393 Co-secant 0.645729 Latitude In 49 35 N...... Co-secant. 0.118352.... Co-sine.. 9.811655 Co-secant . 457384. . . . 20^5 / arc A. H. M. S. Arc A in time 1 21 40 Half elapsed time 54 59 Time from noon, April llth 26 41 24 00 00 Apparent time at ship, April 10th 23 33 19 Equation of time + 103 Mean time at sMp, April 10th 23 34 22 Mean time at Greenwich, April ICth... 23 59 16 Longitude in time 24 54.. Long., G 13' 30" W. NOTE. Take out the equation for the llth of April. NameUie latitude same namt as latiwde ly account, DOUBLE ALTITUDE. 99 Ex. 3. April 23, 1878, A. M. ship time at greater, and P.M. at lesser altitude, in latitude by account 39 30' S., and longitude 30 12' \V. Time by chronom- eter, Hi: 36m: 15s. P.M., which was fast for Greenwich mean time 7m: 15s. when first' altitude of the sun's upper limb was observed to be 38 10' 30", and at Gli: 3m:36s. P.M. the second altitude of the sun's lower limb was 36 20' 45". Sun's bearing N. byW.f. Ship's course between the observations N.N.E.-iE. Dis- tance rim during the interval 10 miles. Index error 2' 30" to subtract. Height cf the eye 22 feet. Kequired the latitude of the ship at the time of taking the greater altitude. H. M. 8. April 23, chr. showed... 1 3G 15 Fast for G. M. time 1 15 1 29 00 24 00 00 Sun's dec. April 23.... 12 34 56 1 H Hourly diff Correct declination.... 12 36 10 49.85 1,5 24925 4985 G. M. time, April 22.... 2.) 29 00 6.0)7.4.775 1' 14" Sun's bearing when last observation was taken _.N.byW. % W.=N. 1% points W. Ship's course during the elapsed time N.N.E. J$ E.=N. 2M points E. Angle between the ship's course and sun's bearing 4^ The angle between the ship's course and sun's bearing 4?4 points is to be taken as a course in Table III., and the distance run during tlie elapsed time (10 miles), as a distance, gies in the latitude column, C' 7"=6' 42, whicliis to be subtracted from the less altitude, the angle being less than eiyfit points, and the less altitude having been taken in the afternoon. UPPER LIMB, o < ,// LOWER LIMB. o , First obs. alt 38103) Second obs. alt b6 20 45 Index error ,2 30 Index error 2 30 33 03 00 36 18 15 Dip 430 Dip 430 33 < 3 30 30 13 45 Kef 113 Kef 118 33 02 17 3(5 12 27 Parallax + 08 Parallax + 8 38 02 25 36 12 35 Semi-diameter 1356 Semi-diameter + 1556 True altitude. ^..^.^-^..^ 37 46 29 True altitude sun's center 3628 31 . Correct.on for change of position . . 6 42 Sun's correct altitude 36 2) 49 ALTITUDES. TIMES. o / // H. M. s. First alt 37 40 29 1 3<> 15 P.M. Greater alt. obs. Second alt ... .3(5 21 49 3 03 36 P.M. Less alt. obs. Sum 74 08 18 Half sum. 37 04' 09" 1 27 21 Elapsed time. Difference 1 24 40 Half diff. .. 42' 20" 43 40 Half elapsed time ..10 55' Half elapsed time fo 55 Co-secant.. 0.7226G3 Jjeclmatiou 1236 Secant 0.010587 Sine 9.338742 Arc first 1039 Co-secant.. 0. 733250.... Secant. .. 0.007546... Secant... 0.00734C Hulf sum of alt 3704 Co-sine 9.9011)67 Sine 9.780133 Half diff. of alt 42 Sine 8.08288 Arc fifth 50 43.... Secant 0.19R489 Arc second 301 Secaut 0.000009 LATITUDE IN 39 13 S.. Co-secant. . 0.199098 100 PRACTICAL "NAVIGATION. Ex. 4. September 8, 1878, A.M., at ship in latitude GO 10' S. by account, and longitude 178 45' E., the altitude of the sun's lower limb was observed to be 19 42' at 10h:04m:20s: apparent time, the sun's center bearing N.N.E. by com- pass, and at Ih: 32m: 36s: P.M. by same chronometer, the second altitude was 21 08' 10" (being the greater). The ship's course during the elapsed time was S.W. by S., and the distance run in the interval was 31 miles. Height of the eye 16 feet. Required the latitude of the ship at the time of taking the greater altitude. H. M. 8. , Ap. time at ship at greater altitude. 13236P.M. Sun's dec. Sept. 7th. 6 01 44 Hourly dif. 56.23 Long. 178 45' E. 24 00 00 Correction 1245 13.6 253236 Correct declin 5 48 59 N. 33738 60)71500 Long, in time... 11 5500 E. " =11 55 G. M.T. Sept. 7..13S736 3G8G9 5623 bhip's course during the elapsed Angle between the ship's course To be taken out as a course, Tab First observed altitude (least) . . Dip time was { 5."W. by S.=N! 13 points^ 15 points. 16 1 point. and sun's be: le II, (and di . 194200 . 3 50 iring [stance 31 miles) Second observed alt. Dip , (greatest).. . . 21 08 10 350 Refraction Refraction It) 38 10 . 2 40 21 04 20 2 27 19 35 30 . + 8 21 01 53 -|- 8 19 35 38 Semi-diameter +1555 21 02 01 Semi-diameter + 15 55 True altitude 195133 Correction for change of position. 30 24 Correct altitude ... . . 1 9 21 09 A.M. True altitude.... 21 17 56 P.M. NOTE. The observation being in the forenoon, and angle, more than 8 points, subtract the correc- tion, 3U 24'. TRUE ALTITUDES. First obs. alt..l9 2'l 09 Sec'd obs. alt.. 21 17 56 Sum 40 39 05 Half Bum. 20 19' 32" Difference... . 1 56 57 Half dif .. 58' 33" TIMES. E. M. s. 10 04 20 A.M. less altitude observed. (Add 12 hours..) 1 32 3G P.M. greater altitude obs. 3 28 16.. Elapsed time. 1 44 08. .Half elap. time, 26 02'. Half clapped time.. 2602 Co-secant . 0.357640 Correct declination. 549 Secant.... 0.002242 ..Sine 9.C05805 Arc first Half Burn of alt.. Half dif. of ait... Arc second... 2554 Co-secant. 0. 353882.... Secant .. 0.045971 Secant.. 0.045971 20 19j....Co-sine.. . 9.972081 Sine .... 58J$ Sine 8.230029 Co-sine 9.540772 9.999937 205 Sine 8. 561992.... Secant .. 0.000287 Arcthird 6716 Co-sine. 9.586967 Arc fourth 96 28= (180 83 32') X3o-sine Arc fifth 2912 Secant.... 0.059025 Arc second ... 205 Secant 0.000287 LATTTCDEIN 60 44 S.... Co-secant . 0.059312 9.051776 DOUBLE" ALTITUDE. 101 Ex. 5. September 9, 1878, A.M. at ship in latitude by account 630'N., at ISh: 16m: 20s: by a chronometer showing Greenwich mean time, the altitude of the sun's lower limb was 35 10' 30", and at 20h: 36: 20s: by the same chronom- eter the altitude was 69 49' 30" ; the height of the observer's eye 18 feet. Re- quired the latitude at the time of taking the greater altitude. H. M. 8. o / // // Gr. mean time Sept 8. .20 80 20 (at greater alt.) Sun's dec. Sept. 9. . 6 16 33 Hourly dif . 60.70 =^=. Cor. for ah: 24m 313 3.4 Corrected declin. . . 6 19 46 N. 22G80 17010 60)19.2.780 3f -I t\ff I-OA la . I oU Correction for Zh.-llm: from noon of the 9th to be added, as the declination is decreasing from noon of the Stk, ana therefore we correct for the nearest noon. First obs. alt. Bun's lower limb 35 10 30 Second observed altitude 69 49 'M Dip 404 Dip 404 35 06 26 69 45 26 Refraction 121 Refraction 21 Parallax. 35 05 05 69 45 05 + 08 Parallax + 03 35 05 13 69 45 08 Semi-diameter + 1555 Semi-diameter -f 1565 Sun's true altitude at first obs 35 21 C8 Second true altitude.... .. 7001 03 TEOE ALTITUDES. First iiltitude... 35 21 Second altitude. 70 01 TIME BY CHHOXOMETEB. H. M. s. 18 16 20 20 36 20 Sum 105 22 Half sum alt.. 52 41' 2 20 CO Elapsed time. 1 10 Ou Half elap. time=17 SO' Difference 34 40 Half dif. alt.. 17 20' Half elapsed time. Sun's declination . Arcfir=t Half sum of ait Half dif. of alt... 17 30 Co-secant . . 521858 5 20 Secant 001884 .Sine .... 8.968249 17 25 .Co-secant. 523742 Secant.. 0. 020382.... Secant .. 0.020382 6241 Co-sine.. . 9.782630 Sine 9.900529 17 2i Sine 9. 474115... .Co-sine . 9.979816 Arc second. Arc third... 37 OCJj.... Sine 9. 780487.... Secant .. 0.098271 3 54 Co-sine . 9.998998 When latitude and declination of same name, '\ take the difference between third and fourth [ arcs for fifth arc. ) Arc fourth 84 24. .Co-Bine . 8.988G31 Arc fifth Arc second 8020 Secant.... 0.782391 37 06 Secant.... 0.098224 Latitude in 7 S4N....Co-sccaut . 0.880615 XOTE. The sum of the third and fourth arcs being less than 90, thisexample admits of two answers. Read carefully the note in rules. 102 PRACTICAL NAVIGATION. Ex. 6. November 10, 1878, in latitude by account 32 32' K, at 9h: 30m. A.M. the altitude of the sun's lower limb was 28 14', the bearing of its center by com- pass being S.E4E.; and at the llh: 17m: 42s. A.M. the altitude of the upper limb was 39 08', the height of the observer's eye being 18 feet, and the ship's course between the observations S. by E., running 7 knots per hour; required the lati- tude of the ship at the time of the greater altitude. H. M. S. , Timebychro 11 17 42A.M. Sun's declination Nov. 10.... 17 12 11.. S. hourly diff. 42" .08 120000 Correction for 42m: 18s 29" 7 M. T. G. Nov. 9 ... 23 17 42 Correct declination Nov. 9 17 11 42 S. ly'AoC, Sun's bearing at first observation S.E.^E. or S.4J6 points E. Ship's course during the elapsed time S. by E. or S. 1 point E. Angle between the ship's course and sun's bearing 33^ points. The elapsed time between the observation is 1? hours nearly, and the rate of sailing 7 miles per hour; that will give the distance run 12 miles, to be taken out as in example 3. First obs. alt. sun's lower limb 28 14 00 Second obs. alt. of sun's upper limb. . . 39 08 66 Dip of the horizon 4 4 Dip of horizon , t . 4 4 28 09 56 3D 03 50 Refraction 147 Eefraction 110 28 08 09 39 02 46 Parallax 8 Parallax 7 28 08 17 39 02 53 Semi-diameter +1612 Semi-diameter 1012 True alt. sun's center 28 24 29 True alt. sun's center ~ . . 38 40 41 Correction for change of position +918 irzzzzz: Sun's corrected alt .. 28 33 47 TKUE ALTITUDES. First alt ..... 28 33 47.. Less altitude. Second alt.. 38 46 41.. Greater altitude. Sum ......... 67 20 28 .. Half sum alt . 3340 / 24 Difference... 10 12 54.. Half diff. alt.. 5 6' 27" TIMES. a. M. B. 9 30 00 AM. 11 17 42A.M. 1 47 42 . . Elapsed time. 53 51.. Half elapsed time =13 27' 45" Half elapsed time.. 1328 Co-secant.. 0.632869.... Sun's declination. .. 17 12 Secant 0.019870 Sine 9.470S63 Arcfirst 12 51}$ Co-secant.. 0.652739.... Secant... 0.011044.... Secant... 0.011044 Half sum of alt 3340 Co-sine.... 9.920268.... Sine 9.743792 Half difference alt. 506 Sine 8.949509. ...Co-sine.. 9.998277 Arc second 1927 Sine 9.522516 Secant... 0.025519 Arcthird 5305 Co-sine.. 9.778G32 Arcfourth 10739 .= (180 72 21') Co-sine.. 9.481907 Arc fifth fi4 34 Secant 0.236755 Arc second 19 27 Secant 0.025519 Latitude in 33 09 N.. . . Co-secant. . 0.262274 DOUBLE ALTITUDE. 103 Ex. 7. JulyTth, 1878, in latitude by account 58 25' N. and longitude 122 30' W. at llh:02m:OOs: A.M. per watch, the altitude of the sun's loM'er limb was 52 53', and at lh:25m:OOs: r.M. the altitude was 52 44', the sun at that time bearing S.W. by W. by compass; height of the observer's eye being 20 feet, and the ship's course during the elapsed time S.S.W.^W., the distance made in the interval was 18 miles; required the ship's true latitude at the time the greater altitude was observed. , j Declination 22 33' 36" N. 1 I Latitude in 57 22' N. Ex. 8. August 30th, 1878, in latitude 12 43' S. by account, and longitude 24 15' E. time by watch, lh:J3m:30s: P.M., the altitude of the sun's lower limb was 66 09' 30", and at 3h:15m:12s: r.M it was 62 00' 15", bearing at that time N. W. $W. ; course during the elapsed time S.W. by W. and distance sailed being 8 miles; height of the observer's eye, 28 feet; required the true latitude at the time of taking the greater altitude. . j Declination 8 58' 28" N. Ans ' 1 Latitude in 11 37' S. Ex. 9. November llth, 1878, in latitude by account 32 34' N. at 9h:30m: A. M., the altitude of the sun's lower limb was 28 18', bearing by compass S.E., and at llh:17m:42s: A.M., the second altitude of the sun's tipper limb was 39 10'; height of the observer's eye, 18 feet; and the ship's course between the observa- tions was S. byE.; distance run during the interval, 12 miles. Required the latitude and longitude of the ship at the time of taking the greater altitude. ( Declination 17 28' 24" S. Ans. \ Latitude in 32 J 51' N. ( Longitude in. 3 10 15' W. Ex. 10. February 25th, 1878, latitude in by account 49 3G' N.; time by chro- nometer Oh:33m:OOs: P.M., the observed altitude of the sun's lower limb was 28 53', and at 2h:43m:OOs: P.M., by the same chronometer, the second altitude was 19 14', the height of the observer's eye being 14 feet. Required the latitude and longitude in at the time of taking the greater altitude. (Declination 9 01' 02" S. Ans. \ Latitude in 51 17' N. ( Longitude in o } 12' 45" E. 104: , PRACTICAL NAVIGATION. TO FIND THE LATITUDE BY THE POLE STAE. The latitude by the meridian altitude of the pole star can be found at any time on a clear night in the northern hemisphere, by the following rules: First. Correct the altitude for index error, if any, dip of the horizon and refraction; after being thus corrected, the altitude is increased if the star is below the pole, or decreased if the star is above the pole. This correction is found in Table XV, and applied thus: Second. Find the sun's right ascension for the given day in the Nautical Almanac, to which add the apparent time at ship; if the sum of these exceeds 24 houre, reject 24 hours, and that will be the right ascension of the meridian. Third. Enter Table XV, and in one of the side columns, opposite in the center column, will be found the correction in degrees and minutes. Fourth. If the right ascension of the meridian is found in one of the right-hand columns, add the correction to the altitude; but if found in one of the left-hand columns, subtract the correction, and you have the latitude to be named North, always. Ex. 1. December 31, 1878, mean time at ship lOh: 50m: OOs. P.M., in longitude 32 3 30' \V. The observed altitude of the Pole star out of the meridian was 40 20' 10". Index error, + 1' 10", eye 20 feet. Required the latitude in. H. M. s. / // Sun's right ascen., Dec. 10. . . 18 42 49 Obs. alt , 40 20 10 Time of observation.. . 105000 Index error. .. + 1 10 29 32 49 40 21 20 24 00 00 Dip - - 417 Right ascension of meridian . 5 32 49 40 17 13 = Ref 1 08 Stars true alt 40 1C 05 Correction for table XV 36 00 Latitude in . . 39 40 05N. Ex. 2. February 12, 1878, mean time at ship, at llh:09:OOs. P.M. in longi- tude 35 12' W. The observed altitude of the Pole star was 41 12'. Required the latitude. Eye 17 feet. H. M. S. , Sun's right ascension 21 44 07 Obs. alt 41 12 00 Time of obs 11 09 00 Dip 3 57 32 53 07 41 08 03 24 00 00 Ref. . 1 05 R. A. of Meridian 8 53 07 41 06 58 = Correction + 36 00 Latitude in.. ..41 42 58N. LATITUDE BY THE POLE STAB. 105 Ex. 3. September 10, 1878, mean time at ship at 2h:30m: los. A.M. in longi- tude 30 17' W. The observed altitude of the Pole star, out of the meridian was 54 Off 30"; eye 18 feet; required the latitude in. H. M. S. Time of observation 2 30 15A.M. Obs. alt 64 00 30 (Add 12 hours) 120000 Dip 4 4 14 30 15 Sun's R. Ascension +11 14 42 Ref 53 56 26 41 25 44 57 24 00 00 53 55 45 Correction.. ,..12300 R. A. of Meridian. . 1 44 57 Latitude. . . .52 32 45N. Ex. 4. July 16, 1878, mean time at ship at 4h:37m: 11s. A.M. longitude 18 30' W. The observed altitude of the Pole star out of the meridian was 39 54" 20"; eye at 16 feet; index error + 5' 10"; required the latitude in. Time of observation . , Sun's R. Ascension . . , H. M. S. . 4 37 11A.M. + 12 00 00 Obs. alt 39 54 20 Index error + 510 16 37 11 + 7 42 33 24 19 44 24 00 00 Dip. Ref. 39 59 30 3 50 39 55 40 1 08 R. A. of Meridian.. 19 44 39 54 32 Correction 1 29 00 Latitude in.. . 38 25 32X. Ex. 5. August 31, 1878, mean time at 2h:40in:20s: A.M. in longitude 85 30' E.; the observed altitude of the Pole star off the meridian was 20 10' 40". Index error 1' 10". Eye 20 feet. Required the latitude in. Ahs. Latitude in, 18 38' 38" N. Ex. 6. December 10, 1878, mean time at ship at 2h:16:04s: A.M. in longi- tude 76 12' E. ; the observed altitude of the Pole star off the meridian was 47 50' 20". Index error -4' 05". Eye 13 feet. Required the latitude in. Ans. Latitude in, 47 48' 57" N. Ex. 7. March 6, 1878, mean time at ship at 7h: 43m: 40s: P.M. in longitude 36 58' 45" W. ; the observed altitude of the Pole star off the meridian was 44 30' 30". Eye 20 feet. Required the latitude in. Ans. Latitude in, 44 08' 14" N. Ex. 8. January 16, 1878, mean time at ship at 9h:38m:OOs: P.M. in longitude 59 15' E.; the observed altitude of the Pole star off the meridian was 67 30' 22". Eye 20 feet. Required the latitude in. Ans. Latitude in, 66 49' 41" N. 106 PRACTICAL NAVIGATION. TO FIND THE TIME OF A STAR'S PASSING THE MERIDIAN, ALSO, ITS APPROXIMATE ALTITUDE. First. Find the star's right ascension as given in pages 242 to 245 in the American Nautical Almanac, nest the sun's right ascen- sion in page one for the month in the Almanac. Second. Subtract the sun's right ascension from the star's right ascension, increasing the star's right ascension by 24 hours when the sun's right ascension is greater than the star's right ascension. Ex. At what time will Arcturus be on the meridian on April 27, 1878. H. M. S. Right ascension of Arcturus, April 27 14 10 05 Sun's right ascension, April 27 2 15 06 Time of Arcturus' meridian passage 11 54 59 By this method the time of any particular star passing the meridian can be found, and knowing at what time a star will pass the me- ridian, and having its approximate altitude at that time (as shown in the following example) there will be no difficulty in determining the latitude. Third. To find the approximate altitude of a star, subtract the lati- tude in by account at the time of observation, from 90 which will give the co-latitude of the place of observation, find the star's de- clination in Nautical Almanac, as per rule, and remember that the sign thus placed before the declination stands for south declina- tion, and thus -f stands for north declination. Fourth. If the co-latitude and the star's declination are of the same name, take their sum, but if contrary names take their differ- ence, for the altitude; the star will be found in the south part of Ihe Heavens when the latitude is north, and in the north part when the latitude is south. When the sum of the co-latitude and the star's declination exceed 90, subtract it from 180 and the remainder will be the altitude, but in this case the star will be found in the north part of the Heavens in north latitude and in the south part when the latitude is ;outh. Fifth. To find the star from its approximate altitude and meridian passage, set the index of the sextant to the approximate altitude, and a few minutes before the time of its meridian passage, direct the sight towards the north or south points of the horizon and the reflected image of the star will be perceived in the horizon glass, upon or near the horizon, the star then being brought in contact with the horizon and kept so until it arrives at its greatest or TIME OF A STAIl'S PASSING THE MEKIDIAN. 107 meridian altitude. There is not the least danger of mistaking the star as no two stars will have the same meridian altitude at the same time. NOTE. The best time for obtaining a correct altitude of a star is at twilight, for the horizon Is then distinctly visible, and the latitude thus found is nearly cs true as that obtained by an altitude of the sun, in dark nights, and in consequence of the obscurity of the horizon a Isrge errcr may be found in the altitude; to counteract this the latitude should be found from an altitude of a star to the southward, end another to the northward, and half the sum of the two latitudes thus found will be the correct latitude, Ex. 1. February 27, 1878, at ship in latitude by account, 40 50' 10" N., re- quired the time of the meridian passage of the star Aldebaran, and its approxi- mate altitude. February 27. Right ascension of Aldebaran from page 242 Nauti- IT. M. s. cal Almanac 4 28 55 Add 24 hours as the snn?s right ascension is greater 24 00 00 28 28 55 Sun's right ascension (page 1, Nautical Almanac) 22 41 41 Time of Aldebaran meridian passage 5 47 14p.ai. Latitude by account 40 50 ION. 90 00 00 Co-latitude 49 09 50 N. Star's declination, Nautical Almanac page 242 16 05 45 + N. Approximate altitude 65 15 35 Set the index of the sextant to this altitude and sweep the horizon to the southward, as the latitude is north, and the star will be distinctly seen near the horizon; watch it closely, and when it has ceased to rise, it is on its meridian, then apply the usual rules to find the latitude. Ex. 2. March 21, at ship, in latitude by account, 1 30' 25" S., at what time will the star Sirius pass the meridian, and what will be its approximate alti- tude ? H. M. s. March 21. Sirius' right ascension 6 39 46 Sun's right ascension 2 47 Time of Sirius' meridian passage 6 36 59P.M. Latitude in by account 1 30 25 S. 90 00 00 Co-latitude 88 29 35 S. Star's declination 16 32 59 S. 105 02 34 180 00 00 Approximate altitude 74 57 26 Toward the south KOTK. See page 71 for finding the latitude by a star. 108 PBACTICAL NAVIGATION. Ex. 3. May 1, 1878, at ship, in latitude by account, 20 00' 00" N., required the meridian passage of the star, Vega, and its approximate altitude. May 21. Vega right ascension 18 32 48 Sun's right ascension 2 34 06 15 58 43 12 00 00 Time of Vega meridian passage 3 58 43 A.M. Latitude in by account 20 00 00 N. 90 00 00 Co-latitude 70 00 00 N. Star's declination 38 40 16 + N. 108 40 16 180 00 00 Approximate altitude ................................. 71 19 TO FIND THE TIME AT ANY GIVEN MERIDIAN BY THE SUN'S ALTITUDE. Take any number of altitudes with their corresponding times by watch, or chronometer, when the sun bears as nearly east or west as possible, of which take the " means," add them all together and divide the number of observations. To these means of the altitudes apply the corrections, as usual, and get the true altitude of the sun's centre. Take the sun's declination (page 2, Nautical Almanac), and cor- rect it by the hourly difference for the mean time at Greenwich, and get the sun's polar distance, adding the declination to 90 when the latitude and declination are of contrary names; subtracting it from 90 when they are of the same name, N. or S. Correct the equation (page 1, Nautical Almanac) for the mean time at Greenwich. Add together the sun's polar distance, ship's latitude and sun's true altitude; take half the sum, and, lastly, the difference between^ that and the true altitude; call this the remainder. Add together the secant of the latitude; co-secant of the polar dis- tance; co-sine of the half sum; sine of the remainder; and the sum, rejecting tens in the index, will be the log. (Table XVIII.) answer- ing to the hour angle or apparent time, from noon, at which the ob- servation was taken. If the observations be made in the morning, the time thus found TO FIND THE TIME BY THE SUN 7 S ALTITUDE. 109 must be taken from 24 hours to obtain the apparent time from the preceding noon. To ,the apparent time thus found, apply the reduced equation of time, by addition or subtraction, as directed at the head of its column on page 1 of the Nautical Almanac, and the sum or remainder will be the mean time at the ship or place of observation. Hence, the error of the watch at the meridian of the place may be found for both apparent and mean time. Ex. 1. August 16th, apparent time at ship 4h: 42m: 06s: in latitude 36 31' N. and longitude by account 152 00' E., the observed altitude of the sun's lower limb was 23 a 50' 24"; height of the observer's eye being 18 feet. Required the true, apparent and mean time at ship, and the error of the watch. Apparent time at ship, August 16.... 4 42 00 Longitude 152 00' 4 6.0)60.8 00 10h:08m. Longitude in time. Greenwich apparent time, Aug. 15. 24 00 00 28 42 00 10 03 00 Sun's dec. Aug. 16.. 13 43 02 Cor. for 5h : 26m 4 1C Hr. dif. 47.46 54 Dec. at Gr. M. T... IS 47 18 N. 90 00 00 Sun's polar distance 76 1 2 42 18984 2:i730 6.0)25.6.281 4' 16" Talce the declination out for the IGth of Autjwt, and correct it for 5h: Wm ; from the noon of the Kith, towards the \5tli, tht Jint beintj the nearest noon, and add the correction as the declination is decreasing, tliat will give the declination at Green- wich mean time on Auyust 15th. Observed altitude ..... 23 50 24 Dip .................. 4 17 23 46 07 Correction Table XHI. 2 00 23 44 07 Sun's semi-diameter. . . 15 50 Sun's true altitude.... 23 59 57 Latitude ............. 36 31 00. ...Secant Polar distance ........ 761242 ____ Co-secant Sum ................ 2)136 43 39 Half sum ............. 68 21 49.... Co-sine Eemaiuder ............ 44 21 52. ...Bine M. s. Equation of time .. 4 05 . 56 2.74 4 03.30 0.094915 0.012699 9.566691 9.8446U Hourly dif. 509 54 2036 2545 2". 7486 H. M. S. B. It. 8. Apparent time at Bhip. 44039 ____ Log. Table XVIII. 9.518919 ........................ 44039 Equation of time ...... 408 Time by watch ............. 44206 Mean time at ship ..... 44447 Time bywatch ........ 44206 Watch slow for M. T. . . 2 41 Watch fatt for app. time... 127 110 PRACTICAL NAVIGATION. Ex. 2. March 15, 1878, A.M. at ship, when a watch showed 6h: 44m: 49s: lati- tude in at time of observation 16 29' N., and longitude 99 30' W., the observed altitude of the sun's lower limb was 10 36' 10"; the error of the sextant was 2' 50" to subtract; eye 22 feet. Required the apparent and mean time at the meridian of ship, and the error of the watch. II. M. s. Time by watch . . G 44 49 A. M. 12 00 00 Apparent time at ship, March 14.184449 Long, in time.. . G 38 00 W. 25 22 49 24 00 00 Apparent time at Greenwich . , . 1 22 49 Sun's dec. March 15. . 2 04 07 Hr. dif. 59.18 Correction for lh: 23m 1 17 1.3 Sun's declination at Green, mean time . 2 02 50 S. 90 00 00 17754 5918 Sun's polar distance.. 92 02 50 60)7.6.934 1'16"934 2 50 .93 10 33 20 Correct equation. 9 03.62 4 30 == 10 28 50 4 53 10 23 57 Sun's semi-diameter. . + 1606 10 40 03 13 Observed altitude 10 36 10 Equation of time. 9 04.55 H. dif. 717 Index error , Dip Correction Table XIII.. 2151 717 9321 Sun's true altitude 10 40 03 Latitude 16 29 00 Secant 0.018226 Polar distance 92 02 50 Co-secant 0.00027S Sum 2)119 11 53 Half sum 59 35 56. . . .Co-sine 9.704179 Remainder 485553 Sine 9.877340 H. M. S. . Appparent time from noon ... 5 12 59 .... Log. Table XVIII 9 . 600023 24 00 00 ===== H. M. s. Apparent time at ship 18 47 01 18 47 01 Equation of time + 9 03 Time by watch 18 44 49 Mean time at ship 18 56 04 Watch slow for app. time. 2 12 Time by watch 18 44 49 Watch slow for mean time .. 11 15 TO FIND THE ERKOB OF A WATCH. Ill TO FIND THE ERROR OF A WATCH OR CHRONOMETER BY EQUAL ALTITUDES OF THE SUN. Subtract the first time from the second, for the interval. Add the two times, and divide the sum by 2, for the middle time by chronometer. Get the difference between the declination of the day before and day after, for the change of declination in two days, and multiply the difference by GO, which will give seconds. Correct the sun's declination for the Greenwich time and date, and the longitude in time, if west, it is the Greenwich time; but if east, take the longitude in time from 24 hours, and call the day one back. Correct the equation of time for the Greenwich time, as usual; taking it out of page 2, Nautical Almanac. From Table XVI. take out log. A. and B. for the interval, and place the log. of natural number (Table I.), for the change of declination in two days under both log. A. and B. The log. tangent (Table II.) of the latitude un- der log. A. and log. tangent of the declination under log. B. *See note for Table XVI. The sum of the first three logs, is the log. in logarithms of num- bers (Table I.) of the first part of the equation of equal altitudes, and the sum of the last three logs., that is, log. B., log. of change of declination, and log. tangent (Table II.) of the corrected declination, will bo the second part of the equation of equal altitudes. The first part of the equation is additive when the declination is decreasing, and of the same name with the latitude, or increasing', and of a different name from the latitude; but subtractive when the declination is increasing, and of the same name with the latitude, or decreasing, and of a different name from the latitude. The second part of the equation is additive when the declination is increasing, but subtractive when the declination is decreasing. "When both parts are additive or subtractive, get the sum of them and apply them to the middle time by chronometer (according to the sign -f or ). But if one is additive and the other subtractive, take their difference and apply it to the middle time by chronometer, according to the sign of the greater. Apply the equation of time corrected for longikide to the apparent noon at place, as directed at head of column, page 1 of the month Nautical Almanac, for the mean time at place of observation. Get the difference between the time by chronometer at apparent noon and mean time at place, and call the chronometer fast or slow, as shown by the times. NOTE. Table XVI. contains but four place of figures, besides the index figures; therefore, In taking out tlie logarithms from Table I., only take out the first four figures, increasing the fourth figure by one when the remaining figures exceed CO. Do the game with the log. taugeut. 112 PRACTICAL NAVIGATION. EQUATIONS OF EQUAL ALTITUDES. Ex. 1. August 5, 1878, in latitude 37 35' N. and longitude 6000'"W., the following times were noted down when the sun had equal altitudes. Requhed the error of the watch for mean time at place of observation. A.M. P.M. H. M. S. H. M. S. 7 25 40 1 33 06 7 26 23 1 32 23 7 27 06 1 31 40 3)97 09 Means 1 32 23 Add 24 hours.. 24 00 00 3)79 09 jj eang 7 26 23 Add 12 hours 12 00 00 August 4 19 26 23 August 5 25 32 23 H. M. S. H. M. S. 25 32 23 P. M 25 32 23 19 26 23 A.M 19 26 23 Interval . . . 6 06 00 Sum of times 2)44 58 46 Middle time by chronometer. 22 29 23 Sun's declination August 4 17 13 41 N. Sun's declination August 6 16 41 08 N. Difference of declinations in two days. 32 33 x CO In seconds 1953 Dec. Aug. 5. 16 57 33 N. H. dif. 40."70 Cor. for long. 2 40 Reduced dec. 16 54 53 N. 6)162"SO 2' 40" M. S. Eq. of time Aug. 5. 5 46.73 H. dif. 248 Cor. for Ion. in time .99 4 Red'd eq. of time. . 5 45.74 99.2 Longitude 60 00' 4 60)240 00 4h:OOW. Interval of time (Table XVI). Gh:06m:. .Log. A. 7.7719.. Opp. Log. B.. 7.6156 Change of declination for two days, log. of numbers Ta. I. 1953. .Log. . . 3.2907. .Same Log. . . . 3.2907 Latitude (Tangent Table II). 37 35' 9.8863. .Dec. tan. T. II. 9.4831 + S".S9 0.9489 -2".45 Log. 0.3894 First part Second part Equation of equal altitudes. . 6". 44 H. M. S. H. M. S. Middle time by chron 22 29 23.0. .Middle app. time at ship. . . 24 00 00 Equation of equal altitudes. + 6.5. .Equation of time -f- 545 Time by chron. at ap. noon. 22 29 29.5. .Mean middle time at ship. . 24 5 45 Mean middle time at ship. 24 05 45 Chron. slow for mean time . 1 36 16 at place of observation. EQUATIONS OP EQUAL ALTITUDES. 113 Ex. 2. October 4, 1878, in latitude 39 19' S. and longitude 90'' 00' E., the following times were noted when the sun had equal altitudes. Required the error of the watch for mean time at place of observation. A.M. P.M. H. M. S. H. M. S. 7 00 05 11 50 03 7 00 55 11 50 53 7 01 30 11 51 34 Add 12 hours. . Octobers 3)2 30 7 00 50 ...12 00 00 19 00 50 3)152 30 11 50 50 Add 12 hours.. 12 00 00 October 3.. . 23 50 50 H. M. S. H. M. S. 23 50 50 Second time 23 50 50 A.M. 19 00 50 First time 19 00 50 A.M. Interval ... 4 50 00 Sum of times 2)42 51 40 Middle time by chronometer. 21 25 50 Declination October 3 4 01 Ob* S. Declination October 5 4 47 27 S, Change of declination in two days 4G 21 x 60 In seconds. 2781 Declin. Oct. 3. . 4 01 98 Hr. dif. 58.06 Cor. for 18h. ..+ 1725 18 Reduced dec... 4 18 31 46448 5806 90 00' 4 )3GO Long, in time. 6h:00m. 24h:00in, 6,0)1045,08 17' 25" 18h:00m. M. S. Equation of time. 10 57.41 Hr. dif. 770 + 13.86 v. IS Correct equation. 11 11.27 6]t>0 770 \60)13".860 Take the longitude in time from 24 hours as the ship is to the east of Green- wich, and take the decimation out for the 3rd of October. Interval 4h: 50m:. .Log .A. . 7.7541. .Log. B 7.C60f> Change of declin. in 2 days. . 2781 . .Log S.4442 . 3.4442 Latitude 36" 19' S. .. Tangent 9.8663. .Dea T't 4 19' sisTTS First part 11". 60.. Leg 1.0646 Second part -f- 0".96 . 0.9P2G Equation equal altitudes. . .. 10". 64 H. M. s. H. M. S. 11. jYi *3. Middle time by chron 21 25 50.0. .Mid. ap. time at ship noon. . 240000.0 Equation of equal altitudes. - 10.6. .Equation of time 11 27.2 Time by chron. at ap. noon. 21 25 39.4. .Mean middle time at ship. . 23 48 32.S Mean middle time at ship, 23 48 32.8 Chr. slow for M. T. at place. 2 22 53.4 Nav. 8 114 PRACTICAL NAVIGATION. Ex. 3. April 6, 1878, in latitude 32 40' S. and longitude 153" 00' E., the fol- lowing times were noted when the sun had equal altitudes. Required the error of the watch for mean time at place of observation. A.M. P.M. H. M. S. H. M. S. 9 28 20 2 33 43 9 29 01 2 33 02 9 29 58 2 32 05 9 30 56 2 31 07 9 31 44 . 2 32 39 Means Add 12 hours . . 5)149 59 . . . 9 29 59 . . . 12 00 00 21 29 59 A.M. 5)160 36 Means 2 32 07 Add 24 hours ..24 00 00 2G 32 07 P.M. II. M. S. First time. . 2G 32 07 P. M Second time 21 29 59A.M... H. M. S. 26 32 07 21 29 59 Interval . . 5 02 08 Sum of times 2)48 0? OG Middle time by chronometer. 24 01 03 Declination April 5 6 08 03 N. Declination April 7 6 53 21 Difference of declination in two days .... 45 18 x 60 In seconds 2718 Dec. Aril 5. G 08 03 N. Hr. dif. 56.89 Cor. 13h:48m+ 1305 Reduced dec. 6 21 08 N. 13.8 Longitude.... 153 00' E. 4 6,0)61,2 00 45512 170G7 5689 6,0)78,5,082 13' 05" Long, in time 10h:12m: From 24 hours 24h:00m: Gr. time 5th. 13h:48m: M. S. Equation of time. 2 44 05 Hr. dif. 728 10 04 138 Correct-equation. 23461 5824 2184 728 6,0)10,0464 Interval of time ........ .5h:02m:OSs: .Log. A . . 7.7566. .Log. B ...... 7.6546 Change of dec. in 2 days. 2718.Log.of No.3.4342 .............. 3.4342 Latitude ............... 32 40' S. . Tangent . 9. 8070 . . Dec. tan. 6 21' 9. 04(J4 First part Second part Equation of equal alt .... + 9". 95. Log ..... 0.9978 + 1".36. . . .. H. M. S. H. M. S. Middle time by chron 24 1 03. . Mid. ap . time at ship noon. .. 24 00 00. Equation of equal altitudes. 4- 11. 3. Equation of time .. + 234.6 Time by chron. at ap. noon. 24 01 14. 3. Mean middle time at ship. . . 24 02 34.6 Mean middle time at place. 24 02 34. 6 Chronometer slow.. .... 120.3 SHIP'S POSITION FROM TWO BEARINGS. 115 TO FIND THE SHIP'S POSITION FKOM TWO BEAKINGS OF THE SAME OBJECT. This method of finding the position of the ship when in sight of land, by two bearings of the same object, will be found of great value when a cross-bearing cannot be obtained: Select an object, the latitude and longitude of which is known; take a correct bearing of it by the compass (apply the variation and deviation due the compass bearing), and note the time by watch. After the bearing has altered not less than three points, take a sec- ond bearing, and note the time by watch. Having the interval of time between the first and second bearings, and the rate of sailing per hour, the distance sailed in the interval of time between the first and second bearings, and the rate of sailing per hour, the distance sailed in the interval may easily be obtained, and the ship's correct latitude and longitude found, as explained in the following example and table: Ex. 1. April 15. at 8h. P.M., a light-house bore by compass N.\V. ^ N.; ship's course, W. ; sailing at the rate of 7 miles per hour till lOh: P.M., when the same light bore N.N.E. ^ E. Required her distance at both places: First bear., N.W. JN. ) Second bear. N.N.E. JE. ) Course west > Angle 4J pts. Course west > Angle 10 pts. Found at top of table. } Found .at side of the table. } With 4J pts. at the top of table, and 10J pts. at the side of table, give the tabular number 84 Distance sailed in 2 hours + 14 11 76 The tabular number multiplied by 14, the distance run in two hours, and the two right-hand figures struck off (being .decimals) gives the distance off at lOh: P.M., 11 J miles. To find the distance : The first angle being.. 4 ?3 pts The second angle.. 10 J$ pts. The tabular number Is .. 095 Subtracted f rom 16 Subtracted from... 16 Distance made 14 Taken from Bide table. . 11 M Taken at the top . . . 6 M 380 1330 Gives the distance at 8h: P.M., 13^ miles. Ex. 2. At 5 o'clock A.M., a light-house bore by compass W. by S. J S. Ship then sailed on a S. \ W. course, at the rate of 5J knots an hour, until 7 A.M., when the same object bore N.W. by N., variation \ point west. Required the ship's latitude and longitude at the time of each bearing. 1st bearing W. by S. % S. by compass. 2d bearing N.W. by N. by compass. Corr. for M pt. W. var. is W.S.W.) Anc]efiTlts Corr. for M pt. var. N. W. M N.) ,, 19V5 , Course S. M W. South, } An g ]e6 P ts - Course true S. \ Angle 12M pts ' Tabular number 97 2 hours and 5% knots= Distance Bailed 11 Distance off at time of second bearing at 7 A.M 10 07 miles. Theop. pt.to2dbear. is S.E.&S..dtet.lOJlf at time of 1st bear. 5 A.M 7.26', or 7!4 miles, nearly. Theop. pt. to 1st bear. isE.N.E.,dist. 7% gives Dif. Lat. . 3 N. Dep.6.7=D. Long. 8 45 E. Latitude of light-house 40 24 N. Lon. . 73 58 48 W. At 5 A.M. the latitude of the ship was 40 27 N. Lon.. 73 56 8 W. The ship having made her true south course, she has sailed on the meridian of 73 50' 3" west, and was in the same longitude at 7 A.M. as at 5 A.M. and her difference of latitude is equal to the distance sailed. Ex. 3. At noon a point of land bore SE. by E. by compass. Ship then sailed on a south course, at the rate of 10 knots an hour, until 4 P.M., at which time the same point of land bore N. E. by E. % E. , the magnetic variation here being 1^ points westerly. Required the latitude and longitude of the ship at the time of each bearing. The 1st Bear. SE. by E. by compass. 2d Bear. N.E. by E. % E. by compass. Cor.forl^pts. W.var.=E.byS.J$S.l . - t Cor. forlJS pts. var.=N.E. ) . , - ^ . Course south, corr.=S. by E. % E. } Ang ' 5 pts 'True course. . . .8. by E. K E. j Angle 10 ^ P ts ' Tabular number 0.94 4 hours at 10 knots 40 Dist. off at the time of the 2d bearing, at 4 P.M 37.CO miles. Theop. pt. to 2dbear.isS.W.dis.37Joff the whole as a decimal. f9.G81241 480^1 T 8.681241 0480 XT , ~ ,. Logs.. ( 7 ( ; 81 . 2 4i .00480 ( Numlt)crs Corresponding. 1 6.681241 !! ! .000480 J 120 PRACTICAL NAVIGATION. TABLE II. To find the log. sine, tangent, etc., of any arc or angle, in degrees and minutes. If the number of degrees is under 45, they will be found at the top of the page, and the minutes in the left-hand column of the page, marked " M." at the top and bottom; the required logarithm will be found opposite the minutes, and in the column with the name of the function that you want to find at the top. But if the number of degrees is over 45, they will be found at the bottom of the page, with the minutes in the right-hand side column of the page, marked " M." at bottom and top; opposite the minutes, and in the column with the name of the required function at the bottom, will be found the required logarithm. If it is required to find the log. co-sine of 9 51', look for the page marked with 9 at the top, and then down the side column for 51'; opposite to this, and in the column marked " Co-sine " at the top, will be found 9.993550, which is the log. co-sine of 9 51'. The log. tangent of 80 IT is found in the same way, with the 80 degrees at the bottom of the page, the minutes in the right-hand side column, and in the column marked ""Tang." at the bottom; it is 10.761880. When the given degrees exceed 90, they are to be subtracted from 180 degrees, and the logarithm of the remainder taken out, as before. Or the logarithmic sine, tangent, etc., of an arc more than 90 is the logarithmic co-sine, co-tangent, etc., of its excess above 90 degrees. Examples: . . . 36 Log. to 6 places. Log. to r- places. 32' 97.74729 9.77473 18 9.681443 9.68144 17 10.143263 lO.mQfi co-sine of ...61 ...54 co-taugent of . .. secant of ...42 ... 19 50 10.032877 10.03288 27 33 36) 21 36) 10.025519 10.025519 9.976702 lu.02552 10.02S52 9.97670 co-secant of. ... ...70 sine, of . . . 108 ...71 .. 18 To find the log. , sine, co-sine, secant, etc. , of any arc or angle, in de- grees, minutes and seconds. Take the difference between the logs, for the given minutes and the next higher number of minutes; multiply this difference by the given number of seconds, and divide by GO; add the quotient to the log. found for degrees and minutes, in the case of sines, tangents and secants; subtract it in the case of co-sines, co-secant and co- tangent. For example. EXPLANATIONS OF THE TABLES. 121 Required the log. secant for 32 44' 34". The log. secant for 32 44' is 10.075103 10.075103 And for 32 J 45' is 10.075184 + 46 Difference 81 Correct log. .10.075149 x 34" ' 324 60)275.4 Correction 45.54 Call the correction 46, as there is 54 over, and add it to the log. secant of 32 44' and the correct log. secant will be for 32 44' 34" 10.075149. Required the log. co-sine to seconds for 81 32' 19". The co-sine for 81 32' is 9.168008 9.168008 And for 81 33' is 9. 167159 Correction . . 269 Difference 849 Correct log. .9.167739 x 19 7641 849 60)1613.1 Correction., 268.51 To find the arc or angle, in degrees and minutes, which corres- ponds the nearest to any given logarithmic sine, tangent, secant, etc. : Look in the column marked at the top or bottom with the name of the given logarithm, and find the logarithm which agrees the nearest with the given logarithm; then, if the name at the top of the column corresponds with the name of the given logarithm, take the degrees from the top of the page and the minutes (opposite the nearest logarithm) in the left-hand side column; but if the name at the bottom of the page corresponds with that of the given log., take the degrees from the bottom of the page, and the minutes (op- posite the nearest logarithm) in the right-hand side column. Required the arc corresponding to log. sine 9.595435. The near- est log. is 9.595432; the arc 23 at the top of the page, and 12"in the left-hand side column. Log. sine 9.595435=23 12'. Required the arc corresponding to log. co-secant, 10.044160. The nearest logarithm in the co-secant column is 10. 044151; the arc is 64, from the bottom of the page, and 36' from the right-hand side column. Log. co-secant 10.044161=64 36'. TABLES III. AND IV. Difference of latitude and departure for })oints and degrees. These tables are the same except one contains points and the other degrees. The difference of latitude and departure are in miles and tenths for distances of less than 300 miles. The courses are set 122 PRACTICAL NAVIGATION. down in points and degrees, at the top of the pages, if they are less than 4 pts. or 45; but the courses are at the bottom of the pages if they are over 4 pts. or 45. The distances are in the column marked " Dist." at the top and bottom; opposite to these distances, and to the right of them, are the difference of latitude and depar- ture. If the courses are under 45, the "Lat." and "Dep." are marked at the top of the columns. But if the courses are over 4 pts. or 45, the "Lat." and "Dep." are at the bottom of the columns; that is, if the course is at the bottom, read the column from the bottom; but if the course is at the top, read the columns from the top. TABLE V. Table of meridional parts. This table is used in solving problems by Mercator's sailing. The meridional parts are found in the columns with the degrees at the top and bottom of the pages, and the minutes at the sides. It is also used in Mercator's projections in constructing charts. The meridional part corresponding to 37 18' is 2415. TABLES VI. , VII. , VIII. Refraction, dip and parallax tables. These are to be applied to all observed altitudes. Kefraction is subtractive from the observed altitude and must be taken out for the altitude which is nearest the given one. Dip is subtractive from a fore observation and additive to a back one. It is given to 100 feet height of the eye. Parallax is always additive and must be taken out to the nearest degree. TABLE XI. For reducing longitude into time, and the contrary. This table has" been added to quicken the reduction of degrees, etc., of longitude into time, or of hours, etc., into longitude. Now suppose you want to convert 160 20' into time, first look in the column marked degrees until you come to 160, then in next column on the right hand and directly opposite 1GO you will see 10h:40m: which is equal in time to 160, then in the seventh column marked minutes of degrees you will find 20 minutes, and directly opposite in the next column on the right hand you will see 1m: 20s: which added to 1 Oh: 40m: will make 10h:41m:20s: in time, which is equal 1GO 20' of longitude. Ex. 1. Required the degrees, etc., corresponding to 8h:32m:45s. H. M. s. , Longitude answering to 8 32 45 is 128 00 Longitude answering to 45 is 3 Hence the longitude answering to ... 8 32 46 is 128 03 EXPLANATIONS OP THE TABLES. 123 TABLE XII. For reducing the sun's declination to noon at any given meridian, and to any time at the meridian of Greenwich. This table contains the corrections to be applied to the sun's declination as given in the Nautical Almanac; which is computed for apparent or mean noon at Greenwich; it is to be entered with the declination for noon of the given day as found in page one or two of the Nautical Almanac, at the top, and the longitude of the place or time at Greenwich, in the side columns; corresponding to these will be found the minutes and seconds to be applied to the above declination by addition or subtraction, as directed at the head of the column table; that is, when the declination is increasing, the correction to be added in west longitude, but to be subtracted in east longitude, or to be added for Greenwich time; but when the declin- ation is decreasing the correction is to be subtracted in west longi- tude but to be added in east longitude, or to be subtracted for Greenwich time. When the declination and longitude, or time at Greenwich, are not nearly found in the table, proportional parts may be used. When the given time at the meridian of Greenwich exceeds 12 hours, the correction must be taken out twice as in ex- ample three. It must be observed that this table is subject to an error of a few seconds, from the sun's unequal motion in the elliptic; but it is nevertheless in general, sufficiently exact for observations taken at sea. Ex. 1. Required the sun's declination at apparent noon on August 17, 1877, in longitude 122 21' west. Sun's declination at apparent noon by p. 1 N. A. (decreasing) 21 09 38 N. Correction for longitude 122 J 21' W - 3 44 Sun's declination when passing the meridian of the given place 21 05 44 N. Ex. 2. Required the sun's declination on Juue 12, 1877, at Gh:24m: apparent time at Greenwich. Sun's dec. on June 12th at apparent noon, p. 1 N. A. (increasing). . 23 11 18 N. Correction Gh: 24m: apparent time + 54 Sun's declination at Greenwich time ' 23 12 12 N. TABLE XIII. Corrections for the apparent altitudes of sun and stars. Enter the columns marked at the top " App. Alt.," with the ap- parent altitude which you have, and find the nearest arc to the one you have. Take the Correction opposite. If the sun was observed, the correction is in the first column to the right of the apparent altitude, but if the altitude is that of star, the correction is in the second column to the right of the app. altitude. This correction is always subtractive, and is only the refraction and parallax combined. TABLE XIV. Natural sines and co-sines. The degrees for the natural sine are found at the top of the page, 124 PRACTICAL NAVIGATION. and the minutes in the left-hand column of the page. But for the co-sines the degrees are at the bottom of the page, and the minutes in the right-hand side column. The sines are under the degrees and opposite the minutes, while the co-sines are over the degrees and opposite the minutes. The natural sine or co-sine of any number of degrees over 90 is the same as the natural sine or co-sine of its supplement, that is, 180 the angle. If the angle or arc is given in degrees, minutes and seconds, mul- tiply the difference at the bottom of the column by the number of seconds, point off two places, and add or subtract the quotient, ac- cording as the natural sine or natural co-sine is increasing or de- creasing. Required the natural sine of 9 30' 10". Natural sine of 9 30' is 165048; difference for 100" is 478, which, multiplied by 10 and point off two places=47.80; 165048+47=165095. Natural sine of 9 30' 10". Arc corresponding to natural co-sine 032289 is 88 9'. TABLE XV. For finding the distance of terrestrial objects at sea. When the eye is elevated above the surface of the adjacent land or water, we not only see the surrounding objects more distinctly, but also see those which are more remote the higher we advance. Now, although the irregularity of the surface of the land will not admit of any one rule that will give the distance to which objects may be seen at different elevations, yet at sea, where the curvature of the water is uniform, those distances may be easily computed by means of this table, in which the distances are exhibited in nautical miles and decimal parts; answering to the height of the eye, or that of the given remote object, allowance having been made for terres- trial refraction. EXAMPLE. Being at the mast head looking out for land, and elevated 130 feet above the .surface of the sea, I discovered the top cf a light-house in the horizon, whose height above the level of the sea is known to he 300 feet : required my distance from the light-house. In the tahle opposite 130 feet is 13. 1 miles. Ditto 300 19.9 Sum gives the distance of the ship from the light-house 33.0 TABLE XVI. Equations of equal altitudes. Observations of the sun, taken when at equal altitudes, afford an easy and accurate method of ascertaining the time shown by a chro- nometer at apparent or mean noon; and from thence its error; but since the sun changes his declination during the interval between the corresponding altitudes, the middle of the times by the chro- nometer when they were taken, will not be that shown by it when the sun passes the meridian; and hence it becomes necessary to apply a correction, called the equation of equal altitudes, to the EXPLANATIONS OP THE TABLES. 125 middle of the times, which may be easily computed as follows, by means of this Table: 1. Opposite the interval between the observations, take out the logarithms marked A and B at the head of the columns. 2. To log. A add the log. (Table I) of the seconds in the change of the sun's declination between the noons of the preceding and following days (taken from the Nautical Almanac), and the log. tangent (Table II) of the given latitude; the sum of these three logs, will be the log. (Table I) of the Jlrst part of the equation. 3. To log. B. add the log. of the above seconds, and the log. co-tangent of the sun's declination to the nearest minute of the given day; their sum will be the log. of the second part of the equation . 4. Tlie/r^part of the equation additive when the declination is decreasing, and of the same name with the latitude; or increasing, and of a different name from the latitude; but subtractive, when the declination is increasing, and of the same name with the latitude; or decreasing, and of a different name from the latitude. 5. The second part of the equation is additive when the declination is increas- ing; but subtractive when the declination is decreasing. TABLES XVII. AND XVIII. Log. rising and horary angle. Enter this table with the hours, minutes and seconds. The hours will be found at the head of the page, the minutes in the left-hand column, and the seconds at the head of the column of logarithms. In the right-hand column will be found a column of proportional parts, there being five seconds of difference between each column. Required the log. rising corresponding to Ih : 55m : 55s. Ans. Index 4.09762=required the log. rising of 57m: 57s. For 57m: 5os: we liave.^. -_ 50190 For 2s: we have x 50 3.50240 TABLE XIX. Required the apparent time corresponding to 8.30270. The angle corresponding this log. islh:05m: 10s. Required the log. corresponding to horay angle 2h: 15m: 36s: 2h: 15ni: 35s: gives 8.92928; Is: gives 10, additive. Log. 8.92928 + 10 8.92938 TABLE XX. To reduce the equation of time to any time under the me- ridian of Greenwich. This table is entered with the daily variation or change of the equation of time (being the difference of the equations at the pre- ceding and the following noons, taken from pages 1 or 2 of the month in the Nautical Almanac, when they are both additive or both subtractive, but their sum when one is subtractive and the other additive) at the top, and the Greenwich time in the left side column. The corresponding correction is then to be applied to the equation at the preceding noon, by addition or subtraction, accord- ing as the equation is increasing or decreasing. But should the , 126 PKACTICAL NAVIGATION. Aquation be less than the correction at the preceding noon, the former is to be substracted from the correction, and the remainder will be the reduced equation of time, to be applied in the same way as directed in the Nautical Almanac, for the equation at the follow- ing noon. When the Greenwich time exceeds twelve hours, the correction must be taken out twice, as in second example. Ex. 1. Required the equation of time, August 17, 1877, at 4 hours apparent time at Greenwich. M. S. Equation of time at app. noon, Aug. 17, page 1, Naiit. Aim 3 49 Equation of time at app. noon, Aug. 18, page 1, Jfaut. Aim 3 36 Daily change of variation (decreasing) 13 Equation of time (as above) Aug. 17 3 49 Correction to difference 13 seconds and 4 hours - 02 Reduced equation time (to be added to apparent time) 3 47 Hence the mean time at 4 hours apparent time at Greenwich on August 17, 1877, is4h: 3m: 47s. Ex. 2. Required the equation of time on September 17, 1877, at 16h: 35m: mean time at St. Helena, in longitude 5 45' "W. H. M. Mean time at St. Helena 16 35 Longitude 5 45' W. in time (Table IX. ) + 23 W. Mean time at Greenwich 16 58 M. S. Equation time at mean noon, Sept. 17, by page 2 N. A 5 40 Correction to daily Variation 21s:and J2h:. . 10 5 I ^ ,. Correction to daily variation 4h: 58m: 3 9 j ' Reduced equation (to be added to mean time) 5 54 TABLE XXI. Amplitude. This table shows a method of finding the variation of the compass by comparing the magnetic with the true amplitude. The true am- plitude is taken from this table, which has the declination at the top of the pages, and the latitude at the left hand. When the minutes of latitude or declination are over 20, the mean of the amplitude for the two nearest degrees will give the required amplitude, nearly. Required the true amplitude in latitude 40 31' N., when the declination is 16. True amplitude for latitude 40, dec. 16 21 05 True amplitude for latitude 41, dec. 16 21 25 2)42 30 True amplitude 21 15 Required the true amplitude in latitude 250'S., declination 10 25'. True amplitude in latitude 3% dec. 10 10 01 True amplitude in latitude 3, dec. 11 11 01 2)21 09 True amplitude lat. 3 3 S. , dec. 10 25' 10 30 TABLES. 127 TABLE I. LOGARITHMIC SINES, TANGENTS, and SECANTS, to every Point and Quarter Point of the Compass. tl hj o o p sr Sine. Co-sine. Tangent Co-tang Secant. Co-sec. 5 0.000000 10.000000 0.000000 Infinite. 10.000000 Infinite. 8 o % 8.690796 9.999477 8.691319 11.308681 10.000523 11.309204 73/ /4 % 8.991302 9.997904 8.993398 11.006602 10.002096 11.008698 7 y* % 9.166520 9.995274 9.171247 10.828753 10.004726 10.833480 7 % 1 9.290236 9.991574 9 298662 10.701338 10.008426 10.709764 7 1 % 9.385571 9.986786 9.398785 10.601215 10.013214 10.614429 6 % 1 % 9.462824 9.980885 9.481939 10.518061 10.019115 10.537176 6 % 1 % 9.527488 9.973841 9.553647 10.446353 10.028159 10.472512 6 % 2 9.582840 9.965615 9.617224 10.382776 10.034385 10.417160 6 2 Ji 9.630992 9.956163 9.674829 10.325171 10.043837 10.3690C8 5 % 2 % 9 673387 9.945430 9.727957 10.272043 10.054570 10.326613 5 y a 2 % 9.711050 9.933350 9.777700 10.222300 10.066650 10.288950 5% 3 9.744739 9.919846 9.824893 10.175107 10.080154 10.255261 5 3 > 9.775027 9.904828 9 870199 10.129801 10.095172 10.224973 4 % 3 y, 9.802359 9.888185 9.914173 10.085827 10 111815 10.197641 4 % 3 % 9.827084 9.869790 9.957295 10.042705 10.130210 10.172916 4 % 4 9 849485 9.849485 10.000000 10.000000 10.150515 10.150515 4 Co-sine Sine. Co-tang Tangent . Co-sec. Secant. LOGARITHMS OF NUMBERS. Ttfn 1 LOO Log. 0.00000 00 000000 No. Log. No. Log. No. Log. No. Log. No. Log. l 0.000000 21 1.322219 41 1.612784 61 1.785330 81 1.908485 2 0.301030 22 1.342423 42 1.623249 62 1.792392 82 1.913814 3 0.477121 23 1.361728 43 1.633468 63 1.799341 83 1.919078 4 O.G02060 24 1.380211 44 1.643453 04 1.806180 84 1.924279 5 0.698970 25 1.397940 45 1.653213 65 1.812913 85 1.929419 6 0.778151 26 1.414973 47 1.662758 66 1.819544 86 1.931498 7 0.845098 27 1.431364 47 1.672098 67 1.826075 87 1.939519 8 0.903090 28 1.447158 48 1.681241 68 1.832509 88 1.944483 9 0.954243 29 1.462398 49 1.690196 69 1.838849 89 1.949390 10 1.000000 30 1.477121 50 1.698970 70 1.845098 90 1 951243 11 1.041393 31 1.491362 51 1.707570 71 1.851258 91 1.959041 12 1.079181 32 1.505150 52 1 716003 72 1.857332 92 1.963788 13 1.113943 33 1.518514 53 1.724276 73 1.863323 93 1. 908483 14 1 146128 34 1.531479 54 1 732394 74 1.869232 94 1.973128 15 1.176091 35 1.544068 55 I. 740363 75 1.875061 95 1.977724 16 1.204120 36 1 556302 56 1.748188 76 1.880814 96 1.982271 17 1.230449 37 1.5G8202 57 1.755875 77 1.886491 97 1 98G772 18 1.255273 38 1 579784 58 1.763428 78 1.892095 98 1.991226 19 1.278754 39 1.591065 5.9 1.770852 79 1.897627 99 1 995635 20 1.301030 40 1.602060 60 1.778151 80 1.903090 100 2 000000 128 TABLE I. LOGARITHMS OF NUMBERS. No. 1 000 1 GOO Log. 00 1000 J04120 No. 1 2 3 4 5 6 7 8 9 Diff. 100 101 102 103 104 105 106 107 103 109 ooooou 004321 008600 012837 017033 021189 025306 0293S4 033424 037426 000434 004751 :009026 01325& 017451 021603 025715 029789 033826 037825 000868001301001734 005180005609006038 009451009876010300 013680014100014520 017868 018284 01870f 022016 022428 022841 026124026533026942 030195030600031004 034227 034628 035029 038223038620039017 002166 006466 010724 014940 019116 023252 027350 031408 035430 039414 ,002598 006894 011147 015360 019532 023664 027757 031812 035830 039811 003029 007321 011570 015779 019947 024075 028164 032216 036229 040207 003460 007748 011993 016197 020361 024486 028571 032619 036629 040602 OU3891 008174 012415 016615 020775 021896 028978 033021 037028 040998 432 428 424 420 416 412 408 404 400 397 110 111 112 113 114 115 116 117 118 119 011393 045323 049218 053078 056905 060698 364458 038186 071882 04177 045714 049606 053463 057286 061075 064832 068557 072250 042182 046105 049993 053846 057666 061452 065206 168928 072617 042575 046495 050380 054230 058046 061829 065580 069298 072985 042969 046885 050766 054613 058426 062*206 065953 069668 073352 077004 043362 047275 051152 054996 058805 062582 066326 070038 073718 07736S 043755 047644 051538 0.>-j:;7S 059185 062958 066699 070407 074085 077731 044148 Oi8053 051924 055760 059563 063333 067071 07077G 074451 078094 044540 048442 052309 056142 059942 063709 067443 071145 074816 o78457 U44D31 048830 052694 056524 060320 064083 067814 071514 075182 078819 393 390 386 383 379 376 373 370 366 363 J7o547 OVoUia 076276:07(5640 120 121 122 123 124 125 126 127 128 129 J79181 082785 )S6360 089905 093422 J96910 100370 103804 107210 110590 079543 083144 086716 09025S 093772 097257 100715 10414G 107549 110926 07 1 J904'08026G 083503083861 087071 087426 090611090963 094122 094471 097604097951 101059 101403 104487 104828 1078S8 108227 111262 111598 080626 084219 087781 091315 094820 098297 101747 105169 108565 111934 080987 084576 08813G 091667 095169 098644 102090 105510 108903 112270 081347 084934 088490 092018 095518 098990 102434 105851 109241 112605 081707 085291 088845 092370 0958G6 099335 102777 106191 109578 112940 082067 085647 089198 092721 096215 099681 103119 108531 109916 113275 08^42b 086004 089552 093071 096562 10002<:i 103462 106870 110253 113609 360 357 355 352 349 346 343 341 338 335 130 131 132 133 134 135 136 137 138 139 113943 117271 120574 123852 127105 130334 133539 136721 139879 143015 1142/v 117603 120903 124178 127429 130G55 133858 137037 140194 143327 114611114944 117934118265 121231121560 124504 124830 127752123076 130977 131298 134177 134496 137354137670 140508 140822 143639 143951 115278 118595 121888 125156 128399 131619 134814 137987 141136 144263 115610 118926 122216 125481 128722 131939 135133 138303 141450 144574 115943 119256 122543 125806 129645 132260 135451 138618 141763 144885 116276 119586 122871 126131 129368 132580 135768 138934 142076 145196 116608 119915 123198 12G45G 129690 132900 136086 139249 142389 145507 116940 120245 123525 126781 130012 133219 136403 139564 142702 145818 332 330 328 325 323 321 318 316 314 311 140 141 142 143 144 145 146 147 148 149 146128 146438 149219 149527 152288 152594 155338 155640 158362158664 161368161667 164353 164650 1G7317 167613 170262 170555 173186173478 146748 149835 152900 155943 158965 161967 164947 167908 170848 173769 147058 150142 153205 15624G 159266 162266 165244 168203 171141 174060 147367 150449 15351Q 156549 1595G7 162564 165541 168497 171434 174351 147676 150756 153815 156852 159868 162863 165838 168792 171726 174641 147985 151063 154119 157154 160168 163161 166134 169086 172019 174932 148294 151370 154424 157457 160468 163460 166430 169380 172311 175222 148603 151676 154728 157759 160769 163757 166726 169674 172603 175512 148911 151982 155032 158061 161088 .64055 167022 1699G8 172895 175802 309 307 305 303 300 298 296 294 292 290 150 151 152 153 154 155 156 157 158 159 17609J 178977 181844 1S4691 187521 190332 193125 195900 198932 201397 176381 179264 182129 184975 187803 190612 193403 196176 198392 201670 176670 179552 182415 185259 188084 190892 193681 196452 199206 201943 176959 179839 182700 185542 188366 191171 193959 196729 199481 202216 177248 180126 182985 185825 188647 191451 194237 197005 199755 202488 177536 180413 183270 186108 188928 191730 194514 197281 200029 202761 177825 180699 183554 186391 189209 192010 194792 197556 200303 203033 178113 180986 183839 186674 189490 192289 195069 197832 200577 203305 178401 181272 184123 186956 189771 192567 195346 198107 200850 203577 178689 181558 184407 187239 190051 192846 195623 198382 201124 203848 288 287 285 283 281 279 278 . 276 274 272 1 '1 2 3 4 5 G 7 | 8 9 TABLE I. 129 LOOAKITHMS OF NUMBERS. No. 1 ftnn ... ,m , - 200 Log. 20- 1 1 !42423 No. 1 2 3 4 5 6 7 8 9 Diff. 160 161 162 1C3 164 165 166 167 168 169 204120 206826 209515 112188 214844 217484 220108 2-22716 225309 227887 204391 207095 209783 212454 215109 217747 220370 222976 225568 228144 21)4662 207365 210051 212720 215373 218010 220631 223236 225826 228400 204933 207634 210318 212986 215638 218273 220892 223496 226084 228657 205204 207903 210586 213252 215902 218535 221153 223755 226342 228913 205475 208172 210853 213518 616166 218798 221414 224015 226600 229170 205745 208441 211120 213783 216430 219060 221675 224274 226,858 229426 206016 208710 211388 214049 216694 219322 221936 224533 227115 229682 206-280 206556 208978 209247 211654211921 214314214579 216957217221 219584219846 222196222456 224792 225051 227372227630 229938J230193 2il 269 267 266 264 262 261 259 258 256 170 171 172 173 174 175 176 177 178 179 23U449 232996 235528 238046 240549 243038 245513 247973 250420 252853 230704 233250 235781 138297 240799 243286 245759 248219 250664 253096 23096U 233504 236033 238548 241048 243534 246006 248464 250908 253338 231215 233757 236285 238799 241297 243782 246252 248709 251151 253580 23147U 234011 236537 239049 241546 244030 246499 248954 251395 253822 231724 234264 236789 239299 241795 244277 246745 249198 251638 254064 231979 234517 237041 239550 242044 244524 246991 249443 251881 254306 232233 234770 237292 239800 242293 244772 247236 249687 252125 254548 232488 235023 237544 240050 242541 245019 247482 249932 252367 254790 23274^ 235276 237795 240300 242790 245266 247728 250176 252610 255031 2>5 253 252 250 249 247 246 245 243 242 ISO 181 182 183 184 185 186 187 183 189 255273 257679 260071 262451 264818 267172 269513 271842 274158 276462 255514 257918 260310 262688 265054 267406 269746 272074 274389 276691 25575j 258158 2B0548 262925 265290 267641 269980 272306 274620 276921 255996 258398 260787 263162 265525 267875 270213 272538 274850 277151 256236 258637 261025 263399 265761 268110 370446 272770 275081 277380 256477 258877 261263 263636 265996 268344 270679 273001 275311 277609 256718 259116 261501 263873 266232 268578 270912 273233 275542 277838 25695S 259355 261738 264109 266467 268812 271144 273464 275772 278067 257198 259594 261976 264345 266702 269046 271377 273696 276002 278296 257439 259833 262214 264582 266937 269279 271609 273927 276232 278525 241 239 238 237 235 234 233 232 230 229 190 191 192 193 194 195 196 197 198 199 278754 281033 283301 285557 287802 290035 292256 294466 ;96665 298853 27898; 281261 283527 285782 288025 290257 292478 294687 296884 299071 279210 281488 283753 286007 288249 290480 292699 294907 297104 299289 279439 281715 283979 286232 288473 290702 292920 295127 297323 299507 279667 281942 284205 286456 288696 290925 293141 295347 297542 299725 279895 282169 284431 286681 288920 291147 263363 295567 297761 299943 280123 282395 284656 286905 289143 291369 293583 295787 297979 300161 280351 282622 284882 287130 289366 291591 293804 296007 298198 300378 280578 282849 285107 287354 289589 291813 294025 296226 298416 300595 2S0806 283075 285332 287578 289812 292034 294246 296446 298635 300813 228 227 226 225 223 222 221 220 219 2)8 200 201 202 203 204 205 206 207 208 209 301030 303196 305351 307496 309630 311754 313867 315970 318063 320146 30 J 247 303412 305566 307710 309843 311966 314078 316180 318272 320354 301464 303628 305781 307924 310056 312177 314289 316390 318481 320562 301681 303844 305996 308137 310268 312389 314499 316599 318689 320769 301898 304059 306211 808351 310481 312600 314710 316809 318898 320977 302114302331302547 304275 304491 304706 306425306639306854 308564308778308991 310693310906311118 312812313023313234 314920315130315340 317018317227317436 319106319314319522 321184321391321598 302764 304921 307068 309204 311330 313445 315550 317645 319730 321805 302980 305136 307282 309417 311542 313656 315760 317854 319938 322012 217 216 214 213 212 211 210 208 208 207 210 211 212 213 214 215 216 217 218 219 322219 324282 326336 328380 330414 332438 334454 336460 338456 340444 322426 324488 326541 328583 330617 332640 334655 336660 338656 340642 322633322839 324694 324899 326745326950 328787 328991 330819331022 332842 333044 334856335056 336860337060 338855339054 340841341039 323046 325105 327155 329194 331255 333246 335257 337260 339253 341237 323252 323458 323665,323871 325310 325516 325721 325926 327359 327563 327767 327972 329398 329601 329805 330008 331427 331630 331832 332034 333447 333649 333850 334051 335458 335658 335859 336059 337459 337659 337858 338058 339451 339650 339849 340047 341435 341632 341830 342028 324077 326131 328176 330211 332236 334253 336260 338257 340246 342225 2U6 205 204 203 202 202 201 200 199 198 1 2 3 4 5 6 7 8 9 130 TABLE I. LOGARITHMS OF NUMBEES. No. 2i Of) 00 Log. M'2 fM 4 47158 No. 1 2 3 4 5 6 7 8 9 Biff. !&U 221 ' 222 223 224 225 226 227 228 229 342423,342620 344392 344589 34(5353346549 348305348500 350248 350442 352182352375 354108354301 353026356217 357935358125 359835360025 342817 344785 346744 348694 350636 352568 354493 356408 358316 360215 343014 344981 1 346939 348889 350829 352761 354685 356599 358506 360404 343214 345178 347135 349083 351023 352954 354876 356790 358696 360593 343409, 345374 347330 349278 351216 353147 355068 356981 358886 360783 343606 345570 347522 349470 351410 353339 355260 357172 359076 360972 343802' 345766 347720 349666 351603 353532 355452 357363 359266 361161 343999 345962 347915 349860 351796 353724 355643 357554 359456 361350 344196 346157 348110 350054 351989 353916 355834 357744 359646 361539 197 196 195 194 193 193 192 191 190 189 230 231 232 233 234 235 236 237 238 239 361728 363612 365488 367356 S69216 371068 372912 374748 376577 378398 361917 363800 365675 367542 369401 371253 373096 374932 376759 378580 362 105 363988 365862 367729 369587 371437 373280 375115 376942 378761 362294 364176 366049 367915 369772 371622 373464 375298 377124 378943 362482 364363 366236 368101 369958 371806 373647 375481 377306 379124 362671362859 364551 364739 366423366610 368287 368473 370143370328 371991 372175 373831374015 375664 375846 377488 377670 379306 379487 363048 364926 366796 368659 370513 372360 374198 376029 377852 379668 363236 365113 366983 368844 370698 372544 374382 376213 378034 379849 363424 365301 367169 369030 370883 372728 374565 376394 378216 380030 188 188 187 186 185 184 184 183 182 181 240 241 242 243 244 245 246 247 248 249 380211 382017 383815 385606 387390 3891 6G 390935 392697 394452 396199 380392 382197 383995 385785 387568 389343 391112 392873 394627 396374 380573 382377 384174 385964 387746 389520 391288 393048 394802 396548 380754 382557 384353 386142 387923 389697 391464 393224 394977 396722 380934 382737 384533 386321 388101 389875 391641 393400 395152 396896 3S1115 382917 384712 386499 388279 390051 391817 393575 395326 397071 381296 383097 384891 386677 388456 390228 391993 393751 395501 397245 381476 383277 385070 386856 388634 390405 392169 393926 395676 397418 381656 383456 385249 387034 388811 390582 392345 894101 395850 397592 381837 383636 385428 387212 388989 390759 392521 394277 396025 397766 181 180 179 178 178 177 176 166 175 174 250 251 252 253 254 255 256 257 258 259 397940 399674 401400 40312I/ 404834 406540 408240 409933 111620 413300 398114 399847 401573 403292 405005 406710 408410 410102 411788 413467 398287 400020 401745 403464 405175 406881 408579 410271 411956 413635 398461 400192 401917 403635 405346 407051 408749 410410 412124 413802 398634 400365 402089 403807 405517 407221 408918 410608 412292 413970 398808 400538 402261 403978 405688 407391 409087 410777 412460 414137 398981 400711 402433 404149 405858 407561 409257 410946 412628 414305 396154 400883 402605 404320 406029 407731 409426 411114 412796 414472 399327 401056 402777 404492 406199 407900 409595 411283 412964 414639 399501 401228 402949 404663 406370 408070 409764 411451 413132 414806 173 173 172 171 171 170 169 169 168 167 260 261 262 263 264 265 266 267 268 269 414973 416640 418301 419956 421604 423246 424882 426511 428135 429752 415140 416807 418467 420121 421768 423410 425045 426674 428297 429914 415307 416973 418633 420286 421933 423573 425208 426836 428459 430075 41U74 417139 418798 420451 422097 423737 42537J 426999 428621 430236 415641 417306 418964 420616 422261 423901 425534 427161 428782 430398 415808 417472 419129 420781 422426 424064 425697 427324 428944 430559 415974 417638 419295 420945 422590 424228 425860 427486 429106 430720 416141 417804 419460 421110 422754 424392 426023 427648 429268 430881 416308 417970 419625 421275 422918 424555 426186 427811 429429 431042 416474 418135 319791 421439 423082 424718 426349 427973 429591 431203 167 - 166 165 165 164 164 163 162 162 161 270 271 272 273 274 275 276 277 278 279 431364 432969 134569 436163 437751 439333 140909 442480 414045 445604 431525 433129 434728 436322 437909 439491 441066 442636 444201 445760 431685 433290 434888 436481 438067 43864g 441224 442793 444357 415915 431846 423450 435048 436640 438226 429806 441381 442950 444513 44C071 432007 433610 435207 436798 438384 439964 441538 443106 444669 446226 432167 433770 435366 436957 438542 440122 441695 443263 444825 446382 432328 433930 435526 437116 438700 440279 441852 443419 444981 446537 432488 434090 435685 437275 438859 440437 442009 443576 445137 446692 432649 432809 434249 434409 435844436003 437433437592 439017439175 440594 440752 442166442323 443732443888 445293445448 446848447003 .160 160 159 159 158 158 157 157 156 155 1 2 3 4 5 6 7 8 9 TABLE I. 131 LOGARITHMS OF NUMBERS. No. 2 HflO '-i 400 Log. 44 71 IS 531479 No. 1 2 3 4 5 6 7 8 9 Diff. 280 281 282 283 284 285 28G 287 288 289 447156 44870G 150249 151786 453318 454845 15636G 457882 459392 460898 44731b 448861 '450403 451940 453471 454997 456518 458033 459543 461048 447466 149015 450557 452093 45C624 455149 45667C 458184 459694 461198 447023 44917C 450711 352247 453777 455302 456821 458336 459845 461348 447 778 447933 44808^ 449324 449478 44963C 450865 451018 451172 452400 452553 45270C 453930 454082 45423c 455454 455606 455758 456973457125457276 458487 458638 45878S 459995460146460296 461498 461649 46179S 44824: 449787 451321 45285 454387 45591 C 457428 45894C 460447 46194S 448397 449941 45147 453012 45454C 456062 45757S 459091 460597 462098 4485o: 45009c 45163c 45316^ 454692 456214 45773C 459242 460747 462248 165 154 154 153 158 152 152 151 151 150 290 291 292 293 294 295 29G 297 298 299 4G23t)b 462548 462(39 1 462847 402997 463893 464042 464191 464340 464489 465383 465532 465680 465829 465977 466868 467016 467164 467312 467460 468347 168495468643468790468938 469822 469969 470116 470263 470410 471292 471438 471585 4717321471878 472756 472903 473049 473195!473341 474216 174362474508474653474799 175671 475816 475962 476107 476252 463146 463296 463445 464639464787464936 466126466274466423 467C08 467756 467904 469085469233469380 463594 465085 466571 468052 469527 463744 465234 466719 468200 469675 471145 472610 474070 475526 476976 150 149 149 148 148 147 147 146 146 145 470557 470704 470851 470996 472025 472171 472317 472464 473487 473633 473779 473925 474944 475090 475235 475381 476397 476542 476687 476832 30J 301 302 303 304 305 3U6 307 308 309 477121477266477411 478566 178711 478855 480007480151480294 481443481586481729 482874483016483159 184300 484442 484584 185721485863486005 487138487280487421 488551 488692 488833 189958490099490239 47 7555 478999 480438 481872 483302 484727 48G147 487563 488973 490380 477700 479143 480582 482016 483445 484869 486289 487704 489114 490520 477844 479287 480725 482159 483587 485011 486430 487845 489255 490661 477989478133 479431 479575 480869481012 482302 482445 483730483872 485153 485295 486572486714 487986488127 489396489537 490801 490941 478278 479719 481156 482588 484015 485437 486855 488269 489677 491081 478422 479863 481299 482731 484157 485579 486997 488410 489818 491222 115 144 144 143 143 142 142 141 141 140 310 311 312 313 314 315 316 317 318 319 491362 492760 494155 195544 496930 498311 199687 501059 502427 503791 491502 492900 494294 495683 497068 498448 499824 501196 502564 503927 491642 491782 493040493179 494433494572 495822 495960 497206497344 498586498724 499962 500099 501333501470 502700 502837 504.063 504199 491922 493319 494711 496099 497482 498862 500236 501607 502973 504335 492062 493458 494850 496237 497621 498999 500374 501744 503109 504471 492201 493597 494989 496376 497759 499137 500511 501880 503246 504607 492341 493737 495128 496514 497897 499275 500648 502017 503382 504743 492481 493876 495267 496653 498035 499412 500785 502154 503518 504878 492621 494015 495406 496791 498173 499550 500922 502290 503654 505014 140 139 139 ' 139 138 108 137 137 136 136 320 321 322 323 324 325 32G 327 328 329 505150 506515 507856 509202 510545 511883 513218 514548 515874 51719G 505286 506640 507991 509337 510679 512017 513351 514680 516006 517328 505421 506775 508125 509471 510813 51215C 513484 514813 516139 517460 505557 506911 508260 509606 510947 512284 513617 514946 516271 517592 505692 507046 508395 509740 511081 512417 513750 515079 516403 517724 505828 505963 507181507316 508530508664 509874510008 511215511348 512551512684 513883514016 515211 515344 516535 516668 517855517987 506099 507451 508799 510143 511482 512818 514149 515476 516800 518119 506234 507586 508933 510277 511616 512951 514282 515609 516932 518251 506370 507721 509068 510411 511750 513084 514415 515741 517064 518382 136 135 135 134 134 133 133 133 132 132 330 331 332 333 334 335 33G 337 338 339 518514518645518777 519828519959520090 521138521269521400 522444522575522705 523746523876524006 525045525174525304 526339526468526598 527630527759527888 528917529045529174 530200530328530456 518909 519040 520221 520352 521530521661 522835 522966 524136524266 525434 525563 526727 526856 528016528145 529302 529430 530584J530712 519171 519303 520483520614 521792 521922 523096523226 524396 524526 525693 525822 526985527114 528274 528402 529559 529687 530840 530968 519434 520745 522053 523356 524656 525951 527243 528531 529815 531095 519565 520876 522183 523486 524785 326081 527372 528660 529943 531223 519697 521007 522314 523616 524915 526210 527501 528788 530072 531351 131 131 131 ISO 130 129 129 129 128 < 128 1 2 3 4 5 6 7 8 9 132 TABLE I. LOGARITHMS OF NUMBERS. No. 3400 4000 Log. 53J 470 02060 No. 1 2 3 4 5 6 7 8 9 Diff. 340 341 342 343 344 345 346 347 348 349 53147 9 531607 531734 531862 532745 532882 533009 533136 534026 534153 534280 534407 535294 535421 535547 535674 536558 536685 536811 536937 537819 537945 538071 538197 539076 539202 539327 539452 540329 540455 540580 540705 541579 541704 541829 541953 542825 542950 543074 543199 531990 532117 533263 533391 534534534661 535800 535927 537063 537189 538322538448 539578 539703 540830 540955 542078 542203 543323543447 532245 53237i 533518 53364E 534787:534914 536053o3617S 537315537441 538574 538699 539829539954 541080541205 542327542452 543571 543696 53250U 533772 535041 536306 537567 538825 540079 541330 542576 543820 53262 r 53389 53516" 536432 537693 538951 540204 541454 542701 543944 1-.8 127 127 126 126 126 125 125 125 124 350 351 352 353 354 355 356 357 358 359 544068544192 545307 545431 546543546666 547775,547898 549003549126 550228550351 551450551572 552668552790 553883,554004 555094555215 544316 544440 544564 544688 545554 545678 545802 545925 546789 546913 547036 547159 548021 548144 548266 548389 549249 549371 549494 549616 550473 550595 550717 550840 551694 551816 551938 552059 552911 553033 553154 553276 554126 554247 554368:554489 555330 555457|555578 555699 544812 544936 546049'546172 547282 547405 548512548635 549739J549861 550962551084 552181J552303 553398,553519 554610,554731 555820,555940 545060 546296 547529 548758 549984 551206 552425 553640 554852 556061 545183 546419 547652 548881 550106 551328 552546 553762 554973 556182 124 124 123 123 123 122 122 121 121 121 360 361 362 363 364 365 366 367 368 369 556302556423 557507:557627 558709558829 559907560026 561101561221 562293562412 563481 563600 564666564784 565848565966 567026 567144 556544 556664:556785 556905 557748 557868,557988 558108 558948 559068 559188:559308 560146 560265 560385 560504 561340 561456 561578 561698 56253r562650 562769 562887 563718 563837 563955 564074 564903 565021 565139 565257 566084 566202 566320 566437 567262 567379 567497 567614 557026,557146 557267 557387 558228,558348 558469 558589 559428,559548559667 559787 560624 560743 560863 560982 561817i561936 562055 562174 563008,563125 563244 563362 564192 564311 564429 564548 565378^65494 565612 565730 566555,566673 566791 566909 567732567849 567967,568084 1-20 120 120 119 119 119 119 118 - 118 118 370 371 372 373 - 374 375 376 377 378 379 568202 568319 568436 569374569491569608 570543570660570776 571709571825571942 572872572988573104 568554568671,568788 569725 569842 5G9959 570893571010571126 572058572174572291 573220573336573452 568905,569023 370076;570193 571243571359 572407:572523 573568573684 574726574841 575880 ! 575996 577032:577147 578181578295 579326579441 569140569257 570309570426 571476571592 372639572755 573800573915 574957 575072 576111 576226 577262;577377 578410 578525 579555579669 117 117 117 116 116 116 115 115 115 114 574031 574147 574263 574379 574494 574610 575188 575303 575419 575534 575650 575765 5763411576457 576572 576687 576802 576917 577492 577607 577721 577836 577951 ! 578066 578639 578754 578868 578983 579097 579212 380 381 382 383 384 385 386 387 388 389 579784 580925 582063 583199 584331 585461 586587 587711 588832 589950 579898:580012 581039581153 582177 582291 583312 583426 584444584557 585574585686 586700 586812 587823587935 588944589056 590061 590173 580126 581267 582404 583539 584670 585799 586925 588047 589167 590284 580240580355 581381 581495 582518582631 583652583765 584783 584896 585912 586024 587037 587149 588160'588272 589279589391 590396 590507 580469,580583 581608581722 582745582858 583879,583992 585009585122 586137,586250 587262587374 588384588496 589503'589615 590619,590730 580697 580811 581836281950 582972 583085 584105584218 585235585348 586362586475 587486587599 588608588720 589726589838 590842 590953 114 114 114 113 113 113 112 112 112 112 390 391 392 393 394 395 396 397 398 399 5'J1065;591176 591287 591399 591510 591621 592177 592288 592399 592510 592621 592732 593286 593397 593508 593618 593729 593840 594393 594503 594613 594724 59^834 594945 595496 595606 595717 595827 595837 596047 596597 596707 596817 596927 597037 597146 597695 597805 597914 598024 598134 598243 598790 598900 599009 599119 599228 599337 599883 599992,600101 600210 600319 600428 600973 601082 601190 601299 601408 601517 591732 591843J591955 592066 592843 592954 593064 593175 593950o94061 594171 594282 595055 595165 595276 595386 596157 596267 596377 596487 597256 597366 597476 597585 598353*598462 598572 598681 599446,599556 599665 599774 600537,600644 600755 600864 601625J601734 601843 601951 111 111 111 110 110 110 110 109 109 109 1 2 3 4 5 | 6 7 8 9 TABLE I. LOGARITHMS OF NUMBERS. 133 No. 4 ono ,1 GOO Log. 602060 ( 562758 No. 1 2 3 4 5 6 7 8 9 Diff. 4UO 401 402 403 404 405 406 407 408 409 u02UGO 603144 604226 605305 6063S1 607455 608526 609594 610660 611723 002109 oO-^77 002386 603253 603361 603469 604334604442604550 605413 G0552r605628 G06489 606596 606704 607562607669607777 60S633 608740 608847 609701 609808 609914 610767610873610979 611829611936612042 002494 oo^oua 603577 603686 604658 60476G 605736605844 606811 606919 607884 G07991 608954609061 600021610128 611086611192 612148612254 60^711 603794 604874 G05951 G0702G 608098 609167 610234 611298 612360 602819 603902 604982 606059 607133 608205 609274 610341 611405 612466 602928,003031 604010604116 305089 605191 606166 606274 607241 60734* 608312!60S41 609381 609488 610447 610554 611511611617 612572,612676 108 108 108 108 107 107 107 107 106 106 410 411 412 413 414 415 416 417 418 419 612784 6128UO 612996 613842613947614053 614897615003615108 615950616055616160 61700o'617105 617210 618048,618153618257 619093619198619302 620136 G20240 620344 621176621280621384 622214622318622421 613101 613207 013313 613419:613525 614159 614264 614370 614475 614581 615213 615319,615424 615529 615634 616265 616370 616475 616580 616685 617315 617420 617524 617629 617734 618362 618466 618571 618675 618780 619406 619511 6i9615 619719 619823 620448 620552 620656 620760 620864 621488 621592 621695 621799 621903 622525 622628 622732 622835,622939 613630,613736 614686614792 615740615845 616790616895 617839,617943 618884618989 619928620032 620968621072 622007622110 623042,623146 106 106 105 105 105 105 104 104 104 104 420 --421 422 423 424 425 426 427 428 429 623249623353 624282624385 625312625415 626340626443 627366627468 628389628491 629410629511 630428 630530 631444631545 632457|63255S 623456 624488 625518 626546 627571 G28593 629613 G30631 331647 G326GO 023559 624591 625621 626648 627673 628695 629715 630733 631748 632761 623663 624694 625724 626751 627775 628797 629817 630834 631849 632862 623766 624798 625827 626853 627878 628909 629919 630936 631951 632963 623869 624901 625929 626956 627980 629002 630021 631038 932052 633064 623972 625004 626032 627058 628082 629104 630123 631139 632153 633165 624076:024179 625107 625209 626135626238 627161 627263 628184628287 629206629308 630224 630326 6312411631342 G32255 632356 833266 6333G7 103 103 103 103 102 102 102 102 101 101 43U 431 432 433 434 435 436 437 438 439 033468633569 634477634578 635484635584 636488636588 637490637590 638489638589 639486639586 640481 640581 641474641573 642464;642563 633670 633771 633872 633973 634074 634175 634276 634679 634779 634880 634981 635081 635182 635283 335685 635785 635886 635986 636086 636187 636287 636688 636789 636889 63G989 637089 637189 637289 637690 637790 637890 637990 638090 638190 63828'J 638689 638789 638888 638988 639088 639188 639287 639686 639785 639885 639984 640084 640183 640283 640680 640779 640879 640978 641077 641176 641276 641672 641771 641870 641970 642069 642168 642267 642662 642761 642860 642959 643058 643156 643255 034376 635383 636388 637390 638389 639387 640382 641375 642366 643354 101 101 100 100 100 100 99 99 99 99 440 441 442 443 444 445 446 447 448 449 643453,643551 643650 643749 644439 644537 644635 644734 645422 645520 645619 645717 (546404 646502 646600 646698 647383 647481 647579 647676 648360 648458 648555 648653 649335649432 649530 649627 650307 650405 650502 650599 651278 651375 651472 651569 652246 652343 652440 652536 643847 643946 644832644931 645815645913 646796 64G894 647774647872 648750648848 649724 649821 650696 650793 651666651762 652633652730 644044 645029 646011 646991 647969 648945 649919 650890 651859 652826 044143644242 645127645226 646109646208 647089647187 648067 648165 649043649140 650016650113 650987 651084 651956652053 G52923 653019 644340 645324 646306 647285 648262 649237 650210 651181 652150 653116 98 98 98 98 98 97 97 97 97 97- 450 451 452 453 454 455 456 457 458 459 653213 653309 653405,653502 653598 653695 653791 653888,653984 054080 654176 654273 654369,654465 654562 654658 654754 654850 654940 655042 655138 655234 655331 655427 G55523 655619 655714 655810 655906 656002 656098656194 656290 656386 656481 656577 656673 656769 656864 656960 657056 657151 657247 657343 657438 657534 657629 657725 657820 657916 658011 658107 658202 658298 658393 C58488 658584 658679 658774 658870 658965 659060 659155 659250 659346 659441 65953G 659631 659726 659821 659916660011 66010G 660201 660296660391 660486660581 660676660771 660865 660960 661055 661150 651245 661399 661434 661529 661G23 661718 661813 661907 662002 662096 652191 662285 662380 662474 662569 662663 96 96 96 96 96 95 95 95 95 95 1 2 3 4 5 6 7 8 9 134 TABLE I. LOGARITHMS OF NUMBERS. No. 4 fiftO ^ 200 Lo#. 662758 716003 No. 1 2 3 4 5 6 7 8 9 Diff. 4GU 401 462 463 464 463 4G6 467 468 469 36^758 6G3701 664642 665581 G66518 667453 668386 669317 670246 371173 66285* 663795 664736 665675 666612 667546 G68479 669410 670339 671265 66^947 663889 664830 665769 666705 667640 668572 669503 670431 671358 603041 663983 664924 665862 666799 667733 668665 669596 670524 671451 6631c5 664078 665018 665956 666892 667826 668758 669689 G70617 671543 663230 664173 665112 666050 666986 667920 668852 669782 670710 671636 6033^4 664''.6G 665206 66614S 667079 668013 668945 669875 670802 671728 1663416 G64360 665299 666237 667173 66R106 669038 669967 670895 671821 60351k 664454 365392 666331 66726C 66819S 669131 67006C 670988 671913 00300" 66454fc 66548" 666424 66735S 668293 669224 670153 67108C 67200J l>'4 94 94 94 94 93 93 93 93 93 470 471 472 473 474 475 476 477 478 479 67*098 673021 673942 (374861 G75778 G76694 G77607 378518 G79428 080335 G72190 673113 G74034 374953 375870 376785 077698 678609 079519 380426 672283 673205 674126 G75045 G75962 676876 G777S9 378700 679610 680517 672375 673297 674218 675136 376053 676968 677881 678791 679700 680607 672467 67339( 674310 675228 676145 677059 677972 678882 679791 680G98 6725bO 673482 674402 675320 676236 677151 678063 678973 679882 680789 67^652 673574 674494 675412 676328 677242 678154 679064 679973 680879 67^744 67366G 674586 67550C 676419 677333 678245 679155 680063 680970 07283L 673758 674677 675595 676511 677424 678336 679246 680154 681060 6729*1] 673850 674769 67568" 67660^ 677516 67842' 67933 r 680245 681151 92 92 92 92 92 91 91 91 91 91 480 481 482 483 484 45 486 487 488 489 681i:41 G82145 (383047 683947 G84845 685742 686636 G87529 688420 G89309 681332 G82235 G83137 684037 684935 685831 G8G726 687618 588509 G89398 08142* 682323 683227 684127 68502L 685921 686815 687707 688598 689486 681513 682416 683317 684217 685114 686010 68C904 687796 688687 689575 G816U3 682506 683407 684307 685204 686100 686994 687886 688776 689664 681693 682596 683497 G84396 685294 686189 687083 687975 688865 689753 681784 682686 683587 684486 685383 686279 687172 688064 688953 689841 681874 682777 683677 684576 685473 686368 687261 688153 689042 689930 681934 6S2867 683767 684666 685563 686457 687351 688242 689131 690019 68205;. 682957 683857 684756 6g5652 686547 68744C 688331 68922C 690107 90 90 90 90 90 89 89 89 89 89 490 491 492 493 494 495 496 497 493 499 G9019G 691081 691965 692847 G93727 G94605 395482 396356 387229 698100 660285 691170 G92053 392935 393815 694693 695569 696444 697317 698188 6903/3 G91258 692142 693023 693903 694781 695657 696531 697404 698275 690461 691347 692230 693111 693991 694868 695744 696618 697491 69S362 690550 691435 692318 693199 694078 694956 695832 69G70G G97578 698448 690639 691524 692406 693287 694166 695044 695919 696793 697665 698535 690727 691612 692494 693375 694254 695131 696007 696880 697752 698622 690810 691700 692583 693463 694342 695219 696094 696968 697839 698709 G90905 691789 692671 693551 694430 695307 696182 697055 69792G 69.S796 69U993 691877 692759 693639 694517 G95394 696269 697142 69801S G9888S 8J 88 88 88 88 88 87 87 87 87 5UJ 501 502 503 504 505 506 507 508 509 J989/0 696838 700704 701568 702430 703291 704150 705008 705864 706718 6U9057 699924 700790 701654 702517 703377 704236 705094 705949 706803 G99144 700011 700877 701741 702603 703463 704322 705179 706035 706888 699236 700098 700963 701827 702689 703549 704408 705265 706120 706974 699317 700184 701050 701913 702775 703635 704494 705350 706206 707059 699404 700271 701136 701999 702861 703721 704579 705436 706291 707144 698491 700358 701222 702086 702947 703807 704665 705522 706376 707229 G99578 700444 701309 702172 703033 703893 704751 705607 706462 707315 699604 700531 701395 702258 703119 703979 704837 705693 706547 707400 690751 700617 701482 702344 703205 704065 704922 705778 706632 707485 67 87 86 86 86 86 86 86 85 85 510 511 512 513 514 515 516 517 518 519 707570 708421 709270 710117 710963 711807 712650 713490 714330 715167 707655 708506 709355 710202 711048 711892 712734 713574 714414 715251 707740 708591 709440 710287 711132 711976 712818 713658 714497 715335 707826 708676 709524 710371 711216 712060 712902 713742 714581 715418 707911 708761 709609 710456 711301 712144 712986 713826 714665 715502 707996 708846 709694 710540 711385 712229 713070 713910 714749 715586 703081 708931 709779 710625 711470 712313 713154 713994 714832 715669 708106 709015 709863 710710 711554 712397 713238 714078 714916 715753 708251 709100 709948 710794 711638 712481 713322 714162 715000 715836 708rfb6 709185 710033 710879 711723 712566 71340G 714246 715084 715920 85 85 85 85 84 84 84 84 84 84 1 2 3 4 5 6 7 8 9 1 TABLE I. LOGARITHMS OF NUMBERS. 135 No. 5 ^00 *V $00 Log. 71( 5003 63428 No. 1 2 3 4 5 G 7 8 9 Diff. MO 521 522 523 524 525 526 527 528 529 710003 716838 717671 718502 719331 720159 720986 721811 722634 723456 71G087 71G921 717754 718585 719414 720242 721068 721893 72271G 723538 716170 717004 717837 7186G8 719497 720325 721151 721975 722798 723620 71G254 717088 717920 718751 719580 720407 721233 722058 722881 723702 716337 717171 718003 718834 719663 720490 721316 722140 7229G3 723784 716421 717254 718086 718917 719745 720573 721398 722222 723045 723866 716504 717338 718169 719000 719828 720655 721481 722305 723127 723948 716588 71GG7J 717421 717504 718253718336 719083719165 719911J719994 720738720821 721563i721646 722387)722469 723209 723291 724030724112 716754 717587 718419 719248 720077 720903 721728 722552 723374 724194 83 83 83 83 83 83 82 82 82 82 550 531 532 533 534 535 53G 537 533 539 72427(5 725095 725912 726727 727541 828354 729165 729974 730782 731589 724358 725176 725993 726809 727623 728435 729246 730055 730863 731G69 7^4440 725258 726075 726890 727704 728516 729327 730136 730944 731750 72452* 725340 72615G 726972 727785 728597 729408 730217 731024 731830 724603 724685 725422725503 726238 726320 727053727134 727866727948 728678 728759 729489729570 730298730378 7311051731186 731911J731991 724767 725585 726401 727216 728029 728841 729651 730459 731266 732072 724849 725667 726483 727297 728110 728922 729732 730540 731347 732152 724931 725748 726564 727379 728191 729003 729813 730621 731428 732233 725013 72583(i 726646 727460 728273 729084 729893 730702 731508 732313 82 82 82 81 81 81 81 81 81 81 54J 541 542 543 544 545 546 5-17 548 549 732394 733197 733999 7348UO 735599 736396 737193 737987 738781 739572 732474732555 733278733358 734079734159 734880734960 735679735759 736476736556 737272737352 738067738146 738860,738939 739651J739730 732635 733438 734240 735040 735838 736635 737431 738225 739018 739810 732715 73351W 734320 735120 735918 736715 437511 738305 739097 739889 732796 733598 734400 735200 735998 73G795 737590 738384 739177 7399G8 732876 733679 734480 735279 736078 736874 737670 738463 739256 740047 73295G 733759 734560 735359 736157 736954 737749 738543 739335 740126 733037 733839 734640 735439 736237 737034 737829 738622 739414 740205 733117 733919 734720 735519 736317 737113 737908 G38701 739493 740284 80 80 80 80 80 80 79 79 79 79 5130 551 552 553 554 555 556 557 558 559 740363 741152 741939 742725 743510 744293 745075 G45855 746G34 747412 740442 741230 742018 742804 743588 744371 745153 745933 746712 747489 740521 741309 742096 742882 743667 774449 745231 746011 746790 747567 740599 741388 742175 742961 743745 744528 745309 746089 746868 747645 740678 741467 742254 743039 743823 744606 745387 746167 746945 747722 740767 741546 742332 743118 743902 744684 745465 746245 747023 747800 740836 741624 742411 74319G 743980 744740 745543 746323 747101 740915 741703 742489 743275 744058 744819 745621 746401 747179 740994 741782 742568 743353 744136 744917 745699 746479 747256 741073 741860 742G47 743431 744215 744997 745777 746556 747334 748110 79 79 79 78 78 78 78 78 78 78 747878 '7479 r >5|748033 5GU 5G1 5G2 563 5G4 565 566 507 568 5G9 748188 748963 74973G 750508 751279 752046 75281C 753583 754348 755112 , 748206 748343 749040,749118 749814749891 750586 7506G3 751356751433 752125752202 752893 75297C 753660 75373C 75442575450] 755189 75526E ,748421 749190 749968 75074C |75151C 752273 ,753047 75381S 754578 75534] i74849b 749272 750045 750817 751587 752350 ,753123 753889 754654 755417 74857G 748653 749350749427 750123750200 750894750971 751664751741 752433 752509 753200753277 753966 754042 754730754807 755494 75557C 748731 |749504 750277 751048 751818 752586 753353 754119 754883 755G46 748808 748885 749582749659 750354]750431 751125751202 751895751972 752663 752740 753430 753506 754195 754272 754960755036 755722 755799 77 77 77 77 77 77 77 77 76 76 570 571 572 573 574 575 576 577 578 579 755875 75595] 75G63G 75671', 757396 75747i 758155 75823( 758912 75898* 759668759741 760422 76049* 7G117G 76125] 76192876200; 762679 76275^ 750027,750103 756180 75G256 75G332|75G408 756484 756560 756788 756864)756940 75701675709217571681757244 757320 757548,757624 757700 757775 757851 757927)758003 758079 758306 758382 758458 758533 758609 758685 758761 758830 ( 759063 759139 759214 759290 759366 759441 759517 759592 1 759819 759894 759970 760045 760121 760196 760272 760347 i 7G0573 760649 760724 760799 760875 760950 761025 761101 761326 761402i761477 761552 761627 761702 761778 761853 } 762078 762153 762228 7G2303 762378 7G2453 762529 762604 [ 762829 762904 762978 763053J7G3128 763203 703278 763353 76 76 76 76 76 75 75 75 75 75 1 2 jxf 4 5 G 7 8 9 136 TABLE I. LOGARITHMS OF NUMBERS. No. 5 300 CM 100 Log. 76 jjoq 306180 No. 1 2 3 4 5 6 7 8 9 Diff. 58U 581 582 533 584 585 586 587 588 589 763428 764176 764923 765669 766413 767156 767898 768638 769377 770115 763oOa 764251 764998 765743 766487 767230 767972 768712 769451 770189 703578 764326 765072 765818 766562 767304 768046 768786 769525 770263 763653 764400 765147 765892 766636 767379 768120 768860 769599 770336 763727 764475 765221 765966 766710 767453 768194 768934 769673 770410 763802 764550 765296 766041 766785 767527 768268 769008 769746 770484 763877 764624 765370 766115 766859 767601 768342 769082 769820 770557 703952 76469t 765445 766190 766933 76767,' 768416 769156 769894 770631 7040^7 764774 765520 766264 767007 767749 768490 769230 769968 770705 7641U1 764848 765594 766338 767082 767823 768564 769303 77004-2 770778 75 75 75 74 74 74 74 74 74 74 59J 591 592 593 594 595 59G 597 598 599 770852 771587 772322 773055 773786 774517 775246 775974 776701 777427 770926 771661 772395 773128 773860 774590 775319 776047 776774 777499 770999 771734 772468 773201 773933 774663 775392 776120 776846 777572 771073 771808 772542 773274 774006 774736 775465 776193 776919 777644 771146 771881 772615 773348 774079 774809 775538 776265 776992 777717 771220 771955 772688 773421 774152 774882 775610 776338 777064 777789 771293 772028 772762 773494 774215 774955 775683 776411 777137 777862 771367 772102 772835 773567 774298 775028 775756 776483 777209 777934 771440 772175 772908 773640 774371 775100 775829 776556 777282 778006 171514 772248 772981 773713 774444 475173 775902 776629 777354 778079 74 73 73 73 73 73 73 73 73 73 GOO 601 602 603 60 i 605 606 607 608 609 778151 778874 779596 780317 781037 781755 782473 783189 783904 784617 7782*4 778947 779669 780389 781109 781827 782544 783260 783975 784689 778296 779019 779741 780461 781181 781899 782616 783332 784046 784760 778368 779091 779813 780533 781253 781971 782688 783403 784118 784831 778441 779163 779885 780605 781324 782042 782759 783475 784189 784902 778513 779236 779957 780677 781396 782114 782831 783546 784261 784974 778585 779308 780029 780749 781468 782166 782902 783618 784332 785045 778658 779380 780101 780821 781540 782258 782974 783689 784403 785116 778738 779452 780173 780893 781612 782329 783046 783761 784475 785187 7788U2 779524 780245 780965 781684 782401 783117 783832 784546 785259 72 72 72 72 72 72 72 71 71 71 610 611 612 613 614 615 616 617 618 619 785330 786041 786751 787460 788168 788875 789581 790285 790988 791691 785401 786112 786822 787531 788239 788946 789651 790356 791059 791761 785472 786183 786893 787602 788310 789016 789722 790426 791129 791831 785543 786254 786964 787673 788381 789087 789792 790496 791199 791901 785615 786325 787035 787744 788451 789157 789863 790567 791269 791971 785686 786396 787106 787815 788522 789228 789933 790637 791340 792041 785757 786467 787177 787885 788593 789299 790004 790707 791410 792111 785828 786538 787248 787956 788663 789369 790074 790778 791480 792181 785899 786609 787319 788027 788734 789440 790144 790848 791557 792252 785970 786680 787390 788008 788804 789510 790215 790918 791620 792322 71 71 71 71 71 71 70 70 70 70 620 621 622 623 624 625 626 627 628 629 792392 793092 793790 794488 795185 795880 796574 797268 797960 798651 792462 793162 793860 794558 795254 795949 796644 797337 798029 798720 792532 793231 793930 794627 795324 796019 796713 797406 798098 798789 792602 793301 794000 794697 795393 796088 796782 797475 798167 798858 792672 793371 774070 794767 795463 796158 796852 797545 798236 798927 792742 793441 794139 794836 795532 796227 796921 797614 798305 798996 792812 793511 794209 794906 795602 796297 796990 797683 798374 799065 792882 793581 794279 774976 795671 796636 797060 797752 798443 799134 792952 793651 794349 795045 795741 796436 797129 797821 798512 799203 793022 793721 794418 795115 795811 796505 797198 797890 798582 799272 70 70 70 70 69 69 69 69 69 69 630 631 632 633 634 635 636 637 638 639 7993411799409 800029800098 800717 800786 801404801472 802089802158 802774802842 803457803525 804139 804208 804821 804889 805501 805569 799478 8001G7 800854 801541 802226 802910 803594 804276 804957 805637 799547 800236 800923 801609 802295 802979 803662 804344 805025 805705 799616 800305 800992 801678 802363 803047 803730 804412 805093 805773 799685, 800373 801060 801747 802432 803116 803798 804480 805161 805841 799754 800442 801129 801815 802500 803184 803867 804548 805229 805908 799823 800511 801198 801884 802568 803252 803935 804616 805297 805976 799892 800580 801266 801952 S02637 803321 804003 S04685 305365 B06044 799961 800648 801335 802021 802705 S03389 304071 304753 805433 300112 69 69 69 69 68 68 68 68 68 68 1 2 3 4 5 6 7 8 9 TABLE I. 137 LOGARITHMS OP NUMBERS. No. 6 /inn i 000 Log. 80 ^1 40 ! 345098 No. 1 2 3 4 5 6 7 8 9 Diff. 640 641 642 643 644 645 646 647 648 649 800180 806858 807535 808211 808886 809560 810233 810904 811575 812245 806248 806310 806926'806994 807603807670 808279808346 808953809021 809627 809694 810300810367 310971811038 811642811709 812312812378 806384 807061 807738 808414 809088 809762 810434 811106 811776 812445 806451 807129 807806 808481 809156 809829 810501 811173 811843 812512 806519 806587 807197 807264 807873807941 808549808616 809223809290 8G9896 8099G4 810569810636 811240811307 811910811977 812579812646 80ob'55 807332 808008 808684 809358 810031 810703 811374 312044 812713 306723 807400 808076 808751 809425 310098 810770 811441 312111 812780 806790 07467 308143 803818 809492 810165 810837 811508 812178 812847 08 68 68 68 67 67 67 67 67 67 650 651 652 653 654 655 656 657 658 659 81*913 813581 814248 814913 815578 816241 316904 817565 818226 818885 812980 813648 814314 8149SO 815644 816308 816970 317631 818292 818951 813047 813714 814381 815046 815711 816374 817036 817698 818358 819017 813114 813781 814447 815113 815777 816440 817102 817764 818424 819083 813181 813848 814514 815179 815843 316506 817169 817830 818490 819149 81324V 813914 814581 815246 815910 816573 817235 81789G 818556 819215 1813314 813981 814647 815312 815976 816639 817301 817962 81S622 819281 813381 814048 814714 815378 81C042 816705 817367 818028 818688 819346 8134481815614 814114814181 814780814847 815445815511 816109816175 816771816838 817433817499 818094 818160 818754818819 819412819478 67 67 <^67 66 66 66 66 66 66 66 (500 661 662 663 664 665 666 6G7 668 669 819J44 820201 820858 821514 822168 S22822 823474 824126 824776 825426 819610 820267 820924 821579 822233 822887 823539 824191 824841 825491 819675 820333 820989 321644 822299 322952 823605 324256 824906 82555G 819741 820399 821055 821710 822364 823018 823670 824321 824971 825621 819807 820464 821120 821775 822430 823083 823735 824386 825036 825686 819873 820530 821186 821841 822495 823148 823800 824451 825101 825751 819939 820595 821251 821906 822560 823213 823865 824516 825166 825815 820004 820070 820661 820727 821317821382 821972 822037 822626822691 823279823344 823930823996 824581 824646 825231 825296 825880825945 82013* 820792 821448 822103 822756 823409 8240G1 824711 825361 826010 66 66 66 65 65 65 65 65 65 65 670 671 672 673 674 675 676 677 678 679 820076 826723 327369 S28015 S28GGO 829304 829947 830589 831230 831870 826140 826787 827434 828080 828724 829368 830011 830653 831294 831934 826204 326852 827498 828144 828789 829432 830075 830717 831358 831998 826269 826917 827563 828209 828853 829497 830139 830781 831422 832062 826334 826981 827628 828273 828918 829561 830204 830845 831486 832126 826399 827046 827692 828338 828982 829625 830268 830909 831550 832189 826464 827111 827757 828402 829046 829690 830332 830973 831614 832253 826528 827175 827821 828467 829111 829754 830396 831037 831678 832317 826593 827240 827886 828531 829175 829818 830460 831102 831742 832381 826658 827305 827951 828595 829239 829882 830525 831166 831806 832445 65 65 65 64 64 64 64 64 64 64 6bO 681 682 683 684 685 686 687 688 689 832509 833147 833784 834421 835056 835691 836324 836957 837588 838219 832573 833211 833848 834484 835120 835754 836387 837020 837652 838282 832637 833275 833912 834548 835183 835817 836451 837083 837715 838345 832700 833338 833975 834611 835247 835881 836514 837146 837778 838408 832764 833402 834039 834675 835310 835944 836577 837210 837841 838471 832828 833466 834103 834739 835373 836007 836641 837273 837904 838534 832892 833530 834166 834802 835437 836071 836704 837336 837967 838597 832956 833593 83423C 834866 835500 836134 836767 837399 838030 838660 833020 833657 834293 834929 835564 836197 836830 837462 838093 838723 833083 833721 834357 834993 835627 836261 836894 837525 838156 838786 64 64 64 64 63 63 63 63 63 63 690 691 692 693 694 695 696 697 698 699 838849 838912 838975 839478839541839604 84010G 840169 840232 840733840796840859 841359 841422 841485 841985842047842110 842609842672842734 343233843295843357 843855843918843980 844477)844539844601 839038839101 339667 839729 840294 ! 840357 840921 840984 841547841610 842172842235 842796842859 843420843482 844042844104 844664844726 839164 839792 840420 841046 841672 842297 842921 843544 844166 844788 839227 839855 840482 841109 841735 842360 842983 843606 844229 844850 839289 839918 840545 841172 841797 842422 843046 843669 344291 844912 839352 839981 840608 841234 841860 342484 343108 343731 344353 343974 839415 840043 840671 841297 841922 842547 843170 343793 344415 345031', 63 63 63 63 63 62 62 62 62 62 1 2 3 4 5 G 7 8 9 138 TABLE I. LOGARITHMS OF NUMBERS. No. 7 000 7 000 Log. 84 ^OQS ! 480814 No. 1 2 3 4 5 6 7 8 9 Diff. 100 701 702 703 704 705 708 707 708 709 34509s 845718 84G337 846955 847573 848189 848805 849419 850033 850646 845100 84522* 845780 845842 846399846461 847017 84707 847634847696 848251848312 848866848928 849481 849542 850095850156 850707850769 845284 845904 84652J 847141 847758 848374 848983 849604 850217 850830 845346 845966 846584 847202 847819 848435 849051 849665 850279 850891 84540* 846028 846646 847264 847881 848497 849112 849726 850340 850952 845471 84609C 846708 84732C 84794c 848551 849174 849788 850401 851014 I84553i 84615J 846771 84738J 848004 85862C 84923S 84984 850462 85107S i 84559^, 846211 346835 847441 84806( 84868'. 84929C 849911 850524 851136 1 84565( (84627; '84689^ 847511 84812* 84874; 849358 849972 85058E 851191 62 62 62 62 62 02 61 61 61 61 7iO 711 712 713 714 715 71G 717 718 710 851258 851870 352480 353090 853698 854306 354913 355519 356124 856729 851320 851931 852541 853150 853759 854367 854974 855580 856185 856789 851381 851992 852602 853211 853820 854427 855034 855640 856245 856850 851442851503 852053852114 852663 852724 853272 853333 853881 853941 854488854549 855095855156 55701 855761 856306856366 856910856970 851564 852175 852785 853394 854002 854610 855216 855822 856427 857031 851625 852236 852846 853455 854063 854670 855277 855882 856487 857091 851686 852297 852907 853516 854124 854731 855337 855943 856548 857151 851747 852358 852968 853576 854185 854792 855398 856003 856608 857212 851808 852419 853029 853637 854245 854852 855459 856064 856668 857272 81 61 61 61 61 61 61 61 60 60 720 721 722 723 724 725 72G 727 728 729 857332 857935 858537 359138 359739 360338 860937 861534 862131 8G2728 857393 857995 858597 859198 859799 860398 860996 861594 862191 862787 857453 858056 858657 859258 859858 860458 861056 861654 862251 862847 857513 858116 358718 859318 859918 860518 861116 861714 862310 862906 857574 858176 858778 859378 859978 860578 861176 861773 862370 862966 857634 858236 858838 859438 360038 860637 861236 861833 862430 863025 857G94 858297 858898 859499 860098 860697 861295 861893 862489 863085 857754 858357 858958 859559 860158 860757 861355 761952 862549 863144 857815 958417 859018 859619 860218 860817 861415 862012 862608 873204 857875 858477 859078 859679 860278 860877 861475 862072 862668 863263 60 60 60 60 60 60 60 60 60 60 730 731 732 733 734 735 736 737 738 739 863323 863917 S64511 865104 865G96 866287 866878, 867467J 868056 868644 S63382 863977 864570 865163 865755 866346 866937 867526 868U5 868703 863442 864036 864630 865222 865814 866405 866996 867585 868174 868762 863501 863561 863620 3G4096 864155 864214 864689864748864808 865282865341865400 865874865933865992 866465866524866583 867055867114867173 867644867703867762 868233868292868350 868821868879868938 863680 864274 864867 865459 866051 866642 867232 867821 868409 868997 863739 864333 864926 865518 866110 866701 867291 867880 868468 869056 863798 864392 864985 865578 866169 866760 867350 867939 868527 869114 863858 864452 865045 865637 866228 866819 867409 867998 868586 869173 59 59 59 59 59 59 59 59 59 59 740 741 742 743 744 745 746 747 748 749 869232 869818 870404 870989 871573 872156 872739, 873321 1 873902 874482 869290 369877 370462 371047 371631 372215 372797 373379 373960 374540 869349 869935 870521 871106 871690 872273 872855 873437 874018 874598 869408 869994 370579 871164 871748 872331 872913 873495 874076 874656 869466 869525 870053870111 870638870696 871223871281 871806:871865 872389872448 872972873030 873553873611 874134874192 874714874772 869584 870170 870755 871339 871923 872506 373088 373669 374250 374830 869642 870228 870813 871398 871981 872564 373146 373727 374308 374887 869701 870287 870872 871456 872040 872622 873204 873785 874366 S74945 8697(50 870345 870930 871515 872098 872681 873262 873844 374424 375003 59 59 58 . 58 58 58 58 58 58 58 1M 751 752 753 754 755 75G 757 758 759 875061875119,875177 875640875698875756 376218-876276876333 376795876853876910 377371877429877486 377947878004878062 B78522 878579 878G37 379096879153879211 379669879726879784 380242880299880356 875235 875293875351 875409 875813875871 875929875987 876391 ! 876449 876507 876564 376968 877026 877083 877141 ! 377544 877602 877659 877717 f B78 1 19 878 177 878234 878292 J 378694 ! 878751 878809 878866 ! 379268:879325 879383 879440 ! 379841 879898 879956 880013 ! 380413,880471 880528 880585 ! 375466 376045 376622 377198 377774 3783491 378924! 379497 1 380070! 380642! 375524 376102 376680 377256! 377832! 378407! 378981 ! 379555! 380127! 380699! 375582 376160 376737 377314 377889 378464 379038 379612 380185 380756 58 58 58 58 58 57 57 57 57 57 1 2 3 4 5 G 7 8 9 TABLE I. 139 LOGARITHMS OF NUMBERS. No. 7 (!() II ft 200 Log. 88 )81 1 313814 No. 1 2 3 4 5 6 7 8 9 Diff. 760 761 762 763 764 765 766 767 7G8 7G9 880814 881385 881955 882524 883093 883661 884229 884795 885361 885926 88U871 881442 882012 882581 883150 883718 884285 884852 885418 885983 8809^8 881499 882069 882638 883207 883775 884342 884909 885474 886039 88u985 881556 882126 882695 883264 883832 884399 884965 885531 886096 881042 881613 882183 88275- 883321 883888 884455 885022 885587 886152 881099881156 881670881727 882240882997 882809 88286G 883377883434 883945884002 884512884560 885078885135 885644^85700 886209886265 881213 881784 882354 882923 88349 J 884059 884625 885192 885757 886321 881271, 881841 882411 882980 883548 884115 884682 885248 885811 886378 881328 881898 882468 883037 883605 894172 884739 885305 885870 886431 57 57 57 57 57 57 57 57 57 56 770 771 772 773 774 775 776 777 778 779 886491 88705-J 887617 888178 888741 389302 8S9862 S90421 890980 $91537 886547 887111 887674 888236 888797 889358 889918 890477 891035 39169S 886604 887167 887730 888292 888853 889414 889974 890533 891091 891649 886MU 887223 887786 888348 688909 889470 890030 890589 891147 891705 886716 887280 88784-2 888404 888965 889526 890086 890644 891203 891760 886773 887336 887898 888460 889021 889582 890141 890700 891259 891816 8808*9 887392 887955 888516 889077 889638 890197 890756 891314 891872 886885 887440 888011 888573 889134 889694 890253 890812 891370 891928 886942 887505 888067 888629 889190 889750 890309 890868 891426 891983 880998 887561 888123 888685 889246 889806 890365 890924 891482 892039 56 56 56 56 56 56 56 56 56 56 780 781 782 783 784 785 786 787 7b8 789 3K2U9,, 392651 593207 893762 394316 J94870 394423 895975 S9652G 397077 S9215U 892707 893262 893817 394371 ^94925 895478 896030 896581 897132 j9220ti 392762 893318 893873 394427 894980 395533 396085 396636 897187 892262 892818 893373 893928 874482 895036 895588 896140 896692 897242 892317 892873 893429 893984 394538 895091 895643 896195 896747 897297 892373 892929 893484 894039 894593 895146 895699 896251 896802 897352 S92429 892985 693540 894094 894648 895201 895754 896306 896857 897407 892484 893040 893595 894150 894704 895257 895809 896361 896912 897462 892540 893096 893651 894250 894759 895312 895864 896416 896967 897517 o92595 393151 893706 894261 894814 895367 895920 896471 897022 897572 56 56 56 55 55 55 55 55 55 55 Tad 791 792 793 794 795 793 797 798 799 S97627 898176 598725 399273 899820 900367 900913 901458 902003 902547 397682 898231 898780 899328 899875 900422 900968 901513 902057 902601 897757 898286 898835 899383 899930 900476 901022 901567 902112 902655 897792 898341 898890 899437 899985 900531 901077 901622 902166 902710 897847 898396 898944 S99492 900039 900586 901131 901676 902221 902764 897902 898451 898999 899547 900094 900640 901186 901731 902275 902818 897957 898506 899054 899602 900149 900695 901240 901785 902329 902873 898012 898561 899109 899o56 900203 900749 901295 901840 902384 902927 8980G7 898615 899164 899711 900258 900804 901349 901894 902438 902981 S98122 898670 899218 899766 900312 900858 901404 901948 902491 903036 55 55 55 55 55 55 55 54 54 54 8UO 801 802 803 804 805 806 807 808 809 J03090 903632 904174 904715 905256 905796 90G335 906873 907411 907948 903144 903687 904228 904770 905310 905850 906389 906927 907465 908002 903198 903741 904283 904824 905364 905904 906443 906981 907519 908056 J05253 903795 904337 904878 905418 905958 906497 907035 907573 908109 903307 903849 904391 904932 905472 906012 906550 907089 907626 908163 903361 903903 904445 904986 905526 90C065 906604 907142 907680 908217 903416 903958 904499 905040 905580 906119 906658 907196 907734 908270 903470 904012 904553 905094 905634 906173 906712 907250 907787 908324 903524 904066 904607 905148 905688 906227 906766 907304 907841 908378 903o78 904120 904661 905202 905742 906281 906820 907358 907895 908431 54 54 54 54 54 54 54 54 54 54 810 811 812 813 814 815 816 817 818 819 908485 909021 909556 910090 910624 911158 911690 912222 912753 913284 908539 909074 909609 910144 910678 911211 911743 912275 912806 913337 908592 909128 909663 910197 910731 911264 911797 912328 912859 913390 908646 909181 909716 910251 910784 911317 911850 912381 912913 913143 908699 909235 909770 910304 910838 911371 911903 912435 912966 913496 908753 909288 909823 910358 910891 911424 911956 912488 913019 913549 908807 909342 909877 910411 910944 911477 912009 912541 913072 913G02 9(.,'S60 909395 909930 910464 910998 91153( 91206S 912494 913125 913655 908914 909449 909984 910518 911051 911584 912116 912647 913178 913708 908967 909502 910037 910571 911104 911637 912169 912700 913231 913761 54 54 53 53 53 53 53 53 53 53 1 2 3 4 5 G 7 8 9 140 TABLE I. LOGARITHMS OF NUMBERS. No. 8200 8800 Log. 91 ^81 \ ' )44483 No. 1 2 3 4 5 6 7 8 9 Diff. 820 821 822 823 824 825 826 827 828 829 913814 914343 914872 915400 915927 916454 916980 917505 918030 918555 913SG7 91 4396 914925 915453 915980 916507 917033 917558 918083 918607 91392U 914449 914977 915505 916033 916559 917085 917610 918135 918659 913973 914502 915030 915558 916085 916612 917138 917663 918188 918712 914U2G 914079 914555914608 915083915136 915611915664 916138916191 916664916717 917190917243 917715917768 918240918292 918764918816 914131914184 914660914713 915189915241 915716915769 916243916296 916770916822 917295917348 917820917873 918345918397 918869918921 914237 914766 915294 915822 91634P 916875 917400 917925 918450 918973 914^90 914819 915347 9 J 5874 916401 916927 917453 917978 918502 919026 53 53 53 53 53 53 53 52 52 52 830 831 832 833 834 835 830 837 838 839 91907t> 919601 920123 920645 921166 921686 922206 922725 923244 9237654 919130 919653 920175 920697 921218 921738 922258 922777 923296 923814 919183 919705 920228 920749 921270 921790 922310 922829 923348 923865 919235 919758 920280 920801 921322 921842 922362 922881 923399 923917 919287 919810 920332 920853 921374 921894 922414 922933 923451 923969 91934UI919392 919444 91949t> 919862 919914 919967 920019 920384 920436 920489 920541 920906 920958 921010 921062 921426 921478 921530 921582 921946 921998 922050 922102 922466 922518 922570 922622 922985 923037 923088 923140 923503 923555 923607 923658 924021|924072 924124 924176 919549 920071 920593 921114 921634 922154 922674 923192 923710 924228 52 52 52 52 52 52 52 52 52 52 840 841 842 843 844 845 846 847 848 849 924279 924796 925312 925828 926342 926857 927370 927883 928396 928908 924331 924848 925364 925879 926394 926908 927422 927935 928447 928959 924383 924899 925415 925931 926445 926959 92747S 927986 928498 929010 924434 924951 925467 925982 926497 927011 927524 928037 928549 929061 924486 925002 925518 926034 926548 927062 927576 928088 928601 929112 924538 925054 925570 926085 926600 927114 927627 928140 928652 929163 924589 924041 1924093 925106 925157,925209 925621925673925724 926137926188926239 926651926702926754 927165 927216 927268 927678927730927781 928191928242928293 928703 928754 928805 929214J929266 929317 924744 925260 925776 926291 926805 927319 927832 928345 928856 929368 52 52 52 51 51 51 51 51 51 51 850 851 852 853 854 855 856 857 858 859 929419 929930 930440 930949 931458 931966 932474 932981 933487 933993 929470 929981 930491 931000 931509 932017 932524 933031 933538 934044 929521 930032 930541 931051 93156G 932068 932575 933082 933588 934094 929572 930083 930592 931102 931610 932118 932626 933133 933639 934145 929023 930134 930643 931153 931661 932169 932677 933183 933690 934195 929674 930185 930694 931203 931712 932220 932727 933234 933740 934246 929725 930236 930745 931254 931763 932271 932778 933285 933791 934296 929770 930287 930796 931305 931814 932321 932829 933335 933841 934347 929827 930338 930847 931356 931864 932372 932879 933386 933892 934397 929878 930389 930898 931407 931915 932423 932930 933437 933943 934448 51 51 51 51 51 51 51 51 51 51 860 861 862 863 864 865 866 867 868 8G9 934496 935003 935507 936011 936514 937016 937518 938019 938520 939020 934549 935054 935558 936061 936564 937066 937568 938069 938570 939070 9345U9 935104 935608 936111 936614 937116 937618 938119 938620 939120 934050 935154 935658 936162 936664 937167 937668 938169 938670 939170 934700 935205 935709 9L6212 936715 937217 937718 938219 938720 939220 934751 935255 935759 936262 936765 937267 937769 938269 938770 939270 934801 935306 935809 936313 936815 937317 937819 938319 938820 939319 934852 935356 935860 936363 936865 937367 937869 938370 938870 939369 934902 935406 935910 936413 936916 937418 937919 938420 938920 939419 U34953 935457 935960 936463 936966 937468 937969 938470 938970 939469 50 50 50 50 50 50 50 50 50 50 870 871 872 873 874 875 876 877 878 879 939519 940018 940516 941014 941511 942008 942504 943000 943494 943989 939509 940068 940566 941064 941561 942058 942554 943049 943544 944038 939019 940118 940616 941114 941611 942107 942603 943099 943593 944088 939669 940168 940666 941163 941660 942157 942653 943148 943643 944137 939719 940218 940716 941213 941710 942206 942702 943198 943692 944186 939769 940267 940765 941263 941760 942256 942752 943247 943742 944236 939819 940317 940815 941313 941809 942306 942801 943297 943791 944285 939808 940367 940865 941362 941859 942355 942851 943346 943841 944335 93991893996s 940417940467 940915940964 941412941462 941909941958 942405942454 942900942950 943396943445 943890943939 944384944433 50 50 50 50 50 50 50 49 49 49 1 2 3 4 5 6 7 8 9 TABLE I. LOGARITHMS OP NUMBERS. 141 No. 8 ROO ') 100 Log. 944483 973128 No. 1 2 3 4 5 6 7 8 9 Diff. 880 881 882 883 884 885 886 887 888 889 944483 944976 945469 945961 946452 946943 947434 947924 948413 948902 .J4463* 345025 945518 946010 946501 946992 947483 947973 948462 948951 944681 945074 945567 946059 946550 947041 947532 948021 948511 948999 944631 945124 945616 946108 946600 947090 947581 948070 948560 949048 94468u 945173 945665 946157 946649 947139 947630 948119 948608 949097 9447*9 945222 945715 946207 946698 947189 947679 948168 948657 949146 944771; 945272 J45764 946256 946747 947238 947728 948217 948706 949195 944828 945321 945813 946305 946796 947287 947777 948266 948755 949244 ; 944s77 1945370 .945862 946354 946845 947336 947826 948315 948804 949292 944927 94541C 945911 946403 946894 947385 947875 948364 948853 949341 49 49 49 49 49 49 49 49 49 49 890 891 892 893 894 895 896 897 898 899 94939U 949878 950365 950851 951337 951823 952308 952792 953276 953760 949459 949926 950413 950900 951386 951872 952356 952841 953325 953808 94948ft J49975 950462 950949 951435 951920 952405 952889 953373 953856 949536 950024 950511 950997 951483 951969 952453 952938 953421 953905 949585 950073 950560 951046 951532 952017 952502 952986 953470 953953 949634 950121 950608 951095 951580 i 952066 952550 953034 953518 954001 954484 954966 955447 955928 956409 956888 957368 949683 950170 950657 951143 951629 952114 952599 953083 953566 954049 949731 950219 950705 951192 951677 952163 952647 953131 953615 954098 949780 950267 950754 951240 951726 952211 952696 953180 953663 954146 9498*9 950316 950803 951289 951774 952259 952744 953228 953711 954194 49 49 49 49 49 48 48 , 48 48 48 900 901 902 903 904 905 906 907 908 909 96424* 954291 954725954773 955206955255 953688 955736 956168956216 956649 956697 957128957176 9o4339 954387 954821 954869 955303 955351 955784 955832 956264 956312 956745 956792 957224957272 954435 954918 955399 955880 956361 956840 957320 964532 955014 955495 955976 956457 956936 957416 954580 955062 955543 956024 956505 956984 957464 957942 958420 958898 9546*8 y 5467 7 955110955158 955592955640 956072 956120 956553956601 957032957C80 957511957559 957990 958038 958468 958516 958946958994 48 48 48 48 48 48 48 48 48 48 957607 957655 958086958134 958564J958612 957703 958181 958659 95/751 958229 958707 957799 957847 958277 958325 958755 958803 957894 958373 958850 910 911 912 913 914 915 9)6 917 918 919 959041 959089 959137 959516 959566 959614 959995960042960090 960471 960518 960566 960946960994 961041 961421 961469 961516 961895.961943961990 962369,962417 962464 962843 962890 962937 963315963363963410 959184 959661 960138 960613 961089 961563 962038 962511 962985 963457 969232 959709 960185 960661 961136 961611 962085 962559 963032 963504 959*80;95y32b 959757 959804 960233960281 960709960756 961184961231 961658961706 962132962180 962606962653 963079963126 9635521963599 95'y375j95945*3 959852959900 960328;960376 960804,960851 961279961326 961753961801 962227 1962275 962701962748 963174963221 963646963693 J59471 959947 960423 960899 961374 961848 962322 962795 963268 963741 48 48 48 48 48 47 47 47 47 47 920 921 922 923 924 925 926 927 928 929 963788963835 964260964307 964731 964776 965202 965249 965672965719 966142966189 966611 966658 967080967127 967548967595 968016968062 96388* 964354 964825 965296 965766 966236 966705 967173 967642 968109 963929 964401 964872 965343 965813 966283 966752 967220 967688 968156 963977 964448 964919 965390 965860 966329 966798 967267 967735 968203 964024 964495 964966 965437 965907 966376 966845 967314 967782 968249 964071 964542 965013 965484 965954 966423 966892 967361 967829 968296 964118 964590 965060 965531 966001 966470 966939 967408 967875 968343 964165964*1* 964637 964684 965108965155 965578965625 966048966095 966517 966564 966986967033 967454967501 967922967969 968389968436 47 47 47 47 47 47 47 47 47 47 930 931 932 933 934 935 936 937 938 939 968483 968530 968576 968623 968950 968996 969043 969090 969416 969462 969509 969556 969882 969928 969975 970021 970347 970393 970440 970486 970812 970858 970904 970951 971276 971322 971369 971415 971740 971786 971832 971879 972203 972249 972295*972342 972666 972712 972758 972804 968670 969136 969602 970068 970533 970997 971461 971925 972388 972851 968716i96870b 969183969229 969649969695 970114970161 970579970626 971044971090 971508971554 971971972018 972434972480 972897972943 908810 969276 969742 970207 970672 971137 971600 972064 972527 972989 968856 968903 969323969369 969788969835 970254 970300 970719970765 971183971229 971647971693 972110972156 972573972619 973035973082 47 47 47 47 47 46 46 46 46 46 1 2 4 5 7 | b y 142 TABLE I. LOGARITHMS OF NUMBERS. No. 9 100 14 3000 Lop. 973128 000000 No. 1 2 3 4 5 6 7 8 9 Diff. 940 941 942 943 944 945 946 947 948 949 973128 973590 974051 974512 97497-2 975432 975891 976350 97680S 977-266 973174^73220 973636:973682 974097 974143 974558 974604 975018975064 975478 075524 975937 975983 976396 976442 976854 976900 977312977358 973266 973728 974189 974650 975110 975570 97C029 976487 976946 977403 973313 973774 974235 974696 975156 975616 976075 976533 976991 977449 973359 973820 974281 974742 975202 975661 976121 976579 977037 977495 973405,9734511973497 973866973913973959 974327:974373974420 974788974834974880 975248 975294 975340 975707 975753 975799 976166976212976258 976625976671976717 977083 977129 977175 977541977586977632 973543 974005 974466 974926 975386 975845 976304 976762 97722C 977678 40 46 46 46 46 46 46 46 46 46 950 951 952 953 954 955 956 957 958 959 97/724 978180 978637 979093 97954* 980003 9S0458 930912 931365 931819 07//69 978226 978683 979138 979594 980049 980503 980957 981411 981864 97/815 978272 978728 979184 979639 980094 980549 981003 98145G 981909 977861 978317 978774 979230 979685 980140 980594 981048 981501 981954 977906 978363 978819 979275 979730 980185 980640 981093 981547 982000 97795^ 978409 978865 979321 979776 980231 980685 981139 981592 982045 977998,978043 978454 978500 978911978956 979366979412 979821979867 980276980322 980730980776 981184981229 081637981683 982090,982135 978089 978546 979002 979457 979912 980367 980821 981275 981728 982181 078135 978591 979047 979503 979958 980412 980867 981320 981773 982226 46 46 46 46 46 45 45 45 45 45 960 961 962 963 964 935 966 967 968 969 9822Y1 982723 933175 983626 984077 984527 984977 985426 985875 986324 982310 982769 983220 983671 984122 9S4572 985022 985471 985920 936369 982362 982814 983265 983716 984167 984617 985067 985516 985965 986413 982407 982859 983310 983762 984212 984662 985112 985561 986010 986458 98*152 982904 983356 983807 984257 984707 985157 985606 986055 986503 982497 982949 983401 983852 984302 984752 985202 985651 986100 986548 982543 082588 982994 983040 983446 983491 983897 983942 984347 984392 984797 984842 985247 985292 985696 985741 986144 986189 986593986637 98-2633 983085 983536 983987 984437 984887 985337 985786 986234 986682 982678 983130 983581 984032 984482 984932 985382 985830 986279 986727 46 45 45 45 45 45 45 45 45 45 970 971 972 973 974 975 97(5 - 977 978 979 9807 Y 2 98721C 98766C 988113 988559 989005 989450 989895 990339 990783 9(30810 987264 987711 988157 93S603 989049 989494 989939 990383 990827 986861 ^86906 987309987353 987756987800 988202 988247 988648988693 989094989138 989539 989583 989983 99002& 990428 990472 990871 990916 986951 987398 987845 988291 988737 989183 989628 990072 990516 990960 986995 987443 987890 988336 988782 989227 989672 990117 990561 991004 987040 987487 987934 988381 988826 989272 989717 990161 990605 991049 987085 987532 987979 988425 988871 989316 989761 990206 990650 991093 987130 987577 988024 988470 988915 989361 989806 990250 990694 991137 987174 987622 988068 988514 988960 989405 989850 990294 990738 991182 45 45 45 45 45 45 44 44 44 44 980 981 982 983 984 985 986 987 988 989 90122U 991669 992111 992553 992995 993436 993877 994317 994757 995196 991270 991713 992156 992598 993039 993480 993921 994361 994801 995240 991315991359 991757 991802 992200992244 992642 992686 993083993127 993524993568 993965994009 994405994449 994845 994889 995284 99532S 991403 991846 992288 992730 993172 993613 994053 994493 994933 985372 991448 991890 9,2333 992774 993216 993657 994097 994537 994977 995416 991492 991536 991934 991979 992377 992421 992818992863 993260993304 993701 993745 994141 994185 994581 994625 995021 995064 995460995504 991580 992023 992465 992907 993348 993789 994229 994669 995108 995547 991625 992067 992509 992951 993392 993833 994273 994713 995152 995591 44 44 44 44 44 44 44 44 44 44 990 991 992 993 994 995 996 997 998 99D J'J5(53o 996074 996512 996949 997386 997823 998259 998695 999130 999565 995079 996117 996555 99G993 997430 997867 998303 998739 999174 999609 995723995767 996161 996205 996599996643 997037 997080 997474 997517 997910 997954 998346 99839C 998782 998826 999218 999261 999652999696 995811 996249 996687 997124 997561 997998 99843 1 998869 999305 999739 995854 996293 996730 997168 997605 998041 998477 998913 999348 999783 995898 995942 995986 996336996380996424 996774996818996862 997212997255997299 997648997692997736 998085998128998172 998521998564998608 998956999000999043 999392999435999478 999826999870999913 996030 996468 996905 997343 997779 998216 998652 999087 999522 999957 44 44 44 44 44 44 44 44 44 43 1 2 3 4 5 6 7 8 9 TABLE II. 143 LOGARITHMIC SINES, TANGENTS, AND SECANTS. Decree. if. Sine. Co-sine. (Tangent. Co-tang. Secant. Co-sec. M. u u.oououo 10.000000 O.UUUOOO lutiuue. 10.0UOUOO lull Bite. GO l 6.463726 10.000000 6.463726 13.531274 10.00.000 13.53(>274 59 2 6.764756 10.000000 6.764756 13 2J5244 10.000000 13 235244 58 3 6 94')847 10.000000 6.940847 13.059153 10. 00 '000 13.059153 57 4 7.065786 10.000000 7.065786 12.934214 10.000000 12 934214 56 5 7.162696 10.000000 7.162696 12.837304 10. 000! 100 12.837304 55 6 7.241877 9.999999 7.241878 12.758122 10.000001 12.758123 54 7 7.308824 9 999999 7.30S825 12.091175 10.000001 12.691176 53 8 7.366816 9.999999 7.366817 12.633183 10.00)U01 12 633184 52 9 7.417968 9.999999 7.417970 12.582030 10.000001 12 58-032 51 10 7 463726 9.993938 7.463727 12 536273 10 (100002 12.536274 50 11 7.5U5118 9.V9999tf 7.5uolzU 12.494(580 1U.OUUUU2 1-^.494862 49 12 7 542906 9.909997 7 54-1909 12 457091 10 000003 12.457094 48 13 7.5776(58 9 999097 7.577(572 12 422328 10.000003 12 422332 47 14 7.609853 9.999996 7 609857 12.390143 10.000004 12 390147 46 15 7.639816 9.999996 7.639820 12 360180 10.000004 12.330184 45 16 7 667845 9.999995 7.667849 12.332151 10 000005 12.332155 44 17 7.694173 9.999995 7.694179 12.305821 10.000005 1-2.305827 43 18 7.718997 9.99:)!'94 7.719003 12.280997 10.000006 12.281003 42 19 7.742478 9.999993 7 742484 12 257516 10.000007 12.257522 41 20 7.764754 9.999993 7.764761 12.235239 10.000007 12.235246 40 VJl V.78o'J43 y.yyyyy-2 7 7So951 12.214U49 10.000008 12.214057 39 22 7.806146 9.999991 7.803155 12.193815 10.000009 12.1938 r )4 8 23 7.825451 9.999990 7.825460 12.174540 10.000010 12.174549 37 24 7 843934 9.999989 7.843944 12.156056 10.000011 12.156066 36 25 7.861662 9.999989 7.861674 12.138326 10.00C011 12.138338 35 26 7,878695 9.999988 7.878708 12.121292 10.000012 12.121305 34 27 7.895085 9.999987 7.895099 12.104901 10.000013 12.104915 33 28 7.910879 9.999986 7.910894 12.089106 10.000014 12.089121 32 29 7.926119 9.999985 7.926134 12.073866 10.000015 12.073881 31 30 7.910842 9.999983 7 910858 12.059142 10.000017 12.059158 30 31 7. 955032 y.9y9982 Y.'Joo 100 12 044'JUO 10.000018 12.044918 29 32 7.968870 9.999981 7.968889 12.031111 10.000019 12.031130 28 33 7.982233 9.999980 7 082253 12.017747 10.000020 12.017767 27 3i 7.995198 9. 999979 7.995219 12.004781 10.000021 12.004802 2(5 35 8 007787 3.999977 8.007809 11.992191 40.000023 11.992213 25 36 8.020021 9.999976 8.020045 11.979955 10.000024 11.979979 24 37 8.031919 y 999975 8.031945 11.968055 10.000025 11.968081 23 33 8 043501 9.999973 8.043527 11.956473 10.000027 11.956499 22 39 8.054781 9.999972 8.054809 11.945191 10.000028 11.945219 21 40 8.065776 9.999971 8.065806 11.934191 10.000029 11.934224 20 | 41 8. 076500 9. 999969 8 076531 11.923469 10.000031 11.923500 19 42 8.086965 9.999968 8.086997 11.913003 10.000032 11.913035 18 43 8.097183 9.999966 8.097217 11.902783 10.000034 11 902817 17 44 8.107167 9.999964 8.107202 11.892798 10.000036 11.892833 1C 45 8.11C926 9.999963 8.116963 11.883037 10.000037 11.883074 15 46 8.126471 9.999961 8.126510 11.873490 10.000039 11.873529 14 47 8.135810 9 999959 8.135851 11.864149 10.000041 11.864190 13 48 8.144953 9.999958 8.144996 11.855004 10.000042 11.855047 12 49 8.153907 9.999956 8.153952 11.846018 10.000044 11.84(i093 11 50 8-162681 9.999954 8.162727 11.837273 10.000046 11.837319 10 51 8.171280 y.yyyy52 8.1713*8 11.828672 1U. 000048 11.828720 y 52 8.179713 9.999950 8.179763 11.820237 10.000050 11 820287 8 53 8.187985 9.999948 8.188036 11.811964 10.000052 11.812015 7 54 8.193102 9 999946 8.196156 11.803844 10.000054 11.80381)8 6 55 8.204070 9 999944 8.204126 11.795874 10.000056 11.795930 5 56 8.211895 9 909942 8.211953 11.788047 10.000058 11.788105 4 57 8.219581 9.999940 8.219641 11.780359 10.000060 11.780419 3 58 8.227134 9.999938 8.227195 11.772805 10.000062 11.772866 2 59 8.234557 9.999936 8.234621 11.765379 10.000064 11.765443 1 CO 8.241855 9.999934 8.241922 11.758078 10.000066 11.758145 M. Co-sine. Sine. |Co-tang. Tangent. Co-sec. Secant. | M. SO Degrees. 144 TABLE II. LOOAEITHM1C SIXES, TANGENTS, AND SECANTS. 1 Degree. M. Sine. Co-sine. |Tangent. Co-tang. Secant. Co-sec. M. u 8.24185s 9.yyyy34 8.241921 11.75SU79 10.0UUOG6 11.758145 GO 1 8.249033 9.999932 8.249102 11.750898 10.000068 11.750967 59 2 8.256094 9.999929 8.256165 11.743835 10.000071 11.743906 58 3 8.263042 9.999927 8.263115 11.736885 10.000073 11.736958 57 4 8 269881 9.999925 8.269956 11.730044 10.000075 11.730119 56 5 8.276614 9.999922 8.276691 11.723309 10.000078 11.723386 55 6 8.283243 9.999920 8.283323 11.716677 10.000080 11.716757 54 7 8.289773 9.999918 8.289856 11.710144 10.000082 11.710227 53 8 8.29G2u7 9.999915 8.296292 11.703708 10.000085 11.703793 52 9 8.302546 9.999913 8.302634 11.697366 10.000087 11.697454 51 10 8 308794 9.999910 8.308884 11.C91116 10.000090 11.691206 50 11 8.314954 9 999907 8.315046 11.684954 1U.OOOU93 11.685046 49 12 8.321027 9.999905 8 321122 11.678878 10.000095 11.678973 48 18 8 327016 9.999902 8.327114 11.672886 10.000098 11.672984 47 14 8.332924 9.999899 8.333025 11.666975 10.000101 11.667076 46 15 8.338753 9.999897 8.338856 11.661144 10.000103 11.661247 45 16 8.344504 9.999b94 8.344610 11.655390 10.000106 11.655496 44 17 8.350181 9.999891 8.350289 11.649711 10.000109 11.649819 43 18 8.355783 9.999888 8.355895 11.644105 10.000112 11.644217 42 19 8.361315 9.999885 8.361430 11.638570 10.000115 11.638685 41 20 8.366777 9.999882 8 366895 11.633105 10.000118 11.633223 40 21 8.37:4171 9.99987'j 8.372292 11.027708 lo.ouul2l ll.b2Y629 39 22 8.377499 9.99J876 8 377622 11.622378 10.000124 11.622501 38 23 8.332702 9.999373 8.382889 11.617111 10.000127 11.617238 37 24 8.3879G2 9.999670 8.388092 11.611908 10.000130 11.612038 36 25 8.393101 9.999867 8.393234 11.606766 10.000133 11.606899 35 26 8.398179 9.999864 8.398315 11.601685 10.000136 11.601821 34 27 8.403199 9.999S61 8.403338 11.596662 10.000139 11.596801 33 28 8.408161 9.993858 8.408304 11.591696 10.000142 11.591839 32 29 8.413068 9.999854 8.413213 11.586787 10.000146 11.586932 31 30 8.417919 9.999851 8.418068 11.581932 10.000149 11.582081 30 31 8.422717 9.99J848 8.4*2869 11.577131 10.000162 11.577283 29 32 8.427462 9.999844 8.427618 11.572382 10.000156 11.572538 28 33 8 432156 9.999841 8.432315 11.567685 10.000159 11.567844 27 34 8.436800 9 999838 8.436962 11.563038 10.000162 11.563200 26 35 8.441394 9.999834 8.441560 11.558440 10.000166 11.558606 25 36 8.445941 9.999S31 8.446110 11.553890 10.000169 11.554059 24 37 8.450440 9.999827 8.450613 11.549387 10.000173 11.549560 23 38 8.454893 9.999824 8.455070 11.544930 10.000176 11.545107 22 39 8.459301 9.993820 8.459481 11.540519 10.000180 11.540699 21 40 8.463665 9.999816 8.463849 11.536151 10.000184 11.536335 20 41 8.467985 9.9U9813 8.4(36172 11.531828 1U.L00187 11.532015 19 42 8.472263 9.999809 8.472454 11.527546 10.000191 11.527737 18 43 8.47649S 9.999S05 8.476693 11.523307 10.000195 11.523502 17 44 8.480693 9.999801 8.480892 11.519108 10.000199 11.519307 16 45 8.484848 9.999797 8.485050 11.514950 10.000203 11.515152 15 46 8.488963 9.999794 8.489170 11.510830 10.000206 11.511037 14 47 8.493040 9.999790 8.493250 11.506750 10.000210 11.506960 13 48 8.497078 9.999786 8.497293 11.502707 10.000214 11.502922 12 49 8.501080 9.999782 8.501298 11.498702 10.000218 11.498920 11 50 8.505045 9.999778 8.505267 11.494733 10 000222 11.494955 10 51 8.508974 9.999774 8.509200 11.490UO 10.0U0220 11.491026 9 52 8.512867 9.999769 8.513098 11.486902 10.000231 11.487133 8 53 8.516726 9.999765 8.516961 11.483039 10.000235 11.483274 7. 54 8.520551 9.999761 8.520790 11.479210 10.000*>39 11.479449 6 55 8.524343 9.999757 8.524586 11.475414 10.000243 11.475657 5 56 8.528102 9.999753 8.528349 11.471651 10.000247 11.471698 4 57 8.531828 9.999748 8.532080 11.467920 10.000252 11.468172 3 58 8.535523 9.999744 8.525779 11.464221 10.000256 11.464477 2 59 8.539186 9.999740 8.539447 11.460553 10.000260 11.460814 1 60 8.542819 9.999735 8.543084 11.456916 10.000265 11.457181 M. Co-sine. Sine. |Co-tang. Tangent. Co-sec. Secant. M. 88 l>grees. TABLE II. 145 LOGARITHMIC SIGNS, TANGENTS AND SECANTS. 2 Degrees. M. Sine. Co-sine. (Tangent. Co-tang. Secant. Co-sec. M. u 8.542819 y. 999/35 8.543U84 11.450916 1U.OU0205 11.46/151 00 1 8.546422 9 999731 8.546691 11.453309 10.000269 11.453578 9 2 8.549995 9.999726 8.550268 11.449732 10.000274 11.450005 58 3 8.553539 9 999722 8.553817 11.440183 10.000278 11.4464G1 57 4 8.557054 9.999717 8.557336 11.442664 10.000283 11.44-2946 56 5 8.5G0540 9.999713 8.560828 11.439172 10.000287 11.439460 55 G 8.56^999 9'999708 8.564291 11.435709 10.000292 11.436001 54 7 8.5G7431 9.999704 8.567727 11.432273 10.000296 11.432569 53 8 8.570836 9 999G99 8.571137 11.428863 10.000301 11.429164 52 9 8.574214 9.999694 8 574520 11.425480 10.000306 11.425786 51 10 8 577566 9.999689 8.577877 11.422123 lO.OOf 311 11.422434 50 11 8 . 550o92 9 999085 8.51208 11.418792 10.000315 11.419108 49 12 0.584193 9.999G80 8 584514 11.415486 10.000320 11.415807 48 13 8.587469 9 999675 8.587795 11.412205 10.000325 11.412531 47 14 8.590721 9 999670 8.591051 11.408949 10.000330 11.409279 46 15 8.593948 9 999665 8.594283 11.405717 10.000335 11.406052 45 1C 8.597152 9.999660 8.597492 11.402508 10.000340 11.402848 44 17 8.600332 9.999655 8.600677 11.399323 10.000345 11.399668 43 18 8.603489 9.999650 8.603839 11.396161 10.000350 11.396511 42 19 8.606623 9.999645 8 606978 11.393022 10.000355 11.393377 41 20 8 609734 9.999640 8.610094 11.389906 10.000360 11.390266 40 21 8.0128*3 9.999635 8.613ifc9 11.380811 10.000305 11.387177 39 22 8.615891 9 999G29 8.616262 11.383738 10.000371 11.3841C9 38 23 8.618937 9.999624 8.619313 11.380687 10.000376 11.3810G3 37 24 8.621962 9.999619 8.622343 11-377657 10.000381 11.378038 36 25 8.624965 9.999614 8.625352 11.374648 10.000386 11.375035 35 2G 8.627948 9.999608 8.628340 11.371660 10.000392 11.372052 34 27 8 630911 9.999603 8.631308 11.368692 10.000397 11.369089 33 28 8.633854 9.999597 8.634256 11.365744 10.000403 11.366146 32 29 8.636776 9.999592 8.637184 11.362816 10.000408 11.363224 31 30 8.639380 9.999586 8.640093 11.359907 10.000414 11.360320 30 31 8.042503 9.999581 8.642982 11.357018 10.000419 11.357437 29 32 8.645428 9.999575 8.645853 11.354147 10.000425 11.354572 28 33 8.648274 9 999570 8.648704 11.351296 10.000430 11.351726 27 34 8.651102 9.999564 8.651537 11.348463 10.000436 11.348898 26 35 8.653911 9.999558 8.654352 11.345648 10.000442 11.346089 25 3G 8.656702 9.999553 8.657149 11.342851 10.000447 11.343298 24 37 8.659475 9.999547 8.659928 11.340072 10.000453 11.340525 23 38 8.6G2230 9.999541 8.662689 11.337311 10.000459 11.337770 22 39 8.664968 9 999535 8.665433 11.334567 10.000465 11.335032 21 40 8.667689 9.999529 8.G68160 11.331840 10.000471 11.332311 20 41 8.070393 9.999524 8.670870 11.329130 10.000470 ' 11.329607 19 42 8.673080 9.999518 8.673563 11.326437 10.C00482 11.326920 18 43 8 G7o751 9.999512 8.676239 11.323761 10.000488 11.324249 17 44 8.678405 9.999506 8.678900 11.321100 10.000494 11.321595 16 45 8.G81043 9.999500 8.681544 11.318456 . 10.000500 11.318957 15 4G 8.683665 9.999493 8.684172 11.315828 10.000507 11.316335 14 47 8.68G272 9.999487 8.686784 11.313216 10.000513 11.31S728 13 48 8.688863 9.999481 8.689381 11.310619 10.000519 11.311137 12 49 8.691438 9.999475 8.691963 11.308037 10.000525 11.308562 11 50 8.693998 9.999469 8.G94529 11.305471 10.000531 11.306002 10 51 S . 690543 9.999403 8.097081 11.302919 10.000537 11.303457 9 52 8.699073 9.999456 8.G99617 11.300383 10.000544 11.300927 8 53 8.701589 9.999450 8.702139 11.297861 10.000550 11.298411 7 51 8.704090 9.999443 8.704646 11.295354 10.000557 11.295910 6 55 8.705577 9.999437 8.707140 11.292860 10.000563 11.293423 5 56 8.709049 9.999431 8.709618 11.290382 10.0005G9 11.290951 4 57 8.711507 9.999424 8.712083 11.287917 10.000576 11.288493 3 58 8.713952 9.999418 8.714534 11.285466 10.000582 11.286048 2 59 8.716383 9.999111 8.716972 11.283028 10.000589 11.283617 1 GO 8.718800 9.999404 8.719390 11.280CO! 10.000596 11.C81200 M. Co-sine. Sine. |Co-tang. Tangent. Co-sec. Secant. M. HI Oesrces. 146 TABLE II. LOGARITHMIC SINES, TANGENTS, AND SECANTS. 8 Degrees. M. Sine. Co-sine. Tangent . Co-tang. Secant. Co-sec. M. U 8.718800 y . 'J99i04 8.719J9U 11 *8UOUi 10.000596 11.28121X) GO 1 8. '72 1-204 9.999398 8.721806 11.278194 10.000602 11.278796 59 2 8.723595 9.999391 8.724-04 11.275796 10.000609 11.276405 58 3 8.725972 9.999384 8.726588 11.273412 10.000616 11.274028 57 4 8 728337 9.999378 8.728959 11.271041 10.000622 11.271663 56 5 8.730688 9.999371 8.731317 11.268683 10.000629 11.269312 55 6 8.733027 9.999364 8.733663 11.266337 10.000636 11.266973 54 7 8.735354 9.999357 8.735996 11.264004 10.000643 11.264646 53 8 8.737667 9.999350 8.738817 11.261683 10.000650 11.262333 52 9 8.739969 9.999343 8.740626 11.259374 10.000657 11.260031 51 10 8.742259 9.999336 8.742922 11.257078 10.0C0664 11.257741 50 11 8.744036 9 999329 8.745207 11.254793 10.000671 11.255464 49 12 8 746802 9.999322 8.747479 11.252521 10.000678 11.253108 48 13 8.749055 9.999315 8.749740 11.250260 10.000685 11.250945 47 14 8.751207 9 999308 8.751989 11.248011 10.000692 11.248703 46 15 8 753528 9.999301 8.754227 11.245773 10.000699 11.246472 45 16 8.755747 9.999294 8.756453 11.243547 10.000706 11.244253 44 17 8.757955 9 999287 8.758668 11.241332 10.000713 11.242045 43 18 8.760151 9.999279 8.760872 11.239128 10.000721 11.239849 42 19 8.762337 9 999272 8 763065 11.236935 10.000728 11.237663 41 20 8.764511 9.999265 8.765246 11.234754 10.000735 11.235489 40 21 8.766t)75 9.999257 8.7U7417 11.232683 10.000743 ll.'2333i.5 3D 22 8.768828 9.999250 8.769578 11.230422 10.000750 11.231172 38 23 8.770970 9.999242 8,771727 11.228273 10.000758 11.229030 37 24 8 773101 9.999235 8.773866 11.226134 10.000765 11.226899 36 25 8.775223 9 999227 8.775995 11.224005 10.000773 11.224777 35 26 8.777333 9 999220 8 778114 11.221886 10.000780 11.222667 34 27 8.779434 9 999212 8.780222 11.219778 10.000788 11.220566 33 28 8.781524 9.999205 8.782320 11.217680 10.000795 11.218476 32 29 8.783605 9.999197 8 784408 11.215592 10.000803 11.216395 31 30 8.785675 9.999189 8.786486 11.213514 10.000811 11.214325 30 31 8.787736 9.999181 8.788554 11.211446 10.000819 11.212-204 5i9 32 8 789787 9 999174 8 790613 11.209387 10.000826 11.210213 28 33 8.791828 9.999166 8.792662 11.207338 10.000834 11.208172 27 34 8.793859 9.999158 8.794701 11.205299 10.000842 11.206141 26 35 8.795881 9.999150 8.796731 11.203269 10.000850 11.204119 25 36 8 797894 9.999142 8.798752 11.201248 10.000858 11.202106 24 37 8.799897 9 999134 8.800763 11.199237 10.000866 11.200103 23 38 8.801892 9.999126 8.802765 11.197235 10.000874 11.198108 22 39 8.803876 9.999118 8.804758 11.195242 10.000882 11.196124 21 40 8.805852 9.999110 8.806742 11.193-258 10.000890 11.194148 20 41 8.807819 9.999102 6.808717 11.191283 10.000898 11.192181 19 42 8.809777 9.999094 8.810683 11.189317 10.000906 11.190223 18 43 8.811726 9.999086 8.812641 11.187359 10.000914 11.188274 17 44 8.813667 9.999077 8.814589 11.185411 10.000923 11.186333 10 45 8.815599 9.999069 8.816529 11.183471 10.000931 11.184401 15 46 8.817522 9.999061 8.818461 11.181539 10.000939 11.182478 14 47 8 819436 9.999053 8.820384 11.179616 10.000947 11.180564 13 48 8.821343 9.999044 8.822298 11.177702 10.000956 11.178657 12 49 8.823240 9.999036 8.824205 11.175795 10.000964 11.170760 11 50 8.825130 9.999027 8.826103 11.173897 10.000973 11.174870 10 1 51 8.8-27011 9.999019 8.8^v 992 11.172008 10.000981 Il.17k.9o9 9 52 8.828884 9.999.ilO 8.829874 11.170126 10.000990 11.171116 8 53 8.830749 9.999002 8.831748 11.168252 10.000998 11.169251 7 54 8.832607 9.998993 8.833613 11.166387 10.001007 11.167393 6 55 8 831456 9.998984 8 835471 11.164529 10.001016 11.165544 5 56 8.836297 9.998976 8.837321 11.162679 10.001024 11.163703 4 57 8.838130 9 998967 8.839163 11.160837 10.001033 11.161870 3 58 8.839956 9.998958 8.840998 11.159002 10.001042 11.160044 2 59 8.841774 9.99S950 8.842825 11.157175 10.001050 11.158226 1 GO 8.843585 9.998941 8.844644 11.155356 10.001059 11.156415 H. Co-sine. Sine. 3 o -tang. Tangent. Co-sec. Secant. 1C. 8(> iX'.srrees. TABLE II. 147 LOGARITHMIC SINES, TANGENTS. AND SECANTS. 4 Decrees. M. Sine. Co-sine. Tangent. Co-tang. Secant. Co-sec. M. u 8.843585 9.998941 . 844U44 11.155356 10.001059 ll.lo(J4lo CO 1 8.845387 9.998932 8.846455 11.153545 10.001068 11.154613 59 2 8.847183 9.99S923 8.848260 11.151740 10.001077 11.152817 58 3 8.848971 9.998914 8.850057 11.149943 10.001086 11.151029 57 4 8 850751 9.998905 8.851846 11.148154 10.001095 11.149249 56 5 8.852525 9.998896 8.853628 11.146372 10.001104 11.147475 5 6 8.854291 9.998887 8.855403 11.144597 10.001113 11.145709 54 7 8 856049 9.998878 8.857171 11.142829 10.001122 11.143951 53 8 8.857801 9.998869 8.858932 11.141068 10.001131 11.142199 52 9 8.859516 9.998860 8. 861 "686 11.139314 10.001140 11.140454 51 10 8.861283 9.998851 8.862433 11.137567 10.001149 11.138717 50 11 8. 865014 9 998841 8.864173 11.135827 10.001159 11.136986 49 12 8.864738 9.998832 8.865906 11.134094 10.001168 11.135262 48 13 8.866455 9.998823 8.867632 11.132368 10.001177 11.133545 47 U 8.868165 9.998813 8 869351 11.130649 10.001187 11.131835 46 15 8.869868 9.993804 8.871064 11.128936 10.001196 11.130132 45 )6 8.871565 9.998795 8.872770 11.127230 10.001205 11.128435 44 17 8.873255 9.998785 8.874469 11.125531 10.001215 11.126745 43 18 8.874938 9.998776 8.876162 11.123838 10.001224 11.125062 42 19 8.876615 9.998766 8.877849 11.122151 10.001234 11.123385 41 20 8.878285 9 993757 8.879529 11.120471 10.001243 11.121715 40 21 8.679949 9.998Y47 8 881202 11.118798 10.001253 1 1.120051 * : *J 22 8.881607 9.998738 8.882869 11.117131 10.001262 11.118393 38 23 8.883258 9 998728 8.884530 11.115470 10.001272 11.116742 37 24 8.884903 9.998718 8.886185 11.113815 10.001282 11.115097 3G 25 8.886542 9.998708 8 887833 11.112167 10.001292 11.113458 35 26 8 888174 9.998699 8.889476 11.110524 10.001301 11.111826 3i 27 8 889801 9.998689 8 891112 11.108888 10.001311 11.110199 33 28 8.891421 9.998679 8.892742 11.107258 10.001321 11.108579 32 29 8.893035 9.998669 8.894366 11.105634 10.001331 11.106965 31 30 8 894643 9.998659 8.895984 11.104016 10.001341 11.105357 30 31 8.896246 9 . 998649 8.897596 11.102404 10.001351 11.1037o4 29 32 8.897842 9.998639 8.899.03 11.100797 10.001361 11.102158 28 33 8.899432 9.998629 8.900803 11.099197 10.001371 11.100568 27 34 8.901017 9.998619 8.902398 11.097602 10.001381 11.098983 26 35 8.902596 9.998609 8.903987 11.098013 10.001391 11.097404 25 3G 8.904169 9.998599 8.965570 11.094430 10.001401 11.095831 24 37 8 905736 9.998589 8.907147 11.092853 10.001411 11.094264 23 38 8.907297 9.998578 8.908719 11.091281 10.001422 11.092703 22 30 8.908853 9.998568 8.910285 11.089715 10.001432 11.091147 21 40 8 9HI404 9.998558 8.911846 11.088154 10.001442 11.089596 20 41 8.911949 9.998548 8.913401 11.086599 10.001452 11.088051 19 42 8.913488 9.998537 8.914951 11.085049 10.001463 11.086512 , 18 43 8.915022 9.998527 8.916495 11.083505 10.001473 11.084978 17 44 8.916550 9.998516 8.918034 11.081966 10.001484 11.083450 16 45 8.918073 9.998506 8.919568 11.080432 10.001494 11.081927 15 4G 8.919591 9.998495 8.921096 11.078904 10.001505 11.080409 14 47 8.921103 9.998485 8.922619 11.077381 10.001515 11.078897 13 48 8.922610 9.998474 8.924136 11.075864 10.001526 11.077390 12 49 8.924112 9.998464 8.925649 11.074351 10.001536 11.075888 11 50 8.925609 9.998453 8.927156 11.072844 10.001547 11.074391 10 51 8.927100 9.998442 8.928658 11.071342 10.001558 11.072900 9 52 8.928587 9.998431 8.930155 11.069845 10.001569 11.071413 8 53 8.930068 9.998421 8.931647 11.068353 10.001579 11.069932 7 54 8.931544 9.998410 8.933134 11.066866 10.001590 11.068456 6 55 8.933015 9.998399 8.934616 11.065384 10.001601 11.066985 5 56 8.934481 9.998388 8.936093 11.063907 10.001612 11.065519 4 57 8.935942 9.998377 8.937565 11.062435 10.001623 11.C64058 3 58 8.937398 9.998366 8.939032 11.060968 10.001634 11.062602 2 59 8.938850 9.998355 8. 94049 i 11.059506 10.001645 11.061150 1 no 8.940296 9. 998:^1 1 8.9<19r,2 11.058048 10.001656 11.059704 M. Co-sine. Sine. Co-tan;?. Tangent. Co-sec. Secant. M. K5 Decree*. 148 TABLE II. LOGARITHMIC SINES, TANGENTS, AND SECANTS. 5 Degrees. M. Sine. Co-sine. Tangent. Co-tang. Secant. Co-sec. | M. U 8.940^1/6 9 . 998344 8.941952 11.058048 10.00i6o6 11.059704 60 1 8 941738 9.998333 8.943401 11.056596 10.001667 11.058262 59 2 8 943174 9.99S322 8.944852 11.055148 10.001678 11.056826 58 3 8 944G06 9.998311 8.946295 11.053705 10.001689 11.055391 57 4 8 946034 9 9983CO 8.947734 11.052266 10.001700 11.053966 56 5 8.947456 9.998289 8 949168 11.050832 10 001711 11.052544 55 6 8.948874 9.998277 8 950597 11.049403 10.001723 11.051126 54 7 8. 950187 9.998266 8.952021 11.047979 10.001734 11.049713 53 8 8.951G93 9.998255 8.953441 11.046559 10.001745 11.048304 52 9 8.953100 9.998243 8.954856 11.045144 10.001757 11.046900 51 10 8 954-199 9.998232 8 956267 11.043733 10.001768 11.045501 50 11 8.955894 9.998220 8.9576/4 11.042326 10.001780 11.044106 49 12 8.957284 9.998209 8.959075 11.040925 10.001791 11.042716 48 13 8.958670 9.998197 8.960473 11.039527 10.001803 11.041330 47 14 8.960052 9.998186 8 961866 11.038134 10.001814 11.039948 46 15 8.961429 9.998174 8.963255 11.033745 10.001826 11.038571 45 16 8.962801 9.998163 8 964639 11.035361 10.001837 11.037199 44 17 8.964170 9.998151 8.966019 11.033981 10.C01849 11.035830 43 18 8 965534 9.998139 8 967394 11.032606 10.001861 11.034466 42 19 8.966893 9.998128 8.968766 11.031234 10.001872 11 033107 41 20 8.988249 9.998116 8 970133 11.029867 10.001884 11.031751 4!) iil 8. 969(30 J 9.998104 8.971496 11.028504 10.001896 11.030400 by 22 8.970947 9.998092 8.972855 11.027145 10.001908 11.029053 38 23 8.972-289 9.998080 8.974209 11.025791 10.001920 11.027711 S7 24 8.973628 9 998068 8.975560 11.024440 10.001932 11.026372 36 25 8.974962 9.993056 8.976906 11.023094 10 001944 11.025038 35 26 8.976293 9.998044 8.978248 11.021752 10.001956 11.023707 34 27 8 977619 9.998032 8.979586 11.020414 10.001968 11.022381 33 28 8.978941 9.998020 8 980921 11.019079 10.001980 11.021059 32 20 8.980259 9.998008 8.982251 11.017749 10.001992 11.019741 31 SO 8.981573 9.997993 8.983577 11.016423 10.002004 11.018427 30 31 8.98:i883 9.997984 8.984899 11.015101 10.002016 11.017117 *9 32 8 981189 9 997972 8.986217 11.013783 10.002028 11.015811 28 33 8.985491 9.997959 8.987532 11.012468 10.002041 11.014509 27 34 8 98G78D 9.997947 8.988842 11.011158 10.002053 11.013211 26 35 8.938083 9.997935 8.990149 11.009351 10.002065 11.011917 25 36 8.9S9G74 9.997922 8.991451 11.008549 10.002078 11.010626 24 37 8.9903:0 9 997910 8.992750 11.007250 10.002090 11.009340 23 38 8.991943 9.997897 8.994045 11.005955 10.002103 11.008057 22 39 8.993222 9.997885 8.995337 11.004663 10.002115 11.006778 21 4Q 8 991407 9.997872 8 996624 11.003376 10.002128 11.005503 1:0 41 8. 99676 J 9 99/8(30 8 997908 11.002092 10.002140 11.00423^ 1'J 42 8.997036 9 997847 8.999188 11.000812 10.002153 11. 00296 i 18 43 8.993299 9.997835 9.000465 10.999535 10.002165 11.001701 17 44 8.9095GO 9 997822 9.001733 10.998262 10.002178 11.000440 16 45 9.000316 9.997809 9.003007 10 996993 10.002191 10.999184 15 46 9.002069 9 997797 9 004272 10.995728 10.002203 10.997931 14 47 9.003318 9.997784 9.005534 10.994466 10002216 10.996682 13 48 9 004563 9.997771 9.006792 10.993208 10.002229 10.995437 12 49 9.005805 9 997758 9.008047 10.991953 10.002242 10.994195 11 50 9 007044 9.997745 9 009298 10.990702 10 002255 10.992956 10 51 9.00^78 9.997732 9.010546 10.989454 10.002268 10.991722 9 52 9.009510 9 997719 9 011790 10.988210 10.002281 10.990490 8 53 9.010737 9.997706 9.013031 10.986969 10.002294 10.989263 7 54 9.011962 9.997693 9.0142G8 10.985732 10.002307 10.988038 6 55 9.013182 9.997680 9.015502 10.984498 10.002320 10.986818 5 56 9.014400 9.997667 9.016732 10.983268 10.002333 10.985600 4 57 9.015613 9.997654 9 017959 10.982041 10.002316 10.984387 3 58 9.016824 9.997641 9.019183 10.980817 10.002359 10.983176 2 59 9.018031 9.997628 9.020403 10.979597 10.002372 10.981969 1 CO 9.019235 9.997614 9.021620 10.978S80 10.002386 10.9807C5 M. | (Jo-siiie. Sine. |Co-tang. Tangent. Co-sec. Secant. | TI. 4 U^jjrccs. TABLE II. 149 LOGARITHMIC SINES, TANGENTS, AND SECANTS. G Degrees. M. Sine. | Co-sine. (Tangent Co-tang. Secant. Co-sec. M. 9.019.^0 y.tjVG14 U. 0-^10^0 I0.9783fc0 10.0Ui:38G 10.980(05 CD l 9.020435 9.997601 9.022834 10.977166 10.002399 10.979565 59 2 9.021632 9.997588 9.024044 10.975956 10.002412 10.978368 58 3 9 022825 9 997574 9.025251 10.974749 10.002426 10 977175 57 4 9.02401G 9.997561 9 026455 10.973545 10.002439 10.975984 C6 5 9.025203 9.997547 9.027655 10.972345 10.002153 10.974797 55 G 9.026386 9.997534 9.028852 10.971148 10.002466 10.973614 54 7 9.027G67 9.997520 9.030046 10.969954 10.002480 10.072433 53 8 9.028744 9 997507 9.031237 10.968763 10.002493 10.971256 52 9 9.029918 9.997493 9.032425 10.967575 10.002507 10.970082 51 10 9.031089 9.997480 9.033G09 10.966391 10 002520 10.968911 50 Jl 9.032257 9.99/406 9.034791 10.9652U9 10.002534 10 907743 49 12 9.033421 9.997452 9.035969 10.964031 10.002548 10.966579 48 13 9.034582 9.997439 9.037144 10.962856 10.002561 10.965418 47 14 9 035741 9.997425 9.038316 10.961684 10.C02575 10.934259 46 15 9.03G89G 9.907411 9.039485 10.960515 10.002589 10.963104 45 1C 9.038048 9.997397 9.040651 10.959349 10.002603 10 961952 44 17 9.039197 9.997383 9.041813 10.958187 10.002617 10.9C0803 43 18 9 010342 9.997369 9.042973 10.957027 10.002631 10.959658 42 19 9.041485 9 997355 9 044130 10.955870 10.002645 10.958515 41 20 9 042625 9.997341 9.045284 10.954716 10.002659 10.957375 40 tl 9.043702 9.997dn7 9.046434 10.953506 10.002073 10.950-38 o9 22 9.044895 9.997313 9.047582 10.952418 10.002687 10.955105 38 23 9.046026 9.997299 9.048727 10.951273 10.002701 10.953974 37 24 9 047154 9.997285 9 049b69 10.950131 10.002715 10.952846 36 25 9.048279 9.997271 9 051008 10.948992 10.002729 10.951721 35 20 9.049100 9.997257 9.052144 10.947856 10.002743 10.950600 3i 27 9.050519 9.997242 9 053277 10.946723 10.002758 10.949481 33 8 9 051635 9 997228 9.054407 10.945593 10.002772 10.948365 32 29 9.052749 9.997214 9.055535 10.944465 10.002786 10.947251 31 30 9 053859 9.997199 9.056659 10.943341 10.002801 10.940141 30 31 9 064906 9.997185 9.057781 10.942219 10.002815 lU.94503i it) 32 9.05G071 9.997170 9.058900 10.941100 10.002830 10.913929 28 33 9.057172 9.997156 9.0G0016 10.939984 10.002844 10.942828 27 31 9 058271 9.997141 9.061130 10.938870 10.002859 10.941729 26 35 9.0593G7 9.997127 9.062240 10.937760 10 002873 10.940633 25 33 9.060460 9.997112 9.063348 10.936652 10.002888 10.939540 24 37 9 061551 9 997098 9.064453 10.935547 10.002902 10.938449 23 38 9.062639 9 997083 9.065556 10 934444 10.002917 10.937361 22 39 9.063724 9 997068 9.066655 10.933345 10.002932 10.936276 21 40 9.06480G 9 997053 9.067752 10.932248 10.002917 10.935194 41 9 005885 9 9970b9 9 063846 10.931154 10.002961 10.934115 J9 42 9.066962 9.997024 9.069938 10.930062 10.C0.976 10.933038 18 43 9 068036 9 997009 9.071027 10.928973 10.002991 10.931964 17 44 9.069107 9.996994 9.072113 10 927887 10.003006 10.930893 16 45 9.070176 9.996979 9.073197 10.926803 10.003021 10.929824 15 4G 9.071242 9.9969G4 9.074278 10.9ii5722 10.003036 10.928758 14 47 9.072306 9.996949 9.075356 10.924644 10.003051 10.927694 13 48 9.073366 9.996934 9.076432 10.923568 10.003066 10.926634 12 49 9.074124 9.99G919 9.077505 10.922495 10.003081 10.925576 11 no 9.075480 9.936904 9.078576 10.921424 10.003096 10.924520 10 51 9.0765jJ 9.9Ju89 9.079044 10 920356 10.003J11 10.923467 9 52 9.077583 9.996874 9.080710 10.919290 10.003126 10.922417 8 53 9.078631 9.996858 9.081773 10.918227 10.003142 10.921369 7 54 9.079676 9.996843 9.082833 10.917167 10.003157 10.920324 G 55 9.080719 9.996828 9.083891 10.916109 10.003172 10.919281 5 5G 9.081759 9.99G812 9.084947 10.915053 10.003188 10.918241 4 57 9.082797 9.996797 9.086000 10.914000 10.003203 10.917203 3 58 9.083832 9.996782 9.087050 10.912950 10 003218 10.916168 2 59 9.084864 9.996766 9.088098 10.911902 10.003234 10.915136 1 CO 9.085894 9.99G7. r )l 9 089144 10 910856 10.003249 J0.91410G M. (Co-nine. Sine. | Co-tang. Tangent. Co-sec. Secant. M. 83 Degree**. 150 TABLE II. LOGAKITHMIO SINES, TANGENTS, AND SECANTS. 7 Degrees. M. Sine. Co-sine. Tangent. Co-tang 1 . Secant. Co-sec. M. 9 08-J6U4 9.9jo7ol 9.U89144 10.910tt^6 lU.COoL-19 10.9141U5 to 1 9.086922 9.996735 9.090-87 10.909813 10.003265 10.913C78 C9 2 9.C87947 9.996720 9 091228 10.908772 10.003280 10.912053 58 3 9.088970 9.996704 9.092266 10.907734 10.003296 10.911030 57 4 9.089990 9.996688 9 093302 10.906698 10.003312 10.910010 56 5 9.091008 9.996673 9.094336 10.905664 10.003327 10.908S92 55 6 9.092024 9.996657 9.095367 10.904633 10.003343 10.907976 54 7 9 093037 9 996641 9.096395 10.903605 10.003359 10.906903 53 8 9.091047 9.996625 9.097422 10.902578 10.003375 10.905953 52 9 9.095056 9.996610 9.098446 10.901554 10.003390 10.904944 51 10 9.096062 9.996594 9.099468 10.900532 10.003406 10.903938 50 11 9.097UG5 9.996578 9.100487 10.899513 10.003422 10.902935 49 12 9.098066 9.996562 9.101504 10.898496 10.003438 10.90 1C454 48 13 9.099065 9.996546 9.102519 10.897481 10.003454 10.9C0935 47 14 9.100062 9.996530 9.103532 10.896468 10.003470 10.899938 46 15 9.101056 9 996514 9.104542 10.895458 10.003486 10.898944 45 16 9.102048 9.996498 9.105550 10.894450 10.003502 10.897952 44 17 9.103037 9.996482 9.106556 10.893444 10 003518 10.896963 43 18 9.104025 9.996465 9.107559 10.892441 10.003535 10.895975 42 19 9.105010 9.996449 9.108560 10.891440 10.003551 10.894990 41 20 9.105992 9.996433 9 109559 10.890441 10.C035G7 10.894008 40 21 9.106973 9.996417 9.110556 10.889444 10.003583 10.8930*7 39 22 9.107951 9.996400 9.111551 10.888449 10.003600 10.892049 38 23 9.108927 9 996384 9.112543 10.887457 10003616 10.891073 37 21 9 . 109901 9.996368 9.113533 10.886467 10.003632 10.890099 36 25 9.119873 9 996351 9.114521 10.885479 10.003649 10.889127 35 26 9.111842 9.996335 9.115507 10.884493 10.003665 10.888158 34 27 9.112809 9.996318 9 116491 10.883509 10.003682 10.887191 33 28 9 113774 9 996302 9.117472 10.882528 10.003698 10.886226 32 29 9.114737 9.996285 9.118452 10.881548 10.003715 10.885263 31 3;) 9.115698 9.996269 9.119429 10.880571 10.003731 10.884302 30 31 9.111565(5 9.996252 9.120404 10.8V 9596 10.003748 10.883344 *9 32 9.117613 9.996235 9.121377 10.878623 10.003765 10.882387 28 33 9.118567 9.936219 9.122348 10.877652 10.003781 10.881433 27 34 9.119519 9.996202 9.123317 10.876683 10.003798 10.880481 26 35 9.120469 9.996185 9.124284 10.875716 10.003815 10.879531 25 36 9.121417 9.996168 9 125249 10.874751 10.003832 10.878583 24 37 9.122362 9.996151 9 126211 10.873789 10.003849 10.877638 23 33 9.123306 9.996134 9.127172 10.872828 10.003866 10.876694 22 39 9.124248 9.996117 9.128130 10.871870 10.003883 10.875752 21 40 9.125187 9.996100 9 . 129087 10.870913 10.003900 10.874813 20 41 9.126125 9.996083 9 130041 10.869959 10.003917 10.873875 19 4'2 9.127060 9 996066 9.130994 10.869006 10.003934 10.872940 18 43 9.127993 9.996049 9 131944 10.868056 10.003951 10.872007 17 44 9.128925 9.996032 9 132893 10.867107 10.003968 10.871075 16 45 9 129854 9.996015 9.133839 10.866161 10.003985 10.870146 15 4G 9 . 130781 9.995998 9.134784 10.865216 10.004002 10.869219 14 47 9.131706 9.995980 9.135726 10.864274 10.004020 10.868294 13 43 9.132630 9.995963 9.136667 10.863333 10.004037 10.867370 12 49 9.133551 9.995946 9.137605 10.862395 10.004054 10.866449 11 CO 9.131470 9.995928 9.138542 10.861458 10.004072 19.865530 10 51 9 . 135387 9.995911 9 . 139476 10.860524 10.004089 10.864613 9 52 9.136303 9.995894 9.140409 10.859591 10.004106 10.863697 8 53 9.137216 9.995876 9.141340 10.858660 10.004124 10.862784 7 54 9.138128 9.995859 9.142269 10.857731 10.004141 10.861872 6 55 9.139037 9.995841 9.143196 10.856804 10.004159 10.860963 5 56 9.139944 9.995823 9.144121 10.855879 10.004177 10.860056 4 57 9.140850 9.995806 9.145044 10.854956 10.004194 10.859150 3 53 9.141754 9.995788 9.145966 10.854034 10.004212 10.858246 2 59 9.142655 9.995771 9.146885 10.853115 10.004229 10.857345 1 60 9.113:5") 9.993753 9.147803 10.852197 10.004247 10.856445 M. Co-sine. Sine. Co-tang. Tangent. Co-sec. Secant. M. M : i ."j;i''s. TABLE II. 151 LOGARITHMIC SINES, TANGENTS, AND SECANTS. 8 Degrees. M. Sine. Co-sine. (Tangent. Co-tang. Secant. Co-sec. M. u 9 . 143555 9.995753 9.147803 10.852197 10004247 10.856445 00 1 9.144453 9.995735 9.148718 10.851282 10.004265 10.855547 59 2 9 . 145349 9.995717 9.149632 10.850368 10.004283 10.854651 58 3 9.146243 9.995699 9.150544 10.849456 10.004301 10.853757 57 4 9.147136 9.995681 9.151454 10.848546 10.004319 10.852864 56 5 9.148026 9.995664 9.152363 10.847637 10.004336 10.851974 55 6 9.148915 9.995646 9.153269 10.846731 10 004354 10.851085 54 7 9.149802 9.995628 9.154174 10.845826 10.004372 10.850198 53 8 9.150686 9.995610 9.155077 10.844923 10.004390 10.849314 52 9 9.151569 9.995591 9.155978 10.844022 10.C04409 10.848431 51 10 9.152451 9.995573 9.156877 10.843123 10.004427 10.847549 50 11 9.153330 9.995555 9.157775 10.842225 10.004445 10.846670 49 12 9 . 154208 9.995537 9.158671 10.841329 10.004463 10.845792 48 13 9.155083 9.995519 9.159565 10.840435 10.004481 10.844917 47 14 9.155957 9.995501 9.160457 10.839543 10.004499 10.844043 46 15 9.156830 9.995482 9.161347 10.838653 10.004518 16 843170 45 16 9.157700 9.995464 9.162236 10.837764 10.004536 10.842300 44 17 9.158569 9.995446 9.163123 10.836877 10.004554 10.841431 43 18 9.159435 9.995427 9.164008 10.835992 10.004573 10.840565 42 19 9.160301 9.995409 9.164892 10.835108 10.004591 10.839699 41 20 9.161164 9.995390 9.165774 10.834226 10.004610 10.838836 4(1 21 9 . 162025 9.995372 9.166654 10.833346 10.004628 10.837975 39 22 9.162885 9.995353 9.167532 10.832468 10.004647 10.837115 38 23 9.163743 9.995334 9.168409 10.831591 10.004666 10.836257 37 24 9 . 164600 9.995316 9.169284 10.830716 10.004684 10.835400 36 25 9.165454 9.995297 9.170157 10.829843 10.004703 10.834546 35 26 9.166307 9.995278 9.171029 10.828971 10.004722 10.833693 34 27 9.167159 9.995260 9.171899 10.828101 10.004740 10.832841 33 28 9.168008' 9 995241 9.172767 10.827233 10.004759 10.831992 32 29 9.168856 9.995222 9.173634 10.826366 10.004778 10.831144 31 30 9 169702 9.995203 9.174499 10.825501 10.004797 10.830298 30 31 9.170547 9.995184 9.175362 10.824638 10.004816 10.829453 K9 32 9.171389 9.995165 9.176224 10.823776 10.004835 10.828611 28 33 9.172230 9 995146 9.177084 10.822916 10.004854 10.827770 27 34 9.173070 9.995127 9.177942 10.822058 10.004873 10.826930 ' 26 35 9.173908 9.995108 9.178799 10.821201 10.004892 10.826092 25 36 9.174744 9.995089 9.179655 10.820345 10.004911 10.825256 24 37 9.175578 9.995070 9.180508 10.819492 10.004930 10.824422 23 38 9.176411 9.995051 9.181360 10.818640 10.004949 10.823589 22 39 9.177242 9.995032 9.182211 10.817789 10.004968 10.822758 21 40 9.178072 9.995013 9.183059 10.816941 10.004987 10.821928 i:0 41 9.178900 9.994993 9.183907 10.816093 10.005007 10.821100 19 42 9.179726 9.994974 9.184752 10.815248 10.005026 10.820274 18 43 9.180551 9.994955 9.185597 10.814403 10.005045 10.819449 17 44 9.181374 9.994935 9.186439 10.813561 10.005065 10.818626 16 45 9.182196 9.994916 9.187280 10.812720 10.005084 10.817804 15 46 9.183016 9.994896 9.188120 10.811880 10.005104 10.816984 14 47 9.183834 9.994877 9.188958 10.811042 10.005123 10.816166 13 48 9.184651 9.994857 9.189794 10.810206 10.005143 10.815349 12 49 9.185466 9.994838 9.190629 10.809371 10.005162 10.814534 11 50 9.186280 9.994818 9.191462 10.808538 10.005182 10.813720 10 51 9.187092 9.994798 9.192294 10.807706 10.005202 10.812908 9 52 9.187903 9.994779 9.193125 10.806876 10.005221 10.812097 8 53 9.188712 9.994759 9.193953 10.806047 10.005241 10.811288 7 54 9.189519 9.994739 9.194780 10.805220 10.005261 10.810481 6 55 9.190325 9.994720 9.195606 10.804394 10.005281 10.809675 5 56 9.191130 9.994700 9.196430 10.803570 10.005300 10.808870 4 57 9.191933 9.994680 9.197253 10.802747 10.005320 10.808067 3 58 9.192734 9.994660 9.198074 10.801926 10.005340 10.807266 2 59 9.193534 9.994640 9.198894 10.801106 10.005360 10.806466 1 60 9.194H32 9.994620 9.199713 10.800287 10.005380 10.805668 M. Co-sine. Sine. | Co-tang. Tangent. Co-sec. Secant. M. SI IM--T <,. 152 TABLE II. LOGARITHMIC SINES, TANGENTS, AND SECANTS. 9 Degrees. M. Sine. Co-sine. Tangent. Co-tang 1 . Secant. Co-sec. M. V 9.194332 9.9946-/0 9.199U3 10.800287 10.005380 10.059 22 9.363954 9.983073 9.375881 10.624119 10.011927 10.636046 38 23 9.364485 9.988043 9.376442 10.623558 10.011957 10.635515 37 24 9 365016 9.988013 9 377003 10.622997 10.011987 10.634984 36 25 9.365546 9.987983 9 377563 10.622437 10.012017 10.634454 35 26 9.366075 9.987953 9.378122 10.621878 10.012047 10.633925 34 27 9.366604 9.987922 9 378681 10.621319 10.012078 10.633396 33 28 9 367131 9.987892 9.379239 10.620761 10.012108 10.632869 32 29 9.367659 9.987862 9.379797 10.620203 10.012138 10.632341 31 30 9 368185 9.987832 9.380354 10.619G46 10.012168 10.631815 30 31 9.U3b7ll 9.987801 9.380910 10.619090 10.012199 10 031289 k.9 32 9.369236 9.987771 9.381466 10.618534 10.012229 10.630764 28 33 9.369761 9.987740 9.382020 10.617980 10.012260 10.630239 .27 34 9.370285 9.987710 9.382575 10.617425 10.012290 10.629715 26 35 9.370C08 9.987679 9.383129 10.616871 10.012321 10.629192 25 36 9.371330 9.987649 9.383682 10.616318 10.012351 10.628670 24 37 9.371852 9.987618 9.384234 10.615766 10.012382 10.628148 23 38 9.372373 9 987588 9.384786 10.615214 10.012412 10.627627 22 39 9.372894 9.987557 9.385337. 10.614663 10.012443 10.627106 21 40 9.373414 9.987526 9.385888 10.614112 10.012474 10.626586 20 41 9 3739J3 9.987496 9.386438 10.613562 l'J.012504 10.0ii6007 19 42 9.374452 9.987465 9.386987 10.613013 10.012535 10.625548 18 43 9 374970 9.987434 9.387586 10.612464 10.012566 10.625030 17 44 9.375487 9.987403 9.388084 10.611916 10.012597 10.624513 16 45 9.376003 9.987372 9.388631 10.611369 10.012628 10.623997 15 46 9.376519 9.987341 9.389178 10.610822 10.012659 10.623481 14 47 9.377035 9.987310 9.389724 10.610276 10.012690 10.622965 13 48 9.377549 9.987279 9.390270 10.609730 10.012721 10.622451 12 49 9.378063 9.987248 9.390815 10.609185 10.012752 10.621937 11 50 9.378577 9.987217 9.391360 10.608640 10.012783 10.621423 10 51 9. 3 i 9089 9.987186 9.391903 10.608097 10.012814 10.6^0911 9 52 9.379601 9.987155 9.392447 10.607553 10.012845 10.620399 8 53 9.380113 9.987124 9.392989 10.607011 10.012876 10.619887 7 54 9.380624 9.987092 9.393531 10.606469 10.012908 10.619376 6 55 9.381134 9.987061 9.394073 10.605927 10.012939 10.618866 5 56 9.381643 9.987030 9.394614 10.605386 10.012970 10.618357 4 57 9.382152 9.936998 9.395154 10.604846 10.013002 10.617848 3 58 9.382661 9.986967 9.395694 10.604306 10.013033 10.617339 2 59 9.383168 9.986936 9.396233 10.603767 10.013064 10.616832 1 CO 9.38H675 9.986904 9 396771 10.603229 10.013096 10.61G325 M. | Co-sine. Sine. | Co-tang. Tangent. Co-sec. Secant. M. 7O Uogrees. TABLE II. 157 LOGAKITH3VIIC SINES, TANGENTS, AND SECANTS. 14 Degrees. M. | Sine. Co-sine. Tangent. Co-tang-. Secant. Co-sec. M. u 9.383675 9.986904 9.390771 10.6032-^9 10.013096 lO.OiGozS 00 l 9.384182 9.986873 9.397309 10.602691 10.013127 10.615318 f9 2 9.384687 9.986841 9.397846 10.602154 10.013159 10.615313 58 3 9.385192 9.986809 9.398383 10.601617 10.013191 10.614808 57 4 9.385697 9.986778 9.393919 10.601081 10.013222 10.614303 56 5 9.386201 9.986746 9.399455 10.600545 10.013254 10.613799 55 6 9.386704 9.986714 9.399990 10.600010 10.013286 10.613296 54 7 9.387207 9.986683 9.400524 10.599476 10.013317 10.612793 53 8 9.387709 9.986651 9.401058 10.598942 10.013349 10.612291 52 9 9.388210 9.986619 9.401591 10.598409 10.013381 10.611790 51 10 9.388711 9.986587 9.402124 10.597876 10.013413 10.611289 50 11 9.3892J1 9.986555 9.402656 10.597344 10.013445 10.610*89 49 12 9.389711 9.986523 9.403187 10.596813 10.013477 10.610289 48 13 9.390210 9.986491 9.403718 10.596282 10.013509 10.609790 47 14 9.390708 9.986459 9.404249 10.595751 10.013541 10.609292 46 15 9.391206 9.986427 9.404778 10.595222 10.013573 10 608794 45 16 9.391703 9.986395 9.405308 10.594692 10.013605 10.608297 44 17 9.392199 9.986363 9.405836 10.594164 10.013637 10.607801 43 18 9.392695 9.986331 9.406364 10.593636 10.013669 10.607305 42 19 9.393191 9.986299 9.406892 10.593108 10.013701 10.606810 41 20 9.393685 9.986266 9.407419 10.592581 10.013734 10.606315 40 21 9.394179 9.986234 9.407945 10.592055 10.013766 10.605821 ij'J 22 9.394673 9.986202 9.408471 10.591529 10.013798 10.605327 38 23 9.395166 9.986169 9.408997 10.591003 10.013831 10.604834 37 24 9.395658 9.986137 9.409521 10.590479 10.013863 10.604342 36 25 9.396150 9.986104 9.410045 10.589955 10.013896 10.603850 35 26 9.396641 9.986072 9.410569 10.589431 10.013928 10.603359 34 27 9.397132 9.986039 9.411092 10.588908 10.013961 10.602868 33 28 9.397621 9 986007 9.411615 10 588385 10.013993 10.602379 32 29 9.398111 9.985974 9.412137 10.587863 10.014026 10.601889 31 30 9.398600 9.985942 9.412658 10.587342 10.014058 10.6014'JO 30 31 9.399086 9.985909 9.413179 10.586821 10.014091 10.600912 i.9 32 9.399575 9.985876 9.413699 10.586301 10.014124 10.600425 28 33 9.400062 9.985843 9.414219 10.585781 10.014157 10.599938 27 34 9.400549 9.935811 9.414738 10.585262 10.014189 10.599451 26 35 9.401035 9.985778 9.415257 10.584743 10.014222 10.598965 25 36 9.401520 9.985745 9.415775 10.584225 10.014255 10.598480 24 37 9.402005 9.985712 9.416293 10.583707 10.014288 10.597995 23 33 9.402489 9.985679 9.416810 10.583190 10.014321 10.597511 22 39 9.402972 9.985646 9.417326 10.582674 10.014354 10.597028 21 40 9.403455 9.985613 9.417842 10.582158 10.014387 10.593545 '20 41 9.403938 9.955(?0 9.418358 10.581642 10.014420 10.596062 19 42 9.404420 9.985547 9 418873 10.581127 10.014453 10.595580 18 43 9.404901 9.985514 9.419387 10.580613 10.014486 10.595099 17 44 9.405382 9.985480 9 419901 10.580099 10.014520 10.594618 16 45 9.405862 9 985447 9.420415 10.579585 10.014553 10.594138 15 46 9.406341 9.985414 9 420927 10.579073 10.014586 10.593659 14 47 9.408820 9.985381 '9.421440 10.578560 10.014619 10.593180 13 48 9.407299 9.985347 9.421952 10.578048 10.014653 10.592701 12 49 9.407777 9.985314 9.422463 10.577537 10.014686 10.592223 11 SO 9.408254 9.985280 9.422974 10.577026 10.014720 10.591746 10 51 9.408731 9.985^47 9.423484 10.576516 10.014753 10.591269 9 52 9.409207 9.985213 9.423993 10.576007 10.014787 10.590793 8 53 9.409682 9.985180 9.424503 10.575497 10.014820 10.590318 7 54 9.410157 9.985146 9.425011 10.574989 10.014854 10.589843 8 55 9.410632 9.985113 9.425519 10.574481 10.014887 10.589368 5 56 9.411106 9.985079 9.426027 10.573973 10.014921 10.588894 4 57 9.411579 9.985045 9.426534 10.573466 10.014955 10.588421 3 58 9.412052 9.985011 9.427041 10.572959 10.014989 10.587948 2 59 9.412524 9.984978 9.427547 10.572453 10.015022 10.587476 1 60 9.412993 9 934944 9.423052 10.571948 10.015056 10.587004 M. Co-sine. Sine. Co-tang. Tangent. Co-sec. Secant. M. 75 l>eKree. 158 TABLE II. LOGARITHMIC SINES, TANGENTS, AND SECANTS. 15 Degrees. M. Sine. Co-sine. Tangent. Co-tang. Secant. Co-sec, j M. u y. 41*99(5 1). 984914 y.4_8oo2 J0.57i9i8 10 OioOoU 10.5bv004 ou 1 9.413467 9.984910 9.428557 10.571443 10.015090 10.586533 59 2 9.41C938 9.984876 9.429062 10.570938 10.015124 10.586062 58 3 9.414403 9.984842 9.429566 10.570434 10.015158 10.585592 57 4 9.414878 9.984808 9.430G70 10.569930 10.015192 10.585122 56 5 9.415347 9.984774 9.430573 10.569427 10.015226 10.5846:3 55 6 9.415815 9.984740 9.431075 10.568925 10 015260 10.584185 54 7 9.416283 9.984706 9.431577 10.568423 10.015294 10.583717 53 8 9.416751 9.984672 9.432079 10.567921 10.015328 10.583249 52 9 9.417217 9.984638 9.432580 10.567420 10.015362 10.582783 51 1C) 9.417G84 9.984C03 9.433080 10.566920 10.015397 10.582316 50 11 9.418150 9.984o69 9.433580 10.5664*0 10.015431 10.5818uU 49 12 9.418615 9.984535 9.434080 10.565920 10.015465 10.581385 48 13 9.419079 9.984500 9.434579 10.565421 10.015500 10.580921 47 14 9.419544 9.984466 9.435078 10.564922 10.015534 10.580456 46 15 9.420007 9.984432 9.435576 10.564424 10.015568 10 579993 45 16 9.420470 9.984397 9.436073 10.563927 10.015603 10.579530 44 17 9.420933 9.984363 9.436570 10.563430 10.015637 10.579067 43 18 9.421395 9.984328 9.437067 10.562933 10.015672 10.578605 42 19 9.421857 9.984294 9.437563 10.562437 10.015706 10.578143 41 20 9.422318 9.984259 9.438059 10.561941 10.015741 10.577682 40 21 9.4*2776 9 . 984224 9.43c>554 10.561446 10.015776 10.5772*2 39 22 9.423238 9.984190 9.439048 10.560952 10.015810 10.576762 38 23 9.423697 9.981155 9.439543 10.560457 10.015845 10.576303 37 24 9.424156 9.984120 9.440036 10.559964 10.015880 10.575844 36 25 9.424615 9.984085 9.440529 10.559471 10.015915 10.575385 35 26 9.425073 9.984050 9.441022 10.558978 '10.015950 10.574927 34 27 9.425530 9.984015 9.441514 10.558486 10.015985 10.574470 33 28 9.425987 9 983981 9.442006 10.557994 10.016019 10.574013 32 29 9.426443 9.983946 9.442497 10.557503 10.016054 10.573557 31 30 9 426899 9.983911 9.442988 10.557012 10016089 10.573101 30 31 9.427354 9.983875 9.443479 10.550521 10.016125 10.57*04(3 19 32 9.427809 9.983840 9.443968 10.556032 10.016160 10.572191 28 33 9.428263 9 983805 9.444458 10.555542 10.016195 10.571737 27 34 9.428717 9.933770 9.444947 10.555053 10.016230 10.571283 26 35 9.429170 9.983735 9.445435 10.554565 10.016265 10.570830 25 ! 36 9.429623 9.983700 9.445923 10.554077 10.016300 10,570377 24 ! 37 9.430075 9.983664 9.446411 10.553589 10.016336 10.569925 k3 38 9.430527 9.983629 9.446898 10.553102 10.016371 10.569473 22 39 9.430978 9.983594 9.447384 10.552616 10.016406 10.569022 21 40 9.431429 9.983558 9.447870 10.552130 10.016442 10.568571 iO 41 9.431679 9.983o23 9.448356 10.551644 10.016477 10.568121 19 ! 42 9.432329 9.983487 9.448841 10.551159 10.016513 10.567671 18 ! 43 9 432778 9.983452 9.449326 10.550674 10.016548 10.567222 17 j 44 9.433226 9.983416 9.449810 10.550190 10.016584 10.566774 16 ! 45 9.433675 9.983381 9.450294 10.549706 10.016619 10.566325 15 i 46 9.434122 9.983345 9.450777 10.549223 10.016655 10.565878 14 47 9.434569 9.983309 9.451260 10.548740 10.016691 10.565431 13 48 9.435016 9.983273 9.451743 10.548257 10.016727 10.564984 12 49 9.435462 9.983238 9.452225 10.547775 10.016762 10.564538 11 50 9.435908 9.983202 9.452706 10.547294 10.016798 10.564092 10 51 9.436353 9.983166 9.453187 10.546813 10.016834 10.563647 9 52 9.436798 9.983130 9.453668 10.546332 10.016870 10.563202 8 53 9.437242 9.983094 9.454148 10.545852 10.016906 10.562758 7 54 9.437686 9.983058 9.454628 10.545372 10.016942 10.562314 6 55 9.438129 9.983022 9.455107 10.544893 10.016978 10.561871 5 56 9.438572 9.982986 9.455586 10.544414 10.017014 10.561428 4 57 9.439014 9.982950 9.456064 10.543936 10.017050 10.560986 3 58 9.439456 9.982914 9.456542 10.543458 10.017086 10.560544 2 59 9.439897 9.982878 9.457019 10.542981 10.017122 10.560103 1 60 9.440338 9.982842 9.457496 10.542504 10.017158 10 559662 M. Co-sine. Sine. Co-tang-. Tangent. Co-sec. Secant. M. 74 l>egrees. TABLE II. 159 LOGAEITHMIC SINES, TANGENTS, AND SECANTS. 16 Degrees. 1C. Sine. Co-sine. Tangent. Co-tang. Secant. Co-sec. M. u y. 440338 y.98_84i5 9.4u74'jO 1U.54_504 1U.017158 10.059602 60 1 9 440778 9.982805 9.457973 10.54-_027 10.017195 10.559222 59 2 9 441218 9. 982709 9.458449 10.541551 10.017231 10.558782 58 3 9.441658 9.98^733 9. 458925 10.541075 10.017267 10.558312 57 4 9 442096 9 982693 9.459400 10.540600 10.017304 10.557904 56 5 9.442535 9.982660 9 459875 10.549125 10 017340 10.557465 55 6 9.44-2973 9.982624 9.460349 10.530651 10.017376 10.557027 54 7 9.443410 9.982587 9.460823 10.539177 10.017-il3 10.55C590 53 8 9.443847 9.982551 9.461297' 10.538703 10.017449 10.556153 52 9 9.444284 9.982514 9.461770 10.538230 10.017486 10.555716 51 10 9.444720 9.982477 9 462242 10.537758 10.017523 10.555280 50 11 9.445155 9.t;82441 9.4u_714 10.5b/L8o iu.ui756y 10.554845 49 12 9.445590 9.982404 9.463186 10.53G814 10.017596 10.554410 48 13 9.446025 9.982367 9.463658 10.536342 10.017633 10.553975 47 14 9.446459 9.982331 9 464128 10.535872 10.017609 10.553541 46 15 9.446893 9.982294 9.464599 10.535401 10.017706 10.553107 45 16 9.447326 9 982257 9 465069 10.534931 10.017743 10.552674 44 17 9.447759 9.982220 9.465539 10.634461 10.017780 10.552241 43 18 9.448191 9.982183 9 4G6G08 10.533992 10.017817 10.551809 42 19 9.448623 9.982146 9.466476 10533524 10.017854 10.551377 41 i '20 9.448054 9. 982 109 9 466945 10.533055 10.017891 10.550946 40 SI 9. 449480 9 . Ubzo72 9.407413 lO.bSzob? 10.0179-^8 10.5oUol5 oU 22 9.449915 9.982035 9.467880 10.532120 10.017965 10.550085 38 | 23 9.450345 9.981998 9.468347 10.531653 10.018002 10.549655 37 24 9.450775 9 981961 9.468814 10.531186 10.018039 10.549225 36 25 9.451204 9.981924 9.469280 10.530720 10.018076 10.548796 35 26 9.451632 9.981886 9 460746 10.B30254 10.018114 10.548368 34 27 9.452060 9.981849 9.470211 10.529789 10.018151 10.547940 33 28 9.452488 9.981812 9 470676 10.529324 10.018188 10.547512 32 29 9.452915 9.981774 9.471141 10.528859 10.018226 10.547085 31 30 9.453342 9.981737 9.471605 10.528395 10.018263 10.546658 30 31 U. 453/08 9.9817LO y.47ilO(J8 10.52/932 10.018300 10.540232 29 32 9.454194 9.981662 9.472532 10.527468 10.018338 10.545806 28 33 9.454619 9.981625 9.472995 10.527005 10.018375 10.545381 27 34 9.455044 9.981587 9.473457 10.526543 10.018413 10.544956 26 35 9.455469 9.981549 9.473919 10.526081 10.018451 10.544531 25 3G 9.455893 9.981512 9.474381 10.525619 10.018488 10.544107 24 37 9.45G316 9 981474 9.474842 10.525158 10.018526 10.543684 23 38 9.456739 9.981436 9.475303 10.524697 10.018564 10.543261 22 39 9.457162 9.981399 9.475763 10.524237 10.018601 10.542838 21 | 40 9.457584 9.981361 9.476223 10.523777 10.018639 10.542416 20 41 9.45bU06 9.9813*3 9 470083 10.523317" 1U.U18677 10.541094 19 42 9.458427 9 981285 9.477142 10 522858 10.018715 10.541573 18 43 9.458848 9.981247 9.477601 10.522309 10.018753 10.541152 17 44 9.459268 9.981209 9.478059 10.521941 10.018791 10.540732 16 45 9*.459C88 9.981171 9.478517 10. C2 1483 10.018829 10.540312 15 46 9.460108 9.981133 9 478975 10.521025 10.018867 10.539892 14 47 9.460527 9.981095 9.479432 10.520568 10.018905 10.539473 13 48 9.460946 9.981057 9.479889 10.520111 10.018943 10.539054 12 49 9.461364 9 981019 9.480345 10.519655 10.018981' 10.538636 11 50 9 461782 9.980981 9 480801 10.519199 10.010019 10.538218 10 51 9.462199 9 . 'JM,94-J 9.481257 1U.518743 10.0lOUii8 10.532 10.529954 50 11 9.4.0i55 9 . 1)80109 9.4902c6 10.509/14 100i9o31 10.529545 49 12 9.470883 9.980130 9 490733 10.C09267 10.019870 10.529137 48 13 9.471271 9.930091 9.491180 10.508820 10.019909 10.528729 47 14 9.471679 9.980052 9.491627 10.508373 10.019948 10.528321 46 15 9.472086 9.980012 9.492073 10.507927 10.01!988 10.527914 45 1C 9.472492 9.979373 9.492519 10.507481 10.020027 10.527508 44 17 9.472898 9 979934 9.492965 10.507035 10.02C066 10.527102 43 18 9.473304 9.979895 9.493410 10.506590 10.0201C5 10.526696 42 19 9.473710 9.979355 9.493854 10.506146 10.020145 10.526290 41 20 9.47-1115 9 979316 9.494299 10.505701 10.020184 10.525885 40 21 St. 474519 9 97;; /76 9.4'J4743 10.50u_57 10.0^0:^4 10.5zo4bl 39 22 9 4749:3 9.979737 9.495186 10.504814 10 020263 10.525077 38 23 9.475327 9 979G97 9.495630 10.501370 10.020303 10.524673 37 24 9.475730 9.979058 9.496373 10.503927 10.020342 10.524270 30 25 9.476133 9.979618 9 49G515 10.503485 10.020382 10.523867 35 26 9 47G5:)6 9.979579 9 49G957 10.503043 10.020421 10.523464 34 27 9 47C938 9.979539 9 497399 10.502601 10.020461 10.523062 33 28 9 477310 9.979499 9 497841 10.502159 10 020501 10.522660 32 29 9.477741 9.979459 9.498282 10.501718 10.02C541 10.522259 31 30 9.478142 9.97D420 9.498722 10.501278 10.020580 10.521858 30 31 9 4vfio42 9.979o80 y.4'JJlo3 10.500837 10.0200*0 10.5^1458 29 32 9.478942 9 979310 9.499G03 10.500397 10.020660 10.521058 28 33 9.479342 9 9793GO 9.50U042 10.409958 10.020700 10.520658 27 31 9.479741 9.979260 9.500481 10.499519 10.020740 10.520259 26 35 9.480140 9.979220 9.500920 10.499080 10.020780 10.519860 25 36 9.480539 9.979180 9 501359 10 498041 10.020820 10.519461 24 37 9 480937 9.979140 9.501797 10.498203 10.020860 10.519063 23 38 9.481334 9.979100 9.502235 10.497765 10.020900 10.518666 22 39 9.481731 9 . 979059 9.502672 10.497328 10.020941 10.518269 21 40 9 482128 9.979019 9 503109 10.496391 10.020981 10.517872 20 41 9.48^525 y y?9/y 9.503546 10.490454 10.0210vil 10.517475 19 42 9.482921 9.978939 9.503982 10.496018 10.021061 10.517079 18 43 9.483316 9.978898 9.504418 10.495582 10.021102 10.516684 17 44 9.483712 9.978858 9.504854 10.495146 10.021142 10.516288 16 45 9.484107 9.978817 9.505289 10494711 10.021183 10.51589S 15 4G 9.484501 9.978777 9.505724 10.494276 10.021223 10.515499 14 47 9.481895 9.978737 9.506159 10.493811 10.021263 10.515105 13 48 9.485289 9.978696 9.506593 10.493407 10.021304 10.514711 12 49 9.435682 9.978655 9.507027 10 492973 10.021345 10.514318 11 50 9.48G075 9.978615 9.507460 10.492540 10 021385 10.51S925 10 51 9.486467 9.978574 9. 007 893 1U.492107 10.021426 10.5135J3 9 52 9.486860 9.978533 9 5l '8326 10.491G74 10.021467 10.513140 8 53 9.487251 9.978493 9.508759 10.491241 10.021507 10.512749 7 54 9.487643 9.978152 9.509191 10 490809 10.021548 10.512357 6 55 9.488034 9.978411 9.509622 10.490378 10.021589 10.511966 5 56 9.488424 9.978370 9.510054 10.489946 10.021630 10.511576 4 57 9.488814 9.978329 9.510485 10.489515 10.021671 10.511186 3 58 9.489204 9.978288 9.510916 10.489084 10.021712 10.510796 2 59 9.489593 9.978247 9.511340 10.488654 10.021753 10.510407 1 60 9.489982 9.978C06 9 511776 10.488224 10.021794 10.510018 M. Co-sine. Sine. | Co-tang. Tangent. Co-sec. Secant. H. 7/4 JUejfrees. TABLE II. 161 LOGARITHMIC SINES, TANGENTS, AND SECANTS. 18 Decrees. M. Sine. Co-sine. Tangent. Co-tang. Secant. Co-sec. M. y. 489982 9.978206 9.511776 10.488224 10.0^1794 10.510018 GO 1 9.490371 9.978165 9.512206 10.487794 10.021835 10.509629 59 2 9.490759 9.978124 9.512635 10.487365 10.021876 10.509241 58 3 9.491147 9.978083 9.513064 10.486936 10.021917 10.508853 57 4 9 491535 9.978042 9.513493 10.486507 10.021958 10.508465 56 5 9.491922 9.978U01 9.513921 10.486079 10. 021999 * 10.508078 55 6 9.492308 9.977959 9 514349 10.485651 10.022041 10.507692 54 7 9.492695 9.977918 9.514777 10.485223 10.022082 10.507305 53 8 9.493081 9 977877 9.515204 10.484796 10.022123 10.506919 52 9 9.493166 9.977835 9.515631 10.484369 10.022165 10.506534 51 10 9.493851 9.977794 9.516057 ld.483943 10.022206 10.506149 50 11 9.494236 9 977752 9.516484 10.483516 10.022248 10.505764 49 12 9.494621 9.977711 9.516910 10.483090 10.022289 10.505379 48 13 9.495005 9.977669 9.517335 10.482665 10.022331 10.504995 47 14 9.495388 9.977628 9.517761 10.482239 10.022372 10.504612 46 15 9.495772 9.977586 9.518185 10.481815 10.022414 10.504228 45 16 9.496154 9.977544 9.518610 10.481390 10.022456 10.503846 '44 17 9.496537 9.977503 9.519034 10.480966 10.022497 10.503463 43 18 9.496919 9.977461 9.519458 10.480542 10.022539 10.503081 42 19 9.497301 9.977419 9.519882 10.480118 10.022581 10.502699 41 20 9.497682 9.977377 9.520305 10 479695 10.022623 10.502318 40 21 9 498064 9.977335 9.520728 10.479272 10.022665 10.501936 39 22 9.498444 9.977293 9.521151 10.478849 10.022707 10.501556 38 23 9.498825 9.977251 9.521573 10.478427 10.022749 10.501175 37 24 9.499204 9.977209 9.521995 10.478005 10.022791 10.500796 36 25 9.499584 9.977167 9.522417 10.477583 10.022833 10.500416 35 26 9.499963 9.977125 9.522838 10.477162 10.022875 10.500037 34 27 9.500342 9.977083 9.523259 10.476741 10.022917 10.499658 33 28 9 500721 9.977041 9.523680 10.476320 10.022959 10.499279 32 29 9.501099 9.976999 9.524100 10.475900 10.023001 10.498901 31 30 9.501476 9.976957 9.524520 10.475480 10.023043 10.498524 30 31 9.501854 9.976914 9.524939 10.475061 10.023086 10.498146 29 32 9.502231 9.976872 9.525359 10.474641 10.023128 10.497769 28 33 9.502607 9.976830 9.525778 10.474222 10.023170 10.497393 27 34 9.502984 9.976787 9.526197 10.473803 10.023213 10.497016 26 35 9.503360 9.976745 9.526615 10.473385 10.023255 10.496640 25 36 9.503735 9.976702 9.527033 10.472967 10.023298 10.496265 24 37 9.504110 9.976660 9.527451 10.472549 10.023340 10.495890 23 38 9.504485 9.976617 9.527868 10.472132 10.023383 10.495515 22 39 9.504860 9.976574 9.528285 10.471715 10.023426 10.495140 21 40 9.505234 9.976532 9.528702 10.471298 10.023468 10.494766 20 41 9.505608 9.976489 9 529119 10.470881 10.023511 10.494392 19 42 9.505981 9.976446 9.529535 10.470465 10.023554 10.494019 18 43 9.506354 9.976404 9 529950 10.470050 10.023596 10.493646 17 44 9.506727 9.976361 9 530366 10.469634 10.023639 10.493273 16 45 9.507099 9.976318 9.530781 10.469219 10.023682 10.492901 15 46 9.507471 9.976275 9.531196 10.468804 10.023725 10.492529 14 47 9.507843 9.976232 9.531611 10.468389 10.023768 10.492157 13 48 9.508214 9.976189 9.532025 10.467975 10.023811 10.491786 12 49 9.508585 9.976146 9.532439 10.467561 10.023854 10.491415 11 50 9.508956 9.976103 9.532853 10.467147 10.023897 10.491044 10 51 9.509326 9.976060 9.533266 10.466734 10.023940 10.490674 9 52 9.509696 9.976017 9.533679 10.466321 10.023983 10.490304 8 53 9.510065 9.975974 9.534092 10.465908 10.024026 10.489935 7 54 9.510434 9.975930 9.534504 10.465496 10.024070 10.489566 6 55 9.510803 9.975887 9.534916 10.465084 10.024113 10.489197 5 56 9.511172 9.975844 9.535328 10.464672 10.024156 10.488828 4 57 9.511540 9.975800 9.535739 10.464261 10.024200 10.488460 3 58 9.511907 9.975757 9.536150 10.463850 10.024243 10.488093 2 59 9.512275 9.975714 9.536561 10.463439 10.024286 10.487725 1 60 9.512642 9.975670 9.536972 10.463028 10.024330 10.487358 M. Co-sine. Sine. | Co-tang. Tangent. Co-sec. Secant. M. 71 JJcjsrees. 162 TABLE II. LOGAKITHMIC SINES, TANGENTS, AND SECANTS. 19 Degrees. M. Sine. Co-sine. Tangent. Co- tang. Secant. Co-sec. M. 9.512642 9.975670 9.5369/2 10 463028 10.0243oO 10.487358 60 1 9.513009 9.975627 9.537382 10.462618 10.024373 10.486991 59 2 9.513375 9.975583 9.537792 10.462208 10.024417 10.486625 58 3 9.513741 9.975539 9.538202 10.461798 10.024461 10.486259 57 4 9.514107 9.975496 9.538611 10.461389 10.024504 10.485893 56 5 9.514472 9.975452 9.539020 10.460980 10.024548 10.485528 55 6 9.514837 9.975408 9.539429 10.460571 10.024592 10.485163 54 7 9.515202 9.975365 9.539837 10.460163 10.024635 10.484798 53 8 9.515566 9.975321 9.540245 10.459755 10.024679 10.484434 52 9 9.515930 9.975277 9.540653 10.459347 10.024723 10.484070 51 10 9.516294 9.975233 9 541061 10.458939 10.024767 10.483706 50 11 9.510657 9.975189 9.541468 10.458532 10.024811 10.483343 49 12 9.517020 9.975145 9.541875 10.458125 10.024855 10.482980 48 13 9.517382 9.975101 9.542281 10.457719 10.024899 10.482618 47 14 9.517745 9 975057 9.542688 10.457312' 10.024943 10.482255 46 15 9 518107 9.975013 9.543094 10.456906 10.024987 10.481893 45 16 9.518468 9.974969 9.543499 10.456501 10.025031 10.481532 44 17 9.518829 9 974925 9.543905 10.456095 10.025075 10.481171 43 18 9.519190 9.974880 9.544310 10.455690 10.025120 10.480810 42 19 9.519551 9.974836 9.544715 10.455285 10.025164 10.480449 41 20 9.519911 9.974792 9.545119 10.454881 10.025208 10.480089 40 21 9.520271 9.974748 9.545524 10.454476 10.025252 10.479729 39 22 9.520634 9.974703 9.545928 10.454072 10.025297 10.479369 38 23 9.520990 9.974659 9.546331 10.453669 10.025341 10.479010 37 24 9 521349 9.974614 9.546735 10.453265 10.025386 10.478651 36 25 9.521707 9 974570 9.547138 10.452862 10.025430 10.478293 35 26 9.522066 9.974525 9.547540 10.452460 10.025475 10.477934 34 27 9.522424 9.974481 9.547943 10.452057 10.025519 10.477576 33 28 9.522781 9.974436 9.548345 10.451655 10.025564 10.477219 32 29 9.523138 9.974391 9.548747 10.451253 10.025609 10.476862 31 30 9.523495 9.974347 9.549149 10.450851 10.025653 10.476505 30 31 9 523852 9.974302 9.549550 10.450450 10.025698 10.476148 29 32 9 524208 9 974257 9.549951 10.450049 10.025743 10.475792 28 33 9.524564 9.974212 9.550352 10.449648 10.025788 10.475436 27 34 9.524920 9.974167 9.550752 10.449248 10.025833 10.475080 26 35 9 525275 9.974122 9.551152 10.448848 10.025878 10.474725 25 36 9 525630 9.974077 9.551552 10.448448 10.025923 10.474370 24 37 9.525984 9 974032 9.551952 10.448048 10.025968 10.474016 23 38 9.526339 9.973987 9.552351 10.447649 10.026013 10.473661 22 39 9.526693 9.973942 9.552750 10.447250 10.026058 10.473307 21 40 9.527046 9.973897 9.553149 10.446851 10.026103 10.572954 20 41 9.527400 9.973852 9.553548 10.446452 10.026148 10.472600 19 42 9.527753 9.973807 9.553946 10.446054 10.026193 10.472247 18 43 9.528105 9.973761 9.554344 10.445656 10.026239 10.471895 17 44 9.528458 9.973716 9.554741 10.445259 10.026284 10.471542 16 45 9.528810 9.973671 9.555139 10.444861 10.026329 10.471190 15 46 9.529161 9.973625 9.555536 10.444464 10.026375 10.470839 14 47 9 529513 9.973580 9.555933 10.444067 10.026420 10.470487 13 48 9.529864 9.973535 9.556329 10.443671 10.026465 10.470136 12 49 9.530215 9.973489 9.556725 10.443275 10.026511 10.469785 11 50 9.530565 9.973444 9.557121 10.442879 10.026556 10.469435 10 51 9.530915 9.973398 9.557517 10.442483 10.026602 10.469085 9 52 9.531265 9.973352 9.557913 10.442087 10.026648 10.468735 8 53 9.531614 9.973307 9.558308 10.441692 10.026693 10.468386 7 54 9.531963 9.973261 9.558702 10.441298 10.026739 10.468037 6 55 9 532312 9.973215 9.559097 10.440903 10.026785 10.467688 5 56 9.532661 9.973169 9.559491 10.440509 10.026831 10.467339 4 57 9.533009 9.973124 9.559885 10.440115 10.026876 10.466991 3 58 9.533357 9.973078 9.560279 10.439721 10.026922 10.466643 2 59 9.533704 9.973032 9.560673 10.439327 10.026968 10.466296 1 60 9.534052 9.972986 9.561066 10.438934 10.027014 10.465948 M. Co-sine. Sine. Co-tang. Tangent. Co-sec. Secant. M. 7O Degrees. TABLE II. 163 LOGARITHMIC SINES, TANGENTS, AND SECANTS. 20 Degrees. M. j Sine. Co-sine. Tangent. Co-tang. Secant. Co-sec. | M. u 9.534052 9.972986 9.5ol066 10.438934 10.027014 10.465948 CO 1 9.534399 9.972940 9.561459 10.438541 10.027060 10.465601 E9 2 9.534745 9.972894 9.561851 10.438149 10.027106 10.465255 58 3 9.535092 9.972848 9.562244 10.437756 10.027152 10.464908 57 4 9.535438 9.972802 9.562636 10.437364 10.027198 10.464562 56 5 9.535783 9.972755 9.563028 10.436972 10.027245 10.464217 55 6 9.536129 9.972709 9.563419 10.436581 10.027291 10.463871 54 7 9.536474 9.972663 9.563811 10.436189 10.027337 10.463526 53 8 9.536818 9.972617 9.564202 10.435798 10.027383 10.463182 52 9 9.537163 9.972570 9.564592 10.435408 10.027430 10.462837 51 10 9.537507 9.972524 9.564983 10.435017 10.027476 10.462493 50 11 9. 537851 9.972478 9.565373 10.434627 10.027522 10.462149 49 12 9.538194 9.972431 9.565763 10.434237 10.027569 10.461806 48 13 9.538538 9.972385 9.566153 10.433847 10.027615 10.461462 47 14 9.538880 9.972338 9.566542 10.433458 10.027662 10.461120 46 15 9.539223 9.972291 9.566932 10.433068 10.027709 10.460777 45 16 9.539565 9.972245 9.567320 10.432680 10.027755 10.460435 44 17 9.539907 9.972198 9.5G7709 10.432291 10.027802 10.460093 43 18 9.540249 9.972151 9.568098 10.431902 10.027849 10.459751 42 19 9.540590 9.972105 9.568486 10.431514 10.027895 10.459410 41 20 9.540931 9 . 972058 9.568873 10.431127 10.027942 10.459069 40 21 9.541272 9.972011 9.569261 10.430739 10.027989 10.458728 39 22 9.541613 9.971964 9.569648 10.430352 10.028036 10.458387 38 23 9.541953 9.971917 9.570035 10.429965 10.028083 10.458047 37 24 9.542293 9.971870 9.570422 10.429578 10.028130 10.457707 36 25 9.542632 9.971823 9.570809 10.429191 10.028177 10.457368 35 26 9.542971 9.971776 9.571195 10.428805 10.028224 10.457029 34 27 9.543310 9.971729 9.571581 10.428419 10.028271 10.456690 33 28 9.543649 9 971682 9.571967 10.428033 10.028318 10.456351 32 29 9.543987 9.971635 9.572352 10.427648 10.028365 10.456013 31 30 9.544325 9.971588 9.572738 10.427262 10.028412 10.455675 30 31 9.544G63 9.9/1540 9.573123 10.426877 10.028460 10.455337 'z9 32 9.545000 9.971493 9.573507 10.426493 10.028507 10.455000 28 33 9.545338 9.971446 9.573892 10.426108 10.028554 10.454662 27 31 9.545674 9.971398 9.574276 10.425724 10.028602 10.454326 26 35 9.546011 9.971351 9.574660 10.425340 10.028649 10.453989 25 36 9.546347 9.971303 9.575044 10.424956 10.028697 10.453653 24 37 9.546683 9.971256 9.575127 10.424573 10.028744 10.453317 23 38 9.547019 9.971208 9.575810 10.424190 10.028792 10.452981 22 39 9.547354 9.971161 9.576193 10.423807 10.028839 10.452646 21 40 9.547689 9.971113 9.576576 10.423424 10.028887 10.452311 20 41 9.546024 9.971066 9.576958 10.423012 10.028934 10.451976 19 42 9.548359 9.971018 9 577341 10.422659 10.028982 10.451641 18 43 9.548693 9.970970 9.577723 10.422277 10.029030 10.451307 17 44 9.549027 9.970922 9.578104 10.421896 10.029078 10.450973 16 45 9.549360 9.970874 9.578486 10.421514 10.029126 10.450640 15 46 9.549693 9.970827 9.578867 10.421133 10.029173 10.450307 14 47 9.550026 9.970779 9.579248 10.420752 10.029221 10.449974 13 48 9.550359 9.970731 9.579629 10.420371 10.029269 10.449641 12 49 9.550692 9.970683 9.580009 10.419991 10.029317 10.449308 11 SO 9.551024 9.970635 9.580389 10.419611 10.029365 10.448976 10 51 9.551356 9.970586 9.580769 10.419231 10.029414 10.448644 9 52 9.551687 9.970538 9.581149 10.418851 10.029462 10.448313 8 53 9.552018 9.970490 9.581528 10.418472 10.029510 10.447982 7 54 9.552349 9.970442 9.581907 10.418093 10.029558 10.447651 6 55 9.552680 9.970394 9.582286 10.417714 10.029606 10.447320 5 56 9.553010 9.970345 9.582665 10.417335 10.029655 10.446990 4 57 9.553341 9.970297 9.583043 10.416957 10.029703 10.446659 3 58 9.553670 9.970249 9.583422 10.416578 10.029751 10.446330 2 59 9.554000 9.970200 9.583800 10.416200 10.029800 10.446000 1 60 9 554329 9. 0701.- -2 9.584177 10.415823 10.029848 10.445671 M. Co-sine. Sine. | Co-tang. Tangent. Co-sec. Secant. M. Ui> Degrees. 164 TABLE II. LOGAKITHMIC SINES, TANGENTS, AND SECANTS. 21 Degrees. M. Sine. Co-sine. Tangent. Co-tang. Secant. Co-sec. M. u 9.554329 9.9/0152 9.584177 10.415823 10.029848 10.44567 i (JO 1 9.554G58 9.970103 9.584555 10.415445 10.029897 10.445342 59 2 9 554987 9.970055 9.584932 10.415068 10.029945 10.445013 58 3 9.555315 9.970006 9.585309 10.414691 10.029994 10.444685 57 4 9.555643 9.969957 9.585686 10.414314 10.030043 10.444357 56 5 9.555971 9.969909 9.586062 10.413938 10.030091 10.444029 55 G 9.556299 9.969860 9.586439 10.413561 10.030140 10.443701 54 7 9.556626 9.969811 9.586815 10.413185 10.030189 10.443374 53 8 9.556953 9.969762 9.587190 10.412810 10.030238 10.443047 52 9 9.557280 9.969714 9.587566 10.412434 10.030286 10.442720 51 10 9.557606 9.969665 9.587941 10.412059 10.030335 10.442394 50 11 9.557932 9.969616 9.588316 10.411684 10.030384 10.442068 49 12 9.558258 9.969567 9.588691 10.411309 10.030433 10.441742 48 13 9.558583 9.969518 9.589066 10.410934 10.030482 10.441417 47 14 9.558909 9.969469 9.589440 10.410560 10.030531 10.411091 46 15 9.559234 9.969420 9.589814 10.410186 10.030580 10.440766 45 1G 9.559558 9.969370 9.590188 10.409812 10.030630 10.440442 44 17 9.559883 9.969321 9.590562 10.409438 10.030679 10.440117 43 18 9.560207 9.969272 9.590935 10.409065 10.030728 10.439793 42 19 9.560531 9.969223 9.591308 10.408692 10.030777 10.439469 41 20 9.560855 9.969173 9.591681 10.408319 10.030827 10.439145 40 21 9.561178 9.969124 9.592054 10.407946 10.030876 10.43882'J 39 22 9.561501 9.969075 9.592426 10.407574 10.030925 10.438499 38 23 9.561824 9.969025 9.592798 10.407202 10.030975 10.438176 37 24 9.562146 9.968976 9.593171 10.406829 10.031024 10.437854 36 25 9.562468 9.968926 9.593542 10.406458 10.031074 10.437532 35 26 9.562790 9.968877 9.593914 10.406086 10.031123 10.437210 34 27 9.563112 9.968827 9.594285 10.405715 10.031173 10.436888 33 28 9 563433 9.968777 9.594656 10.405344 10.031223 10.436567 32 29 9.563755 9.968728 9.595027 10.404973 10.031272 10.436245 31 30 9.564075 9.968678 9.595398 10.404602 10.031322 10.435925 30 31 9 564396 9.968628 9.595768 10.404232 10.031372 10.435604 W 32 9.564716 9.968578 9.596138 10.403862 10.031422 10.435284 28 33 9.565036 9.968528 9.596508 10.403492 10.031472 10.434964 27 34 9.565356 9.968479 9.596878 10.403122 10.031521 10.434644 26 35 9.56567G 9.968429 9.597247 10.402753 10.031571 10.434324 25 36 9.565995 9.968379 9.597616 10.402384 10.031621 10.434005 24 37 9.566314 9.968329 9.597985 10.402015 10.031671 10.433686 23 38 9.566632 9.968278 9.598354 10.401646 10.031722 10.433368 22 39 9.566951 9.968228 9.598722 10.401278 10.031772 10.433049 21 40 9.507269 9.968178 9.599091 10.400909 10.031822 10.432731 20 41 9 5U7587 9.968128 9.599459 10.400541 l'J.031872 10.432413 1U 42 9.567904 9.968078 9.599827 10.400173 10.031922 10.432096 18 43 9.568222 9.968027 9.600194 10.399806 10.031973 10.431778 17 44 9.568539 9.967977 9.600562 10.399438 10.032023 10.431461 16 45 9:568856 9.967927 9.600929 10.399071 10.032073 10.431144 15 46 9.569172 9.967876 9.601296 10.398704 10.032124 10.430828 14 47 9.569488 9.967826 9.601662 10.398338 10.032174 10.430512 13 48 9.569804 9.967775 9.602029 10.397971 10.032225 10.430196 12 49 9.570120 9.967725 9.602395 10.397605 10.032275 10.429880 11 50 9.570435 9.967674 9.602761 10.397239 10.032326 10.429565 10 51 9.57U751 9.967624 9.603127 10.396873 10.032376 10.429249 9 52 9.571066 9.967573 9.603493 10.396507 10.032427 10.428934 8 53 9.571380 9.967522 9.603858 10.396142 10.032478 10.428620 7 54 9.571695 9.967471 9.604223 10.395777 10.032529 10.428305 6 55 9.572009 9.967421 9.604588 10.395412 10.032579 10.427991 5 56 9.572323 9.967370 9.604953 10.395047 10.032630 10.427677 4 57 9.572636 9.967319 9.605317 10.394683 10.032681 10.427364 3 58 9.572950 9.967268 9.605682 10.394318 10.032732 10.427050 2 59 9.573263 9.967217 9.606046 10.393954 10.032783 10.426737 1 CO 9.573575 9.967166 9.606410 10.393590 10.032834 10.426425 M. ) Co-sine. Sine. 3o-tang. Tangent. Co-sec. Secant. M. 68 Degrees. TABLE II. 165 LOGARITHMIC SINES, TANGENTS, AND SECANTS. 22 Degrees. M. Sine. Co-sine. Tangent. Co-tang. Secant. Co-sec. M. 9.573575 9.907106 9.G06410 10.393590 10 032834 10.4264^5 60 ] 9.573888 9.967115 9.606773 10.393227 10.032885 10.426112 59 2 9.574200 9.967064 9.607137 10.392863 10.032936 10.425800 58 3 9.574512 9.967013 9.607500 10.392500 10.032987 10.425488 57 4 9.574824 9.966961 9.607863 10.392137 10.033039 10.425176 56 5 9.575136 9.966910 9.608225 10.391775 10.033090 10.424864 55 6 9.575447 9.966859 9.608588 10.391412 10 033141 10.424553 54 7 9.575758 9.966808 9.608950 10.391050 10.033192 10.424242 53 8 9.576069 9.966756 9.609312 10.390688 10.033244 10.423931 52 9 9.576379 9.966705 9.609674 10.390326 10.033295 10.423621 51 10 9.576689 9.966653 9.610036 10.389964 10.033347 10.423311 50 11 9.57U999 9.9GOC02 9.610397 10.389603 10.033398 10.423001 49 12 9.577309 9.966550 9.610759 10.389241 10.033450 10.422691 48 13 9.577618 9.966499 9.611120 10.388-880 10.033501 10.422382 47 14 9.577927 9.966447 9.611480 10.388520 10.033553 10.422073 46 15 9.578236 9.966395 9.611841 10.388159 10.033605 10.421764 45 1G 9.578545 9.966344 9.612201 10.387799 10.033656 10.421455 44 17 9.578853 9.966292 9.612561 10.387439 10.033708 10.421147 43 18 9.579162 9.966240 9.612921 10.387079 10.033760 10.420838 . 42 19 9.579470 9.966188 9.613281 10.386719 10.033812 10.420530 41 20 9.579777 9.966136 9.613641 10.386359 10.033864 10.420223 40 21 9. 580085 9.966085 9.614000 10.386000 10.033915 10.419915 39 22 9.580392 9.966033 9.614359 10.385641 10.033967 10.419608 38 23 9.580699 9.965981 9.614718 10.385282 10.034019 10.419301 37 24 9.581005 9.965929 9.615077 10.384923 10.034071 10.418995 36 25 9.581312 9.965876 9.615435 10.384565 10.034124 10.418688 35 26 9.531618 9.965824 9.615793 10.384207 10.034176 10.418382 34 27 9.581924 9.965772 9.616151 10.383849 10.034228 10.418076 33 28 9.582229 9 965720 9.616509 10.383491 10.034280 10.417771 32 29 9.582535 9 965668 9.616867 10.383133 10.034332 10.417465 31 30 9 582840 9 965615 9.617224 10.382776 10.034385 10.417160 30 31 9.583145 9.965563 9.617582 10.382418 10.034437 10.416855 29 32 9.583449 9.965511 9.617939 10.382061 10.034489 10.416551 28 33 9.583754 9 965458 9.618295 10.381705 10.034542 10.416246 27 34 9.584058 9 965406 9.618652 10.381348 10.034594 10.415942 26 35 9.584361 9.965353 9.619008 10.380992 10.034647 10.415639 25 36 9.584665 9 965301 9.619364 10.380636 10.034699 10.415335 24 37 9.584968 9.965248 9.619721 10.380279 10.034752 10.415032 23 38 9.585272 9.965195 9.620076 10.379924 10.034805 10.414728 22 39 9.585574 9.965143 9.620432 10.379568 10.034857 10.414426 21 40 9.585877 9.965090 9.620787 10.379213 10.034910 10.414123 2u 41 9.5S6179 9.965037 9.621142 10.378858 10.034963 10.413821 19 42 9.586482 9.964984 9.621497 10.378503 10.035016 10.413518 18 43 9 586783 9.964931 9.621852 10.378148 10.035069 10.413217 17 44 9.587085 9.964879 9.622207 10.377793 10.035121 10.412915 16 45 9.587386 9.964826 9.622561 10.377439 10.035174 10.412614 15 46 9.587688 9.964773 9.622915 10.377085 10.035227 10.412312 14 47 9.587989 9.964720 9.623269 10.376731 10.035280 10.412011 13 48 9.588289 9.964666 9.623623 10.376377 10.035334 10.411711 12 49 9.588590 9.964613 9.623976 10.376024 10.035387 10.411410 11 50 9.588890 9.964560 9.624330 10.375670 10.035440 10.411110 10 51 9.589190 9.904507 9.624683 10.375317 10.035493 10.410810 9 52 9.589489 9.964454 9.625036 10.374964 10.035546 10.410511 8 53 9.589789 9.964400 9.625388 10.374612 10.033600 10.410211 7 54 9.590088 9.964347 9.625741 10.374259 10.035653 10.409912 6 55 9.590387 9.964294 9.626093 10.373907 10.035706 10.409613 5 56 9.590686 9.964240 9.626445 10.373555 10.035760 10.409?14 4 57 9.590984 9.964187 9.626797 10.373203 10.035813 10.409016 3 58 9.591282 9.964133 9.627149 10.372851 10.035867 10.408718 2 59 9.591580 9.964080 9.627501 10.372499 10.035920 10.408420 1 60 9.591878 9.961026 9.627852 10.372148 10.035974 10.408122 M. Co-sine. Sine. | Co-tang. | Tangent. Co-sec. Secant. M. O7 Degrees. 166 TABLE II. LOGARITHMIC SINES, TANGENTS, AND SECANTS. 23 Degrees. M. Sine. Co-sine. |Tangent.| Co-tang. Secant. Co-sec. M. 1 2 3 4 5 6 7 8 9 10 y. 5^1878 9 592176 9 592473 9.592770 9.593067 9.593363 9.593659 9.593955 9.594251 9.594547 9.594842 9.904026 9.963972 9.963919 9.963865 9 963811 9.963757 9.963704 9.963650 9.963596 9.963542 9.963488 9.6z7852 9.628203 9.628554 9.628905 9.629255 9 629606 9.629956 9.630306 9.630656 9.631005 9.631355 10.37^148 10.371797 10.371446 10.371095 10.370745 10.370394 10.370044 10.369694 10.369344 10.368995 10.368645 10.035974 10.036028 10.036081 10.036135 10.036189 10.036243 10.036296 10.036350 10.036404 10.036458 10.036512 10.408122 10.407824 10.407527 10.407230 10.406933 10.406637 10.406341 10.406045 10.405749 10.405453 10.405158 60 59 58 57 56 55 54 53 52 51 -50 11 12 13 14 15 16 17 18 19 20 9.59,3137 9.595432 9.595727 9.596021 9.596315 9.596609 9.596903 9.597196 9.597490 9.597783 9.963434 9.963379 9.963325 9.963271 9.963217 9.963163 9.963108 9.963054 9.962999 9.962945 9.631704 9.632053 9.632401 9 632750 9.633098 9 633447 9.633795 9 634143 9.634490 9 634838 10.368296 10.367947 10.367599 10.367250 10.366902 10.366553 10.366205 10.365857 10.365510 10.365162 10.036566 10.036621 10.036675 10.036729 10.036783 10.036837 10.036892 10.036946 10.037001 10.037055 10.404863 10.404568 10.404273 10.403979 10.403685 10.403391 10.403097 10.402804 10.402510 10.402217 49 48 47 46 45 44 43 42 41 40 21 22 23 24 25 26 27 28 29 30 9.598075 9.598368 9.598660 9.598952 9.599244 9.599536 9.599827 9.600118 9.600409 9.G00700 9.962890 9.962836 9.962781 9.962727 9.962672 9.962617 9.962562 9.962508 9.962453 9.962398 9.635185 9.635532 9.635879 9.636226 9.636572 9.636919 9.637265 9 637611 9.637956 9.638302 10.364815 10.364468 10.364121 10.363774 10.363428 10.363081 10.362735 10.362389 10.362044 10.361698 10.037110 10.037164 10.037219 10.037273 10.037328 10.037383 10.037438 10.037492 10.037547 10.037602 10.401925 10.401632 10.401340 10.401048 10.400756 10.400464 10.400173 10.399882 10.399591 10.399300 3y 38 37 36 35 34 33 32 31 30 31 32 33 34 35 36 37 38 39 40 9.60U990 9.601280 9.C01570 9.601860 9.602150 9.602439 9.602728 9.603017 9.603305 9.603594 9.962343 9.962288 9.962233 9.962178 9.902123 9.962067 9 962012 9.961957 9.961902 9.961846 9.638647 9.638992 9.639337 9.639682 9.640027 9.640371 9.640716 9.641060 9.641404 9.641747 10.361353 10.361008 10.360663 10.360318 10.359973 10.359629 10.359284 10.358940 10.358596 10.358253 10.037657 10.037712 10.037767 10.037822 10.037877 10.037933 10.037988 10.038043 10.038098 10.038154 10.399010 10.398720 10.398430 10.398140 10.397850 10.397561 10.397272 10.396983 10.396695 10.396406 29 28 27 26 25 24 23 2 ! 2 21 20 41 42 43 44 45 46 47 48 49 50 U. 00388 2 9.604170 9.604457 9.604745 9.605032 9.605319 9.605606 9.605892 9.606179 9 606465 9.961791 9 961735 9.961680 9.961624 9.961569 9.961513 9.961458 9.961402 9.961346 9.961290 9.642091 9.642434 9.642777 9.643120 9.643463 9 643806 9.644148 9.644490 9.644832 9 645174 10.357909 10.357566 10.357223 10.356880 10.356537 10.356194 10.355852 10.355510 10.355168 10.354826 10.038209 10.038265 10.038320 10.038376 10.038431 10.038487 10.038542 10.038598 10.038654 10038710 10.396118 10.395830 10.395543 10.395255 10.394968 10.394681 10.394394 10.394108 10.393821 10.393535 19 18 17 16 15 14 13 12 11 10 51 52 53 54 55 56 57 58 59 60 9.606751 9.607036 9.607322 9.607607 9.607892 9.608177 9.608461 9.608745 9.609029 9.609313 9.961235 9.961179 9.961123 9.961067 9.961011 9.960955 9.960899 9.960843 9.960786 9.960730 9.645516 9.645857 9.646199 9.646540 9.646881 9.647222 9 647562 9.647903 9.648243 9.648583 10.354484 10.354143 10.353801 10.353460 10.353119 10.352778 10.352438 10.352097 10.351757 10.351417 10.038765 10.038821 10.038877 10.038933 10.038989 10.039045 10.039101 10.039157 10.039214 10.039270 10.393249 10.392964 10.392678 10.392393 10.392108 10.391823 10.391539 10.391255 10.390971 10.390687 9 8 7 6 5 4 3 2 1 M. Co-sine. Sine. Co-tahg. Tangent. Co-sec. Secant. M. 66 Decrees. TABLE H. 1G7 LOGARITHMIC SINES, TANGENTS, AND SECANTS. 24 Degrees. M. Sine. Co-sine. (Tangent. Co- tang. Secant. Co-sec. M. 1 J. 609313 9.9(50730 9.648583 10.351417 10.039270 10.390687 60 1 9.609597 9.960674 9.648923 10.351077 10.039326 10.390403 59 2 9.609880 9.960618 9.649263 10.350737 10.039382 10.390120 58 3 9.610164 9.960561 9.649602 10.350398 10.039439 10.389836 57 4 9.610447 9.960505 9.649942 10.350058 10.039495 10.389553 56 5 9.610729 9.960448 9.650281 10.349719 10.039552 10.389271 55 6 9.611012 9.960392 9.650620 10.349380 10.039608 10.388988 54 7 9.611294 9.960335 9.650959 10.349041 10.039665 10.388706 53 8 9.611576 9 960279 9.651297 10.348703 10.039721 10.388424 52 9 9.611858 9.960222 9.651636 10.348364 10.039778 10.388142 51 10 9.612140 9.960165 9.651974 10.348026 10.039835 10.387860 50 11 9.6124-21 9.960109 9.652312 10.347688 10.039891 10.387579 49 12 9.612702 9.960052 9.652650 10.347350 10.039948 10.387298 48 13 9.612983 9.959995 9.652988 10.347012 10.040005 10.387017 47 14 9.613264 9.959938 9.653326 10.346674 10.040062 10.386736 46 15 9.613545 9.959882 9.653663 10.346337 10.040118 10.386455 45 ]6 9.613825 9.959825 9.654000 10.346000 '10.040175 10.386175 44 17 9.614105 9.959768 9.654337 10.345663 10.040232 10.385895 43 18 9.614385 9.959711 9.654674 10.345326 10.04028y 10.385615 42 19 9.614665 9.959654 9.655011 10.344989 10.040346 10.385335 41 20 9 614944 9.959596 9.655348 10.344652 10.040404 10.385056 40 21 9.615223 9.959539 9.655684 10.344316 10.040461 10.384777 39 22 9.615502 9.959482 9.656020 10.343980 10.040518 10.384498 38 23 9.615781 9.959425 9.656356 10.343644 10.040575 10.384219 37 24 9.616060 9.959368 9.656692 10.343308 10.040632 10.383940 36 25 9.616338 9.959310 9.657028 10.342972 10.040690 10.383662 35 26 9.616616 9.959253 9.657364 10.342636 10.040747 10.383384 34 27 9.616894 9.959195 9.657699 10.342301 10.040805 10.383106 33 28 9 617172 9.959138 9.658034 10.341966 10.040862 10.382828 32 29 9.617450 9.959080 9.658369 10.341631 10.040919 10.382550 31 30 9 617727 9.959023 9.65.8704 10.341296 10.040977 10.382273 30 31 9.618004 9.958965 9.659039 10.340961 10.041035 10.381996 *9 32 9.618281 9.958908 9.659373 10.340627 10.041092 10.381719 28 33 9.618558 9.958850 9.659708 10.340292 10.041150 10.381442 27 34 9.618834 9.958792 9.660042 10.339958 10.041208 10.381166 26 35 9.619110 9.958734 9.660376 10.339624 10.041266 10.380890 25 36 9.619386 9.958677 9.660710 10.339290 10.041323 10.380614 24 37 9.619662 9.958619 9.661043 10.338957 10.041381 10.380338 23 38 9.619938 9.958561 9.661377 10.338623 10.041439 10.380062 22 39 9.620213 9.958503 9.661710 10.338290 10.041497 10.379787 21 40 9.620488 9.958445 9.662043 10.337957 10.041555 10.379512 '20 41 9.620763 9.958387 9.662376 10.3376*4 10.041613 10.379237 19 42 9.621038 9.958329 9.662709 10.337291 10.041671 10.378962 18 43 9.621313 9.958271 9.663042 10.336958 10.041729 10.378687 17 44 9.621587 9.958213 9 663375 10.336625 10.041787 10.378413 16 45 9.621861 9.958154 9.663707 10.336293 10.041846 10.378139 15 46 9.622135 9.958096 9.664039 10.335961 10.041904 10.377865 14 47 9.622409 9.958038 9.664371 10.335629 10.041962 10.377591 13 48 9.622682 9.957979 9.664703 10.335297 10.042021 10.377318 12 49 9.622956 9.957921 9.665035 10.334965 10.042079 10.377044 11 50 9.623229 9.957863 9.665366 10.334634 10.042137 --- 10.376771 10 51 9.623502 9.957804 9.665697 10.334303 10.042196 10.376498 9 52 9.623774 9.957746 9.666029 10.333971 10.042254 10.376226 8 53 9.624047 9.957687 9.666360 10.333640 10.042313 10.375953 7 54 9.624319 9.957628 9.666691 10.333309 10.042372 10.375681 6 55 9.624591 9.957570 9.667021 10.332979 10.042430 10.375409 5 56 9.624863 9.957511 9.667352 10.332648 10.042489 10.375137 4 57 9.625135 9.957452 9.667682 10.332318 10.042548 10.374865 3 58 9.625406 9.957393 9.668013 10.331987 10.042607 10.374594 2 59 9.625677 9.957335 9.668343 10.331657 10.042665 10.374323 1 60 9.G25948 9.957270 9.668672 10.331328 10.042724 10.374052 M. Co-sine. Sine. | Co-tang. Tangent. Co-sec. Secant. M. 65 I)egreH. 108 TABLE II. LOGARITHMIC SIGNS, TANGENTS AND SECANTS. 25 Degrees. M. Sine. Co-sine. Tangent. Co-tang. Secant. Co-sec. M. 9.625948 9.9-37^(5 9. (5(5867 J 10.331327 10.042724 10.3740^ GO 1 9.626219 9 957217 9.669002 10.330998 10.042783 10.373781 59 2 9.626490 9.957158 9.669332 10.330668 10.042842 10.373510 58 3 9.620760 9.957099 9.669661 10.330339 10.042901 10.373240 57 4 9 627030 9.957040 9.669991 10.330009 10.042960 10.372970 56 5 9.627300 9.956981 9.670320 10.329680 10.043019 10.372700 55 6 9.627570 9.956921 9.670649 10.329351 10.043079 10.372430 54 7 9.627840 9.956862 9.670977 10.329023 10.043138 10.372160 53 8 9.628109 9.956803 9.671306 10.328694 10.043197 10.371891 52 9 9.628378 9.956744 9.671634 10.328366 10.043256 10.371622 51 10 9.628647 9.956684 9.671963 10.328037 10.043316 10.371353 50 11 9.028916 9.956625 9.672291 10.327709 10.043375 10.371084 49 12 9.629185 9.956566 9.672619 10.327381 10.043434 10.370815 48 13 9.629453 9.956506 9.672947 10.327053 10.043494 10.370547 47 14 9.629721 9.956447 9.673274 10.326726 10.043553 10.370279 46 15 9.629989 9.956387 9.673602 10.326398 10.043613 10.370011 45 16 9.630257 9.956327 9.673929 10.326071 10.043673 10.369743 44 17 9.630524 9 956268 9.674257 10.325743 10.043732 10.369476 43 18 9.630792 9.956208 9.674584 10.325416 10.043792 10.369208 42 19 9.631059 9.956148 9.674910 10.325090 10.043852 10.368941 41 20 9.631326 9.956089 9.675237 10.324763 10.043911 10.368674 40 21 9.631593 9.956029 9.675564 10.324436 10.043971 10.368407 39 22 9.631859 9.955969 9.675890 10.324110 10.044031 10.368141 38 23 9.632125 9.955909 9.676217 10.323783 10.044091 10.367875 37 24 9.632392 9.955849 9.676543 10.323457 10.044151 10.367608 3G 25 9.632658 9.955789 9.676869 10.323131 10.044211 10.367342 35 26 9 632923 9.955729 9.677194 10.322806 10.044271 10.367077 34 27 9.633189 9.955669 9 677520 10.322480 10.044331 10.366811 33 28 9.633454 9.955609 9.677846 10.322154 10.044391 10.366546 32 29 9.633719 9.955548 9.678171 10.321829 10.044452 10.366281 31 30 9.633984 9.955488 9.678496 10.321504 10.044512 10.366016 30 31 9. (534249 9.955428 9.678821 10.321179 10.044572 10.365751 29 32 9.634514 9.955368 9.679146 10.320854 10.044632 10.365486 28 33 9.634778 9.955307 9.679471 10.520529 10.044693 10.365222 27 34 9.635042 9.955247 9.679795 10.320205 10.044753 10.364958 26 35 9.635306 9.955186 9.680120 10.319880 10.044814 10.364694 25 36 9.635570 9.955126 9.680444 10.319556 10.044874 10.3644GO 24 37 9.635834 9.955065 9.680768 10.319232 10.044935 10.364166 23 38 9.636097 9.955005 9.681092 10.318908 10.044995 10.383903 22 39 9.636360 9.954944 9.681416 10.318584 10.045056 10.363640 21 40 9.636623 9.954883 9.681740 10.318260 10.045117 10.363377 20 41 9. 63(5886 9.954823 9. 6S2063 10.317937 10.045177 10.3(53114 19 42 9.637148 9.954762 9.682387 10.317613 10.045238 10.362852 18 43 9.637411 9.954701 9.682710 10.317290 10.045299 10.362589 17 44 9.637673 9.954640 9.683033 10.316967 10.045360 10.362327 16 45 9.637935 9.954579 9.683356 10.316644 10.045421 10.362065 15 46 9.638197 9.954518 9.683679 10.316321 10.045482 10.361803 14 47 9.638458 9.954457 9.684001 10.315999 10.045543 10.361542 13 48 9.638720 9.954396 9.684324 10.315676 10.045604 10.361280 12 49 9.638981 9.954335 9.684646 10.315354 10.045665 10.361019 11 50 9.639242 9.954274 . 9.684968 10.315032 10.045726 10.360758 10 51 9.639503 9.954213 9.685290 10.314710 10.045787 10.360497 9 52 9.639764 9.954152 9.685612 10.314388 10.045848 10.360236 8 53 9.640024 9.954090 9.685934 10.314066 10.045910 10.359976 7 54 9.640284 9.954029 9.686255 10.313745 10.045971 10.359716 6 55 9.640544 9.953968 9.686577 10.313423 10.046032 10.359456 5 56 9.640804 9.953906 9.686898 10.313102 10.046094 10.359196 4 57 9.641064 9.953845 9.687219 10.312781 10.046155 10.358936 3 58 9.641324 9.953783 9.687540 10.312460 10.046217 10.358676 2 59 9.641583 9.953722 9.687861 10.312139 10.046278 10.358417 1 60 9.641842 9.953660 9.688182 10.311818 10.046340 10.358158 M. Co-sine. Sine. Co-tang. Tangent. Co-sec. Secant. M. O4 Degrees. TABLE II. 169 Z/OGABITHMIC SINES, TANGENTS, AND SECANTS. 26 Decrees. M. | Sine. Co-sine. Tangent. Co-tang. Secant. Co-sec. | M. u 9.641842 9.953660 9.688182 1U. 311818 10.04(3340 10.35158 00 1 9.642101 9.953599 9.688502 10.311498 10.046401 10.357899 59 2 9.642360 9.953537 9.688823 10.311177 10.046463 10.357640 58 3 9.642618 9.953475 9.689143 10.310857 10.046525 10.357382 57 4 9.642877 9.953413 9.689463 10.310537 10.046587 10.357123 56 3 9.643135 9.953352 9.689783 10.310217 10.046648 10.356865 55 6 9.643393 9.953290 9.690103 10.309897 10.046710 10.356607 54 7 9.643650 9.953228 9.690423 10.309577 10.046772 10.356350 53 8 9.643908 9.953166 9.690742 10.309258 10.046834 10.356092 52 9 9.644165 9.953104 9.691062 10.308938 10.046896 10.355835 51 10 9 644423 9.953042 9.691381 10.308619 10.046958 10.355577 50 11 9.644680 9.952980 9.691700 10.308300 10.0470*0 10.3553^:0 49 12 9.644936 9.952918 9.692019 10.307981 10.047082 10.355064 48 13 9.645193 9.952855 9.692338 10.307662 10.047145 10.354807 47 14 9.645450 9.952793 9.692656 10.307344 10.047207 10.354550 46 15 9.645706 9.952731 9.692975 10.307025 10.047269 10.354294 45 16 9.645962 9.952669 9.693293 10.306707 10.047331 10.354038 44 17 9.646218 9.952606 9.693612 10.306388 10.047394 10.353782 43 18 9.646474 9.952544 9.693930 10.306070 10.047456 10.353526 42 19 9.646729 9.952481 9.694248 10.305752 10.047519 10.353271 41 20 9.646984 9.952419 9.694566 10.305434 10.047581 10.353016 40 21 9.647240 9.952356 9.694883 10.305117 10.047644 10.35^700 39 22 9.647494 9.952294 9.695201 10.304799 10.047706 10.352506 38 23 9.647749 9.952231 9.695518 10.304482 10.047769 10.352251 37 24 9.648004 9.952168 9.695836 10.304164 10.047832 10.351996 36 25 9.648258 9.952106 9.696153 10.303847 10.047894 10.351742 35 26 9.648512 9.952043 9.696470 10.303530 10.047957 10.351488 34 27 9.648766 9.951980 9 696787 10.303213 10.048020 10.351234 33 28 9.649020 9.951917 9.697103 10.302897 10.048083 10.350980 32 29 9.649274 9.951854 9.697420 10.302580 10.048146 10.350726 31 30 9.649527 9.951791 9.697736 10.302264 10.048209 10.350473 30 31 9 649781 9.951728 9.698053 10.301947 10.048272 10.350219 29 32 9.650034 9.951665 9.698369 10.301631 10.048335 10.349966 28 33 9.650287 9.951602 9.698685 10.301315 10.048398 10.349713 27 34 9.650539 9.951539 9.699001 10.300999 10.048461 10.349461 26 35 9.650792 9.951476 9.699316 10.300684 10.048524 10.349208 25 ' 36 9.651044 9.951412 9.699632 10.300368 10.048588 10.348956 24 37 9.651297 9.951349 9.699947 10.300053 10.048651 10.348703 23 38 9.651549 9 951286 9.700263 10.299737 10.048714 10.348451 22 39 9.651800 9.951222 9.700578 10.299422 10.048778 10.348200 21 40 9.652052 9.951159 9.700893 10.299107 10.048841 10.347948 20 H~ 9 652304 9.951096 9.701208 10.298792 10.048904 10.347696 iy 42 9.652555 9.951032 9.701523 10.298477 10.048968 10.347445 18 43 9 652806 9.950968 9.701837 10.298163 10.049032 10.347194 17 44 9.653057 9.950905 9.702152 10.297848 10.049095 10.346943 16 45 9.653308 9.950841 9.702466 10.297534 10.049159 10.346692 15 46 9.653558 9.950778 9.702780 10.297220 10.049222 10.346442 14 47 9.653808 9.950714 9.703095 10.296905 10.049286 10.346192 13 48 9.654059 9.950650 9.703409 10.296591 10.049350 10.345941 12 49 9.654309 9.950586 9.703723 10.296277 10.049414 10.345691 11 50 9.654558 9.950522 9.704036 10.295964 10.049478 10.345442 10 51 9.654808 9.950458 9.704350 10.295650 10.049542 10.345192 9 52 9.655058 9.950394 9.704663 10.295337 10.049606 10.344942 8 53 9.655307 9.950330 9.704977 10.295023 10.049670 10.344693 7 54 9.655556 9.950266 9.705290 10.294710 10.049734 10.344444 6 55 9.655805 9.950202 9.705603 10.294397 10.049798 10.344195 5 56 9.656054 9.950138 9.705916 10.294084 10.049862 10.343946 4 57 9.656302 9.950074 9.706228 10.293772 10.049926 10.343698 3 58 9.656551 9.950010 9.706541 10.293459 10.049990 10.343449 2 59 9.656799 9.949945 9.706854 10.293146 10.050055 10.343201 1 60 9.657047 9.949881 9.707166 10.292834 10.050119 10.342953 M. Co-sine. Sine. Co-tang. Tangent. Co-sec. Secant. M. O3 Degrees. 170 TABLE II. LOGABITHMIC SINES, TANGENTS, AND SECANTS. 27 Degrees. M. Sine. Co-sine. Tangent. Co-tang. Secant. Co-sec. M. 9. 667 047 9.949881 U. 707 106 10.292831 10.050119 10.342953 00 1 9.657295 9.949816 9.707478 10.292522 10.050184 10.342705 E9 2 9.657542 9.949752 9.707790 10.292210 10.050248 10.342458 58 3 9.657790 9.949688 9.708102 10.291898 10.050312 10.342210 57 4 9.658037 9.949623 9.708414 10.291586 10.050377 10.341963 56 5 9.658284 9.949558 9.708726 10.291274 10.050442 10.341716 55 6 9.658531 9.949494 9.709037 10.290963 10.050506 10.341469 54 7 9.658778 9.949429 9.709349 10.290651 10.050571 10.341222 53 8 9.659025 9.949364 9.709660 10.290340 10.050636 10.340975 52 9 9.659271 9.949300 9.709971 10.290029 10.050700 10.340729 51 10 9.659517 9.949235 9.710282 10.289718 10.050765 10.340483 50 11 9.059763 9.949170 9.710593 10.289407 10.050850 10.340237 49 12 9.660009 9.949105 9.710904 10.289096 10.050895 10.339991 48 13 9.66Q255 9.949040 9.711215 10.288785 10.050960 10.339745 47 14 9.660501 9.948975 9.711525 10.288475 10.051025 10.339499 46 15 9.660746 9.948910 9.711836 10.288164 10.051090 10.339254 45 10 9.660991 9.948845 9.712146 10.287854 10.051155 10.339009 44 17 9.661236 9.948780 9.712456 10.287544 10.051220 10.338764 43 18 9.661481 9.948715 9.712766 10.287234 10.051285 10.338519 42' 19 9.661726 9.948650 9.713076 10.286924 10.051350 10.338274 41 20 9.661970 9.948584 9.713386 10.286614 10.051416 10.338030 40 21 9.6(52214 y. 948519 9. 7 13690 10.286304 10.051481 10.337780 b9 22 9.662459 9.948454 9.714005 10.285995 10.051546 10.337541 38 23 9.662703 9.948388 9.714314 10.285686 10.051612 10.337297 37 24 9.662946 9.948323 9.714624 10.285376 10.051677 10.337054 36 25 9.663190 9.948257 9.714933 10.285067 10.051743 10.336810 35 26 9.663433 9.948192 9.715242 10.284758 10.051808 10.336567 34 27 9.663677 9.948126 9.715551 10.284449 10.051874 10.336323 33 28 9.663920 9 948060 9.715860 10.284140 10.051940 10.336080 32 29 9.664163 9.947995 9.716168 10.283832 10.052005 10.335837 31 30 9.664406 9.947929 9.716477 10.283523 10.052071 10.335594 30 31 9. 004048 9.947803 9.716785 10.283215 10.052137 10.335352 29 32 9.664891 9.947797 9.717093 10.282907 10.052203 10.335109 28 33 9.6G5133 9.947731 9.717401 10.282599 10.052269 10.334867 27 34 9.665375 9.947605 9.717709 10.282291 10.052335 10.334625 26 35 9.665617 9.947600 9.718017 10.281983 10.052400 10.334383 25 36 9.665859 9.947533 9.718325 10.281675 10.052467 10.334141 24 37 9.666100 9.947467 9.718633 10.281367 10.052533 10.333900 23 38 9.666342 9.947401 9.718940 10.281060 10.052599 10.333658 22 39 9.666583 9.947335 9.719248 10.280752 10.052665 10.333417 21 40 9.6G6824 9.947269 9.719555 10.280445 10.052731 10.333176 20 41 9.007065 9.947203 9.719862 10.280138 10.052797 10.332935 19 42 9.6G7305 9.947136 9 720169 10.279831 10.052864 10.332695 18 43 9.667546 9.947070 9.720476 10.279524 10.052930 10.332454 17 44 9.667786 9.947004 9 720783 10.279217 10.052996 10.332214 10 45 9.668027 9 946937 9.721089 10.278911 10.053063 10.331973 15 46 9.638267 9.946871 9 721396 10.278604 10.053129 10.331733 14 47 9.668506 9.946804 9.721702 10.278298 10.053196 10.331494 13 48 9.668746 9.946738 9.722009 10.277991 10.053262 10.331254 12 49 9.668986 9.946671 9.722315 10.277685 10.053329 10.331014 11 50 9.669225 9.946604 9.722621 10.277379 10.053396 10.330775 10 51 9.669464 9.946538 9.722927 10.277073 10.053462 10.330536 y 52 9.669703 9.946471 9.723232 10.276768 10.053529 10.330297 8 53 9.669942 9.946404 9.723538 10.276462 10.053596 10.330058 7 54 9.670181 9.946337 9.723844 10.276156 10.053663 10.329819 6 55 9.670419 9.946270 9.724149 10.275851 10.053730 10.329581 5 56 9.670658 9.946203 9.724454 10.275546 10.053797 10.329342 4 57 9.670896 9.946136 9.724759 10.275241 10.053864 10.329104 3 58 9.671134 9.946069 9.725065 10.274935 10.053931 10.328866 2 59 9.671372 9.946002 9.725369 10.274631 10.053998 10.328628 1 60 9.671609 9 915935 9.725674 10.274326 10.054065 10.328391 M. Co-sine. Sine. | Co-tan.?. Tangent. Co-sec. Secant. M. W$ Degrees. TABLE II. 171 LOGABITHMIC SINES, TANGENTS, AND SECANTS. 28 Degrees. M. Sine. Co-sine. Tangent. Co-tang. Secant. Co-sec. M. 1 2 3 4 5 6 7 8 9 10 9.6716U9 9.671847 9.672084 9.672321 9.672558 9.672795 9.673032 9.673268 9.673505- 9.673741 9 673977 9.945935 9.945868 9.945800 9.945733 9.945666 9.945598 9.945531 9.945464 9.945396 9.945328 9.945261 9.725674 9.725979 9.726284 9.726588 9.726892 9.727197 9.727501 9.727805 9.728109 9.728412 9 728716 10 274326 10.274021 10.273716 10.273412 10.273108 10.272803 10.272499 10.272195 10.271891 10.271588 10.271284 10.054065 10.054132 10.054200 10.054267 10.054334 10.054402 10.054469 10.054536 10.054604 10.054672 10.054739 10.328391 10.328153 10.327916 10.327679 10.327442 10.327205 10.326968 10.326732 10.326495 10.326259 10.326023 60 59 58 57 56 55 54 53 52 51 50 11 12 13 14 15 16 17 18 19 20 9.674213 9 674448 9.674684 9.674919 9 675155 9.675390 9.675624 9.675859 9.676094 9.676328 9.945193 9.945125 9.945058 9 944990 9.944922 9.944854 9 944786 9.944718 9 944650 9.944582 9.729020 9.729323 9.729626 9.729929 9.730233 9.730535 9.730838 9.731141 9.731444 9.731746 10.270980 10.270677 10.270374 10.270071 10.269767 10.269465 10.269162 10.268859 10.268556 10.268254 10.054807 10.054875 10.054942 10.055010 10.055078 10.055146 10.055214 10.055282 10.055350 10.055418 10.325787 10.325552 10.325316 10.325081 10.324845 10.324610 10.324376 10.324141 10.323906 10.323672 49 48 47 46 45 44 43 42 41 40 21 22 23 24 25 26 27 28 29 30 9.676562 9.676796 9.677030 9.677264 9.677498 9.677731 9.677964 9.678197 9.678430 9.678663 9.944514 9.944446 9.944377 9.944309 9 944241 9.944172 9.944104 9.944036 9.943967 9.943899 9.732048 9.732351 9.732653 9.732955 9.733257 9.733558 9.733860 9.734162 9.734463 9.734764 10.267952 10.267649 10.267347 10.267045 10.266743 10.266442 10.266140 10.265838 10.265537 10.265236 10.055486 10.055554 10.055623 10.055691 10.055759 10.055828 10.055896 10.055964 10.056033 10.056101 10.323438 10.323204 10.322970 10.322736 10.322502 10.322269 10.322036 10.321803 10.321570 10.321337 39 38 37 36 35 34 33 32 31 30 31 32 33 34 35 36 37 38 39 40 9.678895 9.679128 9.679360 9.679592 9 679824 9 680056 9.680288 9.680519 9.680750 9.680982 9.943830 9.943761 9.943693 9.943624 9.943555 9.943486 9 943417 9.943348 9.943279 9.943210 9.735056 9 735367 9.735668 9.735969 9.736269 9.736570 9.736871 9.737171 9.737471 9.737771 10.264934 10.264633 10.264332 10.264031 10.263731 10.263430 10.263129 10.262829 10.262529 10.262229 10.056170 10.056239 10.056307 10.056376 10.056445 10.056514 10.056583 10.056652 10.056721 10.056790 10.321105 10.320872 10.320640 10.320408 10.320176 10.319944 10.319712 10.319481 10.319250 10.319018 29 28 27 26 25 24 23 22 21 20 41 42 43 44 45 46 47 48 49 50 9.681213 9.681443 9.681674 9.681905 9.682135 9.682365 9.682595 9.682825 9.683055 9.683284 9.943141 9.943072 9.943003 9.942934 9.942864 9.942795 9.942726 9.942656 9.942587 9.942517 9.738071 9.738371 9.738671 9.738971 9.739271 9.739570 9.739870 9.740169 9.740468 9.740767 10.261929 10.261629 10.261329 10.261029 10.260729 10.260430 10.260130 10.259831 10.259532 10.259233 10.056859 10.056928 10.056997 10.057066 10.057136 10.057205 10.057274 10.057344 10.057413 10.057483 10.318787 10.318557 10.318326 10.318095 10.317865 10.317635 10.317405 10.317175 10.316945 10.316716 19 18 17 16 15 14 13 12 11 10 51 52- 53 54 55 56 57 58 59 60 9.683514 9.683743 9.683972 9.684201 9 684430 9.684658 9.684887 9.685115 9.685343 9.685571 9.942448 9.942378 9.942308 9.942239 9.942169 9.942099 9 942029 9.941959 9.941889 9.941819 9.741066 9.741365 9.741664 9.741962 9.742261 9.742559 9.742858 9.743156 9.743454 9.743752 10.258934 10.258635 10.258336 10.258038 10.257739 10.257441 10.257142 10.256844 10.256546 10.256248 10.057552 10.057622 10.057692 10.057761 10.057831 10.057901 10.057971 10.058041 10.058111 10.058181 10.316486 10.316257 10.316028 10.315799 10.315570 10.315342 10.315113 10.314885 10.314657 10.314429 9 8 7 6 5 4 3 2 1 M. | Co-sine. Sine. Co-tang. Tangent. Co-sec. Secant. M. til Degrees. 172 TABLE II. LOGARITHMIC SIXES, TANGENTS', AND SECANTS. 29 Degrees. M. Sine. Co-sine. [Tangent. Co-tang. Secant. (Jo-sec. M. i 2 3 4 5 6 7 8 9 10 9.685571 9.685799 9 686027 9.686254 9.686482 9.686709 9.68G936 9.6871G3 9.687389 9.687616 9.687843 9. 941819 9.941749 9.941679 9.941609 9.941539 9.941469 9.941398 9.941328 9.941258 9.941187 9.941117 9.743752 9.744050 9.744348 9.744645 9.744943 9.745240 9.745538 9.745835 9.746132 9.746429 9.746726 10.256248 10.255950 10.255652 10.255355 10.255057 10.254760 10.254462 10.254165 10.253868 10.253571 10.253274 10.0olSl 10.058251 10.058321 10.058391 10.058461 10.058531 10.058602 10.058672 10.058742 10.058813 10.058883 10.3144J9 10.314201 10.313973 10.313746 10.313518 10.313291 10.313064 10.31--837 10.312611 10.312384 10.312157 bU 59 58 57 56 55 54 53 52 51 50 11 12 13 14 15 16 17 18 19 20 9.688069 9.688295 9.688521 9.688747 9.688972 9.689198 9.689423 9.689648 9.689873 9.690098 9.941046 9.940975 9.940905 9.940834 9.940763 9.940693 9.940622 9.940551 9.940480 9.940409 9.747023 9.747319 9.747616 9.747913 9.748209 9.748505 9.748801 9.749097 9.749393 9.749689 10.252977 10.252681 10.252384 10.252087 10.251791 10.251495 10.251199 10.250903 10.250607 10.250311 10.058954 10.059025 10.059095 10.059166 10.059237 10.059307 10.059378 10.059449 10.059520 10.059591 10.311931 10.311705 10.311479 10.311253 10.311028 10.310802 10.310577 10.310352 10.310127 10.309902 49 48 47 46 45 44 43 42 41 40 21 22 23 24 25 26 27 28 29 30 9.69J323 9.690548 9.690772 9.690996 9.691220 9.691444 9.691668 9.691892 9.692115 9 692339 9.940338 9.940267 9.940196 9.940125 9.940054 9.939982 9.939911 9 939840 9.939768 9.939697 9.749985 9.750281 9.750576 9.750872 9.751167 9.751462 9.751757 9.752052 9.752347 9.752642 10.250015 10.249719 10.249424 10.249128 10.248833 10.248538 10.248243 10.247948 10.247653 10.247358 10.059662 10.059733 10.059804 10.059875 10.059946 10.060018 10.060089 10.060160 10.060232 10.060303 10.309677 10.309452 10.309228 10.309004 10.308780 10.308556 10.308332 10.308108 10.307885 10.307661 39 38 37 36 35 34 33 32 31 30 31 32 33 34 33 36 37 38 39 40 9.692562 9.692785 9.693008 9.693231 9.693453 9.693676 9.693898 9.694120 9.694342 9.694564 9.939625 9.939554 9.939482 9.939410 9.939339 9.939267 9.939195 9.939123 9.939052 9.938980 9.752937 9.753231 9.753526 9.753820 9.754115 9.754409 9.754703 9.754997 9.755291 9.755585 10.247063 10.246769 10.246474 10.246180 10.245885 10.245591 10.245297 10.245003 10.244709 10.244415 10.060b75 10.060446 10.060518 10.060590 10.060661 10.060733 10.060805 10.060877 10.060948 10.061020 10.307438 10.307215 10.306992 10.306769 10.306547 10 306324 10.306102 10.305880 10.305658 10 305436 29 28 27 26 25 24 23 22 21 20 41 42 43 44 45 46 47 48 49 50 9.G94786 9.695007 9 . 695229 9.695450 9.695G71 9.695892 9.696113 9.G96334 9.696554 9.696775 9.938908 9.938836 9.938763 9.938691 9.938619 9.938547 9.938475 9.938402 9.938330 9.938258 9.755878 9.756172 9.756465 9.756759 9.757052 9.757345 9.757638 9.757931 9.758224 9.758517 10.244122 10.243828 10.243535 10.243241 10.242948 10.242655 10.242362 10.242069 10.241776 10.241483 10.061092 10 061164 10.061237 10.061309 10.061381 10.061453 10.061525 10.061598 10.061670 10.061742 10.305^14 10.304993 10.304771 10.304550 10.304329 10.304108 10.303887 10.303666 10.303446 10.303225 19 18 17 16 15 14 13 12 11 10 51 52 53 54 55 56 57 58 59 60 9.696995 9.697215 9.697435 9.697654 9.697874 9.698094 9.698313 9.698532 9.698751 9.698970 9.938185 9.938113 9.938040 9.937967 9.937895 9.937822 9.937749 9.937676 9.937604 9.937531 9.758810 9.759102 9.759395 9.759687 9.759979 9.760272 9.760564 9.760856 9.761148 9.761439 10.241190 10.240898 10.240605 10.240313 10.240021 10.239728 10.239436 10.239144 10.238852 10.2385G1 10.001815 10.061887 10.061960 10.062033 10.062105 10.062178 10.062251 10.062324 10.062396 10.062469 10.303005 10.302785 10.302565 10.302346 10.302126 10.301906 10.301687 10.301468 10.301249 10.301030 9 ' 8 7 6 5 4 3 2 1 M. Co-sine. Sine. Co-tang. Tangent. Co-sec. Secant. M. GO Degrees. TABLE II. 173 LOGARITHMIC SINES, TANGENTS, AND SECANTS. 30 Degrees. M. Sine. Co-sine. Tangent. Co-tang. Secant. Co-sec. M. y.6d97u 9. 93 < 531 9.7(31439 10.238561 10.0(324(39 10.301030 60 1 9.G99189 9.937458 9.761731 10.238269 10.062542 10.300811 59 2 9.699407 9.937385 9.762023 10.237977 10.062615 10.300593 58 3 9.699626 9.937312 9.762314 10.237686 10.062688 10.300374 57 4 9.699844 9.937238 9.762606 10.237394 10.062762 10.300156 56 5 9.700062 9.937165 9.762897 10.237103 10.062835 10.299938 55 6 9.700280 9.937092 9.763188 10.236812 10.062908 10.299720 54 7 9.700498 9.937019 9.763479 10.236521 10.062981 10.299502 53 8 9.700716 9.936946 9.763770 10.236230 10.063054 10.299284 52 9 9.700933 9.936872 9.764061 10.235939 10.063128 10.299067 51 10 9.701151 9.936799 9.764352 10.235648 10.063201 10.298849 50 11 9.7013(38 9.936725 9.764643 10.235357 10.063275 10.298632 49 12 9.701585 9.936652 9.764933 10.235067 10.063348 10.298415 48 13 9.701802 9.936578 9.765224 10.234776 10.063422 10.298198 47 14 9.702019 9.936505 9.765514 10.234486 10.063495 10.297981 46 15 9.702236 9.936431 9.765805 10.234195 10.063569 10.297764 45 16 9.702452 9.936357 9.766095 10.233905 10.063643 10.297548 44 17 9.702669 9.936284 9.766385 10.233615 10.063716 10.297331 43 18 9.702885 9.936210 9.766675 10.233325 10.063790 10.297115 42 19 9.703101 9.936136 9.766965 10.233035 10.063864 10.296899 41 20 9.703317 9.936062 9.767255 10.232745 10.063938 10.296683 40 21 9.703533 9.9J5988 9,767545 10.232455 10.0(34012 10.296407 39 22 9.703749 9.935914 9.767834 10.232166 10.064086 10.296251 38 23 9.703964 9.935840 9.768124 10.231876 10.064160 10.296036 37 24 9.704179 9.935766 9.768414 10.231586 10.064234 10.295821 36 25 9.704395 9.935692 9.768703 10.231297 10.064308 10.295605 35 26 9.704610 9.935618 9.768992 10.231008 10.064382 10.295390 34 27 9.704825 9.935543 9.769281 10.230719 10.064457 10.295175 33 28 9.705040 9.935469 9.769570 10.230430 10.064531 10.294960 32 29 9.705254 9.935395 9.769860 10.230140 10.064605 10.294746 31 30 9.705469 9.935320 9.770148 10.229852 10.064680 10.294531 30 31 9.705683 9.935246 9.770437 10.229563 10.064754 10.294317 29 32 9.705898 9.935171 9.770726 10.229274 10.064829 10.294102 28 33 9.706112 9.935097 9.771015 10.228985 10.064903 10.293888 27 34 9.706326 9.935022 9.771303 10.228697 10.064978 10.293674 26 35 9.706539 9.934948 9.771592 10.228408 10.065052 10.293461 25 36 9.706753 9.934873 9.771880 10.228120 10.065127 10.293247 24 37 9.706967 9.934798 9.772168 10.227832 10.065202 10.293033 23 38 9.707180 9.934723 9.772457 10.227543 10.065277 10.292820 22 39 9.707393 9.934649 9.772745 10.227255 10.065351 10.292607 21 40 9.707606 9.934574 9.773033 10.226967 10.065426 10.292394 20 41 9.707819 9.934499 9 773321 10.226679 10.065501 10.29/11 19 42 9.708032 9.934424 9.773608 10.226392 10.065576 10.291968 18 43 9.708245 9.934349 9 773896 10.226104 10.065651 10.291755 17 44 9.708458 9.934274 9 774184 10.225816 10.065726 10.291542 16 45 9.708670 9.934199 9.774471 10.225529 10.065801 10.291330 15 46 9.708882 9.934123 9.774759 10.225241 10.065877 10.291118 14 47 9.709094 9.934048 9.775046 10.224954 10.065952 10.290906 13 48 9.709306 9.933973 9.775333 10.224667 10.066027 10.290694 12 49 9.709518 9.933898 9.775621 10.224379 10.066102 10.290482 11 50 9.709730 9.933822 9.775908 10.224092 10.066178 10.290270 10 51 9.709941 9.933747 9.776195 10.223805 10.066253 10.290059 9. 52 9.710153 9.933671 9.776482 10.223518 10.066329 10.289847 8 53 9.710364 9.933596 9.776769 10.223231 10.066404 10.289636 7 54 9.710575 9.933520 9.777055 10.222945 10.066480 10.289425 6 55 9.710786 9.933445 9.777342 10.222658 10.066555 10.289214 5 56 9.710997 9.933369 9.777628 10.222372 10.066631 10.289003 4 57 9.711208 9.933293 9.777915 10.222085 10.066707 10.288792 3 58 9.711419 9.933217 9.778201 10.221790 10.066783 10.288581 2 59 9.711629 9.933141 9.778487 10.221513 10.066859 10.288371 1 GO 9.711839 9.933066 9.778774 10.221226 10.066934 10.288161 M. Co-sine. Sine. | Co-tang. Tangent. Co-sec. Secant. M. Gi) Degrees. 174 TABLE II. LOGARITHMIC SINES, TANGENTS, AND SECANTS. 31 Degrees. M. Sine. Co-sine. Tangent.) Co-tang. Secant. Co-sec. M. 9.711839 9.9b30b6 9.7/8774 10.221226 10.0(J0934 10.288161 60 1 9.712050 9.932990 9.779060 10.220940 10.067010 10.287950 59 2 9 712260 9.932914 9.779346 10.220654 10.067086 10.287740 58 3 9.712469 9.932838 9.779632 10.220368 10.067162 10.287531 57 4 9.712679 9 932762 9.779918 10.220082 10.067238 10.287321 56 5 9.712889 9.932685 9 780203 10.219797 10.067315 10.287111 55 6 9.713098 9.932609 9.780489 10.219511 10.067391 10.286902 54 7 9.713308 9.932533 9.780775 10.219225 10.067467 10.286692 53 8 9.713517 9.932457 9.781060 10.218940 10.067543 10.286483 52 9 9.713726 9.932380 9.781346 10.218654 10.067620 10.286274 51 10 9.713935 9.932304 9.781631 10.218369 10.067696 10.286065 50 11 9.714144 9.932228 9.781916 10.218084 10.007772 10.285856 49 12 9.714352 9.932151 9.782201 10.217799 10.067849 10.285648 48 13 9.714561 9.932075 9.782486 10.217514 10.067925 10.285439 47 14 9.714769 9.931998 9 782771 10.217229 10.068002 10.285231 46 15 9.714978 9.931921 9.783056 10.216944 10.068079 10.285022 45 16 9.715186 9.931845 9 783341 10.216659 10.068155 10.284814 44 17 9.715394 9.931768 9.783626 10.216374 10.068232 10.284606 43 18 9.715602 9.931691 9 783910 10.216090 10.068309 10.284398 42 19 9.715809 9.931614 9.784195 10.215805 10.068386 10.284191 41 20 9.716017 9.931537 9 784479 10.215521 10.068463 10.283983 40 21 9.716224 9.931460 y. 784764 10.215236 10.00*540 10.283776 by 22 9.716432 9.931383 9.785048 10.214952 10.068617 10.283568 38 23 9.716639 9.931306 9.7d5332 10.214668 10.068694 10.283361 37 24 9.716846 9.931229 9.785616 10.214384 10.068771 10.283154 36 25 9.717053 9.931152 9.785900 10.214100 10.068848 10.282947 35 26 9.717259 9.931075 9.786184 10.213816 10.068925 10.282741 34 27 9.717466 9.930998 9.786468 10.213532 10.069002 10.282534 33 28 9.717673 9.930921 9.786752 10.213248 10.069079 10.282327 32 29 9.717879 9.930843 9.787036 10.212964 10.069157 10.282121 31 30 9.718085 9.930766 9.787319 10.212681 10.069234 10.281915 30 31 9.718291 9.930688 y. 787603 10.212397 10.069312 10.2817U9 29 32 9.718497 9.930611 9.787886 10.212114 10.069389 10.281503 28 33 9.718703 9.930533 9.788170 10.211830 10.069467 10.281297 27 34 9.718909 9.930456 9.788453 10.211547 10.069544 10.281091 26 35 9.719114 9.930378 9.788736 10.211264 10.069622 10.280886 25 36 9.719320 9.930300 9.789019 10.210981 10.069700 10.280680 24 37 9.719525 9 930223 9.789302 10.210698 10.069777 10.280475 23 38 9.719730 9.930145 9.789585 10.210415 10.069855 10.280270 22 39 9.719935 9.930067 9.789868 10.210132 10.069933 10.280065 21 40 9.720140 9.929989 9.790151 10.209849 10.070011 10.279860 20 41 9.720345 9.92i;911 9.790433 10.209567 10.07 OU89 10.279655 19 42 9.720549 9 929833 9.790716 10.209284 10.070167 10.279451 18 43 9.720754 9.929755 9.790999 10.209001 10.070245 10.279246 17 44 9.720958 9.929677 9.791281 10.208719 10.070323 10.279042 16 45 9.721162 9.929599 9.791563 10.208437 10.070401 10.278838 15 , 46 9.721366 9.929521 9.791846 10.208154 10.070479 10.278634 14 47 9.721570 9.929442 9.792128 10.207872 10.070558 10.278430 13 48 9.721774 9.929364 9.792410 10.207590 10.070636 10.278226 12 49 9.721978 9.929286 9.792692 10.207308 10.070714 10.278022 11 50 9 722181 9.929207 9 792974 10.207026 10.070793 10.277819 10 51 9.722385 9.929129 9.793256 10.206744 10.070871 10.277615 9 52 9.722588 9.929050 9.793538 10.206462 10.070950 10.277412 8 53 9.722791 9.928972 9.793819 10.206181 10.071028 10.277209 7 54 9.722994 9.928893 9.794101 10.205899 10.071107 10.277006 6 55 9.723197 9.928815 9.794383 10.205617 10.071185 10.276803 5 56 9.723400 9.928736 9.794664 10.205336 10.071264 10.276600 4 57 9.723603 9.928657 9.794945 10.205055 10.071343 10.276397 3 58 9.723805 9.928578 9.795227 10.204773 10.071422 10.276195 2 59 9.724007 9.928499 9.795508 10.204492 10.071501 10.275993 1 60 9.724210 9.928420 9.795789 10.204211 10.071580 10.275790 M. Co-sine. Sine. Co-tang. Tangent. Co-sec. Secant. M. 58 Degrees. TABLE II. 175 LOGARITHMIC SINES, TANGENTS, AND SECANTS. 32 Degrees. M. Sine. Co-sine. Tangent. Co- tang. Secant. Co-sec. M. u y. 724210 9.928420 9.795789 10.204211 10.071080 10.275790 GO 1 9.724412 9.928342 9.796070 10.203930 10.071658 10.275588 59 2 9.724614 9.928263 9.796351 10.203649 10.071737 10.275386 58 3 9.724816 9.928183 9.796632 10.203368 10.071817 10.275184 57 4 9.725017 9.928104 9.796913 10.203087 10.071896 10.274983 56 5 9.725219 9.928025 9.797194 10.202806 10.071975 10.274781 55 6 9.725420 9.927946 9 797475 10.202525 10.072054 10.274580 54 7 9.725622 9.927867 9.797755 10.202245 10.072133 10.274378 53 8 9.725823 9 927787 9.79803G 10.201964 10.072213 10.274177 52 9 9.726024 9.927708 9.798316 10.201684 10.072292 10.273976 51 10 9.726225 9.927629 9.798596 10.201404 10.072371 10.273775 50 11 y. 7264*6 9 927549 9.798877 10.2U1123 10.072451 10.273574 49 12 9.726626 9.927470 9.799157 10.200843 10.072530 10.273374 48 13 9.726827 9.927390 9.799437 10.200563 10.072610 10.273173 47 14 9.727027 9.927310 9.799717 10.200283 10.072690 10.272973 46 15 9.727228 9.927231 9.799997 10.200003 10.072769 10.272772 45 16 9.727428 9.927151 9.800277 10.199723 10.072849 10.272572 44 17 9.727628 9.927071 9.800557 10.199443 10.072929 10.272372 43 18 9.727828 9.926991 9.800836 10.199164 10.073009 10.272172 42 19 9.728027 9.926911 9.801116 10.198884 10.073089 10.271973 41 20 9.728227 9.926831 9.801396 10 198604 10.073169 10.271773 40 21 9.728427 9.926751 9 801U75 10.19c>325 10.073249 10.271573 3 1 J 22 9.728626 9.926671 9.801955 10.198045 10.073329 10.271374 38 23 9.728825 9.926591 9.802234 10.197766 10.073409 10.271175 37 24 9.729024 9.926511 9.802513 10.197487 10.073489 10.270976 36 25 9.729223 9.926431 9.802792 10.197208 10.073569 10.270777 35 26 9.729422 9.926351 9.803072 10.196928 10.073649 10.270578 34 27 9.729621 9.926270 9 803351 10.19G649 10.073730 10.270379 33 28 9 729820 9.926190 9.803630 10.19G370 10.073810 10.270180 32 29 9.730018 9.92G110 9.803908 10.196092 10.073890 10.269982 31 30 9.730217 9.92G029 9.804187 10.195813 10.073971 10.269783 30 31 9 730415 9. 925949 9.8044G6 10.195534 10.074051 10.209585 29 32 9.730613 9.925868 9.804745 10.195255 10.074132 10.269387 28 33 9.730811 9.925788 9.805023 10.194977 10.074212 10.269189 27 34 9.731009 9.925707 9.805302 10.194698 10.074293 10.268991 26 35 9.731206 9.925626 9.805580 10.194420 10.074374 10.268794 25 3G 9.731404 9.925545 9.805859 10.194141 10.074455 10.268596 24 37 9.731602 9.925465 9.806137 10.193863 10.074535 10.268398 23 38 9.731799 9 925384 9.806415 10.193585 10.074616 10.268201 22 33 9.731996 9.925303 9.806693 10.193307 10.074697 10.268004 21 40 9.732193 9.925222 9.806971 10.193029 10.074778 10.267807 20 41 9 732390 9 925141 9.807249 10.1U2751 l'J.074859 10.267610 19 42 9.732587 9.925060 9.807527 10.192473 10.074940 10.267413 18 43 9.732784 9.924979 9.807805 10.192195 10.075021 10.267216 17 44 9.732980 9.924897 9.808083 10.191917 10.075103 10.267020 16 45 9.733177 9.924816 9.808361 10.191639 10.075184 10.266823 15 46 9.733373 9.924735 9.808638 10.191362 10.075265 10.266627 14 .47 9.733569 9.924654 9.808916 10.191084 10.075346 10.266431 13 48 9.733765 9.924572 9.809193 10.190807 10.075428 10.266235 12 49 9.733961 9.924491 9.809471 10.190529 10.075509 10.266039 11 50 9.734157 9.924409 9.809748 10.190252 10.075591 10.265843 10 51 9.734353 9. 9243*8 9.810025 10.189975 10.075672 10.265647 9 52 9.734549 9.924246 9.810302 10.189698 10.075754 10.265451 8 53 9.734744 9.924164 9.810580 10.189420 10.075836 10.265256 7 54 9.734939 9.924083 9.810857 10.189143 10.075917 10.265061 6 55 9.735135 9.924001 9.811134 10.188866 10.075999 10.264865 5 56 9.735330 9.923919 9.811410 10.188590 10.076081 10.264670 4 57 9.735525 9.923837 9.811687 10.188313 10.076163 10.264475 3 58 9.735719 9.923755 9.8119G4 10.188036 10.076245 10.264281 2 59 9.735914 9.923673 9.812241 10.187759 10.076327 10.264086 1 GO 9.736109 9.923591 9.812517 10.187483 10.076409 10.263891 M. Co-sine. Sine. | Co-tang. Tangent. Co-sec. Secant. M. 57 Degrees. 176 TABLE II. LOGARITHMIC SINES, TANGENTS, AND SECANTS. 33 Decrees. M. Sine. Co-sine. Tangent. Co-tang. Secant. Co-sec. M. 1 2 3 4 5 6 7 8 9 10 9.736109 9.736303 9.736498 9.736692 9 736886 9.737080 9.737274 9.737467 9.737661 9.737855 9.738048 9.923591 9.923509 9.923427 9.923345 9.923263 9.923181 9.923098 9 923016 9.922933 9.922851 9 922768 9.812517 9.812794 9.813070 9.813347 9.813623 9.813899 9.814175 9.814452 9.814728 9.815U04 9.815279 10.187483 10.187206 10.186930 10.186653 10.186377 10.186101 10.185825 10.185548 10.185272 10.184996 10.184721 10.076409 10.076491 10.076573 10.076655 10.076737 10.076819 10.076902 10.076984 10.077067 10.077149 10.077232 10.263891 10.263697 10.263502 10.263308 10.263114 10.262920 10.262726 10.262533 10.262339 10.262145 10.261952 60 59 58 57 56 55 54 53 52 51 50 11 12 13 14 15 16 17 18 19 20 22 23 24 25 26 27 28 29 30 9.738241 9.738434 9.738627 9.738820 9.739013 9.739206 9.739398 9.739590' 9.739783 9.739975 9.922086 9.922603" 9.922520 9.922438 9 922355 9.922272 9.922189 9.922106 9.922023 9.921940 9.815555 9.815831 9 816107 9.816382 9.816658 9.816933 9.817209 9.817484 9.817759 9 818035 10.184445 10.184169 10.183893 10.183618 10.183342 10.183067 10.182791 10.182516 10.182241 10.181965 10!077397 10.077480 10.077562 10.077645 10.077728 10.077811 10.077894 10.077977 10.078060 I0.'2617o9 10.261566 10.261373 10.261180 10.260987 10.260794 10.260602 10.260410 10.260217 10.260025 49 48 47 46 45 44 43 42 41 40 9.740107 9.740359 9.740550 9.740742 9.740934 9.741125 9.741316 9.741508 9.741699 9.741889 9.921857 9.921774 9.921691 9.921G07 9.921524 9.921441 9.921357 9.921274 9.921190 9.921107 9.818310 9.818585 9.818860 9.819135 9.819410 9.819884 9.819959 9.820234 9.820508 9 820783 10.181690 10.181415 10.181140 10.180865 10.180590 10.180316 10.180041 10.179766 10.179492 10.179217 10.0*8143 10.078226 30.078309 lu.078393 10.078476 10.078559 10.078643 10.078726 10.078810 10.078893 10.259833 10.259641 10.259450 10.259258 10.259066 10.258875 10.258684 10.258492 10.258301 10.258111 38 37 36 35 34 33 32 31 30 31 32 33 34 35 36 37 38 39 40 9.742080 9.742271 9.742462 9.742652 9.742842 9.743033 9.743223 9.743413 9.743602 9.743792 9.921023 9.920939 9.920856 9.920772 9.920688 9.920604 9 920520 9.920436 9.920352 9.920268 9.821057 9.821332 9.821606 9.821880 9.822154 9.822429 9.822703 9.822977 9.823250 9.823524 10.178943 10.178668 10.178394 10.178120 10.177846 10.177571 10.177297 10.177023 10.176750 10.176476 I0.07o977 10.079061 10.079144 10.079228 10.079312 10.079396 10.079480 10.079564 10.079648 10.079732 10.257920 10.257729 10.257538 10.257348 10.257158 10.256967 10.256777 10.256587 10.256398 10.256208 28 27 26 25 24 23 22 21 20 41 42 43 44 45 46 47 48 49 50 9.743982 9.744171 9.744361 9.744550 9.744739 9.744928 9.745117 9.745306 9.745494 9.745683 9.920184 9.920099 9.920015 9.919931 9.919846 9.919762 9.919677 9.919593 9.919508 9.919424 9 ! 824072 9.824345 9.824619 9 824893 9.825166 9.825439 9.825713 9.825986 9.826259 10.176202 10.175928 10.175655 10.175381 10.175107 10.174834 10.174561 10.174287 10174014 10.173741 10.079816 10.079901 10.079985 10.080069 10.080154 10.080238 10.080323 10.080407 10.080492 10080576 10.256018 10.255829 10.255639 10.255450 10.255261 10.255072 10.254883 10.254694 10.254506 10.254317 19 18 17 18 15 14 13 12 11 10 51 52 53 54 55 56 57 58 59 60 9.745871 9.746060 9.746248 9.746436 9.746624 9.746812 9.746999 9.747187 9.747374 9.747562 9.919339 9.919254 9.919169 9.919085 9.919000 9.918915 9.918830 9.918745 9.918659 9.918574 9.826532 9.826805 9.827078 9.827351 9.827624 9.827897 9.828170 9.828442 9.828715 9.828987 10.173468 10.173195 10.172922 10.172649 10.172376 10.172103 10.171830 10.171558 10.171285 10.171013 10.080661 10.080746 10.080831 10.080915 10.081000 10.081085 10.081170 10.081255 10.081341 10.081426 10.254129 10.253940 10.253752 10.253564 10.253376 10.253188 10.253001 10.252813 10.252626 10.252438 9 8 7 6 5 4 3 2 1 M. Co-sine. Sine. Co-tang. Tangent. Co-sec. Secant. M. 56 Degrees. TABLE II. 177 LOGAEITHMIC SINES, TANGENTS, AND SECANTS. 34 Degrees. M. Sine. Co-sine. Tangent Co-tang. Secant. Co-sec. M. u 9.747562 9. 9 J 8574 9.82897 10.171013 10.081426 10.252438 60 1 9.747749 9.918489 9.829260 10.170740 10.081511 10.252251 9 2 9.747936 9.918404 9.829532 10.170468 10.081596 10.252064 58 3 9.748123 9.918318 9.829805 10.170195 10.081682 10.251877 57 4 9.748310 9.918233 9.830077 10.169923 10.081767 10.251690 56 5 9.748497 9.918147 9.830349 10.169651 10.081853 10.251503 55 6 9.748683 9.918062 9.830621 10.169379 10.081938 10.251317 54 7 9.748870 9.917976 9.830893 10.169107 10.082024 10.251130 53 8 9.749056 9.917891 9.831165 10.168835 10.082109 10.250944 52 9 9.749243 9.917805 9.831437 10.168563 10.082195 10.250757 51 10 9.749429 9.917719 9.831709 10.168291 10.082281 10.250571 50 11 9.749615 9.9)7634 9.831981 10.168019 10 08*366 10.250385 49 12 9.749801 9.917548 9.832253 10.167747 10.082452 10.250199 48 13 9.749987 9.917462 9.832525 10.167475 10.082538 10.250013 47 14 9.750172 9.917376 9.832796 10.167204 10.082624 10.249828 46 15 9.750358 9.917290 9.833068 10.166932 10.082710 10.219642 45 16 9.750543 9.917204 9.833339 10.166661 10.082796 10.249457 44 17 9.750729 9.917118 9.833611 10.166389 10.082882 10.249271 43 18 9.750914 9.917032 9.833882 10.166118 10.082968 10.249086 42 19 9.751099 9.916946 9.834154 10.165846 10.083054 10.248901 41 20 9.751284 9.91C859 9.834425 10.165575 10.083141 10.248716 40 21 1). 75 1469 9.916773 9.834696 10.165304 10.033227 10.248531 39 22 9.751654 9.916687 9.834967 10.165033 10.083313 10.248346 38 23 9.751839 9.916600 9.835238 10.164762 10.083400 10.248161 37 24 9.752023 9.916514 9.835509 10.164491 10.083486 10.247977 36 25 | 9.752208 9.916427 9.835780 10.164220 10.083573 10.247792 35 26 9.752392 9.916341 9.836051 10.163949 10.083659 10.247608 34 27 9.752576 9.916254 9.836322 10.163678 10.083746 10.247424 33 28 9.752760 9 916167 9.836593 10 163407 10.083833 10.247240 32 29 9.752944 9.916081 9.836864 10.163136 10.083919 10.247056 31 30 9.753128 9.915994 9.837134 10.162866 10.084006 10.246872 30 31 9.753312 9.915907 9.837405 10.162595 10.084093 10.246688 k9 32 9.753495 9.915820 9 837675 10.162325 10.084180 10.246505 28 33 9.753679 9.915733 9.837946 10.162054 10.084267 10.246321 27 34 9.753862 9.915646 9.838216 10.161784 10.084354 10.246138 26 35 9.754046 9.915559 9.838487 10.161513 10.084441 10.245954 25 36 9.754229 9.915472 9.838757 10.161243 10.084528 10.245771 24 37 9.754412 9.915385 9.839027 10.160973 10.084615 10.245588 23 38 9.754595 9.915297 9.839297 10.160703 10.084703 10.245405 22 39 9.754778 9.915210 9 839568 10.160432 10.084790 10.245222 21 40 | 9.754960 9.915123 9.839838 10.160162 10.084877 10.245040 20 41 9.755143 9.915035 9.840108 10.159892 10.084965 10.244857 19 42 9.755326 9.914948 9 840378 10.159622 10.085052 10.244674 18 43 9 . 755508 9.914860 9.840647 10.159353 10.085140 10.244492 17 44 9 755690 9.914773 9 840917 10.159083 10.085227 10.244310 16 45 9.755872 9.914685 9.841187 10.158813 10.085315 10.244128 15 46 9.756054 9.914598 9 841457 10.158543 10.085402 10.243946 14 47 9.756236 9.914510 9.841726 10.158274 10.085490 10.243764 13 48 9.756418 9.914422 9.841996 10.158004 10.085578 10.243582 12 49 9.756600 9.914334 9.842266 10.157734 10.085666 10.243400 11 50 9.756782 9.914246 9.842535 10.157465 10.085754 10.243218 10 51 9.756963 9.914158 9.842805 10.157195 10.085842 10.243037 9 52 9.757144 9.914070 9.843074 10.156926 10.085930 10.242856 8 53 9.757326 9.913982 9.843343 10.156657 10.086018 10.242674 7 54 9.757507 9.913894 9.843612 10.156388 10.086106 10.242493 6 55 9.757688 9.913806 9.843882 10.156118 10.086194 10.242312 5 56 9.757869 9.913718 9.844151 10.155849 10.086282 10.242131 4 57 9.758050 9.913630 9.841420 10.155580 10.086370 10.241950 3 58 9.758230 9.913541 9.844689 10.155311 10.086459 10.241770 2 59 9.758411 9.913453 9.844958 10.155042 10.086547 10.243589 1 60 9 758591 9 913365 9.845227 10.154773 10.086635 10.241409 M. Co-sine. Sine. | Co-tang. Tangent. Co-sec. Secant. M. 55 Degrees. 178 TABLE II. LOGARITHMIC SIGNS, TANGENTS AND SECANTS. 35 Degrees. II. Sine. Co-sine. Tangent. Co-tang. Secant. Co-sec. M. 9.758591 9.913365 9.845227 10.154773 10.086635 10.241409 60 1 9.758772 9 913276 9.845496 10.154504 10.086724 10.241228 59 2 9.758952 9.913187 9.845764 10.154236 10.086813 10.241048 58 3 9.759132 9.913099 9.846033 10.153967 10.086901 10.240868 57 4 9 759312 9.913010 9.846302 10.153698 10.086990 10.240688 56 5 9.759492 9.912922 9.846570 10.153430 10.087078 10.240508 55 6 9.759672 9.912833 9.846839 10.153161 10.087167 10.240328 54 7 9.759852 9.912744 9.847107 10.152893 10.087256 10.240148 53 8 9.760031 9.912655 9.847376 10.152624 10.087345 10.239969 52 9 9.760211 9.912566 9.847644 10.152356 10.087434 10.239789 51 10 9.760390 9.912477 9.847913 10.152087 10.087523 10.239610 50 11 9.760569 9.912388 9.848181 10.151819 10.0S7612 10.239431 49 12 9.760748 9.912299 9.848449 10.151551 10.087701 10.239252 48 13 9.760927 9.912210 9.848717 10.151283 10.087790 10.239073 47 14 9.761106 9.912121 9.848986 10.151014 10.087879 10.238894 46 15 9.761285 9.912031 9.849254 10.150746 10.087969 10.238715 45 16 9.761464 9.911942 9.849522 10.150478 10.088058 10.238536 44 17 9.761642 9 911853 9.849790 10.150210 10.088147 10.238358 43 ]8 9.761821 9.911763 9.850058 10.149942 10.088237 10.238179 42 19 9.761999 9.911674 9.850325 10.149675 10.088326 10.238001 41 20 9.762177 9.911584 9.850593 10.149407 10.088416 10.237823 40 21 9.762356 9.911495 9.850861 10.149139 10.0S8505 10.237644 39 22 9.762534 9.911405 9.851129 10.148871 10.088595 10.237466 38 23 9.762712 9 911315 9.851396 10.148604 10.088685 10.237288 37 24 9.762889 9.91J226 9.851664 10.148336 10.088774 10.237111 36 25 9.763067 9.911136 9 851931 10.148069 10.088864 10.236933 35 26 9 763245 9.911046 9 852199 10.147801 10.088954 10.236755 34 27 9.763422 9.910956 9 852466 10.147534 10.089044 10.236578 33 28 9.763600 9.910866 9.852733 10.147267 10.089134 10.236400 32 29 9.763777 9.910776 9.853001 10.146999 10.089224 10.236223 31 30 9.763954 9.910686 9.853268 10.146732 10.089314 10.236046 30 31 9.764131 9.910596 9.853535 10.1464(35 10.089404 10.235b(5 l J 29 32 9.764308 9.910506 9.853802 10.146198 10.089494 10.235692 28 33 9.764485 9.910415 9.854069 10.145931 10.089585 10.235515 27 34 9.764662 9.910325 9.854336 10.145664 10.089675 10.235338 26 35 9.764838 9.910235 9.854603 10.145397 10.089765 10.235162 25 36 9.765015 9.910144 9.854870 10.145130 10.089856 10.234985 24 37 9.765191 9.910054 9.855137 10.144863 10.089946 10.234809 23 38 9.765367 9.909963 9.855404 10.144596 10.090037 10.234833 22 39 9.765544 9.909873 9.855671 10.144329 10.090127 10.234456 21 40 9.765720 9.909782 9.855938 10.144062 10.090218 10.234280 20 41 9.765896 9.909691 9.856204 10.143796 10.090309 10.234104 19 42 9.766072 9.909601 9.856471 10.143529 10.09,0399 10.233928 18 43 9.766247 9.909510 9.856737 10.143263 10.090490 10.233753 17 44 9.766423 9.909419 9.857004 10.142996 10.090581 10.233577 16 45 9.766598 9.909328 9.857270 10.142730 10.090672 10.233402 15 46 9.766774 9.909237 9.857537 10.142463 10.090763 10.233226 14 47 9.766949 9.909146 9.857803 10.142197 10.090854 10.233051 13 48 9.767124 9.909055 9.858069 10.141931 10.090945 10.232876 12 49 9.767300 9.908964 9.858336 10.141664 10.091036 10.232700 11 50 9.767475 9.908873 9.858602 10.141398 10.091127 10.232525 10 51 9.767649 9.908781 9.858868 10.141132 10.091219 10.232351 9 52 9.767824 9.908690 9.859134 10.140866 10.091310 10.232176 8 53 9.767999 9.908599 9.859400 10.140600 10.091401 10.232001 7 54. 9.768173 9.908507 9.859666 10.140334 10.091493 10.231827 6 55 9.768348 9.908416 9.859932 10.140068 10.091584 10.231652 5 56 9.768522 9.908324 9.860198 10.139802 10.091676 10.231478 4 57 9.768697 9.908233 9.860464 10.139536 10.091767 10.231303 3 58 9.768871 9.908141 9.860730 10.139270 10.091859 10.231129 2 59 9.769045 9.908049 9.860995 10.139005 10.091951 10.230955 1 60 9.769219 9 907958 9.861261 10.138739 10.092042 10.230781 M. 1 Co-sine. Sine. Co-tang. Tangent. Co-sec. Secant. M. 54 Degrees. TABLE II. 179 LOGARITHMIC SIXES, TANGENTS, AND SECANTS. 36 Degrees. M. Sine. Co-sine. Tangent. Co-tang. Secant. Co-sec. M. y. 7692 19 9.907958 9.861261 10.138739 10.092042 10.23U761 60 1 9.769393 9.9078G6 9.861527 10.138473 10.092134 10.230607 59 2 9.769566 9.907774 9.861792 10.138208 10.092226 10.230434 58 3 9.769740 9.907682 9.862058 10.137942 10.092318 10.230260 57 4 9.769913 9.907590 9.862323 10.137677 10.092410 10.230087 56 5 9.770087 9.907498 9.862589 10.137411 10.092502 10.229913 55 6 9.770260 9.907406 9.862854 10.137146 10.092594 10.229740 54 7 9.770433 9.907314 9.863119 10.136881 10.092686 10.229567 53 8 9.770G06 9.907222 9.863385 10.136615 10.092778 10.229394 52 9 9.770779 9.907129 9.863650 10.136350 10.092871 10.229221 51 10 9.770952 9.907037 9.863915 10.136085 10.092963 10.229048 50 11 9. 771125 9.906945 9.864180 10.135820 10.093055 10.228875 49 12 9.771298 9.906852 9.864445 10.135555 10.093148 10.228702 48 13 9.771470 9.906760 9.864710 10.135290 10.093240 10.228530 47 14 9.771643 9.906667 9.864975 10.135025 10.093333 10.228357 46 15 9.771815 9.906575 9.865240 10.134760 10.093425 10.228185 45 16 9.771987 9.906482 9.865505 10.134495 10.093518 10.228013 44 17 9.772159 9.906389 9.865770 10.134230 10.093611 10.227841 43 18 9.772331 9.906296 9.866035 10.133965 10.093704 10.227669 42 19 9.772503 9.906204 9.866300 10.133700 10.093796 10.227497 41 20 9.772675 9.906111 9.866564 10.133436 10.093889 10.227325 40 21 9.772847 9.90U018 9.8G6829 10.133171 10.093982 10.227153 39 22 9.773018 9.905925 9.867094 10.132906 10.094075 10.226982 38 23 9.773190 9.905832 9.867358 10.132642 10.094168 10.226810 37 24 9.773361 9.905739 9 867623 10.132377 10.094261 10.226639 36 25 9.773533 9.905645 9.867887 10.132113 10.094355 10.226467 35 26 9.773704 9.905552 9.868152 10.131848 10.094448 10.226296 34 27 9.773875 9.905459 9.868416 10.131584 10.094541 10.226125 33 28 9.774046 9.905366 9.8686SO 10.131320 10.094634 10.225954 32 29 9.774217 9.905272 9.868945 10.131055 10.094728 10.225783 31 30 9.774388 9.905179 9.869209 10.130791 10.094821 10.225612 30 31 9.774558 9.905U85 9.869473 10.130527 10.094915 10.225442 *9 32 9.774729 9.904992 9.869737 10.130263 10.095008 10.225271 28 33 9.774899 9.904898 9.870001 10.129999 10.095102 10.225101 27 34 9.775070 9.904804 9.870265 10.129735 10.095196 10.224930 26 35 9.775240 9.904711 9.870529 10.129471 10.095289 10.224760 25 36 9.775410 9.904617 9.870793 10.129207 10.095383 10.224590 24 37 9.775580 9.904523 9.871057 10.128943 10.095477 10.224420 23 38 9.775750 9T904429 9.871321 10.128679 10.095571 10.224250 22 39 9.775920 9.904335 9.871585 10.128415 10.095665 10.224030 21 40 9.776090 9.904241 9.871849 10.128151 10.095759 10.223910 20 41 9. 7 76259 9.904147 9.872112 10.127888 10.095853 10.223741 19 42 9.776429 9.904053 9.872376 10.127624 10.095947 10.223571 18 43 9.776598 9.903959 9 872640 10.127360 10.09G041 10.223402 17 44 9.776768 9.903864 9 872903 10.127097 10.096136 10.223232 16 45 9.776937 9.903770 9.873167 10.126833 10.096230 10.223063 15 46 9.777106 9.903676 9.873430 10.126570 10.096324 10.222894 14 47 9.777275 9.903581 9.873694 10.126306 10.096419 10.222725 13 48 9.777444 9.903487 9.873957 10.126043 10.096513 10.222556 12 49 9.777613 9.903392 9.874220 10.125780 10.096608 10.222387 11 50 9.777781 9.903298 9.874484 10.125516 10.096702 10.222219 10 51 9. 77 7950 9.903203 9.874747 10.125253 10.096797 10.222050 y 52 9.778119 9.903108 9.875010 10.124990 10.096892 10.221881 8 53 9.778287 9.903014 9.875273 10.124727 10.096986 10.221713 7 54 9.778455 9.902919 9.875536 10.124464 10.097081 10.221545 6 55 9.778G24 9.902824 9.875800 10.124200 10.097176 10.221376 5 56 9.778792 9.902729 9.876063 10.123937 10.097271 10.221208 4 57 9.778960 9.902634 9.876326 10.123674 10.097366 10.221040 3 58 9.779128 9.902539 9.876589 10.123411 10.097461 10.220872 2 59 9.779295 9.902444 9.876851 10.123149 10.097556 10.220705 1 60 9.7794G3 9.902349 9.877114 10.122886 10.097651 10.220537 M. Co-sine. Sine. | Co-taug. Tangent. Co-sec. Secant. M. 53 Degrees. 180 TABLE II. LOGAKITHMIC SINES, TANGENTS, AND SECANTS. 37 Degrees. M. Sine. Co-sine. Tangent. Co- tang. Secant. Co-sec. M. 9. 779463 9.902349 9.877114 10 122886 10.097051 10.220537 60 1 9.779631 9.902253 9.877377 10.122623 10.097747 10.220369 59 2 9.779798 9.902158 9.877640 10.122360 10.097842 10.220202 58 3 9.779966 9.902063 9.877903 10.122097 10.097937 10.220034 57 4 9 780133 9.901967 9.878165 10.121835 10.098033 10.219867 56 5 9.780300 9.901872 9.878428 10.121572 10.098128 10.219700 55 6 9.780467 9.901776 9.878691 10.121309 10.098224 10.219533 54 7 9.780634 9.901681 9.878953 10.121047 10.098319 10.219366 53 8 9.780801 9.901585 9.879216 10.120784 10.098415 10.219199 52 9 9.780968 9.901490 9.879478 10.120522 10.098510 10.219032 51 10 9.781134 9.901394 9 879741 10.120259 10.098606 10.218866 50 11 9.781301 9 901298 9.880003 10. 119997 10.098702 10.218699 49 12 9 781468 9.901202 9.880265 10.119735 10.098798 10.218532 48 13 9.781G34 9.9C1106 9.880528 10.119472 10.098894 10.218366 47 14 9.781800 9 901010 9.880790 10.119210 10.098990 10.218200 46 15 9 781 966 9.900914 9.881052 10.118948 10.099086 10.218034 45 16 9.782132 9.900818 9.881314 10.118686 10.099182 10.217868 44 17 9.782298 9 900722 9.881576 10.118424 10.099278 10.217702 43 18 9.782464 9.900626 9.881839 10.118161 10.099374 10.217536 42 19 9.782630 9.900529 9.882101 10.117899 10.099471 10.217370 41 20 9.782796 9.900433 9.882363 10.117637 10.099567 10.217204 40 21 9. 782961 9.900337 9.882625 10.117375 10.0996G3 10.217039 39 22 9.783127 9.900240 9.882887 10.117113 10.099760 10.216873 38 23 9.783292 9.900144 9.883148 10.116852 10.099856 10.216708 37 24 9 783458 9.900047 9.883410 10.116590 10.099953 10.216542 36 25 9.783623 9 899951 9.883672 10.116328 10.100049 10.216377 35 26 9.783788 9.899854 9.883934 10.116066 10.100146 10.216212 34 27 9.783953 9.899757 9.884196 10.115804 10.100243 10.216047 33 28 9.784118 9.899660 9.884457 10.115543 10.100340 10.215882 32 29 9.784282 9.899564 9.884719 10.115281 10.100436 10.215718 31 30 9.784447 9.899467 9.884980 10.115020 10.100533 10.215553 30 31 9.784612 9.899370 9.885242 10.114758 10.100630 10.215388 29 32 9.784776 9.899273 9 855503 10.114497 10.100727 10.215224 28 33 9.784941 9.899176 9.885765 10.114235 10.100824 10.215059 27 34 9.785105 9.899078 9.886026 10.113974 10.100922 10.214895 26 35 9 785269 9.898981 9.886288 10.113712 10.101019 10.214731 25 36 9.785433 9.898884 9.886549 10.113451 10.101116 10.214567 24 37 9.785597 9 898787 9.886810 10.113190 10.101213 10.214403 23 38 9.785761 9.898689 9.887072 10.112928 10.101311 10.214239 22 39 9.785925 9.898592 9.887333 10.112667 10.101408 10.214075 21 40 9.786089 9.898494 9.887594 10.112406 10.101506 10.213911 20 41 9.786252 9.898397 9.887855 10.112145 10.101603 10.213748 19 42 9.786416 9.898299 9.888116 10.111884 10.101701 10.213584 18 43 9.786579 9.898202 9.888377 10.111623 10.101798 10.213421 17 44 9.786742 9.898104 9 888639 10.111361 10.101896 10.213258 16 45 9.786906 9.898006 9.888900 10.111100 10.101994 10.213094 15 46 9.787069 9.897908 9.889160 10.110840 10.102092 10.212931 14 47 9.787232 9.897810 9.889421 10.110579 10.102190 10.212768 13 48 9.787395 9.897712 9.889682 10.110318 10.102288 10.212605 12 49 9.787557 9.897614 9.889943 10.110057 10.102386 10.212443 11 50 9.787720 9.897516 9.890204 10.109796 10.102484 10.212280 10 51 9.787883 9.897418 9.890465 10.109535 10.102582 10.212117 9 52 9.788045 9.897320 9.890725 10.109275 10.102680 10.211955 8 53 9.788208 9.897222 9.890986 10.109014 10.102778 10.211792 7 54 9.788370 9.897123 9.891247 10.108753 10.102877 10.211630 6 55 9.788532 9.897025 9.891507 10.108493 10.102975 10.211468 5 56 9.788694 9.896926 9.891768 10.108232 10.103074 10.211306 4 57 9.788856 9 896828 9.892028 10.107972 10.103172 10.211144 3 58 9.789018 9.896729 9.832289 10.107711 10.103271 10.210982 2 59 9.789180 9.896631 9.892549 10.107451 10.103369 10.210820 1 GO 9.789342 9.896532 9.892810 10.107190 10.103468 10.210658 M. Co-sine. Sine. Co-tang. Tangent. Co-sec. Secant. M. 52 l>cgrees. TABLE II. 181 LOGARITHMIC SINES, TANGENTS, AND SECANTS. 38 Degrees. M. Sine. Co-sine. [Tangent. Co-tang. Secant. Co-sec. M. 9.78934a 9.89o532 9.81)2810 10.107J90 10.103468 10.210658 60 1 9.7S9504 9.896433 9.893070 10.106930 10.103567 10.210496 59 2 9.789G65 9.896335 9.893331 10.106669 10.103665 10.210335 58 3 9.789827 9.896236 9.893591 10.10(5409 10.103764 10.210173 57 4 9.789988 9.896137 9.893851 10.106149 10.103863 10.210012 56 5 9.790149 9.896038 9.894111 10.105889 10.103962 10.209851 55 6 9.790310 9.895939 9.894371 10.105629 10.104061 10.209690 54 7 9.790471 9.895840 9.894632 10.105368 10.104160 10.209529 53 8 9.790632 9 895741 9.8)4892 10.105108 10.104259 10.209368 52 9 9.790793 9.895641 9.895152 10.104848 10.104359 10.209207 51 1U 9.790954 9.895542 9.895412 10.104588 10.104458 10.209046 50 11 9.791115 9 895443 9.895672 10.104328 10.104557 10.208885 49 12 9.791275 9.895343 9.895932 10.104068 10.104657 10.208725 48 13 9.791436 9.895244 9.896192 10.103808 10.104756 10.208564 47 14 9.791596 9.895145 9.896452 10.103548 10.104855 10.208404 46 15 9.791757 9.895045 9.896712 10.103288 10.104955 10.208243 45 16 9.791917 9.894945 9.S96971 10.103029 10.105055 10.208083 44 17 9.792077 9.894846 9.897231 10.102769 10.105154 10.207923 43 18 9.792237 9.894746 9.897491 10.102509 10.105254 10.207763 42 19 9.792397 9.894646 9.8U7751 10.102249 10.105354 10.207603 41 20 9.792557 9.891546 9.898010 10.101990 10.105454 10.207443 40 21 9.793716 9.894446 9.898270 10.101730 10.105554 10.207284 39 22 9.792876 9.894346 9.898530 10.101470 10.105654 10.207124 38 23 9.793035 9.894246 9.898789 10.101211 10.105754 10.206965 37 24 9.793195 9.894146 9.899049 10.100951 10.105854 10.206805 36 25 9.793354 9.894046 9.899308 10.100692 10.105954 10.206646 35 2(5 9.793514 9.893946 9.899568 10.100432 10.106054 10.206486 34 27 9.793673 9.893846 9 899827 10.100173 10.106154 10.206327 33 28 9 793832 9.893745 9.900086 10.099914 10.106255 10.206168 32 29 9.793991 9.893645 9.900346 10.099654 10.106355 10.206009 31 30 9.794150 9.893544 9.900605 10.099395 10.106456 10.205850 30 31 9 794308 9.893444 9.900864 10.099136 10.106556 10.205692 29 32 9.794467 9.893343 9.901124 10.098876 10.106657 10.205533 28 33 9.794626 9.893243 9.901383 10.098617 10.106757 10.205374 27 34 9.794784 9.893142 9.901642 10.098358 10.106858 10.205216 26 35 9.794942 9.893041 9.901901 10.098099 10.106959 10.205058 25 36 9.795101 9.892940 9.902160 10.097840 10.107060 10.204899 24 37 9.795259 9.892839 9.902419 10.097581 10.107161 10.204741 23 38 9.795417 9.892739 9.902679 10.097321 10.107261 10.204583 22 33 9.795575 9.892638 9.902938 10.097062 10.107362 10.204425 21 40 9.795733 9.892536 9.903197 10.096803 10.107464 10.204267 20 41 9 795891 9.892435 9.903455 10.096545 1'J. 107565 10.204109 19 42 9.796049 9.892334 9.903714 10.096286 10.107666 10.203951 18 43 9.796206 9.892233 9.903973 10.096027 10.107767 10.203794 17 44 9.796364 9.892132 9.904232 10.095768 10.107868 10.203636 16 45 9.796521 9.892030 9.904491 10.095509 10.107970 10.203479 15 46 9.796679 9.891929 9.904750 10.095250 10.108071 10.203321 14 47 9.796836 9.891827 9.905008 10.094992 10.108173 10.203164 13 48 9.796993 9.891726 9.905267 10.094733 10.108274 10.203007 12 49 9.797150 9.891624 9.905526 10.094474 10.108376 10.202850 11 50 9.797307 9.891523 9.905784 10.094216 10.108477 10.202693 10 51 9.797464 9.891421 9.906043 10.093957 10.1U8579 10.202536 9 52 9.797621 9.891319 9.906302 10.093698 10.108681 10.202379 8 53 9.797777 9.891217 9.906560 10.093440 10.108783 10.202223 7 54 9.797934 9.891115 9.906819 10.093181 10.108885 10.202066 6 55 9.798091 9.891013 9.907077 10.092923 10.108987 10.201909 5 56 9.798247 9.890911 9.907336 10.092664 10.109089 10.201753 4 57 9.798403 9.890809 9.907594 10.092406 10.109191 10.201597 3 58 9.798560 9.890707 9.907852 10.092148 10.109293 10.201440 2 59 9.798716 9.890605 9.908111 10.091889 10.109395 10.201284 1 60 9.798872 9.890503 9,908369 10.091631 10.109497 10.201128 M. j Co-sine, j Sine. | Co-tang. Tangent. Co-sec. Secant. M. 51 Degrees. 182 TABLE II. LOGARITHMIC SINES, TANGENTS, AND SECANTS. 39 Degrees. M. Sine. Co-sine. Tangent. Co-tang. Secant. Co-sec. M. 9.798872 9.89U503 9.908369 10.091631 10.109497 10.201128 60 l 9.799028 9.890400 9.908628 10.091372 10.109600 10.200972 .59 2 9 799184 9.890298 9.908886 10.091114 10.109702 10.200816 58 3 9.799339 9.890195 9.909144 10.090856 10.109805 10.200661 57 4 9 799495 9 890093 9.909402 10.090598 10.109907 10.200505 56 5 9.799651 9.889990 9 909660 10.090340 10.110010 10.200349 55 6 9.799806 9.889888 9.909918 10.090082 10.110112 10.200194 54 7 9.799962 9.889785 9.910177 10.089823 10.110215 10.200038 53 8 9.800117 9.889682 9.910435 10.089565 10.110318 10.199883 52 9 9.800272 9.889579 9.910693 10.089307 10.110421 10.199728 51 10 9.800427 9.889477 9.910951 10.089049 10.110523 10.199573 50 11 9.800582 9.889374 9.911209 10.088791 10.110626 10.199418 49 12 9.800737 9.889271 9.911467 10.088533 10.110729 10.199263 48 13 9.800892 9.889168 9.911724 10.088276 10.110832 10.199108 47 14 9.801047 9.889064 9 911982 10.088018 10.110936 10.198953 46 15 9.801201 9.888961 9.912240 10.087760 10.111039 10.198799 45 16 9.801356 9.888858 9.912498 10.087502 10.111142 10.198644 44 17 9.801511 9.888755 9.912756 10.087244 10.111245 10.198489 43 18 9.801C65 9.888G51 9 913014 10.086986 10.111349 10.198335 42 19 9.801819 9.888548 9.913271 10.086729 10.111452 10.198181 41 20 9.801973 9.888444 9 913529 10.086471 10.111556 10.198027 40 21 9.802128 9.888341 9.913787 10.086213 10.111659 10.197672 i*9 22 9.802282 9.888237 9.914044 10.085956 10.111763 10.197718 38 23 9.802436 9.888134 9.914302 10.085698 10.111866 10.197564 37 24 9.802589 9.888030 9.914560 10.085440 10.111970 10.197411 36 25 9.802743 9.887926 9.914817 10.085183 10.112074 10.197257 35 26 9.802897 9.887822 9.915075 10.084925 10.112178 10.197103 34 27 9.803050 9.887718 9.915332 10.084668 10.112282 10.196950 33 28 9.803204 9.887614 9.9115590 10.084410 10.112386 10.196796 32 29 9.803357 9.887510 9.915847 10.084153 10.112490 10.196643 31 30 9.803511 9.887406 9.916104 10.083896 10.112594 10.196489 30 31 9.803664 9.887302 9.916362 10.083638 10.112698 10.196336 29 32 9.803817 9.887198 9.916619 10.083381 10.112802 10.196183 28 33 9.803970 9.887093 9.916877 10.083123 10.112907 10.196030 27 34 9.804123 9.886989 9.917134 10.082866 10.113011 10.195877 26 35 9.804276 9.886885 9.917391 10.082609 10.113115 10.195724 25 36 9.804428 9.886780 9.917648 10.082352 10.113220 10.195572 24 37 9.804581 9 886676 9.917905 10.082095 10.113324 10.195419 23 38 9.804734 9.886571 9.918163 10.081837 10.113429 10.195266 22 39 9.804886 9.886466 9.918420 10.081580 10.113534 10.195114 21 40 9.805039 9.886362 9.918677 10.081323 10.113638 10.194961 20 41 9.805191 9.886257 9.918934 10.081066 10.113743 10.1948U9 19 42 9.805343 9 886152 9.919191 10.080809 10.113848 10.194657 18 43 9.805495 9.886047 9.919448 10.080552 10.113953 10.194505 17 44 9.805647 9.885942 9.919705 10.080295 10.114058 10.194353 16 45 9.805799 9.885837 9.919962 10.080038 10.114163 10.194201 15 46 9.805951 9.885732 9.920219 10.079781 10.114268 10.194049 14 47 9.806103 9.885627 9.920476 10.079524 10.114373 10.193897 13 48 9.806254 9.885522 9.920733 10.079267 10.114478 10.193746 12 49 9.806406 9.885416 9.920990 10.079010 10.114584 10.193594 11 50 9 806557 9.885311 9.921247 10.078753 10.114689 10.193443 10 51 9.806709 9.885205 9.921503 10.078497 10.114795 10.193291 9 52 9.806860 9.885100 9.921760 10.078240 10.114900 10.193140 8 53 9.807011 9.884994 9.922017 10.077983 10.115006 10.192989 7 54 9.807163 9.884889 9.922274 10.077726 10.115111 10.192837 6 55 9.807314 9.884783 9.922530 10.077470 10.115217 10.192686 5 56 9.807465 9.884677 9.922787 10.077213 10.115323 10.192535 4 57 9.807615 9.884572 9 923044 10.076956 10.115428 10.192385 3 58 9.807766 9.884466 9.923300 10.076700 10.115534 ' 10.192234 2 59 9.807917 9.884360 9.923557 10.076443 10.115640 10.192083 1 60 9.808067 9.884254 9.923813 10.076187 10.115746 10.191933 M. Co-sine. Sine. Co-tang, j Tangent. Co-sec. Secant. M. SO l>?grees. TABLE II. 183 LOOAEITHMIC SINES, TANGENTS, AND SECANTS. 40 Degrees. M. Sine. Co-sine. jTangeni Co-tang. Secant. Co-sec. M. 9.80S067 9.884254 9.923813 10.076167 10.115746 10.191933 60 1 9.808218 9.884148 9.924070 10.075930 10.115852 10.191782 Q cj 2 9.808368 9.884042 9.924327 10.075673 10.115958 10.191632 58 3 9.808519 9.883936 9.924583 10.075417 10.116064 10.191481 57 4 9.8086G9 9.883829 9.924840 10.075160 10.116171 10.191331 56 5 9.808819 9.883723 9.925096 10.074904 10 116277 10.191181 55 6 9.808969 9.883617 9.925352 10.074648 10.116383 10.191031 54 7 9.809119 9.883510 9.925609 10.074391 10.116490 10.190881 53 8 9.809269 9.883404 9.925865 10.074135 10.116596 10.190731 52 9 9.809419 9.883297 9.926122 10.073878 10.116703 10.190581 51 10 9.809569 9.883191 9.926378 10.073622 10.116809 10.190431 50 11 9.809718 9.883U84 9.926634 10.073366 10.116916 10.190282 49 12 9.809868 9.882977 9.926890 10.073110 10.117023 10.190132 48 13 9.810017 9.882871 9.927147 10.072853 10.117129 10.189983 47 14 9.810167 9.882764 9.927403 10.072597 10.117236 10.189833 46 15 9.810316 9.882657 9.927659 10.072341 10.117343 10.189684 45 16 9.810465 9.882550 9.927915 10.072085 10.117450 10.189535 44 17 9.810614 9.882443 9.928171 10.071829 10.117557 10.189386 43 18 9.810763 9.882336 9.928427 10.071573 10.117664 10.189237 42 19 9.810912 9.882229 9.928683 10.071317 10.117771 10.189088 41 20 9.811061 9.882121 9.928940 10.071060 10.117879 10.188939 40 11 9.811210 9.882014 9.9*9196 10.07U804 10.117U86 10.188790 39 22 9.811358 9.881907 9.929452 10.070548 10.118093 10.188642 38 23 9.811507 9.881799 9.929708 10.070292 10.118201 10.188493 37 24 9.811655 9.881692 9.929964 10.070036 10.118308 10.188345 36 25 9.811804 9.881584 9.930220 10.069780 10.118416 10.188196 35 26 9.811952 9.881477 9.930475 10.069525 10.118523 10.188048 34 27 9.812100 9.881369 9.930731 10.0G9269 10.118631 10.187900 33 28 9.812248 9.881261 9.930987 10069013 10.118739 10.187752 32 29 9.812396 9.881153 9.931243 10.068757 10.118847 10.187604 31 30 9.812544 9.881046 9.931499 10 068501 10.118954 10.187456 30 31 9.812694 9.880958 9.931755 10.068245 10.119062 10.187308 9 32 9.812840 9.880830 9.932010 10.067990 10.119170 10.187160 28 33 9 812988 9.880722 9.932266 10.067734 10.119278 10.187012 27 34 9.813135 9.880613 9.932522 10.067478 10.119387 10.186865 26 35 9.813283 9.880505 9.932778 10.067222 10.119495 10.186717 25 36 9.813430 9.880397 9.933033 10.066967 10.119603 10.186570 24 37 9.813578 9.880289 9.933289 10.066711 10.119711 10.186422 23 38 9.813725 9.880180 9.933545 10.066455 10.119820 10.186275 22 39 9.813872 9.880072 9.933800 10.066200 10.119928 10.186128 21 40 9.814019 9.879963 9.934056 10.065944 10.120037 10.185981 20 41 9. 8 14166 9.879855 9.934311 10.065089 10.120145 10.185834 19 42 9.814313 9.879746 9 934567 10.065433 10.120254 10.185687 18 43 9.814460 9.879637 9.934823 10.065177 10.120363 10.185540 17 44 9 814607 9.879529 9 935078 10.064922 10.120471 10.185393 16 45 9.814753 9.879420 9.935333 10.064667 10.120580 10.185247 15 46 9.814900 9.879311 9 935589 10.064411 10.120689 10.185100 14 47 9.815046 9.879202 9.935844 10.064156 10.120798 10.184954 13 48 9.815193 9.879093 9.936100 10.063900 10.120907 10.184807 12 49 9.815339 9.878984 9.936355 10.063645 10.121016 10.184661 11 50 9.815485 9.878875 9.936610 10.063390 10.121125 10.184515 10 51 9 . 815632 9.878766 9.936866 10.063134 10.121234 10.184308 9 52 9.815778 9.878656 9.937121 10.062879 10.121344 10.184222 8 53 9.815924 9.878547 9.937376 10.062624 10.121453 10.184076 7 54 9.816069 9.878438 9.937632 10.062368 10.121562 10.183931 8 55 9.816215 9.878328 9.937887 10.062113 10.121672 10.183785 5 56 9.816361 9.878219 9.938142 10.061858 10.121781 10.183639 4 57 9.816507 9.878109 9.938398 10.061602 10.121891 10.183493 3 58 9.816652 9.877999 9.938653 10.061347 10.122001 10.183348 2 59 9.816798 9.877890 9.938908 10.061092 10.122110 10.183202 1 60 9 816943 9 877780 9.939163 10.060837 10.122220 10.183057 M. Co-sine. Sine. Co-tang. Tangent. Co-sec. Secant. M. 49 Degrees. 184: TABLE II. LOGARITHMIC SINES, TANGENTS, AND SECANTS. 41 Decrees. M. Sine. Co-sine. Tangent. Co-tang. Secant. Co-sec. M. y. 816943 9.877780 9.939163 10.060837 10.1222*0 10.183057 60 1 9.817088 9.877670 9.939418 10.060582 10.122330 10.182912 59 2 9.817233 9.877560 9.939673 10.060327 10.122440 10.182767 58 3 9.817379 9.877450 9.939928 10.060072 10.122550 10.182621 57 4 9.817524 9.877340 9.940183 10.059817 10.122660 10.182476 56 5 9.817668 9.877230 9.940438 10.059562 10.122770 10.182332 55 6 9.817813 9.877120 9.940694 10.059306 10.122880 10.182187 54 7 9.817958 9.877010 9.940949 10.059051 10.122990 10.182042 53 8 9.818103 9.876899 9.941204 10.058796 10.123101 10.181897 52 9 9.818247 9.876789 9.941458 10.058542 10.123211 10.181753 51 10 9.818392 9.876678 9.941714 10.058286 10.123322 10.181608 50 11 9.818536 9.876568 9.941968 10.058032 10. 123432 10.181464 49 12 9.818681 9.876457 9.942223 10.057777 10.123543 10.181319 48 13 9.818825 9.876347 9.942478 10.057522 10.123653 10.181175 47 14 9.818969 9.876236 9.942733 10.057267 10.123764 10.181031 46 15 9.819113 9.876125 9.942988 10.057012 10.123875 10.180887 45 16 9.819257 9.876014 9.943243 10.056757 10.123986 10.180743 44 17 9.819401 9.875904 9.943498 10.056502 10.124096 10.180599 43 18 9.819545 9.875793 9.943752 10.056248 10.124207 10.180455 42 19 9.819689 9 875682 9.944007 10.055993 10.124318 10.180311 41 20 9.819832 9 875571 9 944262 10.055738 10.124429 10.180168 40 21 9.81997(5 9.875459 9.944517 10.055483 10.124541 I0.18u0ki4 39 22 9.820120 9.875348 9.944771 10.055229 10.124652 10.179880 38 23 9.820263 9.875237 9.945026 10.054974 10.124763 10.179737 37 24 9.820406 9.875126 9.945281 10.054719 10.124874 10.179594 36 25 9.820550 9.875014 9.945535 10.054465 10.124986 10.179450 35 26 9.820693 9.874903 9.945790 10.054210 10.125097 10.179307 34 27 9.820836 9.874791 9.946045 10.053955 10.125209 10.179164 33 28 9.820979 9.874680 9.946299 10.053701 10.125320 10.179021 32 29 9.821122 9.874568 9.946554 10.053446 10.125432 10.178878 31 30 9.821265 9.874456 9.946808 10.053192 10.125544 10.178735 30 31 9.821407 9.874344 9.947003 10.052937 10.125656 10.178593 '29 32 9.821550 9.874232 9.947318 10.052682 10.125768 10.178450 28 33 9.821693 9.874121 9.947572 10.052428 10.125879 10.178307 27 34 9.821835 9.874009 9.947826 10.052174 10.125991 10.178165 26 35 9.821977 9.873896 9.948081 10.051919 10.126104 10.178023 25 36 9.822120 9.873784 9.948336 10.051664 10.126216 10.177880 24 37 9.822262 9.873672 9.948590 10.051410 10.126328 10.177738 23 38 9.822404 9.873560 9.948844 10.051156 10.126440 10.177596 22 39 9.822546 9.873448 9.949099 10.050901 10.126552 10.177454 21 40 9.822688 9.873335 9.949353 10.050647 10.126665 10.177312 20 41 9.822831) 9.873223 9.949607 10.050393 10.126777 10.177170 19 42 9.822972 9.873110 9.949862 10.050138 10.126890 10.177028 18 43 9.823114 9.872998 9.950116 10.049884 10.127002 10.176886 17 44 9.823255 9.872885 9.950370 10.049630 10.127115 10.176745 16 45 9.823397 9.872772 9.950625 10.049375 10.127228 10.176603 15 46 9.823539 9.872659 9.950879 10.049121 10.127341 10.176461 14 47 9.823680 9.872547 9.951133 10.048867 10.127453 10.176320 13 48 9.823821 9.872434 9.951388 10.048612 10.127566 10.176179 12 49 9.823963 9.872321 9.951642 10.048358 10.127679 10.176037 11 50 9.824104 9.872208 9.951896 10.048104 10.127792 10.175896 10 51 9.824245 9.8720U5 9.952150 10.047850 10.127905 10.175755 9 52 9.824386 9.871981 9.952405 10.047595 10.128019 10.175614 8 53 9.824527 9.871868 9.952659 10.047341 10.128132 10.175473 7 54 9.824668 9.871755 9.952913 10.047087 10.128245 10.175332 6 55 9.824808 9.871641 9.953167 10.046833 10.128359 10.175192 5 56 9.824949 9.871528 9.953421 10.046579 10.128472 10.175051 4 57 9.825090 9.871414 9.953675 10.046325 10.128586 10.174910 3 58 9.825230 9.871301 9.953929 10.046071 10.128699 10.174770 2 59 9.825371 9.871187 9.954183 10.045817 10.128813 10.174629 1 60 9.825511 9.871073 9.954437 10.015563 10.128927 10.174489 M. Co-sine. Sine. Co-tang. Tangent. Co-sec. Secant. M. 48 Decrees. TABLE H. 185 LOGARITHMIC SINES, TANGENTS, AND SECANTS. 42 Degrees. M. Sine. Co-sine. Tangent. Co-tang. Secant. Co-sec. M. 9.825511 9.871073 9.954437 10.045563 10.128927 10.174489 60 1 9.825651 9.870960 9.954691 10.045309 10.129040 10.174349 59 2 9 825791 9 870846 9.954945 10.045055 10.129154 10.174209 58 3 9.825931 9.870732 9.955200 10.044800 10.129268 10.174069 57 4 9.826071 9.870618 9 955454 10.044546 10.129382 10.173929 56 5 9.826211 9.870504 9 955707 10.044293 10.129496 10.173789 55 6 9.826351 9.870390 9.955961 10.044039 10.129610 10.173649 54 7 9.826491 9.870276 9.956215 10.043785 10.129724 10.173509 53 8 9.826631 9.870161 9.956469 10.043531 10.129839 10.173369 52 9 9.826770 9.870047 9.956723 10.043277 ]0. 129953 10.173230 51 10 9.826910 9.869933 9.956977 10.043023 10.13U067 10.173090 50 11 9.837049 9.869818 9.95/231 10.042769 10.130182 10.17iJ951 49 12 9.827189 9.869704 9.957485 10.042515 10.130296 10.172811 48 13 9.827328 9.869589 9.957739 10.042261 10.130411 10.172672 47 H 9.827467 9.869474 9.957993 10.042007 10.130526 10.172533 46 15 9.827606 9.869360 9.958246 10.041754 10.130640 10.172394 45 16 9.827745 9.869245 9.958500 10.041500 10.130755 10.172255 44 17 9.827884 9.869130 9.958754 10.041246 10.130870 10.172116 43 18 9.828023 9.869015 9.959008 10.040992 10.130925 10.171977 42 19 9.828162 9.868900 9.959262 10.040738 10.131100 10.171838 41 20 9.828301 9.868785 9.959516 10.040484 10.131215 10.171699 40 21 9.8^8439 9.868670 9.959769 10.040231 10.131330 10.171501 39 22 9.828578 9.868555 9.960023 10.039977 10.131445 10.171422 38 23 9.828716 9.868440 9.960277 10.039723 10.131560 10.171284 37 24 9.828855 9.868324 9.960531 10.039469 10.131676 10.171145 36 25 9.828993 9.868209 9.960784 10.039216 10.131791 10.171007 35 26 9.829131 9.868093 9.961038 10.038962 10.131907 10.170869 34 27 9.829269 9.867978 9.961291 10.038709 10.132022 10.170731 33 28 9.829407 9 867862 9.961545 10.038455 10.132138 10.170593 32 29 9.829545 9.867747 9.961799 10.038201 10.132253 10.170455 31 30 9 829683 9.867631 9.962052 10.037948 10.132369 10.170317 30 31 9.8298^1 9.867515 9.962306 10.057694 10.132485 10.170179 29 32 9.829959 9.867399 9.962560 10.037440 10.132601 10.170041 28 33 9.830097 9.867283 9.962813 10.037187 10.132717 10.169903 27 34 9.830234 9.867167 9.963067 10.036933 10.132833 10.169766 26 35 9.830372 9.867051 9.963320 10.036680 10.132949 10.169628 25 36 9.830509 9.866935 9.963574 10.036426 10.133065 10.169491 24 37 9.830646 9.866819 9.963827 10.036173 10.133181 10.169354 23 38 9.830784 9.866703 9.964081 10.035919 10.133297 10.169216 22 39 9.830921 9.866586 9.964335 10.035665 10.133414 10.169079 21 40 9.831058 9.866470 9.964588 10.035412 10.133530 10.168942 20 41 9.831195 9.866353 9.964842 10.035158 10.133647 10.108805 19 42 9.831332 9.866237 9.965095 10.034905 10.133763 10.168668 18 43 9.831469 9.866120 9.965349 10.034651 10.133880 10.168531 17 44 9.831606 9.866004 9.965602 10.034398 10.133996 10.168394 16 45 9.831742 9.865887 9.965855 10.034145 10.134113 10.168258 15 46 9.831879 9.865770 9.966109 10.033891 10.134230 10.168121 14 47 9.832015 9.865653 9.966362 10.033638 10.134347 10.167985 13 48 9.832152 9.865536 9.966616 10.033384 10.134464 10.167848 12 49 9.832288 9.865419 9.966869 10.033131 10.134581 10.167712 11 50 9.832425 9.865302 9.967123 10.032877 10.134698 10.167575 10 51 9.832561 9.865185 9.967376 10.032624 10.134815 10.167439 9 52 9.832697 9.865068 9.967629 10.032371 10.134932 10.167303 8 53 9.832833 9.864950 9.967883 10.032117 10.135050 10.167167 7 54 9.832969 9.864833 9.968136 10.031864 10.135167 10.167031 6 55 9.833105 9.864716 9.968389 10.031611 10.135284 10.166895 5 56 9.833241 9.864598 9.968643 10.031357 10.135402 10.166759 4 57 9.833377 9.864481 9.968896 10.031104 10.135519 10.166623 3 58 9.833512 9.864363 9.969149 10.030851 10.135637 10.166488 2 59 9.833648 9.864245 9.969403 10.030597 10.135755 10.166352 1 60 9.833783 9.864127 9.969656 10.030344 10.135873 10.166217 M. Co-sine. Sine. Co-tang. Tangent. Co-sec. Secant. M. 47 Degrees. 186 TABLE II. LOGARITHMIC SINES, TANGENTS, AND SECANTS. 43 Degrees. M. Sine. Co-sine. Tangent. Co-tang. Secant. Co-sec. M. y. 633783 9.864127 y.'jiwooo 10 030344 10.135873 10.166217 60 1 9.833919 9.864010 9.969909 10.030091 10.135990 10.166081 59 2 9.831054 9.863892 9 970162 10.029838 10.136108 10.165946 58 3 9.834189 9.863774 9.970416 10.029584 10.136226 10.165811 57 4 9 834325 9.863656 9.9706G9 10.029331 10.136344 10.165675 56 5 9.831460 9.863538 9.970922 10.029078 10.136462 10.165540 55 6 9.834595 9.863419 9.971175 10.028825 10.136581 10.165405 54 7 9.834730 9.863301 9.971429 10.028571 10.136699 10.165270 53 8 9.834865 9.863183 9.971682 10.028318 10.136817 10.165135 52 9 9.834999 9.863064 9.971935 10.028065 10.136936 10.165001 51 10 9 835134 9.862946 9 972188 10.027812 10.137054 10.164866 50 11 9.8352G ( J y . 862827 9.972441 10.0^:7559 10.137173 10.164731 49 12 9 835403 9.862709 9.972694 10.027306 10.137291 10.164597 48 13 9.835538 9.862590 9.972948 10.027052 10.137410 10.164462 47 14 9.835672 9 862471 9.973201 10.026799 10.137529 10.164328 46 15 9 835S07 9.862353 9.973454 10.026546 10.137647 10.164193 45 16 9.835941 9.862234 9.973707 10.026293 10.137766 10.164059 44 17 9.836075 9 862115 9.973960 10.026040 10.137885 10.163925 43 18 9.836209 9.861996 9.974213 10.025787 10.138004 10.163791 42 19 9.836343 9 861877 9 974466 10.025534 10.138123 10.163657 41 20 9.836477 9.861758 9.974719 10.025281 10.138242 10.163523 40 21 9.8J6611 9.8ol638 9.y/jy/3 10.025027 10.138362 10.103369 39 22 9.836745 9.861519 9.975226 10.024774 10.138181 10.163255 38 23 9.836878 9.861400 9.975479 10.024521 10.138600 10.163122 37 24 9 837012 9.861280 9.975732 10.024268 10.138720 10.162988 36 25 9.837146 9 861161 9.975985 10.024015 10.138839 10.162854 35 26 9.837279 9.861041 9.976238 10.023762 10.138959 10.162721 34 27 9.837412 9.860922 9.976491 10.023509 10.139078 10.162588 33 28 9.837546 9.860802 9.976744 10.023256 10.139198 10.162454 32 29 9.837679 9.860682 9.976997 10.023003 10.139318 10.162321 31 30 9.837812 9.860562 9.977250 10.022750 10.139438 10.162188 30 31 9.37945 9.8(30442 9.9/7503 10.022497 10.139558 10.102055 29 32 9 833078 9.860322 9 977756 10.022244 10.139678 10.161922 28 33 9.838211 9.860202 9.978009 10.021991 10.139798 10.161789 27 34 9.838344 9.860082 9.978262 10.021738 10.139918 10.161656 26 35 9 838477 9.859962 9.978515 10.021485 10.140038 10.161523 25 36 9 838310 9.859842 9.978768 10.021232 10.140158 10.161390 24 37 9.838742 9 859721 9.979021 10.020979 10.140279 10.161258 23 38 9.838875 9.859601 9.979274 10.020726 10.140399 10.161125 22 39 9.839007 9.859480 9.979527 10.020473 10.140520 10.160993 21 40 9.839140 9.859360 9.979780 10.020220 10.140640 10.160860 20 41 9.8.J92/2 9.859239 9.960033 lo.oiyyo7 10.140761 10.1GO/28 19 42 9.839404 9.859119 9.980286 10.019714 10.140881 10.160596 18 43 9.839536 9.858998 9.980538 10.019462 10.141002 10.160464 17 44 9.839668 9.858877 9 980791 10.019209 10.141123 10.160332 16 45 9.839800 9.858756 9.981044 10.018956 10.141244 10.160200 15 46 9.839932 9.858635 9.981297 10.018703 10.141365 10.160068 14 47 9.840064 9.858514 9.931550 10.018450 10.141486 10.159936 13 48 9.840196 9.858393 9.981803 10.018197 10.141607 10.159804 12 49 9.840328 9.858272 9.982056 10.017944 10.141728 10.159672 11 50 9.840459 9.858151 9.982309 10.017691 10.141849 10.159541 10 51 9.840591 9. 658029 9.925U2 10.017438 10.141971 10.159409 9 52 9.840722 9.&57908 9.982814 10.017186 10.142092 10.159278 8 53 9.840854 9.857786 9.983067 10.016933 10.142214 10.159146 7 54 9.840985 9.857665 9.983320 10.016680 10. 142335 10.159015 6 55 9 8U116 9.857543 9.983573 10.016427 10.142457 10.158884 5 56 9.841247 9.857422 9.983826 10.016174 10.142578 10.158753 4 57 9.841378 9 857300 9.984079 10.015921 10.142700 10.158622 3 58 9.841509 9.857178 9.984331 10.015669 10.142822 10.158491 2 59 9.841640 9.857056 9.984584 10.015416 10.142944 10.158360 1 60 9.841771 9.856934 9.981837 10.015163 10.143066 10.158229 M. Co-sine. Sine. Co-tang. Tangent. Co-sec. Secant. M. 4O Degrees. TABLE II. 187 LOGARITHMIC SIGNS, TANGENTS AND SECANTS. 44 Degrees. M. Sine. Co-sine. Tangent. Co-tang. Secant. Co-sec. If. 9.841771 9.850934 9.98437 10.015103 10.14oOOO 10.168229 00 l 9.841902 9 856812 9 985090 10.014910 10.143188 10.158098 59 '2 9.842033 9.856690 9.985343 10.014657 10.143310 10.157967 58 3 9.842163 9.856568 9.985596 10.014404 10.143432 10.157837 57 4 9 842294 9.856446 9.985848 10.014152 10.143554 10.157706 56 5 9.S42424 9.85G323 9.986101 10.013899 10.143677 10.157576 55 6 9.842555 9.856201 9.986354 10.013646 10.143799 10.157445 54 7 9.842685 9.856078 9.986607 10.013393 10.143922 10.157315 53 8 9.842815 9.855956 9.986860 10.013140 10.144044 10.157185 52 9 9.842946 9.855833 9.987112 10.012888 10.144167 10.157054 51 10 9.843076 9.855711 9.987365 10.012635 10.144289 10.150924 50 11 9.843206 9.85,3588 9.987018 10.012382 10.144412 10.1567U4 49 12 9.843336 9.855465 9 987871 10.012129 10.144535 10.150664 48 13 9.843466 9.855342 9.988123 10.011877 10.144658 10.156534 47 14 9.843595 9.855219 9.988376 10.011624 10.144781 10.156405 46 15 9.843725 9.855096 9.988629 10.011371 10.144904 10.156275 45 16 9.843855 9.854973 9.S88882 10.011118 10.145027 10.156145 44 17 9.843984 9 854850 9.989134 10.010866 10.145150 10.156016 43 18 9.844114 9.854727 9.989387 10.010613 10.145273 10.155886 42 19 9.844243 9.854603 9.989640 10.010360 10.145397 10.155757 41 20 9.844372 9.854480 9.989893 10.010107 10.145520 10.155628 40 21 9.844502 9.854356 9.990145 10.009*55 I0.14a044 10.155498 39 22 9 844631 9.854233 9.990398 10.009602 10.145767 10.155369 38 23 9.8447CO 9 854109 9.990651 10.009349 10.145891 10.155240 37 24 9.844889 9.853986 9.990903 10.009097 10.146014 10.155111 36 25 9.845018 9.853862 9 991156 10.008844 10.146138 10.154982 35 26 9 845147 9.853738 9.991409 10.008591 10.146262 10.154853 34 27 9 845276 9.853614 9 991662 10.008338 10.146386 10.154724 33 28 9.845405 9.853490 9 991914 10.008086 10.146510 10.154595 32 29 9.845533 9.853366 9.992167 10.007833 10.146634 10.154467 31 30 9.845662 9.853242 9.992420 10.007580 10.146758 10.154338 30 31 9.845790 9.853118 9.992G72 10.0073*8 10.1408S2 10.154210 29 82 9.845919 9.852994 9.992925 10.007075 10.147006 10.154081 28 33 9.846047 9.852869 9.993178 10.006822 10.147131 10.153953 27 34 9.846175 9.852745 9.993430 10.006570 10.147255 10.153825 26 35 9.84G304 9.852620 9.993683 10.006317 10.147380 10.153696 25 36 9.846432 9.852496 9.993936 10.006064 10.147504 10.153568 24 37 9.846560 9.852371 9.994189 10.005811 10.147629 10.153440 23 38 9.846688 9.852247 9.994441 10.005559 10.147753 10.153312 22 39 9.846816 9.852122 9.994G94 10.005306 10.147878 10.153184 21 40 9.846944 9.851997 9.994947 10.005053 10.148003 10.153056 20 41 9.847071 9.851872 9.995199 10.004801 10.148128 10.15*929 19 42 9.847199 9.851747 9.995452 10.004548 10.148253 10.152801 18 43 9.847327 9.851622 9.995705 10.004295 10.148378 10.152673 17 44 9.847454 9.851497 9.995957 10.004043 10.148503 10.152546 16 45 9.847582 9.851372 9.996210 10.003790 10.148628 10.152418 15 46 9.847709 9.851246 9.996463 10.003537 10.148754 10.152291 14 47 9.847836 9.851121 9.996715 10.003285 10.148879 10.152164 13 48 9.847964 9.850996 9.996968 10.003032 10.149004 10.152036 12 49 9.848091 9.850870 9.997221 10.002779 10.149130 10.151909 11 50 9.848218 9.850745 9.997473 10.002527 10.149255 10.151782 10 51 9.848345 9. 8500 19 9.997726 10.002274 10.149381 10.151655 9 52 9.848472 9.850493 9.997979 10.002021 10.149507 10.151528 8 53 9.848599 9.850368 9.998231 10.001769 10.149632 10.151401 7 54 9.848726 9.850242 9.998484 10.001516 10.149758 10.151274 6 55 9.848852 9.850116 9.998737 10.001263 10.149884 10.151148 5 56 9.848979 9.849990 9.998989 10.001011 10.150010 10.151021 4 57 9.849106 9 849864 9.999242 10.000758 10.150136 10.150894 3 58 9.849232 9 849738 9.999495 10.000505 10.150262 10.150708 2 59 9.849359 9.849611 9.999747 10.000253 10.150389 10.150641 1 60 9.849485 9.849485 0.000000 10.000000 10.150515 10.150515 M. | Co-sine. Sine. Co-tang. Tangent. Co-sec. Secant. M. 45 1 >.; r<-.--.. 188 TABLE III. DIFFERENCE OF LATITUDE AND DEPARTURE FOR ^ POINT. Dist. Lat. Dep Dist. Lat. Dep Dist. Lat. Dep Dist. Lat Dep. Dist. Lat. Dep. l 01.0 00.0 61 60.9 03.0 121 120.9 05.9 181 180.8 08.9 241 240.7 11.8 2 02.0 00.1 62 61.9 03.0 122 121.9 06.0 182 181.8 08.9 242 241.7 11.9 3 03.0 00.1 63 62.9 03.1 123 122.9 06.0 183 182.8 09.0 243 242 7 11.9 4 04.0 00.2 64 63.9 03.1 124 123.9 06.1 184 183.8 09.0 244 243.7 12,0 5 05.0 00.2 65 64.9 03.2 125 124.9 06.1 185 184.8 09.1 245 244.7 12.0 6 06.0 00.3 66 65.9 03.2 126 125.8 06.2 186 185.8 09.1 246 245.7 12.1 7 07.0 00.3 67 66.9 03.3 127 126.8 06.2 187 186.8 09.2 247 246.7 12.1 8 08.0 00.4 68 67.9 03.3 128 127.8 06.3 188 187.8 09.2 248 247.7 12.2 9 09 00.4 69 68.9 03.4 129 128.8 06.3 189 188.8 09.3 249 248.7 12.2 10 10.0 00.5 70 69.9 03.4 130 129.8 06.4 190 189.8 09.3 250 249.7 12.3 11 11.0 00.5 71 70.9 03.5 131 130.8 06.4 191 190.8 09.4 251 250.7 12.3 12 12.0 00.6 72 71.9 03.5 132 131.8 06.5 192 191.8 09.4 252 251.7 12.4 13 13.0 00. G 73 72.9 03.6 133 132.6 06.5 193 192.8 09.5 253 252.7 12.4 14 14.0 00.7 74 73.9 03.6 134 133.8 06.6 194 193 8 09.5 254 253.7 12.5 15 15.0 00.7 75 74.9 03.7 135 134.8 06.6 195 194.8 09.6 255 254.7 12.5 16 16.0 00.8 76 75.9 03.7 136 135.8 06.7 196 195.8 09.6 256 255.7 12.6 17 17.0 00.8 77 76.9 03.8 137 136.8 06.7 197 196.8 09.7 257 256.7 12.6 18 18.0 00.9 78 77.9 03.8 138 137.8 06.8 198 197.8 09.7 258 257.7 12.7 19 19.0 00.9 79 78 9 03.9 139 138.8 06.8 199 198.8 09.8 259 258.7 12.7 20 20.0 01.0 80 79. < 03 9 140 139.8 06.9 200 199.8 09.8 260 259.7 12.8 21 21.0 01.0 81 80.9 04.0 141 140. b 06.9 201 200.8 09.9 261 260.7 12.8 22 22.0 01.1 82 81.9 04.0 142 141.8 07.0 202 201.8 09.9 262 261.7 12.9 23 23.0 01.1 83 82.9 04.1 143 142.8 07.0 203 202.8 10.0 263 262.7 12.9 24 24.0 01.2 84 83.9 04.1 144 143.8 07.1 204 203.8 10.0 264 263.7 13.0 25 25.0 01.2 85 84.9 04.2 145 144.8 07.1 205 204.8 10.1 265 264.7 13.0 26 26.0 01.3 86 85.9 04.2 146 145.8 07.2 206 205.8 10.1 266 265.7 13.1 27 27.0 01.3 87 86.9 04.3 147 146.8 07.2 207 206.8 10.2 267 266.7 13.1 28 28.0 01.4 88 87.9 04.3 148 147.8 07.3 208 207.8 10.2 268 267.7 13.2 29 29.0 01.4 89 88.9 04.4 149 148.8 07.3 209 208.8 10.3 269 268.7 13.2 30 30.0 01.5 90 89.9 04.4 150 149.8 07.4 210 209.8 10.3 270 269.7 13.3 31 31.0 01.5 91 90.9 04.5 151 150.8 07.4 211 210.7 10.4 271 270.7 13.3 32 32.0 01.6 92 91.9 04.5 152 151.8 07.5 212 211.7 10.4 272 271.7 13.3 33 33.0 01.6 93 92.9 04.6 153 152.8 07.5 213 212.7 10.5 273 272.7 13.4 34 34.0 01.7 94 93.9 04.6 154 153.8 07.6 214 213.7 10.5 274 273.7 13.4 35 35.0 01.7 95 94.9 04.7 155 154.8 07.6 215 214.7 10.6 275 274.7 13.5 36 36 01.8 96 95.9 04.7 156 155.8 07.7 216 215.7 10.6 276 275.7 13.5 37 37.0 01.8 97 96.9 04.8 157 156.8 07.7 217 216.7 10.7 277 276.7 13.6 38 38.0 01.9 98 97.9 04.8 158 157.8 07.8 218 217.7 10.7 278 277.7 13.6 39 39.0 01.9 99 98.9 04.9 159 158.8 07.8 219 218.7 10.8 279 278.7 13.7 40 40.0 02.0 101 99. C J 04.9 160 159.8 07.9 220 219.7 10.8 280 279.7 13.7 41 41.0 02.0 101 100.9 05.0 161 160.8 07.9 221 220.7 10.8 281 280.7 13.8 42 41.9 02.1 102 101.9 05.0 162 161.8 08.0 222 221.7 10.9 282 281.7 13.8 43 42.9 02.1 103 102.9 05.1 163 162.8 08.0 223 222.7 10.9 283 282.7 13.9 44 43.9 02.2 104 103 9 05.1 164 163 8 08.1 224 223.7 11.0 284 283.7 13.9 45 44.902.2 105 104.9 05.2 165 164.8 08.1 225 224.7 11.0 285 284.7 14.0 46 45.9 02.3 106 105.9 05.2 166 165 8 08.2 226 225.7 11.1 286 285.7 14.0 47 46.9 02.3 107 106.9 05.3 167 166.8 08.2 227 226.7 11.1 287 286.7 14.1 48 47.9 02.4 108 107.9 05.3 168 167.8 08.2 228 227.7 11.2 288 287.7 14.1 49 48.902.4 109 108.9 05.4 169 168.8 08.3 229 228.7 11.2 289 288.7 14.2 50 49.902.5 110 109.9 05.4 170 169 8 08.3 230 229.7 11.3 290 289.7 14.2 51 50.902 5 111 110.9 05.5 171 170.8 08.4 231 230.7 11.3 291 290.7 14.3 52 51.902.6 112 111.9 05.5 172 171.8 08.4 232 231.7 11.4 292 291 7 14.3 53 52.902.6 113 112.9 05.5 173 172.8 08.5 233 232.7 11.4 293 292.7 14.4 54 53.902.7 114 113.9 05.6 174 173.8 08.5 234 233.7 11.5 294 293.6 14.4 55 54.902.7 115 114.9 05.6 175 174.8 08.6 235 234.7 11.5 295 294.6 14.5 56 55.902.8 116 115.9 05.7 176 175.8 08.6 236 235.7 11.6 296 295.6 14.5 57 56.902.8 117 116.9 05.7 177 176.8 08.7 237 236.7 11.6 297 296.6 14.6 58 57.902.9 118 117.9 05.8 178 177.8 08.7 238 237.7 11.7 298 497.6 14.6 59 58.902.9 119 118 9 05.8 179 178.8 08.8 239 238.7 11.7 299 298.6 14.7 60 59.9 02 9 120 119.9 05.9 180 179.8 08.8 240 239.7 11.8 300 299.6 14.7 Dist. Dep Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dcp. Lat. Dist. 1 Dep. Lat. For 7f Points. TABLE III. 189 DIFFERENCE OF LATITUDE AND DEPARTURE FOR ^ POINT. Dist. Lat. Dep Dist. Lat. Dep Dist. Lat. Dep Dist. Lat. Dep. Dist. Lat. Dep. 1 1 01.000.1 61 60.7 06.0 121 120.4 11.9 181 180.1 17.7 241 239.8 23.6 2 02.0 00.2 62 61 7 06 1 122 121.4 12.0 182 181.1 17.8 242 240.8 23.7 3 03.0 00.3 63 62.7 06.2 123 122.4 12.1 183 182.1 17.9 243 241.8 23.8 4 04.0 00.4 64 63.7 06.3 124 123.4 12.2 184 183.1 18.0 244 242.8 23.9 5 05. G 00.5 65 64.7 06.4 125 124.4 12.3 185 184.1 18.1 245 243.8 24.0 6 06.0 00.6 66 65.7 06.5 126 125.4 12.3 186 185.1 18.2 246 244.8 24.1 7 07. G 00.7 67 66.7 06 6 127 126.4 12.4 187 186.1 18.3 247 245.8 24.2 8 08.0 00.8 68 67.7 06.7 128 127.4 12.5 188 187.1 18.4 248 246 8 24.3 9 09. G 00.9 69 68.7 06 8 129 128.4 12.6 189 188.1 18.5 249 247.3 24.4 Id 10. G 01. G 70 69.7 06.9 130 129.4 12.7 19( 189.1 18.6 250 248.8 24.5 11 10.9 01.1 71 70.7 07.0 131 130.4 12.8 191 190.1 18.7 251 249.8 24.6 12 11.9 01.2 72 71.7 07.1 132 131.4 12.9 192 191.1 18.8 252 250.8 24.7 13 12.9 01.3 73 72.6 07.2 133 132.4 13.0 193 192.1 18.9 253 251. b 24.8 14 13 9 01.4 74 73.6 07.3 134 133.4 13.1 194 193.1 19.0 254 252.8 24.9 15 14.9 01.5 75 74.6 07.4 135 134. 13.2 195 194.1 19.1 255 253.8 25.0 16 15.9 01.6 76 75.6 07.4 136 135. 13.3 196 195.x 19.2 256 254.8 25.1 17 16.9 01.7 77 76.6 07.5 137 136. 13.4 197 196.1 19.3 257 255.8 25.2 18 17.9 01.8 78 77.6 07.6 138 137. 13.5 198 197.0 19.4 258 256. b 25.3 19 18.9 01.9 79 78.6 07.7 188 138. 13. G 199 198.0 19.5 259 257.8 25.4 20 19.9 02 80 79.6 07.8 140 139. 13.7 200 199.0 19.6 260 258 7 25.5 21 20.9 02.1 81 80.6 07.9 1411 140. 13.8 201 200. G 19.7 *261 259. 25.6 22 21 6 02.2 82 81.6 08.0 142 141. 13.9 202 201.0 19.8 262 260. 25.7 23 22.9 02.3 83 82.6 08.1 143 142. 14. G 203 202.0 19.9 263 261. 25.8 24 23.9 02.4 84 83.6 08.2 144 143. 14.1 204 2G3.0 20. G 264 262. 25.9 25 24.9 02.4 85 84.6 08.3 145 144. 14.2 205 204. G 20.1 265 263. 26.0 26 25.9 02 5 86 85.6 08.4 146 145. 14.3 206 205.0 20.2 266 264. 26.1 27 26.9 02.6 87 86.6 08.5 147 146. 14.4 207 206. G 20.3 267 265. 26.2 28 27.9 02.7 8b 87.6 08.6 148 147. 14.5 208 207.0 20.4 268 266. 26.3 29 28.9 02.8 89 88.608.7 149 148. 14.6 209 208.0 20.5 269 267 26.4 30 29.9 02.9 90 89.6,08.8 150 149. 14.7 210 209.0 20.6 270 268. 26.5 31 30.9 03.0 91 90.608.9 151 150. 14. b 211 210.0 20.7 271 209. 26.6 32 31.8 03.1 92 91.609.0 152 151. 14.9 212 211.0 20.8 272 270. 26.7 33 32.8 03.2 93 92 609.1 153 152. 15. G 213 212.0 20.9 273 271. 26.8 34 33.8 03.3 94 93 509.2 154 153. 15.1 214 213.0 21.0 274 272. 26.9 35 34.8 03.4 95 94 509.3 155 154. 15.2 215 214.0 21.1 275 273. 27.0 36 35.8 03.5 96 95.509.4 156 155. 15.3 216 215.0 21.2 276 274. 27.1 37 136.8 03.6 97 96.509.5 157 156.2 15.4 217 216.0 21.3 277 275.7 27.2 38 37.8 03.7 98 97.509.6 158 157.2 15.5 218 216.9 21.4 278 276.7 27.3 39 38.8 03.8 99 98.5 09.7 159 158.2 15.6 219 217.9 21.5 279 277.7 27.3 40 39.8 03.9 100 99.5 09.8 160 159.2 15.7 220 218.9 21.6 280 278.7 27.4 41 40. b 04. G 101 1G0.5 09.9 161 160.2 15.8 221 219.9 21.7 281 279. G 27 5 42 41.8 04.1 102 101.5 10.0 162 161.2 15.9 222 220.9 21.8 282 280.6 27.6 43 42.8 04.2 103 102.5 10.1 163 162.2 16.0 223 221.9 21.9 283 281.6 27.7 44 43.8 04.3 104 103.5 10.2 164 163.2 16.1 224 222.9 22.0 284 282.6 27.8 45 44.8 04.4 105 104.510.3 165 164.2 16.2 225 223.9 22.1 285 283.6 27.9 46 45.8 04.5 106 105.510.4 166 165.2 16.3 226 224.9 22 2 286 284.6 28.0 47 46.8 04.6 107 106.5110.5 167 166.2 16.4 227 225.9 22~2 287 285.6 28.1 48 47.8 04.7 108 107.5 10.6 168 167.2 16.5 228 226.9 22.3 288 286.6 28.2 49 48.8 04.8 109 108.5 10.7 169 168.2 16.6 229 227.9 22.4 289 287.6 28.3 50 49.8 04.9 110 109.5 10.8 170 169.2 16.7 230 228.9 22.5 290 288.6 28.4 51 150.8 05.0 111 110.5 10.9 171 170.2 16.8 231 229.9 22.6' 291 289.6 28.5 52 51.7 05.1 112 111.5 11.0 172 171.2 16.9 232 230.9 22.7 292 290.6 28.6 53 52.7 05.2 113 112.5 11.1 173 172.2 17.0 233 231.9 22.8 293 291.6 28.7 54 53.7 05.3 114 113.5 11.2 174 173.2 17.1 234 232.9 22. 9 : 294 292.6 28.8 55 54.7 05.4 115 114.4 11.3 175 174.2 17.2 235 233.9 23.0 295 293.6 28.9 56 55.7 05.5 116 115.4 11.4 176 175.2 17.3 236 234.9 23.1 296 294.6 29.0 57 56.7 05.6 117 116.4 11.5 177 176.1 17.4 237 235.9 23.2 297 295.6 29.1 58 57.7 05.7 118 117.4 11.6 178 177.1 17.4 238 236.9 23. 3 1 298 296.6 29.2 59 58.7 05.8 119 118.4 11.7 179 178.1 17.5 239 237.8 23.4 299 297.6 29.3 60 59.7 05.9 120 119.4 11.8 180 179.1 17.6 240 238.8 23.5 300 298.6 29.4 Dist. Dep Lat. Dist. Dcp. Lat. Dist. Dep. Lat. Dist. Dcp. Lat. Dist. Dcp. Lat, For 7 Points. 190 TABLE III. DIFFERENCE OF LATITUDE AND DEPARTURE FOR J POINT. Dist, Lat. Dep Dist, Lat. Dep Dist, Lat. Dep Dist. Lat. Dep. Dist. Lat. Dep. 1 Jl.G 00.1 61 60.3 09.0 121 119.7 17.8 181 179.0 26.6 241 238.4 35.4 2 02.0 00.3 62 61.3 09.1 122 120.7 17.9 182 180.0 26.7 242 239.4 35.5 3 03.0 00.4 63 62.3 09.2 123 121.7 18.1 183 181.0 26.9 243 240.4 35.7 4 04'. I 00.6 64 63.3 08.4 124 122.7 18.2 184 182.0 27.0 244 241.4 35.8 5 04.9 00.7 65 64.3 09.5 125 123.7 18.3 185 183.0 27.2 245 242.4 36.0 6 05.8 00.9 66 65.3 09.7 126 124.6 18.5 186 184.0 27.3 246 243.3 36.1 7 06.9 Jl.O 67 66.3 09.8 127 125.6 18.6 187 185.0 27.4 247 244.3 36.2 8 07.9 01.2 68 67.3 10.0 128 126.6 18.8 188 186.0 27.6 248 245.3 36.4 9 J8.9 01.3 69 68.3 10.1 129 127. C 18.9 189 187.0 27.7 249 246.3 36.5 10 09.9 J1.5 70 69.2 10.3 131 128. C 19.1 19ii 187.9 27.9 250 247.3 36.7 11 10.9 Ol.b 71 70.* 10.4 131 129.6 19. '2 19 1 188.9 28.0 251 148.3 36.8 12 11.9 01.8 72 71.2 10.6 132 130.6 19.4 192 189.9 28.2 252 249.3 37.0 13 12.9 01.9 73 72.2 10.7 133 131.6 19.5 193 190.9 28.3 253 250.3 37.1 14 13.9 02 1 74 73.2 10.9 134 132.6 19.7 194 191.9 28. 254 251.3 37.3 15 14. 8 02.2 75 74.2 11.0 135 133.5 19.8 195 192.9 28.6 255 252.2 37.4 16 15.8 02.3 76 75.2 11.2 136 134.5 20.0 196 193.9 28.8 256 253.2 37.6 17 16.8 02.5 77 76.2 11.3 137 135.5 20.1 197 194.9 28.9 257 254.2 37.7 18 17.8 02.6 78 77.2 11.4 138 136.5 20.3 198 195.9 29.1 258 255.2 37.9 19 18.8 02.8 79 78.1 11.6 139 137.5 20.4 199 196.8 29.2 259 256.2 38.0 '20 19.8 02.9 80 79.1 11.7 140 138.5 20.5 200 197.8 29.4 260 257.2 38.2 21 20.8 J3.1 81 80.1 11.9 141 139.5 20.7 201 198.8 29.5 261 *58 . 2 38.3 22 21> 03.2 82 81.1 12.0 142 140 5 20.8 202 199.8 29.6 262 259 .'2 38.4 23 22.8 03.4 83 82.1 12.2 143 141.5 21.0 203 200.8 29.8 263 260.2 38.6 24 23.7 03.5 84 83.1 12.3 144 142.4 21.1 204 201.8 29.9 264 261.1 38.7 25 24.7 03.7 85 84.1 12.5 145 143.4 21.3 205 202.8 30.1 265 262.1 38.9 26 25.7 03.8 86 85.1 12.6 146 144.421.4 206 203.8 30.2 266 263.1 39.0 27 26.7 04.0 87 86.1 12.8 147 145.4 21.6 207 204.8 30.4 267 264.1 39 2 28 27.7 04.1 88 87.1 12.9 148 146.4 21.7 208 205.8 30.5 268 265.1 39.3 29 28.7 04.3 89 88.0 13.1 149 147.4 21.9 209 206.7 30.7 269 266.1 39.5 30 29.7 04.4 90 89.0 13.2 150 148.4 22.0 210 207.7 30.8 270 267.1 39.6 31 30.7 04.6 91 90.013.4 151 19.4 22. '2 211 208.7 31.0 271 268.1 39.8 32 31.7 04.7 92 91.013.5 152 150.4 22.3 212 209.7 31.1 272 269.1 39.9 33 32.604.8 93 92.013.7 153 151.3 22.5 213 210.7 31.3 273 270.0 40.1 34 33.6 05.0 94 93.013.8 154 152.3 22.6 214 211.7 31.4 274 271.0 40.2 35 34.6 05.1 95 94.0 ! 13.9 155 153.3 22.7 215 212.7 31.6 275 272.0 40.4 36 35.6 05.3 96 95.014.1 156 154.3 22.9 216 213.7 31.7 276 273.0 40.5 37 36.6 ()5.4 97 96.014.2 157 155.3 23.0 217 214.7 31.8 277 274.0 40.6 38 37.6 05.6 98 96.914.4 158 156.3 23.2 218 215.6 32.0 278 275.0 40.8 I 39 38.6 05.7 99 97.914.5 159 157.3 23.3 219 216.6 32.1 279 276.0 40.9 40 39.6 05.9 100 98.914.7 160 158.3 23.5 220 217.6 32.3 280 277.0 41.1 41 40.6 06.0 101 99.9114. 8 161 159.3 23.6 221 218.6 32.4 281 278.0 41.2 42 41.6 06.2 102 100.915.0 162 160.3 23.8 222 219.6 32.6 282 279.0 41.4 43 42.5 06.3 103 101.915.1 163 161.2 23.9 223 220.6 32.7 283 279.9 41.5 44 43.5 06.5 104 102.915.3 164 162.2 24.1 224 221.6 32.9 284 280.9 41.7 45 44.5 06.6 105 103.9 15.4 165 163.2 24.2 225 222.6 33.0 285 281.9 41.8 46 45.5 06.8 106 104.9 15.6 166 164.2 24.4 226 223.6 33.2 286 282.9 42.0 47 46.5 06.9 107 105.8 15.7 167 165.2 24.5 227 224.5 33.3 287 283.9 42.1 48 47.5 07.0 108 106.815.9 168 166.2 24.7 228 225.5 33.5 288 284.9 42.3 49 48.5 07.2 109 107.816.0 169 167.2 24.8 229 226.5 33.6 289 285.9 42.4 50 49.5 07.3 110 108.816.1 170 168.2 24.9 230 227.5 33.8 290 286.9 42.6 51 50.5 07.5 111 109.8 16.3 171 169.2 25.1 231 228.5 33.9 291 287.9 42.7 52 51.4 07.6 112 110.8 16.4 172 170.1 25.3 232 229.5 34.0 292 288.8 42.9 53 52.4 07.8 113 111.8 16.6 173 171.1 25.4 233 230.5 34.2 293 289.8 43.0 54 53.4 07.9 114 112.8 16.7 174 172.1 25.5 234 231.5 34.3 294 290.8 43.1 55 54.4 08.1 115 113.8 16.9 175 173.1 25.7 235 232.5 34.5 295 291.8 43.3 56 55.4 08.2 116 114.7 17.0 176 174.1 25.8 236 233.4 34.6 296 292.8 43.4 57 56.4 08.4 117 115.7 17.2 177 175.1 26.0 237 234.4 34.8 297 293.8 43. fc 58 57.4 08.5 118 116 7 17.3 178 176.1 26.1 238 235.4 34.9 298 294.8 43.7 59 58.4 08.7 119 117.7 17.5 179 177.1 26.3 239 236.4 35.1 299 295.8 43.0 60 59.4 08.8 120 118.7 17.6 180 178.1 26.4 240 237.4 35.2 300 296.8 44. ( Dist. Dep Lat. Dist, Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist, Dep. L^t. For 7 Points. , TABLE III. 191 DIFFERENCE OF LATITUDE AND DEPARTURE FOR 1 POINT. Dep Lat. Dist. Dist. Lat. Dep Dist. Lat. Dep Dist. Lat. Dep. Dist, Lat. Dep. 1 01.0 00.2 61 59.8 11.9 121 118.7 23.6 181 177.5 35.3 241 236.4 47.0 2 02.0 00.4 62 60.8 12.1 122 119.7 23.8 182 178.5 35.5 242 237.4 47.2 3 02.9 00.6 63 61.8 12.3 123 120.6 24.0 183 179.5 35.7 243 238.3 47.4 4 03.9 00.8 64 62.8 12.5 124 121.6 24.2 184 180.5 35.9 244 239.3 47.6 5 04.9 01.0 65 63.8 12.7 125 122.6 24.4 185 181.5 36.1 245 240.3 47.8 6 05.9 01.2 66 64.7 12.9 '126 123.6 24.6 186 182.4 36.3 246 241.3 48.0 7 06.9 01.4 67 65.7 13.1 127 124.6 24.8 187 183.4 36.5 247 242.3 48.2 8 07.8 01.6 68 66.7 13.3 128 125.5 25.0 188 184.4 36.7 248 243.2 48.4 9 08.8 01.8 69 67.7 13.5 129 126.5 25.2 189 185.4 36.9 249 244.2 48.6 10 09.8 02.0 70 68.7 13.7 130 127.5 25.4 190 186.4 37.1 250 245.2 48.8 11 10.8 U2.2 71 69.6 13.9 131 128.5 25.0 19 1 187.3 37.3 251 246.2 49.0 12 11.8 02.3 72 70.6 14.0 132 129 5 25.8 192 188.3 37.5 252 247.2 49.2 13 12.8 02. L 73 71.6 14.2 133 130.5 26.0 19J 189.3 37.7 253 248.1 49.4 14 13.7 02.7 74 72. C 14.4 134 131.4 26.1 194 190.3 37.8 254 249.1 49.6 15 14.7 02.9 75 73. C 14.6 135 132.4 26.3 195 191.3 38.0 255 250.1 49.7' 16 15.7 03.1 76 74.5 14.8 136 133.4 26.5 196 192.2 38.2 256 251. 1 49.9 17 16.7 03.3 77 75.5 15.0 137 134.4 26.7 197 193.2 38.4 257 252.1 50.1 18 17.7 03.5 78 76.5 15.2 138 135.4 26.9 198 194.2 38.6 258 253.0 50.3 19 18.6 03.7 79 77.5 15.4 139 136.3 27.1 199 195.2 38.8 259 254.0 50.5 20 19.6 03.9 80 78.5 15.6 140 137 3 27.3 200 196.2 39.0 260 255.0 50.7 21 20.6 04.1 81 79.4 15. b 141 138.3 27.5 201 197.1 39.2 261 256.0 50.9 22 21.6 04.3 82 80.4 16.0 142 139.3 27.7 20'2 198.1 39.4 262 257.0 51.1 23 22. C 04.5 83 81.4 16.2 143 140.3 27.9 203 199.1 39.6 263 258.0 51.3 24 23.5 04.7 84 82.4 16.4 144 141.2 28.1 204 200.1 39.8 264 258.9 51.5 25 24. & 04.9 85 83.4 16.6 145 142.2 28.3 205 201.1 40.0 265 259.9 51.7 26 25.5 05.1 86 84.4 16.8 146 143.2 28.5 206 202.0 40.2 266 260.9 51.9 27 26.5 05.3 87 85.3 17.0 147 144.2 28.7 207 203.0 40.4 267 261.9 52.1 28 27.5 05. C 88 86.3 17.2 148 145.2 28.9 208 204.0 40.6 268 262.9 52.3 29 28.4 05.7 89 87.3 17.4 149 146.1 29.1 209 205.0 40.8 269 263.8 52.5 30 29.4 05.0 90 88.3 17.6 150 147.1 29.3 210 206.0 41.0 270 264.8 52.7 31 30.4 06.0 91 89.3 17.8 151 148.1 29.5 211 207.0 41.2 271 265.8 52.9 32 31.- i 06.2 92 90.2 18.0 152 149.1 29.7 212 207.9 41.4 272 266.8 53.1 33 32.4 06.4 93 91.2 18.1 153 150.1 29.9 213 208.9 41. 6 1 273 267.8 53.3 34 33.4 06.6 94 92. * 18.3 154 151.0 30.0 214 209.9 41.8 274 268.7 53.5 35 34.3 ^6.8 95 93.2 18.5 155 152.0 30.2 215 210.9 41.9 275 269.7 53.6 36 35.3 07.0 96 94.2 18.7 156 153.0 30.4 216 211.9 42.1 276 270.7 53.8 37 36.3 07.2 97 95.1 18.9 157 154.0 30.6 217 212.8 42.3 277 271.7 54.0 38 37.3 07.4 98 96.1 19.1 158 155.0 30.8 218 213.8 42.5 278 272.7 54.2 39 38.3 07.6 99 97.1 19.3 159 156.0 31.0 219 214.8 42.7 279 273.6 54.4 40 39.2 07.8 100 98.1 19.5 160 156.9 31.2 220 215.8 42.9 280 274.6 54.6 41 40.2 08.0 101 99.1 19.7 161 157.9 31.4 221 216.8 43.1 281 275.6 54.8 42 41.2 08.2 102 100.0 19. 9 162 158.9 31.6 222 217.7 43.3 282 276.6 55.0 43 42.2 08.4 103 101.0 20.1 163 159.9 31. & 223 218.7 43.5 283 277.6 55.2 44 43.2 08.6 104 102.020.3 164 160.9 32.0 224 219.7 43.7 284 278.5 55.4 45 44.1 08.8 105 103.020.5 165 161.8 32.2 225 220.7 43.9 285 279.5 55.6 46 45.1 09.0 106 104.020.7 166 162.8 32.4 226 221.7 44.1 286 280.5 55.8 47 46.1 09.2 107 104.920.9 167 163.8 32 6 227 222.6 44.3 287 281.5 56.0 48 47.1 09.4 108 105.921.1 168 164.8 32.8 228 223.6 44.5 288 282.5 56.2 49 48.1 09.6 109 106.921.3 169 165.8 33.0 229 224.6 44.7 289 283.5 56.4 50 49.0 09.8 110 107.921.5 170 166.7 S3. 2 230 225.6 44.9 290 284.4 56.6 51 50.0 10.0 111 108.9:21.7 171 167.7 33.4 231 226.6 45.1 291 285.4 56. b 52 51.0 10.1 112 109 921.9 172 168.7 33.6 232 227.5 45.3 292 286.4 57.0 53 52.0 10.3 113 110.822.0 173 169.7 33.8 233 228.5 45.5 293 287.4 57.2 54 53.0 10.5 114 111.822.2 174 170.7 34.0 234 229.5 45.7 294 288.4 57.4 55 53.9 10.7 115 112.822.4 175 171.6 34.1 235 230.5 45.9 295 289.3 57.6 56 54.9 10.9 116 113. 822. C 176 172.6 34.3 236 231.5 46.0 296 290.3 57.7 57 55.9 11.1 117 114.822.8 )77 173. C 34.5 237 232.5 46.2 297 291.3 67.9 58 56.9 11.3 118 115.7 23.0 178 174.6 34.7 238 233.4 46.4 298 292.3 58.1 59 57.9 11.5 119 116.7 23.2 179 175.6 34.9 239 234.4 46.6 299 293.3 58.3 60 58.8 11.7 120 117.7 23.4 180 176.5 35.1 240 235.4 46.8 300 294.2 58.5 Dist, Dep Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist, Dep. Lat. Dist. Dep. Lat. For 7 Points. 192 TABLE III. DIFFERENCE OF LATITUDE AND DEPARTURE FOR 1J POINT. Dist. Lat. Dep Dist. Lat. Dep 'Dist. Lat. Dep Dist. Lat. Dep. Dist. Lat. Dep. 1 01.000.2 61 59.2 14.8 121 117.4 29.4 181 175.6 44.0 241 233.8 58.6 2 01.900.5 62 60.1 15.1 122 118.4129.6 182 176.5 44.2 242 234.8 58.8 3 02.900.7 63 61.1 15.3 123 119.329.9 183 177.5 44.5 243 235.7 59.0 4 03.9 01.0 64 62.1 15.6 124 120.330.1 184 178.5 44.7 244 236.7 59.3 5 04.9 01.2 65 63.1 15.8 125 121.330.4 185 179.5 45.0 245 237.7 59.5 6 05.8 01.5 66 64.0 16.0 126 122.2 30.6 186 180.4 45.2 246 238.6 59.8 7 06.8 01.7 67 65.0 16 3 127 123.2 30.9 187 181.4 45.4 247 239.6 60.0 8 07.8 01.9 68 66.0 16.5 128 124.231.1 188 182.4 45.7 248 240.6 60.3 9 08.7 02.2 69 66.9 16.8 129 125.1 31.3 189 183.3 45.9 249 241.6 60.5 10 09.7 02.4 70 67.9 17.0 130 126.1J31 6 190 184.3 46.2 250 242.5 60.8 11 10.7 02.7 71 6a.y 17.3 131 127.1 31.8 191 185.3 46.4 251 243.5 61.0 12 11.6 02.9 72 69.9 17.5 132 128.1 32.1 192 186.2 46.7 252 244.5 61.2 13 12.6 03.2 73 70.8 17.7 133 129. Oi 32. 3 193 187.2 46.9 253 245.4 61.5 14 13.6 03.4 74 71.8 18.0 134 130.032.6 194 188.2 47.1 254 256.4 61.7 15 14.6 03.6 75 72.8 18.2 135 131.032.8 195 189.2 47.4 255 247.4 62.0 16 15.5 03.9 76 73.7 18.5 136 131.933.1 196 190.1 47.6 256 248.3 62.2 17 16.5 04.1 77 74.7 18.7 137 132.933.3 197 191.1 47.9 257 249.3 62.5 18 17.5 04.4 78 75.7 19.0 138 133.933.5 198 192.1 48.1 258 250.3 62.7 19 18.4 04.6 79 76.6 19.2 139 134 833.8 199 193.0 48.4 259 251.3 62.9 20 19.4 04.9 80 77.6 19.4 140 135.834.0 200 194.0 48.6 260 252.2 63.2 21 20.4 05.1 81 78.6 19.7 141 136.834.3 201 195.0 48.8 261 253.2 63.4 22 21.3 05 4 82 79.6 19.9 142 137.834.5 202 196.0 49.1 262 254.2 63.7 23 22.3 05.6 83 80.5 20.2 143 138.7 34.8 203 196.9 49.3 263 255.1 63.9 24 23.3 05.8 84 81.5 20.4 144 139.735.0 204 197.9 49.6 264 256.1 64.2 25 24.3 06.1 85 82.5 20.7 145 140.7 35.2 205 198.9 49.8 265 257.1 64.4 26 25.2 06.3 86 83.4 20.9 146 141.6 35.5 206 199.8 50.1 266 258.0 64.6 27 26.2 06 6 87 84.4 21.1 147 142.6 35.7 207 200.8 50.3 267 259.0 64.9 28 27.2 06.8 88 85.4 21.4 148 143.6 36.0 208 201.8 50.5 268 260.0 65.1 29 28.1 07.1 89 86.3 21.6 149 144.5 36.2 209 202.7 50.8 269 261.0 65.4 30 29.1 07.3 90 87.321.9 150 145.5 36.5 210 203.7 51.0 270 261.9 65. 6^ 31 30.1 07.5 91 88.322.1 151 146.536.7 211 204.7 51.3 271 262.9 65.9 32 31.0 07.8 92 89.3 22.4 152 147.4 36.9 212 205.7 51.5 272 263.9 66.1 33 32.0 08.0 93 90.222.6 153 148.4 37.2 213 206.6 51.8 273 264.8 66.3 34 33.0 08.3 94 91.222.8 154 149.4 ! 37.4 214 207.6 52.0 274 265.8 66.6 35 34.0 08.5 95 92.223.1 155 150.437.7 215 208.6 52.2 275 266.8 66.8 36 34.9 08.8 96 93.1 23.3 156 151.337.9 216 209.5 52.5 276 267.7 67.1 37 35.9 09.0 97 94.1 23.6 157 152.338.2 217 210.5 52.7 277 268.7 67.3 38 36.9 09.2 98 95.1 23.8 158 153.3J38.4 218 211.5 53.0 278 269.7 67.6 39 37.8 09.5 99 96.0 24.1 159 154.2 38.6 219 212.5 53.2 279 270.7 67.8 40 38.8 00.7 100 97.0 24.3 160 155. 2| 38. 9 220 213.4 53.5 280 271.6 68.0 41 39.8 10.0 101 9S.O 24.5 161 156.239.1 221 214.4 53.7 281 272.6 68.3 42 40.7 10.2 102 99.0 24.8 162 157.2 39.4 222 215.4 53.9 282 273.6 68.5 43 41.7 10.5 103 99.9 25.0 163 158.1 39.6 223 216.3 54.2 283 274.5 68.8 44 42.7 10.7 104 100.9 25.3 164 159.1 39.9 224 217.3 54.4 284 275.5 69.0 45 43.7 10.9 105 101.9 25.5 165 160.1 40.1 225 218.3 54 7 285 276.5 69.3 46 44.6 11.2 106 102.8 25.8 166 161.0 40.3 226 219.2 54.9 286 277.4 69.5 47 45.6 11.4 107 103.8 26.0 167 162 40.6 227 220.2 55.2 287 278.4 69.7 48 46.6 11.7 108 104.8 26.2 168 163.0 40.8 228 221.2 55.4 288 279.4 70.0 49 47.5 11.9 109 105.7 26.5 169 163.9 41.1 229 222 2 55 6 289 280.4 70.2 50 48 512.2 110 106.7 26.7 170 164.9 41.3 230 223.1 55.9 290 281.3 70.5 51 49.512.4 111 107.7 27.0 171 165.9 41.6 231 224.1 56.1 291 282.3 70.7 52 50.412.6 112 108.7 27.2 172 166.9 41.8 232 225.1 56.4 292 283.3 71.0 53 51.412.9 113 109.6 27.5 173 167.842.0 233 226.0 56.6 293 284.2 71.2 54 52.413.1 114 110.6 27.7 174 168.842.3 234 227.0 56.9 294 285.2 71 4 55 53.413.4 115 111.6 27.9 175 169.8 42.5 235 228.0 57.1 295 286.2 71.7 56 54.313.6 116 112.5 28.2 176 170.7 42.8 236 228.9 57.3 296 287.1 71.9 57 55.313.9 117 113.5 28.4 177 171.7 43.0 237 229.9 57.6 297 288.1 72.2 58 56.314.1 118 114.5 28.7 178 172.7 43.3 238 230.9 57.8 298 289.1 72.4 59 57.214.3 119 115.4 28.9 179 173.6 43.5 239 231.8 58.1 299 290.1 72.7 60 58.2 14.6 120 116.4 29.2 180 174.6 43.7 240 232.8 58.3 300 291.0 72.9 Dist. Dep Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. For 6| Points. TABLE HI. 193 DIFFERENCE OF LATITUDE AND DEPARTURE FOR 1^ POINT. Dist. Lat. Dep 1 Dist. Lat. Dep Dist. Lat. Dep Dist. Lat. Dep. Dist. Lat. Dep. 1 01.0'00.3 61 58.4 17.7 121 115.8 35.1 181 173.2 52.5 241 230.6 70.0 2 H.900.6 62 59 3 18 0| 122 116.8 35.4 182 174.2 52.8 242 231.6 70.3 3 02.900.9 63 60.3 18.3 123 117.7 35.7 183 175.1 53.1 243 232.5 70.5 4 03.801.2 64 61.2 18.6 124 118.7 36.0 184 176.1 53.4 244 233.5 70.8 5 04.801.5 65 62.2 18.9 125 119.6 36.3 185 177.0 53.7 245 234.5 71.1 6 05.701.7 66 63.2 19.2 126 120. G 36.6 186 178.0 54.0 246 235.4 71.4 7 06.702.0 67 64.1 19 5 127 121 5 36.9 187 179.0 54.3 247 236.4 71.7 8 07.702.3 68 65.1 19.7 128 122.5 37.2 188 179.9 54.6 248 237 3 72.0 9 08.602.6 69 66 20.0 129 123.5 37.5 189 180.9 54.9 249 238.3 72.3 10 09.602.9 70 67.0 20.3 130 124.4 37.7 190 181.8 55.2 250 239.2 72.6 11 10.503.2 71 67.9 20.6 131 125.4 38.0 191 182.S 55.4 '2ul 240.2 72.9 12 11.503.5 72 68.9 20.9 132 126.3 38.3 192 183.7 55.7 252 241.2 73.2 13 12.403.8 73 69.9 21.2 133 127.3 38.6 193 184.7 56.0 253 242 . 1 73.4 14 13.404.1 74 70.8 21.5 134 128.2 38.9 194 185.7 56.3 254 243.1 73.7 15 14.4,04.4 75 71.8 21.8 135 129.2 39.2 195 186.6 56.6 255 244.0 74.0 16 15.304.6 76 72.7 22.1 136 130.1 39.5 196 187.6 56.9 256 245.0 74.3 17 16.304.9 77 73.7 22.4 137 131.1 39.8 197 188.5 57. '2 257 245.9 74.6 18 17.2'05.2 78 74 6 22.6 138 132.1 40.1 198 189.5 57.5 258 246.9 74.9 19 18.205.5 79 75.6 22.9 139 133.0 40.4 199 190.4 57.8 259 247.9 75.2 20 19.1|05 8 80 76. G 23.2 140 134.0 40.6 200 191.4 58.1 260 248.8 75.5 21 20.106.1 81 77.5 23.5 141 134. y 40.9 201 192.3 58.4 '261 249.8 75.8 22 21.106.4 82 78.5 23.8 142 135.9 41 2 202 193.3 58. G 262 250.7 76.1 23 22.006.7 83 79.4 24.1 143 136.8 41.5 203 194.3 58.9 263 251.7 76.3 24 23.0 07.0 84 80.4 24.4 144 137.8 41.8 204 195.2 59 2 264 252.6 76.6 25 23.9 07.3 85 81.3 24.7 145 138.8 42.1 205 196.2 59.5 265 253.6 76.9 26 24.9 07 6 86 82 3 25.0 146 139.7 42.4 206 197.1 59.8 266 254.6 77.2 27 25.8 07.8 87 83.3 25.3 147 140.7 42.7 207 198.1 60.1 267 255.5 77.5 28 26.8 08.1 86 84.2 25.5 148 141.6 43.0 208 199.0 60.4 268 256.5 77.8 29 27.8 08.4 89 85.2 25.8 149 142.6 43.3 209 200.0 60.7 269 257.4 78.1 30 28.7 08.7 90 86.1 26.1 150 143.5 43.5 210 201.0 61.0 270 258.4 78.4 31 29.7 09.0 91 87.1 26.4 151 144.5 43.8 '211 201.9 61.3 271 259.3 78.7 32 30.6 09.3 92 88.0 26.7 152 145.5 44.1 212 202.9 61.5 272 260 3 79.0 33 31.6 09.6 95 89.0 27 153 146.4 44.4 213 203.8 61. & 273 261.2 79.3 34 32.5 09.9 94 90 27 3 154 147.4 44.7 214 204.8 62.1 274 262.2 79.5 35 33.5 10.2 95 90.9 27.6 155 148.3 45.0 215 205.7 62.4 275 283.2 79.8 36 34.5 10.5 96 91.9 27.9 156 149.3 45.3 216 206.7 62.7 276 264.1 80.1 37 35.4 10 7 97 92.8 28.2 157 150.2 45.6 217 207.7 63 277 2G5.1 80.4 38 3G.4 11.0 98 93.8 28.5 158 151.2 45.9 218 208.6 63.3 278 266.0 80.7 39 37. 1 11.8 99 94.7 28.7 159 152.2 46.2 219 209. G 63.6 279 267.0 81.0 40 33.3 11. G 100 95.7 29.0 160 153.1 46.4 220 210.5 63.9 280 2G7.9 81.3 41 39. ^ 11.9 101 96.7 29.3 161 154.1 46.7 2'21 211.5 64.2 281 268.9 81.6 42 40.2 12.2 102 97.6 29. G 162 155.0 47.0 222 212.4 64.4 282 269.9 81.9 43 41.2 12.5 103 98.6 29.9 163 156.0 47.3 223 213.4 64.7 283 270.8 82.2 44 42.1 12. b 104 99.5 30.2 164 156.9 47. C 224 214.4 65.0 284 271.8 82.4 45 43.1 13.1 105 100.5 30.5 165 157.9 47.9 225 215.3 65.3 285 272.7 82.7 46 14.0 13.4 106 101.4 30.8 166 158.9 48.2 226 216.3 65.6 286 273.7 83.0 47 45.013.6 107 102.4 31.1 167 159.8 48.5 227 217.2 65.9 287 274.6 83.3 48 415.913.9 108 103.4 31.4 168 160.8 48.8 228 218.2 66.2 288 275.6 83.6 49 46.9 14.2 109 104.3 31.6 169 161.7 49.1 229 219.1 66.5 289 276.6 83.9 50 17.914.5 110 105.3 31.9 170 162.7 49.4 230 220.1 66.8 290 277.5 84.2 51 48.814.8 111 106.2 32.2 171 163.6 49.6 231 221.1 67.1 291 278.5 84.5 52 49.815.1 112 107.2 32.5 172 164.6 49.9 232 222.0 67.3 292 279.4 84.8 53 50.715.4 113 108.1 32.8 173 165.6 50.2 233 223.0 67. G 293 280.4 85.0 54 51.715.7 114 109.1 33.1 174 166.5 50.5 234 223.9 67.9 294 281.3 85.3 55 52.616.0 115 110.1 33.4 175 167.5 50.8 235 224.9 68.2 295 282.3 85.6 56 53.616.3 116 111.0 33.7 176 168.4 51.1 236 225.8 68.5 296 283.3 85.9 57 54.616.6 117 112.0 34.0 177 169.4 51.4 237 226.8 68.8 297 284.2 86.2 58 55.516.8 118 112.9 34.3 178 170.3 51.7 238 227.8 69.1 298 285.2 86.5 59 36.517.1 119 113.9 34.5 179 171.3 52.0 239 228.7 69.4 299 86.1 86.8 60 57.4 17.4 120 114.8 34.8 180 172.3 52.3 240 229.7 69.7 300 287.1 87.1 Dist. Dep Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. i'Dist. Dep. Lat. For 6 Points. 194 TABLE III. DIFFERENCE OF LATITUDE AND DEPARTURE FOR If POINT. [list. Lat. DcpDist. Lat. Dep;.Dist. Lat. Dep Dist. Lat. Dep. Dist. Lat. Dep. 1 00.9 00.3 61 , 57.420.6 121 113.940.8 181 170.4 61.0 241 226.9 81.2 2 01.9 00.7 62 58.420.9 122 114.9 41.1 182 171.4 61.3 242 227.9 81.5 3 02.8 01.0 63 59.321.2 123 115.8 41.4 183 172.3 61.7 243 228.8 81.9 4 03.8 01.4 64 60.321.6 124 116.8 41.8 184 173.2 62.0 244 229.7 82.2 5 04.7 01.7 65 61.221.9 125 117.7 42.1 185 174.2 62.3 245 230.7 82.5 6 05.7 02.0 66 62.1J22.2 126 118.6 42.5 186 175.1 62.7 246 231.6 82.9 7 06.6 02.4 67 63.122.6 127 119.6 42.8 187 176.1 63.0 247 232.6 83.2 8 07.5 02.7 68 64.022.9 128 120.5 43.1 188 177.0 63.3 248 233.5 83.6 9 08.5 03 69 65.023.3 129 121.5 43.5 189 177.9 63.7 249 234.4 83.9 10 09.4 03.4 70 65.923.6 130 122.4 43.8 190 178.9 64.0 250 235.4 84.2 11 10.4 03. 7 71 66.923.9 131 123.3 44.1 191 179.8 64.4 251 *36.3 84.6 12 11.3 04.0 72 67.824.3 132 124.3 44.5 192 180.8 64.7 252 237.3 84.9 13 12.2 04.4 73 68.724.6 133 125.2 44.8 193 181.7 65.0 253 238.2 85.2 14 13.2 04.7 74 69.7r24.9 134 126.2 45.1 194 182 7 65.4 254 239.1 85.6 15 14.1 05.1 75 70.625.3 135 127.1 45.5 195 183.6 65.7 255 240.1 85.9 16 15.1 05.4 76 71.6 25.6 136 128.1 45.8 196 184.5 66.0 256 241.0 86.2 17 16.0 05.7 77 72.525.9 137 129.0 46.2 197 185.5 66.4 257 242.0 86.6 18 17.0 06.1 78 73.426.3 138 129.9 46.5 198 186.4 66.7 258 242.9 86.9 19 17.9 06.4 79 74 426.6 139 130.9 46.8 199 187.4 67.0 259 243.9 87.3 20 18.8 06.7 80 75.327 140 131.8 47.2 200 188.3 67.4 260 244.8 87.6 21 19.8 07.1 81 76.3 27.3 141 132.8 47.5 201 189.3 67.7 261 245.7 87.9 22 20.7 07.4 82 77.2 27.6 142 133.7 47.8 202 190.2 68.1 262 246.7 88.3 23 21.7 07.8 83 78.2128.0 143 134.6 48.2 203 191.1 68.4 263 247.6 88.6 21 22.6 08.1 84 79.128.3 144 135.6 48.5 204 192.1 68.7 264 248.6 88.9 25 23.5 08.4 85 80.028.6 145 136.5 48.9 205 193.0 69.1 265 249.5 89.3 26 24.5 08.8 86 81.029.0 146 137.5 49.2 206 194.0 69.4 266 250.5 89.6 27 25.4 09.1 87 81.929.3 147 138.4 49.5 207 194.9 69.7 267 251.4 90.0 28 26.4 09.4 88 82.929.7 148 139.4 49.9 208 195.8 70.1 268 252.3 90.3 29 27.3 09.8 89 83.830.0 149 140.3 50.2 209 196.8 70.4 269 253.3 90.6 30 28.3 10.1 90 84.7 30.3 150 141.2 50.5 210 197.7 70.8 270 254.2 91.0 31 29.2 10.4 91 85.730.7 151 142.2 50.9 211 198.7 71.1 271 255.2 91.3 32 30.1 10.8 92 86.631.0 152 143.1 51.2 212 199.6 71.4 2T2 256.1 91.6 33 31.1 11.1 93 87.6 31.3 153 144.1 51.5 213 200.6 71.8 273 257.0 92.0 34 32.0 11.5 94 88.5 31.7 154 145.0 51.9 214 201.5 72.1 274 258.0 92.3 35 33.0 11.8 95 89.532.0 155 145.9 52.2 215 202.4 72.4 275 258.9 92.6 36 33.9 12.1 90 90.432.3 156 146.9 52.6 216 203.4 72.8 276 259.9 93.0 37 34.8 12.5 97 91.332.7 157 147.8 52.9 217 204.3 73.1 277 260.8 93.3 38 35.8 12.8 98 92.333.0 158 148.8 53.2 218 205.3 73.4 278 261.8 93.7 39 36.7 13.1 99 93.233.4 159 149.7 53.6 219 206.2 73.8 279 262.7 94.0 40 37.7 13.5 100 94.233.7 160 150.7 53.9 220 207.1 74.1 280 263.6 94.3 41 38.6 13.8 101 95.134.0 161 151.6 54.2 221 208.1 74.5 281 264.6 94.7 42 39.5 14.2 102 96.034.4 162 152.5 54.6 222 209.0 74.8 282 265.5 95.0 43 10.5 14.5 103 97.034.7 163 153.5 54.9 223 210.0 75.1 283 266.5 95.3 44 41.4 14.8 104 97.935.0 164 154 4 55.3 224 210.9 75.5 284 267.4 95.7 45 42.4 15.2 105 98.935.4 165 155.4 55.6 225 211.9 75.8 285 268.3 96.0 46 43.3 15.5 106 99.835.7 166 156 3 55.9 226 212.8 76.1 286 269.3 96.4 47 44.3 15.8 107 100.736.1 167 157.2 56.3 227 213.7 76.5 287 270.2 96.7 48 45.2 16.2 108 101.736.4 168 158.2 56.6 228 214.7 76.8 288 271.2 97.0 49 46.1 16.5 109 102.636.7 169 159.1 56.9 229 215.6 77.2 289 272.1 97.4 50 47.1 16.8 110 103.637.1 170 160.1 57.3 230 216.6 77.5 290 273.0 97.7 51 48.0 17.2 111 104.537.4 171 161.0 57.6 231 217.5 77.8 291 274.0 98.0 52 49.0 17.5 112 105.537.7 172 161.9 58.0 232 218.4 78.2 292 274 9 98.4 53 49.9 17.9 113 106.438.1 173 162.9 58.3 233 219.4 78.5 293 275.9 98.7 54 50.8 18.2 114 1Q7.338.4 174 163.8 58.6 234 220.3 78.8 294 276.8 99.0 55 51.8 18.5 115 108.338.7 175 164.8 59.0 235 221.3 79.2 295 277.8 99.4 56 52.7 18.9 116 109.239.1 176 165.7 59.3 236 222.2 79.5 296 278 7 99.7 57 53.7 19.2 117 110.239.4 177 166.7 59.6 237 223.1 79.8 297 279.6 100 1 58 54.6 19.5 118 111.139.8 178 167.6 60.0 238 224.1 80.2 298 280.6 100 4 59 55.6 19.9 119 112.040.1 179 168.5 60.3 239 2'25.0 80.5 299 281.5 100.7 60 56.5 20.2 120 113.0 40.4 180 169.5 60.6 240 226.0 80.9 300 282.5 101.1 Dist. Dep Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. For 6| Points. TABLE III. 195 DIFFERENCE OF LATITUDE AND DEPARTURE FOR 2 POINTS. Dist, LatJDep Dist. Lat. ] Dep Dist. Lat Dep Dist. Lat. Dep. ist. Lat, Dep. 1 KK900.4 61 56.423.3 121 111.8 i6.3 181 167.2 69.3 241 222.7 92.2 2 J1.9U0.8 62 57.323.7 122 112.7 46.7 182 168.2 69.7 242 223.6 92.6 3 J2.8;01.2 63 58.224.1 123 113.647.1 183 169.1 70.0 243 224.5 93.0 4 J3.701.5 64 59.124.5 124 114.647.5 184 170.0 70.4 244 225.4 93.4 5 34.601.9 65 60.124.9 125 115.547> 185 170.9 70.8 245 226.4 93 8 6 J5.502.3 66 61.025.3 126 116.448.2 186 171 8 71.2 246 227.3 94.1 7 36.502.7 67 61.925.6 127 117.3 48.6 187 172.8 71.6 247 228.2 94.5 8 1)7.403.1 68 62.826.0 128 118.3 49.0 188 173.7 71.9 248 229.1 94.9 9 08. 303. 4 69 63.826.4 129 119.249.4 189 174.6 72.3 249 230.1 95.3 10 09.203.8 70 64.7126.8 130 120.149.8 190 175 5 72.7 250 231.0 95.6 11 10.204.2 7J 65.6 27.2 131 121 050.1 191 176 5 73.1 251 231.9 96.1 12 11.104.6 72 66.5 27.6 132 122.050.5 192 177.4 73 5 252 232.8 96.4 13 12.0 [)5.0 73 67.4 27.9 133 122.950.9 193 178.3 73 9: 253 233.7 96.8 14 12.9 J5.4 74 68.4 28.3 134 123.8 51 3 194 179.2 74. 2 ! 254 234.7 97.2 15 13.9 05.7 75 69.3 28.7 135 124.7 51.7 195 180.2 74.6, 255 235.6 97 6 16 14.8 06.1 70 70.2 29.1 136 125.7 52.0 196 181.1 75.0 256 236.5 98.0 17 15.7 06.5 77 71.1 29.5 137 126.6 52.4 197 182.0 75.4 257 237.4 98.4 18 16.6 J6.9 78 72.1 29.9 138 127.5 52.8! 198 182.9 75. 8 1 258 238.4 98.7 19 17.6 07.3 79 73 30.2 139 128.4 53.2 199 183.9 76. 2 ! 259 239.3 99.1 20 18.5 07.7 80 73.9 30.6 140 129.3 53.6 200 184.8 76. 6| 260 240 2 99.5 ill 19.4 08.0 81 74.8 31.0 141 130.3 54.0 201 185.7 76.9) 261 241.1 99.9 22 20 3 08 4 82 75.8 31.4 142 131.2 54.3 202 186.6 77.3 262 242.1 100.3 23 21.3 08.8 83 76.7 31.8 143 132.154.7: 203 187.6 77.7' 263 243.0 100.6 24 22.2 09.2 84 77.6 32.2 144 133.055.1 204 188.5 78.1 264 243.9 101.0 25 23.1 09.6 85 78.5 32.5 145 134.055.5 205 189.4 78.5, 265 244.8 101.4 26 24.0 10.0 86 79.5 32.9 146 134.955.9 206 190.3 78.8 266 245.8 101.8 27 24.9 10.3 87 80.4 33.3 147 135.856.3 207 191.2 79.2 267 246.7 102.2 28 25.9 10.7 88 81.3 33.7 148 136.7 56.6 208 192.2 79.6 268 247.6 102.6 29 26.8 11.1 89 82.2 34.1 149 137.7 57.0 209 193.1 80. 0| 269 248.5 102.9 30 27.7 11.5 90 83.2 34.4 150 138.6 57.4 210 194.0 80.4 270 249.5 103.3 31 Ji.G 11.9 91 84.1 34.8 151 139.5 57.8, 211 194.9 80.8 271 250.4 103.7 32 29.6 12.3 92 85.0 35.2 152 140.4 58.2 212 195.9 81.1 272 251.3 104.1 33 30.5 12.6 93 85.935.6 153 141.458.6 213 196.8 81.5 273 252.2 104.5 34 31.4 13.0 94 86.9 36.0 154 142.358.9 214 197.7 81 9 274 253.1 104.9 35 32.3 13.4 95 87.8 36.4 155 143.259.3 215 198.6 82.3 275 254.1 105.2 3G 33.3 13.8 96 88.7 36.7 156 H4.159.7 216 199.6 82.7 27G 255.0 105 6 37 34.2 14.2 9" 89.6 37.1 157 145 160.1 217 200.5 83.0 277 255.9 106.0 38 35.1 14.5 98 90.5 37.5 158 146.060.5 218 201.4 83.4 278 256.8 106.4 39 36.0 14.9 99 91.5 37.9 159 146.9 60.9 219 202.3 83.8 279 257.8 106.8 40 37. G 15.3 100 92.4 38.3 160 147.8 61.2 220 203 3 84 2 280 258.7 107.2 a 37.9 lo.7 101 93.3 38.7 161 148.7 01.6 221 204.2 84.6 281 259.6 107.5 42 38.8 16.1 102 94.2 39.0 162 149.7 62.0 222 205.1 85.0 282 260.5 107.9 43 39.7 16 5 103 95.2 39.4 163 150.6 62.4 223 206.0 85.3 283 261.5 108.3 44 40.7 16.8 104 96.1 39.8 164 151.5 62.8 224 207.0 85.7 284 262.4 108.7 45 41.6 17.2 lOo 97.0 40.2 165 152 4 63.1 225 207.9 86.1 285 263.3 109.1 46 42.5 17.6 106 97.9 40.6 166 153 4 63.5 226 208 8 86.5 286 264.2 109.5 47 43.4 ia.o 107 98.8 41.0 167 154.3 63 9 227 209.7 86 9 287 265.2 109.8 48 44.4 18.4 108 99.8 41.3 168 155.2 64.3 228 210.6 87.3 288 266.1 110.2 49 45.3 18.8 10 100.7 41.7 169 156.1 64.7 229 211.6 87.6 289 267.0 110.6 50 46.2 19.1 11C 101.6 42.1 170 157.1 65.1 230 212.5 88.0 290 267.9 111.0 51 47.1 19.5 11 102.6 42.5 171 158.065.4 231 213.4 88.4 291 268.9 111.4 52 48.019.9 11 103.542 9 172 158.965.8 232 214.3 88.8 292 269.8 111.7 53 49.020.3 11 104.4 43.2 173 159.866.2 233 215.3 89.2 293 270.7 112.1 54 49.9 20.7 11 105.3 43.6 174 160.866.6 234 216.2 89.6 294 271.6 112.5 55 50.8 21.1 11 106.3 44.0 175 161.767.0 235 217.1 89.9 295 272.5 112.9 56 51.7 21.4 11 107.2 44.4 176 162. 67.4 236 218. C 90.3 296 273.5 113.3 57 52.7 21.8 11 108.1 44.8 17 r 163. 67.7 237 219. C 90.7 297 274.4 113.7 58 53.6 22.2 11 109. C 45.2 17 164.568.1 238 219.8 91.1 298 275.3 114.0 59 54.5 22.6 11 109.8 45.5 17 165.468.5 238 220. fc 91.5 299 276.2 114.4 CO 55.4 23.0 12 110. 45.9 18C 166. J 168.9 24C 221.7 91.8 300 277.2 114.8 DistJDep Lat. His* Dep. Lat Dist Dep. Lat. Dist Dep. Lat. Dist. Dep. Lat, For 6 Points. 196 TABLE III. DIFFERENCE OF LATITUDE AND DEPARTURE FOR 2J POINT. Dist. Lat. Dep Dist. Lat. Dep Dist. Lat. Dep Dist. Lat. Dep. Dist. Lat. Dep. 1 00.9 J0.4J 61 55.1 26.1 121 109.4 51.7 181 163.6 77.4 241 217.9 103. C 2 01.8 30.9 62 56.0 26.5 122 110.3 52.2 182 164.5 77.8 242 218. h 103.5 3 02.7 01.3 63 57.0 26.9 123 111.2 52.6 183 165.4 78.3 243 219.7 103.9 4 03.6 01.7 64 57.9 27.4 124 112.1 53.0 184 166.3 78.7 244 220.6 104.3 5 04.5 02.1 65 58.8 27,8 125 113.0 53.5 185 167.2 79.1 245 221.5 104.8 6 05.4 02.6 66 59.7 28.2 126 113.9 53.9 186 168.1 79.5 246 222.4 105.2 7 06.3 03.0 67 60.6 28.7 127 114.8 54.3 187 169.0 80.0 247 223.3 105.6 8 07.2 J3.4 68 61.5 29.1 128 115.7 54.7 388 169.9 80.4 248 224.2 106.1 9 u8.1 03.8 69 62.4 29.5 129 116.6 55.2 189 170.9 80.8 249 225.1 106.5 10 09.0 04.3 70 63.3 29.9 130 117.5 55.6 190 171.8 81.3 250 226.0 106.9 11 U9.9 04.7 71 ti4.2 30.4 131 118.4 66.0 191 172.7 81.7 251 2*6.9 107.3 12 10.8 05. 1 72 65.1 30.8 132 119.3 56.5 192 173.6 82.1 252 227.8 107.8 13 11.8 05.6 73 66.0 31.2 133 120.2 56.9 193 174.5 82.5 253 228.7 108.2 14 12.7 06.0 74 66.9 31.6 134 121.1 57.3 194 175.4 83.0 254 229.6 108.6 15 13.6 06.4 75 67.8 32.1 135 122.0 57.7 195 176.3 83.4 255 230.5 109.0 16 14.5 06.8 70 68.7 32.5 136 122.9 58.2 196 177.2 83.8 25C 231.4 109.5 17 15.4 07.3 77 69.6 32.9 137 123.8 58.6 197 178.1 84.2 257 232.3 109.9 18 16.3 07.7 78 70.5 33.4 138 124.7 59.0 198 179.0 84.7 258 233.2 110.3 19 17.2 08.1 79 71.4 33.8 139 125.7 59.4 199 179.9 85.1 259 234.1 110.8 20 18.1 08.6 80 72.3 34.2 140 126.6 59.9 200 180.8 85.5 260 235.0 111.2 21 19.0 09.0 81 73.2 34.6 141 127.5 OU.3 201 181.7 85.9 261 235.9 111.6 22 19.9 09.4 82 74.1 35.1 142 128.4 60 7 202 182. C 86.4 26; 236.8 112.0 23 20.8 09.8 83 75.0 35.5 143 129.3 61.2 203 183..: 86.8 263 237.7 112.5 24 21.7 10.3 84 75.9 35.9 144 130.2 61.6 204 184.4 87.2 264 238.7 112.9 25 22.6 10.7 85 76.8 36.3 145 131.1 62.0 205 185.3 87.7 265 239.6 113.3 26 23.5 11.1 86 77.7 36.8 146 132.0 62.4 206 186.2 88.1 266 240.5 113.7 27 24.4 11.5 87 78.7 37.2 147 132.9 62.9 207 187.1 88.5 267 241.4 114 2 28 25.3 12.0 88 79.6 37.6 148 133.8 63.3 ^08 188.0 88.9 268 242.3 114.6 29 26.2 12.4 89 80.5 38.1 149 134.7 63.7 209 188.9 89.4 269 243.2 115.0 30 27.1 12.8 90 81.4 38.5 150 135.6 64.1 210 189.8 89.8 270 244.1 115.5 31 28.0 13.3 91 82.3 38.9 151 136.5 eTe 211 190.7 90.2 27 J 245.0 lib. 9 32 28.9 13.7 92 83.2 39.3 152 137.4 65.0 212 191.6 90.7 272 245.9 116.3 33 29.8 14.1 93 84.1 39.8 153 138.8 65.4 213 192.6 91.1 273 246.8 116.7 34 30.7 14.5 94 85.0 40.2 154 139.2 65.9 214 193.5 91.5 274 247.7 117.2 35 31.6 15.0 95 85.9 40.6 155 140.1 66.3 215 194.4 91.9 275 248.6 117.6 36 32.5 15.4 96 86.8 41.1 156 141.0 66.7 216 195.3 92.4 276 249.5 118.0 37 33.4 15.8 97 87.7 41.5 157 141.9 67.1 217 196.2 92.8 277 250.4 118.5 38 34.4 16.3 98 88.6 41.9 158 142.8 67.6 218 197.1 93.2 278 251.3 118.9 39 35.3 16.7 99 89.5 42.3 159 143.7 68-0 219 198.0 93.7 279 252 2 119.3 40 36.2 17.1 100 90.4 42.8 160 144.6 68.4 220 198.9 94.1 280 253.1 119.7 41 37.1 17.5 101 91.3 43.2 161 145.5 68.8 221 199.8 94.5 28] 254.0 TiO.2 42 38.0 18.0 102 92.2 43.6 162 146.4 69.3 222 200.7 94.9 282 254.9 120.6 43 38.9 18.4 103 93.1 44.1 163 147.3 69.7 223 201.6 95.4 283 255.8 121.0 44 39.8 18.8 104 94.0 44.5 164 148.3 70.1 224 202.5 95.8 284 256.7 121.5 45 40.7 19.2 105 94.9 44.9 165 149.2 70.6 225 203.4 96.2 285 257.6 121.9 46 41.6 19.7 106 95.8 45.3 166 150.1 71.0 226 204.3 96.6 286 258.5 122.3 47 42.5 20.1 107 96.7 45.8 167 151.0 71.4 227 205.2 97.1 287 259.4 122.7 48 43.4 20.5 108 97.6 46.2 168 151.9 71.8 228 206.1 97.5 288 260.3 123.2 49 44.3 21.0 109 98.5 46.6 169 152.8 72.3 229 207.0 97.9 289 261.3 123.6 50 45.2 21.4 110 99.4 47.0 170 153.7 72.7 230 207.9 98.4 290 262.2 124.0 51 46.1 21.8 111 100.3 47.5 171 154.6 73.1 231 208.8 98.8 291 263.1 124.4 52 47.0 22.2 112 101.2 47.9 172 155.5 73.6 232 209.7 99.2 292 264.0 124.9 53 47.9 22.7 113 102.2 48.3 173 156.4 74.0 233 210.6 99.6 293 264.9 125.3 54 48.8 23.1 114 103.1 48.7 174 157.3 74.4 234 211.5 100.1 294 265.8 125.7 55 49.7 23.5 115 104.0 49.2 175 158.2 74.8 235 212.4 100.5 295 266.7 126.2 56 50.6 23.9 116 104.9 49.6 176 159.1 75.3 236 213.3 100.9 296 267.6 126.6 57 51.5 24.4 117 105.8 50.0 177 160.0 75.7 237 214.2 101.4 297 268.5 127.0 58 52.4 24.8 118 106.7 50 5 178 160.9 76.1 238 215.1 101.8 298 269.4 127.4 5'J 53.3 25.2 119 107.6 50.9 179 161.8 76.5 239 216.1 102.2 299 270.3 127.9 60 54.2 25.7 120 108.5 51.3 180 162.7 77.0 240 217.0 102.6 300 271.2 128.3 Dist. Den Lat. Dist, Dcp. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. For 5 Points. TABLE III. 197 DIFFERENCE OP LATITUDE AND DEPARTURE FOR 2J POINT. Dist. Lat. Dep list. Lat. Dep list. Lat. Dep Dist. Lat. Dep. Dist. Lat. Dep. 1 00.9 00.5 61 53.828.8 121 106.7 57.0 181 159.6 85.3 241 212.5 113.6 a 01.8 00.9 6-2 54.729.2 122 107.6 57.5 182 160.5 85.8 242 213.4 114.1 3 02.6 01.4 63 55.629.7 123 108.5 58.0 183 161.4 86.3 243 214.3 114.6 4 03.501.9 64 56.430.2 124 109.4 58.4 184 162.3 86.7 244 215.2 115.0 5 04.402.4 65 57.3 30.6 125 110.2 58.9 185 163.2 87.2 245 216.1 115.5 G 05.3 02.8 66 58.2 31.1 126 111.1 59.4 186 164.0 87.7 246 217.0 116.0 7 06.2 03.3 67 59.131.6 127 112.0 59.9 187 164.9 88.1 247 217.8 116.4 8 07.1 03.8 68 60.032.1 128 112.9 60.3 188 165.8 88.6 248 218.7 116.9 9 07.9 04.2 69 60.932.5 129 113.8 60.8 189 166.7 89.1 249 219.6 117.4 10 08.8 04.7 70 61.733.0 130 114.7 61.3 190 167.6 89.6 250 220.5 117.8 11 09.7 05.2 71 62.633.5 131 115.5 61.71 191 168.5 90.0 251 221.4 118.3 12 10.6 05.7 72 63.533.9 132 116.4 62 2 192 169.3 90.5 252 222.2 118.8 13 11.5 06.1 73 64.434.4 133 117.3 62.7 193 170.2 91.0 253 223.1 119.3 14 12.3 06.6 74 65.334.9 134 118.2 63.2 194 171.1 91.4 254 224.0 119.7 15 13.2 07.1 75 66.1 35.4 135 119.1 63.6 195 172.0 91.9 255 224.9 120.2 16 14.1 07.5 76 67.0 35.8 136 119.9 G4.1 196 172.9 92.4 256 225.8 120.7 17 15.0 08.0 77 67.9 36.3 137 120.8 64.6 197 173.7 92.9 257 226.7 121.1 18 15.9 08.5 78 68.8 36.8 138 121.7 05. 198 174.6 93.3 258 227.5 121.6 19 16.8 09.0 79 69.7 37.2 139 122.6 65.5 199 175.5 93.8 259 228.4 122.1 20 17. C 09.4 80 70.6 37.7 140 123.5 66.0 200 176.4 94.3 260 229.3 122.6 21 18.5 09.9 81 71.4 38-.*2 141 124.4 66.5 201 177.3 94.7 261 230.2 123.0 22 19.4 10.4 82 72.3 38.6 142 125.2 66.9 202 178.2 95.2 262 231.1 123.5 23 iO;3 10.8 83 73.2 39.1 143 126.1 67.4 203 179.0 95.7 263 231.9 124.0 24 21.2 11.3 84 74.1 39.6 144 127.0 67.9 204 179.9 96.2 264 232.8 124.4 25 22.1 11.8 85 75.0 40.1 145 127.9 68.3 205 180.8 96.6 265 233.7 124.9 26 22.9 J2.3 86 75.9 40.5 146 128.8 68.8 206 181.7 97.1 266 234.6 125.4 27 23.8 12.7 87 76.7 41.0 147 129.6 69.3 207 182.6 97.6 267 235.5 125.9 28 24.7 13.2 88 77.6 41.5 148 130.5 69.8 208 183.4 98.0 268 236.4 126.3 29 25. C 13.7 89 78.5 41.9 149 131.4 70.2 209 184.3 98.5 269 237.2 -126.8 30 26.5 14.1 90 79.4 42.4 150 132.3 70.7 210 185.2 99.0 270 238.1 127. 3 31 i7.b 14.6 91 80.3 42.9 151 133.2 71.2 211 186.1 99.5 271 239 127.7 32 28.2 15.1 92 81.1 43.4 152 134.1 71.6 212 187.0 99.9 272 239.9 128.2 33 29.1 15.6 93 82.0 43.8 153 134.9 72.1 213 187.8 100.4 273 240.8 128.7 34 30.0 16.0 94 82.9 44.3 154 135.8 72.6 214 188.7 100.9 274 241.7 129.2 35 30.9 16.5 95 83.8 44.8 155 136.7 73.1 215 189.6 101.3 275 242.5 129.6 36 31.8 17.0 96 84.7 45.2 156 137.6 73.5 216 190.5 101.8 276 243.4 130.1 37 32.6 17.4 97 85.6 45.7 157 138.5 74.0 217 191.4 102.3 277 244.3 130. C 38 33.5 17.9 98 86.4 46.2 158 139.3 74.5 218 192.3 102.8 278 245.2 131.0 39 34.4 18.4 99 87.3 46.7 159 140.2 74.9 219 193.1 103.2 279 246.1 131.5 40 35. c 18.9 100 88.2 47.1 160 141.1 75.4 220 194.0 103.7 280 246.9 132.0 41 36.2119.3 101 89.1 47.6 161 142.0 75.9 221 194.9 104.2 281 247.8 132.5 42 37.019.8 102 90.0 48.1 162 142.9 76.4 222 195.8 104.6 282 248.7 132.9 43 37.9 20.3 103 90.8 48.5 163 143.8 76.8 223 196.7 105.1 283 249.6 133.4 44 38.8 20.7 104 91.7 49.0 164 144.6 77.3 224 197.6 105.6 284 250.5 133.9 45 39.7 21.2 105 92.6 49.5 165 145.5 77.8 225 198.4 106.1 285 251.4 134.3 46 40. 621. 7 106 93.550.0 166 146.4 78.2 226 199.3 106.5 286 252.2 134.8 47 41.522.2 107 94.450.4 167 147.3 78.7 227 200.2 107.0 287 253.1 135.3 48 42.322.6 108 9o.350.iJ 168 148.2 79.2 228 201.1 107.5 288 254.0 135.8 49 43.223.1 109 96.151.4 169 149.0 79.7 229 202.0 107.9 289 254.9 136.2 50 44.123.6 110 97.051.8 170 149.980.1 230 202.8 108.4 290 255.8 136.7 51 45.0 24.0 111 97.952.3 171 150.880.6 231 203.7 108.9 291 256.6 137.2 52 45.9 24.5 112 98.852.8 172 151.781.1 232 204.6 109.4 292 257.5 137.6 53 46.7 25.0 113 99.753.3 173 152.681.5 233 205.5 109.8 293 258.4 138.1 54 47. C 25.5 114 100.553.7 174 153.582.0 234 206.4 110.3 294 259.3 138.6 55 48. G 25.9 115 101.454.2 175 154.382.5 235 207.3 110.8 295 260.2 139.1 56 49.4 26.4 116 102.354.7 176 155.2 83.0 236 208.1 111.2 296 261.1 139.5 57 so. a 26.9 117 103.2 55.1 177 156.1 83.4 237 209.0 111.7 297 261.9 140.0 58 51.2 27.3 118 104.1 55.6 178 157. C 83.9 238 209.9 112.2 298 262.8 140.5 59 52. C 27.8 119 105.056.1 179 157.984.4 239 210.8 112.7 299 263.7 140.9 CO 52. 28. 12C 105.856.6 180 158.8 84.8 240 211.7 113.1 300 264.6 141.4 Dint. Dep Lat Dist Dep. Lnt Dist Dep. Lat. Dist Dep. Lat. Dist. Dep. Lat. For 5 Points. 198 TABLE III. DIFFERENCE OF LATITUDE AND DEPARTURE FOR 2f POINT. [list. Lat. Dep ist. Lat. Dep Dist. Lat. Dep Dist. Lat. Dep. Dist. Lat. Dep. 1 00.9 00.5 61 52.3 31. 4 1 121 103.8 62.2 181 155.3 93.0 241 206.7 123.9 2 01.7 01.0 62 53 2131.9' 122 104.6 62.7 182 156.1 93.6' 242 207 6 124.4 3 02.6 01.5 63 54.0 32.4 123 105.5 63.2 183 157.0 94.1; 243 208.4 124.9 4 03.4 02 1 64 54.9 32.9! 124 106.4 63.7 184 157.8 94.6 244 209.3 125.4 5 04.3 02.6 65 55.8 J3.4 125 107.2 64.3 185 158.7 95.1 245 210.1 125.9 6 05.1 03.1 66 56.6 33.9 126 108.1 64.8 186 159.5 95. 6 1 246 211.0 126 5 7 06 03 6 67 57.5 34.4 127 108 9 65.3 187 160.4 96. li 247 211.9 127.0 8 06.9 04.1 68 58.335.0 128 109.865.8 188 161.2 96.6 248 212.7 127.5 9 07.7 04.6 69 59.235.5 129 110.6 66.3 189 162.1 97.2 249 213.6 128.0 10 08.6 05.1 70 60.036.0 130 111.5 66.8! 190 163.0 97.7 250 214.4 128.5 11 09.4 05.7 71 60.936.5 131 112.4 67.31 191 163.8 98.2 251 215.3 1-29.0 12 10.3 06.2 72 61.837.0 132 113.2167.9 192 164.7 98.7 252 216.1 129.5 13 11.2 06.7 73 62.637.5 133 114.1 68.4 193 165.5 99.2 253 217.0 130.1 14 12.0 07.2 74 63.538.0 134 114.9 68.9 194 166.4 99.7 254 217.9 130.6 15 12.9 07.7 75 64.338.6 135 115.8 69.4 195 167.3 100.2 255 218.7 131.1 16 13.7 08.2 76 65.239.1 136 116.6 69.9 196 168.1 100.8 256 219.6 131.6 17 14.6 08.7 77 66.039.6 137 117.5 70.4 197 169.0 101.3 257 220.4 132.1 18 15.4 09.3 78 66 940.1 138 118.4 70.9 198 169.8 101.8 258 221.3 132.6 19 16.3 09.8 79 67.840.6 139 119.2 71.5 199 170.7 102.3 259 222.2 133.1 20 17.2 10.3 80 68.641.1 140 120.1 72.0 200 171.5 102.8 260 223.0 133.7 21 18.0 10.8 81 69.541.6 141 120.9 72.5 201 172.4 103.3 261 223.9 134.2 22 18.9 11.3 82 70.3 42.1 142 121.8 73 202 173.3 103.8 262 224.7 134.7 23 19.7 11.8 83 71.2 42.7 143 122.7 73.5 203 174.1 104.4 263 225.6 135.2 24 20.6 12.3 84 72.0 43.2 144 123.5 74.0 204 175.0 104 9 264 226.4 135.7 25 21.4 12.9 85 72.943.7 145 124.4 74.5 205 175.8 105.4 265 227.3 136.2 26 22.3 13 4 86 73.844.2 146 125.2 75.1 206 176.7 105.9 266 228.2 136.7 27 23.2 13.9 87 74.644.7 147 126.1 75.6 207 177.5 106.4 267 229.0 137.3 28 24.0 14.4 88 75.545.2 148 126 9 76.1 208 178.4 106.9 268 229.9 137.8 29 24.9 14.9 89 76.345.7 149 127.8 76.6 209 179.3 107.4 269 230 7 138.3 30 25.7 15.4 90 77.2 46.3 150 128.7 77.1 210 180.1 108.0 270 231. t 138.8 31 26.6 15. i/ 91 78.1 46.8 151 129.5 77.6 kill 181.0 108.5 271 232.4 139.3 32 27.4 16.5 92 78.947.3 152 130.4 78.1 212 181.8 109.0 272 233.3 139.8 33 28.3 17.0 93 79.8 47.8 153 131.2 78.7 213 182.7 109.5 273 234.2 140.3 34 29.2 17.5 94 80.6 48 3 154 132.1 79.2 214 183.5 110.0 274 235.0 140.9 35 30.0 18.0 95 81.5 48.8 155 132.979.7 215 184.4 110.5 275 235.9 141.4 3o 30.9 18.5 96 82.3 49.3 156 133.8|80.2 216 185.3 111.0 276 236.7 141.9 37 31.7 19.0 97 83.2 49.9 157 134.7 80.7 217 186.1 111 6 277 237.6 142.4 38 32.6 19.5 98 84.1 50.4 158 135.5 81.2 218 187.0 112.1 278 238.4 142.9 39 33.5 20.1 99 84.9 50.9 159 136.4 81.7 219 187.8 112.6 279 239.3 143.4 40 34.3 20.6 100 85.8 51.4 160 137.2 82.3 220 188.7 113.1 280 240.2 143.9 41 35.2 21.1 101 86.6'51.9 161 138.1 82.8 221 189.6 113.6 281 241.0 144.5 42 36.0 21.6 102 87.5 52.4 162 138.9 83.3 222 190.4 114.1 282 241.9 145.0 43 36.9 22.1 103 88.3 52.9 163 139.8 83.8 223 191.3 114.6 283 242.7 145.5 44 37.7 22.6 104 89.2 53.5 164 140.7 84.3 224 192.1 115.2 284 243.6 146.0 45 38.6 23.1 105 90.1 54.0 165 141.5 84.8 225 193.0 115.7 285 244.4 146.5 46 39.5 23.6 106 90.9 54.5 166 142.4 85.3 228 193.8 116.2 286 245.3 147.0 47 40.3 24.2 107 91.8 55.0 167 143 2 85.8 227 194.7 116.7 287 246.2 147.5 48 41.2 24.7 108 92.6 55.5 168 144.1 86.4 228 195.6 117.2 288 247.0 148.1 49 42.0 25.2 109 93.5 56.0 169 145.0 86.9 229 196.4 117 7 289 247.9 148.6 50 42 9 25.7 110 94.3 56.5 170 145.8 87.4 230 197.3 118.2 290 248.7 149.1 51 43.7 26.2 111 95.2 57.1 171 146.7 87.9 231 198 1 118.8 291 249.6 149.6 52 44.6 26.7 112 96.1 57.6 172 147.5 88.4 232 199.0 119 3 292 250 5 150.1 53 45.5 27.2 113 96.9 58.1 173 148.4 88.9 233 199.8 119.8 293 251.3 150.6 54 46.3 27.8 114 97.8 58.6 174 149.2 89.4 234 200.7 120.3 294 252.2 151.1 55 47 2 28.3 115 98.6 59.1 175 150.1 90.0 235 201.6 120.8 295 253.0 151.7 56 48.0 28.8 116 99.5 59.6 176 151.0 90.5 236 202.4 121.3 296 253.9 152.2 57 48.9 29 3 117 100.4 60.1 177 151.8 91.0 237 203.3 121.8 297 254.7 152.7 58 49.7 29.8 118 101.2 60.7 178 152.7 91.5 238 204.1 122.4 298 255.6 153.2 59 50.6 30.3 119 102.1 61.2 179 153.5 92.0 239 205.0 122.9 299 256.5 153.7 60 51.5 30.8 120 102.9 61.7 180 154.4 92.5 240 205.9 123.4 300 257.3 154.2 [list. Dep Lat. Dist. Dep. Lat. Dist. Dep. Lat, Dist. Dep. Lat. Dist. Dep. Lat. For 5J Points. TABLE III. 199 DIFFERENCE OF LATITUDE AND DEPAETUKE FOR 3 POINTS. Dist. Lat. Dep Dist. Lat. Dep Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. l 00.8 00.6 61 50.7 33.9 121 100.6 67.2 181 150.5 100.6 241 200.4 133.9 2 01.7 01.1 62 51.5 34.4 122 101.4 67.8 182 151.3 101.1 242 201.2 134.4 3 02.5 01.7 63 52.4 35.0 123 102.3 68.3 183 152.2 101.7 243 202.0 135.0 4 03.3 02.2 64 53.2 35.6 124 103.1 68.9 184 153.0 102.2 244 202.9 135.6 5 04.2 02.8 65 54.0 36.1 125 103.9 69.4 185 153.8 102.8 245 203.7 136.1 6 05.0 03.3 66 54.9 36.7 126 104.8 70.0 186 154.6 103.3 246 204.5 136.7 7 05.8 03.9 67 55.7 37 2 127 105.6 70.6 187 155.5 103.9 247 205.4 137.2 8 06.7 04.4 68 56.5 37.8 128 106.4 71.1 188 156.3 104 4 248 206.2 137.8 9 07.5 05.0 69 57.4 38.3 129 107.3 71.7 189 157.1 105.0 249 207.0 138.3 10 08.3 05.6 70 58.2 38.9 130 108 1 72.2 190 158.0 105.6 250 207.9 138 9 11 09.1 06.1 71 59.0 39.4 131 108.9 72.8 191 158.8 106.1 251 2U8.7 139.4 12 10.0 06.7 72 59.9 40.0 132 109.7 73.3 192 159.6 106.7 25* 209.5 140.0 13 10.8 07.2 73 60.7 40.6 133 110.6 73.9 193 160.5 107.2 253 210.4 140.6 14 11.6 07.8 74 61.5 41.1 134 111.4 74.4 194 161.3 107.8 254 211.2 141.1 15 12.5 08.3 75 62.4 41.7 135 112.2 75.0 195 162.1 108.3 255 212.0 141.7 16 13.3 08.9 76 63.2 42.2 136 113.1 75.6 196 163.0 108.9 256 212.9 142.2 17 14.1 09 4 77 64.0 42.8 137 113.9 76.1 197 163.8 109.4 257 213.7 142.8 18 15.0 10.0 78 64.8 43.3 138 114 7 76.7 198 164.6 110.0 258 214.5 143.3 19 15 8 10.6 79 65.7 43.9 139 115.6 77 2 199 165.5 110. 6 1 259 215.3 143.9 20 16.6 11.1 80 66.5 44.4 140 116.4 77.8 200 166.3 111.1 260 216.2 144.4 21 17.5 11.7 81 67.3 45.0 141 117.2 78.3 201 ib7.1 111.7 261 217.0 145.0 22 18.3 12 2 82 68.2 45.6 142 118.1 78.9 202 168.0 112.2 262 217.8 145.6 23 19.1 12.8 83 69.0 46.1 143 118 9 79.4 203 168.8 112.8 263 218.7 146.1 24 20.0 13.3 84 69.8 46.7 144 119.7 80.0 204 169.6 113.3 264 219.5 146.7 25 20.8 13.9 85 70.7 47.2 145 120.6 80.6 205 170.4 113.9 265 220.3 147.2 26 21.6 14.4 86 71.5 47.8 146 121.4 81.1 206 171.3 114.4 266 221.2 147.8 27 22.4 15.0 87 72.3 48.3 147 122.2 81.7 207 172.1 115.0 267 222.0 148.3 28 23.3 15.6 88 73.2 48.9 148 123.1 82.2 208 172.9 115.6 268 222.8 148 9 29 24.1 16.1 89 74.0 49.4 149 123 9 82.8 209 173.8 116.1 269 223.7 149.4 30 24.9 16.7 90 74.8 50.0 150 124.7 83.3 210 174.6 116.7 270 224.5 150.0 31 2o.8 17.2 91 75.7 50.6 151 125.5 83.9 211 175.4 117.2 271 225.3 160.6 32 26.6 17.8 92 76.5 51.1 152 126.4 84.4 212 176.3 117.8 27i 226.2 151.1 33 27.4 18.3 93 77.3 51.7 153 127.2 85.0 213 177.1 118.3 273 227.0 151.7 34 28.3 18.9 94 78.2 52.2 154 128.0 85.6 214 177.9 118.9 274 227.8 152.2 35 29.1 19.4 95 79.0 52.8 155 128.9 86.1 215 178.8 119.4 275 228.6 152.8 36 29.9 20.0 96 79.8 53.3 156 129.7 86.7 216 179.6 120.0 276 229.5 153.3 37 30.8 20.6 97 80.6 53.9 157 130.5 87.2 217 180.4 120.6 277 230.3 153.9 38 31.6 21.1 98 81.5 54.4 158 131.4 87.8 218 181.3 121.1 278 231.1 l- r )4.4 39 32.4 21 7 99 82.3 55.0 159 132.2 88.3 219 182.1 121.7 279 232.0 155.0 40 33.3 22.2 100 83.1 55.6 160 133.0 88.9 220 182.9 122.2 280 232.8 155.6 41 34.1 22.8 101 84.0 56.1 1U1 133.9 89.4 221 183.7 122.8 281 233.6 156.1 42 34.9 23.3 102 84.8 56.7 162 134.7 90.0 222 184.6 123.3 282 234.5 156.7 43 35.8 23.9 103 85.6 57.2 163 135.5 90.6 223 185.4 123.9 283 235.3 157.2 44 36.6 24.4 104 86.5 57.8 164 136.4 91.1 224 186.2 124.4 284 236.1 157.8 45 37.4 25.0 105 87.3 58.3 165 137.2 91.7 225 187.1 125 285 237.0 158.3 46 38.2 25.6 106 88.1 58.9 166 138.0 92.2 226 187.9 125.6 286 237. fe 158.9 47 39.1 26.1 107 89.0 59.4 167 138 9 92.8 227 188.7 126.1 287 238.6 159.4 48 39.9 26.7 108 89.8 60.0 168 139.7 93.3 228 189.6 126.7 288 239.5 160.0 49 40.7 27.2 109 90.6 60.6 169 140.5 93.9 229 190.4 127.2 289 240.3 160.6 50 41.6 27.8 110 91.5 61.1 170 141.3 94.4 230 191.2 127.8 290 241.1 161.1 51 42 4 28.3 111 92.3 61.7 171 142.2 95.0 231 192.1 128.3 291 242.0 161.7 52 43.2 28.9 112 93.1 62.2 172 143.0 95.6 232 192.9 128.9 292 242 8 162.2 53 44.1 29.4 113 94.0 62.8 173 143.8 96.1 233 193.7 129.4 293 243.6 162.8 54 44.9 30.0 114 94.8 63.3 174 144.7 96.7 234 194.6 130.0 294 244.4 163.3 55 45.7 30.6 115 95.6 63.9 175 145.5 97.2 235 195.4 130.6 295 245.3 163.9 56 46.6 31.1 116 96.4 64.4 176 146.3 97.8 236 196.2 131.1 296 246 1 164.4 57 47.4 31.7 117 97.3 65.0 177 147.2 98.3 237 197.1 131.7 297 246.9 165.0 58 48.2 32.2 118 98.1 65 6 178 148.0 98.9 238 197.9 132.2 298 247.8 165.6 59 49.1 32.8 119 98 9 66.1 179 148.8 S9.4 239 198.7 132.8 299 248.6 166.1 60 49 9 33.3 120 99.8 66.7 180 149.7 100.0 240 199.5 133.3 300 249.4 166.7 Dist. Dep Lat. Dist. Dep Lat. Dist, Dep. Lat. Dist, Dep. Lat. Dist. Dep. Lat. For 5 Points. 1 200 TABLE III. DIFFERENCE OF LATITUDE AND DEPARTURE FOR 3J POINT. Hist. Lat. Dep Dist. Lat. Dep Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 00.8 00.6 61 49.0 36 3 121 97.2 72.1 181 145.4 107.8 241 193.6 143.6 2 01.6 01.2 62 49.836.9 122 98.0 72.7 182 146.2 108.4 242 194.4 144.2 3 02.4 01.8 63 50.637.5 123 98.8 73.3 183 147.0 109.0 243 195.2 144.8 4 03.2 02.4 64 51.438J 124 99.6 73.9 184 147.8 109.6 244 196.0 145.4 5 04.0 03 65 52.238.7 125 100.4 74.5 185 14*. 6 110.2 245 196.8 146 6 04.8 03.6 66 53.039 3 126 101.2 75.1 186 149 4 110.8 24.6 197.6 146.5 7 05.6 04.2 67 53.839.9 127 102.0 75.7 187 150.2 111.4 247 198 4 147.1 8 06.4 04.8 68 54.640.5 128 102.8 76.3 188 151.0 112.0 248 199 2 147.7i 9 07.2 05.4 69 55.441.1 129 103.6 76.9 189 151.8 112.6 249 200.0 148.3 10 08.0 06 70 56.241.7 130 104.4 77.4 190 152.6 113.2 250 200.8 148.9 11 08.8 06.6 71 57.042.3 131 105.2 78 191 153.4 113.8 251 201.6 149.0 12 09.6 07.1 72 57.842.9 132 106.0 78.6 192 154.2 114.4 252 202.4 150.1 13 10.4 07.7 73 58.6*43.5 133 106.8 79.2 193 155.0 115.0 253 203.2 150.7 14 11.2 08.3 74 59.444.1 134 107 6 79.8 194 155.8 115.6 254 204.0 151.3 15 12.0 u8.9 75 60.244.7 135 108.4 80.4 195 156.6 116.2 255 204.8 151 9 16 12.9 09.5 76 61.045.3 136 109.2 81.0 196 157.4 116.8 256 205 6 152.5 17 13.7 10.1 77 01.845.9 137 110.0 81.6 197 158.2 117.4 257 206.4 153.1 18 14.5 10.7 78 62.646.5 138 110.8 82.2 198 159.0 118.0 258 207.2 153.7 19 15.3 11.3 79 63.447.1 139 111.6 82.8 199 159.8 118.5 259 208 154.3 20 16.1 11.9 80 64.347.7 140 112.4 83.4 200 160.6 119.1 260 208 8 154.9 21 16.9 12.5 81 65.148.3 141 113.2 84.0 201 161.4 119.7 261 209.6 155.5 22 17.7 13 1 82 65.948.9 142 114.0 84.6 202 162.2 120.3 262 210.4 156.1 23 18.5 13.7 83 66.749.4 143 114.9 85.2 203 163.0 120.9 263 211.2 156.7 24 19.3 14 3 84 67.550 144 115.7 85.8 204 163.9 121.5 264 212.0 157.3 25 20.1 14.9 85 68.350.6 145 116.5 86.4 205 164.7 122.1 265 212.8 157.9 26 20.9 15.5 86 69.151.2 146 117.3 87.0 206 165.5 122.7 266 213.6 158.5 27 21.7 16.1 87 69.9151.8 147 118.1 87.6 207 166.3 123.3 267 214.5 159.1 28 22.5 16.7 88 70.752.4 148 118.9 88.2 208 167.1 123.9 268 215.3 159 6 29 23.3 17.3 89 71.5 53.0 149 119.7 88.7 209 167.9 124.5 269 216.1 160.2 30 24.1 17.9 90 72.3 53.6 150 120.5 89.4 210 168.7 125.1 270 216.9 160.8J 31 24.9 18^ 91 73.1 54.2 151 121.3 90.0 211 109.5 125.7 271 217.7 161.4 32 25.7 19.1 92 73.9 54.8 152 122.1 90.5 212 170.3 126.3 272 218.5 162.0 33 26.5 19.7 93 74.7 55.4 153 122.9 91.1 213 171.1 126.9 273 219 3 162.6 34 27.3 20.3 94 75.5 56.0 154 123.7 91.7 214 171.9 127.5 274 220.1 163.2 35 28.1 20.9 95 76.3 56.6 155 124.5 92.3 215 172.7 128.1 275 220.9 163.8 36 28.9 21.4 96 77.1 57.2 156 125.3 92.9 216 173.5 128.7 276 221.7 164.4 37 29.7 22.0 97 77.9 57.8 157 126.1 93 5 217 174.3 129.3 277 222.5 165.0 38 30.5 22.6 98 78.7 58.4 158 126.9 94.1 218 175.1 129.9 278 223.3 165.6 39 31.3 23.2 99 79.5 59.0 159 127.7 94.7 219 175.9 130.5 279 224.1 166.2 40 32.1 23.8 100 80.3 59.6 160 128.5 95.3 220 176.7 131.1 280 224.9 168.8 41 32.9 24.4 101 81.1 60.2 161 129.3 95.9 221 177.5 131.7 281 225.7 167.4 42 33.7 25.0 102 81.9 60.8 162 130.1 96.5 222 178.3 132.2 282 226-5 168.0 43 34 L 25.6 103 82.7 61.4 163 130.9 97.1 223 179.1 132.8 283 227.3 168.6 44 35.3 26.2 104 83.5 62.0 164 131.7 97.7 224 179.9 133.4 284 228J 169.2 45 36.1 26 8 105 84.3 62.6 165 132.5 98.3 225 180.7 134.0 285 228.9 169.8 46 36.9 27.4 106 85.1 63.1 166 133.3 98 9 226 181.5 134.6 286 229.7 170.4 47 37.7 28.0 107 85.9 63.7 167 134 1 99.5 227 182.3 135.2 287 230.5 171.0 48 38.6 28.6 108 86.7 64.3 168 134.9 100.1 228 183.1 135.8 288 231.3 171.6 49 39.4 29.2 109 87.5 64.9 169 135.7 100.7 229 183.9 136.4 289 232.1 172.2 50 40.2 29.8 110 88.4 65.5 170 136.5 101.3 230 184.7 137.0 290 232.9 172.8 51 41.0 30.4 111 89.2 66.1 171 137.3 101.9 231 185.5 137.6 291 233.7 173.3 52 41.8 31.0 112 90.0 66.7 172 138.1 102.5 232 186.3 138.2 292 234.5 173.9 53 42.6 31.6 113 90.8 67.3 173 138.9 103.1 233 187.1 138.8 293 235.3 174.5 54 43.4 32.2 114 91.6 67.9 174 139.8 103.7 234 187.9 139.4 294 236.1 175.1 55 44.2 32.8 115 92.4 68.5 175 140.6 104.2 235 188.8 140.0 295 236.9 175.7 56 45.0 33.4 116 93.2 69.1 176 141.4 104.8 236 189.6 140.6 296 237.7 176.3 57 45.8 34.0 117 94.0 69.7 177 142.2 105.4 237 190.4 141.2 297 238.5 176.9 58 46.6 34.6 118 94.8 70.3 178 143.0 106.0 238 191.2 141.8 298 239.4 177.5 59 47.4 35.1 119 95.6 70.9 179 143.8 106.6 239 192.0 142.4 299 240.2 178.1 60 48.2 35.7 120 96.4 71.5 180 144.6 107.2 240 192.8 143.0 300 241.0 178.7 Dist. Dep Lat. Dist. Dep Lat. Dist. Dep. Lat, Dist. Dep. Lat. Dist. Dep. Lat. For 4f Points. TABLE III. 201 DIFFERENCE OF LATITUDE AND DEPARTURE FOR 3^ POINTS. Dist. Lat. Dep Dist. Lat. Dep Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat, Dep. l 00.8 00.6 61 47.138.7 121 93.5 76.8 181 139.9 114.8 241 186.3 152.9 2 01.5 01. b 62 47.9 39.3 122 94.3 77.4 182 140.7 115.5 242 187.1 153.5 3 02.3 01.9 63 48.7 40 123 95.1 78.0 183 141.5 116.1 243 187.8 154.2 4 03.1 02.5 64 49.5 40.6 124 95.8 78.7 184 142.2 116.7 244 188.6 154 8 5 03.9 03.2 65 50.2 41.2 125 96.6 79.3 185 143.0 117.4 245 189.4 155.4 6 04.6 03.8 66 51.0 41.9 126 97.4 79.9 186 143.8 118.0 246 190.2 156.1 7 05.4 04.4 67 51.8 42.5 127 98.2 80.6 187 144.5 118.6 247 190.9 156.7 8 06. 2 05.1 68 52.6 43.1 128 98.9 81.2 188 145.3 119.3 248 191.7 157.3 9 07.0 05.7 69 53.3 43.8 129 99.7 81.8 189 146.1 119.9 249 192.5 158.0 10 07.7 06.3 70 54.1 44.4 130 100.5 82.5 190 146.9 120.5 250 193.2 158.6 il- 08.5 07.0 71 54.9 45.0 131 101.3 83.1 191 147.6 121.2 251 194. U 159. ii ia 09.3 07.6 72 55.7 45.7 132 102.0 83.7 192 148.4 121.8 25'2 194.8 159.9 13 10.0 08 2 73 56.4 46.3 133 102.8 84.4 193 149.2 122.4 253 195.6 160.5 14 10.8 08.9 74 57.2 46.9 134 103.6 85.0 194 150 123.1 254 196.3 161.1 15 11.6 09.5 75 58.0 47.6 135 104.4 85.6 195 150.7 123.7 255 197.1 161.8 16 12.4 10.1 76 58.7 48.2 136 105.1 86.3 196 151.5 124.3 256 197.9 162.4 17 13.1 10.8 77 59.5 48.8 137 105.9 86.9 197 152.3 125.0 257 198.7 163.0 18 13.9 11.4 78 60.3 49.5 138 106.7 87.5 198 153.1 125.6 258 199.4 163.7 19 14.7 12.0 79 61.1 50 1 139 107.4 88.2 199 153.8 126.2 259 200.2 164.3 20 15.5 12.7 80 61.8 50.7 140 108.2 88.8 200 154.6 126.9 260 201.0 164.9 21 16.2 13. b 81 62.6 51.4 141 109.0 89.4 201 155.4 127.5 261 201.8 165.6 22 17.0 14.0 82 63.4 52.0 142 109.8 90.1 202 156.1 128.1 262 202.5 166.2 23 17.8 14.6 83 64.2 52.7 143 110.5 90.7 203 156.9 128.8 263 203.3 166.8 24 18. C 15.2 84 64.9 53.3 144 111.3 91.3 204 157.7 129.4 264 204.1 167.5 25 19.3 15.9 8565.7 53.9 145 112.1 92.0 205 158.5 130.0 265 204.8 168.1 26 20.1 16.5 86 36.5 54.6 146 112.9 92.6 206 159.2 130.7 266 205.6 168.7 27 20.9 17.1 87 67.2 55.2 147 113.6 93.3 207 160.0 131.3 267 206.4 169.4 28 21.6 17.8 88 38.0 55.8 148 114.4 93.9 208 160.8 132.0 268 207.2 170.0 29 22.4 18.4 89 68.8 56.5 149 115.2 94.5 209 161.6 132.6 269 207.9 170.6 30 23.2 19.0 90 69.6 57.1 150 115.9 95.2 210 162.3 133.2 270 208.7 171.3 31 24.0 19,7 91 70.3 57.7 151 116.7 95.8 211 163.1 133.9 271 209.5 171.9 32 24.7 20.3 92 71.1 58.4 152 117.5 96.4 212 163.9 134.5 272 *210.3 172.6 33 25.5 20.9 93 71.9 59.0 153 118.3 97.1 213 164.6 135.1 273 211.0 173.2 34 26.3 21.6 94 72.7 59.6 154 119.0 97.7 214 165.4 135.8 274 211.8 173.8 35 27.1 22.2 95 73.4 60.3 155 119.8 98.3 215 166.2 136.4 275 212.6 174.5 36 27.8 22.8 96 74.2 60.9 156 120.6 99.0 216 167.0 137.0 276 213.3 175.1 37 28.6 23.5 97 75.0 61.5 157 121.4 99.6 217 167.7 137.7 277 214.1 175.7 38 29.4 24.1 98 75.7 62.2 158 122.1 100.2 218 168.5 138.3 278 214.9 176.4 39 30.1 24.7 99 76.5 62.8 159 122.9 100.9 219 169.3 138.9 279 215.7 177.0 40 30.9 25.4 100 77.3 63.4 160 123.7 101.5 220 170.1 139.6 280 216.4 177.6 41 31.7 26.0 101 78.1 64.1 161 124.4 102.1 221 170.8 140.2 281 217.2 178.3 42 32.5 26.6 102 78.8 64.7 162 125.2 102.8 222 171.6 140.8 282 218.0 178.9 43 33.2 27.3 103 79.6 65.3 163 126.0 103.4 223 172.4 141.5 283 218.8 179.5 44 34.0 27.9 104 80.4 66.0 164 126.8 104 224 173.1 142.1 284 219.5 180.2 45 34.8 28.5 10o|81.2 66.6 165 127.5 104.7 225 173.9 142.7 285 220.3 180.8 46 35.6 29.2 106 81.9 67.2 166 128.3 105 3 226 174.7 143.4 286 221.1 181.4 47 36.3 29.8 107 82.7 67.9 167 129.1 105.9 227 175.5 144.0 287 221.8 182.1 48 37.1 30.4 108 83.5 68.5 168 129. a 106.6 228 176.2 144.6 288 222.6 182.7 49 37.9 31.1 109 84.3 69.1 169 130.6 107.2 229 177.0 145.3 289 223.4 183.3 50 38.6 31.7 110 85.0 69.8 170 131.4 107.8 230 177.8 145.9 290 224.2 184.0 51 39.4 32.3 111 85.8 70.4 171 132.2 108.5 231 178.6 146.5 291 224.9 184.6 52 40.2 33.0 112 86.6 71.0 172 133.0 109.1 232 179.3 147.2 292 225.7 185.2 53 41.0 33.6 113 87.3 71.7 173 133.7 109.7 233 180.1 147.8 293 226.5 185.9 54 41.7 34.3 114 88.1 72.3 174 134.5 110.4 234 180.9 148.4 294 227.3 186.5 55 42.5 33.9 115 88.9 73.0 175 135.3 111.0 235 181.7 149.1 295 228.0 187.1 56 43.3 35.5 116 89.7 73.6 176 136.0 111.6 236 182.4 149.7 296 228.8 187.8 57 44.1 36.2 117 90.4 74.2 177 136.8 112.3 237 183.2 150.3 297 229.6 188.4 58 44.8 36.8 118 91.2 74.9 178 137.6 112.9 238" 184.0 151.0 298 230.4 189.0 59 45.6 37.4 119 92.0 75.5 179 138.4 113.6 239 184.7 151.6 299 231.1 189.7 60 46.4 38.1 120 92.8 76.1 180 139.1 114.2 240 185.5 152.3 300 231.9 190.3 Dist. Dep Lat. Dist. Dep Lat. Dist. Dep. Lat, Dist. Dep. Lat. Dist. Dep. Lat, For 4 Points. 202 TABLE III. DIFFERENCE OF LATITUDE AND DEPARTURE FOR 3f POINT. Dist. Lat. Dep Dist. Lat. Dep Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. l 00.7 00.7 61 45.2 41.1 121 80.6 81.3 181 134.1 121.5 241 178.6 161.8 2 01.5 01.3 6i 45.9 41.6 122 90.4 81.9 182 134.8 122.2 242 179.3 162.5 3 02.2 02.0 63 46.7 42.3 123 91.1 82.6 183 135.6 122.9 243 180.0 163.2 4 03.0 02.7 64 47.4 43.0 124 91.9 83.3 184 136.3 123.6 244 180.8 163.8 5 03.7 03.4 6548.2 43.6 125 92.6 83.9 185 137.1 124.2 245 181.5 164.5 6 04.4 04.0 6648.9 44.3 126 93.4 84.6 186 137.8 124.9 246 182.3 165.2 7 05.2 04.7 6749.6 45.0 127 94.1 85.3 187 138.6 125.6 247 183.0 165.9 8 05.9 05.4 6850.4 45.7 128 94.8 86.0 188 139.3 126.2 248 183.8 166.5 9 06.7 06.0 6951.1 46.3 129 95.6 86.6 189 140.0 126.9 249 184.4 167.2 10 U7.4 06.7 7051.947.0 130 96.3 87.3 190 140.8 127.6 250 185.2 167.9 11 08.2 07.4 71j52.647.7 131 97.1 88.0 191 141.5 128.3 251 186.0 108.5 12 08.9 08.1 7253.348.3 132 97.8 88.6 192 142.3 128.9 252 186.7 169.2 13 09.6 08.7 7354.149.0 133 98.5 89.3 193 143.0 129.6 253 187.5 169.9 14 10.4 09.4 7454. 849. 7i 134 99.3 90.0 194 143.7 130.3 254 188.2 170.6 15 11.1 10.1 7555.650.4 135 100.0 90.7 195 144.5 130.9 255 188.9 171.2 16 11.9 10.7 7656.351.0 136 100.8 91.3 196 145.2 131.6 256 189.7 171.9 17 12.6 11.4 7757.051.7 137 101.5 92.0 197 146.0 132.3 257 190.4 172.6 18 13.3 12.1 78,77.852.4 138 102.2 92.7 198 146.7 133.0 258 191.2 173.2 19 14.1 12.8 7958.553.0 139 103.0 93.3 199 147.4 133.6 259 191.9 173.9 20 14.8 13.4 8059.353.7 140 103.7 94.0 200 148.2 134.3 260 192.6 174.6 21 15.6 14.1 8160.054.4 141 104.5 94.7 201 148.9 135.0 261 193.4 175.3 22 16.3 14.8 8260.8,55.1; 142 105 2 95.4 202 149.7 135.6 262 194.1 175.9 23 17.0 15.4 8b61.5 : 55.7j 143 106.0 96.0 203 150.4 136.3 263 194.8 176.6 24 17.8 16.1 8462.256.4 144 106.7 96.7 204 151.1 137.0 264 195.6 177.3 25 18.5 16.8 8563.057.1 145 107.4 97.4 205 151.9 137.7 265 196.3 178.0 26 19.3 17.5 8663.757.7 146 108.2 98.0 206 152.6 138.3 266 197.1 178.6 27 20.0 18.1 8764.558.4 147 108.9 98.7 207 153.4 139.0 267 197.8 179 3 28 20.7 18.8 8865.259.1 148 109.7 99.4 208 154.1 139.7 268 198.6 180.0 29 21.5 19.5 8965.959.8 149 110.4 100.1 209 154.9 140.3 269 199.3 180.6 30 22.2 20.1 9066.760.4 150 111.1 100.7 210 155.6 141.0 270 200.1 181.3 31 23.0 20.8 91 67. 4)61.1 151 111.9 101.4 211 156.3 141.7 271 200.8 182.0 3-2 23.7 21.5 9268.261.8 152 112.6 102.1 21'2 157.1 142.4 272 201.5 182.7 33 24.4 22.2 93 68.962.4 153 113.4 102.7 213 157.8 143.0 273 202.3 183.3 34 25.2 22.8 94 69.663.1 154 114.1 103.4 214 158.6 143.7 274 203.0 184.0 35 25.9 23.5 95' ( 70.463.8 155 114.8 104.1 215 159.3 144.4 275 203.8 184.7 36 26.7 24.2 9671.164.51 156 115.6 104.8 216 160.0 145.0 276 204.5 185.3 37 27.4 24.8 9771.9 65.1 157 116.3 105.4 217 160.8 145.7 277 205.2 186.0 38 28.2 25.o 9872.6 65.8 158 117.1 106.1 218 161.5 146.4 278 206.0 186.7 39 28 9 26.2 9973.3 66.5 159 117.8 106.8 219 162.3 147.1 279 206.7 187.4 40 29.6 26.9 10074. 167A 160 118.5 107.4 220 163.0 147.7 280 207.5 188.0 41 30.4 27.5 101 74.867.8 161 119.3 1U8.1 221 103.7 148.4 281 i;08.2 168.7 42 31.1 28.2 102 75.668.5 162 120.0 108.8 222 164.5 149.1 282 208.9 189.4 43 31.9 28.9 103 76. 369. L 163 120.8 109.5 223 165.2 149.7 283 209.7 190.0 44 32.6 29.5 10477.169.8 164 121.5 110.1 224 166.0 150.4 284 210.4 190.7 45 33.3 30.2 10577.870.5 165 122.3 110.8 225 166.7 151.1 285 211.2 191.4 46 34.1 30. J 10678.571.2 166 123.0 111.5 226 167.4 151.8 286 211.9 192.1 47 34.8 31.6 10779.371.8 167 123.7 112.1 227 168.2 152.4 287 212.6 192.7 48 35.6 32.2 10880.072.5 168 124.5 112.8 228 168.9 153.1 288 213.4 193.4 49 36.3 32.9 10980.873.2 169 125.2 113.5 229 169.7 153.8 289 214.1 194.1 50 37.0 33.6 11081.573.9 170 126.0 114.2 '230 170.4 154.5 290 214.9 194.7 51 37.8 34.2 11182.274.5 171 126.7 114.8 231 171.2 155.1 291 215.0 195.4 52 38.5 34.9 11283.075.2 172 127.4 115.5 232 171.9 155.8 292 216.4 196.1 53 39.3 35.6 11383.775.9 173 128.2 116.2 233 172.6 156.5 293 217.1 196.8 54 40.0 36.3 11484.576.5 174 128.9 116.8 234 173.4 157.1 294 217.8 197.4 55 40.7 36.9 115 85.277.2 175 129.7 117.5 235 174.1 157.8 295 218.6 198.1 56 41.5 37.6 116 85.977.9 176 130.4 118.2 236 174.9 158.5 296 219.3 198.8 57 42.2 38.3 11786.778.6 177 131.1 118.9 237 175.6 159.1 2S7 220.1 199.4 58 43.0 38.9 11887 479.2 178 131.9 119.5 238 176.3 159.8 298 220.8 200.1 59 43.7 39.6 11988.279.9 179 132.6 120.2 239 177.1 160.5 299 221.5 200.8 60 44.5 40. J 12088.9 80.6 180 133.4 120.9 240 177.8 161.2 300 222.3 201.5 Dist. Dep Lat. Dist. Dep Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist, Dep. Lat, For 4J Points. TABLE III. 203 DIFFERENCE OF LATITUDE AND DEPARTURE FOR 4 POINTS. Dist. Lat. Dep Dist. Lat. Dep Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. l 00.7 00.7 61 43.1 43.1 121 85. C 85.6 181 128.0 128.0 241 170.4 170.4 2 01.4 01.4 62 43.843.8 122 86.3 86.3 182 128.7 128.7 242 171.1 171.1 3 02.1 02.1 63 44.5 44.5 123 87.0 86.0 183 129.4 129.4 243 171. 8 171.8 4 02.8 02.8 64 45.3 45.3 124 87.7 87.7 184 130.1 130.1 244 172.5 172.5 5 03.5 03.5 /if; 46.0 46.0 125 88.4 88.4 185 130.8 130.8 245 173.2 173.2 6 04.2 04.2 66 46.7 46.7 126 89.1 89.1 186 131.5 131.5 246 173.9 173.9 7 04.9 04.9 67 47.4 47.4 127 89.8 89.8 187 132.2 132.2 247 174.7 174.7 8 05.7 05.7 68 48.1 48.1 128 90.5 90. 188 132.9 132.9 248 175.4 175.4 9 06.4 06.4 69 48.8 48.8 129 91.2 91. 189 133.6 133.6 240 176.1 176.1 10 07.1 07.1 70 49.5 49.5 130 91.9 91. 190 134.3 134.3 250 176.8 176. b 11 o7.b 07.8 71 50.2 50.2 131 92. b 92. 191 135.1 135.1 251 177.5 177.5 12 08.5 08.5 72 50.9 50.9 132 93.3 93. 192 135.8 135.8 252 178.2 178.2 13 09.2 09.2 73 51.6 51.6 133 94.0 94. 193 136.5 136.5 253 178.9 178.9 14 09.9 09.9 74 52.3 52.3 134 94.8 94. 194 137.2 137.2 254 179.6 179.6 15 10.6 10.6 75 53.0 53.0 135 95.5 95. 195 137.9 137.9 255 180.3 180.3 16 11.3 11.3 76 53.7 53.7 136 96.2 96. 196 138.6 138.6 256 181.0 181.0 17 12.0 12.0 77 54.4 54.4 137 96.9 96. 197 139.3 139.3 257 181.7 181.7 18 12.7 12.7 78 55.2 55.2 138 97.6 97. 198 140.0 140.0 258 182.4 182.4 19 13.4 13.4 7 55.9 55.9 139 98.3 98. 199 140.7 140.7 259 183.1 183.1 20 14.1 14.1 80 56.6 56.6 140 99.0 99.0 200 141.4 141.4 260 183.8 183.8 21 14.8 14.8 81 57.3 57.3 141 yy.7 99.7 201 142.1 142.1 261 184. b 184.6 22 15.6 15.6 82 58.0 58.0 142 100.4 100.4 202 142.8 142.8 262 185.3 185.3 23 16.3 16.3 83 58.7 58.7 143 101.1 101.1 203 143.5 143.5 263 186.0 186.0 24 17.0 17.0 84 59.4 59.4 144 101.8 101.8 204 144.2 144.2 264 186.7 186.7 25 17.7 17.7 85 60.1 60.1 145 102.5 102.5 205 145.0 145.0 265 187.4 187.4 26 18.4 18.4 86 60.8 60.8 146 103.2 103.2 206 145.7 145.7 266 188.1 188.1 27 19.1 19.1 87 61.5 61.5 147 103.9 103.9 207 146.4 146.4 267 188.8 188.8 28 19.8 19.8 88 62.2 62.2 148 104.7 104.7 208 147.1 147.1 268 189.5 189.5 29 20.5 20.5 89 62.9 62.9 149 105.4 105.4 209 147.8 147.8 269 190.2 190.2 30 21.2 21.2 90 63.6 63.6 150 106.1 106.1 210 148.5 148.5 270 190.9 190.9 31 21.9 21.9 91 64.3 64.3 151 106.8 106.8 211 149.2 149.2 271 191.6 191.6 32 22.6 22.6 92 65.1 65.1 152 107.5 107.5 212 149.9 149.9 272 192.3 192.3 33 23.3 23.3 93 65.8 65.8 153 108.2 108.2 213 150.6 150.6 273 193.0 193.0 31 24.0 24.0 94 66.5 66.5 154 108.9 108.9 214 151.3 151.3 274 193.7 193.7 35 24.7 24.7 95 67.2 67.2 155 109. 6 109.6 215 152.0 152.0 275 194.5 194.5 36 25.5 25.5 9C 67.9 67.9 156 110.3 110.3 216 152.7 152.7 276 195.2 195.2 37 26.2 26.2 97 68.6 68.6 157 111.0 111.0 217 153.4 153.4 277 195.9 195.9 38 26.9 26.9 98 69.3 69.3 158 111.7 111.7 218 154.1 154.1 278 196.6 196.6 39 27.6 27.6 99 70.0 70.0 159 112.4 112.4 219 154.9 154.9 279 197.3 197.3 40 28.3 28.3 100 70.7 70.7 160 113.1 113.1 220 155.6 155.6 280 198.0 198.0 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 29.7 102 72.1 72.1 162 114.5 114.5 222 157.0 157.0 282 199.4 199.4 43 30.4 30.4 103 72.8 72.8 163 115.3 115.3 223 157.7 157.7 283 200.1 200.1 44 31.1 31.1 104 73.5 73.5 164 116.0 116.0 224 158.4 158.4 284 200.8 200.8 45 3L.8 31.8 105 74.2 74.2 165 116.7 116.7 225 159.1 159.1 285 201.5 201.5 46 32.5 32.5 106 75.0 75.0 166 117.4 117.4 226 159.8 159.8 286 202.2 202.2 47 33.2 33.2 107 75.7 75.7 167 118.1 118.1 227 160.5 160.5 287 202.9 202.9 48 33.9 33.9 108 76 4 76.4 168 118.8 118.8 228 161.2 161.2 288 203.6 203.6 49 34.6 34.6 109 77.1 77.1 169 119.5 119.5 229 161.9 161.9 289 204.3 204.3 50 35.4 35 4 110 77.8 77.8 170 120.2 120.2 230 162.6 162.6 290 205.1 205.1 51 3J.1 36.1 111 78.5 78.5 17J 120.9 120.9 231 163.3 163.3 291 205.8 205.8 52 36.8 36.8 112 79.2 79.2 172 121.6 121.6 232 164.0 164.0 292 206.5 206.5 53 37.5 37.5 113 79.9 79.9 173 122.3 122.3 233 164.8 164. & 293 207.2 207.2 54 38.2 38.2 114 80.6 80.6 174 123.0 123.0 234 165.5 165.5 294 207.9 207.9 55 38.9 38.9 115 81.3 81.3 175 123.7 123.7 235 166.2 166.2 295 208.6 208.6 56 39.6 39.6 116 82.0 82.0 176 124.4 124.4 236 166.9 166.9 296 209.3 209.3 57 40 3 40.3 117 82.7 82.7 177 125.2 125.2 237 167.6 167.6 297 210.0 210.0 58 41.0 41 118 83.4 83.4 178 125.9 125.9 238 168.3 168.3 298 210.7 210.7 59 41.7 41.7 119 84.1 84.1 179 126.6 126.6 239 169.0 169.0 299 211.4 211.4 60 42.4 42.4 120 84.8 84.8 180 127.3 127.3 240 169.7 169.7 300 212.1 212.1 5ist. Dep Lat. Dist. Dep Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. For 4 Points. 204 TABLE IV. DIFFERENCE OF LATITUDE AND DEPARTURE FOR 1 DEGREE. Dist. Lat. Dep Dist. Lat. Dep Dist. Lat. Dep !Dist, Lat. Dep. Dist. Lat. Dep. 1 01.0 00.0 61 61.0 01.1 121 121.0 02.1 181 181.0 03.2 241 241.0 04.2 2 02.0 00.0 62 62.0 01.1 122 122 02.1 182 182.0 03.2 242 242.0 04.2 3 03.0 00.1 63 63.0 01.1 123 123.0 02.1 183 183.0 03.2 243 243.0 04.2 4 04.0 00.1 64 64.0 01.1 124 124.0 02.2 184 184.0 03.2 244 244.0 04.3 5 05.0 00.1 65 65.0 01.1 125 125.0 02.2 185 185.0 03.2 245 245.0 04.3 6 06.0 00.1 66 66.0 01.2 126 126.002.2 186 186.0 03.2 246 246.0 04.3 7 07.0 00.1 67 67.0 01.2 127 127.0 02.2 187 187.0 03.3 247 247.0 04.3 8 08.0 00.1 68 68.0 01.2 128 128.0 02.2 188 188.0 03.3 248 248.0 04.3 9 09.0 00.2 69 69.0 01.2 129 129.0 02.2 189 189.0 03.3 249 249.0 04.3 10 10.0 00.2 70 70.0 01.2 130 130.0 02.3 190 190.0 03.3 250 250.0 04.4 11 11.0 00.2 71 71.0 01.2 131 131. (i 02.3 191 191.0 03.3 251 251.0, 04.4 12 12.0 00.2 72 72.0 01.3 132 132.0 02.3 192 192.0 03.4 25-2 252.0 04.4 13 13.0 00.2 73 73.0 01.3 133 133.0 02.3 193 193.0 03.4 253 253.0 04.4 14 14.0 00.2 74 74.0 01.3 134 134.0 02.3 194 194.0 03.4 254 254.0 04.4 15 15.0 00.3 75 75.0 01.3 135 135.0 02.4 195 195.0 03.4 255 255.0 04.4 16 16.0 00.3 76 76.0 01.3 136 136.0 02.4 196 196.0 03.4 256 256.0 04.5 17 17.0 00.3 77 77.0 01.3 137 137.0 02.4 197 197.0 03.4 257 257.0 04.5 18 18.0 00.3 78 78.0 01.4 138 138.0 02.4 198 198.0 03.5 258 258.0 04.5 19 19.0 00.3 79 79.0 01.4 139 139.0 02 4 199 199.0 03.5 259 259.0 04.5 20 20.0 00.3 80 80.0 01.4 140 140.0 02.4 200 200.0 03.5 260 260.0 04.5 21 21.0 00.4 81 81.0 01.4 14-1 141.0 U2.5 201 201.0 03.5 '/til 261.01 04.5 22 22.0 00.4 82 82. C 01.4 142 142.0 02.5 202 202.0 03.5 262 262.0 04.6 23 23. ( 00.4 83 83.0 01.4 143 143.0 02.5 203 203.0 03.5 263 263.0 04.6 24 24.0 00.4 84 84.001.5 144 144.0 02.5 204 204.0 03.6 264 264.0 04. G 25 25.0 00.4 85 85.001.5 145 145.0 02.5 205 205.0 03.6 265 265.0 04.6 2G 26.0 00.5 86 86.001.5 146 146.0 02.5 206 206.0 03.6 266 266.0 04.6 27 27.0 00.5 87 87.001.5 147 147.002.6 207 207.0 03.6 267 267.0 04.7 28 28.0 00.5 88 88.001.5 148 148.0 02.6 208 208.0 03.6 268 268.0 04 7 29 29.0 00.5 89 89.001.6 149 149.0 02.6 209 209.0 03.7 269 269.0 04.7 30 30.0 00.5 90 90.0 01.6 150 150.0 02.6 210 210.0 03.7 270 270.0 04.7 31 31.0 00.5 91 91.0 01.6 151 151.0 02.6 211 211.0 03.7 271 271.0 04.7 32 32.0 30.6 92 92.0 01.6 15'2 152 02.7 212 212.0 03.7 272 272.0 04.7 33 33.0 00.6 93 93.0 01.6 153 153.0 02.7 213 213.0 03.7 273 273.0 04.8 34 34.0 00.6 94 94.0 01.6 154 154.0 02.7 214 214.0 03.7 274 274.0 04.8 35 35.0 00.6 95 95.0 01.7 155 155. 1 02.7 215 215.0 03.8 '275 275.0 04.8 3G 36.000.6 96 96.0 01.7 156 156.0 02.7 216 216.0 03.8 276 276.0 04.8 37 37.000.6 97 97.0 01.7 157 157.0 02.7 217 217.0 03.8 277 277.0 04.8 38 38.000.7 98 98.0 01.7 158 158.0 02.8 218 218.0 03.8 278 278.0 04.9 39 39.000.7 99 99.0 01.7 159 159.0 02.8 219 219.0 03.8 279 279.0 04.9 40 40.0 00.7 100 100.0 01.7 160 160.0 02.8 220 220.0 03.8 280 280.0 04.9 41 41.0 00.7 101 101.0 01.8 161 161.0 02.8 221 221.0 03.9 281 281.0 04 9 42 42.000.7 102 102.0 01.8 162 162.0 02.8 222 222.0 03.9 282 282.0 04.9 43 43.000.8 103 103.0 01.8 163 163.0 02.8 223 223.0 03.9 283 283.0 04.9 44 44.000.8 104 104.0 01.8 164 164.0 02.9 224 224.0 03.9 284 284.0 05.0 45 45.000.8 105 105.0 01.8 165 165.0 02.9 225 225.0 03 9 285 285.0 05.0 46 46.000.8 106 106.0 01.8 166 166.0 02.9 226 226.0 03.9 286 286.0 05.0 47 47.000.8 107 107.0 01.9 167 167.0 02.9 227 227.0 04.0 287 287.0 05.0 48 48.000.8 108 108.0 01.9 168 168.0 02.9 228 228.0 04.0 288 288.0 05.0 49 49.0 00.9 109 109.0 01.9 169 169.0 02.9 229 229.0 04.0 289 289.0 05.0 50 50.0 00.9 110 110.0 01.9 170 170.0 03.0 230 230.0 04.0 290 290.0 05.1 51 51.000.9 111 111.0 01.9 171 171.0 03.0 231 231.0 04. 291 '291.0 05.1 52 52.000.9 112 112.0 02.0 172 172.0 03.0 232 232.0 04.0 292 292 05.1 53 53.000.9 113 113.0 02.0 173 173.0 03.0 233 233.0 04.1 293 293.0 05.1 54 54.000.9 114 114.0 02.0 174 174.0 03.0 234 234.0 04.1 294 294.0 05.1 55 55.0 01.0 115 115.0 02.0 175 175.0 03.1 235 235.0 04.1 295 295.0 05.1 56 56.0 01.0 116 116.0 02.0 176 176.0 03.1 236 236.0 04.1 296 296 05.2 57 57.0 01.0 117 117.0 02.0 177 177.0 03.1 237 237.0 04.1 297 297 05.2 58 58.0 01.0 118 118.0 02.1 178 178.0 03.1 238 238.0 04.2 298 298.0 05.2 59 59.0 01.0 119 119.0 02.1 179 179.0 03.1 239 239.0 04.2 299 299.0 05.2 60 60.0 01.0 120 120.0 02.1 180 180.0 03.1 240 240.0 04.2 300 300.0 05.2 Dist. Dep Lat, Dist. Dep. Lat. Dist. Dep. Lat. Dist, Dep. Lat. Dist, Dep. Lat, For 89 Degrees. TABLE IV. 205 DIFFERENCE OF LATITUDE AND DEPARTURE FOR 2 DEGREES. [list. Lat. Dep I'M. Lat. Dep Dist. Lat. Dep Dist. Lat. Dep. Dist. Lat. Dep. 1 01.0 00.0 61 61 002.1 121 120. C J 04.2 181 180.9 06.3 241 240.9 08.4 2 02.0 00.1 62 62.0:02 2 122 121.9 04.3 182 181.9 06.4 242 241.9 08.4 3 03.0 UO.l 63 63.002.2 123 122.9 04.3 183 182.9 06.4 243 242.9 08.5 4 04.0 00.1 64 64 002.2 124 123.9 04.3 184 183.9 06.4 244 243.9 08.5 5 05.0 00.2 65 65.0 02.3 125 124.9 04.4 185 184.9 06.5 245 244.9 08.6 6 06.0 00.2 66 66.0 02.3 126 125.9 04.4 186 185.9 06.5 246 245.8 08.6 7 07.0 00.2 67 67.0 02.3 127 126.9 04 4 187 186.9 06.5 247 246.8 08.6 8 OS.O 00.3 68 68.0 02.4 128 127.9 04.5 188 187.9 06.6 248 247.8 08.7 9 >9.0 00.3 69 69.0 02 4 129 128.9 04.5 189 188. 9 06.6 249 248 8 08.7 10 10. 00.3 70 70.0 02.4 130 129.9 04.5 190 189.9 00.6 250 249.8 08.7 11 11 00.4 71 71.0 02.5 131 130.9 04.6 191 190.9 00.7 251 250.6 OS.H 12 12.0 )0.4 72 72.0 02.5 132 131.9 04.6 192 191.9 06.7 252 251.8 08.8 13 13.0 00.5 73 73.0 02.5 133 132.9 04.6 193 192.9 06.7 253 252.8 08.8 14 14.0 0.5 74 74.0 02.6 134 133.9 04.7 194 193.9 06.8 254 253.8 08.9 15 15.0 00.5 75 75.002.6 135 134.9 04.7 195 194.9 06.8 255 254.8 08.9 1C 16.0 00.6 76 76.002.7 136 135.9 04.7 196 195.9 06.8 256 255.8 08.9 17 17.0 00. C 77 77.0 02.7 137 136.9 04.8 197 196.9 06.9 257 256.8 Oi) 18 18.0 00.6 78 78.0 02 7 138 137.9 04.8 198 197.9 06.9 258 257.8 09.0 19 19.0 00.7 79 79.0 02.8 139 138.9 04.9 199 198.9 06.9 259 258.8 09.0 20 20 00.7 80 80.0 02.8 140 139.9 04.9 200 199.9 07.0 26d 259 8 09.1 iii Ji.O 00.7 81 81.0 02.8 141 140.9 04.9 201 200.9 07:0 261 260. 8 09.1 22 22.0 00.8 8i 81.9 02.9 142 141 9 05 202 201.9 07.0 262 261.8 09.1 23 23. ( 00.8 83 82.902.9 143 142.9 05.0 203 202.9 07.1 263 262.8 09.2 24 24.0 00.8 84 83.902.9 144 143.9 05. 204 203.9 07 1 264 263.8 09.2 25 25.0 JO. 9 85 84 9 03.0 145 144.9 05.1 205 204.9 07.2 265 264.8 09. i 26 26 00.9 86 85.9 03 146 145.9 05.1 206 205.9 07.2 266 265.8 09.3 27 27. (' 00.9 87 86.9 03.0 147 146.9 05.1 207 206.9 07.2 267 266.8 09.3 28 28.0 01.0 8s 87.9 03.1 148 147 9 05 2 208 207.9 07.3 268 267.8 09.41 29 29.0 01.0 89 88.9 03.1 149 148.9 05.2 209 208.9 07.3 269 268.8 09 4 30 30.0 01.0 90 89 9 03.1 150 149.9 05.2 210 209.9 07.3 270 269.8 09.4 31 Jl.O 01.1 91 90.9 03.2 151 150.9 05.3 211 210.9 07.4 271 H70.b 09.5 32 32. G 01.1 92 91.9 03.2 152 151.9 05 3 212 211.9 07.4 272 271.8 09.5 33 33.0 01.2 93 92.9 03.2 153 152.9 05.3 213 212.9 07.4 273 272.8 09.5 34 34.0 01.2 94 93 9 03.3 154 153.9 05.4 214 213.9 07.5 274 273.8 09.6 35 55. 01.2 95 94 9 03.3 155 154.9 05.4 215 214.9 07.5 275 274.8 09.6 33 33.0 01.3 96 95.9 03.4 156 155.9 05.4 216 215.9 07 5 276 275.8 09.6 37 37. G 01.3 97 96.9 03.4 157 156.9 05.5 217 216.9 07 C 277 276.8 09.7 38 38. G 01.3 98 97.9 03.4 158 157.9 05.5 218 217.9 07.6 278 277.8 09.7 39 39.0 01.4 99 98.9 03.5 159 158.9 05.5 219 218.9 07.6 279 278.8 09.7 40 to.o 01.4 100 99.9 03.5 160 159.9 05.6 220 219.9 07.7 280 279.8 09.8 41 41 A 01.4 101 100.9 03.5 161 160.9 05.6 2-21 220.9 07.7 "281 280 b 09.8 42 4-2.0 01.5 102 101.903.6 162 161.9 05.7 222 221.9 07.7 282 281.8 09.8 43 43.0 01.5 103 102.9 03.6 163 162.9 05.7 223 222.9 07.8 283 282.8 09.9 44 44.0 01.5 104 103.9 03.6 164 163.9 05.7 224 223.9 07.8 284 283.8 09.9 45 45.0 01.6 105 104.903.7 165 164.9 05.8 225 224.9 07.9 285 284.8 09.9 40 46.0 01.6 106 105.903.7 166 165.9 05.8 226 225.9 07.9 286 285.8 10.0 47 47.0 01.6 107 106 903 7 167 166.9 05 8 227 226.9 07.9 287 286.8 10.0 48 48 01.7 108 107.903.8 168 167.9 05.9 228 227.9 08.0 288 287.8 10.1 49 49.0 01.7 109 108.903.8 109 168.9 05.9 229 228.9 08.0 289 288.8 10.1 50 50 01.7 110 109.903.8 170 169.9 05.9 230 229.9 08.0 290 289.8 10.1 51 51.0 01.8 111 110.903.9 171 170.9 00.0 231 230.9 08.1 291 290.8 10.2 52 52.0 01.8 112 111.903.9 172 171.9 06.0 232 231.9 08.1 292 291.8 10.2 53 53.0 01.8 113 112.903.9 173 172.9 06.0 233 232.9 08.1 293 292.8 10.2 54 54.0 01.9 114 113.904.0 174 173.9 06.1 234 233.9 08.2 294 293.8 10.3 55 55. C 01.9 115 114.904.0 175 174.9 06.1 235 234.9 08.2 295 294.8 10.3 5G 56.0 02.0 116 115.904.0 176 175.9 00.1 236 235.9 08.2 296 295.8 10.3 57 57.0 02.0 117 116.904.1 177 176.9 06.2 237 236.9 08.3 297 296.8 10.4 58 58.0 02.0 118 117.904.1 178 177.9 06.2 238 237.9 08.3 298 297.8 10.4 59 59.0 02.1 119 118.904.2 179 178.9 06.2 239 238.9 08.3 299 298.8 10.4 60 60 02.1 120 119.9 04.2 180 179.9 06.3 240 239.9 08.4 300 299.8 10.5 Dist. Dep Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. For 88 Degrees. 206 TABLE III. DIFFERENCE OF LATITUDE AND DEPABTUBE FOB 3 DEGREES. Mst, Lat. Dep Dist. Lat. Dep Dist. Lat. Dep Bist. Lat. Dep. I Dist. Lat. Dep. 1 01.0 00.1 61 60.9 03.2 121 120.8 06.3 181 180.8 09. 5 ! 241 240.7 12.6 2 02.0 00 1 62 61.9,03.2 122 121.8 06.4 182 181.8 09. 5J 242 241.7 12.7 3 03.0 00.2 63 62.903.3 123 122.8 06.4 183 182.7 09.6 243 242.7 12.7 4 04.0 00.2 64 63.903.3 124 123.8f06.5 184 183.7 09.6 244 243 7 12.8 5 05.0 00.3 65 64.903.4 125 124.806.5 185 184.7 09.7 245 244.7 12.8 6 06.0 00.3 66 65.903.5 126 125.8 06.6 186 185.7 09.7 246 245.7 12.9 7 07.0 00.4 67 66.903.5 127 126.8 06.6 187 186.7 09.8' 247 246.7 12.9 8 08.0 00.4 68 67.903.6 128 127.8 06.7 188 187.7 09.8 248 247.7 13.0 9 09.0 00 5 69 68.903.6 129 128.8 06.8 189 188.7 09.9 249 248.7 13.0 10 |10.0 00.5 70 69.903.7 130 129.8 06.8 190 189.7 09.9 250 249.7 13.1 11 11.0 00.6 71 70.903. 7 131 130.8 06.9 191 190.7 10. Oj 251 250.7 13.1 12 12.0 00.6 72 71.903.8 132 131.8 06. 9 192 191.7 10.0 252 251.7 13.2 13 13 00.7 73 72.903.8 133 132.8 07.0 193 192.7 10.1 253 252.7 13.2 14 14.0 00.7 74 73.903.9 134 133.8 07.0 194 193.7 10 2 254 253.7 13.3 15 15.0 00.8 75 74.903.9 135 134.8 07.1 195 194.7 10.2 255 254.7 13.3 16 16.0 00. b 76 75.904.0 136 135.8 07.1 196 195.7 10.3 256 255.6 13.4 17 17.0 00.9 77 76.904.0 137 136.8 07.2 197 196.7 10.3 257 256.6 13.5 18 18.0 00.9 78 77.904.1 138 137.8 07.2 198 197.7 10.4 258 257.6 13.5 19 19.0 01.0 79 78 904.1 139 138.8 07.3 199 198.7 10.4 259 258.6 13.6 20 20.0 01.0 80 79 9104.2 140 139.8 07.3 200 199.7 10.5 260 259.6 13.6 21 21.0 01.1 81 80.904.2 141 140.8 07.4 '201 200.7 10.5 261 260.6 13.7 2-2 22.0 01.2 82 81.904.3 142 141.8 07.4 202 201.7 10.6 262 261.6 13.7 23 23.0 01.2 83 82.904.3 143 142.8 07.5 203 202.7 10.6 263 262.6 13.8 24 24.0 01.3 84 83.904.4 144 143.8 07.5 204 203.7 10.7 264 263. C 13.8 25 25.0 01.3 85 84.904.4 145 144.8 07.6 205 204.7 10.7 265 264.6 13.9 26 26.0 01.4 86 85.904.5 146 145 8 07.6 206 205.7 10.8 266 265.6 13.9 27 27.0 01.4 87 86.904.6 147 146.8 07.7 207 206.7 10.8 267 266.6 14.0 28 28.0 01.5 88 87.904.6 148 147.8 07.7 208 207.7 10.9 268 267.6 14.0 29 29.0 01.5 89 88.904.7 149 148.8 07.8 209 208.7 10.9 269 268.6 14 1 30 30.0 01.6 90 89.904.7 150 149.8 07.9 210 209.7 11.0 270 269.6 14.1 31 31.0 01.6 91 90.904.8 151 150.8 07.9 211 210.7 11.0 271 270.6 14.2 32 32.0 01.7 92 91.904.8 152 151.8 08.0 212 211.7 11.1 272 271.6 14.2 33 33.0 01.7 93 92.9.04.9 153 152.8 08.0 213 212.7 11.1 273 272.6 14.3 34 34.0 01.8 94 93.904.9 154 153.8 08.1 214 213.7 11.2 274 273.6 14.3 35 35.0 01.8 95 94.905.0 155 154.8 08.1 215 214.7 11.3 275 274.6 14.4 36 36.0 01.9 96 95.905.0 156 155.8 08.2 216 215.7 11.3 276 275.6 14.4 37 36.9 01.9 97 96.905.1 157 156.8 08.2 217 216.7 11.4 277 276. (i 14.5 38 37.9 02.0 9h 97.905.1 158 157.8 08.3 218 217.7 11 4 278 277.6 14.5 39 38.9 02.0 99 98.9 ; 05.2 159 158.8 08.3 219 218.7 11.5 279 278.6 14.6 40 39.9 02.1 100 99.905.2 160 159.8 08.4 220 219.7 11.5 .280 279.6 14.7 41 |40.9 02.1 101 100. 905. 3 161 160.8 08.4 221 220.7 11.6 281 2SO.O 14.7 42 41.9 02.2 102 101.905.3 162 161.8 08.5 222 221.7 11.6 282 281.6 14.8 43 42.9 02.3 103 102.905.4 163 162.8 08.5 223 222.7 11.7 283 282.6 14.8 44 43.9 02.3 104 103 905.4 164 163 8 08.6 224 223.7 11.7 284 283.6 14.9 45 44.9 02.4 105 104.9,05.5 165 164.8 08.6 225 224.7 11.8 285 284.6 14.9 46 45.9 02.4 106 105.905 5 166 165 8 08.7 226 225.7 11.8 286 285.6 15.0 47 46.9 02.5 107 106.905.6 167 166.8 08.7 227 226.7 11.9 287 286. C 15.0 48 47.9 02.5 108 107.905.7 168 167.8 08.8 228 227.7 11.9 288 287.6 15.1 49 48.9 02.6 109 108.905.7 169 168.8 08.8 229 228.7 12.0 289 288.6 15.1 50 49.9 02.6 110 109.805.8 170 169.8 08.9 230 229.7 12.0 290 289.6 15.2 51 50.9 02.7 111 110.805.8 171 170.8 08.9 231 230.7 12.1 291 290.6 15. '2 52 51.9 02.7 112 111.805 9 172 171.8 09.0 232 231.7 12.1 292 2i>1.6 15.3 53 52.9 02.8 113 112.805.9 173 172.8 09.1 233 232.7 12.2 293 292.6 15.3 54 53.9 02.8 114 113.806.0 174 173.8 09.1 234 233.7 12.2 294 293.6 15.4 55 54.9 02.9 115 114.806.0 175 174.8 09.2 235 234.7 12.3 295 294.6 15.4 56 55.9 02.9 116 115.806.1 176 175.8 09.2 236 235.7 12.4 296 295.6 15.5 57 56.9 03.0 117 116.8'06.1 177 176.8 09.3 237 236.7 12.4 297 296.6 15.5 58 57.9 03.0 118 117.806.2 178 177.8 09.3 238 237.7 12.5 298 297.6 15.6 59 58.9 03.1 119 118.806.2 179 178.8 09.4 239 238.7 12.5 299 298.6 15.6 60 59.9 03.1 120 119.8 06.3 180 179.8 09.4 240 239.7 12.6 300 299.6 15.7 Dist. Dep Lat. D~ist Dep. lLat. Dist. Dep. Lat. Dist. Dep. Lat, Dist. Dep. Lat. For 87 Degrees. TABLE IV. 207 DIFFERENCE OF LATITUDE AND DEPARTURE FOR 4 DEGREES. )ist. ..at. Dep Dist. Lat. |Dep list. Lat. Dep ist. Lat. Dep. Dist. Lat. Dep. 1 )1.0 30.1 61 60.90^.3 121 120. 708. 4 1 181 180.6 12.6 241 240.4 16.8 2 )2.0 30.1 62 61.804.3 122 121.708.5 182 181.6 12.7 242 241.4 16.9 3 )3.0 30.2 63 62.804.4 123 122.708.6 183 182.6 12.8 243 242.4 17.0 4 )4.0 30.3 64 63.804.5 124 123.708.6 184 183.6 12.8 244 243.4 17.0 5 5.0 30.3 65 64.804.5 125 124.708.7 185 184.5 12.9 245 244.4 17.1 6 )6.0 JO. 4 66 65.804.6 126 125.708.8 186 185.5 13.0 246 245.4 17.2 7 37.0 (30.5 67 66.804.7 127 126.708.9 187 186.5 13.0 247 246.4 17.2 8 38.0 00.6 68 67.804.7 128 127.708.9 188 187.5 13.1 248 247.4 17.3 9 J9.0 JO. 6 69 68.804.8 129 128.709.0 189 188.5 13.2 249 248.4 17.4 10 10.0 00.7 70 69.8:04 9 130 129.709.1 190 189.5 13.3 250 249.4 17.4 11 ii.O [JO. 8 71 70.805.0 131 130.709.1 191 190.5 13.3 251 ii50.4 17.5 12 12.0 00.8 72 71.805.0 132 131.709.2 192 191.5 13.4 252 251.4 17.6 13 13.0 00.9 73 72.805.1 133 132.709.3 193 192.5 13.5 253 252.4 17.6 14 14 01.0 74 73.805.2 134 133.7U9.3 194 193.5 13.5 254 253.4 17.7 15 15.0 01.0 75 74.805.2 135 134.709.4! 195 194.5 13.6 255 254.4 17.8 16 16.0 01.1 76 75.805.3 136 135.7 J9.5 196 195.5 13.7 256 255.4 .17.9 17 17.0 01.2 77 76.805.4 137 136.709.6 197 196.5 13.7 257 256.4 17.9 18 18.0 01.3 78 77.805.4 138 137.7|09.6 198 197.5 13.8 258 257.4 18.0 19 19.001.3 79 78.805.5 139 138. 7 09.7! 199 198.5 13.9 259 258.4 18.1 20 20.0|01.4 80 79.805.6 140 139.7 09.8; 200 199.5 14.0 260 259.4 18.1 21 ZO.901.5 81 80.805.7 141 140.7 09. 8, 201 200.5 14.0 261 260.4 18.2 22 21.901.5 82 81.805.7 142 141.7 09 9 20'2 201.5 14.1 262 261.4 18.3 23 22.901.6 83 82.805.8 143 142.7 10.0 203 202.5 14.2 263 262.4 18.3 24 23.901.7 84 83.805.9 144 143.6 10.0, 204 203.5 14.2 264 263.4 18.4 25 24.901.7 85 84.805.9 145 144.610.1 205 204.5 14 3 265 264.4 18.5 26 25.901.8 86 85.806.0 146 145.610.2! 206 205.5 14.4 266 265.4 18.6 27 26.901.9 87 86.806.1 147 146.6 10.3 207 206.5 14.4 267 266.3 18.6 28 27.902.0 88 87.806.1 148 147.6 10.3 208 207.5 14.5 268 267.3 18.7 29 28.902.0 89 88.806.2 149 148.6 10.4 209 208.5 14.6 269 268.3 18.8 30 29.902.1 90 89.806.3 150 149.6 10.5 210 209.5 14.6 270 269.3 18.8 31 30.902.2 91 90.806.3 151 150. (i 10.5 211 210.5 14.7 271 270.3 18.9 32 31.902.2 92 91.806.4 152 151.6 10.6 212 211.5 14.8 272 271.3 19.0 33 32.902.3 93 92.806.5 153 152.6 10.7 213 212.5 14.9 273 272.3 19.0 34 33.902.4 94 93.806.6 154 153.610.7 214 213.5 14.9 274 273.3 19.1 35 34.902.4 95 94.806.6 155 154.610.8 215 214.5 15.0 275 274.3 19.2 36 35.902.5 96 95.806.7 156 155.610.9 216 215.5 15.1 276 275.3 19.3 37 36.902.6 97 96.806.8 157 156.611.0 217 216.5 15.1 277 276.3 19.3 38 37.902.7 98 97.806.8 158 157.611.0 218 217.5 15.2 278 277.3 19.4 39 38.902.7 99 98.806.9 159 158.6 11.1 219 218.5 15.3 279 278.3 19 5 40 39.902.8 100 99.8 07.0 160 159.6 11.2 220 219.5 15.3 280 279.3 19.5 41 40.902.9 101 100.8 J7.0 161 160.611.2 221 220.5 15.4 28] 280.3 19.6 42 41.902.9 102 101.807.1 162 161.6 11.3 222 221.5 15.5 282 281.3 19.7 43 42.903.0 103 102.7107.2 163 162. G 11.4 223 222.5 15.6 283 282.3 19.7 44 43.903.1 104 103.7 07.3 164 163.6 11.4 224 223.5 15.6 284 283.3 19.8 45 44.903.1 105 104.7 07.3 165 164.6 11.5 225 224.5 15.7 285 284.3 19.9 46 45.9 03.2 106 105.7 07.4 166 165.6 11.6 2'26 225.4 15.8 286 285.3 20.0 47 46.9 03.3 107 106.7 07.5 167 166.6 11 6 227 226.4 15.8 287 286.3 20.0 48 47.903.3 108 107.7 07. 5 168 167.6 11.7 228 227.4 15.9 288 287.3 20.1 49 48.903.4 109 108.7 07.6 169 168.6 11.8 229 228.4 16.0 289 288.3 20.2 50 49.903.5 11C 109.7 07.7 17C 169.6 11.9 230 229.4 16.0 29C 289.3 20.2 51 50. 03. G 111 110.7 07.7 171 170. b 11.9 231 230.4 16.1 291 290.3 20.3 52 51. i 03.6 115 111.7 07.8 172 171.6 12.0 l)0f) vi 231.4 16.2 292 291.3 20.4 53 52. i 03.7 IK 112.7 07.9 17S 172. C 12. 233 232.4 16.3 29S 292.3 20.4 54 53. i 03.8 114 113.7 08.0 174 173.6 12. 234 233.4 16.3 294 293.3 20.5 55 54. { 103.8 HE 114.7 08.0 111 174. C 12. 23E 234.4 16.4 29c 294.3 20.6! 56 55.1 103.9 IK 115.7 08. 176 175.6 12. 23C 235.4 16.6 29t 295.3 20.6 57 56.1 >04.0 I 11" 116.7 08. ITi 176. C 12. 23 r 236.4 16. E 297 296.3 20.7 58 57.1 >04.0 i lit 117.7 08. 17* 177. e 12. 236 237.4 16.6 296 297.3 20.8 59 58.1 >04.1 111 118.7 08. 171 178.6 12. 231 238.4 16.7 291 298.3 20.9; 60 59.1 >04.2 12( 119.7 08.4 18( 179.612. 24( 239.4 16.7 30C 299.3 20.9 Dist Dej: Lat. Dist Dcp. Lat Dist Do,). Lat Dist DCP. Lat. Dist. Dcp. Lat, For 86 Degrees. 208 TABLE IV. DIFFERENCE OF LATITUDE AND DEPARTURE FOR 5 DEGREES. [list. Lat. Dep Dist. Lat. Dep Dist. Lat. Dep Dist. Lat. Dep. Dist. Lat. Dep. 1 Ol.O 00.1 61 60.8 05.3 121 120.5 10.5 181 180. 15.8 241 240.1 21.0 2 02.0 00.2 62 61.8 05.4 122 121.5 10.6 182 181. 15.9 242 241.1 21.1 3 03.0 00.3 63 62.8 05.5 123 122.5 10.7 183 182. 15.9 243 242.1 21.2 4 04.0 00.3 64 63.805.6 124 123.5 10.8 184 183. 16.0 244 243.1 21.3 5 05.0 00.4 65 64.8 05.7 125 124.5 10.9 185 184. 16.1 245 244.1 21.4 6 06.0 00.5 66 65.7 05.8 126 125.5 11.0 186 185. 16.2 246 245.1 21.4 7 07.0 00.6 67 66.7 05.8 127 126.5 11.1 187 186. 16.3 247 246.1 21.5 8 08.0 00.7 68 67.7 05.9 128 127.5 11.2 188 187. 16.4 248 247.1 21.6 9 09.0 J0.8 6'J 68.7 06.0 129 128.5 11.2 189 188. 16.5 249 248.1 21.7 10 10.0 00.9 70 69.7 06.1 130 129.5 11.3 190 189. 16.6 250 249.0 21.7 11 11.0 01. 7i 70.7 06.2 131 130.5 11.4 191 190. 16.6 251 25J.O 21.9 12 12.0 01.0 72 71.7 06.3 132 131.5 11.5 192 191. 16.7 252 251.0 22.0 13 13.0 01.1 73 72.7 06.4 133 132.5 11.6 193 192. 16.8 253 252.0 22.1 14 13.9 01.2 74 73.7 lJ-6.4 134 133.5 11.7 194 193.3 16.9 254 253.0 22.1 15 14.9 01.3 75 74.7 06.5 135 134.5 11.8 195 194.3 17.0 255 254.0 22.2 16 15.9 01.4 76 75.7 06.6 136 135.5 11.9 196 195.3 17.1 256 255.0 22.3 17 16.9 01.5 77 76.7 06.7 137 136.5 11.9 197 196.3 17.2 257 256.0 22.4 18 17.9 01.0 78 77.7 06.8 138 137.5 12.0 198 197.2 17.3 258 257.0 22.5 19 18.9 01.7 79 78.7 06.9 139 138.5 12.1 199 198.2 17.3 259 258.0 22.6 20 19.9 dl.7 80 79.7 07.0 140 139.5 12.2 200 199.2 17.4 260 259.0 22.7 21 20.9 01.8 81 . V 07.1 141 140.5 12.3 201 200.2 1775 261 260.01 22.7 22 21.9 Jl.9 82 81.7 07.1 142 141.5 12.4 202 201.2 17.6 262 261.0 22.8 23 22.9 02.0 83 82.7 07.2 143 142.5 12.5 203 202.2 17.7 263 262.0 22.9 24 23.9 02.1 84 83.7 07.3 144 143.5 12.6 204 203.2 17.8 264 263.0 23.0 25 24.9 02.2 85 84.7 07.4 145 144.4 12.6 205 204.2 17.9 265 264.0 23.1 26 25.9 02.3 86 85.7 07.5 146 145.4 12.7 206 205.2 18.0 266 265.0 23.2 27 26.9 02.4 87 86.7 07.6 147 146.4 12.8 207 208. '2 18.0 267 266.0 23.3 28 27.9 02.4 88 87.7 07.7 148 147.4 12.9 208 207.2 18.1 268 267.0 23.4 29 28.9 02.5 89 88.7 07.8 149 148.4 13.0 209 208.2 18.2 269 268.0 23.4 30 29.9 02. G 90 89.7 07.8 150 149.4 13.1 210 209.2 18.3 270 269.0 23.5 31 30.9 02. 'i 91 90. 'i 07.9 151 150.4 13.2 211 '2 10. 2 18.4 271 270.0 23.6 32 31.9 02. b 92 91. 08.0 15i 151.4 13.2 212 211.2 18.5 272 271.0 23.7 33 32.9 02.9 93 92. C 08.1 153 152.4 13.3 213 212.2 18.6 273 272.0 23.8 34 33.9 03.0 94 93. C 08.2 154 153.4 13.4 214 213.2 18.7 274 273.0 23.9 35 34.9 03.1 95 94. G 08.3 155 154.4 13.5 215 214.2 18.7 275 274.0 24.0 36 35.9 03.1 9G 95.6 08.4 15b 155.4 13.6 216 215.2 J8.8 276 274.9 24.1 37 36.9 03:2 97 .96.6 08.5 157 156.4 13.7 217 216.2 18.9 277 275.9 24.1 38 37.9 03.3 98 97.6 08.5 158 157.4 13.8 218 217.2 19.0 278 276.9 24.2 39 38.9 03.4 99 98.6 08.6 159 158.4 13.9 219 218.2 19.1 279 277.9 24.3 40 39.8 03.5 100 99. G 08.7 160 159.4 13.9 220 219.2 19.2 280 278.9 24.4 41 40.8 03.6 101 100.G 08.8 16i ICO. 4 14.0 221 220.2 19.3 281 279.9 24.5 42 41.8 03.7 102 101.6 08.9 162 161.4 14.1 222 221.2 19.3 282 280.9 24.6 43 12.8 03.7 103 102.6 09.0 163 162.4 14.2 223 222.2 19.4 283 281.9 24.7 44 43.8 03. b 104 103. C 09.1 164 163.4 14.3 224 223.1 19.5 284 282.9 24.8 45 44.8 03.9 105 104. G 09.2 165 164.4 14.4 225 224.1 19.6 285 283.9 24.8' 46 45.8 04.0 106 105.6 09.2 166 165.4 14.5 226 225.1 19.7 286 284.9 24.9 47 46.8 04.1 107 106.6 09.3 167 166.4 14.6 227 226 1 19.8 287 285.9 25.0 48 47.8 04.2 108 107. C 09 4 ]68 167.4 14.6 228 227.1 19.9 288 286.9 25.1 49 48.8 04.3 109 108. C 09.5 169 168.4 14.7 229 228 1 20.0 289 287.9 25.2 50 49 8 04.4 110 109. G 09.6 170 169.4 14.8 230 229.1 20.0 290 288.9 25.3 51 50.8 04.4 111 110.6 09.7 171 170.3 14.9 231 230.1 20 1 291 289.9 25.4! 52 51.8 04.5 112 111.6 09.8 172 171.3 15.0 232 231.1 20.2 292 290.9 25.41 53 52.8 04.6 113 112. C 09.8 173 172.3 15.1 233 232.1 20.3 293 291.9 25.5 54 53.8 04.7 114 113. C 09.9 174 173.3 15.2 234 233.1 20.4 294 292.9 25.6 55 51.8 04.8 115 114.6 10.0 175 174.3 15.3 235 234.1 20.5 295 293.9 25.7 56 55.8 04.9 116 115.6 10.1 176 175.3 15.3 236 235.1 20.6 296 294.9 25 8 57 56.8 05.0 117 116.6 10.2 177 176.3 15.4 237 236. 1 20.7 297 295.9 25.9 58 57.8 05.1 118 117. C 10.3 178 177.3 15.5 238 237.1 20.7 298 296.9 26.0 59 58.8 05.1 119 118.5 10.4 179 178.3 15.6 239 238.1 20.8 299 297.9 26.1 60 59.8 05.2 120 119.5 10.5 180 179.3 15.7 240 239.1 20.9 300 298.9 26.1 [list. Dep Lat. Dist. Dep. Lat. )ist. Dep. Lat. Dist, Dep. Lat. Dist. Dep. Lat. For 85 Degrees. TABLE IV. 209 DIFFERENCE OF LATITUDE AND DEPARTURE FOR 6 DEGREES. Dist. Lat, Dep Dist. Lat. Dep Dist, Lat. Dep Dist. Lat. Dep. Dist. Lat. Dep. 1 01.000.1 61 60.706.4 121 120.3 12.6 181 180.0 18.9 241 239.7 25.2 2 02.000.2 62 61.7 06.5 122 121.3 12.8 182 181.0 19.0 242 240.7 25.3 3 03.0 00.3 63 62.706.6 123 122.3 12.9 183 182.0 19.1 243 241.7 25.4 4 04.000.4 64 63.606.7 124 123.3 13.0 184 183.0 19.2 244 242.7 25.5 5 05.000.5 65 64.606.8 125 124.3 13.1 185 184.0 19.3 245 243 7 25.6 6 06.0 00.6 66 65.606.9 126 125.3 13.2 186 185.0 19 4 24.6 244.7 25.7 7 07.0 00.7 67 66.607.0 127 126.3 13.3 187 186.0 19.5 247 245. 1) 25.8 8 J8.0 00.8 68 67.607.1 128 127.3 13.4 188 187.0 19.7 248 246.6 25.9 9 09.0 00.9 69 6*. 6 07. 2 129 128.3 13.5 189 188.0 19.8 249 247.6 26.0 10 09.9 01.0 70 69.607.3 130 129.3 13.6 190 189.0 19.9 250 248.6 26.1 11 10.9 01.1 71 70.607.4 131 130 3 13.7 191 190.0 'M 251 249.6 ^0.2 12 11.9 01.3 72 71.607.5 132 131.3 13.8 192 190.9 2o!i 252 250.6 20.3 13 12.9 01.4 73 72.607.6 133 132.3 13.9 193 191.9 20.2 253 251.6 26.4 14 13.9 01.5 74 73.607.7 134 133.314 194 192.9 20.3 254 252.0 26.6 15 14.0 01.6 75 74.607.8 135 134.3 14.1 195 193.9 20.4 255 253 6 26.7 16 15.9 01.7 76 75.6|07.9 136 135.3 14.2 196 194.9 20.5 256 254.6 26.8 17 16.9 01.8 77 76.608.0 137 136.2 14.3 197 195.9 20.6 257 255.6 26.9 18 17.9 01.9 78 77.608.2 138 137.2 14.4 198 196.9 20.7 258 250.0 27.0 19 18.9 02.0 79 78.6'08.3 139 138. '2 14.5 199 197.9 20.8 259 257.6 27.1 20 19.9 12.1 80 79.608.4 140 139.2 14.6 200 198.9 20.9 260 258. <) 27.2 Ul M.9 01. -L 81 80.608.5 141 140.2 14.7 201 199.9 21.0 201 259.6 27.3 22 21 9 02 3 82 81.6i08.6 142 141.2 14.8 202 200.9 21.1 262 200.6 27.4 23 22.9 02.4 83 82.508.7 143 142.2 14.9 203 201.9 21.2 263 261.6 27.5 24 23.9 02.5 84 83 5 ! 08.8 144 143.2 15.1 204 202.9 21.3 264 262.6 27.6 25 24.9 02.6 85 84.508.9 145 144.2 15.2 205 203.9 21.4 265 263.5 27.7 26 25.9 02.7 86 85.509.0 146 145 2 15.3 206 204.9 21.5 266 264.5 27.8 27 26.9 02.8 87 86.5U9.1 147 146.2 15.4 207 205.9 21.6 267 265.5 27.9 28 27.8 02.9 88 87.509.2 148 147.2 15". 5 208 206.9 21.7 268 266.5 28.0 29 28.8 03.0 89 88.509.3 149 148.2 15. C 209 207.9 21.8 269 267.5 28.1 30 29.8 03.1 90 89.509.4 150 149.2 15.7 210 208.8 22 270 268.5 28.2 31 30.8 03.2 91 90.509.5 151 150.2 15.8 211 209.8 22.1 271 269.5 28.3 32 31.8 03.3 92 91.509.6 152 161.2 15.9 212 210.8 22.2 272 270.5 28.4 33 33.* 03.4 93 92.509.7 153 152.2 16.0 213 211.8 22.3 273 271.5 28.5 34 33.8 03.6 94 93.509.8 154 153.2 16.1 214 212.8 22.4 274 272.5 28.6 35 34 8 03.7 95 94.509.9 155 154.2 16.2 215 213.8 22.5 275 273.5 28.7 36 Jo. 8 03.8 96 95.510.0 156 155.1 16.3 216 214.8 22.6 276 274.5 28.8 37 30.8 03.9 97 96.510.1 157 156 1 16.4 217 215.8 22.7 277 275.5 29.0 38 37.8 04.0 98 97.5J10.2 158 157.1 16.5 218 216.8 22.8 278 276.5 29.1 39 38.8 04.1 99 98.510.3 159 158.1 16.6 219 217.8 22.9 279 277.5 29.2 40 39. 8 04.2 10U 99.510.5 160 159.1 16.7 220 218.8 23.0 280 278.5 29.3 41 10.8 04.3 101 100.410.0 101 160.1 16.8 221 219.8 23.1 281 279.5 29.4 42 41.8 04.4 102 101.410.7 162 161.1 16.9 222 220.8 23.2 282 280.5 29.5 43 42.8 04 5 103 102.410.8 163 162.1 17.0 223 221.8 23.3 283 281.4 29.6 44 43.8 04.6 104 103.4 10.9 164 163.1 17.1 224 222.8 23.4 284 282.4 29.7 45 14 8 04.7 105 104.4 11.0 165 164.1 17.2 225 223.8 23.5 285 283.4 29.8 46 15.7 04.8 106 105.4 11.1 166 165 1 17.4 226 224.8 23.6 286 284.4 29.9 47 46.7 04.9 107 106^411.2 167 166.1 17 5 227 225.8 23.7 287 285.4 30.0 48 47.7 05.0 108 107.4 11.3 168 167.1 17.6 228 226.8 23.8 288 286.4 30.1 49 48.7 05.1 109 108.4 11.4 169 168.1 17.7 229 227.7 23.9 289 287.4 30.2 50 19.7 05.2 110 109.411.5 170 169.1 17.8 230 228.7 24.0 290 288.4 30.3 51 50 7 05.3 111 110.4 11.6 171 170.1 17.9 231 229.7 24.1 291 2ts9.4 30.4 52 51.7 05.4 112 111.4 11.7 172 171.1 18.0 232 230.7 24.3 292 290.4 30.5 53 52.7 05.5 113 112.411.8 173 172.1 18.1 233 231.7 24.4 293 291.4 30.6 54 53.7 05.6 1 1 4 113.411.9 174 173.0 18.2 234 232.7 24.5 294 292.4 30.7 55 54.7 05.7 115 114.412.0 175 174.0 18.3 235 233.7 24.6 295 293.4 30.8 56 55.7 05.9 116 115.4 12.1 176 175.0 18.4 236 234.7 24.7 296 294.4 30.9 57 56.7 06.0 117 116.4 12.2 177 176.0 18.5 237 235.7 24.8 297 295.4 31.0 58 57.7 06.1 118 117.412.3 178 177.0 18.6 238 236.7 24.9 298 296.4 31.1 59 58.7 06.2 119 118 312 4 179 178.0 18.7 239 237.7 25.0 '2!)',) 297.4 31.3 60 59 7 06.3 120 119.3 12.5 180 179.0 18.8 240 238.7 25.1 300 198.4 31.4 Dist, Dep Lat. Dist, Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. For 84 Degrees. 210 TABLE IV. DIFFERENCE OF LATITUDE AND DEPARTURE FOR 7 DEGREES. Dist. Lat. Dep Dist. Lat. Dep Dist. Lat, Dep Dist. Lat. Dep. Dist. Lat. Dep. 1 01.0 00.1 61 60.5 07.4 121 120.1 14.7 181 179.7 22.1 241 239.2 29.4 2 02.0 00. i 62 61 5 07.6 122 121.1 14.9 182 180.6 22.2 242 240.2 29 5 3 03.0 00.4 63 62.5 07.7 123 122.1 15.0 183 181.6 22.3 243 241.2 29.6 4 04 00.6 64 63.507.8 124 123.1 15.1 184 182.6 22.4 244 242.2 29.7 5 05.0 00.6 63 64.5 07.9 125 124.1 15.2 185 183.6 22.5 245 243.2 29.9 6 06.0 00.7 66 65.5 08.0 126 125.1 15.4 186 184.6 22.7 246 244.2 30 7 03 9 00.9 67 66.5 08.2 127 126 1 15.5 187 185.6 22.8 247 245.2 30.1 8 07.9 01. 68 67.5 08.3 128 127.0 15.6 188 186.6 22.9 2-18 246.2 30.2 9 08.9 01.1 69 68.5 08.4 129 128.0 15.7 189 187.6 23 249 247.1 30. C 10 09.9 01. i 70 69.5 08.5 130 129.0 15.8 190 188.6 23.2 250 248.1 30.5 11 10. y Ol.o 71 70. & 08.7 131 130. 16.0 191 iy.(j 23. b 251 249.1 30.6 ia 11.9 01.5 72 71.5 08.8 132 131.0 16.1 192 190.6 23.4 252 250.1 30.7 13 12.9 01. 73 72.5 08.9 133 132.0 16.2 193 191.6 23.5 253 251.1 30.8 14 13 9 01.7 74 73.4 09.0 134 133.0 16.3 194 192.6 23.6 254 252.1 31.0 15 14.9 01.8 75 74.4 09.1 135 134.0 16.5 195 193.5 23.8 255 253.1 31.1 10 15.9 01.9 76 75.4 09.3 136 135.0 16.6 196 194.5 23.9 256 254.1 31.2 17 1G.9 02.] 77 76.4 09.4 137 136.0 16.7 197 195.5 24.0 257 255.1 31.3 18 17.9 02.2 I 8 77 4 09.5 138 137.0 16.8 198 196.5 24.1 258 256.1 31.4 19 18.9 02.3 79 78.4 09.6 139 138.0 16.9 199 197.5 24.3 259 257.1 31.0 20 19.9 02 4 80 79.4 09.7 140 139.0 17.1 200 198.5 24.4 260 258.1 31.7 iJi 20.8 02.6 81 80.4 09.9 141 139.9 17.2 201 199.5 24.5 261 259.1 31.8 22 21.8 02.7 82 81.4 10.0 142 140.9 17.3 202 200.5 24.6 262 260.0 31.9 23 22.8 02.8 83 82.4 10.1 143 141.9 17.4 203 201.5 24.7 263 261.0 32.1 24 23.8 02.9 81 83.4 10.2 144 142.9 17.5 204 202.5 24.9 264 262.0 32.2 25 24.8 03.0 85 84.4 10.4 145 143.9 17.7 205 203.5 25.0 265 263.0 32.3 2G 25.8 C3 i. 86 85.4 10. f. 146 144.9 17.8 206 204.5 25.1 260 264.0 32.4 27 26.8 03.3 87 86.4 10.6 147 145.9 17.9 207 205.5 25.2 2G7 265.0 32.5 28 27.8 03.4 88 87.3 10.7 148 146 9 18.0 208 206.4 25.3 268 266.0 32.7 29 28.8 03.5 89 88.3 10.8 149 147.9 18.2 209 207.4 25.5 269 267 32.8 30 29.8 03.7 90 89 3 11.0 150 148.9 18.3 210 208.4 25.6 270 268.0 32.9 3i 30.8 03.8 9i 90.3 11.1 151 149.9 18.4 211 209.4 25.7 271 269 . 33.0 32 31.8 03.9 92 91.3 11.2 152 150 9 18.5 212 210.4 25.8 272 270.0 33.1 33 32.8 04.0 93 92.3 11.3 153 151.9 18.6 213 211.4 26.0 273 271.0 33.3 3i 33.7 04.1 94 93.3 11.5 154 152.9 18.8 214 212.4 26.1 274 272.0 33.4 35 34.7 04.3 95 94.3 11.6 155 153.8 18.9 215 213.4 26.2 275 273.0 33.5 33 35.7 04.4 90 95.3 11.7 156 154.8 19.0 216 214 4 26.3 276 273.9 33.6 37 33.7 04.5 97 96.3 11.8 157 155.8 19.1 217 215.4 26.4 277 274.9 33.8 38 37.7 04.6 98 97.3 11.9 158 156.8 19.3 218 216.4 26. G 278 275.9 33.9 39 38.7 04.8 99 98.3 12.1 159 157.8 19.4 219 217.4 26.7 279 276.9 34.0 40 39.7 04.9 100 99.3 12.2 160 158.8 19.5 220 218.4 26.8 280 277.9 34.1 41 40. '< 05.0 101 100.* 12.3 161 159.8 19.6 221 219.4 26.9 281 278.9 34.2 42 41.7 05.1 102 101.2 12.4 162 160.8 19.7 222 220.3 27.1 282 279.9 34.4! 43 42.7 05.2 103 102.2 12.6 163 161.8 19.9 223 221.3 27.2 283 280,9 34.5 4i 43.7 05.4 101 103.2 12.7 164 162.8 20.0 224 222.3 27.3 284 281.9 34.C 45 44.7 05.5 105 104.2 12.8 165 163.8 20.1 225 223.3 27.4 285 282.9 34.7 40 45.7 05.6 106 105.2 12.9 166 164.8 20.2 228 224.3 27.5 28G 283.9 34.9 47 46.6 05.7 107 106.2 13.0 167 165.8 20.4 227 225.3 27.7 287 284.9 35.0 43 17.6 05. b 108 107.2 13.2 168 166.7 20.5 228 226.3 27.8 288 285.9 35.1 49 18. C 06.0 109 108.2 13.3 169 167.7 20.6 229 227.3 27.9 289 286.8 35.2 50 49.6 06 1 110 109.2 13.4 170 168.7 20.7 230 228.3 28.0 290 287.8 35.3 5i 50. b 0(3.2 111 110.2 13.5 171 169.7 20.8 231 229.3 28.2 29ll 288.8 35.5 52 51.6 06.3 112 111.2 13.6 172 170.7 21.0 232 230.3 28.3 292 289.8 35.6 53 52.6 06.5 113 112.2 13.8 173 171.7 21.1 233 231.3 28.4 293 290.8 35.7 54 53.6 06.6 114 113. 2 13.9 174 172.7 21.2 234 232.3 28.5 294 291.8 35.8 55 54.6 06.7 115 114.1 14-0 175 173.7 21.3 235 233.2 28.6 295 292.8 30.0 58 55.6 06.8 116 115.1 14.1 176 174.7 21.4 236 234.2 28.8 296 293.8 36.1 57 56.6 06.9 117 116.1 14.3 177 175.7 21.6 237 235.2 28.9 297 294.8 36.2 58 57.6 07.1 118 117.1 14.4 178 176.7 21.7 238 236.2 29.0 298 295.8 36.3 59 58.6 07.2 119 118.1 14.5 179 177.7 21.8 239 237.2 29.1 299 296.8 36.4 CO 59.6 07.3 120 119.1 14.6 180 178.7 21.9 240 238.2 29.2 300 297.8 36.6 Dist. Dcp Lat. Dist, Dep. Lat.iflist, Dep. Lat. Dist, Dep. Lat. Hist. Dep. Lat. For 83 Degrees. TABLE IV. 211 DIFFERENCE OF LATITUDE AND DEPARTURE FOR 8 DEGREES. Dist.lLat.JDep Dist. Lat, Dep Dist. Lat. Dep Dist. Lat. Dep. Dist. Lat, Dep. 1 01.000.1 61 60.4 08.5 121 119.8 16.8 181 179.2 25.2 241 238.7 33.5 2 02.000 3 62 61.4 08.6 122 120.817.0 182 180.2 25.3 242 239.6 33.7 3 03.000.4 63 62 4 08.8 123 121.817.1 183 181.2 25.5 243 240.6 33.8 4 04.000.6 64 63.408.9 124 122.817.3 184 182.2 25.6 244 241.6 34.0 5 05.0J00.7 65 64.409.0 125 123.817.4 185 183.2 25.7 245 242.6 34.1 6 05.900.8 66 65.409.2 126 124.817.5 186 184.2 25.9 246 243.6 34.2 7 06 901.0 67 66.309.3 127 125.817.7 187 185.2 26.0 247 244.6 34.4 8 07.901.1 68 67.309.5 128 126.817.8 188 186.2 26.2 248 245.6 34.5 9 08.901.3 69 68.309.6 129 127.718.0 189 187.2 26.3 249 246.6 34.7 10 09.901.4 70 69.309.7 130 128.718.1 190 188.2 26.4 250 247.6 34.8 11 10.901.5 71 70.3 09.9 131 129.7 18.2 191 189.1 26.6 251 248 6 34.9 12 11 901.7 72 71.3 10.0 132 130.7 18.4 192 190.1 26.7 252 249^5 35.1 13 12.901 8 73 72.3 10.2 133 131.7 18.5 193 191.1 26.9 253 250.5 35.2 14 13.901.9 74 73 3 10.3 134 132.7 18.6 194 192.1 27 254 251.5 35.3 15 14.802.1 75 74.3 10.4 135 133.7 18.8 195 193.1 27.1 255 252.5 35.5 16 15.802.2 76 75.3 10.6 136 134.7 18.9 196 194.1 27.3 256 253.5 35.6 17 16.802.4 77 76.3 10.7 137 135.7 19.1 197 195.1 27.4 257 254.5 35.8 18 17.8'02.5 78 77.2 10.9 138 136.7 19.2 198 196.1 27.6 258 255.5 35.9 19 18.802.6 79 78 2 11.0 139 137.7 19.3 199 197.1 27.7 259 256.5 36.0 20 19.802.8 80 79.2 11.1 140 13-!. 6 19.5 200 198.1 27.8 260 257.5 36.2 21 20.802.9 81 80.2 11.3 141 13J.6 19.6 201 199.0 28.0 261 258 . 5 36.3 22 21.803.1 82 81.2 11.4 142 140.6 19.8 202 200.0 28.1 262 259.5 36.5 23 22.803.2 83 82.2 11.6 143 141.6 19.9 203 201.0 28.3 263 260.4 36.6 24 23.803.3 84 83.2 11.7 144 142.6 20.0 204 202.0 28.4 264 261.4 36.7 25 24.803.5 85 84.2 11.8 145 143.6 20.2 205 203.0 28.5 265 262.4 36.9 -26 25.703.6 86 85.2 12.0 146 144.6 20.3 206 204 28.7 266 263.4 37.0 27 26.703.8 87 86.2 12.1 147 145.6 20.5 207 205.0 28.8 267 264.4 37.2 28 27.703.9 88 87.1 12.2 148 146.6 20.6 208 206.0 28.9 268 265.4 37.3 29 28.704.0 89 88.1 12.4 149 147.5 20.7 209 207.0 29.1 269 266.4 37.4 30 29.704.2 90 89.1 12.5 150 148.5 20.9 210 208.0 29.2 270 267.4 37.6 31 30. 7 04. ii 91 90.1 12.7 151 14y.5 21.0 211 208.9 29 4 271 268.4 37.7 32 31.704.5 92 91.1 12.8 152 150.5 21.2 212 209.9 29.5 272 269.4 37.9 33 32.704.6 93 92.1 12.9 153 151.5 21.3 213 210.9 29.6 273 270.3 38.0 34 33.704.7 94 93.1 13.1 154 152.5 21.4 214 211.9 29.8 274 271.3 38.1 35 34.704.9 95 94.1 13.2 155 153.5 21.6 215 212.9 29.9 275 272.3 38.3 36 35.605 9G 95.1 13.4 156 154.5 21.7 216 213.9 30.1 276 273.3 38.4 37 J6. 605.1 97 96.1 13.5 157 155.5 21.9 217 214.9 30.2 277 274.3 38.6 38 37.605.3 98 97.0 13.6 158 156.5 22.0 218 215.9 30.3 278 275.3 38.7 39 H8.605.4 99 98.0 13.8 159 157.5 22.1 219 216.9 30.5 279 276.3 38.8 40 39.605.6 100 99.0 13.9 160 158.4 22.3 220 217.9 30.6 280 277.3 39.0 41 40.605.7 101 100.0 14.1 101 159.4 22.4 221 218 8 30.8 281 278.3 39.1 42 11.605.8 102 101.0 14.2 162 160.4 22.5 222 219.8 30.9 282 279.3 39.2 43 42.606.0 103 102.0 14.3 163 161.4 22.7 223 220.8 31.0 283 280.2 39.4 44 43.606.1 104 103 14.5 164 162 4 22.8 224 221.8 31.2 284 281.2 39.5 45 44.606.3 105 104.0 14.6 165 163.4 23.0 225 222.8 31.3 285 282.2 39.7 46 45.606.4 106 105.0 14 8 166 164.4 23.1 226 223.8 31.5 286 283.2 39.8 47 46.506.5 107 106.0 14.9 167 165.4 23.2 227 224.8 31.6 287 284.2 39.9 48 47.506.7 108 106.9 15. 168 166.4 23.4 228 225.8 31.7 288 285.2 40.1 49 48.506.8 109 107.9 15.2 169 167.4 23.5 229 226.8 31.9 289 286.2 40.2 50 49.507.0 110 108.9 15.3 170 168.3 23.7 230 227.8 32.0 290 287.2 40.4 51 50.507.1 111 109.9 15.4 171 109.3 23.8 231 228.8 32.1 291 288.2 40.5 52 51.507.2 112 110.9 15 6 172 170.3 23.9 232 229.7 32.3 292 289.2 40.6 53 52.507.4 113 111.9 15.7 173 171.3 24.1 233 230.7 32.4 293 290.1 40.8 54 53.507.5 114 112.9 15.9 174 172.3 24.2 234 231.7 32.6 294 2yl 1 40.9 55 54.507.7 115 113.9 16.0 175 173.3 24.4 235 232.7 32.7 295 292'.! 41.1 56 55.507.8 116 114.9 16.1 176 174.3 24.5 236 233.7 32.8 296 293.1 41.2 57 56.407.9 117 115.9 16.3 177 175.3 24.6 237 234.7 33.0 297 294.1 41.3 58 57.408.1 118 116.9 16.4 178 176.3 24.8 238 235.7 33.1 298 295.1 41.5 59 58.408.2 119 117.8 16.6 179 177.3 24.9 239 236.7 33.3 299 296.1 41.6 60 59.408.4 120 118.8 16.7 180 178.2 25.1 240 237.7 33.4 300 297.1 41.8 Dist. Dep Lat. Dist. Dep. Lat. Dist. Dep. Lat. (list. Dep. Lat. Dist. Dep. Lat. For 82 Degrees. 212 TABLE IV. DIFFERENCE OF LATITUDE AND DEPARTURE FOR 9 DEGREES. Dist, Lat. Dep Dist. Lat. JDep Dist. Lat, Dep Dist, Lat. Dep. jDist. Lat. Dep. l 01.0 00.2 61 60.209.5 121 119.5 18.9 181 178.8 28.3 241 238,0 37.7 2 02.0 00.3 62 61.209.7 122 120.5 19.1 182 179.8 28.5 242 239.0 37.9 3 03.0 00.5 63 62.209.9 123 121.5 19.2 183 180.7 28.6 243 240.0 38.0 4 04.0 00.6 64 63.210.0 124 122.5 19.4 184 181.7 28.8 244 241.0 38.2 5 04.9 00.8 65 64.210.2 125 123.5 19.6 185 182.7 28.9 245 242.0 38.3 6 05.9 00.9 66 65.210.3 126 124.4 19.7 186 183.7 29.1 246 243.0 38.5 7 00. 9 01.1 67 66.210.5 127 125.4 19.9 187 184.7 29.3 247 244.0 38.6 8 07.9 01.3 68 67.2 : 10.6 128 126.4 20.0 188 185.7 29.4 248 244.9 38.8 9 08.9 01.4 69 68.210.8 129 127.4 20.2 189 186.7 29.6 249 245.9 39.0 10 09.9 01.6 70 69.111.0 130 128.420.3 190 187.7 29.7 250 246.9 39 1 11 10. 9 01.7 71 70.111.1 131 129.4 20.5 191 188.6 29.9 251 247.9 39.3 12 11.9 01.9 72 71.111.3 132 130.4 20.6 192 189.6 30.0 25. 248.9 39.4 13 12.8 02.0 73 72.111.4 133 131.4 20.8 193 190.6 30.2 253 249.9 39.6 14 13.8 02.2 74 73.111.6 134 132.4 21.0 194 191.6 3'J.3 254 250.9 39.7 15 14.8 02.3 75 74. 1 1 !!. 7 135 133.3 21.1 195 192.6 30.5 255 251.9 39.9 16 15.8 02.5 76 75.1 11.9 136 134.3 21.3 196 193.6 30.7 256 252.8 40.0 17 16.8 02.7 77 76.112.0 137 135.3 21.4 197 194.6 30.8 257 253.8 40 2, 18 17.8 02.8 78 77.012.2 138 136.3 21.6 198 195.6 31.0 258 254.8 40.4 19 18 8 03.0 79 78.012.4 139 137.3 21.7 199 196. 81.1 259 255.8 40.5' 20 19.8 03.1 80 79.012.5 140 138.3 21.9 200 197. 31.3 260 256.8 40.7 21 20.7 03.3 81 80.012.7 141 139.3 22.1 201 198. 31.4 261 '257.8 4U.8, 22 21.7 03 4 82 81.012.8 142 140.3 22.2 202 199. 31.6 262 258.8 41.0 23 22.7 03.6 83 82.013.0 143 141.2 22.4 203 200. 31.8 263 259.8 41.1 24 23.7 03.8 84 83.013.1 144 142.2 22.5 204 201. 31.9 264 260. 41.3 25 24.7 03.9 85 84.0 13.3 145 143.2 22.7 205 202. 32.1 265 261. 41.5 26 25.7 04.1 86 84.913.5 146 144.2 22.8 206 203. 32.2 266 262. 41.6 27 26.7 04.2 87 85.913.6 147 145.2 23.0 207 204. 32.4 267 263. 41 8 28 27.7 04.4 88 86.913.8 148 146.2 23.2 208 205.4 32.5 268 264. 41 9 29 28.6 04.5 89 87.9jl3.9 149 147 2 23.3 209 206.4 32.7 269 265. 42.1 30 29.6 04.7 90 88.9 14.1 150 148.2 23.5 210 207.4 32.9 270 266. 42.2 31 JO. 6 04.8 91 89.9 14.2 151 149.1 23.6 211 208.4 33.0 271 267. 42.4 32 31.6 05.0 92 90.914.4 152 150.1 23.8 212 209.4 33.2 272 268. 4-2.6 33 32. C 05.2 93 91.914.5 153 151.1 23.9 213 210.4 33.3 273 269. 42.7 34 33.6 05.3 94 92.814.7 154 152.1 24.1 214 211.4 33.5 274 '270.6 42 9 35 34.6 05.5 95 93.814.9 155 153.1 24.2 215 212.4 33.6 275 271.6 43.0 36 35.6 05.6 96 94.8 15.0 156 154.1 24.4 216 213.3 33.8 276 272.6 43 .2 37 36.5 05.8 97 95.8 15.2 157 155.1 24.6 217 214.3 33.9 277 273.6 43 3 38 37.5 05.9 98 96.815.3 158 156.1 24.7 218 215.3 34.1 278 274.6 43.5 39 38.5 06 1 99 97.815.5 159 157.0 24.9 219 216.3 34.3 279 275.6 43.6 40 39 5 06.3 100 98.815.6 160 158.0 25.0 220 217.3 34.4 280 276.6 43 8 41 10.5 06.4 101 99.815.8 1G1 159.0 25.2 221 218.3 34.6 281 277.5 44 42 41.5 06.6 102 100.7 16.0 162 160.0 25.3 222 219.3 34.7 282 278.5 44.1 43 42.5 06.7 103 101.7 16.1 163 161.0 25.5 223 220.3 34.9 283 279.5 44 3 44 43.5 06.9 104 102.7 16.3 164 162.0 25.7 224 221.2 35.0 284 280.5 44.4 45 14.4 07.0 105 103.7 16.4 165 163.0 25.8 225 222.2 35 2 285 281.5 44 6 46 45.4 07.2 106 104.7 16.6 166 164.0 26.0 226 223.2 35.4 286 282.5 44.7 47 46.4 07.4 107 105.7 16.7 167 164 9 26.1 227 224.2 35.5 287 283.5 44.9 48 47.4 07.5 108 106.7 16.9 168 165.9 26.3 228 225.2 35.7 288 284.5 45.1 49 48.4 07.7 109 107.7 17.1 169 166.9 26.4 229 226.2 35 8 289 285.4 45.2 50 49.4 07.8 110 108.6 17.2 170 167.9 26.6 230 227.2 36.0 290 286.4 45.4 51 30.4 08.0 111 109.6 17.4 171 168.9 26.8 231 228.2 36.1 291 287.4 45.5! 52 51.4 08.1 112 110.6 17.5 172 169.9 26.9 ooo 229.1 36.3 292 288.4 45.71 53 52.308.3 113 111.6 17.7 173 170.9 27.1 233 230.1 36.4 293 289.4 45.8 54 53.308.4 114 112.6 17.8 174 171.9 27.2 234 231.1 36.6 294 290.4 46.0 55 54.3'08.6 115 113.6 18.0 175 172.8 27.4 235 232.1 36.8 295 291.4 46.1 56 55.3 08.8 116 114.6 18.1 176 173.8 27.5 236 233.1 36.9 296 292.4 46.3 57 56.3 08.9 117 115.6 18.3 177 174.8 27.7 237 234.1 37.1 297 293.4 46.5 58 57.3 09.1 118 116.5 18 5 178 175.8 27.8 238 235.1 37.2 298 294 3 46.6 59 58.3 09.2 119 117.5 18.6 179 176.8 28.0 239 236.1 37.4 299 295.3 46.8 60 59.309.4 120 118.5 18.8 180 177.8 28.2 240 237.0 37.5 300 296.3 46.9 Dist. Dep Lat. Dist, Dcp. Lat. Dist. Dep. Lat, Dist. Dep. Lat. Mst. Dep. Lat. For 81 Degrees. FABLE iv. 213 DIFFERENCE OF LATITUDE AND DEPARTURE FOR 10 DEGREES. Dist, Lat. Dep Dist. Lat. Dep Dist. Lat. Dep Dist. Lat. Dep. Dist. Lat. Dep. 1 01.0 00.2 61 60.1 10.6 121 119.2 21.0 181 178.3 31.4 241 237.3 41.8 2 02.000.3 62 61.1 10.8 122 120.1 21.2 182 179.2 31.6 242 238.3 42.0 3 03.000.5 63 62.0 10.9 123 121.1 21.4 183 180.2 31.8 243 239.3 42.2 4 03.900.7 64 63.0 11.1 124 122.1 21.5 184 181.2 32.0 244 240.3 42.4 6 04.900.9 65 64.0 11.3 125 123.1 21.7 185 182.2 32.1 245 241.3 42 5 6 05.9 01.0 66 65.0 11.5 126 124.1 21.9 186 183.2 32.3 246 242.3 42.7 7 06.9 01.2 67 66.0 11.6 127 125.1 22.1 187 184.2 32.5 247 243.2 42.9 8 07.9 01.4 68 67.0 11.8 128 126.1 22.2 188 185.1 32.6 248 244.2 43.1 9 08.901.6 69 68.0 12.0 129 127.0 22.4 189 186.1 32.8 249 245.2 43.2 10 09.801.7 70 68.9 12.2 130 128.0 22.6 190 187.1 33.0 250 246.2 43.4 11 10.801.9 71 69.9 12.3 131 129 22.7 191 188.1 33 2 251 247.2 43.6 12 11.802.1 72 70.9 12.5 132 130.0 22.9 192 189.1 33.3 252 248.2 43.8 13 12.8 02.3 73 71.9 12.7 133 131.0 23.1 193 190.1 33.5 253 249.2 43.9 14 13.8 02.4 74 72.9 12.8 134 132.0 23 3 194 191.0 33.7 254 250.1 44.1 15 14.8 02.6 75 73.9 13.0 135 132.9 23.4 195 192.0 33.9 255 251 1 44.3 16 15.8 02.8 76 74.8 13.2 136 133.9 23.6 196 193.0 34.0 256 252.1 44.5 17 16.7 03.0 77 75.8 13.4 137 134.9 23.8 197 194.0 34 2 257 253.1 44.6 18 17.7 03.1 78 76.8 13.5 138 135.9 24.0 198 195.0 34.4 258 254.1 44. 8j 19 18.7 03.3 79 77.8 13.7 139 136.9 24.1 199 196.0 34.6 259 255.1 '45.0 20 19.7 03.5 80 78.8 13.9 140 137.9 24.3 200 197.0 34.7 260 256.1 45 1 21 20.7 03.6 81 79.8 14.1 141 138.9 24.5 201 197.9 34.9 261 257.0 45.3 22 21 7 03 8 82 80.8 14.2 142 139.8 24.7 202 198.9 35.1 262 258.0 45.5 23 22.7 04.0 83 81.7 14.4 143 140.8 24.8 203 199.9 35.3 263 259.0 45.7 24 23.6 04.2 84 82.7 14 6 144 141.8 25.0 204 200.9 35.4 264 260.0 45.8 25 24.6 04.3 85 83.7 14.8 145 142.8 25.2 205 201.9 35.6 265 261.0 46.0 26 25.6 04.5 86 84.7 14.9 146 143.8 25.4 206 202.9 35.8 266 262.0 46.2 27 26. G 04.7 87 85.7 15.1 147 144.8 25.5 207 203.9 35.9 267 262.9 46.4 28 27.6 04.9 88 86.7 15.3 148 145.8 25.7 208 204.8 36.1 268 263.9 46.5 29 28.6 05.0 89 87.6 15 5 149 146.7 25.9 209 205.8 36.3 269 264.9 46.7 30 29.5 05.2 90 88.6 15.6 150 147.7 26.0 210 206.8 36.5 270 265.9 46.9 31 30.5 05.4 91| 89.6 15.8 151 148.7 26.2 211 207.8 36.6 271 266. 9 47.1 32 31.5 05.6 92 90.6 16.0 152 149.7 26.4 212 208.8 36.8 272 267.9 47.2 33 32.5 05.7 93 91.6 16.1 153 150.7 26.6 213 209.8 37.0 273 268.9 47.4 34 33.5 05.9 94 92.6 16.3 154 151.7 26.7 214 210 7 37.2 274 269.8 47.6 35 34.5 06.1 95 93.6 16.5 155 152.6 26.9 215 211.7 37.3 275 270.8 47.8 3G 35.5 06.3 96 94.5 16.7 156 153.6 27.1 216 212.7 37.5 276 271.8 47.9 37 36.4 06.4 97 95.5 16.8 157 154.6 27 3 217 213.7 37.7 277 272.8 48.1 38 37.4 06.6 98 96.5 17.0 158 155.6 27.4 218 214.7 37.9 278 273.8 48.3 39 38.4 06.8 99 97.5 17.2 159 156.6 27.6 219 215.7 38.0 279 274.8 48.4 40 39.4 06.9 100 98.5 17.4 160 157.6 27.8 220 216 7 38.2 280 275.7 48.6 41 40.4 07.1 101! 99.5 17.5 161 158.6 28.0 '221 217.6 38.4 281 276.7 48.8 42 41.4 07.3 102 100.5 17.7 162 159.5 28.1 222 218.6 38.5 282 277.7 49.0 43 42.3 07 5 103 101.4 17.9 163 160.5 28.3 223 219.6 38.7 283 278.7 49.1 44 43.3 07.6 104 102.4 18.1 164 161.5 28.5 224 220.6 38 9 284 279.7 49.3 45 44 3 07.8 105 103.4 18.2 165 162.5 28.7 225 221.6 39.1 28o 280.7 49.5 4G 45.3 08.0 106 104.4 18.4 160 163.5 28 8 226 222.6 39.2 286 281.7 49.7 47 46.3 08.2 107 105.4 18.6 167 164 5 29.0 227 223.6 39.4 287 282.6 49.8 48 47.3 08.3 108 106.4 18.8 168 165.4 29.2 228 224.5 39.6 288 283.6 50.0 49 48.3 08.5 109 107.3 18.9 169 166.4 29.3 229 225.5 39.8 289 284.6 50.2 50 49.2 08.7 110 108.3 19.1 170 167.4 29.5 230 226.5 39.9 290 285.6 50.4 51 50.2 08.9 111 109.3 19.3 171 168.4 29.7 '231 227.5 40.1 291 286.6 50.5 52 51.2 09.0 112 110.3 19.4 172 169.4 29.9 23'2 228.5 40.3 292 287 6 50.7 53 52.2 09.2 113 111.3 19.6 173 170.4 30.0 233 229.5 40.5 293 288.5 50.9 54 53.2 09.4 114 112.3 19.8 174 171.4 30.2 234 230.4 40.6 294 289.5 51.1 55 54.2 09.6 115 113.3 20.0 175 172.3 30.4 235 231.4 40.8 '295 290.5 51.2 5G 55.1 09.7 116 114.2 20.1 176 173.3 30.6 236 232.4 41.0 296 291.5 51 4 57 56. 1 09.9 117 115.2 20.3 177 174.3 30.7 237 233.4 41.2 297 292.5 51 6 53 57.1 10.1 118 116 2 20.5 178 175.3 30.9 238 234.4 41.3 298 293 5 51.7 59 58.1 10.2 119 117 2 20 7 179 176.3 31.1 239 235.4 41.5 299 294.5 51.9 60 59 1 10.4 120 118.2 20.8 180 177.3 31.3 240 236.4 41.7 300 295.4 52.1 Dist. Dep Lat. Dist, Dep. Lat. Dist. Dep. Lat. Dist, Dep. Lat. Dist, Dep. Lat, For 80 Degrees. 214 TABLE IV. DIFFERENCE OF LATITUDE AND DEPARTURE FOR 11 DEGREES. Dist. Lat. Dep Dist. Lat. Dep Dist. Lat. Dep Dist. Lat. Dep. Dist, Lat. Dep. l 01.0 00.2 61 59.9 11.6 121 118.8 23.1 181 177.7 34.5 241 236.6 46.0 9 02.0 00.4 62 60.9 11.8 122 119.8 ,23.3 182 178.7 34.7 242 237.6 46.2 3 02.9 00.6 63 61.8 12.0 123 120.7 23.5 183 179.6 34.9 243 238.5 46.4 4 03.9 00.8 64 62.8 12.2 124 121.7 23.7 184 180.6 35.1 244 239.5 46.6 5 04.9 01.0 65 63.8 12.4 125 122.7 23.9 185 181.6 35.3 245 240.5 46.7 6 05.9 01.1 66 64.8 12.6 126 123.7 24.0 186 182.6 35.5 246 241.5 46.9 7 06.9 01.3 67 65.8 12.8 127 124.7 24.2 187 183.6 35.7 247 242.5 47.1 8 07.9 01.5 68 66.8 13.0 128 125.6 24.4 188 184.5 35.9 248 243.4 47.3 9 U8.8 01.7 69 67.7 13.2 129 126.6 24.6 189 185.5 36.1 249 244.4 47.5 10 09.8 01.9 70 68.7 13.4 130 127.6 24.8 190 186.5 36.3 250 245.4 47.7 11 10.8 02. J 71 69.7 13.5 131 128.6 25.0 191 187.5 36.4 251 246.4 47.9 12 11.8 02.3 72 70.7 13.7 132 129.6 25.2 192 188.5 36.6 252 247.4 48.1 13 12.8 02.5 73 71.7 13.9 133 130.6 25.4 193 189.5 36.8 253 248.4 48.3 14 13.7 02.7 74 72.6 14.1 134 131.5 25.6 194 190.4 37.0 254 249.3 48.5 15 14.7 02.9 75 73.6 14.3 135 132.5 25.8 195 191.4 37.2 255 250.3 48.7 16 15.7 03.1 76 74.6 14.5 136 133.5 26.0 196 192.4 37.4 256 251.3 48.8 17 16.7 03.2 77 75.6 14.7 137 134.5 26.1 197 193.4 37.6 257 252.3 49.0 18 17.7 03.4 78 76.6 14.9 138 135.5 26.3 198 194.4 37.8 258 253.3 49.2 19 18.7 03. C 79 77.5 15.1 139 136.4 26.5 199 195.3 38.0 259 254.2 49.4 20 19.6 03.8 80 78.5 15.3 140 137.4 26.7 200 196.3 38.2 260 255.2 49 6 81 20.6 04.0 81 79.5 15.5 141 138.4 26.9 ^01 197.3 38.4 261 256 . 2 49.8 22 21.6 04. '2 82 80.5 15.6 142 139.4 27 1 202 198.3 38.5 262 257.2 50.0 23 22.6 04.4 '83 81.5 15.8 143 140.4 27.3 203 199.3 38.7 263 258.2 50.2 24 23.6 04.6 84 82.5 16.0 144 141.4 27.5 204 200.3 38.9 264 259.1 50.4 25 24.5 04.8 85 83.4 16.2 145 142.3 27.7 205 201.2 39 1 265 260.1 50.6 26 25.5 05.0 86 84.4 16.4 146 143.3 27.9 206 202.2 39.3 266 261.1 50.8 27 26.5 05.2 87 85.4 16.6 147 144.3 28.0 207 203.2 39.5 267 262 1 50.9 28 27.5 05.3 88 86.4 16.8 148 145.3 28.2 208 204.2 39.7 268 263.1 51.1 29 28.5 05.5 89 87.4 17.0 149 146.3 28.4 209 205.2 39.9 269 264.1 51.3 30 29.4 05.7 90 88.3 17.2 150 147.2 28.6 210 206.1 40.1 270 265.0 51.5 31 30.4 05.9 91 89.3 17.4 151 148.2 28.8 211 207 . 1 40.3 27J 266.0 51.7 32 31.4 06.1 92 90.3 17.6 152 149.2 29.0 212 208.1 40.5 272 267.0 51.9 33 32.4 06.3 93 91.3 17.7 153 150.2 29.2 213 209.1 40.6 273 268.0 52.1 34 33.4 06.5 94 92.3 17.9 154 151.2 29.4 214 210.1 40.8 274 269.0 52.3 35 34.4 06.7 95 93.3 18.1 155 152.2 29.6 215 211.0 41.0 275 269.9 52.5 3G 35.3 06.9 96 94.2 18.3 156 153.1 29.8 216 212.0 41.2 276 270.9 52.7 37 36.3 07.1 97 95.2 18.5 157 154.1 30.0 217 213.0 41.4 277 271.9 52.9 38 37.3 07.3 98 96.2 18.7 158 155.1 30.1 218 214.0 41.6 278 272.9 53.0 39 38.3 07.4 99 97.2 18.9 159 156.1 30.3 219 215.0 41.8 279 273.9 53 2 40 39.3 07.6 100 98.2 19.1 160 157.1 30.5 220 216.0 42.0 280 274.9 53.4 41 iO.2 07.8 101 99.1 19.3 161 158.0 30.7 221 216.9 4^ 281 275.8 53.6 42 41.2 08.0 102 100.1 19.5 162 159.0 30.9 222 217.9 42.4 282 276.8 53.8 43 12.2 08.2 103 101.1 19.7 163 160.0 31.1 223 218.9 42.6 283 277.8 54.0 44 43.2 08.4 104 102.1 19.8 164 161.0 31.3 224 219.9 42.7 284 278.8 54.2 45 44.2 08.6 105 103.1 20.0 165 162.0 31.5 225 220.9 42.9 285 279.8 54.4 40 45.2 08.8 106 104.1 20.2 166 163.0 31.7 226 221.8 43.1 286 280.7 54.6 47 46.1 09.0 107 105.0 20.4 167 163.9 31.9 227 222.8 43.3 287 281.7 54.8 48 47.1 09.2 108 106.0 20.6 168 164.9 32.1 228 223.8 43.5 288 282.7 55.0 49 48.1 09.3 109 107.0 20.8 169 165.9 32.2 229 224.8 43.7 289 283.7 55.1 50 49.1 09.5 110 108.0 21.0 170 166.9 32.4 230 225.8 43.9 290 284.7 55.3 51 50.1 09.7 111 109.0 21.2 171 167.9|32.6 231 226.8 44.1 291 285.7 55.5 52 51.0 09.9 112 109.9 21.4 172 168.832.8 232 227.7 44.3 292 286.6 55 7 53 32.0 10.1 113 110.9 21.6 173 169.8 33.0 233 228.7 44.5 293 287.6 55.9 54 53.0 10.3 114 111.9 21.8 174 170.8 33.2 234 229.7 44.6 294 288.6 56.1 55 54 10.5 115 112.9 21.9 175 171.8 33.4 235 230.7 44.8 295 289.6 56.3 5G 55.0 10.7 116 113.9 22.1 176 172.8 33.6 236 231.7 45.0 296 290.6 56.5 57 56.0 10.9 117 114.9 22.3 177 173.7 33.8 237 232.6 45.2 297 291.5 56.7 58 56 9 11.1 118 115.8 22.5 178 174.7 34.0 238 233.6 45.4 298 292.5 56.9 59 57.9 11.3 119 116.8 22.7 179 175.7 34.2 239 234.6 45.6 299 293.5 57.1 60 58.9 11.4 120 117.8 22.9 180 176.7 34.3 240 235.6 45.8 300 294.5 57.2 Dist. Dep Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist, Dep. Lat. Dist. Dep. Lat. For 79 Degrees. TABLE IV. 215 DIFFERENCE OF LATITUDE AND DEPARTURE FOR 12 DEGREES. Hist. Lat. Dei, list. Lat. Dcp Dist. Lat. Dep ist. Lat. Dep. Dist. Lat. Dep. 1 31.0 00. 2 1 61 59.7 12.7 121 118.4 25.2 181 177.0 37. 6- 241 235.7 50.1 I 3-2.0 00.4! 6i 60.612.9 122 119.3 25. 4 1 182 178.0 37.8 212 236.7 50.3 3 32.9 00. 6 1 63 61.6 13.1 123 120.3 25.6! 183 179.0 38.0 243 237.7 50.5 4 )3.9 00.8 64 62.6 13.3 124 121.3 25.8? 184 180.0 38.3 244 238.7 50.7 5 54.9 01.0 65 63.6 13. 5i 125 122.3 26. 0| 185 181.0 38.5 245 239.6 50.9 6 1)5.9 01.2 66 64.6 13.7 126 123.2 26.2' 186 181.9 38.7; 246 240.6 51.1 7 06.8 01.5 67 65.5 13.9 127 124.2 26.4 187 182.9 38.9 247 241.6 51.4 8 07.8 01.7 68 66.5 14.1 128 125.2 26.6| 188 183.9 39.1 248 242.6 51.6 9 08.8 01.9 69 67.5 14.3 129 126.2 26.8 189 184.9 39.3! 249 243.6 51.8 10 J9.8 12.1 70 68.5 14.6 130 127.2 27. 0' 190 185.8 39.5 250 244.5 52.0 11 10.8 J2 . 3 71 69.4 14.8 131 128.1 27. 2| 191 186.8 39.7 251 245.5 52. V 13 11.7 02.5 72 70.4 15.0 132 129.1 27 4 192 187.8 39.9 252 246.5 52.4 13 12.7 02.7 73 71.4 15.2 133 130.1 27.7 193 188.8 4.0.1 253 247.5 52.6 14 13.7 02. 9 74 72.4 15.4 134 131.1127.9 194 189.8 40.3; 254 248.4 52.8 13 14.7 03.1 75 73.4 15.6 135 132.0 28. 1' 195 190.7 40.5 255 249.4 53.0 16 15.7 03.3 76 74.3 15.8 136 133.0 28.3' 196 191.7 40.8 256 25'3.4 53.2 17 16.6 )3.5 77 75.3 16.0 137 134.0 28. 5 1 197 192.7 41.0 257 251.4 53.4 18 17.6 03.7 78 76.3 16.2 138 135.0 28.7: 198 193.7 41.2 258 252.4 53.6 19 18.6 04.0 79 77.3 16. 4 1 139 136.0 28.9: 199 194.7 41. 4 1 259 253.3 53.8 20 19. (3 04.2 80 78.3 16.6 140 136.9 29 1 200 195.6 41. 6 260 254.3 54.1 21 ^0.5 04.4 81 79.2 10.6 141 137.9 29.3 201 196.6 "iTTS; 261 255 . 3 54.3 22 21.5 04.6 82 80.2 17.0 142 138.9 29.5 202 197.6 42.0 262 256.3 54.5 23 22.5 04.8 83 81.2 17.3 143 139.9 29.7' 203 198.6 42.2 263 257.3 54.7 '24 23.5 05.0 81 82.2 17.5 144 140.9 29.9 204 199.5 42.4 264 258.2 54.9 25 24.5 J5.2 85 83.1 17.7 145 141.8 30.1 205 200.5 42.6 265 259.2 55.1 ii6 25.4 05.4 86 84.1 17.9 146 142.8 30.4 206 201.5 42.8 266 260.2 55.3 27 26.4 05.6 87 85.1 18.1 147 143.8 30.6 207 202.5 43.0 267 261.2 55.5 28 27.4 05.8 88 86.1 18.3 148 144.8 30.8 208 203.5 43.2 268 262.1 55.7 29 28.4 06.0 89 87.1 18.5 149 145.7 31.0 209 204.4 43.5 269 263.1 55.9 30 29. ;-> 06.2 90 88.0 18.7 150 146.7 31.2 210 205.4 43.7 270 264.1 56.1 31 30,3 06.4 9i 89.0 18.9 151 147.7 31 4 211 206.4 43.9 271 265.1 56.3 32 31.3 06.7 92 90.0 19.1 152 148.7 31.6 212 207.4 44.1 272 266.1 56.6 33 32.3 06.9 93 91.0 19.3 153 149.7 31.8 213 208.3 44.3 273 267.0 56.8 34 33.3 07.1 94 91.9 19.5 154 150.6 32.0 214 209.3 44.5 274 268.0 57.0 35 34.2 07.3 95 92.9 19.8 155 151.6 32.2! 215 210.3 44.7 275 269.0 57.2 So 35.2 07.5 96 93.9 20.0 156 152.6 32.4 216 211.3 44.9 276 270.0 57.4 37 3(5.2 07.7 97 94.9120.2 157 153.6 32.6 217 212.3 45.1 277 270.9 57.6 38 37.2 07.9 98 95.920.4 158 154.5 32.9 218 213.2 45.3 278 271.9 57.8 39 38.1 08.1 99 96.8 20.6 159 155.5 33.1 219 214.2 45.5 279 272.9 58.0 40 39.1 08.3 100 97.8 20.8 160 156.5 33.3 220 215.2 45.7 280 273.9 58.2 41 40. J u8.5 101 98.8J21.0 161 157.5 33.5 221 216.2 45.9 281 274.9 58.4 42 11.1 08.7 102 99.8121.2 162 158.5 33.7 222 217.1 46.2 282 275.8 58.6 43 12.1 08.9 103 100.7 21.4 163 159.4 33.9 223 218.1 46.4 283 276.8 58.8 44 43.0 09.1 104 101.7 21. ( 164 160.4 34.1 224 219.1 46.6 284 277.8 59.0 45 44.0 09.4 105 102.7 21.8 165 161.4 34.3 225 220.1 46.8 285 278.8 59.3 46 45.0 09.6 106 103.7 22.0 166 162.4 34.5 226 221.1 47.0 286 279.8 59.5 47 46.0 09.8 107 104.7 22.2 167 163.4 34.7 22" 222 47.2 287 280.7 59 7 48 47.0 10.0 108 105. C 22 5 168 164.3 34.9 228 223.0 47 4 288 281.7 59.9 49 47.9 10.2 109 106. C 22.7 169 165.3 35.1 229 224 47.6 289 282.7 60.1 50 48 9 10.4 110 107. C 22.9 170 166.3 35.3 230 225.0 47.8 290 283.7 60.3 51 19. 9 10.0 111 108.623.1 171 167.2 35. fa 231 226.0 48.0 291 284.6 60.5 52 50.9 10.8 112 109.623.3 172 168. 2 35.8 232 226.9 48.2 292 285.6 60.7 53 51.8 11.0 113 110.523.5 173 169. S 36.0 233 227.0 48.4 293 286.6 60.9 54 52. 8 11.2 114 111.523.7 174 170. i 36.2 234 228.9 48.7 294 287. C 61.1 55 53.8 11.4 115 112.523.9 175 171. S 36.4 235 229.9 48.9 295 288. C 61.3 56 54.8 11.6 11C 113.524.1 176 172.5 36.6 236 230.6 49.1 29G 289.5 61.5 57 55.8 11.9 117 114.424.3 177 173.] 36.8 237 231.8 49.3 297 290.5 61.7 58 56.7 12.1 lie 115.424.5 178 174.1 37.0 238 232.8 49.5 298 291. E 62.0 59 57.7 12.3 11 116.424.7 179 175.] 37.2 23 f 233.8 49.7 298 292. C 62.2 60 58.7 12 5 12( 117.4 124.9 ISO 176.] 37.4 24C 234.8 49.9 30C 293.4 62.4 Dixt !Dep Lat Dist. Dcp. Lat ftist Dcp. Lat Dist Dcp. Lat. Dist. Dcp. Lat. For 78 Degrees. 216 TABLE IV. DIFFERENCE OF LATITUDE AND DEPARTURE FOR 13 DEGREES. Dist. Lat. Dep 'Dist. Lat. Dep Dist. Lat. Dep Dist. Lat. Dep. Dist. Lat. Dep. l 31.0 30.2 61 59.413.7 121 117.9 27.2 181 176.4 40.7 241 234.8 54.2 2 91.900.4 62 60 413.9 122 118.927.4 182 177.3 40.9 242 235.8 54 4 3 D2.900.7 63 61.414.2 123 119.827.7 183 178.3 41.2 243 236.8 54.7 4 03.900.9 64 62.4 14.4 124 120.827.9 184 179.3 41.4 244 237.7 54.9 5 04.901.1 65 63.3 14.6 125 121.828.1 185 180.3 41.6 245 238.7 55.1 6 05-801.3 66 64.3 14.8 126 122.828.3 186 181.2 41.8 246 239.7 55 3 7 06.8 01.6 67 65.3 15 1 127 123 7 28.6 187 182.2 42.1 247 240.7 55.6 8 07.8 )1.8 68 66.3 15.3 128 124.7 28.8 188 183.2 42.3 248 241. C 55.8 9 >8.8 02.0 69 67.2 15.5 129 125.7 29.0 189 184.2 42.5 249 242.6 56.0 1(1 09.7 02.2 70 68.2 15.7 130 126.7 29.2 190 185.1 42.7 250 243.6 56.2 11 10.7 02.5' 71 t>y.2 iO.O 131 127.629.5 191 180.1 43.0 251 244.6 50.5 12 11.7 02.7 72 70.2 16.2 132 128.6 29.7 192 187.1 43.2 252 245.5 56.7 13 12.7 02.9 73 71.1 16.4 133 129.6 29.9 193 188.1 43.4 253 246.5 56.9 14 13 6 03.1 74 72.1 16. G 134 130.6 30.1 194 189.0 43.6 254 247.5 57.1 15 14.6 03.4 75 73.1 16.9 135 131.5 30.4 195 190.0 43.9 255 248.5 57.4 16 15.6 03.6 76 74.1 17.1 136 132.5 30.6 196 191.0 44.1 256 249.4 57.6 17 16.6 03.8 77 75.0 17.3 137 133.5 30.8 197 192.0 44.3 257 250 4 57.8 18 17.504.0 78 76.0 17.5 138 134.5 31.0 108 192.9 44.5 258 251.4 58.0 19 18.5 04.3 79 77.0 17.8 139 135.4 31.3 199 193.9 44.8 259 252.4 58.3 20 19.5 04.5 80 77.9 18.0 140 136.4 31.5 200 194.9 45.0 260 253.3 58.5 21 20.504.7 81 78.9 18.2 141 137.431.7 '201 195.8 45.2 261 254.3 58.7 22 21.404.9 82 79.9 18.4 142 138.431 9 202 196.8 45.4 262 255.3 58.9 23 22.4 05.2 83 80.9 18.7 143 139.332.2 203 197.8 45.7 263 256.3 59.2 24 23.4 05.4 84 81.8 18.9 144 140.3'32.4 204 198.8 45.9 264 257.2 59.4 25 24.405.6 85 82.8 19.1 145 141.332.6 205 199.7 46.1 265 258.2 59.6 26 25.305 8 86 83.8 19 3 146 142.332.8 20G 200.7 46.3 266 259.2 19.8 27 26.306.1 87 84.8 19.6 147 143.233.1 207 201.7 46.6 267 260.2 60.1 28 27.306.3 88 85.7 19.8 148 144.233.3 208 202.7 46.8 268 261.1 60.3 29 28.306.5 89 86.7 20.0 149 145.2 33.5 209 203.6 47.0 269 262 1 60.5 30 29 206.7 90 87.7 20.2 150 146.2 33.7 210 204.6 47.2 270 263.1 60.7 31 30.2 07.0 91 88.7 20.5 151 147.1 34.0 211 205.6 47.5 27 i| 204.1 61.0 32 31.2 C7.2 92 89.6 20.7 152 148.1 34.2 212 206.6 47.7 2721 265.0 61.2 33 32.2 07.4 93 90.6 20.9 153 149.1 34.4 213 207.5 47.9 273 266.0 61.4 34 33.1|07.6 94 91 6 21.1 154 150.1 34.6 214 208.5 48.1 274 267.0 61.6 35 34.107.9 95 92.6 21.4 155 151.0 34.9 215 209.5 48.4 275 268.0 61.9 36 35.1 08.1 96 93.5 21.6 156 152.035.1 216 210.5 48.6 276 268.9 62.1 37 36.1 08.3 97 94.5 21.8 157 153.0 35.3 217 211.4 48.8 277 269.9 62.3 38 37.0 08.5 98 95.5 22.0 158 154.0 OO . L 218 212.4 49.0 278 270.9 62.5 39 38.0d8.8 99 96.5 22.3 159 154.9 35.8 219 213.4 49.3 279 271.8 62.8 40 39.009.0 100 97.4 22.5 160 155.9 36.0 220 214.4 49.5 280 272.8 63.0 41 39.9|09.2 101 98.4 22.7 161 156.9 36.2 221 215.3 49.7 281 273.8 03.2 42 40.909.4 102 99.4 22.9 162 157.8 36.4 222 216.3 49.9 282 274.8 63.4 43 41.9 09.7 103 100.4 23.2 163 158.8 36.7 223 217.3 50.2 283 275.7 63.7 44 42.9 09.9 104 101.3 23.4 164 159.8 36.9 224 218.3 50.4 284 276.7 63.9 45 43.8 10.1 105 102.3 23.6 165 160.8 37.1 225 219.2 50.6 285 277.7 64.1 46 44.8 10.3 106 103.3 23.8 166 161.7 37.3 226 220.2 50.8 286 278.7 64.3 47 45.8 10.6 107 104.3 24.1 167 162.7137.6 227 221.2 51.1 287 279.6 64.6 48 46.8 10.8 108 105.2 24.3 168 163.737.8 228 222.2 51.3 288 280. C 64.8 49 47.7 11.0 109 106.2 24.5 109 164.7 38.0 229 223.1 51.5 289 281.6 65.0 50 48 7 11.2 110 107.2 24.7 170 165.6 38.2 230 224.1 51.7 290 282.6 65.2 51 49.7 11.5 111 108.2 25.0 171 166.638.5 231 225.1 52.0 291 283.5 65.5 52 50.7 11.7 112 109.1 25 2 172 167.6 38.7 232 226.1 52.2 292 284.5 65.7 53 51.6 11.9 113 110.1 25.4 173 168.6 38.9 233 227.0 52.4 293 285.5 65.9 54 52.6 12.1 114 111.1 25.6 174 169.539.1 234 228.0 52.6 294 280.5 66.1 55 53.6 12.4 115 112.1 25.9 175 170.5 39.4 235 229.0 52.9 295 287.4 66.4 56 54.6 12.6 116 113.0 26.1 176 171.5 39.6 236 230.0 53.1 296 288.4 66.6 57 55.5 12.8 117 114.0 20.3 177 172.539.8 237 230.9 53.3 297 289.4 66.8 58 56.5 13.0 118 115.0 26.5 178 173.440.0 238 231.9 53.5 298 290.4 67.0 59 57.5 13.3 119 116.0 26.8 179 174.440.3 239 232.9 53.8 299 2al.3 67.3 CO 58.5 13.5 120 116.9 27.0 180 175.4 40.5 240 233.8 54.0 300 292.3 67.5 Dist. Dep Lat. Dist. Dep. Lat. 'Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. For 77 Degrees. TABLE IV. 217 DIFFERENCE OF LATITUDE AND DEPARTURE FOR 14 DEGREES. Dist. Lat. Dep Dist. Lat. Dep Dist. Lat. Dep Dist. Lat. Dep. Dist. Lat. Dep. 1 01.0 00.2 61 59.2 14.8 121 117.4 29.3 181 175.6 43.8 241 233.8 58.3 2 01.9 00.5 62 60.2 15.0 12'2 118.4 29.5 182 176.6 44.0 242 234.8 58.5 3 02.9 00.7 63 61.1 15.2 123 119.3 29.8 183 177.6 44.3 243 235.8 58.8 4 03.9 01.0 64 62.1 15.5 124 120.3 30.0 184 178.5 44.5 244 236.8 59.0 5 04.9 01.2 65 63.1 15.7 125 121.3 30.2 185 179.5 44.8 245 237.7 59.3 6 05.8 01.5 66 64.0 16.0 126 122.3 30.5 186 180.5 45.0 246 238.7 59.5 7 06.8 01.7 67 65.0 16.2 127 123.2 30.7 187 181.4 45.2 247 239.7 59.8 8 07.8 01.9 68 66.0 16.5 128 124.2 31.0 188 182.4 45.5 248 240.6 60.0 9 08.7 02.2 69 67.0116.7 129 125.2 31.2 189 183.4 45.7 249 241.6 60.2 10 09.7 02.4 70 67.9!l6.9 130 126.1 31.4 190 184.4 46.0 250 242.6 60 5 11 10.7 02.7 71 68.917.2 131 1-27.1 31.7 191 1S5.3 46.2 251 243.5 60.7 12 1.6 02.9 72 69.9J17.4 132 128.1 31.9 192 186.3 46.4 25. 244.5 61.0 13 12.6 03.1 73 70.817.7 133 129.0 32.2 193 187.3 46.7 253 '245.5 61.2 14 13.6 03.4 74 71.817.9 134 130.0 32.4 194 188.2 46.9 254 246.5 61.4 15 14.6 03.6 75 72.8'l8.1 135 131.0 32.7 195 189.2 47.2 255 247.4 61.7 16 15.5 03.9 76 73.718.4 136 132.0 32.9 196 190.2 47.4 256 248.4 61.9 17 16.5 04.1 77 74.718.6 137 132.9 33.1 197 191.1 47.7 257 249.4 62 2 18 7.5 04.4 78 75.7 18.9 138 133 9 33.4 198 192.1 47.9 258 250.3 62.4 19 8 4 04.6 79 76.719.1 139 134.9 33 6 199 193.1 48.1 250 251.3 62.7 20 19.4 04.8 80 77.619.4 140 135.8 33.9 200 194.1 48.4 260 252.3 62.9 21 20.4 05.1 81 78.619.6 141 136.8 34.1 201 195.0 48.6 261 253 . i: (33.1 22 21.3 05 3 82 79.6 19.8 142 137.8 34.4 202 196.0 48.9, 262 254.2 63.4 23 22.3 05.6 83 80.5 20.1 143 138.8 34.6 203 197.0 49.1 263 255.2 63.6 24 23.305.8 84 81.5 20.3 144 139.7 34.8 204 197.9 49.4 264 256 . 2 63.9 25 24.3 06.0 85 82.5 20.6 145 140.7 35.1 205 198.9 49.6 265 257.1 64.1 26 25.2 06.3 86 83.4 20.8 146 141.7 35.3 206 199.9 49.8 266 258.1 64.4 27 26.2 06.5 87 84.421.0 147 142.6 35.6 207 200.9 50.1 267 259.1 64.6 28 27.2 06. 81 88 85.421.3 148 143.6 35.8 208 201.8 50.3 268 260.0 64 8 29 28.1 07. 0| 89 86.421.5 149 144.6 36.0 209 202.8 50.6 269 261.0 65.1 30 29.1 07.3 90 87.321.8 150 145.5 36.3 210 203.8 50.8 270 262.0 65.3 31 30.1 17.5 91 88. 322. U 151 146.536.5 211 204.7 51.0 27 J 203.0 65.6 32 31.0 07.7 92 89.3 22.3 152 147.5 36.8 212 205.7 51.3 272 263.9 65.8 33 32.0 08.0 93 90.222.5 153 148.5 37.0 213 206.7 51 5 27b 264.9 66.0 34 33.0 08.2 94 91.2*2.7 154 149.4 37.3 214 207.6 51.8 274 265.9 66.3 35 34.0 08.5 95 92.223.0 155 150.4 37.5 215 208.6 52.0 275 2G6.8 66.5 36 34.9 08.7 96 93.1 23.2 156 151.4 37.7 216 209.6 52.3 276 267.8 66.8 37 35.9 09.0 97 94.1 23.5 157 152.3 38.0 217 210.6 52.5 277 268 8 67.0 38 36.9 09.2 98 95.1 23.7 158 153.3 38.2 218 211.5 52.7 278 269.7 67.3 39 37.8 09.4 99 96.1 24.0 159 154.3 38.5 219 212.5 53.0 279 270.7 67.5 40 38.8 09.7 100 97.0 24.2 160 155.2 38.7 220 213.5 53.2 280 271.7 67 7 41 39.8 09.9 101 98.0 24.4 161 156.2 38.9 221 214.4 53.5 281 2 2 . 7 U8.0 42 40.8 10.2 102 99.0 24.7 162 157.2 39.2 222 215.4 53.7 282 273.6 68.2 43 41.7 10.4 103 99.924.9 163 158.2 39.4 223 216.4 53.9 283 274.6 68 5 44 42.7 10.6 104 100.925.2 164 159.1 39.7 224 217.3 54.2 284 275. b 68.7 45 43.7 10.9 105 101.925.4 165 160.1 39.9 225 218.3 54 4 285 276.5 68.9 46 44.6 11.1 100 102.925.6 166 161.1 40.2 226 219.3 54.7 286 277.5 69.2 47 45.6 11.4 107 103.825.9 167 162.0 40.4 227 220.3 54.9 287 278. i 69.4 48 46.6 11.6 108 104.826.1 168 163.0 40 6 228 221.2 55.2 288 279.4 69.7 49 47.5 11.9 109 105.826.4 169 164.0 40.9 229 222.2 55 4 289 280.4 69.9 50 48.5 12.1 110 106.726.6 170 165.0 41.1 230 223.2 55.6 290 281.4 70.2 51 49.5 12.3 111 107.726.9 171 165.9 41.4 231 2^4.1 55.9 291 282.4 70.4 52 50.5 12.6 112 108.727.1 172 166.9 41.6 232 225.1 56.1 292 283 . 3 70.6 53 51.4 12.8 113 109.6'27.3 173 167.9 41.9 233 226.1 56.4 293 284.3 70.9 54 52.4 13.1 114 110.6 27.6 174 168.8 42.1 234 227.0 56.6 294 25.3 71.1 55 53.4 13.3 115 111.6 27.8 175 169.8 42.3 235 228.0 56.9 295 286.2 71.4 56 54.3 13.5 116 112. G 28.1 176 170.8 42.6 236 229.0 57.1 296 287.2 71.6 57 55. > 13.8 117 113.5 28.3 177 171.7 42.8 237 230.0 57.3 297 288.2 71.9 58 56.3 14.0 118 114.5 28 6 178 172.7 43.1 238 230.9 57.6 298 289.1 72.1 59 57.2 14.3 119 115.5 28. 8 179 173.7 43.3 239 231.9 57.8 299 290.1 72.3 60 58.2 14.5 120 116.4 29 180 174.7 43.5 240 232.9 58.1 300 291.1 72.6 Dist Dep Lat. Dist Dep. Lat IHst. Dep. Lat, Dist. Dep. Lat. Dist. Dep. Lat. For 76 Degrees. 218 TABLE IV. DIFFERENCE OF LATITUDE AND DEPARTURE FOR 15 DEGREES. Dist, Lat. Dep Dist. Lat. Dep Dist. Lat. Dep Dist, Lat. Dep. Dist. Lat. Dep. l 1.0 U0.3 61 58.9 15.8 121 116.9 31.3 181 174.8 46.8 241 232.8 62.4 2 01 9 1)0.5 62 59.9 16.0 122 117.8 31.6 182 175.8 47.1 242 233.8 62.6 3 32.9 00.8 63 60.9 16.3 123 118 8 31.8 183 176.8 47.4 243 234.7 62.9 4 J3.9 01.0 64 61.8 16.6 124 119.8 32 1 184 177.7 47.6 244 235 7 63.2 5 J4.8 01.3 65 62.8 16.8 125 120.7 32.4 185 178.7 47.9 245 236.7 63.4 6 j5.8 01.6 66 63.8 17.1 126 121.7 32.6 186 179.7 48.1 246 237.6 63.7 7 6.8 01.8 67 64.7 17.3 127 122.7 32.9 187 180.6 48.4 247 238.6 63.9 8 37.7 02.1 68 65.7 17.6 128 123.6 33.1 188 181.6 48.7 248 239.5 64.2 9 J8 7 02.3 69 66.6 17.9 129 124.6 33.4 189 182.6 48.9 249 240.5 64.4 10 39.7 02.6 70 67.6 18.1 130 125.6 33.6 190 183.5 49.2 250 241.5 64.7 11 10.6 02.8 71 68.6 18.4 131 126.5 33.9 191 184.5 49.4 251 242.4 65.0 IS 1 6 03.1 72 69.5 18.6 132 127.5 34.2 192 185.5 49.7 252 243.4 65.2 18 2.6 03 4 73 70.5 18.9 133 128.5 34.4 193 186.4 50.0 253 244.4 65.5 14 3.5 03.6 74 71.5 19.2 134 129.4 34.7 194 187.4 50 2 254 245.3 65.7 15 4.5 03.9 75 72.4 19.4 435 130.4 34.9 195 188.4 50.5 255 246.3 66.0 16 15.5 04.1 76 73.4 19.7 136 131.4 35.2 196 189.3 50.7 256 247.3 66.3 17 16.4 04.4 77 74.4 19.9 137 132.3 35.5 197 190.3 51.0 257 248.2 66.5 18 7.4 04.7 78 75.3 20.2 138 133.3 35.7 198 191.3 51.2 258 249.2 66.8 19 8.4 04.9 79 76 3 20.4 139 134.3 36.0 199 192.2 51.5 259 250.2 67.0 20 19.3 05.2 80 77 3 20.7 140 135.2 36.2 200 193.2 51.8 260 251 . 1 67.3 21 20.o 05.4 81 78.2 21.0 141 136.2 36.5 201 194.2 52.0 261 252.1 67.6 22 21.3 05.7 82 79.2 21 .2 142 137.2 36.8 202 195.1 52.3 262 253.1 67.8 23 22.2 06.0 83 80.2 21.5 143 138.1 37.0 203 196.1 52.5 263 254.0 68.1 24 23.2 06.2 84 81.1 21.7 144 139.1 37.3 204 197.0 52.8 264 255.0 68.3 25 24.1 06.5 85 82.1 22.0 145 140.1 37.5 205 198.0 53.1 265 256.0 68.6 2G 25.1 06.7 86 83.1 22.3 146 141.0 37.8 206 199.0 53.3 266 256.9 68.8 27 26.1 07.0 87 84.0 22.5 147 142.0 38.0 207 199.9 53.6 267 257.9 69.1 28 27.0 07.2 88 85.0 22.8 148 143.0 38.3 208 200.9 53.8 268 258.9 69.4 29 28.0 07.5 89 86.0 23.0 149 143.9 38.6 209 201.9 54.1 269 259.8 69.6 30 29.0 07.8 90 86.9 23.3 150 144.9 38.8 210 202.8 54.4 270 260.8 69.9 31 29.9 08.0 91 87.9 23.6 151 145.9 39.1 211 203.8 54.6 271 261.8 70.1 32 30.9 08.3 92 88.9 23.8 152 146.8 39.3 212 204.8 54.9 272 262.7 70.4 33 31.9 08.5 93 89.8 24.1 153 147.8 39.6 213 205.7 55.1 273 263.7 70.7 34 32.8 08.8 94 90.8 24.3 154 148.8 39.9 214 206.7 55.4 274 264.7 70.9 35 33.8 09.1 95 91.8 24.6 155 149.7 40.1 215 207.7 55.6 275 265.6 71.2 36 34.8 09.3 96 92.7 24.8 156 150.7 40.4 216 208.6 55.9 276 266.6 71.4 37 35.7 09.6 97 9a.7 25.1 157 151.7 40.6 217 209.6 56.2 277 267.6 71.7 38 36.7 09.8 98 94.7 25.4 158 152.6 40.9 218 210.6 56.4 278 268.5 72.0 39 V7.7 10.1 99 95.6 25.6 159 153.6 41.2 219 211.5 56.7 279 269.5 72.2 40 38.6 10.4 100 96.6 25.9 160 154.5 41.4 220 212.5 56.9 280 270.5 72.5 41 39.6 10.6 101 97.6 26.1 161 155.5 41.7 221 213 5 57.2 281 271.4 72.7 42 40.6 10.9 102 98.5 26.4 162 156.5 41.9 222 214.4 57.5 282 272.4 73.0 43 1.5 11.1 103 99.5 26.7 163 157.4 42.2 223 215.4 57.7 283 273.4 73.2 44 42.5 11.4 104 100.5 26.9 164 158 4 42.4 224 216.4 58.0 284 274.3 73.5 45 43.5 11.6 105 101.4 27.2 165 159.4 42.7 225 217.3 58.2 285 275.3 73.8 46 44.4 11.9 106 102.4 27.4 166 160 3 43.0 226 218.3 58.5 286 276.3 74.0 47 45.4 12.2 107 103.4 27.7 167 161.3 43.2 227 219.3 58.8 287 277.2 74.3 48 46.4 12.4 108 104.3 28.0 168 162.3 43. b 228 220.2 59.0 288 278.2 74.5 49 47.3 12.7 109 105.3 28.2 169 163.2 43.7 229 221.2 59.3 289 279.2 74.8 50 48.3 12.9 110 106.3 28.5 170 164.2 44.0 230 222.2 59.5 290 280.1 75.1 51 49. a 13.2 111 107.2 28.7 171 165.2 44.3 231 223.1 59.8 291 281.1 75.3 52 o0.2 L3.5 112 108.2 29.0 172 166.1 44.5 232 224.1 60.0 292 282.1 75.6 53 51.2 13.7 113 109.1 29.2 173 167.1 44.8 233 225.1 60.3 293 283.0 75.8 54 52.2 14.0 114 110.1 29.5 174 168.1 45.0 234 226.0 60.6 294 284.0 76.1 55 53.1 14.2 115 111.1 29.8 175 169.0 45.3 235 227.0 60.8 295 284.9 76.4 56 54.1 14.5 116 112. C '30.0 176 170.0 45.6 236 228.0 61.1 296 285.9 76 6 57 55.1 14.8 117 113. C 30.3 177 171.0 45.8 237 228.9 61.3 297 286.9 76 9 58 56. C 15.0 118 114 C 30.5 178 171.9 46.1 238 229.9 61.6 298 287.8 77.1 59 57. ( 15.3 119 114. S 30 8 17S 172.9 46.3 239 230.9 61.9 299 288.8 77 4 60 68 C 15.5 120 115. S 31.1 18CJ 173.9 46.6 240 231.8 62.1 30U 289.8 77.6 Dist Der Lat Dist. Dep. Lat Dist. Dep. Lat Dist Dep. Lat. Dist Dep. Lat. For 75 Degrees. TABLE IV. 219 DIFFERENCE OF LATITUDE AND DEPARTURE FOR 16 DEGREES. Dist. Lat. Dep Dist. Lat. Dep Dist. Lat. Dep Dist. Lat. Dep. Dist, Lat. Dep. 1 01.0 00.3 61 58.6 16.8 121 116.3 33.4 181 174.0 49.9 241 231.7 66.4 2 01.900.6 62 59.6 17.1 122 117.3 33.6 18J 174.9 50.2 242 232.6 66.7 3 02.900.8 63 60.6 17.4 123 118.2 33.9 183 175.9 50.4 243 233.6 67.0 4 03.801.1 64 61.5 17.6 124 119.2 34.2 184 176.9 50.7 244 234.5 67.3 5 04.8 01.4 65 62.5 17.9 125 120.2 34.5 185 177.8 51.0 245 235.5 67.5 G 05.8 01.7 66 63.4 18.2 126 121.1 34.7 186 178.8 51.3 246 236.5 67.8 7 06.7 01.9 67 64.4 18.5 127 122.1 35.0 187 179.8 51.5 247 237.4 68.1 8 07.7 02.2 68 65.4 18.7 128 123.0 35.3 188 180.7 51.8 248 238.4 68.4 9 ,8.7 02.5 69 66.3 19.0 129 124.0 35.6 189 181.7 52.1 249 239.4 68.6 10 ')9.6 02.8 70 67.3 19.3 130 125.035.8 19,. 182.6 52.4 250 240.3 68.9 11 10. b U3.0 71 68.2 19.6 131 125.936.1 191 163.6 52.6 251 241.3 69.2 12 11.5 03.3 72 69.2 19.8 132 126.9 36.4 192 184.6 52.9 252 242.2 69.5 13 12.5 03.6 73 70.2 20.1 133 127.8 36.7 193 185.5 53.2 253 243.2 69.7 14 13.5 J3 9 74 71.1 20.4 134 128.8 36.9 194 186.5 53.5 254 244.2 70.0 15 14.4 04.1 75 72.1 20.7 135 129.8 37.2 195 187.4 53.7 255 245.1 70.3 1C 15.4 04.4 7C 73.1 20.9 136 130.7 37.5 196 188.4 54.0 256 246.1 70.6 17 16.3 04.7 77 74.0 21.2 137 131.7 37.8 197 189.4 54.3 257 247.0 70.8 18 17.3 05.0 78 75.0 21.5 138 132.7 38.0 198 190.3 54.6 258 248.0 71.1 19 18.3 05.2 79 75.9 21.8 139 133.6 38.3 199 191.3 54.9 259 249.0 71.4 '^0 19.2 J5.5 80 76.9 22.1 140 134.6 38.6 200 192.3 55.1 260 249.9 71.7 21 .0.2 05.8 81 77.9 22.3 141 135.5 38.9 20i 193.2 55.4 2(51 25u . 9 71.9 22 21.1 06.1 82 78.8 22.6 142 136.5 39 1 202 194.2 55.7 262 251.9 72.2 23 22.1 06.3 83 79.8 22.9 143 137.5 39.4 203 195.1 56.0 263 252.8 72.5 24 23.1 06.6 84 80.7 23.2 144 138.4 39.7 204 196.1 56.2 264 253.8 72.81 25 24.0 06.9 85 81.7 23.4 145 139.4 40.0 205 197.1 56 5 265 254.7 73.0 26 25.0 07.2 86 82.1 23.7 146 140.3 40.2 206 198.0 56.8 266 255.7 73.3 27 26.0 07.4 87 83.6 24.0 147 141.3 40.5 207 199.0 57.1 267 256.7 73.6 28 26.9 07.7 88 84.6 24.3 148 142.3 40.8 208 199.9 57.3 268 257.6 73.9 29 27.9 08.0 89 85.6 24.5 149 143.2 41.1 209 200.9 57.6 269 258.6 74.1 30 28.8 08.3 90 86.5 24.8 150 144.2 41.3 210 201.9 57.9 270 259.5 74.4 31 29.8 08.5 91 87.5 25.1 161 145.2 41.6 211 202.8 58.2 27 J 260.5 74.7 32 30.8 08.8 92 88.4 25.4 152 146.1 41.9 212 203.8 58.4 272 261.5 75.0 33 31.7 09.1 93 89.4 25.6 153 147.1 42.2 213 204.7 58.7 273 262.4 75.2 34 32.7 09.4 94 90.4 25.9 154 148.0 42.4 214 205.7 59.0 274 263.4 75.5 35 33.6 09.6 95 91.3 26.2 155 149.0 42.7 215 206.7 59.3 275 264.3 75.8 36 34.6 09.9 96 92.3 26.5 156 150.0 43.0 216 207.6 59.5 276 265.3 76.1 37 35.6 10.2 97 93.2 26.7 157 150.9 43.3 217 208.6 59.8 277 266.3 76.4 38 36.5 10.5 98 94.2 27.0 158 151.9 43.6 218 209.6 60.1 278 267.2 76.6 39 37.5 10.7 99 95.2 27.3 159 152.8 43.8 219 210.5 60.4 279 268.2 76 9 40 38.5 11.0 100 96.1 27.6 160 153.8 44.1 220 211.5 60.6 280 269.2 77.2 41 39.4 11.3 101 97.1 27.8 161 154.8 44.4 221 212.4 60.9 281 270.1 77.5 42 40.4 11.6 102 98.0 28.1 162 155.7 44.7 222 213.4 61.2 282 271.1 77.7 43 11.3 11.9 103 99.0 28.4 163 156.7 44.9 223 214.4 61.5 283 272.0 78.0 44 42.3 12.1 104 100.0 28.7 164 157.6 45.2 224 215.3 61.7 284 273.0 78.3 45 43.3 12.4 105 100.9 28.9 165 158.6 45.5 225 216.3 62.0 285 274.0 78.6 46 44.2 12.7 106 101.9 29.2 166 159.6 45.8 226 217.2 62.3 286 244.9 78.8 47 45.2 13.0 107 102.9 29.5 167 160.5 46.0 227 218.2 62.6 287 275.9 79.1 48 46.1 13.2 108 103.8 29.8 168 161.5 46.3 228 219.2 62.8 288 276.8 79.4 49 47.1 13.5 109 104.8 30.0 169 162.5 46.6 229 220.1 63.1 289 277.8 79.7 50 48.1 13.8 110 105.7 30.3 170 163.4 46.9 230 221.1 63.4 290 278.8 79.9 51 49.0 04.1 111 106.7 30.6 171 164.4 47.1 231 222.1 63 7 291 279.7 80.2 52 50.0 14.3 112 107.7 30.9 172 165.3 47.4 232 223.0 63.9 292 280.7 80 5 53 30.9 14.6 113 108.6 31.1 173 166.3 47.7 233 224.0 64.2 293 281.6 80.8 54 51.9 14.9 114 109.6 31.4 174 167.3 48.0 234 224.9 64.5 294 282.6 81.0 55 52.9 15 2 115 110.5 31.7 175 168.2 48.2 235 225.9 64.8 295 283.6 81.3 56 53.8 15.4 116 111.5 32.0 176 169.2 48.5 236 226.9 65.1 296 284.5 81.6 57 54.8 15.7 117 112.5 32.2 177 170.1 48.8 237 227.8 65.3 297 285.5 81.9 58 55.8 16.0 118 113.4 32.5 178 171.1 49.1 238 228.8 65.6 298 286.5 82.1 59 56.7 16.3 119 114.4 32.8 179 172.1 49.3 239 229.7 65.9 299 287.4 82.4 60 57.7 16.5 120 115.4 33.1 180 173.0 49.6 240 230.7 66.2 300 288.4 82.7 Dist. Dcp Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. For 74 Degrees. 220 TABLE IV. DIFFERENCE OF LATITUDE AND DEPARTURE FOR 17 DEGREES. Dist. Lat. Dep Dist. Lat. Dep Dist. Lat. Dep Dist. Lat. Dep. Dist. Lat. Dep. 1 oi.oloo.s 61 58 3 17.8 121 115.7 35.4 181 173.1 52.9 241 230.5 70.5 2 01 900.6 62 59.3 18.1 122 116.7 35.7 182 174.0 53.2 242 231.4 70.8 3 02.9U0.9 63 60.2 18.4 123 117.6 36.0 183 175.0 53.5 243 232.4 71.0 4 03.801.2 64 61.2 18.7 124 118.6 36.3 184 176.0 53 8 244 233.3 71.3 5 04.801 5 65 62.2 19.0 125 119.5 36.5 185 176.9 54.1 245 234.3 71 6 6 05.701.8 66 63.1 19.3 126 120.5 36.8 186 177 9 54.4 246 235.3 71.9 7 06.702.0 67 64.1 19.6 127 121.5 37.1 187 178.8 54.7 247 236 2 72.2 8 07.7 02.3 68 65.0 19.9 128 122.4 37.4 18S 179.8 55.0 248 237.2 72.5 9 08.6 02.6 69 66.0 20.2 129 123.4 37.7 189 180.7 55.3 249 238.1 72.8 10 09.602.9 70 66.9 20.5 130 124.3 38.0 190 181.7 55.6 250 239.1 73.1 11 10.5 03.2 7J 67.920.8 131 125 338.3 191 182.7 55 8 251 240.0 73.4 12 11.5 03.5 72 6S. 921.1 132 126.2 38.6 192 183.6 56.1 252 241.0 73.7 13 12.4 03.8 73 69.8 21.3 133 127.2 38.9 193 184.6 56 4 253 241.9 74.0 14 13.4 04.1 74 70.8 21.6 134 128.1 39 2 194 185.5 56.7 254 242.9 74.3 15 14.3 04.4 75 71.7 21.9 135 129.1 39.5 195 186.5 57.1 255 243 9 74.6 16 15.3 04 .7 7(5 72.7 22.2 136 130.1 39.8 196 187.4 57.3 256 244 8 74.8 17 16.3 05.0 77 73 6 22.5 137 131.0 40.1 197 188.4 57 6 257 245.8 75.1 18 17.2 05.3 78 74.6 22.8 138 132.0 40.3 198 189.3 57.9 258 246.7 75.4 19 18.2 05.6 79 75.5 23.1 139 132.9 40.6 199 190.3 58.2 259 247.7 75.7 20 19.1 05.8 80 76.5 23.3 140 133.9 40.9 200 191 3 58.5 260 248.6 76 541 20.1 06.1 81 77.5 23.7 141 134.841.2 201 192.2 58.8 261 249.6 76.3 22 21 006 4 82 78.4 24.0 142 135.8 41.5 202 193.2 59.1 262 250.6 76.6 23 22.006.7 83 79.4 24.3 143 136.8 41.8 203 194.1 59.4 263 251 5 76.9 24 23.0 07.0 84 80.3 24 6 144 137.7 42.1 204 195.1 59.6 264 252.5 77.2 25 23.9 07.3 85 81.3 24.9 145 138.7 42.4 205 196.0 59.9 265 253.4 77.5 26 24.907.6 86 82.2 25.1 146 139 6 42.7 206 197.0 60.2 266 254.4 77.8 27 25.807.9 87 83.2 25.4 147 140.6 43.0 207 198.0 60.5 267 255.3 78.1 28 26.8 08.2 88 84.2 25.7 148 141.5 43.3 208 198.9 60.8 268 256.3 78.4 29 27.7 08.5 89 85.1 26 149 142.5 43.6 209 199. & 61.1 269 257.2 78.6 30 28.7 08.8 90 83.1 26.3 150 143.4 43.9 210 200.8 61.4 270 258.2 78.9 31 29. b 0971 91 87.0 26.6 151 144.4 44.1 iill 201.8 61.7 271 259 2 79.2,' 32 30.6 09.4 92 88.0 26.9 152 145.4 44.4 212 202.7 62.0 272 260.1 79.51 33 31.6:09.6 93 88.9 27.2 153 146.3 44.7 213 203.7 62.3 273 261.1 79.8 34 32.509.9 94 89.927.5 154 147.3 45.0 214 204.6 62.6 274 262.0 80.1 35 33.510.2 95 90.8 27.8 155 148.2 45.3 215 205.6 62.9 275 263.0 80.4 3G 34.4110.5 96 91.8 28.1 156 149.2 45.6 216 206.6 63.2 276 263.9 80.71 37 35.4 10.8 97 92.8 28.4 157 150.1 45.9 217 207.5 63.4 277 264.9 81.0 38 36.3 11.1 98 93.7 28.7 158 151.1 46.2 218 208.5 63.7 278 265.9 81.3 39 37.3 11.4 99 94.7 28.9 159 152.1 46.5 219 209.4 64.0 279 266.8 81.6 40 38.3 11.7 100 95.6 29.2 160 153.0 46.8 220 210.4 64.3 280 267.8 81.9 41 39.2 12.0 101 96.6 29.5 161 154.0J47.1 221 211.3 64.6 281 208. 7 82.2 42 40.2 12.3 102 97.5 29.8 162 154.9|47.4 222 212.3 64.9 282 269.7 82.4 43 41 1 12.6 103 98.5 30.1 163 155.9 47.7 223 213.3 65.2 283 270.6 82.7 44 42.1 12.9 104 99.5 30.4 164 156.8 47.9 224 214.2 65.5 284 271.6 83.0 45 43.0 13 2 105 100.4 30.7 165 157.8 48.2 225 215.2 65.8 285 272.5 83.3 46 14.0 13.4 106 101.4 31.0 166 158.7 48.5 226 216.1 66.1 286 273.5 83.6 47 44.9 13.7 107 102.331.3 167 159 7 48.8 227 217.1 66.4 287 274.5 83.9 48 45.9 14.0 108 103.331.6 168 160.7 49.1 228 218.0 66.7 288 275.4 84.2 49 46.9 14.3 109 104.231.9 169 161.6 49.4 229 219.0 67.0 289 276.4 84.5 50 47.8 14.6 110 105.2 32.2 170 162.6 49.7 230 220.0 67.2 290 277.3 84.8 51 48.8 14.9 111 106.1 32.5 171 163.5 50.0 231 220.9 67.5 291 278.3 &5.1 52 49.7 15.2 112 107.1 32.7 172 164.5 50.3 232 221.9 67.8 292 279.2 85.4 53 50.7 15.5 113 108.1 33.0 173 165.4 50.6 233 222.8 68.1 293 280.2 85.7 54 51.6 15.8 114 109.0 33.3 174 166.4 50.9 234 223.8 68.4 294 281.2 86.0 55 52.6 16.1 115 110.0 33.6 175 167.4 51.2 235 224.7 68.7 295 282.1 86.2 56 53.6 16.4 116 110.9 33.9 176 168.3 51.5 236 225.7 69.0 296 283.1 86.5 57 54.5 16.7 117 111.9 34.2 177 169.3 51.7 237 226.6 69.3 297 284.0 86.8 58 55.5 17.0 118 112.8 34.5 178 170.2 52.0 238 227.6 69.6 298 285.0 87.1 59 56.4 17.2 119 113.834.8 179 171.2 52.3 239 228.6 69.9 299 285.9 87.4 60 57.4 17.5 120 114.8 35.1 180 172.1 52.6 240 229.5 70.2 300 286.9 87.7 Dist, Dep Lat. Dist. Dep. Lat. 'Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat, For 73 Degrees. TABLE IV. 221 DIFFERENCE OF LATITUDE AND DEPARTURE FOR 18 DEGREES. Dist. Lat. Dep Dist. Lat, Dep Dist. Lat. Dep Dist. Lat. Dep. jj)ist. Lat. Dep. 1 01.0 00.3 61 58.0 18.9 121 115.1 37.4 181 172.1 55. y| 241 229.2 74.5 2 01.9 00.6 62 59.0 19.2 122 116.037.7 182 173.1 56.2| 242 230.2 74.8 3 02.9 00.9 63 59.919.5 123 117.0 38.0 183 174.0 56.6 243 231.1 75.1 4 03.8 01.2 64 60.919.8 124 117.9 38.3 184 175.0 56.9 244 232.1 75.4 5 04.8 01.5 65 61.820.1 125 118.9 38.6 185 175.9 57.2 245 233.0 75.7 6 05.7 01.9 66 62.820.4 126 119.8 38.9 186 176.9 57.5 246 234.0 76.0 7 06.7 02.2 67 63.720.7 127 120.8 39.2 187 177.8 57.8 247 234.9 76.3 8 07.6 02.5 68 64.7 21.0 128 121.7 39.6 188 178.8 58.1 248 235.9 76.6 9 08.6 02.8 69 65.6 21.3 129 122.7 39.9 189 179.7 58.4 249 236.8 76.9 10 09.5 03.1 70 66.6 21.6 ]30 123.6 40.2 190 180.7 58.7 250 237.8 77.3 11 10.5 03.4 71 67.5 21.9 131 124.6 40.5 191 181.7 59.0 251 238.7 77.6 12 11.4 03.7 72 68.5 22.2 132 125.5 40.8 192 182.6 59.3 252 239.7 77.9 13 12.4 04. ( 73 69.4 22 6 133 126.5 41.1 193 183.6 59.6 253 240.6 78.2 14 13.3 04.3 74 70.4 22^9 134 127.4 41.4 194 184.5 59.9 254 241.6 78.5 15 14.3 04. ( 75 71.3 23.2 135 128.4 41.7 195 185.5 60.3 255 242.5 78.8 16 15.2 04.9 76 72.3 23.5 136 129.3 42.0 196 186.4 60.6 256 243.5 79.1 17 16.2 05.3 77 73.223.8 137 130.3 42.3 197 187.4 60.9 257 244.4 79.4 18 17.1 05.6 78 74.2 24.1 138 131.2 42.6 198 188.3 61.2 258 245.4 79.7 19 18.1 05.9 79 75.1 24.4 139 132.2 43.0 199 189.3 61.5 259 246.3 80.0 20 19.0 06.2 80 76.1 24.7 140 133.1 43 3 200 190.2 61.8 260 247.3 80.3 21 M.O U6.5 81 77.0 25.0 141 134.1 43.6 201 191.2 62.1 '261 24*. 2 80.7 22 20.9 06.8 82 78.0 25.3 142 135.1 43.9 202 192.1 62.4 262 249.2 81.0 23 21.9 07.1 83 78.9 25.6 143 136.0 44.2 203 193.1 62.7 263 250.1 81.3 24 22.8 07.4 84 79.9 26.0 144 137.0 44.5 204 194.0 63.0 264 251.1 81.6 25 23.8 07.7 85 80.8 26.3 145 137.9 44.8 205 195.0 63.3 265 252.0 81.9 20 24.7 08.0 86 81.8 26.6 146 138.9 45.1 206 195.9 63.7 266 253.0 82.2 27 25.7 08.3 87 82.7 26.9 147 139.8 45.4 207 196.9 64.0 267 253.9 82.5 28 26. G 08.7 88 83.7 27.2 148 140.8 45.7 208 197.8 64.3 268 254.9 82.8 29 27.6 09.0 89 84.6 27.5 149 141.7 46.0 209 198.8 64.6 269 255.8 83.1 30 28.5 09.3 90 85.6 27.8 150 142.7 46.4 210 199.7 64.9 270 256.8 83.4 31 29. b 09.6 91 86.5 28.1 151 143.6 46.7 "211 200.7 65.2 271 257.7 83.7 32 30.4 09.9 92 87.5 28.4 152 144.6 47.0 212 201.6 65.5 272 258.7 84.1 33 31.4 10.2 93 88.4 28.7 153 145.5 47.3 213 202.6 65.8 273 259.6 84.4 34 32.3 10.5 94 89.4 29.0 154 146.5 47.6 214 203.5 66.1 274 260.6 84.7 35 33.3 10.8 95 90.4 29.4 155 147.4 47.9 215 204.5 66.4 275 261.5 85.0 33 34.2 11.1 96 91.3 29.7 156 148.4 48.2 216 205.4 66.7 276 262.5 85.3 37 35.2 11.4 97 92.3 30.0 157 149.3 48.5 217 208.4 67.1 277 263.4 85.6 38 36.1 11.7 98 93.2 30.3 158 150.3 48.8 218 207.3 67.4 278 264.4 85.9 39 37.1 12.1 99 94.2 30.6 159 151.2 49.1 219 208.3 67.7 279 265.3 86.2 40 38.0 12.4 100 95.1 30.9 160 152.2 49.4 220 209.2 68.0 280 266.3 86.5 41 39.0 12.7 101 96.1 31.2 161 153.1 49.8 221 210.2 68.3 281 267.2 86.8 42 39.9 13.0 102 97.0 31.5 162 154.1 50.1 222 211.1 68.6 282 268.2 87.1 43 40.9 13.3 103 98.0 31.8 163 155.0 50\4 223 212.1 68.9 283 269.1 87.5 44 41.8 13.6 104 98.9 32.1 164 156.0 50.7 224 213.0 69.2 284 270.1 87.8 45 42.8 13.9 105 99.9 32.4 165 156.9 51.0 225 214.0 69.5 285 271.1 88.1 46 13.7 14.2 106 100.8 32.8 166 157.9 51.3 226 214.9 69.8 286 272.0 88.4 47 44.7 14.5 107 101.8 33.1 167 158.8 51.6 227 215 9 70. l! 287 273 88 7 48 45.7 14.8 108 102.7 33 4 168 159 8 51.9 228 216.8 70.5 288 273.9 89.0 49 46.6 15.1 109 103.733.7 169 160.7 52.2 229 217 8 70.8 289 274.9 89.3 50 47.6 15 5 110 104.634.0 170 161.7 52.5 230 218.7 71.1 290 275.8 89.6 51 18.5 15.8 111 105.634.3 171 162.6 52.8 231 219.7 71.4 291 276.8 89.9 52 49.5 16.1 112 106.534.6 172 163.6 53.2 232 220.6 71. 7> 292 277.7 90.2 53 50.4 16.4 113 107.534.9 173 164.5 53.5 233 221.6 72.0, 293 278.7 90.5 54 51.4 16.7 114 108.435.2 174 165.5 53.8 234 222.5 72.3 294 279.6 90.9 55 52.3 17.0 115 109.435.5 175 166.4 54.1 235 223.5 72.6 295 280.6 91.2 56 53.3 17.3 116 110.335.8 176 167.4 54.4 236 224.4 72.9 296 281.5 91.5 57 54.2 17.6 117 111.336.2 177 168.3 54.7 237 225.4 73.2 297 282.5 91.8 58 55.2 17.9 118 112.236.5 178 169.3 55.0 238 226.4 73.5 298 283.4 92.1 59 56.1 18.2 119 113.236.8 179 170.2 55.3 239 227.3 73.9 299 284.4 92.4 GO >7.1 18.5 120 114.1 37.1 180 171.2 55.6 240 228.3 74.2 300 285.3 92.7 Dist. Dep Lat. Dist. Dcp. iLat, Dist. Dep. Lat. Dist. Dcp. Lat. Dist. Dep. Lat, For 72 Degrees. 222 T1BLE IV. DIFFERENCE OF LATITUDE AXD DEPARTURE FOR 19 DEGREES. Dist. [Lat. Dep Dist. Lat. Dep| Dist. Lat, Dep ! Dist. Lat. Dep. Dist. Lat. Dep. 1 00.9 00.3 61 57.7 19 9 121 114.4 39.4 181 171.1 58.9 241 227.9 78.5 2 01.9 JO. 7 62 58 6 :0.2 122 115.4 39.7 182 172.1 59.3 242 228.8 78 8 3 02.8 01.0 63 59.6 20.5 123 116.3 40.0 183 173.0 59.6 243 229.8 79.1 4 33.8 01.3 64 60.5 20.8 124 117.2 40.4 184 174.0 59.9 244 230.7 79.4 5 04.7 01.6 6J 61.5 21.2 125 118.2 40. 7, 185 174.9 60.2 245 231.7 79.8 6 05.7 02.0 66 62.4 21.5 126 119.1 41.0 186 175.9 60.6 246 232.6 80.1 7 06.6 02.3 67 63.3 21.8 127 120 1 41.3 187 176.8 60.9 247 233.5 80.4 8 07. 6 02.6 68 64.3 22.1 128 121.0 41.7 188 177.8 61.2 248 234.5 80.7 9 )8.5 02.9 69 65.2 22.5 129 122.0 42.0 189 178.7 61.5; 249 235.4 81 1 10 J9.5 03.3 70 6J.2 22.8 130 122.9 42.3 190 179.6 61.9' 250 236.4 81.4 11 iO.4 M 6 71 67.1 z3.1 131 123.9 42.6 191 ISO. 6 62.2 251 237.3 84.7 12 11.3 03.9 7z 68.1 23.4 132 124.8 43.0 192 181.5 62.5 252 238.3 82.0 13 12.3 J4.2 73 69.0 23.8 133 125.8 43.3 193 182.5 62.8 253 239.2 82.4 14 13.2 04.6 74 70.0 24.1 134 126.7 43.6: 194 183.4 63.2 254 240.2 82.7 15 14.2 04.9 75 70.9 24.4 135 127.6 44.0 195 184.4 63.5 255 241.1 83.0 1C 15.1 05.2 76 71.9 24.7 136 128.6 44.3 196 185.3 63.8 256 242.1 83.3 17 16.1 05.5 77 72.8 25.1 137 129.5 44.6 197 186.3 64.1 257 243.0 83.7 18 17.0 05.9 78 73.8 25.4 138 130.5 44.9 198 187.2 64.5 258 243.9 84.0 19 18.006.2 79 74.7 25.7 139 131.4 45.3 199 188.2 64.8 259 244.9 84.3 20 18 906.5 80 75.6 26.0 140 132.4 45.6 200 189.1 65.1 260 245. b 84.6 zi 19.9J06.8 81 76. (3 26.4 141 133.3 45.9 201 190.0 65.4 261 246.8 85.0 22 20.8 07.2 82 77.5 26.7 142 134.3 46.2 202 191.0 65.8 262 247.7 85.3 23 21.7 07.5 83 78.5 27.0 143 135.2 46.6 203 191.9 66.1 263 248.7 85.6 24 22.7 07.8 84 79.4 27.3 144 136.2 46.9 204 192.9 66.4 264 249.6 86.0 25 23.608.1 85 80.427.7 145 137.1 47.2 205 193.8 66.7 265 250.6 86.3 26 24 608.5 86 81.328 146 138.0 47.5 206 194.8 67.1 266 251.5 86.6 27 25.508.8 87 82.3 28.3 147 139.0 47.9 207 195.7 67.4 267 252.5 86.9 28 26.5 09.1 88 83.2 28.7 148 139.9 48.2 208 196.7 67.7 268 253.4 87.3 29 27.4 09.4 89 84.229.0 149 140.9 48.5 209 197.6 68.0 269 254.3 87.6 30 23.4 09 8 90 85.1 29.3 150 141.8 48.8 210 198.6 68.4 270 255.3 87.8 31 29.3 10.1 91 86.0 29.6 151 142.8 49.2 211 199.5 68.7 27 J 256. 68.2 32 30.3 10.4 92 87.030.0 152 143.7 49.5 212 200.4 69.0 272 257.2 88.6 33 31.2 10.7 93 87.9 30.3 153 144.7 49.8 213 201.4 69.3 273 258.1 88.9 34 32.1 11.1 94 88.9 30. C 154 145.6 50.1 214 202.3 69.7 274 259.1 89.2 35 33.1 11.4 95 89.8 30.9 155 146.6 50.5 215 203.3 70.0 275 260.0 89.5 30 34.0 11.7 96 90.8 31.3 150 147.5 50.8 216 204.2 70.3 276 261.0 89.9 37 35.0 12. (J 97 91.7 31.6 157 148.4 51.1 217 205.2 70.6 277 261. i, 90.2 38 35.9 12.4 98 92.7 31.9 158 149.4 51.4 21b 206.1 71.0 278 262.9 90.5 39 36.9 12.7 99 93.6 32.2 159 150.3 51.8 219 207.1 71.3 279 263.8 90.8 40 37.8 13.0 100 94.6 32.6 160 151.3 52.1 220 208.0 71.6 280 264.7 91.2 41 38. b 13.3 101 95.5 32.9 161 152.2 52.4 221 209.0 7-2.0 281 265. '< 91.5 42 39.7 13.7 102 96.4 33.2 162 153.2 52.7 222 209.9 72.3 282 266.6 91.8 43 40.7 14.0 103 97.4 33.5 163 154.1 53.1 223 210.9 72.6 283 267.6 92.1 41 41.0 14.3 104 98.3 33.9 164 155.1 53.4 224 211.8 72.9 284 268.5 92.5 45 42.5 14.7 105 99.3 34.2 165 156.0 53.7 225 212.7 73.3 285 269.5 92.8 4G 43.5 15.0 106 100.2 34.5 166 157.0 54.0 226 213.7 73.6 28G 270.4 93.1 47 44.4 15.3 107 101.2 34.8 167 157.9 54.4 227 214.6 73.9 287 271.4 93.4 48 45.4 15.6 108 102.1 35.2 168 158.8 54.7 228 215.6 74.2 288 272.3 93.8 49 46.3 16.0 109 103.1 35.5 169 159.8 55.6 229 216.5 74.6 289 273.3 94.1 50 47.3 16.3 110 104.0 35.8 170 160.7 55.3 230 217.5 74.9 290 274.2 94.4 51 48.2 16.6 111 105.0 36.1 171 161.7 55.7 231 218.4 75/2 291 275.1 94.7 52 49.2 1619 112 105.9 36.5 172 162.6 56.0 232 219.4 75.5 292 276.1 95.1 53 50.1 17.3 113 106.8 36.8 173 163.6 56.3 233 220.3 75.9 293 277.0 95.4 54 51.1 17.6 114 107.8 37.1 174 164.5 56.6 234 221.3 76.2 294 278.0 95.71 55 52.0 17.9 115 108.737.4 175 165.5 57.0 235 222.2 76.5 295 278.9 96.0 56 52.9 18.2 116 109.7 37.8 176 166.4 57.3 236 223.1 76.8 296 279.9 96.4 57 53.9 18.6 117 110.6 38.1 177 167.4 57.6 237 224.1 77.2 297 280.8 96.7 58 54.8 18.9 118 111.6 38 4 178 168.3 58.0 238 225.0 77.5 298 281.8 97.0 59 55.8 19.2 119 112.5 38.7 179 169.2 58.3 239 226.0 77.8 299 282.7 97.3 60 56.7 19.5 120 113.5 39.1 180 170.2 58.6 240 226.9 78.1 300 283.7 97.7 riist. Dep Lat. m. Dep. Lat. Dist. Dep. Lat, Dist. Dep. Lat. Dist. Dep. Lat. For 71 Degrees. TABLE IV. 223 DIFFERENCE OF LATITUDE AND DEPARTURE FOR 20 DEGREES. Dist. Lat. Dep Dist. Lat. Dep Dist. Lat. Dep Dist. Lat. Dep. Dist. Lat. Dep. 1 00.9 00.3 61 57.3 20.9 121 113.7 41.4 181 170.1 61.9 241 226.5 82.4 2 01.900.7 62 58.3 21.2 12-2 114.6 41.7 182 171.0 62.2 242 227.4 82.8 3 02.8 01.0 63 59.2 21.5 123 115.6 42.1 183 172.0 62.6 243 228 3 83.1 4 03.8 01.4 64 60.1 21.9 124 116.5 42.4 184 172.9 62.9 244 229.3 83.5 5 04.7 01.7 65 61.1 22.2 125 117.5 42.8 185 173.8 63.3 245 230.2 83.8 6 05.6 02.1 66 62.0 22.6 126 118.4 43.1 186 174.8 63.6 246 231.2 84.2 7 OG.6 02.4 67 63 22 9 127 119.3 43.4 187 175.7 64 247 232.1 84.5 8 107.5 02.7 68 63.9 23.3 128 120.3 43.8 188 176 7 64.3 248 233.0 84.8 9 08.5 03.1 69 64.8 23.6 129 121.2 44.1 189 177.6 64.6 249 234.0 85.2 10 |09.4 03.4 70 65.8 23.9 130 122 2 44.5 190 178.5 65.0 250 234.9 85 5 11 i0.3 j3.8 71 66.7 24.3 131 123.1 44.8 191 179.5 65.3 251 235.9 85.8 13 11.3 04. 1 72 67.7 24.6 132 124.0 45.1 192 180.4 65.7 252 236.8 86.2 13 12.2 04.4 73 - 68 6 25.0 133 125.0 45.5 193 181.4 66.0 253 237 7 86.5 14 13.2 04 8 74 69.5 25.3 134 125.9 45.8 194 182.3 66 4 254 238.7 86.9 15 14.1 05.) 75 70 5 25.7 135 126.9 46. 5s 195 183.2 66.7 255 239.6 87.2 16 15.0 0:>.5 76 71.4 26.0 136 127.8 46.5 196 184.2 67.0 256 240.6 87.6 17 16 05.8 77 72.4 26.3 137 128.7 46.9 197 185.1 67.4 257 241.5 87 9 18 16.9 06.2 78 73.3 26.7 138 129 7 47.2 198 186.1 67.7 258 242.4 88.2 19 17.9 06 5 79 74.2 27.0 139 130.6 47 5 199 187.0 68.1 259 243.4 88.6 20 18.8 <)6.8 80 75.2 27.4 140 131.6 47.9 200 187.9 68.4 260 244 3 88.9 21 19.7 07.2 81 70.1 27.7 141 132.5 48.2 201 18W.9 68.7 261 245.3 89.3 22 20 7 07.5 82 77.1 28.0 142 133.4 48.6 202 189.8 69 1 262 246.2 89.6| 23 21.6 07.9 83 78.0 28.4 143 134.4 48.9 203 190 8 69.4 263 247.1 90.0 24 22.6 08.2 84 78.9 28.7 144 135.3 49.3 204 191.7 69.8 264 248.1 90.3 25 23.5 08.6 85 79.9 29.1 145 136.3 49.6 205 192.6 70.1 265 249.0 90.6 26 24.4 08-9 86 80.8 29.4 146 137.2 49.9 206 193.6 70.5 266 250.0 91.0 27 25.4 09.2 87 81.8 29.8 147 138.1 50.3 207 194.5 70.8 267 250.9 91 3 28 26.3 09.6 88 82.7 30.1 148 139.1 50.6 208 195.5 71.1 268 251.8 91 7 29 27.3 J9.9 89 83.6 30.4 149 140 ol.O 209 196.4 71.5 269 252.8 92.0 30 2S.2 10.3 90 84.6 30.8 150 141.0 51.3 210 197.3 71.8 270 253.7 92.3 31 29.1 10.6 91 85.5 31.1 151 141.9 51.6 211 198. b 72.2 271 254.7 92.7 32 30.1 10.9 92 86.5 31.5 152 142.8 52.0 212 199.2 72.5 272 255.6 93.0 33 31.0 11.3 93 87.4 31.8 153 143.8 52.3 213 200.2 72.9 273 256.5 93.4 34 31.9 11.6 94 88.3 32.1 154 144.7 52.7 214 201.1 73.2 274 257.5 93.7 35 32.9 i2.0 95 89.3 32.5 155 145.7 33.0 215 202.0 73.5 275 258.4 94.1 36 33.8 12.3 96 90.2 32.8 156 146.6 53.4 216 203.0 73.9 276 259.4 94.4 37 34.8 12.7 97 91.2 33.2 157 147.5 53.7 217 203.9 74.2 277 260.3 94.7 38 35.7 13.0 98 92.1 33.5 158 148.5 54.0 218 204. y 74.6 278 261.2 95.1 39 36.6 13 3 99 93.0 33.9 159 149.4 54.4 219 205.8 74.9 279 262.2 95.4 40 37.0 13 7 100 94.0 34.2 160 150.4 54.7 220 206.7 75.2 280 263.1 95.8 41 38. fa 14.0 101 94.9 34.5 161 151.3 -35.1 221 207.7 75.6 281 264.1 96.1 42 39 5 14.4 102 95.8 34.9 162 152.2 55.4 222 208.6 75.9 282 265.0 96.4 43 40.4 14.7 103 96.8 35.2 163 153.2 55.7 223 209.6 76.3 283 265.9 96.8 44 41.3 15.0 104 97.7 35.6 164 154.1 56.1 224 210.5 76.6 284 266.9 97.1 45 42.3 15.4 105 98.7 35.9 165 155.0 56.4 225 211.4 77 285 267.8 97.5 46 43.2 15.7 106 99.6 36.3 166 156.0 56.8 226 212.4 77 ..3 286 268.8 97.8 47 44. it 16.1 107 100.5 36.6 167 156.9 57.1 227 213.3 77.6 287 269.7 98.2 48 45.1 16.4 108 101.5 36.9 168 157.9 57 5 228 214.2 78.0 288 270.6 98.5 49 46.0 16.8 109 102.4 37.3 169 158.8 57.8 229 215.2 78.3 289 271.6 98.8 50 47.0 17.1 110 103.4 37.6 170 159.7 58.1 230 216.1 78.7 290 272.5 99.2 61 4V .y IV. 4 111 104.3 38.0 171 160.7 58.5] 231 217.1 79.0 291 273.5 99.5 52 48.9 17.8 112 105.2 38.3 172 161.6 .38.8 232 218 79.3 292 274.4 99 9 53 49.8 18.1 113 106.2 38.6 173 162.6 39.2 233 218.9 79.7 293 275.3 100.2 5i 50.7 18.5 114 107.1 39.0 174 163.5 59.5 234 219.9 80.0 294 276.3 100.6 55 51 7 18.8 115 108.1 39.3 175 164.4 59.9 235 220.8 80.4 295 277.2 100.9 56 52.6 19.2 116 109.0 39.7 176 165.4 60.2 236 221 . 8 80.7 296 278.1 101.2 57 53.6 19 5 117 109.9 40.0 177 166.3 60.5 237 222.7 81.1 297 279.1 101.6 58 54.5 19.8 118 110.9 40.4 178 167.3 60.9 238 223.6 81.4 298 280.0 101.9 59 55.4 20.2 119 111.8 40.7 179 168.2 61.2 239 224.6 81.7 299 281.0 102.3 60 56.4 20.5 120 112.8 41.0 180 169.1 61.6 240 225.5 82.1 300 281.9 102.6 DistJDep Lat, Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. 1 Lat. Dist. Dep. Lat. For 70 Degrees. 224 TABLE IV. DIFFERENCE OF LATITUDE AND DEPARTURE FOR 21 DEGREES. Dist. Lat, Dep Dist. Lat. Dep Dist. Lat. Dep Dist. Lat. Dep. Dist. Lat. Dep. l 00.9 00.4 61 56.9 21.9 121 113.0 43.4 181 169.0 64.9 241 225.0 86.4 2 01.9 00.7 62 57.9 22.2 122 113.9 43.7 182 169.9 65.2 242 225.9 86.7 3 02.8 01.1 63 58.8 22.6 123 114 8 44.1 183 170.8 65.6 243 226.9 87.1 4 03.7 01.4 64 59.7 22.9 124 115.8 44 4 184 171.8 65.9 244 227 8 87.4 5 04.7 01.8 65 60.7 23.3 125 116.7 44.8 185 172.7 66.3 245 228.7 87.8 6 05.6 02.2 66 61.6 23.7 126 117.6 15.2 186 173.6 66.7 246 229.7 88.2 7 16.5 02.5 67 62.5 24.0 127 118.6 45.5 187 174.6 67.0 247 230.6 88.5 8 07.5 02.9 68 63.5 24.4 128 119.5 45.9 188 175.5 67.4 248 231.5 88.9 9 08 4 J3.2 69 64.4 24.7 129 120.4 16.2 189 176.4 67.7 249 232.5 89.2 10 09.3 03.6 70 65.4 25.1 130 121.4 46. C 190 177.4 68.1 250 233.4 89.6 11 10.3 03.9 71 66.3 25.4 131 li-2.3 16.91 191 178.3 68.4 25 1 234.5 90.0 12 11.2 J4.3 72 67.2 25.8 132 123.2 47.3 192 179.2 68.8 252 235.3 90.3 13 12.1 04 7 73 68.2 26.2 133 124.2 47.7 193 180.2 69.2 253 236.2 90.7 14 13.1 05.0 74 69.1 26.5 134 125.1 48.0 194 181.1 69 5 254 237.1 91.0 15 14.0 05.4 75 70.0 26.9 135 126.0 48.4 195 182.0 69.9 255 238.1 91.4 16 14.5) 05. 7 76 71.0 .,7.2 136 127.0 48.7 196 183.0 70.2 256 239.0 91.7 17 15.9 06.1 77 71.9 27.6 137 127.9 49.1 19? 183.9 70.6 257 239.9 92.1 18 16.8 06.5 78 72.8 28.0 138 128.8 49.5 198 184.8 71.0 258 240.9 92.5 19 17.7 06.8 79 73 8 28.3 139 129.8 49.8 199 185.8 71.3 259 241.8 92.8 20 18.7 07.2 80 74 7 28.7 140 130.7 50.2 200 186.7 71.7 260 242.7 93.2 21 19.6 07.5 81, 75.6 29.0 141 131.6 oO.o '2ul 167.6 72. U 261 243. V 93.5 22 20.5 07.9 82 76.6 29.4 142 132.6 30.9 202 188.6 72.4 262 244.6 93.9 23 21.5 08.2 83 77.5 29.7 !<* 133.5 51.2 203 189.5 72.7 263 245.5 94.3 24 22.4 08.6 84 78.4 30.1 14* 134.4 51.6 204 190.4 73.1 264 246.5 94.6 25 23.3 09.0 85 79.4 30.5 145 135.4 12.0 205 191.4 73.5 265 247.4 95.0 2G 24.3 09.3 86 80.3 30.8 146 136.3 52.3 206 192.3 73.8 266 248.3 95.3 27 25.2 09. 7 87 81.2 31.2 147 137.2 32.7 207 193.3 74.2 267 249.3 95.7 28 26.1 10.0 88 82.2 31.5 148 138.2 53.0 208 194.2 74.5 268 250.2 96.0 29 27.1 10.4 89 83.1 31.9 149 139.1 33.4 209 195.1 74.9 269 251 . 1 96.4 3J 28.0 10.8 90 84.0 32.3 150 140.0 53.8 210 196.1 75.3 270 252.1 96.8 31 28. y 11.1 91 85.0 32.6 151 141.0 54.1 211 197.0 75.6 271 253 97.1 32 29.9 11.5 92 85.9 33.0 152 141.9 54.5 212 197.9 76.0 272 253.9 97.5 33 30.8 11.8 93 86.8 33.3 153 142.8 54.8 213 198.9 76.3 273 254.9 97.8 34 31.7 12.2 94 87.8 33.7 154 143.8 55.2 214 199.8 76.7 274 255.8 98.2 35 32.7 12.5 95 88.7 34.0 155 144.7 55.5 215 200.7 77.0 275 256.7 98.6 36 33.6 12 9 96 89.6 34.4 156 145.6 35.9 216 201.7 77.4 276 257.7 98.9 37 J4.5 13.3 97 90.6 34.8 157 146.6 56.3 217 202.6 77.8 277 258.6 99.3 38 35.5 13.6 98 91.5 35.1 158 147.5 56.6 218 203.5 78.1 278 259.5 99.6 39 36.4 14.0 99 92.4 35.5 159 148.4 57.0 219 204.5 78.5 279 260.5 100.0 40 37.3 14.3 100 93.4 35.8 160 149.4 57.3 220 205.4 78.8 280 261.4 100.3 41 38 3 14. V 101 94.3 36. '2 161 150.3 57.7 221 206.3 79.2 281 262.3 100.7 42 39.2 15.1 102 95.2 36.6 162 151.2 58.1 222 207.3 79.6 282 263.3 101.1 43 10.1 15.4 103 96.2 36.9 163 152.2 58.4 223 208.2 79.9 283 264.2 101.4 44 11.1 15.8 104 97.1 37.3 164 153 1 58.8 224 209.1 80.3 284 265.1 101.8 45 42.0 16.1 105 98.0 37.6 165 154.0 59.1 225 210.1 80.6 285 266.1 102.1 46 42.9 16.5 106 99.0 38.0 166 155 59.5 226 211.1) 81.0 286 267.0 102.5 47 43.9 16.8 107 99.9 38.3 167 155.9 59.8 227 211.9 81.3 287 267.9 102.9 48 14.8 17.2 108 100.8 38.7 168 156:8 60.2 228 212.9 81.7 288 268.9 103.2 49 45.7 17.6 109 101.8 39.1 169 157.8 60.6 229 213.8 82.1 289 269.8 103.6 50 16.7 17.9 110 102.7 39.4 170 158.7 60.9 230 214.7 82.4 290 270.7 103.9 51 47.6 18.3 111 103.6 39.8 171 159.6 61.3 231 215.7 82.8 291 271.7 104.3 52 18.5 18.6 112 104.6 40.1 172 160.6 61.6 232 216.6 83.1 292 272 6 104.6 53 49.5 19.0 113 105.5 40.5 173 161.5 62.0 233 217.5 83.5 293 273.5 105.0 54 50.4 19.4 114 106.4 40.9 174 162.4 62.4 234 218.5 83.9 204 274.5 105.4 55 51.3 19.7 115 107.4 41.2 175 163.4 62.7 235 219.4 84.2 295 275.4 105.7 50 52.3 20.1 116 108.3 41.6 176 164.3 63.1 236 220.3 84.6 296 276.3 106.1 57 53.2 20.4 117 109.2 41.9 177 165.2 63.4 237 221.3 84.9 297 277.3 106 4 58 54.1 20.8 118 110 2 42.3 178 166.2 63.8 238 222.2 85.3 298 278 2 106.8 59 55.1 21.1 119 111.1 42 6 179 167.1 64.1 239 223.1 85.6 299 279.1 107 2 60 56.0 21.5 120 112 43.0 180 168.0 64.5 240 224.1 86.0 300 280.1 107.5 Dist; Dep Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. For 69 Degrees. TABLE IV. 225 DIFFERENCE OF LATITUDE AND DEPARTURE FOR 22 DEGREES. Dist, Lat. Dep Dist. Lat. Dep Dist. Lat. Dep Dist. Lat. Dep. Dist. Lat. Dep. 1 00.9 00.4 61 56.6 22.9 121 112.245.3 181 167.8 67.8 241 223.5 90.3 2 01.9 00.7 62 67.523.2 122 113.1 45.7 182 168.7 68.2 242 224.4 90.7 3 02.8 01.1 63 58.423.6 123 114.0J46.1 183 169.7 68.6 243 225.3 91.0 4 03.7 01.5 64 59.324.0 124 115.046.5 184 170.6 68.9 244 226.2 91.4 5 04.6 01.9 65 60.324.3 125 115.946.8 185 171.5 69.3 245 227.2 91.8 6 05.6 02.2 66 61.224.7 126 116.847.2 186 172.5 69.7 246 228.1 92.2 7 16.5 02.6 67 62.1'25.1 127 117.847.6 187 173.4 70.1 247 229.0 92. 8 07.4 03.0 68 63.025.5 128 118.747.9 188 174.3 70.4 248 229.9 92. 9 J8.3 03.4 69 64.0,25.8 129 119.648.3 189 175.2 70.8 249 230.9 93.3 10 09.3 03.7 70 64.9!'26.2 130 120.548.7 190 176.2 71.2 250| 231.8 93.7 11 10.2 04.1 71 65.826.6 131 121.549.1 ~19~1 177.1 71.5 251 232.7 94. 1 12 11.1 04.5 72 66.8'27.0 132 122.449.4 192 178.0 71.9 252 233.7 94.4 13 12.1 04.9 73 67.7127.3 133 123.349.8 193 178.9 72.3 253 234.6 94.8 14 13.0 05.2 74 68.627.7 134 124.250.2 194 179.9 72.7 254 235.5 95.2 15 13.9 05.6 75 69.528.1 135 125.2 50.6 195 180.8 73.0 255 236.4 95.5 16 14.8 06.0 76 70.528.5 136 126.150.9 196 181.7 73.4 256 237.4 95. 17 15.8 06.4 77 71.428.8 137 127.05l.3j| 197 182.7 73.8 257 238.3 96.3 18 16.7 06.7 78 72.329.2 138 128.051.7 198 183.6 74.2 258 239.2 96.6 19 17.6 07.1 79 73.2:29.6 139 128.9 52.1 199 184.5 74.5 259 240.1 97. C 20 18.5 07.5 80 74.230.0 140 129.852.4 200 185.4 74.9 260 241.1 97.4 21 19.5 07. y 81 75.130.3 141 130.7|52.8 201 186.4 75.3 261 242.0 97. fc 22 20.4 08.2 82 76.0 30.7 142 131.7 53 2 202 187.3 75.7 262 242.9 98.1 23 21.3 08.6 83 77.0 31.1 143 132.653.6 203 188.2 76.0 263 243.8 98.5 24 22.3 09.0 84 77.9 31.5 144 133.553.9 204 189.1 76.4 264 244.8 98. 1 25 23.2 09.4 85 78.8 31.8 145 134.454.3 205 190.1 76 8 265 245.7 99. 1 26 24.1 09.7 86 79.732.2 146 135.454.7 206 191.0 77.2 266 246.6 99.6 27 25.0 10.1 87 80.732.6 147 136.3 55.1 207 191.9 77.5 267 247 6 100.0 28 26.0 10.5 88 81.633.0 148 137.255.4 208 192.9 77.9 268 248.5 100.4 29 26.9 10.9 89 82.533.3 149 138.255.8 209 193.8 78.3 269 249.4 100.8 30 27.8 11.2 90 83.433.7 150 139.156.2 210 194.7 78.7 270 250.3 101.1 31 28.7 11.6 91 84.434.1 151 140.056.6 211 195.6 79.0 271 251 . b 101. 32 29.7 12.0 92 85.334.5 152 140.9 ( 56.9 212 196.6 79.4 272 252.2 101. t 33 30.6 12.4 93 86.234.8 153 141.957.3 213 197.5 79.8 273 253.1 102. 34 31.5 12.7 94 87.2 35.2 154 142.857.7 214 198.4 80.2 274 254.0 102. C 35 32.5 13.1 95 88.1 35.6 155 143.758.1 215 199.3 80.5 275 255.0 103. C 36 33.4 13.5 96 89.0 36.0 156 144.658.4 216 200.3 80.9 276 255.9 103.4 37 34.3 13.9 97 89.9 36.3 157 145.658.8 217 201.2 81.3 277 256.8 103.8 38 35.2 14.2 98 90.9 36.7 158 146.5 59.2 218 202.1 81.7 278 257.8 104.1 39 36.2 14.6 99 91.8 37.1 159 147.459.6 219 203.1 82.0 279 258.7 104 5 40 37.1 15.0 100 92.737.5 160 148.359.9 220 204.0 82.4 280 259.6 104.9 41 138.0 15.4 101 93.6 37.8 161 149.360.3 221 204.9 82.8 281 260.5 106.3 42 38.9 15.7 102 94.6 38.2 162 150.260.7 222 205.8 83.2 282 261.5 105.6 43 39.9 16.1 103 95.5 38.6 163 151.1 61.1 223 206.8 83.5 283 262.4 106. t 44 40.8 16.5 104 96.4 39.0 164 152.1 61.4 224 207.7 83.9 284 263.3 106.4 45 41.7 16.9 105 97.439.3 165 153.0 61.8 225 208.6 84.3 285 264.2 106.8 46 12.7 17.2 106 98.339.7 166 153.9 62.2 226 209.5 84.7 286 265.2 107.1 47 43.6 17.6 107 99.240.1 167 154.8 62.6 227 210.5 85.0 287 266.1 107.5 48 44.5 18.0 108 100.140.5 168 155.862.9 228 211.4 85.4 288 267.0 107.9 49 45.4 18.4 109 101.140.8 169 156.7163.3 229 212.3 85.8 289 268.0 108.3 50 46.4 18.7 110 102.041.2 170 157.6J63.7 230 213.3 86.2 290 268.9 108.6 51 17.3 19.1 111 102.941.6 171 158.5 64.1 231 214.2 86.5 291 269.8 109.0 52 48.2 19.5 112 103.842.0 172 159.5 64.4 232 215.1 86.9 292 270.7 109.4 53 49.1 19.9 113 104.842.3 173 160.4 64.8 233 216.0 87.3 293 271.7 109.8 54 50.1 20.2 114 105.742.7 174 161.3 65.2 234 217.0 87.7 294 272.6 110.1 55 51.0 20.6 115 106.643.1 175 162.3 65.6 235 217.9 88.0 295 273.5 110.5 56 51.9 21.0 116 107.643.5 176 163.2 65.9 236 218.8 88.4 296 274.4 110.9 57 52.8 21.4 117 108.543.8 177 164.1 66.3 237 219.7 88.8 297 275.4 111.3 58 53.8 21.7 118 109.444.2 178 165.066.7 238 220.7 89.2 298 276.3 111.6 59 54.7 22.1 119 110.344.6 179 166.067.1 239 221.6 89.5 299 277.2 112. C 60 55.6 22 5 120 111.3 45.0 180 166.9 67.4 240 222.5 89.9 300 278.2 112.4 Dist. Dep Lat. Dist. Dep. Lat. Dist. Dep. Lat, Dist. Dep. Lat. Dist. Dep. Lat For 08 Degrees. 226 TABLE IV. DIFFERENCE OF LATITUDE AND DEPARTURE FOR 23 DEGREES. Bist. Lat. Dep Dist. Lat. Dep Dist. Lat. Dep Dist. Lat. Dep. Dist. Lat. Dep. 1 00.9 00.4 61 56 2 23.8 121 111.447.3 181 166.6 70.7 241 221.8 94.2 2 01.8 00.8 62 57.1 24.2 122 112.347.7 182 167.5 71.1 242 222.8 94.5 3 )2.8 01.2 63 58.0 24.6 123 113.248.1 183 168.5 71.5 243 223.7 94.9 4 03.7 01.6 64 58.9 25.0 124 114.148.5 184 169.4 71.9 244 224.6 95.3 5 01. 602.0 65 59.8 25.4 125 115.148.8 185 170.3 72.3 245 225.5 95 7 6 05.502.3 66 60.8 25.8 126 116.049.2 186 171 2 72.7 246 226.4 96.1 7 06.402.7 67 61.7 26.2 127 116.9 19.6 187 172.1 73.1 247 227.4 96.5 8 07.403.1 68 62.6 26.6 128 117.8 50.0 188 173.1 73.5 24.8 228 3 96.9 9 08.303.5 69 63.5 27.0 129 118.7 50.4 189 174.0 73.8 249 229.2 97.3 10 09 203.9 70 64.4 27.4 130 119.7 50.8 190 174 9 74.2 250 230.1 97.7 ll' 10.] 04.3 71 65.4 27.7 131 120 6 51/2 191 175.8 74.6 251 231.0 98.1 12 11. 04.7 72 66.3 28.1 132 121.5 51.6 192 176.7 75.0 252 232.0 98.5 13 12.005.1 73 67.2 28.5 133 122.4 52.0 193 177.7 75 4 253 232.9 98 9 14 12.905.5 74 6H.1 28.9 134 123.3")2 4 194 178.6 75.8 254 233.8 99.2 15 13.805.9 75 69.0 29.3 135 124.3 52.7 195 179 5 76.2 255 234 7 99.6 16 14.706.3 70 70.0 29.7 136 125.2 53.1 196 180.4 76.6 256 235.6 100.0 17 15.606.6 77 70 9 30.1 137 126 1 53.5 197 181.3 77 257 236.6 100.4 18 16.607.0 78 71.8 30.5 138 127.0 53.9 198 182.3 77.4 258 237.5 100.8 19 17.5 07.4 79 72.7 30 9 139 128.0 54.3 199 183.2 77.8 259 238.4 101.2 20 18.4 07.8 80 73.6 31.3 140 128.954 7 200 184.1 78.1 260 239.3 101.6 21 19.308/2 81 74.631.6 141 129.855.1 201 185.0 78.5 261 240.3 102.0; 22 20 308 6 82 75.5 32.0 142 130.755.5 202 185.9 78.9 262 241.2 102.4 23 21.209.0 83 76.4 32.4 143 131.655.9 203 186.9 79.3 263 242.1 102-.8 24 22.109.4 84 77.3 32 8 144 132.656.3 204 187.8 79.7 264 243.0 103/2 25 23.0 09.8 85 78.233.2 145 133.556.7 205 188.7 80.1 265 243.9 103.5 26 23.9 10 2 8G 79.2 33.6 146 134 457.0 206 189.6 80.5 266 244.9 103.9 27 24.9 10.5 87 80.1 34.0 147 135.357.4 207 190.5 80.9 267 245.8 104.3 28 25.8 10.9 88 81.0 34.4 148 136.257.8 208 191.5 81.3 268 246.7 104 7 29 26.7 11.3 89 81.9 34.8 149 137.258.2 209 192.4 81.7 269 247.6 105.11 30 27.6 11.7 90 82.8 35.2 150 138.1 58.6 210 193.3 82.1 270 248.5 105.5 31 28.5 12.1 91 83. 835. C 151 139.059.0 '211 194.2 82.4 271 249.5 105.9 32 29.5 12.5 92 84.7 35.9 152 139 959.4 212 195.1 82.8 272 250.4 106.3 33 30.4 12.9 93 85.6 36.3 153 140.859.8 213 196.1 83.2 273 251.3 106.7 34 31.3 13.3 94 86.5 36.7 154 141 860.2 214 197 83.6 274 252.2 107.1 35 32.2 13.7 95 87.4 37.1 155 142.7 60.6 215 197.9 84.0 275 253.1 107.5 3G 33.1 14.1 96 88.4 37.5 156 143.661.0 '216 198.8 84.4 276 254.1 107.8 37 34.1 14.5 97 89.3 37.9 157 144.561 3 217 199.7 84.8 277 255.0 108.2 33 35.0 14.8 98 90.2 38.3 158 145.461.7 218 200.7 85.2 278 255.9 108.6 39 35.9 15.2 99 91.1 38.7 159 146.462.1 21ist. Lat. Dep Dist. Lat. Dep. Dist. Lat. Dep. 1 00.9:00.4 61 55.724.8 121 110.5 49.2 181 165.4 73.6 241 220.2 y8.0 2 01.800.8 62 56.625.2 122 111.5 49.6 182 166.3 74.0 242 221.1 98.4 3 02.7,01.2 63 57.625.6 123 112.4 50.0 183 167.2 74.4 243 222.0 98.8 4 13.701.6 64 58.526.0 124 113.3 50.4 184 168.1 74.8 244 222.9 99.2 5 04.602.0 65 59.426.4 125 114.2 50.8 185 169.0 75.2 245 223.8 99.7 6 15.502.4 6G 60. 326.8 126 115.1 51.1 186 169.9 75.7 246 224.7 100.1 7 16.4 02.8 67 61.227.3 127 116.0 51.7 187 170.8 76.1 247 225.6 100.5 8 07.303.3 68 62.1 27.7 128 116.9 52.1 188 171.7 76.5 248 226.6 100.9 9 08.203.7 69 63.028.1 129 117.8 52.5 189 172.7 76.9 249 227.5 101.3 10 09.1 04.1 70 63.9,28.5 130 118.8 52.9 190 173.6 77.3 250 228.4 101.7 Jl 10.004.5 71 04.9,28.9 131 119.7 53.3 191 174.5 77.7 251 229.3 102.1 12 11. (04. 9 72 65.829.3 132 120.6 53 7 192 175.4 78.1 252 230.2 102.5 13 11.9.05.3 73 6G.7i29.7 133 121.5 54.1 193 176.3 78.5 253 231.1 102.9 14 12.805.7 74 67.630.1 134 122.4 54.5 194 177.2 78.9 254 232.0 103.3 15 13.7 06.1 75 68.530.5 135 123.3 54.9 195 178.1 79.3 255 233.0 103.7 16 14.6 06.5 76 69.430.9 136 124.2 55.3 196 179.1 79.7 256 233.9 104.1 17 15.5 06.9 77 70.331.3 137 125.2 55.7 197 180.0 80.1 257 234.8 104.5 18 1G.4 07.3 78 71.331.7 138 126.1 56.1 198 180.9 80.5 258 235.7 104.9 19 17.4 07.7 79 72.232.1 139 127.0 56.5 199 181.8 80.9 259 236.6 105.3 20 18.308.1 80 73.132.5 140 127.9 56.9 200 182.7 81.3 260 237.5 105.8 21 19. '2 08.5 81 74.032.9 141 128.8 57.3 201 183.6 81.8 261 238.4 106.2 22 20.1 08.9 82 74.933.4 142 129.7 57.8 202 184.5 82.2 262 239.3 106.6 23 21.0 09.4 83 75.833.8 143 130.6 58.2 203 185.4 82.6 263 240.3 107.0 24 21.9 09.8 84 76.734.2 144 131. C 58.6 204 186.4 83.0 264 241.2 107.4 25 22.8 10.2 85 77.734.6 145 132.5 59.0 205 187.3 83.4 265 242.1 107.8 2G 23.8 10.6 86 78.635.0 146 133.4 59.4 206 188.2 83.8 266 243.0 108.2 27 24.7 11.0 87 79.535.4 147 134.3 59.8 207 189.1 84.2 267 243.9 108.6 28 25.6 11.4 88 80.4:35.8 148 135.2 60.2 208 190.0 84.6 268 244.8 109.0 29 26.5 11.8 89 81.336.2 149 136.1 60.6 209 190.9 85.0 269 245.7 109.4 30 27.4 12 . -2 90 82.236.6 150 137.0 61.0 210 191.8 85.4 270 246.7 109.8 31 28. b 12.0 91 83. 137.0 151 137.9 61 4 211 192.8 85.8 271 247.6 110.2 32 29.2 13.0 92 84.037.4 152 138.9 61.8 212 193.7 86.2 272 248.5 110.6 33 30.1 13.4 93 85.037.8 153 139.8 62.2 213 194.6 86.6 273 249.4 111.0 34 31.1 13.8 94 85.938.2 154 140.7 62.6 214 195.5 87.0 274 250.3 111.4 35 32.0 14.2 95 86.8 38.6 155 141. C 63.0 215 196.4 87.4 275 251.2 111.9 3C> 32.9 14.6 9G 87.739.0 156 142.5 63.5 216 197.3 87.9 276 252.1 112.3 37 33.8 15.0 97 88.6|39.5 157 143.4 63.9 217 198.2 88.3 277 253.1 112.7 38 34.7 15.5 98 89.539.9 158 144.3 G4.3 218 199.2 88.7 278 254.0 113.1 39 35.6 15.9 99 90.4 40.3 159 145.3 64.7 219 200.1 89.1 279 254.9 113.5 40 36.5 1G.3 100 91.4 40.7 160 14G.2 65.1 220 201.0 89.5 280 255.8 113.9 41 37.5 16.7 101 92.3 41.1 161 147.1 65.5 221 201.9 89.9 281 256.7 114.3 42 38.4 17.1 102 93.2 41.5 162 148.0 65.9 222 202.8 90.3 282 257.6 114.7 43 39.3 17.5 103 9i.l 41.9 163 148.9 66.3 223 203.7 90.7 283 258.5 115.1 44 40.2 17.9 104 95.0 42.3 164 149.8 66.7 224 204.6 91.1 284 259.4 115.5 45 41.1 18.3 105 95.9 42.7 165 150.7 67.1 225 205.5 91.5 285 260.4 115.9 4G 42.0 18.7 106 96.8 43.1 166 151.6 67.5 226 208.5 91.9 286 261.3 116.3 47 42.9 19.1 107 97.7 43.5 167 152.6 67.9 227 207 4 92.3 287 262.2 116 7 48 43 .9 19.5 108 98.7 43 9 168 153 5 68.3 228 208.3 92.7 288 263.1 117.1 49 44.8 19.9 109 99.6 44.3 169 154.4 68.7 229 209 2 93.1 289 264.0 117.5 50 45 7 20.3 110 100.5 44.7 170 155 3 69.1 230 210.1 93.5 290 264.9 118.0 51 4(3.0 20.7 111 101.4 4571 171 15G.2 Gb. 6 231 211.0 94.0 291 265.8 118.4 52 47.5 21.2 112 102.3 45.6 172 157.1 70.0 232 211.9 94.4 292 266 8 118.8 53 48.4 21.6 113 103.2 46.0 173 158.0 70.4 233 212.9 94.8 293 267.7 119.2 54 49.3 22.0 114 104.1 46.4 174 159.0 70.8 234 213.8 95.2 294 268.6 119.6 55 50.2 22.4 115 105.1 46.8 175 159.9 71.2 235 214.7 95.6 295 269.5 120.0 56 51.2 22.8 116 106.0 47.2 176 160.8 71.6 236 215.6 96.0 296 270.4 120 4 57 52.1 23.2 117 106.9 47.6 177 161.7 72.0 237 216.5 96.4 297 271.3 120 8 53 53.0 23.6 118 107 8 48.0 178 162.6 72.4 238 217.4 96.8 298 272.2 121.2 59 53.9 24.0 119 108 7 48 4 179 163:5 72.8 239 218.3 97.2 299 273.2 121 6 GO 54 8 24.4 120 109.6 48.8 180 164.4 73.2 240 219.3 97.6 300 274.1 122.0 [list. Dep Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat, Dist. Den Lat, For GG Degrees. 228 TABLE IV. DIFFERENCE OF LATITUDE AND DEPARTURE FOR 25 DEGREES. Dist, Lat. Dep Dist, Lat. Dep Dist. Lat. Dep Dist, Lat. Dep. i Dist, Lat. Dep. l 00.9 10.4 61 55.3 25.8 121 109.751.1 181 164.0 76.5 241 218.4 101.9 2 01.8 00.8 62 56 2 26.2 122 110.651.6 182 164.9 76.9' 242 219.3 102.3 3 02.7 01.3 63 57.1 26.6 123 111.552.0 183 165.9 77.3, 243 220.2 102.7 4 03.6 01.7 64 58.0 27.0 124 112.452.4 184 166.8 77.8 244 221.1 103.1 5 04.5 02.1 65 58.9 27.5 125 113.352.8 185 167.7 78. 2' 245 222.0 103.5 6 05.4 02.5 66 59.8 27.9 126 114.2 53.2 186 168.6 78.6 246 223.0 104 7 06.3 03 67 60.7 28.3 127 115 1 53.7 187 169.5 79.0 247 223.9 104.4 8 07.3 03.4 68 61.6 28.7 128 116.0 54.1 188 170.4 79. 5i 248 224.8 101.8 9 08.2 03.8 69 62 5 29.2 129 116.954.5 189 171.3 79.9 249 225.7 105 2 10 09.1 04.2 70 63.4 29.6 130 117.854.9 190 172.2 80.3, 250 226.6 105.7 11 10.0J4.6 71 64.3 30.0 131 118.7 55.4 191 173.1 80.7 251 227.5 106.1 12 10.905.1 72 65.3 30.4 132 119.6 55.8 192 174.0 81.1; 252 228.4 106 5 13 11.805.5 73 66.2 30 9 133 120.5 56.2 193 174.9 81.6 253 229.3 106.9 14 12.705 9 74 67.1 31.3 134 121.4 56.6 194 175.8 82. 0' 254 230.2 107.3 15 13.606.3 75 68.0 31.7 135 122.4 57.1 195 176.7 82.4 255 231.1 107.8 16 14.5 06.8 76 68.932.1 136 123.3 57.5 196 177.6 82.8 256 232.0 108.2 17 15.4 07.2 77 69.8 32.5 137 124.2 57.9 197 178.5 83.3 257 232 9 103. 6 18 16.307.6 78 70.733.0 138 125.1 58.3 198 179.4 83. 7] 258 233.8 109 4 19 17.2 08.0 79 71.633.4 139 126.0 58.7 199 180.4 84.1 259 234.7 1C9.5 20 18.1 08.5 80 72.533.8 140 126.9 59.2 200 181.3 84. 5 260 235.6 101) 9, '21 19.008.9 81 73.434.2 141 127.8 59.6 201 182.2 84.9, 261 236 . 5 11U.3 22 19.909.3 82 74.334.7 142 128.7 60.0 202 183.1 85. 4 ! 262 237.5 110.7 23 20.809.7 83 75.235.1 143 129.6 60.4 203 184.0 85. 8i 263 238.4 111.1 24 21.810.1 84 76.135.5 144 130.5 60.9 204 184.9 86. 2 1 264 239.3 111.6 25 22.7 10.6 85 77.0 35.9 145 131.4 61.3 205 185.8 86.6 265 240.2 112.0 26 23.611.0 86 77.936.3 146 132.3 G1.7 206 186.7 87. 1 ! 266 241.1 112.4 27 24.511.4 87 78.836.8 147 133.2 62.1 207 187.6 87.5! 267 242.0 112.8: 28 25 4 11.8 88 79.837.2 148 134.1 62.5 208 188.5 87. 9 268 242.9 113.3 29 26.3 12.3 89 80.737.6 149 135.0 63.0 209 189.4 88.3 269 243 8 113.71 30 27. If 12.7 90 81.638.0 150 135.9 63.4 210 190.3 88. 7| 270 244.7 114. Ij 31 28.1 13.1 91 82.538.5 151 136.9 63.8 211 191.2 89. 2 : 271 245.6 114.5 32 29 013.5 92 83.438.9 152 137.8 64.2 212 192.1 89.6 272 246.5 115.0 33 29.913.9 93 84.339.3 153 138.7 64.7 213 193.0 90.0 273 247.4 115.4 34 30.814.4 94 85 239.7 154 139.6 65.1 214 193.9 90.4 274 248.3 115.8 35 31.7 14.8 95 86.1 40.1 155 140.5 65.5 215 194.9 90.9 275 249.2 116.2 36 32.615.2 96 87.040.6 156 141.4 65.9 216 195.8 91.3 276 250.1 116.6 37 33.5 15. i; 97 87.941.0 157 142.3 66.4 217 196.7 91.1 277 251.0 117.1 38 34.4 16.1 98 88.841.4 158 143.2 66.8 218 197.6 92. l' 278 252.0 117.5 39 35.3 16.5 99 89.741.8 159 144.1 67.2 219 198.5 92.6 279 252.9 117.9 40 36.316.9 100 90.642.3 160 145.0 67.6 220 199.4 93.0 280 253.8 118.3 41 37. '217. 3 10J 91.542.7 161 145.9 68.0 221 200.3 93.4 281 254.7 118.8, 42 38.1 17.7 102 92.443.1 162 146.868.5 222 201.2 93. 8 1 282 255.6 119.21 43 39.0 IS. '2 103 93.343.5 163 147.768.9 223 202.1 94.2' 283 256.5 119.6 44 39.918.6 104 94.344.0 164 148.669.3 224 203.0 94.7 284 257.4 120.0 45 40. 819.0 105 95.244.4 165 149.569.7 225 203.9 95.1 285 258.3 120.4 43 41.7 19.4 106 96.1 44.8 166 150.4 70.2 228 204.8 95.5 286 259.2 120.9 47 42.6 19.9 107 97.045.2 167 151.4 70 6 227 205.7 95.9 287 260.1 121.3 48 43.5 20.3 108 97.945.6 168 152.3 71.0 228 206.6 96.4 288 261.0 121.7 49 44.420.7 109 98.846.1 169 153.2 71.4 229 207.5 96.8; 289 261.9 122.1 50 45 321.1 110 99.746.5 170 154.1 71.8 230 208.5 97.2 290 262.8 122.6 51 46.221.6 111 100.646.9 171 155.0 72.3 231 209.4 97.6 291 263.7 123.0 52 47.1 22.0 112 101.547.3 172 155.9 72.7 232 210.3 98.0 292 264.6 123.4 53 48.0 22.4 113 102.447.8 173 156.8 73.1 233 211.2 98.5; 293 265.5 123.8 54 48.922.8 114 103.348.2 174 157.7 73.5 234 212.1 98.9 .294 266.5 124.2 55 49.823.2 115 104.248.6 175 158.6 74.0 235 213.0 99.3 295 267.4 124.7 56 50.823.7 116 105.1 49.0 176 159.5 74.4 236 213.9 99.7 296 268.3 125.1 57 51.724.1 117 106.049.4 177 160.4 74.8 237 214.8 100.2 297 269.2 125.5 53 52.6 24.5 118 106.949 9 178 161.3 75.2 238 215.7 100.6 298 270.1 125.9 59 53.5 24.9 119 107.950.3 179 162.2 75.6 239 216.6 101.0 299 271.0 126.4 60 54.4 25.4 120 108.8 50.7 180 163.1 76.1 240 217.5 101.4 , , ' 300 271.9 126.8 Dist. Dep Lat. 'Dist. Dep. Lat. Dist. Dep." Lat, Dist. Dep. Lat. iDist, Dep. Lat, For 65 Degrees. TABLE IV. 229 DIFFERENCE OF LATITUDE ASD DEPARTURE FOR 26 DEGREES. [list. Lat. Dep Dist. Lat. Dep Dist, Lat. Dep Dist. Lat. Dep. Dist. Lat. Dep. 1 30.9 00.4 61 54.8 26.7 121 108.8 53.0 181 162.7 79.3 241 216. G 105.6 2 01.8 00.9 62 55.7 27.2 122 109.7 53.5 182 163.6 79.8 242 217.5 106.1 3 02.7 01.3 63 56.0 27.6 123 110. G 53.9 183 164.5 80.2 243 218.4 106.5 4 03. G 01.8 64 57.5 28.1 124 111.5 54.4 184 165.4 80.7 244 219.3 107.0 5 04.5 02.2 65 58.4 28.5 125 112.3 54.8 185 166.3 81.1 245 220.2 107.4 6 05.4 02.6 66 59.3 28.9 126 113.2 55.2 186 167.2 81.5 246 221.1 107.8 7 03.3 03.1 67 60.2 29 4 127 114.1 55.7 187 168.1 82.0 247 222.0 108.3 8 07.2 03.5 68 61.1 29.8 128 115.0 56.1 188 169.0 82.4 248 222.9 108.7 9 08.1 03.9 G9 62.0 30.2 129 115.9 56.5 189 169.9 82.9 249 223.8 109.2 10 09.0 04.4 70 62.9 30.7 130 116.8 57.0 190 170.8 83.3 250 224.7 109 6 11 09 9 04.8 71 G3.6 31. Ill 131 117.7 37.4 191 171 7 83.7 251 225.6 110.0 12 10.8 05.3 72 64.7 31. G 132 118.6 57.9 192 172.6 84.2 252 226.5 110.5 13 11.7 05.7 73 65.6 32.0 133 119. C 58.3 193 173.5 84.6 253 227.4 110.9 14 12.0 06.1 74 66.5 32.4 134 120.4 58.7 194 174.4 85 254 228.3 111.3 15 13.5 06.6 75 67.4 32.9 135 121.3 59.2 195 175.3 85.5 255 229.2 111.8 1C 14.4 07.0 76 68 3 33.3 136 122.2 59.6 196 176.2 85.9 256 230.1 112.2 17 15 3 07.5 77 69.2 33.8 137 123.1 60.1 197 177.1 86.4 257 231.0 112.7 18 16.2 07.9 78 70.1 34.2 138 124 60.5 198 178.0 86.8 258 231.9 113.1 19 17 1 08.3 79 71.0 34. G 139 124.9 60 9 199 178.9 87.2 259 232.8 113.5 20 18.0 08.8 80 71.9 35.1 140 125.8 61.4 200 179.8 87.7 260 233.7 114.0 21 18.9 09.2 81 72.6 35.5 141 126.7 61.8 201 180.7 88.1 261 234.6 114.4 22 19 8 09 G 82 73.7 35.9 142 127.6 62.2 202 181.6 88.6 262 235.5 114.9 23 20.7 10.1 83 74.6 36.4 143 128.5 62.7 203 182.5 89.0 263 236.4 115.3 24 21. C 10.5 84 75.5 36.8 144 129.4 63.1 204 183.4 89.4 264 237.3 115.7 25 22. C 11.0 85 76.4 37.3 145 130.3 63.6 205 184.3 89.9 265 238.2 116.2 26 13.4 11.4 86 77.3 37.7 146 131.2 64.0 206 185.2 90.3 266 239.1 116.6 27 24.3 11.8 87 78.2 38.1 147 132.1 64.4 207 186.1 90.7 267 240.0 117.0 28 25.2 12.3 88 79.1 38.6 148 133.0 64.9 208 186.9 91.2 268 240.9 117 5 29 :e.i 12.7 89 80.0 39.0 149 133.9 65.3 209 187.8 91.6 269 241.8 117.9 30 27.0 13.2 90 80.9 39 5 150 134.8 65.8 210 188.7 92.1 270 242.7 118.4 31 27.9 13.6 91 81.8 39.9 151 135.7 66.2 211 189.6 92.5 271 243.6 118.8 32 28.8 14.0 92 82.7 40.3 152 136.6 66.6 212 190.5 92.9 272 244.5 119.2 3:3 :9.7 14.5 93 83. C 40.8 153 137.5 67.1 213 191.4 93.4 273 245.4 119.7 34 30.0 14.9 94 84.5 41.2 154 138.4 67.5 214 192.3 93.8 274 246.3 120.1 35 31.5 15.3 95 85.4 41. C 155 139.3 67.9 215 193.2 94.2 275 247.2 120.6 36 32.4 15.8 96 86.3 42.1 150 140.2 68 4 216 194.1 94.7 276 248.1 121.0 37 33.3 16.2 97 . 87.2 42.5 157 1 11 . 1 (?O O DO.O 217 195.0 95.1 277 249.0 121.4 33 34.2 16.7 98 88.1 43. C 158 142.0 69.3 218 195. 9 95.6 278 249.9 121.9 39 35.1 17.1 99 89.0 43.4 159 142.9 69.7 219 196.8 96.0 279 250.8 122.3 40 36 17.5 100 89.9 43.8 1GO 143.8 70.1 220 197.7 96.4 280 251.7 122.7 TT 30. t> 18.0 101 90. b 44.3 1G1 144.7 71. (5 221 198. G 96.9 281 252.6 123.2 42 37.7 18 4 102 91.7 44.7 162 145.6 71.0 222 199.5 97.3 282 253.5 123.6 43 33. C 18.8 103 92.6 45.2 163 146.5 71.5 223 200.4 97.8 283 254.4 124.1 44 39.5 19.3 104 93.5 45. G 1G4 147.4 71.9 224 201.3 98.2 284 255.3 124.5 45 iO.4 19.7 105 94.4 46.0 165 148.3 72.3 225 202.2 98 G 285 256.2 124.9 46 41.3 20.2 100 95.3 46.5 1GG 149.2 72.8 226 203.1 99.1 286 257.1 125.4 47 42.2 20.6 107 96.2 46.9 167 150.1 73.2 227 204.0 99.5 287 258.0 125.8 48 13.1 21.0 108 97.1 47.3 168 151.0 73 6 228 204.9 99.9 288 258.9 126.3 49 44.0 21.5 109 93.0 47.8 169 151.9 74.1 229 205.8 100.4 289 259.8 126.7 50 44.9 21.9 110 93.9 48.2 170 152.8 74 5 230 206.7 100.8 290 260.7 127.1 51 45.8 22.4 111 99.8 48.7 171 153.7 75.0 231 207. G 101.3 291 2G1.5 127.6 52 46.7 22.8 112 100.7 49.1 172 154.6 75.4 232 208.5 101.7 292 262.4 128.0 53 47. C 23.2 113 101. G 49.5 173 155.5 75.8 233 209.4 102.1 293 263.3 128.4 61 48.5 23.7 114 102.5 50.0 174 156.4 76.3 234 210.3 102.6 294 264.2 128.9 55 19.4 24 1 115 103.4 50.4 175 157.3 76.7 235 211.2 103.0 295 265.1 129.3 56 50.3 24.5 116 104.3 50.9 176 158.277.2 236 212.1 103.5 296 266.0 129.8 57 31 2 25.0 117 105.2 51.3 177 159.1 77.6 237 213.0 103.9 297 266.9 130.2 58 52.1 25.4 118 10G.1 51.7 178 160. 78.0 238 213.9 104.3 298 267.8 130. G 59 53.0 25.9 119 107.0 52.2 179 1G0.9 78.5 239 214.8 104.8 299 268.7 131.1 GO 53.9 26.3 120 107.9 52. G 180 1G1.8 78.9 240 215.7 105.2 300 269.6 131.5 list, Dep Lat. Dist. Dep. Lat, Dist. Dep. LatJDist. Dep. Lat. Dist. Dep. Liit. For 64 Degrees. 230 TABLE IV. DIFFERENCE OF LATITUDE AND DEPARTURE FOR 27 DEGREES. [list. Lat. Dep Hist. Lat. Dep Dist. Lat. Dep Dist. Lat. Dep. Dist. Lat. Dep. 1 00.9 00.5 61 54.4 27.7 121 107.8 54.9 181 161.3 82.2 241 214.7 109.4 2 01.8 00.9 62 55.2 28.1 122 108.755.4 182 162.2 82.6 242 215. C 109.9 3 02.7 01.4 63 56 1 28.6 123 109.655.8 183 163.] 83.1 243 216.5 110.3 4 03.6 01.8 64 57.029.1 124 110.556 3 184 163.9 83.5 244 217.4 110.8 5 04.5 02.3 65 57.9 29.5 125 111.456.7 185 164.8 84.0 245 218.3 111.2 6 05.3 02.7 66 58.8 30.0 126 112.357.2 186 165.7 84.4 24G 219.2 111.7 7 )6.2 03.2 67 59.7 30.4 127 113.257.7 187 166.6 84.9 247 220.1 112.1 8 07.1 03.6 68 60.6 30.9 128 114.058.1 188 167.5 85.4 248 221.0 112.6 9 08 04.1 69 61.5 31.3 129 114.958.6 189 168.4 85.8 249 221.9 113.0 10 08.9 04.5 70 62.431.8 130 115.859.0 190 169.3 86.3 250 222.8 113.5 11 09.8 05.0 71 63.3 32.2 131 116.759.5 191 170.2 86.7 251 223.6 114.0 12 10.7 05.4 72 64.2 32.7 132 117.659.9 192 171.1 87.2 252 224.5 114.4 13 11 6 05.9 73 65.0 33.1 133 118.560.4 193 172.0 87.6 253 225.4 114.9 14 12.5 06.4 74 65.9 33.6 134 119.460.8 194 172.9 88 1 254 226.3 115.3 15 13.4 06.8 75 66.8 34.0 135 120.3 61.3 195 173.7 88.5 255 227.2 115.8 16 14.3 07.3 76 67.7 34.5 136 121.2 61.7 196 174.6 89.0 256 228.1 116.2 17 15.1 J7.7 77 68.6 35.0 137 122.162.2 19? 175.5 89.4 257 229.0 116.7 18 16.0 08.2 78 69.5 35.4 138 123.062.7 198 176.4 89.9 258 229.9 117. 1 ! 19 16.9 08. 6 79 70 4 35.9 139 123.863.1 199 177.3 90.3 259 230.8 117.6 20 17.8 09.1 80 71 3 36.3 140 124.763.6 200 178.2 90.8 260 231.7 118.0 21 18.7 09.5 81 72.2 36.8 14i 125. U 64.0 201 179.1 91.3 26 1 232.6 118.51 22 19.6 10.0 82 73.1 37.2 142 126.564.5 202 180.0 91.7 262 233.4 118.9 23 20.5 10.4 83 74.0 37.7 143 127.464.9 203 180.9 92.2 263 234.3 119.4 24 21.4 10.9 84 74.8 38.1 144 128.3 65.4 204 181.8 92.6 264 235.2 119.9 25 22.3 11.3 85 75.7 38.6 145 129.2 65.8 205 182.7 93.1 265 236.1 120.3 2G 23.2 11.8 86 76.6 39.0 146 130 1 66.3 206 183.5 93.5 266 237.0 120.8 27 24.1 12.3 87 77.5 J9.5 147 131.066.7 207 184.4 94.0 267 237.9 121.2 28 24 C 12.7 88 78.4 40.0 148 131.967.2 208 185.3 94.4 268 238.8 121.7 29 25.8 13.2 89 79.3 40.4 149 132.867.6 209 186.2 94.9 269 239.7 122.1 30 26.7 13.6 90 80.2 40.9 150 133.7|G8.1 210 187.1 95.3 270 240. G 122.6 31 27. G 14.1 91 81.1 41.3 151 134.568.6 211 188.0 95.8 271 241.5 123.0 32 28.5 14.5 92 82.0 41.8 152 135.469.0 212 188.9 96.2 272 242.4 123.5 33 .9.4 15.0 93 82.9 42.2 153 136.369.5 213 189.8 96.7 273 243.2 123.9 3i 30.3 15.4 91 83.8 42.7 154 137.269.9 214 190 7 97.2 274 244.1 124.4 35 31.2 15.9 95 84.6 43.1 155 138.1 70.4 215 191 6 97.6 275 245.0 124.8 36 32.1 16.3 96 85.5 43.6 156 133.070.8 216 192.5 98.1 276 245.9 125.3 37 33.0 16.8 97 86.4 44.0 157 139.971.3 217 193.3 98.5 277 246.8 125.8 38 33.0 17.3 98 87.3 44.5 158 140.871.7 218 194.2 99.0 278 247.7 126.2 39 34.7 17.7 99 88.2 44.9 159 141.7 72.2 219 195.1 99.4 279 248.6 12G.7 40 35.6 18.2 100 89.1 45.4 160 142.6 72.6 220 196.0 99.9 280 249.5 127.1 41 3(3.5 18.6 101 90.0 45.9 161 143.5 73 J 221 196 9 100.3 281 250.4 127.6 42 37.4 19.1 102 90.9 46.3 162 144.3 73.5 222 197.8 100.8 282 251.3 128.0 43 38.3 19.5 103 91.8 46 8 163 145.2 74.0 223 198.7 101.2 283 252.2 128.5 44 39.2 20.0 104 92 7 47.2 164 146 1 74.5 224 199.6 101.7 284 253.0 128.9 45 40.1 20.4 105 93.6 47.7 165 147.074.9 225 200.5 102.1 285 253.9 129.4 46 41.0 20.9 106 94.448 1 166 147 9 75.4 226 201.4 102.6 286 254.8 129.8 47 41.9 21.3 107 95.348.6 167 148.8 75.8 227 202.3 103.1 287 255.7 130.3 48 42. b 21.8 108 96.2 49.0 168 149.7 76.3 228 203.1 103.5 288 256.6 130.7 49 43.7 22.2 109 97.1 49.5 169 150.676.7 229 204.0 104.0 289 257.5 131.2 50 14.6 22.7 110 98.0 49.9 170 151.5 77. 230 204.9 104.4 290 258.4 131.7 51 45.4 23.2 111 93.9 50.4 171 152.4 77.6 231 205.8 104.9 291 259.3 132.1 52 46.3 23.6 112 99.8 50.8 172 153.378.1 232 206.7 105.3 292 260.2 132.6 53 47.2 24.1 113 100.7 51.3 173 154.1 78.5 233 207.6 105.8 293 261.1 133.0 54 48.1 24.5 114 101.6 51.8 174 155.079.0 234 208.5 106.2 294 262.0 133.5 55 49.0 25.0 115 102.5 52.2 175 155.979.4 235 209.4 106.7 295 262.8 133.9 56 49.9 25.4 116 103.4 52.7 176 156.879.9 236 210.3 107.1 296 263.7 134.4 57 50.8 25.9 117 104.253.1 )77 157.780.4 237 211.2 107.6 297 264.6 134.8 58 51.7 26.3 118 105.153.6 178 158.680.8 238 212.1 108.0 298 265.5 135.3' 59 52.6 26.8 119 106.054.0 179 159.581.3 239 213.0 108.5 299 266.4 135.7 60 53.5 27.2 120 106.9 54.5 180 160.4 81.7 240 213.8 109.0 300 267.3 136.2 Hist. Dcp Lat. Dist. Den. Lat. Dist. Dep. Lat, Dist. Dep. Lat. Dist. Dep. Lat. For 63 Degrees. TABLE IV. 231 DIFFERENCE OF LATITUDE AND DEPARTURE FOR 28 DEGREES. DistJLat. Dep Dist. Lat. Dep Dist. Lat. Dep Dist. Lat. Dep. Dist. Lat. Dep. 1 00.9 00.5 61 53.9 28.6 121 106.8 56.8 181 159.8 85.0 241 212.8 113.1 2 01.8 00.9 62 54.729.1 122 107.7 57.3 182 160.7 85.4 242 213.7 113.6 3 02. G 01.4 63 55.629.6 123 108.6 57.7 183 161.6 85.9 243 214.6 114.1 4 03.5 01.9 64 56.530.0 124 109.5 58.2 184 162.5 86.4 244 215.4 114.6 5 04.4 02.3 65 57.430.5 125 110.4 58.7 185 163.3 86.9 245 216.3 115.0 6 05.3 02.8 66 58.331.0 126 111.3 59.2 186 164.2 87.3 246 217.2 115.5 7 06.2 03.3 67 59.231.5 127 112.1 59. G 187 165.1 87.8 247 218.1 116.0 8 07.1 03.8 68 60.031.9 128 113.0 60.1 388 166.0 88.3 248 219.0 116.4 9 07.9 04.2 69 60.932.4 129 113.9 60.6 189 166.9 88.7 249 219.9 116.9 10 08.8 04.7 70 61.832.9 130 114.8 61.0 190 167.8 89.2 250 220.7 117.4 11 09.7 05.2 71 62.733.3 131 115.7 61.5 191 168.6 89.7 251 221.G 117.9 12 10. G 05. G 72 63.633.8 132 116.5 62.0 192 169.5 90.1 252 222.5 118.3 13 11.5 06.1 73 64.534.3 133 117 4 62.4 193 170.4 90.6 253 223.4 118.8 14 12 4 06.6 74 65.334.7 134 118.3 62.9 194 171 3 91.1 254 224.3 119.2 15 13.2 07.0 75 66.235.2 135 119.2 G3.4 195 172.2 91.5 255 225.2 119.7 1G 14.1 07.5 76 67.135.7, 136 120.1 63.8 196 173.1 92.0 256 226.0 120.2 17 15.0 08.0 77 63.036.1 137 121.0 64.3 197 173.9 92.5 257 226.9 120.7 18 15.9 08. 5 78 68.936.6 138 121.8 64.8 198 174.8 93.0 258 227.8 121.1 19 1G.8 08.9 79 69.837.1 139 122.7 65.3 199 175.7 93.4 259 228.7 121.6 20 17.7 09.4 80 70.637.6 140 123.6 G5.7 200 176.6 93.9 2GO 229. G 122.1 21 J'8.5 09.9 81 71.538.0 141 124.5 GG.2 201 177.5 94.4 261 230.4 122.5 22 19.4 10.3 82 72.438.5 142 125.4 CG 7 202 178.4 94.8 262 231.3 123.0 23 20.3 10.8 83 73.339.0 143 126.3 (37.1 203 179.2 95.3 263 232.2 123.5 24 21.2 11.3 84 74.2 39.4 144 127.1 67.6 204 180.1 95.8 264 233.1 123.9 25 22.1 11.7 85 75.1 39.9 145 128.0 68.1 205 181.0 96 2 265 234.0 124.4 26 23.0 12.2 86 75.9 40.4 14G 128.9 68.5 206 181.9 96.7 266 234.9 124.9 27 23.8 12.7 87 76.8 40.8; 147 129.8 69.0 207 182.8 97.2 267 235 .7 125.3 28 21.7 13.1 88 77.7 41.3 148 130.7 69.5 208 183.7 97.7 268 236.6 125.8' 29 25. G 13.6 89 78.6 41.8 149 131.6 70.0 209 184.5 98.1 269 237.5 126.3 30 2G.5 14.1 90 79.542.3i 150 132.470.4 210 185.4 98.6 270 238.4 126.8 31 27.4 14.6 91 80.3 42.7 151 133.3 70.9 211 18G.3 99.1 27J 239.3 127.2 32 28.3 15.0 92 81.2 43.2 152 134.2 71.4 212 187.2 99.5 272 240.2 127.7 33 29.1 15.5 93 82.1 43.7 153 135.1 71.8 213 188.1 100.0 273 241.0 128.2 34 30.0 16.0 94 83.0 44.1 154 136.0 72.3 214 189.0 100.5 274 241.9 128.6 35 30.9 16.4 95 83.944.6! 155 136.9 72 8 215 189.8 100.9 275 242.8 129.1 36 31.8 16.9 96 84.845.1 156 137.7 73.2 216 190.7 101.4 276 243.7 129. G 37 32.7 17.4 97 85.645.5 157 138. G 73.7 217 191.6 101.9 277 244.6 130.0 38 33.6 17.8 98 86.546.0 158 139.5 74.21 218 192.5 102.3 278 245.5 130.5 39 34.4 18.3 99 87.446.5 159 140.4 74.6 219 193.4 102.8 279 246.3 131 40 3>.3 18.8 100 88.346.9 160 111.375.1 220 194.2 103.3 280 247.2 131.5 41 36.2 19.fc 101 69.247.4 101 142. 2 75. G 221 195.1 103.8 281 248.1 131.9 42 .i7.1 19.7 102 90.147.9 162 143.0 76.1 222 196.0 104.2 282 249.0 132.4 43 38.0 20.2 103 90.948.4 1G3 143.9 76.5 223 196.9 104.7 283 249.9 132.9 44 33.8 20.7 104 91.848.8 1G4 144.8 77.0 224 197.8 105.2 284 250.8 133.3 45 39.7 21.1 105 92.749.3 165 145.7 77.5 225 198.7 105.6 285 251. G 133.8 4G 40.6 21 .-G 106 93.G49.8 166 146.6 77.9 226 199.5 106.1 286 252.5 134.3 47 41.6 22.1 107 94.550.2 167 147.5 78.4 227 200.4 10G.6 287 253.4 134.7 48 42.4 22.5 108 95.4 50.7 168 148.3 78.9 228 201.3 107.0 288 254.3 135.2 49 43.3 23.0 109 96.251.2 169 149.2 79.3 229 202.2 107.5 289 255.2 135.7 50 44.1 23.5 110 97.1 51.6 170 150.1 79.8 230 203.1 108.0 290 256.1 136.1 51 15. U 23.9 111 98.052.1 171 151.0 80.3 231 204.0 1U8.4 291 256.9 13G.G 52 45.9 24.4 112 98.9 52. C 172 151.9 80.7 232 204.8 108.9 292 257.8 137.1 53 46.8 24.9 113 99.8 53.1 173 152.7 HI. 2 233 205.7 109.4 293 258.7 137.6 54 47.7 25.4 114 100.7 53.5 174 153.6 81.7 234 206.6 109.9 294 259.6 138.0 55 48.6 25.8 115 .101.5 54.0 175 154.5 82.2 235 207.5 110.3 295 260.5 138.5 5G 19.4 26.3 11G 102.4 54.6 176 155.4 82.6 236 208.4 110.8 296 261.3 139.0 57 50.3 26.8 117 103.3 54.9 177 156.3 83.1 237 209.3 111.3 297 262.2 139.4 58 51.2 27.2 118 104.2 55.4 178 157.2 83.6 238 210.1 111.7 298 263.1 139.9 59 52.1 27.7 119 105.1 55.9 179 158.0 84.0 239 211.0 112.2 299 264.0 140.4 GO 53.0 28.2 120 106.0 56.3 180 158.9 84.5 240 211.9 112.7 300 264.9 140.8 Dixt. Dep Lat. Dist. Dep. Lat. Dist. Dep. l.at. Dist. Dep. Lat. Dist. Dep. Lat. For G2 Degrees. 232 TABLE IV. DIFFERENCE OF LATITUDE AND DEPARTURE FOR 29 DEGREES. Dist, Lat. Dep Dist. Lat. Dep Dist. Lat. Dep Dist. Lat Dep. Dist. Lat. Dep. 1 00.9 00.5 61 53.4 29.6 121 105.8 58.7 181 158.3 87.8 241 210.8 116.8 2 01.7 01.0 62 54.2 30.1 122 106.7 59.1 182 159.2 88.2 242 211.7 117.3 3 02.6 01.5 63 55.1 30.5 123 107.6 59.6 183 160.1 88.7 243 212.5 117.8 4 03.5 01.9 64 56.0 31.0 124 108.5 60.1 184 160.9 89.2 244 213.4 118.3 5 01.4 02.4 65 56.9 31.5 125 109.3 60.6 185 161.8 89.7 245 214.3 118 8 6 05.2 02.9 66 57.7 32.0 126 110.2 61.1 186 162.7 90.2 246 2l5.L> 119.3 7 06.1 03.4 67 58.6 32.5 127 111.1 61.6 187 163.6 90.7 247 216.0 119.7 8 07.0 03.9 68 59.5 33.0 128 112.0 62.1 188 164.4 91.1 248 216.9 120.2 9 07.9 04.4 69 60.3 33.5 129 112.8 62.5 189 165.3 91.6 249 217.8 120.7 10 08.7 04.8 70 61.2 33.9 130 113.7 63.0 190 166.2 92.1 250 218.7 121.2 11 09.6 05.3 71 62.1 34.4 131 114 6 63.5 191 167.1 92.6 251 219.5 121.7 W 10.5 05.8 72 63.0 34.9 132 115.4 64.0 192 167.9 93.1 252 220.4 122.2 13 11.4 06.3 73 63.8 35.4 133 116.3 64.5 193 168.8 93.6 253 221.3 122.7 14 12.2 06.8 74 64.7 35.9 134 117.2 65.0 194 169.7 94.1 254 222.2 123J 15 13.1 07.3 75 65.6 36.4 135 118.1 65.4 195 170.6 94.5 255 223 123.6 16 14.0 07.8 76 66.5 36.8 136 118.9 65.9 196 171.4 95.0 256 223.9 124.1 17 14.9 08.2 77 67.3 37.3 137 119.8 66.4 197 172.3 95.5 257 224.8 124.6 18 15.7 08.7 78 68.2 37.8 138 120.7 66.9 198 173.2 96.0 258 225.7 125.1 19 16.6 09.2 79 69.1 38.3 139 121.6 67.4 199 174.0 96.5 259 226.5 125 6 20 17.5 09.7 80 70.0 38.8 140 122.4 67.9 200 174.9 97.0 260 227.4 126.1 21 18.4 10.2 81 70.8 39.3 141 123.3 68.4 201 175.8 97.4 261 228.3 126.5 22 19 2 10.7 82 71.7 39.8 142 124.2 68.8 202 176.7 97.9 262 229.2 127.0 23 20.1 11.2 83 72.6 40.2 143 125.1 69.3 203 177.5 98.4 263 230.0 127.5 24 21.0 11.6 84 73.5 40.7 144 125.9 69.8 204 178.4 98.9 264 230.9 128.0 25 21.9 12.1 85 74.3 41.2 145 126.8 70.3 205 179.3 99.4 265 231.8 128.5 26 22.7 12.6 86 75.2 41.7 146 127.7 70.8 206 180.2 99.9 266 232.6 129.0 27 23.6 13.1 87 76.1 42.2 147 128.6 71.3 207 181.0 100.4 267 233.5 129.4 28 24.5 13.6 88 77.0 42.7 148 129.4 71.8 208 181.9 100.8 268 234.4 129 9 29 25.4 14.1 89 77.8 43.1 149 130.3 72.2 209 182.8 101.3 269 235.3 130.4 30 26.2 14.5 90 78.7 43.6 150 131.2 72.7 210 183.7 101.8 270 236.1 130.9 31 27.1 15.0 91 79.6 44.1 151 132.1 73.2 211 184.5 102.3 271 237.0 131.4 32 28.0 15.5 92 80.5 44.6 152 132.9 73.7 212 185.4 102.8 272 237.9 131.9 33 28.9 16.0 93 81.3 45.1 153 133.8 74.2 213 186.3 103.3 273 238.8 132 4 34 29.7 16.5 94 82.2 45.6 154 134.7 74.7 214 187.2 103.7 274 239.6 132.8 35 30.6 17.0 95 83.1 46.1 155 135.6 75.1 215 188.0 104.2 275 240.5 133.3 36 31.5 17.5 96 84.0 46.5 156 136.4 75.6 216 188.9 104.7 276 241.4 133.8 37 32.4 17.9 97 84.8 47.0 157 137.3 76 1 217 189.8 105.2 277 242.3 134 3 38 33.2 18.4 98 85.7 47.5 158 138.2 76.6 218 190.7 105.7 278 243.1 134.8 39 34.1 18.9 99 86.6 48.0 159 139.1 77.1 219 191.5 106.2 279 244.0 135.3 40 35.0 19.4 100 87.5 48.5 160 139.9 77.6 220 192.4 106.7 280 244.9 135.7 41 35.9 19.9 101 88.3 49.0 161 140.8 78.1 221 193.3 107.1 281 245.8 136.2 42 36.7 20.4 102 89.2 49.5 162 141.7 78.5 222 194.2 107.6 282 246.6 136.7 43 37.6 20 8 103 90.1 49.9 163 142.6 79.0 223 195.0 108.1 283 247.5 137.2 44 38.5 21.3 104 91.0 50.4 164 143.4 79.5 224 195.9 108.5 284 248.4 137.7 45 39.4 21.8 105 91.8 50.9 165 144.3 80.0 225 196.8 109.1 285 249.3 138.2 40 40.2 22.3 106 92.7 51.4 166 145.2 80 5 226 197.7 109.6 286 250.1 138.7 47 41.1 22.8 107 93.6 51.9 167 146 1 81.0 227 198.5 110.1 287 251.0 139.1 48 42.0 23.3 108 94.5 52.4 168 146.9 81.4 228 199.4 110.5 288 251.9 139.6 49 42.9 23.8 109 95.3 52.8 169 147.8 81.9 229 200.3 111.0 289 252.8 140.1 50 13.7 24.2 110 96.2 53.3 170 148.7 82.4 230 201.2 111.5 290 253.6 140 6 51 44.6 24 7 111 97.1 53.8 171 149.6 82.9 231 202.0 112.0 291 254 5 141.1 52 45.5 25.2 112 98.0 54.3 172 150.4 83.4 232 202.9 112.5 292 255 4 141.6 53 16.4 25.7 113 98.8 54.8 173 151.3 83.9 233 203.8 113.0 293 256.3 142.0 54 47.2 26.2 114 99.7 55.3 174 152.2 84.4 234 204.7 113.4 294 257.1 142.5 55 48.1 26.7 115 100.6 55.8 175 153.1 84.8 235 205.5 113.9 295 258 143.0 56 49.0 27.1 116 101.5 56.2 176 153.9 85.3 236 206.4 114.4 296 258.9 143 5 57 49.927.6 117 102.3 56.7 177 154.8 85.8 237 207.3 114.9 297 259.8 144 58 50.7 28.1 118 103 2 57.2 178 155.7 86.3 238 208.2 115.4 298 260 6 144.5 59 51.6 28.6 119 104 1 57 7 179 156.6 86.8 239 209.0 115.9 299 261.5 145 60 52.5 29 1 120 105.0 58.2 180 157.4 87.3 240 209.9 116.4 300 262.4 145.4 Dist. Dep Lat. Hist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist, Dep. Lat. For 61 Degrees. TABLE IV. 233 DIFFERENCE OF LATITUDE AXD DEPARTURE FOR 30 DEGREES. Dist, Lat. Dep Dist. Lat. Dep Dist. Lat. Dep Dist. Lat. Dep. Dist. Lat. Dep. 1 00. S 00.5 61 52.8 30.5 121 104.8 60.5 181 156.8 90.5 241 208.7 120.5 2 01.7 01. C 62 53.7 31.0 122 105.7 61.0 182 157.6 91.0 242 209.6 121.0 3 02.6 01.5 63 54.6 31.5 123 106.5 61.5 183 158.5 91.5 243 210.4 121.5 4 03.5 02.0 64 55.4 :^2.0 124 107.4 62.0 184 159.3 92.0 244 211.3 122.0 5 04.3 02.5 65 56.3 32.5 125 108.3 62.5 185 160.2 92.5 245 212.2 122.5 6 05.2 03.0 66 57.2 33.0 126 109.1 63.0 186 161.1 93.0 246 213.0 123.0 7 06.1 03.5 67 58.0 33.5 127 110.0 63.5 187 161.9 93.5 247 213.9 123.5 8 06.9 04.0 68 58.9 34.0 128 110.9 64.0 188 162.8 94.0 248 214.8 124.0 9 07.8 04.5 69 59.8 34.5 129 111.7 64.5 189 163.7 94.5 249 215.6 124.5 10 08.7 05.0 70 60.6 35.0 130 112.6 65.0 190 164.5 95.0 250 216.5 125.0 11 09.5 05.5 71 61.5 35.5 131 113.4 65. 5 191 165.4 95.5 251 217.4 125.5 12 10.4 06.0 72 62.4 36.0 132 114.3 66 192 166.3 96.0 252 218.2 126.0 13 11.3 06.5 73 63.2 36.5 133 115.2 66.5 193 167.1 96.5 253 219.1 126.5 14 12.1 07.0 74 64.1 37.0 134 116.0 67.0 194 168.0 97.0 254 220.0 127.0 15 13.0 07.5 75 65.0 37.5 135 116.9 67.5 195 168.9 97.5 255 220.8 127.5 16 13.9 08.0 76 65.8 38.0 136 117.8 G8.0 196 169.7 98.0 256 221.7 1-28.0 17 14.7 08.5 77 66.7 38.5 137 118.6 68.5 197 170.6 98.5 257 222.6 128.5 18 15.6 09.0 78 67.5 39.0 138 119.5 69.0 198 171.5 99.0 258 223.4 129.0 19 16.5 09.5 79 68.4 39.5 139 120.4 69.5 199 172.3 99.5 259 224.3 129.5 20 17.3 10.0 80 69.3 40.0 140 121.2 70.0 200 173.2 100.0 260 225.2 130.0 21 18. '2 10.5 81 70.1 40.5 141 122.1 70.5 201 174.1 100.5 261 226.0 130.5 22 19.1 11.0 82 71.0 41.0 142 123.0 71.0 202 174.9 101.0 262 226.9 131.0 23 19.9 11.5 83 71.9 41.5 143 123.8 71.5 203 175.8 101.5 263 227.8 131.5 24 20.8 12.0 84 72.7 42.0 144 124.7 72.0 204 176.7 102.0 264 228.6 132.0 25 21.7 12.5 85 73.6 42.5 145 125.6 72.5 205 177.5 102.5 265 229.5 132.5 26 22.5 13.0 86 74.5 43.0 146 126.4 73.0 206 178.4 103.0 266 230.4 133.0 27 23.4 13.5 87 75.3 43.5 147 127.3 73.5 207 179.3 103.5 267 231.2 133.5 28 24.2 14.0 88 76.2 44.0 148 128.2 74.0 208 180.1 104.0 268 232.1 134.0 29 25.1 14.5 89 77.1 44.5 149 129.0 74.5 209 181.0 104.5 269 233.0 134.5 30 26.0 15.0 90 77.9 45.0 150 129.9 75.0 210 181.9 105.0 270 233.8 135.0 31 26.8 15.5 91 78.8 45.5 151 130.8 75.5 211 182.7 105.5 271 234.7 135.5 32 27.7 16.0 92 79.7 46.0 152 131.6 76.0 212 183.6 106.0 272 235.6 136.0 33 28.6 16.5 93 80.5 46.5 153 132.5 76.5 213 184.5 106.5 273 236.4 136.5 34 29.4 17.0 94 81.4 47.0 154 133.4 77.0 214 185.3 107.0 274 237.3 137.0 35 30.3 17.5 95 82.3 47.5 155 134.2 77.5 215 186.2 107.5 275 238.2 137.5 36 31.2 18.0 96 83.1 48.0 156 135.1 78.0 216 187.1 108.0 276 239.0 138.0 37 32.0 18.5 97 84.0 48.5 157 136.0 78.5 217 187.9 108.5 277 239.9 138.5 38 32.9 19.0 98 84.9 49.0 158 136.8 79.0 218 188.8 109.0 278 240.8 139.0 39 33.8 19.5 99 85.7 49.5 159 137.7 79.5 219 189.7 109.5 279 241.6 139.5 40 34.6 20.0 100 86.6 50.0 160 138.6 80.0 220 190.5 110.0 280 242.5 140.0 41 35.5 20.5 101 87.5 50.5 161 139.4 80.5 221 191.4 110.5 281 243.4 140.5 42 36.4 21.0 102 88.3 51.0 162 140.3 81.0 222 192.3 111.0 282 244.2 141.0 43 37.2 21.5 103 89.2 51.5 163 141.2 81.5 223 193.1 111.5 283 245.1 141.5 44 38.1 22.0 104 90.1 52.0 164 142.0 82.0 224 194.0 112.0 284 246.0 142.0 45 39.0 22.5 105 90.9 52.5 165 142.9 82.5 225 194.9 112.5 285 246.8 142.5 46 39.8 23.0 106 91.8 53.0 166 143.8 83.0 22G 195.7 113.0 286 247.7 143.0 47 40.7 23.5 107 92.7 53.5 167 144.6 83.5 227 196 6 113.5 287 248.5 143 5 48 41.6 24.0 108 93.5 54 168 145 5 84.0 228 197.5 114 288 249.4 144.0 49 42.4 24.5 109 94.4 54.5 169 146.4 84.5 229 198 3 114.5 289 250.3 144.5 50 43.3 25 110 95.3 55.0 170 147 2 85.0 230 199.2 115.0 290 251.1 145.0 51 44.2 25.5 111 96.1 55.5 171 148.1 85.5 231 200.1 115.5 291 252.0 145.5 52 45.0 26.0 112 97.0 56.0 172 149.0 86.0 232 200.9 116.0 292 252.9 146.0 53 45.9 26.5 113 97.9 56.5 173 149.8 86.5 233 201.8 116.5 293 253.7 146.5 54 46.8 27.0 114 98.7 57.0 174 150.7 87.0 234 202.6 117.0 294 254.6 147.0 55 47.6 27.5 115 99.6 57.5 175 151.6 87.5 235 203.5 117.5 295 255.5 147.5 56 48.5 28.0 116 100.5 58.0 176 152.4 88.0 236 204.4 118.0 296 256.3 148.0 57 49.4 28.5 117 101.3 58.5 177 153.3 88.5 237 205.2 118.5 297 257.2 148.5 58 50.2 29.0 118 102.2 59 178 154.2 89.0 238 206.1 119.0 298 258.1 149.0 59 51.1 29.5 119 103.1 59.5 179 155.0 89.5 239 207.0 119.5 299 258.9 149.5 60 52.0 30.0 120 103.9 60.0 18b 155.9 90.0 240 207.8 120.0 300 259.8 150.0 Dist, Dep Lat. Dist, Dep. Lat, Dist, Dep. Lat. Dist, Dep. Lat. Dist. Dep. Lat. For 60 Degrees. 234 TAJBLE IV. DIFFERENCE OF LATITUDE AND DEPARTURE FOR 31 DEGREES. Dist. Lat. Dep Dist. Lat. 3ep is!. Lat. [)0]I Dist. Lat. Dep. Dist. Lat. Dep. 1 30.900.5 ! 61 52.3 31.4 121 103.7 52.3 181 155.1 93.2 241 206.6 124.1 2 31. 701.0, 62 53 1 31.9 122 104.662.8 182 156.0 93.7 242 207.4 124.6 3 32.6 31.5 63 54.0 32.4 123 105.4 33.3 183 156.9 94.3 243 208.3 125.2 4 33.4 32. i; 64 54.9 33.0 124 106.3 33.9 184 157.7 94.8 244 209.1 125.7 5 84.302.6 65 55.7 33.5! 125 107.1 34.4 185 158.6 95.3 245 210.0 126.2 6 05.103.1 66 56.6 34.0 126 108.0 >4.9 186 159.4 95.8 246 210.9 126.7 7 06.003.6 67 57.4 34.5 127 108 9 35.4 187 160.3 96.3 247 211.7 127.2 8 06.9 34.1 68 58.3 35.0 128 109.7 55.9 188 161.1 96.8 248 212.6 127.7 9 >7.7 34.6: 69 59.1 35.5 129 110.6 56.4 189 162.0 97.3 249 213.4 128 2 10 08.6 35. '2 70 60. U 36.1 130 111.4 57.0 190 162.9 97.9 250 214.3 128.8 11 ljy.405.7| 71 60.9 36. Gj 131 112.3 S7.5 191 163.7 98. 4 ! 251 215.1 129.3 12 10.306.2 72 61.7 37.1 132 113.1 68.0 192 164.6 98.9 252 216.0 129.8 13 11.1 06.7 73 62. C 37.6 133 114.0 68.5 193 165.4 99.4 253 216.9 130.3 14 12.0 )7.2 74 63.4 38.1 134 114.969.0 194 166.3 99.9 254 217.7 130.8 15 12.9 07.7 75 64.3 38. 6 ! 135 115.7 69.5 195 167.1 100.4 255 218.6 131.3 16 13.7 08.2 76 65.1 39.1 136 116.6 70.0 196 168.0 100.9! 256 219.4 131.8 17 14. C 08.8 77 66. (,. 39.7 137 117.470.6 197 168.9 101. 5| 257 220.3 132.4 18 15.4 09.3 78 66.9 40.2 138 118.371.1 198 169.7 102.0 258 221.1 132.9 19 16.3 09.8 79 67.7 40.7 139 119.171.6 199 170.6 102.5 259 222.0 133.4 20 17.1 10 'A 80 68. ( 41.2 140 120.072.1 200 171.4 103.0 260 222.9 133.9 > 25.2 16.3 90 75.549.0 150 125.8 81.7 210 176.1 114.4 270 226.4 147.1 31 26.0 16.9 91 76.3 49.6 151 126.682.2 211 177.0 114 9 271 227.3 147.6 32 26.8 17.4 92 77.250.1 152 127.582.8 212 177.8 115.5 272 228.1 148.1 33 -7.7 18.0 93 78.050.7 153 128.383.3 213 178.6 116.0 273 229.0 148.7 34 28.5 18.5 94 78.851.2 154 129.2 83.9 214 179 5 116.6 274 229.8 149.2 35 29.4 19.1 95 79.7 51.7 155 130.0 84.4 215 180.3 117.1 275 230.6 149.8 36 30.2 19 6 96 80.5 52.3 156 130.8185.0 216 181.2 117.6 276 231.5 150.3 37 31.0 20.2 97 81.452.8 157 131.785.5 217 182.0 118.2 277 232.3 150.9 38 31.9 20.7 98 82.253.4 158 132.586.1 218 182.8 118 7 278 233.2 151.4 39 32.7 21.2 99 83.053.9 159 133.386.6 219 183.7 119.3 279 234.0 152.0 40 33.5 21.8 100 83.954.5 160 134.287.1 220 184.5 119.8 280 234.8 152.5J 41 34 4 22.3 101 84.755.0 161 135.0*7.7 221 185.3 120.4 281 235.7 153.0 42 35.2 22.9 102 85.555.6 162 135.988.2 222 186 2 120.9 282 236.5 153.6 43 36.1 ! 23.4 103 86.456.1 163 136.788.8 223 187.0 121.5: 283 237.3 154.1 44 36.924.0 104 87 256.6 164 137 589.3 224 187.9 122.0 284 238.2 154.7 45 37.724.5 105 88.157.2 165 138.489.9 225 188.7 122. 5 ! 285 239.0 155.2 46 38.6 25.1 106 88.957 7 166 139 2 ! 90.4 226 189.5 123.1 286 239.9 155.8 47 39.4 25.6 107 89.7 58.3 167 140.191.0 227 190.4 123.6 287 240.7 156.3 48 40.3 26.1 108 90.6 58.8 168 140.991.5 228 191.2 124.2 288 241.5 156.9 49 41.1 26.7 109 91.4 59.4 169 141.792.0 229 192.1 124.7 289 242.4 157.4 50 41.9 27.2 110 92.3 59.9 170 142.692.6 230 192.9 125.3 290 243.2 157.9 51 42.8 27.8 111 93.1 60.5 171 143.493.1 231 193.7 125.81 291 244.1 158.5 52 43.6'28.3 112 93.9 61 172 144.393.7 232 194.6 126.4 292 244.9 159.0 53 44.428.9 113 94.8 61.5 173 145.194.2 233 195.4 126.9 293 245.7 159.6 54 45.329.4 114 95.6 62.1 174 145.994.8 234 196.2 127.4! 294 246.6 160.1 55 46.130.0 115 96.462.6 175 146.895.3 235 197.1 128. 1 295 247.4 160.7 56 47.030.5 116 97.363.2 176 147.695.9 236 197.9 128.5 296 248.2 161.2 57 47.831.0 117 98.1 63.7 177 148.4196.4 237 198.8 129.1 297 249.1 161.8 58 48.631.6 118 99.0 64.3 178 149.396.9 238 199.6 129.6, 298 249.9 162.3 59 49.532.1 119 99.8 64.8 179 150.197.5 239 200.4 130.2 299 250.8 162.8 60 50.332.7 120 100.6 65.4 180 151.0 98.0 240 201.3 130.7 300 251.6 163.4 Dist. Dep Lat. Dist, Dep. Lat. Dist, Dep. Lat. Dist, Dep. Lat. Dist, Dep. Lat. For 57 Degrees. TABLE IV. 237 DIFFERENCE OF LATITUDE AND DEPARTURE FOR 34 DEGREES. Dist. Lat. Dep Dist. Lat. Dep Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. l 00.8 00. C 61 50. C 34.1 121 100.3 67.7 181 150.1 101.2 241 199.8 134.8 2 01.7 01.1 62 51.4 34 7 122 101.1 68.2 182 150.9 101.8 242 200.6 135.3 3 02.5 01.7 63 52.2 35.2 123 102.0 68.8 183 151.7 102.3 243 201 5 135.9 4 03.3 00.2 64 53.1 35.8 124 102.8 69.3 184 152.5 102.9 244 202.3 136.4 5 04.1 02.8 65 53.9 36.3 125 103.6 69.9 185 153.4 103.5 245 203.1 137.0 G 05.0 03.4 66 54.7 36.9 126 104.5 70.5 186 154.2 104.0 246 203.9 137.6 7 05.8 03.9 67 55.5 37 5 127 105.3 71.0 187 155.0 104.6 247 204.8 138.1 8 06.6 04.5 68 56.4 38.0 128 106.1 71.6 188 155 9 105.1 248 205.6 138.7 9 07.5 H5.0 69 57.2 38.6 1-29 106.9 72.1 189 156.7 105.7 249 206.4 139.2 10 08.3 05.6 70 5K.O 39.1 130 107 8 72.7 190 157.5 106.2 250 207.3 139 8 11 09 1 06.2 71 58 9 39.7 131 108.6 73.3 191 158.3 106.8 iS51 208.1 140.4 12 09.9 06.7 72 59.7 40.3 132 109.4 73.8 192 159.2 107.4 252 208.9 140.9 13 10.8 07.3 73 60.5 40.8 133 110.3 74.4 193 160.0 107.9 253 209.7 141.5 14 11.6 07.8 74 61.3 41.4 134 111.1 74.9 194 160.8 108 5 254 210.6 142.0 15 12.4 08.4 75 62 2 41.9 135 111.9 75.5 195 161.7 109.0 255 211.4 142.6 16 13.3 08.9 76 63 42.5 136 112.7 76.1 196 162.5 109.6 256 212.2 143.2 17 14.1 09.5 77 63.8 43.1 137 113.6 76.6 197 163.3 110.2 257 213.1 143.7 18 14.9 10.1 78 64.7 43.6 138 114.4 77.2 198 164.1 110.7 258 213.9 144.3 19 15.8 10 6 79 65.5 44.2 139 115.2 77 7 199 165.0 111.3 259 214.7 144.8 20 16.6 11.2 80 66.3 44.7 140 116.1 78.3 200 165.8 111.8 260 215.5 145.4 21 17.4 11.7 81 67.2 45.3 141 116.9 78.8 201 166.6 112.4 *61 216.4 145.9 22 18 2 12.3 82 68 45.9 142 117.7 79.4 202 167.5 113.0 262 217.2 146.5 23 19.1 12.9 83 88.8 46.4 143 118.6 80 203 168.3 113.5 263 218.0 147.1 24 19 9 13.4 84 69.6 47.0 144 119.4 80.5 204 169.1 114.1 264 218 9 147.6 25 20.7 14.0 85 70.5 47.5 145 120.2 81.1 205 170:0 114.6 265 219.7 148.2 26 21.6 14.5 86 71.3 48.1 146 121.0 81.6 206 170. & 115.2 266 220.5 148.7 27 22.4 15.1 87 72.1 48.6 147 121.9 82.2 2$>7 171.6 115.8 267 221.4 149.3 28 23.2 15.7 88 73.0 49.2 148 122.7 82.8 208 172.4 116.3 268 222.2 149 9 29 24.0 16.2 89 73.8 49.8 149 123.5 83.3 209 173.3 116.9 269 223.0 150.4 30 24.9 16.8 90 74 6 50.3 150 124.4 83.9 210 174.1 117.4 270 223.8 151.0 31 23.7 17.3 91 75.4 50.9 151 l&i. 2 84.4 211 1Y4.9 118. U ML 224.7 151.5 32 26.5 17.9 92 76.3 51.4 152 126.0 85.0 212 175.8 118.5 272 225.5 152.1 3.3 27.4 18.5 93 77.1 52.0 153 126.8 85.6 213 176.6 119.1 273 226.3 152.7 34 28.2 19.0 94 77.9 52.6 154 127.7 86.1 214 177.4 119.7 274 227.2 153.2 35 29.0 19.6 95 78.8 53.1 155 128.5 86.7 215 178.2 120.2 275 228.0 153.8 36 29.8 20.1 96 79.6 53.7 156 129.3 87 2 216 179.1 120.8 276 228.8 154.3 37 30.7 20.7 97 80.4 54.2 157 130.2 87.8 217 179.9 121.3 277 229 6 154.9 38 31. 5 21.2 98 81.2 54.8 158 131. C 88.4 218 180.7 121.9 278 230.5 155.5 39 32.3 21.8 99 82.1 55.4 159 131.8 88.9 219 181.6 122.5 279 231.3 156.0 40 33.2 22.4 100 62.9 55.9 160 132.6 89.5 220 182.4 123.0 280 232.1 156 6 41 34.0 22.9 101 83.7 56.5 101 133.5 90.0 221 183.2 123.6 H81 V36. 157.1 42 34.8 23.5 102 34.6 57.0 162 134.3 90.6 222 184.0 124.1 282 233.8 157.7 43 35.6 24.0 103 85.4 57.6 163 135.1 91.1 223 184.9 124.7 283 234.6 158.3 44 36.5 24.6 104 86.2 58.2 164 136.0 91.7 224 185.7 125.3 284 235.4 158.8 45 37.3 25.2 105 87.0 58.7 165 136.8 92.3 225 186.5 125 8 285 236.3 159.4 46 38.1 25.7 106 87.9 59.3 166 137.6 92.8 226 187.4 126.4 286 237.1 159.9 47 39.0 26.3 107 88.7 59.8 167 138 4 93.4 227 188.2 126.9 287 237.9 160.5 48 39.8 26.8 108 89.5 00.4 168 139.3 93.9 228 189.0 127.5 288 238.8 161.0 49 10.6 27.4 109 90.4 61.0 169 140.1 94.5 229 189.8 128 1 289 239.6 161.6 50 11.6 28.0 110 91.2 61.5 170 140.9 95.1 230 190.7 128.6 290 240.4 162.2' 61 12.328.5 111 92.0 62.1 ~m 141.8 95.6 231 191.5 129. -I 291 241.2 102. 7i 52 43.1 29.1 112 92.9 62.6 172 142.6 96.2 232 192 3 129.7 292 242.1 163 3 53 43.9 29.6 113 93.7 63.2 173 143.4 96.7 233 193.2 130.3 293 242.9 163.8' 51 44.8 30.2 114 94.5 63.7 174 144.3 97.8 234 194.0 130.9 294 243.7 164.4 55 15.6 30.8 115 95.3 64.3 175 145.1 97.9 235 194.8 131.4 295 244.6 165.0 56 16.4 31.3 116 96.2 64.9 176 145.9 98.4 236 195.7 132.0 296 245.4 165.5 57 17.3 31.9 117 97.0 65.4 177 146.7 99.0 237 196.5 132.5 297 246.2 166.1 58 18.1 32.4 11897.8 66.0 178 147.6 99.5 238 197.3 133.1 298 247.1 166.6 59 18 9 33.0 11998.7 66.5 179 148.4 100.1 239 198.1 133.6 299 247.9 167.2 60 19.7 33.6 120 99.5 67.1 180 149.2 100.7 240 199.0 134.2 300 248.7 167.8 DisL Dcp Lat. Dist. Dcj) Lat. D~iZ Dcp. Lat. Dist. Dcp. Lat, Dist. Dcp. Lat. For 5G Degrees. 238 TABLE IV. DIFFERENCE OF LATITUDE AND DEPARTURE FOR 35 DEGREES. Hist. Lat. Dep Dist. LatJDepj Dist. Lat. Dep. ftjst Lat. Dep. 'Dist Lat. Dep. l 00.8 00. C 6150.0 ! 35.0 121 9D.1 69.4 181 148.3 103.8 241 197.4 138.2 2 01.6 01.1 6250.8*35.6 122 99.9 70.0 182 149.1 104.4 242 198.2 138 8 3 02.5 01.7 6351.6:36.1 123 100.8 70.5 183 149.9 105.0 243 199.1 139.4 4 03.302.3 6452.4,36.7 124 101.6 71.1 184 150.7 105.5 244 199.9 140.0 5 04.102.9 6553.2 ! 37.3 125 102.4 71.7 185 151.b 106.1 245 200.7 140.5 6 104.903. 4 60 54.137.9 126 103.2 72.3 186 152.4 106.7 246 201.5 141.1 7 05.704.0 67 54.938.4 127 104 72.8 187 153.2 107.3 247 202.3 141.7 8 06.604.6 6855.739.0 128 104.9 73.4 188 154.0 107.8 248 203.1 142.2 9 07.405.2 6956 539.6 129 105.7 74.0 189 154.8 108.4 249 204.0 112 8 10 03.205.7 70 57.340.2 130 106.5 74.6 19( 155.6 109.0 250 204.8 143.4 11 09.0,06.3 71 58. 2J40.7 131 107.3 75.1 191 156.5 109.0 251 205.6 144. ; 12 09.806.9 72 59.041.3 132 103.1 75.7 192 157.3 110.1 252 206.4 144.5 13 10.607.5 73 6Q.8I41 9 133 108.9 76.3 193 158.1 110.7 253 207.2 145.1 14 11.508.0 74 60.642.4 134 109.8 76.9 194 158.9 111.3 254 208.1 145.7 15 12.3 08.6 75 61.443.0 135 110.6 77.4 195 159.7 111.8 255 208.9 146.3 10 13.1 09.2 76 62.343.6 136 111.4 78.0 196 160.6 112.4 256 209.7 146.8 17 13 9 09.8 77 63.144.2 137 112.2 78.6 197 161.4 113.0 257 210.5 147.4 18 14.7 10.3 78 63 944.7 138 113.0 79.2 198 162.2 113.6 258 211.3 148.0 19 15.6 10.9 7964.715.3 139 113.9 79.7 199 163.0 114.1 259 212.2 148.6 20 16 4 11.5 80 65.5j45.9 140 114.7 80.3 200 163.8 114.7 260 213.0 149.1 21 17.2 12.0 81 66.4]46.5 141 115.5 80.9 201 164.0 115.3 261 213.8 149.7 22 18.0 12.6 82 67.2147.0 142 116.3 81.4 202 165.5 115.9 262 214.6 150.3 23 18.8 13.2 83 68.0J47.6 143 117.1 82.0 203 166.3 116.4 263 215.4 150.9 24 19.713.8 81 68.848.2 144 118. ( 82.6 204 167.1 117.0 264 216.3 151.4 25 20.5 14.3 85 69.648.8 145 118.8 83.2 205 167.9 117.6 265 217.1 152.0 26 21.3 14.9 8G 70 449.3 146 119. ( 83.7 206 168.7 118. 266 217.9 152.6 27 22.1 15.5 87 71.349.9 147 120.4 84.3 207 169.6 118. 267 218.7 153.1 28 22 9 16.1 88 72.1:50.5 148 121 2 84.9 208 170.4 119. 268 219.5 153.7 29 23.8 16.6 8972.9)61.0 149 122.1 85.5 209 171.2 119. 269 220 4 154.3 30 24.6 17.2 90 73.751 6 150 122.9 86.0 210 172.0 120. 270 221.2 154.9: 31 25.4 17.8 91 74.552.2 151 123.7 86.6 211 172.8 121. 271 222. C 155.4 32 26.2 18.4 92 75.452.8 152 124 5 87.2 212 173.7 121. 272 222.8 156.0 33 27.0J18.9 93 76.253.3 153 125.3 87.8 213 174.5 122. 273 223.6 156.6 34 27.919.5 94 77 053.9 154 126.1 88.3 214 175.3 122. 274 224.4 157.2 35 28.7120.1 95 77.854.5 155 127.0 88.9 215 176.1 123. 275 225.3 157.7 36 29.5,20.6 9(i 78.C55.1 156 127. b 89.5 216 176.9 123. 276 226.1 158.3 37 30.321.2 97 79.555.6 157 128.6 90 1 217 177.8 124. 277 226 9 158.9 38 31.121.8 98 SO. 356. 2 158 129.4 90.6 218 178.6 125.0 278 227.7 159 5 39 31.922.4 99 81.156.8 159 130.2 91.2 219 179.4 125.6 279 228 5 160 40 32. 22. 9 100 81.957.4 160 131.1 91.8 220 180.2 126.2 280 229.4 160.6 41 33.6 23.5 101 82.757.9 101 131.9 92.3 22i 181.0 126.8 281 230.2 161.2 42 31.4 24.1 10283.658.5 162 132.7 92.9 222 181.9 127.3 282 231.0 161.7 43 33.2 24.7 10384.459.1 163 133.5 93.5 223 182.7 127.9 283 231.8 162.3 4i 36.025.2 10J85.259.7 164 134.3 94.1 224 183.5 128.5 284 232.6 162.9 45 36.925.8, 10586.060.2 165 135.2 94.6 225 184.3 129.1 285 233.5 163.5 46 37.7i'26.4 10686.860.8 166 136 95.2 226 185.1 129.6 286 234.3 164.0 47 38.527.0 107 87 661 4 167 136.8 95 8 227 185.9 130.2 287 235.1 164 6 48 39.327.5 108 88.561.9 168 137. 0.2 14.7 8568.850.0 145 117.3 85.2 205 165.8 120 5 265 214.4 155.8 26 21.0 15.3 8669.650.5 146 118.1 85.8 206 166.7 121.1 266 215.2 156.4 27 22.8 15.9 8770.451.1 147 118.9 86. 4| 207 167.5 121.7 267 216.0 156.9 23 22.7 16.5 8871.251.7 148 119.7 87.0 208 168.3 T22.3 268 216.8 157.5 29 23 5 17.0 8972.0 52.3 149 120.5 87. G; 209 169.1 122.8 2C9 217. G 158.1 33 24.3 17. G 90 72.8 52.9 150 121.4 83.2 210 169.9 123.4 270 218.4 158.7 31 25.1 18.2 9i 73.6 53.5 151 122.2 83. 211 170.7 124.0 271 219.2 159.3 32 25.9 18.8 92 74.4 54.1 152 123.0 89.3 212 171.5 124.6 272 220.1 159.9 33 26.7 19.4 93 75.2 54.7 153 123.8 89.9 213 172.3 125.2 273 220.9 160.5 34 27.5 20.0 94 76.0 55.3 154 124.6 90.5 214 173.1 125.8 274 221.7 161.1 35 23.3 20.6 95 76.9'55.8 155 125.4 91. 1 1 215 173.9 126.4 275 222.5 161. G 33 29.1 21.2 90 77.7156.4 156 123.2 91.7, 216 174.7 127.0 276 223.3 162.2 37 29.9 21.7 9778.557.0 157 127.0 92.3 217 175. G 127.5 277 224.1 162.8 33 3'J.7 22.3 98 79. 3 57. C 158 127.8 92.9 218 176.4 128.1 278 224.9 163.4 33 31. G 22.9 9083.158.2 159 128.6 93.5 219 177:2 128.7 279 225.7 164 40 32.4 23.5 100 30.958.8 160 129.4 94.0 220 178.0 129.3 280 226.5 164.6 41 33. i! 24.1 101 81.7159.4 161 130.3 94.0 221 178. b 129.9 281 '227.3 165.2 42 34.0 24.7 102 32.560.0 162 131.1 95.2 222 179. C 130.5 282 228.1 165.8 43 34.8 25.3 103 83.360.5 163 131.9 95.8 223 180.4 131.1 283 229.0 166.3 44 35.6 25.9 104 84.161.1 164 132.7 96.4 224 181.2 131.7 284 229.8 166.9 45 36.4 26.5 105 84.961.7 165 133.5 97.0 225 182.0 132.3 285 230. C 167.5 43 37.2 27.0 106 85.862.3 166 134.3 97. C 226 182.8 132.8 286 231.4 168.] 47 33.0 27.6 107 86.662.9 167 135.1 98.2 227 183. G 133.4 287 232.2 168.7 48 33.8 28.2 103 87.463.5 168 135.9 98.7 228 184.5 134.0 288 233.0 169.3 49 39. G 28.8 109 83.264.1 169 136.7 99.3 229 185.3 134.6 289 233.8 169.9 50 40.5 29.4 110 89.061.7 170 137.5 99.9 230 186.1 135.2 290 231.6 170.5 TT 11.3 30.0 111 89.865.2 171 138.3 100. b 231 186.9 135.8 291 235.4 171.0 52 12.1 33.6 112 90.665.8 172 139.2 101.1 23* 187.7 136.4 292 236.2 171.6 53 42.9 31.2 113 91.466.4 173 140.0 101.7 233 183.5 137.0 293 237.0 172.2 54 43.7 31.7 114 92.267.0 174 140.8 102.3 234 189.3 137.5 294 237.9 172.8 55 11.5 32.3 115 93. 067. C 175 141.6 102.9 235 190.1 133.1 295 238.7 173.4 56 45.3 32.9 116 93.868.2 176 142.4 103.5 236 190.9 138.7 296 239.5 174.0 57 46.1 33.5 117 94.768.8 177 143.2 104.0 237 191.7 139.3 297 240.3 174. G 58 46.9 34.1 118 95.569.4 178 144.0 104.6 238 192.5 139.9 298 241.1 175.2 59 47.7 34.7 11996.369.9 179 144.8 105.2 239 193.4 140.5 299 241.9 175.7 60 48.5 35.3 12097.170.5 180 145.6 105.8 240 194.2 141.1 300 242,. 7 176.3 Lat. Dist. Dep Lat. DistJDep Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. For 54 Degrees. 240 TABLE IV. DIFFERENCE OF LATITUDE AXD DEPARTURE FOR 37 DEGREES. Dist. Lat. Dep Dist. Lat. Dep Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 00.800.6 61 48 7 36.7 121 96.6 72.8 181 144.6 108.9 241 192.5 145.0 2 01.601.2 62 49.5 37.3 122 97.4 73.4 182 145.4 109.5 242 193.3 145.6 3 )2.4'01.8 63 50.3 37.9 123 98.2 74.0 183 146.2 110.1 243 194.1 146.2 4 03.202.4 64 51.1 38.5 124 99.0 74.6 184 146.9 110 7 244 194.9 146.8 5 01 003 65 51.9 39.1 125 99.8 75.2 185 147.7 111.3 245 195.7 147 4 6 04.8 03.6 66 52.7 39.7 126 100.6 75.8 186 148 5 111.9 246 196.5 148.0 7 05 6 04.2 67 53.5 10.3 127 101.4 76.4 187 149.3 112.5 247 197.3 148.6 8 1)6.4 01.8 68 54.3 10.9 128 102.2 77.0 188 150.1 113.1 248 198.1 149.3 9 07.2 05.4 6955.1 41 5 129 103.0 77.6 189 150.9 113.7 249 198.9 119.9 10 08.0 06 7055.9 42.1 130 103.8 78.2 190 151.7 114.3 250 199.7 150.5 11 U8.8 OG.G 7J 50.7 42.7 131 Io4 G 78.8 191 152.5 114 9 251 200.5 151.1 12 09. G 07.2 7257.5 43.3 132 105.4 79.4 192 153.3 115.5 252 201.3 151.7 13 10.4 07.8 7358.3 43.9 133 103.2 80.0 193 154.1 116 2 253 202.1 152.3 14 11. 2 08.4 7459.1 44.5 134 107.0 80.6 194 154.9 116.8 254 202.9 152.9 15 12.0 09.0 7559.9 45.1 135 107.8 81.2 195 155 7 117.4 255 203 7 153.5 1C 12.8 J9 6 7660.7 45.7 136 108.6 81.8 196 156.5 118. ( 256 204.5 154.1 17 13.6 10.2 7761.; 46 3 137 109.4 82.4 197 157.3 118 6 257 205.2 154.7 18 14.4 10.8 7862.3 tG.9 138 110.2 83.1 198 158.1 119.2 258 206.0 155.3 19 15.2 11.4 7963 1 47.5 139 111.0 83.7 199 158.9 119.8 259 206.8 155.9 20 16. 12.0 8063.9 43.1 140 111.8 84 3 200 159 7 120.4 260 207.6 156 5 21 10.8 12.0 8104 7 48.7 141 H2.6 84.9 201 160.5 121.0 261 208.4 157.1 22 17 G 13 2 8265.5 49.3 142 113.4 85.5 202 161.3 121.6 262 209.2 157.7 23 18.4 13.8 8366.3 50 143 1J4.2 86.1 203 1G2.1 122.2 263 210 158.3 24 19.2 14.4 8467 1 50. C 144 115.0 86.7 204 162.9 122.8 264 210.8 158.9 25 20.0 15.0 8567.9 51.2 145 115 8 87.3 205 163.7 123.4 265 211.6 159.5 20 20.8 15. G 866H.7 51.8 146 116 6 87.9 206 164.5 124.0 266 212.4 160.1 27 21.6 16.2 87169.5 52.4 147 117.4 88.5 207 165.3 124.6 267 213.2 160.7 28 22.4 16.9 8870.3 53.0 148 118 2 89.1 208 16G.1 125.2 268 214.0 161 3 29 23.2 17.5 89,71.1 53 6 149 119 89.7 209 163.9 125.8 269 214.8 161.9 30 24.0 18.1 9071.9 54.2 150 119.8 90.3 210 167.7 126.4 270 215.6 162.5 31 24.6 18.7 9172.7 54.8 151 120.0 90.9 211 108.5 127.0 271 216.4 103.1 32 25. C 19.3 92^73.5 55.4 152 121.4 91.5 212 169.3 127.6 272 217.2 163.7 33 26.4 19.9 93,74.3 56.0 153 122.2 92.1 213 170.1 128.2 273 218.0 164.3 34 27.2 20.5 9475 1 56. G 154 123 92.7 214 170 9 128.8 274 218.8 164.9 35 28.0 21.1 9575.9 57.2 155 123.8 93 3 215 171.7 129.4 275 219.6 165.5 3G 28.8 21.7 9676.7 57.8 156 124.6 93.9 216 172.5 130.0 276 220.4 166.1 37 29.5 22.3 97,77.5 58.4 157 125.4 94 5 217 173.3 130.6 277 221.2 166.7 38 30.3 22.9 9878.3 59.0 158 126.2 95.1 218 174.1 131.2 278 222.0 107.3 39 31.1 23.5 9979.1 59.6 159 127.0 95.7 219 174.9 131.8 279 222.8 167.9 40 31.9 24.1 100'79.0 60.2 160 127.8 96.3 220 175 7 132.4 280 223.6 168.5 41 32.7 24.7 10180.7 60.8 161 128.0 90 9 221 176.5 133.0 281 224.4 109.1 42 33.5 25.3 10281.5 61.4 1G2 129.4 97.5 222 177 3 133.6 282 225.2 169.7 43 34 3 25.9 10382.3 62.0 16b 130.2 98.1 223 178.1 134.2 283 226.0 170.3 44 35.1 26.5 10483.1 62 6 164 131.0 98.7 224 178.9 134 8 284 226.8 170.9 45 35 9 27.1 10583.9 63.2 165 131.8 99.3 225 179.7 135.4 285 227.6 171.5 46 36.7 27.7 10G84.7 G3.8 160 132.6 99 9 2-26 180.5 136.0 286 228.4 172.1 47 37.5 28.3 10785.5 64.4 167 133 4 100.5 227 181.3 136.6 287 229.2 172.7 48 38.3 28.9 108 88. 3 65.0 168 134.2 101.1 228 182.1 137.2 288 230.0 173.3 49 39.1 29.5 10987.1 65. G 169 135.0 101.7 229 182.9 137.8 289 230.8 173.7 50 39.9 30.1 11087.8 66.2 170 135.8 102.3 230 183.7 138.4 290 231. G 174 5 51 40 7 30.7 11188.6 60.8 171 130.0 102.9 '231 1*4.5 139.0 291 232.4 175.1 52 11.5 31.3 11289.4 67.4 17-2 137.4 103.5 232 185.3 139.6 292 233 2 175.7 53 12.3 31.9 11390.2 68.0 173 138.2 104.1 233 186.1 140.2 293 234.0 176.3 54 43.1 32.5 11491.0 68.6 174 139.0 104.7 234 186.9 140.8 294 234.8 176.9 55 43.9 33.1 11591.8 69.2 175 139.8 105.3 235 187.7 141.4 295 235.6 177.5 5G 44.7 33.7 11692.6 69.8 17G 140.6 105.9 236 188.5 142.0 296 236.4 178 1 57 45.5 34.3 117 93.4 70.4 177 141.4 106.5 237 189.3 142.0 297 237.2 178 7 58 46.3 34.9 118 94 2 71.0 178 142.2 107.1 238 190.1 143.2 298 238 179.3 59 47.1 35.5 119 95 71 6 179 143.0 107.7 239 190.9 143.3 299 238.8 179 9 GO 47 9 36.1 120 95.8 72.2 180 143.8 108. c 240 191.7 144.4 300 239.6 180.5 Dist. Dep Lat. Dist. Dep Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. For 53 Degrees. TABLE IV. 241 DIFFERENCE OF LATITUDE A$D DEPARTURE FOR 38 DEGREES. Dist. Lat. Dep| ! Dist. Lat. Dep Dist, Lat. Dep. Dist. Lat. Dep. 1 Dist, Lat. Dep. l 00.800.6 1 61 48.1 37.6 121 95.3 74.5 181 142.6 111.4 241 189.9 148.4 2 01 601.2 62 48.938.2 122 9J.1 75.1 182 143.4 112. 1' 24'2 190.7 149.0 3 02.401.8 63 49.638 8 123 96.9 75 7 183 144.2 112.7 243 191.5 149.6 4 03.202.5 64 50.439.4 124 97.7 76 3 184 145.0 113.3 244 192 3 150.2 5 03.903.1 65 51.240.0 125 98.5 77.0 185 145.8 113.9 245 193.1 150.8 6 04.703.7 66 52.040.6 126 99.3 77. G 186 146.6 214.5 246 193.9 151.5 7 05.504.3 67 52.841.2 127 100.1 78.2 187 147.4 115.1 247 194.6 152.1 8 06.304.9 68 53.6 41.0 128 100.9 78.8 188 148.1 115.7 248 195.4 152.7 9 07.105 5 6954.4 42.5 129 101.7 79.4 189 148.9 116.4 249 196.2 153.3 10 07.906.2 70 55.243.1 130 102.4 80.0 190 149.7 117.0 250 197.0 153.9 11 108.7,00.8 71 55.9 43.7 131 103. 2i 80.7 191 150.5 117.6 251 197 > 154.5 12 09 507.4 72 56.7 14.3 132 104. (i 81.3 192 151.3 118.2 252 198.6 155.1 13 10.2 08.0 73 57.5 44.9 133 104.8 81.9 193 152.1 118.8 253 199.4 155.8 14 11.0 08.6 74 58.3 45.6 134 105.6 82.5 194 152.9 119 4 254 200.2 156.4 15 11.8 09.2 75 59.146.2 135 106.4 83.1 195 153.7 120.1 255 200.9 157.0 16 12.6 09.9 76 59.946.8 136 107.2 83.7 196 154.5 120.7 256 201.7 157.6 17 13.4 10.5; 77 60.747.4 137 108.0 84.3 197 155.2 121.3 257 202.5 158.2 18 14.2 11.1 78 61.548.0 138 108.7 85.0 198 156.0 121.9 258 203.3 158.8 19 15.0 11.7 79 62 348.6 139 109.5 85.6 199 156.8 122.5 259 204.1 159.5' 20 15.8 12.3 80 63.049 3 140 110.3 86.2 200 157.6 123.1 260 204.9 160.1 21 16.5 1279 81 63.849.9 141 111.1; 86.8 201 158.4 123.7 261 205 7 160.7' 22 17.3 13.5 82 G4.G50.5 142 111.9 87.4 202 159.2 124.4 262 206.5 161.3 23 18.1 14.2 83 65.451.1 143 112.7 8S.O 203 160.0 125. : 263 207.2 161.9 24 18.9 14.8 84 66.2 51.7 144 113.5 88.7 204 160.8 125.6 264 208.0 162.5 25 19.7 15.4 85 67.0 52.3 145 114.3 89.3 205 161.5 126.2 265 208.8 1G3.2 26 20.5 1G.O 8G 67.852.9 146 115.0 89.9 206 162.3 126.8 266 209.6 163.8 27 21 3 16.6 87 68.6 53.6 147 115.8 90.5 207 163.1 127.4 267 210.4 164.4 28 22.1 17.2 88 69. b 54.2 148 116.6 91.1 208 163.9 128.1 268 211.2 1G5.0 29 22.9 17.9 89 70.1 54.8 149 117.4 91.7 209 164.7 128.7 269 212 165.6 30 23.6 18.5 90 70.955.4 150 118.2 92.3 210 165.5 129.3 270 212.8 1GG.2 31 24.4J19.1 91 71.7 56.0 151 119.0 93.01 211 166.3 129.9 271 213.6 166.8 32 25.219.7 92 72.5 56.6 152 119.8 93.6 212 167.1 130.5 272 214 3 167.5 33 .6.020.3 93 73.3 57.3 153 120.6 94.2 213 167.8 131.1 273 215.1 1G8.1 34 26.820.9 94 74.1 57.9 154 121.4 94.8 214 168 6 131.8 274 215.9 168.7 35 27.621.5 95 74.9 58.5 155 122.1 95.4 215 169.4 132.4 275 216.7 169.3 36 28.4 22.2 96 75.6 59.1 156 122.9 96.0 216 170.2 133.0 276 217.5 169.9 37 29.222.8 97 76.459.7 157 123.7 96.7 217 171.0 133.6 277 218.3 170.5 38 29.923.4 98 77.260.3 158 124.5 97.3 218 171.8 134 2 278 219.1 171.2 39 30.724.0 99 78.061.0 159 125.3 97.9 219 172.6 134.8 279 219.9 171.8 40 31.524.6 100 78.861.6 160 126.1 98.5 220 173.4 135.4 280 220.6 172.4 41 32.3 25.2 101 79.662.2 161 126.9 99 1 221 174 2 136.1 281 221.4 173.0 42 33.1 25.9 102 80.462.8 162 127.7 99.7 222 174.9 136.7, 282 222.2 173.6 43 33.9 26.5 103 81.263.4 163 128.4 100.4 223 175.7 137.3 283 223.0 174.2 44 34.727.1 104 82 064.0 164 129 2 101.0 224 176.5 137.9 284 223.8 174.8 45 35.527.7 105 82.7G4.6 165 130.0 101.6 225 177.3 138.5 285 224.6 175.5 46 ;36.228.3 106 83 565.3 166 130 8 102.2 226 178.1 139.1 286 225.4 176.1 -17 37.028.9 107 84.365.9 167 131.6 102.8 227 178.9 138.8 287 226.2 176.7 48 37.829.6 108 85.166.5 168 132.4 103.4 228 179.7 140.4 288 226.9 177.3 49 38.630.2 109 85.967.1 169 133.2 104.0 229 180.5 141.0! 289 227.7 177.9 50 39.430.8 110 86.767.7 170 134.0 104.7 230 181.2 141.6 290 228.5 178.5 51 10.231.4 111 87.568.3 171 131.7 105.3 231 182.0 142.2 291 229 . 3 179.2 52 41.032.0 112 88.369 172 135.5 105.9 232 182.8 142.8 292 230.1 179.8 53 41.8 32.6 113 89.069.6 173 136.3 106.5 233 183.6 143.4 293 230.9 180.4 54 42.6 33.2 114 89.870.2 174 137.1 107.1 234 184.4 144.1 294 231.7 181.0 55 43.3 33.9 115 90.670.8 175 137.9 107.7 235 185.2 144.7 295 232.5 181.6 56 11. 1 34.5 116 91.471.4 176 138.7 108.4 236 186.0 145.3 296 233.3 182.2 57 44.9 35.1 117 92.272.0 377 133.5 109.0 237 186.8 145.9 297 234.0 182.9 58 15. 7 35.7 118 93.072.6 178 140.3 109.6 238 187.5 146.5 298 234.8 183.5 59 46.5 36.3 119 93.873.3 179 141.1 110.2 239 188.3 147.1 299 235.6 184.1 60 47.3 36.9 120 94. C 73.9 180 141.8 110.8 240 189.1 147.8 300 236.4 184.7 Dist.! Dep Lat. D~isl Dep Lat. iDist. Dep. Lat. Dist. Dep. Lat. Dist, Dep. Lat, For 52 Degrees. 242 TABLE IV. DIFFERENCE OF LATITUDE AND DEPARTURE FOR 39 DEGREES. Dist, Lat. Dep Dist. Lat. Dep Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 00.8 00.6 61 47.4 38.4 121 94.0 76.1 181 140.7 113.9 241 187.3 151.7 2 01.601.3 62 48 2 39.0 122 94.8 76.8 182 141.4 114.5 242 188.1 152.3 3 02.3 01.9 63 49.0 39.6 123 95.6 77.4 183 142.2 115.2' 243 188.8 152.9 4 03.1 02.5 64 49.7 40.3 124 96.4 78.0 184 143.0 115. 8' 244 189.6 153.6 5 03.903.1 65 50.5 40.9 125 97.1 78.7 185 143.8 116.4 245 190.4 154.2 6 04.703.8 66 51.3 41.5 126 97.9 79.3 186 144.5 117.1 246 191.2 154.8 7 03.404 4 67 52.1 42.2 127 98 7 79.9 187 145.3 117.7 247 192.0 155.4 8 06.2K)5.0 68 52.8 42.8 128 99.5 80.6 188 146.1 118.3 248 192.7 156.1 9 >7.0 05.7 69 53 643.4 129 100.3 81.2 189 146.9 118.9 249 193.5 156.7 10 07.8 06.3 70 54.444.1 130 101.0 81.8 190 147.7 119. 6' 250 194.3 157.3 11 08 5 0(5.9 71 35.2 44.7 131 101.8 8^.4 191 148.4 120.2 251 195.1 158.0 12 J9.3 07.6 72 56.0 45.3 132 102.6 83.1 '192 149.2 120.8 252 195.8 158.6 13 10.1 08.2 73 56.7 45.9 133 103.4 83.7 193 150.0 121.5, 553 196.6 159.2 14 Kh 9 08.8 74 57.5 46.6 134 104.1 84.3 194 150.8 122.1' 254 197.4 159.8 15 11.7 09.4 75 58.3 17.2 135 104.9 85.0 195 151.5 122. 7, 255 198.2 160.5 16 12.4 10.1 76 59.1 47.8 136 105.7 85.6 196 152.3 123.3 256 198.9 161.1 17 13.2 10.7 77 39.848.5 137 106.5 86.2 197 153.1 124.0 257 199.7 161.7 18 14.0 11.3 78 60 649.1 138 107.2 86.8 198 153.9 124. 6! 258 200.5 162.4 19 14.8 L2.0 79 61.4 49.7 139 108.0 87.5 199 154.7 125.2 259 201.3 163.0 20 15.5 12.6 80 62.2 50.3 140 108.8 88.1 200 155.4 125.9 260 202.1 163.6 ZL 10. -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 51.6 142 110.4 89 4 202 157.0 127.1 262 203.6 164.9 23 17.9 14.5 83 64.5 52.2 143 111.1 90.0 203 157.8 127.8 263 204.4 165.5 24 18.7 15.1 84 65.3 52.9 144 111.9 90.6 204 158.5 128.4 264 205.2 166.1 25 19.4 15.7 85 66.1 53.5 145 112.7 91.3 205 159.3 129.0 265 205.9 166.8 26 :o 2 16.4 86 66 8 54.1 146 113.5 91.9 206 160.1 129.6 266 206.7 167 4 27 21.0 17.0 87 67.6 54.8 147 114.2 92.5 207 160.9 130.3 267 207.5 168.0 28 21.8 17.6 88 68.4 55.4 148 115 93.1 208 161.6 130.9 268 208.3 168.7 29 22.5 18.3 89 G9.2 56.0 149 115.8 93.8 209 162.4 131.5 269 209 1 169.3 30 23.3 18.9 90 69.9 56.6 150 116.6 94.4 210 163.2 132.2 270 209.8 169.9 31 24.1 19.5 91 70.7 57.3 151 117.3 95.0 211 164 132.8 271 210.6 170.5 32 24.9 20.1 92 71.5 57.9 152 118.1 95.7 212 164.8 133.4 272 211.4 171.2 33 25.6 20.8 93 72.3 58.5 153 118.9 96.3 213 165.5 134.0 273 212.2 171.8 34 26.4 21.4 94 73 1 59.2 154 119.7 96.9 214 166.3 134.7 274 212.9 172.4 35 27.2 22.0 95 73.8 59.8 155 120.5 97.5 215 167.1 135.3 275 213.7 173.1 36 28.0 22.7 90 74.660.4 156 121.2 98.2 216 167.9 135.9 276 214.5 173.7 37 28.8 23.3 97 75.461.0 157 122.0 98.8 217 168.6 136.6 277 215.3 174.3 38 29.5 23.9 98 76.261.7 158 122.8 99.4 218 169.4 137.2 278 216.0 175 39 30.3 24.5 99 76.962.3 159 123.6 100.1 219 170.2 137.8 279 216.8 175 6 40 31.1 25.2 100 77.762.9 160 124.3 100.7 220 171.0 138.5 280 217.6 176.2 41 31.9 25. 8 101 78.563.6 161 125 . 1 101.3 221 171.7 139.1 281 218.4 176.8 42 32.6 26.4 102 79.364.2 162 125.9 101.9 222 172.5 139.7 282 219.2 177.5 43 33.4 27.1 103 80.064.8 163 126.7 102.6 223 173.3 140.3 283 219.9 178.1 44 34.2 27.7 104 80.865.4 164 127.5 103.2 224 174.1 141.0 284 220.7 178.7 45 35.0 28.3 105 81.666.1 165 128.2 103.8 225 174.9 141.6 285 221.5 179.4 46 35.7 28.9 106 82.466.7 166 129.0 104.5 226 175.6 142.2 286 222.3 180.0 47 36.5 29.6 107 83.267.3 167 129.8 105 1 227 176.4 142.9 287 223.0 180.6 48 37.3 30.2 108 83.968.0 168 130.6 105.7 228 177.2 143.5 288 223.8 181.2 49 33.1 30.8 109 84.768.6 169 131.3 106.4 229 178.0 144.1 289 224.6 181.9 50 38.9 31 5 110 85.569.2 170 132.1 107.0 230 178.7 144.7 290 225.4 182.5 51 39.6 32.1 111 86.369.9 171 132.9 107.6 231 179.5 145.4 291 226 . 1 183.1 52 JO. 4 32.7 112 87.070.5 172 133.7 108.2 232 180.3 146.0 292 226.9 183.8 53 il.2 33.4 113 87.871.1 173 134.4 108.9 233 181.1 146.6 293 227.7 184.4 54 42.0 34.0 114 88.671.7 174 135.2 109.5 234 181.9 147.3 294 228.5 185.0 55 42.7 34.6 115 89.472.4 175 136.0 110.1 235 182.6 147.9 295 229.3 185.6 56 43.5 35.2 116 90.173.0 176 136.8 110.8 236 183.4 148.5 296 230.0 186.3 57 44.3 35.9 117 90.9 73.6 177 137.6 111.4 237 184.2 149.1 297 230.8 186.9 58 45.1 36.5 118 91.7 74 3 178 138.3 112.0 238 185.0 149.8 298 231.6 187.5 59 45.9 37.1 11992.5 74.9 179 139.1 112.6 239 185.7 150.4 299 232.4 188.2 60 46.6 37.8 120 93.3 75.5 180 139.9 113.3 240 186,5 151.0 300 233.1 188.8 Dist. Dep Lat. Dist. Dep Lat. Dist. Dep. Lat. Dist. Dep. Lat, Dist. Dep. Lat. For 51 Degrees. TABLE IV. 243 DIFFERENCE OF LATITUDE AND DEPARTTTBE FOR 40 DEGREES. Dist. Lat. [)ep list. Lat.! Dep Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 DO. 8 00. C 61 40.739.2 121 92.7 77.8 181 138.7 116.3 241 184.6 154.9 2 01.5 01.3 62 47. 5:39.9' 122 93.5 78.4 182 139.4 117.0 242 185.4 155.6 3 [)2.3 01.9 6348.340.5 123 94.2 79.1 183 140.2 117.6 243 186.1 156.2 4 03.1 02.0 64 49. dil.l 124 95.0 79.7 184 141.0 118.3 244 186.9 156.8 5 13.8 03.2 6549.8.41.8 125 95.8 80.3 185 141.7 118.9 245 187.7 157.5 6 )4.6 03. y 6650.642.4 126 96.5 81.0 180 142.5 119.6 246 188.4 158.1 7 05.4 04.5 67 31.343.1 127 97.3 81.6 187 143.3 120.2 247 189.2 158.8 8 06.1 05.1 68 52.143.7 128 98.1 82.3 188 144.0 120. 8| 248 190.0 159.4 9 06.9 05.8 6952.944.4 129 98.8 82.9 189 144.8 121.5 249 190.7 100.1 10 37.7 06.4 7053.645.0 130 99.6 83. C 190 145.5 122.1 250 191.5 160.7 11 U8.4 07.1 71 34.4i45.6 131 1U0.4 84.2 191 146.3 122.8 251 192.3 161.3 12 09.2 07.7 72 55.246.3 132 101.1 84.8 192 147.1 123.4 252 193.0 162.0 13 10. 08.4 73 55.946.9 133 101 9 85.5 193 147.8 124.1 253 193.8 162.6 14 10.7 09.0 74 56.747.6 134 102.6 86.1 194 148.0 124.7 254 194.6 163.3 15 11.5 09.6 75 57.548.2 135 103.4 86.8 195 149.4 125.3 255 195.3 163.9 16 12.3 10.3 76 58.248.9 136 104.2 87.4 196 150.1 126.0 256 196.1 164.6 17 13.0 10.9 77 39.049.5 137 104.9 88.1 197 150.9 126.6 257 196.9 165.2 18 13.8 11.6 78 59.850.1 138 105.7 88.7 198 151.7 127.3 258 197.6 165.8 19 14.6 12.2 79 GO.550.8 1 139 106.5 89.3 199 152.4 127.9 259 198.4 166.5 20 15.3 12.9 80 61.351.4 140 107.2 90.0 200 153.2 128.6 260 199.2 167.1 21 16.1 13.5 81 62. 0,52. 1| 141 108.0 90.6 201 154.0 129.2 261 199.9 167.8 22 16.9 14.1 82 62.852.7 142 108.8 91 3 202 154.7 129.8 26'2 200.7 168.4 23 17.6 14.8 83 63.653.4 143 109.5 91.9 203 155.5 130.5 263 201.5 169.1 24 18.4 15.4 84 64.354.0 144 110.3 92.6 204 156.3 131.1 264 202.2 169.7 25 19.2 16.1 85 65.154.6 145 111.1 93.2 205 157.0 131 8 265 203.0 170.3 26 19.9 16.7 86 65.955.3 146 111.8 93.8 206 157.8 132.4 266 203.8 171.0 27 20.7 17.4 87 G6.655.9 147 112.6 94.5 207 158.6 133.1 267 204 5 171.6 28 21.4 18.0 88 G7.4'56.6 148 113.4 95.1 208 159.3 133.7 268 205.3 172.3 29 22.2 18.6 89 63.257.2 149 114.1 95.8 209 160.1 134.3 269 208.1 172.9 30 23.0 19.3 90 68.957.9 150 114.9 96.4 210 160.9 135.0 270 206.8 173.6 31 23.7 19.9 91 69.758.5 151 115.7 97.1 211 101.6 135.6 271 207.6 174.2 32 24.5 20.6 9270.559.1 152 116.4 97.7 212 162.4 136.3 272 208.4 174.8 33 25,3 21.2 9371.259.8 153 117.2 98.3 213 163.2 136.9 273 209.1 175.5 34 26.0 21.9 9472.060.4 154 118.0 99.0 214 163.9 137.6 274 209.9 176.1 33 26.8 22.5 9572.961.1 155 118.7 99.0 215 164.7 138.2 275 210.7 176.8 33 27.6 23.1 9073.561.7 156 119.5 100.3 216 165.5 138.8 276 211.4 177 .4 37 28.3 23.8 9774.372.4 157 120.3 100.9 217 166.2 139.5 277 212.2 178.1 38 29.1 24.4 9875.163.0 158 121.0 101.6 218 167.0 140.1 278 213.0 178.7 39 29.9 25.1 9975.863.0 159 121.8 102.2 219 107.8 140.8 27.9 213.7 179 3 40 30.6 25 . 7 10076.664.3 160 122.6 102.8 220 108.5 141.4 280 214.5 180.0 41 31.4 26.4 10177.404.9 161 123.3 103.5 221 169.3 142.1 281 215.3 180.6 42 32.2 27.0 10278.165.6 162 124.1 104.1 222 170.1 142.7 282 216.0 181.3 43 32.9 27.6 10378.966.2 163 124.9 104.8 223 170.8 143.3 283 216.8 181.9 44 33.7 28.3 10479.7G6.8 164 125.6 105.4 224 171.6 144.0 284 217.0 182.6 43 34.5 28.9 10580.467.5 165 126.4 106.1 225 172.4 144.6 285 218.3 183.2 46 35.2 29.6 10681.268.1 166 127.2 106.7 226 173.1 145.3 286 219.1 183.8 47 36.0 30.2 107 82. 068. 8 167 127.9 107.3 227 173.9 145.9 287 219.9 184.5 48 36.8 30.9 10882.769.4 168 128.7 108.0 228 174.7 146.6 288 220.6 185.1 49 37.5 31.5 10983.5,70.1 109 129.5 108.6 229 175.4 147.2 28!) 221.4 185.8 50 38.3 32.1 11084.370.7 170 130.2 109.3 230 176.2 147.8 290 222.2 186.4 ~sT 39.1 32.8 11185.071.3 171 131.0 109.9 231 177.0 148.5 291 222.9 187.1 52 39.8 33.4 11285.872.0 172 131.8 110.0 232 177.7 149.1 292 223.7 187.7 53 40.6 34.1 11386. C72.G 173 132.5 111.2 233 178.5 149.8 293 224.5 188.3 54 41.4 34.7 11487.373.3 174 133.3 111.8 234 179.3 150.4 294 225.2 189.0 55 42.1 35.4 11588.173.9 175 134.1 112.5 235 180.0 151.1 295 226.0 189.6 56 12.9 36.0 11688.974.6 176 134.8 113.1 236 180.8 151.7 290 226.7 190.3 57 43.1 36.6 1 17 89. r, 75. 2 177 135.6 113.8 237 181.6 152.3 297 227.5 190.9 58 44.4 37.3 11890.475.8 178 136.4 114.4 238 182.3 153.0 298 228.3 191.6 59 45.2 37.9 11991.276.5 179 137.1 115.1 239 183.1 153.6 299 229.0 192.2 60 46.0 38 6 12C 91.977.1 180 137.9 115.7 240 183.9 154.3 300 229.8 192.8 Dist Dep Lat Dist Dep Lat. Dist. Dep. Lat, Dist. Dep. Lat. !;Dist. Dep. Lat, For 50 Degrees. 244 TABLE IV. DIFFERENCE OP LATITUDE AND DEPARTURE FOR 41 DEGREES. Dist, Lat. Dep Dist. Lat. Dep Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. l 00.6 00.7 6116.0 40.0 121 91.3 79.4 181 136.6 118.7 241 181.9 158.1 2 01.5 01.3 6246.8 40.7 122 92.1 80.0 182 137.4 119.4 242 182.6 158.8 3 D2.3 02.0 6347.5 41.3 123 92.8 80.7 183 138.1 120.1 243 183.4 159.4 4 03.0 02.6 6448.3 42.0 124 93.6 81.4 184 138.9 120.7 244 184.1 160.1 5 03.8 03.3 6549.1 42. G 125 94.3 82.0 185 139.6 121.4 245 184.9 160 7 6 04.5 03.9 6649.8 43.3 126 95.1 82.7 186 140.4 122.0 246 185.7 161.4 7 05.3 04.6 6750.6 44.0 127 95.8 83.3 187 141.1 122.7 247 186.4 162.0 8 06.005.2 6851.3 44.6 128 96.6 84.0 188 141.9 123.3 248 187.2 162.7 9 06. & 05.9 6952.1 45.3 129 97.4 84.6 189 142.6 124.0 249 187.9 163.4 10 07.5 06.6 7052.8 45.9 130 98.1 85.3 190 143 4 124.7 250 188.7 164.0 11 08.3 07.2 7153.6 46.6 131 98 9 85.9 191 144.1 125 3 251 189.4 104.7 12 09.1 07.9 7254.3 47.2 132 99.6 86.6 192 144.9 126.0 252 190.2 165.3 13 09.8 08.5 7355.1 47.9 133 100.4 87.3 193 145.7 126.6 253 190.9 166.0 14 10. C 09.2 7455.8 48.5 134 101.1 87.9 194 146.4 127.3 254 191.7 166.6 15 13.3 09.8 7556. G 49.2 135 101.9 88.6 195 147.2 127.9 255 192 5 167.3 16 12.1 10 5 7657.4 49.9 136 102.6 89.2 19G 147.9 128.6 256 193. i 168.0 17 12.8 11.2 7758.1 0.5 137 103 4 89.9 197 148.7 129 2 257 194.0 168.6 18 13.6 11.8 7858.9 51.2 138 104.1 90.5 198 149.4 129.9 258 194.7 169.3 19 14.3 12.5 7959 6 51.8 139 104.9 91.2 199 150.2 130.6 259 195.5 1G9 9 20 15.1 13.1 8060.4 52.5 140 105.7 91.8 200 150 9 131.2 260 196.1 170 6 21 15> 13.8 8161.1 53.1 141 10JJ.4 92.5 201 151.7 131.9 '261 197.0 171.2! 22 16 6 14.4 8261.9 53.8 142 107.2 93.2 202 152.5 132.5 262 197.7 171.9' 23 17.4 15.1 8362.6 54.5 143 107.9 93.8 203 153.2 133.2 263 198 5 172 5 24 18 1 15.7 8463 4 55.1 144 108.7 94.5 204 154. ( 133.8 264 199.2 173.2 25 18.9 16.4 8564.2 55.8 145 109.4 95.1 205 154.7 134.5 265 200.0 173.9 26 19. G 17.1 8664.9 56.4 146 110 2 95.8 206 155.5 135.1 266 200.8 174.5 27 20.4 17.7 8765.7 57.1 147 110.9 96.4 207 156.2 135.8 267 201.5 175.2 28 21.1 18.4 8866.4 57.7 148 111 7 97.1 208 157.0 136.5 268 202.3 175 8 29 21.9 19.0 8967.2 58 4 149 112 5 97.8 209 157.7 137.1 269 203.0 176.5 30 22.6 19.7 9067.9 59.0 150 113.2 98.4 210 158.5 137.8 270 203.8 177.1 ~3T 23.4 20.3 916N.7 59.7 151 114.0 99.1 211 159.2 138.4 271 204.5 177.8 32 24.2 21.0 9269.4 60.4 152 114.7 99.7 212 160.0 139.1 272 205.3 178.4 33 24.9 21.6 9370.2 61.0 153 115.5 100.4 213 1G0.8 139.7 273 206 179.1 34 25.7 22.3 9470.9 61.7 154 116 2 101.0 214 161 5 140.4 274 206.8 179.8 35 26.4 23.0 9571.7 62.3 155 117.0 101.7 215 162.3 141.1 275 207.5 180.4 36 27.2 23.6 9672.5 63.0 156 117.7 102.3 216 163.0 141.7 276 208.3 181.1 37 27.9 24.3 9773.2 63.6 157 118.5 103 217 163.8 142.4 277 209.1 181.7 38 28.7 24.9 9874.0 64.3 158 119.2 103.7 218 164.5 143.0 278 209.8 182.4 39 29.4 25.6 9974.7 64.9 159 120.0 104.3 219 165.3 143.7 279 210.6 183.0' 40 30.2 26.2 10075.5 65.6 160 120.8 105.0 220 166.0 144.3 280 211.3 183.7 41 30.9 26.9 10176.2 66.3 161 121.5 105. G 221 166.8 145.0 281 212.1 184.4 42 31.7 27.6 10277.0 66.9 162 122.3 106. 3 222 167.5 145.6 282 212.8 185.0 43 32.5 28 2 10377.7 67.6 163 123.0 106.9 223 168.3 146.3 283 213. G 185.7 44 33.2 28.9 10478.5 68.2 164 123.8 107.6 224 169.1 147.0 284 214.3 186.3 45 34.0 29 5 10579.2 68.9 165 124.5 108.2 225 1G9.8 147.6 285 215.1 187.0 40 34.7 30.2 10680.0 69.5 16G 125.3 108 9 226 170.6 148.3 286 215.8 187.6 47 35.5 30,8 10780.8 70.2 167 126 109.6 227 171.3 148.9 287 216.6 188.3 48 36.2 31.5 10881.5 70.9 168 126.8 110.2 228 172.1 149.6 288 217.4 188.9 49 37.0 32.1 10982.3 71.5 169 127.5 110.9 229 172.8 150.2 289 218.1 189.6 50 37.7 32.8 11083.0 72.2 170 128.3 111.5 230 173.6 150.9 290 218.9 190.3 51 38.5 33 5 11183.8 72.8 171 129.1 112.2 231 174.3 151.5 291 219.6 190.9 52 39.2 34.1 11284.5 73.5 172 129.8 112.8 232 175.1 152.2 292 220 4 191.6, 53 40.0 34.8 11385.3 74.1 173 130.6 113.5 233 175.8 152.9 293 221J 192 2 54 40.8 35.4 11486.0 74.8 174 131.3 114.2 234 176.6 153.5 294 221.9 192.9 55 41.5 36.1 11586.8 75.4 175 132.1 114.8 235 177.4 154.2 295 222.6 193.5 56 42.3 36.7 11687.5 76.1 176 132.8 115.5 236 178.1 154.8 296 223.4 194 2 57 43.0 37.4 11788.3 76.8 177 133.6 116.1 237 178.9 155.5 297 224.1 194 8 58 43.8 38.1 11889 1 77.4 178 134.3 116.8 238 179.6 156.1 298 224 9 195.5; 59 44.5 38.7 11989 8 78 I 179 135.1 117.4 239 180.4 156.8 299 225.7 196 2 60 45.3 39 4 12090.6 78.7 180 135.8 118.1 240 181.1 157.5 300 226.4 196.8 Oist. Dep Lat. Dist. Dep Lat. Dist, Dep. Lat. Dist, Dep. Lat. Dist, Dep. Lat. For 49 Degrees. TABLE IV. 245 DIFFERENCE OF LATITUDE AND DEPARTURE FOR 42 DEGREES. Dist. Lat. Pep Dist. Lat. Pep IMst. Lat. Pep. Dist. Lat. Pep. Dist. Lat. Pep. \ '0.700.7' 61 15.8*0:8 121 89.9 81.0 181 134.5 121. 1 ! 241 179.1 161.3 2 01 501.3 62 16.141.5 122 90.7 81.6 182 135.3 121.8! 242 179.8 161.9 3 02.202.0 63 46.8,42 2 123 91.4 82.3 183 136.0 122.5 243 180.6 162.6 4 03.002.7 64 17.642.8 124 92.1 83 184 136.7 123 . 1 244 181 3 163.3 5 13.703.3 65 18.343.5 125 92.9 83.6 185 137.5 123.8 245 182.1 163.9 6 04.5 >4.0 66 49.044.2 126 93.6 84.3 186 138.2 124.5 246 182.8 164.6 7 5.204.7 67 19 844.8 127 94.4 85.0 187 139.0 125.1 247 183.6 165.3 8 05.905.4 68 50 . 5 15 . 5 128 95.1 85.6 188 139.7 125.8 248 184.3 165.9 9 06.706.0 69 31.346.2 12!) 95.9 86.3 189 140.5 126.5 249 185.0 166.6 10 07.4-06.7; 70 32.046.8 130 96.6 87.0 190 141.2 127.1 250 185.8 167.3 11 08.207.4 71 V2.847.5 131 97.4 87.7 191 141.9 127.8 251 186.5 168.0 12 08.9 >8 72 53.5 48.2 132 98.1 88.3 192 142.7 128.5 252 187.3 168.6 13 09 708.7 73 54.2 48.8 133 98.8 89.0 193 143.4 129.1 253 188.0 169.3 14 10.409.4 74 55 49.5 134 99.6 89.7 194 144.2 129 8 254 188.8 170. (i 15 11.1 10. 75 55.7 50.2 135 100 3 90.3 195 144.9 130.5 255 189.5 170.6 16 11.910.7 76 56.5 50.9 136 101.1 91.0 196 145.7 131.1 256 190.2 171.3 17 12.6,11.4 77 57.2 51.5 137 101.8 91.7 197 146.4 131.8 257 191.0 172.0 18 13.412.0 : 78 58.0 52.2 138 102.6 92.3 198 147.1 132.5 258 191.7 172.6 19 14.1 12. 7j 79 58 7 52.9 139 103.3 93.0 199 147.9 133.2 259 192.5 173.3 20 U.913.4 80 59.5 53 5 140 104.0 93.7 200 148.6 133.8 260 193.2 174.0 ~2T 15.614.1 81 30 254.2 141 104.8 94.3 201 149.4 134.5 261 194.0 174.6 22 16.314.7 82 30 . 9 54 . 9 142 105.5 95.0 202 150.1 135.2 262 194.7 175.3 23 17.1 15.4 83 61.755.5 143 106.3 95.7 203 150.9 135.8 263 195.4 176.0 24 17.816.1 84 62.456.2 144 107.0 96.4 204 151.6 136.5 264 196.2 176.7 25 18.616.7 85 63.256.9 145 107.8 97.0 205 152.3 137.2 265 196.9 177.3 2C> 19.317.4 86 63.957.5 146 108 5 97.7 206 153.1 137.8 266 197.7 178.0 27 20 1 18.1 87 34.7 58.2 147 109.2 98.4 207 153.8 138 5 267 198.4 178.7 js 20.818.7 88 65.4 58 9 148 110.0 99.0 208 154.6 139.2 268 199.2 179.3 29 21.619.4 89 66.1 59.6 149 110.7 99.7 209 155.3 139.8 269 199 9 180.0 30 2-2.320.1 90 36.9 60.2 150 111.5 100.4 210 156.1 140.5 270 200.6 180.7 ~3T 23.0:20.7. 91 87. 6]60.9 151 112.2 101.0 211 156.8 141 2 271 201.4 181. 3j 32 23. 8 21. 4 1 92 <58.4'61.6 152 113.0 101.7 212 157.5 141.9 272 202.1 182.0! 33 .'4.5,22.1 93 69.162.2 153 113.7 102.4 213 158.3 142.5 273 202.9 182.7, 34 25.322.8 94 69.962.9 154 114.4 103.0 214 159 143.2 274 203.6 183.3 35 26.0'23.4 95 70.663.6 155 115.2 103.7 215 159 8 143.9 275 204. 4 184.0 30 126.824 1 9(J 71.364.2 156 115.9 104.4 216 160.5 144.5 276 205.1 X 184.7 37 27.524.8 97 72.164.9 157 116 7 105.1 217 161.3 145.2 277 205.9 185.3 38 28.225.4 98 72.865.6 158 117.4 105.7 218 162.0 145.9 278 206.6 186.0 39 29.026.1 99 73.666.2 159 118.2 106.4 219 162.7 146.5 279 207.3 186.7 40 29.726.8 100 74.3;66.9 160 118.9 107.1 220 163.5 147.2 280 208.1 187.4 41 J30 5,27.4 101 75.1;67.6 161 119.6 107.7 221 164.2 147.9 2811 208.8 188.0 42 31.228.1 102 75.868 3 162 120.4 108.4 222 165.0 148.5 282 209.6 188.7 43 32.0:28.8 103 76.568.9 163 121.1 109 . 1 223 165.7 149.2 283 210.3 189.4 44 32.729.4 104 77 369 6 164 121 9 109.7 224 166.5 149.9 284 211.1 190.0 45 33 4;30.1 105 78.070.3 165 122.6 110.4 225 167.2 150.6 285 211.8 190.7 46 34.230.8 106 78 870.9 166 123 4 111.1 226 168.0 151.2 286 212.5 191.4 47 St. 931. 4 107 79.5 71.6 167 124.1 111.7 227 168.7 151.9 287 213.3 192.0 48 35.73-2.1 108 80.3 72.3 168 124.8 112.4 228 169.4 152.6 288 214.0 192.7 49 36.432.8 109 81.072.9 169 125.6 113.1 229 170.2 153.2 289 214.8 193.4 50 37.233.5 110 81.7 73.6 170 126.3 113 8 230 170.9 153.9 290 215.5 194.0 51 37.934.1 111 82.5 74.3 171 127 . 1 114.4 231 171.7 154.6 291 216.3 194.7 52 38.634.8 112 83.2 74 9 172 127.8 115.1 232 172.4 155.2 292 217.0 195.4 53 39.435.5 113 84.0 75.6 173 128.6 115.8 233 173.2 155.9 293 217.7 196.1 .'.I 10.136.1 114 84.7 76.3 174 129.3 116.4 234 173.9 156.61 294 218.5 196.7 55 40.936.8 115 85.5 77.0 175 130.1 117.1 235 174.6 157.2 295 219.2 197.4 56 41.6,37.6 116 86.2 77.6 176 130.8 117.8 236 175.4 157.9] 296 220.0 198.1 .',7 12.438.1 117 86.9 78.3 J77 131.5 118.4 237 176.1 158.6, 297 220.7 198.7 58 43.1138.8 118 87.7 79.0 178 132.3 119.1 238 176.9 159.3* 298 221.5 199.4 59 l;i. *:!'. r, 119 88.4 79.6 179 133.0 119.8 239 177.6 159.91 299 222.2 200.1 60 44.640.1 120 89.2 80.3 1HI 133.8 120.4 240 178.4 160.6 300 222.9 200.7 Dist. Pep Lat. Dist. Pei> Lilt. Dist. Pep. Lat. Dist. Pep. Lat. Dist. Pep. Lat For 48 Degrees. 246 TABLE IV. DIFFERENCE OF LATITUDE AND DEPARTURE FOR 43 DEGREES. iDist. Lat. Dep Dist. Lat. Dep Dist. Lat, Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 00.7 00.7 61 44.6 41. 6 121 88.5 82. 5' 181 132.4 123.4 241 176.3 164.4 2 01.5 01.4 62 45.3 42.3 12'2 89 2 83.2 182 133.1 1-24.1 242 177.0 165.0 3 02.2 02.0 63 46.1 43.0 123 90.0 83. 9 1 183 133.8 124.8 243 177.7 165.7 4 02.9 02.7 64 46.8 43.6 124 90.7 84.6 184 134.6 125.5 244 178.5 166.4 5 03.7 03.4 65 47.5 44.3 125 91.4 85. 2i 185 135.3 126.2 245 179.2 167.1 6 04.4 04.1 66 48.3 45.0 126 92.2 85.9 186 136.0 126.9 246 179.9 167.8 7 05.1 04.8 67 49.0 45.7 127 92.9 86.6 187 136.8 127.5 247 180.6 168.5 8 05.9 05.5 68 19.7 46.4 128 93.6 87.3; 188 137.5 128.2 248 181.4 169.1 9 06.6 06.1 69 50.5 47.1 129 94.3 88.0; 189 138.2 128.9 249 182.1 169.8 10 07.3 06.8 70 51.2 47.7 130 95 1 88. 7| 190 139.0 129.6 250 182.8 170 5 11 08.0 07.5 71 51.9 48.4 131 95.8 b'9.3 191 139.7 130.3 251 183.6 171.2 12 08.8 08.2 72 52.7 49.1 132 96.5 90.0 192 140.4 130.9 252 184.3 171.9 13 09.5 08.9 73 53.4 49.8 133 97.3 90. ?! 193 141.2 131.6 253 185.0 172.5 14 10.2 09.5 74 o4.1 50.5 134 98.0 91.4 194 141.9 132 3 254 185.8 173.2 15 11.0 10.2 75 54 9 51. ] 135 98.7 92.1 195 142.6 133 255 186.5 173.9 16 11.7 10.9 76 55 6 51.8 136 99.5 92.8 196 143.3 133.7 256 187.2 174.6 17 12 4 11.6 77 56.3 52.5 137 100.2 93.4 197 144.1 134.4 257 188.0 175.3 18 13.2 12 3 78 57.0 53.2 138 100 9 94.1 198 144.8 135.0 258 188.7 176.0 19 13 9 13.0 79 57.8 53.9 139 101.7 94.8 199 145.5 135.7 259 189.4 176.6 20 14.6 13.6 80 58.5 54.6 140 102.4 95.5 200 146.3 136.4 260 190 2 177.3 21 15.4 14.3 81 59.2 55.2 141 103.1 96.2 201 147.0 137.1 261 190.9 178,0 22 16.1 15 82 60 55.9 142 103.9 96.8 202 147.7 137.8 262 191.6 178.7 23 16.8 15.7 83 60.7 56.6 143 104.6 97.5 203 148.5 138.4 263 192.3 179.4 24 17.6 16.4 84 61.4 57.3 144 105.3 98.2 204 149.2 139.1 264 193.1 180.0 25 18.3 17.0 85 62.2 58. (i 145 106.0 98.9 205 149.9 139.8 265 193.8 180.7 26 19.0 17.7 86 62.9 58.7 146 106.8 99.6 206 150.7 140.5 266 194.5 181.4 27 19.7 18.4 87 63.6 59.3 147 107.5 100.3 207 151.4 141.2 267 195.3 182.1 28 20.5 19.1 88 64.4 60.0 148 108.2 100.9 208 152.1 141.9 268 196.0 182 8 29 21.2 19.8 89 65'. 1 60.7 149 109 101.6 209 152.9 142.5 269 196.7 183.5 30 21.9 20.5 90 65.8 61 4 150 109.7 102.3 210 153.6 143.2 270 197.5 184.1 31 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 62.7 152 111.2 103.7 212 155.0 144.6 272 198.9 185.5 33 24.1 22.5 93 68.0 63.4 153 111.9 104.3 213 155.8 145 3 273 199.7 186.2 34 24.9 23.2 94 68.7 64.1 154 112.6 105.0 214 156.5 145.9 274 200.4 186.9 35 25.6 23.9 95 69.5 64.8 155 113.4 105.7 215 157.2 146.6 275 201.1 187.5 36 26.3 24.6 96 70.2 65.5 156 114.1 106 4 216 158.0 147.3 276 201.9 188.2 37 27.1 25.2 97 70.9 66.2 157 114.8 107.1 217 158.7 148.0 277 202. G 188.9 38 27.8 25.9 98 71.7 66.8 158 115.6 107.8 218 159.4 148.7 278 203.3 189.6 39 28.5 26 6 99 72.4 67.5 159 116.3 108.4 219 160.2 149.4 279 204.0 190.3 40 29.3 27.3 100 73.1 68.2 160 117.0 109.1 220 160.9 150.0 280 204.8 191.0 41 30.0 28.0 101 73.9 68.9 161 117.7 109.8 2i!l 161.6 150.7 281 205.5 191.6 42 30.7 28.6 102 74.6 69.6 162 118.5 110.5 222 162.4 151.4 282 206.2 192.3 43 31.4 29 3 103 75.3 70.2 163 119.2 111.2 223 163.1 152.1 283 207.0 193.0 44 32.2 30.0 104 76.1 70.9 164 119.9 111.8 224 163.8 152.8 284 207.7 193.7 45 32.9 30.7 105 76.8 71.6 165 120.7 112.5 225 164.0 153 4 285 208.4 194.4 46 33.6 31.4 106 77.5 72.3 166 121.4 113.2 226 165.3 154.1 286 209.2 195.1 47 34.4 32.1 107 78.3 73.0 167 122 1 113.9 227 166.0 154.8 287 209.9 195.7 48 35.1 32.7 108 79.0 73.7 168 122.9 114 6 22s 166.7 155.5 288 210.6 196.4 49 35.8 33.4 109 79.7 74.3 169 123.6 115.3 2-29 167.5 156.2 289 211.4 197.1 50 36.6 34.1 110 80.4 75.0 170 124 3 115.9 230 168.2 156.9 290 212.1 197.8 51 37.3 34.8 111 81.2 75.7 171 1*5.1 116. 6i 231 168 . y 157 5 291 212.8 198.5 52 38.0 35.5 112 81.9 76.4 172 125.8 117. 3 1 232 169.7 158 2 292 213.6 199 1 53 38.8 36.1 113 82.6 77.1 173 126.5 118.0 233 170.4 158.9 293 214.3 199.8 54 39.5 36.8 114 83.4 77.7 174 127.3 118. 7i 234 171.1 159.6 294 215.0 200.5 55 10 2 37.5 115 84.1 78 4 175 128.0 119.3 235 171.9 160.3 295 215.7 201.2 56 41.0 38.2 116 84.8 79.1 176 128.7 120.0 236 172.6 161.0 296 216.5 201.9 57 41.7 38 9 117 85.6 79.8 177 129.4 120.7 237 173.3 161.6 297 217.2 202.6 58 42.4 39.6 11886.3 80.5 178 130.2 121.4! 238 174.1 162.3 298 217.9 203.2 59 43.140 2 11987.0 81.2 179 130.9 122.1 239 174.8 163.0 299 218.7 203.9! 60 43.9 40.9 120 87.8 81.8 180 131.6 122.8 240 175.5 163.7 300 219.4 204.6 Dist. Dcp Lat. Dist. Dep Lat. Dist. Dep. Lat. i Dist, Dep. Lat. Dist. Dep. Lat. For 47 Degrees. TABLE IV. 247 DIFFERENCE OF LATITUDE AND DEPARTURE FOR 44 DEGREES. Dist, Lat. Dep Dist, Latfoep Dist. Lat. Dep. Dist, Lat. Dep. Dist. Lat. Dep. 1 00.7 00.7 6143.942.4 121 87.0 84.1 181 130.2 125.7 241 173.4 167.4 2 01.4 01.4 6244.643.1 122 87.8 84.7 182 130.9 126.4 242 174.1 168.1 3 02.2 02.1 6345.343.8 123 88.5 85.4 183 131.6 127 1 243 174.8 168.8 4 02.9 02.8 6446.044.5 124 89.2 86.1 184 132.4 127.8 244 175.5 169.5 5 03.6 03.5 6546.845.2 125 89.9 86.8 185 133.1 128.5 245 176.2 170.2 6 04.3 04.2 6647.545.8 126 90.6 87.5 186 133.8 129.2 246 177.0 170.9 7 05.0 04.9 6748.246.5 127 91.4 88.2 187 134.5 129.9 247 177.7 171.6 8 05.8 05.6 6848.947.2 128 92.1 88.9 188 135.2 130.6 248 178.4 172.3 9 06.5 06.3 6949.647.9 129 92.8 89.6 189 136.0 131.3 249 179.1 173.0 10 07.2 06.9 7050.448.6 130 93.5 90.3 190 136.7 132.0 250 179.8 173.7 11 07.9 07.6 71151.149.3 131 94.2 91.0 191 137.4 132.7 251 180.0 174.4 12 08.6 08.3 72,51.850.0 132 95.0 91.7 192 138.1 133.4 252 181.3 175.1 13 09.4 09.0 73,52.550.7 133 95 7 92.4 193 138.8 134.1 253 182.0 175.7 14 10.1 09.7 7453.251.4 134 96.4 93.1 194 139.6 134.8 254 182.7 176.4 15 10.8 10.4 75 54.052.1 135 97.1 93.8 195 140.3 135.5 255 183.4 177.1 16 11.5 11.1 76 54.752.8 136 97.8 94.5 196 141.0 136.2 256 184.2 177.8 17 12.2 11.8 7755.453.5 137 98.5 95.2 197 141.7 136.8 257 184.9 178.5 18 12.9 12.5 7856.154.2 138 99.3 95.9 198 142.4 137.5 258 185.6 179.2 19 13.7 13.2 7956.854.9 139 100.0 96.6 199 143.1 138.2 259 186.3 179.9 20 14.4 13.9 80 57.555.6 140 100.7 97.3 200 143.9 138.9 260 187.0 180.6 21 15.1 14.6 81 58.3i56.3 141 101.4 87.9 201 144.6 139.6 261 187.7 181.3 22 15.8 15.3 82 59.057.0 142 102.1 98 6 202 145.3 140.3 26-2 188.5 182.0 23 16.5 16.0 8359.7 57.7 143 102.9 99.3 203 146.0 141.0 263 189.2 182.7 24 17.3 16.7 8460.4 58.4 144 103.6 100.0 204 146.7 141.7 264 189.9 183.4 25 18.0 17.4 8561.1 59.0 145 104.3 100.7 205 147.5 142 4 265 190.6 184.1 26 18.7 18.1 8661.959.7 146 105.0 101.4 206 148.2 143.1 266 191.3 184.8 27 19.4 18.8 8762.660.4 147 105.7 102.1 207 148.9 143.8 267 192.1 185.5 28 20.1 19.5 8863.361.1 148 106.5 102.8 208 149.6 144.5 268 192.8 186.2 29 20.9 20.1 8964. 061. & 149 107.2 103.5 209 150.3 145.2 269 193.5 186.9 30 21.6 20.8 9064.762.5 150 107.9 104.2 210 151.1 145.9 270 194.2 187. Gj 31 22.3 21.5 91G5.563.2 151 108.6 104.9 211 151.8 146.6 271 194.9 188.3 32 23.0 22.2 9266.263.9 152 109.3 105.6 212 152.5 147.3 272 195.7 188.9 33 23.7 22.9 9366.9,64.6 153 110.1 106.3 213 153.2 148.0 273 196.4 189.6 34 24.5 23.6 9467.665.3 154 110.8 107.0 214 153.9 148.7 274 197.1 190.3 35 25.2 24.3 9568.366.0 155 111.5 107.7 215 154.7 149.4 275 197.8 191.0 36 25.9 25.0 9669.1 66.7 156 112.2 108.4 216 155.4 150.0 276 198.5 191.7 37 26.6 25.7 97 69. 8 67.4 157 112.9 109.1 217 156.1 150.7 277 199.3 192.4 38 27.3 26.4 9870.5 68.1 158 113.7 109.8 218 156.8 151.4 278 200.0 193.1 39 28.1 27.1 9971.268.8 159 114.4 110.5 219 157.5 152.1 279 200.7 193 8 40 28.8 27.8 10071. 9,69. 5 160 115.1 111 1 220 158.3 152.8 280 201.4 194.5 41 29.5 28.5 101 72.7 70.2 161 115.8 111.8 221 159.0 153.5 281 202.1 195.2 42 30.2 29.2 102 73.4 70.9 162 116.5 112.5 222 159.7 154.2 282 202.9 195.9 43 30.9 29.9 10374.1 71.5 163 117.3 113.2 223 160.4 154.9 283 203.6 196.6 44 31.7 30.6 104i74.8 72.2 164 118.0 113.9 224 161.1 155.6 284 204.3 197.3 45 32.4 31.3 10575.5 72.9 165 118.7 114.6 225 161.9 156.3 285 205.0 198.0 46 33.1 32.0 10676.3 73.6 166 119.4 115.3 226 162.6 157.0 286 205.7 198.7 47 33.8 32.6 10777.0 74.3 167 120.1 116:0 227 163.3 157.7 287 206.5 199.4 48 34.5 33.3 10877.7 75.0 168 120.8 116.7 228 164.0 158.4 288 207.2 200.1 49 35.2 34.0 10978.4 75.7 169 121.6 117.4 229 164.7 159.1 289 207.9 200.8 50 36.0 34.7 11079.176.4 170 122.3 118.1 230 165.4 159.8 290 208.6 201.5 51 36.7 35.4 111 79.877.1 171 123.0 118.8 231 166.2 160.5 291 209.3 202.1 52 37.4 36.1 11280.677.8 172 123.7 119.5 232 166.9 161.2 292 210.0 202.8 53 38.1 36.8 11381.378.5 173 124.4 120.2 233 167.6 161.9 293 210.8 203.5 54 38.8 37.5 114 82.079.2 174 125.2 120.9 234 168.3 162.6 294 211.5 204.2 55 39.6 38.2 115 82.7 79.9 175 125.9 121.6 235 169.0 163.2 295 212.2 204.9 56 40.3 38.9 116 83.4 80.6 176 126.6 122.3 236 169.8 163.9 296 212.9 205.6 57 41.0 39.6 117 84.2 81.3 177 127.3 123.0 237 170.5 164.6 297 213.6 206.3 58 41.7 40 3 118 84.982.0 178 128.0 123.6 238 171.2 165.3 298 214.4 207.0 59 42.4 41.0 119 85.682.7 179 128.8 124.3 239 171.9 166.0 299 215.1 207.7 60 43 2 41.7 120 86.3 83.4 180 129 5 125.0 240 172.6 166.7 300 215.8 208.4 Dist. Dep Lat. Dist, Dep Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist, Dep. Lat, For 4G Degrees. 248 TABLE IV. DIFFERENCE OF LATITUDE AXD DEPARTURE FOR 45 DEGREES. Dist. Lat. Dep Dist. Lat. Dep Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 00.7 00.7 61 43.1 43.1 121 85.6 85.6 181 128.0 128.0 241 170.4 170.4 2 01.4 01.4 62 43.8 43.8 122 86.3 86.3 182 128.7 128.7 242 171.1 171.1 3 02.1 02.1 63 44.5 41.5 123 87.0 87.0 183 129.4 129.4 243 171.8 171.8 4 02.8 02.8 64 45.3 45.3 124 87.7 87.7 184 130.1 130.1 244 172.5 172.5 5 03.5 03.5 65 46.0 46.0 125 88.4 88.4 185 130.8 130.8 245 173.2 ]73.2 6 04.2 04.2 66 16.746.7 126 89.1 89.1 186 131.5 131.5 246 173.9 173.9 7 04.9 04.9 67 47.4 47.4 127 89.8 89.8 187 132.2 132.2 247 174.7 174.7 8 05.7 05.7 68 48.1 48.1 128 90.5 90.5 188 132.9 132.9 248 175.4 175.4 9 06.4 06.4 69 48.8 48.8 129 91.2 91.2 189 133.6 133.6 249 176.1 176.1 10 07.1 07.1 70 49.549.5 130 91.9 91.9 190 134.3 m.3 250 176.8 176.8 11 U7.8 07.8 71 50.250.2 131 92.6 92. ( 191 135.1 135.1 '251 177.5 177.5! 12 08.5 08.5 72 50.950.9 132 93 3 93.3 192 135.8 135.8 252 178.2 178.2 13 09.2 09.2 73 51.651.6 133 94.0 94.0 193 136.5 136.5 253 178.9 178.9 14 09.9 09.9 74 52.352.3 134 94.8 94.8 194 137.2 137.2 254 179.6 179.6 15 10.6 10.6 75 53.053.0 135 95.5 95.5 195 137.9 137.9 255 180.3 180.3 16 11.3 11.3 76 53.753.7 136 96.2 96.2 196 138.6 138.6 256 181.0 181.0 17 12.0 12.0 77 54.454.4 137 96.9 96.9 197 139.3 139.3 257 181.7 181.7 18 12.7 12.7 78 55.255.2 138 97.6 97.6 198 140.0 140.0 258 182.4 182.4 19 13.4 13.4 79 55.955.9 139 98.3 98.3 199 140.7 140.7 259 183.1 183.1 20 14.1 14.1 80 56.656.6 140 99.0 99 200 141.4 141.4 260 183.8 183.8 21 14.8 14.8 81 57.357.3 141 99.7 99.7 201 142.1! 142.1 261 184.0 184.6 22 15 6 15 6 82 58.058.0 142 100.4 100.4 202 142.8 142.8 262 185. 185.3 23 16.3 16.3 83 58.758.7 143 101.1 101.1 203 143.5 143.5 263 186 186.0 24 17.0 17.0 84 59 459.4 144 101.8 101.8 204 144.2 144.2 264 186. 186.7 25 17.7 17.7 85 60.160.1 145 102.5 102.5 205 145.0 145.0 265 187. 187.4 26 18.4 18.4 86 60.860.8 146 103.2 103.2 206 145.7 145.7 266 188. 183.1 27 19.1 19.1 87 61.561.5 147 103.9 103.9 207 146.4 146.4 267 188. 188.8 28 19.8 19.8 88 62.262.2 148 104.7 104.7 208 147.1 147.1 268 189. 189 5 29 20.5 20.5 89 62.962.9 149 105.4 105.4 209 147.8 147.8 269 190. 190.2 30 21.2 21.2 90 63.6 63.6 150 106.1 106.1 210 148.5 148.5 270 190. 190 9 31 21.9 21.9 91 64.3 64.3 151 106. b 106.8 211 149.2 149.2 271 191. 191.0 32 22.6 22.6 92 65.1 65.1 152 107.5 107.5 212 149.9 149.9 272 192. 192.3 33 23.3 23.3 93 65.8 65.8 153 108.2 108.2 213 150.6 150.6 273 193. 193.0 34 24.0 24.0 94 66.5 66.5 154 108.9 108.9 214 151.3 151.3 274 193. 193.7 35 24.7 24.7 95 67.2 67.2 155 109.6 109.6 215 152.0 152.0 275 194. 194.5 36 25.5 25.5 96 67.9 67.9 156 110.3 110.3 216 152.7 152.7 276 195. 195.2 37 26.2 26.2 97 68. 6 68.6 157 111.0 111 217 153.4 153.4 277 195. 195.9 38 26.9 26.9 98 69.3 69.3 158 111.7 111.7 218 154.1 154.1 278 196. 196.6 39 27.6 27.6 99 70.0 70.0 159 112.4 112.4 219 154.9 154.9 279 197. 197.3 40 28.3 28.3 100 70.7 70.7 160 113.1 113.1 220 155.6 155.6 280 198.0 198.0 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 29.7 102 72.1 72.1 162 114.5 ]14.5 222 157.0 157.0 282 199.4 199.4 43 30.4 30.4 103 72.8 72.8 163 115.3 115.3 223 157.7 157.7 283 200.1 200.1 44 31.1 31.1 104 73.5 73.5 164 116.0 116.0 224 158.4 158.4 284 200.8 200.8 45 31.8 31.8 105 74.2 74.2 165 116.7 116.7 225 159.1 159.1 285 201.5 201.5 46 32.5 32.5 106 75.0 75.0 166 117.4 117 4 226 159.8 159.8 286 202.2 202.2 47 33.2 33.2 107 75.7 75.7 167 118 1 118.1 227 160.5 160.5 287 202.9 202.9 48 33.9 33.9 108 76.4 76.4 168 118.8 118.8 228 161.2 161.2 288 203.6 203.6 49 34.6 34.6 109 77.1 77.1 169 119.5 119.5 229 161.9 161.9 289 204.3 204.3 50 35.4 35.4 110 77.8 77.8 170 120.2 120.2 230 162.6 162.6 290 205.1 205.1 51 36.1 36.1 111 78.5 78.5 171 120.9 120.9 231 163.3 163.3 291 205.8 '2U5 8 52 36.8 36.8 112 79.2 79.2 172 121.6 121.6 232 164.0 164.0 292 206 5 206.5 53 37.5 37.5 113 79.979.9 173 122.3 122.3 233 164.8 164.8 293 207.2 207.2 54 38.2 38.2 114 80.680.6 174 123.0 123.0 234 165.5 165.5 294 207.9 207.9 55 38.9 38.9 115 81.381.3 175 123.7 123.7 235 166.2 166.2 295 208.6 208.6 56 39.6 39.6 116 82.082.0 176 124.4 124.4 236 166.9 166.9 296 209.3 209 3 57 10.3 40.3 117 82.7 82.7 177 125.2 125.2 237 167.6 167.6 297 210.0 210 58 41.0 41.0 118 83 4 83.4 178 125.9 125.9 238 168.3 168.3 298 210.7 210 7 59 41.7 41.7 119 84.1 84.1 179 126.6 126.6 239 169.0 169.0 299 211.4 211 4 60 42 4 42.4 12084.9 84.9 180 127.3 127.3 240 169.7 169.7 300 212.1 212.1 Dist. Dep Lat. DistJDep Lat. Dist, Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat, For 45 Degrees. TABLE V. 249 MERIDIONAL PARTS. M. 1 2 3 40 5 6 70 8 9 10 11 12 13 14D 15 1C. 60 120 IbO 240 300 361 421 482 542 003 064 725 787 849 910 1 1 61 121 181 241 301 362 422 483 543 6041 665 726 788 850 912 1 2 2 62 122 182 242 302 363 423 484 544 605 666 727 789 851 913 2 3 3 63 123 183 243 303 864 424 485 545 606 667 728 790 852 914 3 4 4 G4 124 184 244 304 365 425 486 546 607 668 729 791 853 915 4 5 5 65 125 185 245 305 366 426 487 547 608 669 730 792 854 916 5 6 6 66 126 186 246 306 367 427 488 548 609 670 731 793 855 917 6 7 7 67 127 187 247 307 368 428 489 549 610 671 732 794 856 918 7 8 8 68 128 188 248 308 369 429 490 550 611 672 734 795 857 919 8 9 9 69 129 189 249 309 370 430 491 551 612 673 735 796 858 920 9 10 10 70 130 190 250 3iO 371 431 492 552 613 6V4 V36 797 859 9J4 10 11 11 71 131 191 251 311 372 432 493 553 614 675 737 798 860 922 11 12 12 72 132 192 252 312 373 433 494 554 615 676 738 799 861 923 12 13 13 73 133 193 253 313 374 434 495 555 616 677 739 800 862 924 13 14 14 74 134 194 254 314 375 435 496 556 617 678 740 801 863 925 14 15 15 75 135 195 255 315 376 436 497 557 618 679 741 802 864 926 15 16 16 76 136 196 256 316 377 437 498 558 619 680 742 833 865 927 16 17 17 77 137 197 257 317 378 438 499 559 620 681 743 804 866 928 17 18 18 78 138 198 258 318 379 439 500 560 621 682 744 805 867 92S 18 19 19 79 139 199 259 319 380 440 501 561 622 683 745 806 868 930 19 20 20 80 140 200 260 320 381 441 502 562 623 684 746 807 869 931 20 21 21 81 141 201 261 321 382 442 503 564 624 685 747 808 870 932 21 22 22 82 142 202 262 32-2 383 443 504 565 625 687 748 809 871 933 22 23 23 83 143 203 263 323 384 444 505 566 626 688 749 810 872 934 23 24 24 81 144 204 264 324 385 445 506 567 627 689 750 811 873 935 24 25 25 85 145 205 265 325 386 446 507 568 628 690 751 812 874 936 25 26 26 86 14C 200 266 326 387 447 508 569 629 691 732 813 875 937 26 27 27 87 147 207 267 327 388 448 509 570 631 692 753 815 876 938 27 28 28 8S 148 208 268 328 389 449 510 571 632 693 754 816 877 939 28 29 29 89 149 209 269 330 390 450 511 572 633 694 755 817 878 941 29 30 30 90 150 210 270 331 391 451 512 573 634 695 756 "818 879 942 30 31 31 91 151 211 271 332 392 452 513 574 635 696 757 819 880 943 31 32 32 92 152 212 272 333 393 453 514 575 636 697 758 820 882 944 32 33 33 93 153 213 73 334 394 454 515 576 637 698 759 821 883 915 33 34 34 94 154 214 274 335 395 455 516 577 638 699 760 822 884 946 34 35 35 95 155 215 275 336 396 456 517 578 639 700 761 823 885 947 35 3G 36 96 156 216 276 337 397 457 518 579 640 701 762 824 886 948 36 37 37 97 157 217 277 338 39$ ,458 519 580 641 702 763 825 887 949 37 38 38 98 158 218 278 339 399 459 520 581 642 703 764 826 888 950 38 39 39 99 159 219 279 340 400 460 521 582 643 704 765 827 889 951 39 40 40 10U 160 "2M 280 341 401 461 522 583 644 705 766 8*8 890 952 40 41 41 101 161 221 281 342 402 462 523 584 645 706 767 829 891 953 41 42 42 102 162 222 282 343 403 463 524 585 646 707 768 830 892 954 42 43 43 103 163 223 283 344 404 464 525 586 647 708 769 831 893 955 43 44 44 104 104 224 284 345 405 465 526 587 648 709 770 832 894 956 44 45 45 105 165 225 285 346 406 466 527 588 649 710 771 833 895 957 45 46 46 lOb 166 226 286 347 407 467 528 589 650 711 772 834 896 958 46 47 47 107 167 227 287 348 408 468 5'29 590 651 712 773 835 897 959 47 48 48 108 168 228 288 349 409 469 530 591 652 713 774 836 898 960 48 49 49 10'J 169 229 289 350 410 470 531 592 653 714 776 837 899 961 49 50 50 110 170 230 290 361 411 471 532 593 654 715 777 838 900 962 50 51 51 111 171 231 291 352 412 472 533 594 655 716 778 839 901 963 51 52 52 112 172 232 292 353 413 473 534 595 656 717 779 840 DOi 964 52 53 53 113 173 233 293 354 414 474 535 596 657 718 780 811 903 965 53 54 54 114 174 234 294 355 415 476 536 597 668 719 781 842 904 966 54 55 55 115 175 235 295 356 410 477 537 598 659 720 782 843 905 968 55 56 56 116 176 236 296 357 417 478 538 599 660 721 783 844 906 96'. 56 57 57 117 177 237 297 358 418 479 539 600 661 722 784 845 907 970 57 58 58 118 178 238 298 359 41i 480 510 601 662 723 785 846 908 971 58 69 59 119 179 239 299 3GO 4-20 481 541 602 G63 724 786 847 909 972 59 M. 1 2 3 4 J 5 G 70 8 9 10 11 12 13 14 ISO M. 250 TABLE V. MERIDIONAL PARTS. M. 16 17 18 19 20 21 22 23 24 25 26 M. ( ,)7:i 1035 1098 1161 1225 1289 1354 1419 1484 1550 1616 1 974 1036 1099 1163 1226 1290 1355 1420 1485 1551 1618 1 2 975 1037 1100 1164 1227 1291 1356 1421 1486 1552 1619 2 3 976 1038 1101 1165 1228 1292 1357 1422 1487 1553 1620 3 4 977 1039 1102 1166 1229 1293 1358 1423 1488 1554 1621 4 5 978 1041 1103 1167 1230 1295 1359 1424 1490 1556 1622 5 6 979 1042 1105 1168 1232 1290 1360 1425 1491 1557 1623 6 7 980 1043 1106 1169 1233 1297 1361 1426 1492 1558 1624 7 8 981 1044 1107 1170 1234 1298 1362 1427 1493 1559 1625 8 9 982 1045 1108 1171 1235 1299 1363 1428 1494 1560 1626 9 10 983 1046 1109 1172 1236 1300 1364 1430 1495 1561 1628 10 11 984 1047 1110 1173 1237 1301 1366 1431 1496 1562 1629 11 12 985 1048 1111 1174 1238 1302 1367 1432 1497 1563 1630 12 13 986 1049 1112 1175 1239 1303 1368 1433 1498 1564 1631 13 14 987 1050 1113 1176 1240 1304 1369 1434 1499 1565 1632 14 15 988 1051 1114 1177 1241 1305 1370 1435 1500 1567 1633 15 10 989 1052 1115 1178 1242 1306 1371 1436 1502 1568 1634 16 17 990 1053 1116 1179 1243 1307 1372 1437 1503 1569 1635 17 18 991 1054 1117 1181 1244 1308 1373 1438 1504 1570 1637 18 19 993 10.35 1118 1182 1245 1310 1374 1439 1505 1571 1638 19 20 994 1056 1119 1183 1240 1311 1375 1440 1506 1572 1639 20 21 995 1057 1120 1184 1248 1312 1376 1441 1507 1573 1640 21 22 996 1058 1121 1185 1249 1313 1377 1443 1508 1574 1641 22 23 997 1059 1122 1186 1250 1314 1379 1444 1509 1575 1642 23 24 998 1060 1123 1187 1251 1315 1380 1445 1510 1577 1643 24 25 999 1061 1125 1188 1252 1316 1381 1446 1511 1578 1644 25 2G 1000 1063 1126 1189 1253 1317 1382 1447 1513 1579 1645 26 27 1001 1064 1127 1190 1254 1318 1383 1448 1514 1580 1647 27 28 1002 1065 1128 1191 1255 1319 1384 1449 1515 1581 1648 28 29 1003 1066 1129 1192 1256 1320 1385 1450 1516 1582 1649 29 30 1W04 1067 1130 1193 1257 1321 1386 1451 1517 1583 1650 30 31 1005 1068 1131 1194 1258 1322 1387 1452 1518 1584 1651 31 32 1006 1069 1132 1195 1259 1324 1388 1453 1519 1585 1652 32 33 1007 1070 1133 1196 1260 1325 1389 1455 1520 1586 1653 33 34 1008 1071 1134 1198 1261 1326 1390 1456 1521 1588 1654 34 35 1009 1072 1135 1199 1262 1327 1392 1457 1522 1589 1656 35 36 1010 1073 1136 1200 1264 1328 1393 1458 1524 1590 1657 36 37 1011 1074 1137 1201 1265 1329 1394 1459 1525 1591 1658 37 38 1012 1075 1138 1202 1266 1330 1395 1460 1526 1592 1659 38 39 1013 1076 1)39 1203 1267 1331 1396 1461 1527 1593 1C60 39 40 1014 1077 1140 1204 1268 1332 1397 1462 1528 1594 1661 40 41 1015 1078 1141 1205 1269 1333 1398 1463 1529 1595 1662 41 42 1016 1079 1142 1206 1270 133i 1399 1464 1530 1596 1G63 42 43 1018 1080 1144 1207 1271 1335 1400 1465 1531 1598 1664 43 44 1019 1081 1145 1208 1272 1336 1401 1467 1532 1599 1666 44 45 1020 1082 1146 1209 1273 1338 1402 1468 1533 1600 1667 45 46 1021 1084 1147 1210 1274 1339 1403 1469 1535 1601 1668 46 47 1022 1085 1148 1211 1275 1340 1405 1470 1536 1602 1669 47 48 1023 1086 1149 1212 1276 1341 1406 1471 1537 1603 1670 48 49 1024 1087 1150 1213 1277 1342 1407 1472 1538 1604 1671 49 50 1025 1068 1151 1215 1278 1343 1408 1473 1539 1605 1672 50 51 1026 1089 1152 1216 1280 1344 1409 1474 1540 1606 1673 51 52 1027 1090 1153 1217 1281 1345 1410 1475 1541 1608 1675 52 53 1028 1091 1154 1218 1282 1346 1411 1476 1542 1609 1676 53 54 1029 1092 1155 1219 1283 1347 1412 1477 1543 1610 1677 54 55 1030 1093 1156 1220 1284 1348 1413 1479 1544 1611 1678 55 5G 1031 1094 1157 1221 1285 1340 1414 1480 1546 1612 1679 56 57 1032 1095 1158 1222 1286 1350 1415 1481 1547 1613 1680 57 58 1033 1096 1159 1223 1287 1352 1416 1482 1548 1614 1681 58 59 1034 1097 1160 1224 1288 1353 1418 1483 1549 1615 1682 59 M. 1G 3 17 18 J 19 20 21 22 23 24 25 2G U M. TABLE V. 251 MERIDIONAL PARTS. M, 27 28 29 30 31 32 33 34 35 36 37 M. 1684 1751 1819 1888 1958 2028 2100 2171 2244 2318 2393 1 1685 1752 1821 1890 1959 2030 2101 2173 2246 2319 2394 1 2 1686 1753 1822 1891 1960 2031 2102 2174 2247 2320 2395 2 3 1687 1755 1823 1892 1962 2032 2103 2175 2248 2322 2396 3 4 1688 1756 1824 1893 1963 2033 2104 2176 2249 2323 2398 4 5 1689 1757 1825 18J4 1964 2034 2105 2178 2250 2324 2399 5 6 1690 1758 1826 1895 1965 2035 2107 2179 2252 2325 2400 6 7 1691 1759 1827 1896 1966 2037 2108 2180 2253 2327 2401 7 8 1693 1760 1829 1898 1967 2038 2109 2181 2254 2328 2403 8 9 1694 1761 1830 1899 1969 2039 2110 2182 2255 2329 2404 9 10 1695 1762 1831 1900 1970 2040 2111 2184 2257 2330 2405 10 11 1696 1764 1832 1901 1971 2041 2113 2185 2258 2332 2406 11 12 1697 1765 1833 1902 .1972 2043 2114 2186 2259 2333 2408 12 13 1698 1766 1834 1903 1973 2044 2115 2187 2260 2334 2409 13 14 1699 1767 1835 1905 1974 2045 2116 2188 2261 2335 2410 14 15 1700 1768 1837 1906 1976 2046 2117 2190 2263 2337 2411 15 16 1701 1769 1838 1907 1977 2047 2119 2191 2264 2338 2413 16 17 1703 1770 1839 1908 1978 2048 2120 2192 2265 2339 2414 17 18 1704 1772 1840 1909 1979 2050 2121 2193 2266 2340 2415 18 19 1705 1773 1841 1910 1980 2051 2122 2194 2268 2342 2416 J9 20 1706 1774 1842 1912 1981 2052 2123 2196 2209 2343 2418 20 21 1707 1775 1843 1913 1983 2053 2125 2197 2270 2344 2419 21 22 1708 1776 1845 1914 1984 2054 2126 2198 2271 2345 2420 22 23 1709 1777 1846 1915 1985 2056 2127 2199 2272 2346 2422 23 24 1711 1778 1847 1916 1986 2057 2128 2200 2274 2348 2423 24 25 1712 1780 1848 1917 1987 2058 2129 2202 2275 2349 2424 25 26 1713 1781 1849 1918 1988 2059 2131 2203 2276 2350 2425 26 27 1714 1782 1850 1920 1990 2060 2132 2204 2277 2351 2427 27 28 1715 1783 1852 1921 1991 2061 2133 2205 2279 2353 2428 28 29 1716 1784 1853 1922 1992 2063 2134 2207 2280 2354 2429 29 3u 1717 1785 1854 1923 1993 2064 2135 2208 2*81 2355 2430 30 31 1718 1786 1855 1924 1994 2065 2137 2209 2282 2356 2432 31 32 1720 1787 1856 1925 1995 2066 2138 2210 2283 2358 2433 32 33 1721 1789 1857 1927 1997 2067 2139 2211 2285 2359 2434 33 34 1722 1790 1858 1928 1998 2069 2140 2213 2286 2360 2435 34 35 1723 1791 1860 1929 1999 2070 2141 2214 2287 2361 2437 35 36 1724 1792 1861 1930 2000 2071 2143 2215 2288 2363 2438 36 37 1725 1793 1862 1931 2001 2072 2144 2216 2290 2364 2439 37 38 1726 1794 1863 1932 2002 2073 2145 2217 2291 2365 2440 38 39 1727 1795 1864 1934 2004 2075 2146 2219 2292 2366 2442 39 40 1729 1797 1865 1935 2005 2076 2147 2220 2293 2368 2443 40 41 1730 1798 1866 1936 2006 2077 2149 2221 2295 2369 2444 41 42 1731 1799 1868 1937 2007 2078 2150 2222 2296 2370 2445 42 43 1732 1800 1869 1938 2008 '2079 2151 2224 2297 2371 2447 43 44 1733 1801 1870 1939 2010 2080 2152 2225 2298 2373 2448 44 45 1734 1802 1871 1941 2011 2082 2153 2226 2293 2374 2449 45 46 1735 1803 1872 1942 2012 2083 2155 2227 2301 2375 2451 46 47 1736 1805 1873 1943 2013 2084 2156 2228 2302 2376 2452 47 48 1738 1806 1875 1944 2014 2085 2157 2230 2303 2378 2453 48 49 1739 1807 1876 1945 2015 2086 2158 2231 2304 2379 2454 49 50 1740 IbOS 1877 l'J4i> 2017 2088 2109 2232 2306 2380 2456 50 51 1741 1809 1878 1948 2018 2089 2161 2233 2307 2381 2457 51 52 1742 1810 1879 1949 2019 2090 2162 2235 2308 2383 2458 52 53 1743 1811 1880 1950 2020 2091 2163 2236 2309 2384 2459 53 54 1744 1813 1881 1951 2021 2092 2164 2237 2311 2385 2461 54 55 1746 1814 1883 1952 2022 2094 2165 2238 2312 2386 2462 55 56 1747 1815 1884 1953 2024 2095 2167 2239 2313 2388 2463 56 57 1748 1816 1885 1955 2025 2096 2168 2241 2314 2389 2464 57 58 1749 1817 1886 1956 2026 2097 2169 2242 2316 2390 2466 58 59 1750 1818 1887 1957 2027 2098 2170 2243 2317 2391 2467 59 M. 27 28 21P 30 31 32 33 34 35 3G 37 M. 252 TABLE V. MERIDIONAL PARTS. M. 38 39 40 41 42 43 44 45 4G 47 48 M. 2408 2545 2023 27u2 2782 2803 2946 3U30 3116 3203 3292 1 2470 2546 2624 2703 2783 2864 2947 3031 3117 3204 3293 1 2 2471 2548 2625 2704 2784 2866 2949 3033 3118 3206 3295 2 3 2472 2549 2627 2706 2786 2867 2950 3034 3120 3207 3296 3 4 2473 2550 2628 2707 2787 2869 2951 3036 3121 3209 3298 4 5 2475 2551 2629 2708 2788 2870 2953 3037 3123 3210 3299 5 6 2476 2553 2G31 2710 2790 2871 2954 3038 3124 3212 3301 6 7 2477 2554 2632 2711 2791 2873 2956 3040 3126 3213 3302 7 8 2478 2555 2K33 2712 2792 2874 2957 3041 3127 3214 3303 8 9 2480 2557 2634 2714 2794 2875 2958 3043 3129 3216 3305 9 10 2481 2558 2606 27 1 5 2795 2877 2900 3044 3130 3217 3306 10 11 2482 2559 2637 2716 2797 2878 2961 3046 3131 3219 3308 11 12 2484 2560 2638 2718 2798 2880 2963 3047 3133 3220 3309 12 13 2485 2562 2640 2719 2799 2881 2964 3048 3134 3222 3311 13 14 2186 2563 2641 2720 2801 2882 2965 3050 3136 3223 3312 14 15 2487 2564 2642 2722 2802 2884 2967 3051 3137 3225 3314 15 1G 2489 256G 2G44 2723 2803 2885 2968 3053 3139 3226 3316 16 17 2490 25G7 2645 2724 2805 2886 2970 3054 3140 3228 3317 17 18 2491 2568 264G 2726 2806 2888 2971 3055 3142 3229 3319 18 19 2492 2569 2648 2727 2807 2889 2972 3057 3143 3231 3320 19 20 24U4 2571 2649 2728 2809 2891 2974 3058 3144 3232 3322 20 21 2495 2572 2650 2729 2810 2892 2975 3060 3146 3234 3323 21 22 2496 2573 2C51 2731 2811 2893 2976 3061 3147 3235 3325 22 23 2498 2575 2653 2732 2813 2895 2978 3063 3149 3237 3326 23 2-4 2499 2576 2G54 2733 2814 2896 2979 3064 3150 3238 3328 24 25 2500 2577 2655 2735 2815 2897 2981 3065 3152 3240 3329 25 26 2501 2578 2657 2736 2817 2899 2982 3067 3153 3241 3331 26 27 2503 2580 2658 2737 2818 2900 2983 3068 3155 3242 3332 27 28 2504 2581 2659 2739 2820 2902 2985 3070 3156 3244 3334 28 29 2505 2582 2661 2740 2821 2903 2986 3071 3157 3245 3335 29 30 25u6 2584 '2002 2742 2822 2904 2988 30/3 3159 3247 3337 30 31 2*08 2585 26G3 2743 2824 2906 2989 3074 3160 3248 3338 31 32 2509 2586 2665 2744 2825 2907 2991 3075 3162 3250 3340 32 33 2510 2588 2666 2746 2826 2908 2992 3077 3163 3251 3341 33 34 2512 2589 2667 2747 2828 2910 2993 3078 3165 3253 3343 34 35 2513 2590 26G9 2748 2829 2911 2995 3080 3166 3254 3344 35 36 2514 2591 2670 2750 2830 2913 2996 3081 3168 3256 3346 36 37 2515 2593 2671 2751 2832 2914 2998 3083 3169 3257 3347 37 38 2517 2594 2673 2752 2833 2915 2999 3084 3171 3259 3349 38 39 2518 2595 2674 2754 2834 2917 3000 3085 3172 3260 3350 39 40 2519 2597 20(5 27o5 2836 2918 3002 3087 3173 3202 3352 40 41 2521 2593 2676 2756 2837 2919 3003 3088 3175 3263 3353 41 42 2522 2599 2678 2758 2839 2921 3005 3090 3176 3265 3355 42 43 2523 2G01 2679 2759 2840 2922 3006 3091 3178 3266 3356 43 44 2524 2602 2680 2760 2841 2924 3007 3093 3i79 3268 3358 44 45 2526 2603 2682 2762 2843 2925 3009 3094 3181 3269 3359 45 46 2527 2G04 2683 2763 2844 2926 3010 3095 3182 3271 3361 46 47 2528 2606 2684 2764 2845 2928 3012 3097 3184 3272 3362 47 48 2530 2607 2686 2766 2847 2929 3013 3098 3185 3274 3364 48 49 2531 2608 2687 2767 2848 2931 3014 3100 3187 3275 3365 49 50 2532 2610 2088 2708 2849 2932 3010 3101 3188 3277 3307 50 ' 51 2533 2611 2690 2770 2851 2933 3017 3103 3190 3278 3368 51 52 2535 2612 2691 2771 2852 2935 3019 3104 3191 3280 3370 52 53 2533 2614 2692 2772 2854 2936 3020 3105 3192 3281 3371 53 54 2537 2615 2694 2774 2855 2937 3021 3107 3194 3283 3373 54 55 2538 2616 2695 2775 2856 2939 3023 3108 3195 3284 3374 55 56 2540 2617 2696 2776 2858 2940 3024 3110 3197 3286 3376 56 57 2541 2619 2698 2778 2859 2942 3026 3111 3198 3287 3378 57 58 2542 2620 2699 2779 2860 2943 3027 3113 3200 3289 3379 58 59 2544 2621 2700 2780 2862 2944 3029 3114 3201 3290 3381 59 M. 38 39 40 41 o 42 43 44 45 46 470 48 M. TABLE V. 253 MERIDIONAL PARTS. M. 49 50 51 52 53 54 55 56 57 58 59 M. 3382 3474 3569 3665 3764 3665 3968 4074 4183 4294 4409 1 3384 3476 3570 3667 3765 3866 3970 4076 4184 4296 4411 1 2 3385 3478 3572 3668 3767 3868 3971 4077 4186 4298 4413 2 3 3387 3479 3574 3670 3769 3870 3973 4079 4188 4300 4415 3 4 3388 3481 3575 3672 3770 3871 3775 4081 4190 4302 4417 4 5 3390 3482 3577 3673 3772 3873 3977 4033 4192 4304 4419 5 6 3391 3484 3578 3675 3774 3875 3978 4085 4194 4306 4421 6 7 3393 3485 3580 3677 3775 3877 3980 4086 4195 4308 4423 7 8 3394 3487 3582 3678 3777 3878 3982 4088 4197 4309 4425 8 9 3396 3488 3583 3680 3779 3880 3984 4090 4199 4311 4427 9 10 3397 3490 3585 3681 3780 3882 3985 4092 4*01 4313 4429 10 11 3399 3492 3586 3683 3782 3883 3987 4094 4203 4315 4431 11 12 3400 3493 3588 3685 3784 3885 3989 4095 4205 4317 4433 12 13 3402 3495 3590 3686 3785 3887 3991 4097 4207 4319 4434 13 14 3403 3496 3591 3688 3787 3889 3992 4099 4208 4321 4436 14 15 3405 3498 3593 3690 3789 3890 3994 4101 4210 4323 4438 15 16 3407 3499 3594 3691 3790 3892 3996 4103 4212 4325 4440 16 17 3408 3501 3596 3693 3792 3894 3998 4104 4214 4327 4442 17 18 3410 3503 3598 3695 3794 3895 3999 4106 4216 4328 4444 18 19 3411 3504 3599 3696 379o 3897 4001 4108 4218 4330 4446 19 20 3413 3506 3601 3098 3797 3899 40U3 4140 4220 4332 4448 20 21 3414 3507 3602 3699 3799 3901 4005 4112 4221 4334 4450 21 22 3416 3509 3604 3701 3800 3902 4006 4113 4223 4336 4452 22 23 3417 3510 3606 3703 3802 3904 4008 4115 4225 4338 4454 23 24 3419 3512 3607 3704 3804 3906 4010 4117 4227 4340 4456 21 , 25 3420 3514 3609 3706 3806 3907 4012 4119 4229 4342 4458 25 26 3422 3515 3610 3708 3807 3909 4014 4121 4231 4344 4460 26 27 3423 3517 3612 3709 3809 3910 4015 4122 "4232 4346 4462 27 28 3425 3518 3614 3711 3811 3913 4017 4124 4234 4347 4464 28 29 3427 3520 3G15 3713 3812 3914 4019 4126 4236 4349 446G 29 30 3428 3521 3617 3714 3814 3916 4021 4128 4238 4354 44G8 30 31 3430 3523 3618 3716 3816 3918 4022 4130 4240 4353 4470 31 32 3431 3525 3620 3717 3817 3919 4024 4132 4242 4355 4472 32 33 3433 3526 3622 3719 3819 3921 4026 4133 4244 4357 4474 33 34 3434 3528 3623 3721 3821 3923 4028 4135 4246 4359 4476 34 35 3436 3529 3625 3722 3822 3925 4029 4137 4247 4361 4478 35 36 3437 3531 3626 3724 3824 3926 4031 4139 4249 4363 4480 36 37 3139 3532 3628 3726 3826 3928 4033 4141 4251 43(55 4482 37 38 3440 3534 3630 3727 3827 3930 4035 4142 4253 4367 4484 38 39 3442 3536 3631 3729 3829 3'i32 4037 4144 4255 4369 4486 39 40 3443 3537 3633 3731 383 L 3933 4038 4446 4257 4370 4488 40 41 3445 3539 3634 3732 3832 3935 4040 4148 4259 4372 4490 41 42 3447 3540 3636 3734 3834 3937 4042 4150 4260 4374 4492 42 43 3448 3542 3638 3736 3836 3938 4044 4152 4262 4376 4494 43 44 3450 3543 3639 3737 3838 3940 4045 4153 4264 4378 4495 44 45 3451 3545 3G41 3739 3839 3942 4047 4155 4266 4380 4497 45 46 3453 3547 3643 3741 3841 3944 4049 4157 4268 4382 4499 46 47 3454 3548 3644 3742 3843 3945 4051 4159 4270 4384 4501 47 48 3456 3550 3646 3744 3844 3947 4052 4161 4272 4386 4503 48 49 3457 3551 3647 3746 3846 3949 4054 4162 4274 4388 4505 49 50 3459 3553 3649 3747 348 3951 4056 4164 4275 4390 4507 50 51 3460 3555 3651 3749 3849 3952 4058 4166 4277 4392 4509 51 52 3462 3556 3652 3750 3851 3954 4060 4168 4279 4394 4511 52 53 3164 3558 3654 3752 3853 3956 4061 4170 4281 4396 4513 53 54 3465 3559 3655 3754 3854 3958 4063 4172 4283 4398 4515 54 55 3467 3561 3657 3755 3856 3959 4065 4173 4285 4399 4517 55 56 3468 3562 3659 3757 3858 3961 4067 4175 4287 4401 4519 56 57 3470 3564 3660 3759 3860 3963 4069 4177 4289 4403 4521 57 58 3471 3566 3662 3760 3861 3964 4070 4179 4291 4405 4523 58 59 3473 3567 3664 3762 3863 3966 4072 4181 4292 4407 4525 59 M. 49 5(P 51 52 53 54 55 56 57 58 59 M. 254 TABLE V. MERIDIONAL PARTS. M. 60 61 62 63 64 65 66 67 68 69 70 M. 4527 4649 4775 4905 5059 5179 5324 5474 5631 5795 59GO 1 4529 4651 4777 4907 5042 5181 5326 5477 5633 5797 59G9 1 2 4531 4653 4779 4909 5044 5184 5328 5479 5G36 5800 5972 2 3 4533 4655 4781 4912 5046 5186 5331 5482 5639 5803 5975 3 4 4535 4657 4784 4914 5049 5188 5333 5484 5642 5806 5978 4 5 4537 4660 4786 4916 5051 5191 5336 5487 5644 5809 5931 5 6 4539 4662 4788 4918 5053 5193 5338 5489 5647 5811 5984 6 7 4541 4664 4790 4920 5055 5195 5341 5492 5650 5814 5986 7 8 4543 4666 4792 4923 5058 5198 5343 5495 5652 5817 5989 8 9 4545 4668 4794 4925 5060 5200 5346 5497 5655 5820 5992 9 la 4547 4070 4796 4927 5062 5203 5348 5500 5658 5823 5995 10 11 4549 4672 4798 4929 5065 5205 5351 5502 5660 5825 5998 11 12 4551 4674 4801 4931 5067 5207 5353 5505 5663 5828 6001 12 13 4553 4676 4803 4934 5069 5210 5356 5507 5666 5831 6004 13 14 4555 4678 4805 4936 5071 5212 5358 5510 5668 5834 6007 14 15 4557 4680 4807 4938 5074 5214 5361 5513 5671 5837 6010 15 1C 4559 4682 4809 4940 5076 5217 5363 5515 5674 5839 6013 16 17 4562 4684 4811 4943 5078 5219 5368 5518 567G 5842 6016 17 18 4564 4687 4814 4945 5081 5222 5368 5520 5679 5845 6019 18 19 45GG 4689 4816 4947 5083 5224 5371 5523 5682 5848 6022 19 20 4568 4691 4818 4949 5085 5226 5373 5526 5685 5851 6025 20 21 4570 4693 4820 4951 5088 5229 5376 5528 5687 5854 6028 21 22 4572 4695 4822 4954 5090 5231 5378 5531 5690 5856 6031 22 23 4574 4697 4324 4956 5092 5234 5380 5533 5693 5859 6034 23 24 4576 4699 4826 4958 5095 5236 5383 5536 5695 5862 6037 24 25 4578 4701 4829 4960 5097 5238 5385 5539 5C98 5865 6040 25 26 4580 4703 4831 4963 5099 5241 5388 5541 5701 5868 6043 26 27 4582 4705 4833 4985 5102 5243 5390 5544 5704 5871 6016 27 28 4584 4707 4835 4967 5104 5246 5393 5546 5706 5874 6049 28 29 4586 4710 4837 49G9 5106 5248 5395 5549 5709 5876 6052 29 30 4588 4712 48^9 4972 51U8 5250 5398 5552 5712 5879 6055 30 31 4590 4714 4812 4974 5111 5253 5401 5554 5715 5882 6058 31 32 4592 4716 4844 4976 5113 5255 5403 5557 5717 5885 6061 32 33 4594 4718 4846 4978 5115 5258 5406 5559 5720 5888 6064 33 34 4596 4720 4848 4981 5118 5260 5408 5562 5723 5891 60G7 34 35 4598 4722 4850 4983 5120 5263 5411 5565 5725 5894 6070 35 36 4600 4724 4352 4985 5122 5265 5413 5567 5728 5896 6073 36 37 4602 4726 4855 4987 5125 5267 5116 5570 5731 5899 6076 37 38 4604 4728 4857 4990 5127 5270 5418 5573 5734 5902 6079 38 39 4606 4731 4859 4992 5129 5272 f421 5575 5736 5905 6082 39 40 4608 4733 4301 4994 5132 5275 5423 5578 5739 5908 6085 40 41 4610 4735 4863 4996 5134 5277 5426 5580 5742 5911 6088 41 42 4612 4737 4865 4999 5136 5280 5428 5583 5745 5914 6091 42 43 4614 4739 4868 5001 5139 5282 5431 5586 5747 5917 6094 43 44 4616 4741 4870 5003 5141 5284 5433 5588 5750 5919 6097 44 45 4618 4743 4872 5005 5143 5287 5436 5591 5753 5922 6100 45 46 4620 4745 4874 5008 5146 5289 5438 5594 5756 5925 6103 46 47 4623 4747 4876 5010 5148 5292 5441 5596 5758 5928 6106 47 48 4625 4750 4879 5012 5151 5294 5443 5599 5761 5931 6109 48 49 4627 4752 4881 5014 5153 5297 5446 5602 5764 5934 6112 49 50 4629 4754 4883 5017 5155 5299 5448 5604 5767 5937 6115 ~50~ 51 4631 4756 4885 5019 5158 5301 5451 5607 5770 5940 6118 51 52 4633 4758 4887 5021 5160 5304 5454 5610 5772 5943 6121 52 53 4635 4760 4890 5023 5162 5306 5456 5612 5775 5946 6124 53 54 4637 4762 4892 5026 5165 5309 5459 5615 5778 5948 6147 54 55 4639 4764 48tf4 5028 5167 5311 5461 5617 5781 5951 6130 55 56 4641 4766 4896 5030 5169 5314 5464 5620 5783 5954 6133 56 57 4643 4769 4898 5033 5172 5316 5466 5623 5786 5957 6136 57 58 4645 4771 4901 5035 5174 5319 5469 5625 5789 59GO 6140 58 59 4647 4773 4903 5037 5176 5321 5471 5628 5792 5963 6143 59 If. 60 61^ 62^ 03 64 G5 66 67 68 09 70 H. TABLE V. 235 MERIDIONAL PARTS. 1C. 71 72 73 74 75 | 76 77 78 79 80 81 | M. 6146 0335 0534 0746 0970 7210 Uo7 7745 6046 8375 8739 1 6149 6338 6538 6749 6974 7214 7472 7749 8051 8381 8745 1 2 6152 6341 6541 6753 6978 7218 7476 7754 8056 8387 8752 2 3 6155 6345 6545 6757 6982 7222 7481 7759 8061 8393 8758 3 4 6158 6348 6548 6760 6986 7227 7485 7764 8067 8398 8r*ft /Go 4 5 6161 6351 6552 6764 6990 7231 7490 7769 8072 8404 8771 5 6 6164 6354 6555 6768 6994 7235 7494 7774 8077 8410 8778 6 7 6167 6358 6558 6771 6997 7239 7498 7778 8083 8416 8784 7 8 6170 6361 6562 6775 7001 7243 7503 7783 8088 8422 8791 8 9 G173 6364 6565 6779 7005 7247 7507 7788 8093 8427 8797 9 10 6177 630/ 0509 0/62 7009 7252 7512 7793 8099 8433 8801 JO 11 6180 6371 6572 6786 7013 7256 7516 7798 8104 8439 8810 11 12 6183 6374 6576 6790 7017 7260 7521 7803 8109 8445 8817 12 13 6186 6377 6579 6793 7021 7264 7525 7808 8115 8451 8823 13 14 6189 6380 6583 6797 7025 7268 7530 7813 8120 8457 8830 14 15 6192 6384 6586 6801 7029 7273 7535 7817 8125 8463 8836 15 16 61915 6387 6590 6804 7033 7277 7539 7822 8131 8469 8843 16 17 6198 6390 6593 6808 7037 7281 7544 7827 8136 8474 8849 17 18 6201 6394 6597 6812 7041 7285 7548 7832 8141 8480 8856 18 19 6205 6397 6600 6815 7045 7-289 7553 7837 8147 8486 8863 19 20 6208 0400 6G03 0819 70i8 7zy4 7ooV 7842 8152 8492 8869 20 21 6211 6403 6607 6823 7052 7298 7562 7847 8158 8498 8876 21 22 6214 6407 6610 6826 7056 7302 7566 7852 8163 8504 8883 22 23 6217 6410 6614 6830 7060 7306 7571 7857 8168 8510 8889 23 24 6220 6413 6617 6834 7064 7311 7576 7862 8174 8516 8896 24 25 6223 6417 6621 6838 7GG8 7315 7580 7867 8179 8522 8903 25 2G 6226 6420 6624 6841 7072 7319 7585 7872 8185 8528 8909 26 27 6230 6423 6628 6845 7076 7323 7589 7877 8190 9534 8916 27 28 6233 6427 6631 6849 7080 7328 7594 7882 8196 8540 8923 28 29 6236 6430 6635 6853 7084 7332 7599 7887 8201 8546 8930 29 30 G:i39 0433 OGo9 0850 70S8 '<3o6 7603 V892 8207 8552 8936 30 31 6242 6437 6642 6860 7092 7341 7608 7897 8212 8558 8943 31 32 6245 6140 6646 6864 7096 7345 7612 7902 8218 8565 8950 32 33 6249 6443 6649 6868 7100 7319 7617 7907 8223 8571 8957 33 34 6252 6447 6653 6871 7104 7353 7622 7912 8229 8577 8963 34 35 6255 6450 6656 6875 7108 7358 7626 7917 8234 8583 8970 35 36 6258 6453 C660 6879 7112 7362 7631 7922 8240 8589 8977 36 37 6261 6457 6663 6883 7116 7366 7636 7927 8245 8595 8984 37 38 6264 6460 6667 6886 7120 7371 7640 7932 8251 8601 8991 38 39 6268 6463 6670 6890 7124 7375 7645 7937 8256 8607 8998 39 40 0271 046 / 6074 0894 7128 73'<9 7050 7942 8202 8014 9005 40 41 6274 6470 6677 6898 7132 7384 7654 7948 8267 8620 9012 41 42 6277 6473 6681 6901 7136 7388 7659 7953 8273 8626 9018 42 43 6280 6477 6685 6905 7140 7392 7664 7938 8279 8632 9025 43 44 6283 6480 6688 6909 7145 7397 7668 7963 8284 8638 9032 44 45 6287 6483 6692 6913 7149 7401 7673 7968 8290 8644 9039 45 46 6290 6187 6695 6917 7153 7406 7678 7973 8295 8651 9046 46 47 6293 6490 6699 6920 7157 7410 7683 7978 8301 8657 9053 47 48 6296 6494 0702 6924 7161 7414 7687 7983 8307 8663 9060 48 49 6>99 6497 6706 6928 7165 7419 7692 7989 8312 8669 9067 49 50 6303 6500 6710 6U32 7169 7423 7097 7994 8318 8070 9074 50 51 6306 6504 6713 6936 7173 7427 7702 7999 8324 8682 9081 51 52 6309 6507 6717 6940 7177 74-32 7706 8004 8329 8688 908S 52 53 6312 6511 6720 6943 7181 7436 7711 8009 8335 8695 9096 53 54 6315 6514 6724 6947 7185 7441 7716 8014 8341 8701 9103 54 55 6319 6517 6728 6951 7189 7445 7721 8020 8347 8707 9110 55 56 6322 6521 6731 6955 7194 7449 7725 8025 8352 8714 9117 56 57 6325 6524 6735 6959 7198 7454 7730 8030 8358 8720 9124 57 58 6328 6528 6738 69G3 7202 7458 7735 8035 8364 8726 9131 58 59 6332 6531 6742 6966 7206 7463 7740 8040 8309 8733 9138 59 M. 71 o 72 73 74 75 76 770 78 J 79 80 81 M. 256 TABLE V. MERIDIONAL PARTS. M. 82 83 84 85 86 87 88 89 1C. 91-15 9006 1U137 1U765 11533 12522 13916 16300 1 9153 9614 10147 10776 11547 12541 13945 16357 1 2 91CO 9622 10156 10788 11561 12561 13974 16416 2 3 9167 9631 10166 10799 11576 12580 14004 16476 3 4 9174 9639 10175 10811 11590 12599 14033 16537 4 5 9182 9647 10185 10823 11605 12G19 14063 D6599 5 6 9189 9655 10195 10834 11620 12639 14093 16662 6 7 9196 9664 10205 10846 11634 12659 14123 16726 7 8 9203 9672 10214 10858 11649 12679 14154 16792 8 9 9211 9G80 10224 10870 11664 12699 14185 16858 9 ID 9218 9689 10^34 10881 11679 T/719 14216 169.6 10 11 9225 9G97 10244 10893 11694 12739 14247 16996 11 12 9233 9706 10254 10905 11709 12759 14279 17067 12 13 9240 9714 10264 10917 11724 12780 14311 17139 13 14 9248 9723 10274 10929 11739 12801 14343 17213 14 15 9255 9731 10284 10941 11755 12821 14376 17289 15 16 9262 9740 10294 10953 11770 12842 14409 17366 16 17 9270 9748 10304 10965 11785 12863 14442 17445 17 18 9277 9757 10314 10978 11801 12885 14475 17526 18 19 9285 9765 10324 10990 11816 12906 14509 17609 19 20 9292 97/4 10334 11002 11832 12927 14543 17G94 20 21 9300 9783 10344 11014 11848 12949 14578 17781 21 22 9307 9791 10354 11027 11863 12970 14G13 17870 22 23 9315 9800 10364 11039 11879 12992 14648 17962 23 24 9322 9809 10374 11052 11895 13014 14684 18056 24 25 9330 9817 10385 11064 11911 13036 14720 18153 25 26 9337 9826 10395 11077 11927 13059 14756 18252 26 27 9345 9835 10405 11089 11943 13081 14793 18355 27 28 9353 9344 10416 11102 11959 13104 14830 18461 28 29 9360 9852 10426 11115 11976 13126 14868 18570 29 oO 9368 9861 10437 11127 11992 13149 14906 18683 30 31 9376 9870 10447 11140 12008 13172 14944 18799 31 32 9383 9879 10457 11153 12025 13195 14983 18920 32 33 9391 9888 10468 11166 12041 13219 15022 19045 33 34 9399 9897 10478 11179 12058 13242 15062 19174 34 35 9407 9903 10489 11192 12075 13266 15102 19309 35 36 9415 9915 10500 11205 12092 13290 15143 19450 36 37 9422 9924 10510 11218 12109 13314 15184 19596 37 38 9430 9933 10521 11231 12126 13338 15226 19749 38 39 9437 9942 10532 11244 12143 13362 15268 19909 39 40 9445 9951 1U542 11257 12160 13366 15311 20076 40 41 9453 99GO 10553 11270 12177 13411 15354 20253 41 42 9461 9969 10564 11284 12194 13436 15398 20439 42 43 94G9 9978 10575 11297 12212 13461 15442 20635 43 44 9477 9987 10586 11310 12229 13486 15487 20844 44 45 9485 9996 10597 11324 12247 13511 15532 21065 45 4G 9493 10005 10608 11338 12265 13537 15579 21303 46 47 9501 10015 10619 11351 12282 13563 15625 21557 47 48 9509 10024 10630 11365 12300 13589 15673 21833 48 49 9517 10033 10641 11378 12318 13615 15721 22132 49 , 50 9525 10U43 10652 11392 12336 13G41 15770 22459 50 51 9533 10052 10663 11406 12354 136G8 15819 22822 51 52 9541 10061 10674 11420 12373 13695 15869 23226 52 53 9549 10071 10u85 11434 12391 13722 15920 23685 53 54 9557 10080 10696 11448 12409 13749 15972 24215 54 55 9565 10089 10708 11462 12428 13776 16024 24842 55 56 9573 10099 10719 11476 12440 13804 16078 25609 56 57 9581 10108 10730 11490 12465 13832 16132 26598 57 58 9589 10118 10742 11504 12484 13860 16187 27992 58 59 9598 10127 10753 11518 12503 13888 16243 30375 59 M. 82 83 84 85 86 J 87 88 89 M. TABLE VI. MEAN REFRACTION. 257 TABLE VII. DIP OF THE HORIZON. 4 PP Alt. Rcfr. 4P P Alt. Ref. App. Alt. Ref. App. Alt, Ref. App. Alt. Ref. Height. Dip. O / 5 10 15 20 25 30 35 40 45 33 32 10 31 22 30 35 29 50 29 6 28 23 27 41 27 26 20 o / 5 5 5 5 10 5 15 |5 20 5 25 5 30 5 35 j5 49 5 45 9 54 9 46 9 33 9 30 9 23 9 15 9 8 9 1 8 54 8 47 o / 10 10 10 10 20 10 30 10 40 10 50 11 11 10 11 20 11 30 5' 15 5 10 5 5 5 4 56 4 51 4 47 4 43 4 39 4 34 o / 20 20 10 20 20 20 30 20 40 20 50 21 21 10 21 20 21 30 2' 35 2 34 2 32 2 31 2 29 2 28 2 27 2 26 2 25 2 24 o / 34 34 30 35 35 30 3(5 36 30 37 37 30 38 38 30 1 24 1 23 1 21 1 20 1 18 1 17 1 16 1 14 1 13 1 11 1 10 1 9 1 8 1 5 1 3 1 1 59 57 55 53 Feet. , 1 2 3 4 5 6 7 8 9 10 58 1 21 1 40 1 56 2 9 2 21 2 33 2 44 2 53 3 2 50 55 1 1 5 1 10 1 15 1 20 1 25 1 30 1 3" 25 42 25 5 24 29 23 54 23 20 22 47 22 15 21 41 21 15 20 46 5 50 5 55 ,6 ,6 5 6 10 6 15 6 20 6 25 6 30 6 35 8 41 8 34 8 28 8 21 8 15 8 9 8 3 7 57 7 51 7 45 11 40 11 50 12 12 10 12 20 12 30 12 40 12 50 13 13 10 4 31 4 27 4 23 4 20 4 16 4 13 4 9 4 6 4 3 4 21 40 21 50 22 22 10 22 20 22 30 22 40 22 50 23 23 Id 2 23 2 21 2 20 2 19 2 18 1 17 2 16 1 15 2 14 1 13 ,59 39 30 40 41 42 43 44 45 46 47 11 12 13 14 15 16 17 18 19 20 3 10 3 19 3 27 3 36 3 42 3 50 3 57 4 4 4 11 4 17 1 4U 1 45 1 50 1 55 2 2 5 2 10 2 15 2 20 2 25 20 18 19 51 19 25 19 18 35 18 11 17 48 17 26 17 4 ]6 44 6 40 6 45 !6 50 :c 55 7 7 5 7 10 7 15 7 20 ,7 25 7~30 7 35 7 40 7 45 7 50 7 55 8 8 5 8 10 ; 8 15 7 40 7 35 7 30 7 25 7 20 7 15 7 11 7 6 7 2 6 57 13 20 13 30 13 40 13 50 14 14 10 14 20 14 30 14 40 14 50 3 57 3 54 3 51 3 48 3 45 3 43 3 40 3 38 3 35 3 33 23 20 23 30 23 40 23 50 24 24 10 24 20 24 30 24 40 24 50 I 12 1 11 2 10 2 9 2 8 2 7 2 6 2 5 2 4 2 3 48 49 50 51 52 53 54 55 56 57 51 49 48 46 44 43 41 40 38 35 21 22 23 24 26 28 30 35 40 45 4 23 4 30 4 36 4 42 4 52 5 5 5 15 5 39 6 4 6 27 2 30 2 35 2 40 2 45 2 50 2 55 3 3 5 3 10 3 15 16 24 16 4 15 45 15 27 15 9 14 52 14 36 14 20 14 4 13 49 6 53 6 49 6 45 6 41 6 37 6 33 6 29 6 25 6 22 6 18 15 15 10 15 20 15 30 15 40 15 50 16 16 10 16 20 16 30 3 30 3 28 3 26 3 24 3 21 3 19 3 17 3 15 3 12 3 10 25 25 10 25 20 25 30 25 40 25 50 26 26 10 26 20 26 30 2 2 2 1 2 1 59 1 58 1 57 1 56 1 55 1 55 1 54 58 59 60 61 62 C 63 64 65 66 67 35 34 33 32 30 29 28 26 25 24 50 60 70 80 90 100 6 46 7 25 8 1 8 34 9 6 9 35 TABLE VIII. SUN'S PARALLAX IN ALTITUDE. 3 20 3 25 3 30 3 35 3 40 3 45 3 50 3 55 4 4 5 13 34 13 20 13 6 12 53 12 40 12 27 12 15 12 3 11 51 11 40 8 20 8 25 8 30 8 35 8 40 8 45 8 50 8 55 9 9 5 6 15 6 11 6 8 6 5 6 1 5 58 5 55 5 52 5 48 5 45 16 40 16 50 17 17 10 17 20 17 30 17 40 17 50 18 18 10 3 8 3 6 3 4 3 3 3 1 2 59 2 57 2 55 2 54 2 52 26 40 26 50 27 27 15 27 30 27 45 28 28 15 28 30 28 45 1 53 1 52 1 51 1 50 1 49 1 48 I 47 1 46 1 45 1 44 08 69 70 71 72 73 74 75 76 77 23 22 21 19 18 17 16 15 14 13 Altitude. Parallax. 10 20 30 40 50 55 9 9 8 8 7 6 5 4 JO 4 15 4 20 4 25 4 30 4 35 4 40 4 45 4 50 4 55 11 29 11 18 11 8 10 58 10 48 10 39 10 29 10 20 10 11 10 2 9 10 9 15 9 20 9 25 9 30 9 35 9 40 9 45 9 50 9 55 5 42 5 39 5 36 5 34 5 31 5 28 5 25 5 23 5 20 5 18 18 20 18 30 18 40 18 50 19 19 10 19 20 19 30 19 40 19 50 2 51 2-49 2 47 2 46 2 44 2 43 2 41 2 40 2 38 2 37 29 29 30 30 30 30 31 31 30 32 32 30 33 33 30 1 42 1 40 1 38 1 37 1 35 1 33 1 31 1 30 1 28 1 26 78 79 80 81 82 83 84 86 88 90 12 11 10 9 8 7 6 4 2 00 65 70 75 80 85 'JO 4 4 3 2 2 1 258 TABLE IX. TO REDUCE THE EQUATION OF TIME TO ANY TIME UNDER THE MERIDIAN OF GREENWICH. Green Time. DAILY VARIATION. Is. 2s. 4s. 6s. 8s. 10s. 12s. 14s. 16s. 18s. 20s. 22s 24s. 26s. 28s. 30s. h. m. 30 1 1 30 2 2 30 3 3 30 4 s. 8. s. 1 s. 1 s. 9 s. 9 s. 3 s. 3 s. 3 s. 4 8. 4 8. R 8. R s. 5 s. fi s. 6 1 9 9 3 4 R fi 7 8 8 9 1 1 1 1 9 1 2 01 0.1 1 0.1 0.2 9 0.2 0.3 4 0.4 0.5 o r, 0.5 7 8 0.6 8 0.8 1 9 1 9 1.0 1 3 1.1 1 R 1.3 1 7 1.4 1 8 1 5 9 1.6 9 9 1.7 9 3 1.8 2.5 1 1 3 1 R 1 7 1 9 9 1 9 3 9 R 9 7 9 9 3 1 1 3 R 7 1 1 9 1 R 1 8 9 9 9 9 R 9 7 3 3 9 3 R 3 7 0.1 0.2 0.3 3 0.6 7 0.9 1 1.2 1 3 1.5 1 7 1.8 2 2.0 9 3 2.3 9 fi 2 6 3 2.9 3 3 3. '2 3 7 3.5 4 3.7 4 3 4.1 4 7 4.4 5.0 4 30 5 5 30 6 6 30 7 7 30 8 0.2 0.2 02 9 0.4 0.4 0.5 5 0.7 0.8 0.9 1 1.1 1.2 1 4 1 5 1.7 1 8 1.9 2.1 2 3 2.3 2.5 9 8 2.6 2 9 3 2 3.0 3.3 3 7 3.4 3.8 4 1 3.7 4.2 4 fi 4.1 4.6 R 4 5 5.0 R R 4.9 5 4 R 9 5.2 5.8 fi 4 5.6 6.2 6.8 1 R 9 9 R 3 3 R 4 4 R R R R fi fi R 7 7.5 3 5 1 1 i r. 9 9 9 7 3 3 3 8 4 3 4 9 R 4 5 9 fi R 7 7 fi 8 1 0.3 0.3 3 0.6 0.6 0.7 "OV7 7 1.2 1.2 1 3 1 7 1 9 9 9 3 9 9 3 5 4 1 4 7 5 9 R 8 6 4 7 7 R 8 1 8.7 2.5 9 7 3.1 3 3 3.8 4 4.4 4 7 5.0 R 3 5 6 fi 6.3 6 7 6.9 7 3 7.5 8 8.1 8 fi 8.7 9 3 9.4 10.0 8 30 9 9 30 10 10 30 11 11 30 12 0.4 4 1.4 1 5 2.1 9 9 2.8 3 3 5 3 7 4.3 4 R 5.0 R 9 5.7 6 6.4 fi 8 7.1 7 R 7.8 8 9 8.5 9 9.2 9 7 9.9 10 4 10.6 11.2 0.4 0.4 4 0.8 0.8 9 1.6 1.7 1 7 2.4 9 R 3.2 3 3 4.0 4 9 4.8 5 5 5 5 8 6.3 6 7 7.1 7 R 7.9 8 3 8.7 9 9 9.5 10 10.2 10 8 11.0 11 fi 11.8 12 5 9 fi 3 R 4 4 R 3 6 1 7 7 9 8 7 9 fi 10 5 11 11.4 11 9 12.2 19 8 13.1 13.7 0.5 ft 09 1 1 8 9 7 3 7 4 fi R 5 6 4 7 3 8 9 9 9 10 1 9 9 9 3 8 4 8 R 8 fi 7 7 7 8 fi 9 fi 10 R 11 R 19 4 13 4 14.4 R 1 9 3 4 R fi 7 8 9 10 11 19 13 14 15.0 TABLE X. TO OBTAIN THE PROPORTIONAL PART OF THE RATE OF A CHRONOMETER, FROM NOON, TO ANY GIVEN HOUR AT GREENWICH. Green Time. DAILY RATE OF CHRONOMETER. Is. 2s. 4s. 6s. 8s. 10s. 12s. 14s. 16s. 18s. 20s. 22s. 24s. 26s. 28s. 30s. h. m. 30 1 1 30 2 2 30 3 3 30 4 a. s. s. 1 s. 1 s. 9 s. 9 s. 3 s. 3 s. 3 8. 4 s. 4 8. 5 s. R s. R s. fi s. 6 1 9 9 3 4 R 6 7 8 8 9 1 1 1 1 9 1 2 1 1 9 4 R 6 8 9 1 1 1 1 3 1 4 1 5 1 fi 1 7 1 8 1 9 3 R 7 8 1 1 9 1 3 1 5 1 7 1 8 9 9 9 9 3 2 5 0.1 1 0.2 3 0.4 R 0.6 7 0.8 1 1.0 1 9 1.3 1 5 1.5 1 8 1.7 9 1.9 9 9 2.1 9 R 2.3 9 7 2.5 3 2.7 3 9 2.9 3 R 3.1 3 7 0.1 0.2 0.3 0.3 0.6 0.7 0.9 1.0 1.2 1.3 1.5 1.7 1.8 2.0 2.0 2 3 2.3 2.6 2.6 3.0 2.9 3.3 3.2 3.7 3.5 4.0 3.7 4.3 4.1 4.7 4.4 5.0 4 30 5 5 30 6 6 30 7 7 30 8 0.2 9 4 4 (1 7 1 1 1 R 1 9 9 :i 9 fi 3 3 4 S 7 4 1 4 R 4 9 R 9 5 6 8 1 9 1 7 9 1 9 R 9 9 3 3 3 8 4 9 4 fi R R 4 R 8 6.2 6.8 7 5 02 9 0.5 R 0.9 1 1.4 1 R 1.8 9 2.3 9 R 2.8 3 3.2 3 R 3.7 4 4.1 4 5 4.6 R 5.0 5 R 5.5 fi 5.9 fi R 6.4 70 o 3 R 1 1 1 P 29 9 7 3 3 3 8 4 3 4 9 R 4 R 9 fi R 7 7 fi 8 1 0.3 3 o a 0.6 6 1.2 1 9 1.7 1 9 2.3 9 5 2 9 3 1 3.5 3 8 4.1 4 4 4.7 R 5.2 5 fi 5.8 fi 3 6.4 fi-9 7.0 7 R 7.5 8 1 8.1 8 7 8.7 9 4 7 1 3 9 9 7 3 3 4.0 4 7 5 3 fi fi 7 7 3 8 8 fi 9 3 10.0 8 30 9 9 30 10 10 30 11 .11 30 12 0.4 0.4 4 0.7 0.7 fl 1.4 1.5 1 fi 2.1 2.2 9 4 2.H 3.C 3 9 3.5 3.7 4 4.3 5.0 4.5 5.2 4.8 5.5 5.7 6.0 fi 3 6.4 6.8 7 1 7.1 7.5 7 9 7.8 8.2 8 7 8.5 9.0 9 R 9.2 9.7 10 9 9.9 10.4 11 10. G 11.2 11 8 0.4 0.4 F 0.8 0.9 <1 1.7 1.7 1 fi 2.5 2.C 9 7 3.3 3.5 3 7 4.2 4.4 4 6 5.0 5.8 53 6.1 5 5 fi 4 6.7 7.0 7 3 7.5 7.9 8 9 8.3 8.7 9 9 9.2 9.6 10 10.5 11 f 10.0 10.5 11.0 11.5 19 10.8 11.4 11.9 12.4 13 ( 11.6 12.2 12.8 13 4 14 12.5 13.1 13.7 14.4 15 0.5 o r 1.0 1 (I 1.9 9 f 2.8 3 ( 3.8 4 ( 4.8 r> c 5.8 6 6.7 7 n 7 7 8 f 8.6 9 ( 9.6 10 TABLE XI. 259 TO TURN DEGREES INTO TIME, OR TIME INTO DEGREES. Degrees. Time. Degrees. Time. Degrees. Time. Minutes of Deg. Time. Seconds of Deg. Time. H. M. H. M. H. M. M. 8. B. T. 1 2 3 4 5 0. 4 0. 8 0.12 0.16 20 61 62 63 64 65 4. 4 4. 8 4.12 4.16 4.20 121 122 123 124 125 8. 4 8. 8 8.12 8.16 8.20 1 2 3 4 5 0. 4 0. 8 0.12 0.16 0.20 1 2 3 4 5 0. 4 0. 8 0.12 0.16 0.20 6 7 8 9 10 0.24 0.28 0.32 0.36 0.40 66 67 68 69 70 4.24 4.28 4.32 4.36 4.40 126 127 128 129 130 b.24 8.28 8.32 8.36 8.40 6 7 8 9 10 0.24 28 0.32 0.36 0.40 6 7 8 9 10 0.24 0.28 0.32 0.36 40 11 12 13 14 15 0.44 0.48 0.52 0.56 1. 71 72 73 74 75 4.44 4.48 4 52 4.56 5 131 132 133 134 135 8.44 8.48 8 52 8.56 9. 11 12 13 14 15 0.44 0.48 0.52 0.56 1. 11 12 13 14 15 0.44 0.48 0.52 0.56 1. 16 17 18 19 20 1. 4 1. 8 1.12 1.16 1.20 76 77 78 79 80 5. 4 5. 8 5.12 5.16 5.20 136 137 138 139 140 y. 4 9. 8 9 12 9.16 9.20 16 17 18 19 20 1. 4 1. 8 1.12 1.16 1.20 16 17 18 19 20 1. 4 1. 8 1.12 1 16 1.20 21 22 23 24 25 1.24 1.28 1.32 1.36 1.40 81 82 83 ,- 84 85 5.24 5.28 5.32 5.36 5 40 141 142 143 144 145 9.24 9.28 9.32 9.36 9.40 21 22 23 24 25 1.24 1.28 1.32 1.36 1.40 21 22 23 24 25 1.24 1.28 1.32 1.36 1.40 '26 27 28 29 30 1.44 1.48 1.52 1.56 2. 86 87 88 89 90 5.44 5.48 5.52 5.56 6. 146 147 148 149 150 y.44 9.48 9.52 9.56 10. 26 27 28 29 30 1.44 1.48 1.52 1 56 2. 26 27 28 29 30 1.44 1.48 1.52 1.56 2. 31 32 33 34 35 2. 4 2, 8 2.12 2.16 2.20 91 92 93 94 95 6. 4 6. 8 6.12 6.16 6.20 151 152 153 154 155 10. 4 10. 8 10.12 10.16 10.20 31 32 33 34 35 2. 4 2. 8 2.12 2.16 2.20 31 32 33 34 35 2. 4 2. 8 2.12 2.16 2.20 36 37 38 39 40 2.24 2.28 2.32 2.36 2.40 96 97 98 99 100 6.24 6 28 6.32 6.36 6.40 156 157 158 159 1GO 10.24 10.28 10.32 10.36 10.40 36 37 38 39 40 2.24 2.28 2.32 2.36 2.40 /36 37 38 39 40 2.24 2.28 2.32 2.36 2.40 41 42 43 44 45 2.44 2.48 2.52 2.56 3. 101 102 103 104 105 6.44 6.48 6.52 6.56 7. 161 162 163 164 165 10.44 10.48 10.52 10.56 11. 41 42 43 44 45 2.44 2.48 2.52 2.56 3 41 42 43 44 45 2.44 2.48 2.52 2.56 3. 46 47 48 49 50 3. 4 3. 8 3.12 3.16 3.20 106 107 108 109 110 7. 4 7. 8 7.12 7.16 7.20 16i 167 168 169 170 11. 4 11. 8 11.12 11.16 11.20 46 47 48 49 50 3. 4 3. 8 3.12 3.16 3.20 46 47 48 49 50 3. 4 3. 8 3.12 3.16 3.20 51 52 53 54 55 3.24 3.28 3 32 3.36 3.40 111 112 113 ll4 115 7.24 7.28 7.32 7.36 7.40 171 172 173 174 175 11.24 11.28 11.32 11.36 11.40 51 52 53 54 55 3.24 3.28 3.32 3.36 3.40 51 52 53 54 55 3.24 3.28 3.32 3.36 3.40 56 57 58 59 CO 3.44 3.48 3.52 3.56 4. 116 117 118 119 120 7.44 7.48 7.52 7.56 8. 176 177 178 179 180 11.44 11 48 11.52 11.56 12 56 57 58 59 60 3.44 3.48 3.52 3.56 4. 56 57 58 59 60 3.44 3.48 3.52 3.56 4. 2GO TABLE XII. FOB REDUCING THE SUX's DECLINATION TO NOON AT ANY GIVEN MERIDIAN, AND TO ANY TIME AT THE MERIDIAN OF GREENWICH. When Sun's dec. ( add in W. Ion. ) Add tor 1 1 When Sun's dec. sub. in W. Ion. ) Sub. for is increasing, (sub. in E. lou. ) Green, time. |[ is decreasing. add in E. Ion.) Green, time. SUN'S DECLINATION. Time Long. from 2 4 6 8 9 10 11 12 13 14 15 16 Noon . O'O" O'O" O'O" O'O" O'O" O'O" 0' 0" O'O" O'O" O'O" O'O" O'O" O'O" Oh Om 3 12 12 12 11 11 11 11 11 10 10 9 9 9 12 6 24 24 24 23 23 22 22 21 20 20 18 18 18 24 9 35 35 35 34 34 33 32 32 31 30 28 27 27 36 12 47 47 47 46 45 44 43 42 41 40 38 37 36 48 15 59 59 58 57 56 55 54 53 51 50 48 46 44 1 18 1 11 1 10 1 10 1 9 1 7 1 6 1 5 1 3 1 1 1 58 55 53 1 12 21 1 22 1 22 1 22 1 21 1 18 1 17 1 16 1 14 1 12 1 9 1 7 1 5 1 2 1 24 u 1 34 1 34 1 33 1 32 1 29 1 28 1 27 1 24 1 22 1 19 1 17 1 14 1 11 1 36 27 1 46 1 45 1 44 1 43 1 41 1 39 1 38 1 35 1 32 1 29 1 27 1 23 1 20 1 48 30 1 58 1 57 1 56 1 54 1 51 1 49 1 48 1 45 .1 43 1 39 1 36 1 32 1 28 2 33 2 10 2 10 2 8 2 6 2 3 2 1 1 59 1 55 1 53 1 49 1 46 1 42 1 37 2 12 36 2 22 2 21 2 19 2 17 2 14 2 12 2 Id 2 6 2 3 1 59 1 56 1 51 I 46 2 24 39 2 33 2 32 2 31 2 29 2 25 2 23 2 20 2 16 2 14 2 9 2 5 2 1 1 55 2 36 42 2 45 2 44 2 43 2 40 2 36 2 34 2 31 2 27 2 24 2 19 2 15 2 10 2 4 2 48 45 2 57 2,56 2 54 2 51 2 47 2 44 2 41 2 38 2 34 2 29 2 24 2 19 2 12 3 48 3 9 3 -8 3 6 3 3 2 59 2 55 2 52 2 49 2 44 2 39 2 34 2 28 2 21 3 12 51 3 20 3 19 3 18 3 15 3 10 3 6 3 3 3 2 55 2 49 2 44 2 38 2 30 3 24 54 3 32 3 31 3 30 3 26 3 21 3 17 3 14 3 10 3 5 2 59 2 53 2 47 2 39 3 36 57 3 43 3 42 3 41 3 37 3 32 3 28 3 25 3 21 3 15 3 9 3 3 2 56 2 48 3 48 GO 3 55 3 54 3 52 3 48 3 43 3 39 3 35 3 31 3 25 3 19 3 13 3 5 2 56 4 03 4 7 4 G 4 4 4 it 3 54 3 50 3 46 3 42 3 35 J 29 3 22 3 14 3 5 4 12 G6 4 19 4 18 4 16 4 12 4 5 4 1 3 57 3 52 3 46 3 39 3 32 3 23 3 14 4 24 G9 4 31 4 30 4 27 4 23 4 16 4 12 4 8 4 3 3 56 3 49 3 4i 3 32 3 23 4 36 72 4 43 4 42 4 39 4 34 4 27 4 23 4 19 4 13 4 G 3 59 3 51 3 41 3 32 4 48 75 4 54 4 53 4 50 4 45 4 38 4 34 4 29 4 23 4 16 1 9 4 1 3 51 3 40 5 78 5 6 5 5 5 2 4 57 4 50 4 45 4 40 4 34 4 27 4 19 4 11 4 3 49 5 12 81 5 18 5 17 5 14 5 9 5 1 4 56 4 51 4 44 4 37 4 29 4 20 4 9 3 58 5 2t 84 5 30 5 28 5 26 5 20 5 12 5 7 5 2 4 55 4 47 t 39 1 30 4 18 4 7 5 36 87 5 41 5 40 5 37 5 31 5 23 5 18 5 13 5 5 4 58 t 49 4 40 4 27 4 16 5 48 90 5 53 5 52 5 48 5 42 5 34 5 29 5 23 5 16 5 8 4 59 4 49 4 37 4 25 6 'J3 G 5 G 4 6 5 54 5 40 5 41 5 34 5 27 5 18 9 4 59 4 4U 4 34 G 12 93 6 17 6 15 6 12 6 6 5 57 5 52 5 45 5 37 5 28 19 5 9 4 55 4 43 G 24 99 G 28 6 27 6 23 6 17 6 8 G 3 5 56 5 48 5 39 29 5 18 5 5 4 52 G 36 102 6 40 6 39 6 35 6 28 6 19 G 14 6 7 5 58 5 49 39 5 28 5 14 5 G 48 105 6 52 6 51 G 46 6 39 G 30 G 24 6 17 6 9 5 59 49 5 37 5 23 5 8 7 108 7 4 7 2 6 58 G 51 6 41 6 35 6 28 6 19 6 9 59 5 47 5 32 5 17 7 12 111 7 15 7 14 7 10 7 3 G 52 G 46 G 39 6 30 6 20 9 5 50 5 42 5 26 7 24 114 7 27 7 26 7 22 7 15 7 3 6 57 6 50 6 40 G 30 19 6 G 5 51 5 35 7 3G 117 7 39 7 37 7 33 7 26 7 14 7 8 7 1 6 51 6 40 29 6 15 6 1 5 44 7 48 120 7 51 7 49 7 44 7 37 7 25 7 18 7 11 7 1 6 51 39 6 25 6 10 5 53 8 12.J 8 3 8 1 7 56 7 49 7 37 7 29 7 22 7 12 7 1 6 49 G 35 6 19 6 2 8 J2 126 8 11 8 13 8 8 8 7 48 7 40 7 33 7 22 7 11 6 59 G 44 6 28 6 11 8 24 129 8 26 8 21 8 20 8 11 7 59 7 51 7 43 7 33 7 22 7 9 6 54 G 37 6 19 8 36 132 8 38 8 36 8 31 8 22 8 10 8 2 7 54 7 43 7 32 7 18 7 4 3 46 6 28 8 48 135 8 50 8 48 8 42 8 33 8 21 8 13 8 4 7 54 7 42 7 28 7 13 G 56 6 33 9 138 9 1 8 59 8 54 8 45 8 33 8 24 8 15 8 5 7 52 7 38 7 23 7 5 6 45 9 12 141 9 13 9 11 9 6 8 57 8 44 8 35 8 26 8 15 8 3 7 48 7 33 7 14 6 54 9 24 144 9 25 9 23 9 18 9 8 8 55 8 46 8 37 8 26 8 13 7 58 7 42 7 23 7 3 9 36 117 9 37 9 35 9 29 9 19 9 6 8 57 8 48 8 3G 8 23 8 8 7 52 7 32 7 12 9 48 550 9 48 9 45 9 40 9 30 9 17 9 8 8 58 8 47 8 33 8 18 8 2 7 42 7 21 10 153 10 9 57 U 52' 9 42 9 28 9 19 9 9 8 57 8 43 8 28 8 12 7 51 7 30 10 12 156 10 12 10 9 10 4 9 54 9 39 9 30 9 20 9 8 8 54 8 38 8 21 8 7 39 10 24 159 10 24 10 21 10 16 10 5 9 50 9 41 9 31 9 18 9 4 8 48 8 31 8 10 7 48 10 36 162 10 36 10 33 10 27 10 16 10 1 9 52 9 42 9 29 9 14 8 58 8 41 8 19 7 57 10 48 165 10 47 10 44 10 38 10 27 10 12 10 3 9 52 9 39 9 24 9 8 8 50 8 28 8 5 11 168 10 59 10 56 10 50 10 39 10 24 10 14 10 3 9 50 9 35 9 18 9 8 38 8 14 H 12 171 11 11 11 8 11 2 10 51 10 35 10 25 10 14 10 9 45 9 28 9 10 8 47 8 23 U 24 171 11 23 11 2011 14 11 310 46 10 36 10 25 10 11 9 55 '.) 38 J. J 8 57 3 32 U 33 177 11 34 11 31 1 1 25 11 14 10 57 10 47 10 36 10 21 10 G 9 48 9 29 9 6 8 41 11 48 180 11 4G 11 43 11 37 11 25 11 8 10 58 10 46 10 32 10 16 J 58 9 389 15 S 49 12 TABLE XII. 261 FOB REDUCING THE SUN*S DECLINATION TO NOON AT ANY GIVEN MERIDIAN, AND TO ANY TIME AT THE MERIDIAN OF GREENWICH. When Sun's dec. i add in W. Ion. 1 Add for When Snn's dec. j sub. in W. Ion. ) sub. for is increasing, (sub in E. Ion. J Green, time. is decreasing, (add in E. Ion. J Green, time. SUN'S DECLINATION. Time Lon from 17- 18 19 19 30 20 20 30 21 21 30 22 22 30 '23' 23 15 23 28' Noon. o- 0'0"0'0"0'0" 0' 0" O'O' 0' 0' O'O' 0' 0"0'0" 0' 0"0'0' 0' 0' O'O" OhOm 3 80 80 7 7 o e 6 5 4 3 2 2 12 6 160 160 14 13 12 11 1C 9 8 6 4 4 24 9 240 240 21 20 18 17 15 14 12 10 n 5 36 12 35 31 ! 28 27 25 23 21 19 16 14 9 7 48 15 41 490 35 34 32 29 27 24 21 18 12 9 18 4 460 42 40 38 35 32 29 25 21 14 10 1 12 '21 57 540 4S 47 44 41 38 34 29 24 17 12 1 24 24 1 1 '2 5G 54 50 47 44 39 34 28 19 14 1 36 27 I 14 I 1C 1 j 1 1 57 53 50 44 39 32 22 15 1 48 30 1 23 1 18 1 11 1 8 1 4 59 55 49 43 36 25 17 2 33 1 31 1 25 1 Ib 1 14 1 10 1 4 1 .(J 53 4" 39 27 19 2 12 3u 1 39 I 33 1 25 1 21 L 16 1 10 1 5 58 5 42 30 20 2 24 39 1 47 I 41 1 32 1 28 1 2'2 1 16 1 10 1 3 5o 46 32 22 2 36 42 1 5G 1 49 I 39 1 35 1 29 1 22 1 16 1 8 59 50 34 24 2 48 45 2 5 1 57 1 46 1 42 1 36 1 28 1 22 1 13 1 4 54 36 25 3 48 2 13 2 4 1 53 1 48 I 42 1 33 1 27 1 18 1 8 57 39 27 3 12 51 2 21 2 12 2 1 55 1 48 1 39 1 32 1 23 1 12 1 42 29 3 24 54 2 29 2 20 2 7 2 2 1 54 1 45 1 38 1 28 1 16 1 3 44 30 3 36 57 2 38 2 28 2 15 2 9 2 1 1 52 1 44 1 33 1 21 1 7 47 32 3 48 CO 2 47 2 36 2 23 2 16 2 8 1 59 1 49 1 39 1 26 1 11 49 34 4 03 2 55 2 43 2 29 2 '22 2 14 2 4 1 54 1 4J 1 30 1 14 51 3-5 4 12 CG 3 3 2 51 2 36 2 29 2 20 2 10 1 59 1 48 1 34 1 17 54 37 4 24 69 3 11 2 59 2 43 2 36 2 26 2 16 2 4 1 53 1 38 1 21 56 39 4 36 72 3 19 3 7 2 5U 2 43 2 33 2 21 2 10 1 58 1 4'^ 1 25 59 40 4 48 75 3 28 3 15 2 58 2 50 2 40 2 27 2 16 2 3 1 47 1 29 1 1 42 5 78 3 36 3 2. 3 5 2 56 2 46 2 33 2 21 2 8 1 51 1 32 1 4 44 5 12 81 3 44 3 30 3 12 3 3 2 52 2 39 2 26 2 13 1 55 1 35 1 6 45 5 21 84 3 52 J 3.->3 19 3 10 2 58 2 45 2 32 2 18 1 59 1 39 1 9 47 5 36 87 4 1 3 463 20 3 17 3 5 2 52 2 38 2 23 2 4 1 43 1 11 49 5 48 90 4 10 3 51 3 34 3 24 3 12 2 59 2 41 2 28 2 1 1 47 1 14 50 6 93 4 181 13 41 3 30 3 18 3 4 ^ 49 2 32 2 13 1 50 1 16 52 6 J2 96 4 264 93 48 3 37 3 24 3 9 2 54 2 37 2 17 1 53 1 19 54 6 24 90 4 344 17 3 55 3 44 3 30 3 15 2 59 2 42 2 21 1 57 1 21 55 6 36 102 4 43 1 25 4 2 3 51 3 37 3 21 3 5 2 47 2 25 2 1 1 24 57 6 48 105 4 524 33 4 9 3 58 3 44 3 27 3 11 2 52 2 30 2 5 1 26 59 7 108 5 04 404 16 4 4 3 50 3 33 3 16 2 57 2 34 2 9 1 29 1 7 12 111 5 84 484 23 4 11 3 56 3 39 3 21 3 2 2 38 2 12 1 31 1 2 7 24 114 16 4 56 4 30 4 18 4 2 3 46 3 27 3 7 2 43 2 16 1 34 1 4 7 36 117 25 5 44 38 4 25 4 9 3 52 3 33 3 12 2 48 2 20 1 37 1 5 7 48 120 31 .5 12 4 46 4 32 4 16 3 59 3 39 3 17 2 53 2 23 1 39 1 7 8 123 42 5 19 4 53 4 38 i 22 4 4 3 41 3 22 2 57 2 20 1 41 1 9 8 12 12G 50 5 27 5 4 45 4 28 4 10 3 49 3 27 3 1 2 29 1 44 1 10 8 24 129 58 5 30 5 7 4 52 1 34 4 16 3 54 3 32 3 5 2 33 1 4G 1 12 8 36 132 6 5 43 5 14 4 59 1 41 4 22 3 59 3 37 3 9 2 36 1 49 1 14 8 48 185 15 5 51 5 21 5 6 1 48 4 28 4 5 3 42 13 2 40 1 51 1 15 9 138 23 3 58 5 2b 5 12 4 54 4 34 4 10 3 47 17 2 43 1 54 1 17 9 12 141 31 6 6 5 3? 5 19 5 4 40 4. 15 3 52 21 2 46 1 56 1 19 9 24 lit 39 a 14 5 42 5 2G 3 4 46 4 21 3 57 26 2 50 1 59 1 20 9 36 147 48 6 22 5 49 5 33 5 13 4 52 4 27 4 2 30 2 54 2 1 1 22 9 48 150 G 57 6 30 5 57 5 40 5 20 4 58 4 33 4 7 35 2 58 2 4 1 24 10 153 7 5 G 37 G 4 5 4G 3 '26 5 3 i 38 4 11 39 3 1 I 6 1 25 10 12 156 7 13 6 45 G 11 5 53 3 32 5 9 t 43 4 16 43 3 4 2 9 1 27 10 24 159 7 21 6 53 G 18 6 3 38 5 15 4 48 4 21 47 3 8 2 11 1 29 10 36 162 7 29 7 1 G 25 6 7 3 45 5 21 4 54 4 26 51 3 12 2 13 1 30 10 48 1G5 7 38 7 9 6 32 G 14 5 52 5 26 3 4 31 56 3 16 2 15 1 32 LI 168 7 4G 7 1C G 39 6 20 3 58 5 32 5 6 4 36 t 3 19 2 17 1 34 11 12 171 7 54 7 24 G 40 G 27 > 4. 5 38 3 11 4 41 1 4 3 22 2 20 1 35 11 24 174 8 3 7 3 G 53 G 34 j 10 5 4t 3 17 4 46 I 9 3 26 2 22 1 37 11 36 177 s i-j 1 4d 7 1 6 41 j 17 :, .M 5 23 4 51 I 14 3 30 2 25 1 39 11 48 180 8 21 7 48 7 9 6 48 3 24 5 58 5 29 4 56 t 19 3 34 2 28 1 40 12 262 TABLE XIII. CORRECTIONS OF THE APPARENT ALTITUDES OF THE SUN AND STARS. App, Alt. Sun's Corr. Star's Corr. Diff. to 1' App. Alt. Sun's Corr. Star's Corr. App. AH. Sun's Corr. Star's Corr. App. Alt. Sun's Corr. Star's Corr. o / 5 10 15 20 25 32 51 32 1 31 13 30 26 29 41 28 56 33 32 10 31 22 30 35 29 49 29 5 10.0 9.6 9.4 9.1 8.9 8.6 5 1 2 3 4 5 9 44 9 42 9 41 9 39 9 37 9 36 9 52 9 51 9 49 9 48 9 46 9 44 6 1 2 3 4 5 8 18 8 17 8 15 8 14 8 13 8 12 8 26 8 25 8 24 8 23 8 22 8 20 7 1 2 3 4 5 7 12 7 11 7 10 7 9 7 8 7 7 7 21 7 20 7 19 7 18 7 17 7 16 30 35 40 45 50 55 28 13 27 31 26 51 26 11 25 33 24 55 28 22 27 40 26 59 26 20 25 41 25 4 8 4 8.1 7.9 7.7 7.4 7.2 5 6 7 8 9 10 11 9 34 9 32 9 31 9 29 9 28 9 26 9 43 9 41 9 40 9 38 9 36 9 35 6 6 7 8 9 10 11 8 10 8 9 8 8 8 7 8 6 8 4 8 19 8 18 8 17 8 15 8 14 8 13 7 6 7 8 9 10 11 7 6 7 6 7 5 7 4 7 3 7 2 7 15 7 14 7 13 7 12 7 11 7 10 1 5 10 15 20 25 24 19 23 44 23 10 22 38 22 6 21 35 24 28 23 53 23 19 22 46 22 15 21 44 7.0 6.7 6.5 6.4 6.2 6.1 5 12 13 14 15 16 17 9 25 9 23 9 21 9 20 9 18 9 17 9 33 9 32 9 30 9 29 9 27 9 25 6 12 13 14 15 16 17 8 3 8 2 8 1 8 7 59 7 57 8 12 8 11 8 10 8 8 8 7 8 6 7 12 13 14 15 16 17 7 1 7 6 59 6 58 6 57 6 56 7 10 7 9 7 8 7 7 7 6 7 5 1 30 35 40 45 50 55 21 5 20 36 20 8 19 41 19 15 18 50 21 14 20 45 20 17 19 50 19 24 18 59 5.7 5.6 5.3 5.2 5.0 .4.9 5 18 19 20 21 22 23 9 15 9 14 9 12 9 11 9 9 9 8 9 24 9 22 9 21 9 19 9 18 9 16 6 18 19 20 21 22 23 7 56 7 55 7 54 7 53 7 52 7 50 8 5 8 4 8 3 8 1 8 7 59 7 18 19 20 21 22 23 6 55 6 55 6 54 6 53 6 52 6 51 7 4 7 3 7 2 7 1 7 1 7 2 5 10 15 20 25 18 25 18 2 17 39 17 17 16 55 16 34 18 34 18 10 17 48 17 25 17 4 16 43 4.7 4.5 4.5 4.3 42 4.0 5 24 25 26 27 28 29 9 6 9 5 9 3 9 2 9 8 59 9 15 9 13 9 12 9 11 9 9 9 8 6 24 25 26 27 28 29 7 49 7 48 7 47 7 46 7 45 7 44 7 58 7 57 7 56 7 55 7 54 7 53 7 24 25 26 27 28 29 6 50 6 49 6 48 6 48 6 47 6 46 6 59 6 58 6 57 6 56 6 55 6 54 2 30 35 40 45 50 55 16 14 15 55 15 36 15 17 15 14 43 16 23 16 3 15 44 15 26 15 8 14 51 3.9 3.8 3.6 3.5 3.4 3 4 5 30 31 32 33 34 35 8 58 8 56 8 55 8 53 8 52 8 51 9 6 9 5 8 3 9 2 9 1 8 59 6 30 31 32 33 34 35 7 43 7 42 7 41 7 40 7 38 7 37 7 51 7 50 7 49 7 48 7 47 7 46 7 30 31 32 33 34 35 6 45 6 44 6 43 6 42 6 42 6 41 6 54 6 53 6 52 6 51 6 50 6 49 3 5 10 15 20 25 14 26 14 10 13 54 13 39 13 24 13 10 14 35 14 19 14 3 13 48 13 33 13 19 3.3 3.2 3.1 3.0 2.8 2.8 5 36 37 38 39 40 41 8 49 8 48 8 46 8 45 8 44 8 42 8 58 8 56 8 55 8 54 8 52 8 51 6 36 37 38 39 40 41 7 36 7 35 7 34 7 33 7 32 7 31 7 45 7 44 7 43 7 42 7 41 7 40 7 36 37 38 39 40 41 6 40 6 39 6 38 6 37 6 37 6 36 6 49 6 48 6 47 6 46 6 45 6 44 3 30 35 40 45 50 55 12 56 12 43 12 30 12 17 12 5 11 53 13 5 12 51 12 38 12 26 12 13 12 1 2.7 2.6 2.6 2.5 2.4 2.3 5 42 43 44 45 46 47 8 41 8 40 8 38 8 37 8 36 8 34 8 50 8 48 8 47 8 46 8 44 8 43 6 42 43 44 45 46 47 7 30 7 29 7 28 7 27 7 26 7 25 7 39 7 38 7 37 7 36 7 35 7 34 7 42 43 44 45 46 47 6 35 6 34 6 33 6 33 6 32 6 31 6 44 6 43 6 42 6 41 6 40 6 40 4 5 10 15 20 25 11 41 11 30 11 19 11 8 10 58 10 48 11 50 11 38 11 27 11 17 11 6 10 56 2.3 2.2 2.1 2.1 2.0 2.0 5 48 49 50 51 52 53 8 33 8 32 8 30 8 29 8 28 8 27 8 42 8 40 8 39 8 38 8 36 8 35 6 48 49 50 51 52 53 7 24 7 23 7 22 7 21 7 20 7 19 7 33 7 32 7 31 7 30 7 29 7 28 7 48 49 50 51 52 53 6 30 6 29 6 29 6 28 6 27 6 26 6 39 6 38 6 37 6 36 6 36 6 35 4 30 35 40 45 50 55 10 38 10 28 10 19 10 10 10 1 9 52 10 46 10 37 10 28 10 18 10 10 10 1 1.9 1.9 1.8 1.8 1.7 1.7 5 54 55 56 57 58 59 8 25 8 24 8 23 8 21 8 20 8 19 8 34 8 33 8 31 8 30 8 29 8 28 6 54 55 56 57 58 59 7 18 7 17 7 16 7 15 7 14 7 13 7 27 7 26 7 25 7 24 7 23 7 22 7 54 55 56 57 58 59 6 25 6 25 6 24 6 23 6 22 6 22 6 34 6 33 6 33 6 32 6 31 6 30 TABLE XIII. 263 CORKECTIONS OF THE APPAEENT ALTITUDES OF THE SUN AND STARS. App. Alt. Sun's Corr. Star's Corr. App. Alt. Sun's Corr. Star's Corr. App. Alt. Sun's Corr. Star's Corr. App. Alt. Sun's Corr. Star's Corr. O ' 8 1 2 3 4 5 6 21 6 20 6 19 6 19 6 18 G 17 6 30 6 29 6 28 6 27 6 27 6 26 9 2 4 6 8 10 5 40 5 39 5 37 5 35 5 34 5 34 5 48 5 47 5 46 5 45 5 44 5 42 11 2 4 6 8 10 4 38 4 37 4 37 4 36 4 35 4 34 4 47 4 46 4 45 4 44 4 43 4 43 o / 13 2 4 6 8 10 3 54 3 54 3 53 3 53 3 52 3 51 4 3 4 2 4 2 4 1 4 1 4 8 G 7 8 9 10 11 6 1G 6 16 6 15 6 14 6 13 6 13 G 25 6 24 6 24 6 23 6 22 6 21 9 12 14 16 18 20 22 5 33 5 31 5 30 5 29 5 28 5 27 5 41 5 40 5 39 5 38 5 36 5 35 11 12 14 16 18 20 22 4 33 4 32 4 32 4 31 4 30 4 29 4 42 4 41 4 40 4 89 4 39 4 38 13 12 14 16 18 20 22 3 51 3 50 3 50 3 49 3 48 3 48 3 59 3 59 3 58 3 57 3 57 3 56 8 12 13 14 15 16 17 G 12 6 11 6 10 6 10 6 9 6 8 6 21 6 20 6 19 6 18 6 18 6 17 9 24 26 28 30 32 34 5 iiG 5 24 5 23 5 22 5 21 5 20 5 34 5 33 5 32 5 31 5 30 5 29 11 24 26 28 30 32 34 4 28 4 28 4 27 4 26 4 25 4 24 4 37 4 36 4 35 4 35 4 34 4 33 13 24 26 28 30 32 34 3 47 3 47 3 46 3 45 3 45 3 44 3 5G 3 55 3 54 3 54 3 53 3 53 8 18 19 20 21 22 23 6 8 6 7 6 6 6 5 6 5 6 4 6 JG 6 16 6 15 6 14 6 13 6 13 9 3G 38 40 42 44 46 5 1U 5 18 5 17 5 16 5 15 5 13 5 'z7 5 26 5 25 5 24 5 23 5 22 11 36 38 40 42 44 46 4 24 4 23 4 22 4 21 4 21 4 20 4 32 4 31 4 31 4 30 4 29 4 28 13 3G 38 40 42 44 46 3 44 3 43 3 43 3 42 3 41 3 41 3 52 3 52 3 51 3 51 3 50 3 49 8 24 25 26 27 28 29 G 3 6 3 6 2 6 1 6 1 6 6 la 6 11 6 11 6 10 6 9 G 9 9 48 60 52 54 56 58 5 12 5 11 5 10 5 9 5 8 5 7 5 21 5 20 5 19 5 18 5 17 5 16 11 48 50 52 54 56 58 4 19 4 18 4 18 4 17 4 16 4 15 4 28 4 27 4 26 4 25 4 25 4 24 13 48 50 52 54 56 58 3 40 3 40 3 39 3 39 3 38 3 38 3 49 3 48 3 48 3 47 3 47 3 46 8 u() 31 32 33 34 35 5 59 5 59 5 58 5 57 5 57 5 56 6 8 6 7 6 7 6 6 6 5 6 5 10 2 4 6 8 10 5 6 5 5 5 4 5 3 5 2 5 1 5 15 5 14 5 13 5 12 5 11 5 10 12 2 4 6 8 10 4 15 4 14 4 13 4 12 4 12 4 11 4 23 4 22 4 22 4 21 4 20 4 20 14 2 4 6 8 10 3 37 3 36 3 36 3 35 3 35 3 34 3 45 3 45 3 44 3 44 3 43 3 43 8 30 37 38 39 40 41 5 55 5 55 5 54 5 53 5 53 5 52 o 4 6 3 6 3 6 2 6 1 6 1 10 12 14 16 18 20 22 5 4 59 4 58 4 57 4 56 4 55 5 9 5 8 5 7 5 6 5 5 5 4 12 12 14 16 18 20 22 4 1U 4 10 4 9 4 8 4 8 4 7 4 19 4 18 4 17 4 17 4 16 4 15 14 12 14 16 18 20 22 3 34 3 33 3 33 3 32 3 32 3 31 3 42 3 42 3 41 3 41 3 40 3 40 8 42 43 44 45 46 47 5 51 5 51 5 50 5 49 5 49 5 48 G 5 59 5 59 5 58 5 57 5 57 10 24 26 28 30 32 34 4 54 4 53 4 53 4 52 4 51 4 50 5 3 5 2 5 1 5 4 59 4 58 12 24 26 28 30 32 34 4 6 4 6 4 5 4 4 4 3 4 3 4 15 4 14 4 13 4 13 4 12 4 11 14 24 26 28 30 32 34 3 31 3 30 3 30 3 29 3 29 3 28 3 39 3 39 3 38 3 38 3 37 3 37 8 48 49 50 51 52 53 5 47 5 47 5 46 5 45 5 45 5 44 5 56 5 55 5 55 5 54 5 53 5 53 10 36 38 40 42 44 46 4 49 4 48 4 47 4 46 4 45 4 44 4 57 4 57 4 56 4 55 4 54 4 53 12 3G 38 40 42 44 46 4 2 4 2 4 1 4 4 3 59 4 n 4 10 4 9 4 9 4 8 4 7 14 3G 38 40 42 44 46 3 28 3 27 3 27 3 26 3 26 3 25 3 36 3 36 3 35 3 35 3 34 3 34 8 54 55 56 57 58 59 5 44 5 43 5 42 5 42 5 41 5 40 5 52 5 52 5 51 5 50 5 50 5 49 10 48 50 52 54 56 58 4 43 4 43 4 42 4-41 4 40 4 39 4 52 4 51 4 50 4 49 4 49 4 48 12 48 50 52 54 56 58 3 58 3 58 3 57 3 56 3 56 3 55 4 7 4 6 4 5 4 5 4 4 4 4 14 48 50 52 54 66 68 3 25 3 24 3 24 3 23 3 23 3 22 3 33 3 33 3 32 3 32 3 31 3 31 264 TABLE XIII. CORRECTIONS OF THE APPARENT ALTITUDES OF THE SUN AND STARS. App. Alt. Sun's Corr. Star's Corr. App. Sun's Alt. Corr. Star's Corr. App. Alt. Sun's Corr. Star's Corr. App. Alt. Sun's Corr. Star's Corr. O / 15 5 10 15 20 25 3 22 3 21 3 19 3 18 3 17 3 16 3 30 3 29 3 28 3 27 3 26 3 24 20 10 20 30 40 50 2 27 2 26 2 25 2 23 2 22 2 21 2 35 2 34 2 33 2 31 2 30 2 29 30 20 40 31 20 40 1 31 1 30 1 28 1 27 1 26 1 25 1 38 1 37 1 36 1 35 1 33 1 32 50 30 51 30 52 30 42 41 41 40 39 38 48 47 46 45 44 44 15 30 35 40 45 50 55 3 15 3 14 3 13 3 11 3 10 3 9 3 23 3 22 3 21 3 20 3 19 3 18 21 10 20 30 40 50 2 TJ 2 18 2 17 2 16 2 14 2 13 '2 'z7 2 26 2 25 2 24 2 23 2 21 32 20 40 33 20 40 1 '24 1 22 1 21 1 20 1 19 1 18 1 31 1 30 1 29 1 27 1 26 1 25 53 30 54 30 55 30 38 37 36 36 35 34 43 42 41 41 40 39 16 5 10 15 20 25 3 8 3 7 3 6 3 5 3 4 3 3 3 17 3 16 3 15 3 14 3 13 3 12 22 10 20 30 40 50 2 12 2 11 2 10 2 9 2 8 2 7 2 20 2 19 2 18 2 17 2 16 2 15 34 20 40 35 20 40 1 17 1 16 1 15 1 14 1 13 1 12 1 24 1 23 1 22 1 21 1 20 1 19 56 30 57 30 58 30 34 33 32 32 31 30 38 38 37 36 36 35 16 30 35 40 45 50 55 3 2 3 1 3 2 59 2 58 2 57 3 11 3 10 3 9 3 8 3 7 3 6 23 10 20 30 40 50 2 6 2 4 2 3 2 2 2 1 2 2 14 2 13 2 11 2 10 2 9 2 8 36 20 40 37 20 40 1 11 1 10 1 9 1 9 1 8 1 7 1 18 1 17 1 16 1 15 1 15 1 14 59 30 60 30 61 30 30 29 29 5-8 27 '27 34 34 33 32 32 31 17 5 10 15 20 25 2 56 2 55 2 54 2 54 2 53 2 52 3 5 3 4 3 3 3 2 3 1 3 24 10 20 30 40 50 1 59 1 58 1 57 1 57 1 56 1 55 2 7 2 6 2 5 2 4 2 4 2 3 38 20 40 39 20 40 1 6 1 5 1 4 1 3 1 3 1 2 1 13 1 12 1 11 1 10 1 9 1 9 62 30 63 30 64 30 U 26 26 25 24 24 23 30 30 29 28 28 27 17 30 35 40 45 50 55 2 51 2 50 2 49 2 48 2 47 2 46 2 59 2 58 2 57 2 56 2 56 2 55 25 10- 20 30 40 50 1 54 1 53 1 52 1 51 1 50 1 49 2 2 2 1 2 1 59 1 58 1 57 40 20 40 41 20 40 1 1 1 59 59 58 57 I 8 1 7 1 6 1 5 1 5 1 4 65 30 66 30 67 30 '23 22 22 21 21 20 '27 26 25 25 24 24 1 5 10 15 20 25 2 46 2 45 2 44 2 43 2 42 2 41 2 54 2 53 2 52 2 51 2 51 2 50 26 10 20 30 40 50 1 49 1 48 1 47 1 46 1 45 1 44 1 56 1 56 1 55 1 54 1 53 1 52 4'2 U 20 40 43 20 40 57 56 55 55 54 53 1 3 1 2 1 2 1 1 1 1 68 69 70 71 72 73 20 19 18 17 16 15 23 22 21 20 18 17 18 30 35 40 45 50 55 2 41 2 40 2 39 2 38 2 38 2 37 2 49 2 48 2 47 2 47 2 46 2 45 27 10 20 30 40 50 1 44 1 43 1 42 1 41 1 41 1 40 1 51 1 51 1 50 1 49 1 48 1 48 44 20 40 45 20 40 53 52 51 51 50 49 59 58 58 57 56 56 74 75 76 77 78 79 14 13 12 11 10 9 16 15 14 13 12 11 19 5 10 15 20 25 2 36 2 35 2 35 2 34 2 33 2 32 2 44 2 44 2 43 2 42 2 41 2 41 28 10 20 30 40 50 1 39 1 38 1 38 1 37 1 36 1 35 1 47 1 46 1 45 1 45 ] 44 1 43 46 20 40 47 20 40 o 49 48 48 47 47 46 55 54 54 53 52 52 bO 81 82 83 84 85 8 8 7 6 5 4 10 9 8 7 6 5 19 30 35 40 45 50 55 2 32 2 31 2 30 2 29 2 29 2 28 2 40 2 39 2 38 2 38 2 37 2 36 29 10 20 30 40 50 1 35 1 34 1 33 1 33 1 32 1 31 1 42 1 42 1 41 1 40 1 40 1 39 48 20 40 49 20 40 45 45 44 44 43 43 51 51 50 49 49 48 86 87 88 89 90 3 3 2 1 4 3 2 1 TABLE XIV. 265 TO FIND LATITUDE BY REDUCTION TO THE MERIDIAN. Natural Sines. M. 1 2 3 40 5 6 7 8 9 M. 1 2 3 4 5 6 7 8 9 10 UOOOOO 000291 000582 000873 001164 001454 001745 002036 002327 002618 002909 017452 017743 oisoai 018325 018616 018907 019197 019488 019779 020070 020361 034899 035190 035481 035772 036062 036353 036644 036934 037225 037516 037806 052336 052626 052917 053207 053498 053788 054079 054369 05466(i 054950 055241 069756 070047 070337 070627 070917 071207 071497 071788 072078 072368 072G58 087156 087446 087735 088025 088315 088605 088894 089184 089474 089763 090053 104528 104818 105107 105396 105686 105975 106264 106553 106843 107132 107421 121809 122158 122447 122735 123024 123313 123601 123890 124179 124467 124756 139173 139461 139749 140037 140325 140613 140901 141189 141477 141765 142053 156434 156722 157009 157296 157584 157871 158158 158445 158732 159020 159307 60 59 58 57 56 55 54 53 52 51 50 11 12 13 14 15 16 17 18 19 20 U03200 003491 003782 004072 004363 004G54 004945 005236 005527 005818 02065i: 020942 021233 021524 021815 022106 022397 022687 022978 023269 03b097 038388 038678 038969 039260 039550 039841 040132 040422 040713 055531 055822 056112 056402 056693 056983 057274 057564 C57854 058145 072948 073238 073528 073818 074108 074399 074689 074979 075269 075559 OU0343 090633 090922 091212 091502 091791 092081 092371 092660 092950 107710 107999 108289 108578 108867 109 156 109445 109734 110023 110313 125045 125333 125622 125910 126199 126488 126776 127065 127353 127G42 142341 142629 142917 143205 143493 143780 144068 144356 144644 144932 159594 159881 160168 160455 160743 161030 161317 161604 161891 162178 49 48 47 46 45 44 43 42 41 40 21 22 23 24 25 26 27 28 29 30 006109 006399 006690 006981 007272 007563 007854 008145 008436 008727 023560 023851 024141 024432 024723 025014 025305 025595 025886 026177 041004 041294 041585 041876 042166 042457 042748 043038 043329 043619 058435 058726 059016 059306 059597 059887 060177 060468 060758 061049 075849 076139 076429 076719 077009 077299 077589 077879 078169 078459 093-39 093529 093819 094108 094398 094687 094977 095267 095556 095846 110602 110891 111180 111469 111758 112047 112336 112625 112914 113203 127930 128219 128507 128796 129084 129373 129661 129949 130238 130526 145220 145507 145795 146083 146371 146659 146946 147234 147522 147809 162465 162752 163039 163326 163613 163900 164187 164474 164761 165048 39 38 37 36 35 34 33 32 31 30 31 32 33 34 35 36 37 38 39 40 009017 009308 009599 009890 010181 01047-2 010763 011054 011344 011635 026468 026759 027049 027340 027631 027922 028212 028503 028794 029085 043910 014201 044491 044782 045072 0453G3 045654 045944 046235 046525 061339 061629 061920 062210 062500 062791 063081 063371 063661 063952 078749 079039 079329 079619 079909 080199 080489 080779 081069 081359 090135 096425 096714 097004 097293 097583 097872 098162 098451 098741 113492 113781 114070 114359 114648 114937 115226 115515 115804 116093 130815 131103 131391 131680 131968 132256 132545 132833 133121 133410 148097 148385 148672 148960 149248 149535 149823 150111 150398 150686 165334 165621 165908 166195 166482 166769 167056 167342 167629 167916 29 28 27 26 25 24 23 22 21 20 41 42 43 44 45 46 47 48 49 50 011926 012217 012508 012799 013090 013380 013671 013962 014253 014541 029375 029666 029957 030248 030539 030829 031120 031411 031702 031992 046816 047106 047397 047688 047978 048269 048559 048850 049140 049431 064242 064532 064S23 065113 065403 065693 065984 066274 066564 066854 081649 081939 082228 082518 082808 083098 083388 083678 083968 084258 (199030 099320 099609 099899 100188 100477 100767 101056 101346 101635 116382 116671 116960 117249 117537 117826 118115 118404 118693 118982 133698 133986 134274 134563 134851 135139 135427 135716 136004 136292 150973 151261 151548 151836 152123 152411 152698 152986 153273 153561 168203 168489 168776 169063 169350 16963G 169923 170209 170496 170783 19 18 17 16 15 14 13 12 11 10 51 52 53 54 55 56 57 58 59 GO 014835 015126 015416 015707 015998 016289 016580 016871 017162 017452 03-2283 032574 032864 033155 033446 033737 034027 034318 034609 034899 049721 050012 050302 050593 050883 051174 051464 051755 052045 052336 067145 067435 067725 068015 068306 068596 068886 069170 069466 069750 084547 084837 085127 085417 085707 085997 086286 086576 086866 087156 101924 102214 102503 102793 103082 103371 103661 103950 104239 104528 119270 119559 119848 120137 120426 120714 121003 121292 121581 121869 136580 136868 137156 137445 137733 138021 138309 138597 138885 139173 153848 154136 154423 154710 154998 155285 155572 155860 156147 156434 171069 171356 171643 171929 172216 172502 172789 173075 173362 173648 9 8 7 6 5 4 3 2 1 BE. 89 1 88 87 86 85 I 84 83 | 82 1 81 | 80 1C. Natural Co-sines. 266 TABLE XIV. TO FIND LATITUDE BY SEDUCTION TO THE MERIDIAN. Natural Sines. M. 10 11 12 13 14 15 16 17 18 19 M. 1 2 3 4 5 6 7 8 9 10 73(548 73935 74221 74508 74794 75080 75367 75653 75939 76226 76512 L90609 191095 L91380 191666 L91951 L92237 192522 192807 193093 193378 193664 07912224951 08196,225234 08481225518 08765 225801 09050226085 09334226368 09619226651 09903226935 10187227218 10472227501 10756227784 24192-2 242204 242486 242769 243051 243333 243615 243897 244179 244461 244743 ^58819 259100 259381 259662 259943 260224 260505 260785 261066 261347 261628 275637 275917 276197 276476 276756 277035 277315 277594 277874 278153 278432 2923721 292650 292928 293206 293484 293762 294040 294318 294596 294874 295152 3U9017 3-255681 3092941325843 309570326118 309847326393 310123226668 310400326943 310676327218 310953327493 311229327768 311506328042 311782328317 00 59 58 57 56 55 54 53 52 51 50 11 12 13 14 15 16 17 18 19 20 76798 77085 77371 77657 77944 78230 78516 78802 179088 179375 193949 194234 194520 194805 195090 195376 195661 195946 196231 196517 11040228068 11325228351 11609 228634 11893228917 212178229200 212462 229484 -12746229767 213030230050 213315230333 213599230616 245025 245307 245589 245871 246153 246435 246717 246999 247281 247563 261908 262189 262470 262751 263031 263312 263592 263873 264154 264434 278712 278991 279270 279550 279829 280108 280388 280667 280946 281225 295430 295708 295986 296264 296542 296819 297097 297375 297653 297930 311059328592 312335 i 328867 312611)829141 312888,329416 313164329691 313440329965 313716330240 313992330514 314269:330789 314545,331063 49 48 47 46 45 44 43 42 41 40 21 22 23 24 25 26 27 28 29 30 179061 179947 180233 180519 180805 181091 181377 181663 181950 182236 196802 197087 197372 197657 197942 198228 198513 198798 199083 199368 213883230899 214167231182 214451231465 214735231748 215019232031 215303232314 215588232597 215872-232880 216156233163 216440233445 247845 248126 248408 248690 248972 249253 249535 249817 250098 250380 264715 264'J95 265276 265556 265837 266117 266397 266678 266958 267238 281504 281783 282062 282341 282620 282900 283179 283457 283736 284015 298208 298486 298763 299041 299318 299596 299873 300151 300428 300706 314821331338 316097331612 315373331887 315649|332161 316928332435 3162011332710 316477|332984 316753333258 317029,333533 317305,333807 49 38 37 36 35 34 33 32 31 30 31 32 33 34 35 36 37 38 39 40 18252-2 182808 183094 183379 183665 183951 184237 184523 184809 185095 199053 199938 200223 200508 200793 201078 201363 201648 201933 202218 21(5724233728 217008234011 217292234294 217575234577 217859234859 218143235142 218427235425 218711235708 218995235990 219279236273 250662 250943 251225 2515Gb 251788 252069 252351 252632 252914 253195 207519 267799 268079 268359 268640 268920 269200 269480 269760 27004G 284294 284573 284852 285131 285410 285688 285967 286246 286525 j-286803 300983 301261 301538 301815 302093 302370 302647 302924 303202 303479 317580|334081 317856,334355 318132334629 318408334903 318684335178 318959335452 319235335726 319511336000 319786336274 320062;336547 29 28 27 26 25 24 23 22 21 20 41 42 43 44 45 46 47 48 49 50 185381 185667 185952 186238 186524 18681C 187096 187381 187667 187953 202502 20278" 203072 203357 203642 20392" 20421 204496 20478 20506 2195U2 236556 219846236838 220130237121 220414237403 220697 237686 220981237968 221265238251 221548 238533 221832238816 222116239096 253477 253758 254039 254321 254602 25488? 255165 255446 255727 256008 27032U 27060C 27088C 27116C 27144C 27172C 27200C 27228C 27256C 272841 287082 287361 287639 287918 28819G 288475 288753 289032 28931C 28958S 303750 304033 304310 304587 304864 305141 305418 305695 305972 300249 320337i336821 320613:337095 320889337369 321164:337643 321439337917 3217151338190 321990338464 322266338738 322541339012 322816339285 19 18 17 16 15 14 13 12 11 10 51 52 53 54 55 56 57 58 59 60 188238 188524 18881C 18909S 189381 189667 189952 190238 190522 19080S 20535 20563 20592 20620 20648 20677 20705 20734 20762 20791 222399 2393U1 222683239665 222967 23994C 223250240228 223534 24051C 223817 24079; 224101 24107E 22438424135'J 224668 24164C 224951 24192: 256*89 256571 256852 25713S 257414 25769c 25797C 258257 258538 25881 27312C 27340C 27367i 27395 274231 27451J 274798 275078 27535* 27563 r 289867 29014E 290424 290705 290981 29125C !'29153'J J29181 ( 292094 292375 30052d 306803 30708(1 307357 307633 3079K 308187 308464 30874C 309017 323092 33955S3 323367 339832 323642340106 32391734038C 324193340653 324468340927 324743 34120C 325018341472 325293341747 325568 34202C 9 8 7 6 5 4 3 2 1 M. | 79 78 77 76 75 74 73 72 ! 71 70 M. Natural Co-sines. TABLE XIV. 267 TO FIND LATITUDE BY REDUCTION TO THE MERIDIAN. Natural JSincs. M. 20 210 22' 23 24 25 26 27 28 29 M. 2 3 4 5 6 7 8 9 10 342020 342293 342567 342840 343113 343387 343660 343933 344206 344479 344752 358368 358640 358911 359183 359454 359725 359997 360268 360540 360811 361082 374607 374876 375146 375416 375685 375955 376224 376494 376763 377033 377302 390731 406737 390999407002 391267 407268 391534407534 391802407799 392070408065 392337408330 392605408596 392872 408861 393140409127 393407 409392 4226181438371 4228821438633 423145438894 423409 439155 423673439417 423936:439678 424199 439939 424463440200 424726 440462 424990440723 425253440984 453990 454250 454509 454768 455027 45528G 155545 455804 456063 456322 456580 46947v 469728 469985 470242 470499 470755 471012 471268 471525 471782 472038 484810 485064 485318 485573 485827 486081 486335 486590 486844 487098 487352 60 59 58 57 56 55 54 53 52 51 50 11 12 13 14 15 16 17 18 19 20 345025 345298 345571 345844 346117 346390 346G63 346936 347208 347481 301353 361625 361896 362167 362438 3G2709 362980 363251 363522 363793 377571 377841 37H110 378379 378649 378918 379187 379456 379725 379994 393675 393942 394209 394477 394744 395011 395278 395546 395813 396080 409G58 409923 410188 410454 410719 410984 411249 411514 411779 412045 425516441245 425779 441506 426042|441767 426306,442028 426569 442289 426832 442550 427095442810 427358443071 427621 443332 427884443593 456839 457098 457357 457615 457874 458133 458391 458650 458908 459166 472294 472551 472807 473063 473320 473576 473832 474088 474344 474GOO 487606 487860 488114 488367 488621 488875 489129 489382 489636 489890 49 48 47 46 45 44 43 42 41 40 21 22 23 24 25 26 27 28 29 30 347754 348027 348299 348572 348845 349117 349390 349662 349935 350207 364U64 364335 364606 3C4S77 365148 365418 365689 365960 366231 366501 380263 380532 380801 381070 381339 381608 381877 382146 382415 382683 396347 396614 396881 397148 397415 397682 397949 398215 398482 398749 412310 412575 412840 413104 413369 413634 413899 414164 414429 414693 428147 443853 428410444114 428672444375 428935444635 429198444896 429461 445156 429723445417 429986445677 430249 445937 430511 446198 459425 459683 459942 460200 460458 460716 460974 461232 461491 461749 474856 475112 475368 475624 475880 476136 476392 476647 476903 477159 490143 490397 490650 490904 491157 491411 491664 491917 492170 492424 39 38 37 36 35 34 33 32 31 30 31 32 33 34 35 36 37 38 39 40 350480 350752 351025 351297 351569 351842 352114 35238G 352658 352931 366772 367042 367313 367584 367854 368125 368395 368665 368936 369206 382952 383221 383490 383758 384027 384i95 384564 384832 385101 385369 399016 399283 399549 399816 400082 400349 400616 400882 401149 401415 414958 415223 415487 415752 416016 416281 416545 416810 417074 417338 430774 446458 431036 146718 431299446979 431561 447239 431823 447499 432086447759 432348 448019 432610 448279 432873 448539 433135448799 462007 462265 462523 462780 463038 463296 463554 463812 464069 464327 477414 477670 477925 478181 478436 478692 478947 479203 479458 479713 492677 492930 493183 493436 493689 493942 494195 494448 494700 494953 29 28 27 26 25 24 23 22 21 20 41 42 43 44 45 46 47 48 49 50 353203 353475 353747 354019 354291 3545G3 354835 355107 355379 355651 cft'.947G 369747 370017 370287 370557 370828 371098 371368 371G38 371908 385638 385906 386174 386443 386711 386979 387247 387516 387784 388052 401681 417603 401948417867 102214418131 402480 418396 402747 4186GO 403013418924 403279419188 403545 419452 403811419716 404078419980 433397,449059 433659 449319 433921 449579 434183449839 434445 450098 434707 450358 434969450618 435231 450878 435493451137 435755451397 464584 464842 465100 465357 4G5615 465872 466129 466387 466644 466901 479968 480223 480479 480734 480989 481244 481499 481754 482009 482263 495206 495459 495711 495964 496217 49G469 496722 496974 497226 497479 19 18 17 16 15 14 13 12 11 10 51 52 53 54 55 56 57 58 59 GO 355923 356194 3564GG 356738 357010 357281 357553 357825 35809G 3583R8 37217S 372448 372718 372988 373258 373528 373797 374067 374337 374607 388320 388588 388856 389124 389392 389660 389928 390196 390463 390731 4043444-20244 404610420508 404876'420772 405142421036 405408421300 405G73 421563 405939421827 406205 422091 406471 422355 406737 422618 436017 451656 436278451916 436540452175 436802452435 437063 452694 437325452953 437587453213 437848453472 438110453731 438371 453990 467158 467416 467673 467930 468187 468441 468701 468958 469215 469472 482518 482773 483028 483282 483537 483792 484046 484301 484555 484810 497731 497983 498236 498488 498740 498992 499244 499496 499748 500000 9 8 7 6 5 4 3 2 1 M. | 69 C 68 67 66 65 64 63 >J 62 Gl 60 M. Natural Co-sines. 268 TABLE XIV. TO FIND LATITUDE BY KEDUCTION TO THE MERIDIAN. Natural Sines. M. 30 31 32 33 34 35 36 37 38 39 M. 1 2 3 4 5 6 7 8 9 10 50000U 500252 .300504 500756 501007 501259 501511 501762 502014 502268 502517 515038 515287 515537 515786 516035 516284 516533 516782 517031 517280 517529 5-^9919 530166 530413 530659 530906 531152 531399 531645 531891 532138 532384 544639 544883 545127 545371 545615 545858 546102 546346 546589 546833 547076 559193 573576 559434 573815 559675 574053 559916 574291 560157 574529 560398574767 560639 575005 560880575243 561121 575481 561361 575719 561602 575957 587785 588021 588256 588491 588726 588961 589196 589431 589666 589901 590136 601815 602047 602280 602512 602744 60297G 60320b 603440 603672 603904 604136 615661 615891 616120 616349 616578 616807 617036 617265 617494 617722 617951 629320 629546 629772 629998 630224 630450 630676 630902 631127 631353 631578 60 59 58 57 56 55 54 53 52 51 50 11 12 13 14 15 16 17 18 19 20 502769 503020 503271 503523 503774 504025 504276 504528 504779 505030 517778 518027 518276 518525 518773 519022 519271 519519 519768 520016 532630 532876 533122 533368 533615 533861 534106 534352 534598 534844 547320 547563 547807 548050 548293 548536 548780 549023 549266 549509 561843 562083 562324 562564 562805 563045 563286 563526 563766 564007 576195 576432 576670 576908 577145 577383 577620 577858 578095 578332 59037 1 590606 590840 591075 591310 591544 591779 592013 592248 592482 604367 604599 60483! 605062 605294 605526 6G5757 605988 606220 606451 018180 618408 618637 618865 619094 619322 619551 619779 620007 620235 631804 632029 632255 632480 632705 632931 633 15c 633381 633606 633831 49 48 47 46 ' 45 44 43 42 41 40 21 22 23 24 25 26 27 28 29 30 505281 505532 505783 506034 506285 506535 506786 507037 507288 507538 520265 520513 520761 52101G 521258 521506 521754 522002 522251 522499 53509U 535335 535581 535827 536072 536318 536563 5J6809 537054 537300 549752 549993 550238 550481 550724 550966 551209 551452 551694 551937 564247 564487 564727 564967 565207 565447 565687 565927 566166 566406 578570 578807 579044 579281 579518 579755 579992 580229 580466 580703 592716 592951 593185 593419 593653 593887 594121 594355 594589 594823 60668^ 606914 607145 607376 607607 607838 608069 608300 608531 608761 620464 620692 620920 621148 621376 621604 621831 622059 622287 622515 634056 634281 634506 634731 634955 635180 635405 635629 635854 636078 39 38 37 36 35 34 33 32 31 30 31 32 33 34 35 36 37 38 39 40 507789 508040 508290 508541 508791 509041 509292 50954-2 509792 510043 522747 537545 522995 537790 523242538035 523490538281 523738 538526 523986538771 524234 539016 524481539261 524729;539506 524977 539751 55218U 552422 552664 552907 553149 553392 553634 553876 554118 554360 566646 566886 567125 567365 567604 567844 568083 568323 568562 568801 580940 581176 581413 581650 581886 582123 582359 582596 582832 583069 595057 595290 595524 595758 595991 596225 596458 596692 596925 597159 608992 609223 609454 609684 609915 610145 610376 610606 610836 611067 62274* 622970 623197 623425 623652 623880 624107 624334 624561 624789 636303 636527 636751 636976 637200 637424 637648 637872 638096 638320 29 28 27 26 25 24 23 22 21 20 41 42 43 44 45 46 47 48 49 50 510293 510543 510793 511043 511293 511543 511793 512043 512293 512543 525224539996 525472 540240 525719 540485 525967 540730 526214540974 526461 541219 526709 541464 526956541708 527203 541953 527450542197 554602 554844 555086 555328 555570 555812 556054 556296 556537 556779 56904U 569280 569519 569758 569997 570236 570475 570714 570952 571191 583305 583541 583777 584014 584250 584486 584722 584958 585194 585429 597392 597625 597858 598092 598325 598558 598791 599024 599256 599489 611297 611527 611757 611987 612217 612447 612677 612907 613137 613367 625016 625243 625470 625697 525923 626150 626377 626604 626830 627057 638544 638768 638992 639215 639439 639663 639886 640110 640333 640557 19 18 17 16 15 14 13 12 11 10 51 52 53 54 55 56 57 58 59 fiO 512792 513042 513292 513541 513791 514040 514290 514539 514789 515038 527697 527944 528191 528438 528685 528932 529179 529426 529673 529919 542242 542886 542930 543174 543419 543663 543907 544151 544395 544639 557021 557262 557504 557745 557987 558228 558469 558710 558952 559193 571430 571669 571907 572146 572384 572623 572861 573100 573338 573576 585665599722 585901 599955 586137600188 586372 600420 586608 600653 586844600885 587079601118 587314601350 587550601583 587785601815 613596 613826 614056 614285 614515 614744 614974 615203 615432 615G61 627284 627510 627737 627963 628189 628416 628642 628868 629094 629320 640780 G41003 641226 641450 641673 641896 642119 642342 642565 642788 9 8 7 6 5 4 3 2 1 M. 59 58 57 | 56 | 55 54 | 53 52 51 50 M. Natural Co-sines. TABLE XIV. 269 TO FIND LATITUDE BY REDUCTION TO THE MERIDIAN. Natural Sines. M. 40 41 42 43 44 45 46 47 48 49 M. 1 2 3 4 5 6 7 8 9 10 4-2788 650059 43010 656279 43233656498 43456656717 43679 65G937 43901 657156 44124657375 44346657594 44569657814 44791 658033 45013,658252 669131 669347 669563 669779 669995 670211 670427 670642 670858 671074 671289 081998 682211 682424 682636 682849 683061 683274 683486 683698 G83911 684123 594658 694868 695077 69528G 695495 695704 695913 696122 696330 696539 69G748 707107 707312 707518 707723 707929 708134 708340 708545 708750 708956 709161 719340 719542 '19744 "19946 720148 720349 720551 720753 720954 721156 721357 731354 731552 731750 731949 732147 732345 732543 732741 732939 733137 733334 743145J754710 743339,754900 743534755091 743728755282 743923755472 744117755663 744312 755853 744506 756044 744700 756234 744894756425 745088j756615 00 59 58 57 56 55 54 53 52 51 50 11 12 13 M 15 16 17 18 19 20 045^36658471 645458658689 45680 658908 645902 659127 46124,659346 >46346 659565 646568659783 646790660002 647012 660220 647233 G60439 671505 671721 671936 672151 672367 672582 672797 673013 673228 673443 684335 684547 684759 684971 685183 685395 685607 685818 686030 686242 696957 697165 697374 697582 G97790 687999 698207 698415 698623 698832 7U9366 709571 709776 709981 710185 710390 710595 710799 711004 711209 721559 721760 721962 722163 722364 722565 722766 722967 723168 723369 733532 733730 733927 734125 734323 734520 734717 734915 735112 735309 745282 756805 745476756995 745670757185 745864 757375 746057757565 746251 757755 7464451757945 7466381758134 746832(758324 747025:758514 49 48 47 46 45 44 43 42 41 40 21 22 23 24 25 26 27 28 29 30 647455 G6U657 647677 660875 647898 661094 648120661312 648341 661530 648563661748 648784661966 649006662184 649227 662402 649448662620 673658 673873 674088 674302 674517 674732 674947 675161 675376 675590 686453 686665 686876 687088 687299 687510 687721 687932 688144 688355 699J40 699248 699455 699663 699871 700079 700287 700494 700702 700909 711413 711617 711822 712026 712230 712434 712639 712843 713047 713250 723570 723771 723971 724172 724372 724573 724773 724974 725174 725374 7^5506 735703 735900 736097 736294 736491 736687 736884 737081 73777 747218 758703 747412 758893 747605759082 747798759271 747991 759461 748184759650 748377 1759839 748570J760028 748763760217 748956,760106 39 38 37 36 35 34 33 32 31 30 31 32 33 34 35 36 37 38 39 40 64%6'J 662838 649890663056 650111663273 650332 663491 650553 663709 650774663926 650995664144 651216664361 651437664579 651657|66479G 675805 G76019 G7G233 676448 676662 676876 677090 677304 677518 677732 G88566 688776 688987 689198 689409 689620 689830 690041 690251 690462 701117 701324 701531 701739 701946 702153 702360 702567 702774 702981 713454 713658 7138G2 714066 714269 714473 714676 714880 715083 715286 725575 725775 725975 726175 726375 726575 72G775 726974 727174 727374 737474 737670 7378G7 738063 738259 738455 738651 738848 739043 739239 749148760595 749341 '760784 749534,760972 749726761161 749919761350 750111761538 750303761727 750496761915 750688762104 750880,762292 29 28 27 26 25 24 23 22 21 20 41 42 43 44 45 46 47 48 49 60 651878 6651)13)677940 652098665230678160 652319 665448 678373 652539665665678587 652760665882678801 652980666099679014 653200 666316 G79228 653421666532679441 653641 666749 67965E 653861666966679868 690672 690882 G91093 691303 691513 691723 691933 692143 692353 69256! 703188 703395 703601 703808 704015 704221 704428 704634 704841 705047 715490 715693 715896 716099 71630-2 716505 716708 716911 717113 717316 727573 727773 727972 728172 728371 728570 728769 728969 729168 729367 739435 739631 739827 740023 740218 740414 740609 740805 74100U 741195 751072762480 7512641762668 751456762850 7516481763044 751840763232 752032,763420 752223)763608 752415,763796 752606763984 752798764171 19 18 17 16 15 14 13 12 11 10 51 52 53 54 55 56 57 58 59 60 654081667183680081 654301 667399 68029i 654521 667616 68050i 654741 667833 68072] 654961668049680934 655180 668265 G8114 r 655400 668482 68136( 655620668698081571 655839 668914 68178( 656059 669131 68199! 692771 69298c 693192 69340-2 1693611 69382] )69403( !694*24C 5 694441 J 69465* 705253 705453 705665 705872 706078 706284 70648S 70669L 1 706901 (707107 717519 717721 717924 718126 718328 718531 71873S 71893C 719136 71934C 729560 729763 729963 730162 730361 73056C 730756 730957 73115C 731354 741391 74158G 741781 741976 742171 742361 742561 74275E 74295C 74314E 752989764359 753181764547 753372764734 753563,764921 753755765109 753946,765290 754137,765483 754328,765670 754519765857 754710|766044 9 8 7 6 5 4 3 2 1 M. 49 1 48 47 46 I 45 1 44 1 43 1 42 1 41^ 1 40 M. Natural Co-sines. 270 TABLE XIV. TO FIND LATITUDE BY REDUCTION TO THE MERIDIAN. Natural Sines. M. 50 51 52 53 54 55 56 57 58 59 M. 1 2 3 4 5 6 7 8 9 10 760044 766231 766418 766605 76G792 766979 767165 767352 767538 767725 767911 777146,7b8011 777329788190 777512788369 777695788548 777878788727 778060788905 778243789084 778426789263 778608789441 778791789620 778973789798 798636 798811 798985 7991CO 799335 799510 799685 799859 800034 800208 800383 809017 809188 809359 8C9530 809700 809881 810042 810212 810383 810553 810723 819152 819319 819486 819652 819819 8199S5 820152 820318 820485 820651 820817 8-^9038 829200 829363 829525 829688 829850 830012 830174 830337 830499 830661 838671 838829 838987 839146 839304 839462 839620 839778 839936 840094 840251 848048J857167 848202 857317 848356 857467 848510857616 848664 857766 848818857915 848972 858065 849125858214 849279858364 849433858513 849586 858662 GO 59 58 57 56 55 54 53 52 51 50 11 12 13 14 15 16 17 18 19 20 7G8097 768284 768170 768656 768842 769028 769214 769400 769585 769771 779156789977 779338790155 779520790333 779702790511 779884790690 780067 790868 780249 791046 780430791224 780612791401 780794791579 801)557 800731 800906 801080 801254 801428 801602 801776 801949 802123 810894 811064 811234 811404 811574 811744 811914 812084 812253 812423 820983 821149 821315 821481 821647 821813 821978 822144 822310 822475 830823 830984 831146 831308 831470 831631 831793 831954 832115 832277 840409 840567 840724 840882 841039 841196 841354 841511 841668 841825 849739858811 849893 858960 85004C 859109 850199859258 850352859406 850505 859555 850658859704 850811 859852 850964 860001 851117 8G0149 49 48 47 46 45 44 43 42 41 40 21 22 23 24 25 26 27 28 29 30 769957 770142 770328 770513 770699 770884 771069 771254 771440 771625 780976791757 781157791935 781339792112 781520792290 781702792467 781883792644 782065792822 782246792999 782427793176 782608793353 802297 802470 802644 802817 802991 803164 803337 803511 803684 803857 812592 812762 812931 813101 813270 813439 813608 813778 813947 814116 822641 822806 822971 823136 823302 823467 823632 823797 823961 824126 832438 832599 832760 832921 833082 833243 833404 833565 833725 833886 841982 84-2139 842296 842452 842609 842766 842922 843079 843235 843391 851269860297 851422860446 851575860594 851727 860742 851879860890 852032,861038 852184861186 852336861334 852488861481 852640861629 39 38 37 36 35 34 33 32 31 30 31 32 33 34 35 36 37 38 39 40 771810 771995 772179 772364 772549 772734 772918 773103 773287 773-472 782789793530 782970793707 783151793881 78333279106] 783513 79423S 783693794415 783874794591 784055794768 784235794944 784416795121 80403U 804203 804376 804548 804721 804894 805066 805239 805411 805584 814^84 814453 814622 814791 314959 815128 S1529G 815465 815633 815801 824291 824456 824620 824785 824949 825113 825278 825442 825606 825770 834046 834207 8343G7 834527 834688 834848 835008 835168 835328 835488 843548 843704 843860 844016 844172 844328 844484 844640 844795 844951 852792:861777 852944 861924 853096862072 853248862219 853399862366 853551 862514 853702862661 853854 862808 854005,862955 854156863102 29 28 27 26 25 24 23 22 21 20 41 42 43 44 45 46 47 48 49 50 773656 773840 774024 774209 774393 774577 774761 774944 775128 775312 784596 795297 784776795473 784957 795650 785137795826 785317796002 785497796178 785677796354 785857796530 786037 796706 786217796882 805756 805928 806100 806273 806445 806617 806788 806960 807132 807304 615969 816138 816306 816474 816642 816809 816977 817145 817313 817480 825934 826098 826262 826426 826590 826753 826917 827081 827244 827407 835648 835807 835967 836127 836286 836446 836605 836764 836924 837083 845106 845262 845417 845573 845728 845883 846038 846193 846348 846503 854308863249 854459863396 854610863542 854761 863689 854912863836 855063863982 855214:864128 855364 ; 864275 855515:864421 855665J864567 19 18 17 16 15 14 13 12 11 10 51 52 53 54 55 56 57 58 59 60 775496 775679 775863 776046 776230 776113 776596 776780 77G963 777146 786396 786576 786756 786935 787114 787294 787473 787652 787832 788011 797057 797233 797408 797584 797759 797935 798110 798285 798460 798636 807475 807647 807818 807990 808161 808333 808504 808675 808846 809017 817648 817815 817982 818150 818317 818484 818651 818818 818985 819152 827571 827734 827897 828060 828223 828386 828549 828712 828875 829038 837242 837401 837560 837719 837878 838036 838195 838354 838512 838671 846658 846813 846967 847122 847277 847431 847585 847740 847894 848048 855816864713 855966864860 856117865006 856267865151 856417 865297 856567865443 856718865589 856868;805734 857017865880 857167866025 9 8 7 6 5 4 3 2 1 M. 39 38 37 36 35 34 33 1 32 31 30 M. Natural Co-sines. TABLE XIV. 271 TO FIND LATITUDE BY REDUCTION TO THE MERIDIAN. Natural Sines. M. 60 61 62 63 64 65 66 67 -68 69 M. 866025 874620,882948 891007!898794|9063U8i913545| ( J2U5u5 927184:933580 866171874761 883084 891139 898922 906431 913664 920618 92729J 933685 866316,874902:883221891270899049906554913782920732927402933789 866461875042883357891402,899176906676,913900920846,927510933893 8GGG07 875183 883492 891534|899304|906799!914018l920959te27619!033997 i70Q077 866752W5324 883629 8916668994311906922,914136 921072 927728 934101 869897,875465883766891798,899558:9070449142549211859278361934204 867042J875605|883902 891929,8996851907166 914372 921299,927945 934308 867187,375746 884038 892061 893812 907289914490 921412 928053 934412 867331,875886 884174 892192j899939j907411 914607 921525 928161 934515 367476 876026 884309 892323 ! 900065 907533 914725 921638 928270 934619 60 59 58 57 56 55 54 53 52 51 50 11 12 13 14 15 IG 17 18 19 20 867621 8701GY 884445 892455jlKJ0192j ( J07u55,914842 921750 928378:934722 867765^876307 884581 892586,900319 907777,914960 921863 928486 934826 867910,876447 884717 892717,900445,907899 915077 921976 9285941934929 808054 876587 384852 892848,900572 908021,915194,922088 928702935032 868199^876727 884988 892979,900698 908143,915311192220119288101935135 868487J87700G 88525: 868632.877146 885394 8933711901077 9085081915663 922588I929133J936444 868776877286 885529 893502,901203 908630 915779 922650 929240 935547 8G8920 877425 ! 885664 893633 901329 90875l'915896 922762 ! 929348 ! 935650 49 48 47 46 45 44 43 42 41 40 21 22 23 24 25 26 27 28 29 30 8G9064 877565 88579U 893763 901455 90887 869207!377704!S85934 893894 901581 2^16013922874;929455935752 908994 ;916130 922986 929562'935855 3693511877844 886069 894024:901707 909115 916246 923098 929669,935957 869495;877983 ! 886204 894154J901833 909236 9163G3 923210 929776:936060 869639,878122 886338 894284'901958 909357 916479 923322 9298841936162 869782 878261 886473 894415,902084 909478,916595 923434 929990*936264 809926 8784001886608 894545,902209 909599 916712 923545 742 894675 902335 909720 916826 923G57 930204 936468 878678 886876 894805 902460 909841916944 923768 930311 936570 917060 923880 930418 936672 8700G9 878539 88 87021 870356 878817 887011 834934'902585 909961 930097 9363G6 39 38 37 36 35 34 33 32 31 30 31 32 33 34 35 36 37 38 39 40 870199 87 8956 387145 89d004;yU27iU940U82s91717Gl923991 930524 936774 870642 879095 887279 895194 902836 910202 917292 924102 930631 936876 870785879233887413895323,902961910323917408924213930737936977 870928 879372 887548 395453 903086 910443,917523 924324 930843 937079 871071 879510 887681 8955S2 903210 910563,917639 924435 930950 937181 8712141879649 887815 895712 903335 910684 917755 924546 931056 937282 8713578797871887949895841903460910804917870924657 871499879925 871642 881)063 888217 888083 895970,903585 89C099,90370'J 911044 918101 924878 931374 937586 8717841880201 888350 896229903834 911164 318216924989 931480:937687 910924 931162937383 917986 924768 931268,937485 29 28 27 26 25 24 23 22 21 20 41 42 43 44 45 46 47 48 49 50 871 l J27j88033 ( J;868484 896358 903958J911284918331I92509JJ931586 937788 872069 880477 888617 896486,904083 911403 918446 925210 93169l'937889 87221 2 880615 888751 896615,904207 872354 S80753 888834 87249G 880891 889017 396744 904331 911528Bl8561 925320 931797 937990 911643918676925430931902938091 896873904455911762918791 925541 932008,938191 872638 881028 889150 897001 904579 911881018906 925651 982118938292 872780881166889283 897130,904703 912001 919021 925761 932219938393 8729221881303 88941618972581904827 912120 919135 925871 932324 938493 912239B19260 925980 932429 938593 912358 919364 926090 932534 938694 389.349897387:904951 873206:881578 889632 897515,905075 19 18 17 16 15 14 13 12 11 10 51 52 53 54 55 56 57 58 59 60 873347 881716 889815 9 i'G43 903198,912477 919479 92621HH932639 938794 373489881853889948397771905322912596,919593926310932744938894 873631 881990j890030 397900 905445 912715 91 9707.926419 9328491938994 873772 882127,89021 3 898028'905569 9 12834'91982 1926529 932954 939094 873914J882264 890345 898156:905692 912953 919936'926638 933058 939194 874055;882401 390478 898283 905815 913072 920050 920747 933*63 939294 874196:882038|890610 898411 905939 913190'920164 926857 933267'939394 874338 882674 890742 898539 906062 913309'920277,926966 933372 939493 874479,882811 890874 898666906185 913427,920391 927075 933476 939593 874620^882948 891007 898794 ! 90G308 913545920505 927184 933580939693 M. 29 I 28 1 27 I 26 25^ 24 I 23 22 21 I 20 I M. Natural Co-sines. 272 TO FIND TABLE XIV. LATITUDE BY REDUCTION TO THE MERIDIAN'. Natural Sines. St. 70 71 72 73 74 75 76 77 78 79 M. 1 2 3 4 5 6 7 8 9 10 939693 339792 339891 939991 910090 t)40189 940288 3403S7 940186 340585 J40684 945519 945613 945708 345802 945897 945991 946085 346180 946274 946388 94646-2 951057 951146 951236 951326 951415 351505 951594 951684 951773 951862 951951 956305 956390 956175 356560 956614 956729 956814 956898 956983 957067 957151 961262 961342 961422 961502 961582 961662 981741 961821 961901 961980 962059 965926 9C6001 966076 966151 966226 966301 966376 966451 966526 966600 966675 970290 970366 97043G 970506 970577 970647 970711 97078G 970856 970920 970995 974370 974435 974501 974566 974631 974696 974761 37182C 974891 97495. 975020 9781489*1027 378208 981683 378268981738 978329 981793 978389981849 978449981904 978509 981959 3785G9 982014 978629982069 978689 982123 978748982178 60 59 58 57 56 55 54 53 52 51 50 11 12 13 14 15 16 17 18 19 20 940782 940881 340979 J41078 341176 941274 941372 941471 9415G9 941666 94(3655 946649 916743 946837 946930 947024 947117 947210 947301 947397 352040 952129 952218 952307 952396 952484 35257,3 952661 952750 952838 957235 957319 957404 357487 957571 957655 957739 957822 957906 957990 962139 9G2218 962297 962376 962455 962534 962613 962692 962770 962819 J66719 966823 966898 366972 967046 967120 967194 967268 967342 967415 971065 971134 971204 971273 971312 971111 971480 971519 971618 971687 375085 975119 375214 975278 975312 975106 975171 975535 975598 375662 978608 378867 978927 978980 979045 979105 979164 979223 979282 970341 982233 982287 982342 98239G 982450 982505 982559 982613 982667 982721 49 48 47 46 45 44 43 42 41 40 21 22 23 24 25 26 27 28 29 30 941764 341862 941960 942057 942155 942252 942350 942447 942544 942641 947490 95-920 947583 953015 94767C 953103 947768953191 947861953279 947954953366 918016 953454 918139953512 918231 953629 918321 953717 9580/3 958156 958239 958323 958406 958489 958572 958651 958737 958820 962928 96300G 963084 963163 963241 963319 963397 963475 963553 9G3630 967489 967562 987636 967709 967782 957856 967929 968002 968075 968148 971755 971824 971893 971961 972030 972098 972166 972234 972302 972370 975726 975790 975853 975917 975980 976014 976107 976170 976233 97629G 979399 982774 979458 982828 979517 982882 979575982935 979634982989 979692983042 979750 983096 979809983149 9798671983202 979925983255 39 38 37 36 35 34 33 32 31 30 31 32 33 34 35 36 37 38 39 40 942739 942836 942932 943029 943126 943223 943319 943416 943512 943609 918416 9538U1 918508 953892 918600 953979 948692951066 948784954153 948876 944240 ,918968951327 919059951411 949151 954501 949243954588 958902 958985 959067 959150 959232 959314 959396 959478 959560 959842 963708 963786 963863 963941 964018 961095 961173 964250 964327 964404 968220 968293 968366 968438 968511 968583 968656 968728 968800 968872 972438 972500 972573 972641 972708 972776 972843 972911 972978 973015 976359 976422 976485 976547 976610 976672 976735 976797 976859 976921 979983 980041 980098 980156 980214 980271 980329 980386 980443 980500 983308 983361 983414 983466 983519 983571 983624 983670 983729 983781 29 28 27 26 25 24 23 22 21 20 41 42 . 43 44 45 46 47 48 49 50 943705919331951674 943801 949425 9547G1 943897 949517 954847 943993949608954934 944089949699955020 944185 949790 955103 944281 949881 955192 944376949972955278 944472 950063'955364 944568950154955450 959724 959805 959887 959968 960050 960131 980212 960294 960375 960456 964181 964557 964G34 9G4711 964787 964864 964940 935016 9G5093 9G5169 968944 969016 969088 969159 969231 989302 969374 969445 969517 9G95S8 97311k 973179 973210 973313 973379 97311G 973512 973579 973345 973712 976984 977046 977108 977169 977231 977293 977351 977416 977177 977539 980558 980615 980672 980728 980785 380842 980899 980955 981012 981088 983833 983885 983937 983989 984041 984092 984144 9S4196 984247 984298 19 18 17 16 15 14 13 12 11 10 51 52 53 54 55 56 57 58 59 60 944663 950244 955530 944758950335955622 944854950425955707 944949 950516 955793 945044 950606'955879 945139,950696 955964 945234950786956049 945329'950877 956134 945424950967956220 945519951057956305 960537 960618 9G0898 960779 960860 960940 961021 961101 961181 961262 965245 965321 965397 965473 965548 965624 965700 965775 935850 965926 9o9659:97377b 969730973844 969801973910 969872 973970 969943 974042 970014 974108 970084974173 970155974239 970225974305 970296 97437C 9 < 7600 977661 977722 977783 977844 977905 977936 978026 978087 978148 981124984350 981181 981401 981237984452 981293984503 981349'984554 981405984605 981460984656 981516984707 981572984757 981027)984808 9 8 7 6 5 4 3 2 1 M. 1 19 18 17 10 | 15 I 14 1 13 12 11 10 M. Natural Co-sines. TABLE XIV. 273 TO FIND LATITUDE BY REDUCTION TO THE MERIDIAN. Natural (Sines. M. 80 81 82 | 83 84 85 86 87 88 89 M. 1 2 3 4 5 6 7 8 9 10 3tf4SO 384858 384909 384959 383009 385059 385109 J85159 1385209 985259 9S5309 97G8b 'J9U268 987734990309 987779990349 987824 990389 987870990429 987915990469 987930 990509 98S005 990549 988050990589 988094 990629 988139 990G69 392540 392582 992617 992652 992687 992722 992757 992792 992827 992862 992890 994522 99G 1 95 997564 994552996220997584 994583 396245 997004 994613996270997625 994643996295997645 994673 996320 997664 994703996345997684 994733996370997704 994762996395997724 99479-2 99G419 397743 994822996444997763 998030 998045 398660 998675 998690 998705 998719 998734 998749 998763 998778 999391 999401 999411 999421 999431 999441 999450 9994GO 9994G9 999479 999488 999848 999853 999858 999803 999867 999872 999877 999881 999386 999890 999894 60 59 58 57 56 55 54 53 52 51 50 11 12 13 14 15 16 17 18 19 20 J85358 93540S 985457 985507 no""- r*/ 'OOOUO 985G05 985G54 9S5703 985752 985801 988184 988226 988273 988317 988362 968400 988450 988494 988538 988582 990708 990746 990787 990827 990866 990905 990944 990983 991022 991061 99*931 9929G6 993000 993034 993086 993103 993137 993171 993205 993238 994851990408997782 994881 99G493 997801 994910996517997821 984939996541997841 994969 996565 997859 994998 996589 997878 9950279966 14 997897 99505G 993637 997910 995084996661997934 995113993685997953 996792 998806 998820 998834 998818 99S862 998870 998890 998904 998917 999497 999507 999516 999525 999534 999542 999551 999560 999568 999577 i>99t>98 999903 999907 999910 999914 999918 999922 999925 999929 999932 49 48 47 46 45 44 43 42 41 40 21 22 23 24 25 26 27 28 29 30 985850 985899 985947 985996 936045 986093 986141 986189 986238 986280 988620 988669 988713 98875C 988800 988843 98888G 98893C 988973 98901G 991 10U 991138 991177 991216 991254 991292 991331 991369 991407 991445 993272 993300 993339 993373 993406 993439 993473 99350G 993539 993572 995142 9907o9 997972 998931 995170 996732 997990 998944 995199 996756 998008 998957 995227 996779 998027 998971 995256 996802 998045 998984 993284 996825 998063 998997 995312 99G848 998081 999010 995340 996872 998099 999023 995368 996894 993117 999035 99539G 990917 998135 999048 999585 999594 999602 999610 999618 899620 999634 99964'2 999650 999657 9999oG 999939 999942 999915 999948 999951 999954 999957 999959 999962 39 38 37 36 35 34 33 32 31 30 31 32 33 34 35 36 37 38 39 40 980334 989059 986381 989102 986429989145 986477 989187 986525989230 986572989272 986620989315 986667989357 986714989399 98G762 98944-2 991483 991521 991558 991596 991634 991671 991709 991740 991783 991820 993005 993638 993C70 993703 993735 993768 993800 993833 393865 993897 995424 990940 998153 995452996963998170 995479996985998188 995507 997008 998205 995535997030998223 995562997053998240 995589997075998257 995617 997097 998274 995644997119998291 995671:997141998308 999061 999005 999073999672 399086 999680 999098999687 999111999694 999123 999701 999135 999709 999147:999710 999 15 f J|999722 999171;999729 999904 999967 9999G9 999971 999974 999970 999978 999980 999931 999983 29 28 27 26 25 24 23 22 21 20 41 42 43 44 45 46 47 48 49 50 966809 989484J991857 98685G 989526,991894 986903 989568 991931 986950989610991968 98G99G 989651 992005 987043989693992042 987090989735.992078 987136989776992115 987183,989818992151 987229,989859 9921 87 993929 993961 993993 994025 994050 994088 994120 994151 994182 994214 995098:997163998325 995725997185998342 995752997207998259 99577b 997229 998375 995805997250998392 995832 997272 998408 995858997293998425 995884*997314 998441 995911997336998457 995937997357998173 999183 999736 999194999743 999206999749 999218 99975G 999229999762 999240999768 999252999775 999263999781 999274 999787 999285999793 999985 999986 999988 999989 999990 999992 999993 999994 999995 999990 19 18 17 16 15 14 13 12 11 10 51 52 53 54 55 56 57 58 59 CO 987275,989900992224 987322,989942 .992200 987368989983992290 987414990024:992332 987460990065992368 987506990105992404 98755l'990146 992433 987597i990187;992475 987643,990228992511 937688,990268,992540 |994245 995903 997378 998489 99427G 995989 997399 998505 994307,990015 997420 998521 994338.9960-11 997441 998537 994369 99G067 9974G2 998552 994400 99G093 997482 0985C8 994430 996118 997503 998583 994461 996144 997523 998599 994491 996169 997544 998614 99452; 99G195 997564 998030 999296:999799 999307,999804 999318999810 999328999810 999339999821 999350999827 999360999832 999370 999837 999381999813 999391 999846 999997 999997 999998 999998 999999 999999 1000000 ,1000000 1000000 1000000 9 8 7 6 5 4 3 2 1 X. 9 1 8 1 7 1 G 5 1 4 3 2 1 1 1 M. Natural Co-sines. 274 TABLE XV. FOB FINDING THE DISTANCE OF TEREESTRIAL OBJECTS AT SEA. Height in Distance in Height in Distance in Height in Distance in Feet. Miles. Feet. Miles. Feet. Miles. 1 1.15 85 10.6 660 29.5 2 1.62 90 10.9 680 30.0 3 1.99 95 11.2 700 30.4 4 2.30 100 11.5 720 30.8 5 2.57 105 11.8 740 31.2 6 2.81 110 \ 12.1 760 31.7 1 3.04 115 12.3 780 32.1 8 3.25 120 12.6 800 32.5 9 3.45 125 12.8 820 32.9 10 3.63 130 13 1 840 33.3 11 3.81 135 13.3 860 33.7 12 3.98 140 13.6 880 34.1 13 4.14 145 13.8 900 34.5 14 4.30 150 14.1 920 34.8 15 4.45 160 14.5 940 35.2 16 4.60 170 15.0 960 35.6 17 4.73 180 15.4 980 36.0 18 4.87 190 15.8 1000 36.3 19 5.01 200 16.2 1100 38.1 20 5.14 210 16.6 1200 39.8 21 5.26 220 17.0 1300 41.4 22 5.39 230 17.4 1400 43.0 23 5.51 240 17.8 1500 44.5 24 5.62 250 18.2 1600 46.0 25 5.74 260 18.5 1700 47.3 26 5.86 270 18.9 1800 48.7 27 5.97 280 19.2 1900 50.1 28 6.08 290 19.6 2000 51.4 29 6.18 300 19.9 2100 52.6 30 6.30 310 20.2 2200 53.9 31 6.40 320 20.6 2300 55.1 32 6.50 330 20.9 2400 56.2 33 6.60 340 21.2 2500 57.4 34 6.70 350 21.5 2600 58.6 35 6.80 3GO 21.8 2700 59.7 36 6.90 370 22.1 2800 60.8 37 6.99 380 22.4 2900 61.8 38 7.09 390 22.7 3000 63.0 39 7.17 400 23.0 3100 64.0 40 7.27 410 23.3 3200 65.0 41 7.36 420 23.5 3300 66.0 42 7.44 430 23.8 3400 67.0 43 7.54 440 24.1 3500 . 68.0 44 7.62 450 24.4 3600 69.0 45 7.70 460 24.6 3700 69.9 46 7.79 470 24.9 3800 70.9 47 7.88 480 25.2 3900 71.7 48 7.96 490 25.4 4000 72.7 49 8.0 500 25.7 4100 73.6 50 8.1 520 26.2 4200 74.4 55 8.5 540 26.7 4300 75.4 60 8.9 560 27.2 4400 76.2 65 9.3 580 27.7 4500 77.0 70 96 600 28.1 4700 88.8 75 9.0 620 28.6 5000 81.2 80 10.3 640 29 1 1 mile 83.5 275 DIP OF THE HORIZON AT DIFFERENT DISTANCES FROM THE OBSERVER. Distance T ,1 HEIGHT OF THE EYE IN FEET. of Land, in Miles. 5 10 15 20 25 30 35 40 45 50 M". o.i 28 56 84 112 140 169 19'7 22'5 252 28'0 0.2 14 28 42 56 70 85 99 113 126 140 0.3 9 19 28 3 7 47 56 65 75 84 93 0.4 7 14 21 28 35 42 49 56 63 70 0.5 6 11 17 22 28 34 39 45 50 56 0.6 5 9 14 19 23 28 33 37 42 47 0.7 4 8 12 16 20 24 28 32 36 40 6 8 4 7 10 14 17 21 25 28 31 35 9 3 6 9 12 15 19 22 25 28 31 1.0 3 6 8 11 14 17 20 23 25 27 12 3 5 7 9 12 14 16 19 21 23 1.4 3 4 6 8 10 12 14 16 18 20 L.6 3 4 5 7 9 11 13 14 16 18 1.8 2 3 5 6 8 10 12 13 14 16 2.0 2 3 5 6 7 9 11 12 13 15 2.2 2 3 5 6 7 8 10 11 12 14 2.4 2 3 5 6 7 8 9 11 12 13 2.6 2 3 4 5 6 8 9 10 11 12 2.8 2 3 4 5 6 7 8 9 10 11 3.0 2 3 4 5 6 7 8 8 9 10 3.5 2 3 4 5 6 6 7 8 9 9 4.0 2 3 4 4 5 6 7 7 8 8 4.5 2 3 4 4 5 5 6 6 7 8 5.0 2 3 4 4 5 5 6 6 7 7 6.0 2 3 4 4 5 5 6 6 7 , 7 7.0 2 3 4 4 5 5 6 6 7 7 TABLE, SHOWING THE NUMBER OF MINUTES AND SECONDS CONTAINED IN EACH DEGREE OR 60 MILES OF LONGITUDE FOR EVERY DEGREE OF LATITUDE. LAT. MIN. SEC. LAT. MIN. SEC. LAT. MIN. SEC. LAT. MIN. SEC. LAT. MIN. SEC. O , // O ' " O , O / // O , // 1 59.59 19 56.44 37 47.55 55 34.25 73 17.33 2 59.58 20 56.23 38 47.15 56 33.30 74 16.33 3 59.55 21 56.00 39 46.38 57 32.41 75 15.31 4 59.51 22 55.38 40 45.58 58 31.48 76 14.31 5 59.46 23 55 14 41 45.17 59 30.54 77 13.30 6 59 40 24 54.49 42 44.35 60 30.00 78 12.28 7 59.33 25 54.23 43 43.53 61 29.06 79 11.27 8 59.25 26 53.56 44 43.10 62 28.10 80 10.25 9 59.16 27 53.28 45 42.26 63 27.15 81 9.24 10 59.06 28 52.59 46 41.41 64 26.18 82 8.21 11 58.54 29 52.29 47 40.55 65 25 22 83 7.19 12 58.41 30 51.58 48 40.09 66 24.24 84 6.16 13 58.28 31 51.26 49 39.22 67 23.26 85 5.14 14 58 14 32 50.53 50 38.44 68 22.28 86 4.12 15 57.58 33 50.19 51 37.46 69 21.30 87 3.09 16 57.41 34 49.45 52 36.57 70 20.31 88 2.02 17 57.23 35 49.09 53 36.07 71 19 32 89 1.03 18 57.04 36 48.33 r,i 35.13 72 18.33 90 0.00 276 TABLE XYI. LOGARITHMS FOE COMPUTING- THE EQUATION OF EQUAL ALTITUDES. Inter- val. Log A Log B Inter- val. Log A Log B Inter- val. Log A LogB Inter- val. Log A Log B h. m. li. m. la. m. n. m. 2 7.7297 7.7146 4 7.7447 7.6823 6 07.7703 7.6198 8 7.8072 7.5062 2 7.7298 7.7143 2 7.7451 7.6815 2 7.7708 7.6184 2 7.8079 7.503C 4 7.7300 7.7139 4 7.7454 7.6807 4 7.7713 7.6170 4 7.8080 7.5010 6 7.7302 7 7136 6 7.7458 7.6800 6 7.7719 7.6156 6 7.8094 7.4983 8 7.7304 7.7132 8 7.7461 7.6792 8 7.7724 7.6142 8 7.8101 7.4957 10 7.73057.7128 10 7.7464 7.6784 10 7.7729 7.6127 10 7.81087.4930 12 7.73077.7125 12 7.7468 7.6776 12 7.7735 7 6113 12 7.81167.4902 14 7.7309 7.7121 14 7.7472 7.6768 14 7.7740 7.6098 14 7.8123(7.4874 16 7.7311 7.7117 167.7475 7.6759 16 7.7745 7.6083 16 7.81307.4846 18 7.73137.7113 18 7.7479 7.6751 18 7.7751 7.6068 18 7.81387.4818 2 20 7.7315 7.7109 4 fcO 7.7482 7.6743 6 20 7.7756 7 . 6053 8 2U 7.8l457.47t9 22 7.7317 7.7105 22 7.7486 7.6734 22 7.7762 7.6038 22 7. 8153 7. 4700 24 7.7319 7.7101 24 7.7490 7.6726 24 7.7767 7.6023 24 7.81607.4731 26 7.7321 7.7097 26 7.7494 7.6717 26 7.7773 7.6007 26 7.81687 4701 28 7.7323 7.7092 28 7.7497 7.6708 28 7.7779 7.5991 28 7.8176 7.4671 30 7.7325 7.7088 30 7.7501 7.6700 30 7 7784 7.5975 30 7.8183 7. 4640 32 7.7327 7.7083 32 7.7505 7.6691 32 7.7790 7.5959 32 7.8191 7.4600 34 7.7329 7.7079 34 7.7509 7.6682 34 7.7796 7.5943 34 7.8199 7.4578 36 7.7331 7. 7075 36 7.7513 7. 6673 36 7.7801 7.5927 36 7.8206 7.4546 38 7.7333 7.7070 38 7.7517 7 6663 38 7.7807 7.5910 38 7.8214 7.4514 2 40 7.7330 7.7065 4 4U 7.7521 7.6654 6 40 7.7843 7.5894 8 40 7.8^k. V.4482 42 7.7338 7.7061 42 7.7525 7.6645 42 7.7819 7.5877 42 7.8230 7.4449 44 7.7340 7.7056 44 7.7529 7.6635 44 7.7825 7.5860 44 7.8238 7.4415 46 7.7342 7.7051 46 7.7533 7.6626 46 7.7831 7.5843 46 7.8246 7.43811 48 7.7345 7.7046 48 7.7537 7.6616 48 7.7836 7.5825 48 7 8254 7.4347 50 7.7347 7.7041 50 7.7541 7.6606 50 7.7812 7.5808 50 7.8262 7.4312 52 7.7349 7.7036 52 7.7545 7.6597 52 7.7848 7.5790 52 7 8270 7.4277 54 7.7352 7.7031 54 7.7549 7.6587 54 7.7854 7.5772 54 7.82787.4241 56 7.7354 7.7026 56 7.7553 7.6577 56 7.7860 7.5754 56 7.8286 7.4205 58 7.73577.7021 58 7.7557 7.6567 58 7.78G7 7.5736 58 7.8294 7.4168 3 7.7359 7.7015 5 7.7562 7.0556 7 7.7873 7.5717 9 7.83027.4131! 2 7.7362 7.7010 2 7.7566 7.6546 2 7.7879 7.5699 2 7.8311 7.4093 4 7.7364 7.7005 4 7.7570 7.6536 4 7.7885 7.5680 4 7.83197.4055 6 7.7367 7.6999 6 7.7575 7.6525 6 7.7891 7.5661 6 7.83.8 7.4016 8 7.7369 7.6993 8 7.7579 7.6514 8 7.7898 7.5641 8 7.8336 7.3977 10 7.7372 7.6988 10 7.7583 7.6504 10 7.7904 7.5622 10 7.8344 7.3937 12 7.7374 7.6982 12 7.7588 7.6493 12 7.7910 7.5602 12 7.8353 7.3896 14 7.7377 7.6976 14 7.7592 7.6482 14 7.7916 7.5582 14 7.8361 7.3855 16 7.7381; 7.6970 16 7.7597 7.6471 16 7.7923 7.5562 16 7.8370 7.3813 18 7.7383 7 6964 18 7.7601 7.6460 187.7929 7 5542 18 7 8378 7 377] 3 20 7.7380 7.0958 5 2U 7.7606 7.6448 7 20 7.7930 7.5522 9 20 7.83S7 7 BV28 22 7.7388 7.6952 22 7.7610 7.6437 22 7.7942 7.5501 22 7.8396 7.3684 24 7.7391 7.6946 24 7.7615 7.6425 247.7949 7.5480 24 7.8404 7.36o9 26 7.7394 7.6940 26 7.7620 7.6414 26 7.7955 7.5459 26 7.8413 7.3591 28 7.7397 7.6934 28 7.7624 7.6402 28 7.7962 7.5437 28 7.8422 7.3548 30 7.7400 7.6927 30 7.7629 7.6390 30 7.7969 7.5416 30 7.8430 7.3501 32 7.7403 7 6921 32 7.7634 7.6378 32 7.7975 7.5394 32 7.8439 7.3454 34 7.7406 7.6914 34 7.7638 7.6366 34 7.7982 7.5372 34 7.8448 7 3400 36 7.7409 7.6908 36 7.7643 7.6354 36 7.7989 7.5350 36 7.8457J7.3357 38 7.7412 7.6901 387.7648 7.6342 38 7.7995 7.5327 38 7.84667.3307 3 4U 7.7415 7 . 6894 5 407.7653 7.03i:9 7 40 7.8002 7.5304 9 40 7.84757.3-^56 42 7.7-418 7.6888 42'7.7658 7.6317 42 7.8009 7.5281 42 7.848417.3205 44 7 7421 7.6881 44 7.7663 7.6304 44 7.8016 7. 5258 44 7.8493j7.3152 46 7.7424 7.6874 46 7.7668 7.6291 46 7.8023 7.5234 46 7.8502|7.3099 48 7.7428 7.6867 48 7.7673 7.6278 487.8030 7.5211 48 7.85117.3045 50 7.7431 7.6859 . 50 7.7678 7.6265 50 7.8037 7.5186 50 7.85207.2989 5-2 7 7434 7.6852 52 7.7683 7.6252 52 7.8044 7.5162 52 7.85307.2931 54 7.7437 7.6845 54 7.7688 7.6239 54 7.8051 7.5137 54 7.85397 2876 56 7.7411 7 6838 50 7.7693 7.6225 56 7.8058 7.5112 567.85487.2817 58 7.7444 7.6830 58 7.7698 7.621i 587.80657.5087 58 7.8558.7.2758 4 7.7447 7.6823 G 7.7703 7. 6198 8 7.8072 7.5062 10 7.8567 7.2697 TABLE XVII. 277 LOG RISING TO FIND THE LATITUDE BY REDUCTION TO THE MERIDIAN. Hour. M. Os. 5s. 10s. 15s. 20s. 25s. 30s. 35s. 40s. 45s. 50s. 55s. P.P. 1 2 3 4 u. J .97860 0.5806G J. 93284 1.18271 04813 61612 95664 20062 11250 65019 97980 21817 17242 68297 00236 23537 02136 22848 71455 J2435 25224 2181S 28114 74503 04580 2G878 37654 33079 77448 06673 28502 51044 37775 80296 08717 30095 62642 4223(J 83054 10714 31660 72873 463G8 85726 12666 33198 82024 50509 88319 14575 34708 90303 54370 90837 16443 36193 5 6 7 8 9 1.37053 53488 66877 78474 88703 39088 40501 41*90 54686 55868 57034 67905 68920 69924 79374 -(0265,81147 89504 90297 j91083 43256 58184 70917 S2019 91862 44G05 59320 71898 32884 92634 45931 60440 72869 33739 93399 47237 61547 73829 84587 94157 48524 62639 74778 8542G 91909 19794 63718 75717 86257 95655 51041 64784 76646 87080 9G394 52273 65837 77565 87896 97127 10 11 12 13 14 1.97854 2.06131 13687 20638 27073 98574 06786 14288 21192 2758S i)9289te999a 07437 08082 14885 15477 21744 22292 28100(28609 0070 J : 18723 1606G 22836 29116 0139U 09359 16651 23377 29619 02091 09991 17232 23915 30120 0^777 10618 17809 24449 30617 03456 11240 18382 2498G 31112 04134 11859 18951 25508 31604 04805 12472 19517 26033 32093 05470 13082 20079 26554 32579 s 1 a 3 4 119 238 368 476 15 1G 17 18 19 2.33063133544 38G67 39118 4393044355 48893 49294 5338653966 34023 39567 44777 19693 54344 34498 40013 45198 50090 54721 34972 40457 45616 5048G 55096 35442 40S99 46033 50879 55469 35910 41339 46447 51271 55841 3637G 1177C 46859 51661 56211 36839 42211 4727C 52050 56580 37299 42644 47678 52436 56947 37756 43075 48085 52821 57313 38213 43504 48490 53205 57676 s 1 2 3 1 84 168 252 336 20 21 22 23 24 2.5803958400 62274 62618 6631266640 70170 70483 7386374164 3875959117 6296063302 66967 67292 7079G 71108 74464 74762 59474 33641 67617 71418 75060 59829 G3979 67940 71728 75357 60182 64316 68262 72036 75652 60534 64652 G8583 72343 75947 60885 64987 68903 72649 76241 61234 65320 69221 72954 76533 61582 65652 69538 73258 76825 61929 65982 69855 73561 77116 s 1 2 3 4 65 130 195 260 25 26 27 28 29 2.7740577694 8080981086 8408384350 8723887496 9028290531 77982:76269 8136381639 84617 84883 8775388009 9077991027 7855578840 8191482188 85148,85412 8826588519 9127891520 79124 82461 85675 88773 91765 79407 82734 85937 89027 92010 79689 83005 86199 89279 92254 79970 83276 86460 89531 92497 80251 83546 8G72G 89782 92739 80530 83815 86979 90032 92981 s 1 2 3 4 53 106 159 212 30 31 32 33 34 2 . 93223 93463 93703 93942 96067962999653296763 g . 98820 99045 99270 99-195 3.01488017070192502143 04077042890450104712 94161 96994 99719 02360 04922 94419 97224 99942 02576 05133 94656 97454 00164 02792 05342 94893 97683 00386 03008 05551 95129 97912 00608 03222 1)5760 95364 98140 0062.9 03437 05968 95599 95833 98367 98594 0104901269 G3651 03864 0617606383 s 1 2 3 4 45 90 134 178 35 36 37 38 39 3.06590 09032 11406 13718 15969 0679(3 09232 11601 13908 16154 0700107207 0943209632 11796 11990 14097 14286 16338 16522 07411 09831 12184 14475 16706 07616 10029 12377 14663 16889 07819 10227 12570 14850 17072 06023 10425 12762 15038 17255 08225 10622 12954 15225 17437 08428 10819 13146 15411 17619 08629 11015 13337 15597 17800 08831 11211 13527 15783 17982 s s I 30 77 116 154 40 41 42 43 44 3.18162 20301 22389 24427 26418 18343 20477 22560 24594 26581 18522 18702 20653 20828 22732 22903 2476224929 26745 26908 18881 21003 23073 25095 27071 19060 21177 23244 25262 27234 19238 21351 23414 25428 27396 19417 21525 23583 25594 27558 19594 21699 23753 25759 27720 19771 21872 23922 25924 27881 19949 22044 24090 26089 28042 20125 22217 24259 26253 28203 s 1 2 1! 1 34 68 102 137 45 46 47 48 49 3.28363 30266 32128 33950 35734 28524 30423 32281 34100 35881 28683 28843 30579 30735 32434 32587 34250 34400 36028 36175 2900229161 30891 31047 32739 32892 3454934698 36321 36467 29320 31202 33044 34847 36613 29478 31357 33195 34995 36758 29637 31512 33347 35144 36903 29i94 31666 33498 35292 37048 29952 31820 33649 35439 37193 30109 31974 33801 35587 37338 I 1 2 3 t 31 62 92 122 50 51 52 53 54 3 . 37482 37626 37770 37914 39195 39336 39477 39618 40875410134115241290 42522426584279442929 44138442724440544537 36057138200 3975939899 41427 41565 4306443199 1467044803 38343 40039 11702 43334 44935 38486 40179 41839 43469 45067 38628 40319 41976 43603 45199 38770 38912 4045840597 1211342250 43737 43871 15331 45462 39054 40736 42386 44005 45593 a 1 2 3 1 27 55 82 no 55 56 57 58 59 3.45724 47282 48811 50314 51791 45855 45986 46116 474104753947667 489381906449190 504385056250686 519135203552156 46247,46377 4779537923 1931549441 50809 50933 5227852399 46507 48050 1956G 51056 52520 46636 48177 49691 51179 52641 46766 48305 49816 51301 52761 46895 47024 4843248558 49941 50066 5142451547 5288253002 47153 48685 50190 51669 53122 s 1 a 3 i 25 50 75 100 278 LOG EISING TO FIND THE TABLE XVII. LATITUDE BY REDUCTION TO THE MERIDIAN. 1 Hour. M. Os. 5s. 10s. 15s. 20s. 25s. 30s. 35s. 40s. 45s. 50s. 55s.P. P. U 1 2 3 4 3 . 53243 533G2 c 5467054788, 5G074 56190, 5745557569, 58814 5892G >S48id 54905 5630G 57683 59038 33602 35023 56421 37797 59150 5372153840,53959 55140o5258 55375 56537 56652 56767 57910 58024 58137 59262 59374 59486 54u7 35492, 56S82 . 58250 59597 54197 i 55608 1 56997 . 38363 . 59708, 54^15:54434 55725 55841 5711257226 5847G 58589 59819,59930 54552 55958 37341 58702 30041 s 1 2 3 4 23 46 70 93 5 6 7 8 9 3.6015260202 G1469 61578 62766 62873 6404364149 65302 6540G 30373 31686 32980 34254 35510 130483 J1795 G3087 64360 65614 60593 60703 6190362012 63194 63301 6446564570 6571765821 130813 52120 63407 64675 65924 3092D 52228 53513 64780 G6028 31032 32336 33620 34885 36131 3114361251 3244362551 3372G 63832 3498965094 36234 66337 313uO 32659 33938 35198 56440 s 1 a a 4 21 42 63 85 10 11 12 13 14 3.6054266645 67765 6786G 689G9690G9 7015870256 71329 71426 136747 G7967 G9169 70354 71523 6'J849 68067 692G8 70452 71620 6695-2 68168 G93G7 70550 71716 37054 G715G 38269 68369 39467 695GG 7064870745 7181371909 672-57 G84G9 69665 70843 72005 37359 38570 59763 70940 72101 37461 675G2 3867068770 398G2 G9961 7103871135 72197 72294 57663 68870 70059 71232 72389 s 1 2 3 4 20 40 60 80 15 16 17 18 19 3.7248572580J 73G25 73719 74750,74843 75860 75952 7695577046 7267G 73813 7493G 76043 77137 7277 1I728G7I 73907:74001 7502975121 76135 76227 77227 77318 72962 73057 73152 74095 74189 74283 752147530775399 763187640976501 774087749877588 73247 7437G 75491 76592 77678 73341 74470 75584 76683 77768 7343G 74563 75676 76774 77858 73530 74657 75768 76865 77947 s 1 9 3 4 18 37 55 74 20 21 22 23 24 3.78037|78127 7919579193 8015980247 81201 81287 82230 82315 78210 79282 80331 81373 82400 78305 79370 80421 8145S 82485 :78395 78484 79458 79546 8050880595 8154581631 82570 82655 78573 79634 80682 81717 82739 78GG2 79722 80768 81802 82824 78750J78839 78928|7901G 79809798977998580072 80855809428102881115 81888819748205982144 82908:829938307783162 s 1 2 3 1 17 35 52 70 25 26 27 28 29 3.8324G 84250 85242 86223 87192 83330 84333 85325 86304 87272 83414 8441G 8540G 86385 87352 83498 8449S 85488 8646C 87432 83582 84582 85570 86547 87513 83G6G 83749 83833 84G65 84748 84830 85652 85734 8581G 86628 86709 86790 87593 87672 S7752 83917 84000 8491384995 85897 85979 8687086951 8783287912 84083 85078 86060 87031 87991 841G7 85160 86111 87112 88071 s 1 2 3 4 16 33 49 65 30 31 32 33 34 3.88150J88229 8909789176 90034 90112 9096091037 9187C;91952 88309 89254 90189 91114 92028 88388 88467 8933389411 90267 90344 9119091267 9210492179 88540 89489 90421 91343 92255 88G25 88704 895G7 89645 9049890576 91420 9149G 92331 J9240C 88783 89723 90653 9157z 92482 88862 89801 90730 91648 92557 88940 89879 90807 91724 92632 89019 S9956 90884 91800 92707 1 2 3 1 15 31 46 62 35 36 37 38 39 3.9278292858 93679,93753 94566J9463S 9544395515 96311J96383 92933 93827 94712 95588 96455 93007 93082 9390193975 94786 94859 9566 1)95733 96527 96599 93157 94043 94932 9580C 96G7C 93232 94123 95005 95878 96742 9330G 94197 95078 95950 96813 93381 94271 95152 96023 96885 93456 94345 95224 96095 9G956 93530 93G05 9441894492 95297 95370 9016796239 9702897099 s 1 2 3 'i 15 29 44 58 40 41 42 43 44 3.97170,97242 9802198091 9886298932 %99696 99765 4.00521005SS 9731c 9816k 9900: 99834 0065-i 97384,97455 9823298302 9907299141 9990399972 0072G 00794 97521 98372 99211 0004C 00862 97597 97GG7 9844398513 9928099350 0010900178 0093000998 j977ob 98583 99419 00247 010G6 97809 9788(J 98653 98723 99488 99557 0031500384 0113401202 ,97950 98793 99627 00452 01270 s 1 2 3 4 14 28 42 5G 45 46 47 48 49 4.0133701405 02146 02212 02947.0301S 03740.0380C 0452604591 101471 0228( 0308C 0387J 0465( ;01540 01608 10234702414 ) 03146 03212 03937,04003 > 04721 0478C 01075 02481 03278 0406* 04851 01742 0254 1 ; > 03344 (04134 049K 01810 02614 03411 0419S 0498C 01877 02681 03477 04265 0504i] 01945 02747 0354i 0433C 05111 02012 02814 03608 04395 05175 0207 b 0288C 03674 0446C 05231 s 1 2 3 4 13 26 40 53 50 51 52 53 54 4.053040536!: 0607406138 06838:06901 07595,0765'i 08344 0840( 05433 05497 05561 06202 06266 0633C 06965 07028,07091 077200778307845 084680853008592 05026 0509C 06393 0645 r 07154 0721 r 0790807971 08654 087K 105754 06521 0728C 108032 ) 08778 U5S18 06581 07342 08095 0884C U5882!o594t 0664806713 07406 07461. 081570822( 0890208964 0601C 06775 07532 0828$ 09025 s 1 2 3 4 13 25 38 50 55 53 57 58 59 i. 09087,0914* 09823 098& 10552 10611 11275 1133; 119921205- S092K t0994, iiOG7 51139 L 1211 ) 09272,0933311)9394 0945* 3 10006 10067 10128 10181 3 10734 10794 10854] 10U1, 31145511515115751163 L 12170' 1222912289 1234 509517 > 1024$ 5 1097; 1 1169^ 5l240 r 09578 1 103K iiioai 1 11754 HJ246( 09640,0970] 103711043] > 11095 1115( [1181311871 .125251258- 0976'. 1049: 511215 $1193$ L 12641 s ! 1 , 2 \ 3 5 4 12 24 36 48 TABLE XVII. 279 LOG RISING TO FIND THE LATITUDE BY REDUCTION TO THE MERIDIAN. 2 Hours. M. Os. 5s. 10s. 15s. 20s. 25s. 30s. 35s. 40s. 45s. 50s. 55s. P.P. 1 2 3 4 4.1270212761 13406 134G5 14104 1416-2 14797114854 15483J15540 12820 13523 14220 14911 15597 12879 13o81 14278 14969 15652 12938 13640 14336 15026 15710 12996 13696 14394 15083 15767 13055 13750 14451 15140 15824 13114 13814 14508 15198 15880 13172 13872 14567 15255 15937 13231 13931 14625 15312 15994 13283 13989 1468'2 15369 16050 13348 14047 14739 15420 16107 s 1 2 3 1 11 23 34 46 5 6 7 8 9 4.1610316220 1683816894 17507 17563 18171 18226 18829 18883 16276 16950 17618 18281 18938 1633-2 17006 17673 18336 18992 16389 17062 17729 18391 19047 16145 17117 17784 18445 19101 16501 17173 17840 18500 19156 16557 17229 17895 18555 19210 16614 17285 17950 18610 19265 16070 17340 18005 18665 19319 107-20 17396 18060 18719 19373 10782 17451 18116 18774 19427 s 1 2 3 4 11 22 33 44 10 11 12 13 14 4.19482:19536 201-29 20183 20771120825 '2140921461 22041 22093 19590 20236 20878 21514 22146 19641 20290 20931 21567 22198 19698 20344 20984 21620 22250 19/52 20397 21037 21673 22303 19806 20451 21091 21725 22355 19800 20505 21144 21778 22407 19914 20558 21197 21831 22459 19968 20611 21250 21883 22511 20022 20665 21303 21936 22564 20075 20718 21356 21988 22610 H ] 2 3 4 11 21 32 '42 15 16 17 18 19 4.22668 23290 23907 24520 25128 2ii72u 23342 23959 24571 25178 2277* 23393 24010 24622 25229 22824 23445 24061 24673 25279 22876 23496 24112 24723 25330 22928 23548 24163 24774 25380 2296'0 23599 24214 24825 25430 23031 23051 24265 24875 25481 23083 23702 24316 24926 25531 23135 23754 24367 24977 25581 23187 23805 24418 25027 25631 23238 23850 24469 25078 25681 B 1 2 3 4 10 20 31 41 20 21 22 23 24 4. 25731 25761 2633026380 2692426974 27514 27563 2803928148 25831 26429 27023 27612 28197 25881 26479 27072 27661 28245 25931 26529 27121 27710 28294 25981 26578 27171 27759 28342 26031 26628 27220 27807 28391 26031 26677 27269 27856 28439 26131 26727 27318 27905 28487 26181 26776 27367 27954 28536 2u231 26826 27416 28002 28584 26281 26875 27465 28051 28632 s 1 2 3 4 10 20 29 39 25 26 27 28 29 4.2866128729 29257 29305 29830 29877 3039830445 30963 31009 28777 29353 29925 30493 31050 .:88Z5 29401 29973 30540 31103 28873 29449 30020 30587 31150 28921 29496 30067 J0034 31197 2896U 29544 J0115 JOG81 31243 ^9017 29592 30162 30728 31290 29060 29639 30209 30775 31337 29114 29687 30257 308-22 31383 29161 29735 30304 30869 31430 29209 29782 30351 30916 31476 s 1 2 3 1 10 19 29 38 30 31 32 33 34 4.31523 32079 32631 33180 33724 31569 32125 32677 33225 33770 31610 32171 32723 33271 33815 31602 32217 32769 33316 33800 31709 32264 32815 33362 J3905 31755 32310 32860 33407 33950 31801 32356 32906 33453 33995 31848 32402 32952 33498 34040 31b91 32448 32997 33543 34085 31940 32491 33043 33589 34130 31987 32540 33089 33634 34175 3203o 32586 33134 33679 34220 a 1 '2 1! 1 9 18 28 37 35 36 37 38 39 4.34205 34802 35335 35865 36391 31310 34847 35380 35909 36435 34355 34891 35424 35953 36476 34400 34936 35468 35997 36522 34444 34980 35512 36041 30565 34489 35025 35556 36085 36609 34534 35069 35601 36128 36053 34579 35114 35645 36172 36696 340.i3 35158 35689 36216 36740 34008 35202 35733 36260 36783 34713 35247 35777 36303 36827 34757 35291 35821 36347 36870 s 1 2 9 l 9 18 27 36 40 41 42 43 44 4.36913 37432 37948 38460 389G8 369o7 37475 3799U 38502 3J010 3700U 37518 38033 38545 39052 37043 37561 38076 38587 39095 37087 37604 38119 38629 39137 37130 37647 38161 38672 39179 37173 37690 38204 38714 39221 37216 37733 38247 38757 39263 37200 37776 38289 38799 39305 37303 37819 38332 38841 39347 37340 37862 38374 38884 39389 37389 37905 38417 38920 39431 s 1 2 3 1 9 17 26 35 45 46 47 48 49 4.39473395io 3997540017 40474 40515 4096941010 41461 41502 39557 40058 40550 41051 41543 39599 40100 40593 41092 41583 39641 40142 40639 41133 41624 39683 10183 10680 11174 11065 39725 40225 40722 41215 41706 39700 40260 40763 41256 41746 39ci08 40308 40804 41297 41787 39850 10349 40845 11338 41828 39892 40391 40887 41379 41868 39930 4043-2 10928 41420 41909 s 1 1 ;; -i 8 17 25 34 50 51 52 53 51 4.41950'4199U 4243542476 4291842958 4339843437 4387443914 42031 42516 42998 43477 43953 42071 42556 43038 43517 43993 421la 42597 43078 43557 44032 42153 42637 43118 43597 44072 42193 42677 43158 43636 44111 42233 12717 43198 43676 14151 42274 42758 43238 43716 44190 42314 42798 43278 43755 44229 42355 42838 43318 43795 44269 42395 42878 43358 43835 44308 s I a 3 i 8 If 24 32 55 56 57 58 59 4.4434 : 44387 4481844857 4528645325 45750 45789 4621240250 44426 44405 4489644935 453G3 45402 45827 15860 46289'46327 44505 14974 15141 45905 46365 44544 44583 4501345052 45480 45518 4594345982 4640i!46442 44022 45091 45557 46020 16480 44662 45130 1559G 16058 46518 44701 45169 45634 46097 ior>r,i; 44740 15208 45673 46135 46595 44779 45247 45712 46174 46633 s ] _' B -I 8 15 23 30 280 TABLE XVII. LOG RISING TO FIND THE LATITUDE BY REDUCTION TO THE MERIDIAN. 3 Hours. M. Os. 5s. 10s. 15s. 20s. 25s. 30s. 35s. 40s. 45s. 50s. 55s. P.P. 1 2 3 4 4.40671 47127 47580 48031 48479 46709 47165 47618 48068 48516 46747 47203 47656 48106 48553 46785 46823 4686146899 47241472784731647354 47693477314776847806 48143 4818048218 48255 48590 48627 48664 48701 40937 47392 47843 48292 48739 40975 47013 47051 47089 47430 47467^750547543 47881479184795647993 4833048367,4840448441 48776488134885048887 s ] 9 :; 4 7 15 22 30 5 6 7 8 9 4.48924 49360 49806 50243 50677 43961 49403 49842 50279 50714 4899S 49440 49879 50316 50750 49035 49476 49915 50352 50786 49071,4910849145 495134955049586 49952 49988 50025 503885042450461 50822 5085850894 49182 49623 50061 50197 o0930 4921949256 49293 49329 49660 4969649733 497G9 50098501345017050207 50533 50569 50605 50641 50966510025103851073 s 1 2 I 1 7 14 22 29 10 11 12 13 14 4.51109 51539 51966 52390 52812 51145 51574 52001 52425 52847 51181 51610 52037 52461 528S2 31217 51646 52072 52496 52917 5125351289,51324 516815171751753 521075214352178 5253r52566'52601 52952j5k987 53022 513GO 51788 52213 52636 53057 5139651432:5146751503 51824 51859 51895'51930 52249522845231952355 52672 52707 52742 52777 53092 53127 53162 53197 8 I 2 3 4 7 14 21 28 15 1(3 17 18 19 4.53231 53648 54063 54475 54885 53266 53683 54097 53301 53718 54132 53330 53752 54166 533715340553440 5378753821153856 54201 54235,54269 53475 53891 54304 53510 53544 53579 53614 53925 53960 53994 54029 54338 54372;54407>54441 8 1 2 3 4 7 14 20 27 54509 54919 54544 54953 54578 54987 5461254646 55021 55055 o4680 55089 54715 55123 54749 54783,54817 54851 55157551915522555259 20 21 22 23 24 4 . 55293 55G98 56101 56501 56900 55327 55732 56134 56534 56933 55360 55765 56168 56568 56966 55394 55799 56201 56G01 56999 55428 55832 56235 56635 57032 55402 55496 5586655900 56268,56301 56668'56701 57065,57098 55529 55933 56335 56734 57131 55563 55597j55630,55664 55967 56000 56034 56067 56368 56401 56435 56468 56767 56800,56834 56867 57164571975723057263 I j 2 3 4 7 13 20 26 25 20 27 28 29 4.57296 57690 58082 58471 58859 57329 57723 58114 58504 58891 57362 57755 58147 58536 58923 57395 57788 58179 58568 58955 57428 57821 58212 58601 58988 57460 57493 57854 57886 58244 58277 58633 58665 5902059052 57526 57919 58309 58698 59084 57559 57592jo7625 57057 57951579845801758049 58342583745840758439 58730587625879458827 59116591485918059212 s 1 2 3 4 6 13 19 26 30 31 32 33 34 4.59244 59627 60008 60388 60764 5927(j 59659 60040 60419 60796 59308 59691 60072 60450 60827 59340 59723 60103 60482 60858 59372594045943(3 597555978659818 601356016760198 60513 60545 G0576 608906092160952 59408 59850 60230 6060-- 60983 59500 59532 59564 59596 59882599135994559977 60261 60293 60324J60356 60639606706070160733 61015610466107761108 s 1 2 3 4 6 12 18 25 35 36 37 38 39 4.01139 61512 61883 62252 62619 G1171 61543 61914 62283 62650 61202 61574 61945 62313 62680 61233 61605 61976 62344 62711 61264 6163G 62006 62375 62741 6129561326 6166761698 62037 62068 6240562436 62771 62802 01357 61729 62099 62466 62832 6138861419,6145061481 61760617916182261852 6212962160,6219162222 62497 62528 62558 62589 62863 62893 62923 62954 s 1 2 3 4 6 12 18 24 40 41 42 43 44 4.62984 63347 63708 640G8 64425 63014 63377 63738 64097 64455 63045 63407 63768 64127 64484 63075 63438 63798 64157 64514 631056313663160 63468 63498 63528 638286385863888 64187 64217 64246 G4544 64573 64603 63196 63226 G3257J63287jG3317 J3558 63588 63618 63648 63678 63918 63948 63978 64008 64038 64276 64306 64336 64365 ! 64395 64632 64662 64692 64721 64751 s 1 2 3 4 6 12 18 24 45 46 47 48 49 4.64780 65134 65486 65836 66184 64810 65163 65515 65865 66213 64839 65193 65544 65894 66242 64869 65222 65573 65923 66270 64898 65251 65603 65952 G6299 6492864957 65281 65310 6563265661 65981 '66010 6632866357 64987 65339 65690 66039 66386 65016650456507565105 65369653986542765456 65719 65748 65777 65806 66068660976612666155 66415664446647266501 s 1 2 3 4 c 12 17 23 50 51 52 53 54 4.66530 66875 67217 67558 67897 66559 66903 67246 67587 67925 66588 66932 67274 67615 67954 66616 66960 67303 67643 67982 66645 66989 67331 67672 68010 G6674'66702 6701867046 6736067388 6770067728 6803868066 66731 67075 67416 67756 68094 66760 66789J66817 66846 6710367132J6716067189 6744567473:6750267530 67785678136784167869 68123681516817968207 B 1 2 3 4 6 12 17 23 55 56 57 58 59 4.68235 68571 68905 69237 69568 68283 68599 68933 69265 69595 68291 68627 68960 69292 69623 68319 68654 68988 69320 69650 68347 68682 69016 69348 69678 68375,68403 68431 68459 68487,68515 68543 6871068738 68766 68794 68821 68849 68877 69043 69071 69099 69127,69154 69182 69210 69375 69403:69430 69458 69486,69513 69540 69705 69733169760 69788 69815 69842 69870 s 1 a 3 4 6 11 17 22 TABLE XVII. LOG RISING TO FIND THE LATITUDE BY REDUCTION 281 TO THE MERIDIAN. 4 Hours. M. Os. 5s. 10s. 15s. 20s. 25s. 30s. 35s. 40s. 45s. 50s. 55s. P.P. 1 2 3 4 4.G9897 70224 70550 70874 71197 6JW24 70252 70577 70901 71224 G9952 69979 7027970306 70G04 70631 70928'70955 7125071277 70000 70333 70658 70932 71304 70031 70061 70U88 70115 70143 70360 70387 70415 70442 70469 70685 70712 70739 70766 70793 71009 71036,71063 71089 71116 7133l'71357,71384 71411 71438 70170 70496 70820 71143 71464 70197 70523 70847 71170 71491 8 1 2 3 4 5 11 16 22 5 6 7 8 9 4.71518 71837 72155 72471 72785 71544 71864 72181 72497 72812 71571J71598 7189071917 7220872234 7252372550 72838 72864 71624 71G51 71678 719437197071996 72260 7228772313 7257C 72602 72628 7289072916,72942 7170417173171757 7202372049,72075 72339 723GG 72392 726557268172707 729687299473020 71784 72102 72418 72733 7304C 71810 72128 72445 72759 73072 s 1 2 3 i 5 10 16 21 10 11 12 13 14 4 . 73099 73410 73720 74028 74335 73125 73436 73746 74054 74361 73151 73462 73772 74080 74386 73177 73438 73797 74105 74412 73203 73514 73823 74131 74437 7322873254 73539 73565 73849 73874 7415774182 744G3 74488 73280 73591 73900 74208 74514 73306,7333* 73G17 73643 73926 73951 7423374259 7453974565 73358 73668 73977 74284 74590 73384 73694 74003 74310 7461G s 1 2 3 4 5 10 15 20 15 16 17 18 19 4.74041 74945 75247 75549 75S48 74666 74970 75273 75574 75873 74692 74995 75298 75599 75898 74717 75021 75323 75624 75923 74742 75046 75348 75649 75948 74768 75071 75373 75674 75973 74793 75096 75398 75G99 75997 748181 74844 174869 75122175147(75172 754237544875473 75723 7574875773 76022 76047 76072 74894 75197 75498 75798 76097 74920 75222 75523 75823 76121 s 1 2 3 4 5 10 15 20 20 21 22 23 24 4.76146 76443 76738 77032 77325 76171 76468 76763 77057 77349 761% 76492 76787 77081 77373 76221 76517 76812 77105 77398 76245 76542 7G83C 77130 77422 70270170295 76566 76591 76861 76885 77154 77179 774-16,77470 76320 76615 769K 77203 77495 76344 763G9 76640 76665 76934 76959 77227 77252 7751977543 76394 76689 76983 77276 77567 76418 76714 77008 77300 77592 s 1 2 3 4 5 10 15 20 25 26 27 28 29 4.77G16 77906 78194 78481 78767 77640 77930 78218 78505 78790 77604 77954 78242 78529 78814 77088 77978 78266 78552 78838 7771ci 78002 78290 78576 78861 77737|77701I?7785 780267805078074 78314 78338 78361 78600.7862478648 78885;78909 78933 77809 78098 78385 78671 78956 77833 78122 78409 78G95 78980 77857 78146 78433 78719 79004 77882 78170 78457 78743 79027 s 1 2 3 4 5 10 14 19 30 31 32 33 34 4.79U51 79334 79615 79896 80175 790747909879122 79357 79381 79404 796397966279686 79919 79942 799G5 80198 80221 S0244 79145 79428 79709 79989 80267 79109,79192 79451 79475 79732 7975G 80012 80035 8029080314 79210 79498 79779 80059 80337 7924079263 79522 79545 79802179826 8008280105 8036080383 79287 79568 79849 8012& 80406 79310 79592 79872 80151 80429 s 1 2 3 -i 5 9 14 19 35 3G 37 38 39 4.80452 80729 81004 81277 81550 80475 30752 81027 31300 81573 80498,30521 8077580797 8104981072 8132381346 8159581618 30545 80820 81095 81368 81641 80508 80591 30014 808438086680889 811188114181163 813918141481437 816638168681708 80637,80660180683 80912 80935 80958 811868120981232 814598148281505 81731 81754 81776 80706 80981 81255 81527 81799 s 1 2 3 4 5 9 14 18 40 41 42 43 44 4.81821 82091 82360 82628 82894 31844 82114 82382 82650 82916 8186681889 8213682159 3240582427 8267282694 8293882960 81911819348195081979 82181 82203 82226 82248 82449 82472 82494 825 1C 82716827398276182783 82982830048302683049 82001182024 820408.1069 822711822938231582338 82538 82561 82583 8260S 82805828278285082872 83071|83093 83115 83137 s ] a 3 1 4 9 13 18 43 46 47 48 49 4.83159 83423 83685 83947 84207 83181 83445 8320383225 83467 83488 8324783269 8351083532 83291 83313 8355483576 8381683838 84077 84099 84337 84358 83335:83357 8359883620 8386083881 8412084142 8438084401 83379 83642 83903 81164 84423 83401 83663 83925 84185 84444 s 1 2 a i 4 9 13 18 837078372983751 839688399084012 842298425084272 8377383794 8403484055 8429384315 50 51 52 53 f>4 4.84406 84724 81981 85236 85490 84488 84745 85002 85257 85512 8450984531 8476784788 8502385044 8527885300 8553385554 8455284574,8459584617 84810848318485284874 8506G85087j85108,85130 85321 85342,85363 85385 85575855968561785638 8463884659 8489584916 85151 85172 8540685427 85659 85680 34081 84938 85194 85448 85701 84702 81959 85215 85469 85722 s 1 2 :; 1 4 9 13 17 55 56 57 < 58 59 4.85744 85996 86247 86496 86745 85765 86017 86267 86517 86766 8578685807 8603886058 8628886309 86538 8655D 8678686807 85828 85849 85870 85891 85912:85933 86079 86100 86121 86142lS6163 86184 86330 8G35l'8G372 86392 8G413 86434 86579 36600 8662 1 866 1 1 |S6GG2 I 8GG83 86828 86848 86869 86889 86910 86931 35954J85975 86205 86226 MM .I.-. 36475 8670486724 86951 86972 s 1 a :i i 4 8 13 17 282 TABLE XVII. LOG RISING PO FIND THE LATITUDE BY REDUCTION TO THE MERIDIAN. 5 Hours. M. Os. 5s. 10s. ]5s 20s. 25s. 30s. 35s. 40s. 45s. 50s. 55s. P. P. 1 2 3 4 4 . 8b992 87013 87034 87054 87239 87259 87280 87300 87484875058752587545 87728 87749 877G9 87789 87971 87992 88012|88032 87075 87321 87566 87809 88052 87u l JiJ 87341 87586 87830 88072 871Hi 87362 87606 87850 88093 87136J8715787177 873828740287423 876278764787667 878708789087911 881138813388153 87198 87443 87688 87931 88173 87218 87464 87708 67951 88193 s 1 4 8; 12 16 5 r> 7 8 9 4.882138823488254 88454 88474 88494 886948871488734 889338895388973 891718919089210 88274 88514 88754 88992 89230 88^94 88534 83774 89012 89250 88314 88554 88794 89032 89269 88334 88574 88814 89052 89289 88354 88594 88834 89072 88309 88374 88394 88614 88634 8885388873 89C91 89111 8932889348 88414 88654 88893 89131 89368 88434 88674 88913 89151 89388 8 1 2 3 4 4 8 12 16 10 11 1'2 13 14 4.89407(894^789447 89G4389G62 89682 898778989789916 901119013090150 90343,90363 90382 89460 89702 89936 901G9 90401 S9486 89721 S9955 90188 90421 89500 89741 89975 90208 90440 89525 89760 89994 90227 90459 89545 89564:89584 897808979989819 900149003390053 90247 90266 90285 904789049890517 89604 89838 90072 90305 90536 896^3 89858 90091 90324 90555 8 1 2 3 4 4 8 12 16 15 1G 17 18 19 4 . 90575 90594 90613 90632 90805.9082419084390883 91034 91051 91073J91092 91263912829130191320 91490915099152891517 90u5_ 90882 91111 91339 91566 90671 90901 91130 91358 91585 90690 90920 91149 91377 91603 90709 90939 91168 91396 91622 9072890748 90958,90977 91187,91206 9141491433 9164191660 90767 90996 91225 91452 91679 90786 91015 91244 91471 91698 s 1 2 3 4 4 S 11 15 20 21 2-2 23 24 4.917169173o 9194291961 9216692185 92390 132408 9261292630 91754 91979 92203 92427 92649 91773 91998 92222 92145 926G7 31792 92017 92241 92464 9268G 91811 92035 92259 92483 92704 91829 92054 92278 92501 92723 91848 92073 92297 92519 92741 91867,91886 9209292110 9231592334 9253892556 92760,92778 91904 91923 9212992148 9235292371 92575 92593 92796 92815 S 1 2 3 1 4 7 11 15 25 26 27 28 29 4.9.8339285J 93054'93072 93273 93291 93492 93510 93709 93727 92870 93090 93310 93528 93745 92888 93109 93328 33546 93763 J2907 93127 93316 93564 93781 92925 93145 93364 93582 93809 92944 93164 93382 93600 93817 92962 93182 93401 93619 93836 92980,92999 9320093218 9341993437 93637,93655 93854 ! 93872 93017 93237 93455 93673 93890 93035 93255 93473 93691 93908 s 1 2 3 -i 4 7 11 15 3J 31 32 33 34 4.U3926 94141 94356 91570 94782 93944 94159 94374 91587 94800 939o293980 94177 94195 94392 94410 91605 91623 34818 94833 93998 94213 94427 34641 94853 '94016 94231 94445 94658 94871 94034 94249 94463 94G7G 94888 9405294069,94088 94267 94284,94302 94481 94498 94516 946919471194729 94906 94924^4941 94105 94123 94320 94338 94534 94552 94747 94765 9495994976 8 1 2 3 4 4 7 11 14 35 38 37 38 39 4.919949501^ 95205 95223 95415 95433 95624 95642 95832 95850 95029 95240 95450 95659 95867 95047 95258 J54GS 95676 95884 35005 95275 95485 35694 95902 35082 95293 95502 95711 95919 95100 95310 95520 95728 95936 95117i95135 95153 95328,95315J95363 95537 95555 95572 95746 35763*95780 959539597195988 95170 95380 95589 95798 96005 95188 95398 95607 95815 3.6022 8 1 2 3 4 3 7 1C 14 40 41 42 43 44 4.96040'9G057 96246 96263 96451 93469 96656 96673 9686093877 06074 96280 96486 9G690 96894 96091 96297 96503 96707 9G910 36109 96315 96520 9G724 9G927 96126 96332 36537 96741 36944 9614S 96349 96551 96758 96961 36160 96366 96571 96775 96978 96177,96195 9638396400 9658896605 9679296809 9G995 97012 96212 96417 9G622 96826 97029 96229 96434 9GG39 96843 37046 s 1 2 1! 4 3 7 10 14 4o 4G 47 48 49 4.97002:37079 9726497281 9746597482 97665 97682 97865 97881 97090 97113 97298 97315 9749997515 9769997715 9789897914 37130 97331 97532 97732 97931 97147 97348 97549 97749 37947 37163 97365 97565 97765 97964 97180 97382 97582 97782 97981 9719797214 9739897415 97599,97615 97798,97815 97997|98014 97231 97247 97432 97449 97G32 97649 97832 97848 9803098047 s 1 2 3 4 3 7 10 13 50 51 5-2 53 5t 4 . 98063 98080 98096 98113 98261982779829398310 98457984749849098506 98653986699868698702 98848988649888098897 9812998145 9832698343 9852398539 9871898734 3891398929 9816z 38359 98555 98751 38945 98178 98375 18572 98767 98961 98195.9S211 9.S39298408 9858898G04 9878398799 9897798994 98228 98425 38620 38816 39010' )8244 )8441 )8637 )S832 )902G s 1 2 3 4 3 7 10 13 55 5G 57 58 59 4 . 99042 9905S 99074^99090 99235 9925l!99267|99284 99423J99444 99460 99 476 99G19 99635 99651 99667 99310 99826 9984^99858 39107199123 3930099316 39492 99508 39683 99690 3987399889! 391399915599171199187 99332 99348 993G4 99380 99524995409955699572 997159973199747,99763 99905 9992 ll99937;99953 9920399219 3939699312 39587 99603 3977899794 39968199984 1 s 1 2 9 4 3 6 10 13 TABLE XVII. 283 LOG RISING TO FIND THE LATITUDE BY REDUCTION TO THE MERIDIAN. 6 Hours. M. Os. 5s. 10s. 15s. 20s. 25s. 30s. 35s. 40s. 45s. 50s. 55s. P.P. 1 2 3 4 5.0000000010 00189 00205 00377100393 0056500580 00751 D0767 00032 00221 00409 J0596 00782 00047 00236 00424 0061* 00798 00063 0007900095J00110 00252 002G8 00283 00298 00440004560047100487 00627006430065800674 00813008290084400860 u01*G 00315 00502 00689 00875 0014* 00330 00518 00705 0089J 0015800173 0034000362 0053400549 U0720 00730 0090600922 8 1 2 8 4 3 6 9 12 5 6 7 8 9 5.0093700953 0112201138 0130601322 0149001505 01672,01688 009G8 01153 01337 01520 01703 00984 01168 01352 01536 01718 00999 01184 01368 01551 01733 01014 01199 01383 01566 0174& 0103001045 01214 0123C 0139801413 01581 0159C 0176301779 01061 01245 01429 01612 01791 01076 01260 01444 01627 01809 01091 01276 01459 dl642 01824 01107 01291 01474 01657 01839 8 1 2 ;; 3 6 9 12 10 11 12 13 14 5.01854,01869 0203502050 02215 02230 0239502410 0257402588 01884 02065 02245 02425 02603 01900 02080 02260 02440 02618 01915 02095 02275 02455 02633 0193001945 0211002125 02-29002305 0246902484 0264802663 01960 02140 02320 02499 02677 01975 02155 02335 02514 02692 01990 02.1.70 02350 02529 02707 02005 02185 02365 .'2544 02722 02020 022UO 02380 02559 02737 s 1 2 3 4 3 C 9 12 15 16 17 18 19 5.02751502766 02928 02943 0310503119 0328003295 03455 03470 02781 02958 03134 0331G 03484 H2796 02973 03149 03324 03499 02811 02987 03163 03339 03513 02825!0*840 02855 03002 03017 03031 031780319303207 03353 03368 03382 0352803542,03557 02870 03046 03222 03397 03571 02884 03061 03237 03412 03586 02899 03075 03251 03426 03600 0*914 03090 03266 03441 03615 s 1 2 3 4 3 6 9 12 20 21 22 23 24 5.03629103644 0380203817 03975|03989 04147 04161 0431804332 03658 03831 04004 04175 04346 0367 z 03846 04018 04190 04360 03687 03860 04032 04204 04375 0370103710 03874 03889 04047 04061 0421804232 0438904403 0373003745 0390303918 0407504090 0424704261 0441704431 03759 03932 04104 04275 04445 03774 03946 04118 0428t 04460 03788 03961 04132 04303 04474 s 1 2 3 4 3 6 9 12 25 26 27 28 29 5.04488:04502 04657 04672 0482604840 0499405008 0516205175 04516 04686 04854 05022 05189 04530 04700 04868 05036 05203 04545 04714 0488* 05050 05217 045590457301587 047280474204756 048960491004924 050640507805092 052310524505259 04601 04770 04938 05106 05273 04615 04784 04952 05120 05286 04629 04798 04966 05134 05300 04G43 04812 04980 05148 05314 s 1 2 3 4 3 5 8 11 30 31 32 33 34 5.0532805342 0549405508 0565905673 0582305837 05987J06001 05356 05521 05686 05851 06014 05370 05535 05700 05864 06028 05383 05549 05714 05878 06041 05397J0541 105425 05439 05563055770559005604 05728057410575505769 05892 05905 05919 05933 06055060690608206096 05452 05618 05782 05946 06109 05460 05632 05796 05960 06123 05480 05645 05810 05973 06136 s 1 2 3 4 3 5 8 10 35 36 37 38 39 5.061500616306177 C6312 06326 06339 06474,06487 06500 066340664806661 067940680806821 06191 03353 06514 06674 06834 06204 06368 06527 06688 06848 06218 06379 06541 06701 06861 06231J06245 06258 063930640606420 06554065670G581 067140672806741 068740688706901 06272 06433 06594 06754 06914 06285 06447 06608 067G8 OG927 06299 06460 06621 06781 06941 K 1 2 3 4 3 5 8 10 40 41 42 43 44 5.0695406967 0711207126 0727007284 07428:07441 07584 07597 OH980 07139 07297 07454 07610 06994 07152 07310 07467 07623 U7007 07165 07323 07480 07636 07020 07178 0733G 07493 07649 07033 0704G 07060 071920720507218 073490736207375 07506.0751907532 076620767507688 07073 07231 07388 07545 07701 07086 07244 07401 07558 07714 07099 07257 07415 07571 07727 s \ 3 5 8 10 45 46 47 48 49 5.077400775307766 078950790807921 080500806308075 08204 08216,03229 083570836908382 0777907792 07934 07947 0808808101 0824208255 0839508408 07805 07818|07831 0784407857 07960 07973j07985j07998 08011 081 14 08127 08140 081 52 08165 08267 08280 08293 0830G 08318 08420 08433 08446 08458,08471 07869 08024 08178 08331 08484 07882 08037 08191 08344 08496 s 1 2 ;s i 3 5 8 10 50 51 52 53 54 5.085090852208534 086610867308686 088120882408837 089620897508987 091120912409137 08547 08560 0869908711 0385008862 0900009012 0914909162 085720858508598,08610 087240873608749,08762 08875088870890008912 09025 09037 09050 09062 09174091870919909211 08623 08774 08925 09075 09224 08636 08787 08937 09087 09236 08648 08799 08950 09100 09249 s 1 2 3 4 2 5 7 10 55 56 57 58 59 5 . 09261 09273 09286 09298 0931 1 09323'09335 09348 09360 09372 09385 09397 0940909422,09434 09446 09459 09471 09483 09496 09508 09520 09533 09545 09557 095C9 09582 095D4 09606 09618 09631 0964309655 09667 091580 09692 09704 09716 09729 09741 09753 09765 09777 09790 ( 09802 09814 09826 09838 09851 09863 09875 09887 09899 0991 1 0992 109936 099 48 099C.O 09972 09984 s 1 2 3 4 2 *- 7 10 284 TABLE XVII. LOG RISING TO FIND THE LATITUDE BY REDUCTION TO THE MERIDIAN. 7 Hours. M. Os. 5s. 10s. 15s. 20s. 25s. 30s. 35s. 40s. 45s. 50s. 55s. P.P. 1 2 3 4 5.09996 10141 1028C 10430 1057S 0006 015L 029, 0441 0585 oo^j 0166 0310 0454 0597 0033 0178 032i 0465 060!: L0045 10190 L0334 L0477 10620 10057 L0202 1034C 10489 10632 10069 L0214 L0358' 10501 10644 10081 10226 10370 10513 1065C 10093 10238 10382 10525 10G68 L0105 10250 10394 L0537 L0680 10117 10262 10400 10549 10691 L0129 10274 10418 L05G1 10703 s 1 2 3 4 2 5 7 9 5 6 7 8 9 5.10715 10S57 10998 1113^ 11271; 1072. 08GL 1101C 11150 11290 0739 0881 1022 116i 1302 0751 089L 103. 1174 1314 LO/03 L0904 11045 11185 11325 10774 1091C 11057 11197 11337 10786 10928 11069 11209 11348 10798 10941, 11080 11220 1136C 10810 10951 11092 11232 11372 10822 10963 11104 11244 11383 10833 10975 11115 11255 11395 10845 10986 11127 11267 11406 S 1 2 3 4 2 5 7 9 10 11 12 13 14 5.1141b 11557 11G95 1183i 11969 11429 11568 1170C 11843 11980 1411 1580 1717 1855 1991 1453 1591 1729 11866 2003 11464 11603 11740 11878 12014 11476 11614 11752 11889 12025 11467|114'J9 1162611637 1176311775 1190011912 12037|12048 11510 11649 1178G 11923 12059 11522 11660 11793 11934 12071 11533 11672 11809 11946 12082 11545 11683 11820 11957 12093 s 1 2 3 4 2 5 7 9 15 16 17 18 19 5.12100 12240 12375 1-2500 12643 12110 12251 1238G 12520 12654 2127 2263 2397 2532 2665 12139 12274 12409 12543 12676 12150 12285 12420 12554 12687 12161 12296 12431 12565 12698 12173 12184 12308 1231& 1244212453 12576 12587 12709 12721 12195 12330 12465 12598 12732 1220G 12341 1247G 12610 12743 12218 12353 12487 12621 12754 122-^9 12364 12498 12632 12765 s 1 2 3 4 2 4 7 9 20 21 22 23 24 5.12770 12908 13040 13171 13302 12787 12919 13051 13182 13313 2796 2930 3062 3193 3323 12809 12941 13073 13204 13334 12820 12952 13084 13215 13345 12831 12963 13095 13226 13356 1284212853 1297412985 1310613117 13237 13248 13367,13378 12864 12996 13128 13258 13388 12875 128SG 13007 13018 13139 13149 132G9 13280 13399 13410 12897 13029 13160 13291 13421 s 1 2 3 4 2 4 7 9 25 26 27 28 29 5.1343. 13561 13690 13818 13945 1344. 13572 13701 1382& 13956 345b 3582 13711 13839 13967 13464 13593 13722 13850 13977 13475 13604 13732 13860 13988 13486 13615 13743 13871 13998 1349o 13507 13625 I 13G36 1375413765 13882' 13892 14009 14019 13518 13647 13775 13903 14030 13529 13658 13786 13914 14041 13539 136G8 13797 13924 14051 13550 13679 13807 13935 14062 s 1 2 3 4 2 4 7 9 30 31 32 33 34 5.1407. 1419G 14324 14449 14574 I408b 14209 14330 14460 14584 14093 14220 14345 14470 14595 14104 14230 14356 14481 14605 14114 14241 14366 14491 14615 14125 14251 14377 14501 14626 14136 14262 14387 14512 14636 14146 14157 14272 14282 14397 14408 1452214533 14646' 14657 14167 14293 14418 14543 14667 14178 14303 14429 14553 14677 14186 14314 14439 14564 146S8 s 1 2 3 4 2 4 6 8 35 36 37 38 39 5 . 14096 1482 14944 1506C 15188 14708 14832 14954 15076 1519& 14719 14842 149G4 1508" 15208 14729 14852 14975 15097 15218 14739 14862 14985 15107 15228 14750 14872 14995 15117 15238 14760 14771 1488314893 15005 1501E 15127 15137 15248 15258 14780 14903 15026 15147 15269 14790 14913 1503G 15157 15279 14801 14924 15016 15168 15289 14811 14934 15056 15178 15299 s 1 2 3 4 2 4 6 8 40 41 42 43 44 5.15309 1542 C 15549 1566 1578 15319 15439 15559 15678 1579 1532U 15449 15569 15G88 1580" 15339 15459 15579 15698 15817 15349 15469 15583 15708 15827 15359 15479 15599 15718 15837 153691537915389 15489 15499 15509 15609 15619 15629 15728 15738 15748 15846 15856 15866 15399 15409 15519 15529 15639 1564S 15758 15767 15876 1588C 154 li 15539 15659 1577 1 " 15896 1 2 3 4 2 4 6 8 45 46 47 48 49 5.1590c 1602c 1614C 1625t 1637$ 1591 1603 1614 1626 1638 1592 1604 1615 1627 1639 15935 16052 16169 16285 16401 15944 1606$ 1617 1629i 164K 15954 1607$ 16188 16304 1642C 1596^ 1608" 16191 1631' 16481 1 15974 15984 1 16091116101 * 16208 13217 [ 16324 16332 ) 16439 1644C 15991 1611] 1622 r 1634; 16451 ( 16002 1612C 16237 i 16352 ) 16468 16013 16130 16246 163G2 16478 s 1 2 3 4 2 4 6 8 50 51 52 53 54 5. 1648 < 16605 167H 16831 1694J 1649 .1661 J1672 J1683 51695 16501 16621 1673c 1684 16961 16516 16631 1674c 16856 16971 1652t 1664( 1675^ 1686 r 1698( 1653c 1665C 1 1676^ ' 1687 r ) 1699( 165451655416564 16659 16G69 16676 16773167821679$ ' 16886 16896 1690t ) 16999 17008 1701* 1657; 16685 1680 1691; 1 1702' 5'16582 J 16697 1 16813 5 16924 1703( 16592 16707 16820 1693 >1704 s 1 2 3 4 2 4 6 8 55 56 57 . 58 59 5.1705; 1716' 1727* 1738! 17495 >1706 ri7i7 S 1728 )1739 )1750 1707^ 1718( 1729 r 1740* 1751 f 1708; > 1719c ' 1730C } 1741 P j 1752 r ! 1709; . 1720' > 1731, ' 17421 "1753 5 1710; 1 1721^ 5 1732J J 1743; 5 1754, ! 17111 17121 1713( U7223 17232 1724] 517334173431735'. 517444174541746; 5117554175631757; >1713' 1725 > 1736! ] 1747- ] 1758- ) 1714* 1726( 21737] 2 1748] 217591 51715 )172G 1738C L1749 L1760 s 1 2 3 4 2 4 6 8 TABLE XVIII. 285 LOGARITHMS FOR FINDING THE APPARENT TIME OR HORARY ANGLE. Hour. M. Os. 5s. 10s. 15s. 20s. 25s. 30s. 35s. 40s. 45s. 50s. 55s. P.P. 1 2 3 4 % . 51921 5.6775774710 5.2796331509 6318165561 6.8816889959 12127 47345 72333;91715 81147,871399274598011 34916381944135244400 6787770133 72332 74477 91714934349512196775 07551 02976 46345 76570 98399 20941 07672 50193 78614 99992 32539 12127 52951 80611 01557 42770:5192160200 16365 20406 24267 5562358216,60734 8256384172.86340 03095 0460S|OC090 5 6 7 8 9 6.0755008985 23385 24583 3G774 37802 48372 49271 58600 59401 10398 11787 13155 257652693128081 38817 3982W0814 50162 5104J 51916 601946098061759 14502 29217 41795 52780 62531 15828 30337 4276C 53636 6329G 17134 31444 43726 54484 64054 18421 32536 44675 55323 64806 19689 33615 45614 56154 65552 2093822170 3468135734 4654347462 56977 57792 66291 J67024 10 11 12 13 14 6.67751JG847.L 7602876683 8358484185 9053591089 ". 96970 97485 69186 69895 70598 773347797978620 847828537485963 91641 92189,92733 979979850699013 71296 79256 86548 93274 99516 7 1988 79888 87129 93812 00017 72674 80515 87706 94346 00514 73355 81137 88279 94877 01009 74031 81756 88848 95405 01501 7470275367 8236982979 89414*89976 9593096451 01990'02476 8 1 2 3 1 119 238 358 476 15 16 17 18 19 7.02960 08564 13827 18790 23483 03441 09015 14252 19191 23863 03920 04395 0946409910 1467415095 19590 19987 24241 24618 04S69 10354 15513 20383 24993 05339 10796 15930 20776 25366 05807 11236 16344 21168 25738 06273 11673 16756 21558 26108 06736 12108 17167 21947 26477 07196 12541 17575 22333 26844 0765508110 12972113401 1798218387 2271923102 2721027573 3 1 2 3 1 84 168 25',: 336 20 21 22 23 24 7.27986 32171 36209 40067 43760 28297 32515 36537 40380 44061 28656 32857 36864 40693 44361 2901429371 29726 331983353833876 371893751437837 410054131541625 44659,44957(45254 30079 34213 38159 41933 45549 30431 34519 38480 42240 45844 30782 34884 3880d 42546 46138 31131 35217 39118 42851 46430 3147931826 3554935879 3943539752 4315543458 46722 47013 B \ ''I 65 130 195 200 25 26 27 2* 29 7.47302 50706 53980 57135 60179 47591 50983 54247 57393 60428 47879 51260 54514 57650 60676 4816(5 51536 54780 57906 60924 48452 51811 55045 58162 61170 48737 52085 55308 58416 61417 49021 52358 55572 58670 61662 49304 52631 55834 58924 61907 4958(5 52902 56096 59176 62151 49867 53173 56357 59428 62394 5014850427 5344353712 56617 56870 59679,59929 6263662878 s 1 2 3 4 53 106 159 212 3U 31 32 33 34 7.63120 65964 68717 71385 73974 633(50 66196 68942 71604 74186 63600 63839,64078 G6429 66660 66891 69167 69392 69616 71822 72040J72257 7439874609,74819 64310 67121 69839 72473 75030 64553 67351 70061 72689 75239 61790 67580 70283 72904 75448 65026 67809 70505 73119 75657 65261 68037 70726 73334 75865 65490 65730 6826468491 70946i71166 7354873760 7607376280 s 1 2 3 1 45 90 134 178 35 36 37 38 39 7 . 76487 76693 7892979129 8130381498 8361583804 85866 86050 76898 77104|77308|77513 79329 79529f79728 79926 8169381887,8208182274 83994841838437281560 86235864198660386786 77716 7792(JJ78122 801248032280519 824678265982851 847478493585122 869698715287334 78325 78526 772b 807168091281108 83043 83234 83424 853088549485680 8751C 87697,87876 8 1 2 a 4 39 77 116 154 40 41 42 43 44 7.8805988240 90198J90374 9228692457 9432494491 9G315 96478 88419:88599^877888957 90550 90725 90900 91074 92629928009297093141 94659948269499295159 96642968059696897131 8913589314 9124891422 9331193480 95325 95491 97293 97455 89491 91596 93650 95656 97617 89668,89846 90022 917699194192114 9381993987,94156 958219598696150 977789793998100 s 1 2 3 ! 34 68 102 137 45 46 47 48 49 -/ a . 98260,98421 98580 98740 98899 99058 8 . 00163100320 00476 00632 00788 00944 02025:02178 02331 02484 02636 02789 03847 03997 04147 04297 04446 04595 05631:05778 0592506072 06218 06364 99217 01099 02941 04744 06510 99375 01254 03092 04892 06655 99534 01409 03244 05041 06800 99^91 99849 00000 015630171701871 03395 03546,03697 051890533605484 0694507090,07235 s 1 2 3 ! 31 62 92 122 50 51 52 53 54 8.07379,07523 09092 09233 10772 10910 12419 12555 14035 14169 07G67 0781 107934 08097 09374 09515 09656 09796 11048111871132411462 12691 12826 12961 13096 14302 14434 14567 14700 08240 09936 11599 13231 14832 08383 10076 11736 13366 14964 08525 10216 11873 13500 15096 08667 10355 12010 13634 15228 0880908951 1049410633 12147 12283 13768 1390 i 15359 15490 s 1 2 3 1 27 55 82 110 55 56 57 58 59 8.15621 15752 17179 173)7 1870818835 20211J20335 21(588 21810 15883il6013il0144 16274 16404110533 17436 17564' 1769217820 17947 18074 1 8961 19087 : 19212' 1 9338 19463 19588 20459 20583 20706 20830 20953 21076 21932 22053 22175 22296122417(22538 16603 18202 19713 21198 22<;r,;- 1679216921 17i>5< 18329 18455:1858-2 19838 199G3 20087 21321 21444 21560 22779122899:23019 s 1 2 r ; i 25 K< 75 10 286 TABLE XVIII. LOGARITHMS FOR FINDING THE APPARENT TIME OR HORARY ANGLE. 1 Hour. M. Os. 5s. 10s. 15s. 20s. 25s. 30s. 35s. 40s. 45s. 50s. 55s. P. P. 1 2 3 4 8.23140 245G7 25971 27352 28711 23259 24685 26087 27466 28823 23379 24802 26203 27580 28935 23499 24920 26318 27691 29047 23618 25037 26434 27607 29159 .^3737 25155 26549 27921 29271 23856 23975 24094 25272 25389 25505 26664 26779 26894 280342814728260 293S3'29494|29605 24212j24331 2562225738 -7009 27123 28373 28486 29716 29827 24449 25855 27238 28599 29938 s 1 2 3 4 28 46 70 93 5 6 7 8 9 8 . 30049 31366 32G63 33940 35199 3015930270 3147531583 3277032877 3404631151 35303,35407 30380 31692 32984 34257 35511 30490 31800 33091 34362 35614 30GOO .30710 3190932016 33198 33304 3446731572 3571835821 30820 309-9 3212532233 3341033517 34677 34782 35925 36028 31039 32340 33623 34886 36131 31148 32448 33729 34991 36234 31257 32556 33835 35095 36337 s 1 2 3 4 21 42 63 85 10 11 12 13 14 8.3(3439 37062 38866 40055 41226 36542 377(53 3896(5 10153 11323 36044 37864 39066 40251 4J420 36746 37964 39165 10349 41517 36849 36951J37053 37154 38065 38166 38266 3836C 39261 39364 39463 39562 10447405454064240740 41613117101180611902 37256 38467 39660 10837 41998 37358 38567 39759 40935 12094 37459 386G7 39858 41032 12191 37560 38767 39956 41129 12286 s 1 2 3 4 20 40 60 80 15 16 17 18 19 8.4-2382 43522 44647 45757 46852 42177 1361C 14740 15849 16943 12573 437K 14833 15940 17031 12668 13804 14926 4G032 47124 12764 42859 42954 138984399244086 450184511145204 16124 46215 16306 172154730547395 43049 44180 45296 46398 47485 43144 4427C 15388 16489 47575 13236 44367 15481 16580 17665 43333 44460 15573 16671 17755 13427 44554 45665 46762 47844 s 1 2 3 4 18 37 55 74 20 21 22 23 24 8.47934 4900-2 5005G 51098 52127 18024 19090 30144 5118:1 52212 18113 19179 50231 31270 32297 48202 19267 30318 51356 52382 18292 19355 30405 51442 32467 18381 49443 50492 51528 52552 .48470 49531 50579 51614 52636 48559 19619 50G65 51699 52721 18647 19706 50752 51785 52805 1873G 19791 50839 51871 52890 48825 19882 50925 51950 32974 48913 19969 51012 52041 53059 B 1 2 3 4 17 35 52 70 25 26 27 28 29 8.5314b 54147 55139 56120 57089 53227 53311 33395 33479,53563 53646 53730 53814 53897 53981 54064 s 1 2 3 -1 16 33 49 65 34230 35221 54313 55303 54396 35385 34479 54562 54645 554675554955631 54727 55713 54810 55794 54892 5587C 54975 55957 55057 56038 36201 06282 56363 36144 56525 a6G06 36687 56707 56848 56928 57009 37169 o'/249 57330 37410 57490 57569 57619 57729 57809 jV88b 57968 30 31 32 33 34 8.58047 53991 59931 60857 6177^ J812GI 58206 39078 59151 50009 30086 30934 31011 31849 31925 38285 59230 30164 31087 62001 38364 59308 60241 31164 32076 5841358522 5938359464 6031860395 6124061317 62152 62228 58601 39542 60473 31393 32303 58680 59620 60550 61469 62379 38759 59698 G0627 61545 62451 58837 5977( 6070J 61621 62529 58916 59853 60781 G1697 32G04 s 1 2 3 4 15 31 46 62 35 36 37 33 39 8.62671 6357G 64463 65340 66208 32755 33650 34536 65412 6G280 G2830 63724 64609 G5485 66352 32901 G3798 34G83 35558 66424 6-979 63872 34756 65630 .36496 63054 63946 G4829 65703 66567 63129 61020 61902 65775 66639 J3203 64094 G4975 65817 6G710 63278 64168 G5048 65920 66782 63353 64242 65121 35992 66853 63427 G4315 65194 66064 G6925 63502 64389 65267 66136 6699G 3 1 2 3 4 15 29 44 58 40 41 42 43 44 8.07067 67918 6S759 G9593 70418 (5713967209 3798868059 3882968899 G9362 69731 70486,70554 67*81 68129 6S969 G9SOO 70623 07352 68199 39038 39869 70691 67423 68269 69108 G9937 70759 67491 G8340 69177 70006 70827 67561 68110 69247 70075 70895 67635 68480 69316 70141 70963 67706 68550 G9385 7021-2 71031 68620 G9154 7028] 71099 67847 68690 69524 70349 71167 1 2 3 4 14 28 42 56 45 46 47 48 49 8.71234 72043 72814 73637 74123 713u2 71370 7211072177 72910,72977 73703 73768 74488,74553 71437 72244 73043 73834 74618 7150571572 72311 72378 7310973175 73900739G5 74683,74748 71640 72444 73241 74031 74813 71707 72511 73308 7J096 74877 71774 72578 73374 74162 74942 71812 72644 73439 74227 75007 71909 72711 73505 74292 75072 71976 72777 73571 74357 75136 s 1 o 3 4 13 26 40 53 50 51 52 53 51 8.75201 75971 76735 7749- 78241 752657533075391 760357609976163 767987686276925 77551 77617|77680 78303 78365 78427 75458 75523 76227.76290 76988:77051 7774277805 7848978551 75587 76354 77114 77867 78613 75651 76418 77177 77930 78675 75715 76481 77240 77992 78737 75779 76545 77303 78054 78799 75843 76608 77366 78117 78861 75907 76672 77429 78179 78922 K 1 2 a 4 13 25 38 50 55 56 57 58 59 8.78984 79720 80149 81172 81889 79015 79107 79109,79230 79291 79781 79842 79903179964 80025 8051C'80570 80631 80691 80751 31232 31292 81352 81412 81472 81948 82008 82067 32126 82186 79353 80085 80812 81531 82245 79114 80146 8087-2 81591 82304 79475179537 8020780268 8093280992 8165181710 82363182422 79598 80328 81052 81770 824811 79659 80389 81112 81829 82540 s 1 2 3 4 12 21 36 48 LOGARITHMS TABLE XVIII. 287 FOR FINDING THE APPARENT TIME OR HORARY ANGLE. 2 Hours. M. Os. 5s. 10s. 15s Ms 35s 80s 85s 40s 45s 50s 55s. P.P. 1 2 3 4 8.8259i) 83303 84001 84G94 8538(1 82658 32 1 17 3336:; 83420 8405984117 84751 84808 8543785194 82770 83478 84175 84866 85550 8J835 83537 84233 34923 85607 3289L 5 359J 84291 8493C 85664 ( 82952 83653 84348 85037 85721 83011 83711 84406 331 109 33769 44464 ,831^ft 83828 84521 83187 '3388L S457S 8526G 35947 83245 83944 84636 85323 86004 s 1 2 3 4 11 23 34 46 85095 85777 35152 35834 85*09 85891 5 6 7 8 9 8.860GU 83735 87404 830G8 8872G 86117 36791 87460 88123 S8780 36173 86347 87515 88178 S8835 86229 86903 37570 88233 38889 8628d 86959 87626 88288 88944 86342 87014 87681 88342 88938 8639s 87070 37730 88397 8905. 86454 37126 37792 88452 39107 36511 87182 37847 88507 89162 86567 8662; 87237 87293 8790287957 88562*38616 89216*89270 86679 87348 88013 88671 89324 1 2 3 1 11 22 33 44 10 11 .12 13 14 8.89J79 9002G 90668 91306 91938 8943.J 90080 30722 91358 91991- 89487 90133 9077C 91411 92043 89541 90187 J0328 31464 92095 89595 90241 90881 91517 92147 89649 90294 30934 9157( 92200 39/03 90348 90988 91622 92252 89757 90401 91041 91675 92304 89811 90455 91094 91728 92356 89865,89918 9050890562 91147 91200 9178091833 9240892461 89972 90615 91253 91885 92513 s 1 2 3 1 11 21 32 42 lo 16 17 18 19 . 92-j6o 93187 93804 94417 93025 J261V 93239 93856 34488 95075 9266J 93290 93907 94519 9512G 92721 93342 93958 94570 35176 927 /a 93393 94009 94620 95227 9282u 93445 9406C 94671 95277 928/7 9349G 94111 91722 93327 92928 93548 94162 94772 95378 92980 93599 94213 94823 95428 93032 93084 9365193702 9426494315 94874 94924 9547895528 9313.3 93753 94366 94975 95578 s 1 2 3 1 10 20 31 41 '20 21 22 23 21 8 . 95628 96227 93821 97411 9799G 95678 9G277 96871 974GO 980 45 957^8 96326 93920 97503 98091 93/78 96376 96969 97558 98142 95828 96426 97018 97607 98191 95878 9G475 97038 97656 98239 95928 9G525 37117 97701 38288 95978 93574 97166 97753 9833G 36028 9GG24 97215 97802 98384 9607896128 9667396723 9726497313 37851 97893 98433 38481 93178 96772 97362 97948 98529 R 1 2 3 4 10 20 29 39 25 26 27 28 29 8 . 9857s 99154 9.99727 9.00295 008GO 98626 : 98674 99201 93250 99774 09822 00342 00390 00906 00953 3872v 99298 99869 00437 01000 9877U 993 1C 99917 00481 01017 98816 99393 9996 1 00331 01094 98806 93441 00012 00578 01140 98914 99489 00059 00825 01187 98903 9933G 00108 00672 01234 99011J99058 9958439332 0015400201 0071900766 01280J01327 991U6 99G7G 00248 00813 01373 s 1 2 3 i 10 19 29 38 30 31 32 33 34 9.014UO 01976 02528 03077 03G21 0146601513 0202202065 0257402620 0312203168 03667 0371-2 J1559 02114 02366 03213 03757 01606 02161 02712 03259 03802 01G52 02207 02757 03304 03847 01693 02253 02803 03350 03892 0174501791 02299 02345 02849 02894 03395 03140 0393703982 01837101884 0239102437 0294002986 03486:03531 04027,04072 01930 02483 03031 03576 04117 s 1 2 3 4 9 18 28 37 35 33 37 38 39 9. 04162 04G99 04207,04252 0474404788 0429 i 04833 04341 04877 04386 04922 04431 34936 04476 05011 0452004565,04610 0505505099,05144 04651 05188 s 1 2 9 4 9 18 27 36 05232 05762 06288 05277,05321 0580605850 06332'OG375 05365 05894 06419 05409 05938 06462 03453 05982 03506 05493 06025 06550 05542 060G9 06593 05586 06113 06637 0,j630,05674 06157,06200 0668006724 05718 08244 067G7 40 41 42 43 44 9.0381U 07329 07845 08357 08865 OG854 00897 0737207415 07887 07930 0839908442 08907 08949 06940 07458 07973 03484 08992 05934 07501 08016 08526 09034 07027 07544 08058 03569 0907G 070/0 07587 08101 03611 09118 07113 07630 08141 08654 09160 0715707200,07243 G7673 077 16 07759 081860822908271 086960873808781 0923209244:09236 07286 07802 08314 08823 09328 s 1 2 a i 9 17 26 35 45 46 47 48 49 9.09370 09872 10371 10866 11338 09412;09454 0991409955 1041210453 10907| 10948 11399,11440 09496 09997 10495 10989 11480 09538 10039 1053G 11030 11521 09580 10030 10577 11071 11562 09G22 10122 10319 11112 11603 09363. 10163 10630 11153 11643 09705 10205 10701 11194 11684 09747 09789 10246 10288 10742 10784 1123511276 1172511765 09830 10329 10825 11317 11806 s 1 2 9 1 8 17 25 34 50 51 52 53 54 9.11847 12332 12815 13295 13771 118871192811968 12373,12113 12453 12855 12895 12935 13334,13374113414 13811 13850 13S90 12009 12494 12975 13454 13929 12050 12534 13015 13491 13969 12090 12574 13055 13533 MOOS 12130 12614 13095 13373 14048 12171! 12655 13135 13613 14037 1221112252 12695 12735 13175 13215 13652 13692 14126 141G6 12292 12775 13255 13732 14205 s 1 1 I! 1 8 16 24 32 55 56 57 53 59 9.14215 14715 15183 15647 16109 14284 1 1754 15221 15686 16147 11323 14793 15260 15724 16186 14362 14832 15299 15763 16224 14102 14871 15338 15802 16262 14441 14910 15377 15840 16301 14430 14919 15415 1587S) 16339 14519 14988 15151 15917 10377 11559J 14593 15027 15066 15193 15531 15935 15994 16415116453 14637 15105 15570 16032 16492! 14676 15144 15609 16071 16530 s 1 J 3 1 8 15 23 30 288 LOGABITHMS TABLE XVIII. FOE FINDING THE APPAEENT TIME OB HOEAEY ANGLE. 3 Hours. M. OS. 5s. 10s. 15s. 20s. 25s. 30s. 35s. 40s. 45s. 50s. 55s. P.P. 1 2 3 4 9 . 16568 17024 17477 17928 18376 16GU8 16644 1706217100 17515,17553 17963 18003 18413 18450 16682 17138 17590 18040 18487 167ZOJ1G758 16796 171751721317251 17628 17665 17703 18077|18115 18152 18524 18561 18598 1G834 17289 17740 18189 18636 16872 17326 17778 18227 18G73 16J10 17364 17815 18264 18710 1694816986 17402 17440 17853 17890 1830118338 18747 18784 s 1 2 3 4 7 15 22 30 5 6 7 8 9 9.18821 19263 19703 20140 2057J 18858 18o'95 19300 19337 19739,19776 20176:20213 2061120647 189Jz 19373 19812 20249 20683 189G8irJOUO 19042 19410 19447 19483 198491988519922 2028520321^0358 207192075520791 19079 19520 19958 20394 20827 19116 19557 19995 20430 20863 19153 19593 20031 2046G 20899 1919U 19226 19630 19666 20067 20104 20502 20538 20935 20970 s 1 2 3 4 7 14 22 29 10 11 12 13 14 9.2100G 21436 21863 22287 22709 2104221078 2147121507 21898 21934 22322 22358 22744 22779 21513 219G9 22393 22814 2115021186,212^1 21578'21G14 21650 22001)2204022075 2242822463 22498 228492288422919 21257 21685 22111 22533 22934 21293 21721 22146 22569 22989 21329 21756 22181 22604 23024 213G4 ; 21400 21792)21827 2221622252 22639 22674 2305923094 s 1 2 3 1 7 14 21 28 15 16 17 18 19 9.23128 23345 23960 24372 24782 2316323198 2358023615 23994 24029 2440G 24441 2481G 24850 23233 23649 24063 24475 24884 23268 23684 24098 24509 2i918 23302 23337 2371823753 24132124166 24543 24577 24952 2498G 23372 23788 24201 24612 25020 23407 23822 24235 24646 25054 23441 23857 2426C 24680 25088 23470 23891 24304 24714 25122 23511 23926 24338 24748 25156 8 1 2 ,1 20 27 20 21 22 23 24 9.25190 25595 25998 2G398 26797 25224 25629 26031 26432 26830 25257 256G2 2GOG5 26465 26863 25291 25696 26098 26498 2G89G 25325 25359 25393 25729:25763 2579C 261322616526198 265322656526598 26929 2G9G2 26995 25420 25830 26232 26631 27028 25460 25864 26265 26664 27061 25494 25897 26298 26697 27094 25527 25931 26332 26731 27127 25561 25964 26365 26764 27160 s I I 7 13 20 26 25 '26 27 28 29 9.27193 27587 27979 28368 28756 27226 27620 28011 28401 28788 27259 27652 28044 28433 28820 27292 27685 28076 28465 28852 ^7325)27357 27718)27751 2810928141 2819828530 2888528917 27390 -.7783 28174 28562 28949 27-423 27816 28206 28595 28981 27456 27848 28239 28627 29018 27489 27881 28271 28659 29045 27521 27914 28304 28691 29077 27554 27946 2833G 28724 29109 s I 3 4 6 13 19 26 30 31 32 33 34 9.29141 29524 29905 30285 30661 2917329205 29550 29588 29937 29969 30316 30347 3069330721 29237 29620 30000 30379 30755 29269 29652 30032 30410 30787 29301 29683 30064 30442 30818 29333 29715 30095 30173 30849 29365 29747 30127 30505 30880 29397 29779 30158 30536 30912 29429 29810 30190 30567 30913 29461 29493 29842 29874 30221 30253 30599:30630 30974J31005 s 1 2 3 4 6 12 18 25 35 36 37 38 39 9.31036 31409 31780 32149 32516 31068 31099 3144031471 31811 31842 3218032210 32547 32577 31130 31502 31873 32241 3260S 311613119231223 315333156431595 319033193431965 32272 32302 32333 32638 32668 32699 31254 31626 31996 32363 32729 34285 31657 32020 32394 32760 31310 31688 32057 32425 32790 31347 31378 3171931749 3208832119 32455 32486 3282032851 s 1 2 3 4 6 12 18 24 40 41 42 43 44 9.32881 33244 33603 33965 34322 32911132942 33274 33304 33635,33665 33994 34024 34352 34381 329 // 33002 33033 33063 33335333653339533425 33695 33725 33755 33785 34054340843411434143 34411 34441 34470 34500 33093 33455 33815 34173 34529 33123 33485 33845 34203 34559 33154 33515 33875 34233 34589 3318433214 33545J33575 33905133935 3426234292 3461834648 s 1 2 3 i 6 12 18 24 45 46 47 48 49 9.34677 35031 3538C 35733 36081 34707 34736 35060 35090 3541235441 35762:35791 3G110|36139 34766 35119 35470 35820 36167 347953482534854 351483517835207 35499 35529 35S58 3584935878:35907 36196|36225|36254 31884 35236 35587 3593G 36283 34913 3526C 35616 35965 36312 349433497235002 35295 35324 35353 ?5645 35674 35703 35994 36023 36052 3634136369,36398 s 1 2 3 4 6 12 17 23 50 51 52 53 54 9.36427 36771 37114 37455 37794 36456)36485 3680036829 37143:37171 3748437512 3782337851 36513 36857 37200 37540 37879 3G542 36886 37228 37568 37907 j3657Jj36599 3691536943 37257:37285 37597J37625 3793537963 36628 36657136686 36714.36743 36972 37000 37029 37057 37086 37313 37342 37370 37C99 37427 37653 37682 37710 37738,37766 37991 38020 38048 38076 38104 s 1 2 3 4 6 11 17 23 55 66 57 58 59 9.38132 38468 38802 39134 39465 38100J38188I38216 38496 38524'38551 38830,38857 38885 391623918939217 39492'39520'39547 38244 I 38272 I 38300 38328 38579 38607|38635 38663 38913389403896838996 39245392723930039327 39575 39602 t 39630l39657 3835(j 38691 39024 39355 39684 38384 38412:38440 3871838746)38774 390513907939107 393823941039437 I39712I39739'39767 s 1 2 3 4 (i 1 22 TABLE XVIII. 289 LOGARITHMS FOB FINDING THE APPARENT TIME OR HORARY ANGLE. 4 Hours. M. Os. 5s 10s 15s 90s 9,5s 80s 35s 40s 45s 50s 55s P.P. u 1 2 3 4 y 39794'3962 1 M6-i\) 3957(3.39903 39931 39958 39985 40012 40040 40007 40121 40149 10176 40203 40230 40257 40281 40312 10339 40366 40393 40447 : 40474 10501 40528 40555 40582 4060'J 10636 40663 40690|40717 40771 40798 10825 40852J40879 40906 40933 4096040986 4101341041 41094411214114741174:41201412281125441281413084133541361 40094 40420 10741 41067 41388 s 1 2 3 4 5 11 16 22 5 6 7 8 9 9.4141511411 4173441761 4205242078 42368 12394 42682 42709 41468 4149-3 41521 41048 41787 J 1814 41840 41867 42105421311215742181 424-2042447 1247342499 12735 4276 1 14277 428 1 3 41575 41893 42210 42525 42839 1160141628 41920 4194G 4223642263 42562^2578 42865 42891 11654 41972 1228'J 12604 42917 41681 41999 42315 42630 12943 41707 42020 42312 12606 42969 s 1 2 3 i 5 10 16 21 10 11 ia 13 14 9. 42996 43307 43617 43925 44232 13022 43333 43643 43951 44258 430184307443100 43359 43385 ! 13111 4366943691 1372( 33977 44002 44028 442834430944334 43125 13436 43746 44054 14360 43151 43462 43771 44079 4438.3 4317743203 4348843514 43797 43823 1410544130 4441144436 13229 43540 43848 44156 41462 43255 43565 43874 44181 44487 43-81 43591 43900 44207 44513 s 1 2 3 1 5 10 15 20 lo 16 17 18 19 9.4403S 44842 45144 45416 45745 44563 14867 45m 15471 45770 14-J8944614 4489244918 1519545220 4519845.321 457954.3820 1463'J 41943 45245 1554G 45845 146uO 44968 4-3270 15571 15870 11690 14993 15295 15595 45894 14715 14741 4501945011 45320 45340 45620 45645 40919 15944 41760 45069 45370 45670 45969 44791 45094 45395 45695 45994 44817 15119 15420 45720 46018 s 1 2 3 i 5 10 15 20 20 21 22 23 24 9.4G043 46340 4G635 46929 47222 4G006 46360 46660 46954 1724G 160934611S 4638946414 16G84 46709 1697847002 172704729.3 16142 46439 4.J733 17027 47319 46167 16163 16758 17051 47343 4619- 46488 16782 47076 47367 4621746241 46512 46537 4G807 46831 4710047124 47392 474 1C 46266 46-^91 46562 46586 4685G 46880 47149 47173 47440 47464 46315 46611 46905 47197 47489 s 1 2 3 1 5 10 15 20 26 26 27 28 89 9.4751317537 47803 17827 48091 18115 48378 4S10L 4866448687 4756147585 1785147875 1813918163 1812648449 1871l'48735 47610 47899 48187 48473 48758 17634 1792o 18211 48497 48782 47658 47947 48235 18521 18806 17682 47706 47971 17995 4825848282 48540 485G8 4883018853 47/30 48019 48306 48592 48877 47754 48043 48330 48616 48900 17779 18067 48351 48640 48924 s 1 2 3 1 5 10 11 19: 30 31 32 33 34 9.4894848971 49231 4925J 49512! 19536 4979349816 50071|50095 18995 19019 19278'493Q1 19-359 19583 1983919862 5011850141 19042 19325 19GOU 19S8G 50164 49066 49348 49629 19909 30187 49089 19372 49653 49932 50211 19113,49137 49395.49419 1967G'49699 49956149979 0023450257 49160 19442 49723 50002 50280 19181 49465 49746 00025 50303 19_07 49489 497G9 50048 50326 a I 3 i 5 9 14 19 35 36 37 38 39 9.50349 50626 50901 51174 51447 50372 30649 50924 31197 31470 5039550418 3067250391 30916 50969 3122051243 3149251515 50441 50717 30992 51265 31538 50465 30740 51015 51288 31560 50188 50763 51038 51311 51583 0001150531 50786 00809 3106051083 5133451356 5160551628 50057 50832 51106 51379 51651 00580 50855 51129 51402 51673 50603 50878 51102 51424 51696 s 1 2 3 ! J 18 4U 41 42 43 44 9.51718 51988 52257 52525 52791 31741 52011 32279 52547 52813 31763 51766 32033 5205G 32302 52324 52569,52591 52835;52857 31808 52078 52346 52G13 52879 31831 52100 32369 52636 32901 51853 52123 52391 52658 52923 51876,51898 52145,52168 5241352435 5268052702 52946 02968 31921 52190 52458 52724 52990 51943 52212 52480 52747 53012 519G6 52235 52502 52769 53034 s I 2 3 l 4 9 13 18 45 46 47 48 49 9.5305653078 5332053342 5358253604 5384453865 54104 54126 53100,53122 533154 53385 5362653648 .3388753909 54147 541G9 53144 .33107 53670 33931 54190 33166 33429 53691 53952 54212 331885321053232 .334515347353195 53713 53735 33757 339745399654017 54234 54255)54277 53254 33517 53778 54039 54298 53276 53539 53800 54061 54320 33298 53560 53822 54082 54341 a 1 2 3 i 4 9 13 18 4 9 13 17 50 51 52 53 54 9 . 54363 54385|54406 54428 54449 54621 54642 54GG4o4685 54707 5487854899 5492054941 549G3 5513355154551755519755218 55387 55409,55430 55151 55472 34471 54728 54984 35239 55493 544925451454535 547495477154792 54556 54813 54578 54835 34599 54856 s 1 2 :; i 35005 55027 55048 55069 55260 -55282 55303(55324 35514155535 55-5.5i; ">.">. >77 55091 55345 55598 55112 35366 55619 55 56 57 58 59 9.55641 55893 56144 56393 56642 55662155683 55914 -3.3934 56164B6185 5641456435 56663 ! 56683 3.370 1: 35725 5574(5 35955 55976 55997 3620056227 56248 55767J55788 55809 56018 56039 56060 562695628956310 55830 56081 56331 55851 56102 56352 5GG01 56818! 55872 3612;) 36372 56621 56Sr,'.) s 1 9 3 1 4 8 13 17 36156.36476 5670156725 66497 56745 565185653856559:56080 56766156786 56807 56828 290 . TABLE XVIII. LOGARITHMS FOR FINDING THE APPARENT TIME OR HORARY ANGLE. 5 Hours. 1C. Os. 5s 10s 15s 20s. 35s 80s 35s 40s 45s 50s. 55s P. P. 1 2 3 4 ( J. 5(5889 5713G 573S1 57G25 578G8 36910 57156 37402 57646 37889 56931 37177 57422 57666 37909 56951 57197 57442 57686 57929 56972 56992 5721857238 574G3 57483 57706 57727 57949 57969 57013 57259 57503 57747 37990 57033 37279 57524 57767 58010 57054 57299 57544 57787 38030 57074 57320 57564 57808 58050 5709557115 57340 57361 57585 57605 57828 57848 58070 58090 a l 2 3 4 4 8 12 16 5 6 7 8 9 9.58110 5835J 58591 58830 590G8 38131 58371 58611 38850 39087 38151 58391 58631 58870 59107 38171 3$411 38651 38889 59127 58191 58431 58671 58909 59147 58211 58451 38691 58929 39166 18231 38471 58711 38949 39186 58251 58491 58731 58969 59206 38271 58511 58750 38988 39225 38291 58531 58770 59008 59245 5831158331 58551 58571 5879058810 5902859048 59265 59285 s 1 2 3 4 4 8 12 16 10 11 12 13 14 9.59304 59540 59774 G0008 G0240 59324 59559 59794 30027 30260 59344 59579 59813 60017 60279 393G3 59599 59833 30066 (50298 59383 59618 59852 60085 30318 59403 59638 59872 60105 G0337 59422 39657 59891 30124 6035C 59442 59677 59911 60144 G0375 39461 5969G 39930 60163 60395 594S1 59716 59950 60182 60414 59501-59520 5973559755 59969 59988 6020260221 60433,60452 s 1 2 3 4 4 8 12 16 15 1G 17 18 19 9.60472 G0702 60931 61160 G1387 6049 J 30721 30951 31179 3140G 3051U 60740 G0370 31198 G1425 60529 60760 60989 61217 151444 60549 30779 61008 G123G 61463 60568 60798 61027 61255 G1482 U0j&7 60817 31046 61274 61500 GOG06 60833 G1065 G1293 61519 60625 60855 61084 61311 31538 G0645 60874 61103 61330 61557 6066460083 6089360912 6112261141 6134961368 6157G 61595 s 1 2 3 4 4 8 11 15 20 21 22 23 24 9.61013 61839 62063 62287 62509 G103- 31858 G2082 G2305 32527 61651 G1876 62100 62324 G2546 31670 131895 62119 G2342 G2564 G1G89 61914 32138 62361 32583 61708 61932 62156 62379 62601 G172G 31951 G2175 32398 62620 61745 G1970 G2194 G2416 G2G38 131764 6198& 62212 62435 62657 61783 62007 62231 62453 62675 G1801 61820 62026 62045 62249 62268 6247262490 6269362712 s 1 2 3 4 4 7 11 15 25 26 27 28 29 9.62730 62951 63170 G3389 63606 J2749 62969 .33188 G3407 63624 32767 32987 63207 63425 63G42 32785 33006 33225 63443 33660 32804 33024 33243 33461 G3C78 62822 63042 63261 33479 63696 G2841 63061 63279 63497 63715 G2859 63079 63298 63516 63733 G2877 63097 63316 63534 G3751 62896 63115 63334 63552 63769 62914;62932 G3134 63152 6335263370 63570 63588 63787 63805 s 1 2 3 4 4 7 11 1C 30 31 32 33 34 9.63823 64038 64253 64467 64G79 63841 3405G 34271 34484 64G97 G3859 64074 64289 64502 61715 G3877 84092 64307 64520 64732 (3389563913 6411064128 3432464342 G4538 64555 3475064768 G3931 64146 64360 G4573 G4785 63949 64164 64378 64591 64803 639GG 64181 64395 64609 64821 639856400264020 641996421764235 64413 64431 64449 G4G26 64644 64662 64838 G485G 64873 s 1 2 3 4 4 7 11 14 35 3G 37 38 39 9.64891 65102 65312 65521 65729 34909 65120 65330 65539 G5747 G492G 65137 65347 G555G 65764 G4944 65155 35365 65573 65781 64962 35172 65382 65591 S5799 64979 65190 65399 65608 65816 64997 65207 65417 65625 65834 65014 65225 65434 65643 65850 65032 G5242 65452 65660 65868 65050 65260 654G9 G5677 65885 65067 G5085 6527765295 6548G ! G5504 6569565712 65902 G5919 s 1 2 3 4 7 10 14 40 41 42 43 44 9.65937 6G143 66348 66553 G6757 35954 G6160 66366 66570 66774 65971 66177 66383 6G587 GG791 65986 36194 66400 66604 36807 66000 GG212 66417 66621 6G824 66023 G6229 66434 66638 66841 GG040 66246 66451 66655 G685S GG057 66263 66468 66672 66875 G6074 66280 66485 66689 6G892 66092 66297 66502 66706 66909 06109.66126 66314G633J 6651966536 6672366740 6692666943 s 1 2 3 4 7 10 14 45 4G 47 48 49 9.66959 67161 67362 67562 67762 66976 67178 67379 67579 67778 66993 67195 67396 G759G 67795 67010 G7027G7044 G72 12 67228 67245 G7412'G7429 G7446 67612 67629 G7646 678116782867844 67060 67262 67462 67662 67861 67077 G7279 G7479 67679 67878 67094 67295 67496 67G95 67894 67111 67312 67512 67712 67911 67 128 67 144 6732967346 67529;67546 6772967745 67927,67944 8 1 2 3 4 1 1 50 51 52 53 54 9.67960 68158 68354 68550 68745 67977 68174 68371 68566 68761 67993 68190 68387 68583 68777 680106802668042 G8207 68223 68240 684036842068436 685996861568631 68794 G8810 68826 68059 6825G 68452 68648 68842 G8075 68272 G84G9 686G4 G8858 0809L 68289 68485 68680 68874 681U8 68305 68501 68696 68891 68125,68141 6832268338 68517|G8534 68713,68729 6890768923 s 1 2 3 4 1 1 55 56 57 58 59 9.68939 69132 69325 69516 69707 68955 G9148 G9341 G9532 69723 68971 69164 69357 69548 69739 168987 69004 69020 6918169197 G9213 G9373 69389 69405 69564 G9580G9596 IG9755G9770G9786 69036 69052 6922969245 69421 G9437 69G12 G9C28 !69802l6981b 69068 69261 69453 69614 69834 69084 69277 69469 69G60 169850 69100,69116 6929369309 6948169500 6967569691 69866169881 8 1 2 3 4 6 10 18 TABLE XVIII. 291 LOGARITHMS FOR FINDING THE APPARENT TEME OR HORARY ANGLE. 6 Hours. M. Os. 5s. 10s. 15s. 20s. 25s. 30s. 35s. 40s. 45s. 50s. 55s. P.P. 1 2 3 4 9.098976991369929 7008670102,70118 70274 70-29070306 70462:7047770193 70618170664 70G80 69944 70133 70321 70539 70695 69960 70149 70337 70524 70710 69976 70165 70353 70540 70726 69992 70007 7018070196 7036870384 70555 70571 7074170757 70023 70211 70399 70586 70772 700397005570070 702277024370259 70415,7043170446 70602j706 17 70633 707887080370819 s 1 2 3 4 3 6 9 12 5 6 7 8 9 9.7U8347085070865 710197103571050 712037121971234 713877140271417 715697158.J71GOO 70881 71065 71249 71433 71615 70896 71081 71265 7 1448 7163J 70911 71096 71280 71463 71645 70927 70942 7111171127 7129571310 7147871493 7166071676 78958 71142 71326 71509 71691 709737098871004 711577117371188 713417135671371 715247153971554 7170671721 71736 B 1 2 a 4 3 6 9 12 10 11 12 13 14 9.717517176671781 719327194771962 721127212772142 72292 72307:72322 72471 7248572500 71797 71977 72157 72337 72515 71812 71992 72172 72352 72530 71827 72007 72187 72366 72545 71842 72022 72202 72381 72560 71857 72037 72217 72396 72574 71872 72052 72232 72411 72589 71887 7190271917 720677208272097 7224772262^72277 72426,72441 72456 72604,7261972634 s 1 2 3 4 3 6 9 12 15 16 17 18 ia 9. 72648 72663/2678 728257284072855 730027301673031 731777319273207 73352 73367 73381 72693 72870 73046 73221 73396 72708 72881 73060 73236 73410 72722 72899 73075 73250 73425 7273772752 72914 72928 73090 73104 73265 73279 73439 73454 72767 72943 73119 73294 73468 72781 7279672811 729587297272987 731347314873163 733097332373338 734837349773512 s r 2 3 4 3 6 9 12 20 21 22 23 24 9 .73526 73541 73555 73699 73714 73728 738727388673901 74044 74058i7-4072 74215 74229,74243 73569 73743 73915 74087 74257 73584 73757 73929 74101 74272 73598 73771 73944 74115 74286 7361373627 73786 73800 7395S 73972 7412974144 7430074314 73642 73656 73671 73685 73815738297384373858 73987 74001 74015 74029 74158741727418674200 74328 74342,74357 74371 s 1 2 3 4 3 6 9 12 25 26 27 28 29 9.74385 74554 74723 74891 75059 74399 74413 7456974583 74737 74751 7490574919 75072 75086 74427 74597 74765 74933 75100 74442 74611 74779 74947 75114 74456 74625 74793 74961 75128 74470 74639 74807 74975 75142 74484 74653 74821 74989 75156 74498 74667 74835 75003 75170 74512 74526)74540 74681J74695 74709 74849,74863174877 75017 75031 75045 75183 75197J75211 s 1 2 3 4 3 5 8 11 30 31 32 33 34 y. 75225 75239 75253 753917540575418 7555G 75570,75583 75720 75734 75748 75884 7589S 75911 75267 75432 75597 75761 75925 7528U 75446 75611 75775 7593S 75294 75160 75625 75789 75952 75308 75322 7547475487 75638 75652 7580275816 75966 75979 75336 75501 75666 75830 75993 75349,7536,; 7551575528 75679 75693 75843 75857 76006 76020 753V7 75542 75707 75870 76033 B J 9 -1 3 5 8 10 35 36 37 38 39 9.76047 76209 76371 76531 76691 7606076074 76223 76236 7638476397 76545 76558 76705 76718 76088 76250 76411 76571 76731 76101 76263 76424 76585 76745 76115 76276 76438 76598 76758 76128 76290 76451 76611 76771 76142 76303 76464 76625 76784 76155 76317 76478 76638 76798 761697618276196 763307634476357 7649l'76505 76518 760517666576678 768117682476838 s 1 2 3 4 3 5 8 10 40 41 42 43 44 9.76851 77009 77167 77325 77481 76864 76877 7702377036 7718177194 7733877351 77494 77507 76891 77049 77207 77364 77520 76904 77062 77220 77377 77533 76917 77075 77233 77390 77546 7693076943 7708977102 77246 77259 7740377416 7755977572 76957 77115 77272 77429 77585 76970 77128 77285 77442 77598 76983 77141 77298 77455 77611 76996 77154 77312 77468 77624 s 1 2 3 -1 3 5 8 10 45 4G 47 48 49 9.776377765077663 77792 77805 77s is 779477796077972 781017811378126 782547826678279 77676 77831 77985 78139 78292 77689 77844 77998 78152 78305 77702 77857 78011 78164 78317 77715J77728 7787077882 7802478037 78177J78190 7833078343 77741 77895 78019 78203 78355 7775477766 7790877921 7806278075 78215,78228 7836878381 77779 77934 78088 78241 78393 s 1 a 3 ! 3 5 8 10 50 51 52 63 54 y. 78406:78419 78431 78558,7857078583 787097872178734 78859 78872J78884 79009 7902 1J79034 78444 7859G 78747 78897 79046 78457 78608 78759 78909 79059 78469 78621 78772 78922 79071 78482 78495 7863378646 7878478797 7893478947 7908479096 78507 78659 78809 78959 79108 78520 78533 78671 78684 78822,78834 78972 78984 79121J79133 78545 78696 78S47 78997 79146 s 1 a 3 1 2 5 7 10 55 56 57 58 59 9.791587917079183 79306,7931979331 794547946679179 79601 79613 7962G 79748 79760^79772 79195 79343 79491 79638 79784 79^08 79356 79503 79650 79796 79220 79368 79515 796G2 7: (SO* 7923279245 79380,79393 795287954(1 79674 79687 7982179833 79257 79405 79552 79699 79845 792697928279294 794177943079442 79564,7937779589 797117972379735 798577986979881 8 1 9 3 1 2 5 7 10. 7 . _ , . 292 TABLE XVIII. LOGARITHMS FOR FINDING THE APPARENT TIME OR HOEAEY ANGLE. 7 Hours. M. Os. 5s. 10s. 15s., .20s. 25s. 30s. 35s. 40s. 45s. 50s. 55s. P.P. 1 2 3 4 9.7989379905 800C8 30050 80183 80195 80327 80338 8047080482 79918 80063 80207 80350 30494 (9930*9942 8007580087 302,1980231 8036288874 30505 80J17 7'J954 80099 80243 S0386 S0529 79966 30111 80255 S0398 80541 79978 80123 80267 30410 80553 79990 80135 30279 80422 80565 80602 80147 80291 30434 80577 80014 80159 30303 30446 30588 80J-^6 80171 30315 30453 30600 s 1 2 3 4 2 5 7 9 5 6 7 8 9 9.80612 80754 80895 81036 81176 80624 80766 S0907 8L047 81187 80636 80778 30910 81059 31199 S0648 307S9 80930 31071 31211 80660 30801 80942 31082 81222 30671 80813 80954 31094 31234 30633 30695 8082580836 8096C 80977 8110681117 3124531257 30707 80848 80989 81129 81269 30719 80860 81001 31141 31280 30730 30872 81012 31152 31292 8UV42 30883 81024 81161 81303 s 1 2 3 4 2 5 7 9 10 11 12 13 14 9.81315 81454 81592 81729 818% 31326 31465 81600 81740 31877 J133S 81477 81614 81752 31888 31350 31488 31626 31763 31900 81361 31500 31637 31775 81911 81373 31511 31649 31786 31922 8138431396 3152331534 3166081672 31797 31809 8193^81945 81407 31546 8168S 8182C 81956 31419 31557 31695 31831 31968 81430 81569 3170C 31843 81979 3144-2 31580 31717 31854 319CO s 1 a 3 4 2 5 7 9 15 16 17 18 19 9.82002 82137 8-2272 82406 82540 82013 32148 82283 32417 32551 82024 321GC 32294 82429 32562 32036 82171 32306 32440 32573 82047 82182 32317 32451 8258] 32058 82193 82328 32462 32595 32070 32205 82339 82473 82606 32081 82216 32350 82484 32618 82092 $2227 82362 82495 82629 32103 82238 32373 32507 32640 82115 82250 82334 82518 32651 32126 82261 32395 32529 32662 s 1 2 3 4 2 4 7 9 20 21 22 23 24 9.82673 82805 82937 83068 83199 82G84 32810 82948 83079 33210 32695 82827 82959 33090 83220 8-706 82838 32970 33101 83231 82717 82849 32981 83112 33242 82728 82860 32992 83123 83253 32739 32871 33003 83134 83264 82750 32882 330W 83144 83275 32761 82893 83025 83155 83285 3-772 82901 83035 83166 33296 32785 82915 83046 83177 33307 82794 32926 33057 83188 83318 s ! | 2 4 7 9 25 26 27 28 29 9.83329 83458 83587 83715 83842 83339 83469 S3597 33725 33853 33350 33179 3360S 83736 33863 33361 33490 33619 33747 33874 83372 83501 836-29 83757 3388Z 33383 83512 33640 33768 83895 33393 33522 83651 83779 83906 34031 84159 34284 84409 84533 83101 33533 83662 83789 83916 83415 83544 83672 83800 33927 8342683436 8355583565 8368383691 33811 53821 33938 83948 33447 83576 33704 83832 33959 B I I 2 4 7 9 30 31 32 33 34 9.83969 8409G 84221 84346 84471 <3980 81106 34232 84357 34481 3399U 34117 34242 34367 84492 84001 84127 84253 84378 84502 34011 8413& 84:163 34388 84512 34022 34148 34274 84398 84523 84013 84169 34294 84419 34543 84054 84179 84305 34430 84554 34064 84075 34190 34200 84315 8432C 84440 84450 J4564 84574 84U85 84211 34336 34461 84585 S 1 2 3 -i 2 4 6 8 35 36 37 38 39 9.84595 84718 84841 84983 85085 3400.: J4729 84851 84973 35095 34616 31739 318G1 84984 85105 84626 34636 3474984759 8187234882 34994'85004 8511585125 84646 84769 34891 35014 35135 34657 34780 81902 35024 35145 84667 84790 84912 85034 85155 84677 84800 84923 85044 85166 31687 34810 34933 85051 85176 84696 34821 84943 85065 85186 84708 84S31 84953 85075 35196 s 1 2 3 4 2 4 6 8 40 41 42 43 44 9. 155206 85216J85226 35236 85246 85256 85266 85276 85286 35296 85306 65316 s ] 2 3 4 2 4 6 8 85326185336I35346 8544G 83456 85466 85565 85575 85585 85684 8569-185704 85356 35366 8547685486 8559585605 8571485724 85376 85496 85615 85733 8538C 85396 8550G 85516 85625 85635 8574b 85753 85406 8552C 85645 85763 35416 85426 8553685546 8565485661 8577385783 85436 85555 85674 85792 45 46 ' 47 t 48 49 9.85802 85920 86037 86153 8G269 35812 85822 85930 35939 3604686056 861633617k 86279 86288 8583285841 85949 35959 86066 8G07C 861823619; 8629886307 35851 85969 86085 86201 36317 8-38(51 85871 85978 85988 8609586105 86211 86221 8632786336 85881 85998 86114 86230 86346 85890 85900 8600886017 8612486134 8624086250 8635686365 85910 86027 86143 86259 86375 s 1 2 3 4 2 4 6 8 50 51 5 3 53 54 9.86384 86499 86613 86727 86840 86394'3G403 8650986518 86623 86632 8673686746 8684986858 86413*6423 8652*6537 8664S86651 8675586764 86868,86877 86432 S6547 86661 86774 86887 8644286451 8655686566 8667086679 8678386793 8689686905 86461 86575 86689 86802 86915 86470|36480 86585,86594 8669886708 8681286821 8692486933 86439 86604 86717 86830 86943 s 1 2 3 4 2 4 6 8 55 56 57 58 59 9.869528696286971 87064 3707387083 871758718587194 87286 37295 87305 8739G8740G 87415 3698086990 8709287101 8720337212 87314 87323 37424:87433 86999 87008 87018 87027 37111871208712987138 87222 87231 87240 87249 87332873113735187360 87442874518746087470 87036 87045 87055 871488715787166 87259,8726887277 873698737887387 874798748887497 s 1 2 3 4 ! 2 4 6 8 -I TABLE XVIII. 293 fJARITHMS FOR FINDING THE APPARENT TIME OR HORARY ANGLE. 8 Hours. M. Os. 5s. 10s. 15s. 20s. 25s. 30s. 35s. 40s. 45s. 50s. 55s. P. P. 1 2 3 4 9.8750687515 87G15 87624 8772487733 8783287841 87939,87948 87524 87633 87742 87850 87957 87534 87643 87751 87859 8796G 87543 87652 8776C 87868 87975 ;87552,75G1 87661 187670 877G9 37778 87877,87886 87984 3799.3 87570 87679 87787 37895 38002 87579 37688 3779G 87904 88011 87588 87697 87805 87913 8802C 87597 8770G 87814 37921 88029 87606 87715 87823 87930 88038 8 1 2 3 1 2 4 5 7 5 G 7 8 9 9.86046 88153 83259 88364 884G9 88055 8316-2 88268 38373 88478 88064 88170 38270 88381 88486 88073 38179 38285 38390 88495 88082 38188 38294 38399 38503 38091 88197 88303 38408 88512 88100 38206 88311 3841G 38521 88109 88215 38320 38425 88530 38117 88223 38329 38434 88538 8812li 88232 88338 38443 88547 88135 38241 38346 88451 38556 88144 38250 88355 88460 88565 s 1 2 3 4 2 4 5 7 10 11 12 13 14 9.88o73 83677 88780 83882 83984 88582 8868( 88789 38891 8899S 88590 3809.1 33797 3389D 89001 33591 88703 3880G 38908 3901C 88GO< 38711 88814 88910 =9018 586 It 38720 88823 38925 39027 88025 387-28 38831 38933 89035 38634 38737 88840 38942 39044 j864k 88745 88848 88950 J905-2 38651 88754 88857 83959 39061 3865'J 38763 38865 38967 89069 38068 88772 38874 38976 39078 8 1 2 3 4 2 4 5 7 15 16 17 18 19 9.83080 89187 89287 89387 80487 3909. 89196 39296 89396 89495 39lOo 39204 8930J 39401 89503 39112 89213 39313 3941S 39512 3912CJ 89221 39321 39421 89520 39129 39229 39330 39429 89528 39137 89237 39338 89437 39536 39145 39246 8934C 39446 89545 39l5o 39254 39354 89454 39553 39102 3926S 39363 39462 89561 39170 89271 39371 89470 39569 3917U 33279 89379 39479 39577 s 1 2 3 4 2 4 5 7 20 21 22 23 24 9.89580 89684 89782 89879 8997G 39o96 89693 39790 89888 3998J 39602 39701 J979S 39S9G 3999-1 39611 3970C 89807 80904 9000C 39019 39717 39815 399K 9000S 89o27 89725 39823 39920 9001C j9G35 39733 89831 ,9926 90024 39643 89741 39839 89936 90032 89651 89749 39847 39944 9004( 396GC 89758 8985C 8995-2 9004!- 89GGb 3976G 898G3 89960 90056 89676 39774 89871 89968 90064 s 1 2 a 4 2 3 5 6 25 26 27 28 29 9.9iJ072 90168 90263 90358 90452 30080 90176 90271 9036C 90460 JUOob 9018J 90279 J037,! 901G8 900% 3019- 30287 90382 3017( 90104 30200 30295 90390 90484 90112 30208 30303 30398 9049. 90120 90216 90311 30405 30499 30128 30224 90319 90413 90507 3013G 30232 90327 90421 90515 90144 30240 90335 9042C 3052E 90152 90248 90342 30437 30531 90160 90256 90350 90445 90539 s 1 2 3 1 2 3 5 6 3'J 31 32 33 34 9.90546 90639 90732 90824 90916 90551 90647 90740 90832 90921 90562 90655 90747 90840 J0331 30570 90663 30755 90848 30939 J0577 30670 .30763 30855 30946 90585 90678 90771 90863 90954 90593 90686 90778 30870 90962 30G01 30694 90786 30878 90970 30G08 90701 90794 90885 90977 90610 .30708 90802 90893 )0985 90624 90717 90809 90901 30992 30032 90725 90817 90909 91000 s 1 2 3 1 2 3 5 6 35 36 37 38 39 9. 9 1007 91098 91188 91277 913G7 31015 31106 9119G 31285 91374 9102:; 91113 91203 31292 31331 31030 31121 91211 31300 91389 91037 31128 91218 31307 9139G 31015 91136 31226 31315 91104 9105291060 9114331151 9123391241 3132291330 9141191419 31067 91158 91248 91337 9142G 31075 9116C 91255 91345 91433 31083 91173 91262 91352 31440 91091 91181 91270 91360 91448 s 1 a 3 i 2 3 5 6 40 41 4-2 43 44 9.91455jt>14'J3 9154391531 91631I91638 91718^91725 91805,91812 3147U 31558 91645 91732 91819 31478 91566 91653 31740 9182G 3148u 31573 91660 91747 31833 91492 91580 91667 91754 91841 91499 E)1587 31674 31761 31848 31507 91595 31682 31769 31855 91514 91602 91689 91776 31862 91522 91609 91696 31783 91869 3152y 91616 31703 91790 91870 91536 91624 91711 31798 31884 s 1 a a 4 2 3 5 6 4j 46 47 48 49 9.9189191898 91976 91984 92061 92069 9214692153 3^80,92237 91900 31991 92076 92160 92244 91912 91938 92083 92167 92251 31919 92005 92090 32174 92258 31927 91934 919411 920129201992026 920979210492111 92181 9218892195 922G5 92272 92279 31948 32033 32118 32202 32286 91955 92040 92125 92209 92293 31962 92047 92132 92216 92300 31969 32054 32139 32223 92307 s 1 2 3 4 1 3 4 6 50 51 52 53 54 9. 92314 923-21 92397 92404 9248092487 9256292569 9264392650 92328 92411 92493 92575 9265? 32335 92418 32500 92582 92664 32342 32425 92507 325.N9 12070 92349 92355 92302 924329243892445 925149252192528 9259G92G03 92610 92677,92684 92691 32369 32452 32534 32616 32698 92370 92459 92541 92623 32705 32383 92466 92548 92630 32711 32390 32473 32555 J2637 32718 s 1 9 :i I 1 3 4 6 55 56 57 58 59 9 . 92725 92732 92738 92745 92805928129281992826 92885928929289992906 929G5 92972 92978 92985 93041;93051 93057193064 32751 92832 92912 92992 93071! 327589-276592772 928399284592852 929199292592932 929999300593012 930789308493091 32778 32859 32939 33018 33097 32785 32866 32j)46 33025 (3101 32792 92872 32952 33031 93110 32799 32879 32959 33038 33117 s 1 2 a 4 1 1 3 4 6 294 TABLE XIX. ^ TO FIND THE LATITUDE BY AN ALTITUDE OF THE POLE STAB.- Subtracted if the R. A. is found in this column. Correction. Added if the R. A. is found in this column. H. M. H. M. H. M. H. M. 7 10 19 10 7 10 19 10 7 00 19 20 3 7 20 19 00 G 50 19 30 7 7 30 18 50 6 40 19 40 1 11 7 40 18 40 G 30 19 50 15 7 50 18 30 G 20 20 00. 18 8 00 18 20 G 10 20 10 21 8 10 18 10 6 00 20 20 25 8 20 18 00 5 50 20 30 29 8 30 17 50 5 40 20 40 32 8 40 17 40 5 30 20 50 36 8 50 17 30 5 20 21 00 39 9 00 17 20 5 10 21 10 42 9 10 17 10 5 00 21 20 45 . 9 20 17 00 4 50 21 30 48 9 30 16 50 4 40 21 40 51 9 40 16 40 4 30 21 50 54 9 50 16 30 4 20 22 00 56 10 00 16 20 4 10 22 10 59 10 10 16 10 4 00 22 20 1 02 10 20 16 00 3 50 22 30 1 04 10 30 15 50 3 40 22 40 1 06 10 40 15 40 3 30. 22 50 1 08 10 50 15 30 3 20 23 00 1 10 11 00 15 20 3 10 23 10 1 13 11 10 ^- 10 2 50 23 30 1 17 11 30 14 50 2 30 23 50 1 19 11 50 14 30 2 10 10 1 21 12 10 14 10 1 40 40 1 23 12 40 13 40 1 10 1 10 1 24 13 10 13 10 TABLE XX. 295 AMPLITUDES. DECLINATION. Lat. 1 2 3 4 5 6 70 8 9 1

THE SUN'S RIGHT ASCENSION AND DECLINATION. Equation of Time, to be added to Apparent Time. Var. in 1 hour. Apparent Right Ascension Var. in 1 hour Apparent Declination. Var. in 1 hour Friday . . . 1 h. in. s. 22 49 11.96 S. 9.360 S. 7 30 56' 4 57.05 m. s. 12 32.33 s. 0.495 Saturday . Sunday . . 2 O 22 52 56.35 22 56 40.25 9.339 9.319 7 8 4.0 6 45 5.6 57.31 57.55 12 20.20 12 7.58 0.516 0.536 Monday . Tuesday . Wednes'y 4 r\ G 23 23.68 23 4 6.66 23 7 49.20 9.300 9.282 9.264 6 22 1.5 5 58 52.2 5 35 38.0 57.78 57.99 58.18 11 54.49 11 40.95 11 26.98 0.555 0.573 0.591 Thursday Friday . . . Saturday . 7 8 23 11 31.32 23 15 13.04 23 18 54.37 9.247 9.230 9.215 5 12 19.4 4 48 56.8 4 25 30.5 58.36 58.52 58.66 11 12.58 10 57.79 10 42.61 0.608 0.624 0.640 Sunday . . Monday . Tuesday . 10 11 1-2 23 22 35.34 23 26 15.97 23 29 56.26 9.200 9.18G 9.172 4 2 1.0 3 38 28.7 3 14 53.9 58.79 58.90 58.99 10 27.07 10 11.19 9 54.97 0.655 0.669 0.682 Wednes'y Thursday Friday . . . 13 14 23 33 36.24 23 37 15.94 23 40 55.36 9.160 9.148 9.137 2 51 17.0 2 27 38.4 2 3 58.6 59.07 5913 59.18 9 38.45 9 21.63 9 4.55 0.695 0.706 0.717 I Saturday . Sunday . . Monday . 1C 17 18 23 44 34.53 23 48 13 48 23 51 52.23 9.127 9.119 9.111 1 40 17.7 1 16 36.2 52 54.4 59.22 5924 59.24 8 47.22 8 29.66 8 11.90 0.727 0.736 0.744 Tuesday . Wednes'y Thursday 19 20 21 23 55 30.80 23 59 9.23 2 47.54 9.104 9.099 9.094 29 12.6 S. 5 31.2 N. 18 9.6 59.23 59.21 59.18 7 53.97 7 35.89 7 17.70 0.750 0.756 0.760 Friday . . . Saturday . Sunday . . 22 23 24 6 25.75 10 3.89 13 41.99 9.091 9.088 9.087 41 49.5 1 5 28.1 1 29 5.1 59.14 59.08 59.00 6 59.41 6 41.05 6 22.64 0.764 0.766 0.768 Monday . Tuesday . Wednes'y 25 2(5 27 17 20.05 20 58.10 24 36.16 9.086 9.086 9.086 1 52 40.0 216 12.5 2 39 42.3 58.90 58.80 58.68 6 4.20 5 45.75 5 27.31 0.769 0.769 0.768 Thursday Friday . . . Saturday . Sunday . 28 21) JO Jl 28 14.25 31 52.38 35 30.58 39 8.85 9.088 9.090 9.093 9.097 3 3 9.0 3 26 32.2 3 49 51.6 4 13 6.7 58.54 58.39 58.22 58.03 5 8.89 4 50.52 4 32.21 4 13.98 0.766 0.764 0.7C1 0.757 303 TABLE XXI. MARCH, 1878. Page 2. AT MEAN NOON. * o M O 1 o o o p THE SUN'S RIGHT ASCENSION AND DECLINATION. Equation ot Time, to be subtracted from Mean Time. Apparent light Ascension Apparent Declination. Semi- diameter. Friday ..... 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1*7 18 19 20 21 22 23 24 25 26 27 28 29 30 31 h. m. s. 22 49 10.00 22 52 54.43 22 56 38.37 23 21.83 23 4 4.85 23 7 47.43 23 11 29.59 23 15 11.35 23 18 52.73 23 22 33.74 23 26 14.41 23 29 54.74 23 33 34.77 23 37 14.51 23 40 53.98 23 44 33.20 23 48 12.19 23 51 50.98 23 55 29.60 23 59 8.08 2 46.43 6 24.69 10 2.88 13 41.02 17 19.13 20 57.23 24 35.34 28 13.47 31 51.65 35 29.89 39 8.21 S. 7 3l' 8.3 7 8 15.8 6 45 17.2 6 22 13.0 5 69 3.5 5 35 49.1 5 12 30.3 4 49 7.5 4 25 41.0 4 2 11.3 3 38 38.7 3 15 3.6 2 51 26.5 2 27 47.7 2 4 7.5 1 40 26.4 1 16 44.6 53 2.5 29 20.4 S. 5 38.7 N. 18 2.4 41 42.6 1 5 21.5 1 28 58.8 1 52 34.1 2 16 6.9 2 39 37.0 3 3 4.0 3 26 27.5 3 49 47.2 4 13 2.6 16 I0''l 16 9.9 16 9.6 16 9.4 16 9.1 16 8.9 16 8.6 16 8.4 16 8.1 16 7.9 16 7.6 16 7.3 16 7.1 16 6.8 16 6.5 16 6.3 16 6.0 16 5.7 16 5.5 16 5.2 16 4.9 16 4.7 16 4.4 16 4.1 16 3.8 16 3.5 16 3.2 16 3.0 16 2.7 16 2.4 16 2.1 in. s. 12 32.44 12 20.31 12 7.69 11 54.60 11 41.06 11 27.09 11 12.69 10 57.90 10 42.73 10 27.19 10 11 30 9 55.08 9 38.56 9 21.74 9 4.66 8 47 32 8 29.76 8 12.00 7 54.07 7 35.99 7 17.79 6 59.50 6 41 13 6 22.72 6 4.27 5 45 82 5 27.38 5 8.96 4 50.58 4 32.27 4 14.04 Saturday .... Monday Tuesday Wednesday . Thursday . . . Friday Saturday .... Sunday Monday .... Tuesday .... Wednesday Thursday . . . Friday Saturday Sunday Monday Tuesday Wednesday . Thursday . . . Friday Saturday Sunday Monday .... Tuesday .... Wednesday . Thursday . . Friday . . Saturday . . . Sunday 304 TABLE XXI. APRIL, 1878. Page 1. AT APPARENT NOON. i o o !>> c5 ft Day of the Month. THE SUN'S RIGHT ASCENSION AND DECLINATION. Equation of Time . to be added to Var. in 1 hour. Apparent Right Ascension Var. in 1 hour. Apparent Declination. Var. in 1 hour. subt. from Apparent Time. Monday . Tuesday . Wednes'y 1 2 8 h. in. s. 42 47.23 46 25.72 50 4.34 8. 9-101 9.106 9.112 N. 4 36 17 '2 4 59 22.8 5 22 23.1 57.84 57.62 57.39 m. s. 3 55.85 3 37.84 3 19.95 8. 0.753 0.748 0.742 Thursday Friday . . . 4 5 53 43.11 57 22.04 9.119 9.126 5 45 17.7 6 8 6.2 57.15 56.89 3 2.22 2 44.65 0.735 0.728 Saturday . e 1 1 1.16 9.134 6 30 48.3 56.61 2 27.26 0.720 Sunday . . Monday . Tuesday . 7 8 9 1 4 40.47 1 8 20.00 1 11 59.75 9.143 9.152 9.161 6 53 23.7 7 15 52.0 7 38 12.8 56.33 56.02 55.70 2 10.07 1 53.08 1 36.33 0.712 0.703 0.693 Wednes'y Thursday Friday. . . to 11 12 1 15 39.74 1 19 19.99 1 23 0.50 9.172 9.182 9.194 8 25.7 8 22 30.'4 8 44 26.7 55.36 55.02 54.66 1 19.81 1 3.55 47.55 0.683 0.672 0.661 Saturday. Sunday . . Monday . Tuesday . Wednes'y Thursday 13 14 15 1G 17 18 1 26 41.30 1 30 22.41 1 34 3.84 1 37 45.62 1 41 27.77 1 45 10.30 9.206 9.220 9.234 9.249 9.264 9.281 9 6 14.1 9 27 52.4 9 49 21.2 10 10 40 2 10 31 49.2 10 52 47.8 54.29 53.90 53.50 53.08 52.66' 52.22 31.84 16.44 1.36 0.648 0.635 0.621 0606 0.591 0.574 13 38 27.75 41.73 Friday . . . Saturday . 19 20 1 48 53.24 1 52 36.61 9.298 9.316 11 13 35.9 11 34 13.0 51.77 51.31 55.31 1 8.46 0.557 0.539 Sunday . . 21 1 56 20.42 9.335 11 54 38 8 50.84 1 21.17 0.520 Monday . Tuesday . Wedues'y 22 23 24 2 4.69 2 3 49.42 2 7 34.63 9.354 9.374 9.394 12 14 53.1 12 34 55.4 12 54 45.5 50.35 49.85 49.33 1 33 43 1 45.22 1 56.53 0.501 0.481 0.461 Thursday Friday . . . Saturday . 25 20 27 2 11 20.34 2 15 6.55 2 18 53.26 9.415 9.436 9.457 13 14 23.0 13 33 47.5 13 52 58.7 48.79 48.24 47.69 2 7.35 2 17.67 2 27.48 0.440 0.419 0.398 Sunday . . Monday . Tuesday . 2H 21) 30 2 22 40.50 2 26 28.27 2 30 16.57 9.479 9.501 9.524 14 11 56.4 14 30 40.0 14 49 9.4 47.11 46.52 45.92 2 36.77 2 45.53 2 53.76 0.376 0.354 0.332 305 TABLE XXI. APRIL, 1878. Pages. AT MEAN NOON. i u * -u 3 >> a Q Day of the Month. THE SUN'S EIGHT ASCENSION AND DECLINATION. Equation of Time, to be subtracted from Apparent Right Ascension Apparent Declination. Semi- diameter. added to Mean Time. Monday .... Tuesday .... Wednesday . Thursday . . . Friday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 h. m. s. 42 46.63 46 25.16 50 3.83 53 42.65 57 21.63 1 1 0.79 1 4 40.14 1 8 19.71 1 11 59.50 1 15 39.54 1 19 19.83 1 23 0.38 1 26 41.22 1 30 22.37 1 34 3.84 1 37 45.66 1 41 27.84 1 45 10.41 1 48 53.39 1 52 36.79 1 56 20.63 2 4.93 2 3 49.69 2 7 34.94 2 11 20.67 2 15 6.91 2 18 53.65 2 22 40.92 2 26 28.71 2 30 17.03 N. 4 36 13.4 4 59 19.3 5 22 19.9 5 45 14.8 6 8 3.6 6 30 46.0 6 53 21.7 7 15 50.3 7 38 11.3 8 24.5 8 22 29.5 8 44 26.0 9 6 13.6 9 27 52.1 9 49 21.1 10 1.0 40.4 10 31 49.6 10 52 48.4 11 13 36.7 11 34 14.0 11 54 40.0 12 14 54.4 12 34 56.9 12 54 47.1 13 14 24.7 13 33 49.3 13 53 0.7 14 11 58.4 14 30 42.2 14 49 11.6 16 l.S 16 1.6 16 1.3 16 1.0 16 0.7 16 0.5 16 0.2 15 59.9 15 59.7 15 59.4 15 59.1 15 58.9 15 58.6 15 58.3 15 58.1 15 57.8 15 57.6 15 57,3 15 57.0 15 56.8 15 56.5 15 56.2 15 56.0 15 55.7 15 55.5 15 55.2 15 55.0 15 54.7 15 54.5 15 54.2 m. s. 3 55.90 3 37.88 3 19.99 3 2.25 2 44.68 2 27.29 2 10.09 1 53.10 1 36.34 1 19.82 1 3.56 47.56 31.85 16.44 1.36 Saturday .... Sunday Monday .... Tuesday .... Wednesday . Thursday . . . Friday Saturday .... Sunday Monday Tuesday .... Wednesday . Thursday . . . Friday 13.38 27.76 41.74 55.32 1 8.47 1 21.18 1 33.44 1 45.23 1 56.54 2 7.36 2 17.68 2 27.49 2 36.78 2 45.55 2 53.78 Saturday . . . Sunday Monday .... Tuesday .... Wednesday . Thursday . . . Friday Saturday .... Sunday ' Monday .... Tuesday .... 306 TABLE XXI. MAY, 1878. Page 1. AT APPARENT NOON. V 9 O Q c X M- z > c; THE SUN'S RIGHT ASCENSION AND DECLINATION. Equation of Time, to be subtracted from Apparent Time. Var. in 1 hour. Apparent Right Ascension Var. in 1 hour Apparent Declination. Var. in 1 hour Wednes'y Thursday Friday . . . 1 9 r h. m. s. 2 34 5.42 2 37 54.81 2 41 44.76 s. 9.547 9.570 9.593 m. s. S. 0.309 0.286 0.263 N.15 7 24.1 15 25 23.9 15 43 8.5 45.29 44.67 44.03 3 1.45 3 8.59 3 15.19 Saturday . Sunday . . Monday . 4 5 6 2 45 35.26 2 49 26.31 2 53 17.91 9.616 9.639 9.662 16 37.4 16 17 50.3 16 34 47.0 43.37 42.70 42.02 3 21.23 3 26.72 3 31.65 0.240 0.217 0.194 Tuesday . Wednes'y Thursday 7 8 c 2 57 10.07 3 1 2.79 3 4 56.06 9.685 9.708 9.731 16 51 27.1 17 7 50.3 17 23 56.4 41.32 40.61 39.89 3 36.04 3 39.87 3 43.15 0.171 0.148 0.125 Friday. . . Saturday . Sunday . . 10 11 12 3 8 49.88 3 12 44.25 3 16 39.17 9.754 9.777 9.800 17 39 44.9 17 55 15.7 18 10 28.3 39.15 38.40 37.64 3 45.87 3 48.06 3 49.69 0.102 0.080 0.056 Monday . Tuesday , Wednes'y 13 14 15 3 20 34. G5 3 24 30.70 3 28 27.31 9.824 9.847 9.870 18 25 22.6 18 39 58.4 18 54 15.3 36.88 3610 35.31 3 50.76 3 51.27 3 51.22 0.033 0.010 0.014 Thursday Friday . . . Saturday . 1C 17 18 3 32 24.48 3 36 22 23 3 40 20.54 9.894 9.918 9.941 19 8 13.1 19 21 51.6 19 35 10.5 34.51 33.70 32.87 3 50.60 3 49.41 3 47.66 0.038 0.061 0.085 Sunday . . Monday . Tuesday . 19 20 21 3 44 19.42 3 48 18.86 3 52 18.86 9.965 9.988 10.012 19 48 9.5 20 48.4 20 13 7.0 32.04 31.20 30.34 3 45.35 3 42.47 3 39.04 0.108 0.131 0.155 Wednes'v 22 3 56 19.42 10.035 20 25 4.9 29.48 3 35.05 0.178 Thursday Friday . . . 23 24 4 20.52 4 4 22.15 10.057 10.079 20 36 42.0 20 47 57.9 28.60 27.72 3 30.52 3 25.46 0.200 0.222 Saturday . Sunday . . Monday . 25 27 4 8 24.31 4 12 26.98 4 16 30.17 10.101 10.122 10.143 20 58 52.4 21 9 25.3 21 19 36.3 26.82 25.91 25.00 3 19.87 3 13.76 3 7.15 0.244 0.265 0.286 Tuesday . Wedues'y Thursday Friday . . . 28 29 3, Jl 4 20 33.86 4 24 38.01 4 28 42.62 4 32 47.68 10.163 10.182 10.201 10.220 21 29 25.3 21 38 51.9 21 47 56.1 21 56 37.5 24.08 23.14 22.20 21.25 3 0.05 2 52.48 2 44.45 2 35.97 0.306 0.325 0.344 0.362 307 TABLE XXI. MAY, 1878. Page 2, AT MEAN NOON. 4 3 *o * n Day of the Month. THE SUM'S RIGHT ASCENSION AND DECLINATION. Equation of Time, to be added to Mean Time. Apparent Right Ascension Apparent Declination. Semi- diameter. "Wednesday Thursday . . . Friday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 20 27 28 29 30 31 h. m. s. 2 34 5.90 2 37 55.31 2 41 45.28 2 45 35.79 2 49 26.8G 2 53 18.48 2 57 10.65 3 1 3.38 3 4 56.66 3 8 50.49 3 12 44.86 3 16 39.79 3 20 35.28 3 24 31.33 3 28 27.94 3 32 25.11 3 36 22.86 3 40 21.17 3 44 20.04 3 48 19.48 3 52 19.47 3 56 20.02 4 21.11 4 4 22.73 4 8 24.87 4 12 27.53 4 16 30.70 4 20 34.36 4 24 38.49 4 28 43.09 4 32 48.12 N.15 i 26". 4 15 25 26.3 15 43 10.9 16 39.8 16 17 52.8 16 34 49.5 16 51 29.6 17 7 52.8 17 23 58.9 17 39 47.4 17 55 18.1 18 10 30.7 18 25-25.0 18 40 0.7 18 54 17.5 19 8 15.3 19 21 53.7 19 35 12.5 19 48 11.5 20 50.4 20 13 8.9 20 25 6.7 20 36 43.7 20 47 59.5 20 58 53.9 21 9 26.7 21 19 37.6 21 29 26.5 21 38 53.0 2L 47 57.1 21 56 38.5 15 54~0 15 53.7 15 53.5 15 53.3 15 53.1 15 52.8 15 52.6 15 52.4 15 52.2 15 52.0 15 51.8 15 51.6 15 51.4 15 51.2 15 51.0 15 50.8 15 50.6 15 50.4 15 50.2 15 50.0 15 49.9 15 49.7 15 49.5 15 49.3 15 49.2 15 49.0 15 48.8 15 48.7 15 48.5 15 48.4 15 48.2 m. s. 3 1.46 3 8.61 3 15.20 3 21.24 3 26.73 3 31.67 3 36.05 3 39.88 3 43.16 3 45.88 3 48.06 3 49.69 3 50.76 3 51.27 3 51.21 3 50 60 3 49.41 3 47.66 3 45.34 3 42.46 3 39.03 3 35.04 3 30 51 3 25.44 3 19.85 3 13.75 3 7.14 3 0.04 2 52.47 2 44.43 2 35.96 Saturday Sunday Monday Tuesday .... Wednesday . Thursday . . . Friday . . Saturday .... Sunday Monday .... Tuesday Wednesday . Tluirsday . . . Friday Saturday .... Sunday Monday .... Tuesday .... Wednesday . Thursday . . . Fiiday Saturday .... Sunday Monday .... Tuesday .... Wednesday . Thui'sday . . . Friday 308 TABLE XXI. JUNE, 1878. Page 1. AT APPARENT NOON. 1 g c8 P S c THE SUN'S RIGHT ASCENSION AND DECLINATION. Equation of Time to be subt. from Var. in 1 hour. IE Apparent light Ascension Var. in 1 hour. Apparent Declinati'on. Var. in 1 hour. added to Apparent Time. Saturday . Sunday . . Monday . 1 2 3 h. m. s. 4 36 53.16 4 40 59.04 4 45 5.30 S. 10.237 10.253 10.268 N.22 4 56' 1 22 12 51.5 22 20 23.7 20.29 19.32 18.35 m. s. 2 27.07 2 17.78 2 8.10 s. 0.379 0.395 0.411 Tuesday . Wednes'y Thursday 4 5 4 49 11.92 4 53 18.87 4 57 26.13 10.283 10.296 10.308 22 27 32.4 22 34 17.6 22 40 39.1 17.37 16.39 15.40 1 58.07 1 47.70 1 37.03 0.425 0.438 0.451 Friday . . . Saturday . 7 8 5 1 33.67 5 5 41.48 10.320 10.331 22 46 36.6 22 52 10.1 14.40 13.40 1 26.07 1 14.85 0.462 0.473 Sunday . . c 5 9 49.54 10.341 22 57 19.6 12.39 1 3.38 0.483 Monday . Tuesday . Wedues'y 10 11 12 5 13 57.83 5 18 6.33 5 22 15.03 10.350 10.358 10.366 23 2 4.8 23 6 25.7 23 10 22.3 11.38 10.36 9.35 51.68 39.77 27.67 0.492 0.500 0.508 Thursday Friday . . . Saturday . 13 14 15 5 26 23.90 5 30 32.92 5 34 42.09 10.373 10.379 10.385 23 13 54.5 23 17 2.1 23 19 45.1 8.33 7.30 6.28 15.39 2.96 0.515 0.521 0.526 9.62 Sunday . . Monday . Tuesday . 10 17 18 5 38 51.38 5 43 0.76 5 47 10.23 10.389 10.393 10.396 23 22 3.5 23 23 57.3 23 25 26.4 5.25 4.23 3.19 22 31 35.10 47.97 0531 0.535 0.537 Wednes'y Thursday Friday . . . 19 2( 21 5 51 19.75 5 55 29.31 5 59 38.88 10.398 10.399 10.399 23 26 30.6 23 27 10.1 23 27 24.7 2.16 1.13 0.09 1 0.90 1 13.86 1 26.84 0.539 0.540 0.541 Saturday Sunday . . Monday ir 2, 6 3 48.45 6 7 57.98 6 12 7.47 10.398 10.397 10.394 23 27 14.5 23 26 39.5 23 25 39.6 0.94 1.98 3.01 1 39 81 1 52.76 2 5.65 0.540 0.538 0.535 Tuesday Wednes'y Thursday 25 21 2" 6 16 16.88 6 20 26.18 6 24 35.36 10.390 10.385 10.379 23 24 15.0 23 22 25.6 23 20 11.5 4.04 5.07 6.10 2 18. 4G 2 31.1" 2 43. 7G 0.532 0.527 0.521 Friday . . ' Saturday Sunday . 2S 2! 3( 6 28 44.39 6 32 53.25 6 37 1.90 10.373 10.365 10.356 23 17 32.7 23 14 29.4 23 11 1.0 7.13 8.15 9.17- 2 56.20 3 8.4f 3 20.52 0.515 0.507 0.498 309 TABLE XXI. JUNE, 1878. Page 2, AT MEAN NOON. 3 * < -u "8 i- Q Day of the Month. THE SUN'S RIGHT ASCENSION AND DECLINATION. Equation of Time, to be added to Apparent Right Ascension Apparent Declination. Semi- diameter. subtracted from Mean Time. Saturday .... Sunday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 h. m. s. 4 36 53.57 4 40 59.43 4 45 5.67 4 49 12.26 4 53 19.18 4 57 26.40 5 1 33.92 5 5 41.70 5 9 49.73 5 13 57.98 5 18 6.45 5 22 15.11 5 26 23.94 5 30 32.93 5 34 42.06 5 38 51.31 5 43 0.66 5 47 10.09 5 51 19.57 5 55 29.09 5 59 38.63 6 3 48.16 6 7 57.66 6 12 7.11 6 16 16.48 6 20 25.75 6 24 34.89 6 28 43.89 6 32 52.71 6 37 1.32 N.22 i 56.9 22 12 52.3 22 20 24.4 22 27 33.0 22 34 18.1 22 40 39.5 22 46 37.0 22 52 10.4 22 57 19.8 23 2 5.0 23 6 25.9 23 10 22.4 23 13 54.5 23 17 2.1 23 19 45.1 23 22 3.5 23 23 57.3 23 25 26.3 23 26 30.6 23 27 10.1 23 27 24.7 23 27 14.5 23 26 39.5 23 25 39.7 23 24 15.1 23 22 25.8 23 20 11.8 23 17 33.1 23 14 29.8 23 11 2.1 15 48~1 15 48.0 15 47.9 15 47.7 15 47.6 15 47.5 15 47.4 15 47.3 15 47.2 15 47.1 15 47.0 15 46.9 15 46.8 15 46.7 15 46.6 15 46.6 15 46.5 15 46.5 15 46.4 15 46.3 15 46.3 15 46.2 15 46.2 15 46.1 15 46.1 15 46.1 15 46.0 15 46.0 15 46.0 15 46.0 m. s. 2 27.06 2 17.76 2 8.08 1 58.05 1 47.69 1 37.02 1 26.06 1 14.84 1 3.37 51.68 39.77 27.67 15.39 2.96 Monday Tuesday .... Wednesday . Thursday . . . Friday. . Saturday . . . Sunday Monday Tuesday .... Wednesday . Thursday . . . Friday Saturday Sunday 9.62 22.31 35.10 47.96 1 0.89 1 13.85 1 26.83 1 39.80 1 52.74 2 5.63 2 18.44 2 31.15 2 43.74 2 56.18 3 8.44 3 20.50 Monday Tuesday Wednesday . Thursday . . . Friday Saturday Sunday Monday .... Tuesday .... Wednesday . Thursday . . . Friday Saturday .... Sunday 310 TABLE XXI. JULY, 1878. Page 1. AT APPARENT NOON. jj o o HJ 'o fr p Day of the Month. THE SUN'S RIGHT ASCENSION AND DECLINATION. Equation of Time, to be added to Apparent Time. Var. in 1 hour. Apparent Right Ascension Var. in 1 hour. Apparent Declination. Var. in 1 hour Monday . Tuesday . Wednes'y 1 2 3 h. m. s. 6 41 10.32 6 45 18.47 6 49 26.33 s. 10.345 10.331 10.321 N.23 7 9' 4 23 2 53.0 22 58 12.4 10.18 11.19 12.19 m. s. 3 32.35 3 43.91 3 55.18 S. 0.487 0.476 0.463 Thursday 4 6 53 33.88 10.307 22 53 7.7 13.19 4 6.14 0.450 Friday . . . Saturday . 5 G 6 57 41.09 7 1 47.94 10.293 10.278 22 47 39.2 22 41 46.9 14.18 15.17 4 16.77 4 27.03 0.435 0.420 Sunday . . Monday . Tuesday 7 8 9 7 5 54.41 7 10 0.48 7 14 6.14 10.261 10.244 10.227 22 35 31.0 22 28 51.7 22 21 49.3 16.15 17.12 18.09 4 36.91 4 46.40 4 55.48 0.404 0.387 0.369 Wednes'v 10 7 18 11.37 10.209 22 14 23.5 19.05 5 4.13 0.351 Thursday Friday. . . 11 12 7 22 16.16 7 26 20.50 10.190 10.171 22 6 35.0 21 58 23.7 20.00 20.94 5 12.34 5 20.10 0.333 0.314 Saturday . Sunday . Monday . 13 11 15 7 30 24.37 7 34 27.77 7 38 30.67 10.151 10.131 10.110 21 49 49.9 21 40 53.7 21 31 35.3 21.87 2280 23.72 5 27.39 5 34.21 5 40.54 0.294 0.274 0.253 Tuesday . Wedues'y Thursday 10 17 Ib 7 42 33.07 7 46 34.96 7 50 36.34 10.089 10.068 10.047 21 21 55.0 21 11 52.8 21 1 29.1 24.64 25.54 26.43 5 46.37 5 51.69 5 56.49 0.232 0.211 0.189 Friday . . . Saturday . Sunday . . ID 20 21 7 54 37.20 7 58 37.52 8 2 37.30 10.025 10.002 9.979 20 50 44.0 20 39 37.7 20 28 10.6 27.32 28.20 29.06 6 0.78 6 4.53 6 7.74 0.167 0.145 0.122 Monday . Tuesday . Wednes'y 22 23 21 8 6 36.53 8 10 35.21 8 14 33.33 9.957 9.933 9.910 20 16 22.7 20 4 14.3 19 51 45.7 29.92 30.77 31.61 6 10.41 6 12.53 6 14 09 0.100 0.077 0.053 Thursday Friday . . . Saturday . 25 2G 27 8 18 30.89 8 22 27.87 8 26 24.27 9.886 9.862 9.838 19 38 57.2 19 25 49.0 19 12 21.4 32.43 33.25 34.05 6 15.09 6 15.51 6 15.36 0.030 0.006 0.019 Sunday . . Monday . Tuesday . Wednes'y 28 2!) 3 31 8 30 20.08 8 34 15.30 8 38 9.91 8 42 3.90 9.813 9.788 9. 762 9.737 18 58 34.6 18 44 29.1 18 30 5.1 18 15 22.8 34.84 35.61 36.38 37.14 6 14.61 6 13.27 6 11.33 6 8.77 0.044 0.068 0.094 0.119 311 TABLE XXI. JULY, 1878. Page 2. AT MEAN NOON. Day of the Week. Day of the Month. THE SUN'S RIGHT ASCENSION AND DECLINATION. Equation of Time, to be subtracted from Mean Time. Apparent Right Ascension Apparent Declination. Semi- diameter. Monday .... Tuesday .... Wednesday . Thursday . . . Friday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 h. m. s. 6 41 9.71 6 45 17.83 6 49 25.66 6 53 33.17 6 57 40.35 7 1 47.17 7 5 53.61 7 9 59.66 7 14 5.30 7 18 10.51 7 22 15.28 7 26 19.60 7 30 23.45 7 34 26.82 7 38 29.71 7 42 32.10 7 46 33.98 7 50 35.35 7 54 36.19 7 58 36.50 8 2 36.28 8 6 35.51 8 10 34.18 8 14 32.30 8 18 29.86 8 22 26.84 8 26 23.25 8 30 19.06 8 34 14.28 8 38 8.90 8 42 2.90 N.23 1 id'.O 23 2 53.7 22 58 13.2 22 53 8.6 22 47 40.2 22 41 48.1 22 35 32.3 22 28 53.1 22 21 50.7 22 14 25.1 22 6 36.7 21 58 25.5 21 49 51.8 21 40 55.8 21 31 37.6 21 21 57.4 21 11 55.3 21 1 31.7 20 50 46.7 20 39 40.6 20 28 13.5 20 16 25.7 20 4 17.5 19 51 49.0 19 39 0.6 19 25 52.5 19 12 24.9 18 58 38.3 18 44 32.8 18 30 88 18 15 26.6 15 4G"0 15 46.0 15 46.0 15 46.0 15 46.0 15 46.0 15 46.0 15 46.1 15 46.1 15 46.1 15 46.2 15 46.2 15 46.3 15 46.3 15 46.4 15 46.4 15 46.5 15 46.5 15 46.6 15 46.7 15 46.7 15 46.8 15 46.9 15 47.0 15 47.1 15 47.2 15 47.3 15 47.4 15 47.5 15 47.6 15 47.7 m. s. 3 32.32 3 43.88 3 55.15 4 6.11 4 16.73 4 27.00 4 36.88 4 46.37 4 55.45 5 4.10 5 12 31 5 20.07 5 27.37 5 34.18 5 40.51 5 46 34 5 51.66 5 56.47 6 0.76 6 4.51 6 7.73 6 10.40 6 12.52 6 14.08 6 15.08 6 15.51 6 15.36 6 14.62 6 18.28 6 11. ;U 6 8.78 Saturday Sunday Monday .... Tuesday .... Wednesday . Thursday . . . Friday Saturday .... Sunday Monday .... Tuesday Wednesday . Thursday . . . Friday . . Saturday .... Sunday Monday .... Tuesday .... Wednesday Thursday . . . Friday Saturday Sunday Monday .... Tuesday .... Wednesday . 312 TABLE XXI. AUGUST, 1878. Page 1, AT APPARENT NOON. J O> 0> "8 ft Day of the Month. THE SUN'S RIGHT ASCENSION AND DECLINATION. Equation of Time to be added to Var. in 1 hour. Apparent irlight Ascension Var. in 1 hour. Apparent Declination. Var. in 1 hour. sitbt. from Apparent Time. Thursday Friday . . . Saturday . 1 2 3 h. m. s. 8 45 57.27 8 49 50.02 8 53 42.15 S. 9.711 9.685 9 659 X.18 22 '6 17 45 4.8 17 29 29.8 37.88 38.60 39.31 m. s. 6 5.60 6 1.80 5 57.39 8. 0.145 0.171 0.197 Sunday . . Monday . Tuesday . 4 5 8 57 33.66 9 1 24.55 9 5 14.83 9.633 9.608 9.582 17 13 37.8 16 57 29.1 16 41 4.1 40.01 40.70 41.38 5 52.36 5 46.70 5 40.44 0.223 0.248 0.274 Wednes'y Thursday Friday . . . 7 8 9 9 9 4.49 9 12 53.55 9 16 42.01 9.557 9.532 9.507 16 24 23.0 16 7 26.1 15 50 13.8 42.04 42.69 43.33 5 33.57 5 26.09 5 18.02 0.299 0.324 0.349 Saturday . Sunday . . Monday . LO 11 12 9 20 29.88 9 24 17.16 9 28 3.88 9.482 9.458 9.435 15 32 46.4 15 15 4.0 14 57 7.1 43.95 44.57 45.17 5 9.35 5 0.11 4 50.29 0.373 0.397 0.421 Tuesday . Wednes'y Thursday 13 14 15 9 31 50.03 9 35 35.63 9 39 20.70 9.411 9.389 9.367 14 38 55.8 14 20 30.6 14 1 51.6 45.76 46.34 46.90 4 39.92 4 29.00 4 17.54 0.444 0.466 0.488 Friday. . . Saturday . Sunday . . 1(5 17 18 9 43 5.25 9 46 49.28 9 50 32.82 9.345 9.324 9.304 13 42 59 2 13 23 53.6 13 4 35.2 47.46 48.00 48.53 4 5 56 3 53.08 3 40.10 0510 0.530 0.551 Monday . Tuesday . Wedues'y 19 20 21 9 54 15.88 9 57 58.47 10 1 40.60 9.284 9.265 9.246 12 45 4.1 12 25 20.8 12 5 25.7 49.05 49.55 50.04 3 26.64 3 12.71 2 58 33 0.571 0.590 0.609 Thursday Friday. . . Saturday . 22 23 24 10 5 22.29 10 9 3.55 10 12 44.39 9.228 9.210 9.193 11 45 18.9 11 25 0.8 11 4 31.7 50.52 50.98 51.43 2 43 50 2 28.25 2 12.58 0.627 0.644 0.661 Sunday . . Monday . Tuesday . 25 26 27 10 16 24.82 10 20 4.86 10 23 44.51 9.176 9.160 9.144 10 43 52.0 10 23 2.0 10 2 2.1 51.87 52.29 52.70 1 56.50 1 40.02 1 23.16 0.678 0.695 0.710 Wednes'y Thursday Friday. . . Saturday. 28 29 30 31 10 27 23.78 10 31 2.69 10 34 41.24 10 38 19.46 9.129 9.114 9.099 9.086 9 40 52.6 9 19 33.8 8 58 6.1 8 36 30.0 53.09 53.47 53.83 54.18 1 5.93 48.33 30.38 12.09 0.726 0.741 0.755 0.769 313 TABLE XXI. AUGUST, 1878. Page 2, AT MEAN NOON. O "8 Q *3 d c8 ft THE SUN'S RIGHT ASCENSION AND DECLINATION. Equation of Time, to be subtracted from Apparent Right Ascension Apparent Declination. Semi- diameter. added to Mean Time. Thursday . . . Friday .... Saturday .... Sunday .... 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 h. m. s. 8 45 56.29 8 49 49.05 8 53 41.20 8 57 32.72 9 1 23.63 9 5 13.92 9 9 3.61 9 12 52.69 9 16 41.17 9 20 29.06 9 24 16.37 9 28 3.12 9 31 49.30 9 35 34.93 9 39 20.03 9 43 4.61 9 46 48.68 9 50 32.25 9 54 15.35 9 57 57.97 10 1 40.14 10 5 21.87 10 9 3.17 10 12 44.05 10 16 24.52 10 20 4.60 10 23 44.29 10 27 23.61 10 31 2.57 10 34 41.17 10 38 19.43 N.18 0' 26.5 17 45 8.7 17 29 33.7 17 13 41.7 16 57 33.0 16 41 8.0 16 24 26.9 16 7 30.0 15 50 17.7 15 32 50.1 15 15 7.7 14 57 10.7 14 38 59.4 14 20 34.0 14 1 54.9 13 43 2.4 13 23 56.7 13 4 38.1 12 45 7.0 12 25 23.5 12 5 28.2 11 45 21.2 11 25 2.9 11 4 33.6 10 43 53.7 10 23 3.5 10 2 3.3 9 40 53.5 9 19 34.5 8 58 6.6 8 36 30.1 15 47~9 15 48.0 15 48.1 15 48.3 15 48.4 15 48.6 15 48.7 15 48.9 15 49.0 15 49.2 15 49.4 15 49.5 15 49.7 15 49.9 15 50.1 15 50.2 15 50.4 15 50.6 15 50.8 15 51.0 15 51.2 15 51.4 15 51.6 16.51.8 15 52.0 15 52.2 15 52.4 15 52.6 15 52.8 15 53.1 15 53.3 m. s. 6 5.61 6 1.82 5 57.41 5 52.38 5 46.73 5 40.47 5 33.60 5 26.12 5 18.04 5 9.38 5 0.14 4 50.33 4 39.95 4 29.03 4 17.58 4 5.60 3 53.11 3 40.13 3 26.67 3 12.74 2 58.36 2 43.53 2 28.27 2 12.60 1 56.52 1 40.04 1 23.18 1 5.94 48.34 30.39 12.10 Monday Tuesday .... Wednesday . Thursday . . . Friday . . Saturday .... Sunday Monday .... Tuesday .... Wednesday . Thursday . . . Friday Saturday .... Sunday Monday .... Tuesday .... Wednesday . Thursday . . . Friday. . Saturday .... Sunday Monday Tuesday .... Wednesday . Thursday . . . Friday Saturday . . 314 TABLE XXI. SEPTEMBER, 1878. Page 1. AT APPARENT NOON. ^ V i M *0 >> cj 5 < o "^ 9 >. es Q THE SUN'S EIGHT ASCENSION AND DECLINATION. Equation of Time, to be subtracted from Apparent Time. Var. in 1 hour. Apparent Right Ascension Var. in 1 hour. Apparent Declination. Var. in 1 hour. Sunday . . Monday . Tuesday 1 2 3 h. m. s. 10 41 57.35 10 45 34.93 10 49 12.22 S. 9.072 9.060 9.048 N. 8 14 45" 6 7 52 53.4 7 30 53.6 54.51 54.83 55.14 m. s. 6.52 25.44 44.65 S. 0.782 0.794 0.806 Wednes'v 4 10 52 49.23 9.037 7 8 46.7 55.43 1 4.14 0.817 Thursday Friday. . . 6 6 10 56 25.98 11 2.49 9.026 9.017 6 46 32.9 6 24 12.6 55.71 55.97 1 23.89 1 43.88 0.828 0.838 Saturday . Sunday . Monday . 7 8 9 11 3 38.78 11 7 14.86 11 10 50.76 9.008 9.000 8.993 6 1 46.1 5 39 13.7 5 16 35.6 56.23 56.47 56.70 2 4.10 2 24.51 2 45.11 0.846 0.854 0.861 Tuesday . Wednes'y Thursday 10 11 12 11 14 26.50 11 18 2.10 11 21 37.59 8.986 8.981 8.977 4 53 52.2 4 31 3.8 4 8 10.7 56.91 57.11 57.30 3 5.86 3 26.76 3 47.76 0.868 0.873 0.877 Friday. . . Saturday . Sunday . . 13 14 15 11 25 12.99 11 28 48 32 11 32 23.61 8.974 8.971 8.970 3 45 13.2 3 22 11.5 2 59 6.1 57.48 57 65 57.80 4 8.86 4 30.03 4*51.24 0.881 0.883 0.884 Monday . Tuesday . Wednes'y 10 17 18 11 35 58.87 11 39 34 13 11 43 9.41 8.969 8.970 8.971 2 35 57.2 2 12 45.1 1 49 30.2 57.94 5806 58.17 5 12.47 5 33.70 5 54.91 0.885 0.884 0.883 Thursday Friday . . . Saturday . 19 20 21 11 46 44.74 11 50 20.13 11 53 55.61 8.973 8.976 8.980 1 26 12.8 1 2 53.2 39 31.7 58.27 58.36 58.43 6 16.08 6 37.19 6 58 21 0.881 0.878 0.874 Sunday . . Monday . Tuesday . 22 23 24 11 57 31.19 12 1 6.89 12 4 42.73 8.985 8.990 8.997 16 8.8 7 15.3 30 40.1 58.48 58.52 58.54 7 19.12 7 39.92 8 0.58 0.869 0.864 0.858 Wednes'y Thursday Friday . . . 25 20 27 12 8 18.73 12 11 54.89 12 15 31.25 9.003 9. OH 9.019 54 5.3 1 17 30.5 1 40 55.3 58.55 58.54 58.52 8 21.08 8 41.41 9 1.55 0.851 0.843 0.835 Saturday . Sunday . . Monday . 28 2!) 3u 12 19 7.82 12 22 44.61 12 26 21.65 9.028 9.038 9.049 2 4 19.4 2 27 42.4 2 51 3.9 58.48 58.43 58.36 9 21.48 9 41.18 10 0.64 0.826 0.816 0.8U6 315 TABLE XXI. SEPTEMBER, 1878. Page 2. AT MEAN NOON. i 1 i IM O > A Day of the Month. THE SUN'S RIGHT ASCENSION AND DECLINATION. Equation of Time, to be added to Mean Time. Apparent Right Ascension Apparent Declination. Semi- diameter. Sunday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19. 20 21 22 23 24 25 26 27 28 29 30 h. m. s. 10 41 57.37 10 45 35.00 10 49 12.33 10 52 49.39 10 56 26.19 11 2.75 11 3 39.09 11 7 15.22 11 10 51.17 11 14 26.97 11 18 2.62 11 21 38.16 11 25 13.61 11 28 48.99 11 32 24.33 11 35 59.64 11 39 34.96 11 43 10.30 11 46 45.68 11 50 21.12 11 53 56.65 11 57 32.29 12 1 8.04 12 4 43.93 12 8 19.98 12 11 56.20 12 15 32.61 12 19 9.23 12 22 46.07 12 26' 23.16 N.8 14 45'. 5 7 52 53.0 7 30 52.9 7 8 45.7 6 46 31.6 6 24 11.0 6 1 44.2 5 39 11.4 5 16 33.0 4 53 49.2 4 31 0.5 4 8 7.0 3 45 9.2 3 22 7.2 2 59 1.4 2 35 52.2 2 12 39.8 1 49 24.5 1 26 6.7 1 2 46.7 39 24.9 N. 16 1.6 S. 7 22.8 30 47.9 54 13.5 1 17 39.0 1 41 4.2 2 4 28.6 2 27 51.8 2 51 13.6 15 53 '5 15 53.8 15 540 15 54.2 15 54.5 15 54.7 15 55.0 15 55.2 15 55.5 15 55.7 15 56.0 15 56.3 15 56.5 15 56.8 15 57.0 15 57.3 15 57.5 15 57.8 15 58.0 15 58.3 15 58.6 15 58.8 15 59.1 15 59.4 15 59.6 15 59.9 16 0.2 16 0.5 16 0.7 16 1.0 m. s. 6.52 25.44 34.66 1 4.16 1 23.91 1 43.91 2 4.13 2 24.55 2 45.15 3 5.91 3 26 81 3 47.82 4 8.92 4 30.09 4 51.31 5 12 55 5 33 79 5 55.00 6 16.18 6 37.29 6 58.31 7 19.23 7 40.03 8 69 8 21.19 8 41.53 9 1.68 9 21.61 9 41.31 10 0.77 Monday .... Tuesday .... Wednesday . Thursday . . . Friday Saturday Sunday .... Monday .... Tuesday .... Wednesday . Thursday . . . Friday . . Saturday .... Sunday Monday Tuesday .... Wednesday Thursday . . . Friday Saturday Sunday Monday Tuesday .... Wednesday . Thursday . . . Friday Saturday Sunday Monday 316 TABLE XXI. OCTOBEK, 1878. Page 1, AT APPARENT NOON. jjj o * 2 +3 "o >> e3 ft Day of the Month. THE SUN'S RIGHT ASCENSION AND DECLINATION. Equation of Time to be subtracted from Apparent Time. Var. in 1 hour. Apparent Right Ascension Var. in 1 hour. Apparent Declination. Var. in 1 hour. Tuesday . Wednes'y Thursday 1 2 3 h. m. s. 12 29 58.95 12 33 36.52 12 37 14.39 s. 9.060 9.072 9.084 S. 3 14 23'' 5 3 37 40.8 4 55.6 58.27 58.17 58.0G m. s. 10 19.85 10 38.78 10 57.41 S. 0.795 0.783 0.770 Friday. . . Saturday . Sunday . . 4 5 G 12 40 52.57 12 44 31.09 12 48 9.96 9.098 9.112 9.127 4 24 7.5 4 47 16.0 5 10 20.9 57.93 57.78 57.62 11 15.73 11 33.72 11 51.35 0.756 0.742 0.727 Monday . Tuesday . Wednes'y 7 8 9 12 51 49.21 12 55 28.86 12 59 8.93 9.144 9.161 9.179 5 33 21.8 5 56 18.4 6 19 10.3 57.45 57.26 57.06 12 8.61 12 25.47 12 41.91 0.711 0.694 0.676 Thursday Friday . . . Saturday . 10 11 12 13 2 49.45 13 6 30.43 13 10 11.91 9.198 9.218 9.239 6 41 57.2 7 4 38.7 7 27 14.5 56.84 56.61 56.36 12 57.90 13 13.43 13 28.46 0.657 0.637 0.616 Sunday . . Monday . Tuesday . 13 14 15 13 13 53.90 13 17 36.43 13 21 19.51 9.261 9.284 9.307 7 49 44.2 8 12 7.5 8 34 24.0 56.10 55.83 55.54 13 42.99 13 56.98 14 10.41 0.594 0.571 0.548 Wednes'y Thursday Friday. . . 1G 17 18 13 25 3.16 13 28 47.42 13 32 32.29 9.331 9.357 9.383 8 56 33 4 9 18 35.2 9 40 29.2 55.23 54.91 54.57 14 23.27 14 35.54 14 47.19 0524 0.498 0.472 Saturday . Sunday . . Monday . 19 20 21 13 36 17.79 13 40 3.94 13 43 50.75 9.409 9.437 9.465 10 2 14.8 10 23 51.8 10 45 19.6 54.26 53.85 53.46 14 58.22 15 8.60 15 18.31 0.446 0.419 0.390 Tuesday . Wednes'y Thursday 22 23 24 13 47 38.24 13 51 26.43 13 55 15.33 9.493 9.523 9.552 11 6 37.9 11 27 46.3 11 48 44.3 53.06 52.63 52.19 15 27 34 15 35.69 15 43.33 0.362 0.333 0.303 Friday. . . Saturday. Sunday . . 25 2G 27 13 59 4.94 U 2 55.29 14 6 46.37 9.582 9.613 9.644 12 9 31.5 12 30 7.5 12 50 31.9 51.73 51.26 50.76 15 50.24 15 56.44 16 1.90 0.274 0.243 0.212 Monday . Tuesday . Wednes'y Thursday 28 29 30 3] 14 10 38.20 14 14 30.78 14 18 24.11 14 22 18.21 9.675 9.706 9.738 9.770 13 10 44.2 13 30 44.0 13 50 30.9 14 10 4.G 50.25 49.72 49.18 48.62 16 6.61 16 10.58 1.6 13.78 16 16.23 0.181 0.149 0.118 0.086 317 TABLE XXI. OCTOBEK, 1878. Page 2. AT MEAN NOON. x u t & Day of the Month. THE SUN'S RIGHT ASCENSION AND DECLINATION. Equation of Time, to be added to Mean Time. Apparent Right Ascension Apparent Declination. Semi- diameter. Tuesday .... Wednesday . Thursday . . . Friday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 h. m. s. 12 30 0.51 12 33 38.13 12 37 16.05 12 40 54.28 12 44 32.85 12 48 11.77 12 51 51.06 12 55 30.76 12 59 10.87 13 2 51.44 13 6 32.47 13 10 13.99 13 13 56.02 13 17 38.58 13 21 21.70 13 25 5.40 13 28 49.69 13 32 34.60 13 36 20.13 13 40 6.32 13 43 53.17 13 47 40.69 13 51 28.91 13 55 17.83 13 59 7.47 14 2 57.84 14 6 48.95 14 10 40.80 14 14 33.40 14 18 26.75 14 22 20.86 S. 3 U 33.5 3 37 51.2 4 1 6.2 4 24 18.3 4 47 27.1 5 10 32.3 5 33 33.4 5 56 30.2 6 19 22.4 6 42 9.5 7 4 51.2 7 27 27.1 7 49 57.0 8 12 20.5 8 34 37.1 8 56 46.6 9 18 48.6 9 40 42.6 10 2 28.3 10 24 5.3 10 45 33.2 11 6 51.6 11 28 0.0 11 48 57.9 12 9 45.1 12 30 21.1 12 50 45.4 13 10 57.6 13 30 57.4 13 50 44.2 14 10 17.7 16 3 16 1.6 16 1.9 16 2.1 16 2.4 16 2.7 16 3.0 16 3.3 16 3.6 16 3.8 16 4.1 16 4.4 16 4.7 16 4.9 16 5.2 16 5.5 16 5.7 16 6.0 16 6.3 16 6.5 16 6.8 16 7.0 16 7.3 16 7.6 16 7.8 16 8.1 16 8.4 '16 8.6 16 8.9 16 9.1 16 9.4 m. 8. 10 19.98 10 38.92 10 57.55 11 15.87 11 33.86 11 51.50 12 8.76 12 25.61 12 42.05 12 58.04 13 13.57 13 28.60 13 43.12 13 57.11 14 10.54 14 23.40 14 35.66 14 47.31 14 58 33 15 8.70 15 18.41 15 27.44 15 35.77 15 43.40 15 50.31 15 56.50 16 1 . 95 16 6.66 16 10.62 1 16 13 b-2 16 16.26 Saturday Sunday .... Monday .... Tuesday .... Wednesday . Thursday . . . Friday . . Saturday Sunday Monday Tuesday .... Wednesday . Thursday . . . Friday ...... Saturday Sunday Monday .... Tuesday Wednesday . Thursday . . . Friday Saturday .... Sunday .... Monday .... Tuesday .... Wednesday . Thursday . . . 318 TABLE XXI. NOVEMBER, 1878. Page 1. AT APPARENT NOON. 4 V * 53 *o & B 3 s > THE SUN'S RIGHT ASCENSION AND DECLINATION. Equation of" Time, to be subtracted from Apparent Time. Var. in 1 hour. Apparent Right Ascensioi Var. in 1 hour. Apparent Declination. Var. in 1 hour Friday. . . Saturday . Sunday . . I n 4 h. m. s. 14 26 13.09 14 30 8.74 14 34 5.19 S. 9.803 9.835 9.869 S.14 29 24" 5 14 48 30.3 15 7 21.5 48.04 47.44 46.83 m. s. 16 17.91 16 18.81 16 18.92 S. 0.054 0.021 0.012 Monday . Tuesday . Wednes'y 4 c 6 14 38 2.43 11 42 0.49 14 45 59.3G 9.902 9.936 9.970 15 25 57.9 15 44 18.9 16 2 24.2 46.20 45.55 44.89 16 18.23 16 16.74 16 14.43 0.045 0.079 0.114 Thursday Friday . . . Saturday . 7 8 , ci fi Day of the Month. THE SUN'S RIGHT ASCENSION AND DECLINATION. Equation of Time, to be added to Mean Time. Apparent light Ascension Apparent Declination. Semi- diameter. i Friday. ..... 1 2 3 4 5 G 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 2G 27 28 29 30 h. m. s. 14 26 15.75 14 30 11.42 14 34 7.87 14 38 5.12 14 42 3.18 14 46 2.06 14 50 1.76 14 54 2.29 14 58 3.66 15 2 5.88 15 6 8.95 15 10 12.88 15 14 17.66 15 18 23.30 15 22 29.80 15 26 37.16 15 30 45.38 15 34 54.45 15 39 4.36 15 43 15.12 15 47 26.71 15 51 39.12 15 55 52.33 16 6.33 16 4 21.10 16 8 36.61 16 12 52.85 16 17 9.79 16 21 27.40 16 25 45.68 S. 14 29' 37". 5 14 48 43.1 15 7 34.2 15 26 10.4 15 44 31.2 16 2 36.3 16 20 25.3 16 37 57.9 16 55 13.5 17 12 11.9 17 28 52.7 17 45 15.5 18 1 19.8 18 17 5.4 18 32 31.7 18 47 38.5 19 2 25.3 19 16 51.8 19 30 57.5 19 44 42.0 19 58 4.9 20 11 6.0 20 23 44.8 20 36 0.9 20 47 54.0 20 59 23.8 21 10 29.9 21 21 12.0 21 31 29.8 21 41 23.0 16 9~7 16 9.9 16 10.2 16 10.4 16 1D.6 16 10.9 16 11.1 16 11.3 16 11.6 16 11.8 16 12.0 16 12.3 16 12.5 16 12.7 16 12.9 16 13.1 16 13.3 16 13.5 16 13.7 16 13.9 16 14.1 16 14.3 16 14.4 16 14.6 16 14.8 16 15.0 16 15.1 16 15.3 16 15.5 16 15.6 m. s. 16 17.92 16 18.81 16 18.92 16 18.22. 16 16.71 16 14.39 16 11.25 16 7.28 16 2.46 15 56.80 15 50 28 15 42.91 15 34.69 15 25.60 15 15.66 15 4 85 14 53.19 14 40.68 14 27.32 14 13.12 13 58.09 13 42.24 13 25.59 13 8 15 12 49.94 12 30.98 12 11.30 11 50.92 11 29.86 11 8.14 Saturday .... i Monday .... Tuesday .... Wednesday Thursday . . . Friday Saturday Sunday Monday Tuesday .... Wednesday . Thursday . . . Friday Saturday .... Sunday .... Monday .... Tuesday .... Wednesday Thursday . . Friday . . Saturday . . . Sunday .... Monday .... Tuesday . . . Wednesday Thursday . . Friday Saturday . . 320 TABLE XXI. DECEMBER, 1878. Page 1, AT APPARENT NOON. j * o ^ "o p e Month. THE SUN'S RIGHT ASCENSION AND DECLINATION. Equation of Time to be snbt from Var. in 1 hour. **H O ce Apparent Right Ascension Var. in 1 hour. Apparent Declination. Var. in 1 hour. added to Apparent Time. Sunday . . Monday . Tuesday . 1 2 3 h. m. S. 16 30 2.66 16 34 22.27 16 38 42.47 S. 10.804 10.829 10.854 S.2l 50 47 'l 21 59 50.4 '22 8 28.4 23.16 22.11 21.05 m. s. 10 45.95 10 22.96 9 59.38 S. 0.944 0.970 0.994 Wednes'y Thursday Friday . . . 4 5 G 16 43 3.25 16 47 24.59 16 51 46.46 10.878 10.900 10.922 22 16 40.7 22 24 27.0 22 31 47.0 19.97 18.88 17.79 9 35.23 9 10.52 8 45.27 1.018 1.041 1.063 Saturday . Sunday . . Monday . 7 8 9 16 56 8.84 17 31.71 17 4 55.04 10.943 10.963 10.981 22 38 40.7 2245 7.7 22 51 8.0 16.68 15.57 14.45 8 19.52 7 53.28 7 26.58 1.083 1.103 1.122 Tuesday . Wednes'y Thursday 10 11 12 17 9 18.81 17 13 42.99 17 18 7.55 10.999 11.013 11.031 22 56 41.2 23 1 47.3 23 6 26.0 13.32 12.18 11.04 6 59.44 6 31.90 6 3.98 1.139 1.155 1.171 Friday. . . Saturday. Sunday . . 13 U 15 17 22 32.46 17 26 57.71 17 31 23.25 11.045 11.058 11.070 23 10 37.2 23 14 20.8 23 17 36.6 9.89 8.74 7.58 5 35.70 5 7.09 4 38.19 1.185 1.198 1.210 Monday . Tuesday . Wednes'y 1C 17 18 17 35 49.06 17 40 15.11 17 44 41.36 11.080 11.090 11.098 23 20 24 4 23 22 44.1 23 24 35.7 6.41 5.24 4.06 4 9 02 3 39.61 3 9.99 1 220 1.230 1.238 Thursday Friday . . . Saturday . 19 20 21 17 49 7.78 17 53 34.35 17 58 1.01 11.104 11.109 11.112 23 25 59.1 23 26 54.1 23 27 20.8 2.88 1.70 0.52 2 40.21 2 10.29 1 40.26 1.244 1.249 1.252 Sunday . . Monday . Tuesday . Wednes'y Thursday Friday . . . 22 23 24 25 20 27 18 2 27.74 18 6 54.49 18 11 21.21 18 15 47.87 18 20 14.43 18 24 40.84 11.114 11.114 11.112 11.109 11.104 11.097 23 27 19.2 23 26 49.2 23 25 50.9 23 24 24.3 23 22 29 4 23 20 6.3 0.66 1.84 3.02 4.20 5.37 6.55 1 10.18 40.07 9.99 1.254 1.254 1.252 1.249 1.244 1.237 20.03 49.95 1 19.73 Saturday . Sunday . . Monday . Tuesday . 28 29 30 31 18 29 7.08 18 33 33.11 18 37 58.88 18 42 24.38 11.089 11.079 11.068 11.056 23 17 15.1 23 13 55.8 23 10 8.6 23 5 53.6 7.72 8.89 10.05 11.20 1 49.32 2 18.71 2 47.85 3 16.71 1.229 1.219 1.208 1.196 321 TABLE XXI. DECEMBER, 1878. Page 2. AT MEAN NOON. jj 9 5 t Day of the Month. THE SUN'S EIGHT ASCENSION AND DECLINATION. Equation of Time, to be added to Apparent Right Ascensioi Apparent Declination. Semi- diameter. subt. J'rom Mean Time. Sunday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 2G 27 28 29 30 31 h. m. s. 16 30 4.60 16 34 24.14 16 38 44.28 16 43 4.99 16 47 26.25 16 51^48.05 16 56 10.36 17 36.15 17 4 56.41 17 9 20.09 17 13 44.19 17 18 8.66 17 22 33.49 17 26 58.65 17 31 24.10 17 35 49.82 17 40 15.78 17 44 41.94 17 49 8.28 17 53 34.75 17 58 1.32 18 2 27.95 18 6 54.61 18 11 21.24 18 15 47.81 18 20 14.28 18 24 40.60 18 29 6.75 18 33 32.68 18 37 58.37 18 42 23.78 S.21 50' 5l'.2 21 59 54.2 22 8 31.9 22 16 43.9 22 24 29.8 22 31 49.6 22 38 43.0 22 45 9.8 22 51 9.8 22 56 42.8 23 1 48.7 23 6 27.2 23 10 38.2 23 14 21.5 23 17 37.1 23 20 24.8 23 22 44.4 23 24 35.9 23 25 59.2 23 26 54.2 23 27 20.9 23 27 19.2 23 26 49.2 23 25 50.9 23 24 24.3 23 22 29.5 23 20 6.5 23 17 15.3 23 13 56.2 23 10 9.1 23 5 54.2 16 15~8 16 15.9 16 16.1 16 16.3 16 16.4 16 16.5 16 16.6 16 16.8 16 16.9 16 17.0 16 17.1 16 17.2 16 17.3 16 17.4 16 17.5 16 17.5 16 17.6 16 17.7 16 17.7 16 17.8 16 17.9 16 17.9 16 18.0 16 18.0 16 18.1 16 18.1 16 18.1 16 18.2 16 18.2 16 18.2 16 18.2 m. s. 10 45.78 10 22.80 9 59.22 9 35.07 9 10.36 8 45.12 8 19.37 7 53.13 7 26.44 \- 6 59(.31 6 31V78 6 3.86 5 35.59 5 6.99 4 38.09 4 8.93 3 39.53 3 9.93 2 40.15 2 10.24 1 40.23 1 10.15 40.06 9.98 Monday Tuesday .... "Wednesday . Thursday . . . Friday Saturday .... Sunday Monday .... Tuesday Wednesday . Thursday . . . Friday Saturday .... Sunday Monday .... Tuesday .... Wednesday . Thursday . . . Friday Saturday .... Sunday Monday .... Tuesday .... Wednesday. Thursday . . . Friday 20.03 49.93 1 19.70 1 49.29 2 18.66 2 47.79 3 16.64 Saturday Sunday Monday Tuesday .... 322 , TABLE XXII. LATITUDES AND LONGITUDES Of the Principal Ports, Capes, and Lights in the World. EAST COAST OF UNITED STATES OF AMERICA. Qnoddy-head Light. . Mt. Desert-rock " . Martinicus Island Lt. Portland Li"ht LAT. LONG. Philadelphia (St. H.) Cape Charles LAT. LONG. 44 49 N 43 58 43 47 43 37 42 38 42 31 42 20 42 21 42 02 41 16 41 35 41 29 41 13 41 19 41 04 40 43 40 28 40 24 38 56 38 47 ISL 10 ION 11 20 12 00 13 03 14 27 15 38 16 30 18 29 18 28 ] 19 12 N 17 29 19 49 9 34 10 26 10 39 10 28 10 30 6 49 5 48 4 56 1 10 \ 33 02 S 12 03 12 04 2 13 8 57 N EAST 43 24 N 44 39 45 19 45 57 45 42 66 58 W 68 08 68 51 70 12 70 34 70 54 70 53 71 04 70 03 . 70 04 70 54 71 18 71 34 72 05 71 51 74 00 74 00 73 59 74 57 75 05 LNDS IN THI 61 00 W 60 27 61 49 59 37 60 55 61 26 61 29 66 07 69 52 }AST COAST 96 09 W 88 12 90 33 79 40 75 38 71 45 68 07 67 01 58 11 55 00 52 13 50 00 VEST COAST 71 41 W 77 06 77 13 79 53 79 31 COAST OF 65 36 W 63 55 60 55 59 48 61 29 39 67 N 37 07 36 55 37 32 38 53 39 18 35 15 34 37 33 52 33 13 32 42 32 01 32 05 28 28 25 40 24 33 30 21 30 14 29 57 29 20 18 33 N 19 46 17 58 19 58 20 20 23 09 23 03 25 51 32 22 1 28 S 8 04 5 28 8 21 13 01 22 03 23 01 22 56 34 53 34 36 55 59 16 55 N 37 48 49 36 70 29 46 39 N 47 34 46 49 59 49 75 09 W 75 58 76 00 77 26 77 00 76 37 75 31 76 31 78 00 79 11 79 52 80 51 81 05 80 34 80 09 81 48 87 17 88 00 90 00 94 45 72 16W 72 11 76 46 75 52 77 11 82 22 81 40 77 11 64 38 48 29 W 34 52 35 17 34 57 38 32 41 00 41 59 43 09 . 56 13 58 22 67 16 99 48 W 122 26 126 35 161 42 53 05 W 52 43 71 16 43 54 Cape Henry Light. . . Richmond Cape Ann (Thatcher's Island) Light. .... Washington City .... Baltimore Salem (City Hall) . . . Boston L. H Cape Hatteras Cape Lookout Light . Cape Fear ' ' Georgetown " Charleston " Tybee " Savannah Boston (State House) Capo Cod Li^ht Nantucket harbor Lt. Xc w Bedford L. H. . Newport Spire Block Island Light . . New London L. II .. Montauk Point L. H. New York (City Hall) Sandy Hook Light . . Neversink Light Cape May Light .... Cape Henlopen L. H. Trinidad (Pt. Galiote) Tobago (N.E. Point) Grenada(S.W. Point) Barbadoes (S. Point) Martinico " Dominica (N. Point). Guadeloupe (NE.Pt.) Porto Rico (St. A. Bt.) St. Domingo Light . . Vera Cruz Cape Carnaveral Cape Florida Light . . Key West Pensacola " Mobile Point " New Orleans Galveston (entrance) . : WEST INDIES. Port au Prince Cape Hayti City .... Kingston St. Jago de Cuba Lt. Manzanillo Havana (the Moro). . Matanzas Hole-in-the-wall Lt. . Georgetown OF AMERICA. Para Balize . . Pernambuco Campeche Cape St. Roque Porto Bello Cape St. Angustin . . Bahia, St. Antonio Lt. Cape St. Thomas Cape Frio Cartagena Maracaybo Porto Cabello Caraccas Rio Janeiro Georgetown Light . . . Paramaribo Monte Video iBuenos Ayres Cayenne Cape Horn River Amazon OF AMEBICA. Acapulco Valparaiso Lima San Francisco Callao Nootka Guayaquil Icy Cape Panama NORTH AMERICA. Cape Race Cape Sable . ... Halifax St. Johns Cape Canso ' . . Quebec Cape Breton Cape Farewell Gut of Canso 323 TABLE XXII. LATITUDES AND LONGITUDES Of the Principal Ports, Capes, and Lights in the \Vorld. ENGLAND, SCOTLAND, AND IRELAND. Lizard Point ....... LAT. LONG. Glasgow LAT. LONG. 49 58 N 50 22 50 47 51 C8 51 31 52 37 53 45 55 46 56 00 55 57 57 09 58 40 FBO 36 07 N 36 32 36 59 37 03 38 42 41 09 43 22 43 30 43 30 43 15 43 29 44 50 45 35 45 56 46 09 47 13 48 23 SotTND, THE 57 38 N 59 55 57 42 55 41 56 02 56 10 59 21 53 52 36 07 N 36 43 37 36 38 20 39 28 41 09 41 23 43 18 43 07 44 24 43 46 43 32 41 54 40 50 43 38 5 12 W 4 10 1 06 1 19 E 06 W 1 44 E 20 W 1 59 2 29 3 12 2 08 3 08 M GlBEALTA 5 21 W 6 18 5 58 9 00 9 09 8 37 8 24 8 13 3 47 2 54 1 29 34 1 10 58 1 09 1 33 4 29 BALTIC, AST 7 02 E 10 43 11 55 12 34 12 37 15 36 18 04 10 42 THE MEDI 5 21 W 4 26 1 01 26 24 1 18E 2 11 5 22 5 56 8 53 11 16 10 18 12 27 14 16 13 30 55 52 N 54 54 53 25 51 27 51 26 52 40 55 00 54 35 53 23 51 48 51 29 48 29 N 49 38 48 50 49 29 50 44 50 58 51 03 51 14 51 13 51 27 51 54 52 22 53 22 53 05 53 33 57 43 AND BOTHN 54 22 N 54 43 56 57 54 25 59 26 59 59 59 56 65 51 45 26 N 45 39 42 38 37 54 37 58 40 39 41 01 38 26 36 11 30 03 31 12 32 54 36 47 36 47 35 47 4 16\V 2 56 3 00 2 35 9 29 8 39 7 19 5 57 6 20 8 15 9 22 5 03 W 1 37 2 20 E 06 1 37 1 51 2 22 2 55 4 24 3 35 4 29 4 53 7 12 8 49 9 58 10 37 IA. 18 41 E 20 30 24 C6 13 28 24 45 29 47 30 19 24 14 12 21 E 13 46 18 07 22 52 23 44 22 57 28 59 27 07 37 10 31 18 29 53 13 11 10 06 3 04 5 50 W Plymouth Carlisle Portsmouth Liverpool Dover Bristol London Cape Clear Light. . . . Limerick Yarmouth Hull Londonderry Berwick Li^ht. . . . Belfast ". Dunbar. Dublin Edinburgh Cork Aberdeen ... Baltimore Duncansby Head .... Gibraltar R TO THE SCAW. Ushant Light Cadiz Light Cherbourg Seville Paris Cape St. Vincent Lt . Lisbon Havre de Grace Boulogne Oporto Li^ht Calais Corunna " Dunkirk Ferrol Ostend Santander Li^ht Antwerp Bilbao ' Flushing ^ Bavonnc Rotterdam Bordeaux Amsterdam Cordouau Light > Embden . Rochefort Bremen. ... Ilochelle Light Hamburgh Nantes . Scaw Light Brest D THE GTTLFS OF FINLAND Dantzig CATTEGAT AND The Naze Li^ht Christiana Konigsberg Gothenburf'h Rica . . Copenhagen Bergen (Isl'd Rugen) Revel Elsineur Carlscrona Cronstadt. .... Stockholm Petersburg Lubeck Tornea Gibraltar TERRANEAN. Venice Alala^a, ... Trieste Cartha^ena Ransa Alicante Corinth Valencia Athens Terra ^ona Salonica Barcelona Constantinople Marseilles Smyrna. Toulon Genoa Cairo Florence . ..... Alexandria Leghorn Tripoli Rome Tunis Naples Algiers Ancona LiMit Tangier TABLE XXII. LATITUDES AND LONGITUDES Of the Principal Ports, Capes, and Lights in the World. 324 WEST COAST OF AFRICA. CapeSpartel. Mogador. Senegal Cape Verde . . LAT. 35 48 N 31 31 16 01 14 44 LONG. 5 54 W 9 46 16 32 17 32 Sierra Leone Cape. . Capetown Cape of Good Hope . Cape Lagullas LAT. ISLANDS IN IHE ATLANTIC OCEAN. Fayal, S.E. point Funchal . . Santa Cruz(Teneriffe) " (St. Anthony) Cape Lagullas Mozambique Suez Mocha Bassora Surat Bombay Goa Mangalore Cape Comorin Ceylon (Columbo Lt. ) Pondicherry Madras . . 38 30 N 32 38 28 28 17 02 28 42 W 16 55 16 16 25 15 Porto Praya Ascension St. Helena ( James- town ) FROM CAPE OF 34 508 15 03 29 59 N 13 20 30 30 21 11 18 54 15 28 12 51 8 05 6 56 11 56 13 04 ISLANDS IN THE Madagascar Cape St. Mary . . Cape Amber Mauritius (Pt. Louis) Sumatra (Bencoolen) Java (Batavia) Banca (South Point) . Singapore (East Pt. ) . Borneo (Road) Celebes (Macassar).. Amboyna (Ft. Viet.) Formosa (S. Cape) . 25 39 S 11 58 20 10 3 48 6 08 3 08 1 22 N 5 00 5 09 S 3 41 21 56 N 45 49 57 102 106 106 104 115 119 128 120 GOOD 01 E 48 34 12 00 47 52 52 49 30 49 50 16 INDIAN AND PACIFIC OCEANS. [Niphon (Yeddo) Jesso (Matzumay). . . Australia Cape York N.W. Cape Sydney Botany Bay Melbourne Sandwich Islands Owhyhee(N.Pt.) " (E. Pt.) Honolulu HOPE TO KAMISKATKA. Masulipatam Ballasore Calcutta Pegu Point Romania Siam Hong Kong Canton Shanghai Nankin Pekin St. Peter and St. Paul North Cape 07 E 19 30 19 50 28 00 00 23 10 56 8 30 N 33 56 S 34 22 34 50 14 54N 7 56 S 15 55 16 09 N 21 30 22 34 18 00 1 23 14 55 22 15 23 07 31 12 32 02 39 54 53 00 68 56 35 40 N 41 32 10 44 S 21 50 33 52 34 02 37 49 20 23 N 19 34 21 19 LONG. 13 18 W 18 29 E 18 30 20 01 23 30 W 14 25 5 45 81 08 E 87 10 88 20 96 52 104 16 100 00 114 22 113 14 121 28 118 49 116 29 158 44 179 47 W 140 00 E 140 04 142 33 114 04 151 14 151 13 144 58 155 54 W 154 54 157 52 COAST OF CALIFORNIA. St. Diego, Point Loma St. Catalina Island. Santa Cruz Island, W. end * Point Conception Mount Buchon Point Pinos Monterey Fort Farallones Rocks peak San Francisco Fort, S. side entrance Mt. Bolbones, 3765 ft, 10 leag. inland Cape Mendocino Cape Perpetiia Pt. Adam entrance, Columbo River Cape Disappointment Astoria City Pacific City Gray's Harbor, N. Head Cape Flattery S. side ent, of Straits of Juan de Fuca . LAT. 32 38. 8 N 33 28 34 10 34 31 35 18 36 38.5 36 36.4 37 42 37 48.5 37 52.9 40 29 44 12 46 12 16 16 46 10 46 20 47 48 9 LONG. 117 14.7 118 38 119 47 120 30 120 50 121 55 121 53 122 59 122 28.5 121 54.5 124 32 124 17 124 1 124 5 123 49 124 3 124 7 124 46 TESTIMONIALS. From a long list of subscribers we select the following names as evidencing that our " GUIDE " has won the patronage of the best nautical men : YV. B. Seabury, Commanding Steamship Alaska, P. M. S. S. Co. W. H. McLean, First Officer T. E. Thompson, Second Officer " " " James E. Hunter, Third Officer " " D. E. Friele, Commanding Steamship China, P. M. S. S. Co. Thos. Golding, First Officer " " " C. Basset, Second Officer " " " I. M. Dow, Third Officer " " " H. C. Dearborn, Commanding Steamship City of Sydney. F. H. Johnson, First Officer " " WiUiam Danol, Second Officer " " A. H. Panzes, Third Officer J. Metcalfe, Commanding Steamship Belgic, 0. 0. S. S. Co. Louis Meyer, First Officer " " " Daniel Joyce, Second Officer " " " G. A. Williams, Fourth Officer " " " A. G. Jones, Commanding Steamship Salvador, P. M. S. S. Co. D. Clark, First Officer M. Connolly, Commanding Steamship Granada, P. M. S. S. Co. F. W. Hart, First Officer " G. Foster, Second Officer " " C. T. Rode, Third Officer D. C. Griffiths, First Officer Steamship Dakota, P. M. S. S. Co. W. Lascombe, Second Officer " " " D. Berry, Third Officer L. B. Walls, First Officer Steamship City of Tokio, P. M. S. S. Co. J. H. Powell, Second Officer " ' " " J. Luke, Third Officer " " " " D. S. Austin, Commanding Steamship Wilmington, P. M. S. S. Co. A. N. M. Tnlloh, First Officer Steamship Australia, P. M. S. S. Co. Francis Connor, Commanding Steamship Oregon, Oregon S. S. Co. W. H. Kidley, Commanding Steamship Gaelic, O. & O. Line. H. Davison, First Office* " " T. Suafton, Second Officer J. M. Cavarly, Commanding Steamship Georgia. Wm. CargiLl, Commanding P. M. S. Australia. Robert It. Searle, Commanding Steamship Colima, P. M. S. S. Co. Thos. Chapman, First Officer " " " Thos. P. Deering, Second Officer " " " W. Ward, Third Officer " " " G. G. Berry, Commanding Steamship China, P. M. S. S. Co. J. T. Mulcohm, First Officer Steamship Los Angeles, P. M. S. S. Co. TESTIMONIALS. This work, the first of its kind published within the last half-century, seems, upon even cursory glance, admirably calculated to effect the professed object, viz., to enable the navigator to find at any time, quickly and accurately, his position at sea. The text-matter is exceedingly clear and concise. The rules and instructions, throughout, though based on theory, are altogether practical, and will in no wise repel the non-scientific seafarer from attaining (as far as can be done from a book), a trustworthy knowledge of what he most needs. Only a man who knows by experience the sailor's wants, could have written this book, which, from the arrangement of its matter as well as from its numerous original prob- lems all carefully worked out and valuable practical suggestions, will AVC think, make it prized wherever it finds its way. We certainly think that all naviga- tors, no matter what their attainments, but especially those who have yet to ad- vance in their profession, will find it advantageous to make themselves acquainted with the contents of this work. Its typographical execution is admirable, and reflects great credit on the publishers. Alta California, May 20, 1878. This book, prepared by Captain E. McNevin, appears, after a careful survey of its pages, to be all that it claims on its title page. It gives the rules for solv- ing all necessary nautical problems in the simplest and most practical manner, and enables the seaman to find, without other aid than that of an ordinary edu- cation, his position at sea. It attracts from the first, beginning with the matter that a sailor should first know, viz., the compass and a table of the angles which its points and quarter-points make with the meridian. The book is interspersed with practical and original suggestions that cannot fail to be appreciated by sea- men. The method of finding simultaneously, latitude and longitude by double altitudes has not, we believe, heretofore been published in any American work . The same good judgment is observable in the arrangement of the the tables as of the text. The first gives the logarithmic lines, tangents, etc., for the points and quarter-points of the compass, and the second the logarithms of the natural numbers. The typographical appearance of the tables is excellent, the columns being so well spaced and the figures so distinct that they can be used with facil- ity and without danger of error an important point for both student and navi- gator. A great deal has been written about the deviation of the compass; but we venture to say that the few paragraphs of this book on the subject will be all that the student need ever seek to know, either as to its theory or use. We pre- dict for this book, which must have cost its author much time and thought, a large patronage. Morning Call, June 7, 1878. MARINE DRUG COMPANY, JAMESJ3URTIS DRUGGIST, CORNER MARKET AND SPEAR STS. SAN FRANCISCO. Particular attention paid to furnishing and refitting Ship's Medicine Chests -WiZtTES .A-lsTX) LI QUOINS. MARINE DRUG STORE. N. S. THOMPSON g DRUGGIST, $ COR. STEUART AND MARKET STS. Particular Attention paid to replenishing Ship's Chests ivitJi Pi:re Medicine A Cood Assortment of Medicine Chests always on hand, at Reasonable f 'rial's. SAN FRANCISCO CORDAGE CO. ESTABLISHED 1856. MANUFACTURERS OF ALL SIZES OF CORDAGE AND HAY ROPE A full assortment constantly on hand, and extra sizes and lergths made st short notice. TTJBTSS cfc OO. 6n AND 613 FRONT ST. SAN FRANCISCO, CAL. Rubber Goods for Steamboat Use! HOSE, PACKING, VALVES, GASKETS, ETC. WE MAKE VALVES AND GASKETS TO ORDER, Thus saving the waste which occurs by cutting them from the sheet. ALSO, AM. KINDS OK RUBBER CLOTHING, INCLUDING SOU-WESTERS, LEGGGINS HIV., KIT. Factory and Warerooms; ! 501 Market Street ' cor ' First ' San Francisco, I 327 Broadway, New York. The Gutta Percha and Ruhhcr Manufacturing Company, JOHN \V. TAYLOR, M AXAC.HR, I. L. MERRELL & CO. WIRE-BOUND Utilized Asbestos AND STEATITE OR SOAP STONE BOILEK COVEKING AND ROOFINQ MATERIAL. (Patented November i6th, 1875.) Office and Factory, 314 Townsencl St. SAN FRANCISCO, CALIFORNIA. This is the best non-conductor of heat in use. For covering Steam Boilers and Pipes it has no equal. It has the highest endorsement for durability, lightness, elasticity, ease of application, and all desirable qualities. It effects a LARGE SA VI NG OF FUEL, Itut* a* lomj a* the iron on <'/