1 ■.'■■■J %s 1^ GIFT OF V A NEW TKEATISE ON THB PRACTICE OF NAVIGATION AT SEA CONTAINING ALL THE DETAILS NECESSARY TO ENABLE THE MARINER TO BECOME A GOOD PRACTICAL NAVIGATOR. ILLUSTRATED BY A NEW MODE OF ENGKAVED DIAGRAMS AND FIGURES, DESIGNED WITH THE INTENTION OF MECHANICALLY INSTRUCTING THE LEARNER IN THE . MEANING AND USE OF THE VARIOUS PROBLEMS IN NAVIGATION AND NAUTICAL ASTRONOMY, in room of the tedious solutions of geometry and trigonometry. the usuai Tables are given which are indispensable in a work of this kind, SOME OF which ARE IMPROVED, AND NEW ONES INTRODUCED FO^ THE FIRST TIME, WITH A VIEW OF SHORTENING THE LABOR OF COMPUTATION. THE WHOLE BEING x^XPRESSLY ADAPTED FOR THE USE OF SEAMEN. BY CAPTAIN WILLIAM THOMS, TWENTY-FIFTH EDITION. NEW YORK: PRINTED FOR THE AUTHOR AND SOLD BY JOHN BLISS & CO.. IIAVIGATION WARKHOUSE, '28 FRONT STREET, KEW YORK; F. A. ASHTON, 259 WINTHROP STREET, BROOKLrN, AND ALJi THE PRINCIPAL NAUTICAL BOOKSTORES IN NEW TORK AND THROUGHOUT THE UNION. 1902. 7 v^jf 4,' . Sntered according to Act of Congress, in the Year One Thousand Eight Hundred and Eighty BY WILLIAM THOMS, In the office of the Librarian of Congress at Washiusitoa TO THE COMMANDERS, OFFICERS, AND SEAMEN, EMPLOYED IN THE MERCHANT MARINE OF THE UNITED STATES, Cljis i'olume, (THJB FIRST ATTEMPT OF THE KIND BY A MEMBER OF THAT SERVICE,) IS RESPECTFULLY DEDICATED, •T THE AUTHOR. 288104 PREFACE. This work is intended exclusively for the use of seamen, and has been compiled by the author from, an experience of more than twenty-five years, in the practice of navigating a ship at sea, ia nearly all parts of the world. Consequently, a competent knowledge has been acquired, during that period, of what is actually required to be known, in order to become an expert practical navigator. This work is, therefore, confined to the practice at sea ; that is, navigation proper, or that which has reference to the ship's place on the ocean. Thus knowing what is required, and also the distaste which seamen have for long and tedious calculations. I have endeavored to simplify the various rules and tables, and to strike out all jnnecessary matter, which is not required, and in the room of which, introduced diagrams of the various cases, which will convey mechanically the whole state of the case to the mind of the reader at once. The tedious and unprofitable solutions of geometry and triginometry are, therefore, abolished, together with the tables of the logarithms of numbers, which are never used at sea, even by those persons who have previously studied the subject, and who have eventually to fall back upon the method now used in this work. The sailings are therefore explained by diagrams, and worked out by inspection of the traverse table; only, the same as we actually do at sea, and which is correct enough for all practica] purposes ; thus relieving the learner from the embarrassment of having several methods given of doing the same thing. The names of the parts of the diagram are inserted against them, which makes it easier to comprehend the meaning of the case, and will be found an improvement upon the old system of marking them alphabetically for the purpose of reference. Every diagram in this work is drawn on the same scale, that is, with the chord of 60", taken from the plane scale, (and which is in general use on board ship.) Instructions are also given how to construct the diagrams, so that the learner may teach himself in a mechanical manner, and which will give him more insight into the nature of the problem than the study of geometry and trigonometry will. In Parallel and Middle Latitude Sailings, diagrams of semi-hemispheres are introduced, showing the contraction of the meridians towards the poles, and the comparative length of the degrees of longitude in the various parallels of latitude. And in Mercator's Sailing, a diagram showing the meridians all parallel to each other, and the expansion of the degrees of latitude towards the poles. Current sailing is gone into at some length, and rules given as they are applied in the practice at sea, m this difficult branch of the study. Taking departures, or ascertaining the ship's place by the bearing of the land, is introduced, and a table given to find the ship's position by two bearings of the same object, having the course and distance sailed between them. This will be found very useful to a ship coasting along shore, a* her distance oif shore can be easily found by the use of this table ; and upon the same prinoipla ber distance off shore may be ascertained by projecting the accompanying diagram. n PREFACE The time of high water is found by the usual rules, and is only an approximation. Local tid« table only can show the time of high water with any degree of certainty. The navigator will naturally consult those tables in preference to any general rule, where accuracy is required. A short account of the prevailing winds and currents in the various parts of the world are introduced, chiefly derived from my own experience, and will be found interesting and useful to ne young navigator. The cause and effect of hurricanes are also explained in a short and familiar manner, and practical rules given to avoid their fatal effects, illustrated by diagrams of the storm circles in both North and South latitude, and which, by giving the subject a little attention, will be easily understood. The rules given to avoid the focus, and the general handling of a ship, on approach ing the verge of the storm circle, the falling of the barometer, etc., are also derived from my own experience, the facts having been recorded in the journals I have kept of many voyages, where they prevail. The usual rules are given for the construction of a general chart on Mercator's projection, illustrated by a diagram chart of part of the North Atlantic Ocean. The use of it is explained, and a number of questions proposed, and the answers given, so as to citable the learner by himself to obtain a thorough knowledge of this most important subject. Rules are also given to construct a coasting chart on a large scale, illustrated by a diagram, and the use of it explained, under all the possible circumstances in which a ship may be placed, and questions and answers given in like manner, which will be found of much importance to the learner The manner of sounding with the lead recommended, on a ship's approaching the coast in thick weather, and the method of tracing out her track, by soundings, on the chart, when no observations of the heavenly bodies can be obtained, and will be found of much service to the young navigator. Nautical astronomy is then introduced, containing the various methods of finding the ship's place on the ocean from astronomical observations, and commences with a diagram of the solar system, showing the real state of the case, and the motion of the earth, and of those planets only which are used in navigation, round the sun. Nautical astronomy is then defined, and diagrams of the sphere given, showing the case reversed and the earth is treated as a mere speck in the centre of the universe, and all the heavenly bodies revolving round it, the spectator being supposed to be situated at an immense distance to the Eastward of it. These diagrams will be found of great importance in giving the learner a mechanical knowledge of the nature of the circles and angles supposed to be drawn in the heavens, and will show at once the meaning of the various terms used in nautical astronomy, and which any amount of descrip- tion would fail to do without them. The manner of constructing those diagrams, from the use of the plane scale, and the measuring of the various circles and angles, are also given, with the view of exercising the learner, and to impress the figure on his mind ; and they are generally so arranged that the description is given on the page facing them. The projection of the heavens in two hemispheres, shows at once the nature of the right a.scension and declination of the heavenly bodies, the sun's path in the heavens, the signs of the zodiac, etc. And the diagram of motion round the pole will give a distinct idea of the movement of the hour angles of the heavenly bodies in an opposite direction to their movements in right ascension. As it is of much importance to seamen to be able to find the latitude from the meridian altitude of a star, 1 have introduced several diagrams, showing the nature of a meridian altitude, and how It may be computed, and also a new table, containing the meridian passages of those stars of the first magn'tudfe which are t^enerally used at sea, for avery third day throughout the year, by which means a person otherwise unacquainted with the stars in the heavens may be enabled to tind any star on the meridian without knoM'ing it, and find his latitude thereby. The planets are also found by the same method, having the time they pass the meridian from the \autical Almanac. Diagrams showing the effect of the dip of the horizon, refraction, and parallax, which is fully explained on the opposite page PREFACE. Tit A diagram showing the manner of observing altitudes of the he&venly bodies and the nature of the correction for semi-diameter. The instruments of navigation and nautica. astroncmy are then explained, and the manner of reading off and adjusting them. The use of the quadrant for taking altitudes, and the sextant for measuring angular distance* Detween the sun and the moon, or the moon and stars, are fully explained, together with a ne-w method of causing the moon to measure her own distance from the sun or a star. The artificial horizon is explained, and a diagram showing the cause of the double reflection, this being a most useful instrument for rating a chronometer on shore, when the sea horizon ia not visible. The use of the chronometer is now explained, and the various practical rules given for its management on board ships at sea, which will be found of great service to the young navigator. The azimuth compass is next explained, and the manner of taking azimuths and amplitudes, aa practiced at sea. Then follow remarks on the action of the barometer and thermometer, derived from experience in the use of these instruments for the last twenty-five years. The action of the new or Aneroid Barometer is also explained. The sun being the most important of all the heavenly bodies on which observations are made, the manner of correcting his declination is first introduced, and the latitude deduced from his meridian altitude, illustrated by diagrams of all the various cases, which will give the learner a complete insight into the meaning and nature of finding the latitude, not only by the sun, but by the meridian altitude of any other heavenly body. • Finding the latitude by an altitude of the sun out of the meridian, is then introduced, having the time from noon, or, which may be deduced from the Greenwich time by chronometer, and bv the help of a new table for that purpose, a correction is found, which, added to the observe •Ititude, gives the meridian altitude. The latitude is then found in the usual manner. The latitude is also found by two altitudes of the sun, misnamed double altitudes, by a new method of using the hour angle of the lesser altitude, to which is applied the interval of time between the observations, corrected for the ship's change of longitude in time, and the result is the inner hour angle, or the time from noon, at which the greater altitude was observed, it now becomes the same case as if only one altitude had been observed. This will be found a more direct and easier mode of solving the problem than by the old and tedious methods of double altitudes given in works of this kind. A method is also given of finding the latitude by measuring the change of altitude of any of th5 heavenly bodies on the prime vertical in one minute of time ; and this portion of altitude found in a table constructed for the purpose, will point out the latitude corresponding, within certain limits. The latitude by the meridian altitude of the moon is found in the usual manner, only it is much simplified by the introduction of a new table, containing the correction for the moon's parallax in altitude, given in minutes and tenths of minutes, and taken out for the nearest degree of apparent altitude and the nearest minute of parallax, which is sufficiently near enough for all practical purposes. Becaurff , if the Greenwich time be not accurately known, the moon's declination cannot be found within ten times the amount of the difference between this table and the most rigorous method of finding this correction, a new table is also given to correct the moon's declination to the Green wich date. The method of finding the planets on the meridian, and the latitude obtained from their meridian allitudv^ also the mode of finding the stars on the meridian, further explained, with the manner of finding the latitude from their meridian altitudes fully explained, and which may be put in practice by any person, otherwise unacquainted with the stars in the heavens, ly p'mply followintr the direc- tions g'ven in this work. The manner of finding the latitude by the meridian altitude of the pole star, both above and below the pole, and the usual table for finding the latitude by that stjir At any other time of the night, which has heai constructed for this year, but will serve for several years hereafter. nil ^ PREFACE. A method of finding the correct latitude in the night time, when the horizon :s often obsour«d and doubtful, by observing stars both North and South of the meridian, and can be practiced io either hemisphere, will be found of great use, from its extreme simplicity, as will also the finding of the latitude by the moon, planets, or stars out of the meridian. For instance, if the latitude is required to be known at twilight, (which is the best time for taking altitudes of the stars, the horizon being then distinctly visible,) it may happen that there are no stars on the meridian al that time. Now, if an altitude of a star, which is nearest to the meridian, be observed, and th* apparpnt time of the observation noted, (as in the case of the sun,) the apparent time at ship ma^ be deduced from the Greenwich time by chronometer, it is easy to find the star's distance from the meridian, (which with the sun is the time from noon,) and is used in the tables in the same manner, by which means we obtain a correction to be added to the observed altitude of the star Thence the meridian altitude is obtained and the latitude is found as correctly as if the meridiaD altitude had been actually observed. The finding the variation of the compass at sea by amplitudes and azimuths, is now introduceo, illustrated by diagrams showing the real state of the case, and also why the variation is called easterly and westerly. Then follows a diagram showing the effect of local attraction on a ship's compass, the mannet of detecting the same, and the best means of remedying the erro;, and remarks on fixing up r standard compass. Diagrams showing the nature of hour angles, and the terms used in the computation, clearlj explained, and the apparent time at ship found from a set of altitudes of the sun, the corresponding time being noted by a watch or chronometer, as is usually done at sea. The time tables used in /his work are simply the co-secants for degrees and minutes of the polar distance, the secants for ihe latitude, the co-sines of the half sum, and the sines of the difference or remainder. The apparent time from the preceding noon or midnight, in the case of the sun, or the hour anglea of the other bodies, may be taken out at once from these tables. The logarithms in these tables are also used for other purposes in this work. The old standard tables of logarithms, sines, tangents, secants, etc., are not required. Finding the time at sunrise and sunset is illustrated by diagrams showing the nature of the case, and the degree of dependence to be placed thereon. The method of finding the apparent time at noon from equal altitudes of the sun, is also intro- duced, and is valuable from its extreme simplicity. The finding the time on shore by the use of the artificial horizon. •«► The mode of finding the time at sea by an altitude of the moon, planets, and stars, and also the manner of finding any particular planet or star in the heavens at any given time, when abore the horizon ; in like manner, the name of any star of the first magnitude, or planet, whose altitude has been observed, may be known. After thus having given all the various modes of finding the time at ship, the longitude by chronometer is then gone into, and every possible case is taken notice of and exemplified, first by the sun, in which the cases are all worked out in full, and every necessary correction fully explained, to which are added the practical rules as they are worked out at sea. A new table ia here added, to correct the longitude by chronometer, when the latitude used in computing the time at ship is proved to have been in error ; thus saving the time and trouble of working i over again. ITie longitude by chronometer is found at sun rising and setting, and also from equal altitude* at noon, and from the altitudes of the moon, planets, and stars. The mode is also given of com- bining observations of two different bodies, with the view of finding both latitude and longitude by chronometer, at the same instant <^f time. Sumner's method is now introduced, explained and exemplified, according to the mode [ have been in the habit of using myself at sea, and illustrated by a diagram, showing its great utility and use to the navigator, when the ship is approaching land or a danger. Tlie method of rating chronometers at sea, from time "^o time during the voyage, when in sight of land, is full) explained and exemplified, and also when in port, either by the spa or by ■■ PREFACE. ts artificial honzon. This is worthy the attention of navigators who carry chronometers, from th» (act that chronometers generally alter their rate after being received on board, and acquire what is termed a sea rate, and which is easily ascertained by the above method. In treating of lunar observations, diagrams have been introduced, showing the nature of the oorroctiins required in clearing the lunar distance, and a case projected exhibiting the relative positions of the two bodies in the heavens, and the hour angle of one of them used in finding the time at ship. The various methods of observing and writing down this observation is given as practiced at sea, and distances exemplified in a.i the various cases^ between the sun and moon, and between the moon and planets and stars. In clearing the lunar distance, one method only has been adopted, which is that by Lyons, and IS nearly the same as that given in Thompson's Tables, and which I have found from experience to be the most simple and easiest understood of any mode now in use, and is correct enough in practice. Much precision in clearing the lunar distance is not aimed at in this work, therefore many tedious corrections are omitted, which only tend to embarrass the navigator, and which are seldona applied in practice, and from the nature of errors in observing the distance itself, they do not seem to be required. The lunar observation in this work is therefore considered only as a means of detecting any Tery gross error in the longitude by chronometer, during a long voyage. A method is here also given of finding the longitude by a lunar observation on shore, on» altitude being observed in the artificial horizon, and the other computed. I have also introduced a new method of my own, which I have often used at sea, which is that of finding the longitude by measuring the moon's declination, illustrated by diagrams of the meridian altitudes of the moon and a star. The principle of this method is simply to observe th» distance between the bodies on the meridian. Then the star's declination being known, (taken from the almanac or table,) furnishes the moon's declination. Or, the meridian altitudes of the bodies being observed, (though not necessarily on the meridian together,) the star's declination applied to the difference of the altitudes, gives the moon's declination. Now, where this declina- tion so measured is found in the nautical almanac, will give the Greenwich time. Then the dif- ference between this time and the mean time of the moon's passing the meridian of the ship, i» the longitude in time, etc. The method of working days works and keeping the ship's reckoning at sea, adapted to the present age, is thoroughly explained and exemplified, and the various rules given in the first part of this work are now applied, as are also those in nautical astronomy, to find her position from celestial observations. The method of navigating a ship is now introduced, showing the mode of applying all the details which have been previously gone through, and many useful suggestions given, which have been derived from my own experience of a sea life, and will be found of service to the young navigator in times of peril and danger. Amongst which the rules given for avoiding a collision on ships meeting each other at sea, will be found of great importance, and should be thoroughly understood by every seaman. I have» therefore, put them into a practical shape. These rules are recognized by courts of law in deciding cases of collision. The method of keeping a log-book is explained, and various remarks made thereon, exemplified y a harbor log, the manner of keeping the log at sea by civil time, and also in the usual mod* by sea time. The whole is then wound up by the journal of a voyage in a clipper ship, in which every circumstance is noted in the log-book, as it would actually be done at sea, and showing th» care and circumspection necessarily required in navigating a fast^sailing vessel, from the fact that an error in the course of such a vessel will produce an error in the dead reckoning, in one day'» run, of from two to three times the amount greater than what the same error in the course of & ■Jow-sailing vessel would produce. Many new tables have been introduced into this work, with the view of shortening the compa » PREFACE. tations, and they are so arranged as to be easily referred to in practice, the one following the othet •8 they are required to be used at sea. The tables usually given in works of this kind are rejected, except those only which have • direct bearing upon the practice of navigation at sea. The tables containing the times of high water at full and change, the variation of the compass in early all parts of the world, deduced from actual observation at sea, and the very important one f the position of places, which is taken from the best English authorities on those subjects, in which the principal headlands, ports and islands only are given, with the view of enabling the navigator to verify his chronometer on sighting the land at any time during the voyage, or rating it while in port, the position of shoals, etc., are not given, the navigator will naturally look for information on this subject from his chart, which will furnish the most proper and correct delineation of their extent and position, which cannot be obtained from a table. From the foregoing prefatory remarks, it will be perceived that no very great amount of mathematical knowledge is required, beyond the common rules of arithmetic, to become a good practical navigator. Practical navigation does not, therefore, consist of a tedious set of oalculations, with a view of obtaining a very nice precision at any given time, but in the tact with which the navigator can single out and employ the heavenly bodies, in finding his ship's position therefrom, either by day ■or by night, and by increasing the number of observations, serve as a check upon each other, and thus verify her position in short intervals of time, in the shortest and simplest manner possible, having a due regard at the same time to its general correctness ; and which has been the aim of this work to accomplish. Having been engaged for some years in the instruction of seamen in navigation, I find that the chief difficulty lies in the fact that the generality of them cannot spare time sufficient on shore for the purpose of studying, and that they are obliged to pick up scraps of it here and there, as they best can, from whatever book falls in their way ; and not being able to discriminate between what i really useful in practice or otherwise, many of them form very erroneous ideas, in their laudable attempt at self-instruction. Therefore the chief inducement I had in writing this work, was to place it within their reach, iivested of everything but what has a direct bearing on the practice at sea, whereby they might instruct themselves with greater ease than formerly, as it will lead them step by step from the Vowest up to the highest branches of the science, and it embraces everything that is required to form a good practical navigator. Here 1 may remark, that the entire work has been computed and written by myself, from the observations and memoranda contained in the journals of many voyages I have made to nearly all parts of the world, the examples having been reduced to the present year of 1854, for the sake of uniformity ; and to accommodate those persons who may not have an almanac for that year at hand, I have added a table of extracts from the Nautical Almanac, containing the data for working the examples. Seamen will please to bear in mind that the work has been written by one of themselves, and with a sincere desire for their improvement and instruction, and should it meet with their approval, ^equal to the amount of labor bestowed on it,) would leave nothing more to be desired. And, without meaning any disrespect to the generality of navigators, I may add, that from nQ.y «wn experience I know that there are many who are very deficient, not from the want of the capacity of becoming so, but from the want of the proper means of instruction, and which would (Beem to verify the words of the ancient sage, on being interrogated by the youth. " My son" said he, '■ when you come to the years of manhood, you will be astonished to find how little wisdom it used in the governing of the worlds 1 cannot close the preface to a work of such immense labor, without soliciting the indulgence of the reader to any errors or inaccuracies which may have unavoidably crept in, notwithstanding the extreme care I have taken in revising the work over several times, both before and after com' mitting it to the press. I, however flatter myself that few will be found to ex'jst of much importance. WILLIAM THOMSl CONTENTS. PAGE ImkOMicnoif to tbe Practice of Navigation at Sea. 1 Diagram of the Earth — its description and dimen- eious. 2 Definition of the imaginary Circles on the Earth's surface — Latitude, etc^ explained S do. do. Longitude explained. 4 Diagram of the Earf. h 'wo Hemispheres Definition of Plant • 2 and the properties of a Right-angled Tr. - explained 6 Instruments of Naviga„ u defined and explained.. . 6 Mariner's Compass, and a Table of the Angles each point makes with the Meridian 7 The Sailings — Great Circle described on the Chart. 8 Plane Sailing, by Projection and Inspection 9 •Questions for Exercise in Plane Sailing 13 IVaverse Sailing by Projection and Inspection 14 Parallel Sailing by Projection and Inspection, with a Table showing the number of minutes and seconds of Departure contained in one degree of Longitude, f t every degree of Latitude. ... 18 Middle Latitude Sailing by Projection and Inspection 20 Questions for Exeicise in Case Ist, Mid. Lat Sailing 22 do. do. in Case 2d, Mid. Lat. Sailing 24 Mercator's Sailing by Projection and Inspection .... 25 Questions for Exercise in Car", 1st, Mercator's Sailing 26 do. do. in Case 2d, Mercator's Sailing 28 Current Sailing explained 29 Questions for Elxercise in Current Sailing 30 Taking Departures, or finding the Ship's Position from the Bearing of known objects on the Land 31 Table for finding the Ship's Position by two Bear- ings of the same object on the Land, with the Rules 82 Projection of a case of finding the Ship's Position by two Bearings 33 Questions for Exercise in finding the Ship's Position from Beaiings 84 Tides — Description and Cause of explained 35 First Method of finding the Time of High Water.. . 36 Second Method of finding the Time of High Water. 87 Winds in different parts of the World described. . . SB Currents of the Ocean described 39 Hurricanes — their Nature and Cause described. ... 41 Diagram of the Storm Circle in North Latitude.. . . 42 do. do. South Latitude.... 43 Remarks on Handling a Ship in a Hurricane 44 The Construction of MercJitor's Chart 46 Diagram of a Chart of Part of the Atlantic Ocean, and Ship's Track Construction of a Coasting Chart on a large scale. . 47 fhe Use of Mercator's Chail, Pricking off the Ship, Shaping a Course, etc_ 48 Questions for Exercise in Using the Chart 49 (J«e of the Coasting Chart and Questions for Exer- cise. 60 Span lings on the Coast, witli Remarks *^reon. ... 62 NAUTICAL ASTRONOMY. Diagram of the Solar System, and explanation ... 54 Description of the Planets used in Navigation 6fi Diagram of the Sphere, projected and explained. . 56 Definition of Nautical Astronomy 67 Diagram of the Sf^-'re, and the definitions explained 58 Projection of the Heavens in two Hemispheres 60 Signs of the Zodiac, and the Change in the Seasons explained fil Diagram of the Motions of the Heavenly Bodies round the Pole 6S Definitions of Tmie •"••... 68 Diagrams, showing the Method of finding the Stars in the heavens from their computed Altitude and Meridian Passage 64 Diagrams, showing tbe Dip, Refraction and Parallax 66 Definitions of the Dip, Refraction and Parallax 67 Diagram, showing the manner of taking Altitudes . f.8 The Instruments of Nautical Astronomy explained 69 To Adjust the Quadrant 70 To Measure Altitudes with the Quadrant 71 To Adjust the Sextant 72 To find the Index Error of the Sextant 73 The Use of the Sextant in measuring Angular Dis- tances 74 To find any Heavenly Body (used in the Lunar Dis- tance) by computing its Distance from the Moon 75 Remarks on Telescopes, and a New Method of tak- ing Lunars 7(j The Artificial Horizon explained 77 Diagram, showing the prinxjiples of the Artificial Horizon 7 g The Chronometer explained — stopping, setting ago- ing, etc 79 General Remarks on tbe Use of the Chronometer. . 80 The Azimuth Compass explained — Taking Azi- muths and Amplitudes 81 Use of the Thermometer, and General Remarks on the same §2 Use of the Barometer, and Practical Remarks on the same 88 To Correct the Sun's Declination, with Remarks. . . 84 Questions foi' Exercise in Correcting the Declination 86 Finding the Latitude by the Sun's Meridian Alti- tude 85 Diagrams and Examples of finding the Latitude by the Sun 87 Questions for Exercise gg Diagram of tiie Sun in the Zenith, and Examples. . 89 Finding tlie Latitude by observing the Sun's centre 89 Finding the Latitude by a back observation with a Sextant ^ Finding the Latitude by a Meridian Altitude of the "^un below the Pole ,,,. %f CONTENTS, FAOE Fio.liDg the Latitad« on Shore bj the Artificial Horizon 92 Fiiuling the Latitude by the Sun out of the Meridian 98 Questioos for Exercise in findiog the Latitude out of the Meridian 94 Finding the Latitude by two Altitudes of the Sun. . 96 QuertUoni^ tor Exercise in finding the Latitude by two Altitudes 99 Fiiiiiiiig the Latitude from the Sun's change of Alti- tude on the Prime Vertical, with a Tjible con- taining the Sun's change of Altitude in one minute of time for ev^rj degree of Latitude. . . 100 Finding the Latitude by the Meridian Altitude of the Moou .' 101 Examples of finding the Latitude by the Moon. . . . 103 Finding the Latitude by the Meridian Altitude of a Planet 104 Examples of finding the Latitude by a Planet .... 105 Finding the Latitude by the Meridian Altitude of a Star 106 To find the Star in the heavens from its computed Altitude and Meridian Passage 107 Examples of finding the Latitude by a Star. 108 Finding the Latitude by the Meridian Altitude of the Pole Star, and also at any other time when risible 109 Finding the Latitude by the Meridian Altitude of two Stars, North and South of the Meridian, when the horizon is obscured 110 Finding the Latitude by an Altitude of a Star out of the Meridian Ill To compute the Logarithm of the Latitude and De- clination when the latter exceeds 26* 112 Finding the Latitude by two Stars, one of them out of the Meridian 118 Finding the Latitude by an Altitude of the Moon out of the Meridian 114 Finding the Latitude by an Altitude of a Planet out of the Meridian 116 Diagram of an Amplitude, and solred by Inspec- tion 116 Finding the Variation of the Compass by an Ampli- tude. 117 Diagraui of an Azimuth, and Rule for computing the same 118 Finding the Variation by an Azimuth 119 Diagram, showing the EflFect of Local Attraction on the Ship's Compass 120 Remedy, when Local Attraction exists on board Ship at Sea 121 Finding the Time at Sea by the Sun 122 Diagrams of the Hour Angles, with North and South Declinations 123 Method of Obserring Altitudes of the Sun for Time, and Gkneral Rules for finding the Time at Ship, with Examples 124 Diagram of the Hour Angles, when both the Sun and the Ship are on the Equator, with Exam- plea of finding the Time 127 Finding the Time by the Sun's Rising or Setting. . 128 Diagrams of the Hour Angles at Rising or Setting. 128 Finding the Time from Equal Altitudes of the Sun near Noon 130 Finding the Time on Shore by the Artificial Horizon 181 Finding the Time by an Altitude of the Moon 132 Finding the Time by an Altitude of a Planet 134 Finding the Time by an Altitude of a Star 1 36 Remarks on finding the Longitude by Chronometer 138 Finding the Longitude by Chronometer by the Sun 140 Fizamples of the Ship crossing the Opposite Merid- ian to Orcenwich 148 To Correct the Longitude at Noon, wben the Lati- tude worked with is in error. 144 Finding the Longitude by Gbrononaeter at Sunri»« or Sunset Finding the Longitude by Chronometer at Noon, from Equal Altitude* Finding the Latitude bv the Sun, and the Longitude by the Chroiioineter "jy the Meon Finding the Latitude by a Star, and the Longitude by Chronometer b} Planet Finding the Longitude b) Chronometer, and the Variation of the Compass by an Azimuth, from the same Altitude ot the Sub Finding the Ship's Positioi at Sea by Sumner's Method Diagram of Sumner's Method Continuation of the same Example Rating the Chronometer at Sea Examples in West Longitude do. East Longitude Rating the Chronometer on Shore Questions for Exercise in finding the Longitude by Chronometer Lunar Observations. Diagram showing the Efi'ect of Parallax on the Lunar Distance Remarks on Lunar Observations Methods of Observing a Lunar, with or without as- sistants Diagrams of a Lunar Observation Finding the Longitude by a Lunar Observation by the Sun do. do. Lunar Ob8<»'v"'ion by a Star. . do. do. do. by a Planet To find the Error in the Meap' .distance The Bodies being too near the ...pridian to get the correct time from their Altitude. Time found afterwards and applied Rule to Compute the Altitude of any heavenly body To Compute the Altitudes at the time of observing the Distance Finding the Longitude by Lunar Observations on Shore New Method of finding the Longitude from the measurement of the Moon's Declination Diagram of the Moon and a Star on the Meridian . . New Method of finding the Longitude from the Me- ridian Altitudes of the Moon and a Star Diagram of the Meridian Altitudes of the Moon and Star ,;,.. Method of Keeping a Ship s Reckoning at Sea.. . . . The Log Board explained Allowing for Leeway and Variation Remarks on Keeping the Reckoning at Sea Rules for Working a Day's Work Example of a Day's Work, outward bound do. do. at Sea do. do. inward bound Finding the Departure and Longitude from Equal Distances of Sun or Star from the Meridian . . Navigating the Ship, appUcationof the above Rules, etc. do Indications of Stormy weather, discovery of Danger Rules to Prevent CollisiM on meeting Ships at Sea, etc. Lying to under a Drag. Construction of a Tempo- porary Rudder Making the Land. Signs of Land being near. Methods of Keeping the Log-Book Keeping the Harbor Log, outward bound Method of Keeping the Log-Book in Civil Time . . Usual Method of Keeping the Log in Sea Time, ex- emplified in a Journal from Santa Cruz to St John's Abstract of the Journal 147 148 14« 150 151 159 154 15C 156 158 169 160 161 163 168 164 16& 167 168 169 170 172 178 174 176 177 178 17» 180 181 182 188 184 185 186 187 188 188 18» 1»> 19) 19i 193 194 19fi 19« 9M NOTICE TO THE THIRD EDITION. This edition has been furtker revised and corrected ; and a new and complete set of Tablei, for finding the Time at Ship (and thence the Longitude by Chronometer), have been added. NOTICE TO THE SECOND EDITION. This work has been revised and corrected, and an addition made of a separate Explana- tion of the Tables^ and it is hoped that no error of importance will now be found to exist. It may be necessary here to say, that the author, in writing this work, did not consider a separata Explanation of the Tables requisite, as he had beep particular irt explaining them in difftrent parts of the work when they were used. But as some navigators have recommended it, the fol- lowing has been added, which will be found useful, as by glancing over tliem you can rapidly see, what the book contains, where the tables can be found, how and where they are used. EXPLANATION AND USE OF THE TABLES. Note. — The number of the page, which is placed on the same line with the number of the table, refers to the second part of this work, where the table will be found, and the numbers of pages in the margin refer to the first part of this work, where the table is used and explained. TABLES I. AND II.— Page 1 to 6L Difference of Latitude and Departure. These tables are of very extensive use in Navigation, afibrding an easy and expeditious method of solving problems in right-angled plane trigonometry, and consequently applicable to every variety of sailing. Table I. contains the difference of latitude and departure (m whole numbers And tenths) answering to distances not exceeding 300, and for courses to every point p „ of the compass. Table II. is of the same nature and extent, but for courses consisting °„ of whole degrees. The courses are set down at the top of the pages when they do not exceed 4 points or 4.^ degrees, and at the bottom when they are greater than these quantities; and it must be observed that when the courae is taken from the /o/> of the page, the diff. of Lat. and Dip. must be taken 'from the top also, but when the course is taken from the bottom the diff. of Lat. and D(p. must be taken from the bottom. Hence, wnen these tables are „ ,„ applied in Farallcl or Middle Latitude sailing the co. lat. or co. mid. lat. is taken as a ''i'f course, the departure or meridional distance is found in the Dep. coiumn, and the dif- ference of longitude in the Dist. column. In Mercator's sailing, the meridional dif- p „. ference of latitude is taken out in the Lat. column, and difference of longitude in the "^* ^ Dep. column. When any of the given parts (excepting the courses,) exceed the limits of the table, any aliquot part, as a half, third, fourth, &c., is to be taken ; and those found cor responding are to be multiplied by the same figure that the given number is divided by. TABLE III.— Page 62 to G7. Meridional Parts. This table is used in resolving problems by Mereator's sailing, and in constru' ting „ „_ eharts on Mereator's projection. The meridional parts are to be taken out fo» the ^nl degrees answering to the given latitude, at the top or bottom, and for the minutes at either side colunm. • 1* TABLE IV.— Page 68. Mean Refraction Thl.* table contains the mean refraction of the heavenly bodies, in minutes and p «- •econis, at a mean state of the atmosphere, and corresponding to their observed alti- °f an tudes This correction is always to be substracted from the observed altitude of the " ohject. tn EXPLANATION AND USZ OF THE TABLES. •2 TABLE v.— Paqb 69. Dip of the Horizon _ ^^_ The corrections taken out from this table, answering to the height of the eye, ftboT* ^fl_ the sea in feet, are to be subtracted, from an altitude taken by a fore observation, or ***** ' added to those taken by a back one. *3 TABLE VL— Paok 69. Sun^s Parallax in Altitude. Foffe 67 This correction is to be taken out opposite the Sun's altitude, and is always ad and 86, ditive to it. • Ifot* — ^Th« joint effect of the oorrections taken from theBe three tables, togetb«r with the Sun's semi-diameter,, tma b« taken at onoe from Table IX. when the altitude of the Sun's lower limb is tr.ken by a fore obaerTation. TABLE VIL-Page 69. Moon^s Augmentation. _ .f.. The Moon's apparent horizontal semi-diameter, as given in the Nautical Almanacs, t^age . j^ ^.^ ^^ increased by a number of seconds, called the augmentation, taken out from this table, answering nearest to her altitude. I^ote. — In practice this is seldom used, except in working a Lunar. See page 165. TABLE VIII.— Page 69. Dip at Different Distances. p _» When that part of the horizon immediately under the Sun is obstructed by land,. "^ ' the dip is to be taken fi-om this table, (with the height of the eye at the top, and th« estimated distance from the land in miles in the side column) instead of Table V. TABLE IX.— Page 70. To Correct the Observed Altitude of the Sun''s Lower Limb. n Qrt This table is intended to simplify the usual method of correcting the observed altitude "^* ■ of the Sun's lower limb, when taken by a fore observation, by showing the correc- tion at once for the joint effect of the Sun's semi-diameter, dip of the horizon, refraction, and parallax. These corrections I ing computed to minutes and tenths, the tenths may easily be reduced to seconds by multiplymg them by six. In this table the Sun's semi-diameter is assumed at 16 minutes, and its variation from that quantity in each month of the year, given at the bottom of the tal)le, is to be applied to the corrections found in the table according to the sign -|- or — prefixed it. TABLE X.— Page 71 and 72. Sun's Declination. The Sun's declination is given in this table in degrees and mmutes for the years 1854-55- 66-57, at noon on each day of the year under the meridian of Greenwich ; but will answer for leveral subsequent years, by applying the corrections from Table XII. TABLE XL— Page 73. To Correct the Suit's Declination for Longitude and for Time. T* Al "^^ ^^^ Sun's declination in table X. is adapted to the meridian of Greenwich at ^Qfr noon, when the ship is to the eastward or westward of that meridian, it should be corrected by this table; also when it is required for any other time than noon, it can oe corrected by this table, and applied as directed below the table. J!iote. — Rules for correcting the declination (taken from the Nautical Almanac") to Greenwich time, at page 124 EXPLANATION AND IISK OK II IK TABLKS. «•• TABLE XII.— Page 73. Correction of the Sun's Declinatu n evert/ 4 years. This table is intended to correct the Sun's declination given in Table X-, for the chanc[e that takes place in periods of four years. See note below the Uible. TABLE XIIL— Paok 74. Sun's Right Ascension. * The Sun's mean right ascension contained in this table, is to be taken out with the p ^»^ month at the top, and the day in the side column. When great accuracy is necessary, ' it must be taken from Nautical Almanac. TABLE XIV.— Page 74. Equation of Time and Table of Corrections. The Equation of time for apparent noon at Greenwich, is given in this table for the years 1854-55-i56 and '57, and which will answer nearly for sixteen years. A table adjoin- „ ,j>^ ing is given for correcting the Equation of time for Longitude and for time. This table " is entered with the daily change of the variation at the top, and the Longitude at the left side, (or if for time, at the right side) and the angle of meeting points out the correction in sec. and tenths of sec. to be applied as directed at the bottom of the table. Note. — Rule for correcting th» Equation of time from the Nautical Almanac is given at page 124. TABLE XV.— Page 75 to 80. J'hr Finding the Latitude out of the Meridian. This table was first calculated and published by the author in a separate form, (call- „ ^j- ed Thorn's Tables) but on writing this work was introduced in it ; it is divided into ^ five parts, and explained at Page 93. TABLE XVI.— Page 81 to 83. Apparent Time, of Sun's Rising and Setting. This table is entered with the declination at the top and the latitude at the side, and the angl* tC meeting will point out the time of rising and setting from the top when the Latitude and de- clination are of the same name, or from the bottom when they are of contrary names. To Find the Time of Rising and Setting of any other Celestial Object. This table also exhibits half the time that an object continues above the horizon in Moon^s the column of Sett., and half the time that it continues below in the column of Ris., M. P., from the top of the page, when the latitude and declination of the object are of the FagelOl. same name, and from the bottom when they are of contrary names. Therefore, to Star's find the time of the object's rising, subtract half the time that it continues above the M. P., horizon, from the time of t7s passing the meridian, and to find the time of setting Fage \0Q. add half the time that it continues above the horizon to the time of its passing the Planet's meridian. Note. — The rule for computing the meridian passage of the Stars is given M. P. It page in. Table XVIIL al^o gives the Mn. Passages of the Stars Page 85 to 90. Page 115. TABLE XVII.— Page 84. Altitudes by which the Apjyarent Time may be found with the greaictit accuracy. When the latitude and declination of an object are of the same name, by entering this tabU with the declination at top or bottom, and the latitude at the side, the angle of meeting p^^ j23, points out the altitude of the object nearly, when it is in the prime vertical, or at its nearest approach thereto, and which is the best altitude for ascertaining the apparent time. When the latitude and declination of an object are of contrary names the olject is nearest the prinw vertical, when in the horizon, but an altitude less than 6° or 7° stould not be used on account ot \ite uncertainty of refraction at low altitudes. «T» EXPLANATION AND USE OF THE TABLES, TABLE XVIII.— Page 85 to 90. Fof finding the Apparent Time of 24 Principal Stars passing the Meridian throughout th» Page 106. year. TABLE XIX.— Paob 9L "age 106. Sight Ascension and Declination of 24 Principal Start. TABLE XX.— Page 91. Fbr Correcting the Observed Altitude of a Star or Planet. Page 108. Pag 109 mtdll. This table contains the corrections in minutes and tenths to be subtracted from th» observed altitude of a Star or Planet to find its true altitude, being the joint effect of refraction and dip of the horizon. TABLE XXI.— Page 92. To find the Latitude by an Altitude of the Polar Star. This table is explained on its own page, and on the right hand column is the varia- tion of the correction in 10 years, which is to be substracted from the correction for that period of time. TABLE XXII.— Page 93. For Correcting the Time of the Moon's M. Passage at Greenwich to the time of her passing over any other Meridian. This table is entered with the daily variation of Moon's M. Passage to the nearest „ i<\j minute at the top, and the longitude of the place in the left side colunm, and the angle ^ of meeting points out the minutes to be added to the time of Moon's passing the Meridian of Greenwich in west longitude or subtracted in east. The sum or remainder will be the time of her passing the Meridian of the place. TABLE XXIII— Page 94. For Reducing the MoorCs Declination to the Greenwich Time of the Observation. Page 102. This table is only used with an Almanac that has the Moon's Declination given for every noon and midnight. TABLE XXIV.— Page 95. To Correct the Moon''s Semi-diameter and Horizontal Parallax. Pag§ 101. This table is explained at Page 95, below the table. TABLE XXV.— Page 9G. Bage 102, To Cor'-ect the Moon's Apparent Altitude. TABLE XXVI.— Page 97. To Turn Time into Degrees or Degrees into Time. p \At\ T^s table is entered with degrees in one column, and opposite the time correspond rage 14U. j^^ .^ ^^^^^ TABLE XXVIL— Page 98 to 106. logarithms of the Latitude and Polar Distances. P 1«M» T^& table contains Logs, of latitude and polar distance for finding the time, and ^ ' thence the longitude by chronometer. The latitude in degrees is taken from the top and miles from left hand side, the polar distance in degrees is taken from the bottom and miles from right hand side, except when the polar distance is above 90°. it is then taken from the top. EXPLANATION AND USE OF THE TABLES. TABLE XXVIIl.— Paob 107, 115. Logarithms of the Half Sum a«td Difference. This table contains the Logs, of the half sum and difference for finding Jie time, p j^^ 4nd thence the longitude by chronometer. The half sum is tak«jn from the top and ^ difference from bottom. TABLE XXIX.— Page 116 to 124. Logarithms of Apparent Tin\e or Hour Angle. For explanatioa, sm note at bottom of page 125, first part of this work. Paiye 12S. TABLE XXX.— Page 125. ^or Correcting the LongihuU hy Chronometer for the effect of an error in the Latitude used m finding Time. TTiis tabl* saves the trouble of working the sights over again at noon, when you Page 144 €nd you have used a wrong latitude in finding the time at s«»» in the morning. and 145. TABLE XXXI.— Page 126 to 137. Logarithms of the Apparent Lunar Distance. This table 0(mtains the Logs, sines and Logs, tangent of the apparent lunar distances. Page 165. TABLE XXXII.— Page 138 to 152. Logarithms of the First and Second Corrections. Tliis table contains the first and second corrections to be applied to the apparent „ .__ bude when not on the Prime Vertical. JAMES H. BROWNLOW PRACTICAL NAVIGATION INTRODU.CTION. Navig A.TION is the art of conducting a ship from one port to another, through the wide and trackless ocean, with the greatest safety, in the shortest time possible, and to find her position on the globe at any given time. To be able to do this, the mariner is required to have a knowledge of certain imaginary circles, Bupposed to be drawn on the surface of the earth, together with the most practical and easy method of finding a ship's position thereon, from the course steered by the compass, and lier distance sailed, and also the course and distance to her intended port. This constitutes what is called Navigating by Dead Reckoning; but as it is liable to be greatly in error, even in short dis- tances run, from many causes (which will be explained in this work), it cannot therefore safely be depended on. Consequently, the mariner must have some other resource to apply to, with the view of ascer- taining his ship's true positioa. This can only be derived from the observations of the heavenly bodies ; but to do this, he is required to have e knowledge of certain imaginary circles supposed to be drawn in the heavens, corresponding to those already supposed to be drawn on the earth's surface ; by which means he obtains the positions of the heavenly bodies themselves, in the same manner as the position of the ship is indicated by the circles on the earth ; and it will be the object of this work to instruct him how to find his ship's position, from the observations of any of the heavenly bodies which may be visible, either by day or by night, and avoiding all the tedious details and intricate calculations which are not necessary, thereby saving much valuable time and labor ; the results, by this method, having been found from actual experience to be sufficiently accurate for all practical purposes. In this work the mariner will therefore not be required to go through a tedious training in decimal and logarithmical arithmetic, nor is it required that he should have a previous knowledge of either geometry or trigonometry, which are usually given in works of this kind ; all the matter which treats on those subjects is therefore discarded, except such part of it as has a direct bearing on the practice of navigation at sea. All that is then required of him is to have a previous knowledge of the common rules of arith- metic; that is, addition, subtraction, multiplication, division, the rule of three, and the practice of aliquot parts ; or that amount of education only which would be required to fit a person to ful- fil the ordinary business of life. In the room of the above-mentioned discarded matter. Diagrams or figures of the subject under consideration will be introduced in their proper places, and the explanation of each Diagram facing it on the same or opposite pages, thereby enabling thf learner to comprehend mechanically the whole case at one view. The construction and use of both General and Coasting Charts, with the manner of taking Sound- ings on the Coast, tiie prevailing Winds and Currents in different parts of the world, and Storms and Hurricanes, will all be explained, and practical rules given to avoid the latter, derived from actual experience. The Instruments of Navigation will also be explained, and the manner of adjusting, correcting, and using them at sea. In treating of Nautical Astronomy, the subject will be illustrated by Diagrams, and the case* proved by projection only, in the room of going into the tedious solutions of Spherical Trigonom- etry, except in those cases where a Rule is required ; and much new matter on this subject will W introduced, in connection with the use of the Chronometer. Many new Tables will also b« -Dtroduced, with a view of shortening the labor in the computations. Although this work is intended to treat only on those subjects which have reference to the place of the Ship on the Ocean, nevertheless much useful matter will be found which will be interesting to the young officer, in regard of Navigating the Ship. The who.e being original matter, which the author of this work has derived f^om a personal experience of more than a quarter of a cen- tury, in Navigating Ships to nearly all parts of the world. The work will be closed with the methods of Keeping a Log-Book, exemplified by a journal of a Voyage, with remarks on th» same, as would actually be done at sea. fJEOGRAPHY. /♦ ,1. .^ DIAGKAM OF THE EARTH, Aowng Ut inclination to the Plane of its Orbit of 23* 28', and. the imaginary Circles drawn or. it mtfjtt FlQ. 1. DESCRIPTION AND DIMENSIONS OF THE EARTH. The Polar Diameter is 7899, and the Equatorial Diameter 7926 miles; the latter being the greatest, it Mtosed by the revolution of the Earth on its axis, and as the greater portion of the surface is covered with water, it recedes from the poles towards the Equator, until its tendency to run back towai-ds the poles just balances the effects of the centrifugal force. This causes the Equatorial Diameter to be about 27 miles greater than the Polar Diameter. If the Earth should stop revolving on its axis, the water at the Equator would ■ettle away towards the Poles until it assumed the form of a Globe as near as possible. Thus, large por- tions of land in the Torrid Zone which are now covered by the ocean would be left dry, and new conti* Bents and islands formed. The Polar Axis is not perpendicular, but inclines to the plane of its orbit at an angle of 23° 28', and per- forms its revolution round the sun in one year, or 365 days 6 hours, or at the rate of 68,000 miles an hour; at the same time it performs its daily revolution round its axis at the rate of 15° to the hour — equal to 90* miles, or 15 miles in 1 minute of time. Latitude is measured in Degrees, Minutes, and Seconds from the Equator towards the Poles, from which H is 90* distant ; each Degree contains 60 Minutes, and each Minute contains 60 Seconds. 1 Minute ©r Nautical Mile contains 6082 feet, or 1013 fathoms, and therefore a Second is about 101 feet, or 17 fathomi nearly. The Circumference of the Earth at the Equator is 360 Degrees of the same length as the Degrees of Lati- tude ; consequently, Degrees of Latitude and Longitude are the same length on the Equator. But on sail- ing North or South from the Equator, the Meridians contract, and the Degrees of Longitude become less, (but still contain or are divided into 60 minutes,) until they finally meet at the Poles, where there is ne Longitude. The Earth revolves from West to East, which if th/* '•aiise of all the heavenly bodies appearing to rise in the East and set in the West. DEFINITIONS OF GEOGRAPHT. GEOGRAPHY, iS APPLIED TO THE PRACTICE OF NAVIGATIOW AT SEA. DEFINITIONS. Practical Navigation relates to two methods, independent of each other — the first is that usually called Oead Reckoning, and the other by Astronomical Observations ; but in practice they are generally carried ♦n together, as a check upon each other. The first of these methods requires a knowledge of the imaginary lines and Circles on the surface of the Globe, or Earth, which we inhabit, and which turns round once in every 24 hours ; the line round which it revolves, and which is the shortest diameter, is called the Polar Axis, and drawn between the North and South Poles 90° from the Poles is the great Circle, called the Equator, passing round the earth and dividing it into "two equal parts, or Hemispheres. At all places on this circle the sun rises and sets at 6 o'clock all the year round, and the days and nights are equal, being divided into 12 hours each. A Meridian is a circle passing through both poles, and cutting the Equator at right angles. Places situ- ated on this Circle are said to be on the same meridian North or South of each other. Latitude is the distance from the Equator, measured in Degrees and Minutes, on a meridian towards Ihe North or South Poles, and named accordingly. The Co-latitude is the difference between a given Latitude and 90*. or the Pole. Parallels of Latitude are Circles parallel to the Equator, running East and West. Places on this circle .*re said to lie on the same parallel of latitude. The Difference of Latitude of two places is the portion of the meridian included between their parallels. The Difference of Latitude of a Ship is therefore the distance she makes good in a North or South direc- 'Uon. It is evident that when two places are on the same side of the Equator, their difference of Latitude u ifound by subtracting the lesser latitude from the greater, and that when they are on opposite sides of tha Equator, that is, when one place is in North Latitude, and the other in South Latitude, the sum of their l«alitudes is the difference of Latitude. EXAMPLE 1. Find the difference of Latitude between New York tnd CharleatoD, S. C. New York, Latitude 40* 43' N. Charleston " • 32 46 N. Difference of Latitude. . . 7° 67'. EXAMPLE 2. Find the difference of Latitude between Cape Henry 8', or 63 milta N. of th« Equator, munt evidently be in South Latitude after nutkisg 128 miles southinff. Thus, in subtracting one of the quantities from tba oinar, the difference takes the name of the greater. GEOGRAPHY. Longitude is th« distance xneasured on the Equator, between the Meridian of a giren plaoe and another^ •ailed the first meridian. The choice of a first meridian is arbitrary. The Americans, English, and othat nations adopt Greenwich Observatory in England as the first Meridian. The Longitude of a place is named East or West, according as it is East or West of Greenwich, as far w- J 80', and which is the opposite meridian to Greenwich, or one-half of the circumference of the Earth. A Ship sailing East beyond 180° East Longitude, would then be in West Longitude, and sailing West beyond 180* West Longitude, would then be in East Longitude. Longitude is measured either in Degrees, Minutes, and Seconds, or in Time, that is, in Hours, Minutes, and Seconds, each hour being equal to 15° ; for the Sun, which regulates the time, returns to the same- meridian again after describing a complete circle, or 360 , in 24 hours, and 15* multiplied by 24, makes 360*. The Difference of Longitude of two places is the portion of the Equator included between their meridians. To measure, therefore, the difference of Longitude between two places, we must follow down their meridian* to the Equator, and then take the included portion of the Equator itself, The Degrees of Latitude and Longitude are of the same length on the Equator ; but as the meridians contract and meet at the Poles, the greater the Latitude the Degrees of Longitude become less ; that is, the space contained in a Degree of Longitude becomes less as the Latitude increases, until at the Poles the Longitude ceases altogether. When two places are on the same side of the first meridian, their difference of Longitude is found by subtracting the lesser from the greater. When two places are on opposite sides of the first meridian, that is, when one place is in East Longitude and the other in West Longitude, the sum of their Longitudes is the difference of Longitude. When one Longitude is East and the other West, and their sum exceeds 180°, subtract from 360' will fire their difference of Longitude. EXAMPLE 5. Find the difference of Longitude between New York and )£anilla. New York, Longitude 74° 1' W. Manilla " 121 2 B Sum EXAMPLE 1. Find the difference of Longitude between New York and CbailestoD, S. C. New York, Longitude 14' 0' W. Charle«ton " 79 64 W. Difference of Longitude. ... 6* 64'. EXAMPLE 2. Find tk« differenee of Longitude between the Cap« of )ood Hope and Cape St Roque. Cape of Good Hope, Longitude 18* 30' E. Oape St Roque " 86 17' W. Difference of Longitude, 63* 47'. EXAMPLE 8. A Ship sails from Longitude 60* 10' W. to 60° 80* W, find the difference of Longitude. Longitude left 60* 10' "W. Longitude in .60 30 W. Difference of Longitude. . 10* 20'. EXAMPLE 4. A Ship sails from Longitude 6° 40' W. to 2* 10' R find her difference of Longitude. Longitude left 6* 40* W. Longitude in 210 £. Difference of Longitude. . .7* 60'. 195" 3'. Subtract ftom 360 . Difference of Longitude.. 164° 57' Fig. 2. THE EQTUTOR. NoTB.— A Ship in East Longitude sailing East, or in West Longkuda sailing "We8t, increases her Longitude, b-n ir But Longitude sailing West, or in West Longitude sailin^r Eastj she dimir.iahea her longitude ; and when the Lonir' ide exoeedg 180", subtract it from 860, will give the Longitude m of a contrary name. EXAMPLE 7. EXAMPLE 6. A Ship from Longitude 85* 26' "W. sails East 8* 40', fad the Longitade in. Longitude left 86' 26' W. Difference of Longitude 8 40 E. longitude in 81* 46' W. A Ship from Longitude 179' 32' E. sails East 2° find the Longitude in. Longitude left 179' 32' K. Difference of Longitude . . 2 30 B. Sum sy. 182° Subtract from 360 2' Longitude in 177° 68' W, DEFINITIONS Or PLANE SAILING Fic. 4. DIAGRAM OF THE RIGHT-ANGLED TRIANGLE. ' -^ 1 1 1 TcvralZel -f £. •'■^ , '1 .A(pr> r^t )^ /h'^y/'i i/ & if t ^/ t/c .'r m • \\i/ 1 CO'Mf' if j - — ^ "f ./.'fJ ^! il r/ i,yrrr/r ">^ ; ^ 1 ' vi i 5 3 su II 1^ t i ' /r//,y//./ ^"^Z /^'/' Jf'// The length of a nautical mile being about 6,080 feet, the 30 Second Glass should have a length of T *t oearly 51 feet To determine the length of Knot to any length of glass, the Rule is, as 3f Seconds u tc SI feet, so is 38 Seconds to the Knot of 47 feet, and so on. But in practice a 45 feet length of Knot is found to correspond best with a 28 Second Glass. The dif- ference is caused by the Log Ship coming home when hove, ana 47 feet gives the Distance run too small. Before the line is measured it should be well stretched, and then made wet. Nails should be placed in •Hie Deck at the proper length of the measured Knot, so as to verify the marks frequently, as the line is !hable either to stretch or run up. Sometimes the Knots and half Knots only are inserted in the Log Board, but in general the Knot is •divided into 10 fathoms, and the odd fathoms inserted for handiness in adding up. This laihom is noi i feet, but the tenth part of the Knot only. The Log line, after being thus measured, is fastened to a Reel and wound up. ready for use. The mail- ner of heaving the Log can only be learned at. Sea, but it may be useful to remark that the line is faked in the hand, not coiled, and the Log Ship is to be thrown well out to Leeward of the Ship's wake, and in such a manner that it may take hold of the water at once, and that before a heavy Sea the line should be paid out rapidly wlien the Stern is rising, and retarded a little when the Stern is falling. Whichever length of Glass is adopted, there should always be another of half the length, usually called the short glass, and used when the Ship is going rapidly through the water, as only half of the length of line is required, and by doubling the number of Knots run out, the same result is obtained as if the whols •line had been used. The Glass should be kept dry, and verified occasionally with the second hands of a Chronometer. THE COMPASS. The Mariner's Compass consists of a circular card, the edge being divided into 32 Points, Half Points »nd Quarter Points, and into 360 Degrees. The four principal points, or, as they are called, the cardinal points, are North, South, East, aad Waal,, the East being towards the right when facing the North. A farther description of this well-known Instrument is not required, except that in North Latitude the North Pole of the magnetizpd bar is drawn or attracted in that direction, and in South Latitude the South Pole is attracted towards the South. The Dip, or attraction towards the centre of the Earth is greatest in high Latitudes, and is frequently the cause of a sluggish movement of the Card in common compasses* The magnetic pole dipping, a balance-weight of Sealing- Wax or other substance is required at the othei «nd of the bar, to make it swing freely round, which can be removed again in low Latitudes. The pin on which the card is balanced sometimes becomes blunt by constant use, which can be sharpened with a fine- grained file or a set stone. The Lubber's Point is a perpendicular mark in the centre of the forward part of the Compass Bowel uid represents the line of the Ship's Keel, (or a line parallel to it) By endeavoring to keep a given poin< «f the Compass cam at this mark, constitutes what is called steering a course by Compass. THE VARIATION OF THE COMPASS. The Needle points to the Magnetic North, which in few pajts of the world agrees with the true Nerth, oint representing the given course or bearing. A True course or bearing is reduced to the Compass course or bearing by applying the variation the con- Irary way. LOCAL ATTRACTION. The Compass in every Ship is more or less affected by the Iron used in her construction, and by Iron on Iward as cargo. It is most sensibly felt when the Ship's head is East or West, because in North Latitude the North Point is drawn forward, and the reverse in South Latitude ; but when her head is North and ■ Bouth, the Magnetic and true meridians nearly coincide with the disturbing force, situated in the forward part of the Ship, and the effect is not so sensible. It may be detected by taking frequent observations to find the variation of the Compass, (which will include the Local Attraction ;) then the difference between that and the variation laid down on the Chart will be the Local Attraction. Th'S subject will be found treated of more at length at page 120. PRACTICAL NAVIGATION. INTRODUCTION TO THE SAILINGS. Th« Methods used in navigating a Ship by Dead Reckoning are the Plane and Traverse Sailings, Paral lei, Middle Latitude, a,nd Mercator Sailings ; Current Sailing being merely a modification of the others, all •f "Which will be explained and exemplified under their proper heads. It has not been deemed necessarily •vrithin the scope of this work to include Great Circle Sailing, simply because the track of a Ship, as given by the general rules in Great Circle Sailing, cannot be practicallT'' adopted by a Sailing Vessel, from many causes which it is not necessary here to explain, and which ha* been the cause of leading many vessels astray that had adopted it. A Ship may, however, adopt a modification of the Track on the Great Circle without reference to any- general rules, as follows : Great Circle Sailing supposes a Ship to Sail on a circle on the Earth's surface, having the Centre of th» Earth as a Centre. When a Ship sails true North or South, she sails on the Arc of a Great Circle; and when she sails true East or West on the Equator, she also sails on the Arc of a Great Circle, because these Circles have the Earth's Centre for a Centre ; but in sailing on a straight Rhumb line in any other direo- tion, which, although it may appear perfectly straight on the Chart, nevertheless, if her positions at Nooa were laid off on a Terrestrial Globe, it would be found that she had described a Curve with its back to- wards the Equator, and been sailing on a Small Circle. Now the object to be attained in Great Circle- Sailing is to adopt a curve or track on the Chart, the back of which shall be turned towards the Pole of that Latitude in which she is Sailing. Then, supposing her positions at Noon to be laid off on the Globe as be- fore, it will be found that she has been sailing on a circle which has the centre of the Earth as a centre,, the distance measured between any two places on this Great Circle is the least distance between them j. but, as before observed, this is not always practical. A modification may be adopted by tracing upon a Chart of the intended voyage a curved Track from Port to Port, having its back towards the North in North Latitude, or towards the South in South Latitude, and which shall keep the Ship free from being entangled with the Land, and at the same time placing her in the most favorable position to take advantage of the prevailing Winds and Currents. The manner of doing this is simply to draw a line between the two places on the Chart, and to mark the extent to which the curve may be judiciously made on the polar side of the middle of that line ; thei* through th«>se three points trace a curved line, which will approximate to that of a Great Circle. Now it is evident that to sail on this curved track, the course must be shaped accordingly, and that it will be required to be reshaped or changed at the end of every 60 or 100 miles of Distance run by the Ship. The- extent < f this curve must be greatest in high Latitudes, and on crossing the Equator it changes to the oppo- site side of the straight line. See the Great Circle track from Santa Crux to St. Johns, on the Chart a^ Dace 4* PLANE SAILING. Plane Sailing is the Art of Navigating a Ship on ^lano surface, supposing the surface of the Earth M ♦© an extended plane, and the meridians all parallel to each other. This supposition is nearly true foi •mall portions of the Earth's surface, and for a considerable space on each side of the Equator. But as the Meridians contract in Sailing from the Equator towards the Poles, the sides of the Right ijogled Triangle do not bear the same relation to each other on large portions of the Earth's surface. Plane Sailing also supposes the parallels of Latitude to be at right angles to the Meridians, and th i»ngth of a degree on the Meridian, Equator, and parallels of Latitude, everywhere equal. CASE L , The Course and Distance given to find the Difference in Latitude and Departure. Example. — A Ship from Latitude 48° 30' N. Sails North-East by North 300 miles. Required he' Latitude an and Departure from the Meridian. BY PROJECTION ON THE PLANE SCALE. Fig. 6. Draw a horizontal line representing the parallel of Latitude sailed from ; then with the Chord of 6P ' u the dividers, and one foot on this line, describe a Semicircle ; divide this Semicircle ,into equal parts of fO" each, (oi a Quadrant) ; divide the right hand Quadrant into 8 equal parts, which transfer to a line dravvTi aoroai the Quad.-ant, will give the line of Rhumbs. Divide the left hand Quadrant into 9 equal parts, and transfer them to a line drawn across the Quadrant in like manner, will give l^e line of Chords. Those figures ar« always drawn so that the upper part represents the North, and the ship is supposed to sail from the centre on a given course towards the circumference or horizon, the course North-East by North, 300 miles given. Taka 3 points from the line of Rhumbs and lay it off from the North towards the East, and draw the Rhumb line, which will represent the Ship's Course, and on which measure off the Distance Sailed ; this will give the Ship's place. Draw a parallel of Latitude through this place, and through the Meridian wailed from, and the space between the Parallels of Latitude is the Difference of Latitude made, measured on the Meridiaa. f>raw a Meridian through the Ship's place parallel to the Meridian sailed from, and the space between the Meridians is the Departure made. BY INSPECTION. TRAVERSE TABLE. Conroe North-East by North, or 3 Points, and Distance 300 miles. In the Traverse Table gives Difference of Latitude. , . . )249.4 miles, and the Departure 167 mfle*. — 4° 9' N Latitude left 48 30' N. Latitude in... 52° 39' N Note. — ^These Tables contain/ui/r terms, any two of which being given, the other two can be found by inspecJuni . md it must be observed that in using these Tables the terms Distance, Latitude, Departure, must be found at the top, if the Course is found there : but if the Course is found at the bottom, those names or terms must be found at the bottom Thus, the Course North-East by North, or 8 Point*, is found at the top, and the columns headed Latitude and Departure •re to be used from the top, and against Distance 800 stands Difference of Latitude 249.4, and Departure 1M.7. £n practice, should the tenths bo less than 6, we throw them away ; if more than 6, we call the sum one mile more. When the Dibtance is more than 800, or if any of the other terms be too great for the Tables, we take one half, enft third, one-fourth, or on«-tenth, and multiply the termu thus found by the same quantity that they were reduced ^r- 10 PLANE SAILING CASE II. The Dijfference of Latitude and Course given to find the Distance and Dep. • 'ure. Example. — A Ship from Latitude 52° 39' North, sails South- West by South until her Latitude obserred 48* 30' North. Required the Distance run and her Departure from the Meridian. Fio. 7. Latitude left. Latitude in . . ,52' 48 39' N. 30 N. Fio. 8. Latleft..82* 81' >. Latin... 30 10 N 2° 21' • 60 Diffi Lat 141 PROJECTION BY THE PLANE SCALE. Draw a Horizontal line to represent the parallel of Latitude sailed from, then with the Chord of 6( ' a the dividers, and one foot on this line as a Centre, make the Arc of a Circle towards the right hand d<-wn- firards, and which will represent the South-East quarter of the Compass. Take 90° in the dividerb, and *ith one foot on the line where the circle meets it. extend the other downwards, and mark the Circle ; thei A line drawn through this mark to the Centre will form a Right Angle with the oth"- line, and represent* the Meridian sailed from. Lay off the Difference of Latitude, 141, oa the Meridian. 'Jom the parallel of Latitude sailed from downwards, or towards the South, and draw the parallel of Lativr de come to. 4° 9' N. 60 T3iff. of Lat.. . . 249 miles. PROJECTION BY THE PLANE SCALE. Draw a horizontal line to represent the parallel of Lati- tude Sailed from ; then with the Chord of 60° in the divi- ders, and one foot on this line as a Centre, make the Arc of a Circle towards the left hand downwards, which will represent the Southwest Quadrant. Take 90° in the divi- ders, and with one foot on the line where it joins the Cir- cle, extend the other downwards, and mark the Circle. A line drawn through this mark to the Centre will form a Right Angle with the other line, and represents the Meridian sailed from. Lay off the Difference of Latitude on this Meridian towards the South, and draw the parallel of Latitude come to. Take 3 Points from the line of Rhumbs, and lay it off from the Meridian South, towards the West, and draw the Rhumb line, and where it cuts the parallel of Latitude is the Ship's place, and gives her Distance Sailed. Draw a line parallel to the Meridian through the Ship's place, will give the Meridian come to. and the space between the Meridians is th* Departure, BY INSPECTION. TRAVERSE TABLES. I open the Table at a 3-Point Course, and find the Difference of Latitude 249 miles in its column, (a ne top ot the page, marked Latitude,) and against it, in the Distance column, stands 300 miles, the Di» tance required, and opposite, in the column marked Departure, stands the Departure required, 167 CASE III. The Difference of Latitude and Departure given to find the Course and Distance. ExAMPLi. — A Ship from Latitude 32° 81' North sails between the South and East until her Latitude in is 80" 10' * N ortih, having made 265 miles of Departure. Required her Course and Distance sailed. PLANE SAILING. n From the meridian line towards the East, or right hand, lay off the Departure, 265 miles, and dra\» th* meridian come to parallel with it. Then where this meridian cuts the parallel of Latitude come to is th* Bliip's place. Draw the Rhumb-line between th« Ship's place and the centre, which will give the Distano* Sailed ; and where this line cuts the Circle will be the Course 5i Points measured from the meridian lin*^ w from the South towards the East. BY INSPECTION. TRAVERSE TABLES With tlie difference Latitude 141, and the Departure 265, I enter the Table for Points, and I find theM © agree nearly to the Course 5^ Points, and the Distance opposite is 300 miles. Or, in the Table for Degrees the nearest is 264.9 and 140.8, which gives the Course Sailed 62* E., ai^ •stance 300 miles. The Departure being the greatest the C^ourse is found at the bottom of the page CASE IV. The Difference of Latitude and Distance Sailed, given, to find the Course and Departure. A Ship from Latitude 38* 20' N. sails 296 miles between the North and West, until the Latitude ofc» •••rred was 40" 13' N. Required her Course and Departure. Fig. 9. J?ara/lcly(/'/ Za^ co-rtiS' io / Jfe/o ^7^ Lat. left, Lat. in, 380 40 20 13 N N 1* 60 53 Dif. Lat. 113' J^uretUel ef Zai. tween this place and the Centre, will give the Distance sailed 396 miles. Through the Ship's place draw the parallel of Latitude come to. and the space hetween the parallels of Latitude is the Difference of Lati- tude, 187, or 3° 7' South, and the Latitude in is 1° 00' South. In this case the Ship has crossed the Equator. B^ INSPECTION. TRAVERSE TABLES. Find the Course 5^ Points at the bottom of the page of the Table for Points. Take half the Departure, JJ50 miles, which is 175, in its column, the nearest to it, is 174.6; opposite, in the Distance column, standi 198, and in the Latitude column 93.3, which is half the Distance and half the Departure, which, being doubled gives the whole Distance, 396 miles, and the whole Difference of Latitude 186.6, or divided by 60, 3° 7' South. The Latitude sailed from was 2° 7' North, which, subtracted from the Difference of Lati- tude made, gives the Latitude in 1 ° 0' South, and the Ship in this case has crossed the Equaior CASE VI, The Distance and Departure given to find the Course and Difference of Latitude ExiMPLE. — A Ship from Latitude 1° 0' South sails between the North and East 896 miles, until her D«partar» ii 860 miles. Required the Ootirse steered and her Latitude in. Fio. 11. J^i:'ju//('/ r/ Acy. ':<'r,,< /< ""-^ llf/> jy/T I' f /, f ''//..■■/ r/" /^aJ^ SufU<^^- ^y't'iTh PLANE SAILING IS PROJECTION BY THE PLANE SCALE. Draw a horizontal line to represent the parallel of Latitude sailed from. Take the Chord of 60' in th« dividers, and with one foot on this line as a centre, make the Arc of a circle towards the right hand upwards, which will represent the North-East quarter of the Compass. Take 90° in the dividers, and with one foot on this line where the Circle joins it, extend the other upwards, and mark the Circle. A lina drawn thTough this mark to the Centre will form a Right Angle with the other line, and which will rep- resent the Meridian sailed from. Lay off the Departure 350 miles from the Meridian towards the right oi the Ea=t, and draw the Meridian come to i)arallel with the other. Take the Distance, 396 miles, in the dividers, and with one foot on the centre, extend the other, and cut the Meridian come to, which will be the Ship's place. Draw the Rhumb line between the Ship's place and the centre, and where it cuts the Circle will be the Course North 5i Points East, and measured on the line of Rhumbs. Through the Ship's place draw the parallel of Latitude come to, and the space between the parallels is the Difference of Latitude, 487 miles, or 3° 7', the Latitude in being 2° 7' North. In this case the Ship has crossed the Equator. BY INSPECTION. TRAVERSE TABLES. Take half the Distance, 198. and half the Departure, 175. Seek in the Tables till opposite the former, the nearest to the latter is found to be 174.6, adjoining to which stands half the Difference of Latitude, ■93.3, which doubled is 186.6, or 3° 7' North, from which subtract the Latitude left, 1° 0' South, gives the Latitude m 2° 7' North, and the Departure being greater than the Difference of Latitude, the Course i* found at the bottom of the page to be North 5i Points East, or North 62° E. in the Table for Degrees. The above Six cases comprehend all the varieties of Plane Sailing, but as it is of great importance tt have a thorough knowledge of the principles of Plane Sailing before going into the other Sailings, (because it is us^d in all the other Sailings,) and also to exercise the learner in the use of the Traverse Tables, the following questions are given for exercise. Question 1. A Ship from Latitude 36° 30' North sails South-West by West 420 miles. Required her Latitude in and her Departure from the Meridian. Answer. Latitude in 32° 37' North, and Departure 349.2 West. Question 2. A Ship from Latitude 3° 54' South sails North- West i West until her Latitude in is 2* 14 North. Required her Distance run and Departure made good. Answer. Distance 618 miles, and Departure 496.4 West. Question 3. A Ship from St. Helena, in Latitude 15° 55' S sails South-South-East i East till she has made 115 miles of Departure. Required her Latitude in and the Distance run. Answer. Latitude iji 19° 30' South, and Distance 244 miles. Question 4. A Ship from Latitude 28° 20' North sails between the North and East 486 miles, and finds ty Observation that she is in Latitude 32° 17' North; what Course has she steered, and what Departure feas she made ? AxswEii. Course N. 61° East, or North-East by East i East nearly, and Departure 425 East. Question 5. A Ship sails between the North and West 170 Leagues from a Port in Latitude 38° 42' North until her Departure be 98 leagues. Required her Course and Latitude in. A.nswer. Course North 35° West, or North- West by North i West nearly, and Latitude in 45° 40' North. Question 6. A Ship from Sandy Hook in Latitude 40° 28' North, sails between the South and East until her Latitude observed is 38° 20' North, and having made 100 miles Departure. Required the Course and Distance Sailed. Answer. Course South 38° East, Distance 163 miles. Question. 7. A Ship off Cape Henry in Latitude 36° 56' North, is bound to Bermuda, in Latitude 32° 19' North, and which lays 552 miles to the Eastward of the Cape. Required her Course and Distance to it. Answer. Course South 63° East, or South-East by East i East nearly, and the Distance 618 miles. Question 8. Five Days ago we were in Latitude 3° 10' North, and since then have sailed on a South- West Course, at the rate of 10 knots an hour. Required the Latitude in and the Departure made to the A'estward. Answer. The Latitude in is 10° 59' South, and the Departure made is 849 to the Westward. Question 9. A Ship from Latitude 4° 10' South is bound to a Port in Latitude 3° 10' North, and bearing trom the Ship North-North- West. Required how far that Port lies to the Westward, and the Ship's Dis- tance from it. Answer. The Port lies 183 miles to the Westward, and the Distance is 478 miles. Question 10. Required the Bearing and Distance between Neversink Light in Latitude 40° 24' North .,// i/ .A' With the Chord of 60° describe a Circle. Take 90' in the dividers, and mark the circumferenoe of il mto lour equal parts, representing the Points of the Compass, and mark it North at the top. South at th^bot- »K I on the Right, and West on the left hand, and mark the Centre as the place of the Island Tak« ^LTfvf w'*? ^ ^i*'."*^ ^^'*' ^" ^^^ dividers, from the line of Rhumbs and lay it off from the North ^r^hiM ' !' e" '?''*V-^^"® *° *^® ^^"*'"®' ^^'«^' prolonged to the opposite side, will pass through the Ship s pxace to South 6 Points East. Take the distance of the Ship from the Island, 10 miles in^a aimers, and lay it off from the centre on this line, which will be the Ship's place at the time of taking ber aeparture. 1 ake 4 Points in the dividers, and lay it off from the North towards the East, and mark it oa Pnnilo*; iu L f ^?='' ""^ ^^® parallel ruler over this mark, and that of the Centre, and transfer thi« frnm tt cl- > P ' P ?^' ^"^ ^^'^^' ^ ^^"^^ ^'^ *^^* direction; take 30 miles, in the dividers, and lay it off W fi f n ^^ ^ P^Tt.'' "^^P^rture on this line, and which will be the Ship's second place after corapletin- ner first Course and Distance. fio"", thi'l«!l't>r''''°f lu^l.''^ """ 1^^ ''*^^'' ^^"'■'*' ^"^ Distances. Then draw a parallel of Latitude throagb nr.» v% u J,"P' ^"^ ^^®'"® "^ <="t^ t^« Meridian will be the Difference of Latitude made 49 n^^r ^A^ u cf ^^"^''^to the Ship's place, and where it cuts the Circle will be the Course made good.' Z^Zt. T M ' -^"''^ ?' ^^^*' *"^ *^« D'«^^"«^' 5^ '"il^^- ^^ "^« drawn through the Ship's pW KrnL!f )t ^^f"dian of the Island, will give the Meridian come to, and the space between them is the i«S K'k oi^i^'\ }'u ''.^^""^ °^ ^"^^ ^'^^"d ^"■°'" ^^'« Ship is the opposite point to the Course mad« good ' Distance from the Island is 54 miles, which is equal to the Distance madt lA TRAVERSE SAILING. EXAMPLE 2. A Ship from Latitude 43* 10' North, is bouud to a port in Latitude 42° 20' North, and which lies 50 miles to tL Westward of the Ship. But by reason of contrary winds, and other causes, she has sailed on the following Courses^ n*. : N. N. W SO miles, E. S. E. 30, South 20, W. i S. 39, S. E. 15, and W. by S. 22. Required the Bearing and L/istanceof the Port rrom her first position, her Course and Distance made good, her Latitude come to, and tM bourse and Distance to her intended Port. TRAVERSE TABLE. To find the Bearing and Distance of the f\ir1 from the Ship's first position. DIFF. LAT. DEP. 1 COURSES. N. N. W. E. S. E. South. W. i S. S. E. W. by S. DIST. NORTH. SOUTH. EAST. WEST 30 30 20 89 15 22 27.7 11.5 11.5 20.0 3.8 10.6 4.S 27.7 10 6 ■ - . • • • • • 38.8 21.6 1 27.7 5(1.2 27 7 38.3 71.9 38.3 .43° 10' N. .42 20' N. Diff. Lat , Lat left. 43° Lat of the Ship. Lat. of the Port. Diff. Lat 60 Dep. 50, Gives the Bearing S. W And the Distance 70 mile* 22.5 S. and Dep. . . 33.6 W., gives the Course made good, S. 56° W., or S.W. by W 1 0' N. and the Distance 40 miles. Lat. come to 42° 47'. To find the Bearing and Distance of the intended Port. Take the whoI« Difif. of Lat. between the Ship's 1st position and that of the Port, which is 50 miles, and the whole Departure 50. From which subtract the Diff. Lat. made good 23 " and Dep. made good ... .34. Leaves the Difference of Latitude to make 27 " and the Dep. to make. . .16 Port These agree in the Tables to the Course 31°, or 2| points, nearly, and the Distance 31 miles'; and as the inteodW )rt lies to the South and West of the Ship, she must steer S. 31 W., oi or S. S. W. S W., 31 miles. PROJECTION BY THE PLANE SCALE. Fig. 13. II TRAVERSE SAILING. n l>raw a figure as in the preceding example, the Ship's position being in the Centre. Draw her parahel «f Latitude and her Meridian; from the Centre lay off the first Course Norlk 2 Points West 30 miles; lay off 6 Points from the South towards the East for the second Course, and mark it on the Circle. Lay the parallal ruler over this mark and the centre, and transfer this Course to ihe Ship's place, and dra>y a line, on which lay off the Distance, 30 miles. Lay off the other Courses and Distances in like manner, and at the end of the last one is the Siiip's place. From the Ship's place draw a line to the Centre, which will be the Distance made good. 40 miles, and the Angle which thi« line makes with the Meridian is the Course made good South 5 Points West. Through the Ship's place, draw the parallel of Latitude como to, and the ^ace between the parallels of Latitude is the difference of Latitude made good, 23 miles. Draw a Mer.dian line through the Ship's place, and the space between the Meridians is the Departure mad© good, 34 miles. Take the Difference of Latitude between the Latitude saile^ from, and the Latitude of the intended Port, 50 miles. Lay this off to the South on the Meridian sailed from, and draw the parallel of Latitude of the Port on this line. Lay off 50 miles, which the Port lies west of the Meridian of the Ship, and draw the Meridian of the Port ; where these lines intersect each other, is the intended Port. Draw a line between the uitended Port and the Ship's place, will give the Distance from it, 31 miles, and the Angle between this line and the Meridian of the Ship will be the Course. Lay the ruler along this line, and transfer it to the Centre, and where the edge of the ruler cuts the Circle is the measurement of the Course South 31° West to her intended port. Draw a line between the Port and the Ship's first position in the Centre, will give its Distance, 70 miles, and the Angle between this line and the Meridian of the Ship is the bearing of the Port, which is South- West. EXAMPLE 3. A Ship from a Port in Latitude 38° 42' North, bound to another Port, situated in Latitude 36* 32' North, and 137 miles to the Ea.stward, sails on the following Courses; South by West i West 55 miles, South- West by South i West 37 miles. South 60 miles, East-South-East 40 miles, South-East by South i East 32 miles, and North-East by East i East 58 miles. Required her Course and Distance made good, her pres- ent Latitude, and the direct Course and Distance to her intended Port. Answer. The Course made good is South 23° 30' East, and the Distance 169 miles, the Latitude in 36* y North the Course t» the intended Port North 70° East, and the Distance 74 miles. EXAMPLE 4. A Ship takes her Departure from Cape Henry Light House, in Latitude 36° 56' North, bearing West- North- West 7 leagues, bound to the Island of Bermuda, in Latitude 32° 19' North, and which lies 552 miles to the Eastward of the Cape, but by reason of contrary winds has sailed on the following Courses: South- East by East 50 miles, South-South-East 40 miles, South 20 miles, East 60 miles. East by North J- North 30 miles,. North-East i East 40 miles, and East by South i South 50 miles. Required the Difference of Latitude and Departure made good, her direct Course and Distance made good, her present Latitude and the Bearing and Distance of Bermuda Island. COUSSB8. E. S. E. S. E. bv E. S. S. E. South. East. E. by N. i N. N. E. i E. E. by. S. i S. 21 50 40 20 60 30 40 50 8.7 25.4 34.1 8.0 27.8 37.0 20.0 14.5 19.4 41.6 15.3 60.0 28.7 30.9 47.8 WEST. 243.7 of Easting. Difference of Lat made good is or'r 13' S. Latitude of Cape Henry 36 66 N. v.^ c- i o oc? „il«i LaUtud«of theShip... '35° 43' N. by S i S. 254 mile.. 107.3 34J 73.2 and Dep. 243.7, gives the Course and Dis- tance made good E. Latitude of Cape Henry 36° 56' N. Latitude of Bermuda... 32 19 N. 4° 37' 60 Whole Diff. of Latitude 277 S., and Dep. 652 K Diff. of Latitude made, . 73 S., and Dep. 244 E. Leaves Diff of Lat 204' and Dep 308mile8 to make. One-tenth of these Sums are found to agree nearly to a Course of 56° and the Distance correa- ponding 370 miles. The true Bearing of Bermuda from the Ship ia, therefore, South 56° East, or South-Eaat by &*ai nearly distant 370 miles. 18 PARALLEL SAILING. fn Plane Sailing the Earth is considered to be an extended plane, and the Meridians all parallel to eacB other, and the length of a Degree everywhere equal, which supposition will give just conclusions, so far u the Course, Distance, Difference of Latitude and Departure are concerned ; because a Sliip, when sailing on a Rhumb line, makes equal Angles with the Meridian. But as the E-artli is a Globe or Sphere, and the Meridians meet at the Poles, it is evident that the Dis- tance between any two Meridians must vary in every Latitude : their greatest Distance being at the Equator on which tlie Difference of Longitude is measured ; hence tlie difference of Longitude always exceeds the Departure or Meridian Distance, (except on the Equator, where they are the same), in proportion as the given places are situated farther from the Equator. The following Table, showing the number of Minutes and Seconds contained in each Degree or 60 milea •f Longitude for every Degree of Latitude, will be found useful. LAT. MIN. SEC. LIT. MIN. SEC. LAT. MIN. SEC. LAT. MIN. EEC. LAT. MIN. 8EC. • tt • / II o 1 II o 1 II • 1 II 1 59.59 19 66.44 37 47.55 65 34.26 73 17.33 2 69.58 20 66.23 38 47.15 56 33.30 74 16.83 S 59.56 21 66.00 39 46.38 57 32.41 75 15.31 4 59.51 22 65.38 40 45.58 58 31.48 76 14.31 6 59.46 28 55.14 41 46.17 59 30.64 77 13.30 6 59.40 24 54.49 42 44.35 60 30.00 78 12.28 7 69.33 25 54.23 43 43.53 61 29.06 79 11.27 8 69.25 26 53.56 44 43.10 62 28.10 80 10.26 9 69.16 27 53.28 45 42.26 63 27.16 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 66 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 8.14 14 68.14 32 50.53 50 38.44 68 22.28 86 4.12 15 57.68 33 50.19 51 37.46 69 21.30 87 3.09 16 67.41 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 l.OS 18 57.04 36 48.33 54 35.18 72 18.33 90 0.00 DIAGRAM Showing the Contraction of the Meridians from the Equator towards the Pole, and the Parallel! of Lot* tude crossing the Meridians. Fig. Parallel Sailing is the method of finding the Distance between two places in the same Parallel of Latituie when their difference of Longitude is known, or of finding the difference of Longitude answering to th« Distance or Departure made good when a Ship sails due East or West. Distance sailed and Departure ar« Ihe same thing in Parallel Sailing. Note —This Sailing ia particularly useful in making a small or low Is'and, in which case it is usual to run into the Ltttitud'e, and then steer East or West, care being taken that the Ship ia on the proper side of the Meridian of th« Ulaad. PARALLEL SAILING. 19 CASE I. Hu Difference of Longitude between two Places, both in one Parallel of Latitude, given, to find their Du'oncc EXAMPLE. A Ship fc the Latitude of 32* a' N. and Longitude 69* 50' W., and bouud to Bermuda, in the same Latitude, and Longitude 64* 60' W., what distance must she run to the Eastward to arrive at the Island ? BY INSPECTION. Longitude of the Ship. .69° 50' W. ) u i * t ^-^ i e ^\ t i j o^. «- -kt Lon|itude of Bermuda. ^*_50' W. ^ ^ "'■''^"^1 ^^ Latitude of the Island 32* 9' N. 6° 0' 60 Role. — Take the Parallel of Latitude 32* as a Coura« •nd the Difference of Longitude in miles 300 in the Distance Column, and the Distance (or Departure) 264.4 will b« i)und in the Latitude Column. The Ship has, therefore, to run 254 miles to the Eastward to aniye at tb« blaud. CASE II. The Distance between two places given, both in the same Parallel of Latitude, to find the Difference of Lon- gitude. EXAMPLE. A Ship from the Island of Bermuda, in Latitude 32* 9' N. and Longitude 64* 60' W., saild du^ W. 254 miloA E«quirea her Longitude in. Rcu. — Take the Parallel of Latitude 32* as a Course, and the Distance, 254, in the Latitude Oolunco, and UM Difference of Longitude will be found in the Distance Column, 300 miles. Longitude of Bermuda. .64* 60' W. Diff Long, made 300. . — 5 W. Longitude in. . . .69* 60' W CASE III. The Difference of Longitude and Distance between two places in the same Parallel of Latitude given, (• firxd the Latitude of that Parallel. EXAMPLE. A Ship sails due East 264 miles, and then finds she has altered b«r Longitude SOO miles. Required the Paralld •f Latitude she sailed in. Rdlx. — Seek in the Tables until the Difference of Longitude, 300,18 found in the Distance Column, and the Distanes «ailed, 254, is found in the Latitude Column ; then the Course 32', at the top of the page, will be the Parallel of Latitude sailed in, because 254 is found in the Column headed Latitude at the top of the page. QUESTION FOR EXERCISE. A Ship from Latitude 48* 89' N. and Longitude 60° 10' W, sails due "Wept 350 miles. Required her Longitude in. With Latitude 48°, and half the Distance, 175, (the whole being too great for the Tables,) in the Lati- tude Column, I find half the Difference of Longitude, 262, in the Distance Column. Then, with Latitude 49° as a Course, and Distance 175 in the Latitude column, I find 267 in the Distance column. Add these Differences of Longitude together, and take their half Sum for the Difference of Longit ide, corresponding to the Latitude 48° 30', which doubled will give the required Difference of Longitude, 529=8° 49' W and Longitude in 68° 59' W., as follows : Latitude 48* difference Longitude 262 Latitude 49* difference Longitude 267 )529 Half Difference cf Longitude 264.5 2 Whole Difference of Longitude. 629.0 miles. Which divided by 60* gives 8° 49' W. Longitude left fin 10 W. Longitude in 68°59' W. 20 MIDDLE LATITUDE SAILING. This method is founded upon the same principle as Parallel Sailmg ; that is, of converting the Depart ore into Difference of Longitude, and Difference of Longitude into Departure. When the Ship's Courst lies obliquely across the meridians, that is, when, besides Departure, she makes Difference of Latitude she leaves a certain Parallel of Latitude and arrives at another, the Space or Departure between the Meridians •ailed from and come to differ, the one being greater than the other, and it is evident neither of these Departures can be used singly, to find the Difference of Longitude. But if we take the Middle Parallel of Latitude between the Latitudes sailed from and come to, we get the middle Departure between them. In the greater Latitude the Departure is less, and in the less Lati- tnde the Departure is greater, than the Departure corresponding to the Middle Latitude. Hence thi» method, which is compounded of Plane and Parallel Sailings, is called Middle Latitude Sailing. The Middle Latitude is half the Sum of the two Latitudes when they are of the same name. Near the Equator, when the Latitudes are of contrary names, no sensible error can arise from taking the Departure itself, made good from day to day as the Difference of Longitude, because the Degrees of Latitude and Lon- gitude are of the same length on the Equator, and the latter is only diminished by 1 mile at the lOtb Parallel of Latitude; therefore in practice at Sea, Longitude and Departure may be considered the same for several Degrees on each side of the Equator. In using the Traverse Tables, it is enough to take the Latitude for the nearest Degree. In greater distances between places whose Latitudes are of contrary names, the proper rule is to take half the greater Latitude as the Middle Latitude* (See the annexed Diagram.) The Difference of Longitude found by this Sailing is true at the Equator, and very nearly true for short distances in all Latitudes, especially when the course is nearly East or West. In High Latitudes, when the Distance is great and the Course oblique, the error becomes considerable ; but the result may be made nearly true by subdividing the Distance Sailed into small portions, and finding the Difference of Longitude for each portion separately, and then adding the whole together. In like manner the Bearing and Distance between places near the Equator by this Sailing are correcl But in High Latitudes the result cannot be rendered accurate by subdividing the Distance into small por- tions, as above, because it is not known. Such cases are truly solved by Mercator's Sailing DIAGRAM, Showing the Middle Latitude between the Parallels of Latitude North and South of the Equator Ffo. 15 • Or ndd together the half of the greater Latitude to the half of the less Latitude, and their half sum will J* the Hidcfie Latitide required. See al8.:^ the Note at page 28. I MIDDLE LATITUDE SAILING. SI CASE I. • ihte Latit ide and Longitude^ Course and Distance given, to find the Difference of Latitude arui Longttudt. EXAMPLE L A Ship from Latitude 62* 6' N. and Longitude 36° 6' W_ sailed S. W. by W. 256 u ilea. Required her Latitud* ■nd Longitude in. Course S. 6 pta. W, ) Distance 256 miles, ) gives the Diff. Lat. )142 and the Dep. 212.9, the half, 106.4, taken in the Latitudk ^ Diff. Lat 142 S. Diffi Lat.. .2* 22' S. CoL of Mid. Lat 61*. as a Course, then Half DiH of I Departure 218W. Lat left. 52° 6' N. Long- is found in the Dist Column to be 1 99 Lat in 49° 44' N. Lat in. . 49° 44' )388 '^ Diff Long.... 6° 38' W.- Sum... 101 .60 T • ^.^OiAf Tir \M J T t rr.» r r / Diff Loug. made.. 5' 88' W. Long. m. ... 40 44 W. Mid. Lat 60 66' L^^ ij 35^^ ^ Long. in. . . . 40* 44' W. The Difference of Latitude and Departure are found' a« in Plane Sailing. The Latitude in, and thence the Middle Latitude, by adding the two Latitudes together, and taking their half Sum for the Middle Lati- tude. The Departure being too great for the Tables, the half is taken. Then, with Middle Latitude as » Course and half the Departure in the Latitude column, half the Difference of Longitude is found in the Distance column. This being doubled and divided by 60 gives Degrees and Minutes. Ship in West Lon- gitude sailing West, add Difference of Longitude to Longitude left. This is the usual case at Sea in working a day's work. Two Latitudes and Course given, to find the Distance and Difference of Longitude EXAMPLE 2. A Ship from Latitude 49* 44' N. and Longitude 40* 44' W, sails N. E. by E. until by obserTation she is in Late tade 62* 6' N. Required her Distance run and Longitude in. GoHTse N. 6 pte. E. Lat left . . .45"* 44' N. Lat left 49* 44' N Dist 266 Latin 62* 6 N. Latin 62 6 N Diff. Lat. . 142 N. 2* 22 Sum 101 .50 Dep. 218 K ^0 Mid Lat, . .60* 66' Lat Ob. 62* 6' N. Course 6 pts. and 142 Difference Latitude in its column gives the Dep. )213 and Dist 266-, Diff Long. 6* 88' K Mid. Lat 61* as a Course, and half the Departure, 1 06.5 in tiie Lai- Loa in. .36* 6'W. Column, half the Diff. of Long, is foimd in the Dist Column to b« 169 2 )338 Diff of Long. 6° 38' E. Long, left 40 44 W. Long, in 36° 6' W. In a fast-sailing ship, where it is found difficult to measure the Ship's rate of sailing by the Log thi» Example may be used with advantage. Two Latitudes and Distance given, to find the Course and Difference of Longitude. EXAMPLE 3. A Ship from Latitude 3° 20' N. and Longitude 22* 80' W., runs for 4 days between the South and West, at the- rate of 10 knots an hour, and then by observation finds her Latitude to be 10° 40' S. Requred the Course and the. Longitude in. Lat left 3* 20' N. Greater Lat 10* 40' S. Run. , 4 days. Course & 29* W Latin 10 40 S. The half of which, 6° 20' 24 i^ Diet 960 , Diff of Lat 14° 0' to be taken as Mid Lat . . "96 hours I Diff Lat.... 840 S. _60^ ' 10 knots 'an hour. I Dep 466 W. The 10th part of 840 Differ. Latitude and 10th part of the Distance, "960" are fcund te eg Lat ic 10* 40' S. agree at Course S. 29° W, and gives the tenth part of the Departure 46 5 then witb Diff Long.. 7 47 "W. half the greater Lat 5° for the Middle Latitude as a Course, and the t< nth part of th» Long. in. .30 17 W Dep., 46.5, in the Latitude column, the tenth part of the Diff. of Long, is found in the Distance column to be 46.7, and the whole is )467 Diff Long. 7° 47' W. Long, left 22 30 "W Long, in 80* 17' W. By this Example it appears that there are only 2 miles difference between the Departure and the Differ •Dce pf Longitude as found in the run of noarly 1 000 mi.' aa. «2 MIDDLE LATITUDE SAILING. One Latitude, Ccrnrse and Distance given in a Hi°;h Latittide, to find the Latitude and Longitude tn. EXAMPLE 4. A Ship from Latitude 68* 30' S. and Longitude 178* 10' W., sails S. W, by W. 300 miles. Required Ler Correei Latitude aud Longitude in. By taking Short Distances run, and also the same by the Whole Distance run, in th« oauol way. V TRAVERSK TABLE. D. LAT. DKP. LONGITUDE TABLE. Course. Dist s. W. Lat Left. Lat in. M: 1. Lat Dif. Long. made. S. W. by W. 14 f( M M (( S. W. by W. Diff. Lat Lat left 50 50 50 50 50 50 300 m . 2* 47' 58° 30' 27.8 27.8 27.8 27.8 278 27.8 .=166.8 S. Dep S. 41.6 41.6 41.6 41.6 41.6 41.6 )249.6 124.8 ' 58° 30' 58° 58' 58 58 59 26 59 26 69 54 59 54 60 22 60 22 60 50 60 50 61 18 Summary. W .=249.5 Course. .S. W. by 2 Dist 800 68° 44' 69 12 59 40 60 8 60 36 61 4 W. Diff of ] Long, lei 80' 81 82 83 *84 86 )496' Long. 8° 16' W. ■t..l78* 10' W. 186° 26' 360* 0' . . . 178* 84' E. LaL in 61° 17' S. Diff Lon The Shoit E Whol<» Tlistji )499.0 Diff Lat 167 119° 47' Mid. Lat 59° 54' g...8* 19 W. Dep 250 Lat in 61° 17 istances give Diff. Long 8° 1( iDce do 8* 19 ' S. Long, in )' W. ' W. ' E. Long '. in is. 173* 34 In this Example, by taking Short Distances on the same Course and finding the Difference of Longitude corresponding to each, and adding the whole together, there appears to be a difference of 3 miles between ihat and the Difference of Longitude found from the whole Course and Distance, the former being the correct Difference of Longitude, the Distance in this Example not being great. One Latitude, Course and Departure given, to find the Latitude and Longitude in. EXAMPLE 5. A Ship from Latitude 38* 40' S. and Longitude 1* .16' W, tails N. R i E. jntil her Departar« is 860 mOM Required the Latitud* and Longitude in. Cours« 4i pte. and half the Departure, 125, gives half the Dist 162, and half Diffi Lat 102.8 Z 2 ^ Dist 324 Dht 824 Diff Lat )20S.g 2 Diff Lat. .206 Mid. Lat 87* and half the Dep. 126— D. Long. 167 8* 26' N. I Dep 260 £. Lat left 38* 40' & J Lat in.. . 35° 14' S. J314_ Lat b .85* 14 ' 8. DiffLong. 5* 14'K Diff of I^ng.. .6* 14' K Sum 78° 64 ' Long. in. .3° 59' E. Long, left .1* 18' W, Mid. Lat ... 86* 87' Long, in 8° 59' E. QUESTIONS FOR EXERCISE. Question 1.— A Ship from Latitude 25* 35' N. and Longitude 60* W., sails N. N. E. 296 miles. Re quired her Latitude and Longitude in. Answer. — Latitude in 30* 9' N. and Longitude 57* 52' W, Ques. 2. A Ship from Latitude 3° 10' N. and Longitude 25° 0' W. sails on a S. W. by S. Course until iher Latitude observed was 2° 16' S. Required the Distance run and Longitude in. Jns. — The Distance run is 392 miles and the Longitude in 28° 38' W. Ques. 3. A Ship from Latitude 30* 15' S. and Longitude 178° 10' E., sails on a N. E. Course until her Departure is 150 miles. Required the Distance run and the Latitude and Longitude in. Ans. — Distance sailed 212 miles, Latitude in 27° 45' S. and Longitude in 178* 58' W. Ques 4. A Ship from Sandy Hook, in Latitude 40* 28' N. and Longitude 74* C W., sails between the fiouth and East until her Latitude observed is 37* 6' N. and her Departure made good is 500 miles. Re^ paired the Course and Distanr-e sailed and the Longitude in. Ans. — Course S. 68° E., Distance 540 miles, and the Longitude in 63* '«' W MIDDLE LATITUDE SAILING. St CASE II. Two L *itudes and Longitudes given, to find the Bearing and Distance. EXAMPLE 1 Required the Beaiiug and Distance between Cape Henry, in Latitude 36° 66' N. and Longitude 76' 0' W, and Om IsLnd of Bermuda, iu Latitude 32° 18' N. and Longitude 64° 50' W. LaL Cape Henry 36° 6«' N. 36° 56' N. Long, of Cape Henrv 76° C W Lat Bermuda 32 18 N. 3 2 18 N . Lnjug. of Bermuda. .'. 64 6C W 4° 38' b9M7 " rr° 10 . 60 3^o 37' Middle Latitude. 60 Diffi Lat. in miles 278 ' Diff. Long, iu miles. . . 670 Rule. — With Middle Latitude 34° 30' as a Course, taken out first with 34° and then with 35°, and the tenth pait of the Diifeience of Longitude, 67.0, iu the Distance Columns, the tenth part of the Meau Departure, 55.2, will be found in the Latitude Columns. Then with this Departure, 55.2, and the tenth part of the Dittereuce of Latitude, 57.8, enter the Tables again, and where they are fouud to agree in their columns, gives the Course at the bottom of the pa^, 63°, because the Departure is greater than the Difference of Latitude, and the corresponding Distance opposite is 61.5, which multiplied by 10 gives the Whole Distance, 615 miles. Hence the Bearing of Bermuda from the Cape is S. 63° E., because the"Latitude and Longitude of the former ki to the Southward and Eastward of the latter, aud the Distance beween them is 615 miles. Two Latitudes and Longitudes given^ to find the Course, Distance and Departure. EXAMPLE 2. A Ship from Latitude 30° 15' N. and Longitude 45° 20' W., sails between the North and West until by observa- tion she 18 in Latitude 33° 46' N. and Longitude 60° 10' W. Required the Course and Distance made good, and hoi Departure from the Meridian. ^ Course. . .N. 60° W. Lat. left 30° 15' N Long, left 45° 20' W. I Dist 822 Lat. in .33 45 N. Lat. left 30° 15' N. Long, in 60 10 ' W. I DiflL Lat. 210 3° 30' ^at. in -33 45 N. Difj Long -^ 50' ^ D^p 246 60 Sura 64 .0 60 DifF. Lat 210 N. Mid. Lat .32° as a Course, and 290 in the Distanc* column gives the Departure in the Latitude column 245.9. Then with half the Diiference of Lati ude, 105, and half the Departure, 123, found in their columns, where they agree nearest, and the Course must b« taken from the bottom of the page at 50°, (because the Departure is greater than the Difference of Latitude,) and half the Distance is found opposite to be 161, which doubled gives 322 miles. Hence the True Course and Distanot ■ailed is N. 60* W, or N. W. i W., 822 miles, aad the Departure from the Meridian 246 miles. One Latitude and Longitude, with the Difference of Lct»i.uue and Departure given, to find the Latitude and Longitude in, and the Bearing and Distance of the Inte7id€d Port. EXAMPLE 3. A Ship from Montauk Point, in Lat. 41* 4' N. and Longitude 71* 51' W., and bound to Santa Cruz (one of the Cape Verd Islands) in Latitude 17" 2' N. and Longitude 26* 15' W., sails between the South and East -mtil she has made 800 leagues of Southing and 400 leagues of Easting. Required the Latitude and Longitude in. and the Course and Distance to her intended port Course. .S. 53° E. Diff. Lat 300 Leagues. Dep. 400 Leagues. Dist 1500 miles sailed. 3 3 Dep. in miles. 1200 The tenth part of the Departure, 120, found in the Lat column, of the Middle Latitude, 33, gives the 10th part of the Diff. Long, in Dist. column, 143. Middle Lat 34°, in like manner gives 145, the mean of which is 144 this multiplied bv 10 gives the proper "Diff. of Long.) 1440 m iles. Diff Long 24° 0' E. Long, of Ship 47° 51' W. Long, of Montauk Point. 71 51 W. " Santa Cruz 25 15 W Long, of the Ship 47° 51' W. Diff. Long.... 22° 36' 60 with Mid. Lat 21° and 22°, and the tenth part of the Diff. Lat in miles ) 900 Diff. Lat .15° 0' S. Lat. Montauk Point. .41 4 N. Lat of the Ship. . . . .26° 4'N. Sum .67° 8' Mid. Lat 83° 34' Lat of the Ship 26° 4' N , " Santa Cruz 17 2'N. Lat 26° 4'N. Diff. Lat .. 9° 2' Lat. n 2 N. ^Q Sum 43* 6'" Diff. Lat 642 ^i(j Lat 21° 33 '■ Diff. Long. 135.6 in the Dist. column, the tenth part of the Departure 126, is found in tlie Lat column. Then with the tenth part of the Difference Latitude 54.2, and the Departure 126 the Course to SanCa Cruz is found to be S. 67° E. or E. S. E., and the Distance 1870 miles. Note. — The rule in the Epitomes, which directs that half the Difference of Latitude between two places on opposite Bides of the Equator must be used for the Middle Latitude, beiiip incorrect, (as may be perceived by inspecting Fig. 16, page 20,) the deficiency is supplied by the following Rule : (See Example 4, which is worked out iu the following page.) Add the half of the Grejiter Latitude to the half of the Less Latitude, and take their half Sum for the Middle Latitude. If one Latitude he great and the other small, take the half of the Greater Latitude alone for the Middle Latitude. The Example referred to comes out exactly the same by Mercator's Sailing, which proves this Rule to be correct. But when the Ship sails a greater distance on one side of the Equator than on the other, a greater weight should be given to that li»liturte which corresponds to the greater dislanne. (See the Last Example in this Sai'ing.) ^ MIDDLE LATITUDB SAILIN*. Tvo Places, whose LaiitiuUs and Longitudes are of contrary names, given, tn find the correct Bearing tmS Distance between them. EXAMPLE 4. Required the Bearing and Distance between New York, in Latitude 40° 43' N. and Longitude 74* 0' W, »nd th» Cfep« of Good Hope, in Latitude 84° 22' S. and Longitude 18* 80' E. Lat of New York 40* 48' N. Half of the greater Lat 20' 21' Long, of New York 74* 0' W " Cape G.Hope., 84 22 & .. « less Lat .17 11 " Cape Good Hope. 18 SO EL 75* 5' Sum 37° 82' 92° SO' 60 Half Sum for Mid. Lat. ... 18° 46' ^Q Diflt Lat m miles. . . .4506 Diff. Long, in miles 6551 In this Example we have to take the 100th part of these Sums to get into the Tables, as follows: With Middle Latitude 19* as a Course, and the lOOth part of the Difference of Longitude. 55.5, in the Distance Column. By taking parts we get the Departure in the Latitude Column, 52.45. Then with this Departure and the lOOth part of the Difference of Latitude, 45.05, enter the Table again, and they are found to agree to the Course 49*, and Distance 69°. Multiply this Distance by 100, which is the Distance required. Hence the Bearing of the Cape from New York is S. 49° E., or S. E. k E-, nearly, and that of New York from the Cape N. 49° W., or N. W. k W. Distance 6900 miles. This Example, worked by Mercator Sailing, comes out the same as above ; but by the Old Rule, half the Difference of the Latitudes in this case would be 3* 10' for the Middle Latitude; which is manifestly incorrect. The following Exanaple, though not of much practical utility, may exercise the learner. EXAMPLE 6. A Ship from 36* 32' North Latitude, sails between the Soutn and West until she has made 480 miles of Departure and 560 miles Difference of Longitude. Required her present Latitude, Course steered and Distance rua RiHJC. — -Enter the Table with the 10th part of the Departure, 48, in the Latitude Column, and the 10th part of the Difference of Longitude, 56, in the Distance Column, they are found to agree to the Course at the "Top of the page, 81', and which is the Middle Latitude the ship has sailed in. Take the Difference between this Middl« Latitude and the Latitude left which is 5° 32', and subtract it from the Middle Latitude, because the ship has been sailing S»uth, will give the present Latitude, 25° 28' N. Take the Difference between the Latitudes sailed from and come to, which is 664, and the Depar*,ure, 480, enter the Tables with the tenth part of the Difference of Latitude, 66.4, and the Departut e, 48.0, found in their respeotive columns, the Course is found to be 36°, and the Distance 82, which multiplied by 10 gives 820. Heoo« the Latitude in is 25° 28' N., and the Course S. 36* W., or S. W. i S, Distance 820 miles. Diff. Long. 56 and Dep. gives the Mid. Lat 31° 0' Lat left. .86' 32' N. - Lat left.. 36 32 ' Lat in.. . 25 28 N. Difr. between Mid. Lat and Lat left .T5° 32' N. 11° 4' Mid. La t. 81 60 Lat in ... 25° 28' N. Diff. Lat 664 and Dep. 480»=Cour8e S. 86* W., Dist 820 m QUESTIONS FOR EXERCISE. Question 1.— A Ship from Latitude 60° 10' N. and Longitude 30° 15' W., is bound to a Port in Latitude 49* 10' N. and Longitude 50° 10' W. Required the Course and Distance. Answer. — The Course is S. 46° W., or S. W., nearly. Distance 950. Ques. 2. — A Ship on the Equator, in Longitude 25° 40' W., and bound to the Port of Rio Janeiro, and wishing to shape a Course for Cape Frio, in Latitude 23° 1' S. and Longitude 41* 50' W. Required the correct Course and Distance to it. Ans. — The Course is S. 35° W., or S. W. by S., nearly, and Distance 1685 miles. Ones. 3. — Required the Bearing and Distance between the Cape Verd Islands, (say Cape St. Anthony,} in Latitude 17° 12' N. and Longitude 25° 19' W., and the Island of St. Helena, in Latitude 15' 55' S. and 4° 45' West Longitude. Ans. — Bearing is S. 30* 30' E., and Distance 2300 miles Que*. 4. — Required the Bearing and Distance between Cape Horn, in the Latitude of 55° 59' S. and Lo» gitude 67° 16' W., and San Francisco, in Latitude 37' 48' N. and Longitude 122' 21' W. Ar^. — The Bearing is N. 27' W., and the Distance 6300 miles. NoTB. — In the last Example, half the greater Latitude ie taken as a Middle Latitude, and which is incren«e(' by !•, ttMaose the (jreateat disUnoe had to t)e ran to the Southward of the Equator. The Middle Latitude allowed is 80 aft MERCATOR'S SAILING. Thi« Sailing is used lor the same purposes as Middle Latitude Sailing, and is more correct in long Autances, except when the Course is large ; tliat ie, near the East or West points. Mercator Sailing is the Art of finding on a Plane Surface the position of a Ship, which shall be true ta Course, Distance, Latitude and Longitude. This method is derived from the Projection of Mercator's Chart, in which the Degrees of Longitudfl are «very where equal, the Degrees of Latitude expand towards the Poles, and the Parallels, Meridians, and Rhumb Lines are all represented by straight lines. In Middle Latitude Sailing the Meridians contract and meet at the Poles, and the length of the Degrees of Longitude also decrease from the Equator towards the Poles. But in Mercator Sailing the Meridians are all parallel to each other, and a Degree of Longitude is 60 miles in length, measured on the Equator, in all parts of the World. To remedy this, the Degrees of Latitu le are expanded from the Equator towards the Poles, and the miles of Latitude grow larger ; so that in the Latitude of 60* the miles of Latitude are twice the length they are on the Equator, and the Degree of Longitude is only 30 of these miles long ; near the Pole one mile of Latitude is nearly the length of 60 miles on the Equator, and the Degree of Longitude only 1 mile long. But as the Polar Seas are not navi- gable much above 80°, Charts or Tables on this projection are rarely published beyond that paralleL DIAGRAxM OF MERCATOR'S SAILING, thowing the Expansion of the Parallels of Latitude for every 10 Degrees, and the Meridians (or ParalUU of Longitude) all Parallel \o each other at 10 Degrees Distance. Fio. 16. 90 80 -70 60 50 40 30 W E 5 T L N CT ^ o io ao EAST LOnC PROJECTED BY THE FOLLOWING TABLE And the Measurements taken from the Degrees on the Equator. From the Equator to Lat. 10° the Expansion is 0° 3' From Lat 10° to 20 (( 25 l( 20 to 30 « 1 28 t* 30 to 40 " 3 43 M 40 lo 50 it 7 54 U 50 to 60 t. 15 27 « 60 to 70 ti 29 26 u 70 to 80 u 69 35 Distance of 1st Parallel from the Equate the Expansion of the miles of Latitude from the Equator towards the Poles. To find the Meridiiiiial Difference of Latitude. When the Latitudes are of the same tmme, take the differeno* of tiM Meridianal Parts for the two Latitudes. When of contrary rames, take the sum of the Meridianal Part*. 2d MERCATOR'S SAILING. CASE I. One Latitude and Longitude. Course and Distanit given, to find the Latitude and Longitud4 m. EXAMPLE 1. A Ship from Latitude 62° 6' N. and Longitude 35* 6' W, sails S W. by "W. 266 miles. Required her Latitud* uxi Longitude in. Here, as in Middle Latitude Sailing, the Difference of Latitude and Departure are found from tha Coon* &nd Distance by the rules in Plane Sailing. Course S. 6 pts. W^ ) and Diutance 256 miles f gives the Difference of Lat, )142 and the Dep. 213. Diff. Lat in Degrees 2° 22' S. Lat. left 62* 6' N Meridianal parts 8676 ),p,, jj, Lat. b 49° 44' N Meridianal parts 8460 J Rule. — With the Couise 6 pMnts, and the Meridianal Difference of Latitude 226 in the Difference of Latitude column, (here we find it to be too great for the Tables,) we take the half, 112.5. Then half the Diff ol Longitude. 168.8, is found against it in the Dep. Column, which doubled gives the whole Diff of Long. )327.6 Diff. of Long, in Degrees 5° 38' W Long, left tb' 6' W. Long, b 40° 44' W Two Latitudes and Course gtVen, to find the Distance and Difference of Longitude. EXAMPLE 2. A Ship from Latitude 49° 44' N. and Longitude 40° 44' W., saUa N. R by R until by obserration she is in Lati tuda 62° 6' N. Required her Distance run and Longitude in. Lat. left 49° 44' N. Merid. parts 8460 Lat in 62° 6 ' N. Merid. parts 8676 Diff Lat 2° 22' N. Merid. Diff. Lat , )226 ^Q 112.5 Rule. — With the Course 5 pts. and the Diff. of Lat 142 in its column, then opposite to it in the Dist Column stand* the Distance, 266 miles. Again, with the same Course, 6 points, and half the Merid. Diff. of Latitude, 112.6, taktm in the Latitude column, then half the Difference of Longitude, 168.8, is found in the Departure column, whidi doubled gives the whole Difference of Longitude, 337.6, or, 6° 38' K Long, left 40° 44 ' W. Dbtance sailed, 266 miles, and Long, in 35° 6' W. Two Latitudes and Distance given, to find the Course and Difference of Longttude EXAMPLE 8. A Ship from Latitude 8* 20' N. and Longitude 22* 30' W., runs 4 days between the South and West until her Latitude observed is 10° 40' S. Her rate of sailing -was 10 knots an hour. Required the Course she baa mad« and ber Longitude ia Latleft 8° 20' N. Merid. parts 200 Run of 4 days. Latin 10' 40' S. Merid. part* 644 24 bonra, Diff of Lat 14* "O^ Mer. Diff Lat .. 844 96 hours. 60 10 knot*. Rule. — Enter the Table with the tenth part of Diff Lat, 84.0, and the tenth part of the Distance, 96.0 miIes,aod they will be found to agree at Course 29°. Again, with the same Course, 29*, and the tenth pari of the Meridiaoali Difference of Latitude, 84.4, in the Latitude colimin, then the tenth part of the Difference of Longitude is found ia the Departure column 47, which multiplied by 10 gives, 470, the whole Difference of Lon^^itude. Diff. Long, in Degrees T°~5b' W. Long, left 22° 30 ' W. The Course steered is S. 29' W. and Longitude m, .80° 20' W. NoTK. — The above three Examples are the same as are used in Middle Latitude Sailing, and the answers oome oat wluma The whole Difference of Loogituc'e is 813.8, or 5° 14', and the Longitude in 8° 69' East MERCATOR'S SAILING. Tt CASE II. Tipo Latitudes and Longitudes given, to find the Bearing and Distane4. EXAMPLE L Required the Bearing and Distance of Cape Henry, in Latitude 36* 66' N., and Longitude 76* 0' W, and the leUa^ f Bermuda, in Latitude 32° 18' N, and Longitude 64° 60' W. Latof Cape Henry 36* 66' N. Merid. parts 2388 Long 76* 00' W. Lat. of Bermuda 32 18 N. Merid. parts 2050 Long 64 60 W. 4° 38 Merid. diffi Lat ... ..888 S. 11* 10' W. 60 . 60 Diff. of Lat in miles 278 Diff Long, in miles 670 RUT.E. — Seek in the Tables with the tenth part of the Meridian Difference of Latitude 38.8. and the tenth part of the Difference of Longitude 67.0 until they are found to agree in the Latitude and Departure columns, as if thej were Difference of Latitude and Departure. If the Difference of Longitude be greater than the Meridian Differeno* ©f Latitude, the Course must be taken from the bottom of the page, but if let-i, from the top. They ai"e found to agree in this case nearly to the Course, 63*. Then, with the tenth part of the proper Difference of Latitude, 27.8, in its column on the same page, will be found opposite to it, in the Distance column, the tenth part of the Distaneer •1.6, which, multiplied by 10, gives the whole Distance, 616 miles. Hence, the Bearing is South 63* East, beoauie Bermuda lies towards the South and East from the Cape, and the Distance is 615 miles. Fwo Latitudes and Longitudes given, to find the Course and Distance. EXAMPLE 2, A Ship from Latitude 30* 15' N., and Longitude 46' 20' W., sails between the North and West imtil, by obeerra- tion, she is in Latitude 33° 46' North, and Longitude 60* 10' West Required the Course and Distance mad* ([oo taifled between the second Bearing and the ship's he«d. At the angle of meeting take out the tabular number, which multiply by the number of miles of Distance made good by the ship. The result is the Distance in milea off •bore at the time the last Bearing was taken. Rule 2d. To find the Distance when the first Bearing was observed, enter the table with the differe-Me between] these Bearings and 16 points ; the second Bearing in this case must be taken from the top, and the first Bearing from the side column. Take out the tabular number corresponding and multiply it by the number of miles of Distance made good by the ship. The result is the Distance of the ship off shore at the time of the first Bearing. CASE 1. Finding the Ship*s Position from two Bearings of the same Object. EXAMPLE L At 8 P. M. Fire liknd Light bore N. W. ^ N. by Compass. Ship's course W., at the rat« of 7 knots an hour, and at 10 P. M. the same light bore N. N. E. | E. Required her Distance off at both stations. let Beariner N. W. 4 N. ) . i . , ,. 2d Bearing N. N. E. -J E. ) . , ,^, ^ . xu t u i xr noA Course West. J Angle 4i pts. Course W^st, f Angle lOi pts. gives the Tabular Num. 0.84 Taken at the top of the Table. Taken at the side of the table. Dist sailed 2 h's at 7 knots 14m ~336 The Tabular Number multiplied by 14, the Distance sailed, and the two right hand figures struck off (being "'^ Decimals) gives the Distance off at 10 P. M. llf miles nearly, or - 11.76 To find the distance off at 8 P. M., The first angle being 4-J points, the second angle 10^ points ) The Tabular number is ....... 0.95 Subtract from 16 " subtract from 16 " \ Distance sailed 14iB Taken at the aid* of the Table TTT " Taken at the top' 6^ " ) 880 95 Giv»8 th«> distance off at 8 P. M. l^i miles, or 13.80 / FINDING THE SHIPS xuSiTlON. EXAMPLE 2 At 6 P. M. Barnegat Light came in eiglit, bearing by conipasa S. W. by W. Ship sailed on a S. by W. ^ W iouree, at the rate of 8 kuots an houi-. with n 2kiiot tide in iier favor, until 7h 3f>m P. M., when the same light waa observed to bear N. W. by W. Required her distance off at both stations. Ist. bearing S. W. by W. ) . , 2d bearing N. W. by W. ) , Course S. by W. ^ W. \ ^"^^^ ^* P^" Curse S. by W. ^ W. f ^"^'^ ^* P^ Takeu at tke top of the Table. Taken at the side of the Table, glTes the Tabular Number 0.6» Distmice sailed in 1^ hours. . 12 milea. Multiply by 16 Add for tide 3 ~346 Distance made good 16 miles. 6t» The siiip's distance off the Light at 7h 3(lm P. M. is 10^ milea, or lOM To tiad the distance oflf at 6 P. M., Che first angle was 3^ points, 2d an^le V-^ points. ) 4ub»r<.cl from 16 " Sub. from 16 " \ The Tabular Number is found to be 1.08 l*k8 at the side T2i points. At the top ~6i points. ) Distance made good _16 61fi 10 S The ship's distance off the Light when peen at 6 P. M., was 16^ miles, o. 1*44 PROJECTION OF THE ABOVE EXAMPLES, Skmcing the Distances found by the Tables to be correct, as measured in the Diagram. Fig. 17. Ce^ur.ie ms'l J)isl H^fftlcs SCALE of MILE5 t i 6 T t 2 IC 94 FINDING THK SHIPS POSITION. FINDING THE SHIP'S POSITION FROM TWO BEARINGS OF THE SAME OBJECT. CASE II. Given, two Bearings by Compass of an Object on Shore, with the Distance sailed between them, to ^nd ilu Ship's correct Position in Latitude and Longitude. This case is useful in finding the Sea Rate of the Chronometer. (See page 155.) EXAMPLE 1. At 6 o'clock A. M., Neversink Light-House bore by Compass W. by S. i S. Ship then sailed on a S. | W. Course, «t the rate of 6^ 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. Fbe Ist Bearing W. by S. i S. by Compass. 2d Bearing N. W. by N. by Compass. Corr. for i pt W. var. is W. S. W., j .' „, „ ,.+= Corr. for ^ pt var. N. W. ^ N. | . „„, , „, .. Course S.iW - South, [AngleGpts. Course..!.^ true S. f ^^^" ^^i pts Tabular Number 97 2 hours at 5^ knots=Distance sailed 11 Distance off at time of 2d Bearing at 7 A.M 10.67 miles. Tte op. pt to the 2d Bear, is S. E. i S., Dist. 10^ miles, gives D.L. 0° 8' S., and Dep. 6.7==D. Long.. . 0° 8' 46" K Lat of Neversink, 40 24 N. Long, of Neversink. .78 58 48 "W. At 7 A. M. the Lat of the Ship was 40° 16' N. and Long 73"° 50' ?" W. To find the Position of the Ship at 5 A M., or time of the 1st Bearing. Ist Angle was 6 points. 2d Angle -was 12^ points. ; Subtractfrom 16 " Subtractfrom 16 Take 10 points at the side of the Table, and 3^ at the toj*. Tabular Number 66 Distance Sailed 11 Diet off at time of 1st Bear. 5 A. M 7.26', or 7i miles, nearly. l^e pp. pt to 1st Bear, is E. N. E, and Dist 7i, gives Diff. Lat. . . 0° 8' N. Dep. 6.7— D. Long. 0° 8' 45" E. Lat of Neversink .40 24 N. Long.. . . 73 68 48 W At 5 A. M. the Lat of the Ship was 40° 27' N. Long 73° 60' 8"W. The Ship having made a true South Course, she has sailed on the Meridian of 73° 50' 3" West, and was is Um Hme Longitude at 7 A- M. as at 5 A- M., and her Difference of Latitude is equal to the Distance sailed. EXAMPLE 2. At Noon the N. W. end of St Anthony (one of the Cape Verde Islands) bore S. E. by E. by Compass. Shij) tnen •ailed on a South Course, at the rate of 10 knots an hour, until 4 P. M., at which time it bore N. E. by E. -J E. the Magnetic Variation here being 1^ points "Westerly. Required the Lat and Long, of the Ship at the time of each Beaoing. The Ist Bear. S. E. by E. by Compass. 2d Bear. N. E. by E. ^ K by Compass. Cor. for U pts. W. var. =E by S. i S. ) . , - , Cor. for 1^ pts. var.=N. E. | . , ,„, Course South, corrected,=S. by E. | E. f ^^S^^ ^ P^ True Course. . . .S. by K i K f ^"^le lOi ptiL Tabular Number 0.94 4 hours at 10 knots Dist . . 40 Dist off at the time of the 2d Bear, at 4 P. M .37.60 miles. 'Qie op. pt to the 2d Bear.'is S. W., and Dist 37^ miles, ^ives D. L. 0° 26' 80" S. Dep. 26.5=-D. L. 0° 27' 40^ W Lat of the N. W. Point of St Anthony 17 12 N. and Long. do.. . . 26 19 W At 4 P. M. the Lat of the Ship was 16° 45' 30"N. and Long 25° 46' 40" W To find' the Position of the Ship at Noon, or time of 1st Bearing The 1st Angle was. ... 5 points. 2d Angle was 10^ points. Subtract from .!&_ " Subtract from. . ._16 " ) Tabular No. . . 1.00 Take 11 points at the side of the Table, and . . 5^ at the top. \ Dist sailed . . . 40 Dist off at time of 1st Bearing, or Noon 40.00 miles. The op.pt to the 1st Bear, is W.byN.iN., and Dist40=D. L. 0° 11' 36" N. Dep. 38.3 W.=D. Long. 0° 40' "W Lat N. W. Point of St Anthony is .17 12 N. Long.. . . 25 19 W Lat of the Ship at Noon was 17° 23' 36" N. Long.. . . 25° 59' W This method of finding the Position of the Ship when in .sight of Land, by two bearings of the same •bject, will be found of great value, when a cross-bearing cannot be obtained. All that is necessary to do, is to select an object, the position of which is given in the Table of Latitudes and Longitudes, and to take a correct bearing of it by the Ship's Compass, and note the time by Watch ; and after the bearing has altered not less than 3 points, take a 2d bearing and note the time by the Watch. Thus having the interval of time between the 1st and 2d bearings, and the rate of sailing per hour, the Distance sailed ia the interval may easily be obtained, and the Ship's correct Latitude and Longitude found, as explained in the above Examples, at either of the Bearings. This will be found of importance wnen the Ship's Chronometers require to be verified, at times during a voyage, when in sight of any known land. Because if the Sights are taken for Time, the Bearing of the Land can be taken at the same time, and another Bearing taken either before or after that time, with the Course and Distance run in the interval, will give the Ship's exact Latitude ani Longitude at the time the Sights were taken. ss TIDES. . The Tidal Wave is caused by the joint Attractions of the Sun and Moon, but chiefly of the latter body, whereby the Sea is raised or drawn up by that power, in the form of a Swelling Wave, and following th« motion of the Moon round the Earth, advances at a prodigious rate. This Water does not, however, partaxe of any onward motion, but merely rises and falls. The motion of a Tide Wave is represented by the fluttering of an Awning or the shaking of a Sail. If the Earth was entirely covered with water, the Course of this Wave would be from the East towards the West ; but as large Continents and Islands exist, which obstruct its free passage, it diverges into other directions, and the meeting with those obstructions causes the water to acquire a motion conforming to ths direction m which the land lies ; but still, to a certain extent, under the governing influence of the Sur and Moon, and branching off" in all directions until it finds its level. The -Interval of time which the Moon takes in passing the Meridian of any place, and returning to th« same again, consists of 24 liours 49 mmutes, being the length of a Lunar day. This occasions two floods and two ebbs of the Tide Wave in that time. Therefore one flood and one ebb will occupy about 12 hours 24 minutes, and the Flood tide will run 6 hours 12 minutes, and the Ebb in a contrary direction the same len^iii of time. But as the JMoon comes to the Meridian nearly an hour later every day, the time of High Water is that much later every day. When it is High Water on the shore, or when the Tide has done rising, it continues running longer in the offing. Three hours longer is called Tide and Half Tide, one hour and a half longer, Tide and Quarter Tide. On the day of the full and change of the Moon, the time of High Water is noted at the various Ports and places of the World, and published in a Table, and which is called the E..tablishment of the Port or place And all that would require to be done to find the time of High Water on any other given day, would be to add the time of the Moon's Meridian passage to the fetablishment of the Port. But on account of the irregular influence of the Sun and Moon, and other causes, together with the effect of gales of wind in accelerating or retarding the times of High Water, an approximate result only can be obtained from any general rule. In some parts of the world Local Tide Tables are constructed, containing the times of High Water at the various places on that Coast, predicted from long experience of tidal observations, and which is of great importance to vessels which are about to enter a Harbor where there is a great rise and fall of the Tide. In many parts of the world there is very little rise and fall ; nevertheless, the tide runs with considerable velocity. And where a Bay or Inlet is exposed to the Set of the Flood Tide, which not having any outlet, the water naturally rises to a great height, as we see in the case of the Bay of Fundy, and other places. In inland Seas, such as the Mediterranean, Baltic, &c., which are composed of narrow stripes of water, there is not sufficient room for the formation of the Tidal Wave ; consequently, the tides there are scarcely perceptible. In some rivers, which, on account of tlie great quantity of water they discharge, run longer and with greater velocity on tlie ebb, the flood tide is thereby kept back, until accumulating strength, it rises like a wall above the level of t.ie ebb, and advancing m the form of a Crested Wave, rushes upwards with great strength until it finds its level. This phenomena ic called the Bore of the Tide. When the Sun and Moon are on the Meridian together, their actions concur, and the tide is higher than at any other time. The same holds good when they are in opposition to each other. These highest tides are called Spring Tides, and occur a day or two after New and Full Moon. But when the Sun and Moon are 90° apart, their actions, or power of attraction, neutralize each other, and the tide is lower than at other times. These are called the Neap Tides. The highest tides happen in the month of January ; because the Earth is nearer to the Sun and Moon then, than at any other time of the year ; consequently, the hignest Spring Tides happen in that month. When the Moon's Declination is 0, the tides are equally high on that day ; and while the Moon has Nortk Declination the higest tides are in the Northern Hemisphere, when she is above the horizon, and the reverse when her Declination is South. The Tides risp h'ghest at places where the Moon is in the zenith; they Are also highest at the Equator and lowest at the Poles. The common method of finding the time of High Water is as follows : 1. TO FIND THE MOON'S AGE. Rule. — Add together the Epact of the Year, the Epact of the Month, and the Day of the MontL The Sum, if it does not exceed 30, is* the Moon's Age ; if the Sum exceeds 30, subtract 80 from it, and the remainder will be tb« Moon's Age on that day of the month reauired. M TIDES. TO FIND THE TIME OF THE MOON'S PASSING 1 HE MERIDIAN IhrLK. — Multiply the Moon's Age by 8, and point oflF the right figure under the days, then the left hand figur«, ot figures, yriW be the hours, and multiply the right hand figure (which was pointed off) by 6, will be the minutes past Boon when the Muon passes the Meridian. If the hours exceed 12, subtract 12 uours from it, which will be thf lim« vf her Morning passage. TABLES FOR FINDING THE MOON'S AGE THE KPACT OK THE YEAR. 186S. 1854. 1856. 1866. 1867. 1858. 1859. 1860. 1861. 1862. 1863. 1864. 1865 1866. 1867. 1868. d h. 6. 8 1869. d. h. 20. 1 d. h. I. 3 d. h. 11.18 d. h. 23.10 d. h. 4.12 d. h. 15. 3 d. h. 25.17 d. h. 7.21 d. h. 18.12 d. b. 29. 8 d. h. d. h. 10. 6 21.21 d. h. 2.23 d. h. 13.15 d. h. 24. 6 d. d. 16.23 THE EPACT OF THE MONTH. 1 1 Jkn. Feb. Marcli, April. May. June. July. Aug. Sept. Oct Nov. Dea d. h. 0. d. h. 1.11 d. h. 29.11 d. h. 1.10 d. h. 1.21 d. h. 3. 8 d. h. 3.20 d. h. 6. 7 d. h. 6.18 d. h. 7. 6 d. h. 8.17 d. h. 9. 4 TO FIND THE TIME OF HIGH WATER.— l5t Method. Role. — To the time of the Moon's Meridian passage on the given day, add the time of High Water at the givei pliice on the Full and Change days, or, as it is called, the Establishment of the Port Their Sum is the time of High Water past noon on the given day. If this Sum exceed 1 2 hours 24 minutes, which is the interval between Mich succeeding tide, subtract 12 hours 24 minutes from it ; or, if it exceed 24 hours 48 minutes, subtract 24 boor* 48 minutes from it, and the remainder will be the time of High Water in the afternoon of the given dav. EXAMPLE 1. Required, the time of High Water at Sandy Hook, October 2, 1854, (Civil time.) Epact for the Year, 1854, is 1.3 " " Month, Octf)ber, 7.5 Day of the Month, October 2.0 Moon's Age 10.8 Moon's Age, October 2, 1854 10.8 Multiply by. 8 8h. '2.16 6 Moon's Meridian Passage 8h.l6 Establishment of Sandy Hook 7 36 Time of High Water in the morning 15 51 Subtract.. 12 24 Time of High Water at Sandy Hook. . . . 8h.27 in the aftemooa EXAMPLE 2. itequired, the time of High Water at Cape Henry, December 6th, 1854, (Civil time.) Kpaet for the Year, 1854, is 13 " " Month, December, 9.4 Day of the Month, December, 6.0 Moon's Age 16,7 Moon's Age, December 5th, 16.7 Multiply by 8 13. '0.8 6 Moon's Meridian Passage 13h. 2.0 Establishment of Cape Henry 7 40 Time of High Water in the morning 20 42 Subtract 12 24 do. Do. in the evening 8h.l8 As this Rule gives only a rough estimate of the Time of High Water, and may be as much as two houi» in error, caused by the variation in the time of the Moon's daily passage over the Meridian, and which aries from about 40 minutes to 66 minutes, at different times n the year. This Rule assumes the interval f her Meridian passage to be 48 minutes or four-fifths of au hour. It, however, may be useful when Jiere is no Nautical Almanac at hand. The Second Method is more to be depended on. In this case the Moon's Meridian Passage at Green- wich is taken from the Nautical Almanac, and corrected to the time of her passing the Meridian of tbt Ship, and which is further corrected for her Horizontal Parallax by the annexed Tables. FINDING THE TIME OF HIGH WATER.— 2d to the Meridian passage if the Longitude be Went but subtracted if Eaet, will be the App. time of the Moon's Meridian passage at the place. Take out the Moon's Hor. Pari Dearest to this time on the given day, from the Nautical Aimanaa Enter the Table below, with the time of the Meridian passage at the side and the Hor. Pari, at the top. and take out a correction to be applied as directed in th* table, to the apparent time of the Moon's Meridian passage at the place, to which add the establishment of the port^ and the result is the time of High Water in the afternoon, if less than 12 hours. If it exceed 12 hours, it is the time of High Water next morning ; and to obtain the time for P. M. on the present day, subtract 12h. 24 m. from it If the sum exceeds 24 hours, it is the apparent time of High Water P. M. the next day. For the P. M. of the prc^- poted day, subtract 24h. 48m. Long. Corr. of th« ia TABLE FOR FINDING THE TIME OF HIGH WATER. ?Hce. Min. » , • f Moon'* Moon '• Horizontal Parallax. Moon's Moon's Moon 't Horizontal Parallax. Moon's 10 20 80 1 3 4 Mer. Passage. Mer. Passage. Mer. Passage. Mer. Passage. 64' 56' 68' 60' 64' 66' 68' 60' Add Add Sub. Sub. 40 6 h m h m h m h m h m h m h m h m h ro h ra h m h m 60 6 6 2 1 8 12 6 50 45 42 40 n 38 18 50 60 8 Sub. Sub. 7 37 35 34 33 19 70 9 20 1 4 6 7 12 20 7 10 29 28 28 27 19 10 80 10 40 8 10 11 12 12 40 7 20 22 22 22 22 19 20 90 12 1 16 16 17 17 13 7 30 16 15 16 17 16 30 100 13 1 20 22 22 22 22 13 20 7 40 8 9 11 12 19 40 110 14 1 40 29 28 28 27 13 40 7 60 3 1 6 6 19 60 120 15 2 37 85 33 32 14 Add Add Add 130 17 2 20 43 41 38 37 14 20 8 9 4 1 1 20 140 18 2 40 6C 46 44 42 14 40 Add 160 19 3 56 52 49 46 15 8 20 17 12 8 6 20 20 160 21 S 20 1 3 57 53 51 15 20 8 40 29 22 17 13 20 40 170 22 3 40 1 8 1 2 67 54 16 40 9 31 24 19 15 21 180 23 4 1 13 1 6 1 1 58 16 9 30 36 29 23 19 21 80 4 30 1 18 1 11 1 5 1 2 16 30 10 35 27 22 18 22 5 1 21 1 13 1 7 1 3 17 10 30 30 23 18 15 22 80 5 80 1 18 1 11 1 6 1 2 17 80 11 23 17 13 10 23 6 1 13 1 6 1 1 58 18 11 30 15 10 6 4 23 30 6 20 1 2 56 53 50 18 20 Sub. Sub. 6 40 53 49 46 44 18 40 12 6 2 1 3 24 EXAMPLE 1. Required the time of High Water at Sandy Hook, Oct. 2d, 1854. (Sea time.) Moon's Mer. Passage Oct Ist, N. A 8h 11m " " " ~ • Equa. of Time the contrary way, add 10 Apparent time of Meridian passage 8h 21m Long, of Sandy Hook 74° W., add 10 ^pp. time of the M. Mer. pass, at Sandy Hook. 8h 31m At Sandy Hook, Apparent time of High Water, in the afternoon . Moon's Hor. Pari, at time of the Mer. passage is 59'. Then- with the Mer. pass at the side of the table, and between 68 and 60 at the top, the Corr. is Oh Km to be added to the Meridian passage 8 31 8h 41m Add the Establishment of the place 7 35 Time of High Water in the morning 16h 16m Subtract 12h 24m - 3h 52ui EXAMPLE 2. Required the time of High Water at Cape Henry, December 6th, 1864. (Sea time.) Moon's Mer. passage, December 5th, N. A ISh 8m Moon's Hor. Pari, at time of the Mer. passage 55'. Then with the Moon's Mer. passage at the side of the tal 9_ 18b 12m 10 passage at tiie side oi ine table, and between 64 and 56 at the top, the Corr. is. . . . Oh 22m ■which, subtracted from the Meridian passage .13 22 13h On? Add the Establishment of the place 7 40 At Cape Henry, apparent time of High Water in the morning 20h 40ni 12 24 Equa. of time the contrary way, add. Li)ng. of Cape Henry 76° West, add. App. time of the Moon's Mer. passage 13h 22m TW« of nigh Water oc the afternoon of the same day 8b 16i WINDS. The fjilownng short description of the prevailing Winds may be found useful, in the absence of the regu- alar sailing directions for the voyage, which should contain all the necessary information on this head: The Earth revolving on its axis from West to East, together with the great heat near the Equator, caused toy the Sun being always vertical in some part or other of the Torrid Zone, produces the Trade Winds. The motion of the Earth causes the Wind to blow from East to West, whilst the cold air rushing m from the North and South towards the heated air in the Tropics, produces the N. E. and S. E. Trade Winds, ana which blow continually in those directions Their limits extend to about 30* on each side of the Equator, but near to the coasts of America and Africa they extend to 34° sometimes. The limits of the Trade Winds are very variable, even in the same months of the year. When the Sun has great North Declina- tion, their limits are considerably to the Northward of where they are found when the Sun has great South Deelination. In the month of June, for instance, the Northern limit of the N. E. Trade may be found in about 30° North Latitude, and the Southern limit of the same in about 10° North of the Equator. A space of calms and rain-squalls intervene. Until the Northern limit of the S. E. Trade is reached in about 4° North of the Equator, its Southern limit at this season extends only to about 20* South of thej Eqaator. In the month of December, when the Sun has great South Declination, the Northern limit of the N. L. Trade Wind may be expected in about 20° North Latitude, and its Southern limit in about 4° North of thej Equator. A space of calms and rain-squalls intervene, and the Northern limits of the S. E. Trade will ba found in about 2' North of the Equator, and the Southern limit about 30° South Latitude, It appears, then, that the limits vary to the extent of 10° in 6 months, and that the Northern limit of the S. E. Trade] Wind is always found to the Northward of the Equator. Ships cross the region of calms, &c., between the Trades, quicker bound North, than they do when bound | South, by reason of the airs of wind being more favorable. Ships on approaching the limits of the Trade Wind, fall in with squally weather and heavy rains, a sure ' indication of a change. On entering the Northern limit of the N. E. Trade, the wind will be found far tOj the Northward : but as you advance South, the Wind will draw more to the Eastward. And in like man- ner, the S. E. Trade is found far to the Southward, and draws more to the Eastward as you advance. Ships bound to the Southward should endeavor to cross the Equator in about Long. 25° W., because they^ will meet the S. E. Trade sooner than they would if farther to the Eastward. They must, however, bej careful not to go too far to the Westward before crossing the Equator, on account of meeting tiie S. E. Trade Wind far to the Southward, which heads them off to the Westward, and because of the Equatorial | Current, which sets in towards the coast of Brazil. But in a fast sailing Ship this may be much modified. When the vessel is caught in the variable weather which exists between the N. E. and S. E. Trade Winds,] the rule is to keep on that tack in which she makes the most Southing on, so as to get out of it as quickly j as possible. Far to the Eastward, along the coast of Africa, the S, E. Trade is changed to a S. W. Wind, which blows with little variation throughout the year in that direction, interrupted at times by violent j tornadoes, and the Harmattan or East Wind, close to the coast. A ship taking this Eastern passage to the Cape of Good Hope, vrould certainly have to beat the wholol way, though an advantageous slant is sometimes obtained when the Wind veers at the quarterly changes »f the Moon. After losing the S. E. Trade, the usual variable Winds are met with, but the most prevailing one is from the S. W. When a Ship is bound to the East Indies or Australia, the best parallel of Latitude for running down her Longitude to the East is 39° 0' S., because there the Westerly Winds prevail, and the; weather is not so tempestuous as it is farther South. (See remarks on Great Circle Sailing. Page 6.) If bound to India, and having reached 70° 0' E. Longitude, they steer more to the North, and fall in with I the Southern limit of the S. E. Trade in about 90° E. The limits of the Trade Winds here are governed by the same laws as they are in the Atlaniic Ocean, but do not blow so steadily. The space, between the Northern limits of the S. E. Trade and the Equator is occupied by a Wind which blows 6 months, that is, from May to October, from the Eastward and called the Easterly Monsoon, and the other 6 months of th« fax in an opposite direction, and then called the Westerly Monsoon. CURRENTS. 89 After crossing the Equator and bound up the Bay of Bengal, the region of the r»g,alarMonjoons is reached The S. W. Monsoon commences in May, and brings rain and squally weather, which continues 6 months «r until October. The N. E. Monsoon then commences, and durmg its continuance, from October to May (the other six months of the year), fine dry weather prevails on all the coasts of India. The Monsoons varj their direction according to the locality of the place at which they blow. This includes the China and Arabian Seas. At the changes of the Monsoons, terrific hurricanes frequently occur in all these localities. In the Pacific Ocean, the South East Trade Wind is found to blow very steadily, with fine serene weather, and its limits are about the same as in the Atlantic Ocean. Not so, however, with the North East Trade ; it is generally found light and variable, and hangs far to the Northward, especially when the Sun has great North Declination. Ship's bound to California generally cross the Equator in about 112° West Longitude; but they seldom find the North East Trade blow with the same, force as it does in the Atlantic. These are the principal winds which blow with any degree of certainty ; but where there are larg* Islands or Contments within the limits of the Trade Winds, the surfaces of which becoming violently heated by the tropical Sun, causes the regular wind to diverge into a local Trade. THE CURRENTS OF THE OCEAN. The Trade Wind blowmg continually in one direction, causes the water on which they act to acquire a. movement in the same direction. This is called a Current; but as neither the direction nor the velocity of a Current continues uniform, it becomes one of the most perplexing problems in Navigation, in making the proper allowance for the effect it may have had on the vessel's course. The only true method i.s to keep a careful account of the Ship's way by Dead Reckoning, and compare this frequently with the place of the Ship by Celestial observations. The Set and Drift of the Current may thus be ascertained, and proper allowance made until next observations. (See Current Sailing, page 29.) There are several Currents known to exist in various parts of the world. The one known as the Florida Stream, originates in the Trade Winds which force the Water in towards the West India Islands, and between which it passes into the Gulf of Mexico ; but not finding an outlet there, it rushes out between Cape Florida shore and the Islands of Cuba and Bahama, pursuing its course to the North, nearly parallel with the coast of the United States ; it then diverges to the Eastward and crosses the Atlantic. One part of it is supposed to enter the Straits of Gibraltar, and the other to proceed along the Coast of Africa. Passing the Cape Verde Islands, it rushes along the S. E. Coast into the Gulf of Guinea. It is then called the Guinea Current, and which runs to the Eastward, between this Coast and the Equator, until it strikes the South Coast of Africa, by which cause and the prevailing winds together it is forced in and blended with the great Equatorial Current which sets West to the South of tL Equator. The author of this work has frequently seen the extraordinary phenomena of these two great Ocean Rivers brushing past each other, side by side, the dividing line marked by a streak of foam, exactly on the Equator.* It will be perceived that what is called the Florida Stream makes a complete circuit of the Ocean. For by joining this Current, which is formed by the South East Trade Wind, it is again precipitated into the Gulf of Mexico. The Velocity of the Florida Stream is governed by the force of the Trade Winds and the obstruction it meets with from local causes. About 4 knots an hour is the usual rate of" the Bahamas ; but as it proceeds to the North and East it becomes less. But the most interesting fact of its retaining its heat acquired in the tropics, and preserving its borders from mixing with the surrounding Sea, is very extraordinary. This is of great use to Seamen; because by ascertaining the temperature of the Sea water by the Ther- mometer, he knows whether he is within the influence of the Stream or not. The Sea- weed floating about, usually called the Gulf weed, which although brought down by the Stream, js not always an indication of being in it. The Polar Current is supposed to have its origin in Behring's Straits, in the North Pacific Ocean, and ruuH South through Davis' Straits into the North Atlantic. Rennels' Current runs across the mouth of the British Channel towards the North West, and is caused by the water escaping out of the Bay of Biscay, which had been forced in by continued gales of wind from the West. The action of the Trade Winds in the Indian Ocean produce a Current which sets North West into the Arabian Sea, and having no outlet, the waters make their escape out again in two divisions, one runs to Jhe South East along the Malabar Coast and past the Island of Ceylon, and again joins the Equatorial Current running to the Westward. The other division runs out along the East Coast of Africa, between Ihat Coast and the Island of Madagascar. Pursuing its course to the South West, it passes along the edge jf the AguJhas Bank and round the Cape of Good Hope ; it then runs to Northward and joins the Equato- .•ial Current which runs to the Westward in the Atlantic Ocean. Tliat part of the Current which sets round the Cape of Good Hope i.« called the Agulhas Current, and its velocity varies from 5 knots to 0, and a Current has been found someti >ries to run in the opposite direction. A Ship bound to the Eastward should keep in about the Latitude of 40° South when rounding the Cape By that means they will avoid the Current setting to the Westward. On the other hand, a Ship bound to the Westward should endeavor to get into this Current by steering for the coast to the Eastward of the * Ships on leaving the Gulf of Gniiiea, or the Bi^lit of BiatVa, bound to the Westward, consequently have to Veat to w^indward between tlie Princes Islands and tlie mainland of Africa, where they find a favorable current running to ihe Southward, until tiiey have crossed tlie Equator, when, by then standing to the Westward, they fall in with the regular Eqn&toriai Current running Wast. Thereby avoiding the Guinea Cuirent whijh runs in a contrary direction to Ml* Northwfijd of the Eouator. 40 WINDS AND CURRENTS. Gape. In Westerly gales the Current running against the wind makes the Sea run heary and dangeroo* But a Ship may find smoother water by standing in for the Agulhas Bank and keeping on it until the gaU n»derate» in the ofBug. Two Ships becalmed near each other, one may be in the Agttlhas Current and the other on its Bank, and it frequently happens that in the course of two or three hours the one in th© Current is swept away to the Westward, out of sight of the other, without any visible cause ; and befor« the nature and effect of this Current was understood by Navigators, it gave rise to the superstitious story of the Flying Dutchman. The Trade Winds in the Pacific Ocean also form a Current which runs to the Westward, and thei between the North and West, until it strikes the Coast of China. One division then running throug the Indian Archipelago joins the Westerly Current in the Indian Ocean, and the other sets toward Berhing's Straits. Ships bound to California cross the Equator in about 112° West, which is too far to th« Eastward, because the effect of the North East Trade Wind is deadened by its proximity to the Continent of Nori k America, which has exactly the same effect on the North East Trade here (that is, of causing light wines from the North and baffling weather) as there is found in the South East Trade in the proximity t» the (Continent of Africa, where light Southerly winds are found to prevail, and baffling weather ; but on getting further to the Eastward they have the regular Trade. Consequently, if Ships were to cross the Equator in the Pacific Ocean in about 130° West Longitude, they would find a steady fresh North East Trade, be enabled to cross it quickly, and then afterwards run down their Easting in a high Latitude, where both wind and current would be found more favorable. In the Mediterranean Sea, there exists the curious phenomena of its receiving the Currents from the Black Sea, and large rivers running into it, besides the regular Current from the Atlantic Ocean, which flows in through the Straits of Gibraltar. Those waters have no visible outlet ; but they are known U> make their escape out into the Atlantic Ocean through the Straits of Gibraltar, underneath the Current which runs in on the surface. This has been proved by vessels which have been sunk at eome distance inside of the Straits, the wrecks of which were afterwards cast on shore to the Westward, or outsj-ie of the entrance. The submarine mountains rising from the bottom of the Sea, the tops of which are /.j'/jo« visible in the form of Shoals or Rocks, are no doubt the fertile cause of many of the extraordinary Coirenta whi<* are met with at Sea. Because a body of water striking these elevations at right a-igJ<5? would be tume iiar manner as before stated. DIAGRAM OF THE STORM CIRCLE IN SOUTH LATITUDE. Fig. 19. RULES TO AVOID THE FOCUS. Dim your back to the Wind, and your Right hand will point to the Focus. HaiTioun* Wind. Wbd at "West. N. W. North.. N. E. • East &E. " South. S. W. Bearing of the Focus. Focus bears South. t( II S. W. II u West II II N. W. 11 u North. U 41 N. E. U II East U M S. E. When th« Path is to the W. S. W. Heave to on the Starboard Tack, do do do do do do de do Run 50 miles to N. W. and heave to. Heave to on the Starboard Tack, do do When the Path i» to the 5. B Heave to on the Starboard Tack. do do do do Run 50 miles to the S. W. and heave to, Heave to on the Starboard Tack, do do do do do do Jk"' a^ Hurricanes in the Sonlh Atlantic, after leaving the Latitude of 80* S. recurve to the S. E. ■g these Horncanes in a higher Latitude would be in their direct path, when she has the Wind at N. E., becaose o» ■iraine your back to the Wind, the right hand will point to the Focus bearing N. W., and ita path being 8. 1 ~- •▼•ruke her unless she gets out of its way by running off 50 mile» to the S. W. A Ship mevW >o» wir 44 HURRICANES. REMARKS ON HURRICANES. • The following remarks on handling a Ship in a Hurricane, may be found useful : When a Ship iaj approaching the locality of Hurricanes, the Barometer should be carefully watched, and when it ha« fallen] rapidly from about 30 inches to 29 20, the Ship is then on the verge of a Storm Circle At the same time! ■the weather will appear threatening, with heavy, bluish-looking clouds in the sky. At other times, it sett] in with small rain, and the Wind increases gradually. Now is the time to consider which side of the] Storm Circle the Ship is on, from the direction in which the Wind is theu blowing, by the rules already] .given for that purpose. The most severe Hurricanes, especially those in the Indian Ocean and China Seas, generally give notic«] «f their approach by the rapid falling of the Barometer about an inch, when no other indications in the] ••ky are visible, at from 12 hours to 48 hours before the verge of the Storm reaches the Ship. And in this} «ase no time should be lost in preparing the Ship to encounter it, by sending down on deck all the light] spars and rigging, and the studdmg-sails out of the tops, rigging in the flying-jib and standing-jib booms,] securing the boats and hatchways, and the sails (which are furled to the yards) with double gaskets,] •because after the Hurricane sets in, the violence of the Wind is so great that it will be found impossible] for men to go aloft or to do any work whatever. Upon the same principle the Ship's place in the Storm j •Circle should be ascertained as soon as possible, and arrangements made for her safety by running out of its path, if necessary, before the wind has increased to that degree that no sail can withstand, or to heave] •to on the proper tack. Instances have been known of Ships getting into the Storm Circle, and been obliged to scud before the] Wind under bare poles, and changing their Course as the Wind veered, and have been kept scudding round] 4he Focus tor several days together, and only got liberated after the Meteor had spent itself, and found them- selves several hundreds of miles to the Westward of where they had entered it. A Transport Ship, with troops on board, from Ceylon, bound to the Island of Mauritius, fell in with one ] ^of those Hurricanes on the 26th of March. At midnight the Barometer had fallen to 28.90. Wind blow ing hard at West. And the captain, not being acquainted with the theory of storms, the Ship was kept] on her course to the S. S. W. 50 miles, and next day the centre of the Hurricane burst upon her, and threw ter completely on her beam ends. All three masts went by the board, and she righted a little. The wreck of the masts alongside knocked off her rudder, and caused her also to leak badly ; and so severe was the Hurricane and sea that the men were frequently washed from the pumps, the Ship laying all the time m the trough of the sea, and her decks were continually swept. For three days this Hurricane continued, jind during all that time the hatches had to be kept carefully closed to prevent her going down. And when) the storm abated so that the hatches could be raised a little, 14 of the soldiers were found dead by suftoca- Uon from the want of fresh air in the hold. Now there is not a shadow of a doubt but this was caused by the ignorance of the captain, in allowing] the Ship to stand on to the S. S. W. 50 miles, after the Barometer had fallen to 28.90, and which placed iirN«. i»oo sne been hove to in the first case when the Barometer fell to 29 inches, with her head to the North- ward, on the Port tack, the Meteor would have passed to the Northward of the Ship on its path toward* the W. N. W., and the Wind as usual would have veered to the S. W. and South, and she would then laff up and bow the sea, but would be kept perhaps two or three days in the storm. And in the second case, by heaving to under the same circumstances, the storm would pass to the Soath- •Mtward of the ship, on its path towards the N. E. ; and the Wind veering to thn North and N. W., *h» would luif up as before, but would also be kept 2 or 3 days in the storm laiH *o 4« THE CONSTRUCTION AND USE OF MERCATOR'S CHART. A» the surface of the Globe is round, while that of the paper is flat, every chart exhibiting any extent af surface is necessarily an artificial construction, or, as it is called, projection of the real state of things. The Charts used in navigation are those on Mercator's Projection, because on this alone the track of » Ship always steering the same course appears a straight line ; and thus all calculations respecting the Lati. tude and Longitude of a Ship steering a course which cuts all the Meridians at the same angle, are reduced to the utmost simplicity. On Mercator's Chart all the Meridians are parallel and the degrees of Longitude are all equal, and of the same length throughout, as a degree of Latitude is on the Equator. The degrees of Latitude ar* unequal, being extended at each Latitude beyond their proper lengths, in the same proportion as the degree» of Longitude are diminished on the Globe towards the Poles. The miles of Lati*Tide are consequently increased towards the Poles, so that in the Latitude of 60* » degree of Longitude will measure 30 of these miles only, and near the Poles 1 mile of Latitude is equal !» a degree of Longitude. TO CONSTRUCT A CHART ON MERCATOR'S PROJECTION. Having first determined the limits of the proposed Chart, that is, the number of degrees of Latitude and Longitude it is to contain, and the degree of each it is to commence from, take out the Meridional part* fi»m Table III, corresponding to each degree of Latitude within the intended limits, and find the difference between the Meridional parts of each succeeding degree, or every fifth degree (if the scale is small.) Reduce the difference of the Meridional parts into degrees by dividing them by 60. Draw a line at tb» bottom margin of the paper, to represent the parallel of the least Latitude, on which lay off the proposed •Bmber of Degrees of Longitude, taken from a scale of equal parts, or the space to be occupied by the Lon- gitude can be divided into equal parts. Draw another line at the top margin parallel to the bottom one, and divide it also into the like number of equal parts. This top line or parallel of Latitude must bedraw» at a distance from the bottom one equal to the Meridional Difference of Latitude between the extreme Lat- itude!, taken from the scale of Longitude, which must previously be graduated to Degrees and Minutes. Take the Meridional Difference of Latitude between the least Latitude and the next fifth degree, froni> .he graduated scale of Longitude, and lay it oflf on both sides from the parallel of least Latitude upwards, and draw the parallel of Latitude line for that degree. In like manner lay off the next fifth degree, and draw its parallel of Latitude, and draw the Meridians through every fifth degree of Longitude at top and bottom. Draw Compasses, showing the Rhumb-lines at convenient places on the Chart, and the principal point* •f the coasts are then laid down according to their Latitude and Longitude, and the coast-line filled in by hand. The variation of the Compass, and other matters that are usually inserted, are then introduced. EXAMPLE. Required to construct a Chart, extending from 29 degrees West Longitude to 60 degrees West Longitude fio» <*reenwich, and from the Equator to 50 degrees North Latitude. Take out the Meridional parts for every fifth degree with their Difference as follows : Latitudes. Merid. Parts. Differences. 5* 300 300 — 10 603 SOS — 15 ' 910 307 — 20 1226 316 — 25 1650 325 — 80 1886 338 — 36 2244 S66 — 40 2623 379 — 46 3030 407 — 60 S474 444 — Divide the bottom line into 40 equal parts, which will represent the Degrees of Longitude on the Equat t^ ^ SeLock tSL" O^OSE 1SI.° ^,.^/?-^^--- - t>> -' Jce £*. rojyt S>) - *^i.^ l^arG'-fy- 40 - PARALLEL OF LA-T ■off on the bottom margin line as many Degrees of Longitude as required in the Chart, and divide each into •60 equal parts, and draw Meridians at each side. Enter Table III., and take out the Meridional parts for each Latitude, beginning with the least Latitude^ and take the Differ, between that and the next greater. Take this Meridional Difference of Latitude in the -dividers from the graduated Scale of Longitude, and lay it off on each Meridian from the bottom margin line, or least parallel of Latitude, and draw the next greater parallel of Latitude. From this last parallel of Latitude lay off the Meridional Difference of Latitude between that and the next, and draw the next parallel of Latitude, and so on, to the extent required. Divide the greatest parallel of Latitude, at the top, into the same number of Degrees and Minutes of Longitude as at the bottom margin, and draw Merid- ians through each Degree of Longitude, and number the Degrees of Longitude (whenever the Latitude ie North of the Equator, and the Longitude West from Greenwich,) from Right to Left, and vice versa. When the Chart is to be bounded by Parallels of Latitude on different sides of the Equator, to the extent of a feif Degrees only, the Degrees of Latitude and Longitude being of the same length, we first draw the Equator and lay off the Degrees of Latitude (according to the scale required) North and South of it, and draw the Parallels of Latitude. The Degrees of Longitude on the Equator are then made of the same length, and the Meridians drawn as before. This is called a Plane Chart, and can only be thus constructed oear the Equator. Having thus drawn and graduated the Parallels of Latitude and the Meridians of Lon- gitude, the Latitudes and Longitudes of places are laid down, and the coast-lines sketched by hand. Rocks and shoals are then inserted, with the depth of water at low water, spring tides, the setting of the tides, the tmies of high water, full and change, variation of the compass, &o. ; and one or more Compasses are uis<«rted in the most convenient parts of the Chart. EXAM?L3. Required to eoDBtruet a Chart between the Latitudes of 40* and 43* North and the Lozgitude of 69* and li West 'from Greenwich, on a Scale of 2 inches to the Degree of Latitude. (See P^. 21.) Draw a line at the bottom margin of the paper to represent the parallel of 40' , take 2 inches from the Plane Scale and divide it into 60 equal parts, representing miles of Latitude. Enter the Traverse Table with Latitude 40* as a Course, and 60 miles of Longitude in the Distance Column. Then in the Latitude Column opposite will be found 46 miles, the required length of a Degree of Longitude in that parallel of Latitude. Now take this 46 miles in the dividers, from the two inch scale, and lay off 3° of Longitude, divide them into 60 miles each, and draw a Meridian line at each side. Enter Table III., and take oat the Meridional parts for each Latitude, beginning with the least, as follows : Lat. Diff. 7»'— 1* 19' 40' Merid. Parts . . . . do do do 2628 41 2702 42 2782 • • • . ..43 2863 .80—1 20 .81—1 21 Now take 1* 19' in the dividers, from the Scale of Longitude, and lay it off on the Meridian lines from the narallel of least Latitude, 40*, and draw the parallel of 41°. In like manner, from tne parallel of 41* iay off 1* 20', and draw the parallel of 42*, and 1* 21' laid off will give the parallel of 44*. Divide this last parallel of Latitude into Degrees and Minutes of Longitude, the same as the parallel of 40* at the bottom margin, and draw the Merid'an lines. Divide the Degrees of Latitude into 60 miles each, and number the Degrees of Longitude from Right to Left, because the Longitude is West from Greenwich. Lay )ff the Latitudes and Longitudes of the most prominent parts of the ComI, and fill in the Co««i Une by hand, to. 48 THE USE OF MEKCATOR'S CHART. TO PRICK OFF THE SHIP'S PLACE ON THE CHART. Lay the edge of the parallel ruler along the nearest parallel of Latitude line, and move one ;f its sidot ttntilitc edge is over the Degree and Minute of Latitude required, and as near as possible to t:.e required Longitude. Draw a pencil line, which will represent the Ship's parallel of Latitude. Take the Longitude with a pair of dividers from the scale, one foot being on the nearest less Meridian, and the other at the Degiee and Minute required. Then with one foot on that Meridian, extend the other along the Ship's par- allel of Latitude, and mark the spot, which is the Ship's place required. Or lay the edge of the parallel ruler along the nearest less Meridian line, and move one of its sides until the edge is over the Degree and Minute of Longitude required, and transfer the same to the Ship'* parallel of Latitude. Draw a pencil line, and at the intersection of these two lines will be the Slap'* place. (See Chart, Fig. 20, page 46.) EXAMPLE. Lay oflf the Ship's position on the Chart, Latitude 19° 30' N. and Longitude 42° W. The nearest less parallel of Latitude is 15° ; a ruler on this, and moved up to Latitude 19° 30' on th« Graduated Scale, gives the Ship's parallel of Latitude. Then with one foot of the dividers on the neares less Meridian of 40* on the Scale of Longitude, and the other extended to 42°, transferred to the Ship's par allel of Latitude, points out the Ship's place. This is done at least once every day at noon, and being connected together ■vrith a pencil line, shows the Riip's track on the Chart from day to day. TO SHAPE A COURSE ON THE CHART. Lay the edge of the parallel ruler over the Ship's place and the place she is bound to. Move the ruler «Ter the Chart until its edge is placed over the centre of the nearest Compass, which will give the True Course. Then, if the variation of the Compass is Westerly, it must be allowed to the Right hand of this True Course, but if Easterly, to the Left hand of the True Course, will give the Course required to steer b> Compass. EXAMPLE 1. A Ship in Latitude 19° SO' and Longitude 42* W., is required to shape a Course by Compass to St Antonio, one •r the Cape Verde Islands. (See Chart, Fig. 20, page 46.) Lay the Ruler over the Ship's place and that of the Island, and move the edge of it over the centre of the nearest Compass, gives the True Course E. i S. The variation of the Compass being H points West- erly, which, allowed to the Right hand, gives the Compass Course required E. S. E. EXAMPLE i. Required the Course to the mouth of the River Amazon from the same positioa Lay the ruler over the Ship's place and that of the River Amazon, and refer it to the centre of the Com- paas as before, will give the True Course S. S. W. The Variation being i point Easterly, which allowed to the Left hand gives the Compass Course required S. by W. i W. TO MEASURE THE DISTANCE BETWEEN TWO PLACES ON THE CHART. When the places lie nearly North or South of each other, their Difference of Latitude is the Distance required. Extend the feet of the dividers to the places, and refer this extent to the Scale of Latitude between the parallels, and count the number of Degrees and Minutes contained, which multiplied by 60 (and taking in tJie odd Minutes' will be the Distance required. EXAMPLE 1. Required the Bearing and Distance of St. Mary, one of the Western Islands, from St Antonio, one of the Cape ?^erde Islands, both Islands being on the same Meridians. Answer. — The True Bearing is North, and 2 points Westerly variation allowed to the Right hand givee the Bearing by Compass N. N. E. The extent of their Distance in the dividers, and applied to the Scale •f Latitude from the parallel of 17* 12' N. to 36* 59' N., contains 19* 47', which multiplied by 60 gives tb« True Distance 1187 miles. USK OF MEIfCATOR'S CHAFtT. 4y When the places lie nearly Easi or West, or on the same parallel of Latitude, extend j^t feet of tha dividers betweei? the placets, and refer tins extent to tlie Scale of Latitude, holding the centre or joint of the dividers directly over their parallel of Latitude, so that each foot may reach to equal distances from it Count the number of Degrees and Minutes contained between the feet of the dividers, which multiply by 60, (and taking in the odd Minutes) will be the Distance required. But if the Distance is too great for the dividers, take, say 10° from the scale (5° on each side of the parallel of Latitude) find how many times this extent of 10° can be obtained between the places. Then contract the dividers and measure tha remainder, holding the centre of the dividers over the parallel of Latitude as before, a«d count the number of Degrees and Minutes they contain. Add this to the number of tens of degrees already measured, which multiplied by 60 (and taking in the odd Minutes) will give the Distance required. EXAMPLE 2. , Required the Bearing and Distance of the Island of Barbadoes from the Isle of Brara, one of the Cape Verda blands, in nearly the same parallel of Latitude. Answer. — The True Bearing is W. i S., and i^ a point Westerly variation allowed to the Right hand, gives the Compass bearing W. i N. The distance being too great to be measured at one time, take 10° in the dividers, 5 on each side of the parallel of Latitude, and with one foot of the dividers on Brava, it will take 3 times this extent, or 30°, to reach near to Barbadoes. Then the remainder of the distance taken in the dividers, will be found to measure 4°. Total 34° ; which multiplied by 60, gives the Distance, 2040 miles. ' When the places lie obliquely, neither being in the same Latitude or Longitude. Find the Middle Latitude between the places. Take the distance between them in the dividers, and refer it to the graduated Scale of Latitude, holding the centre or joint of the dividers directly over the Middle Parallel of Latitude, so that each foot may reach to an equal distance from it, and count tha Degrees and Minutes contained in the dividers, and proceed as before. But if the Distance be too great to be taken in the dividers, take an equal number of degrees on each side of the Middle Parallel of Latitude, and proceed as in the last Example. EXAMPLE 8. Required the Bearing and Distance of St John's, Newfoundland, from St Antonio, one of the Cape Verde Islands Answer. — The True Bearing is N.W. i N., and 2 points of Westerly variation allowed to the Right hand, gives the Compass bearing N. by W. i W. The Middle Parallel of Latitude is 32°. Take 10° in the dividers, that is, 5 on each side of 32°, from the Scale of Latitude, and with one foot on St. Antonio, 3 times this extent, or 30°, will reach short of St. John's. The remainder of the Distance taken in tha dividers, middled again at 32°, will give 9° more, or 39°, which multiplied by 60, gives the Distance required, 2340 miles. (See Chart, Fig. 20, page 47.) THE COURSE AND DISTANCE GIVEN, TO FIND THE LATITUDE AND LONGITUDE IN. Allow the variation on the Compass Course steered to the Left hand, if the variation is Westerly, but to the Right hand if Easterly, will give the True Course. Lay the edge of the parallel ruler over the centre of the nearest Compass on this Course, and transfer it to the Ship's place of departure, and draw a pencil track. Take the Distance run from the Scale of Latitude, middled on the Middle Parallel of Latitude the Ship has sailed in. and lay it off on the track, which will be the Ship's place. Take the Distance in the dividers between it and the nearest less Parallel of Latitude line, and refer it to the Scale of Latitude, will give her Latitude in. In like manner, take the Ehstance between the Ship's place and Jhe nearest less Meridian line, and refer it to the Scale of Longitude, will give her Longitude in. EXAMPLE. A Ship from Barbadoes sails N. K by Compass 300 miles. Variation of the Compass J a point Easterly Required her Latitude and Longitude ia Answer. — The True Course is N. E. i E. ; the variation being allowed to the Right hand, because it la Easterly, and the Distance, 300 miles, or 5°, taken in the dividers, from the Scale of Latitude, to the North- ward of the Parallel of Barbadoes, and laid off on this N. E. i E. Track, will give the Ship^s place. The learest less Parallel of Latitude line is 15°. A parallel ruler laid on this line, and moved up to the Ship'a place, and then referred to the Sale of Latitude, will give her Latitude in, 16* 20' N. The nearest less Meridian line is 55°, and the Difference in like manner referred to the Scale of Longitude, gives her Lon. gitude in, 55°40' West. Or the Latitude may be ascertained by taking the Difference between the Ship's place and the nearest less parallel of Latitude, 15°, in the dividers, and applying it to the Scale of Latitude, gives her Latitude in, 16° 20'. And in like manner the Longitude is found by taking the Difference between the Ship's place and the nearest less Meridian line, 15°, in the dividers, and applying it to the Sealt •1 Longitude, gives the Longitude in, 55' 40' W. 50 USE OF THE COASTING CHART To fina the Ship's Position from the Latitude Observed and the Bearing of the Land by Compass Roi.K. — Place the edge of the ruler along the nearest less Parallel of Latitude line, and moTe it up to the requii < «»ne on the Scale of Latitude, and draw a pencil line, which will be the Ship's Parallel of Latitude. Correct thJ ''Compass bearing by allowing the Variation as before directed, whieh will give the True Bearing of the object PlaoJ 'th« edg« of the ruler over the centre of the nearest Compass, and transfer this True Bearing to the object by moviug •the ruler until its edge is placed over it, and draw a pencil line, and where this line cuts the Ship's Parallel of liEtitude is the Ship's place. By this means her Longitude in and Distance off the object is ascertained. EXAMPLK A Ship obeerred her Latitude to be 40° 45' N. At the same time Moutauk Point Light House bore by Conipiu F. W. J N. Variation J point Westerly. Required her Distance off the Point and her Longitude in. (See Chart Fig. 21, page 47.) Answer. — Having drawn the Parallel of Latitude line of 40* 43' N., allowing the variation on tlr Compass bearing, gives the true bearing N. W. A line drawn in that direction from Montauk Point inter-] •^scts the Parallel of Latitude and gives the Ship's place. Her Distance off being 30 .-nilei. and he Longitude in 71° 22' W. To find the Ship^s Position from the Cross Bearing of two Objects on the Land. RaiA — Take the Bearings by the Compass, and correct them for the Variation, as before directed, which will giv« <ht>ihi« J are und fully explained at page 156. 54 SOUNDINGS The Soundings marked on the Chart are those at low -water spring tides, and the depth is noted u. fiithoms (or in feet in some of the harbor plans), and the nature of the bottom inserted. As the Ship's place on the Chart can be determined by the Latitude observed and the Soundings laid down in that parallel of Latitude, it may also be determined within certain limits by a systematic manner of Sounding on approaching the land in foggy weather or in dark stormy nights, which is always a proper precaution, however correctly the reckoning may have been kept, because near the shore the Ship is under the influence of either Tides or Currents, which may^ in the course of a few hours, set her considerably out of her proper course. To obviate this, take Soundings early (when Soundings can be obtained), say at noon. The Ship's position by observation being then marked on the Chart, the Soundings as laid down at the Ship's place may be compared with the depth obtained from Sounding. This may be taken as a point of Departure. Then the Course and Distance sailed, say every 4 hours, projected on the Chart, may be verified by the Soundings at the end of every 4 hours, and in the event of thick weather setting in (as is often the case in making the land) any deviation from the proper Course and Distance allowed, may be at once detected. Even although ne vessel retains her proper Course, it gives greater confidence in the Reckoning, and does away with all doubt and anxiety on the subject. But, as before observed, this system of Sounding must be commenced early, so that the various Soundings obtained may be compared with each other, and also with those laid down on the Chart, from which a judgment may be formed of the Ship's pla»e from the track of Soundings she has passed over. Single Soundings taken without any reference to each other, are seldom of any use, and only tend to perplex the subject, except when the Latitude is known, or when ihe Ship comes suddenly into shoal water REMARKS ON SOUNDING WITH THE LEAD. There are two Leads used for Sounding, the Hand Lead, weighing 14 pounds, and attached to about ib fathoms of line, and the Deep-Sea Lead, weighing 28 or 30 pounds, and attached to 100 fathoms or more of line wound on a reel, and a small Lead of 5 or 6 pounds is sometimes used in shoal water. The lower end of these Leads have a hole in which a lump of tallow is inserted, for the purpose of adhering to the bottom of the sea and bringing up a portion of it for examination. This is called Arming 'the Lead. The Hand Lead is only used in shallow water, and the Leadsman standing in the main channels, throws it as far forward as he can, swingmg it once or twice over his head if necessary, to give it increased force, and endeavoring to draw the line tight from the Lead at the instant the Ship, by her progress, places him directly over it. The hand Lead descends about 10 fathoms in the first 6 seconds, hence when the vessel is going fast it is often difficult to get Soundings, unless her way is deadened. The line is marked as follows : Blue at 3, White at 5, Red at 7, Leather at 10, Blue at 13, White at 15, Red at 17, and 2 knots at 20 fathoms. These numbers are called Marks, and the intermediate ones Deeps. For example : In obtaining 7 fathoms, the Leadsman calls out, " By the Mark seven." In 8 fathoms, " By the Deep eight." Tlie fathom is divided into a half and quarters. 7i fathoms are called " and a quartet seven," 7i fR*,homs " and a half seven." 7J fathoms " a quarter less eight." Id heaving the Deep-Sea Lead, it is carried forward to the weather cat-head, (and sometimes to tho lee cat-head if the Ship is making much leeway.) The line being passed forward to windward an jutside of all, the Ship's way is then reduced, if necessary, and the Lead dropped, and as soon as i is felt to strike the bottom the line is hauled in a little and the bottom struck again. The mark a.1 the surface of the water is then examined and the depth of water ascertained, allowing for the streaming of the line, caused by the vessel's drift when hove to, and which sometimes amounts to 10 fathoms to the 100 of line run out. li. Sounding in deep water in small vessels, wnich drift to leeward rapidly upon losing their way, it is best to drop the Lead before the headway ceases, and to cause the vessel to gather stern- way, so as to pass over the Lead, which will thus have descended through a considerable depth perpendicularly. The deep-sea line is maiKed at each 10 fathoms by the corresponding number of knots, and with 2 single knot at each five fathoms. The error in Sounding is generally in excess, because the line can r^ ely be stretched straight from the Lead. SOUNDINGS. i9 A I^ead-line should be well stretched and thoroughly wetted before it is measured and marked , be«&uufl It has a tendency to shrink up on being used ; and it should afterwards be verified from time to time, to ascertain whether the marks remain correct. Soundings on board of Steam vessels may be made with more accuracy than on board of Sailing vessels ; because they can be kept stationary while the line is running out by the aid of their wheela. Many inventions have been tried from time to time to obviate the inconvenience of rounding the Ship to when under a press of sail for the purpose of Sounding. And amongst them may be mentioned as th« best, Massey's Lead, Burt's Buoy and Nipper, and Enccson's Le^. Massey's Lead registers the depth of water descended through, by wheel-work, set in motion by a fl *cted on by the water as it descends. But in great depths this fly is liable to be crushed. In Burt's Buoy and Nipper, the line being rove through a spring-catch in the buoy, the Lead is dropped (and the buoy afterwards) into the water. The line then cbntinues to run through the catch till the Lead reaches the bottom, or is checked by a pull, when the catch firmly seizes the line attaching the buoy to H mt the depth descended through it by the Lead. Ericcson's Lead measures the depth of water by the space into which the air, (contained in a giaaa tube and reservoir within the Lead,) is condensed by the pressure of the water. The depth is indicated on a graduated scale by the height to which the water rises in the tube. These instruments require a great deal of care and circumspection in their management. For instance, by raising and lowering them alternately, they will be made to show the depth in excess, and they m^ut be lowered gradually to the surface of the water. Moreover, they are all liable to get »ut of order in stormy weather, which is the very time they are most wanted. From these considerations, they have not come much into use amongst merchant vessels, the commanders of which preferring the old and safe method of sounding by the Deep-Sea Lead and Line, and which is more to be relied on in t»a«©8 of emergency. In thick blowing weather, when a Ship is approaching the Coast, common prudence would dictakb iUM she should be under easy sail ; and by the exercise of a little seamanship, Soundings can always b« obtained sufficiently accurate to eusure the voM'.Pa safety, from the use of their old and frjoiliar frieaii the Dcep-Ssa Lead and Lui<> M NAUTICAL ASTKONOMY. DIAGRAM OF THE SOLAR SYSTEM, SHOWING THE PLANETARY ORBITS ROUND THE SUN. Fio. A. EXPLANATION OF THE FIGURE. '^ Arrows show the direction in which they revolve roirwi the Hun tn the centre No. 1 . Orbit of Mercury. No 4. ( Orbit of Mars. « 2. " of Venus. " 5. " of Jupiter. " 3. " of The Earth and her Moon. " 6. " of Saturn. The Solar System is that in which our Earth is placed, and in which the Sun is supposed to bo fixed in the wntre, with several bodies, called Planets, similar to our Earth, revolving round him at different dis- tances from him and from each other, and which shine by the light borrowed from the Sun. The fixed Stars are supposed to be Suns which shine by their own light, and situated in the heavene at DESCRIPTION OF THE PLANETS 55- nioh an immense distance from our system that it is found impossible io measure, or th« human miix)' to conceive it. While the Earth and Planets are thus revolying r«und the Sun, from West to East, they hare also a motion round their own axis in thA same direction, and which, in the case of the Earth, produoei( our day and night. Although to a spectator placed in the Sun, the Planets would appear to move in due order about- him from West to East, yet to a spectator on the Earth their apparent motions appear to be very irregular. Sometimes they appear to move from West to East, and then to stand still. Then they seena to move from East to West, and after standing some time they again move from West to East, and so on continually. This is easily detected by noticing the relative positions of a Planet and a fixed Star in the heavens on a certain night, and then again at an interval of a few nights after. This is caused oy the Earth not being iu the centre of the system. » That is the real state of the case. But in conformity with the impression on the mind of the specta- tor, that the heavenly bodies appear to rise in the East and set in the West, (which in reality is caused by the Eanh's motion on its axis in a contrary direction,) and in treating of Nautical Astronomy as applied U» the purpoi^es of Navigation, we suppose the Earth to be placed in the centre of the Universe, (See Fig. 1, page 56,) and that the Sun and all the other heavenly bodies revolve round it. This supposition accords with the senses of the spectator, which greoily simplifies the whole matter, and the conclusions arrived at come to the same thing. DESCRIPTION OF THE PLANETS: THEIR MAGNITUDE AND DISTANCE FROM THE SUN The Sun is the great centre of our System, and is 890,000 English miles in diameter, and he turns onc«- round on his axis from West to East in 25 days 10 hours. There ai© upwards of 17 Planets which revolve around the Sun as a centre, but many of these ar» invisible lo the naked eye. Some of them have satellites or moons, which revolve round them, and being kttraotea to it, they are carried round the Sun along with the Planet, as in the case of our Earth and' Moon. Out of all this number of Planets and Moons^ only 5 can be made serviceable in the Practice of Naviga- Vton at Sea, viz : Venus, Mars, Jupiter, Saturn, and the Moon. Mercury being always too near the Sun is> ield( m seen on account of the sunlight, and the others are too small or too remote, and shine with such t^ feeble light that they can only be seen and distinguished by using good telescopes on shore. I'Ke path which the Planets describe round the Sun is called their Orbits. Mercury and Venus aro •ftlled Inferior Planets, because their orbits are within that of the Earth, while the Earth, Mars, Jupiter, oA Saturn are called Superior Planets, because their orbits include that of the Earth. Mercury is a small Planet ; his diameter being only 3.200 miles. His distance from the Sun 37 million* o'" miles, and he performs his revolution in his orbit in 87 days 23 hours. Venus is the brightest of all the Planets. Her diameter is 7,687 miles. Her distance from the Sun 6* uiillions of miles, and she performs her revolution in her orbit in 224 days 17 hours. On being viewed through a telescope she appears horned sometimes, like our Moon. When this Planet is in the Western* )i&Tt of her orbit she rises before the Sun, and is then called the Morning Star. When in the Eastern, she iftmes after sunset, as the Evening Star. The Earth is the next Planet in the system, the mean diameter of which is about 7,913 miles (See »>escription of the Earth at page 2d.) Its distance from the Sun is 95 millions of miles, and its period of rjvolution in its orbit, 365 days 6 hours nearly, or one year, which produces the change in our seasons, and (Mining on its axis in 23 hours and 56 minutes, produces our day and night. The Earth is attended by a satellite or moon, whose diameter is 2,161 miles, and her distance from tht *entre of the Earth is 240,000 miles. She goes round her orbit in 27 days 8 hours ; but reckoning from change to change, in 29i days, and she turns round on her axis in the same time, but always presents th© same side to the Earth. And els she shines by the reflected light of the Sun, she appears diflerently according as she is situated with regard to him. When she is on the same side, her dark side is turned towards the Earth and is then invisible. This is called New Moon. When she is on the opposite side, her Ught side is turned towards the Earth. It is then said to be Full Moon. Mars is the next Planet to the Earth. His Diameter is 4,189 miles. His d stance from the Sun is 144- millions of miles. He performs his revolution in his orbit in about 687 days, and turns on his axis once in. 24 hours 40 minutes. Mars may he easily distinguished from the other Planets, by his red appearance, which is supposed to be caused by his dense atmosphere. Eleven small Planets revolve between the orbits of Mars and Jupiter, but as they are of no »^erTice to Navigation, it is useless to describe them. Jupiter is the next and largest of all the Planets, and is easily distinguished by his peculiar magnitude and light. His diameter is 89,170 miles. His distance from the Sun 494 millions of miles He performs his revolution in bis orbit in 4, 3321 days, or 12 years nearly, and he turns on his axis once in 9 hours and 66 minutes. This Planet is attended by 4 satellites or moons, but is invisible to the naked eye. In viewmj Jupiter through a telescope, these "loons make a beautiful appearance, together with the belt over hi*- equator, supposed to be caused by the swiftness of his diurnal motion, in drawing his clouds and vapors into that form. Saturn is the remotest of all the Planets which are useful in Navigation, and may be distinguished by his pale and feeble light. His diameter is 79,042 miles. His distance from the Sun is about 900 millions of miles. He performs his revolution in his orbit in 29 years 167 days, and turns on his axis once in 10- hours 16 minutes, and is attended by 7 moons. Thi.s Planet is different from all the others when viewed tlirough a telescope, being furnished with a broad double luminous ring, which appears intended to increaj» the quantity of light received from the Sun, and which, on account of his vast distance from that body must b# verv feeble. m NAUTICAL ASTRONOMY. DIAGRAM O? -^HF. SPHERE, Drawn on the Plane of the Meridian in 45° NoriJ- Latttu^ Fig. 1. Tkt 9p»€taior is supposed to be situated at a great distance East of the Earth, and lookwg towa^ th* Wed. having North on the Right and South on the Left. TO CONSTRUCT THE FIGURE. Tak. 60- from the line of Chords on the Plane Scale, ind describe a circle, which ^» /•P;!'?: •ent the Circular Dome of the Heavens, and from the centre draw a l«'««\«;':*'i«' J^^'^'^J^J^ represent the Earth in the centre of the Sphere. Draw a horizontal hne through he ««°^' ^^^ will cut the Earth in two halves, and represents the Rational Horizon Draw another line P«JP«°f ^J";" to it, which will divide the Heavens into four equal parts of 90* each. This line or ^irde is calledth* Prime Vertical, and passes through the East and West points in the centre. The top or point overhead i. wiled the Zenith, which i. 90" from the Rational Horizon; and the bottom or point under foot is called the Nadir, also 90* from the Rational Horizon. .,..-:, .. d- v.* Ko^^ «f th* Horizon Take 45- from the line of Chords, and with one foot of the dividers on the Right hand <>/ f « f °"/°^' iay it off upwards, and draw a line from thence through the centre, will represent the Elevated Pole ot tM Hlavens and the Earth's Polar Axis. At 90' from the Pole drawthe Celestial Equator through the cen^. al«o, and it will be perceived that the Poles of the Heavens coincide with the Poles of the Earth, ana me Celestial Equator coincides with the Equator of the Earth. Horizon. Take 2ir from the line of Chords, and with one foot of the dividers on the Left hand of the Horizoi^ lay it oflT upwards, will be the Sun's place on the Meridian to the South of the spectator Th^s is oal led thl Celestial Meridian, and passes through the Poles of the Heavens. Lay 2U- off in ^^ke manner to th. Right; .hen take 2U- from the line of semi-tangents on the Plane Scale and l^J '\«f ff7,.\^X°^ •pwards, and through these three points describe a circle, which is called a P*^^"«l "^ ^^*''"f«; "^J which in this ca^/is the Parallel of the Run's Meridian Altitude, and i. always measured from th. )ns in South Latitude are reversed. •) The Common or Civil Year, sjs most convenient for the affairs of life, includes the succession of th« seasons. It is therefore the interval in which the Sun leaves any Parallel of Declination, and returns to it again, and is called a Tropical Year. Its length, that is, the average length of a number of such years, is 365 days 5 hours 48 minutes 6 seconds of Common or Mean Time. The beginning of this Tropical Year eoinmences on the 1st of January. Declination being the Distance of any Heavenly Body, North or South, of the Celestial Equator, it is used in determining the position of the Fixed Stars, exactly as Latitude is used in determining places on the Earth's surface. Right Ascension of a Celestial Body is an Arc of the Celestial Equator included between the first point of Arie« and the Celestial Meridian of the body, ana is reckoned from West to East. Circles of Right Asceui.:on are drawn from the Poles through the body; and cutting the Celestial Equator at right angles. The Celestial Equator is divided into 360* of Right Ascension, which, at the rate of 15* to the hour make also 24 hours of time. Thus Right Ascension is reckoned on the Celestial Equator, exactly as Lon gitude of places on the Earth is reckoned on the Terrestrial Equator. The first point of Aries being used as a first Meridian, and from which the Right Ascension of all the Heavenly Bo^'les are reckoned in hours and minutes, the same as the first Meridian of Greenwich is used to reckon the Longitude from, in Degrees and Minutes. Right Ascension is therefore used in determining the places of the Heavenly Bodies, and is their distance in time from the first point of Aries. Sidereal Time begins when the first point of Aries is on the Meridian, and is counted through the 84 hours, till the same point returns again, which is called a Sidereal Day, and consists of 23 hours 56 mm- Btes 4 seconds of Common or Mean Time. The Hour Angle of the first point of Aries is the Right Ascension of the Meridian. ft? NAUTICAL ASTRONOMY. DIAGRAM, Sktnnng the Motion of the Heavenly Bodies round the Pole, drawn on the Plane of tht Celestial Equal** Fig. 4. tK th%* Figure the Spectator ts supposed to be standing on the North Pole, facing toward tht South, havinr East on the Right hand and West on the Left. TO CONSTRUCT THE FIGURE. Take 60* from the Chords and describe a circle which will represent the Celestial Equator. Draw a perpendicular line to represent the Meridian. Make HP the first point of Aries, and mark the Hours of Riaht Ascension round the Equator from Right to Left, according to the progression of the Heavenly Bodies, which is, from East to West. Mark the Sun, whose Right Ascension from the first point of Aries is VII h. Then the Sun's Hour Angle West of the Meridian at M is 3 hours. The first point of Aries having passed the Meridian 7 hours before the Sun, the Sun's Hour Angle added to it gires X h. as the Right Ascension of the Meridian, or, as it is called, the Sidereal Time, which com mences when the first point of Aries is on the Meridian, and is counted through the 24 hours, until it again comes to the same Meridian. Suppose a Star, whose Right Ascension is XIX h., which has passed the opposite Meridian at N., its Hour Angle is 15 h., counted from the Meridian round by the West, which, together make 34 h., from which sub- tract 24 h., gives Xh. for the Right Ascension of the Meridian ; or, if counted to the Eastward, its Hour Angle from the Meridian is 9 h. Subtracted from XIX (its Right Ascension) gives the same. Suppose the Moon's Right Ascension to be XIII, and her Hour Angle 21 h., which together make 34, frorn which subtract 24 hours, gives the Right Ascension of the Meridian as before, X h. Or the Moon's dis- tance from the Meridian to the East being 3 h., subtracted from her Right A.scen.sion, gives the same. From the above figure it will be perceived that the Cele.«;tial bodies in their diurnal motion in the Heavens are continually forming Angles with the Meridian around the Pole from West to East, caused by Uie -otatory motion of the Earth on its ax s, contrary to their motion in Right Ascension, which is from East u» We«t. and which is caused bv the Earth revolving round the Sun. DEFINITIONS. 83 AD Hour Angles, which are difTerenccs of Higi.t Ascension of the Meridian and that of a Celch.ial body, {nay oe considered as portions of Sidereal Time. Tlie interval of time in which a body describes a« Hour Angle, depends on the rate at which its Right ascension changes. The Earth's motion round its axis being perfectly uniform, becomes the real standard of a uniform measure of time. But as any Star passes the Meridian nearly 4 minutes earlier every night, the beginning «f the Sidereal Day has no connexion with that of the common, or Civil Day, as determined by light and darkness The Hour Angle of the Sun, reckoned always Westward from the Meridian, is Apparent Time. Thu when the Sun's Meridian has passed over 45° of the Celestial Equator to the Westward of the meridian ot the place, it is said to be 3 hours Apparent Time. The interval between the Sun's passing the Meridian on one day and the next, or the apparent Solar Day, is not always of the same length, the difference being sometimes half a minute between one day and the next. But the time for general use must unite the two advantages of being regulated by the San and of V)eing perfectly uniform. The mean, or average day of 24 hours, must thereiore be an average taken of all the days in the year. That is, such a day as the Sun would regulate if he moved uniformly in Right Ascension, or the time a Solar Clock would show, when set at hours, minutes, seconds, at the instant the Sun was on the first point of Aries, and keeping uniform time until his return to the same point, would again show hours, minutes, seconds. This average day ic called the Mean Solar Day, and the time thus regulated, is calle4 the Mean Time. The Sun being generally either behind or in advance of the position which he would have occupied if ha had moved uniformly. Apparent Time is in general either fast or slow of Mean Time. The correction for this irregularity, that is, the Difference between the Sun-Dial and the Solar Clock, is called the Equation of Time. Mean Time is, therefore, deduced from Apparent Time, by applying the correction for the Equa- tion of Time taken from the Nautical Almanac. Suppose O to be the place of the Sun, in Fig. 4, at 3 P. M. Apparent Time, and m the place he would «e if he moved uniformly. Then the space between O ^^^ "») is the Equation of Time, and M m, the Mean Time from Noon. The Equation is here additive to Apparent Time, as is the case f^om January to March, and from July to August. Referring to Fig. 4 again. While the Sun and Aries revolve, the Sun moves contrary to the diuma rotation, or is always increasing his Right Ascension by nearly 1* a day. The complete revolution of V «onstitutes a Sidereal Day, that of O an Apparent Solar Day, and that of m a Mean Solar Day. After 24 Sidereal hours, the Sun has still to describe about 1*, or one 360th of 24 Sidereal hours, or 4 AiJereal minutes. Thus the Solar Day is longer than the Sidereal Day by about 4 minutes. The Mean Solar day being divided into 24 hours, the Sidereal Day is 23 hours, 56 minutes, 4 seconds of such a day. Since the Sun passes over 15* of the Circle in one Mean hour, he arrives at the Meridian of a place 15* West of M one hour after h« has passed M, that is, at one o'clock of the time at any place, or all places «f which N M i& the Meridian. In like maimer, he passes a Meridian 15* East of M one hour before h« arrives at M, that is, when the time at 3f is 1 1 o'clock in the forenoon, or 23 hours after the nooa of th« •day before. Thus the beginning of the day, and therefore the hour of the day at one place differs from that of another place by the difference of Longitude of the places. The time at the Easternmost of the two being m advance of, that is, greater than the time at the other. Hence, when the Mean Time at two places at th« «ame instant are known, their Difference of Longitude is determined, and also the relative positions of their Meridians. The Civil Day is dated from Midnight, and the 12 hours are computed twice over. The Astronomies. Day is dated from Noon, and runs through the 24 hours. Civil Time is converted into Astrenomieal Tims *rj diminishing it bv 13 hours. g4 NAUTICAL ASTRONOMt DIAGRAM, Shoreing the method of finding the Stars in the Heavens from their Meridian Altitudes, FWD THB MkRIDIAM ALTITUDE OF THK StaR AlDKBARAN IN THK LaTITODE OT 45* NORTW Fxo. 5. Drawn on the Plane of the Meridian. ,//?c^ •V V o Nr^ RATIONAL HORIZON E.^W. POINTS TO CONSTUCT THE FIGURE. With the Chord of 60 describe a semi-circle, and draw the Horizontal and Prime Vertical lines at Right Angles to each other. Elevate the Polar Axis equal to the Latitude of 45* N., and draw the Equator at Right Angles to it. Lay off the Star's Declination, 16° 13', on the Meridian to the North of the Equator, which will be the place of the Star, and its Distance measured from the Horizon, is the Altitude required. Now, as the Elevation of the upper end of the Equator above the Horizon, is equal to the Co-Latitude of the place, which is North, and the Declination of the Star being also North, their Sum is the Meridiaa Ititude of the Star, 61* 13', South of the observer, because his Latitude is North. Find th« Mxridiam Altitude er the Star Antarei in the Latitodk or 30* North. Fig. 6. Drawn on the Plane of the Prime VertieaL TO CONSTRUCT THE FIGURE. With the Chord of 60*, describe a semi-circle as before, which will represent the Prime Vertioal Cirele Draw the Rational Horizon line, and at right angles to it from the centre, draw the Meridan line or Circle. The Spectator is now facing the South. The Prime Vertical Circle passes through the East point of th« Horizon on the Left, and through the West point of the Horizon on the Right. The Elevation of the Celestial Equator above the Horizon being equal to the Co-Latitude, take bO* the Co-Latitude) from the lino of semi-tangents, and lay it off on ihe Meridian line. Then through thia point, and the East and West points of the Horizon, draw the Celestial Equator. From the line of semi- tangents take the Star's Declination, 26* 6' South, (measured from 60* backwards,) and lay it off from th« Equator towards the South point of the Horizon on the Meridian line, and draw the Parallel of Declination parallel to the Equator. Then where it crosses the Meridian line is the Star's place, and its Altitude abore the Horizon is 33* 54' South, measured on the line of semi-tangents ; and where the Parallel of Declinatior •uts the Horizon shows the places of the Star's rising and setting. DEFINITIONS PiMS THK MXRIDIAN ALTITUDE Or CaNOPUS, IR THE LaTITUDB Or 13* SOOTI Fig. 7. TO CONSTRUCT THE FIGURE. Hanng drairn this Figure as in Figure 5, elevate the Polar Axis equal to the Latitude of 30* South, and iimyr the Equator at Right Angles to it. From the Equator, lay off the Star's Declination, 52* 27', on thm Meridian towards the South, which will be the place of the Star, and its distance from the nearest Horizo» ia its Meridian Altitude South. In this case, the elevation of the upper end of the Equator above the Horizon being equal to the Co-Lat- itude of 60* South, and the Declination of the Star 52* 27' South, both of the same name, their Sum 111* 17' exceeds 90*, must be subtracted from 180*, gives the Meridian Altitude of the Star 67* 33', reckontd from the South point of the Horizon. Find the Meridian Altitude or Castor in thk Latitude or 10* North Fig. 8. TO CONSTRUCT THK FIGURK. Elevate th» Polar Axis equal to the Latitude of 10* North, and draw the Equator at right angles to It rom the Equator lay off the Declination of the Star, 32° 18', on the Meridian towards the North, whieb *all be the Star's place. Then its distance from the" nearest Horizon is its Meridian Altitude. In this case, the Sum of the Co-Latitude 80° North, and the Star's Declination 32' 18' North, is 111* 8', which exceeds 90*, must be subtracted from 180*, gives the Altitude 67* 42' North. Thus having the computed Altitude of any Star on the Meridian, the Star itself is found by setting the index of the instrument to this Altitude and facing towards the South or the North, as the case may be, and the Star vrill be seen on the Horizon. On referring to Figure 4, the time at which the Stars pass the Meridian is easily computed by subtrael* ing the Sun's R. Ascension from the Star's R. Aso«n.<«ion, (increasing the latter by 24 hours, if necessary), will be the apparent time of its Meridian passage. For example : Suppose a Star, whose R. A. is XIX k In ¥^g. 4; the Sun's R. A. same time is V[I h ' the differ«nr« '•h or M'dn'sb* '• th*» ^rv th« oaKUHi the ^endiaii iii N «6 NAUTICAL ASTRONOMY. Fig. •. DEFINITIONS. r>T CORRECTIONS OF THE ALTITUDES OF THE HEAVENLY BODIES ORSER\ED AT SEA Dip of the Horizon is the Angle through which the Sea Horizon appears depressed, in consequence oJ the elevation of the spectator's eye above the Sea level. Suppose the observer's eye to be at e (in the figure for Dip of the Horizon) and a perpeudicukr line drawn to his zenith. Then a line drawn at right angles to it will be the True Horizontal Line. But hii- eye being elevated above the Sea, his vision extends over tlie curvature of the Earth's surface, in tlie direction of the Visible Horizon, or the dividing line between the Sea and Sky. And as the Altitudes ol aU Heavenly Bodies are measured to this line, it is evident that the Altitudes so obtained are too great bv ihe amount of the angle of the Dip of the Horizon contained between the True and the Visible Horizons. The distance of the Sea Horizon from the observer is about 6 miles when the eye is elevated 30 feet above ihe Sea ; and if it were possible to observe an Altitude with the eye at the surface of the Sea. as at S. there would be no correction required for Dip because the True and the Visible Horizons are in the same liiif *nd the Rational Horizon is considered r bp also on the same line. The Dip of the Horizon at different - «»' au^np is given in Table V for that purpose, and is always sub Iractive from the observed Altitude. Ke/ruction. The rays of light proceeding fipr r» Heavenly Body when not in the zenith, in traversing th« Earth's atmosphere, become bent or .-etracted more and more, on approaching the surface of the Earth towards the perpendicular, which causes all the bodies to be seen above their true places in the Heavens •onsequently the observed Altitudes are too great by the amount of the Refraction. The rays of ligkt pro- eeeding from the Sun at L (in the figure for Refraction), entering the atmosphere at A, becoming ^ent upwards as it proceeds, the spectator sees the object at U, and the difference between the True and the Apparent places of the Sun is the amount of Refraction. The Refraction is at the zenith, because tin rays of light penetrate directly downwards, and are not bent out of their course. At the Horizon th« Refraction is about 34', because the rays of light enter the atmosphere obliquely, so that all bodies, (except the Moon), when on the Horizon, are raised that much above their true place. In the figure the lower appears in his true place below the Horizon, but the rays of light entering the atmosphere at m are oem ■pwards or refracted, and the © is seen above his true place in the Horizon. Refraction diminishes aa the Altitudes increase from the Horizon to the Zenith, and the correction for Refraction is g'van m Tabic IV for that purpose, and is always subtractive from the observed Altitude. Parallax. As before observed, ths Earth is considered as a mere point in the centre of the Sphere, as regards the Stars, which are situated a great distance from it, but with respect to the S^cn. Moon, and Planets, the Earth's semi-diameter musi be taken into consideration in measuring the Altitudes of these bodies, especially the Moon, which is the nearest to the Earth. Parallax, therefore, is the depression of a Heavenly body, inconsequence of its being seen from the surface instead of from the centre of the Earth , and the nearer any Heavenly body is to the Earth, the greater is the Angle of Depression The Moon, to an observer at the surface, would appear to be situated in the Heavens at A, (in the figure for Parallax), but to an observer at the centre, her place would be at T, her true place in the heavens ; and the difference between the two places is called her Horizontal Parallax, and which ir always greatest at the Horizon. Again, to an observer at the surface, the Moon would appear at a, but to an observer at the centre of the Earth she would be at t. b«r true place in the Heavens. The difference between these two places is called her Parallax in Altitude. The Sun and Planets being at a greater distance from the Earth hare only a very small parallax. S and P represent the Parallax of the Sun and Planet. When a body u in the Horizon its Parallax is greatest The Sun's Parallax is only 9", while the Moon's Parallax is above 1* sometimes. But when a body is in the Zf-nitb Mh Parallax is 0, because it is seen in the same line from the centre as from the surface as at Z. The Sun's Parallax in Altitude is given in Tabls VI. The Moon's Horizontal Parallax, which is in perpetual change, and the Parallax of the Planet*, ar* fiven in the Nautical Almanac. M NAUTICAL ASTRONOMY DIAGRAM, Showing the Manner of Measuring the Altitudes of the Heavenly Bodies ai Sea, and the Correction ftp Semi-diameter. Fio. 10. This figure repreient* the different methods of observing th^ Altitudes of the Sun and Moon by bringinf Iheir upper or lower limbs in contact with the Horizon. No. 1 is an Altitude of the Sun's lower limb brought in contact with the Horizon. This it the usual method practised at Sea, being the most simple and correct mode of doing it. His semi-diameter added giTea his observed Central Altitude. No. S ii an Altitude of the Sun's upper limb brought in contact with the Horizon. This is only resorted to in the event of the lower limb being hidden by clouds. His semi-diameter subtracted gives hia observea Central Altitude. No. 3 is an Altitude of the middle of the Sun brought down to the Horizon. This kind of observation u only used when his limbs are so ill-defined, in consequence of the sky being overcast, as in the case when he shines through a rain-cloud, that no observation can be made with them j the body of the Sun, however, may be visible. By a little practice this method may be turned to a good account in finding the Latitude of the Ship, in the room of a better. At all events, it is more to be trusted to than the Latitude by Dead Reck- oning. In this case no semi-diameter is allowed, because the Central Altitude is observed. No. 4 i« an Altitude of the Moon's lower limb brought in contact with the horizon. In this case the Moon'a semi-diameter added, gives her observed Central Altitude. No. 5 is an Altitude of the Moon's upper limb brought m contact with the Horizon. This is necessary when her horns are turned downwards, and in this case, her semi-diameter subtracted gives her observed Central Altitude. No. 6 IS an Altitude of a Star or Planet bisected on the Horizon. This gives its observed Central Altitude. Tne semi-diameter of the Sun is given in the Nautical Almanac throughout the year. His greatest semi-diameter is 16' 18", at the time the Earth is nearest to the Sun, in December; and his least is 15' 45", at the time the Earth is farthest from the Sun, in June. But in dealing with Altitudes, we generally allow 16' as his mean semi-diameter throughout the year. The Moon's semi-diameter is also given in the Nautical Almanac for the nearest noon and midnight at Greenwich, because it changes very rapidly, her greatest being about 16' 48", and her least about 14' 4^\ ■o that it is necessary to take it from the Almanac when great accuracy is required. But in general ttM lean of the extremes, which is about 16', is taken as the Moon's seihi-diameter. The Stars and Planets require no eorrection of the Altitude for semi-diameter. 69 INSTRUIVtENTS OF NAUTICAL ASTRONOMY. DESCRIPTION, ADJUSTMENTS, AND USE OF THE QUADRANT AND SEXTANT. These are instruments for measuring angles between two objects, by bringing the reflected image of one •f them in contact with that of the other seen direct. They are also necessary for observing Altitudes •f the heavenly bodies at Sea, where the spectator has no fixed point of reference except the horizon. on the Vernier stands at the on the Arch, there is no Index Error. Suppose it stood at 2 on the Arch, that is, to the Left of the on the Arch, then the Index Error is that much subtract) ve , but if it siaiidi^ at 2' otT the Arch, that is, to the Right of the on the Arch, then it is that much additive to all allsle^ liiken hy.the instrument. By the Sun. If the iii>iniMiiiii has no Shade for the Horizon Glass, take the opportunity when the Sun is veiled over by thin cloutls. and u^e them as a substitute for Shades. Hold the instrument vertically, and look through the sight-vane diret'tly at the Sun, and make the reflected sun cover the one seen direct. Then if the on tlie Vernier siands at on the Arch, there is no Index Error. Otherwise it is found as before explained. For the |)urposes of adiusting an instrurnenl, objects should be used which are at least 1 mile distant; because at a nearer object the distance between the glasses produce a sensible parallax, and the ooincidenec doeft not take place MANNER OF MEASURING ALTITUDES WITH THE UUADRANT Tl MANNEH OF MEASURING ALTITUDES WITH THE QUADRANT To Observe the Sun's Altitude at Sea. Set 'fle index at 0, and put do-WTi a screen or shade before the Index Glass. Hold the instrument m a TerlicnJ position, and direct the sight through the sight-vane and Horizon-Glass to that part of the horizoB which is directly under the Sun. Now move the Index onwards with the left hand, and the image of the Sun will appear to descend towards the horizon. Give the instrument a slow motion from side to side^ round the line of sight, and the Sun will appear to sweep the horizon, and it must be made just to touch it at the lowest part of the arch. This gives the Observed Altitude of his lower limb. It is best to commence the pbs'jrvation some time before the Meridian Altitude is expected, and to continue observing until his greatest Altitude is obtained, unless the watch has been previously regulated and the apparent time at the ship known. This last Altitude is sometimes near enough, but for accuracy, having made a rough contact as above, put in the telescope, previously set to distinct vision by looking through it at the horizon, and the tube may be marked at the proper focus of the observer's eye. The image being now magnified, the contact is made more correctly. Clamp the Index, and make the contact perfect by turning the Tangent Screw. This L» the method generally used in taking Altitudes for time. The Tangent Screw should be kept nearly middled when not in use, and the contact should be made in the centre of the field of view of the telescope. To Observe the Altitude of a Star. Turn up the sight-vane or unship the telescope. Set the Index at 0, and direct the sight to the star, antf look with both eyes, as close to the sight-vane or color of the telescope as possible, and move the Indei onwards, when the reflected star will be seen to descend, and which must be followed by the eye until i\ finally reaches the horizon. Now give the instrument a slow motion from side to side, round the line of sight, and the Star will appear to sweep the horizon, which it must be made to touch at the lowest part of the arch To find any particular star on the Meridian, the readiest way is to compute the Meridian Altitude, (Se* pages 64 and 106) and set the Index to it. Then with both eyes, as before observed, look towards that part of the horizon indicated, and the proper star will be seen on or near it. Continue to observe it, until il tains its greatest Altitude. By this means it is impossible to mistake the star, because no other can be on the Meridian at that time. The Altitude of Planets May be observed in the day time, even when the Sun is considerably above the horizon, for though they are invisible to the naked eye, they may readily be found by computing their Meridian Altitude, (see page 104), and set the Index to it. Screw in the telescope, and direct the sight to the true North or South pointc nf the horizon at the time it passes the Meridian, and the Planet will be plainly seen on or near it. To Observe an Altitude of the Moon. The same directions may be followed as given for the stars, to bring her down to the horizon, an4 the telescope afterwards used in making the contact. But sometimes, when she is faintly seen, it is better te use both eyes without the telescope. Her upper limb must be observed when her horns are downwards^ and care must be taken, in making the sweep for the horizon, that her limb just touches it at the lowest part of the arch. The best time for making observations of the Moon and Stars is at twilight, for then the horizon is di»- tinctly visible ; but in cloudy weather at night long dark shadows are sometimes projected on the sea, which, in the case of the Moon, renders it difficult to ascertain the real horizon under her. 72 INSTRUMENTS OF N-4.UTICAL ASTRONOMl THE SEXTANT The Sextant is constructed upon the same principle as the Quadrant, and contains an Arc of more thaa €0' of a circle, but on account of the Double Reflection, it measures Angular Distances of more than 120*. The Arch or limb is divided into degrees, and the degrees into 6 equal parts of 10' each. The Vernier is gen- •crally cut to 10", for the purpose of minute readings, which is thus explained : Suppose a division on the Arch to be J of 1° or 10', and the Vernier to be equal in length to 590 of such divisions, or 9* 50', bu/ ■divided into 600 equal parts. Then each of the divisions on the Vernier is ^^ part less than the 591 ■divisions on the Arch. Therefore the difference between one division on the Arch and one on the \ermei is 10". As the Vernier contains 600", it is divided into 10 equal parts or minutes, and the minute into ■6 equal parts of 10" each. Now suppose the^ or beginning of the Vernier, and the or beginning of the Arch to coincide; then ihe first of the dividing lines of the Vernier fall short of the first dividing line of the Arcfc by 10". If we make these lines coincide, we advance the Index and Vernier 10". Again, to make the second divid- ing line of each to coincide, we must move the Vernier to 20", and so on to 30", 40", 50", and then to 1'. Therefore to make l' on the Vernier coincide with 1' on the Arch, we must advance the Index or Vernier 1'. Hence for an angle on the Arch the number of divisions counted on the Vernier before we arriTe at a coincidence is 10", 20", &c., to be added to the division of the Arch next behind the ^ or to the right of the beginning of the Vernier. For an angle off the Arch we must read from the opposite end of the Vernier And from left to right. The scale on which these divisions are marked is generally made of silver, and in consequence of their minuteness a magnifying glass must be used in reading them off", which is fixed to the Index bar for that purpose. The Adjustment of the Sextant is done in exactly the same manner as that described of the Quadrant The only addition is the following: To set the Line of Sight of the Telescope parallel to the Plane of the Instrument. Thi» is » very important matter, beoaose when the Inverting Telescope is used, as in the case of mearar- ing the Lunar Distance, any defect in this adjustment causes a considerable error in the measurement of the «ngle, and always makes it too great. Place the two wires of the Inverting Telescope parallel to the plane of the instrument. Select two dis- tant objects about 120° apart from each other, such as two stars, or the Sun and Moon, and make an exact contact at the lower wire, or that nearest the instrument. Now move the instrument so as to throw the image in contact upon the upper wire. If the contact is still perfect, (the images continuing the surae in the middle of the field), the adjustment is perfect ; but if they have separated, the object end of the telescope ^oops towards the plane of the instrument ; if they overlap, it rises from the plane of the instrument. The position of the telescope is rectified by the screws in the collar. The adjusting screws are never to be touched, except from necessity, and then with the greatest ponible ■caution. When two screws work against each other, care must be taken in tightening one to loosen the other if necessary. The sides of the colored glasses are sometimes not exactly parallel, and the shades may cause an error in Ihe angle. It is^ therefore, prudent to find the error of each shade or combination of shades from actual 4ri«L ro FIND THE INDEX ERROR OF THE SEXTANT. T9 TO FIND THE INDEX ERROR BY MEASURING THE SUN'S DIAMETER. Ihe Index Error of an instrument being merely the error of the place of the Beginning of the divisioa*, ^hen all the Mirrors or Glasses are pexiectly adjusted, and it aifects all angles alike. >. To Measure the Sun's Diameter. Screw in the Inverting Telescope and adjust it to direct vision; turn up the proper Shades, place the t on the Vernier, about 40' to the Right of 0, on the Arch, and clamp the Index. Then, holding the instru- ment horizontally, bring the direct and reflected Suns in exact contact by the use of the tangent screw, and read off the minutes and seconds, counting from the opposite or Left end of the Vernier, which call off tlie Arch. Next place the f of the Vernier about 40' to the Left of 0, on the Arch, and make the contact of the two Sun's as before, and read off the minutes and seconds in the usual way, which call on the At«k, and set it under the first reading ; then half the difference of the two readings will be the Index Error, which is additive to all angles taken with the Sextant, when the Reading to the Right of is greater than the Reading to the Left of 0, but subtractive when the reading to the Left is the greatest. If the two reading? are equal there is no Index Error to the instrument. The direct and reflected Suns will appear through the Inverting Telescope thus : iVhen the Vernier is to the Right of on the Arch. Keflected Sun. Direct Siin. When the Vernier is to the Left of on the Arch. Direct Sun. Reflected Sun. Suppose the following Observations were taken to determine the Index Error : EXAMPLE 1. EXAMPLE 2. let Jan., 1854. Reading off 31' 65" do on 33 15 )1 20 Index Error O' 40" Sub. Because the reading on the Arch is greater than the feading off. 31st Jan., 1854. Index Error. Reading off S3' 40" do on 31 20 )2 20 1' 10" Add. Because the reading off the Arch is greater ♦ban th« reading on. When both Readings are on the Arch, (which can only happen when the Index Error exceeds half a degree,) the Index Error is the Mean of the two, and subtractive, but when both Readings are off tlie Arch, the Index Error is the mean of the two additive. To prove that the contacts were made correctly, add the Readings together and divide their Sum by 4, find the quotient should be equal to the Sun's semi-diameter as given in the Nautical Almanac for the cbove days of the month. In Example 1, the Sum of the Readings is 65' 10" WhicJi divided by 4 gives the Semi .1,6' 17".5. In Example 2, the Sum of the Readings is 65' 00" Which divided by 4 gives the Semi 16' 16" These agree nearly with that given in the Almanac, namely, 16' 18" on the 1st, and 16' 15".7 on the 31st. It may, therefore, be presumed that the contacts were correctly made. In this manner the error of each colored glass, or Shade, may be found by first measuring the Sun'« diameter at the time when there is a thin veil of clouds over his disc, (which will answer the purpose of Shades,) and as^certain the Index Error as in the above Examples (without using any Shade.) 'Then to measure it again, using, say, the Green Shades. If these two measured diameters agree, the GrcQn Shades are correct. If they do not, then their difference is the error of the Green Shades, which must be applied to the Index Error, when they are n.«ed. In like manner, the Red Shades, or any combination of Red and Green, may be proved by using them in measuring the diameter, and afterwards comparing them with that 'vhich was measured without the Shados. 74 INSTRUMENTS OF NAUTICAL ASTRONOMY. USE OF THE SEXTANT. To Observe the Angular Distance between the Sun and Moon. When the Distance between them is considerable, lind their approximate distance in the Nautical Almanac, corresponding to the Greenwich Time of the observation, (by simply turning the Ship's Longitude Lnto Time, by Table XXVI., and adding it to the Time at the Ship in West, or subtracting it in East Lon- gitude.) Now set this approximate distance on the Sextant, turn up one or more of the Shades before the Index Glass, according to the brightness of the Sun. Screw in the Plane Tube into its collar. Then, hold- ing the Sextant (with its face upward when the Sun is to the Right hand of the Moon, or downward wherv the Sun is to the Left,) with its Plane in the line of Sight of the two objects, and direct the Sight to the Moon, and the Sun's image will be seen near to it. Make the contact roughly. Take out the Tube and screw in the Inverting Telescope, and adjust it to distinct vision, placing the wires parallel to the Plane of the instrument. Raise the Telescope (by the screw behind) to the transparent part of the Horizon Glass. Then, directing the Sight through the Telescope to the Moon, holding the instrument as before directed, make the contact perfect by means of the tangent screw, at the same time moving the Sextant round the axis of the Telescope, by which means the Sun will appear to pass slowly by the Moon, and the contact be more accurately made. Observing always that the point of contact of the limbs should be as near the centre of the field of the Telescope (that is, in the middle between the four wires) as possible. Reading off the Angle. Ascertain the nearest degree on the Arch to the Right of the f , or the beginning of the Vernier, then the nearest division of the degree on the Arch. Then look along the Vernier, and ascertain whicl line coincides with the line on the Arch, then the minutes to the Right of where the coincidence takes place must be added to the division of the degree, and the seconds are counted to the Left of the nearest m:nut« on the Vernier up to the place of coincidence. 1 EXAMPLE, Of finding the Approximate Central Distance between the Sun and Moon. • February 7th, 1854. At 8 hours 20 minutes A. M., Sea Time, in Longitude of 70* 0' West Required the Ap proximate Central Distance of the Sun and Moon. ■nme of Observation 8h 20m. A.M The Distance in N. A. at Noon is 117' 47' 61" West A.dd 12h Acdatlllh. 1 19 8 28 From the preceding Noon 20h. 20m. The Moon's Motion in 3b. is 1° 20' 87" Increaaiiig. Long. 70* in Time .4h 40 m. q t. being Ih. from Noon, or equal to i of it . ,. 26' 52" 26h. 00m. Which added to the Distance at Noon 1 1 7 ° 47 ' 6 1 " Subtract 24h. qj^^ th^ required Distance at 8h. 20m, A-M-llS" 14' 48" Greenwich Time, Feb. 7th Ih. 00m. Now put this on the Arch of the Sextant as follows : Advance the Index until the f on the Vernier has passed the stroke of 118°, and also the first division, or 10', of the adjoining degree on the Arch. Then look along the Vernier, and make the 5' on it coincide with one of the divisions on the Arch. The instru- ment will then have on it 118° 15', or even 118° is near enough for the purpose of bringing the objects into the field of view. Accuracy is not, therefore, required when the Sun is used. After bringing the nearest limbs "n contact, screw in the Telescope, and proceed as directed. In this case, the Sun being to the Right of the Moon, (in North Latitude.) the instrument is held with its face upwards, in the line of Sight, and the Telescope directed to the Moon, when the Sun will appear inverted, or on the Left of the Moon. In South Latitude, by direct view, the Sun will be on the Left of the Moon, and the Sextant roust be \eld face downwards, and the Sight directed to the Moon. TO OBSERVE THE DISTANCE BETWEEN THE MJON AND A STAE. Ti TO OBSERVE THE DISTANCE BETWEEN THE MOON AND A STAR. Turn the Ship's Longitude into time by Table XXVI, and add it lo the time at the Ship in West Longi- tude, or subtract it in East, will give the approximate time at Greenwich. Look into the Nautical Almana* amongst tlie Lunar Distances, agamst the day of the month, and find the given Star's distance from the Moon corresponding to this Greenwich time. Put this distance on the Arch of the Sextant. Turn up one of the green shades before the Index-glass ; then holding the plane of the instrument in the line of sight between the Moon and Star, with its face upwards when the Moon is to the Right of the Star, or downward* when the Moon is to the Left of the Star. Direct the sight through the ring of the collar towards the Star, (without using the Telescope), and the Moon's image will be seen near the Star. Move the Index so as to bisect the Star on the bright limb of the Moon Now screw in the Inverting Telescope, and adjust it to distinct vision, and make the contact perfect by means of the tangent screw, at the same time moving the Arch of the Sextant slowly up and down, by which motion the bright limb of the Moon will appear to pa«s the Star, and the contact be more accurately made, and "which should always be done as nearly at possible in the centre of the field of the telescope. The angle being read off will give the observed dis- tance between the Star and the Moon's bright limb. In the Nautical Almanac, headed Lunar Distance, the Sun, Stars, and Planets are marked according ar they are East or West of the Moon. By attending to this and having the approximate distance on the Arch of the Sextant corresponding to the Greenwich time, any Lunar Star may be easily found by a person otherwise unacquainted with the stars in the heavens, because no other one in that direction will correspond % it in distance. EXAMPLE Of Finding a Lunar Star. January 3l8t, 1854, at lOh. 25m. P. It, Sea Time, in Longitude 60* 0' W. Required th« Bpprozimato distitvM between the Moon and the Star Aldebaran Time of Observation. . . .lOh 25m Distance of Aldebaran at Midnight 86* 88' 38" East of the Moob. Long. 60* W. in time _4 Do. do. XVh....83 63 69 Greenwich time Jan. 30th 14h 26m Moon's motion in 3 hours 1* 44' 89" Pro. Loir., 2855 \^ G. Time past Midniglit 2h 25m Pro. Log.. 098» Past Midnight 2h 26m pp^. of Dist. to be subtracted 1* 24'~18^ Pro. Log.. 829r From the Dist at Midnight 85 88 28 Which gives the Star's Distance from the Moon 84" 14' 10" at lOh 26m P. M. It 18 necessary to be as exact as possible in finding the approximate distance between the Moon ard a Star, for very often it is the only security we have for employing the right star. Now put 84* 14' on the Arch, as follows : Advance the Index until the f on the Vernier has passed the Stroke for 84°, and also that of the first division or 10' of the adjoining degree. Then look along the Vernier and make 4' on it coincide with .some line on the Arch, which will be the required distance. The Star bein^ East or to tho left of the M8on (in North Latitude), the Sextant must be held with its face upwards in the proper line of sight, and the sight directed through the collar in the direction of the Star. Then if it be the right Star it will appear on ihe face of the Moon. Bring it in contact with her bright limb, screw in the Inverting Telescope, and the contact is then made perfect by the tangent screw as before directed. In South Latitude the same Star w^ill be to the right of the Moon, and the Sextant must be held fact downwards, and as a general rule the sight must be directed to th« dimmest object, and the orightest or •rought to it T« INSTRUMENTS OF NAUTICAL ASTRONOMY. REMARKS ON MEASURING THE LUNAR DISTANCE. Of the Inverting Telescope. (jn ftcootirt of all the objects seen through this Telescope being inverted, and the difficulty of keeping them in th<^ tleld of view in consequence of the motion of the Ship at Sea, which is extremely puzzling for a lear»irf, because when the instrument is not held steady they always appear to go out of view on the WT'ng Bid,. This however can only be remedied by practice and by shifting the instrument in the opposite divectic.7 to what he would do if they were seen direct. We are obliged to submit to this »-.nnnyance, becauH«» of the superior power derived from the Inverting, to what could be obtained trom a Direct Telescope, of tM same length. Besides, the cross parallel wires, which are so useful in the Inverting Telescope, could not b« used in a common one. Of the Common Telescope. Those who find a difficulty in observing with the Inverting Telescope may find a good substitute in tht Common one. For although its power is not so great, if the contact is made as near as possible in the eentre of the field, by a little practice a very fair result may be obtained, if distances are observed East and West of the Moon, and the mean of the Longitudes taken. TTie Proper Place of the Ship for taking the Observation, Is as near as possible to the midships of the vessel, because there her motic . is the least felt, and when •he rolls heavy going before the wind, if the yards were braced forward a litl' ^ it would help to keep her ■teady until the observation is completed. The observer should place himself firmly in a corner, and sit or lie down on the deck, whichever is most convenient, so that the least bodily effort may be required to steady himself. The following method I have found of great utility, which does not require the tangent screw to be touched at all, v/hen the contact takes place, consequently both hands can be used to hold and steady the instrument, and the whole atten tion is directed to the time of the contact. It also does away with what is called the springing of th» Index Bar, (after the contact is made with the tangent screw), which is the case even in the best instru- tnenta : NEW METHOD OF MEASURING THE LUNAR DISTANCE. When the Distarut is Increasing (which may be known by inspecting the N. A.), and the Near Limbs to b« Observed, Set the Index rf the Sextant so that the objects may overlap each other a little, and watch for the instant when the Moon, by her motion in the heavens, brings the limbs in contact. Note the time and read off" the ansle. Advance the Index 1', and then watch as before for the contact. Now, as the Moon advances to the Eastward in the heavens at the rate of about 1' in two minutes of time, this will give time to read off the angles and to note down the observation. Then having advanced the Index another 1', proceed a« before, until the required number of distances are observed. Distance Increasing, and the Far Limb of the Moon to be Observed. By advancing the Index 1', the Star will appear separated from the Moon's Limb. The contact is then watched for, and the observation made in the same manner as the above. Distance Decreasing, and the Near Limbs to be Observed. Set the Index so that the limbs may appear a little separated, and watch for the contact taking place. Mote the time and read off. Then set back the Index l', and watch the contact as before. Note the time and read off, and so on. Distance -Decreasing, and the Far Limb to be Observed. By setting back the Index 1', the Star will appear to overlap the Moon's Limb. Watch for the contact a.s before, and in the same manner as the last. By this means the Moon is made to measure her own di». taiice, and all that is required to be done is to note the time of the contact For further remarks on measuring the Lunar Distance, see page 163 THE ARTIFICIAL HORIZON tT THE ARTIFICIAL HORIZON. Whsn an observer has not the advantage of a Sea Horizon for the purpose of measuring Altitudes of the neavenly bodies, or when, for instance, the Ship is in port and the Sea Horizon obstructed by the land around, he is obliged to use an Artificial one, and which is used for finding the Latitude of the place, and also for rating the Chronometer, &c. (See Fig. 11, page 78.) An Artificial Horizon is variously constructed, but the general principle, is to produce a perfectly level surface. The most simple is that of a pool of water on a calm day, or a basin containing water. But the most common in use is a trough filled with quicksilver, and protected from the wind by a roof, in which are fixed two glasses, ground perfectly plane and parallel. Another kind has a plate of glass in the trough, which, when the quicksilver is poured in, floats on the surface, and a roof is not required. But these kind of instruments are troublesome, in having to pour in and out the quicksilver every time they are used. Besides, there is a scum or film gathers on the surface of the fluid. This, however, may be prevented from running into the trough, by holding the bottle bottom op, while it is poured out. Tar, Treacle, and Oil have been tried for this purpose, but they do not give satisfaction j especially when exposed to the strong heat of the Sun, because the fluidity varies from unequal expansion. The best and cleanest kind of Horizon is a brass circular box, of about 5 inches in diameter, supported on three screw legs, having a thick plate of glass glazed into its rim. The under surface of this glass is unpol- ished, and a space left between it and the bottom, this space being nearly filled with spirits of wine, leaving a small portion vacant, so as to produce an air bubble, and which bubble, by the use of the screws is brought under the centre of the glass. This centre must be ascertained from actual trial, and marked, so that the bubble can always be placed under it. The strong heat of the Sun will cause the spirits to expand, but a screw plug is fixed at the side, which can be taken out, and a small bell-shaped funnel put in its place to receive the surplus spirits caused by expansion. This instrument, together with a pocket Sextant, will form a portable Observatory, valuable to those who may have occasion to travel much inland. When one of these instruments is used, it must be placed on firm ground, and the observer, facing towards the Sun, walks backwards until he sees the direct image of the Sun reflected on the surface of the Artificial Horizon. Then, turning down the Shades over both the Index and Horizon Glasses of the Sextant, he directs his sight through the Collar of the Telescope at the reflected image in the Artificial Horizon, at the same time advancing the Index Bar, when the reflected image from the Sextant will appear to descend. He now brings the lower limb of this Sun in contact with the upper limb of the direct Sun already seen. The Telescope is then screwed in and the observation made. It is thus necessary to bring the limbs in contact, before using the Inverting Telescope, as a security against using the wrong limbs. The Image of a heavenly body reflected from the surface of a fluid at rest, appears as much below the true horizonal line as the object itself appears above it. The Angular Distance, measured between the object and its image, is, therefore, Double the Altitude. And in halving the Angle shown by tho iDitrument. we halve at the same time all the errors of the observation. b 78 INSTRUMENTS OF NAUTICAL ASTRONOMV. DESCRIPTION AND USE OF THE ARTIFICIAL HORIZON. Tki foLowing Diagram will illustrate the Method of Observing Altitudes with an Artificial Horizon Fig. 11 ^^x-rm (See the Table on page 100.) j,^ rNSTRUMENTS- OF NAUTICAL ASTRONOMY. REMARKS ON THE CHRONOMETER. Chronometers, when sent on board of Ships, are provided with a Certifica.te of their Error ; that i* what they are fast or slow of Greenwich Mean Time on a certain day of the month, and also their Dail^ Rate, that is, what they are gaining or losing on Mean Uniform Time. Consequently, the Greenwich Time can easily be computed for any subsequent period of time, by multiplying the Daily Rate by the number of days elapsed, and applying it to the original Error. And if Chronometers always kept a uniform steady Rate they Avould answer every purpose required of them. But unfortunately, they do not always keep a steady Rate, at least not the Rate given in the Certificate, or the Shore Rate, as we call it. For it is found by experience that after Chronometers have been placed on board Ships their Rates change, caused. no doubt, by the magnetic action of the iron on board the vessel on the steel work of the Watch, and also by the change of temperature in the weather during the voyage. And as this is difficult to remedy on board a merchant vessel, it becomes necessary to find the Sea Rate at the earliest convenient opportunity, and to rerify it from time to time during the voyage. The method of doing this will be found in its proper place under the head of Rating the Chronometer at Sea. (See page 155.) This method is simply to ascertain the Error of the Chronometer on Greenwich Mean Time when the Ship is in sight of land, the position of which is well laid down. And the difference in the Error ascer- tained at one place and the next, divided by the number of days elapsed between the observations, is the Sea Rate. Or, when the Ship is in port, and the Sea Horizon visible, the Rate may be found by comparing it with M. Time. Or the Artificial Horizon may be used on shore, the times of the Altitudes being taken by a Watch, which, as before explained, must be compared with the Chronometer, both before and after the observations are made, and its Rate (if any) allowed. Rating Chronometers by the Artifical Horizon is a more correct method than by the Sea Horizon, because of the haze and change of Dip, which some- times effects the latter. When there are several Chronometers on board a vessel, the one which keeps the most uniform Rate is taken as a standard one, and with which all the others are compared. The cause which alters the Rate of one Chronometer may likewise alter the Rate of another, so that the agreement of any number of Chronometers cannot be admitted as e\'idenee of the truth of the time which they show. One good Chro Bometer, in the hands of a competent person to manage it, is sufficient for almost any voyage. THE AZIMUTH COMPASS. "* The Azimuth Compass is of a superior construction to the Steering Compass, and is particularly adapted' for observing Bearings. It is fitted with vertical Sight Vanes for the purpose of observing objecta elevated above the horizon, la one of these Vanes there is a long and very narrow slit, and in the other is an opening of the same kind, out wider, and having a wire up and down the middle of it exactly opposite to the slit. The Card is similar to those of the Steering Compass, with this difference only, that a circular ring of silvered brass, divided into four times 90°, or 360°, circumscribes the card. To Observe the Sun^s Amplitude. Turn the Compass Box, until the Vane containing the magnifying-glass is directed towards the Sun, and antil the bright speck or rays of the Sun (collected by the magnifying-glass) falls upon the slit in the other Vane. If the Card vibrates considerably at the time of observation, take the middle between the extrem* vibrations for the Observed Amplitude. Or the sight may be directed through the dark glass towards the Sun, which must be bisected by th* wire in the other Vane. A common spare Steering Compass may be made a very good substitute when a Ship is not furnished with an Amplitude Compass, (and which is frequently the case), as follows : Place the Compass Box as near the Binnacle as possible, and in such a position that the Sun at Rising or Setting may be seen over it. Now take a Plane Scale or a thin straight-edge, and place it over the centre of the Card in the direction of the Sun. Look along the edge of the Scale and see that the far end of it points to the Sun's centre. Then the point, or fraction of a point of the Compass, which is under the edge of the Scale, will be the Observed Amplitude, which must always be reckoned from the East or West points towards the North or South The observation should be made when the Sun's lower limb appears somewhat more than his semi diameter above the horizon, because, on account of the Refraction of the atmosphere his centre is then really in the horizon. THE AZIMT'TH COMPASS. ;^V To Observe the Sun^s Azimuth. In observing the Azimuth of the Sun his Altitude is required to be taken at the same nstant of tim with a Quadrant, in order to obtain his True Azimuth. Raise the magnifying-glass to the upper part of the Vane, and move the box, with the nagnifying-glass^ to the Sun, until the bright speck falls on the other Vane, or on the line on the horizontal bar. The divisions being then read off ■will be the Sun's Magnetic Azimuth. If the Card vibrates considerably at the time of observation, take the middle between the extreme vibrations. The Azimuth is counted generally from the North point of the Compass in North Latitude, and from the South point of the Compass in South Latitude. Towaiids the East in the morning, and towards the West in the afternoon. But sometimes, for convenience sake, it is counted from the South in North Latitude, and from the North in South Latitude. In high Latitudes, the Sun's Azimuth may be observed at Noon at the instant he is on the Meridian , that is, when he is true South or North, and the difference between that and the Azimuth bearing by Com- pass gives the magnetic variation at once. But to do this it is r.eceefary to have the Watch previously regulated to Apparent Time at the Ship, so that the Sun's Azimuth may be observed at the instant the Watch shows 1 2 o'clock , because the Sun then is True South in North Latitude, and True North in South Latitude. And supposing the Bearing by the Azimuth Compass to have been South also, there would, in that case, be no variation. On the other hand, if *.he Bearing by the Azimuth Compass was S. 22° 30' W., then there would be that amount of Magnetic Variation Westerly, But if the Bearing of the Azimuth Compass had been S. B2° 30' E., ther* would be that amount of Magnetic Variation Easterlv, INSTRUMENTS USED IN NAVIGATION, DESCRIPTION AND USE OF THE THERMOMETER. Fahrenh jit's Thermometer is used on board of Ships for the purpose of registeriiier the temperature of th« Oecan at the surface, and also the temperature of the Air on the "'pen Sea. The Zero, or commencement •f the Scale, begins at 32°, or the Freezing-point, and is counted upwards and downwards, according as the «olumn of mercury expands or contracts. When the temperature or heat increases it rises , but when the temperature decreases, or, (which is the same thing), the cold increases, it falls, and the degree opposite th top of the mercury is the reading required. When it is below 32° it is said to stand so many degree* below tne Freezing-point; and during the Winters in the Arctic or Polar regions, the mercury itself freezes from the intense cold. The Thermometer is a most useful instrument in giving warning of the Ship's approach to Ice in thick foggy weather. This is simply done by drawing a bucket of water from alongside and plunging the Ther- tnometer into it at regular intervals in the day, during the voyage, and the readings noted down. And, when it is found that the temperature of the water has fallen, on approaching a locality where Ice may be «xpevjted to be fallen in with, the observations should be repeated every few minutes. And should the mercury in the tube keep sinking, you may conclude that the Ship is approaching Ice, and the precaution should be taken at once to shorten sail. For if it be in the Winler season, and the Thermometer has fallen to 34°, she will then be only half a mile off the Ice. If in the Sum ner season, and the Thermometer has fallen to 42°, she will then be about the same distance off, and on a nearer approach the glass will fall still lower. But when the Ship has passed the Ice, the Thermometer will gradually rise again. In the month of June, near the Bank of Newfoundland, the Thermometer had fallen suddenly from 48* to 42°. Ship was then running with Studding-sails set on both sides, in very thick weather. They were immediately taken in and the Courses hauled up, when the white glare of an immense Iceberg was seen Tight ahead, and she had to be hauled to the wind in order to pass clear to the windward of it at less than a ■quarter of a mile distant; so that by a timely reference to this useful instrument the Ship was rescued from imminent danger. The temperature of the Ocean is higher in deep water, than it is in shoal water near the land, or on banks. Hence, a Ship on approaching land, or on Soundings, the Thermometer falls from 2° to 6°, except on a high bold shore with deep water close to it, when it is not so apparent. The difference of temperature on and off the Banks of Newfoundland is 5°. Currents in the Ocean coming from high Latitudes have their water colder than those which come from low Latitudes, which accounts for the variation in the temperature of the surface water, out on the open Sea On a Ship entering the Eastern edge of the Florida stream, the water will be found to be from 5* to ■8° warmer, and after crossing it and leaving its Western edge, the adjoining Sea will be found that much eolder. and when she gets on soundings, several degrees colder still. So that a careful observer will always be warned of his approach to the coast of the United Stales of America, by consulting this useful instru- ment m thick we?.ther, when no Celestial observations can be obtained. The Plate of the Thermometer should be made of Ivory or Metal, .so that the tube will be less liable to break, and it should be fixed in a square metal box, the bottom of which, as high as the mark 30°, should be water-tight, so that in examining the degree of temperature, the bulb may be kept immersed in the water The remainder of the length should be open in front, with only two or three cross bars to ward off any accidental blow. It would be better to have a spare one also, fixed up in some safe part of the ship, in the •hade, out of the wind, and in as dry a place as possible, ♦' -egister the temperature of the air, while the .«tber may be used for the water. THE JSE OF THE BA.tOMETER. DESCRIPTION AND USE OF THE BAROMETER. iTi* Barometer is used on board of Ships for the purpose of foretelling the state of the weather. By th« ^oBsure of the Atmosphere acting on a column of Mercury, contained in a glass Tube, which has aScala iv. ached to it, marked in inches, and a sliding Vernier, the top of which being set at the height of th« Mercurial column, gives the measurement in inches, and hundredth parts of an inch. In North Latitude it ■itaads highest with N. E. winds, and lowest with S. W. In South Latitude it stands highest with S. E. wiuds, and lowest with N. W. \bout the commencement of a Storm, in North Latitude, from the S. W., with rain, the Barometer oe^ins to fall, and continues to fall as the Storm increases j and when it stops and begins to rise, the rain w.ll 80on cease, and a shift of wind to the Northward maybe expected; but it may continue to blow hard until the Barometer rises to 30 inches. In South Latitude, N. W. winds bring rain, with a falling Barometer; but it rises with Southerly winds. If it rises slowly and gradually, good weather may be expected to follow; but if it rises rapidly, the weather will continue unsettled and stormy. In general, before a heavy fall of snow or sleet, the Barometer falls very low, and the wind commences to biOW from the quarter in which it generally stands the highest in fine weather, and after the fall of snow it riocs rapidly. Rat there are many curious exceptions to these general rules ; for I have seen the Barometer steady at 30 inches, with the wind blowing hard at S. W., with heavy rain falling for several days together, Ship being then in a high Northern Latitude. But the secret of this turned out to be, that an Easterly wind waj. at hand, which followed the S. W. wind, and continued blowing for several weeks afterwards. riie never-failing sign of bad weather is, when daylight breaks high over head, and the clouds to lee- ward look heavy and near ; also, when the Sun rises or sets with a lurid red glare. These appearances should be taken in connexion with the action of the Barometer, before a proper opinion can be formed of the kind of weather that may be expected to follow. The Barometer generally stands about 30 inches in the fine serene weather experienced in the Tropics, except between the Trade Winds, when it falls a little during the rainy weather which prevails there. but, if it falls rapidly near the Northern or Southern limits of the Trade Winds, (that is, between the Lati- tudes of 20° and 30°,) down to 29.50, there is a Hurricane at hand, and by referring to the Diagrams of the Slorra Circle, at pages 43 and 44. measures must be taken at once for the safety of the Ship, where it will be perceived thaj". with the Barometer at 29.50, the Ship will be about 150 miles distant from the Focus , when it falls to 29.20, 100 miles ofl"; to 28.40. 50 miles off; and at the Focus itself it will stand at 27 inches. When the Ship increases her distance from the Focus the Barometer will rise ; so that it is a most valuable instrument in the locality of HurriAnes. THE ANEROID BAROMETER. This instrument is constructed so that the pressure of the Atmosphere acts upon a metalic spring, con- A'ected with a vacuum, and turns a band to the Right, answering to the rising of the Barometer, and to the l^eTt wh^n it is falling. It has a round face, similar to a Chronometer, and the Inches are marked on it and counted in the same manner as tlie Mercurial one. This instrument is very sensitive and exact, very superior to the old ones, which are sorneiiines difficult to read ofi", on account of the Mercury plunging up ajid down in the tube, when the Ship has violent motion. I have used this instrument myself for some years, and in a great many instances it has given me warning of a coming Hurricane more than 24 hours in advance. It is also more portable, and can be hung up, or f laced any where about a Ship's cabin, or in a place where it would be inconvenient to swing a Mercurial Hie. AA NAUTICAL ASTRONOMY. Having thus given a short description of the principal instruments used in Nav eating a Ship, we now proceed to find the Ship's place on the Ocean from Astronomical Observations, and commence with finding the Latitude from the Meridian Altitude of the Sun. The Correct Declination of the Sun must be found at the time of Observation, as follows : The Sun's Declination, found in Table X, to the nearest minute, is calculated for every Noon at Greenwich, for several years in advance, and which will answer for every fourth year afterwards, by applying a small correction found in the adjoining Table ; or it may be taken from the Nautical Almanac. When the Ship is on the Meridian of Greenwich, no correction is required, and the Declination standing asainst the day of the month may be taken out and applied at once, because it is Noon at the Ship and Noon at Greenwich at the same instant of time. But when a Ship is on a Meridian to the Eastward or Westward of Greenwich, that is, when her Longitude is East or West from Greenwich, the Declination must be corrected for the Change of Declination corresponding to the Longitude in time ; because when it is Noon at the Ship, in 15° East Longitude, it wants 1 hour of being Noon at Greenwich, and when it is Noon at the Ship, in 15° West Longitude, it would be 1 hour past Noon at Greenwich. This correction amounts to a considerable quantity when the Longitude is great, and when the Sun changes his Declinatior rapidly in the months adjoining March and September. RULE For Correcting the Sun's Declination at Noon. Enter Table XI with the Longitude at the side column and the Declination at the top, and the angle of meetinf^ loints out the correctaon to be applied, according to the precepts at the bottom of the Table. EXAMPLE 1. Required the Sun's Correct Declination on the Ist of March, 1854, at the Ad ot the Sea Day, in the Longitude of 80* West The Sun'i Declination, March Ist, at Greenwich, at the end of the Sea Day, or the beginning of the day in the Nautical Almanac, by Table X, is 7' 85' S. Conection for the Declination in Table XI, for Longitude 80° "West, is Sulx 6 (Because the Long, is West and Declination Decreasing,) Gives the Correct Declination .7° 80' S. EXAMPLE 2. Required the Sun's Correct Declination on the 1st of April, 1854, at the end of the Sea Day, in the Longitude of 90° East The Sun's Declination, April 1st, at Greenwich, by Table X, is ■#* 32' N The Correction for the Declination in Table XI, for Long. 90° East, is 6'.8 Sub^ 6 Because the Long, is East and Declination Increasing,) Gives the Correct Declination 4° 26' jjjyj5_ 'Phe Corrections in Table XI, are expressed in minutes and tenths of minutes, and it is usual in practice that when the tenths exceed 5, we call the minutes one more, but when the tenths are less than 5, they are not used at alL But when jrreater accuracy is required, multiply the tenths by 6, which will give seconds of Declination. It may also be remarked here, that the Declinations, or any other quantity found in the Nautical Almanac, are all calculated for Astronomical Time at Greenwich ; and that the Astronomical Day begins 24 hours after the Sea Day, and 12 hours after the Civil Day, and is counted through the 24 hours. , . , ^ , -,, • • , .u . . Hence the Noon of the Civil Day, (or that used by the generality of mankuid,) the Begmmng of the Astronomical Day and the End of the Nautical Day, take place at the same period of time. There is no reason why this absurd system of keeping Sea Time should be continued ; because it is just as easy Ic keep Civil Time commencing the day at Midnight, and the Day's Work could still be reckoned from Noon to Ndoh, as before The only difference would be, that one half of it would appear in the preceding day's Log, (where it roallT belongs )' »nd the other half in the following. Many Logs ar; now kept on this principle. (See page 195.) 4 FINDING THE SUN'S CORRECT DECLINATION' gft To Correct the Sun's Declination to any Time of the Day. When the Declination is required at any other time than at the Noon of the Ship, a farther conection is necessary : because, for instance, an observation of the Sun made at 4 hours, either before or after the Noon of tile Ship, his Declination must be corrected for the change of Declination in that time. RULK Correct the Declinaliou for Noon as in the foregoing Examples. 'Then enter Table XI again, with the time from Noon at the Ship in the side column, and the Declination at the top, and the angle of meeting points out the correc- tion in mimites and tenths, to be applied according to the precept at the bottom of the Table. EXAMPLE. ?,. Required to find the Sun's correct Declination on the Istof March, 1854, at 8h 10m in the forenoon, Sea AcrouLu jD the Longitude of 80° West The Sun's Declination, March 1st, at Greenwich Noon, by Table X, is V 35' S. Decreasing Correction for Declination, in Table XI, for Longitude 80° West, Sub. 6 (Because the Long, is West, and the Declination Decreasing), gives theDeel. at Noon 7° 30' S. Correction for 3h 50m, or the time from Noon, Table XI, is 3' 8" = Add 4 (Because the Time was before Noon and Decl. Decreasing.) Correct Decl. at 8h 10m 7° 34' S. EXAMPLE 4. Required to find the Sun's correct Declination on the 1st of Anril, 1854, at 7h 20m in the forenoon, Sea Account in the Longitude of 90° East The Sun's Declination, April 1st at Greenwich Noon, by Table X, is 4° 82' N. Increasing. Correction for the Declination, in Table XI, for Long. 90° East is 5' 8" Sub. 6 (Because the Long, is East and the Decl. Increasing), gives the Decl. at Noon 4° 26' N. Correction for 4h 40m, or Time from Noon, in Table XI, is 4' 5'' Sub. 5 (Because the Time was before Noon and the Decl. Increasing.) Cor Decl. at 7h 20m 4° 21' N. EXAMPLE 5. Required to find the Sun's Declination on the 21st of March, 1854. at 5h 20m in the afternoon, Sea Account id the Long, of 120° West 21st, Sea Account, is March 20th. Declination at Greenwich Noon, Table X, is 0° 10' S. Decreasing, tion for the DecHuation, in Table XI, for Long. 120° W. is 7' 8" Sub. 8 March Correction (Because the Long, is West, and the Decl. Decreasing), gives Decl. at Noon 0° 2' S. Correction for 5h 20m, or the time from Noon, in Table XI, is 5' 2" Sub. 6 Here the Decl. has changed from S. to N., and the Diff. is the Decl. at 5h 20m. P. M. "o° 3^N. Hence, the rule in this case is, that when the Correction Subtract! ve, exceeds the Declination, the differ •nee is the Declination of a contrary name. EXAMPLE 6. Required to find the Sun's correct Declination on the 23d of September, 1854, at lOh Om, in the forenoon, ic Long. 15° 0' East The Sun's Declination on the 23d September, at Greenwich Noon, is 0* 8' S. Increasing. Correction for the Declination in Table XI, for Long 15° East, Sub. 1 (Because the Long, is East and the Declination Increasing.) Declination at Noon .... 0° 2' S. Correction for 2h Om, or the time from Noon, Table XI Sub. 2 (Because the Time was before Noon and the Decl. Increasing.) Correct Decl. at lOh. 0* 0' Sun on the Eqna To Correct the Sun's Declination to the Greenwich Time of Observation. RULE Turn the Ship's Long, into Time by Table XXVI, and add it to the time at the Ship, in West Longitude, oi •ubtract in East The lesult will be the Greenwich Time of the observation. If it is before Noon at Greenwicli, subtract it from 12h; if afternoon, it is the required Time. Take f)ut the Declination against the day of the month, from Table X. Then enter Table XI with this time from Greenwich Noon, in the side column, and the Declination at the top, and at the angle of meeting will be the required correction, to be applied according to the precept at the bottom of the Table /or Time. Suppose, as in Example 3d. the time at Ship to be 8h 10m A M. Long. 80* W., in time, is 5h 20m, which, added, makes 13h 30m, less 12h^ gives Ih 30m, the Greenwich time past Noon, which, with the Declination 7' 35', gives the Correction 1' subtractive. and the cor-ect Declination is 7* 34' S M NAUTICAL ASTRONOMY LATITUDE BY THE MERiDIAN ALTITUDE OF THE SUN. Latitude is the Distance of a place from the Equator either North or South, and is measured by an Are 91 the Meridian contained between the Zenith of the observer and the Celestial Equator. Hence, if the distance of any heavenly body from the Zenith, when on the Meridian, be known, and its Declination found in Table X, that is, the number of degrees and minutes it is to the Northward and Southward of the Celestial Equator, the Latitude may thence be found. As the Pole round which the Celestial Bodies appear to revolve, remains always in the same fixed place m the heavens, from whatever point of the Earth's surface it is viewed, its elevation at any particular place is always the same, and the Celestial Equator is 90° from it. When the observer changes his Lati- tude he changes the distance between his Zenith (which moves with him) and the Pole. He therefore changes the Altitude of the Pole above the Horizon, and which is always equal to the Latitude of the place. The position of the Celestial Equator is changed in like manner. (See Figure 12th, next page.) The simplest and most efficient manner of determining the Latitude is by measuring the Meridian Alti tude of the Sun with a Quadrant, at the time he attains his greatest Altitude. It is then Apparent Noo» at tWe Ship. To Find the Latitude from the Meridian Altitude of the Sun. RULE. RmuI off the Observed Altitude from the Quadrant, and write it down. In practice, three Correctioni only ar^ reauired to be applied to the Sun's Observed Altitude, viz : The Semi-diameter, taken at 16', the Dip found in Table V, and the Refraction found in Table IV. The Sun's Parallax, being small, is omitted. If the lower limb be observed, we find his central Altitude by adding the Semi-diameter 16', and sub- tracting the Dip and Refraction ; or by subtracting the Dip and Refraction from 16', and adding the bal- ance, which comes to the same thing. In Table IX, the balance of all the corrections may be taken out at once by inspection, as follows Enter the Table, with the Observed Altitude, at the side, and the height of the eye above the Sea, in feet, at the top, and at the angle of meeting will be the Correctien required in minutes and tenths, and whicb is always additive when the lower limb is observed. When the tenths amount to more than .5, we call the minutes 1' more, but if less than .5, we throw them away, and the result is the True Central Altitude. But if greater accuracy be required, multiply the tenths by 6, will give seconds of Altitude. If the Sun's upper limb be observed, the whole of the Corrections are to be subtracted, which will give the True Central Altitude. (f the Sun's centre itself be observed, as in figure 10. No. 3, the Semi-diameter is not required to be allowed for. In that case, the Dip and Refraction together, subtracted, will give the True Central Altitude. Subtract the Sun's True Central Altitude from 90°, will give the Zenith Distance. Then if the Sun bear South when on the Meridian, mark his Zenith Distance North, and if he bear North, mark his Zenith Distance South. Take out the Sun's Declination from Table X, and correct it for the Longitude of the Ship by Table XI Write it down under the Zenith Distance, and mark it North or South, as named in Table X ,: or, if taken from the Almanac, in the page containing the day of the month. Then if the Zenith Distance and Declination be both North or both South, their sum is the Latitude of that name. But if one be North and the other South, their difference is the Latitude of the same name a* the greater of the two. Non. When the horizon under the Sun is obstructed by land, the Correctioa for Dip must bo taken from Table Vlll,. when at less distance from the Shore than 6 miles. EXAMPLE 1, Jannary Ist, 1864. In the Longitude of 80* West, the Meridian Altitude of the Sun's Lo^er Limb was observed lo be 26* 62', bearing South, Index Error 2', subtractive Height of the eye above the Sea, 18 feet Required' rho Latitude in. FINDING THE LATITUDE BY MEKIDIAN ALTITUDE. 87 Projection of the Meridian Altitude. Fig. 12. Rule.— With the Chord of 60* describe a semi-circle, to represent the concave Arch of the heavens, and draw the Rational Horizon. Lay off the Sun's Altitude, 27°, on the Left. Take the Declination, 23° S., in the diyiders, (from th« hne of Chords,) and with one foot in the Sun's place, extend the other towards the Zenith, (because the Declina- tion 18 South ) which will mark the place of the upper end of the Equator on the Meridian Circle. Now draw the Equator through the centre and the Polar Axis at right angles to it. Mark the Zenith at gO" from the horrzon, and draw a line from it through the centre, and where it cuts the Earth's surface is the place of the Observer. His Latitude is measured on the Meridian, and is the Distance of his Zenith from the Celestial Equator, which, on the hne of Chords, measures 40°, and the Elevation of the North Pole, 40° above the horizon, is equal to the Latitude of the place. Hence the Distance of the Observer from the Equator of the Earth, which is 40°, is his Latitude North. By Computation. Sun's Declination, Jan. 1st, Table X, 23' Correction Table XI, Long. 80 W Sub. 1' 1 Corr. Declination at Noon of (he Ship 23° S. Sun's Observed Altitude, Lower Limb 26° 52' S. Semi-diam, add, 16' Index Error, Sub.... 2_ Dip. 4, Ref 2=Sub..^ 26° 50' Balance of Corr 10', Add.^^ 10 Sun's true Central Altitude 27* 0' 90 Zenith Distance .63° 0' N Correct Declination. 23 S. Latitude in 716° 0' N. EXAMPLE 2. June 1st, 1854. In the Long, of 90° E., the Meridian Altitude of the Sun's Lower Limb was observed to b« 69* 45', bearing S., Index Errors', additive. Height of the eye above the Sea, 20 feet. Required the Latitude in. Projection of the Meridian Altitude. Fig. 13. R0LK.— Proceed, as in the last Example, to draw the figure. Then lay off the Sun's correct Altitude, 70* on the left. Take the Declination, 22° N., in the dividers, and with one foot in the Sun's place, extend the other downwards, (because the Declination is North,) which will mark the upper end of the Equator. Now draw the Equator and the Polar Axis as before. A line drawn from the Zenith, let fallen the Earth's surface, and through the centre, will be the piece of the Observer, and his Latitude is the Distance of the Celestial Equator from his Zenith, which measures 42° on the line of Chords, and the Elevation of the Pole is equal to th« Latitude. m NAUTICAL ASTRONOMY. Ftfviing the Latitude by the Meridian Altitude of the Sun. BY COMPUTATION.— (See Examfk S., Sun's Observed Altitude, Lower Limb 69° 45' S. Declination, June 1st, 1854, Table X, . . . 22' 8' H Semi-diam. 16' Index Error, Add.. ._ 3 Corr. in Table XI, Long. 90° E.— . Sub.^ 2 Dip. 4, Ref. 0, Sub^ 4 69° 48' Sun's Corr. Dec, Noon of Ship 22° 1 'N Balance of Corr 12 Add 12 Sun's true Central Altitude 70° 0' 90 Zenith Distance 20° 0' N. Sun's Correct Declination 2^ 1 N. Latitudein 42° 1' N. EXAMPLE 3. July 22d, 1854. In Long. 25° "West, the Meridian Alti- tude of the Sun's Lower Limb waa 89° 1' South. Height of the eye, 18 feet Required the Latitude ia Obs. Alt Sun's Lower Limb 89° 1' S. Corr. found in Table IX., Add. . . . 12 True Central Altitude 89° 13' 90 Zenith Distance ..0°47'N. Declij ation. Table X, 22d July, 20° 19' N, ) „^ ,0 vr Corr, fable XL Long. 26°, . .Sub.. . 1 J " ^ Latitude in 21° 5' N. EXAMPLE 5. Aug. 7th, 1854. In Long. 112° W., the Meridian Alti- tude of the Sun's Lower Limb was 74° 27' North. Re- quired the Latitude ia Obs. Alt Sun's Lower Limb 74° 27' N. Corr. from Table IX, Add. ._^ 12 True Central Altitude 74° 39' Zenith Distance ,15° 21' S. Declination, Table X, 7th Aug., 16° 28' N. i ,« „„ vr Corr, Table XI, Lon. 1 1 2° W., Sub . . 5 f ^^ ^ ^^ Latitudein 1" 2' N. EXAMPLE 7. March 20th, 1854, In Longitude 160° W., the Meridian Altitude of the Sun's Lower Lunb was 32° 58' N. Re- quired the Latitude. Obs. Alt Sun's Lower Limb 32° 58' N. Correction, Table IX, Add . . 10 True Central Altitude 33° 8' Zenith Distance 56° 52' S. Jeclination, Table X, March 20th, 0° 10' S. ) ^ . ^^ Corr, Table XL Lon.l60°W.,Sub.O 11 ^ 1 JN. Latitude in 56° 51' S. EXAMPLE 4. ' July 23d, 1854. lu Long. 27° W., the Meridian Alti tude of the Sun's Lower Limb was 88° 4' N. Height of the eye, 18 feet. Required the Latitude. Obs. Alt Sun's Lower Limb 88° 4' N Correction, in Table IX. Add.^ 12 True Central Altitude 88' 16 90 Zenith Distance 1*44 S Declination, Table X, July 23d, 20* 7' N. ) 9^ a V Corr, Table IX, Lon. 27° W., Sub.. .1 f ^" " " Latitude in 18' 22' N EXAMPLE 6. Aug. 8th, 1854. In Long. 140° East the Meridian Alti- tude of the Sun's Lower Limb was 7 2° 46' N. Required the Latitude. Obs. Alt Sun's Lower Limb 72° 46' N. Correction, Table IX, Add. . 12 True Altitude 72° 58' N Zenith Distance 17" 2' S. Declination, Aug. 8th, Table X, 16° 11' ) , ^ Corr, Table XI, for Lon. 140° E., . .Add. 7 )_____ Latitude in 0° 44' S. EXAMPLE 8. ' March 21st 1864. In Long. 1.75° E., the Meridian Alti- tude of the Sun's Lower Limb was 40° 20' N. Required the Latitude. Obs. Alt Suu's Lower Limb was 40° 20' N Correction, Table IX Add. . H True Altitude 40* 31' Zenith Distance 49'' 29' S. Declination, Table X, March 21st 0" 14' N. | n" 9' NT Corr., Table XI, Lon. 175° E, Suh. 12 [____ Latitude in 4 9° 27' S. In the above Examples the height of the eye above the Sea is supposed to be about 16 or 18 feet, which answers very well for vessels of common size ; but in very large Ships the height of the eye will be con siderably above that. On the other hand, in small vessels the height of the eye will be much less than IS feet above the Sea. The Dip, found in 'Table V, or the height of the eye, in Table XI. inusl be regulated fccoordingly TO FIND THE LATITUDE BY THE MERIDIAN ALTITUL E OF THE SUN. 89 FINDING THE LATITUDE BY THE MERIDIAN ALTITUDE OF THE SUN. When the Sun's True Central Altitude is 90', he is in the Zenith, and the correct Lcclination for tk day is th« Latitude of the same name as the Declination. When the Declination is 0° 0', the Zenith Distance is the ISatitude of a contrary name to the Beariiig of the Sun when on the Meridian. When the Zenith Distance and Declination are equal, but of contrary names, the Ship is on th Equator. When the Sun is in the Zenith, and his Declination 0° 0', the Ship is on the Equator, which the follow- ing Diagram will show. Fig. 14. » I aH thig Figure, the Sun appears in the Zenith, and his Declination at the same time being 23° 28' N. from the Equator, is the Latitude of that name, and which is equal to the elevation of the Pole above the Horizon. Now suppose the Sun to be on the Equator, then his Zenith Distance would be 23° 28' N., which is also the Latitude. Again : Suppose the Equator to coincide with the Zenith ; then both North and South Poles would appear in the Horizon, and which is the case when the Ship is on the Equator. Again : if the Sun has, say 23° 28' S. Declination, his Zenith Distance in this case would be 23° 28' N., which being equal and of contrary names, the Ship would be also on the Equator. When the Sun is in the vicinity of the Zenith, it is often difficult to observe his Altitude, in consequence of not knowing on which side of it he will pass the Meridian. But if the Watch be previously regulated to Apparent Time it will be found of great service in indicating the exact time, that is, 12 o'clock, when the Sun will be on the Meridian, because his motion is then very quick, and he requires to be carefully watched to obtain his proper Altitude. It may, however, be obtained to nearly 90° in this way, by th« exercise of a little care. It is nevertheless advisable to verify the Latitude so obtained, by an observation of a Planet or a Star taken at twilight, when the Horizon is distinctly seen, and for which there are good opportunities to be found during the fine serene weather in the tropics. To Find the Latitude by Observing the Sun's Centre. When the Sun shines through watery clouds his limbs may not be distinctly visible, but a good observa- tion may still be obtained by bringing his middle down to the Horizon. (See page 68, Fig 10.) The observation is then worked as follows : EXAMPLE 9, Observed Meridian AIL of the Sun's Centre. ..10° 10' N Dip 4, Refraction 6 Sub. 9 Sue's True Central Altitude 10° 1' Zenith Distance 79° 59' S. DecUnation, June 21st 23 27 N. Ship ofif Gape Horn, Latitude in 56^ 32' S EXAMPLE 10. Observed Merid. Altitude of the Son's Centre. 60' 14' & Dip 4, Refraction 1 Sub. 6 Sun's True Central Altitude 60^ 9* Zenith Distance 29° 51' N. Declination, December 2l8t 23 27 S Latitude in , 6° 24' N M NAUTICAL ASTRONOMY. TO FIND THE LATITUDE FROM A BACK OBSERVATION WITH A SEXTANl RULE. Bring the Lower Limb of the Sun in contact with the Back Horizon, and subtract the Angle so obtained fr«nii 180° , which will give the Meridian Altitude of the Upper Limb Subtract the difference between the Dip and the Semi diameter, (usually taken as 12'), and the result is the True Central Altitude. In thia case, no Correction fo» Refraction is required, because the Sextant can only measure about 120° of an Angle, the supplement of which i» 60* of an Altitude, (for which no Correction for Refraction is required in Praottoe at Sea.) This method is useful ia kw Latitudes when the Horizon uuder the Sun is obstructed by the laud. DIAGRAM OF A BACK OBSERVATION. Fig. 15. • ZENITH D\ST ,0F THE <%:-. VISIBLEl HORIZON EXAMPLE 11 xTie Angle of the Sim's Lower Limb from a back Ob- •ervation with a Sextant, was 119° 32' on the Meridian, the observer facing towards the North. The correct De- clination at the same time was 20° 10' N. Required the Latitude. Observed Angle Sun's Lower Limb 119° 32' N. Subtract from 180 Sun's Meridian Altitude, Upper Limb 60° 28' S. Semi-diameter 16' and Dip 4', subtract Corr. 12 Sun's True Central Altitude 60° 16' Subtracted from 90°, gives the Zenith Distance 29° 44' N. Correct Declination 20 10 N. Latitude in 49° 54' N. EXAMPLE 12. The Angle of the Sun's Lower Limb from a Back Ob servation with a Sextant was 100° 25' on the Meridian, the observer facing towards the South. The Correct De- clination at the same time was 22° 15' N. Required the : Latitude. Observed Angle Sun's Lower Limb 100° 26' & Subtiact from 180 Sun's Meridian Altitude, Upper Limb 79° 36' N Semi-diameter 16' and Dip 4', subtract Corr. 12 Sun's True Central Altitude 79° 23' Subtracted from 90°, gives the Zenith Distance 10° 37' S Correct Declination 22° 16' K Latitude in 11° 38' N To Find the Latitude from an Altitude by the Shore Horizon When the Ship is less than 6 miles from the Shore under the Sun, when on the Meridian, his Lower Limb is brought down to the line which divides the Sea and Land, and a Correction for Dip taken from Table VIII, to be used in the room of the Dip usually taken from Table V. EXAMPLE 13, "With the Bearing of the Land find the Distance off, by •ome one of the Rules given at pages 32 and 33, or by the Soundings on the Chart. Suppose the Distauce off shore to be 1 mile, and the Observed Altitude to be 60° 11' S ; height of the eye 18 feet: Correct Declination 20° 10' N. Required the Lati- tude. Observed Alt Lower Limb to the Sea Line 60° 11' S. 8emid.l6', Dip at 1 mile. Tab. VIII, is 11', Add Diff. 5' Sun's True Central Altitude 6'o°~T6"^ Subtracted from 90°, gives Zenith Distance.. ..29° 44' N. Correct Declination 20 10 N. Ijititude in 49° 54' N. EXAMPLE 14. Find the Distance off shore from the Bearing of th» Land, as before directed, and the correct height of th* eye above the Sea level. Suppose the distance off shore to be -J- a mile, and th» Observed Altitude to be 79* 35' ; height of the eye 2& feet ; Correct Declination 22° 15' N. Reqaired the Lati- tude. Observed Alt. Lower Limb to the Sea Line. . .79° 35' N Semid. 16', Dip at -J m., in Tab VIII, is 28' Sub. Diff. 12 Sun's True Central Altitude 79° 23' Subtracted fiom 90°, gives the Zenith Dist lO" 37' S' Coirect Declination 22 15 N Latitude in .11° 38' I» FINDING THE LATITUDE BY MERIDIAN ALTITUDE. 91 TO FINJ THE LATITUDE FROM A MERIDIAN ALTITUDE BELOW THE POLE When the difference between the Declination of a body and 90°, or the Polar Distance, is less than Um Latitude of the place, and they are both of the same name, the object comes to the opposite Meridian with- out setting, and passes that Meridian below the Pole. If the Altitude be then observed, the Latitude may oe found as follows : RoLK. — Correct the Observed Altitude as usual, and tc the true Central Altitude, add the DiflFerence between U»« D9'' N. at Nooa FINDING THE LATITUDE BY THE SUN. FINDING THE LATITUDE OUT OF THE MERIDIAN. EXAMPLE 8. Oet 20tlv 1854. In Latitude by Dead Reckoning about 40" 0' S., Long, by Chro. 62° E., the Suu'a Obs. Alt waa 69° 30' N., P. M. The Greenwich Time by Chronometer waa 19h. 58m. 54a. A. M. The Couree aince Noon waa S. S. K, going 12 knota an hour. Required the Latitude in at Noun. H. M. s. Green.Time by Chr., 19 58 54 Dec, Oct. 20. . . 10° 20' S. Lou. 62° E. in time. . 4 8 Cor., Ta. XL Sub. 4 24 6 54 Cor. Dec 10° Iti' S. Subtract. . . .24 Ma Time at Ship.. 6 54 Equa. Time.N. A. 16' 6" Eq. of Time,. . Ad d.. 15 6 Ap. Time from Noon. 22m.08.Log 7.862 Part 1st Lat 40° S. and Dec. 10* S . Log 0.480 Part 2d. Cor. in Part 4th, Add 0° 24'= Log777842 Table XV. Oba. Alt 59 30' N. Mer. Altitude 59° 64' N. Corr., Table IX, Add 1_2 True Altitude 60° 6' N. Zenith Dist 29° 64' S. Declination 10 16 S. Latitude in 40° 10' S. at 22' past Noon. S.S.E. 4 m. ■=D.Lat. 4 to the South'd since Noon. Latitude 40° 6' S. at Noon. EXAMPLE. 5 June 22d, 1854. Ship near the Equator, equal Alti- tudes were taken to correct the Watch. Altitude A.M. 66° 4' N. Time by Watch lib. 48m, do. P.M. 66 4 N. do. do 12 18 Watch is 8 min. fast of Apparent Time )24 6 "l2h. 3 m. Required the Latitude in at the time of the P.M. Altitude. Time by Watch, P.M Oh. 18m. Watch fast of App. Time. 3 App.Time from Noon . . .Oh. 15m.Log 7.029 Part let Lat 0° 0', Dec 23° N. Log 0.673 I'ait 2d. Corr. Part 4th, . .Add 17' = Lug 7.702 Table XV. Oba Altitude 66 4 N. Merid. Altitude 66" 21' N. Cor., Table IX, Add. Vl True Altitude 66° 33' N. Zenith Distance 23° 27' S. Declination 23 27 N. Latitude 0° 0' EXAMPLE 4. July 5th, 1864. In Lat by Dead Reckonmg about 50 S., and Long, 90° 36' E„ by Chro., the Sun's Oba. Alt was»l5' 47' N., A.M. The Greenwich Time by Cro. wm 17h. Im. 47s. A.M. The Course to Noon waa N.E., going 10 knots an hour. Required the Latitude at Noon. H. M. 8. Green. T'e by Chr., 17 1 47 Dec, July 5 22' 49' N. Lon.90° 36' E.iu tim e, 6 2 24 Cor., Ta.XI, Add 2 M. Te at Ship, A.M. 23 4 11 Cor. Dec 22° 5] N Equa. of tune. Sub. 4 11' Sub fr. 24h.=Ap.T. ^00 Equa., N. A 4' 11" Log 8.231 Part Ist. Ap. T. f m Noon . . Ih.Om.Os. Lat 50° S., and Dec. 23° N . Cor., Part 4th,. Add 1° 13'== Obs. Altitude 15 47' N. Mer. Altitude 17° O' N. Corr., Table IX, Add 9 True Altitude . . 17° 9 N. Zenith Distauce . . 72° 61' S. Declination 22 51 N. Latitude. Log 0.093 Part 3d. Log 8.324 Table XV \ .60° 0' S. at 11 o'clock A.M. Co. N.E. 10 m.=D.Lat 7 to the Northward. Latitude 49° 53' S. at Noon. ♦ EXAMPLE 6. Nov. 15th, 1854. In Latitude about 56* 5' N., uua^. 15° W., an Altitude of the Sun was observed in the after- noon to be 14° 7' S. Time shown by the watch, lh.8m.46s, which had been regulated in the morning, since which time the Ship had made 64' of Longitude to the West- .ward. Required the Latitude in at the time of the Alti- tude. Time of Alt by Watch Ih. 8m. 468. * D.Lon. ma. 64' W. in time. Sub. 4 16 App. Time at Ship, P. M Ih. 4m. SOs.Log. 8.294 Lat 56° N., and Dec. 18^ S Log. 0.042 Corr. in Part 4th. . Add 1° 14' -= Log. 8.336 Obs. Altitude 14 7 S. Table XV. Merid. Altitude 15° 21' S. Dec 18^30' S. Corr., Table IX . . Add 8 Corr. . . Add 1 True Altitude 1_6° 29' S. Cor. Dec 18° 31 S. Zenith Distance 74°~Tr N. Decimation 18 31 S. Latitude in . . . ^6°~b' N. at Ih. 4m. P. M QUESTIONS FOR EXERCISE. ijuestian 1st.— Dec. 11th, 1854. The Latitude by Dead Reckoning was about 50° 0' N., and the Longi tude by Chronometer 41° 20' W. An Altitude of the Sun was observed in the forenoon to be 15° 28' S and the time by ChronometerlSh. 40m. 6.s, P. M., whicTi was fast of Greenwich 3m. 20s. The Course untii Noon was S. by W., going 8 knots. Required the Latitude at the time of the Altitude and at Noon. Answer. — Latitude at lOh. 58m., or tune of Altitude, was 50° 4' N., and at Noon, 49° 56' N. Ques. 2d.— August 27th. The Latitude by Dead Reckoning was 35* 30' N., and Long. 75' W. An Altitude of the Sun was observed to be 63° 59' S. at 20 minutes past Noon, apparent time at the place Ship running to the Northward, going 9 knots. Required the Latitude as before. Ans — Latitude at 20 minutes past Noon was 35° 27' N. Latitude at Noon, 35' 24' N. • When the Differonc* of Lon^tude made in time is Eaat, it muatbe added to the Time by Watch. »6 NAUTICAL ASTRONOMY. TO FIND THE LATITUDE BY TWO ALTITUDES OF THE SUN, (USUALLY CALLED DOUBLE ALTITUDES,) Having the Measured Interval of Time between the Observations by the Watch. This method will be found more simple and useful than the old and tedious methods of Double Altitudes usually given in works of this kind, many cases of which are of very doubtful utility, besides the time ipent in working them out. The principle of this method is simply to find the Sun's Hour Angle at the time the Altitude was observed, which was farthest from the Meridian, and to measure the interval of time elapsed between it and another Altitude observed near the Meridian, by a good Watch or Chronometer. This interval of time being then corrected for the Ship's change of Longitude in time, and applied to the Outer Hour Angle, the difference between them is the Inner Hour Angle, and which is the Apparent Time from Noon. The observation then becomes the same as if only one Altitude had been observed, and the limits are the same as in the last case. The Time so found is only an approximation, because the Latitude la not known, but it is near enough for this purpose. And as every Navigator, now-a-days, is supposed to know how to find the time at Sea, nothing new is required to be learned. The Rule for findiilg the time at Sea is given at page 124. When both Altitudes are Observed in the Forenoon. RULE. "When the Sun is at a proper distance from the Meridian, or on the Prime Vertical, that is, when he bears nearly true East or West, take an Altitude, and note the time by a good-going Watch, or the Chronometer. Take another Altitude nearer Noon, about the limits given in Part 5th, Table XV, and note the time by the same Watch, and find the Interval of Time elapsed between the observations. Correct the lesser Altitude by Table IX. Compute the Latitude in by the Dead Reckoning at the tim ihe lesser Altitude was observed, and also the Sun's Declination, and find his Polar Distance. Then, with the true Altitude, Latitude, and Polar Distance, find the Sun's Outer Hour Angle. If the Ship has been stationary during the Interval, or been sailing due North or South, no correction of the Interval is neces- sary. But if she has made Easting or Westing, then find the Departure the Ship has made in the Interval, from her true Course and Distance >nade good, and the corresponding Difference of Longitude. Turn this Difference of Longitude made into Time, by Table' XXVI, and add it to the Interval if the Ship has been sailing East, or subtract it from the Interval if she has been sailing West, will give the correct Interval of Time between the observations ; then the Difference between this corrected Interval, and the Sun's Outer Hour Angle, will give the Inner Hour Angle, at the time the greater Altitude was observed, and the result is the Apparent Time from Noon. The Latitude is thence found in exactly the same manner as if only one Altitude had been observed near Noon. When the Lesser Altitude is Observed Before and the Greater Altitude in the Afternoon. The Interval is found in the same manner, and the Outer Hour Angle subtracted from it, gives the Innet Hour Angle, whi®h will be the Apparent T'ime past Noon at the Ship, When Both Altitudes are Observed in the Afternoon* Take an Altitude near Noon, about the limits in Part 5th, Table XV, and another when the Sun is at a Distance from the Meridian, and find his Hour Angle as before, from which subtract the Interval, will give the Inner Hour Angle past Noon. When the Lesser Altitude ts Observed After Noon, and the Greater Altitude Before Noon.* The Interval is found in the same manner, and the Outer Hour Angle subtracted from it, gives the Inner Hour Angle, which will be the Apparent Time from Noon, A. M., at the Ship. Hence it is easy to ascertain at once whether the observations have been made on the same, or on opposite •sides of the Meridian, by comparing the Outer Hour Angle with the Interval of time between the obser- vations. If the Interval bo less, they must have been taken on the same side, that is, both in the fore- noon or both in the afternoon. If greater, they must have been taken on opposite sides of the Meridian, that H, one Altitude has been taken in the forenoon and the other in the afternoon. * When both Altitudes are observed in the Afternoon, or the Greater Altitude before Noonj and the Lesser Alti- tude after Noon, the difference of Long, in time made in t,he interval, should be added to themterval, if the course "lae been Westerly, or subtracted from the interval, if the uourse has been Easterlv. FINDING THE LATITUDE BY TWO ALTITUDES OF THE SUN. »7 ExampUs of Finding the Latitude by two Altitudes of the Sun, ( Usually called Double Altitudes.) EXAMPLE 1 April 1st, 1854, the Latitude Id was 86* 48' N., and the Long. 60* W. by Dead Reckoning. In the morning, at 7b I8ni per Watch, the Sun's Observed Altitude was 20° 10'. Ship* then sailed on a True S. E. course, going 9 kaot* an hour, until llh SOm per Watch, when another Altitude of the Sun was observed to be 67° 28' S. Required the Latitude of the Ship at the time of the last Altitude, and at Noon. Observed Altitude L. Limb 20 10 Corr. Table IX Add 9 Time of Lesser Altitude rime of Greater Alt. . . H. H. 7 28 Decl. in Table X 4*32 N 11 30 Cor.Ln.60°W.,T.XI,Add 4 4 2 Corr. Decl. Noon 4 86 4 True Altitude 20 19 Interval of T. by watch Latitude 36 48 Log. 0.09R61 Rate of Sailing 9 k's Cor.4h32'beforeN. Sub. P. Distance 85 28 Log. 0.00136 Distance SaUed 36 m. Corr. DecL at 7h 28m,. . "432 M Sum 142 85 90 i Sum -, 71 18 Log. 4.50598 . Polar Distance. 86°28' True Altitude 20 19 Difference 50 59 Log. 4.89040 Course S. E. 36 m., Dep. 26.5, D. Long. 32' in time. Oh 2m 88 Add Outer HoiH- Angle 4h 31m 41s = 9.49425 Interval of Time by Watch 4 2 Correct Interval 4 4 8 Inner H. Angle, Correct Interval of Time. ,< 4h 4m Ss AM.. 27m 338 Log. 7.555 Part Ist Lat 36i* N; DecL 4^° N Log . 0.481 Part 2d. Corr. in Pa^ 4th Add 0° 37'=- Log. 8.036 Table XV. Greater Altitude 57 28 Meridian Altitude 58° 6' S. Coui-se S. E., Dist. in 27 min. 4 miles gives D. Lat to Noon 0* 8' & Corr. Table IX 11 Latitude at 27m before Noon 36 20 N True Central Altitude. . . 58° 16''S. Dist. . Latitude at Noon 86° 17' N From 90' Zen. Dist 31 44' N. Corr. Decl. Noor* 4 36 N. The Watch in this case was 2m 278 fast at time of Greater Altitude Latitude 36° 2u' N. at 27 minutes before Nooa EXAMPLE 2. 16th March, 1854, In Latitude 44* 42' Ji, and Long. 50° W. by Dead Reckoning. In the morning at 9h 10m pei Watch, the Sun's Observed Altitude w.ns 25° 8'. Ship then sailed ©n a True W. S. W. course, going 8 knots aa hour, until Ih 11m, per Watch, in the afternoon, when the Sun's Observed Altitude was 42° SO' S. Required tb« Latitude in at the time of the P. M. Altitude, and also at Noou. Observed Altitude L. Limb Corr. Table IX Add 26 8 10 Time of Lesser Altitude Time of Greater Alt Ih ) lira add 12h=. ) H. H. 9 10 13 11 Decl. in Table X 2 9 Corr. Lon. 60° W Sab. 3 S. True Altitude 25 18 Latitude 44 42 Log. 014825 Interval of T. by watch ..41 Polar Distance 92 9 Log. 0.00031 Rate of Sailing 8 ks. Dg^L at 9h A. M. "i Sum 162 9 Sum Distance Bailed. 82m. DecL at Noon 2 6 Corr. 3h before Noon Add. 3 T 90 i Sum 81 5 Log. 4.19038 Altitude 25 18 Difference 66 47 Log. 4.91746 Polar Distance 92° 9' 9.26635 Course W. S. W. 32 miles — Dep. 80 =- D. Lon. in time. Interval of Time by watch . . Correct Interval of Time 3h 58m Ss I Oh ..4 2m 62a Sub 1 Outer Hour Angle 3h 21m 68 Correct Interval S 58 8 Inner Hour Auu;le 37m 28 Log. 7.813 Part Ist Latitude 44^° N. DecL 2° S Log . 0.293 Part 8d. Corr. Part 4th Add 0° 44' Log. 8.106 Table XV. Greatsr Altitude 42 80 Meridian Altitude. 43° 14' S Curr. Table IX Add 11 True Central Altitude. Bub. from 90° Zenith Dist. DecL Noon 2° 6', Corr. for | 37m Sub. 1 f * " °' The W^tch in this case was 83m 588 fast at the time of the Greater Altikod* Latitnde 44° 30' N. at 37 minutes past Nooa Note. In the Ist E.xample, 10 miles of an error in the Latitude, in working the Hour Angle, would produce an error in the time of about 9 seconds, and which does not affect the Corr. for Altitude. In the 2d Example, 10 miles of at error in tlie Latitude, in working the Hour Angle, would pro^> '-« • 5 error cf ii ♦•conds in the time from Noon, and ^n error of only 1' 80" in the Correction for Altitude 48° 25' S. Course W. S. W. 5 miles since Noon D. Lat 0' 2' Latitude at 87m past Noon 44 80 Latitude in at Noon 44° 82' S 46' 2 35' N. 5 S. i'S NAUTICAL ASTRONOMY. FINDING THE LATITUDE BY TWO ALTITUDES OF THE SUN, (Usually called Double Altitudes.) EXAMPLE S. Nov. 80th, 1864, Ship oflf Cape Horn, in Latitude 66° S., Long. 80° W., by the Dead Reckoning. In the after noon, at Oh 36m 523, per Watch, the Observed Altitude of the Suu was 54° 49' N. Ship then sailed on a True N W by W. Course, going 10 knots an hour, until 4h 47m 41 sec, by the same Watch, when the Sun's Observed Alti- tode was 26° 38'. Required the Latitude at the time of the Greater Altitude, and at Nooa • / H. M. a , Lesser Altitude Observed.. 26 88 Time of Lesser Alt. | ^ d7 a.1 Sun's Decl. Nov. 30, 2140 8 Corr. Table IX. Add 10 by Watch J 4 4< 41 Cor. Ln. 80° W. Tab. XI Add 2 True Altitude 26 48 Time of Greater Alt. 86 62 pgcl. at Noon 21 42 a Latitude by Dead Reck 65 38 Log. 0.24835 Interval Time by W. 4 10 49 Cor. for 4h 47m past Noon Add 2 Polar Distance _^i? W- 0.03202 ^iij 4J hours Decl. Time of Lesser Alt. 2T~44 S Sum 150 42 Rate of Sailing 10 knots 90 ^ Sum Ts 21 Log. 4.40297 Distance Sailed. . . .42 miles. Polar Distance 68°16' Difference "48 33 Log. 4.87479 •Outer Hour Angle 4h~55m4'l8 -= 9.55813 Course N. W. by W. 42 miles ) . ,. ^ kaa r.u a ,o Correct Interval. 4 16 1 Dep. 35 = D Lon. = 63. . . f" '"««• Add Oh 4m 128 Time past Noon 40ra 40s Log. 7.895 Part 1st Inte'-^al of Time by Watch 4 10 49 Lat. 56° S., DeeL 22° S Log . 0.268 Pait 2d. Correct Interval of Time. 4h 16m Is Corr. Part 4th Add 0° 50' = Log. 8.163 Table XV. Greater Alt Observed. . 64 49 Merid. Alt 65° 39' N. Course N. W. by W. 7 miles, since Noon, gives =- D. Lat. 0* 4' Ccrr. Table IX- Add 11 Latitude in at 41m past Noon 56° 62 S. True Altitude 55° 60' N. Latitude in at Noon 55° 66' S Zenith Distance 34° 10' S. And the Watch in this case was 3m 488 slow, at the time of the Greater Al* Decl. at Noon ._21 42 S. Latitude 65° 52' S. at Oh 41m past Noon. EXAMPLE 4 August lOth, 1864, Ship off the Cape of Good Hope, in Latitude 38° 20' S., and Long. 20° 10' E. by the Dead Reckoning. At lib 28m in the forenoon, the Sun's Observed Altitude was 36° 2' N. Ship then sailed due East, going 8 faiotj, until 4h 21m 298 in the afternoon, when the Sun's Observed Altitude was 10° 8'. Required the Latitude in at the time of the A. M. Altitude, and also at Noon. Lesser Altitude Observed... 10° 8 Timeof Great Alt K , „„ ^ Decl Aug. 10th 16'37'N Corr. Table IX Add 7_ by Watch p i /» u q^^^ 20° E. Long.. ..Add 1 True Altitude 10 15 Tiraeof Lesser Alt [ jg .^^ ^g Declination Noon UsT Lat Dead Reckoning 38 20 Log. 0.10546 4h 21m 298 add 12h ^ " Corr. for 4h 21m Sub. 8 Polar Distance 105 35 Log. 0.01627 Interval Time by W. 4 53 29 Decl. Time of Lesser Alt.* 16 85 Sum 154 IJO Say 5 hours. 90 \ Sum 77 "6 Log. 4.34934 ^^^e of Sailing.. . . ^_8 p^lar Distance lOe^S^ Altlude 10 15 Distance sailed 40 miles. Difference 66 50 L og. 4.96349 Course True East 40 miles ■= D. Lon. 61' in time Oh Sm 24a Sut Outrtr Hour Angle 4h 11m 29s = 9.434^ Interval of Time by Watch 4 68 29 Cor ect Interval 4 50 5 Correct Interval of Time 4h fiOm 58 Time before Noon 88m 36s Log. 7.851 Part Ist ) rp ui vir Lat 38iS.,Decl. 16i N Log. 0271^ Part 3d \ ^'^'"'^^ ^^ • Corr. Part 4th Add 0° 46' Log. 8.122 Greater Altitude Observed. 35 2 Ship's Course having been due East she is on the name Parallsl Meridian Altitude ~Z^'~^' N. of Latitude at Noon, 38' 23 Corr. Table IX Add 1 1 True Altitude 35° 59' N Zenith Distance 64° IS. In this case the Watch was 6m 868 fast at the time of the Greater Altituae Decl. Noon 16 88 N. liatitude 38° 23^ S. at llh 21m 248 in the forenoon. Note. — In Example 8d, the Lesser Altitude having been observed on the Prime Vertical, an error in the Latitad# does not affect the Hour Aiiirle. In Example 4th, an error of 10' in the Latitude would produce an error of 29 hpc. in working tne Hour Auffle bnl vhich has little or no effect on the correction for Altitude I FINDING THE LATITUDE BY THE SUN 99 FINDING THE LATITUDE BY TWO ALTITUDES OF THE SUN QUESTIONS FOR EXERCISE. Question \st. — October 20th, 1854. Ship becalmed in Latitude 50* 9' N., and Longitude 30* W by Dead Reckoning. In the afternoon at Oh. 34m., per watch, the Sun's observed Altitude, Lower Limb, was 29° 5' S., and at 2h. 46m. it was 19° 54'. Required the time from Noon, when the greater Altitude waa observed, and the Latitude in. Answer. — The time from Noon, when the greater Altitude was observed, is Oh. 28m. 46s., and the Latitude in at that time was 50° 3' N. Ques. 2d. — February 25th, 1854. In Latitude 51° 2' N., Longitude 45* W., by Dead Reckoning. In the afternoon, at Oh. 33m., the Altitude of the Sun's Lower Limb was 28° 53' S. Ship then sailed to the East- ward 20 miles, and at 2h. 43m. P. M., it was 19° 44'. Required the error of the Watch, and the Latitude at the time of the greater Altitude. Ans. — The time from Noon, when the greater Altitude was observed, was Oh. 40m. lis Watch was tra. lis. slow, and the Latitude in 51° 17' N. Ques. 3d. — January 6th, 1854. In Latitude 58° 25' S., and Longitude 138' E., (at Noon, by Dead Reck- oning.) At llh. 2m., A. M., per watch, the Altitude of the Sun's Lower Limb was 52° 13' N. Shipthsa sailed on a S. S. W. i W. Course, (true,) going 8 knots an hour until 4h. 50m. P. M., when his Altitude was 28° 10'. Required the correct time from Noon, when the greater Altitude was observed, the Latitude in at tSiat time, and the Latitude at Noon, brought on by the Dead Reckoning. Ans. — The time from Noon, when the greater Altitude was observed, was Ih. Im. 58s. A. M. Latitude in at that, time 58° 30' S. The Difference of Latitude made to Noon was 7' S., and the Latitude in at Noon was 58° 37' S. {In this case, at the time of the lesser Altitudej the Sun was on the Prime Vertical.) Ques. 4th. — August 30th, 1854. In Latitude 12° 43' S., and Longitude 93° W., Dead Reckoning, at llh. 45m. 12s., A. M., the observed Altitude of the Sun's Lower Limb was 67° 44' N. Ship sailed S. W. by W., going 4 knots an hour, until Ih. 15m. 12s., P. M., (both times being noted by the same watch,) when the Altitude was 62° 0'. Required the time from Noon, when the greater Altitude was observed, and the Latitude in. Atis. — The time from Noon was Oh. 20m. 22s., A. M., and the Latitude observed at that time was 12° 32' S. Note. — In Low Latitudes, the Lesser Altitude may be taken much nearer to Noon than in High Latitudes; because there the Sun's motion is much quicker, and the Time is more correctly found in Low Latitudes • but in all cases the Greater Altitude should be observed as near to Noon as the limits required in Part 6th, Table XV Should there happen to be a very great difference between the Latitude so found, and that by the Dead Reckoning at the lime of the greater Altitude, the Latitude used in finding the Outer Hour Angle must bo corrected accordingly, and the case worked over again, and the Inner Hour Angle found anew, which will .{ire the correct Latitude. In the above Examples the height of the eye is taken at 16 or 18 feet above the Sea Iflvei. 100 NAUTIUAL ASTRONOMY. TO FIND THE -.ATITUDE FROM THE SUN'S CHANGE OF > LTITUUE. This Table contains the Sun's Change of Altitude in One Minute of Time for every Degree of Lmtitud* When on the Prime Vertical, Lat. Change of Alt. L.u. Change of Alt. L..t. Change of Alt. Lilt. Change of Alt. Lat. Change of Alt. Lat. Change of Alt. Lat. Change of Alt. Lat. Change of All. Lat. Change of Alt. O 1 / // 15. O 11 14.44 O 21 14. o 31 / // 12.52 o 41 11.20 O 51 / // 9.27 o 61 7.16 O 71 1 II 4.53 81 / II 2 22 2 16. 12 14.41 22 13.54 32 12.44 42 11.10 52 9.15 62 7. 2 72 4.38 82 2. 6| 8 14.68 13 14.37 23 13.48 33 12.35 43 10.59 63 9. 2 63 6.48 73 4.23 83 1.50 4^ 14.68 14 14.34 24 13.42 34 12.26 44| 10.48 64 8.49 64 6.34 74 4. 8 84 1.34 5 14.57 15 14 80 25 13.36 36 12.17 45 10.37 55 8.36 66 6.20 76 3.53 85 1.18 6 14.56 16 14.26 26 13.29 36 12. 8 46 10.26 56 8.23 66 6. 6 76 3.38 86 1. 2 7 14.64 17 14.21 27 13.22 37 11.59 47 10.15 67 8.10 67 5.52 77 3.23 87 0.46 8 14.51 18 14.16 28 13.15 38 11.60 48 10. 8 58 7.67 68 5.38 78 3. 8 88 0.30 9 14.4'.» 19 14.11 29 13. 8 39 11.40 49 9.51 59 7.44 69 6.24 79 2.52 89 0.15 10 14.46 20 14. 6 30 13. 40 11.30 50 9 . 39 60 7.30 70 5. 9 80 2.36 90 0. When the Sun, or any other heavenly body, is on the Prime Vertical, that is, when it bears true East or iVcst, its change of Altitude is then greatest. If its change of Altitude in one minute of time be then measured with a Sextant, to the nearest second, the Latitude corresponding to it will be found in the abova Table This method depends entirely upon the accuracy with which the change of Altitude is measured, and cannot be much depended on, even in High Latitudes, where the change of Altitude in one minute of time, between any two degrees, differ the most. It is merely given here to illustrate the subject. The Table itself, however, will be found useful when we want to know the change of Altitude of any heavenly body when bearing East or West ; for instance, in observing Altitudes for Time, it may be used as a check on the difference of the observed Altitudes in a given time, and which should agree with the change of Altitude in one minute of time given in the abov© Table, according to the Latitude of the place of observation. But as the heavenly bodies only pass the Prime Vertical above the horizon when the Latitude of the place and the Declination of the body are of the same name, (as in the case of the Sun in the Summer time | the change of Altitude will be slower when they are of contrary names, and in this case the quickest change will take place when the Altitude is from 5° to 10° above the horizon, but there are always som* one or other of the heavenly bodies on the Prime VerticaL which may be observed. To find the Latitude from the Change of the Sun^s Altitude tn One Minute of Time. RULE. Observe with a Sextant an Altitude of the Sun, when he bears true East or West, and note the full mmntc oy th» Watch. Three minutes afterwards, observe another Altitude, at that exact time Divide the Difference of th» Observed Altitudes by the number of minutes ehipsed, will give the Change of Altitude in 1 minnte of time, with ^hich enter the above Table, opposite to which will stand the Latitude required. EXAMPLE 1. The Sun's Change of Altitude in 1 minute, and his tearing East (passing tlie Meridian to the Southward) given. But neither the Declination nor the Latitude by account known. Required the Latitude in. T.by Watch. . 5h 20m. 1st Alt.. 14° 17' 40" do. do. . . 5 23 2d Alt.. 14 52 10 3 m. )34' 30"Diff.of Alt. Bun's Change of Alt in 1 minute. 11' 30" Which corresponds to Lat . . 40° 0' N. in the Table. EXAMPLE 2. Required to find the Latitude by the Sun's Change ot Altitude in 1 minute of time, when on the Prime Ver tical, having passed the Meridian to the North of th» Obsei'ver. T. by Watch. . 5h.4m. Ist Alt.. 21* 6' 20' do. do. .. 5 7 2d Alt. 20 37 2 3 3m )28' 67" Dilf. of Al»' Sun's Change of Alt in 1 minute. 9' 39" Which corresponds to Lat. .60" O' S. b the Table. i FINDING THE LATITUDE BY THE MERIDIAN ALTITUDE 'CF- TUE MOON' 101 The Latitude may be found from the Meridian Altitude of the Mooi>, upon the same pniclple an tbat by the Sun. But as the Moon's Declination changes very rapidly, we must know the exact Grvsehwich data at which the Observation is made, in order to correct her Declination to that date. The Moon's Declination is given in the large Nautical Almanacs for every hour of the day at Greenwich and her change of Declination in seconds for every 10 minutes between the hours, so that the Correction can easily be computed. In the small Almanacs, it is only given for every Noon and Midnight at Greenwich, and we take the proportional part of hpr change iu Declination, corresponding to the hours and minutes past the nearest Noon or Midnight, or enter Table XXIII with the Diff. in 12h at the side, and the tiiHe past Noon or Mid- night at the top, and take out the Correction. But if the Longitude of the Ship be not known, the correct peclination cannot be computed, consequently the Latitude cannot be found by tlie Moon. Ships, however, which carry good Chronometers, have their Longitude always tolerably correct ; hence, the Latitude found by the Moon, in that case, can be depended on, and is sufficiently near the truth for all practical purposes. The Moon being nearer the Earth than any other heavenly body, her place in the heavens is greatly affected by Parallax ; that is, she always appears below her true place in the heavens, by the amount of her Parallax in Altitude. This Correction is given in Table XXV, (and which includes the correction for the Refraction of the Atmosphere), and is always additive to the Apparent Altitude. The Moon's Semi-diameter and Horizontal Parallax is given in the Nautical Ainianac tor every Noon and Midnight at Greenwich, and are generally taken out for the nearest Noon or Midnight corresponding to the Greenwich date of the Observation. When the Moon is in the Zenith, she is nearer to the observer than when'm the Horizon, by the amount of the Earth's Semi-diameter; hence, her Diameter is augmented, or appears 16" larger than when in the Horizon. This Correction is given in Table VII, but is seldom used in the practice of finding the Latitude at Sea. The first thing ri*quired to be done is to find at what time the Moon passes the Meridian of Greenwich, in the Nautical Almanac, on the day before the Sea Date, and correct it to the time she passes the Merid- ian of the Ship ; because, as the Moon is constantly advancing to the Eastward in the Heavens, she will pass any Meridian to the Eastward of Greenwich sooner in the day, or a Meridian to the Westward later in the day, by a certain number of minutes. Therefore, in West Longitude we take out the Meridian passage on that and the following day, but in East Longitude, on that and the preceding day, and take their difference, which is tne daily variation of the Moon's passing the Meridian. Enter Table XXII with the daily variation at the top, and the Longitude of the Ship in the side column, and at the angle of meet- ing will be the number of minutes required, which must be added to the time of her Meridian passage on the day before the Sea Date, if the Longitude be West, or subtracted, if East, will give the Mean Time oi her passing the Meridian of the Ship. This correction may also be found by adding 2 minutes of time for every 15° of Longitude which the Ship is to the Westward of Greenwich, to the Mean Time of her passing the Meridian of Greenwich (by th<< Nautical Almanac), or subtracting the same when the Longitude is East, will give the Mean Time of tier passage at the Ship. Here it may be remarked, that as the Watch is generally regulated to Apparent Time at Ship, and is referred to in ascertaining the time to begin the observation, these two times may differ as much as 16 minutes sometimes, and the observation is frequently lost ; that is, the Moon has passed the Meridian before the observation has been begun. To prevent this happening, take out the Equation of Time given in the Nautical Almanac, and apply it to the Mean Time of passing the Meridian at the Ship the contrary way to what is directed in the precept at the head of the column for Apparent Time, and the result is the Apparent Time of her passing the Meridian at the Ship. Then if the Watch be regulated to Apparent '•'ime at the Ship, it will show the exact time at which the Moon will pass the Meridian, because all the ieavenly bodies pass the Meridian at Apparent Time. i Having thus found the Mean Time of the Moon's Meridian passage at the Ship, as directed above ' 2. To Find the Greenwich Date, Turn the Ship's Longitude into Time by Table XXVI, and add it to the above time, if the Longitude be West, or subtract it if the Longitude^ be East. The Sum or Difference will be the time at Greenwich (usually called the Greenwich Date) when the Moon passes the Meridian of the Ship. But should the lum exceed 24 hours, subtract 24 hours from it, and add one day to the Greenwich Date. On the other hand, when the Longitude is subtractive, and greater than the time of Passing the Meridian, add 24 hours to the latter, for the purpose of subtraction^ and take one day from the Greenwich Date. 3. To Correct the Semi-diameter and Horizontal Parallax From the Nautical Almanac take out the Moon's Semi-diamSter and Horizontal Parallax for the nearest Noon or Midnight corresponding to this Greenwich Date, and correct them if required by Table XXIV, and to the Moon's Semi-diameter add her augmentation found in Table VII. (But this is seldom necessary.) 4. To Find the Apparent Altitude. Add the Difference between the Moon's Semi-diameter and the Dip of the Horizon found in Table V to the Observed Altitude of her Lower Limb, or siil)tract their Sum if the Upper Limb be observed, will gire the Moon's Apparent Central Altitude. (See remarks on taking A.ltitudes at page 71.) 102 NiUTICAL ASTRONOMY. 5, To Find the Moon^s Tru* Altitv.de. Enter Table XXV with the Moon's Horizontal Parallax at the top, and her Apparent Altitude at tb« •ide, and take out the Correction for her Parallax in Altitude, and which ij always additive to her Apparent Altitude. 6. To Correct the Declination by the Large Nautical Almanac To correct the Moon's Declination, taken from the large Nautical Almanac, take out the Declination fo- the day and hour corresponding to the Greenwich Date. And when there are odd minutes, take out th« Diff. of Declination in 10 minutes, found in the side column opposite, and wnich is expressed in seconds and hundred parts of a second ; and when the hundredths are more than 6u, call the seconds one more, but if less, throw them away. Multiply the seconds by the odd minutes, and strike off the right hand figure ; then divide by 60, will give the Correction in minutes and seconds. If the Declination is increasing, add this Correction, but if it be decreasing, subtract it. 7. To Correct the Declination by the Small Nautical Almanac. To Correct the Moon's Declination taken from the small Nautical Almanac, take out the Declination for the nearest Noon or Midnight, if the Greenwich Date be exactly at Noon or Midnight; but if not, take it| out for the nearest Noon or Midnight preceding, and the nearest Noon or Midnight following, the Green- wich Date, and take their difference, which will be that for 12 hours. Enter Table XXIII with the difference for 12 hours at the side, and the hour from Noon or Midnight atj the top, and take out the Correction. If there are odd minutes, enter the right hand side of the table with I the odd minutes at the top and the difference for 12 hours at the side, and take out the Correction. Add\ the Sum of these Corrections to the Declination at the preceding Noon or Midnight, if the Declination ir] increasing, but subtract it if decreasing, will give the Moon's correct Declination at the time of the obser vation. But when the Declination, taken from the Nautical Almanac, for the preceding Hour or the Noon or Mid- 1 night, is decreasing, and the correction subtractive exceeds it, the difference is the Declination of a contrarr^\ name ff 8. To Find the Latitude Thus having the Moon's Correct Altitude, and her Correct Declination, the Latitude is found by thai same rule as for the Sun's Meridian Altitude. That is: Subtract the True Altitude from 90°, will g\y^\ the Zenith Distance of a contrary name to the Moon's Bearing. Place the Correct Declination under it. Then if they are both North or both South, their Sum is the Latitude of that name ; but if one be Nortbj and the other South, their difference is the Latitude of the same name as the greater of the two EXAMPLE 1 Jul J' 12th, 1854, Sea Time, in the Longitude of 75* W., the Meridian Altitude of the Moon's Lower Limb wa« j •bse'-ved to be 40° 85' S. Height of the eye 18 feet Required the Latitude of the Ship. July 12th is July 11th, Astronomical Time. Moon's Men Passage, July 11th, .13h 58m On the following day, July I'ith 14 56 Long. 75° W., and daily variation 58m b Table XXII. Gives the Correction to be added Oh 12m To the Meridian Passage, July 11th .13 58 Mean Time of the Men Passage at Ship. . .14h 10m Long. 75° W. in time Add 5 Greenwich Date, July 11th 19h 10m Less 12h, gives the time past Midnight. . . . 7h 10m Moon's Decliuatiou at Midnight, July Uth.. 21* 21' S. Moon's Declination at Noon, July 12th 19 9 S Diff. of DecUnation in 12 hours 2 Time from Midnight 7h 10m in Table XXIU-Corr. 12' and the ' j- .Sub. 1" 18' Declination at Midnight decreasitig 21 21 S. Correct Declination at time of Observation 20° 3' S Mean Time of Mer. Pass, at Ship. . . .14h 10ra| Equa. of Time N. A. applied con. way Sub. 6 App. Time by Watch of Merid. Pass.. 14h 5n»| Or at 2h 5m in the morning. Moon's Hor. Pari, at Mid. July 1 1th 60' 0" Observed Altitude Moon's L. Limb 40° 35' &| Semid. at Midnight 16' ) Dip of the Horizon 4' \ Moon's Apparent Altitude 40° 47' Co.T. for Alt. in Table XXV.. Add 44 Moon's True Central Altitude 41° 31' Sj 90 Zenith Distance.^ 48° 29' N I Correct Declination 20 3 S | Latitude in '"8° 2«' S i Add Diff. 12 FINDI> G THE LATITUDE BY THE MERIDIAN ALT ITUDE OF THE MOON. \Q» EXAMPLE 2. April 26th, 1864, Sea Time, in the Longitude of 80* East, the Meridian Altitude of the Moon't Upper Limb wm •keerred to be 67* 36' N. Height of the eye 21 feet Required the Latitude of the Ship. April 25th is April 24th, Astronomical Time. Mean Time ot passing the Mer. at Ship. . 22h SSm Moon's Mer. Passage April 24th, 22h 4Sm Equa. of Time, N. A., applied contr'y way -Add 2 • Long. 80* E., which, at the rate of ) ^^^ jq App. Time of the Merid. passage 22h 86m 2m to every 1** — Corr )"" J Legs 12 Mean Time of the Mer. Pass, at Ship 22h 83m ^pp. time by Wat«h of the Mer. passage. . lOh 36m A. M. Long. 80* K in time Sub. 5 ao Greenwich Date, April 24th 17h 13m - Moon's Por. Pari at Midnight, April 24th 6T 0" Lees 12h Time past Midnight at Greenwich "^13 Moon's Obs. Altitude Upper Limb 67* 86' ». Semid Midnight... 16 31 s^^^j^^g^^^^^ ^ Moon's DecL Midnight, April 24th, 0° 61' S. ^'P of <^'^« Horizon. 4 28 J Moon's DecL Noon, April 25th _2 2'N. App. Altitude 67" 16' Diff of DecL in 12 hours 2° 63' ^orr. for Altitude, Table XXV Add 22_ And time fi-om Midnight 6hl3m in Table Un>,"T^ ^°"°'' "^'"^ ^^"*'^^ '^^'^'"*^* ol' ^J ^■ XXnLCorr. ^Suh.l 15 90^_0^ Declination at Midnight decreasing 51 S. Zenith Distance 22" 22' S Correct DecL at the time of GUervation 0° 24' N. Correct Declination • <> ^* ^ Latitude in 21" 68' S • This Correction is found by adding' 2 minutes of Time for every 15* of Longitude which the Ship is to the West- ward of Greenwich, to the time of her passnge in the Nautical Almanac, or subtracting the same in East Longituda, will gfive the Mean Time of her passage at the Ship. Correction of the Declination {used in the above Examples), taken from thf large Nautical Almanac EXAMPLE 1. Decl.,N. A., July 11, 19h.20" 4' 44" S. Diflf: 10m 110".83 DecL Decreasing. ., .Sub. 1 60 10m. Correct Declination 20" 2' 64" S. 60)110.0 Correction for 10 minutes 1' 50" EXAMPLE 2. DecL April 24, 17h 0" 21' 8" N. Diff. 10m 144 60 DecL Increasing . . . Add 8 8 13 Correct Declination 0° 24' U" N. ~~60) 188.5 Correction for 10 minutes 8' 8" QUESTIONS FOR EXERCISK Question 1. — April 6th, 1854, Sea Time, in Longitude 80° 44' W., the Meridian Altitude of the Moon's Upp«r Limb was 76° 15 S. Height of the eye 18 feet Required the Latitude of the Ship. iltwwer.— Latitude in 40" 58' N. Quextion 2. — April 2d, 1864, Sea Time, the Observed Altitude of the Moon's Lower Limb was 64° 39' S. in Lo» gitude 60" W. Required the Latitude ia .4n«u»*r.— Latitude b 54" 31' N. Question 8.— April 13th, 1864, Sea Time, the Observed Altitude of the Moon's Upper Limb wa« 80° 20' &. m Longitude Po° W, Required the Latitude ia. Antft^ — latitude in 64° 18' N. 104 NAUTICAL ASTRONOMY. TO FIND THE LATITUDE BY THE MERIDIAN ALTITUDE OF A PLANET. The Latitude may be found from the Meridian Altitude of the Planets upon the same principle as that fcy the Sun and Moon. Their Declinations are given in the Nautical Almanac for the Noon at Greenwich, for every day of th« month throughout the year. When their Declinations change slowly, they may be taken out for the Noon of the day at once by inspec- tion. But when there is a considerable change in their Declinations between the Noon of one day and the next, we must correct the Declination to the Greenwich time of Observation, in a similar nianner as is done in the case of the Moon, except that their Meridian Passage is taken from the Nautical Almanac and used without being corrected, as the Mean Time of their passing the Meridian at Greenwich, is near enough for general practice at Sea. But to find the Apparent Time, or the Actual Time, they do pass the Meridian by the watch, (regulated to Apparent Time at Ship), the Equation of Time must be applied to the time of passage taken from the Nautical Almanac, the contrary way to what is directed in the precept at the head of the column for Equa tion of Time, in the same manner as it is done in the case of the Moon, so as the Observation may not be iost in consequence of being too late in beginning it. To Find the Planets tn the Heavens when on the Meridian. RULE. 1. Fmd at what time a Planet will pass the Meridian in the Nautical Almanac, select one in preference which will be on the Meridian at twilight, because then the Horizon is distinctly visible ; or even when the Sun is several degrees above the Horizon, some of them may be observed, though invisible to the nakea eye, and they are found as follows : Apply the Equation of Time, as before directed, to the Mean Time of their passage in the N. A., will ijive the Apparent Time of their passage at the Ship, and the Watch must be previously regulated to Apparent Time, or its error known. 2. Subtract the Latitude by Dead Reckoning from 90°, and the remainder will be the Co-Latitude. Take oat the Declination oi that Planet from the Nautical Almanac, which passes the Meridian at the proposed time. Then if the Co-Latitude and its Declination are of the same name, take their sum, but if of con- trary names, take their difference, for the Meridian Altitude of the Planet. Now put this Computed Altitude on the Arch of the Sextant, and if in the day time, screw in the Inverting Telescope, (otherwise use the Direct one), and look towards the South point of the Horizon when the Latitude is North, and towards the North point of the Horizon when the Latitude is South, and the Planet will be distinctly seen, through the Telescope, on or near it. But when the Sum of the Co-Latitude and Declination exceed 90°, it must be subtracted from 180°, and the Planet must be looked for in the North point of Uie Horizon, in North Latitude, and in the South point •f the Horizon in South Latitude. Bring the Planet in contact with the Horizon, and when it attains its greatest Altitude, read off the Arch, and find the Latitude as follows : To Compute the Latitude from the Meridian Altitude of a Planet. RULE Subtract the Sum of the Refraction and Dip, found in Tables IV and V, from the Observed Altituoe, will give the True Altitude, which, subtracted from 90°, gives the Zenith Distance of the contrary name to the Planet's Bearing. Take from the N. A. the Declination, and correct it if required. Then, if th«» Zenith Distance and Declination are of the same name, their Sum, but if of contrary names, their Differ' tnu. u the Latitude of the same name as the reatrr of the two FINDING THK LATITUDE BY THK PLANETS 106 TO COMPUTE THE MERIDIAN ALTITUDE OF THE PLANETS. Pro. for 2h...Sub. 2' Dec Jan. 1st, 1 8° 6 ' Cor. Dec... T3^~~3' S, EXAMPLE 1. January 2d, 1 864. Sea Time. Required the Apparent Ttofl, and the Altitude at which the planet VeuuB will pass the Meridian. Ship off the Cape of Good Hope, in Latitude 84° 0' S, and Longitude 18° O' K II Pas. N.A., Jan. l8t,Sh. 15m. M. Time at Greenwich. Eqa. of Time,. .Sub. 4 H. Pass, at Ship 3h.llm. App. Time P. M. M. Pas, N.A.. Jan.l8t, 3h. 15m. Dec., N'n, Jan.lst, 13° 5' S. Loii.l8° E. in T, Sub._l__12 do. Jan. 2d^240 S. iQaeenwich Date. . . 2h. 3m. Change in 24h.. 25' Lat. of Ship.. . . .34°T'X ^ Cor. Lat 66^' S. Dec. Venus 1£_3 S. €ompu. Alt 69° 3' of Venus at 8h. 11m. P. M. Put this Altitude on the Sextant and look towards the North point of the horizon, (the Latitude being South.) \ EXAMPLE 3, April 14th, 1854. Sea Time. Required the Apparent rime, and tiie Altitude at which the planet Jupiter will pass the Meridian. Ship on the Equator, in Longitude ■25° West M. Pas.N.A.,Ap.l3th,18L24ui. M.Time at Greenwich. Equ. of Time. .Sub. 1 M. Pass, at Ship, . . 'a8L23ra, or 6L23m. A. M by "Watch. M. Pass. April 13. . .18h.24m. Dec, April 13th, 21° 7' S. Lon.25°W. inT.,Add J_40 do. April 14th, 21 6 S. Greenwich Date, . , 20h. 4nx Change of Dec.24h.—1 ' Pro. for 20h . Sub.— 1 Lat of Ship 0° 0' Co-Lat, 90° 0' Dec, Ap.13, 21° T Add Dec of Jupiter 21 6 S . Cor. Dec 21° 6' 111° 6' Subtract from 180 Computed Altitude 68 °54' of Jupiter at6h.23'A3I, Put this Altitude on the Sextant and look towards the South point of the horizon, (because the Declination is SouUl) EXAMPLE 2. June 1th, 1854. Sea Time. Required the Apparent Time, and the Altitude at which tne planet Mars wiD pass the Meridian. In Latitude 40° 20 N, and Lonir' tude 75° West M. Pas. June 6th, N.A.,6h. 2m. M. Time at Greenwiob Equa. of Time....Add 2 M. Pass, at Ship 6h. 4m. App. Time, P. M. M.Pass. N.A.,June 6th, 6h. 2m. Dec, June 6th, 7* 26' N. Lon. 76° W. in T, A dd 5 do. June 7th,7 13 Greenwich Date. . . llh. 2m. Change in 24h.. . 12' Lat of Ship 40 °~2b' N, Pro. for llh.. SubTT' _90 Dec, June 6, . . 7 ° 26' N. Co-Latitude 49° 40' N. Cor .Dec,. . . . 7° 20' N Dec of Mars, ... 7 20 N. Computed Alt. . 67° 0' of Mars at 6h.4m. P. M. Put this Altitude on the Sextant and look towards th« South point of the horizon, (the Latitude being North.) EXAMPLE 4. Feb. 2d, 1854. Sea Time Required the Apparent Time, and the Altitude at which the planet Saturn wiU pass the Meridian in Latitude 30° 20' N- and Lomritude 76° 30' W. ^ M. Pass. Feb. 1st. , 6L 46m. M. Time at Greenwich. Equa. of Time.. Sub. 14 Mer. Pass, at Ship. . . 6h. 82m. App. Time, P. M. M. Pass. Feb. 1st 6h 46m. DecNA., Fcl»t. 17° 4' N Lon. 76° 30' W. in T.J 6 do. Feb. 2d. 17 4 N Greenwich Date. . . llh. 62 m. No Cor. for Dec. required Lat of Ship 30° 20' N. 90 ,59' .17 40' N 4 N, Co-Latitude . . . Dec of Saturn, Computed Alt. 76° 44' of Saturn at 6L 82m. P M. Put this Altitude on the Sextant and look towards the South point of the horizon, (because the Lat is North.) To find the Latitude from the Meridian Altitude of the Planets. EXAMPLE 1. . Jaa 2d, 1864, Sea Time. The observed Altitude •f the planet Venus was 69' 7'N. in Longitude 18° East Required the Latitude. Observed Altitude of Venus 69° 7'N. Dip 4. Ref. Sub . . 4 IVue Altitude 69° 3' N. Zenith Distance 20° 67' S. Declination 13 3 S. LaUtude 34° O' S, EXAMPLE 3. April 14th, 1864. Sea Time. The observea Altitude of Jupiter was 68° 68' S., in Longitude 26° West Required the Latitude Observed Altitude of Jupiter 68° 68' S. Dip 4. Ref. Sub. 4 True Altitude 68° 64' S. Zenith Distance, . 21* 6" N. Declii.ation ^ 6 S. «hip on the Equator "OO^^' EXAMPLE 2. June 7th, 1864. Sea Time The observea Altitude oi Mars was 57° 4' S, b Longitude 76° West Required the Latitude. Observed Altitude of Mars 67* 4' S. Dip 4. Ref. 1 Sub. 6 True Altitude 56° 69' Zenith Distance ~83° ]' JJ Declination ^ 20 N Latitude 40° 21' N EXAMPLE 4. Februaiy 2d, 1854. Sea Time The observed Altitud* of Saturn was 76* 48' S., in Longitude 76* 80' West Required the Latitude. Observed Altitude of Saturn 76° 48' & Dip 4. Ref. Sub. 4 True Altitude 76° 44' g Zenith Distance 13° jq' jf Declination 17 4 N Latitude 80° 20' 5 100 NAUTiLAL ASTRONOMY. TO FIND THE LATITUDE BY THE MERIDIAN ALTITUDE OF A ST.Ul. The Latitude may be found by the Meridian Altitude of a fixed Star, upon the same principle as that hj the Sun. 1. Table XIX contains the Right Ascensions and Declinations of 24 of the principal Fixed Stars, for the year 1854, and the annual variation or change of the same. So that this Table may serve for future years, by simply multiplying the number of years elapsed by the amount of the annual variation, and applying it according to the sign of addition (•+•), or subtraction ( — ), to the Sums taken from the Table. 2. To Find what Star will Pass the Meridian at any Given Hour of the Day, Enter Table XVIII, with the Day of the Month at the top, and follow down the column until we comfr to the required hour, opposite to which will stand the name of the Star. But as the Meridian passages in this Table are only given for every third day, should the day required be between those which are m.arked at the head of the column, take it out for the nearest day preceding the required day, and subtract 4 minutes for each intermediate day. The times shown in this Table are only approximations, but are sulBciently near enough for the purpose of finding the Latitude by the Stars. By the assistance of this Table, the method of finding the Latitude by the Meridian Altitude of a Star will be greatly facilitated ; for when we know at what time, nearly, a Star will pass the Meridian, and the approximate Altitude at that time, there can be no difficulty in making the requisite observation t* determine the Latitude. These opportunities occur frequently in the course of a clear night, and may Ui put in practice by any person otherwise unacquainted with the Stars in the heavens, by reference to tLt Figures at pages 65 and 66, and the following Rules. 3. To Compute the Meridian Altitude of a Star. Subtract the Latitude by Dead Reckoning, (at the proposed time of observation,) from 90', will ?ivp thp ion plement of the Latitude, or Co-Latitude, of the place of observation. Take out the Star's Docl'.nation fronr Table XIX, and correct it for the years elapsed since 1854. Then, if the Co-Latitude and its Derhnation ar» •f the same name, take their Sum, but if of contrary names, take their Difference for the Meridian Altitude and the Star will be found in the South part of the heavens when the Latitude is North, and in th3 Nortu part when the Latitude is South. But when the Sum exceeds 90°, subtract it from 180"" ; the remainde. will be the Altitude, and the Star will be found in the North part of the heavens in North Laticude, and m the South part in South Latitude. (See remarks on taking Altitudes of the Stars, at page 71.) 4. To Find the Star from its Computed Altitude and Meridian Passaf^e. Set the Index of the Quadrant to the Computed Altitude, and at a few minutes before the time of its Meridian passage, direct the sight towards the North or South points of the horizon, as shown above, and the reflected image of the Star will be perceived in the Horizon Glass, upon or near the horizon, which being brought in contact with it, and kept so until it arrives at its greatest, or Meridian Altitude, the angle is then read off the Quadrant. There is not the least danger of mistaking the Star, as no other will have the s^me Meridian Altitudt at that time. (See remarks at page 71.) The best time for observing Altitudes of Stars is at twilight, for then the horizon is distinctly visible, and the Latitude may be found as correctly as by the Sun. But in dark nights an error of from 6 to id miles in the Altitude may be made, in consequence of the obscurity of the horizon. To obviate ttds, the Latitude should be found from an Altitude of a Star to the Southward, and anather to the Northward, and the half Sum of the two Latitudes thus found will be the correct one This will be further explained in the following Examples. FINDING THE LATI'lUUE BV THE STARS. 107 FINOING THE LATITUDE BY THE MERIDIAN ALTITUDE OF A STAR The Meridian passages of the Stars shown in Table XVIII, being for Apparent Astronomical Time which commencea at Noon, one day before the Sea Day begins, and the hours are counted in successioB throughout ; so that when Sea Time is used, the Tables must be entered with the date one day less than Sea Time. If Civil or Common Time is used, the hours less than 12 -w-ill be the time past Noon on that day (and which are the same as Astronomical Time.) But when the hours are greater than 12. subtract 12 hours from it, and it will be the time on the morning of the following Civil Day, and which commences at Mid- night. Because the Noon of the Civil Day, the beginning of the Astronomiaal Day, and the end of th* Sea Day, takes place at the same period of time. To Find the Stars tn the Heavens from their Computed Altitude. EXAMPLE 1 Feb. 28th, 1854, Sea Time, in Latitude by D. R. 40° 10' N. Required what Star will be on the Meridian at twi- light in the evening, and its Computed Altitude. On referring to Table XVTII, and taking the date one day less, or Feb. 27 th, I find the Star Aldebaran will pass at 6h 48m P. M. Latitude by Dead Reck.. 40° 10' N. Subtract from ._90 Co-Latitude 49^~50' N. Declination Table XIX... 16 13 N. Computed Altitude 66° 3'. I now set the Index of the Quadrant to this Altitude, and face towards the South, because the Latitude is North. Flatten down the Sight Vane, and using both eyes, the Star Aldebaran will be distinctly seen upon, or near the Horizon. EXAMPLE 3. March 2l8t, 1854, Civil Time, in Latitude by D. R. 0° 30' S. Required to find a Star b the evening at twi- light. In Table XVIII, I find that the Star Sirius passes the Meridian at 6h 34m P. M. Latitude by Dead Reek- . 0° 30' S. Subtract from 90 Co- Latitude 89° 30' S. Declination, Table XIX.. 16 31 S. 106° 1' Subtract from 180 Computed Altitude 73° 59' towards the South. EXAMPLE 6. May 2d, 1854, Sea Time, in Latitude by D. R. 20° 0' N. Required at what Time and Altitude the Star Vega will pass the Meridian. On the Ist of May, by Table XVIII, Vega passes the Meridian at 15h 59m, or time by Watch at 8h 59m A. M. Latitude by Dead Reck.. 20° 0' N. Subtract from 90 Co-Latitude '70° O' N. Declination, Table XIX. 38 39 N. 108° 39' Subtract from 180 Computed Altitude 71° 21' towards the North. EXAMPLE 2. March 1st, 1854, Sea Time, in Latitude by D. R. 38* 10' N. Required what Star will pass the Meridian at twilight in the morning, and its Computed Altitiide. On referring to Table XVIII, and taking the date one day less, or February 28th, I find that the Star Antares will pass on the 27 tb, at 17h 40m, from which I subtract 4 minutes, gives 17h 3fim, and less 12h gives 6h 36tn, th« time it passes in the morning. Latitude by Dead Reck 38° 10' N. Subtract from 90 Co-Latitude 6T°~50' N. Declination, Table XIX 26 6 S. Computed Altitude 25° 44'. Set the Index ta this Altitude, and face towards South in North Latitudi^ and the Star will be found as before. EXAMPLE 4. March 26th, 1854, Civil Time, in Latil^ido by D. R 30° 25' S. Required to find a Star in the morninff twi light In Table XVIH, I find that the Star Ve^-a passes the Meridian at 18h 20m, on the 24th, from which I subtract 8 minutes, gives 18h 12m, and less 12h gives 6h 12m, ita passage in the morning. Latitude by Dead Reck.. 80° 25' S. Subtract from 90 0_ Co-Latitude. 69° 35' S • Declination, Table XIX.. 38 39 N. Computed Altitude 20° 56' towards the NortL EXAMPLE 6 June 22d, 1854, Sea Time, Ship on or near the Equa- tor. Required at what Time and Altitude the foot Stai of the Southern Cross will pass the Meridian. On the 2 Ist June, by Table XVIII, it passes the Meridian at 6h 21m in the evening. Latitude by Dead Reck.. 0° 0' Co- Latitude 90° 0' Declination, Table XIX.. 62 17 S. Computed Altitude 27° 43' towards the South. because the Declination is South. The Crost alvayt pasxes the Meridian erect. Note. — When the Star's Declination Subtractive is ereater than V the observer. ttie Co-Latitude, the Star is not above the flor 108 NAUTICAL ASTRONOMY TO FIND THE LATITUDE BY THE MERIDIAN ALTITUDE OF A STAR. I RULE. FroK: tie Observed Altitude of the Star, subtract the Dip of the Horizon, and the Refraction, taken from Tablet IV and V ; or the Sum of these Corrections may be taken out at once from Table XX, by entering it with the height of the eye at the top, and the Observed Altitude at the side, and tlie Angle of meeting is the required CorreetioB, iJways subtractive from the Observed Altitude, will give the Star's True Altitude, which, subtracted from 90°, gives the Zenith Distance. Then, if the Star bears South, mark the Zenith North, and if the Star beai-s North, mark the Zenith Distance South. Take out the Star's Declination from Table XIX, and correct it for the years elapsed since 1854, as before shown, and mark it North or South. Then, if the Zenith Distance and Declination are of the same name, take their Sum, but if they are of contrarj Dames, take their Difference, for the Latitude, of the same name as the greater of the two. EXAMPLE L Feb. 28th, 1854, Sea Time, at 5h 48m P. M., the Ob- served Altitude of the Star Aldebaran was 66° 7' S. Required the Latitude. #'8 Observed Altitude 66° 7' S. Corn, Table XX ) g^j^ ^ Height of the eye 16 feet j True Altitude 66° 8' 90 Zenith Distance 23° 67' N. Declinatiou, Table XIX 16 1.3 N. Latitude Observed 40° 10' N. at 5h 48m P. M. EXAMPLE 8. March 2l8t, 1854, Civil Time, at 6h 34m P. M., the Ob- served Altitude of the Star Sirius was 74* 8' S. Height af eye 18 feet Required the Latitude. #'8 Observed Altitude 74° 8' S. Corr, Table XX. Suk 4_ True Altitude .78° 59' Zenith Distance 16* 1' N. Declination, Table XIX 16 ^ S. Latitude Observed ."o^ 80' S. at 6h 84m P. M. EXAMPLE 8. Mar 2d. 1864, Sea Time, at 3h 59m A. M., the Ob- served Altitude of the Star Vega was 7 1° 26' N Height of the eye 20 feet. Required the Latitude. #'8 Observed Altitude 71* 26' N. Corr, Table XX 5 True Altitude .71° 21' Zenith Distance '. .18° 39' S. Declination, Table XIX 88 39 N. Latitude Obeer^ed .2*^° O'N.at 8h 6»m A. M. I EXAMPLE 2. I March Ist, 1854, Sea Time, at 6h 36m A. M., the Ob- served Altitude of the Star Antares was 25° 60' S. Re- quired the Latitude. #'s Observed Altitude 25° 50' S. Corr., Table XX (16 feet) Sub^ 6_ True Altitude .26° U' 90 Zeuith Distance 64° 16' N. Dechnation, Table XIX 26 6 S. Latitude Observed .38° 10' N. at 5h 36m A. M EXAMPLE 4. March 26th, 1864, Civil Time, at 6h 12m A. M., th« Observed Altitude of the Star Vega was 21° 2' N. Height of the eye 16 feet Required the Latitude #'s Observed Altitude 21° 2' N Corr., Table XX Sub. _6 True Altitude 20° 66' Zenith Distance 69° 4' S. Declination, Table XIX ._88_ 89 N. Latitude Obsei-ved 80' 25^ S. at 6h l«m A. M. EXAMPLE 6. June 22d, 1864, Sea Time, at 6b 21m P. M., the Ob- served Alt. of the foot Star of the Southern Cross was 27° 50' S. Height of eye 25 feet Required the Latitude. #'8 Observed Altitude 27* 50' S. Corr., Table XX 7_ True Altitude .27* 43' Zenith Distance .62° 17' N. Declination, Table XIX.. . . .62° 1 7' S Ship on the Equator 0° 0' at 6h 21m P. M. QUESTIONS FOR EXERCISE. Qitest. lit. — April 2d, 1864, Sea Time, what Star, and at what Time and Altitude will it pass the Meridian aboot Twilight in the evening, in Latitude 42° 25' N Antieer. — The Star Castor, April 1st, at 6h 43m, and its Meridian Altitude is 79° 47' S. QiuKt. 2d. — April 2d, 1854, Sea Time, the Meridian Altitude of the Star Castor was observed to be 79* 4»' 8, »• lb 48m in the evening. Height of the eye 16 feet Required the Latitude. Anmctr. — Latitude Observed 42° 27' N. FlNDiNG THh LATITUDE BY THE STARS. 109 TO FIND THE LATITUDE BY THE MERIDIAN ALTITUDE OF THE POLE STAR RULE. Ck»rrect the Observed Altitude for Dip and Refraction by Table XX- Take out the Pole Star's Declination from Table XIX, and correct it for the years elapsed since 1854, and subtract its Declination from 90°, will give iti Polar Distance ; then the Sum of the true Altitude and Polar Distance is the Latitude, when observed below tb« Pole, but the Difference between them is the Latitude when observed above it. To find when the Pole Star passes the Meridian below the Pole, we add half the interval of its revolution, which is llh 58m., to the time at which it passes the Meridian above the Pole, found in Table XVIII, and subtract 24 hours from it, if it exceeds that quantity EXAMPLE 1. July 2d, 1854, Sea Time. At 6h. 20m. in the even- ing the Meridian Altitude of the Pole Star (below the Pole) was oberved to be 43° 10'. Height of the eye, 20 feet Required the Latitude. Bv Table XVIII, it passes the Merid. at 18h. 26m. A.M. Obs. Alt Pole m . 43° 10' Dec, Table XIX, 88° 32' N. Cor., Tab. XX.. Sub. 5 90 00 True Alt . , . 43° 5' Polar Dist .. 1° 28' Polar Dist. . liAtitude iu. .Add.l 28 44° 83' N, EXAMPLE 2. July 2l8t, 1854. Sea Time. At 5h. 9m. in the morn- ing, the Meridian Altitude of the Pole Star (above th« Pole) was observed to be 32° 28'. Height of the eye, 16 feet Required the Latitude. By Table XVIII, it passes the Merid. at 17h. 9m. A. M. Obs. Alt Pole #. . 32° 28' Dec, Table XIX, 88° 32' N Cor., Tab. XX, Sub^ 6 True Alt 32° 23' Polar Dist. . , Polar Dist. . Sub. 1 28 Latitude in 30° 55' N. 90 00 1°28' To Find the Latitude by the Pole Star at any Hour in the Night. RULE. To the Sim's Right Ascension, taken from Table XIII, add the time since Noon, when the Altitude was observed Tlie Sum (rejecting 24 hours if it exceeds that quantity) will be the Right Ascension of the Meridian, with which enter Table XXI, and take out the correction, to be applied as dire<{ted in that Table, and the Sum, or remainder, will be the required Latitude. Remarks on Finding the Latitude by the North Pole Star. This method of finding the Latitude by the Pole Star is only an approximation, and may deviate two ot three miles from the truth ; but from its extreme simplicity it is well adapted to the practice of Seamen, ii cases where an error of a mile or two can be of oo material consequence. If the time at the Ship is not known, that is, if the Watch has not been previously regulated at the time of the Altitude, the Apparent Time at Ship may be deduced from the Greenwich Time by Chronometer, by turning the Ship's Longitude into time, and subtracting it in ^Vest Longitude, or adding it in East, will give the Mean Time at Ship, and the Equation of Time applied the contrary way will give the Apparent Time at Ship. In general, a few minutes error in the time will not affect the result. To Find the North Pole Star Itself The North Pole Star is easily found in the heavens, from the direction of the two lirgo Stars in the coulter of the Plough, that well-known constellation, which is perpetually wheeling round the Pole of the heavens, so that these two Stars, or Pointers, always point to the North Pole Star a« a centre. The Pole Star itself is only a dim object, of the second or third magnitude, and it requires good silvered mirrors in the Quadrant to obtain a tolerable observation, and the glasses should be wiped clean bo*ore. the observation u •wimmenced. (See remarks on taking Altitudes of the Stars, page 71.) EXAMPLE. 1, January 2l8t 1864. Sea Time. At 8h. 25m. P. M. the Altitude of the Polar Star was observed to be 38° 16'. Height of the eye, 18 feet Required the Latitude. #'8 Obs. Alt 38° 15' App. Time at Ship. .8h. 25m. Cor, Tab. XX, Sub^ 5 Sun's R.A. Jan.20th, 20 9 True Alt .38° 10' R. A. Meridian 28h. 34m. Cor, Ta.XXl,Sub.0 53 Less 24 Latitude in "^"7° 17' N. R.A. of Meridian. . 4h. 34m. EXAMPLE 2. February 11th, 1854. Sea Time. The Greenwich Time by Chronometer being 21h. 30m., in Longitude 60° 0' W., an Altitude of the Pole Star was observed to 1x8 32° 45'. Height of the eye, 20 feet Required the Lat- itude. #'s Obs. Alt... 32° 45' Cor., Tab. XX, Sub. 6 True Alt 32° 39' Cor.,Ta.XXI,Addl 18 Latitude in Gr. T. byChro 21 h. 30m. Lon.60° W. in T.,Sub. 4 M. Time at Ship. . . 17h. 80m. Eq. of Time. . Sub. 16 . 83° 67' 1^. App. Time at Ship.l7h. 15m. Sun'a RA. Feb.l0tb .21 86 38h.61m. Less 24h. R. A of Meridian. 14h. 61m. no NAUTICAL ASTRONOM\, FINDING THE LATITUDE BY THE MERIDIAN ALTITUDE OF TWO STARfc In the Northern Hemisphere. 'in the night time, as before observed, errors in the observed Altitudes of the Stars are liable to be made in consequence of the obscurity of the horizon. But if we observe one Altitude of a Star to the Southward and another to the Northward, (md although they may both be in error, the one error will balance the other; that is, the Latitude found from the Alti- tude of both Stars may be erroneous, but if we add the two Latitudes together, their half Sum will be th« correct Latitude. EXAMPLE, March I9th, 1854. Sea Time. At lOh. 10m. P. M., Apparent Time at Ship, the Meridian Altitude of the Stai Regains was observed to be 64° 1' South, and at the same time the Altitude of the Pole Star was 37° 67' North Height of the eye. 18 feet Required the Latitude. Obs. Alt. of the # Regulus. 64° 7' S. Cor., Table XX Sub.. 6 True Alt 64° 2' Zenith Dist 25" Dec, Table XIX 12 58' N. _41'N. "39' N. Lat. by Regulus 38° The Altitudes were ^\m. too great. Obs. Alt. Pole * 37° 57' Cor., Table XX Sub. 5 True Alt 37° 52' Cor., Table XXI Add 1 2 Lat. by Pole Star 38° App. Time at Ship lOh. 10m. Sun's R. A., March 18th,. 23L 51 34h 24 Im Lat. by Regulus 38 54' 39 R. A. of the Meridian. , lOh. Im. Sum ) 77° 33^ Correct Latitude 38° 46' 30" N, at 10b. 10m. P. M In the Southern Hemisphere. There are no Stars near the Pole which will answer the same purpose as the North Pole Star. Cons* • quently, we have to observe~the Meridian Altitudes of two Stars in opposite directions, but which do not pass the Meridian at the same period of time. (The difference of their Meridian passages is shown in Table XVIII.) So that the Altitude of the first Star observed must be reduced to the place where the second was observed, by applying the difference of Latitude the Ship has made in that interval of time, by the following simple Rule, and which is founded on the fact that when a Ship sails South she rises all the Stars in that direction, that is, their Meridian Altitudes increase^ while those to the North gradually smk, that is, their Meridian Altitudes decrease ; and in sailing North, those to the North are raised, while the Stars to the South decline, by a quantity equal to the Difference of Latitude she has made in a given time. RULE Enter the Traverse Table with the Course and Distance made good in the interval between the times of the StAn passing the Meridian, and take out the Difference of Latitude made in that mterval, and apply it as follows : Ship saihng South. Ship sailing NortL . , . , r ,, n J. c^. i_ J i to the Southward, Add Difference of Latitude to it Altitude of the first Star observed, ^ ^ ^^^ Northward, Sub. do. do. from it , . , , , ^ , , , J i to the Noithward, Add do. do. Altitude of the first btar observed, -j ^ ^j^^ Southward, Sub do do. to it from it EXAMPLE, March 18th, 1854. Sea Time. At 12h. 50m. the Meridian Altitude of the foot Star of the Southeru Cross Wiu observed to be 61° 47' South. Ship's Course S. W., (true,) going 10 knots ; and at Ih. 48m. the Meridian Altitude of Spica was 66° 35' North. Required the Latitude. Mer Pass, of the Cross 12h. 50m. First Obs Alt. S. Cross 61° 47' S. do. of Spica 13 48ra. Cor. for Diff Lat Add. 7 Interval of time Oh. 58m. Cor., Table XX Sub 61' 54' 5 Couise S.W., Dist 1 (^ gives D.Lat 7' S. True Alt 61° 49 ' Zenith Dist 28° 11' N. Dec, Table XIX 62 17 S. Latitude by the S. Cross. , 34° 6' S. do. by Spica 33 54 S. Ob.s. Alt of Spica 66' 35' N- Cor., Table XX Sub. 5 True Alt 66° 30 ' Zenith Dist 23° 30' S Dec, Table XIX 10 24 S Latitude by Spica 83° 64' S. Sum )68° 0' Correct Latitude 34° O' S. at Ih. 48m. or time of the last Altituae The Altitudes in this case have been too great by 6 minutes, and which is generally the case in observing Altitudes of Stars in the night time FINDING THE LATITUDE BY THE STARS. Ill FINDING THE LATITUDE BY AN ALTITUDE OF A STAR OUT OP* THE MERIDIAN. • The Latitude may be found by an Altitude of a Star out of the Meridian, upon the same principle bm the method given at page 94, by the Sun, using the Star's Distance from the Meridian in the room of the time from Noon. And it is necessary, in this case, (in obtaining a correct result), to compute the Star's Meridian passage, in the room of taking it from Table XVIII. ,» RULK Turn the Ship's Longitude into Time, and add it in West Longitude, or subtract in East, to or from the Apparent Time of Observation, reckoned from the preceding Noon, -will give the Greenwich Time, nearly. Or the Greenwieb Time may be found at once from the Chronometer. Take out the Sun's Right Ascension from the Nautical Almanac; one day less than the Sea Date, and correct it to the Greenwich Time by multiplying the difference for 1 hour by the time fmm Greenwich Noon, and add it to the Right Ascension at tlae preceding Noon, (because it is always increasing.) Take out the Star's Right Ascension, and correct it, if required. Then subtract the Sun's Right Ascen- aioD from the Star's Right Ascension, (increasing the latter by 24 hours, if necessary, for the purpose of subtraction), and the I'emaiuder will be the correct Apparent Time of the Star's Meridian passage. The limits of the time from the Meridian passage of the Star, are the same as the time from Noon by the Sun, given in Part 5. Table XV, and the rules for using the Tables are the same as given at page 94. If the time of the Altitude of the Star is noted by the Watch, it must be previously regulated, or its error on Apparent Time knowTi. The Chronometer may be used to find the Apparent Time of Observation, as at page 94. EXAMPLE 1 Feb, 28th, 1854, Sea Time, in Latitude by Dead Reck- •ning, about 40° 10' N., and Longitude 60° W., at 6h 5m P. M.. tlie Oliserved Altitude of the Star Aldebaran was 65° 43' S. ; height of the eve 18 feet; the Watch show- ing the correct Apparent Time. Required the Latitude. 1 30 .22h 42m 298 28 27 32 Feb. 27th, the Sun's R. A., N. A. Noon 22h 40m 598 Time of Obs. 6h 6m Change of R. A. in ' Long. 60° W._4_0 Ih = 9s X 10h = Green. Date. lOh 5m 0's Correct R. A. #'8 R. A. 4h 27 ra 328 ) Increased by 24h J' #Aldebaran's Mer. Passage 5h 45m 38 Apparent Time of Observation 6 5 Time past the Meridian # Past the Meridian 19m 57s Part 1st Lat 40° N., #8 Decl. 16s Part •2d..' Corr. for Altitude... Add 0° 24' Log #'s Ohs. Altitude .65 43 Meridian Altitude "66^ 7' S. Corr.. Table XX... Sub. 5 J Log. . . .' f ^°^- 19m 578 7.279 0.559 }■ Table XV. 7.838 True Altitude 66° 2' Zenith Distance .23° 58' N. Declination 16 13 N. Latitude in 40° 11' N. at 6h 5m P. M. EXAMPLE 2. March 22d 1864, Sea Time, in Latitude by Dead Reck ouing about 38° N., aud Longitude 46° W., an Altitude of the Star Sirius was observed to be 34° 36' S., when the Greenwich Time by Chro. was 9h 3m P. M : height of the eye 18 feet. Required the Latitude. March 21st, Sun's R. Ascen., N. A., at Noon Oh 2m 58 G. Time of Obs. 9h 3m Os Corr. for G. ) „ , „, Long. 45° W. ) 3 ^ ^^ T. 9h X 9s f __^_J^ ^ ^^^^^- • • ) ©'8 Cor.R.A. Oh 3m 268 Mer. T. at Ship. 6h 3m Os #'8 R. Ascen. 6 38 43 ' Equa of Time . Sub. 7 15 ^-g Mer. Pas. 6h 35m PTa App. T. at Ship.5h 55m 458 or T. of Obs. 5 55 45 Time before passing the Meridian 39m 32i Time before Mer. Pass. 39m328>T /,n„^' Part 1st.. f ^^- ^-^^^ Lat. 38° N.; #'s Deci 'iVr's.".*.'. [ j ).Tab. XV Part 3d \ ^°^- ^'-^^^ Corr. for Altitude Add 0° 47' Log. 8.187. #'8 Observed Altitude.. . .34 36 Meridian Altitude 35° 23' S. Corr., Table XX Sub 5^ True Altitude 36° 18' Zenith Distance 54° 42' N. #'s Decl., Table XLX... 16 31 S. Latitude in 38° 11' N. at 5h 56m P.M. The same Examples as above, worked with the Star's Meridian Passage taken from Table XVIII. Mer. Passage of Sirius, March 21, Table XVIII. 6b 84m Time of Observation 5 66 Time before passing the Meridian sg^i Time before Mer. 38m Part 1st... Log. 7,8361 Lat. 38° N.,Decl. 16i° S. Part Sd.Log. 0.266 ^ Table XV Mer. Passage of Aldebaran, Feb. 27, Tab. XVIII 6h 48m Time of Observation 6 5 Time past the Meridian 17^ # past tiie Mer. 17m Part 1st.. .Log. 7.138^ Ut. 40° N., #'s Decl. 16° N. . K . , Part 2d \ ^"S- 0.5o9 iTable XV. Corr. for Altitude 17' Log. 7.697 „ Hence an error of nearly 3 minutes of time m the Meridian Passage of Aldebaran would produM m WTor of 7' in tlie Correction for Altitude. And an error of Im 32s of time in tlie Meridian Passage of Sirius would produce an error of 3' in t^ •vorrectioD '-^r Altitude. Corr. for Altitude 44' .Log. 8.102 J 112 NAUTICAL ASTRONOMY. FINDING THE LATITUDE BY AN ALTITUDE OF A STAR OUT OF THE MERIDIAN. As the Parts 2d and 3d of Table XV are only calculated for objects whose Declinations do not exceed 8** : therefore, when the Declination of a Star exceeds that quantity, the Logarithm of the Latitude and Declination must be computed as follows : . I RULE. Compute the Meridian Altitude of the body by adding ita Declination to the Co-Latitude, when they .are of m mM name, or taking their Difference when of contrary names. Enter Table XXVIII with the Latitude and th« Declination, (as if they were Half Sums), and take out three figures of these Logarithms with their Indices. Entei Table XXVll, with the Meridian Altitude, (as a Latitude), and take out its Logarithm in like manner, and write under it the constant Logarithm 0.301. Add these four Logarithms together, and their Sv,m (rejecting lO's in the Index), will be the Logarithm of the Latitude and Declination required. EXAMPLE L Required the Logarithm for Lat 48° 80' N, and the Decimation of the Star Castor 32° 12' N. Latitude 48° Subtract from,.. 90 Co-Lat.'*ude.... AV #'8 DecL 32 Mer. Altitude 30' N. as a half Sum . _0 (Table XXVIII.) 80' N. 12 N. as a half Sum. , .Log. 4.821 .Log. 4.927 ^Log. 0.552 73° 42' S. as a Lat., Table XXVII. . Constant ,'. Log. 0.301 Required Computed Log. 0.601 EXAMPLE 3. March 81 st, 1854. Sea Time, Latitude by Dead Reck- oning 48' 30' N., Long. 30° W., the Observed Altitude of the Star Castor was 73° 1' S., and the Greenwich Time by Chronometer 8h 28m 49^ Required the Latitude. Oh 34m 488 1 16 Oh 36m 48 7 2 5 17 6h 49m 13s 6 24 IS March 30th. Sun's R A., in N. A., Noon. . G. T. by Chro. 8h 28m 49s Cor. for G. T. ) Lon. 80° W. I 2 8ih X 98... f "° *™«- • i ©'8 Cor. R. A.. M. T. at Ship. 6h 28m 49s #'s R Ascen.. . Equa... iSub. ^_86_^-8Mer. Pass... App. Time. . . 6h 24m 138 App. T. of Obs.. Time before the Meridian Passage 26m Os #'s Diet fm. the Mer. 25m, Part 1st, Tab. XV. Log. 7.478 Lat 48° 80' N.. DecL 82* 12' N., Computed. .Log. 0.601 Part 4th, Corr. for Altitude Add 0° 41' Log. 8.074 ♦'s Observed Altitude 78 1 Meridian Altitude 73° 42' S. Corr, Table XX Sub^ ^ True Altitude 78° 88' Zenith Distance ..16° 22' N. #'8 Declination 83 12 N. Latitude Obs^-rved .48° 84' N. At 6h 24m ISs P. M. EXAMPLE 6. Required the Logarithm for Latitude 10' O' S, and the Declination of the Star Dubhe 62' 82' N. Latitude 10° 0' S. as a half Sum Log. 4.998 Sub. fm. 90 Co- Lat.. 80° 0' S. Decl 62 32 N. as a half Sum Log. 4.664 Mflr. Alt"T7'~28' 8. as a Latitude Log. 0.021 Constant Log. 0.301 Required Computed Log. 9.97 9 EXAMPLE 2. Required the Log. for Lat 88° 25' S., and the Decl of the foot Star of the Cross 62° 17' S. Latitude 88° 26' S. as a half Sum., Sub. from, , . ,. 90 (Table XXVII L) Co-Latitude.... 51° 35' S. DecL 6 2 17 S. as a half Sum. . "113° 62' Subtract from.. .180 Mer. Altitude.. 66° .Log. 4.894 .Log. 4.661 8' S. as a Lat, Table ) ^ - „„. XXVII [Log. 0.39» Constant Log. 0.301 Required Computed Log. 0.25f» EXAMPLE 4. Jan. 2d, 1854, Sea Time, in Lat by Dead Reckoning 88° 25' S., Long. 30° E., the Obs. Alt of the foot Star of the Southern Cross was 65° 41' S., and the Greenwich Time by Chro. 16h 2m 40s. Required the Latitude. 2 56h Jan. 1st, Sun's R. A., in N. A., Noon 18h 47m 6> G. T. by Chro.. 16h 2m 408 Cor. for G. T. ) Long. 30° E. ) 2 ^^^ >' ll8= f mtime....) ©'sCor. R. A..18h 50m 2a M.T. at Ship. .18h 2m 408 #"8 R. A.. .. 1 -- - - 61 r2hl8m3l8>86 Equa. of T.Sub. App. Time 18 81 17h 58m 498 +24h - . . ) ^ #'8 Mer. Pass.. 17h 28m 2»« App. T. of Obs. l7 6 8 49 Time past the Meridian 80m 20s #'s Dist from the Mer. 80m 208, Part Ist / Log. 7.641 Lat 88° 26' S., DecL 62' ) Computed Log. 0.265 17 o ) . Corr. for Altitude Add 0' 27' Log. 7.896 #'8 Obs. Altitude .66 41 Meridian Altitude 66* 8' S. Corr., Table XX Sub. 4 Table XV. True Altitude .66' 4 ' Zenith Distance 23° 66' N. Declination 62 17 8. Latitude Observed 88° 21' 8. EXAMPLE 6. Required the Log. tor Latitude 40' 27' 8, and th« Declination of the Star Canopus 52° 37' S. Latitude 40' 27' S. as a half Sum Log. 4.881 Sub. fm.. 90 Co-Lat...."49°"¥3' S. Decl 52 37 8. as a half Sum Log. 4.7 8« 102° 10' Sub. fm., 180 Mer. Alt. 77° 50' S. as a Latitude Log. 0.676 Constant Log. 0.301 Reoiiired Computed Log. 0.64) nNDING THE LATITUDE BY THE STARS ll» FINDING THE LATITUDE BY TWO STARS, ONE OF THEM OUT OF THE MERIDIAN. As before observed, a single Altitude of a Star for Latitude, on a dark night at Sea. is always of a doubt ful character, in consequence of the obscurity of the horizon* but which may be remedied byob.servLng twc Btars on opposite sides of the Meridian. But as no two Stars pass the opposite Meridians at the same period of time, the Ship may have changed her place in the interval of their passing, and a correction must be applied to the first Altitude, to reduce it to the place where the second was observed, (an Example of which is given at page 110.) But when we want to find the Latitude at once from the Altitude of two Stars ott opposite sides of the Meridian, we observe the Meridian Altitude of one, and directly afterwardi observe the Altitude of the other, (not on the Meridian,) and note the time by the Watch or the Chronometer, and reduce it to the Meridian, (as in the Examples on the preceding page.) The limits must be the same a» that given in Part 5th, Table XV. February 12th, 1854. Sea Time. In tlie Meridian Altitude of the Star Spica foot Star of the Cross was 66° 10' South GreenwTi Time by Chr..l5h.34m.20a Long. 25° 16' W.in T.. ._\. 41 4 Mean Time at Ship 13h.63m.168. Equa of T., contrary, Sub^ 14 32 pp. Time at Ship 13h. 38m. 448. Mer. Obs. Alt. of # Spica.. 60° 34' N. Cor., Table XX 4 True Alt. 60° 30' Zenith Dist 29° 80' S. Dec Spica 10 24 S. Lat. Oba. by # Spica. . . . 39° 64' S. do by # S. Cross. . J0_ 6' S. Sum ^)80° 0' Correct Latitude .... 40^^' S. EXAMPLE 1. Liititude, by Detvd Reckoning, about 40° 9' S., and Longitude 26° 16' W.,. wafl observed t<> be 60° 34' North, and at the same time the Altitude of th» . Greenwich Time by Chronometer, 16h. 34m. 20s. Required the Lat'tud* Feb. 11th. Sun's R. Asceu., N. A 21h. 39m. 2Ss.. Corr. for Greenwich Time Add 2 20 • Diff. for lh....98. .Green. Time .I5^h. Sun's Correct R. Aseen 21h. 41m. 48s. # Cross R. A. 12h.l8m.3l8.X24h.=36 18 32 135 b_ )T40 *'8 Meridian Passage 14h. 36m. 448. Time of the Observation 1 3 38 44 Cor. 2m.208 Time before Mer. Passage 58m. 08.= Log. 8.202 Lat 40° S., Dec. 62° 17' S., computed Log. 0.274 Cor. for Alt Add 1 ° Obs. Alt # S. Cross 66 Merid. Alt "67' Cor, Table XX Sub. True Alt _67° Zenith Dist 22' Dec, S. Cross 62 Lat by S. Cross 40^ 48' Log. 8.47ft 10 Table XV. "63' S. 4 "49' TPn. r? s. " 6' S. EXAMPLE 2. March 2d, 1864. S?a Time. In Latitude, by Dead Reckoning, about 40* 80' South, and Longitude 76* SC East, (he Meridian Altitude of the Star Sirius was observed to be 66" 14' North, and at the same time the Altitude of the Star Canopus was 77° 36' South. Greenwich Time by Chronometer, 3h. Om. 248. Required the Latitude. March 1st Sun's R. A. in N. A 22h. 48m. SOs Diff. for Ih.. . 9a» Cor. for Greenwich Time Add 27 Green. Time 8h Correct R. ur.llme by Chro Sh. Lon.75° 30' E. in time. 6 Om. 24s. 2 Mean Time at Ship . .. 8h 2m. 248. Equa. of T., contrary, Sub. 12 87 App. Time at Ship. . . 7h. 49m. 47s. Mer. Alt of # Sirius. . 66° 14' N. Cor. Table XX.. Su , 4 True Alt . 66° 10 Zenith Dist . 23° 16 50' S Dec Sirius 31 S. Lat Obs. by Siiius . . 40~ 21' S. do. by Canopus . 40 32 S. Sum i)80° 63' Correct Latitude 40° 26' 80"S. Aseen 22h. #Canopu8 R.A.6h.20m.448.Add 24h.80 do. Mer. Passage 7h. 31m. Time of Oba 7 49 Time before Mer. Passage 48m. 678 Cor. 20 44 .27* .Log, 7.82» 478. 47 (Table .XV.) 18m. Os Log.~7.188 See Example 6th, page 112, of Computing the. Log, 0.641 Correction for Altitude Add 0° 23' Obs. Alt # Canopus 77 36 S. Mw. Alt 77° 69' Cor., Table XX Sub. 4 True Alt 'nVYb' & Zenith Dist ."Tsi^ 6' N. Dec. Canopus 62 37' S. Lat Obs. by Canopus 40° §2' S. ^r^h7v7T^f\ '"' Example ?iven above is not a jr.ood case, as the time from the Meridian passage exceeds the Umito wu r. '• ""*^,''". ^'■'■'"' '" the time will considerably affect the result. ■>."oo«o i-uo umiw .5 of Stars, take the one whose Declination is of a oontrarv name to the Latitude of the nl Altitnde, beca.ise it can be observed farthest from the Meridian, and an error in the time aff When there is a ch f and which has a low [it the least. In this case an error of 1 minute aoe, ., ^. , , , ' . — ■ • •'■ »"" '■•'■i<= affect* n the time would produce an error of 4 minutes in the correction for Altitude ; and on reversing the case, that is, observincr the Cross on the Meridian, and findincr the correction-'for'tJ^ Altitude of Spica, an error of 1 minute in time would produce an error of 3 minuted in the oorr'ection t^'r SttU/ 1)4 NAUTICAL ASTRONOMY. f:nd.ng the latitude by an altitude of the moon out of the meridian. The Latitude may be found by an Altitude of the Moon, taken either before or after she passes th« Meridian, within the limits of Part 5th, Table XV, upon the same principle as that by the Sua and Stars, as follows : RULK To Find the Apparent Time of the Ohservatton. 1. Note the Greenwich Time by Chronometer, when the Altitude was observed. Turn the Ship's Longitude into Time. Subtract in West or add in East Longitude, will give the Mean Time at Ship. Apply the Equation of Time the cmitrary way to what is directed for Apparent Time in the column of the Nautical Almanac, and we have ih« Apparent Time at Ship at whicli the observation was made. To Find the Time of the Moon's Meridian Passage. 2. Take out the Moon's Meridian Passage from the Nautical Almanac, against the day of the month, and correct H by Table XXI I, which will give the Mean Time of her passing the Meridian of the Sflaip. to which apply the Equation of Time the contrary way, as above directed, and the result will be the Apparent Time of her passmg th« Meridian of the Ship. To Find the Moon^s Distance from the Meridian. 3. Now take the difference between the Apparent Time of her passing the Meridian of the Ship and the Apparent Time of the Observation, with which enter Part Ist, Table XV, as a time from Noon, and take out its Logarithm. To Find the Correction for Altitude. 4. Correct the Moon's Declination, taken from the Nautical Almanac, to the Greenwich time of the observation bj the Rules given at page 102, No. 6, with which, and the Latitude by Dead Reckoning, proceed as before to find the Correction, (as in the case of the Sun and Stars,) to be added to the observed Altitude. The Latitude is then found IB the usual way Sometimes the Meridian Altitude of the Moon is lost, in consequeuee of being too late in beginning th« observation. The Latitude may, however, still be obtained as correctly as by the Meridian Altitude, by the abov« miethod. if the Longitude of the Ship can be ascertained within a few miles of the truth. EXAMPLE. June 3d, 1854. Sea Time. Li Latitude, by Dead Reckoning, 49° 25' North, and Longitude 46° "W., the observed Altitude of the Moon's Lower Limb was 56° 29' South, before her Meridian passage, and the Greenwich time by "Chronometer, 7h. 56m. Os. Height of the eye, 24 feet Required the Latitude of the Ship. > 's Dec. Noon, 18" 24' N, June 2d >'b Mer. Pas., June 2d, N.A., 5h. 21m. Green. Time by Chro.. . 7h. 56m. Os. Ali.lnight, 16 19 ' June 3d, ._& 5 Lon. 45° W. in time. . . 8 0_ Change in 12h. 2° 6') Tab.XXII Lon45°W.,D.Varia. 44m. Mn. Time at Ship 4b. 56m. Os. G. T. from Noon, 8h. [• -' T 22' Gives the correction . . . -"T^^s. ^qua. of Time. . . .Add 2 22 in Table XXIII . ) Mer. Pass., June 2d 5h. 21m. App. Time of Obs 4h. 58m. 22s. Dec, Noon. June 2d 18 24 M.TimeofM.Pas.atShip,-^h:26^.-0i:^PP-l'i'-««fM-P^^^- ^ ^^ ^^ 5 's Cor Dec 17° 2'N Equa. of T., contra. . Add 2 22 Moon's Dist from Mer.. Oh. 30m. Os. Log. 7.631 | ,j,^y^ j-y App.TuneofMer Pas...6h. 28m.228. Lat. D.R 49° 25' N., Dec. . 0° 17' N. Log._a367 f Cor.forAit Add 34=- Log. 7.998 Obs. Alt. D 's L. Limb . . . 56 29 S. Mer. Alt 57" 8' ]) 's semid. 16, Dip 5, Add 10 29 App. AIL 67° 13' Cor. for Hor. Par. 55', A.lt. ) 57°, Table XXV,. Add j" " J-s True Alt 57° 42' S. Zenith Distance 32° 18' N. Correct Dec 17 2 N. Lat. Observed 49° 20' N. at 6h. 28m. P. M. QUESTIONS FOR EXERCISE. ituestton. — August 9th, 1854. Sea Time. In Latitude, by Dead Reckoning, about 56* 0' North, Longi tude 75* 30' West, the observed Altitude of the Moon's Upper Limb was 14° 41' South, (about 1 hour paat the Meridian.) The Greenwich Time by Chronometer being, August 8th, 18h. 52m. SOs. (Height of the eye, T^ feet.) Required the Latitude. Answer. — Latitude 56° 10' North. The Apparent Time of observation at Ship was 13h. 45m. 68. The Apparent Time of the Moon's Meridian Passage, 121". 45m. 6s., the Moon was 1 hour past the Meridiaa, mad the Correction for Altitude, 1° 6', and Meridian Altitude 15* 47' South. FINDING THE LATITUDE BY THE PLANETS 115 FINDING THE LATITUDE BY AN ALTITUDE OF A PLANET OUT OF THE MERIDIAN. The Latitude may be found by an Altitude of a Planet out of the Meridian, upon the same principle, And in a similar manner, a« that by the Moon. RULE To Fwd the Apparent Time of Observation. 1. Note the time by Chronometer, ■when the Altitude of the Planet was observed, and from which, dednoe th« Apparent Time of the Observation, aa directed on the preceding page. To Find the Time of the Planet's Passing the Meridian. • 2. Take out the Planet's Meridian Passage from the Nautical Almanac, against the day of the month, as nsual, and apply the Equation of Time the contrary way to what is directed for Apparent Time, in the column of ih» Nautical Almanac, which will give the Apparent Time of its passing the Meridian of the Ship. To Find its Distance from the Meridian. 3. Now take the DiflFerence between the Apparent Time of its passing the Meridian of the Ship, and the Appa- rent Time of the Observation will be the Planet's Distao?" from the Meridian iu time, the Logarithm of which fin«^ in Part Ist, Table XV. ■ To Find the Correction for Altitude. 4. From the Nautical Almanac take out the Planet's Declination, and correct it to the Greenwich Time of th« Observation, in a similar manner as at page 104, with which, and the Latitude by Dead Reckoning, take out th« Logaritlim from Parts 2d or 3d, Table XV. The Sum of these two Logarithms, in Part 4th, gives the Correction for the Altitude required, which is always additive. EXAMPLE 1. Sept 25th, 1854, Sea Time, in Latitude by Dead Reck. 44° 25' N., Longitude by Chronometer 65° W., an Alti- tude of the Planet Jupiter was observed to be 21° 62' S. (before the Mer. Passage), Greenwich Time by Chronome- ter, lOh 34m 16s, R K Height of the eye 18 feet. Re- •quired the Latitude. Sep. 24th, G. T. ),., „. .. Mer. Pass. ) ^v, a oc of Observation \ ^^"^ 24m 16s j^^^.^^^_ J 7h 4m 368 Long. 65° W. in ) ^ ^^ ^ Equa.ofT. Add 8 7 Time. Sub. ) A pp. T. of / Mean T. at Ship.. . 6h 14m I'eT Pass.' \ '^^ ^^™ ^^^ Equa. of Time. Add 8 7 App. T. at Ship.. ...6h 22m 238" Decl. Jupiter. 22° 44' S. A pp. T. of Passage . 7 1 2 43 Time before Mer.. 7. 50m 208 Log. 8.078 ) Table Lat 44° i N., Decl. 22° 44' S Log. 0.156 f XV. Corr. for Altitude Add 0° 69' = Log. 8.234 Oba. Alt. of Jupiter 21 52 Meridian Altitude "22^ 51' S. Corr., Table XX Sub. 6 True Altitude .22° 4 ? Zenith Distance. .67° 15' N. Declination 22 44 S. Latitude in. ii^ir N. at 6h 23m P. M. EXAMPLE 2. Jan. 29th, 1854, Sea Time, in Latitude by Dead Reck- oning, 25° 10' S., Long, by Chronometer 0° 0' 0", an Alt of the Planet Saturn was observed to be 47°9' N., (past the Meridian), Greenwich Time by Chronometer 7h 31ra 38s, and the height of the eye 18 feet Required th^ Latitude. Jan. 28th, G. T.of ) ^, „, „„_^ Mer. Pass. ) ^, , , . Observation. . . \ ^^ ^^"^ ^^^ Saturn. \ ^^ ^"^ 1^" Long, in time ODD Equa. of T... 13 16 Mean T. at Ship. . .7h 81m 388~App. T. of ) TT".- 7" Equa. of Time . Sub . 13 1 6 Passage f ^^ ^^"^ ^' ^^t"Ship°.*^ .°!*!' [ ''^ ^^"^ 228 Decl. Saturn 17° 2' N App Time of Pass. 6h 48m 28 Time past Mer 30m 201 Log. 7.641 ) Tabl* Lat 25° S., Decl. 17° N Log. 0.413 \ XV Corr. for Altitude Add 0° 39' Log. 8.054 Obs. Altitude of Saturn 47 9 N. Meridian Altitude 47^48^ Corr'., Table XX Sub. 5_ True Altitude 47° iF N. Zenith Distance .42° 17' S. Declination 17 2 N. Latitude in .26° 15' S. at 7h 18m P. M Note. — In all the preceding Examples, where the Chronometer is used in deducing the Apparent time at Ship, the Difference of Longitude the Ship has made in the interval between the time the Long'itude by Chronometer was ascer- tained, and the time the Altitude of the body was observed for Latitude, must be applied, by the rules in Middle Lati- tude Sailincr, in order to get as near as possible the correct Longitude of the Ship at the time the Altitude of the body was observed; bearing in mind that for every 1' of error in the Longitude, there will be a corresponding error of 4 ieconds in time in deducing the Apparent Time at Ship from it. In general, when sights for Chronometers are taken, both morning and afternoon, the error in the Ship's Longitude, brought on by the Dead Reckoning, will rarely exceed 6 miles. And it will be perceived that in thus findincr the Latitude from bodies out of the Meridian, the Chronometer renders valuable assistance in finding the Apparent Time at Ship, at the time the Altitude was observed, when it would be diflioult to get it otherwise. ^ Many of the foreg^oing Examples of finding the Latitude from the Meridian Altitude of the Stars, are given for Twi- ight, because the horizon is then distinctly visible, and the observation can be depended on. But it sometimes hap pens that there are no Stars on the Meridian at Twilight. In that case, if an Altitude be observed at Twilight, either before or after it passes the Meridian, and the time noted by Chronometer, the Latitude is found by the preceding rule* •s correctly as if its Meridian Altitude had been observed. In the two last Examples, the Planet Jupiter p>assed th» Meridian after darkness had set in, but his Altitude was obtained in good Twilight, 50 minutes before that time. Saturn had passed tlie Meridian in stroncj Sun-light, and 30 minutes afterwards, or as soon as he became visible, hia Altit;ul« was observed and the Latitude found as above. Il« NAUTICAL ASTROJNOMY. FINDING THE VARIATION OF THE COMPASS BY AN AMPLITUDE An Amplitude means the Distance of any Heavenly body from the True East or West points of th* Horizon at Rising or Setting, and is found by inspection in Table XXXV, by entering it with the Latitude of the Ship at the side, and the Decimation of the body at the top, and at the angle of meeting will b« th« required Amplitude in degrees and minutes, to be called East in the morning and West in the evening, and towards the North or South, according as the Declination of the body is North or South, as the foilowing figure will show • DIAGRAM Of an Amplitude in 45° North Latitude. A Fig. 17. This Figure represents the North Pole of the Heavens elevated above the Horizon equal to the L«iitaac of the place, and the Celestial Eqaator at Right Angles to it. The line drawn perpendicular to the Hori- zon is called the Prime Vertical Circle, and which passes through the East and West points in the centre. The dotted Circles on each side of the Equator are the Sun's Parallels of Declination North and South. The Circles from the Zenith passing through the Sun's place in the Horizon, are called Amplitude Cirole«» and measure the Sun's Amplitude or Distance from the East or West points of the Horizon. Hence, it will appear that the Sun and all the other Heavenly Bodies Rise and Set to the Northward of the East and West points, when their Declinations are North, and that they Rise and Set to the Southward of the East or West points when their Declii»tions are South. EXAMPLE 1. June 21 fit, 1854. Required the Sun's True Amplitude at Rising and Setting, in Latitude 45° N. Answer. — The Sun's Deelination on the 2lBt of June is 23* 28' N., with which and the Latitude 46°, the true Am- plitude is found in Table XXXV, at Rising, to be E. 34° 18' N., and at setting W 34° 18' N, EXAMPLE 3. March 2l8t, 1 854. Required the Sun's True Amplitude Hising and Setting, in Latitude 45° N. Answer. — The Sun being on the Equator, his Declina- tion is 0° ; he therefore Rises and Sets in the East and West poiuts of the Horizon. EXAMPLE 2. December 21st, 1854. Required the Son's True Afl» plitude at Rising and Setting, in Latitude 46* N. Anstoer. — The Sun's Declination on the 2l8t of Dee is 23° 28' S., with which and Latitude 45*. the True Am plitude is found in Table XXXV, at Rising, to be K 8* 18' S., and at Setting, W. 34° 18' S. EXAMPLE 4. Sept 2l8t, 1854. Required the Sun's True Amplitoa* at Rising and Setting, in Latitude 46° N. Answer. — Tlie Sun being on the Equator, his Dechna tion is 0° ; he therefore Rises and Sets in the East and "West points of the Horizon. Note. — All heavenly bodies whose Declinations are 0° 0', Rise in the True East point of the norizon, and Set in the True West point. Hence, when the Sun's or Moon's Declination is 0° 0', that is, wlien they are on the Celestial Eqaa- tor, and their Bearing be taken by an Amplitude Compasa, when Risinp; or Setting, if they bear by Compa.«is Easv at West, there is no Magnetic Variation. But suppose the Sun was observed to Set by Compass W. 12° N., that would h* the amount of Magnetic Variation Westerly. Or, suppose he was observed to Set West 12° S., that would be tb« Knonnt of Magnetic Variation Easterly, and he would rise in the first case E. 12° S., and in the second case, £. 18° N which would furnish the Variation in the same manner. I 1-hVDING THE VARIATION OF THK COMPASS. IP FINDING THE VARIATION OF THE COMPASS BY AN AMI'LlTUDfi,. The manner of observing the bearing of the Sun, or other heavenly body, at rising or belting, by an Amplitude Compass, and other remarks coimected with the observation, will be found at page 81. When the Magnetic Amplitude, or bearing of the body by the Compass, and the True Amplitude, are both on the same side of the East or West points, that is, when they are both North or both South, their difference is the Variation of the Compass. But when one is North and the other South, their Surn is the Variation, and the following Diagram wii) «bow wliether tiie Vn' ion is Easterly or Westerly. DIAGRAM,.. Showing Easterly and Westerly Variation FiQ. 18. BXAMPLE 1. April 2d. 1864. In latitude 88* 30' North, LoDgi- ♦ode 52' West, ibe Sun -was observed to Set by Ccmpass W. 22° N. Required the Variation of the Compass, April 2d, Sun's Declination 4° 55' N. and Lat. 88° 30' N. In Table XXXV, g:ive3 the True Ampli.. .W. 6 2S N. Sun's bearing by Compass at Sotting W. 22 N. Magnetic Variation 15* 87' W. or 1^ points, (nearly,) Westerly. EXAMPLE 2. Oct 8th, 1854. In Latitude 40° South, Longitude 76 West, the Sun was observed to Rise by Compass E. 9 N. Required the Variation of the Compass. Oct 8th, Sun's Declination 6° 52' S. and Lat 40' 0' S In Table XXXV. gives the True Ampli E. 7 Bearing by Compass at Rising R V Magnetic Variation or 1| points Easterly, 61 S N. le'fti'K Taking the Ist Example, and referring it to the abov« Figure, it will be perceivea that both Amplitude* •re to the North of the West Point, their difference is therefore the Variation ; and looking towards the Sun's bearing by the Compass, the true Amplitude is on the left of the Compass bearing ; the variation is, therefore, Westerly. In the 2d Example, (and referring it to the same figure.) one Amplitude is on the North and the other OP the South of the East Point, and their Sum is the variation. And looking towards the bearing of the Sun by Compass, the true Amplitude is to the right of th« Compass bearing; the ■Variation is, therefo.-e, Easterly. And in the 1st Example, if we make the Compass bearing coincide with the North point in the aboTe Figure, the true Amplitude will then be on the West side of the North ; hence it is called Westerly varia- tion. And in the 2d Example, in like ma-^ner, the true Amplitude will be on the East side of the North , tence it is called Easterly variation. In the above Examples the Latitude used is that brought on from Noon by Dead Reckoning,and the Sun's Declination taken out for the nearest Noon, but if greater accuracy is requii-M, the Declination must be cor fected to the time of the observation, by Table XI} but this is seldom necessary at Sea. QUESTIONS FOR EXERCISE Question let. — July 3d, 1854. In Latitude 9' 36' South, the Sun's bearing by Compass at Rising was E. 12° 42' N. Required the Variation. Answer. — The True Amplitude is E. 23* 22' N., and the Variation 10* 40' Westerly. Question 2d. — Sept. 2l8t, 1854. In Latitude 26" 32' North, the Sun's bearing by Compass at Settinc was West 6° 15' South. Required the Variation. Answer. — The True AmpHtude is W. 1* 7' N., and the Variation 7* 22' Easterly. MA NAUTICAL ASTROPiuMY. FINDING THE VARIATION OF THE COMPASS FROM AN AZIMUTH. An Azimuth means an Angle at the Zenith, contained between the Meridian of the Observer and a Oirah *i Altitude passing through the body. DIAGRAM Of an Azimuth in 381° North Latitude. Fig. 19. Ir this Figure the Sun's True Altitude is 25", his Declination 17° South, and the Latitude 38' SO^Nortl ; •fil 'i will be perceived that the Co-Altitude, or the Sun's distance from the Zenith, the Polar Distance, and the Co-Latitude are given, which form the three sides of an Oblique Spherical Triangle, to find the Angle of Azimuth at the Zenith, which is measured on the Horizon by a Circle of Altitude passing through the body, and cutting the Horizon at right angles. The Azimuth Angle in the above Figure is meas- ured from the North point of the Horizon, because the North Pole of the heavens is elevated, and it contains 141° 46' : but for convenience' sake its Supplement is generally used, that is, what it wants of 180°, and is reckoned from the opposite point of the Horizon, because the Sun is South of the observer in North Lati tude, and North of the observer in South Latitude. RULE. Correct the Sun's observed Altitude by Table IX. Correct the Sun's Declination by Table XI, and find his Polar Distance by adding the Declination to 90°, when the Latitude and Declination are of contrary names, or taking tfae difference between it and 90° when they are of the same name. Then add together the Sun's Polar Distance, his True Altitude, and the Latitude. Take half their Sum, and take the difference between the half Sum and the Polar Distance, which call the difference. Enter Table XXVII, and take out the Log. Secant of the Altitude, and also the Log. Secant of the Latituae. Enter Table XXVIII, and take out the Log. Co-Sine of the Half Sum and the Log. Co-Sine of the Difference. Add together these four Logs., and their Sum found iu Table XXIX, will give an angle in time. Turn this into Degreei and Minutes by Table XXVI, which will be the Angle of Azimuth required. To be reckoned from the South in North Latitude, and from the North in South Latitude ; towards the East in the morning, and towards the West im the afternoon. The Magnetic Azimuth having been observed by the Azimuth Compass, as directed at page 81, at the the time of taking the Altitude. Then the difference between the True Azimuth and the Magnetic Azimuth, (both of which being reckoned from the same Meridian,) is the Variation of the Compass when they are on the same side of the Meridian, that is, both East or both West ; but when one is East and the other West, their Sum is the Variation Finding the Variation at Noon. In High Latitudes, where the Sun's Meridian Altitude is low, the variation may be found at Noon, from the Magnetic Azimuth observed. But to do this, it is necessary to have the watch previously regulated to Apparent Time at the Ship, so that the Sun's Azimuth bearing may be observed at the instant the watch shows 12 o'clock ; because the Sun is then True South in North Latitude, and True North in South Latitude And supposing the bearing by the Azimuth Compass to have been South also, there would in that caae'ne no variation. On the other hand, if the bearing by the Azimuth Compass was S, 22* 30' W., then there would be that amount of Magnetic Variation Westerly ; but if the bearing by Azimuth Compasi lad been S. 22* 30' E., then there would be that amount of Magnetic Variation Eatterlv. _ , FINDING THE VARIATION OF THE COMPASS BY AN AZIMbTH. n» EXAMPLE 1. February 2d, 1864, Sea Time, in Latitude 38" 30' N., Longitude 60' W„ the Altitude of the Sun's Lower Lfaak was observed to be 24° 50', and his Miiijnetic Azimuth S. 16° 0' E., at about 9h 30m in the forenoon. Hei{;ht of tk» eye 18 feet Required the Variation of the CompasB. Sun's Declination, February 1st, Table X., 17* Corr. for Lon. 60° W., Table XI, Subt. 3 ) g^j^ CJorr. for Time before Noon, 2h 30m Add 2 Sun's Correct Declination 17° 90 6' S. 1 Observed Altitude Sun's Lower Limb. . 24* 60' Corr., Table IX Add 10 Sun's True Altitude 25* (f Sun's Polar Distance 107° True Altitude 25 Latitude. 38 5' S. 6' 0' Log. Secant 30 Log. Secant Sum ..170° 36' Half Sum 85° 18'. Log. Co-Sine ) Difference 21° 47' Log. Co-Sine ) Table XXVII Table XXVIII 0.04272 0.10646 3.91849 4.9678S Fig. 19, Supplement of the Angle in Time, 2h 32m 578, Table XXIX Log 9.03050 Tamed into space by Table XXVI, gives the True Azimuth S. 88° 14' R Magnetic Azimuth S. 16 0' R Magnetic Variation 22° 14' Wester^. DIAGRAM, Showing Easterly and Westerly Variation. Fig. 20. In the above fi^re, (to the left), both Azimuths are on the same side of the Meridian, and their Differ ence is the Variation Westerly, because the True Azimuth is to the Left of the Magnetic Azimuth. EXAMPLE 2. April 16th, 1864. Sea Time, in Latitude 40° N., Longitude 120° W.. the Observed Altitude of the Sun was 82° ISf Magnetic Azimuth S 57° 22' W., at about 3 P. M. Required the Variation. April 15th, Sun's Declination 9° 46' N, Add 10 Corr., Long. 120° W., Table XI, 7' ) Corr. for 3h past Noon 3 ) ' ' Sun's Correct Declination 9° 65' N. 90 Sun's Polar Distance 80° 6' Sun's Observed Altitude Lower Limb 32* Ifr' Corr., Table IX Add 10 Sun's T^ue Altitude 82*25 Correct Altitude 82 25 Log. Secant / m ,, yxvtt ^■O'^^'^T Latitude 40 Log. Secant P^^'® -^^^^^^.IIS?* Sum 152° 30 Half Sum ~76 Difference 15' 3° 60' •J;;;|g°;|i°^[ Table XXVIII*' ,87600 gpoQg Angle in Time 4h 68m 10s, Table XXIX Log. 9.6648ft Turned into space by Table XXVI, gives the True Azimuth S. 74° «3' W. Magnetic Azimuth S. 67° 22' W. Magnetic Variation 17° 11' Easterly Because on referring to the above figure on the right, we find the True Azimuth is to the Right of the Magneti* Azimuth. IfO NAbl'lLAl. ASTRONOMY. EFFECT OF LOCAL ATTRACTION ON THE SHIP'S COMPASS. This is a very important matter for investigation, and should be attended to at the earliest possilDle oppor- ^tunity, because, in consequence of not knowing that Local Attraction existed on board, many vesseli have been -wrecked from that very cause. There being large quantities of Iron now used in the construction of Ships, besides the quantities which ithey carry to and fro, and stowed in different parts of the vessel as cargo, renders every Ship liable to nave her Compasses deranged by Local Attraction. And the general effect which Iron, s^ituated in th»» lor- ward part of a vessel, has on the Compass, is to draw the North end of the Needle forward in North Lat» 4tude, and the South end of the Needle forward in South Latitude, and which the following Diagram will <^ow- DIAGRAM, %,owing the Effect of Local Attraction. Fig. 21. fflten the Attracting Force is Forward. In the above figure, the dotted line will show the course intended to be steered, which in the one ca*e u 4!ast. But the North end of the Needle being drawn forward from the effect of the Local Attraction, .{Caused by the Iron forward acting on it), the Ship is actually going E. by S. ; and in the other case, •«teering West, the North end of the Needle being drawn forward in like manner, the Ship is actually going "W. by S. Now suppose the Ship to steer North, the North end of the Needle will point in the direction of the dis- turbing force, and which being then on the same line as the Magnetic Meridian, no Local Attraction will •be perceptible. Hence, when tlie Ship's head is at North or South, little or no deviation will be found in the Compass : but when her head is at East or West, or nearly so, the greatest deviation may be expected. The above figure it irawn for North Latitude, but by sub.«tituting South for North, it will answer for South Latitude. In that case, the South end of the Needle is drawn forward from the effect of Local Attraction, and in steering East, in the one case, the Ship would actually be going E. by N. ; and in the other case, steering West *he Ship would actually be going W. by N. When the Attracting Force ts Abaft. We havt .iitherto been considering the case where the Attracting Force is situated forward in the \ew ii*i it someLimes happens that it is situated abaft the Steering Compass, as in the case of some Steamshipa, waere the Steering Apparatus is placed in the forward part of the vessel ; and in this case, on referring to 4he figur* in North Latitude steering East, the North end of the Needle is drawn aft. when the Ship would nctually be going E. by N. Acain, in steering West, the North end of the Needle being drawn aft, the sShip would actually be going W. by N. ^n South Latitude, and supposing the disturbing force to be abaft the Compass, tJeedle is drawn aft, and in steering East the Ship would be going E. by S., and OM\, FINDING THE TIME AT SEA It will be necessary here again to premise that there are three different modes of reckcning Time, vitli respect to the commencement of the day, viz., Civil, Astronomical, and Nautical. The Civil Day, Which is that used by the generality of mankind, begins at Midnight and ends at the Midnight following. It is divided into two equal parts of twelve hours each. The first is marked A. M , signifying before Noon, and the latter P. M., or afternoon. The Astronomical Day Begins 12 hours after the Civil Day, that is, at Noon, or when the Sun's centre is on the Meridian, and ends at the following Noon ; and it is reckoned through the 24 hours, from Noon to Noon ; and what are called the morning hours of the common day are by Astronomers reckoned in succession from 12, or mid- night, to 24 hours. So that 8 o'clock on the morning of June 5th, CivU Time, is by Astronomers called June 4th, at 20 hours. The Nautical, or Sea Day, Commences at Noon, or 12 hours before the Civil Day, and 24 hours before the Astronomical day, and ends at the Noon of the Civil Day, and at the beginning of the Astronomical Day. It fe divided into two parts of 12 hours each; the former being marked P. M. and the latter A. M., so that occurrences whicii hippened, for instance, on Sunday, the 10th, afternoon. Civil Time, are entered in the Log as Monday, the nth, p. M. Hence it appears that the Noon of the Civil Day, the Beginning of the Astronomical Day, and the End of the Nautical Day take place at the same period of time. Time, as inferred from observations of the Sun, is denominated Apparent and Mean Solar Time. Apparent Time, Is that which is immediately derived from the Sun, either from the middle of the times of his Equu* Altitudes, that is at Apparent Noon, or by observing his Altitude at a proper distance from the Meridian Mean, or Uniform Time, Is thai shown by Clocks, or Watches, which keep a constant, uniform time throughout the year. The reason of these two different modes of dividing Time is explained in Figure 4, page 62, and i» jaused by the unequal motion of the Earth in her orbit, combined with the inclination of its axis to the plane of the Ecliptic. The difference between Apparent and Mean Time is called the Equation of Time, and amounts to over 16 minutes sometimes. It is computed for the Noon at Greenwich, and set down on page Ist of the Nautical Almanac, against the day of the month, throughout the year, and the precept at the head of the- joluran shows whether it must be added to or subtracted from Apparent Time, to obtain Mean Time. The Greenwich Date, Or the Mean Time at Greenwich, is referred to, because it is for the Time at this Meridian that the •lements of Astronomical calculations (which are in perpetual change) are given in the Nautical Almanac. The Greenwich Date is therefore always expressed in Mean Time, (unless the contrary i? notified.) and it may be defined as being the time at Greenwich, corresponding to any given time elsewhere, and in lakiiig observations at Sea, the Noon at Greenwich is referred to, in order to find on which side of Greenwu-h Noon the observation has been made Note. — In observing Altitudes for time, the observation should be made when the body is on or near the Prime Vc. tioal, that is, when it bears true East or West ; because then, errors in both the Latitude of the observer and of the- Altitude observed, produce the least effect on the Hour Angle. In geiieral, the change of Altitude should not be less than 6 minutes to 1 minute of time. An error of 1 minute m the Altitude would then produce an error of about 10 seconds in time. In High Latitudes, an error in the Latitude produces a great effect on the Hour Angle. On the other hand, in the Tropics the time can be more correctly determined when the body is at less than an hoar from the Meridian than when at several hours from it in His'h Latitudes. FINDING THE TIME BY THE SUN. VZ6 FINDING THE APPARENT TIME FROM AN ALTITUDE OF THE SUN. This \B one of the most important problems in Nautical Astronomy, and for the solution of which we require to have the Altitude and Polar Distance of the body, and the Latitude of the place of observation, being three sides of an Oblique- Angled Spherical Triangle given, to find the Hour Angle at the Pole, and which is measured on the Celestial Equator, between the Meridian and the Time Circles. DiAORAM of Qn Hour Angle. Latitude and Declination of the Same Name, Fir.. 22. Diagram of an Hour Angle. Latitude and Declination of Contrary Names. Fui. 23. In Figure 22, the Sun is on the Prime Vertical, the Latitude and Declination being of the same name the Declination subtracted from 90°, gives the Polar Distance. ' In Figure 23, the Latitude and Declination being of contrary names, the Declination added to 90*. gives the Polar Distance. ' RULES FOR USING THE TABLES. Ist Add together the Sun's True Altitude, the Polar Distance, and the Latitude of the place of Observation find the Half Sum, and the Difference between the Half Sum and the Sun's True Altitude. ' 2d. To Uie Loe;8. of the Polar Distance, and Latitude found in Table XXVIL add the Logs, of tie Half Sum and Difference found in Table XXVIIL and the Su7n of these four Logs., found in Table XXIX, will give the Sun'i Hour Angle, at the Top of the Page, and which is also the Apparent Time from Noon, when the Altitude is observed in the Afternoon. But when the Altitude is observed in the Forenoon, the Apparent Time from the preeedine Nooa or Midnight, is found at the Bottom of the page. 5 ". EXAMPLE 1. Figure 22. Given the Sun's True Altitude, 37°, Polar Distance, 66' 33', and Latitude 40° 43' N. Required the Hour Ane:le. Sun's True Altitude 37° 0' Polar Distance 66 33 Log. 0.08744 Latitude in ^0 43 Log. 0.12036 Sum 144M6' Half Sum ~^2' Sun's True Altitude 37 Difference 35 Eoiir Angle 4.48686 8'.... Log. 8' Log. 4.76003 4h. 2m. 48. . . . Log. 9.40469 EXAMPLE 2. Figure 23. Given the Sun's True Altitude, 13* 20 the Polar Distance, 113° 27', and Latitude 40° North Required the Hour Angle. Sun's True Altitude 13° 26' Polar Distance 113 27 . Latitude in 40 00 . Sum 166° 63' Half Sum 83° 27'. Sun's True Altitude 13 26 Difference » 70° ~T'., Hour Angle 8h. 3m.558.' . . .Log. 0.03744 ...Log. 0.1167 ..Log. 4.067 It ..Log. 4.9780» . — 9.18839 124 NAUTICAL ASTRONOMY. FINDING THE TIME AT SEA BY THE SUN. Methoa of Observing Altitudes for Time. Hold the instrument with the right hand and the watch in the left ; bring the Sun's Lower Limb in^ eontact with the Horizon, and clamp the Index, and at the instant the Second-hand of the watch has com- pleted the full minute, bring the Sun's limb in contact by using the Tangent screw ; note the Time by the watch and read off the Altitude, and write them down. When the Second-hand of the watch has again completed the full minute, take the Altitude, &c., as before, and write them down. This may be repeated three or five times. In general, three Altitudes, and their corresponding times, is sufficient. If tha difference between the Altitudes, or the Sun's change of Altitude in one minute of time, correspond with each other, it is a guarantee that the Altitudes have been correctly observed ; but if they do not so agree, add them together, and divide by the number taken, will give the mean of the Altitudes corresponding to the middle of the times they were taken, which may be taken as the correct observed Altitude EXAMPLE. A. M., 2l8t June, in Latitude 40° North. Alt L. Limb 37° 13' 0" Time by Watch, 3h. 58m, 25 30 3 59 38 • _4 Obs. Altitude. . . 37° 26' 30" Time 3h. 59m. 7%t» Altitude has been correctly taken. EXAMPLE. P. M., December 2l8t, in Latitude 40° North. Altof L. Limb 13° 26' Time by Watch, 3h. 3m 19 4 10 5 Number taken . . . 3)55 3)12 Obs. Altitude 13° 18' 20" Time Rh. 4m TTie above Altitudes have not been correctly taken To Find the Apparent Time, and thence the Mean Time, at Skip. RULK To Correct the Altitude. 1 Add the Correction, taken from Table IX, to the Sun's Observed Altitude, will give nis True Central Altitud To Find the Greenwich Date 2. Turn the Ship's Longitude into Time, by Table XXVI, and Add it to the Time of the Observation by Watch a Weet Longitude, or Subtract it in East will give the approximate Greenwich Time, which, if before Noon, Subtract a frum 12h. will give the Time from Greenwich Noon, A. M., otherwise it is the Time from Noon, P. M. To Correct the Declination. 8 Take out the Sun's Declination from the Nautical Almanac, against the Day of the Month, and the Differens;* or Change of the Declination in one hour, found in the adjoining column. Multiply this Difference for 1 hour by th« Time from Greenwich Noon, and divide by 60, will eive the Correction in Minutes and Seconds. To Correct the Equation of Time. 4 Take out the Equation of Time from the Nautical Almanac in hke manner, and the Difference, or Change o^ Equation in one hour, (which is given in Decimal parts of a Thousand,) found in the adjoining column. Multiply tins Difference for 1 hour by the Time from Greenwich Noon, and strike off the Right hand figure, prefix a DecimiJ poiiii to the Left of the next two figures, which are now hundredth parts of a second, and the figure to the Left-hand IS Sfionds of Time, and is the required correction. For Applying the Corrections for Declination and Equation. ^ ft Inspect the oolumns in the Nautical Almanac, and ascertain whether they are Increasing or Decreasing. Greenwich Time. Before Noon. Declination or Equation ■> r)p„,.ea8ino- Add ' Greenwich Time. After Noon. Dechnation or Equation j De^.^n^g, Subtract, to or from the Declination, or the Equation of Time, taken from the page in the Nautical Almanac, will give them 0«.rr<»cted to the Greenwich Time of the Observation. To Find the Sun's Po.ar Disiance. A Subtract the Declination from 90°, when tlie Latitude and Deoliuatioi' are of the same name, or Add the Deeh ixioo t«^ 90" when they are of contrary names FINDING THE TIME AT SEA BY THE SUN. 135 FINDING THE APPARENT TIME, AND THENCE THE MEAN TIME, AT SHIP. To Correct the Latitude to the Time of the Observation. 1. Th« usual mode of doing this at Sea, ia to find the DiffereDce of Latitude the Ship has made in the iaterval be Iweea the time the Sights were taken and Noon, (the correct Latitude having been obtained from the Sun's Meridiai Altitude), and applying it to the Latitude Observed, according to the course the vessel has been Bteering, rii ^ o- Li t u x. e vr • -nt _ii. t t-t. j ( Sailing North, Subtract Difference of Latitude. Sights taken before Noon, in North Latitude j ^^^^^ ^^^^^ ^^^ Difference of Latitude. Q- 1 i * u fl. xr • XT ii. T f4_ J I Sailing North, Add Difference of Latitude. Sights taken after Noon, in North Latitude j g^jj^^ ^^^^^^^ g^^^^^^^ Difference of Latitude. Which will give the correct Latitude of the Ship at the time of the Sights. To apply this Rule in South Latitude, we subetitute South for North. Thus having the Sun's True Altitude, Polar Distance, and the Correct Latitude of the place of Observation, find the Apparent Time by the Rule for using the Tables already given at page 128. To the Apparent Time apply the Equation of Time as directed in the precept at the head of the column headed Equation of Time, in the Nautical Almanac, by Adding or Subtracting it, and the result is the Mean Time at the Ship. EXAMPLE L 4.pnl JJOth, 1864, (Noon at Sea), in Longitude by Dead Reckoning 25° 0' W., the Observed Altitude of the Suns 1 ^er Limb was 22° 7'. Time by Watch, 7h 6m in the Morning. Ship then sailed on a true N. E. by E. Course, %' x\ixtB, until Noon, when the Latitude observed was 86° 82' N. Required the error of the Watch on both Appa- IV 4i and Mean Time. Obs. Alt. . . 22° V T. by Watch. 7h 6m Decl. 80th April. . 14* 46' 81" N. Diffi for Ih 46 " Oorr, Tab. ) j^ Lon. 25° W. ) ^ ^^ Corr Snb . 2 29 G. T. fi-om Noon_8}h I^ ) in Time.. ) Correct DeoL 14° 43' 2" IsF" True Alt. . 22° 17' Greenwich.) _, . 90 11 Polar Dist. 75 17 Log. 0.01449 Time, A. M. ^ "'' ^'"^ Pdar Distance. . . .76° 16' 68" Latitude.... 36 18 Log. 0.09824 Subtfrom.. 12 60)149 Sum 188° 47' G. T. from , „. ,^ 8h 14m Corr. 2' 89, sm ) Half Sum.. 66° 6"7" Log. 4.59366 Noon. ... J **" ^'*'" Equa. of Time 2m 58s-68 Diff. for Ih -828 Difference... 44° 37' Log. 4.84656 Corr. Su b. 1 "06 G. T from Noon. . Zjh App. T.. .7h"8mT9rLog.^9^64795 Correct Equation.. ..2m 62862 -984 Equa. of I o 53 Course N. E. by E. 35 miles = D. Lat. 0° 19' 82 Time.. $■ Latitude observed at Noon 86 82 N. Corr. 1'06'6 Mean T. ) „, . ~ Latitude in at Time of Sights 86° 18' N. at Ship, i- ^^ ^"^ 268 T. bv... Watch. ^^ \ Watch On. bis fast of Mean Time. And Watch . 2m 1 9s slow of Apparent Time. Note.— When the Sights are taken in the Morninor, we look for the sum of the 4 Logarithms in Table XXIX, and take the time from the bottom of the pacje, and if the figures are found exactly, the Hours are found at the bottom, th« Minutes at the right side opposite the Logarithm, and the Seconds in the &ame column at the bottom of the Table. But if the Sum of tlie 4 Logarithms cannot be found exactly, take the nearest Usi Logarithm, and find the differene* between it and the given Logarithm, with which enter the adjoining proportional columns, and take out the correspond- ing Seconds of Time, which must be subtracted from the Seconds found at the bottom of the cohimu fron. wnenoe tlie Dearest leas Logarithm was taken, which will be the Apparent Time from the preceding Noon or Midnight. When the Sights are taken in the Afternoon, the time is taken from the top of the Table. And in like manner, we mnst look for the nearest ^.«s Logarithm, ami find the difference between it and the given one, and the proportional parts for Seconds, found in the adjoining coluniu, must be added to the Seconds found at the top of the column, from whence the nearest less JjOgarithm was taken. All Hour Angleo are taken from the top of the page, and which is also the Apparent Time past Noon by th« Son. 126 NAUTICAL ASTRONOMY. FINDING THE TIME AT SEA BY THE SUN. EXAMPLE 2. April 80th, 1864, (Noon at Sea), in Latitude by Observation 36" 32' N., Longitude 24* 26' W.,the Sun's Obeeriid Ititude was 13° 48'. Time by Watch, 5h SOm in the afternoon, and the Ship had sailed since Noon on a trn* El N. K course, distance 29 miles. Required the Error of the Watch on both Apparent and Mean Time. Obs. Altitude 13° 48' Corr, Table IX... 8 True Altitude 13° 56' Polar Distance 75 9 Latitude 36 43 Time by Watch P. M. . Lon. 24° 26' W. in time Greenh. Time P. M Log. 0.01475 Log. 0.09604 Sh SOm Os Decl. April 30th. 14° 45' 31" N. Diff. for Ih 46" 1 37 448 Decl. Increasing, Add 5 22 7h 7h 7m 448 Correct Decl 14° 50' 53" N. 60)322 Polar Distance. 14' 90 75= 50' 53" 9' 7" Corr., .5' 22" 12_5M_8^ Half Sum 62"^T'Log. 4.65863 Difference 48° 58' Log. 4.87756 App. Time. . .6h 34m Ss Log. 9.64688 Equa Sub. 2 66 Equation of Time April 30th 2m 539 68 Equation Increasing Add 2 29 Correct Equation 2m 568'27 Course E. N. E. 29 miles =■ D. Latitude Diff. for lb -328 7h Corr 2-2»6 0° 11' Latitude observed at Noon 36 32 N. Latitude in at time of Sights. 86° Mean Time. . .5h 31m 78 T. by Watch... 6 SO Watch Im 7a slow of Mean Time, and 4m 38 slow of Apparent Time 43' N. EXAMPLE 3. March 26th, 1864, (Noon at Sea), in Latitude by observation 12° 21' S., Longitude 65° 30' E., the Sun's Observed Altitude was 26° 26'. Time by Watch 7h 47m in the forenoon. Ship had sailed on a N. W. Course, true, 17 miles, since the Sights were taken, until Noon. Required the Error of the Watch on both Apparent and Mean Time. 25° 25' 10 Obs. Altitude. . Corr., Table IX True Altitude.... 26° 35' Polar Distance.. . 92 3 Latitude 12 33 130 ° 11' 65° 6' 39° 81' Log. Log. Log. Log. 4 22 Decl. 26th Mar. 2 Corr. Sub_ Correct Decl Time by... . Kv., Watch A. M. f ^^ *^°^ Lon 65° 3.0' E. ( 0.00028 ■" *'™® ) 0.01050 G. Time A.M. 3h25m Polar Distance 92^ Sub. from. ...12 T. fm G. Noon 11' 40' 8 21 N. Diff. for Ih. Timo fm N. 59 " 2° 90 3' 19" 3' 19" 4.62432 4.80366 8h 35m Equation 5m 60s-02 Diff. for Ih Corr Add 6-52 472 '• 29 6 0)501" Corr. for Decl. 8' 21" •768 8ib App. Time.... 7h 47m 98 Log. Equa Add 6 67 Mean Time.. . 7h 68m 68 T.by Watch. . 7 47 Watch 9.43876 Correct Equa..5m 568-64 Course N. W. 17 miles, D. Lat 0° 12' Latitude by Obs. at Noon 12 21 S. Lat in at time of Sights 12° 33"' S. 6m 68 slow of Mean Time, and Om 9s slow of Apparent Time, •6144 • 384 Corr. for Equa. 6-52-8 QUESTIONS FOR EXERCISR Quest. 1st. — May 12th, 1854, (Noon at Sea), in Latitude Observed at Noon 47° 60' N., Longitude by Dead Reckon- mg 60° 30' W. In the morning the Sun's Observed Altitude was 34° 5'. Time by Watch 8h 6m A. M. The Ship bad made 4' of Diff. Latitude to the Southward since the Sights were takea Required tb** Error of the Watch. Answer. — The Apparent Time is 8h 5m 398, and Watch fast Om 2l8. Mean Time 8h Im 478, and Watch fast 4m 18s. Quest. 2d. — On the same day as above, in Latitude 47° 50' N., Longitude 50° 80' W., in the Afternoon the Sun's Observed Altitude was 10° 14'. Time by Watch 6h 17m' P. M. The Ship had sailed on a true W. by S. ^ & Course, 52 miles since Noon. Required the Erroi if the Watch as before. Answer. — The Apparent Time is 6h 18m 168. Watch slow Im 168. Mean Time, 6h 14m 288. Watoh fast tm 37 s. Quest. Sd — June 1st, 1854, (Noon at Sea), in Latitude 39° 25' S. by Observation, and Longitude 90°E., at Noon. In tbe Morning the Observed Altitude of the Sun was 12° 15'. Time by Watch 8h 35m A. M. The Ship h;id soiled •n a true S. E. Course, 28 miles, until Noon. Required the Error of the Watch. 4»i«M«r.— The Apparent Time is 8h 84m 56s. Watch fast Om 48. Mean Time 8h 82m 208. Watch faal 2m 408. NoTB.— In the foregoing E.xamples, and also those which follow, the height of the eye is supposed to be 18 feet above the Sea level. . - , . ■ , r^ Noon at Sea means the end of the Sea Day, and which also corresponds to Ine beginnmg of the Astronomical U»T uid to the Noon of the Civil Day. FINDING THE APPARENT TIME AT SEA BY THE SUN. 12? FINDING THE APPARENT TIME AT SEA BY THE SUN, W«EN THE SHIP IS ON THF EQUATOR. When the Ship is on the Equator, and the Sun is also on the Equator, that is, when his Declination v 9, the Poles of the Heavens are in the Horizon and the upper end of the Celestial Equator is then in th« l^nith. and the Sun rises and sets vertically. DIAGRAM Of the Hour Angles on the Equator. Fig. 24. In this case, the Son's change of Altitude is 15' in one minute of Time, or 15' in one hour, ttxronghoat the entire day. The time can, therefore, be as correctly found near the Meridian, that is, near Noon, as it can at any other time of the day, and an error in the Latitude, in working out the time, does not affect the result. It will be perceived by this figure, that when a Ship sails to the Southward, after leaving the Equator, she raises the South Pole of the Heavens, and that in sailing North from the Equator, she raises the North Pole, and that the Polar Distance and Hour Angles are always measured from the elevated Pole. But in this case, both Poles being in the Horizon, and the Sun on the Equator, his Polar Distance 90', and the Hour Angles, (measured on the Equator), are the same at both Poles. If we therefore observe the Sun's Altitude at any period of the day, under the above circumstances, and after correcting it in the usual manner, to obtain the True Central Altitude, and then subtract it from 90°, we have the Sun's Hour Angle at once, in space, which, turned into degrees and minutes by Table XXVI, will give the Apparent Time at the Ship in the afternoon, and subtracting it from 12h, will give the Apparent Time in the forenoon. EXAMPLE 1. Jjstitude and Declination ; the Sun's Observed Alti- tude in the forenoon was 74' 48'. Required the Appa- rent Time at the Ship. Obs. Altitude L. Limb 74° 48' Corr, Table IX, \2^ Sun's True Altitude 75' O' 90 Hour Angle in space 15° 0' = Ih, or llh A. M. This may be verified by the Time Tables, as follows True Altitude 75' 0' Polar Distance 90 Log. 0.00000 Latitude Log. 0.00000 Sum 166° 0' Half Sum 82° 80' Log. 4.11570 Altitude 75 Difference Y°~30' Log. 4.11570 Apparent Time llh Om Os Lot?. 8J3140 EXAMPLE 2. Latitude and Declination ; the Sun's Observed Alti- tude was 29° 50' in the afternoon. Required the Appa* 'rent Time at Ship. Obs. Altitude L. Limb 29' 60' Corr., Table IX, 10 Sun's True Altitude 30° 0' 90 Hour Angle in Space 60° = 4h Om P M True Altitude 80* C Polar Distance 90 Log. 0.00000 Latitude Log. 0.00000 120^' Half Sum 60' 0' Log. 4.69897 Altitude 30 Difference 30° 0' Log. 4.698 97 Apparent Time 4h Om Os Log. 9.397^ 128 NAUTICAL ASTRONOMY. FINDING THE APPARENT TIME WHEN THE SUN IS RISING OR SETTING. . This method is upon the same principle as that of measuring the Hour Angle from the Elevated Pole, but in the room of observing his Altitude above the Horizon with a Quadrant, we observe with a Spy- Glass the contact of either of his Limbs with the Horizon at Rising or Setting, and note the time bv thf watoh RULE When the Lower Limb ts Observed. Take the Difference between the Sun's Semi-diameter, N. A., and the Mean Horizontal Refraction, 84' 17", to vhich add the Dip of the Horizon, found in Table V. Call this the Correetion. Correct the Declination, and fiuc'. tbi Polar Distance, as usual Also correct the Latitude to the place of Obser ration by the rules already given. Add together the Latitude and ^o^B.r- Distance, from which tubtract the above Correction. Take half this Sum, Jd which add the same co''r«>ct'OR -*n rc v„.t u r. j r. ,_ • . Dip of the Horizon 4 8 o^.^n t- a \t .^ » « Corr.,..Sub. 3 40 Ht Correction t IlLf' SubTacTrn.^- "" l^^^" T o' '"^- ''^"- '^'^'" «"^)il LaHt d • . . • '''"^ '^'"'•^ «-^«-- • • i^^^S^^ Polar Dist el-TO'"""'*^^^-^ Latitude iM at Sunnse 25' 0'. .. .Log. 0.04272^ i^olar Di8t..68 17 Polar Disbince 68 ... .Lo|. 0.03283 Sum , QQO ni Correction Sub + B4 7,^^^' °^ '^^''' .... 2m. 318-92 Dif. Ih. S-80 —~~ Corr..,..Add.. 4 -1 8 Hl^ Half Sum %-t r .».,oo ^^''^^^tEqua.. . . jtn. 86s-10 Cor..— jj-lfrp-- o .• 4b S .. Loff. 4.84138 CoTection Add f 54 J'^«'':°"« r4FT7'.... Log. 4.86377 ^pp. Time at Ship at Sunrise. 5h. 1 21^7 2777.:!^^:^ 8070 Equation of Time. 2 86 s ■ ." Time by Watch 5 j^ q* Watch Fast of Mean Time. . . . 7^724,. and Fast of Apparent Time 4m. 48.. )m the fact that when the Son's- below it. And when his Upper Ihi. Ub-erV-ai-hliTi'T ''■' "" *«fa«>l»» of ■he"A,;„„7pT,cV,'. •"'""■" "'''"' "* "'""■"•• fti., » b.&r, «.f«., .nd ™, bT£;'isyr:;^;'bf^?„*rdt'r'/^f'sft™i;:' "'"*• ■• «» ''°"»- » ■- >■»''—• -n- tso NAUTICAL ASTRONOMY. FINDING THE APPARENT TIME FROM EQUAL ALTITUDES OF THE SUN NEAR NO<")N. This is a very convenient and simple mode of finding the Apparent Time at Noon, or when the Sun ia on the Meridian, that is, at 12 o'clock Apparent Time at the Ship; and as it is independent of Latitude and Declination, and all the other corrections, it is a useful check on the more regular method of finding the time. This observation can be depended on in Low Latitudes, because the Sun's change of Altitude is very rapid near the Meridian. But in High Latitudes the Sun's change of Altitude near the Meridian is very slow, especially in the Winter months ; hence an error in the time of observation, in the latter case, may be committed which may render it worthless. Besides, the greater the distance of the observer from the Equator, the time from Noon, at which the Altitude is observed, must be greater, (because the correctness of the Time so found depends entirely upon the rapidity with which the Sun rises and falls.) This involves a tedious system of corrections, for the Ship's change of place and the Sun's change of Declination in the interval between the observations, and which is unnecessary labor, because the Time can be found as correctly by one of the Altitudes in the usual manner. When a Ship sails due East or West in the interval between the Altitudes, in that case it becomes a ■question of time only. But when she makes much Northing or Southing, it is evident that the same Alti- tudes will no longer give the correct Middle Time at Apparent Noon. The error in the P. M. Altitude will be equal to the difierence of Latitude made in the interval. Therefore the Rule is, when sailing towards the Sun, we must increase the A. M. Altitude which is on the Quadrant, by advancing the Index ■of the instrument equal to the difference of Latitude made in the interval. But in sailing from the Sun, we must decrease the A. M. Altitude by screwing back the Index equal te the difference of Latitude made in the interval; and when the Sun falls to that Altitude in the afternoon. we note the time by the same watch by which the time of the A. M. Altitude was noted. Limits of the Time from Noon. The. Altitudes should not be taken nearer to Noon than in the proportion of One Minute of Time for everj Oegroe of Latitude the Ship is North or South of the Equator. The Observation. Observe an Altitude of the Sun's Lower Limb according to the above limits before Noon. Note the tira t>\ the Watch, and clamp the Index of the instrument. When the Sun's Lower Limb falls again to th« •ame Altitude in the afternoon, note the time by the watch. RULE. Add together the two times, and take their ITalf Sum for the Middle Time. If the Middle Time is exactly It Iwurs, the Watch is correct for Apparent Time ; because, at the instant of this Middle Time by the Watch, the Sun u on the Meridian and it is Apparent Noon, or 12 o'clock, Apparent Time at the Ship. But should this Middle Time exceed 12 hours, then the excess is what the Watch is Fast of Apparent Time. If the Middle Time be leas than 12 hours, then what it wants of 12 hours is what the Watch is Slow of Apparent Time. And by applying the correct Equation of Time, in the usual manner, to Apparent Noon, or 12b., we have the Mean Noon at Ship, the difference between which and the Middle Time is the error of the Watch on Mean Time. EXAMPLE 1. April 2d, 1864. In Latitude 5° 52' North, and Lon- gitude 28° West, at llh. 64m. by the Watch, the Sun's Altitude was 85° 40' A. M., and at 12h. 20ni. by the same Watch, he had fallen to the same P. M. Required the error of the Watch on both Apparent and Mean Time. Sun's Alt. . 85° 40' A. M. Time by Watch, llh. 54m. Same P. M. do. do. 12 20 Equa. of T.. 3m. 418-71 Dif. •'ZeO Sum )2 4h. 14m . €orr. ..Sub. 1-50 Long. 2h. Mid. Time, 12L 7m. Equa. .Add 3m. 40a. Ap. N'n , 12b.O Mn. N'n, 1211.3 Mid.T. . 12 7 Watch . , 1'50K) App. Noon, 12 Watch Fast, Oh. 7m. 408. 3m.20s. Fast of Mean Time. EXAMPLE 2. April 16th, 1854. In Latitude 30° North, Longitude 45° East, at llh. 20m. by Watch, the Sun's Altitude was 68° 20' A. M., and at 12h. 34m. by the same Watch, be had fallen to the same Altitude P. M. Required the error of the Watch on both Apparent and Mean Time. Sun's Alt. . 68° 20' A.M. Time by Watch, llh. 20m. Same P.M. do. do. 12 34 Equa. of T.. . Om. 1 1887 Di£ .603 Sum . . . . 23h. 54m Corr.. . .Sub. 1 -80 Equa... Sub. Om. lOs. Ap. N'n. 12h. Mn. Nn. llL69m.5'0B! Mid. T... 11 57 Watch. . . . 3h. Mid.Time,llh.67m. 1.80-9 Ap.Noon, 12 Watch Slow, Oh. 8m. 2m. 6Cs. Slow of Mean Time Note. — It is not necessary to read off the Altitude if the Index of the instrument remains untouched, because we have only to wait until the Sun mils again to the same Altitude in the afternoon, unless the Ship makes much Northing or bouthiug in the interval, when it must be corrected as aba/e. But to guard against accident, or if the instrument ii required for use in the interval, we have only to read it ofl and write it down, and set the Index to the same Altitude «cain, ready for the P. M. Altitude, and in case of cloudy weather several Altitudes, and their corresponding timee, «aould be taken before Noon, as a reserve. FINDING THE TIME. 121 FINDING THE TIME ON SHORE FROM ALTITUDES BY THE ARTIFICIAL HORIZON. As a full description of the method of taking Observations with this Instrument is given at page-s 77 and T8, it will only be necessary here to give a few Examples of finding tiie Apparent Time, and thence the Mean Time, on Sliore. EXAMPLE M. March 6th, 185-1. at New York, in Latitude 40° 42' 42" N., and Longitude 74° 0' 1" W., the following Altitude* were observed by an Artificial Horizon iu the Moruiug, to ascertain the Ei-ror of the Watch on Mean Time. Obs. Altitude L. Limb. 24' 14' 30' 35 89 5fi 30 8)106' 39" 24° 35' 2 83' Mean of the Altitudes. Index Error Sub, Angle of Double Reflex. 24^33^33' Suns Obs. Alt. L. L. . . 12M6' 46" Sun's Seinid Add 16 9 Apparent Altitude 12^ 32' 55 Refraction. Sub. 4 18 Suns True Altitude. ... 12° 28' 37- ' Polar Distance 96 2 46 Latitude 40 42 42 Sum 149° 14' 4" Half Sum 74' True Altitude.. _12^ Difference 62 Apparent Tim«. ., 37' 2' 28 37 Time by the Watch. Mean of the Times. Lon. 74° W. iu time- Mean Time at G. . , Sub. T. past Noon at G.. Log. 0.0024S Log. 0.12083 Log. 4.42370 7h 32m 20s Declination. 6' 33 36 Corr..Sub.. __li_Jii Cor. Decl. . ~6^ 3)10Um 268 90 7h 33m 28fl Polar Dist. 96° 4 56 14" S. 29 2' 45" Diff. for Ih 68" G. Time ) ,, pastN. S Correction 29" 2' 45' 12h 29m 28s 12 Equa. of T. 11m 45s-78 Diff. for Ih -684 29m 283 ^orr.. .Sub. •29 Corr. •29-4 Correct Eq. 11m 45849 8' 25" Log. 4.94650 7h 28m 468 = Log. 9.49296 Apparent Time of Observation 7h 28m 468 Equation of Time Add 11 45 Mean Time 7h 40m 3l8 Time by Watch 7 33 28_ Watch slow Oh 7m Ss of Meaa Tune. EXAMPLE 2. p October 20th, 1854, at the Cape of Good Hope, in Latitude 34° 22' S., and Longitude 18° 30' E., the following Altitudes were observed by an Artificial Horizon in the Afternoon, to ascertain the Error of the Watch on Mean Time. Sun's Altitude L. Lunb. 36° 30' 30" Time by Watch 4h 58m 10s Declination 10° 19' 47" S. Diff Ih 54 " 36 6 4 59 20 Corr.. Add 8 22 Sfb lLJi_J^ 6 40 Corr. Decl 10° 28' 9" 162^' 3) 108° 17' 4 0" 3)1 4h 58m 10s 90 0_0 27 Meauof the Altitudes... 36° 5' 53" Mean of Times. ^iT9m~233 Polar Dist. 7'9°"36'~5r' 1£_ jidex Error Add 1^ lo Lon. 18° .30'. ) 60)202" Augle of Double Reflex. 86° "r~l" E. iu time, j" (j^rr 3^2~^ Suns Obs. Alt. L. Limb. 18° 3' siT' G- Time P. M.. 3h 45m 238 U Add Semid 16 6 Apparent Altitude 18° !!»' 38" Equation of Time 15m 68^7 Difflh.. AOt Subtract Refraction 2 58 Correction-. .Add 1 '62 Sfh Sun's True Altitude 18° 16' 40" Correct Eqnatioa 15m 7829 -1218 Polar Distance. 79 36 51 Log. 0.00717 -208 Latitude 34 22 Log. 0.08881 •101 Sum r32^T5"'^" Oorr TmT" HalfSum t;6° 7' 45" Log. 4.60711 True Altitude 18 16 40 Difl'erence 47° 61' 5" Log. 4.87006 App. Time at the Place 4ii 5ym HOs Log.^6766 Equa. of Time. .. .Sub. 15 7 Mean Time 4h 44m 233 Time by Watch 4 59 23 ^ Watch 16m Os fast of Mean Tune at the plao*. I 133 NAUTICAL ASTRONOMY FINDING THE TIME AT SEA FROM AN ALTITUDE OF THE MOON. The Apparent, and thence the Mean Time, at Ship, may be found by an Altitude of the Moon at a di» taooe from the Meridian. In the first place we must hare the txact Greenwich Date at the time of the observation at the Ship, Id order to reduce her Semi-diameter, Horizontal Parallax, Right Ascension, and Declination taken from the Nautical Almanac to that time, and as before stated at Page 101, (in the case of finding the Latitude by th« Moon's Meridian Altitude,) if the Longitude of the Ship be not known, neither the Latitude nor the Time can be found by the Moon. But m cases where a Ship carries a good Chronometer, the Longitudecan at any time be found tolerably correct by applying the Difference of Longitude made by Dead Reckoning to the Longitude last found by Chronometer. The Moon's Observed Altitude must be corrected as usual, to obtain her centre, and another correctioD for her Parallax in Altitude, and which is always additive to her Apparent Altitude, because she alwav* appears below her true place in the heavens. (See page 67.) RULES FOR COMPUTING THE VARIOUS CORRECTIONS, To Find the Greenwich Date. let. Turn the Ship's Longitude into Time by Table XXVI, and add it to the Mean Time at the Ship, (al the time the observation was made), in West, or subtract it in East Longitude, will give the Greenwich Date, which must be always one day less than the Sea Date. Or it may be more correctly found by noting the times of the Altitudes by Chronometer, which, after allowing for its error on Greenwich Time, will give the required Greenwich Date. To Correct the Moon's Altitude. 2d. Take from the Nautical Almanac the Moon's Semi- diameter and Horizontal Parallax, for the near- •et Noon or Midnight correpponding to the Greenwich Date. Then if the Moon's Lower Limb be observed, add the difference between the Dip of the Horizon and her Semi-diameter to the Observed Altitude. But if her Upper Limb be observed, subtract their Sum, will give the Moon's Apparent Central Altitude. 3d. Enter Table XXV with the Apparent Altitude at the side, and the Horizontal Parallax at the top, and take out the Correction, which is expressed in Minutes and tenths of Minutes, and proportion it, if required, for the odd Minutes of Altitude, and the odd Seconds of Parallax. This correction is always additive, and will give the Moon's True Altitude. To Correct the Moon's Right Ascension. ^ 4th. When the large Nautical Almanac is used, and the Greenwich Date, for the full hour, the Right Ascension is found opposite that hour ; but when there are odd Minutes, take the Difference between that and the following hour, and apply the proportion of this difference, corresponding to the odd Minutes, to the Right Ascension at the preceding hour, according as it is increasing or decreasing, will give the Moon's correct Right Ascension. 5th. When the small Almanac is used, and the Greenwich Date exactly at Noon or Midnight, take out the Right Ascension found opposite. But when it is between them, take it out for the nearest Noon or Midnight preceding, and the nearest Noon or Midnight following this Greenwich Date, and take their Dif- ference, which will be that for 12 hours, and note the number of Hours and Minutes which the Green- wich Date is past Noon or Midnight. Then say, as 12 hours is to the Difference in 12 hours, so is the Greenwich Time pa.st Noon or Midnight to ihe required correction, which, applied to the Right AscensioB at the preceding Noon or Midnight, according as it is increasing or decreasmg, will give the Moon's correct Right Ascension. (See the Note on the next page.) To Correct the Moon's Declination. 6th. When the large N. Almanac is used, proceed by the rule already given at page 102, No. 6, for cor- recting the Moon's Declination when on the Meridian. When the small Nautical Almanac is used, proceed in like manner by Rule No. 7, on the same page, and the result will be the Moon's correct Declination, corresponding tc the Greenwich Date. 7b Find the Moon's Polar Distance. 7lh. When the Latitude and the Moon's Declination are of the same name, the Difference between hei Declinaaon and 90° is her Polar Distance. But when of contrary names, their Sum is her Polar Disttnor FINDING THE TIME. 138 To Correct the Latitude to the Time of Observatiim. 8th. Enter the Traverse Tables with the Course and Distance made good, and find the Difference of Lati- tude the Ship has made since the last Observation for Latitude was obtained, and apply it by the Rule given At page 125, which will give the correct Latitude in To Find the Moon's Hour Angle. 9th. Thus having the Moon's True Altitude, Polar Distance, and the Latitude of the place, proceed (a« with the Sun) to find the Moon's Hour Angle, or her Distance from the Meridian, (which with the Sun ii the time from Noon.) this being added to the Moon's Right Ascension, if the Moon be to the Westward of the Meridian, or subtracted from it if the Moon be to the Eastward, the Sum, or remainder, will be the Right Ascension of the Meridian. To Correct the Sm7i's Right Ascension. 10th. Take out the Sun's Right Ascension and the Difference for 1 hour from the Nautical Almanac, mul- tiply this Difference by the Time from Greenwich Noon, and add this correction to the Right Ascension, taken from the Nautical Almanac, (because the Sun's Right Ascension is constantly increasing,) will giv« the Sun's correct Right Ascension. To Find the Apparent Time at Ship 11th. From the Right Ascension of the Meridian, (increased by 24 hours, if necessary,) subtract the Suu'i eorrect Right Ascension, and the remainder will be the Apparent Time. 7b Correct the Equation of Time. 18th. Take out the Equation of Time from the Nautical Almanac, and the Difference for 1 hoar, and eorrect it by the Rules given at page 124, will give the correct Equation of Time. To Find the Mean Time at Ship. 13th. Apply the correct Equation as directed in the precept at the head of the column in the Nautical A.lmanac, to the Apparent Time, by adding or subtracting it, and the result is the Mean Time at the Ship EXAMPLE. Miirch lOtb, 1854. At Noon the Latitude observed was 88° 15' North, Longitude by account 60° 45' West. Ship tad sailed N. E. (true) 40 miles since Noon, when the observed Altitude of the Moon's Lower Limb was 40° 82' to the Eastward of the Meridian, and the Greenwich Time by Chronometer 9h. 44m. 87s. P. M. Required the time at Ship. Ob«. Alt. D's L. Limb. 40° 82' Gr. Time by Chro 9b. 44m. 37 s. J 'b Dec, Noon. 24° 14' N. Semid. 15'. Dip 4 11^ Midnight. 23 4 Hor. Par.65', and.... 40° 43' Lat at Noon 88° 15' N. T.XXIILDit 12h. 1° 10' ) ., .. _^. .., Gives Coi-., Tab. XXV, 40 Course N. E. 40 miles, D.L. 28 and G. T. from Noon. . f »'i-45d^-=-0 Ofl J 'b True Alt 41° 23' Lat. at time of Sights 38° 48' ^^^■' ^00°- • • • ^4 14 N Polar Dist 66 42 Log. 0.03695 > 's Cor. Dec.. . 23° 18'N Latitude 38 43 Log. 0.10777 90 Sum 1 46° 48' J) 's Polar Dist 66° 42' Half Sum 78° 24' Log. 4.45589 ^, t, . >t n-ff oo° T T A^oAAi D'sR. A. Noon.. 8h. 12m. 218. D'ff«^'«Dce •• 82 1 . . . .L og. 4.72441 Midnight. 888 26 I '8 Hour Angle 3h. 38m. 53s Log. 9.32502 g ^ ^gh.^ 26 5i.-9h. 46m. J) sR. Aseen... 8 33 S3 H.A.ofthe Mer.. 4h. 54m. 858. Sun's R. A. 23h. 21m. 588. Dif. lb. 98. * 10.0000 Add 24 Cor... Add 1 30 _10_ Pro. Log 12h.. 1.1761 Table XXXIV R. A. M. Tncrea. 28h. 54m. 35s. Corrected. 23h. 23m. 238. 908. Arth. Co 78!8239 finn's R. Ascen. 23 23 23 Pro.L(>g.26m.5 0.8389 App. T. at Sliip 5L 31m. 128. Equation. . 10m. 3 ls-55 Di£ lh.-665 ^o- 9b. 45m . 1.2663 Eg. of T... Add 10 25 6^5 10 0.9291 Mean Time 5h. 41m. 878. Corrected. 10m. 24890 6 66-0 Pro. Log. OL 21m. 12a. CJor. for 9h. 43a > '8 KA.at N'n 8 12 21 j) 'b Cor. R.A..8h.S3m. 838. • The Proportional Logs., Table XXXIV, are very nseful for the purpose of performing Rule of three qnestiona* bstto make the terms all additive we must eubtract the Pro. Log. of the first term from 10.0000. It is then called Um 4rithmetical Cnnipleinent. But as this Table only extends to 8 hours, we must enter it, (when they exceed that quantity,) with the hourn as ininntos and the minutes as seconds, «fec., Latitude 38 38 Log. 0.10726 Jupiter's Dec N'n. Dec 6th. 21° 15' S. Sum 143°"28' ^Q Half Sum. . . ."71° 44' . Log. 4.49616 Jupiter's Polar Dist 68° 46' Difference . . ."j5^. Log. ^76^ gun's R A. 16h. 46m. 86.. Di£ Ih.. lU ^5- ^^- i l9h. 67m. ISs. Jup.'saA. 4L 0m.293.Log. 9.89953 Correction. 11 Dec 6th I RAscen. 19 67 15 Corrected . leOeSri?^ D^fth } ^^ ^^ * R.A of Mer.23h.57m7?4 Sun'8RA.l6 46 47 LatObs.at N'n 38° 10' S. Long 92" fto' R Say as 24h. is to 6ls.8oi8lh.6ia Ap.T at S'p77hTo^~578. Co. S.W. 40= D.L. 28 S. Dep. 28 — D.L.36W. *91249 A. C. R Log. 24h,T«.XXXlV Eq, of T,Sub. 9_ JU Lat time sight8.38° 38' S. Long.. ... 92* 14' E. ^J J69 go. Log.. . 61^ ^^ Mn. Time, 7h. Im. 468. -'" '^ „ \ ' T. by watch 7 16 App. 'Hme at Ship 7h. 10m. 67s. 3.664/ Pro. Log. Corr. Om. iA. W. fast M, T — 18m. 14s '^™« by Watch 7 15 ^ Ascen, Dec 6th.l 9h. 67 18 "^ *■ ^ Watch fast of App. T. . (*. 4m. 3a. CorrectR. Aacea . . .19h, 67m. 16* • See the Note at page 133. for worklnir bv the Proportional liogm. 136 NAUTICAL ASTRONOMY. FINDING THE TIME AT SHIP FROM AN ALTITUDE OF A STAR. The Time may also be found as correctly by an Altitude of a Star at a distance from the Meridian, twilight, as by the Sun ; and the name of the Star of which the Altitude is observed, may be found in Iik« manner as the Planets, by referring to the Diagrams and Rules for finding the Meridian Altitude of th« Stars, at pages 64 and 65. The names of any of the Stars, in Table XIX, when observed out of the Meridian, may be found by imagining a point in the heavens, in an opposite direction to the elevated Pole, which is equal in Altitude to the Co-Latitude of the place. This point will represent the Upper part or Elevation of the Celestial Equator. Then suppose a semicircle drawn from thence through the true East and West points of the Horizon, will represent the Celestial Equator. Then all the Stais seen to the Northward of this semicircle will have North Declination, and those seen to the Southward of it will have South Declination, and it can at once be determined whether the Star observed has North or South Declination. Now estimate its distance in Degrees from this supposed line or Equator, and enter Table XIX, and find which of the Stars corresponds nearest to this estimated Deoli- oation. The bearing of the Star will show whether it be to the Eastward or Westward of the Meridian. Now •enter Table XVI II with the day of the month, and find at what time it would pass the Meridian on that day. Then, if the Star be to the Eastward when observed, and it is the proper Star, the Table wil' give its Meridian passage later in the day ; but if observed to the Westward, it will give it earlier in the day. Thus the Declination and Meridian passage will point out the name of the Star. And as before stated, all the Stars having North Declination rise and set to the Northward of th^ true East and West points of the Horizon, while those having South Declination rise and set to the Southward ■of the East and West points. And in Hish Latitudes, when their Declinations are of the same name as the Latitude, their Altitudes are high, and they pass the Prime Vertical, that is, they pass the East or West points above the Horizon. But when the Latitude and their Declinations are of contrary names, their Altitudes are low, and they do iiot reach the East or West points (at rising or setting) when above the Horizon. RULES For Computing the Corrections. 1. Turn the Ship's Longitude into Time, and add it to the Time by Watch, in West Longitude, or tubtra&t it in East, will give the Greenwich Date. To Correct the Starts Observed Altitude. 2. Take out the Correction from Table XX. and subtract it from the observed Altitude, will give the Star's true Altitude. To Correct the Star''s Declinatiori. 3. Take out the Star's Declination from Table XIX, and the annual Variation; multiply this by the number of years elapsed since 1854, and divide by 60, if above 60", will give the correction in Minutes and Seconds, and apply it according to the sign of addition (+) or subtraction ( — ) found in the Table. To Find the Star''s Polar Distance. 4. When the Latitude and Declination of the Star are of the same name, the Difference between th« Declination and 90° is the Polar Distance, otherwise their Sum is the Polar Distance. To Find the Latitude at the Time of Observation. 6. Find the Difference of Latitude the Ship has made, and apply it to the Latitude last observed. To Find the Starts Hour Angle. 6 Having thus the True Altitude and Polar Distance of the Star, and the Latitude of the place, pro- •eed as with the Sun to find the Star's Hour Angle, or Distance from the Meridian, (which with the Sun is the time from Noon.) To Correct the Starts Right Ascension. 7. Take out the Star's Right Ascension from Table XIX, and the annual Variation; multiply this by the number of years elapsed sine 1854, and divide by 60, (if above 60s.,) will give the correction, which « always culditive. » •J'O FIND THE TIME. IST FINDING THE TIME AT SHIP FROM AN ALTITUDE OF A STAR. To Find the Right Ascension of the Meridian. 8. If the Star be to the Eastward of the Meridian, subtract its Hour Angle from its Right Ascension, Bat if ta the Westward, add its Hour Angle to its Right Ascension, will give the Right Ascension of the Meridian To Find the Sun's Right Ascension. 9 Take out the Sun's Riglit Ascension, and the Difference for 1 hour, from the Nautical Almanac, for the Nooa of the Greenwich Date. Multiply the Difference for 1 hour by the time from Greenwich Noon, and divide by 60 (fl above 60), This Correction is always additive. To Fi7}(l the Apparent Time at Ship. 10. Fi-om the Right Ascension of the Meridian, (increased by 24 hours, if necessary), subtract the Sun's Oorreot Right Ascension, and the remainder is the Apparent Time. To Find the Mean Time at Ship. 11. Take out the Equation of Time, and the Difference for 1 hour from the Nautical Almanac, and correct it to the Greenwich Date by the rules at page 124, and apply it to the Apparent Time, according to the precept at the head of tlie column in the Nautical Almanac, by adding oi subtracting it, and the result is the Mean Time at Ship EXAMPLE 1. February 10th, 1854, Sea Time, in Latitude 40° 10' N., Longitude 68" 20' W„ in the Evening Twilight, the Obd Altitude of the Star Sirius was 12° 29' to the Eastward of the Meridian. The Time by Watch was 5h 28m. Re quired the error of the Watcli on both Apparent and Mean Time. Elevation 16 feet. Obeei-ve.l Altitude of Sirius 12° 29' Corn, Table XX Sub. 8 True Altitude 12" 21' Polar Distance 106 31 Latitude 40 10 Log. 0,11681 6um Time by Watch 5h 2Sra Oe Sirius's Declination, 1864.. 16° 31' a Long. 68° 20' W. in time 4 33 20 90 Green. Date, Feb. 9th . . lOh Im 20s Polar Distance 106° 81' Log. 0.01830 Sirius's Right Ascension, 1854, 6h 38m 48« 159° 2' Half Sum 79° 31' Oifference 67° 10' Sirius's Hour Angle. . . 3h 48m 409 eiiius's Right Ascen.. .. 6 38 43 A. A«ceo. of the Mer. . 2li 50m 33 Add. 21 increased ti. A. M 2tih 50m Ss Suo'b il. Adcen 21 33 14 Log. 4.25995 Log. 4.96466 Log. 9.35962 Sun's R. A, Feb. 9th 21h 31m 34s DiflF. Ih lOi Add 1 40 10 6 0)100i lm408 Correct Right Asceu. 21 h 33m 148 App. Time at Ship. ... 5h 16m 49b Equation Add 14 32 Mean Time at Ship. . 5h 81m 21b Time by Watch 5h 28m Oa Apparent Time 5 16 49 Watch fast Oh 11m lis of Apparent Time. Time by Watch 5h 28m Os Mean Time 5 31 21 Watch slow Oh 3m 2l8 of Mean Time. EXAMPLE 2. "May 13th. 1854, Sea Time. Ship's position at the preceding Noon was Latitude 37° 44' S, Longitude 68* 9' K She then sailed E. S. S., 120 ti.-'les, until 4h 40m A. M., when the Altitudes of Antares was observed 42° 86', to the Westward. Required the error yj the Watch on both Apparent and Mean Time. Elevation 18 feet. Obs. Alt. of Antares 42° 86' Time by Watch 4h 40m Antares's Declination 1864 26* 6' S Corr.. Table XX... Sub. 5 Add. 12 90 :True Altitude 42° 81' From preced. Noon "l6h 40m Antares's Polar Distance... 63° 64' Polar Distance 63 54 Log. 0.04671 Lon. 70° 30' E.in T.. 4 42 ^^^'^^»B East Longitude, we subtract one day fro'u the Greenwich Date, so that when the Ship arrives again on tW Meridian of Greenwich, the time at Ship, and the Greenwich Time by Chronometer will coincide. FINDING THE LONGITUDE BY CHRONOMETER !»» In Circumnavigating round by the East, one Day is Added to the Greenwich Date. In Circumnavigating round by the East, the general practice is, that on reaching the opposite Mendiai to Greenwich, or the Longitude of 180° E., thence passing into West Longitude, and with the view of making the general rule applicable, which is. that the Greenwich Time should be the greatest in We«l Longitude, we add one day to the Greenwich Date, and on the Ship's arrival again on the Meridiau of Rreenwioh, the time at Ship will coincide with the Greenwich Time by Chronometer. On Ascertaining the Greenwich Ti-ne from the Chronometer. As only 12 hours are given on the face of the Chronometfcr, it shows only the time after Noon or Mid- night, therefore when it is A. M. at Greenwich, by adding 12 hours to it, we have the time since the ))r«- ceding Noon. If it .<;hows P. M. at Greenwich, the Noon of the present day will be the preceding Noon at Greenwich, or tlie beginning of the Astronomical day. which, with the day of the month prefixed, is called the Grren wich Date. To know whether the Time by Chronometer is P. M. or A. M. at Greenwich. To the Astronomical Mean Time at the Ship (which is found by taking one day from the Sea Date, and eounted through the 24 hours), add the Ship's Longitude in time in West Longitude, or subtract it in East . the Sum or DitTerence will be the Mean Time at Greenwich. If it be less than 12 hours, the face of ilie Chronometer will show P. M. at Greenwich ; but if the Greenwich Time be more than 12 hours, the face of ihe Chronometer will show A. M. at Greenwich, to which we must add 12 hours to get the Time from the iireceding Noon. Longitude is the Difference of Time between two Meridians^ and how Found. it will be perceived, from the above remarks that Longitude is merely a question of the difference of Time between two Meridians. If we, therefore, have the correct Mean Time at the first Meridian ♦ Greenwich, shown by a Chronometer, we can at any time find the Longitude of the Ship by simply taking the difference between the Mean Time at Greenwich and the Mean Time at the Ship, fouiid by any of tbe .T.etiiods already given in this work, which, turned into Degrees and Minutes, by Table XXVI, is the Shij » Longitude Then, it the Greenwich Time be greater than the time at the Ship, the Longitude is West; but if the Greenwich Time is the least ^ the Longitude is East. ^'j;.-^^'" When one of the Times is P. M. and the other A. M. on the same day, we must add 24 hours to that at P M., and take their difference for the Longitude in time. And when the P. M. and A. M. Times fall on different dates, their difference, counted from their preced- iu2 Noons, is the Longitude in Time. ) Rate of a Chronometer, The Chronometer would therefore be a most useful instrument, were it to keep a steady uniform rate throughout the voyage, and nothing more would be required ; but as this is seldom the case, (see remarki at Pages 79 and 80), it is necessary that it should be verified from time to time during the voyage, in order to ascertain its error on Greenwich Mean Time, at the place of observation, and its present rate. Th« manner of doing this will be found at page 155. Method of Keeping an Account of the Rate. Calculate the daily error of the Chronometer on Greenwich Mean Time by applying the Rate for each da^i for several days in advance, and write it on the margin of the Nautical Almanac, each day's error opposit* the day of the month. So that the error of the Chronometer can be taken out and applied at once from the same page that the Sun's Declination and Equation of Time are taken from. This will be found a ▼ery convenient mode, and save some time and trouble. To Find the Accumulated Error of a Chronometer , after a lapse of Time. Multiply the Daily Rate, which is generally given in Seconds and Tenths of Seconds, by the days apsed since the last Rate was ascertained, and divide by 60, (if it is above 60), will give the accumula- ted Rate, lu x.Iinutes and Seconds. This applied to the original error, f Fa.st, and the Daily Hate Gaining, Add, ^j^ tb Pt t ' } ^''''^) ^"*^ ^^^ Daily Rate Gaining, Subtract, I Fast, and the Daily Rate Losing, Subtract, [ Slow, and the Daily Rate Losing, Add, will give the whole error of the Chronometer on Greenwich Mean Time on that day; and it is applied la [■ the 8am<) manner as for a common watch, and requires no explanation. 140 J^AtJTIOAL ASTEONOMY. Mode of Observing Altitudes. In taking Altitudes of any of the Heavenly Bodies, for the purpose of finding the time at the Ship, th« times by Chronometer at which they were observed, must be noted, and the Altitudes are then added •together and divided by the number taken. The times by Chronometer are in like manner added together, and divided by the number taken. This gives the Mean of the Altitudes, and the Mean of the Times 'by Chronometer. By this mode we are supposed to obtain a more correct result by taking the Arith- imetical Mean of the Altitudes than can be obtained from one Altitude alone. At all events, it prevent" imistakes in the readings off. (See also the method given at page 1-24.) TTie Times at which the Altitudes were observed to be taken by a Watch. A« the Chronometer must, on no account, be removed from tlie place where it has been fixed for the TOyage, it may not be convenient to note the time direct from the Chronometer at the time of taking the Altitudes, and in that case we use a Hack or common Watch, furnished with a Second Hand, with which the Times of the Altitudes are taken. It is then immediately afterwards compared with the Chronometer, and their difference noted. This difference being then applied to the Mean of the Times by "Watch, at ivhich the Altitudes were observed, will give the Time of the Altitudes by Chronometer. Its error being then appHed, we have the Greenwich Time. The Mean Time at Ship by an Altitude of the Sun is then found in exactly the same manner as that given at Eage 124, using the Greenwich Time by Chronometer, in making the Corrections, in the room of the approx- oate Greenwich Time. The following is an example of the whole process, as is usually done at Sea, and both Latitude and Longitude found at Noon. EXAMPLE 1. March 6th, 1854 (at the end of the Sea Day), a Ship which sailed from her last port 5 days previously had the following observations in the morning: The Error of her Chronometer on Greenwich Time, March 1st, was Oh 2m 148 fast, and the Daily Rate 2s and 6-10 gaining. Ship sailed N. W. 60 miles until Noon, when the Sun's Merid- ian Altitude observed was 46° 32' S., and the Longitude by Dead Reckoning being about 54° W. Required her Latitude and Longitude in at Noon. Bun's Obs. Altitude L. Limb.. 10° 12' Times by the Watch 1h Urn 24a 22 12 30 35 13 60 S)69' 3)37m 443 1 Mean of the Altitudes 10° 23' Mean of the Times by Watch 7h 12m 353 Oorr., Table IX Add 7 Comparison Chro. fast of Watch 3 49 64 Sun'i True Altitude 10° 30' Time by Chronometer A M llh 2m 298 Sun's Polar Distance 96 41 Log. 0.00214 Accumulated Error Fast Sub. 2 27 Latitude ^8 5_Log. 0.10396 Greenwich Time from Midnight llh Om 28 Sum 1 44° 16' Add. 12 HalfSum ^ 2° 8' Log. 4.48686 Greenwich Date, March 5th • 23h Om 23 Difference "6 1V38^ Log. 4.94445 Mer. Alt. Obs 46° 32' S. Difif. Decl, lh=.68 Apparent Time 19h 12m 24s Log. 9.53^41" Corr., Table LX .. Add 11 Cor. for Ln. 5 4°W. S jh Equation of Time Ad d 11 32 True Altitude 45° 43 ' 174 " Mean Time 19h 23m 56s Zenith Distance 44°17'N. ^^ Greenwich Time 23 2 Declination 6 37 S. 60 )203 " Longitude in Time 3h 36m 6s = 54° 1' 30" W. Lat. at Noon 38° 40' N. Corr 3' 23 " Departure made to Noon, 35' — Diflf. Long . 45 W. Course N. W. 50m D. L. 35 Decl 5° 40' S. Long, of the Ship at Noon 64° 46' 30" W. Lat. at Sights 38° 6' N. Decl 5° 36' 37"S. To find the Comparison. Sun's Dec. Noon, March 6th. 5° 40' 2" S. Diflf Ih. .58" Time by Chronometer llh 5m 548 Corr. Ih before Noon. .Add 68 Time by Watch 7 16 Corrected Dec 6° 41' 0" (Jomparison Chro. fast of Watch 3h 49m 54s _90j_0_0 Polar Distance 95° 41' 0" To find the Error of the Chronometer. Chronometer fast March 1st Oh 2m 14s Equation of Time 11m 31s -74 Diflf. Ih 60-J Days elapsed 5, daily rate 2s 6-10 — 13 Corr. Ih before Noon. ...Add '60 Accumulated Error Oh 2m 27s Correct Equa 11m 328 -34 RULE FOR TURNING TIME INTO LONGITUDE BY COMPUTATION. Tom the Hours into Minutes, and divide by 4 This gives Degrees, Minutes, and Seconds. JBrompfc.— 3h 36m 68 is 216m 68, which, divided by 4, gives 54* 1' 30". , RULE FOR TURNING LONGITUDE INTO TIME BY COMPUTATION. Multiply the Longitude by 4. This turns the Degrees into Minutes of Time (which, divided by 60, gives Houri and Minutes), the Minutes of Longitude into Seconds of Time, and the Seconds of Longitude into Thirds of Time. Example.— LougMwdQ 64° 1' 30", multiplied by 4, gives 216m 6s = 3h 36m 6s. FINDING THE LONGITUDi;:. Ul FINDING THE LONGITUDE BY CHRONOMETER FROM THE SUN'S ALTITUDE. Referring to the 1st Example, it will be perceived that the Time shown by the face of the Chronometei it llh 2m. 29s., and the accumulated Error subtracted, would give the Greenwich Time from midnight, 111.. Om. 2s. The Mean Time at Ship, from the preceding midnight, being 7h. 23m. 66s., their Difference, 8h. 36m. 6s., is the Longitude in time. This mode of reckoning the two times from the same midnight '« frequently done at Sea, because it is more convenient than to reckon them from the preceding Noon. Th« result in either case is the same. The Time from Noon, A. M., in the one case is found by subtracting it from 24 hours, and in the other from 12 hours. In the Example referred to, the time from Noon is 1 hour, and the difference of the Sun's Declination and Equation ef Time for 1 laour, in the column of the Nautical Almanac, is the correction required, tc ke applied as directed at page 124, No. 7. RULE For Correcting the Sun's Declination at Noon of the Ship by the Nautical Almanac. Multiply the difference for 1 hour by the Longitude in Time, and divide by 60, if requiised, will give th« correction in Minutes and Seconds, to be applied to that taken from the Nautical Almanac, as follows : In West Longitudt, and Declination . . . ." ( Increasing, Add ( Decreasnig, Subtract, In East Longitude and Declination \ }°«'-«^^ingi ^ub^t'"*''^ '^ ( Decreasing, Add, RULE To Reduce the Longitude by Chionometer at Time of Sights to Noon Take the I ^'-tude in as a Course, and the Departure made in the interval, in the Latitude column, the Hifferenee of Longitude is found in the Distance column. Apply this as follows : Observation taken in the morning, in West Longitude .... { gSlini S' Subtract, Observation taken in the afternoon, in West Longitude .... ] OnHin^ EasV Add ' 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 Longitud*. EXAMPLE 2 April 2d, 1854. (End of the Sea day.) The Latitude observed was 30' S7' North. Ship then sailed S. R(true) 60 miles, when the following observation was made in the afternoon, the Error of her Chronometer on Greenwich Mean Time, on the 23d of March, was ascertained to be Oh. 9m. 3l8. fast, and the daily rate 38 4-lOth losing. Re- quired her Longitude in at time of Sights and Noon. Sun'i Obs. Alt 10° 13' Times by Watch ... 5h. 24m. Os. To find the Comparison^ 10 25 Timeby Chro.. 8h. 42m. 48s 9 47 26 Time by Watch, 6 28 8)80° 0' 3)7 5m. Oa. Comparison . . 8h.l4m.48& Mean of the Alt 10° 0' Mn, of the Times by W,. . 5hr26m. Os. Corr., T»)-,le IX ...Add 7 Comparison 3 14 48 True Alt ...10° 7' Time by Chro 8h.39m.48B. Polar L)i9t 84° 67'. . .Log. 0.00169 Accuma error. .Sub . 8 57 LatitMe 80 2. ... Log. 0.06262 Gr. Vnt^, April 2d . 8h. 80m. f > Sum .'T25° 6' Chr fast, MarcL aivi. Jb. 9m. 81b. Half Sum 62° 33',. . . Log. 4.66368 Days elap. 10. Rate 3s. 4-1 0th =-34 Difference 52° 26'. . . Log. 4.89908 Accumulated error Oh. 8m. 57b. fast App.Time 5h. 24m. 548.. . .Log. 9.62707* „ . ^ ,. . ., , .« =.. rr/' xt T^•* iu ^t,n E^iktion ... Add 8 35 Sun's Declina, April 2d . . . 4° 54' 55' N. D.f. Ih ........ ^1" ,, rp. 71—^ — ^ Correction Add 8 4 Time from Noon . ijk Mean Time 5h. 28m. 298. ^ ^ ,. . ,. ^, , ., rz^ — Green Time .... 8 30 51 Correct Dechnation 5269 466 Long, in Time . . 3h. 2m. 22s.=45° 35' SO" W. ^" ^, \ -„TT^7— Dep. made since Noon 35' =Diff Lon. 40 30 Polar Distance 84 67 1 60)484 Long, in at Noon 46° 16' O" W. F*^ Course S.E. 50 miles, D.Lat 85' Dep. 85' Equation of Time, April 2q . . 8m. 418-71 Dif. Ih . . -760 Lat Obs. at Noon 80° 37 ' N. Correction Sub. 6^ Time fr. N n, 8_ib Lat Time of Sights 30° 2' N. 3m. 368-34 6 000 6-87-6 Note. — Tie Longitude obtained from Morning Altitudes and brought on to Noon, very seldom agrees with the Lon* fitude obtaii ed from Afternoon Altitudes and reduced back to Noon. This is supposed to be caused by uneqaal Mfraction in the Atmosphere, together with errors in the observed Altitudes, errors in the Instrnments, and that oiaa kioorrect Latitude used in the computation. 142 NAUTICAL ASTRONOMY FINDING THE LONGITUDE BY CHRONOMETER FROM THE SUN'S ALTITUDK EXAMPLE 3. May 20th, 1854. (Eud of the Sea day.) A Ship being in South Latitude, and in about 77° East Longitude, ih the morning the Mean of several Altitudes of the Sun was observed to be 12° 10', and the Time by the Watch 8h 10m. 20s., which, on being compared, was found to be fast of the Chronometer 5h 15m 38s, and on the 30th April this Chronometer was found to have been slow on Greenwich Mean Time Oh om 10s, and the rate losing daily 4 sec. and 7-lOth. Ship then sailed on a S. E. Course (true) 20 miles, until Noon, when the Sun's Meridian Altitud« (Sbserved was 33° 14' N. Required her Latitude and Longitude in at Noon. Time by Watch 8h 10m 20s ,7, ^ , ., ^ Comparison 5 15 38 „ To ,fmd the Comparison^ ^ Time by Chronometer, . 2h 57m 42i FaceofChro. A.M 2h 54m 42s -jj^g ^ ^^^^^j^ g ^3 20 Log. 0.02674 Accum. Error Add 6 44 Log. 0.09435 G, Sun's Obs. Alt 12° 10 Cor., Tab. LK . 8 True Alt..... 12° 18' Polar Dist... 109 54 26 158° 37' Latitude 36 Sum Half Sum "•ifference App. T...20h 13m Eq. of T.. 3_ Mn. Tirae20h ' Gr. Time 15 Lon. in T.liT T.fi-omMid 3h Add 12h 79M8y Log. 4.26840 Gr. Date, May 19th 15h Subtract from 24 Time Before Noon 67° Oj' 5s 47 Log. 4.96405 Log. 9.35354 Comparison 6h 15n^ 388 Chro. Slow, April 30th Oh 5m 10a Im 268 Days elapsed 20X4s.7-10th = 1 34 Accumulated Error Oh 6m 44« Im 268 8h 68m 34s 9m 188 1 26 Dep. made | to Noon \ Lon 7m 52 76" 68' 0" 14 . .— D. L. 17' 30 E. Sun's Dec. 20th May 19 Correction Sub. Correct Declination . 58' 19" N. 4 39 19° 90 53' 40" Diff. Ih -81" Before Noon . . 9h 60)279 Correction... 4*39 '"•^fS'^'Pt 77° 16' 30" K at Noon J Eq. of Time.. 3m 468-15 Diflh.-140 Correction... A dd 1 '26 Bef. N 9h Correct Eqa..3m 47s-41 Corr..l-26-O Polar Distance 109° 53' 40" Meridian Altitude 33° 14' N. Dif. Dec. lh= 11 Long... 77°= =31" =. 5h _332 Zenith Distance 56° Declinatinn 19 Lat. of Ship at Noon . . Course S. E. 20 miles. Dif Lat. 36° 39' 14 25' 35' S. 56 N. "" S. Dec. 19' 60)165 2' 35" 58' 19 19° 55' 44" ^f Latitude at Time of Sighta 36° 26' S. EXAMPLE 4. October 10th, 1854. (End of the Sea day.) Latitude observed at Noon 20° 41' South, Longitude in by Dead Reckoning 179° 30' East at Noon. Ship had sailed N. E. 54 miles since Noon, when the Mean of several Altitudes of the Sun was observed to be 18° 45'. Time by Watch 4h40ra 85s, which, on being compared with tlie Chronome- ter, was found to be fast of the Chronometer Oh 14m 223, and on the 10th of September this Chronometer was slow of Greenwich Mean Time Oh 10m 268., and gaining 58. 2-lOth per day. Required the Longitude of the Ship at th« time of the Sights and at Noon. Sun's Obs. Alt Correction, Table IX. 18' Add 45' 9 True Altitude 18° 54' Polar Distance 83 29 Latitude _20 3 Sum 122° 26' Log. 0.00282 Log. 0,02715 Log. 4.68260 Log. 4.82816 App. Time 4h "48m 538 Log. 9.54073 Equation of Time. . . . Sub. 12 60 Mn. Time at Ship, Oct 10th~4h 36m 38 Add 24 Half Sum 61 Difference ; "iP" 3s 3 Mn. Time at Ship, Oct 9th 28h 36m Mn. Time at Green', Oct 9th 16 34 Long, in Time 12h 2m 0=180' Subtract from 360 Long, of Ship at time of Sights 179 Dep. made since Noon 38m — D. Long. 30' 30' 40 0"E. _0 "OsW 30 W Reckoned from Greenwich 180° 10' 0' Subtract from 360 Long, of Ship at Noon 179° 49' 30" K Lat Obs. Noon ;20' 41' S. Course N. K 64 miles=Dif. Lat Sub. 38 Lat at time of Sights 20* S'S. Time by Watch 4h 40m 358 Comparison . . . , 14 22 Face of Chron., A. M 4h 26m 138 Add 1 2 Time by Chronometer "Tch 26m 138 Accum. Error, slow. . . . Add 7 50 Gr. Date, Oct 9th 16h 34m 38 Subtract from 24 0_ Time Before Noon 7h 25m 67b Chron. slow, Sept 10th Oh 10m 268 Days elaps. 30. Rate 5s 2-lOth . 2 86 Accumulated Error Oh 7 m 50'' To find the Comparison. Time by Chronometer. . . 4h 29m iSs Time by Watch 4 43 35 Comparison Oh 14m 22 S Sun'.s Dec, Oct 9th. S. .6° 37' 30" Correction Sub. 6 58 Correct DecUnation. . . .6° 30' 90 32" Polar Distance 83° 29' 28' Equa. of Time 12m 65818 Correction .^. - . Sub. 4 74 Correct Equation. . . .12m 508'44 Di£ lh=-57" 7t t 399 19 60)418 Corr 6' 58" •647 7 >b 4-529 216 Corr 4-74-6 NoTB. — In the 4th E.xample the Ship has crossed the Meridian of 180° Enst, in the interval' between Noon and tlni 4me the Sights were taken in the afternoon, havin? passed from East into West Long-itude, and if bound to the Ea»*- «rard, we would add one day to the Greenwich Date. (See page 139.) FINDING THE LONGITUDE BY CHRONOxMETER. 143 EXAMPLE 5. August 6th, 1854, (end of the Sea day,) a Ship beiug iu North Latitude and about 179° West Longitude. In the Morning the Sun's observed Altitude was 36° 6', and the Time from the Face of the Chronometer was 8h 89m 22s. (beiug P. M. at Greenwich,) which was fast of Green. M. T. Oh 3Uiu 353. Ship then sailed due West 48 mile* until noon, when the Suu3 Meridian Altitude observed was 76° 11' S. Required the Ship's Latitude and Longitud« •n at Noon. Sun's Observed Altitude 36" Corr., Table IX Add. True Altitude 35' Polar Distance 78 Latitude ^ Sum ._13£ Half Sum 69' 6' _n_ ir 4 Log. 0.01925 30 Log. 0.06468 ' 26' Log. 4.54567 Time by Chronometer 8h 39m 228 Chronometer fast of Greenwich 30 35 Difference 34° 9' Log. 4.74924 44' Log. 9.37884 43 Apparent Time 20 5' Equation of Time Add 6 Mean T. Ship Aug. 4 20h 11m 278 Green. Date, Aug. 4 .32 8 47 Longitude m Time llh 57m 20s=179' Departure made to Noon, 48=— Diff. Long. Greenwich Time Aug. 5th 8h 8m 478 F M Add. 24h Om O a Greenwich Date Aug. 4th 32h 8m 478 Meridian Altitude 76° 11' S. Dif. Dec. 41'- Corr. Add. 12 12h True Altitude 76° 23' 60)492 Zenith Distance 13° 37' N. 8' 12" Declination 16 53 S. 17* 1' S. Latitude at Noon. 30° 30' N, D. 16° 51' 48" & 20' 0"W. 55 45 W. Reckoned West from Greenwich. 180° 15' 45" W. Sub. from 360 Long, of the Ship at Noon 179° 44' 15" E. Note. — Here the Ship has crossed the Meridian of 180° West, between the time the Sights were taken and Noon, and she is now in East Longitude. We therefore Sub- tract one day from the Greenwich Date, if the Ship ia bound West. See page 139. Sun's Declination 17° Correction -. . .Sub. 1' 2" N, Dif. Ih 41" 5 28 8h Correct Declination 16° 65' 34 " N. 90 )328 6' 28" Polar Distance 73° 4' 26' Equation of Time 'im 448 64 Dif, Ih 0*268 Corr Sub. 2 "06 8h Correct Equation 6m 428 "68 2-06-4 EXAMPLE 6 November 28th, 1864, (end of the Sea day,) the Sun's Altitude in the Forenoon was observed to be 50° 25', whec the Face of the Chronometer showed 9h 33m 10s A. M. at Greenwich, and which was correct for Greenwich Mean Time. Ship then sailed E. by N. 31 miles, when the Sun's Meridian Altitude observed was 68° 23' S. Required the Ship's Latitude and Longitude at Noon. Sun's Observed Altitude 60° 25' Corr., Table IX 11_ True Altitude 50° 36' Polar Distance 68 42 Log. 0.03073 Latitude _^_2. ^°S- 0.00000 Sum 119° 18' Half Sum 59° 39' Log. 4.70358 Difference 9° 3' Log. 4.19672 Apparent Time 9h 44m 9s Log. 8.93098 Equation 11 54 Mean Time at Ship 9h 32m 15 from Midnight Greenwich Mean Time 9 33 10 from Midnight Long, in Time Oh Om 55s= 0° 13' 45" W. Departure made to Noon 3U=Diff. Lon. 30 E. Long, in at Noon 0° 16' 18" E. Sub. from 12h Om Ss Greenwich Time by Chro 9 33 10 Time before Noon 2h 26m 608 Sun's Meridian Altitude 68° 23' S. Correction 12 True Altitude 68° 35' Zenith Distance 2r° 25' N. Decliuatiou 21 19 S. Latitude in at Noon Course E. by N. 31 miles D. L. Lat time of Sights 0° 6'N. 6 — & Dep. »tl 0° 0' Sun's Declination 21' Correction 19' 21"S. Dif. 26" 1-5 Declination 21° 18' 16" S. Polar Distance 68^° 4I' 44'" Note. — Here the Ship has crossed the Meridian of " Greenwich, between the time the Sights were taken and rjorrectioa Noon, from West into East Longitude. 11m 628 -4 Dif 2 -17 6il 13 •871 24 Equation Hm 543 -21 1742 43 6 217-7 QUESTIONS FOR EXERCISE. Quest. 1. July 20th, 1854. In the Morning the Sun's observed Altitude was 33' 19', when the Face of the Ohroa •hewed 9h 28m 408 A. M. at Green., and which was fast Oh 6m 47s S. Ship sailed on a S. S. W. ^ W. Course 32 mile« •ntil Noon, when the Lat. Obs. was 26° 27' N. Required the Long, of the Shipat the time of the Sights and at Nooa Answer. — Longitude at time of Sights 21° 12' W., and at Noon 21° 29' W. Quext. 2. September 25th, 1854. In the Afternoon the Sun's observed Altitude was 18* 20'. Time by the Chroa Dh 7m 388, beiug P. M. at Greenwich, and which was fast Oh 7ni 2s. The Latitude observed at Noon was 87° 67' S «nd the Course was E. N. E. 29 miles since Noon. Requiied the Long, in at the time of the Sights and at Noon. Antwrr. — Longitude at time of the Sights 64° 49' E,'aud at Noon 64* 15' E. 114 NAUTICAL ASTRONOMY. TO CORRECT THE LONGITUDE BY CHRONOMETER AT NOON WHEN THE LATITUDE IS IN ERROR. 'n the foregoing Six Examples the Latitude used in computing the time at Ship has been deduced from the Latitude by Observation at Noon, and when the Altitudes are observed in the morning we have io ^hat case to wait until Noon, before the Ship's position can be accurately ascertained. And as it is sometimes of importance to know the Longitude by Clironometer as soon as possible after the Sights are taken in the morning, with.in a few minutes of the truth, we have in that case to use the Latitude by Dead Reckoiiinir from the preceding Noon in working the Time, and which may be considerably In error, and as before explained at page 122, greatly affects the Hour Angle, (except when the Sun is on ihe Prime Vertical.) so that after finding the correct Latitude we have to work it over again. To save all this trouble Tables A and B, No. XXX., are given for the purpose of correcting the Longitude iy Chronometer, brought on to Noon for the effect of an error in the Latitude used in computing the time ftt the Ship, and all we have to do is to take out the Correction for the Longitude from the Tables, (which ts expressed in minutes and seconds) for each mile of Latitude. This, multiplied by the mimber of miles »f error in the Latitude worked with, gives the whole correction to be applied to the Longitude brought on m Noon, and the result is the correct Longitude of the Ship at Noon. RULE For Using Table XXX. , Enter Table A with the Latitude worked with at the side, and the Hour Angle at the Top, and at the Angle of meeting take out the Correotion. Enter Table B with the Declination at the Side and the Hour Angle at the Top, and at the Angle of meeting take out the Correction. When the Latitude and Declination are of the same name, the difference between the Corrections found In Tables A and B is the Correction of Longitude for each mile of Latitude in error. And Note whether the Correction found in Table A be greater or less than that found in Table B. When the Latitude nnd Declination are of contrary names the Sum of th« Corrections in Tables A and B IS the Correction of Longitude for each mile of Latitude in error. Multiply the Correction for Longitude by the number of miles of error in the Latitude, which will g iv* the whole Correction for Longitude. To Apply this Correction. When the Corrections in Tables A and B are subtractive and the -one found in Table A is leas than thej one in Table B, apply the Correction as follows : Latitude worked with being too Small, Add in West Longitude, Subtract in East. Latitude worked with being too Great, Subtract in West Longitude, Add in East. When the Corrections in Tables A and B are additive, and also when the Correction in Table A is greattf^ than that in Table B, Subtractive, as follows : Latitude worked with being too Small, Subtract in West Longitude, Add in East. Latitude worked with being too Great, Add in West Longitude, Subtract in East. To or from the Longitude by Chronometer, brought on to Noon by the Dead Reckoning, will give thej Ship's Correct Longitude by Chronometer at Noon. EXAMPLES In Using the Tables Lat worked with 30° 30' N, H. A. 3h 15m Tab. A— 31" Lat. worked with 60" 10' N., H. A. 2h 45m Tab. A 1' 21 Dec 22° 30 N. (same name) H. A. 3h 15m Tab. B 33" Dec. 23° S. (contrary names) H. A. 2h 45m Tab. B 39" The Diflf. is tlie Ccrr. for each mile of Lat 2" The Sum is the Corr. for each mile of Lat 2' 0"' Lat. worked with fouud to be too amall. lOm , Lat. worked with found to be too great 10 Whole CoiT. for Lonsr. to be Added 20" Whole Corr. for Long, to be Subtracted 20' Long by Cliro. brought on to Noon 60° 13' 30" W. Long, by Chro. brought on to Noon 30° 14' 'W , Clorr. Long by Chr... at Noon '^O* 13' 60"W. Coireet Long, by Chro. at Noon 29° 54' Wj The Latitude and Declination being of the same name The Latitude and Declination being of contrary namei the Difference of the Corrections in the Tables io the Cor- the Sum of the Correction in A and B is tbe CorrectiottJ rectioD Additive, because the Latitude was too small and Subtractive, because the Latitude was too great and th»| llie longitude West. . Longitude West TO CORRECT THE LONGITUDE 146 ro CORRECT THE LONGITUDE BY CHRONOiMETER AT NOON WHEN THE LATITUDE IS IN ERROR EXAMPLE 9. March 6th, 1854. (End of the Sea day.) At about 7h 30m in the morning, the Sun s observed Altitude waa 10* Time at the Ship was found, and the correct Longitude by Chronometer at Noon. Sun's Obs. Alt 10° 23 Cor., Tab. LX... Add 7 30' 40 53 Ti-ue Alt 10 Polar Dist 95 Latitude 37 Sum 144° 3 Half Sum 72°_2' 32' Log. 0.00213 Log. 0.10278 Log. 4.48920 Log. 4.94404 Difference 61' H. A.4h47m I j^ 7B-.Log. 9.53815 63s Ap. Time ) ° Equa. of T. . A dd 11 32 Mn. T. at Ship. 19h 23m 398 Gr. Time 23 2 Long, m Time."~3h 36m 238 Lo.54* r45"W. Dep. maiie to Noon 36'«=«=D. L. 45 Approx. Lon.by Chro.at Noon. .54° 50'45"W. Cor. from Taoie XXX Sub. 4 12 W. Gr. T. by Chro. A. M.. llh. Om 28 Same as Examp. Ist, page 141. Add. 12 Sun's Corr. Dec 5° 40' S. Gr, Date, March 5th, 23h. Om 28 90 Polar Dist, 96° 40 ' Equa. of Time. . 11m 32e True Course to Noon N. W. 50, D. Lat 36' N. and Dep, 35 W Lat by D. Reckon, at time of Sights. . . 37° 53 ' N. Lat. by D. Reckon, at Noon 38' Lat by Observation 38 28 40 Error in the Latitude worked with 12' too small. Lat. worked with 38° and H. A. 4h 48m in Table A, Corr. 16" Dec. 5° 40' of (contrary names) H.A. 4h 48m in Tab.B. Corn « Their Sum as the Correction per mile 21 Number of miles error in the Latitude 12 6 0)252" ^ Whole Correction for Longitude 4' 12" Cor, Lon. by v'hro, at Noon 64° 46' 83" W. Agreeing within 3" of the Long, in Example Ist, page 140. EXAMPLE 10. May 20th, 1864. (End of the Sea day.) At about 8 o'clock in the morning, the Sun's observed Altitude wtut 12° 10', and the Greenwich Time by Chronometer 3h Im 268, A. M., or l6h Im 268, from the preceding Noon. The Latitude in by the Dead Reckoning from the preceding Noon was 36° 40' S. Ship then sailed S. E. (true) 20 milet until Noon, when the Latitude observed was 36° 39' S. Required the Error in the Latitude used in finding the Time at the Ship, and the correct Longitude by Chronometer at Noon. Sun's Obs. Alt 12° 10' Corr, Table LX Add 8 True Alt 12° 18' Polar Dist 1C9 54 Latitude 36 40 Sum 1 58° 52 Half Sum 79° 26' Difference 67 Log. 0.02674 Log. 0.09676 Log. 4.26335 Log. 4.96445 H.A.3h46m. Ap. T..20h 14m Os Equa. of Time . . Sub. . 3 47 Mn.Tirae at Ship. , ,20hTom 133 Green. Time 15 1 26 Loner, in Time . , . Log. 9.35030 . . 6h 8m 47& Dep. made to Noon 14'— D. Long. Approx. Long, by Chro.at Noon. . Corr. from Table XXX Correct long, by Chro at Nooo . , Til is agrees exactly with the ;=.Long. 77°11'45" E. made. 17' 46" E. 77' ■ Sub. 29' 30" K 14 K 77° 15' 30" Long, in Example 3, G.T.by Chro., A.M. 3h Im 26s Same as Ex.3d, page 142. Add 12 Sun's Dec cor. 19° 54' It 90 Gr. Date, May 19th, 16h Im 268 Polar Dist.. 109° 54' Equation of Time 3m 478 True Course to Wn S. E. 20 miles. D. L. 0° 14' Dep. 14 Lat. by D. Reck, at the time of Sights. _36 40 Lat. bv D. Reckoa at Noon 36° 54' S. Lat by Obs. at Noon 36 39 S. Error in the Latitude worked with 16' too great, Latworked with 37° S. H. A. 3h 46m in Tab, A. Corr. 80" Dec. 20° N. (eon. name) H. A, 3h 45m Table B. Corr . 26 Their Sum is the Correction per mile 56' Number of miles of error in the Latitude 15 280 56 60)840" Whole Correction for Longitude Sub,. . 14' 0" Note. — When it is of irjportance to know the Ship's trni,' position at Noon directly the Latitude is observed, TabJ* XXX will be found of great service. For instance, after Seven Bells we can estimate the Course and Distance the Ship will have made to Noon new enough, so as to work up the day's work and find the Latitude by Dead Beckoning, and also to bring up the approxi- mate Longitude by Chronometer to Noon. Then the instant the Latitude by Observation is determined, the Error of the Latitude by Dead Beckoning can h9 found, and the approximate Longitude by Chronometer corrected, as in tlie above Examples. This Table will also show at once the effect of an error of one mile of Latitude in produciug an error m the Loo^i hide by Chronometer in any given Latitude; and it will be perceived that an error of this kind has the greatest effeot '~ Tiigh Latitudes. 140 NAUTICAL ASTRONOMY. TO FIND THE LONGITUDE BY CHRONOMETER AT SUNRISE OR SUNSET. The method of finding the Time at the Ship from the Sun's Rising or Setting is given at pages 128 and 129, and the same Examples will answer the purpose of finding the Longitude by Chronometer ; because we have only to compare the Watch with the Chronometer, and thence find the Greenwich Time at which the Sun rose or set, or the Time may be taken at once from the Chronometer without the Watch. Then the difference between the Mean Time so found at the Ship, and the Greenwich Time by Chronometer is tri*-. Longitude in Time. EXAMPLE I.— (See page 128.) Jan. 25th, 1864. Latitude in 38° 42' North, the Sun's Lower Limb was observed to Set, by Watch, at 5h 3m 258, which, on being compared with the Chronometer, was found to be 7h 7ra lis slow of the Chronometer. The Mean Time at the SLip was found to be 5h 11m 16s, and the error of the Chronometer on Greenwich Mean Time 3m 208 too fast Required the Longitude of the Ship. Tim* by Watch at Sunset 6h 3m 258 Watch Slow of Chronometer 7 *? 11 Time by Chron. at Sunset T 12h 10m 36s Green. Mean Time at Sunset, Jan. 26tb. . 12h 7m 16a] Chroa fast of Greenwich Mean Time 3 20s Mean Time at Ship do Jan. 25th.. 5 11 16» Oraen. Mean Time at Sunset 12h 7m 168 Long, of the Ship at Sunset, 104° 0' W. =^^6h~66m~~OiJ EXAMPLE 2.— {Same as at page 129.) June Ist, 1854. In Latitude 26° North, the Sun's Upper Limb was observed to Rise at the instant the Tim«] moted on the Face of the Chronometer was lb 6m 12s A. M. at Greenwich, and which was Slow of Greenwich Mean Time 2m 24s. The Mean Time at the Ship was found to be 5h 9m 36s, the Ship being in East Longitude. Required ibe Longitude of the Ship. Time by Chronometer at Sunrise Ih 6m 12s, being A. M. at Greenwich. Chronometer Slow of Greenwich Mean Time 2 24 Greenwich Mean Time from Midnight, June Ist Ih 8m 36 or May 31st. . 13h 8m 86s Mean Time at the Ship from Midnight, June Ist 6 9 36 or May 31st. . 17 9 86 Longitude of the Ship at Sunrise, 60° 16' 0"E.= 4h Im Os As no reflecting instrument is required in this Observation, (we use in its room the common Spy-Glass.^ its accuracy, therefore, rests entirely upon the instant of time noted by the Chronometer at which the Sun ■ Upper Limb at rising, or his Lower Limb at setting, touches the horizon. This is liable to a small error,! eometimes, in consequence of unequal refraction and mirage at the horizon. (See Note at page 129.) The Latitude of the Ship may also be determined by an Altitude of a Star or Planet at twilight, anjl the Ship's position found as correctly as at Noon, as follows : Enter Table XVIII with the day of the month, and find what Star will pass the Meridian a few minutes before Sunrise, or after Sunset; or inspect the Nautical Almanac, and find what Planet will pass th« Meridian about that time, as directed at page 104, No. 2. Compute the Altitude, and find the Star as directed at page 106, No. 3, or find the Planet as directed page 104, No. 3, and observe the Meridian Altitude. EXAMPLE Of Finding the Latitude at Sunset by a Star. — (See Example 1st.) January 25th, 1854. (End of the Sea day.) The Latitude at Sunset being required, we look into Table XVIH •nd find the nearest Star on the Meridian to be the N. Pole Star, which passes at 4h 37m, and ie not vis'ble on accouni •f the Sun-light, but at 5h 15m, or 15m after Sunset, its Altitude was observed to be 40° 18'. We Cod iia Latitude U) be 88° 42' North. (See this method at page 109.) EXAMPLE Of Finding the Latitude at Sunrise by a Star. — {See Example 2d.) June Ist, 186't. (End of the Sea day.) The Latitude at Sunrise being required, we first add 12 hours to tjh Apparent Time at Ship, 6b 12m, which gives the App. Astrou. Time, May 81st, 17h 12m, and on ref<>rrir.g to Table'' XVIII, we find that the Star Gruis passes the Meriiliuu at 17h 24m, or 12m after Sunrise, and "Cy computing the Meridian Altitude, and setting the Index of the Quadraut at 17° 20', the Star will be found at that Altitude in tha Soutii point of the horizon at a few minutes before Sunrise, and supposing the observed Altitude to have been 17° 27 , the Latitude in would be 25° 0' NortL NoTB. — As the change o Akitiide of these two Stars, when near the Meridian, is very slow, an error of a few minate* ta the time at the Ship wil je of no eonseonenoe. Hence both the Latitude aud Longitud* of the Ship may be found 4T ObserTation, at Suurisa : Sunset. FINDING THE LONGITUDE. 147 FINDING THJ^. LuNoITUDE BY CHRONOMETER AT NOON FROM EQUAL ALTITUDRS OF THE STI>J The method of finding ihe Apparent Noon at the ship from Equal Altitudes of the Sun near the Mcridiaa and thence the Mean Noc o, is given at page 130, and in finding the Longitude by Chronometer at Noor. we have on^y to compare theiWatch with the Chronometer, and apply the comparison to the middle Time by the Wc'ch, which will give the time by Chronometer at apparent Noon. Or if we Note the time by Chrc nomet. - when the Sun's Altitude is the same both before and after Noon, the middle of the times is the time by Chronometer, at apparent Noon, (See Note at the bottiom of the page,) to which its error on Green- wich, applied as usual, gii'es the Greenwich time by Chronometer, when it is Noon at the Ship. The only Correction necessary in this case is for the Equation of Time, which must be Corrected a« usual to the Greenwich Time by Chronometer, and applied as directed in the Nautical Almanac to Apparent Noon, will give the Mean Noon at the Ship. Then the difference between the Mean Noon at Ship and the Greenwicli Mean Time by Chronometer is the Longitude in time, which turned into Degrees and Minutes by Table XXVI., in the Longitude of the Ship at Noon. EXAMPLE l.—{See Page 180.) April 2d, 1854. (Ebd of the Sea day.) The Altitude of the Sun's L. Limb was observed to be 85° 40' at a few minutes before Noon. Tinoe by Chronometer Ih 46m lOs P. M. at Greenwich, and when the Sun fell again to the •ame Altitude in the Afte.uoon, the Time by Chronometer was 2h 12m 168, and its Error 3m SSs Fast. Required the Longitude by Chronom ■Xier at Noon. Sun's Observed Altitude A. M. 85° 40' Time by Chronometer. . . Ih 46m lOs P. M. at Oreea do do P. M. 85 40 do do 2 12 16 do. do. A)3h 58m 26s Lqua. of Time April 2d 3m 4l8 71 Diff. Ih -760 rj.- , o, ,, ,„ — — - CJrr. SuU 1 60 2h 3^:°"« ^7 ^^^^^ • • ' ' ^^ ^^'" ^^s at App. Nooa „ „ . . ,, Chro. Past of Green., Sub. 3 33 Correct Equation Add 3m 40s -21 ISOO ^ ., t,. -rr App. Noon at Ship Oh Green. Mean Time Ih 65m 408 »/ »T r,, • — ; Mean Noon at Ship 3 40 Mean Noon at Ship Oh 3m 408 t r *i 01 ■ • ^- ,. ^, „„„ , „, ^ Lon.of the Ship in time.. Ih52m 08 = 28 O'W. at Noon EXAMPLE 2.— (5« S^^ 56m 40s at App. Nooa ^/'^ ,^ ^,^ Chr. Slow of Green., Add. 3 10 M.-an Noon at bhip llh 6'Jm 50s .^ ,. t,- — ; — r ^ Green. Mean Time 8h 59m oOs Comparison. Mean Noon at Ship 11 59 50 oi:™S°e7stw;d;;:-.::;-.::;-.;::-.::: '? IT ,T ^-■■»'*'^'"p'°^'°- ^^ »■» »•=«• ''•■^■■"•'««» WaiAifa Fast of Chronometer 3h Om 2bs Degree of Dependence. This method, as before observed at page 130, is most suitable for Low Latitudes ranging to 30° on each Bide of the Equator. Because when the Ship makes much way, and the interval between the Altitudes i» great, the First Altitude will not be equal to the Second, on account of the Ship's change of place of Ob- lervation and the Sun's change of Declination. Except when she Sails due East or West, in that ca&e it becomes a question of Time only, and does not affect the result Note.— Bat when she makes much Northing or Southing in the interval, it is evident that the sume Altitudes will no cnger give the correct middle time at Apparent Noon. The Error in the Altitude will be equal to the Difference of Latitcde the Ship has made in the interval. For instance, a Ship Sailing South in North Latitude, the P. M. Altitude would be too small, and Sailing North the P. M. Altitude would be too great by the Amount of the Difference of Lati- tude made in the interval, therefore the Kule is, when Sailing towards the Sun, ve must increase the A. M. Altitude which is on the Quadrant by advancing the Index of the Instrument equal to the Difference of Latitude made in the interval. But in Sailing/rw» the Sun we decrease the A. M. Altitude by screwing back the Index equal to the Diflfer- euce of Latitude made in the interval, and when the Sun falls to that Altitude in the Afternoon, and the time noted by Watch or Chronometer, the correct middle time is found at Apparent Noon as before. But as this method is much used at Sea in its present form, because of its extreme simplicity and independence of both Latitude and Declination »nd which, w.th ordinary caution, it is well adapted for the use of Seamen in detecting any very gross error in the mora rej^iar mod> ?.' working out the Time at Sea. 148 NAUTICAL ASTRONOMY. FINDING THE LATITUDE BY THE SUN, AND THE LONGITaOE BY CHRONOMETER, BY THE MOON'S ALTITUDE AT NOON. When tne Sun is on the Meridian, his Altitude determines the Latitude, and when the Moon is at • proper distance from the Meridian her Altitude will give the Time at the Ship, and thence the Longitud* y Chronometer at Noon. • Or the Moon may be on the Meridian, when her Altitude will give the Latitude, and an Altitude of th« Sun at the same time will give the Longitude by Chronometer. Or Altitudes of the Moon, Planets 'or Stars taken in like manner will give both Latitude and the Longi* tude by Chronometer at the same lime. The advantage of this method is that the Latitude being correctly known at the time of taking the Sights for Chronometer the Altitudes of the object for Time mu.y be taken nearer to the Meridian than other- wise without producing an Error in the H. Angle, alway.s providing that their change of Altitude be not less than 6' in one minute of time. EXAMPLE BY THE SUN AND MOON AT NOON. March 24th, 1854. (End of the Sea day.) The Latitude observed from the Meridian Altitude of the Sun ■wa* 40° 10' S. and at the same time the Altitude of the Moon's Upper Limb was observed to be +1° 40' to the West- ward of the Meridian, and the Greenwich time by Chronometer was 17h 48m 278. Raquired the Longitude in by Chronometer at Noon. Obs. Altitude ]) 's Up Limb 41' 40' Green. Time by Chron., March 23 17h 48m 21i Semid. 16', Dip. 4' Sub. 20_ 12 <> Hor. ParL 59' and Altitude 41° 20' Green. Time past Midnight 5h 48m 27l Gives the Corr., Table XXV ^3 rr, Auv ^ X9' 1' Sun R. A. 23d Oh 9m 228 Diff. Ih 9i True Altitude *z 6 aji o ^o lok PolarDist 66 53 Log. 0.03636 Add 2_J2_ 18h Latitude Observed 4 10 Log. 0.11681 Sun's Cor. R A Oh 12m 48 60)162 gum 149° 6 ' Corr 2m 42i Half Sum 74° 33' Log. 4.42553 '^^"^""^ r-^^, r .nonoo 5 '8 Declination March 23d, Mid 23° 51 & difference 32_^ Log. 4.73022 ^^ March 24th, Noon 22 20 a J '8 Hour Angle, W«8t 3h 34m 878 Log. 9.30891 Difference of Declination in 12h= 1° 34' D 's R Ascen ^0 38 ^20 ^^^.^ rpj^j^j^ xXIII 0° 44' R. Ascen. of the Meridian 24h 12m 578 Declination at Mid 23 61 Sun's K. Ascen Su b. 12 4 Correct Declination 2'3° V'S. App. Time at Ship 24h Om 538 ^yO Equation of Time Add. & 31 ^ .^ p^j^^j. Djgtance 66° 53" Mean T. at Ship, March 23. . .24h 7m 248 G. M. T.by Chr. March 23. ... 17 48 27 p 's R. A. Mar. 23d . ..20h 23m 588 at Mid. Longitude in Time 6b 18m 578 Mar. 24 tb. ..2 63 47 at Noon. T^nmUiAe of the Shin 94° 44' 15" E. at Noon. Say as 12b is to 29m 548 so is 5h 48m T. from Mid ^ ^ Pro. Log. of 12h, Table XXXIV. 1.1761 Arith. Comp 8.8239 Eaustion of Time 6m 458 27 -766 Pro. Log. of 29m 54s 0.7796 ^ Oorr Add 138-7 9 18b Pro. Log. of 5h 48m 1-4918 Correct Equation 6m 318-48 13-78-8 1.0953 Corr. 14m 27l ^ R. Ascen. at Mid 2 0b 23m 53 > '8 Correct R. Ascen 201i 38m^0t Finding the Latitude by a Planet, and the Longitude by Chronometer by the Moon's Altitude at the same time. QUESTION, October Sd, 1354. In North Latitude and West Longitude at Twilight in the evening the Meridian Altitude of the Planet Jupiter was observed to be 39° 8' S. About the time the Altitude of the Moon's L. Limb was la" 19 East of the Meridian, and the Greenwich Time by Chronometer, October 3d, llh 23m 62s P. M. Required the Latitude by Observation and the Longitude by Chronometer. A7iswer.—ln this case the Correct Altitude of the Moon is 14° 24', her Polar Distance 102° 28', her Hour An^le 4h 28m 40s, R. A. 22h 52m 438, R. A. of the Meridian 18h 29m 38, the Sun's R. A. 12h 88rn 198, Apparent Time at Ship 5h s'om 448 P. M., and the Mean Time 6h 39m 40s. The Latitude observed 28° 16' N., and Longitude by Chronometer 86° 3' West Note 1 -av perhaps be necessary here to repeat the remarks already made at pages 101 and 104, wnich iSj that the Meridian psnrMiges of the Moon and Planets are given in the Nautical Almanac for Mean Time, and which must oe turned Into Apparent Time by Applying the Equation of Time the contrary way to what we would do in turning Apparent In the ease of the Planet Jupiter in the above Question he passes the Meridian by the Almanac at 6h 81m. The Eqna- teon of Time, 11m, added, gives the Apparent Time 6h 41m, at whioli lie passes the Meridian, or that shown by ■ W»toh regulated to Apparent Time at the Ship. The Moon's Meridian passage is found in like manner. FINDING THE LATiri)DE AND LONGITUbE 149 riNDING THE LATITUDE BY A STAR, AND THE LONGITUDE BY CHRONOMETER, BV A PLANET. EXAMPLE. Api-U 2d, 1854. (End of the Sea day.) In North Latitude and West Longitude, the Meridian Altitude of thf; Star Castor was observed to be 77° 52' North, and at the same time tLe Altitude of the Planet Saturn was 37° 53' tc the Westward of the Meridian iu the evening twilight, aua the Greenwich Tinje by Chronometer was lOh 68m lOa P. M. Required the Latitude in and the Longitude by Chronometer. Mer. Alt # Castor 77° 52' N. Corr.,'rab. XX.Sub. 4 True Alt 77° 48' Zenith Dist 12° 12' S. #'8 Dec. 1864 .. 32° 12 N Latitude in 20° O'N. at the time Castor passed the Merid., or at 6h 40m P.M. Obs. Alt. Sat 37° 63' Corr.Tab. XX, Sub. 5 True Alt 37° 48 , Polai Dist 71 50 Log. 0.02221 Lat Obs 20 G. T. by Chro. | Ap. 2d, f lOh 6&m 108 DecSat 18' 10 ^0 Polar Dist., 7>° 50 12^° 38 Log. 0.02701 Half Sum Difference 64° 49'Log. 4.62892 27 I'Log. 4.65729 Sat H. Angle 3h 41m 50s. Log. 9.33543 R. Ascen.. . . ■ 3 47 27 R.A. of Mer.. 7h 29m 178 Sun's R. A. . . 47 22 App. Time. . . 6h 41m 658 Equa Add 3 33 Mean Time at Ship. 6h 46m 28s Gr. M. T by Chro. . 10 68 10 Saturn's R. A. \pn^ 2X 8h 47m 153 April ^d, 3 47 41 Say as 24h is tr> to the Ourroctior Right Ascen., Apnl 2q Correct Right Ascen 3h ilis^ 27a 263, so is llh Oh Om 128 3 47 15 Sun's R. A. April 2d. . Oh 45m 43s. Di: Ih, 9» Correction Add 1 39 Un Correct K Ascen.. Oh 47m 229 90* ft Long, of Ship 63* 10' 30" W.— 4h 12m 428 at 6h 41ra 56s [P.M. Equa. of Time 3m 4l8 '71 Dift. ih. .-761 Sub. 8-25 11 Correct Equa 3m 338 47 Finding the Latitude in and the Longitude by Chronometer at the same time by Two Stars. •8-25-C EXAMPLE. August 22d, 1854. (End of the Sea day.) In South Latitude and East Longituds, the Meridian Altitude of thf Star Aldebaran was 63° 26' North, and at the same time the Altitude of the Star Siriua was 63° 47' East of th« Meridian, at twilight in the morning, and the Greenwich Time by Chronometer ^ as, October ilet, 14h 57m 41i Required the Latitude iu and the Longitude by Chronometer. 26' 4 N. Mer. Alt # Aldebaran 63 Correction, Table XX Sub. True Altitude 68° 22' Zenith Distance 26° 38^ S. #'s Deehuation 16 13 N. Latitude iu by Observation 10° 25' S. At the time Aldebaran passed the Meridian, Aug. 21st, ISh 18m, or on the morning of Aug. 22d, at 6h 18m. e Latitude m by Dead Reckoning, Take a Latitude, say 30', to the Southward of the Dead Reckoning, with which •nd the True Altitude, and tlie Sun's Polar Distance, find the Longitude by Chronometer as usual. Again, take a Latitude, say 30', to the Northward of the Latitude by Dead Reckoning, and with the same Altitude and Polar Distance find another Longitude in by Chronometer. I>ay ofi" these two positions on the Chart and Draw a pencil line between them, which, extended t« any Land in the vicinity, will give the true bearing of that place from the Ship, or if the Land trends parallel with the line it will give the Ship's distance from the Shore. At an hour or two or more after the first Altitude was taken, or when the change of Azimuth exceeds 2 points, take another Altitude, and with the «ame Ijatitudea and Polar Distance find two other positions. A line drawn between them will cross the first line, which will be the Ship's true place in Latitude and Longitude by Chronometer. But if the Ship has changed her place between the Observations, lay off the True Course and Distance Sailed in the interval, from any part of the first hue, and through the point so obtained, draw a line parallel to the first hue projected, and at the intersection of tkis line with the second, is the Ship's true place in Latitude and Longitude. EXAMPLE. December 10th, 1854. A ship in Latitude, by Dead Reckoning, 37° N., and Running for Cape Henry, at about 8 o'clock in the Morning observed the Sun's Altitude to be 9° 35', and the Greenwich Time by Chronometer Ih fim 55a P. M. at Greenwich, and after Sailing W. by S. True 20 miles, a second Altitude was observed to be 27° 10', Greenwich Time by Chronometer 3h 39m 16s. Required the Bearing of or Distance from Ae Landin the vicinity, •t the time of each Altitude, and also the Ship's Correct Latitude and Lon^tude in at the tim<9 of the last Altitude. Latitude and Longitude in at the Time of the Last Altitude. ^ Sun's Ist. Obs. Alt. . 9° 35' G. Time by Chro. Ih Corr., Table IS 7 Add 12_ Sun's True Alt 9° 42' Time from Mid. 13h Polar Distance 112 56 Log. 0.03576 Latitude 36 30 Log. 0.09482 159° 8' Half Sum 79° 34 ' Log. 4.25790 Difference 69° 52 ' Log. 4.97262 8hl0m558 Log. 9.36110 Equation Sub. 7 iL Ship Time. . . 8h 3m 55s 1st position. Green. Time... . 13 5 55 with Lat. 36° 30 N. 5h 2m 08=Long. 76° 30 W. Sun's 2d Obs. Alt. ..27° 10' Corn, Table IK. . .^ 1£ True Altitude 27° 20' Polar Distance 112 56 Latitude 36 30 176° 46' Half Sum 88° 23' Difference 61° 3' 1 Oh 3 5m 498 Equation. . .Sub. 6 58 M. Ship Time. . 10h28m51s Green. Time 15 39 16 51ilOm258 G. Tune by Chro. 3h Add 12 Time from Mid. 15h Log. 0.03576 Log. 0.09482 Log. 3.45044 Log. 4.94203 Log. 8.52305 1st Position, with Lat. 36° 30' = Long. 77° 36' W. 5m 558 - Lat. in D. R. 37° 0' N. Dec. 22' 66' S. 90 6m 55s True Altitude 9° 42' Polar Dist. 112° 66' Polar Distance 112 56 Log. 0. 03-6 7 6 Latitude 37 30 Log. 0.10053 160° 8' Equ.Sur.7m08 Half Sum 7~80^' Log. 4.23679 Difference 70° 22' Log. 4.97399 8h 14m 55s Log 9.34707 Equation Sub 7 M. Ship Time. . . . 8h 7m 65s 2d position. Green. Time 13 5 55 withLt.37°30'N.) timeof 4li58m0s=Long.74°30'W.| Ist Alt Lat. in by D. R. 37° 0' N. Dec. 22° 66' S. 39m 16s 90 _2 9 True Altitude 27.^20' Polar Dist. 112° 56' 39m 168 Polar Distance 112 66 Log. 0.03576 Latitude 37 30 Log. 0.10053 177° 46' Equ.Sub.6m588 f Sum 88° 53' Log. 3.28927 'erence 61° 33' Log. 4.94410 10h49m 34s Log. 8.36966 Equation . . . Sub. 6 58 M. Ship Time . . . 1 Oh 42m 36s 2d position. Green. Time 15 39 16s with Lat. 37° 30' N. 4h 56m 403 =- Long 74*10' W. at th» t?me of the 2d Alt See the Projection on the Chart, next page. The positions by the first Altitude laid off' and the first line drawn between them strikes the Shore tbout 10 miles to the Southward of Currituck Inlet, hence the true bearing of that part of the Shore is 3. W. ^S., •sd the Coast of Maryland is 38 miles distant in a N. W. direction. The Positions by the Second Altitude laid off and the second line drawn between them passes through Cap* Henry. Hence its true bearing is W. by | S. from the Ship. The Ship's True Course and Distance W. by S. 20 miles, being now laid off from the first line and a line drawn parallel to it, then where it cuts the second line, is the Ship's True place (at the time of the last Altitude), in Latitude 37° 13' N. and Longitude 75° 8' W., and distant from Cape Henry 50 miles. A line drawn parallel to the Course made in the interval, through the True place of the Ship, back t9 the first line will show the Ship's place on that line, when the first Altitude was observed, in Latitude 37' 18m N. and Longitude 14° 43' W. Hence the Ship's Latitude by Dead Reckoning was found to have been 18 miles in Error, or that much too far to the Northward of her proper position, in running for Cape Henry. FINDING- THE SHIP'S POSITION BY SUMNER'S METHOD. 153 Fm. 27. #' 1 ■^k"- POSITION \T/il/£ P/AC£ AT- THE TIME \ OrTHE SH' ALT? \^W3 2"* POSITION n" POSITION l^wV 2 "i POSITION 20 30 'tO 50 3-7 = 20 30 PROJECTION OF SUMNER'S METHOD ON THE OHAiiT. NAUliJAL ASTRONOMY. FINDING THE SHIP'S POSITION AT SEA BY SUMNER'S METHOD 1 he Ship's place may be found in the same manner in the Afternoon, should the Latitude not have boe» •btsiined from an observation. The Altitude observed in the Afternoon is worked with the same two Latitudes unless she has made much Northing or Southing in the interval, but the Decl. and Equa. of Time is generally corrected to thf time of observation, and two positions are again found, which laid off on the Chart, and a line drawn be- tween them, will give the bearing of the Land or the distance off, as the case may be. The Course and Distance made good in the interval, laid off as before, and another line drawn parallel to the former, will cut the last line projected, at the Ship's true place. But when the Ship has been sailing in the same direction as the former line it is not necessary to lay off either Course or Distance, because the place of intersection of the two lines as above, will give both. Thus the Ship's place on the Chart may be found every hour of the Day from Sunrise to Sunset^ (Seo the method at page 128,) if his change of Azimuth be sufficiently rapid to cause the lines projected on the Chart to cross each other at an angle By this method also the Ship's position may be found every hour of the Night by using the Staris.or Planets, that is, finding the Longitude by Chronometer, by them, using two assumed Latitudes as with the Sun. But unfortunately the Horizon is generally so obscured at night that not much dependence can be placed on the Altitudes observed. In laying off the Course and Distance run in the interval between two Altitudes, when the Ship is in a Tide-way or Current, the Set and Drift of which is known, it can easily be allowed for, by forming a small traverse Table, composed of the true Course and Distance sailed, and the True Set and Drift of the Current. Then the Difference of Latitude and Departure made good -vvill give the Course and ' D-stance made good, which is then laid off as usual. CONTINUATION OF THE FORMER EXAMPLK Decemoer 10th, 1854. No observation for Latitude having been obtained, the Ship had been hauled up W. S. W ou the bearing of Cape Henry, (from the Altitude which had been obtained about an hour before Noon), and at 11 80m in the Afternoon another Altitude was observed to be 26° 15'. Greenwich Time by Chronometer 6h 24m 388, havinK run in the interval W. S. W. True 25 miles, and been Set by the tide in the same direct on 6 miles. Re- quired her true place on the Chart and hei- Bearing and Distance from the Land in the vicinity. Sun's 3d Obs, Alt. 26° 15' G. T. by Chr. 6b 24m 38b Corr, Table IX-. . J^ True Alt 26 25 Polar Dis 112 57 Log. 0.03681 Latitude 36 30 Log. 0.09482 175° 5i ' Half Sum 87 56 Log. 3.55705 Difference 61 31 Log . 4.94397 lb 35m 32s Log. 8.63165 Equa Sub. 6 54 M. Ship Time.Th~28m 38a G. T. by Chro. 6 24 38 with Lat. 36° 30' N. 4h 56m 0= Long. 74° 0' W. Sun's Corn Dec. 22° ^ 90 67' S. Same Alt 26° 25' Polar Dis. 112 57 Log. 0.03581 Lat 37 30 Log. 0.10053 112° 57 176° 52 Equa. 7m Is -53 Diff lb 1-148 Half Sum. 88 26 Log. 3.43680 7 -46 H Diff 62° 1' Log. 4.94600 6m 548 '7 6-888 Ih 23m 47s Log. 8.51914 574 Equa... Sub. 6 54 7.46t M.S. T. Ih 16m 53s G. T. .. 6 24 38 with Lat. 37° 30' N. 5b 7m 45s=.Long. 76° 56' W The above positions being laid off on the Chart as before directed, and a ..ne dvawu through them, w.U e found to pas,s over the Lisht-House on Smith's Island, near to Cape Charles, and as th"* Ship has been sailing on the line of bearing of Cape Henry, obtained from the last Altitude, do parallel line is required to be drawn nor Distance laid off in this case, because at the intersection of, tb^ two last lines is the tru» place of the Ship, at the time of the last Altitude. It now appears from the above that the Li?ht-House on Smith's Ulf^n^ bes«s from the ship W, N. W, nearly 12 mile;?, and Cape Henry W. S. W. /•»~e 29 miles. Hence if the Chronometer is right, and th' j"*a,ol^.r t,^*-a lb« deck. H>«vs»» «»i)i^cts will soon beco; ae viniblo froui HATING THE CHRONOMKTKR. loS RATING THE CHRONOMETER AT SEA. Ab Chronometers are frequently found to alter their rates after having been a few days tin bcful^aa explained at page 80, they should be verified from time to time during the voyage, or in othe-r ff^iO.^, the Sea rate should be found at every convenient opportunity, which is easily done in the followiiii,' r/.j u ittko OACioiise of his mental powers will soon acouir«» the habit of doin"^ the same with ease 15« NAUTICAL ASTRONOMT. HATING THE CHRONOMETER AT SEA. EXAMPLE 1. March 10th, 1854. A Ship bound out from New York Harbor, observed the following set of Altitudes and Times by Chronometer; her True Position at the same time being found from the bearing of the land, as follows. Required the Error of the Chronometer on Greenwich Mean Time. Elevation 18^ feet. Runs Obs. Alt 10° 15' 20" A.K...10 26 30 10 37 50 8)79' 40" Mn. of the Alt 10° 26' Ir,driX Error. Sub. 2 Seniid 16' 7 Dip 4' 12") ,11 Ref.4'59"J^ ^^ True Alt, 33' T.by Ch.Oh 16m 248 17 26 18 28 3)52m 18s Mn.of Ts . Oh 17m 26s by Chroa 10° 24' 33" Add 6 66 10' Polar Dist 94 40 31' 29" 6 15 23 40 145° 1' 24' Log. 0.00111 Log. 0.11827 72° 30' 42 • Log. 4.47787 61° 69' 1 3" iiOg. 4.94589 Ap. I. at Ship 7h 10m 128 Log. 9.64314 Equii. Add 10 31 Mn. T. at Ship .7h 20m 438 Long, in Time 4 55 40 I2h 16m 23a Less 12 sr. Mn. Time Oh I6m 238 Neversink Light-H. bore W. f N. 4 mil»3, or True West. Sandy-Hook Light-House N.W. 7 " or "N.W.fW The Float Light Vessel K f E. 3 " or " North. These Bearings laid off on the Chart gives the Ship's True position at the time of the Sights, Latitude in 40° 23' 40" N. Longitude 73° 65' W And the Longitude in Time 4h 6om 408. Sun's Dec. at Noon 4° 6' 30" S. Correction Sub. 15 Correct Dec 4° 6' 15" 90 Diff. lh..i)69 Polar Distance 94° 6' 16" Equation of Time 10m 3l8 'oS Correction Sub. 16 Correct Equation 10m 3l8 "39 Green. Time of the Observation. .Oh I6m 2. place, and the Local attraction (if any) due to the Ship (See page 121) previous to the Sights beinf W« "u 'oi Chj-T.oaieter, so that the proper Variation mav be allowed on the Compass bearing, for the purpose of iudi- •at T)g tt..« lin;e at which the Object bears* True North or" South. i E erroi of this kind will cause an error in the Longitude so deduced, that is. the Ship will not be on the same M«'*- diai or in ^hr Longitude of that place, and the ereater the Distance from the Object the greater will be the error •• ^arcd, and the nearer to the Object the less will be the error from that cause. 168 NAUTICAL ASTRONn\* RATING THE CHRONOMETER. EXAMPLE B 'September 7th, ld64. Ship oflf the Gape of Good Hope. The Magnetic Variation Observed from ao Amplitude at Sunrise was found to be 80° Westerly, and when the Lion's Head Iwre N. 30* K by Compass, Distant 30 mi)e«^ the Sun's Mean Altitude was ooserved to be 11° 31' 49" in the Morning. Time by Chronometer 6h 8m lOs from Midnight Required the error of the Chronometer on Green. Mean Time. Elevation 18 feet. Sun's Observed Altitude . . Semid 15 55" | D.4' 8" R.4'30" = 8 38 j True Altitude Polar Distance Latitude T. by Chr. 6h 8m lOs Reckoned from Mid't Sub, Half Sum Difference App. Time at Ship. Equa Mean Time at Ship Long in Time Sub, Green. Mean Time Time by Chron , Error of the Chron 11° 31' 49" Add 7 17 . 11° 89' 6" , 96 12 2 142° 17' 8" .71° 8' 34" Log. 4.5095 Log. 0.00255 Log. 08366 Bearing of the Lion's Head N. 30° E. Magnetic Variation 30 West'ly. True Bearing North 30 miles. Lat. Lion's Head . . 33° 66' S. Long. 18° 24' E . Lat of the Ship. ..34° 26' S. in Time Ih 13m 36s Sun's Corr. , Dec. Noon 6° 6' Add. 5 59° 29' 28" Log. 4.93528 7h 14m 603 Log. 9.5310© 1_57_ 7h 12m 588 1 13 36 Correct Deel 6° 12' 2" Polar Distance 96° 12' 2" 26" N. Dif Ih 56" 86 T. fr N oon 6h 2" 60)336 6' 36' Equa. of Time 2m Corr Sub. 28-14 Dif lh-849 6 OST. fr.Noon 6b Correct Equ. Im 57s '5 5h 59m 178 , 6 8 10 8m 538 Faat of Green Mean Time this day, September 7th 6-09-4 EXAMPLE 6 September 30th, 1864. Ship in Sight of St. Paul's Island, in the Indian Ocean, the Variation of the Oompasa M per Amplitude, being 21° Westerly, and when the centre of the Island bore S. 21° W. by Compass, Distant 26 miles, the Sun's Observed Altitude was 8° 26' 15" in the Morning, the Time by Chronometer being Ih 21m 28, reck- oned from Midnight, or 13h 21m 28 from the preceding Noon. Required the error of the Chronometer on Green- wich Mean Time, and its rate since leaving the Cape of Good Hope on the 7 th of September. Elevation 19 feet. Sun's Observed Altitude Semid 16' Dip. 4' 15" R. 6' 8"= 10' 23 Ti-ue Altitude 8 Polar Distance 87 Latitude 38 ^\ 8° 25' 15" T. by Chr. Ih 21m 2s A jj c oo Reckoned from Midt Add 5 38 ' 30 63 23' 56" Log. 0.00046 22' 0'' Log. 0.10564 Bearing of St. Paul's Island S. 21° W. Magnetic Variation S. 21° Wes'ly True Bearing South 25 miles. Lat. of St. Paul's 38° 47' S. Long. 77° 62' E. Lat of the Ship. 38° 22' S.in Time 5h 11m 2«s Half Sum. 134° 16' 49" .67° 8' 24" Log, 4.58987 Difference e'S" 37' 31" Log . 4.93134 App. Time at Ship 6h 36m 18s=Lg. 9.62681 Equation Su b. 9 4 9 Mean Time at Ship 6h 25^ 24s Long, in Time Sub- 5 11 28 Green Mean Time Ih 13m 56s Time by Chron 1 ^^ ^ Chron. Fast, Sep. 30th 7m 68 Chron. Fast, Sep. 7th 8 68 Aflcumnlated Error lm47B 60 Sun's Declination . Corr .Sub. Correct Declination 2° 36' 4" 20 46' 27" S. Dif. Ih 58" 10 23 T. fr. Noon lOJ 580~ Povar Distance 87° 28' 66" 29 14 60)623 10 23" Equa. of Time 9m 67s -32 Dif Ih -808 Corr Sub. 8 68 T fr. Noon lOj 8030 Correct Equa 9m 488 -69 401 20C •ag-l Davi Elapsed . . . 23)1078(4s 6-10 and i Daily Rate Losing, and this day, Sept. SOtn, Fast of l ' '^ 92 Green. M. Time Oh 7m 6a. ( n 28)160(6 188 RATING THE CHRONOMETER. IM RATING THE CHRONOMETER ON SHORE. When a Ship is in Port, and the Sea Horizon visible from the deck, and the Sun is at a proper distanoQ from the Meridian, the Rate of the Chronometer may be found in a similar manner to the foregoing Examples ; or thf differenceof its Error on tlie Mean Time at the place, ascertained after the lapse of several days, will give us Rate per day. When the Sea Horizon is not visible from the Ship's deck, it may happen that 70od Sights can be obtained from the Sea-beach. In that case, compare the Watch (with which the Time li intended to be taken) with the Chronometer, before leaving the vessel, and also on the return on board. If the comparisons are the same, then the Watch has no rate, but if they differ, the difference is the erri/r of the Watch in the interval. Hence its rate may be found, (unless the Chronometer has itself y very large rate.) a proportion of which must be applied to the Time by the Watch when the Altitudes "ve-e observed. The elevation of the Observer's eye above the Sea-level must also, in this case, be carefully ascertained va order to apply the proper correction for the Dip of the Horizon, found in Table V. An Example of doiiig this is not necessary, as it is worked in the same manner as in the preceding Examples. By the Artificial Horizon. The use of this instrument is fully explained at pages 77 and 78, and the manner of finding the Time (s given at page 131. It is, therefore, considered unnecessary to give any more Examples of the same, and we proce^ to give a case of Rating the Chronometer from the Mean Time at the Place, supposed to have been obtained from either of the above methods. EXAMPLE 1. October 3d, 1854. A Ship lying in the Port of Rio Janeiro, her correct position by bearing \ra8 Latitude 22° 64 South, Longitude 43° 9' West At 8h 30m 25s A. M, Mean Time at the place, a Chronometer showed lib 83m 12a Required its Error on Greenwich Meau Time. Mean Civil Time at Rio Janeiro, October 3d 8h 30m 25s Add...» 12 Mean Astronomical Time, October 2d 20h 30m 25s Longitude of the Ship 43° 9' W. in Time Add 2 62 36 Mean Abtronomical Time at Greenwich, October 2d 23h 23m Is Astronomical Time bv Chronometer, October 2d 23 33 12 Chronometer Fast of Greenwich Mean Time Oh 10m 1 Is, Oct. 3d. EXAMPLE 2. i>ov. 2d, 1854. At Rio Janeiro, Ship in the same position as before, the Mean Time at the place was Bh 10m 6t A. M„ the same Chrononifter showed llh 14m 7s. Required its Error on Greenwich Mean Time, and its Rate bIdm Ootober 8d, at which time it was 10m lis too fest Mean Civil Time at Rio Janeiro, Nov. 2d 8h 10m 58 Add 12 Mean Astronomical Time, Nov. 1st 20h 10m os Longitude of the Ship 43° 9' W. in Time Add 2 52 36 Mean Astronomical Time at Greenwich, Nov. Ist 23h 2m 4l8 Astronomical Time by Chronometer, Nov. Ist 23 14 7 Chronometer Fast of Greenwich Mean Time, Nov 2d 11m 26s do. do. Oct. 8d. 10 11 Accumulated Error TmTss 60 Number of days elapsed 30)75( 29 6-1 0th Daily RaU cai»iiiiB go ^ The Chronometer is this day Fast of Greenwich 11m 26«... )160(6 And gaining 2 sea 6-lOtb per day 150 e^^^—l" East Longitude, the Longitude in Time must be subtracted from the Mean Astronomical Tim* at th* MM, to obtain the Greenwich Mean Time ; beoaase the Time at Greenwich most always be the least in East Lonjri- l*?) NAUTICAL ASTRONOMY. FINDING THE LONGITUDE BY CHRONOMETER. Having thus given all the various methods of finding the Longitude hy Chronometer which are of prae lical utility, and also the manner of Rating the same, both at Sea and on Shore, this part of the s ihjeet will be closed by the following Examples for Exercise. QUESTIONS FOR EXERCISE. Queshon 1st. — April 30th, 1854. (Noon at Sea.) Tn North Latitude, and 24* 30' West Loiigitude. in the morning, the observed Altitude of the Sun was 22° 7'. Greenwich Time by Chronometer 8h 46m IDs, reckoned from midnight. Ship then sailed N. E. by E. (True Course) 35 miles until Noon, when the Sun's Meridian Altitude observed was 68° 3' South. Required the Ship's Latitude and Longitude in at the time of the Sights, and al.so at Noon. Answer. — Latitude 36° tude 24° 3r>' W. at Noon 13' N., Longitude 25° 11' W. at time of Sights, and Latitude 36° 32' N., Longi- Ques. 2f/. — April 30th, 1854. (Noon at Sea.) Latitude observed at Noon 36° 32' North. In the after- noon the Sun's observed Altitude was 13° 48'. Greenwich Time by Chronometer 7h 7m 15s. Ship had sailed £. N. E. (True Course) 30 miles since Noon. Required the Latitude and Longitude in at time of the Sights, and also the Longitude of the Ship reduced back to Noon. Ans. — Latitude at time of Sights 36° 43' N., Longitude 24° 2' W., and Longitude at Noon 24° 37' W. Ques. 3d. — March 26th, 1854. (Noon at Sea.) In South Latitude, and 66° 30' East Longitude, by ac- count. In the morning the Sun's observed Altitude was 25° 25'. Time by the face of the Chronometei 3h 29m Is, or which, reckoned from the preceding Noon is. March 25th, 15h 29m Is Astronomical Time, the Chronometer being 2:n 24s fast of Greenwich Mean Time. Ship then sailed N. W. (True) 17 miles nntil Noon, when the Sun's Meridian Altitude observed was 75° 20' North. Required the Latitude and Longitude in at the time of the Sights and at Noon. ^7W.— Latitude 12* 32' S., Longitude 66° 37' E at time of Sights, and Latitude 12* 20' S., Longitude 66' 84' 30" E. at Noon. Qiies. 4th. — March 10th, 1854. (Noon at Sea.) In North Latitude, and 60° 45' West Longitude, the Sun's Meridian Altitude observed at Noon was 47° 32' South. Ship then sailed N»rth East (True; 40 miles, and in the afternoon the Moon's observed Altitude, Lower Limb, was 40° 32' to the Eastward of the Meridian, and the Greenwich Time by Chronometer was 9h 41m 21s. Required the Latitude and Longi- tude in at Noon, and also the Latitude and Longitude in at the time of the Moon's Altitude. Ans. — Latitude observed 38° 14' N., Longitude 60° 33' W. at Noon, and Latitude 38° 42' N., Longitude 59° 57' W. at the time of Sights. Ques. 5th. — April 7th, 1854. (Noon at Sea.) In North Latitude, and West Longitude, at twilight in the morning, the Meridian Altitude of the Star Vega was observed to be 79° 51' North, and at the same time the Altitude of the Planet Venus was 24° 21' to the Eastward of the Meridian, the Greenwich Time bjr Chronometer being lOh 15m 55s from midnight, or April 6th, 22h 15m 55s from the preceding Nooiv. Required the Latitude and Longitude in at the time of the Sights. Ans. — Latitude observed 2o 26' N., Longitude by Chronometer 70° 5' W. Ques. 6th. — February 10th, 1854. (Noon at Sea.) In North Latitude and West Longitude, at twiligl.t in the evening, the observed Altitude of the Star Sirius was 12° 27' to the Eastward of the Meridian, ard the Greenwich Time by Chronometer was lOh 4m 41s, and at li hours afterwards the Meridian Altitude of the Star Aldebaran was observed to be 66° 16' South. Ship had sailed on a true S. W. Course 12 mile* Ui the interval. Required the Latitude in by Observation, and the Latitude and Longitude in at time of lights. ^rw.— Latitude observed by # Aldebaran 40° l' N. Latitude in at time of Sights 40° 10' N., and Lon- eitude 68* 23' W. at the time of the Sights Ques. 7th. — A Chronometer which was 10m 14s Fast of Greenwich Mean Time at New York, on the 10th of March, 1854, showed 3h Om 53s, when the Mean Time at Calcutta was 8h 40m 10s A. M., on the 12th of June, 1854, in Longitude 88° 17' E., or in Time 5h 53m 8s. Required its Error on Greenwich Mean Time, and its Rate since leaving New York. " Ans. — Its Error on Greenwich Mean Time is 13m 51s. Accumulated Error 3m 37s. The number «i 4ava elapsed 94, and its daily Rate 2 see. 3- 10th gaining since leaving New York. NoTi. — In the above Examples the height of the eye above the Sea-level is supposed to be 17 or 18 feet. LUNAR CjhSEllVATinit loi 'iHE LUNAR OBSERVATION Means the measurement of the Angular Distance of the Moon from certain Celestial bodies, and tui the Moon is constantly advancing to the Eastward in the heavens, at the rate of about l' in 2 minutes of time, she overtakes and passes all the other Celestial bodies in her progress, they appearing to remain Btationary in the heavens. The Moon's distance from the Sun, and a fevr bright Stars and Planetp, are calculated for the end of •very 3 hours, (except during about 6 days at the time of each New Moon,) and given in the Nautical Almanac for the Mean Time at Greenwich. The observation of this distance from any part of the Earth'» surface, affords the means of determining the Greenwich Mean Time, the difference between which and the Mean Time at the Ship, is the Longitude in Time. This constitutes a Lunar Observation. If the distance between the Moon and the other body were the same to the spectator, whether viewed at the surface or from the centre of the Earth, there would be nothing m«re to do than to measure the dis- tance, (with an instrument,) and to find from the Nautical Almanac the Greenwich Time corresponding to it, and to compare this with the Time at the place. But the Refraction of the Atmosphere has the ten- dency to raise the Sun, a Star, or a Planet, above its true place in the heavens, and the effect of Parallax is to make them appear lower ; the latter has, however, very little effect, in consequence of their great distance. (See explanation given at page 67.) On the other hand, the Moon being near the Earth, her Parallax in Altitude is greater than her Refraction, and which causes her to appear below her true place in the heavens. Hence the Apparent Distance between the Moon and the other body differ from the True Distance, a» will be seen in the following Diagram. DIAGRAM, • Showing the Effect of Parallax on tne Lunar Distance Fig. 28. A» the Moon must always be raised, and the Sun or Star lowered, to obtain their true places, the Star to the right in the above Figure being higher than the Moon, it is evident that by raising her the True Tft4- tance will be less than the Apparent Distance. Again, the Star to the left being lower than the Moon, by raising her the True Distance will be greater than the Apparent Distance And it is evident from the above, that the difference between the True and the Apparent Distancet depend almost entirely on the correction of Altitudes. It is therefore useful to bear in mind, as a check against gross mistakes, that the True and Apparent Distances cannot differ by more than the Sum of the Corrections of Altitude. Again, when the Moon's Altitude is equal or less than that of the other body, the True Distance is less than the Apparent Distance. Bat the contrary does not always hold good when the Moon's Altitude is greater than the other body Ift2 NAUTICAL ASTRONOMY. THE LUNAR OBSERVATION IS the only independt • it method of finding the Longitude which is practical at Sea, and it requires gr«ai jjractice to measure the distance successfully. (See the Use of the Sextant, and the Remarks on Measur- ing the Lunar Distance^ at pages 72 to 76.) And the application of so many small corrections as are neces- «ary, when accuracy is required, even with extraordinary care and some skill, it is scarcely possible to arrive at extreme precision, although the observation may have been made on shore, with the best instru- ments ; and it is recorded by practical surveyors, and other scientific men, entitled to great credit, that the Mean Longitude deduced from several thousands of Lunar Distances, taken equally on both sides of the Moon at one season of the year, have differed from 10' to 12' from the Mean Longitude deduced from an equal number of Lunar Distances taken in like manner at a different season of the year. And from my own experience in observing Lunar Observations at Sea, during the course of many yearb, I am entirely of the same opinion. The Lunar Observation is certainly an excellent mode of detecting any very gross error in the Chro- nometer, and is valuable on that account alone, and also for correcting the Dead Reckoning within certain limits ; but I am satisfied that a Chronometer cannot be rated by Lunars at Sea, though some authors of Nautical works persist in the contrary opinion. The most rapid change of distance between the Moon and a body is 1° 48' in three hours, and the effect of an error of 1' of distance is 25' of Longitude, or that of 15" error of Distance is 6' of Longitude in the most favorable case. An error in the observed Altitudes, however minute, also affects the True Distance. Then there are the errors in the Shades or Screens, and the parallelism of the Telescope, all which are explained at page 72 and rules given to correct them : and lastly the errors in the Tables, however small, from which the cor rections are taken. , It is usual to take Lunar Distances both East and West of the Moon, and to take the Middle of the Longitudes so found for the True Longitude. This may compensate to a certain extent for some of tlie errors, but it may nevertheless be several minutes of Longitude from the truth. It is, however, more likely to be correct than either of the others. From the above facts it would appear that in general the Longitude by nf set of Lunar Distances is liable to be in error, even with the greatest care and by the most practical observer. This error may not exceed 10', and is in general much less ; but even this amount of precision is a very valuable acquisition to a Ship on a long voyage, and which may not have had an opportunity of verifying her Chronometer by the sight of land. For, if after several sets of Distances have been taken, both East and West of the Moon, and the Longitude deduced from each set differ considerably from the Longitude by Chronometer, and they all point in the same direction, that is, either all to the Eastward or all to the Westward of the Chronometer, it may be concluded that the Chronometer is in error to the amount of nearly the difference between them. And in the case of a Chronometer thus changing its error and rate, it wouid be unsafe to trust to it during the remainder of the voyage. And as the following method of observing and working a Lunar Observation may be done with nearly as little time and trouble as that of finding the Longitude by Chronometer, and in the case of the Chronometer breaking down at Sea, the Longitude may be found sufficiently near for all practical purposes by the Lnnar method, bearing in mind that in Low Latitudes she Degrees of Longitude are large, and where an error of a few minutes of Longitude would be most con •picuously seen, the weather is generally clear and fine, and the land may be seen at a considerable dis- tance off. On the other hand, in High Latitudes the Degrees of Longitude are small, and where an error of a fe"» muxutes of Longi?.:de occupy only a small portion of space, or miles of Departure, consequently *V.y vrocid fcivi ress effect o j the Ship's Distance from the shore than it would in Low Latitudes. LUNAR OBSERVATION ]o3 THE LUNAR OBSERVATION. In taking a Lunar Observation, two assistants may be'employed to observe the Altitudes of tiie objects, ■while the principal observer is taking their Distance, and a fourth notes the Times of each by a Watch or Chronometer. The Observation is then written down in the following order. (See page 76.) June 3d, 1864 In the Afternoon. Height of the Eye, 1 8 feeu Times by Watch. .2h t .^m 668 Sun's Altitude. . 49° 45' Moon's Alt, L. L.,. .41* 10' Dist.© and ]> . ,87° 41' 20'' 2 68 do. 49 17 do. 32 To the Westward 42 20 3 4 do. 48 49 do. 64 43 20 3) 8h 64m 3)147° 61' 3)96 3)127'^0^ Mn of the Times. .2h 58m Sun's Obs. Alt.. . . 49° 17' Moon's Obs. Alt. .~4i'^32' Mean Obs. Dist. 87° 42' 20'' When no assistants are at hand, one person may take the whole observation himself; indeed it is more .satisfactory to de so than to have to trust to others, because it is very rarely possible that the Altitudes of the bodies can be seized at the instant of taking the Distance. By adopting the following method the observer will be independent of all assistants, and learn by experience to trust entirely on himself in using the instruments with precision. Being prepared with two Quadrants to measure the Altitudes of the bodies, and a Sextant to measure their Distance, all previously adjusted, (or their errors known,) and a Watch to note the Time. Set the Index of the Sextant roughly to the Approximate Distance. (See page 74 or 75.) Set the Indices of the ■Quadrants roughly to the Approximate Altitudes of the two bodies. Then, holding the Watch in the hand ar place it where the movement of the second hand can be distinctly seen, take an Altitude of one of the bodies, (generally the one farthest from the Meridian,) at the instant the second hand of the Watch has completed the full minute, and note down the Time and the Altitude of that body opposite. Take up the other Quadrant and observe the Altitude of the other body at the time the second hand of the Watch has ■completed the next two minutes, and note down the Time and Altitude as before. Now take the Sextant and bring the Limbs of the objects in contact, at the instant the second hand of the Watch has completed the next two minutes, and note down the Time and the observed Distance. Shift backward or forward the Index of the Sextant 1', (as directed at page 76,) and await the contact; note the Time and Distance down as before. Shift the Index again 1' in the same direction, and note the time of contact as before, rtiree Distances being sufficient. Take up the Quadrant and observe the Altitude of that body which wag last observed, at the completion of the next two minutes, which note down as before, and finish with observing again the Altitude of the first body observed, at the expiration of the next following two minutes. Thus there will be a uniformity of Time between the Observations, which will render it easy to reduce them all to the Mean of the Times at which the Distance of the bodies were observed, as follows • Form of Writing down the Observation. JuneSd, 1864. T.by Watch 2h 52m Os Alt of the Sun 60° 41' 0" Height of the Eye, 18 feet 2 54 Moons L. Linio.. 40 48 ( 2 56 56 Dist Sun and Moon.. 87 41 20 ) Sun West of the Moon. Mn. of Times 2h 58m 0s.-| 2 58 do. 42 20 \ Mean Distance 87° 41 W (304 do. 43 20 ) 3 2 Alt of Moon's L. Limb 42 16 3 4 Alt of the Sun 47 53 To Reduce the Altitudes to the Mean of the Times that the Distance was Observed. To Find the Sun's Altitude. To Find the Moon's Aliunde. Time of Ist Alt. 2h 62m Alt 50° 41' T. let Alt 2b 52m Time of Ist All 2h 54m Alt 40° 48' T. Ist Alt 2h 54ni 2d .Alt 3 4 Alt 47 53 Mn. of T b 2 68 " 2d Alt 3 2 Alt 42 lo Mn. ofT'8 2 68 Say as r2in is to 2° 48' So is 6m Say as 8in is to 1° 28 so is Ara €m being half of 12m, and the Difference of AIti- Am being half of 8m, and the Diffeieuc«» of Alti- tude bting 2° 48', the half of which sublmct 1° 24' tude being 1° 28', the half of which addded 0* 44 1 8t Alt Obs. ( and decreasing) was 50 41 1 st A It ( increasing) was 40 48 Sun's Alt at the Mean of the Times 49° 17' Moon's Alt at the Mean of the Times 41* 82 Hence we have tbe following Observation • M . .87* 4«' 30* iei4 NAUTICAL ASTRONOMY. TO FIND THE APPARENT ALTITUDES OF THE BODIES AND THEIR APPARENT DISTANCE. • Add 12' to the Observed Altitude of the Sun and Moon, and add their Semidiameter to the Observed Distanott Bon's Oba. Alt .49° 17' Moon's Obs. Alt, L. L..41' 32' Obs. Distance of Sun and Moon 87* 42' 20" 12^ 12 Sun's Semid.15'48" D's Aug. Semi 16' 21". Sum 81 9 Bun's App. Alt. .49' 29' Moon's App. Alt . . . AV'ii Apparent Central Distance 88' 13' 29" June 8d, 1854. At 2h 68m P. M, Latitude in 30' North, Longitude, Dead Reckoning, 70* W, the Sun's Deolin»> lion 22* 21' North, the Moon's Decimation 12° 28' N., given to Project the Figure. DIAGRAM OF A LUNAR, Drawn on the Plane of the Meridian. Fir,. 29. In this Figure th* Sun in on the Prime Vertical, to the Westward of the Meridian, and his Hour Angle measured on the Equator gives the Apparent Time of the Ob.servation, 2h 58m P. M. The Moon having nearly the same Hour Angle to the Eastward of the Meridian, appears to a spectator situated at a great Jistauoe to the Eastward of the Earth, (which is in the centre,) to be nearly in the same line of bearing^ jut the following Figure, drawn with the objects facing the spectator, will place them in a better point of Tiew for showing the nature of the case. DIAGRAM OF A LUNAR, Drawn on the Plane of the Prime Vertical. Fig. 30. 7tNITH tp "L OlST ; 8 7^3^ 12 ISAeci-lA THOKISSCHY. In this last Figure both bodies are seen on the Prime Vertical, East and West of the Meridian, their Altitudes are laid off from the line of Chords, and their Apparent Central Distance measures on the scale 88* 13' 29". Now, it is evident that by raising the Moon (which the correction for Parallax does) wo bring the Moon nearer the Sun, while the correction for Refraction increa.ses the Distance by lowering the bodies ; but as the former has more effect than the latter, the Moon's True Distance, according to the Figure, is less than the Apparent Central Distance. This quantity is found by the Rules given on th© oext page, and which is termed Clearing the Lunar Distance. * This Correction is simply the Difference between the Semidlameters taken at 16', and the Pip of the Horizon, take» »t 4', to be added when the Lower Limbs are taken. LUNAR OBSERVATION. lAf TO FIND THE APPARENT ALTITUDES AND DISTANCE. Turn the LongHude by Dead Reckoning into time by Table XXVI, and aaa if to the Time at the Ship a West Longitude or subtract it in East, will give the Approximate Time at Green ivich. Prefix the day of the month one day less than the Sea date, and call it the Greenwich Date. * Take out the Moon's Semidiameter and Horizontal Parallax from the Nautical Almanac and correct them to the Greenwich Date by Table XXIV, and to the Moon's Semid. add her Augmentation, taken from Table VII. To the observed Altitude of the Sun and Moon's Lower Limbs add 12'. But if the Moon's Upper Limk 06 observed, subtract 20', and if a Star be observed, subtract*^' . Take out the Sun's Semid. from the Nautical Almanac and add both it and the Moon's Augmentation Semidiameter to the observed Distance, will give the Apparent central Distance. If a Star be observed, add the Moon's Augmentation Semidiameter to the observed Distance if the nearest Limbs be observed, but subtract it if the farthest Limbs be taken, will give the apparent Distance. If one of the bodies be at a sufficient distance from the Meridian, correct its Apjmrent Altitude for refrac- tion by Table IV, but if the body be the Moon, by Table XXV, will give its true Altitude, with which find the Mean Time at the Ship as usual ; but if both bodies are too near the Meridian an Altitude taken after- wards will give the Error of the Watch on Mean Time at the Ship, which must be farther corrected for the Difference of Longitude in Time the Ship has made in the interval ; but it is much more convenient and correct to time tho observation, so that one of the Altitudes of the bodies, (the Sun or a Star is pre- ferred) observed with the distance, may also be used to find the Time at the Ship. To Clear the Lunar Distance. RULE 1. To the Pro. Log. of the Moon's Horizontal Parallax, Table XXXIV, add the Log. Co-Secant of tb* Apparent Altitude of the Sun or Star, taken from the bottom of Table XXVII, and the Log. Sine of the Apparent Distance found in Table XXXI, their Sum, will be the Log. of i\iQ first correction. 2. To the Pro. Log. of the Moon's Horizontal Parallax already found, add the Log. Co-Secant of tk« Moon's Apparent Altitude, taken from the bottom of Table XXVII., and the Log. Tangent of the Apparent Distance found in Table XXXI, their Sum will be the Log. of the second correction. 3. Take the first and second corrections from Table XXXII, and place them under the Apparent Distance 4. Take the third correction from Table XXXIII, and alter applying to it the correction taken from TabU P, on the same page, (which is only used when the Sun is observed) and place it under the Second correction, add all these corrections to the Apparent Distance, and their Sum, rejecting lO degrees, will be the true Distance. EXAMPLE 1. June 3d, 1854. In Latitude 30' u N., Longitude by Dead Reckoning 69° 64' W., the Time by Watch was 2b 68ia, Sun's observed Altitude 49° 17', Moon's observed Altitude L. L, 41° 82', and the observed Distance 87° 42' 20". (See page 164.) Required the true Distance, tlie Green. Mean 'Time, the Mean Time at Ship, and the Longitude ia Tnn#atShip 2h 58m ©'sObs.Alt 49° 17' D 's Obs. Alt 41° 32' Obs. Dis 87° 42' 20" Long. 69° 64' W. in time 4 40 Add 12 Add 12 Q'a Semid.... 16 48 G-'»en. Date, June 8 7h 38m ©'sApp. Alt. 49° 29' ]) 's App. Alt 41° 44' P's Aug. Semi d. 16 21 App. Dist 88° IS' 29" Moon's Her. Par. 0° 65' 37" Pro. Log... . 05101 Pro. Log. . . 0.5101 J) 's Sem. Noon... 16' 8" Sun's App. Alt. 49 29 Log. Co-Sec. 0.1191 ]) 's App. Alt 41° 44' Log. Co-Sec. 0.1767 Corr. 7^ hours. . 8_ App. Dist 88° 13' 29^ Log Sine.. 0.9998 Log Tang. . 2.5087 15' H" First Correc. -I- 4 17' 43" Log. 1.6290 ^"S • \^ Second Corr. 4- 5 1 9 Log 8.1955 Aug.Semid 16' 21" Tbird Corr.. -j- 1 61 Less 10°=87° 34' 12" True Distance. H*'^'- Pf Noon. .66' 24'' Cor. 7i hours. . 18 Correct H. Par.. 66' ST** NoTX. — The manner of a.^lnp the Tables for clearing the Lunar Distaaoe are the same a« usually done with others, anc nqnires nc explanation, and in Table XXXII directions are given on the face of the Table for taking out and applying the corrections, and in 'Table P alao the precept Add or Subtract to or from the correction in Table XXXIII, ar<) givca •o the face of the Table. * Tha Moon's Semidiameter and the Horizontal Parallax are taken oat for tie nearest Noon or Midnight, and tbcb Difierence in 12 honrs found, with which we enter Table XXIV at the Top, and the Greenwich Time from Noon or Mi^ ■ight at the aide, aud at the angle of meeting is the cor-«ntio't to be Added or Subtracted, according aa they are ia« (■f or deoraaaing 166 NAUTICAL ASTRONOMY. HAVING THE TRUE LUNAR DISTANCE, TO FIND THE CORRESPONDING GREENWICH TIME. Find in the Nautical Almanac the two distances between wnich the True Distance falls. Take out th« first of these and set it down under the True Distance, and note down the hour taken from the head of th« •ame column, and also its Prop. Log., found opposite in the Nautical Almanac. Take the Difference between the two Distances thus set down, with which enter Table XXXIV, and take out the Pro. Log. of the Difference ; from this, Subtract the Pro. Log. taken from the Nautical Almanac, the remainder is the Pro. Log. of a portion of Time to be Added to the Hour taken from the head of th« column, and the result is the Greenwich Mean Time. True Distance previousl/ found 87° 34' 12" which falls between VI and IX honra Distance at VI Hours 86 48 23 Pro. Log. .3208 Difference 0° 45' 49" Pro. Log. .6942 ^ Portion of Time to be Added Ih 35m 55 Pro. Log. .2734 To the Hour of the preceding Dist N. A .^. . 6 Oreenwich Mean Time, June 8d 7h 85m 55b at the time of the Observation To Find the Mean Time at the Ship, and thence the Longitude. The Sun being at a proper Distance from the Meridian, in this case, at the time the Distance was observed the Mean Time at the Ship is found from his Apparent Altitude, after correcting it for Refraction by Tabl« IV, as follows : Sun's App. Altitude 49° 29' Gr Date. June 8d, 7h 36m Oa. Ref. Table IV Sub. True Altitude 49° ''olar Distance - 67 atitude 30 28 89 147° 7' Half Sum.... 73° 34 ' Difference 24° 6' Log. 0.08892 Log. 0.06247 Log. 4.46163 Log. 4.61101 App. Time at Ship 2h 68m 888=Log. 9.16903 Equa. of Time Sub. 2 10 Mean Time at Ship. 2h 56m 288 Green. Time by Lunar... 7 85m 55 Longitude in Time 4h 39m 828=Longitude in 69" 53' 0" West at about 8 P. M. Sun's Declination Noon. , . 22° 19' N. Dif. Ih 18' , Cor ' Correct Declination. . . . . ...Add 2 7 . 22° 21' N. 60)126 [ Polar Dist Equation Noon 90 'A' . 67° 89' .2m ISs "SS Dif. Ih 410 > Cor Correct Equa . ySub. 3 -07 7^ 2m 108 -26 2870 206 807-5 The Difference between the Mean Time at the Ship and the Greenwich Time by observation is the Lon- gitude in Time, which turned into Space by Table XXVI, oe it may be computed by the rule given at the bottom of cage 140, and the result is the Longitude of the Ship at the time of the observation. REMARKS. If the times of the observation are taken by a Chronometer, or which is the same thing, the time of the Distance by Chronometer obtained from a comparison with, the same Watch used in taking the times of the observation, and the Error of the Chronometer on Greenwich Mean Time applied to it, we have the Greenwich Time by Chron. at the time of the observation ; then if it agrees nearly with the Greenwich rime found by the Lunar Distance, the correctness of the Chronometer is confirmed within certain limits ; but should they differ considerably after several observations, it may be concluded that the Chronometer Has altered its rate. The learner should practice measuring the Lunar Distance when in Sight of Land, or when his Longitude 8 well known, and by that means establish a confidence in himself. But he must not feel discouraged hould it happen that his first attempts fall very wide of the truth, (as is generally the case.) but by a steady perseverance, and profiting by his former errors, he will, after carefully perusing the instructions given at pages from 72 to 76, soon acquire the habit of measuring the Distance tolerably correct. And i1 is easy to know whether the Distance measured has been too great or too small by simply inspecting the columns of the Nautical Almanac and finding whether the Distance between the bodies is increasing ot decreasing: if increasing and the Greenwich Time by Lunar too great, when compared with the Green- wich Date, found as above, then the Distance observed has been too great by the amount of the Difference of Time, say as 3 hours is to the Difference in 3 hours, so is this Difference of Time to a proportion ol Space, will give the amount of the Error. When the Distance is decreasing and the Greenwich Time bj Lunar too great, then the* Distance observed has been too small, and the amount is found in like manner »nd vice versa. (See the Rules on pages 16S and 169.) 7h 51m 30s 7 53 40 7 55 45 7 57 40 7 59 60 8 1 58 8 3 59 LUNAR OBSERVATIf.N. 167 FINDING THE LONGITUDE BY LUNAR OBSERVATION. Distance betweoi the Moon and a Star. In the preceding Example the Sun's Distance was observed W. of the Moon, and in the following Observa- tion the Star's Distance is observed East of the Moon, for the purpose of showing the manner of connectinf the two Longitudes so deduced, in order to obtain the Mean of the two at the time of the last Observation. EXAMPLE 2. June 8d, 1854. On the evening of the same day as in the preceding Example, the following Distances wer« Bbeeived of Antares, East of the Moon, and East of the Meridian. Ship had sailed from Latitude 30° North, and Longitude 69° 52' 45" West, by last Lunar. Course S. E. (true) 40 miles. Required the Longitude in, and also th* Mean of the two Longitudes, at the time of the last Observation. June 3d. Times by Watch 7h 51m 30s Alt of Antares 12° 57' 0" L. Limb of the Moon... 60 2T Dist. remote Limb 85 35 40 ) Mean of the Times 7h 57 ra 45s.. •{ 7 57 40 do. 34 40 V Mean Dist. ... 86° 84' 87"^ do. 33 30 ) Alt. of the Moon 59 31 Altitude of Antares. ... 15 27 The Altitudes are now reduced to the Time of the Mean Distance by Pro. Logs, as follows : To Mild the Star's Altitude. To Find the Moon's Altitude. r. of Ist Alt. 7 51 30 Ist Alt 12° 57' T Ist Alt 7'61 80 T. of Ist Alt 7 53 40 1st Alt. 60° 27' T. Ist Alt7 58 40 " 2d Alt 8 3 59 2d Alt 15 27 Mn. of T's 7 57 45 " 2d Alt 8 1 58 2d Alt 59 31 M. of T's 7 57 46 Then say as~12 29 is to 2° 80' so is 6 15 Then say a^ 8^ is to 66' so is 4 i 12m 298 Pro. Log. 1.1589 8m 18s Pro. Log. 1.3362 Arith. Compli 8.8411 Arith. Compli 8.6638 2° 30' Pro. Log.. . 0.0792 0° 56' Pro. Log.. . 0.5071 6m 16s Pro. Log . 1.4694 1st Alt. Obs. increas. 12° 67' 4m 5s Pro. Log. 1.6443 1st Alt Obs. decreas. 60' 27' 0.3797 Pro. Log. of the Cor r. 1 15' 0.815'Z Pro. Log of the Corr. 028' Ah. of Antares at the Time of the Mean Dist 14° 12' Alt of the Moon at the Time ol the Mean Dist. . .69° 59 To Find the Greenwich Date and the Necessary Preparations for Clearing the Distance. Time at the Ship. . 7 67' 45 Co.S.E. 40=D.L. 0° 28' Dep. 28'=D. L. 0° 32' 45" E. D's Sem. Mid. 16' 13" aPar.66'46' L-in 69° 20'W.in T. 4 37 20 Lat Left 30 Lon. by Lunar 69 52 45 W. Aug. 13 Corr. 1' Gr. Date, June 3d, 12 36 6 Lat In 29° 32N. " brought on 69° 20' 0" W. Aug.Semid. 15' 26" aPar.55'46' Alt of Antares 14° 12' Alt. of Moon's L. L 59° 59' Obs. Dist Moon's remote Limb. . . 85° 34' 87" Dip for 21 feet Sub. 5 Add.. 12 Aug.Semid Sub. 16 26 #'s App. Alt 14° 7' Moon's App. Alt . 60° 11' App. Central Distance 85° 19' 11" To Clear the Lunar Distance and Find the Greenwich Time. > 's Hor. Parallax 0° 55' 46" Pro. Log. 0.5089 Pro. Log 0.6089 #'sApp. Alt 14 7 Co-Sec... 0.6128 B'sApp. Alt 60° 11' Co-Secant 0.0617 App. Distance 86° 19' 11" Sine 0.9985 Tangent 2.0866 First Correction 4 46 21 . . Log. .... 2.1202 Second Corr 6 3 58 2.6679 Third Corr. 3 30 True Dist Less 10°=85° 13' 0" Dist at Midnight, or XII, 85 29 55 Pro. Log. 0.2843 Difference 16' 55" Pro. Lo g. 1.0270 0.7427= Oh 32m 38s portion of Time to be added to the Hour of the precediog Distance, N. A. .12 Gueenwich Mean Time 12h 82m 33s at the Time of the Distance. To Find the Mean Time at the Ship, and thence the Lcmgitude. App. Alt of Antares 14* 7' Gr. Date, June 3d, 12h 35m Sun's R. Ascen. .4h 44m 13s Di£ lh.l08X12h 8^ Corr. for Ret Subu 4 Correction 2 5 #'b True Alt 14° 3' Sun's Corr. R. A.4h 46m 18s Polar Distance 116 6 Log. 0.04671 Equa.. .. 2m 138 Latitude 29 32 Log. 0.06045 Corr 5 #'s Right Ascen., 1854 16h ^Om 24* 159° 41' Corr. Eq. 2m~~88 Half Sum ~79° 60' Log. 4.24677 Wb Declination, 1864 2(;° •' 8 Diflference 66 4 7 Log. 4.96000 90 H. An.', of # East),, ^, ,_ j „„,„„„ #'s Polar Dist 116° 6' p,, ,, J- >■ 3b 85m 588 Log. 9.31393 of the Meridian ) " #'8 R Ascen 16 20 24 Mean Time at Greenwich by Lunar 12h 32m 88i R. A. of the Merid. . 12h 44m 268 Mean Time at Ship 7 56 Sun's R. Ascen 4 46 18 Long, by Lunar 69° 8' 15' — 4h 36m 88» App. Time 7h 58m Ss Long, by last Lunar brought on by D. R.. . . 69 20 Equation of Time .Sub. 2 8. , i)1 38° 28' 16" Mean Time at Ship. 7h 66m Os Mean Long, by Lunar 69* 14' 7 ' W. at time ol [laDt Ob* 468 NAUTICAL ASTRONOMY FINDING THE LONGITUDE BY LUNAR OBSERVATIONS. Distance Observed between the Moon and a Planet. EXAMPLE 8. Jnly 8d, 1864. la Latitude 89° 26' South, Longitude by Dead Reckoning about 80° East, at 8h 80m P. M Apparent Time at Ship, the observed Altitude of the Planet Jupiter was 31° 35' East of the Meridian, the obseryea Altitude of the Moon's Lower Limb 38° 61', and the observed Distance between the centre of Jupiter, East of tho Moon, and the Moon's remote Limb was 102° 31' 43". Index Error 1' 30", subtractive, and the Greenwich Mean Time by Chronometer, being correct, was 3h 14m 28s. Required the Longitude in by the Lunar Distance, and the F''ror (if any) of the measured Distance. Preparation for Clearing the Distance. •Green. Time or Date, by Chrc, July 3d, , . . 3h 14m 28s Moon's Semid. Noon 15' 31" and H. Par 56' 49' ^t T-,- .. «.. i y„u ino" oT Ao" * ' * n > Add 11 Gorr. Gr. Date.. Add 6 Obs. DisL p 8 remote Limb 102 31 43 Augm. 9 J Index Error Sub. 1 30 Aug. Semid 15' 42" Hor. Par 56^55^ Obs. Distance 102° 30' 13" Moon's Aug. Semid Sub. 16 42 Obs. Alt. Jup.. . . 31° 35' Obs. Alt. > 's L. L.. . . 38* 61' Apparent Distance 102° 14' 31" ^^P Sub. 4 Corr. Ad d 12 App. Alt Jup.. . 31° 31' App. Alt. of the > ... 39° 3' To Clear the Distance. |> 's Hor. Parallax 66' 55" Pro. Log. 0.6000 Pro. Log. 0.5000 Jupiter's App. Alt. 31 81 Co-Secant 0.2817 ' D 's App. Alt. ... 89' 8' Co-Sec„ . 0.2007 App. Central Distance 102° 14' 31" Sine 0.9900 Tangent. 1.6687 First Correction 4 29 38 _' 1.7717 Second Correction 4 52 13 2.3644 Third Correction 2 23 True Distance, less 10° 101° 38' 40" Distance, N. A., at Illh 1 01 46 12 Pro. Log. 0.2618 Difference 0° 7 32" Pro. Log. 1.3783 Pro. Lo|. 1.1165— Oh 18m 468 portion of Time V be added to the time of the preceding Distance, Jr. A. ... 3 Greenwich Mean Time by Lunar 3h 18m 468 To Find the Time at Ship, and thence the lo%fritude. App. Alt of Jupiter. . . 31° 81' Green. Date . 3h 14m 28s Sun's R. A. Noon. . . 6)x 48m 34s Dif lh.l0sX3ih— 32i Refraction ... Sub^ 2 Corr A drt_ 32 True Alt of Jupiter... 31° 29' East of the Meridian. Corr. R. Ascen. .. . 6h 49m 6s Polar Distance 68 21 Log. 0.03177 Latitude 89 25 Log. 0.11207 Jup. Dec. . .21° 39' S. Jup. R As^ien.. . . 19h 44m 26a 139° 15' 90 Cor. Gr. Date. .Sub. S flalf Sum 69° 88' Log. 4.64161 Polar Dist. 68° 21' Conevt R. A.. . . lOh 44nr~28i 0'ff«'-^°«« "38^' Log-±7907_9 Equa. of Time . . . . 3m49s-26 .^if. .hw455K3i-l, t- H. Angle of Jup. E. 4h 26m 23s Log. 9.47624 Corr Add 1 '47 R. A. of Jupiter. .. 19 44 23 „ ' '.'' -^rrTT;— I^TTi ^ Correct Equa. .. . 8m oOs "72 R. A. of the Merid_.15h 19m fiun's R. Ascen 6 49 6 App. Time at Ship. 8h 29m 548 Greenwich Mean Tune by Lunar 3h ISm ^6» Equa. of Time. Add 3 51 Mean Time at Ship 8 83 46 Mn. Time at Ship. . 8h 33m 458 Longitude in ... 79° 59' 46" E.— 5h 19m 69<» To Find the Amount of Error in the Measurement of the Lunar Distance. Here the Correct Greenwich Time by Chronometer given being. ...... 8h 14m 28s And the Greenwich Time by Lunar being 3 18 46 Henoe their Difference in Time is 42 sec. The Greenwich Time by Lunar being too small, and the Distance between the bodies decreasing, the N'^mv •baerved has been too great the amount of which is found as follows : Take from the N. A. the Pro. Log. of the Difference of Distance in 3 hours, (already found,). . . 0.2618 Place under it the Pro. Log. of the Difference in 'Time, which is 42s=-2.4102 Their Sum 2.6710 •ts the Pro. Log. of a portion of Space, 0° 0' 28", and which is the error of the measured Distance having been too groat The error of the measured Distance may also be found, as before observed, when in sight of land, the |>08ition of which is well laid down, by first finding the Ship's true position by bearings of the land, and turning her Longitude into Time and adding it to the Mean Time at the Ship in West Longitude, or sub- tracting it in East, will give the true Greenwich Time. Then the comparison between this and the Green- wich Time by the Lunar Observation, as in this case, affords the learner the means of judging of tho eorrectnete of his observed Lunar Distance. In observing with the Planets, the usual practice at Sea is to bisect the middle of the Planet on (h* found limb of the Moon. Thia saves the trouble of allowing for the semidiameter of the Planet. LUNAR OBSERVATIONS. 100 FINDING THE LONGITUDE BY LUNAR OBSERVATIONS. EXAMPLE 4. July 4tb. 1864. Id Latitude 40* 20' S., Longitude at about 81° 30' E., at 2h 62in Os P. M. Apparent Time at tb« Ship, tlie biiu's oliserved Altitude was 15° 0', the Moon's observed Altitude Lower Limb 29° 11 , and the Sun's Dis- tance Wesi of the Moon 100° 12' 24", Index Error 2' 30" Additive, the Greenwich Time by Chronometer, July Sd, 21h 30m 38, and which was known to be correct. Required the Longitude in by the Lunar Distance, and also tb* Error ^if any) o{ the measured Distance. Preparation for Clearing the Distance. Green. Time or Date, July 3d 21h SOni 3s Moon's Semid. Mid 15' 38" and Hor. Par. 57' 14" (By Chronometer.) Corr. G. Date 6" A ug. 8", Add 14" Corr. G. Date, Add 21 Obs. Dist nearest Limbs 100° 12' 24" Corr. Au^. Semid 15' 52" Correct H. Par. . 57' 86^ Index Error Add 2 30 ^ Observed Dist. Corrected 100° 14' 54" Sun's Obs. Alt. 16° 0' Moon's Obs. Alt L. L 29° 11' Sun's Semid 15 46 ^orr Add 1^ Cor Add 12 Moon's Aug. Semid 16 52 Sun's App. Alt 15° 12' Moon's App. Alt 29° 28' Apparent Dist 100°T6' 32" Clearing the Distance. Moon's Hor. Parallax 57' 85" Pro. Log. 0.4950 Pro. Log. . .0.495U Sun's App. Altitude 16° 12 Co-Sec. 0.5814 ( 's App. Alt 29° 23' Co-Sec, . . .0.3092 Apparent Distance 100° 46' 32" Sine.... 0.9923 Tang 1.7205 First Correction 4 44 38 2.0687 Second Correction 4 54 37 2.5247 Third Correction 2 35 True Distance Less 10°=- 100° 28' 22 Dist Nautical Almanac at XXI hours. 100 13 12 Pro. Log. 0.2876 Difference 16' 10" Pro. Log. 1.0744 Pro. Log. 0.7868=- Oh 29m 25s PortioD of Time to be Added To the Hour of the preceding Dist Naut Almanac 21h Green Mean Tim i by Lunar 21h 29m 253 To Find the Time at the Ship and thence the Longitude. Green. Date, July 3d. . . 21h 30m 3s Dec. Noon, July 4th 22° 54' N Sun's App. Alt 15° 12' 24 Corr. for 2ih Add 1 Refraction Sub. Z_ Yn^ie: from Noon. July 4, 2h 29m 578 22^65^ N Sun's True Alt 15° 9" 90 Polar Dist 112 55 Log. 0.03571 Polar Dist 112° 55' Latitude 40 20 Log. 011788 ]^° 24' • Equa.of T...4m Os .If Qif: lb .441 Half Sum "84^T2~ Log. 4.00456 Corr. 2ih, Sub. 1 •1(> 2^ Difference 69° 3' Log. 4.97080 Corr. Equa.. .3m 698 / 882 App. Time at Ship 2b 52m 4s Log"9T2845 _??L Equa. of Time Add 8 69 ' MO-2 M. T. at Ship, July 4th . 2h 56m 3s Add 24 Green. Mean Time by Lunar, July 8d 21h 29m 258 or July 3d 2(ih 56m 8s Mean Time at Ship, July 3d 2 6 >6 8 Longitude in by Lunar 81° 39' 30' E.= 5h 26na 888 To Find the Amount of Error in the Measurement of the Lunar Distance. Here the Correct Greenwich Time by Chronometer given is 21h 30m Ss and the Greenwich Time by Lunar being 21 29 25 Their Difference in Time is 38s The Greenwich Time by Lunar being too Small and the Distance between the bodies increas*^*^ •'^« lJi» lance observed has been too Small, and the amount is found as follows : Set down the Pro. Log. of the Difference of the Distance in 8 hours (already found) 0.2876 And place imder it the Pro. Log. of the Difference 38s in 'Time 2.4536 Their Sum ,.. 2.7412 * the Pro. Log. of a portion of Space 0° 0' 20", and which is the Error of the Measured Distance, bavu»l j • ^ o t ° ( Greenwich lime by Lunar too bmall^ Distance Observed is too Sini^u r»- . r* • f Greenwich Time by Lunar too Great= Distance Observed is too Small nar Distance Decreasing. < ^ • 1 t^ \. -i * o h t^ , nx. 3 .. r^ ^ ° \ Greenwich lime by Lunar too Small= Distance Observed is too Great ky the amrunt of the Error found as above. 170 NAUTICAL ASTRONOMY. FINDING THE LONGITUDE BY LUNAR .BSERVATION. EXAMPLE 6. JV Bodies being too near the Meridian the Mean time at Ship is found Afterwards by an Altitude of tht Sun, and showing the Manner of Applying it. August 15th, 1854, or August 14th, 17h 28m Os Apparent Astronomical Time by Watch, in Latitude 10° 23' N. Longitude 20° 15' W, the observed Altitude of the Star Aldebaran was 69° 24', the Moon's Altitude L. Limli DQ the Meridian 88° 24', and the observed Distance Moon's nearest Limb 19° 16' 6", Index Error 1' 45' Additive. rhe Course and Distance made good was W. by S. 9 miles, until IBh 14m 288 Astroa. Time by the same Watch, when the Sun's observed Altitude was 6° 23'. Required the Latitude in by the Moon's Altitude, the Mean Time bj the Sun's Altitude, and the Longitude in at the Time of the Lunar Distance. Preparation for Clearing the Distance. ' App. Astron. T. ktShip, Aug. 14th. ITh 28m Moon's Semid Mid 15' 15" and Hor. Par. Mid . .. 56' 62'- Long. 20° 15' W. in Time Add. 1 21 Corr. for 7 hours Sub. 3 Corr. for 7h Sub. 18 Greenwich Date, August 14th 18h 49m ~15' 12" Correct Hor Par, ... 65' 89'' # East of the Moon. Observed Distance nearest Limb. 19° 15' 6' Index Error Add 1 46 Observed Distance Corrected Moon's Aug. Semid 16 27 15 Apparent Distance 19° 82' 18" Moon's Aug. Add Aug. Semid 7\b' 27" #'8 Obs. Altitude 69° 24' 19° 16' 51" Dip Sub. 4_ #'8 App. Altitude 69' 20' ]) '8 Obs. Alt. L. L. 83' 24' N Corr Ad d 12 J 'b App. Alt 88° 86' To Clear the Distance Moon's Hor. Pari 56' 89" Pro, Log. 0.5098 Pro, Log. 0.5098 #'b App. Altitude 69° 20 Co-Sec. 0.0289 J 's Apparent Altitude. .. .88' 86' Oo-Sec. 0.0027 App. Distance 19° 32' IS"' Sine 0.5244 . Tang.. . . 0.5602 First Correction 2 24 20 Log. 1.0681 Log..... L0627 Second Correction 7 85 48 Third Correction 21 True Dis. lesB 1 0° 19° 82' 47 " Difl. N. A. at XVIIIh 19 57 86 Pro. Log. 0.8115 24' 49'' Pro. Log. 0.8605 .6490= Oh 50m 5 Is Portion of Time to be Added To the Hour of the preceding Dis. N. A 18 Greenwich Mean Time by Lunar 18h 60m 5l8 To Find the Latitude by Observation and the Mean Time at the Ship when the Distance was Observed. Log. 0.01338 Log. 0.00717 Bun's Obs. Alt 6*23' Oorr., Add 3 Sun's True Altitude 5° 26' Polar Distance 75 51 Latitude 10 23 91° 40' Half Sum „ 45° 60 ' Log. 4.84308 Difference 40° 24 ' Log. 4.81166 App. Time 18h 12m lOs Log. 9.67529 Equa Ad d 4 19 Mean Time 18h 16m 29s at Ship. Time by Watch 18h 14m 288 Sun's Dec. Noon, August 15th ... 14* 6" N Long. 20° 15 W.in T, 1 21 Corr. for 4ih .Add . R Greea Date 19h 85m 288 Correct Dec 14° 9 Sun's Polar Dist 76* 61 ]) 'sApp.Mer. Alt. .88° 36' N. Corr. for Alt. .-Add 6^ True Alt .83° 42' Zen. Distance 6° 18' S. Declination 16 41 N. Equa. Noon 4m 17i Cor4ih _Add 2_ Correct Equa. . . .4m 19f Latitude in 10° 23' N. To Find the Mean Time at Ship at the Time the Distance was Observed. Fake the Difference between the Times shown by the Watch or Chronometer at the Time the Distance was observed and the Time the Altitude of the Sun was observed, which call the Interval Turn the Dif- ference of Longitude (made in the Interval) into Time, and Subtract it from the Interval if Sailing West or add it to Interval when Sailing East, will give the Correct Interval. Subtract the Correct Interval fron the Mean Time obtained from the Sun's Altitude, and the result is the Mean Time at Ship at the Time th Liunar Distance was observed : then the Difference between the Greenwich Mean Time found by Lunar an this Mean Time at Ship reduced back, is the Longitude of the Ship in Time. EXAMPLE IN THE ABOVE CASE. Mean Time at Ship 18h 16m 298 Time of Distance by Watch I7h 28m Corrected Interval Sub. 45 52 Time of Sun's Altitude by Watch 18 14 28 2^ 86 4!Sm 62t Mean Time at Ship when Dist was Obs. . . 17h 30m 378 Measured Interval by Watch 46 Green. Mean Time by Lunar, August 14th. 18 50 51 Course W. by. S. 9="D. Lon. 9' W. in TimcSub. Longitude in 20 3' 30" W.= Ih 20m 14s Corrected Interval. If the Interval is great it will be more correct to measure the Interval by Chronometer but if the Watch keep imiform Time, the Chronometer is not necessary. LUNAR OBSERVATIONS. 171 FINDING THE LONGITUDE BY LUNAR OBSERVATIONS, The Sun being too near the Meridian, the Time is found by the Moon's Altitude. EXAMPLE 6. August 16th, 1854, or August 14th, at 22h 30m Apparent Astronomioal Time at Ship, the Moon's obeerrwd Altitude, Upper Limb, West of the Meridian, was 18° 88', Sun's Altitude 87° 28', and liis observed Distance Eaat of the Mjou 91° 7' 44". Index error 1' 46 ", additive. The face of a Chrouometer at the same time showed Ok lOm 23b. The Ship sailed S. W. (true) 15 miles until Noon, when the Latitude observed was 9° 56' N., the Longi- tude by account at the same time being 21° 30' West Required the Longitude by Luaar Observation, and supposing it to be correct, the error of the Chronometer on Greenwich Mean Time, and also the Longitude by Lunar brought up to Noon by the Dead Reckoning. * Preparation for Clearing the Distance. App. Time at Ship, August 14th, 22h 30m Moon's Semid. Noon ... .16' 9" and Hor. Par. Noon 66' 80" Long. 21° 30" W. in Time Add 1 26 Augment Add 5 Greenwich Date, Aug. 14th 23h 66m 15' 14" Obs. Dist nearest Limb 91° 7' 44" ludex Error Add 1 46 Obs. Dist. corrected 91° 9' 29'' Suu's Semid Add 15 50 Moon's Obs. Alt. Up. Limb 18* 88' Sun's Obs. AIL 67* 28' Moon's Aug. Semid.. . Add 16 14 Sub. 20 Add 12 App. Central Dist 91° 40' 33" J> 's App. Central Alt 18° 18' Sun's App. AIL 67* 40' To Clear the Distance Moon's Hor. Parallax 0° 56' 80" Pro, Log. 0.51 10 Pro. Log. 0.6110 Sun's App. Altitude 67 40 Co-Sec. 0.0339 J)*8 App. Alt 18' 18' Oo-Secant 0.6031 Apparent Distance .. 91° 40' 38" Sine 0.9998 Tangent 2.6840 First Correction 4 8 89 1.5447 " Second Correction 4 59 30. . .... 8.6481 Third Correction 8 8 True Distance, less 10* 90° 51' 60" DiBLN. A. at Noon 90 6 1 60 0° 0' 0" Greea Time, Aug. 14th. . . 84h Cm Oa, or Noon of Aug. IMh. To Find the Mean Time at the Ship, and thence the Longitude. App. Alt of the Moon. ... 18' 18' Time by Face of the Chro. Oh 10m 288. J) 'b R A. Noon, Aug. 16th, 8h 16m 29i Cor. for AIL, Table XXV, A dd 49 > '» True Alt 19' 7' > 's Dec. Noon, Aug. 16th, 17* 38' N. J'sPolarDisL 72 22 Log. 0.02090 Polar Dist 72 22 Latitude 10 7 Log. 0.0068J 101° 86' Suns R. A. Noon, Aug. 16th,. . . 9h 88m 3ii Half Sum 50° 48 ' Log. 4.80074 DiflFerence 81° 41' Log. 4.72084 Equa. of Time, Noon 4m 16i. ]> 's H. A. West of Mer. 4h 52m Os—Log. 9.54879 > s R. Ascen Ad d 3 16 29 Course to Noon S. W. 16 miles D. Lat 11' Dep. 11'— D.Lon.— 0*11' R. A. of the Merid.. Sh 8m 29s Latitude Obi. at Noon 9* 56' N. • Add 24 LaL in at Time of Dist 30^' N. 82h 8m 29s Sun's R. Ascen. .Sub. 9 38 33 App. Time at Ship. . 22h 29m 568 Greenwich Mean Time by Lunar, Aug. 14th 24h Om 0* Equa. of Time. Add 4 16 Mean Time at Ship, Aug. I4th 22 34 12 Mean Time at Ship r~22h 84m 128 Long, in by Lunar 21 ° 27' 0" W.^ Ih 26m 48b. Diff. of Long, made to Noon 11 W. Long, in by Lunar, Noon 21' 38' 0" W To Find the Error of the Chronometer. I^me by Chronometer when the Distance was Observed. ... Oh 10m 288 Past Noon, Aug. 16th. Greenwich Mean Time by Lunar or Noon of Aug. 16th. Hence the Chronometer is Fast of Green. Mean Time Oh 10m 238 In this ca.se, if the Time at Ship had been found from the Sun's Altitude, the error in the Time woul« be 8 seconds too great, the Sun being too near the Meridian. The Moon being the lower body in this case, by raising her the True Distance is 48' 43" less than the Apparent Distance. (See Figure 30.) And as before observed, the Difference betvs-een the Apparent ana the True Distance can never exceed the Sum of the correction for Altitude. (That is, the Moon's parallax in Altitude, found in Table XXV, and Sun or Star's correction for Refraction, found in Table IV.) When the difference between the observed and the true Distance exceeds that quantity, it may be concluded t> «k lomo gross error has been committed in the Clearing of the Lunar Distance. 1^^ NAUTICAL ASTRUNOMI. rO COMPUTE THE ALTITUDES OF THE OBJECTS AT THE TIME THE DISTANCE WAi OBSERVED, Having the Correct Apparent Time, the Latitude of the Place, and thf Approximate Lor.gitude. li nometimes happens at Sea, in taking a Lunar Observation, that the Altitude of one or both of tn» obje&bS are lost in consequence of cloudy weather coming on. In that casr,, if the Apparent Time at th-. SWi., and the correct Latitude of the place are known, the Apparent Altitudes of the objects may be eom* vJted as follows * RULES To Compute an Altitude. lit. If the Time at Ship is not known, and a Chronometer at hand, (and its error on Greenwich known,) take tne Greenwich Time by Chronometer at the time of the Distance, from which subtract the Longitude in Tiiiie in West, or add it in East Longitude, will give the Mean Time at the Ship. From the Nautical Alman&c take out the Equation of Time, and apply it to this Mean Time the contrary waj^ to what is director in the column for Apparent Time, and the result is the Apparent Time at the Ship at the time the Di8tan».« was observed. If an Altitude of one of the objects has been observed at a proper Distance from the Meridian, tbt Apparent Time can at once be found from its Altitude. Or, the Watch may be corrected to Apparent Time by an Altitude taken either before or after the Lunai Distance has been observed, allowing for the difference of Longitude in Time, made in the interval. If the Apparent Time at Ship is A. M., add 12 hours to it ; but if P. M., both will then be the Apparent Astronomical Time from the preceding Noon, which must be dated one day less than the Sea account ; if the Civil day is used, and the Apparent Time is A. M., date it also one day less, but when P. M. dfte it the same as Civil Time. 2d. Find the Hour Angle of the object, which, if it be the Sun, is the Apparent Time from the nearest Noon. If the object be the Moon or a Planet, find the Greenwich Date as usualf and from the Nautical Almanac take out their Right Ascensions and Declinations, and correct them to the Greenwich Date ; but if the object be a Star, take out its Right Ascension and Declination from Table XVIII, and correct th« Sun's Right Ascension taken from the Nautical Almanac to the Greenwich Date, Add the Sun's Right Ascension to the Apparent Time, their Sum (less 24 hours, if it exceed thatquantityj will be the Right Ascension of the Meridian, the difference between which and the Right Ascension of the object in Time will be its Hour Angle ; write under it the Latitude and the Declination of the object. 3d. Then, if the Latitude of the place and the Declination are both of the same name, that is, both North or both South, their difference will be the Meridian Zenith Distance ; but if one be North and *he othe* South, their Sum will be the Meridian Zenith Distance. 4th. Add together the Logs, of the Hour Angle, found in Table XXIX, the Log. Co-Sines of the Latitude and Declination, from the top of Table XXVIII, and the Log. Secant of the Meridian Zenith D:■^tance, from the top of Table XXVII. The Sura of these 4 Logs., (rejecting 10 from the Index,) found in Table XXIX, will give an Arch in Time. 5th. Turn this Arch in Time into Degrees, &c., by Table XXIX, and from the top of Table XXVII take out its Log. Secant, which add to the Log. Secant of the Meridian Zenith Distance, (already found,) the Sum will be the Log. Co-Secant of the True Altitude of the object, found at the bottom of Table XXVlI. 6th. As the Apparent Altitudes are used m correcting a Lunar Distance, it is necessary to reduce lh« True Altitudes thus found as above to the Apparent Altitudes. When the object is the Sun, Planet, or a Star, this is simply the correction for Refraction, taken from Table IV, which must be added to the True Altitude. Their Sum will be the Apparent Altitude. But when the object is the Moon, enter Table XXV with the Moon's Ti ae Altitude at the side, aiid her Horizontal Parallax at the top, and take out her correction for Altitude. This subtracted from the Tru» Altitude will give her Apparent Altitude. In the night time, at Sea, a Lunar Distance may often be correctly observed, while the Altitudes of th< objects may be in great uncertainty from the obscurity of the horizon; and in the case of the M?on. ib cloudy weather, long, dark shadows are sometimes projected on the Sea under her, wliich renders it impos- ■ible to obtain her Altitude correctly. In that case, the Altitudes may be computed by the above Rules. But it rarely happens that a time cannot be chosen to observe the Altitudes correct enough foi Clearing the Lunar Distance, as precision in the Altitudes is not necessary, and thus saviu"' the heavy additional ealeulations of Altitudes in working a Lunar Observation. LUNAR OBSERVATIONS. 178 TO COMPUTE THE ALTITUDES OF THE OBJECTS AT THE TIME THE DISTANCE WAS OBSERVED. To Find the Sun's Altitude. Suppo.se it was required to find the Sun's Apparent Altitude at the Time of the Distance Observed 1q Example 1st, page 166, the Mean Time at Greenwich by Chronometer being, June 3d, 7h 36m Os, Latitude 113 30° 0' N. and Longitude 69° 54' 15" W., we proceed as follows : Green. Time bv Chronometer, June 3d 7h 36m Os Sun's Dee. Noon. 22° 19' N. Equa. of TimeNoou 2m I8f Long. 69° 54' 15" W. in Time Sub. 4 39 37 Corr. for 7|h. Add 2 Con: for 7^. . .Sub. S Mean Time at Ship 2h Stim 23s Correct Dec 22° glM^. Correct Equ 2m lOt Equa. of lime Add 2 10 '* Appa/ent Time at Ship 2h 58m 33s Log. Table XXIX 9.15902 Sun's Declination 22° 21' N. Co-Sine Table XXVIII 4.96608 Latitude 30 X. Co-Sine Table XXVIII 4.93753 Meridian Zenith Distance 7° 39' Sec. Table XXVII 0.00388. . .0.00388 Arch, in Time 2h 39m 423 Log Table XXIX 9.06651 Turned into Degrees by Table XXVI 39° 56' Sec Table XXVII at Top. . ,0.11532 Sun's True Altitude 49 28 Co-Sec. .Table XXVII at Bottom 0.11920 Refraction, Table IV Add 1 Suu'a Apparent Altitude 49° 29' To Find the Moo7i's Altitude. Required to compute the Moon's Altitutle at the time of the Distance observed, in Example 2d, page 167, th« Apparent Time at Ship being, June 3d, 7h 57m 453, the Latitude in 29° 32' N., and Longitude by Acct 69° 20' W. to find the Moon's Apparent Altitude. App. Time at Ship, June 3d. . .7h 57m 458 App. Time at Ship 7h 58m Sun's R. A. at Noon. 4h 44m I3i Sun's R. Ascen , 4 46 18 Lon. 69° 20' W. in Time Add 4 37 Corr. for l?h 35m Add 2 6 R. A. of the Meridian 12h 44m 033 Greenwich Date, June 3d. . 12h 36m Sun's Correct R. A. . 4h 46m 18i Moon's R. Ascen 11 6 13 ^i t^ . ^.., J) 8 R. A. Mid. . . . Ilh4ml8 Moon's Hour Angle Ih 38m 50s Log Table XXIX 8.66664 Con- for Sftm AAA 1 o Moon's Declination 11°27' N. Co-Sine Table XXVIII 4.99127 ^,' " ••^"<^ 1 i Latitude 29^32^J^ Co-Sine Table XXVIII 4.93955 ^ ' Correct R. A. llh 5m .13i Meridian Zenith Distance 18° 5' Sec Table XXVIl 0.02200 0.02200 Arch, in Time Ih 34m lis Log.. ., Table XXIX 8.61946 furned into degrees by Tab. XXVI 23° 33' Sec. . . Table XXVII at Top 0.03777 J) 's Dec. Mid.. 11° 86' W Moon's Tiue Altitude 60° 38' Co-Sec. Table XXVII at bottom 0.05977 Corr 35m Sub 8 Corr. for AIL Table XXV, Sub. 27 ^ '„ n 'i^ - -rr5-;:;r^ J) 8 Corr. Dec. 11° 27 N Moon's Apparent Alt 60° 11' at Time of the Dist. See Ex. 2d, page 167. To Find a Star's Altitude. Required to compute the Altitude of the Star Aldebaran at the Time of the Distance, in Example 5th, page IV o, the Apparent Time at Ship being, August I4th, 17h 28m Os, the Latitude in 10° 23' N., and Longitude by AcoL 20° 15'^ W, to find the Star's Apparent Altitude App. T. at Ship, Aug .14th 17h 28m Os App. Time at Ship I7h 28m Sun'sR.A.Noon, Aug. 14,9h84m488 Suns R. Ascen 9 37 58 Long. 20° 16' W. in T. _J_ 21_ Cor.for G.Date 18h49m Add 3 10 27h 5m 588 Green. Date, Aug. 14... 18h 49m Sun's Correct R. A.. . .9h 37m 58« Sub. 24 K A. of the Meridiai' 3h 5m 588 #'8 R. A. Tab. XIX. .. 4h 27m 8'ii #'b R. Ascen 4 27 32 #'8 Hour Angle Ih 21m 34s Log. Table XXIX 8.49601 *'^ ^^'^ '^^^- ^^^- • ' ^^' ^^' ^ #'8 Declination - 16° 13' N. Co-Sine Table XXVIII 4.98237 Latitude . 10 23' N. Co-Sine Table XXVIII 4.99288 Meridian Zenith Dist 6° 60' S^°- • • '^'^'^l^ XXVI I_0.00226=0.00225 Arch in Time Ih 19m 27s Log. . . Table XXIX 8.47346 Tur. into degrees by T. XXVI 19" 52' Sec. Table XXVIl at Top.. . .0.02665 *'• '^>'« ^'^'^"^« ; V, 69 20 .... Co-Sec Table XXVII at bottom 002890 Oorr. for Ref Add *'8 App. Altitude 69° 20' at the Time of the Dist. See Ex. 5, page 170. It may be remarked here that considerable care is required in correcting the R. A. and DecMnatione to th« Green. Date, and also in having the Apparent Time correct, especially when the object is neai' the Prime Vertical, but an Error in the Latitude at that time will not much affect the result, and when the object ii near the Meridian any probable Error in the Time will not much affect the computation, but an Error ia the Latitude will cause nearly an equal Error in the computed Altitude. Note -An Error of 2' or 3' in the Altitude of a Star has more effect in producing an Error in the True Lnnw 2oS a' LTar ObreVvatrou" ''""'' "' '' '"" "" ^'"'^ ^'"^""^ """"^ ""'''■ '^^'^ '« ™P-'-°' ^° be^rVn a.ind " |f4 NAUTICAL ASTRONOMY. FINDING I'HE LONGITUDE BY LUNAR OBSKaVATIONS ON SHORE. A Lunar Observation may be taken on Shore by the aid of an Artificial Horizon for observing ihe Sun i Altitude (see pages 77 and 78) only ; the Altitude of the Moon can be computed by the preceding ruies, and the observations should be taken when the Sun is at a proper Distance from the Meridian with the Tiew of obtaining the Time at the place, from the same Altitude observed with the Distance. The Observation Compute the Approximate Distance as directed at page 74, ready for use, and proceed first to observe ai. Altitude of the Sun in the Artificial Horizon, note down the Time and the Altitude, set the Index of the Sextant to the Approximate Distance, and when brought into the field of view bring the Limbs in contaci, note down the time and the observed Distance, proceed to take any odd number of Distances and their cor- responding Times, as recommended at page 76, and finish with an Altitude of the Sun, noting down th« Time as before. Find the Mean of the Times of the Distance and the Mean of the Distances, and the Difference be- tween the Times of the Altitudes and the Difference of the Altitudes : then say, as the Difference of the Times is to the Difference of the Altitudes, so is the portion of Time between the Time of the first Altitude and the Mean of the Times of the Distance to a portion of Altitude, which Added or Subtracted to or from the first Altitude, according as it is Increasing or Decreasing, will give the Sun's Altitude at the Time of tha Mean Distance. Having the Sun's observed Altitude, the Latitude of the place (which may be obtained in like manner by the Sun's Meridian Altitude, see page 92,) and the Approximate Longitude, proceed to find the Apparent Time as in the Examples at page ^31. Having the Apparent Time at which the Distance was observed, compute the Moon's Apparent Altitude (by the Rule at page 172), and proceed to work the Lunar as before : EXAMPLE OF WRITING DOWN THE OBSERVATION September 26th, 1854. At 3h 57m 158 P. M. Mean Time at New York, in Latitude 40° 42' 42" N., and Lonjfi- tnde 74° 0' 15" W., the following observation was made to find the Longitude. "nme per Watch Sh 63m ( 3 56 Mean of the Times 3h 57 m 15s. 3 57 25 8 69 10 4 1 28 Os Alt. Sun's L. L. ArL Hor. 1 Dis. of Sun and Moon . . . do. do. do. do. Alt. Sun's.L. L. 41' •32' 0" 66 13 10 14 10 16 10 38 38 Mean Dis 66*14' 10" Index Error.. Add 60 Obs. Dis 56* 16' O" To Find the Sun's Altitude at the Time of the Mean Distance and thence the Time at the Place. Time of the Ist Alt. . do. 2d Alt... Say as 8h 63m Os 4 1 28 8m 28b is to Ist Alt 41° 32' Time of Ist Alt 3h 63m Os 2d Alt 38 33 Mean of the T.. . 3 6 7 16 So is 2° 59' 4m 168 Sun's Obe. Alt Artit Hor. 40' 2' 8" Index Error Add 60 8m 288 Pro. Log 1.8276 Arith. Co 2° 59' Pro. Log. . . 4m 168 Time by Watch 8h 67m 158 1°29' 6 2"= Pro. Log.. Long. 74" W. m Time 4 66 Ist Alt 31 32 Decreasing 8.6724 0.0024 1.6269 0.3017 Observed Angle i)40° 2' 58 ' Greenwich Date. Alt of Sun's L. Limb. . 20° 1' 29" 2' 18 81 Sun's Sem. 16' Ref 2' 29" Sun'e True Altitude 20* 16' 0"~ Polar Distance 91 21 84 Latitude 40 42 42 162° ig'TF Half Sum 76° 9' 38' Log. 0.00012 Log. 0.12038 Log. 4.37876 Log. 4.91812 Difference 66* 64' 88' App. "nme "xt Place 4h 6m 0« =Log 0.41788 Equation of Time... Sub 8 46 Mean TioM tt Plaee .... . Sb 67m Ifie . 8h 63m 08Ob8.Alt40 Sun's Declination Noon . . . . Corr Add. Correct Declinatioa 8" at Time of Diet 1° 12' 52" S. Dif. Ih 68 8 42 G. Date 9b 1* 90 21' 34" S. 60)622 Polar Distance 91° 21' 34' Equation of Time, Noon Correction Add Correct Equation 8m 87fi -87 Di£ Ih -840 7 '66 G. Date 9k 8m 46b -48 7M-0 FINDING THE LONGITl DE ON SHORE. 175 TO FIND THE LONGITUDE BY LUNAR OBSERVATIONS ON SHORE Having the Apparent Time, to Compute the Moon's Altitude at the Time of the Distance. Corr. .Add 1 21 App. Time at place . . 4h 6m Os Sun's Right Ascen 12 12 33 R. A. of the Merid. . . I6b 18m 33s >'b R. Ascen 15 47 12 p 's Hour Angle Oh 81m 2l8 Log. 7.66891 R. A.. . 12h 12ra 838 D's Declination 20° 80' S. Co-Sine 4.97159 Latitude _40 43 N. Co-Sine 4.87964 > 's Mer Zen. Diat. . . 61° 13' . . .Secant_031740=-0.3174O oh 88m 4s Green. Date, Sept. 26tb, 8b 53m Ob . > 's R. A. at Noon 16h 26ra 42i At Midnight 15 54 24 Sun's R.A. 12h'llm 123 Dif. Ih- da Diff. in 12 hours. _9_ Diff. 12h. Pro. Log.. Oh 27m 42< 1.1761 •8.8239 0.8128 Arch iu Time. . In degrees. 9° 81' = Moon's True Alt 28° 21' Corr., Tab. XXV,. .Sub. 49 ' Log. 7.83754 Secant . 0.00602 . Co-Sec .~0.32342 Moon's App. Alt 27° 32' at the Time of the Distance. Hence we have the following Observation to Clear the Distacce and find the Longitude 60)81 8 Arith. Comp Im 2l8 27m 428 Pro. Log.. G. D. 8h 53m Pro. Log. 1.3067 Corr. 20m 308="a9434 R. A I5h 26m 42s > 's R. A.T5 h 47m 128 )'8 Declination, Noon 18° 68' 8. Corr. Q. Date 9h Add 1 87 ]) 's Correct Dec 20° 30' S Sun's Oba. Alt 20° 1' Mn. Time at the place 3h 57m 15s 3h 57m 15s Sun's Obs. Alt 20° 4 56 Semid. Add Mean Time Loa 74° W. in Time Or. Date, Sept 26th 8b 53m 158 Sun's App. Alt 20° 17' 1' 16 D'a App. Alt 27° 82' ]) 's Semid., Noon Corr. 2" and Augm. 8" ]) 's Aug. Semid. . . .T 16^ Sun's Semid. 16 Obs. Dist 55 15' 53 10 15' 0' Hor. Par. 58' 12' Corr. G. D. 8 3" D 's H.Par. 58' 20" Obs. Distance 65° 15 App. Distance 66° 47' 3" Moon's Hon Parallax 68' 20" Pro. Log. 0.4894 Sun's App, Alt 20 17 Co-Secant 0.4601 1>'b App. Alt.. 27* 82' App. Distance 65° 47' 8" First Correction 4 35 83 Second Correction 6 18 20 Third Correction 1 21 Sine 0.9175. . . 1.8670 Pro. Log. 0.4894 Co-Secant 0.3851 Tangent 1J674 1.99S0 True Distance 65* 42' 16" Dist, N. A., at Vlh. ..64 10 41 Difference 1° 31' 35" Pro. Log. 0.2769 Pro. Log. 0.2936 Pro. Log. 0.0166= to the Time of the preceding Distance, N. A., •2h 63m 168 portion of Time to be added 6 Greenwich Mean Time 8h 53m 168 Mean Time at the Place 3 67 15 Longitude of New York in Time 8h 56m 18^74° 0' 15" W Another Example of this method is not necessary, as all the various cases are already given of finding '8 Dea at 13h 26 21 Diff. between the Obs. and ) , „ the Preceding DecL. \ ^^ ^ 13' 20" Then say as 13' 20" is to 1 hour so is 12' 19" to a portion of Timl Difference in 1 hour 18' 20" Pro. Log. 1.1 SOS Arith. Comp. 8.8697 Is to 1 hour Pro. Log. 0.4771 g So is the Diff. betw. the Preced. and Obs. DecL 12' 19" Pro. Log. 1.1648 g Portion of Time to be Added Oh 65m 268 a 0.511* Time of the preceding Declination 13h Grenwich Mean Time 13h 55iu 258 Mean Time at Ship 11 23 29 Longitude in 37' 59' 0" W.= 2h 31m 568 The result is a Diff. of only 1' less than that bv Cbron. hnnucht oii by I). R. from Sights taken in the Aftemomh 178 NAUTICAL ASTRONOMY. FINDING THE LONGITUDE FROM THE MERIDIAN ALTITUDES OF THE MOON AND A STAR The principle of this method is the same as that in the preceding example, that is, of finding the Moon'* Declination by observation ; but in the room of measuring the Distance between the Moon and a Star, we take the Difference between their True Meridian Altitudes. Then the Difference between this and tha Star's Declination is the Moon's observed Declination, which furnishes the Greenwich Time as before. In this case it is not necessary that the Altitudes of the Moon and Star should be observed at the same time, though they necessarily must pass the Meridian within a short time of each other, in order to obviate the necessity of making a correction for the Ship's change of place, especially when making much Northing «r Southing. The Altitudes should be accurately observed with a Sextant to the nearest second, and at Twilight^ when the Horizon is distinctly visible. This method is therefore seldom practical in the Night Time, as it depends entirely on the accuracy of the measured Altitude. By the method given in the 1st Example the Altitudes are not required with precision, as its accuracy depends upon the measured Distance between the Moon and the Star ; an ill defined Horizon in the Night Time is therefore no detriment to the former observation. THE OBSERVATION. The Proper Time for Observing the Moon's Altitude. 1. The Limits are the same as in the preceding example, that is, the Time must be chosen when the Moon's change of Declination is at the greatest, and also the day on which the Moon will be on the Meridian at Twilight, which can be easily ascertained by inspecting the Nautical Almanac, and by inspect- ing Table XVIII, find a Star which passes the Meridian about the same time and on the same side of the Zenith. Find the Mean Time of the Moon's Meridian passage at the Ship, to which apply the Equaticu ->f Time, will give the Apparent Time, and the Watch must be previously regulated to the exact Apparent Time at the Ship, (which can be easily done by an Altitude of the Sun before he sets,) because the Moon's Altitude must be observed at the instant of Apparent Time by Watch, (according to computation) at which she if on the Meridian of the Ship, and the Time and Altitude observed noted down. Observing the Starts Altitude. 2. Find the Star by the rules given at page 106, No. 3, and the Apparent Time of its passing the Meridian oy Table XVIII. Observe its Meridian Altitude at this time, which will be indicated by the Watch, either before or after the Meridian passage of the Moon, or according to which of the objects passes the Meridian fiist. Correcting the Semidiameter and Horizontal Paral^. 3. Find the Greenwich Date as usual, and take out the Moon's Semidiameter and Horizontal Parallax, «orrect them to the Greenwich Date, and to the Semid. add the Moon's Augmentation. To Find the Moon's Apparent Altitude. 4. If the Moon's Lower Limb be observed add the Aug. Semidiameter, if the Upper Limb suitract it, will Ijive the Central Altitude. Take out the Dip of the Horizon accurately from Table V, and Subtract it from the Central Altitude, will give the Apparent Altitude. To Find the Moon^s True Altitude. 5. Add the Log. Sec. of the Apparent Altitude to the Pro. Log. of the Horizontal Parallax, and their Sum will be the Pro. Log. of the Moon's Corr. for Parallax in Altitude, which add to the Apparent Alt. Enter Table IV with the Moon's Apparent Altitude, and take out the Refraction corresponding to it, and which must be subtracted from it, and the result is the Moon's True Altitude. To Find the Star's True Altitude. 6. Enter the same Table with the Star's Observed Altitude, and take out the Refraction, Subtract both Dip and Refraction from the Observed Altitude, will give the Star's True Altitude. Having the True Altitudes to Find the Moon's Declination. 7. From the Large Nautical Almanac take out the Star's correct Declination and mark it N. or S. Take the Difference between the Star's and the Moon's True Altitudes, then the Difference between this portion of Altitude and the Star's Declination is the Moon's Observed Declination. If the Difference of the Altitudes be greater than the Star's Declination the Moon's Declination will be of a contrary name to the Star's. But if the Difference of Altitude be less than the Star's Declination thf Moon's Declination will be of the same name as the Star's. Having the Moon's Observed Declination to Find the Greenwich Mean Time. 8. Find in the Large Nautical Almanac the two Declinations between which the observed Declination fallf, and take their Difference ; take the Difference also between the preceding and the observed Distance ; then •ay SM the hourly Difference is to 1 hour so is the Difference between the preceding and the observed Decli- nations to a portion of Time, which Added to the hour opposite the preceding Declination will give the firaeuwich Mean Time at the time of the observation PINDING THK LONGITUDE. 1751 RNDING THE LONGITUDE FfiOM THE MERIDIAN ALTITUDES OF THE MOON AND A STAR. To Choose a Case. Suppose it was required to find the Longitude by this method, on the evening of tlie 6th of July, 18&4. On inspecting the Nautical Almanac, I find that the Moon's Declination changos at the rate of 123" in 10 minutes of time ; the Moon is also on the Meridian at twilight. And on inspecting Table XVI 1 1, I find that the Star Arcturus will be on the Meridian about the same time. The case is, therefore, practical, and we proceed at once to find the Apparent Time at Ship, and correct the Watch. EXAMPLE 2. July 6th, 1854. lu Latitude 42° 10' North, Lougitude 64° 66' West, at 6h 47m 78 Apparent Time at Ship by Watch, the obseiveil Meridian Altitude of the Moon's Lower Limb was 41° 21' lu", aud about 23ra aftei-warda th« M*-ridian Altitude of the Star Aieturus was observed to be 67° 62' 15 ", the elevation of the eye being 18 feet. Re- quired the Longitude in at the Time of the Moon's Altitude. PROJECTION Of the Meridian Altitudes of the Moon and the Star Arcturus. Fig. .32. I ZENITH jRCLE P;ASS//Wc; t or ' A R CT 'of Vecl' RATI ON A L HORIZON POfNT It will be perceived by the above Diagram, that the Star's Declination (being North of the Celestial Equator) subtracted from the Difference between the Moon and the Star's Altitudes, famishes at once th« Aloon's Declination, South of the Equator. lb Find the Longitude from the Moon's Observed Declination. I'sMer. Pass. N. A. July 6th 6h 42m SOs M. T.of Pass, at Ship 6h 51m SOs ]) 'sSem.lS' 69" H.P.SS'Sg" Say as 360° is to 50m so is L. 64° 56' W. to 9 Lon.64° 56' W.in T. 4 19 44 Oor.G.D. 2 Cor. 14 Mean Time of Pass. Men at Ship 6h 51m SOs Gr. Date, July 6th, llh 11m Us 15' 67" 68^'' Equa. ofTime Sub. 4 23 Augment.. 11 App. Time at Ship 6h 47m 78 Cor. Eq. of Time. . 4m 23s Augm. Semi. 16' 8" Obs. Alt. D 's Lower Limb. . 41" 21' 10" #'s Obs. Alt. . 67° 62' 15" 5 '8 Augm. Semid Add 16 8 Dip 4' 8" R. 24 "=- 4 3 2 Central Altitude 41° 37' 18" #'8 True Alt 67° 47' 43" Dipof theHor. 18 feet 4 8 D 'b App. Alt 41° 33' 10" App. Alt Log. Sec. 0.1259 Corr. for Par. in Alt... Add 43 43 H.P. 58' 25" Pro.Log. 0.4887 Refraction in Alt. 42° 16' 53" > 'a C.43' 43" Pro.Log. 0.6146 Diff. of Obs. and preced. Dec. .Sub. 1 3 2> '8 True Alt 42* 15' 50" %'b True Alt 6 7 47 43 Diff. of Altitudes 25° 31' 58" #'8 Dec. N. A., July 8th. . 19 57 43 N D 's Obs. Declination 5° 34' 10" S D 's Dec. N. A., July 6th, llh. 5 31 56 0^ 2' 14" Moon's True Altitude 42° 15' 50" Bay as 12' 17" is to Ih so is 2' 14" to a portion of Time. Diff. Declination. . 12' 17" Pro. Log 1.1660 Arith. Compli 8.8340 I hour Pro.Log. 0.4771 Diff of Dec. 2' 14" Pro.Log 1.9063 T) '8 Dec. N. Al, July 6th, llh 5° do at 12h 6 31' 5C 44 Itt Diff. of Dec. in 1 hour 0° 12' 17" Time of the preceding Declination. ... llh Om 0» Portion of Time to be added 10 64 Greenwich Mean Time llh 10m 54» Mean Time at Ship 6 51 30 Longitude in 64° 61' 0" W.=-4h 19m 24fl Portion of Time 1 Om 548 Pro. Log. 1.2174 Degree of Dependence. Although the Altitudes are required to be taken with much precision, to insure a tolerable degree of accuracy by Wiis method, still as the errors in the Observation are not multiplied in the computation, it may be used with aavao- iHge in fine serene weather, when the Sea is smooth, and the Dip of the Horizon is correctly ascertained, by thoM persons who may not have had practice in the Lunar method. In this case an error of 10" in computing the Moon'a Declination, will produce an error of 13' in the Longitude deduced therefrom ; and an error of 1' m the Declination will produce an error of 1° 13' in the Longitude. "This method is therefore most suitable for High Latitudes, wbflr« the aegrees of Longitude are small, and where the actual error in space (that is, Departure) would be small in pro- portion. It is, however, much inferior to the Lunar Tup'^^hod as regards accuracy ; but the Observation may be usalbl to those who can take Altitudes accurately enough, bu* who make sad work at measuring a Lunar Distance 180 MEIHOD OF KEEPING A SHIPS RECKONING AT SEA; AND THE MANNER OF WRITING DOWN THE SAME IN A LOG BOOK OR JOURNAL Description of the Log Slate or Board. This is ruled in the follo\ring form, so as to contain an exact account of the Ship's progress during the 24 hours of a Sea Day, and which commences at Noon, that is, when the Sun is on the Meridian of the Ship. The hours are counted to 12 at Midnight, and called the hours P. M. They are then reckoned over again in the same manner, until the following Noon, and called the hours A. M. Mode of Reckoning Time. The Sea Day begins 12 hours before the Civil Day, and 24 hours before the Astronomical Day. So that the end of the Sea Day, the beginning of the Astronomical Day, and the Middle or Noon of the Civil Day, takes place at the same period of time. This mode of reckoning arises from the custom of seamen dating their Day's Work for the preceding 24 hours the same as the Civil Day, so that occurrences which happen, for instance, on Tuesday the 10th in the afternoon, are entered in the Log marked Wednesday the 11th, P. M., and occurrences which happei on the following morning of the Sea Day, are entered in the Log marked A. M., and which also corres ponds to the same hours of the Civil Day What the Log Board should Contain. The Log Board should contain a register of the Courses, Distances, Leeway, and the direction of th*., V^'nA tacking or wearing Ship, making or shortening Sail, and other matters of importance connected with tnc Ship^i» way; and it is the duty of the officer of the Watch to mark the same regularly on the Log Slate (whicn w generally hung up in the Steerage for that purpose) at the expiration of each Watch, so tlia« the Chip's progress may be ascertained at any given hour of ihe day. When land is in sight, the bearing and estimated distance of the most prominent ob'erts, and the time at which the bearing was taken, must be inserted, as also the particulars of speaking vea.sels at Sea, and anT ether memoranda intended to be inserted in the I og Book, as a guard against a tA}, a the memory. Ruling of the Log Board. The Log Board is ruled to contain seven columns ; the first contains the hou'a from Noon to Noon, bemg marked for every hour, similar to a Civil Day ; (or sometimes it is marked for every two hours,) in the second and third columns are inserted the rate of sailing by Log per hour, sU against the hour when the Log was hove ; the fourth column contains the Courses steered by Compass ; the fifth, the direction of the Wind; the sixth, the Leeway; and the seventh contains the transactions, remarks on the weather, and ther memoranda. Setting the Watch at Sea. When a Ship leaves a Port outward bound, the crew are divided into two Watches, termed the Starboard and Larboard Watches, and who do duty 4 hours alternately, except between 4 and 8 o'clock in the evening, when each Watch does duty 2 hours only. These are called the Dog Watches, and are for the purpose of changing the Night Watches, so that the same party will not be on duty at the same interval Oi time on two follovring nights; and it is the custom or rule for the Second Officer, who keeps the Captain's, or Starboard Watch, to take the first Watch, (which is from 8 o'clock in the evening until midnight.) on leaving Port outward bound ; and the First Officer, who keeps the Larboard Watch to take the first Watob »n leaving Port, homeward bound. KEEPING A Si HP'S RECKONING. l«l THE LOG BOARD. 1.. K. F. COURSES. WINDS. L.W. REMARKS. TUESDAY, APRIL IST, 1854. 1 2 3 4 6 6 7 8 9 10 11 12 8 8 8 8 9 10 9 9 7 7 7 6 3 2 6 7 4 5 S. K ti 0. Ther.76'' 1 H 2 At 4h, sent down the royal yards, and made all snug alofL At 6h, strong gale and a high sea running. Vessel shipping much water on deck. At Sh, tacked ship to the Southward; more moderate weather- out double-reefs and set top-gallmt-sails. Spoke the ship Asia, from Manilla to New York, out 85 days ; all well. Noon. Fresh gale and cloudy. Sun obscured. Magnetic variation 1-J^ points Westerly. 5 6 6 5 8 7 8 5 5 9 10 11 12 6 6 6 6 6 8 9 5 The above form of ruling for every hour is the most accurate mode, though sometimes another form u ased, and marked for every two hours, but which is liable to cause considerable error in the reckoning, in having to double the knots marked opposite the hours, thereby doubling the error in the distance sailed. Besides, it is inconvenient for inserting the Course, when it is changed between the hours so marked. On proceeding to work a Day's Work, the Courses by Compass are taken from the Log Board, and cor» reeled lor the Variation of the Compass and for Leeway, when she makes any. This gives the Course made yood between the hours marked on the Board. Cross off the di.stance below the hour at which the Course was changed, (as in the form above,) sum up the fathoms, which divide by 10*, the quotient is knots, and the remainder, if above 5, call 1 knot more, but if less than 5, throw it away ; carry the quotient to ihe column of knots, and their sum, contained between the hourg corresponding to the Course, will be the distance run on that Course. To Correct the Courses for Variation. RULE. " When the Variation is \ Westerly, allow it to the Left hand of the Course steered. ( Easterly, allow it to the Right hand of the Course steered To Correct the Courses for Leeway. RULK When the Shin ia n the \ ^tarboard Tack, allow it to tiie Left hand of the Compass Course. Port Tack, allow it to the Right hand of the Compass Course. EXAMPLE Of Correcting the Courses and Finding the Distance. COMPASS COURSE STEERED. TARIA. L. WAY. WIND. ON WHICH TACK. OOITRSE MADE QOOD. DI8TAN0K. S. E. from Noon to Midnight. H pt. w. S. W. Wind free. S. E. by E. i K 100 E.by S. from Mid to 2 A.M. U M S. by E. Starboard Tack. E. iN. 14 East from 2h to 4 " «< 11 ipt. S. S. E. do. E. N K 18 E. N. E. " 4h to 6 " C( U 1 " S. E. do. N. K i N. 19 i*. E. - 6h to 8 " u tt H " E. S. £. do. N. by E. 10 South " Sh to Noon. tt u 2 " do. Port Tack. S-i W. 27 • Or, oonslder the Sum to be tenths of a mile, note the unit, and carry the tens to the next oolnmn, in the same \v Ml the Sums taken from Tables I and U. 182 KEEPING A SHIPS RECKONING Finditig the Variation of the Compass The Variation of the Compass maybe found by an Amplitude, (see page 116,) or by an Azimuth, '■•• page 118.) It may also be found by inspecting the Chart, or by the Variation Table. The Magueti* Variation is there laid down from actual Observation. (See Remarks, page 120.) Allowing for Leeway. Leeway is the effect of the lateral pressure of the Wind and Waves in forcing a vessel out of the Courst Bhe is endeavoring to make when close-hauled, and it is the angle contained between her wake and the point of the Compass right astern) It may be ascertained after heaving the Log, and before the line i* drawn in, by bringing it over a Half-Compass, constructed for that purpose, on the Taffrail, the diameter of which being at right angles to the Ship's keel, then the angle between the centre point, and the point oi half point over which the line lies, will contain the number of points of Leeway the vessel is then making, providing she has been steered steadily during the time of trial. When a Ship is laying to, the middl* point between what she comes up to, and falls off, is taken as the direction of her head by Compass. The Leeway is then estimated from the angle of her wake, as before. As the correctness of the Reckoning in a great measure depends upon a proper allowance for Leeway, the officer of the Watch should be particular in marking it on the Log Board, or else in reckoning up th« day's work, it will be found difficult for a person who has not been on deck the whole time to make t proper allowance. Correcting the Course for Leeway and Variation. In correcting the Courses for Variation and Leeway, imagine yourself to be in the centre of the CompaM and looking towards that point which represents the Course steered. EXAMPLES Uf Correcting the Courses Steered for the Effect of Leeway and Variation. OOURBE3 STSEEED. WINDS. ON WHICH TACK. LEEWAY. VAKIATION. OODESES MADE GOOD. E. N. E. N.W. Wind free. H pts. W. N. E. i E. W. by S. N. W. by N. N.W. by N. Starboard Tack. 1 pt. » W. s. w. N. E bv N. do. H 2 " W. W. by N. i N. South. E. S. E. Port Tack. i li " E. S. by W. i W. N.W. W. S. W. do. 2 1 « W. N. W. by N. S. S. W. S. E. do. H li " w. S. S. W. E. by N. N. by E. do. n Oi " E. S. E. by E f K West N. N. W. Starboard TacK. 5 1 " E. W.iN. In the above Examples, 6 points of an Angle is allowed between the Ship's head and the point from which the wind blows, this being as near as a square-rigged vessel will lie to the wind when close-hauled in smooth water ; but in blowing weather at Sea, it is the practice to round in the weather-braces, so that the Ship's head, though still close-hauled, is about 7 points from the wind, or as it is termed by seamen, on a Western Ocean bowling, the object being to make greater speed and less Leeway. Fore-and-aft vessels generally lie within from 4 to 5 points of the wind, that is, a point or two higher or nearer the wind than square-rigged vessels do. In allowing for Leeway and Variation, when they both go the same way, it may be done at once by allowing their Sum ; or when in different ways, take their Difference and allow it the same way as that of the greater of the two, whether it be Variation or Leeway. And the learner should keep the figure of the Compass-card in view while making these allowance!, which will be found to greatly assist the memory. Allowing for the Heave of the Sea. A Ship is supposed to make Leeway only when she is close-hauled and a rough sea on. But it some- ♦icnes happens when the wind is free, a heavy beam-sea may be running, which has the effect of heaving tier to leeward of the Course steered. This allowance is called the Heave of the Sea, and will rarely xceed i point ; because, although the waves appear to have a rolling motion, it is only the crest of the -vave which advances, the great body of the water remaining stationary, rising and falling with a motion •imilar to the shaking of a sail. And the greater the speed of the vessel the less will be the effect of the waves; on the other hand, th« less the speed of the vessel the greater will be the effect of the waves in any given distance sailed ; because the fast-sailing vessel will cross any given space in a shorter time than the slow one, and will be subjected to fewer buffetings. So that the allowance for the Heave of the Sea must rest entirely on the judgment of the Navigator Keeping in view the various circumstances of the case. On allowing tor Currents, (see page 29,) and for a description of the Log-Line, Log-Glasa, and inaniiier of using the same, (see page 6.) KREPl^G A SHIP'S RECKONING. 183 METHOD OF KEEPING A SHIPS RECKONING AT SEA. Allowi?}g For Currents. Hnving thuB found the Courses made good and the Distance Sailed by the Log, they are entered in the traverse Table, together with the True Set of the Current as a Course, and its Drift as a Distance whea the Current is actually known to exist, otlierwise much caution is required. (See Remarks at page 29.) Remarks on the First Day's Work after Leaving the Land. If a departure has been taken from the Land, the Variation must be allowed on the Bearng b Compass, and the opposite point entered into the Traverse Table as a Course, and the estimated distance o9 Shore as a Distance, (see page 31) the Difference of Latitude and Departure made good is then found by a case of Traverse Sailing ; then the Difference of Latitude made applied to the Latitude left, (or in the case of taking a departure from the Land applied to the Latitude of that place,) will give the Latitude of the Ship. Then with the middle Latitude as a Course, found in Table II, and the Departure made good taken in the Latitude column, the Difference of Longitude corresponding will be found in the Distance column. This applied to the Longitude left, at the preceding Noon, (or in the case of taking a Departure from the Land, applied to the Longitude of that place,) will give the Longitude of the Ship. Cause of the Errors in the Dead Reckoning. The Latitude and Longitude thus calculated at Noon is called by Seamen the Dead Reckoning, and it u well named, for it frequently happens that it is dead enough as regards the Ship's true position. This it caused by many circumstances, such as bad steerage, local attraction acting on the Steering Compa8s,(for Remark* see page 120,) unknown currents, false distance siven by the Log in squally weather, errors in the Log-Line and Log-Glass, and impioper allowances for Leeway and Variation. Ascertaining the Cause of the Error in the Dead Reckoning. When the discrepancy is great between the Ship's position by Dead Reckoning and that by Observation, a careful Navigator will investigate the matter, and endeavor to ascertain the cause. If the Log-Line and Glass have been found correct, (see page 6) examine the Steering Compass and see that it is free from Local attraction, and if the Ship has been steered her proper course, and the Log has given her proper Distance run, then the discrepancy may be set down as the effect of a Current, the direction and drift of which may be found by the rules given at page 29, Case 1st, and in that case it may be allowed for in the next day's work, as a Course and Distance Sailed, or, it may be counteracted by altering the Ship's course. (Se« method of doing so, page 30, Case 3d.) Allowing for Bad Steerage. When a Ship is scudding in a Gale of wind some Navigators are in the habit of allowing for the heave of the sea, in forcing the vessel, as they imagine, ahead of the distance run by Log. This allowance is of very doubtful utility. In fact, I have always found it the reverse, especially in a badly steered or bad ■teering Ship, because on account of her yawing about she must necessarily waste a considerable portion of her Distance run, and the Log will be found to give the Distance run in excess of the actual place o« the Ship by observation, and it is usual in some cases to deduct 1 mile in 10 for bad steerage. Heaving the Log in Steam Vessels. In Steam Vessels the Log is found to give too much Distance. This is easily accounted for, and caused by the action of the paddle-wheels driving the water astern. The Log in this case should be hove from the paddle-boxes, outside of the influence of this current of water. The Use of Keeping the Dead Reckoning. Nerertheless, the Dead Reckoning even under all these disadvatages should not be neglected, as it some- times is the only mode we have of detecting any very gross error made in deducing the Ship's position from Astronomical observations and in the detection of Currents, and otiier matters. When the Dead Reckoning is Proved to be Erroneous, to take a Fresh Depat Cure. When theLonuitude by Dead Reckoning is proved to have been erroneous from the Sight of Land or by the Chron.. the error and rate of winch has been recently found, or by Lunar Distances observed on both sides of the Moon, il can answer no useful purpose in carrying it on, and a fresh Departure and Longitude should be adopted and then carried on as before. Practice of some Navigators Regarding Dead Reckoning. Some Navigators carry the Longitude by Dead Reckoning on from day to day only, as a means of com paring it with the Longitude made by Chronometer. Others again never keep any Dead Reckoning at all trusting entirely upon the Latitude observed and the Longitude by Chronometer. Practice of Keeping the Reckoning in Fast Sailing Ships. In fast sailing Ships the Distance run is generally estimated, and the Log seldom or ever hove, and u those Ships generally steer well, their Course steered can be depended upon ; and when the Difference of Lat. is obtain'?d from observation, the Distance run and the Departure made good, can also be obtained by a eas« in Plane Sailing, and more correct than if the Distance had been measur«^d in the usual mannvr b) the Log. (See the following rules for working Day's works.) 184 ■ KEEPING THE SHIP'S RECKONING. METHOD OF KEEPING THE SHIP'S RECKONING AT SEA. RULES FOR WORKING A DAY'S WORK. The foUovv.ng rules have been collected with the view of simplifing the matter, and placed so as the) 4an be conveniently referred to by the learner. Correcting the Courses Sailed 1. Correct ea«h Course sailed for Variation and Lee-way by the rules (page 182) already given; entef them in the Traverse Table and set against each the Distance run on that Course. If the Ship is in • Current, the Set and Drift of which is known, allow tiie Variation on its set, and enter it in the Traverse Table as a Course and Distance, but if its Set and Drift is uncertain, it is better to leave it out altogether ; •Iso if the ship has taken a Departure from the Land, correct the Bearing by Compass for Variation, and enter the Table with the Opposite Point as a Course, and the estimated Distance off as a Distance. Finding the Course Made Good. 2. Find the Difference of Latitude and Departure made good, with which enter Table II, and find th« Course and Distance made good, by seeking in its columns until they are found to agree, opposite to which will be found the Distance in its column ; and if the Departure be greater than the Difference of Latitude, tha Course is taken from the bottom of the Table, but if the departure be less than the Difference of Lati- tude, the Course must be taken from the top of the Table. Finding the Latitude In. 3. If the Latitude of the place from which the Ship's Departure has been taken, or yesterday's Latitude, and the Diflference of Latitude made be both North or both South, their Sum will be the Latitude in of that name ; but if the Difference of Latitude be of a contrary name to the Latitude left, their Difference will be the Latitude in. of the same name as the greater of the two. Finding the Difference of Longitude. 4. Add together the Latitude observed yesterday and the Latitude in to-day, and take their Half Sum for the middle Latitude, then with this middle Latitude (taking the nearest Degree) enter Table 11, and seek for the Departure made good in the Latitude column, and the Sum standing opposite in the Distance column will be the Difference of Longitude made, which divided by 60 will give Degrees and Minutes, and mark it of the same name as the Departure. Finding the Longitude In. 5. If the Longitude of the place from which the Ship's Departure has be^an taken, or yesterday's Longi- tude, and the Difference of Longitude made be both East or both West, their Sum will be the Longitude in, of that name ; but if the Difference of Longitude be of a contrary name to the Longitude left, their Dif- ference will be the Longitude in of the same name as the greater of the two ; but when their Sum exceeds 180** the Ship has crossed the opposite Meridian to Greenwich ; in that case Subtract it from 360", the remain- der will be the Longitu''': In, ^"^d of a different name to the first. Mode of Working the Day's Work when the Distance run is Unknown. b. When the Distance run is uncertain or even altogether unknown, take the Difference of the observed Latitudes, and the Course made good, with which enter Tables I or II, as usual, and seek for the ob served Difference of Latitude in its column, and opposite to which will be found the corresponding Distanci run and the Departure. Then proceed as before by rule No. 4, to find the Longitude in by Dead Reckoning General Remarks on Keeping a Ship^s Reckoning, Currents, ^c. If the Latitude yesterday has been observed, the Difference of Latitude made is usually applied to it, the room of the Latitude by Dead Reckoning, and it is called the Latitude in by Dead Reckoning at No(i to-day. Then if it agrees with the Latitude in by observation to-day, the reckoning is said to be ju«t, but it do not so agree the Ship is said to be the amount of the Difference to the Northward or to the Southward a the Dead Reckoning. In like manner, if the Longitude by Chronometer or Lunar observation has been ob served and brought up to Noon yesterday, and the Difference of Longitude made by Dead Reckoning beinj applied to it, then if it agrees with similar observations for Longitude to-day, brought up to Noon, tia reckoning is said to be just, but if they do not so agree then the Ship is said to be the amount of the D'S- ference to the Eastward or Westward of the Dead Reckoning on this day's work. The errors of the Latitude and Longitude so found, furnish the means of Detecting the Set and Drift o/ the Current (always providing that the Course and Distance Sailed are correctly given,^ by taking the Mid Latitude a§ a Course, and the Error of the Longitude in the Distance column; then in the Latitude co)'»ma will stand the Departure, with the Departure and the Error in the Latitude find the Course and Disiance, and which will be the true Set and Drift of the Current, or in that direction in which the Ship is founo ui be by observation, when compared with her place as given by the Dead Reckoning. The Dead Reckoning should not be Altered on Slight Grounds. The Difference of Longitude made by Dead Reckoning being applied daily to the Long, in by Dead Reckon in^ is carried on from the commencement of taking a Departure, independent of that by observation, and should not be altered on slight grounds, because the rate of the Chron. may change or the Lunar Distance may be in Error, and the Dead Reckoning may thus be the means of detecting it ; but wh^n the Dead Reokon< tng has been found to be decidedly in Error then a fresh Departure must be taken. KEEPING A SHIP'S RECKONING. 185 THE DAY'S WORK. EXAMPLE 1. At 1 P. M^ took our Departure from Neversink Light Houses, bearing by Compaea W. N W., distant 9 miles, an« fcave sailed until Noon this day as per Lot? ; the Variation of the Compass being i a point Westerly, and the Sun'i Meridian Altitude observed was 66° 30' South. Required the Latitude in by Observation, he Latitude and Longi tude by Dead Reckoning, and the Bearing and Distance of Wreck Hill, in the Island of Bermuda, at Noon. H. K. F. COURSES. WINDS. L.W. REMARKS ON BOARD, MONDAY, MAT IST, 1854. 1 West. At 1 P. M. Neversink Light-Houses bore W, N. W. 9 miles, in Lati- 2 10 3 S. R by S. t( tude 40° 24' N., Long. 73° 59' W., from which I take my Dep. 3 10 6 M «« Set the starboard studding-sails low and aloft 4 11 M 44 Steady breeze and fine pleasant weather. Stowed the anchors and secured the boats. 6 6 10 9 8 4 <* II •i 7 8 10 10 5 U m At 8h, squally-like in the South. 9 10 6 «• i< At 9h, wind hauled more to the Southward. In all the studding- 10 11 12 9 9 8 8 4 8. W. sails and braced the yards up. u S. W. by S. Midnight Squally. Handed the Ught sails. 1 7 S. K S. S. W. 2 3 7 6 S.Kby E. It S. by W. i At 2 A. M. in top-gallant-sails and first reefs of the topsails. 4 6 U « At 4h, blowing fresh and a head sea. 6 6 4 E. S. K South. 1 Sun's Magnetic Bearing at rising was observed to be E. 14° 18' Nn 6 7 6 5 6 «4 East. S. S. E. 2 which gives the Magnetic Variation 6°, or about i pt Westerly. 8 5 u it At 8h, tacked ship to the Southward and set top-gallant-sails ; 9 6 6 South. E. S. E. H weather more moderate and clear. 10 6 6 ** t( At lOh, many vessels in company. Spoke the ship Jacob Bell, from 11 6 6 S. E. KN. E 1 Boston to Australia. 12 7 3 •' »( Noon. do. weather. Lat. Obs. 38° 25' N. Varia. i pt. Westerly. TVJl VERSE TABLE. DIF. OF LAT. DEPARTURE. COURSES. DIST. N. 8. E. w. E. by S. i S. 9 • • • • 2 -6 8 -6 • • • • S. E. i S. 110 ■ • • • 85 -0 69 -8 • . • . S. E. i E. 14 • • • • 8 9 10 -8 • • ■ • E. S. E. 12 . • • . 4 -6 11 -1 . • . . E. i S. 11 . . . 1 -1 10 -9 • • • ■ N. E. by E. i E. 10 4-7 • • • • 8 -8 • • • • S. by W. 13 .... 12 -7 ■ • • • 2 -5 S. E. i S. 14 .... 10 -8 8 .9 2 -5 4 -7 125 -7 128 -0 4-7 2-5 Southing DifF. of Latitude made . . 60 )r21 126 -40 )fEa8'g. 2° r 3. 1 Lat of Neversink L. Houses 40° 24' N. Lat in by D. Reckoning ... 38° 23' N. Sum of the Latitude 78° 47' Half Sum, or Mid. Lat ,39° 23' taken as a Co., and the Dep., 126 '4, in the Lut. column, and in the Dist Col. stands the Diff. Lon. 163' K= 2° 43' E. Long, of Neversink Light-Houses 73 59 W. Long, of the Ship by D. Reck. 71° 16' W. Difference of Latitude 121, and Departui-e 126, made good, found togetlier in the Traverse Table, gives the Course made good S. 46° E., and the Distance made good 175 miles. 1 To Find the Variation. Lat by D. Reck, at Sunrise about 38|° N., and Sun's Declination 16° N., in Table XXXV, gives the true Amplitude E. 19° 18' N. Magnetic Amplitude at Rising E. 14 18 N. Magnetic Variation 6° o' W To Find the Latitude by Observation. Sun's Mer. Altitude Observed 66° 30' S. Correction, Table IX 12 True Altitude 66° 42' Zenith Distance 23° 18' N. Sun's Correct Declination 15 7 N, Latitude Observed 38° 26' N Summary. Course S. 46° E. Distance 175 Diff. Latitude 121 S. Departure 126 E. . Latitude by D. Reck. ... 38° 23' N. Latitude Observed 38 25 N. Diff. Longitude 2 43 K Long, by D. Reck 71 16 W. Bearing of Bermuda S. 41° E, or S. E. J S, nead fTrue.^ Distuuce 484 miles. To Find the Bearing mid Distance of Bermuda. Lat of the Ship by Observation . . Lat of Wreck Hill, Bermuda. Diff. of Latitude in miles 366 . . . = Sum Middle Latitude 38° 32 25' 19 N. =6° 70 Long. 7 1 ' Lons. 64 16' 50 6' 44 6° 26' 60 35° 22' Di£Lon.386 W. Middle Lat 35°, and half the Diff. Long., 193, i| W. the Dist «ol., gives half the Dep., 168, in the Lat col. Then half the Diff. Lat, 183, and Dep, 158, gives the True Course S. 41° E., and half the Dist. 242, which doubled gives the Irue Distance 484 miles. 186 KEEPING A SHIPS RECKCNING. THE DAY'S WORK. EXAMPLE 2. A Ship from Latitude 85° 42' N. by Observation, and Longitude 51" 2' West by Chronometer, yesterday at Rood has sailed until Noon this day as per Log. The Sun's observed Altitude iu the morning was 10° 23', the Green wich Time by Chronometer llh Om 28, or March 5th, 23h Om 2s, and the Sun's Meridian Altitude was 46° 32' S Required the Latitude and Longitude in, both by Dead Reckoning and Observation, and the Set and Drift of th» Current. In this Example the Fractional parts of the Knots are marked as 1 half knot H. K. H. K. COURSES. 1 ■WINDS. |L.W. TRANSACTIONS ON BOARD, MONDAY, MA&ZH 6TH, 1854. 1 10 N. W. by N. East. -■■'■*■ -^ P. M. Strong gale and squally, with hail anc sleet. Vessel shipping 2 lu (i *t much water on deck. Pumps carefully attended. 3 9 1 i( tt At 3h, moie moderate and clear weather. 4 10 (( t( At 4h, out double reefs arc set top-gallant-sails. 5 10 (t (( Signalized the ship Washington, from New York to Liverpool, out 6 10 li u 10 days. 7 9 1 it It Observed the Sun to set per Compass W. 4° N., which gives the Magnetic Variation 1 1 30', or 1 point Westerly. 8 9 10 11 12 9 10 9 9 8 1 U It 1 <1 At lOh, passing squalls, with showers of haiL 1 Sumi nary. Midnight. Gale moderating. Out all reefs and set the starboabr 1 9 1 Course. . . . ... N. W. foretopmast-studding-sail. 2 3 10 10 Distance . . 281 Diff. Lat... ... 163 N. 4 9 1 Departure . . 163 W. At 4 A. M. set top-gallant and lower studding-sails, royals and fly- 6 9 Lat. D. R.. 38° 25' N. ing-jib. 6 8 1 Lat. Obs.. . 38 40 N. 7 9 Diff. Long... 3 24 W. At 7h, Longitude in by Chronometer 54' 1' 30" W 8 10 Long. D. R .M 26 W. 9 10 Lon. Chr. bA ° 46' 30"V/. Unstowed the anchors and bent the cables. 10 10 Bai-om. 30. Therm. 42° Carpenter employed fixing the windlass. 11 10 Current N. 47° W.rate Fresh breezes and clear weather. Variation 1 point Westerly. M2 10 of 1 knt an hour, nearly. Noon. Cape Sable, N. S., bore N. W. J- N. True, Distance 750 miles. , The Ship has been running on a N. W. by N. Course the whole 24 hours. The variation of 1 point allowed to the left, gives the True Course N. W. The knots being summed up gives 227 miles, and the 8 half knots, equal to 4 whole ones, this added to 227 gives the whole Dis- tance 231. Ti ne Course N. 4 pts. W. 231, gives D. L. 123 Dep. 163 Diff. Latitude made 2° 43' N. Lat. Observed yesterday '. . 35 42 N. Lat by D. Reckon, to-day 38° 25 ' N. Sum )74° 7' Middle Latitude 37° 3' taken as a Course, and the Dep., 163, in the Lat. column, the DifF. of Longitude is found in the Distance column to be 204 3° 24' W. Long, by Chron. yesterday 51 2 W. Long, by D. R. since yesterday. . . . 54° 26' W. To Find the Set of the Current. Lat Obs. 88° 40' N. Long, by Chron. 54° 46' 30" W. LatD. R. 38_25 N. Long, by D. R. 54 26 W. Error in LaTT^ 15' Error in Long. 0° 20' 30" With Latitude 37° as a Course, and Difference of Lon- gitude 20' 30'', in the Dist column, opposite to which, ID the Lat. column, stands the Dep., 16 . Then with Diff. of Lat 15, and Dep. 16, the Set of the Current is found to have been N. 47 W. (true) and its Drift 22 miles. To Find the Magnetic Variation. Diff. Lat made to Sunset 0° 42' N. Latitude at Noon 85 42 N. Latitude at Sunset 36° 24' and th« Sun's Declination corrected, 5° 54' South, found in Tab«» XXXV, gives the Sun's True Amplitude. W. 7° 30' a Magnetic Bearing at Sunset W. 4 N Magnetic Variation 11° 30' V Sights for Chronometer having been taken in the mom ing about 7 o'clock, the necessary corrections are made (see Example Ist, page 140,) and the Meridian Altitud* having been observed, the Latitude iu is found to be 88' 40'. This Latitude is then reduced back to the time the Sights were taken, ana tne Longitude by Chronometer found, which is then brought up to Noon by the Dead Reckoning, and in this case is 64° 46' 80" W. {This will be found worked out at page 140.) Now, as there is a considerable difference between th» place of the Ship by Dead Reckoning and that by Ob- servation, and supposing the Course and Distance run to have been correct, we now proceed to find the Set an Drift of the Current Again : Suppose that the Course steered could be depended on, and the Distance run uncertain. The Latitud« observed yesterday was 86° 42' N., and to-day 38° 40', the Difference of Latitude between the Observations being 178 miles. Then, with the Course N W., and the True Difference of Latitude 178, the True Distance run is found to be 262 miles, and the Departure 178. The Middle Latitude 37°, taken again as a Course, and the Departurt 178, in the Latitude column, gives the correct Difference of Longitude mivde 223, in the Distance column, or 8° 48' lliia, added to the longitude in yesterday, 61° 2' W., gives the Ij0i>^*ude in by Dead Reckoning to day 64° 46', anrf vhidi agrees with that given by Chronometer, nearly. KEEPING A SHIPS RECKONINK. THK DAY'S WORK. IK1 EXAMPLE 3. A Ship from Latitude i5* 60' N. by observation, and Longitude by Chrononoeter 49° 34' -V. yesterday it Nooi^ has Sailea until Noun this day as per Log. An Altitude of the Sun in the Morning was observed to be 26° 8',Tiin« by Chronometer 12h 13ni "ils, and which was Fast of Gieeuwich this day 6m 25s. The Weather being Foggy at Noon tlie Meridian Altitude of the Sun was lost for the day, but an Altitude was obtained afterwards, and oh. •erved to be 42° 30', the Time by Chronometer being 4h 14ra 21s. Required the Sliip's position at Noon, both by Dead Reckoning and Observation, and the bearing and Distance of the nearest Laud. H. 1 K. 8 II. K. CO U USES. "WINDS. L. W. \ REilARKS, WEDNESDAY, MARCH 16tH, 18.54. w. s. w. N. W i P. M. Steady breezes and due pleasant weather, all sail set, close 2 8 «i t( hauled. 3 8 tt u 4 8 i( tt At 4h, Long, in by Chron. 50° 3' 30" W., and Magnetic Vari. as per 6 6 7 7 7 7 1 it (t tt Azimuth 23° or 2 points Westerly. 1 (( ft At 7h, Barom. filling lapidly to 29° 30', Lee clouds appeared near. 8 3 South. W. s. W. 3 and of a threatening appearance. Took in all the small sails, 9 3 •i tt and double-reefed the top-sails, reefed the coursers and stowed 10 3 11 tt the jib and S. M. Sail. 11 2 1 4( (t 4 Wind very unsteady and blowing in gusts. 12 2 (( It At Midnight came on to blow excessive hard, close-reefed the top- 1 2 1 l( \ •» sails and handed the foresail, vessel laboring heavy and shipping 2 3 4 2 2 2 1 11 11 ) of Time. The Time past Noon being Cor>^etcd J7m 34s, fie Correction for Altitude is 45', and Lat. at Noon Corrected is 44* 31' N. 188 NAVIGATING THE SHIP. FINDING THE LONGITUDE FROM THE OBSERVED ALTITUDES OF A BODY ON THE PRIM! VERTICAL AT EQUAL DISTANCES IN TIME FROM THE MERIDIAN. On leaving any known Longitude take an Altitude of the Sun on the Prime Vertical, that is, when h« bears True East or West, which can only be in tht, 6ummer time. But a Star can always be found on the Prime Vertical at any season of the year. Note or find the Apparent Time by Watch when the observation was made, say in the Morning, and find the Time before Noon, (which with the Sun is his Hour Angle,) Then observe another Altitude in the Afieruoon, at the same time past Noon by the Watch. Now, if the Ship has not moved to fhe Eastward or Westward, that is, if she has made no Departure during th« Interval, the Sun's Altitude will be the same as in the Morning. But if the Altitudes do not agree, then the Difference is the number of miles of Departure the Ship has made to the Eastward or Westward. And in Sailing East the P. M. Altitude will be the greatest because the Ship is meeting the Sun, and in Sailing West the P, M. Altitude will be least because she is leaving him. This Departure, so obtamed iurned into Longitude by a case of Middle Latitude Sailing, furnishes the Difference of Longitude, whicn applied to the Longitude left will give the Longitude in. Or one Altitude can be observed on the Morning or Evening of one day, (having the Apparent Time from Noon of the observation), and exactly at the same time on the day following. The Difference between the Altitudes so observed is the Departure made good during the 24 hours, which turned into Longitude and ap- plied to the Longitude left from day to day, will furnish an excellent check on Gross Errors in the Dead Beckoning when there is no Chronometer on board. The daily Variation of the Equation of Time ought in strictness to be Added to the Time from Noon by Watch, at which the last Altitude should be observed, when the Equation is Decreasing, or Subtracted from it when Increasing ; but as this quantity amounts to only a few seconds, it may be neglected. In the case of observing Stars, 3m 56s should be Subtracted from the Time from Noon by Watch, at which the last Altitude should be observed, when P. M., or Added to it when A. M., because the Stars are that much before the Apparent Time by the Sun every day, EXAMPLE 1. Jul e 10th, 1854. A Ship in Latitude 40* 0' N,, and Loogitude 45° 0' W., at 8h 2rQ A. M. observed the Sum Altiti de to be 37° 24', and then Sailed to the "Westward, until 3h 58m P, M. by the same Watch, when the Sun's Alt \t %8 Oba. to be 3fi° 9', Required the Dep. made, the Diffi of Long, and the Long, in at the Time of the last Alt At 8b 2m A, M. Observed Altitude.. 37° 24' Departure 75m -with Latitude 40° = D, Long )98 At 8h 58m P. M. Observed Altitude _36^ 9_ Difference of Longitude made 1° 38' 1° 15' Longitude Left 45 0_ ^0 Longitude in 46° 38' Departure made good .,, . 75 j at 8h 68m P. M. EXAMPLE 2. ^ March SGth, 1854. A Ship took her Departure from Latitude 40° 43' N. and Longitude 74* W,, at 5b 43m P. M, irhen the Sun's Altitude was observed to be 6° 6', and then having Sailed to the Eastward about 265 miles, until tb« next Evening at 5h 42m bv the same "Watch, when the Sun's observed Altitude was 10° 16'. Required the Depar- ture made, the DifFereuce of Longitude, and the Longitude in. a irch 80th, at 5h 42m P. M. Observed Altitude . 6° 6' Departure 250, Latitude 41° = D. Long )332 _ do. Slst, at 5h 42m P, M. Observed Altitude. 10 16 Difference of Longitude made 6° 32' 4° 10' Longitude Left 74 6Q Longitude in.., 68° 28' Departure made .... 250 EXAMPLE 3. By the Stam. April llth, 1854, A Ship in Latitude 30° 0' N. and Longitude 65° O' "W., at 7h 8m P. M. observed the Altitude of Aldebai;-5 METHOD OF KEEPING THE LOG-BOOK. The Log-Book is an official Journal or Record of all the transactions which occur during the T?oyage of • Ship, from the time of her sailing from a port in the country to wliich she belongs, until her returu lo • aome port again, and her cargo discharged ; although it is usual to consider the voyage at an end when she u safely moored in that port, so far as regards the engagements with seamen. It should, therefore, contain a true and faithful account of all matters connected with the duty of the Ship, of daily occurrence, both at Sea and in port. Accidents, or loss in the Ship's material sustained, and also the misconduct of either the crew or officers, should all be entered distinctly, and in as few words as possible. While the Ship is in port, the Harbor Log, as it is called, is kept in the common, or Civil Time at the place, the Day beginning at midnight and ending at midnight. It contains an account of the wind and weather, the number of packages received or discharged, as per Cargo Book, the quantity of stores received on board or discharged, the number of hired laborers employed, and the general employment of the crew and when leave is granted to a portion of them to go on shore, to return again at a stated time, if they do not so return, the fact should be entered in the Log-Book, and the length of time they were absent without leave also. Any occurrence which may have a bearing upon the discipline of the Ship should be taken notice of and noted down; because, m the case 'of trouble wit li the crew, the Log-Book is received as evidence of the facts of the case in a Court of Justice. These entries should all be made in the evening of the day on which they occur, or on the morning of the following day, while the circumstances are fresh in the memory of the officer whose duty it is to record them. The Log-Book is kept by the 1st officer; but in the event of sickness, or in having been put off duty for misconduct, whoever is appointed in his room by the Captain) must keep the Log. Sometimes the Captain writes it himself. This is legal enough, providing nothing but the truth is recorded. This 18 mentioned merely to show that the Chief Mate of a Ship is not justified in retaining the Log- Book after its being demanded from him by the Captain, as some Mates seem to imagine they have a right to do. The Book belongs to the Ship and to her commander. The Sea Log may be kept in Common or Apparent Civil Time, if required. (See the Example following.) The entries comaience at midnight, and are continued nntil the following midnight, liaviug the Noon of the Sea Day in the middle of it. The Log Board is carried on from Noon to Noon, as usual, the preceding 12 hours work on the Board, that is, from the preceding Noon to midnight, and the following 12 hours, from midnight to Noon, constitute the day's work, as before ; the Ship's reckoning up to Noon, in this case, appearing in the middle of the Log. This method is very convenient in case of referring back to dates, and is perfectly easy in practice, because we have only to copy off from the Log Board as above stated. The old- method is still, however, generally used, through the force of habit, and which is an exact copy of the form used on the Log Board. (See page 180.) The Log-Book commences, as before observed, when the Ship is unmoored, or breaks ground, under charge of the Pilot; and the time at which he leaves the vessel is noted, and the bearing and distance of the land taken as a Departure. Suppose the Ship to have sailed in the morning of the 5th of June, and a Departure taken at 6 A. M., in writing the Log up to Noon, we would say, this day's work ends with 12 hours, (being the end of the Sea Day of June 5th,) to begin the Sea Log. The Course and Distance sailed is then reckoned up. and the Ship's position found at Noon. The Log for the afternoon is then dated the 6th of June. Suppose the Ship to sail and take her Departure in the afternoon at 6 P. M., we would commence the Sea Day in like manner, noting that the last Harbor Log contains only 12 hours. On the other hand, when a Ship goes into port in the morning, the Sea Date of the Log and the Civil Date of the place being the same, the entries are continued until midnight, and we say, this day contains 36 hours, to begin the Harbor Log. And when she goes into port in the afternoon, the entries are continued under the same date until the following midnight, when the same remark ia made, tha' this day «uds with 36 hours, to begin the Harbor Log. ipi KEEPING THE LOG-BOOK METHOD OF KEEPING A SHIPS LOG-BOOK IN CIVIL TIME. We shall now proceed to give a few Examples of writing the Harbor Log, and the Log at Sea, by Civil Time, and conclude this work with a short Journal of a voyage, or rather a passage, of a Ship from Santa Cruz to St. John's, N. F. The Harbor Log. DAT OF THE MONTH. WINDS. EEMAEKS ON BOAED THE C. S. DAUNTLESS, LYING AT SANTA OEUZ. Monday, March 18th, 1854. Barom. 30.00 N. K Therm. 80* Throughout this day fresh breezes, with passing showers. Crew and 3 laborers employed taking in cargo, (as oer Cargo Book,) bending light sails, and other duty. James CoUius off duty, sick. Tuesday, March 14th. Barom. 29.85 N. K E. Therm. 79° First part of this day fresh trade, and fine, middle and latter parts. Strong wind and rain squalls. 3 laborers employed. Finished taking on board cargo. Hoisted in the longboat and cleared up the decks. J. Collins returned to bis duty. Wednesday, March 15th, Barom. 80.05 E. N. E. Therm. 81" Throughout this day moderate and fine weather. Employed filling fresh water, bending sails, and taking in Ship's stores, and in the evcLiug got the Ship ready for Sea, and at 6 P. M. unmoored, and hove up the starboard bower anchor, and hove in to 30 fathoms. Shackle on tlie small bowei-. Discharged the laborers. The Clipper Ship Dauntless, W. Griffen, Commander, from Santa Cruz to St. John's, N. F. Thursday, March 16th. Barom. 31.00 N. E. Therm. 82* At 6 A. M. the Pilot came on board. Hove short and made sail. At 5h 80m Weighed from the anchorage at Santa Cruz and pro- ceeded to Sea. Light baffling wind and cloudy. At 7 A. M. discharged the Pilot and made all possible sail. The steady Tiade set in, with fine pleasant weather. kt Noon, the N. E. end of St. Anthony Island, one of the Cape Verde Islands, bore West by Compass, 3 or 4 miles distant Lat. Obs. 17° 9' N. Magnetic Varia. 1| points Westerly. H. E. H. K. oouasE& WINDS. L .W. Log Kept in Civil Time. 1 2 3 4 5 6 1 8 9 10 n 5 5 6 8 9 10 10 11 1-2 IS 1?. 13 1 1 N. W. by N. it a N. N. W tt M U U u tt it a N. E. by N. it it N. E. by K ti u E. N. E. tt U Kby N. u i'. M. Fresh Trade and fine weather. Stowed the anchors, unbent the cables and put them below. At 3h, the N. W. end of St. Anthony bore S. 17" 80' W., distant 15 miles, from which the Dep. is taken in Lat. 17° 12' N, Long. 25° 19' W. At 5h, set the starboard studding-sails. At 6h, the Mag. Vai-iation at sunset was 17° 30' Westerly. Passed several vessels bound West A t 8h, increasing breezes and smooth water. Light squalls from passing clouds. At lOh, in sky-sails and rounded in the weather braces. Midnight. Fresh Trade and clear weather. The Departure is taken from theNorth West end of the Island of S . Anthony, bearing S. 17° 80' West, and the Variation 17° 30' West allowed, gives the true bearing South ; the Ship is, therefore, on the Meridian of that point, distant 15 miles to the N^rth of it. Sights being taken for Chronometer, its error on Greenwich Mean Time is found to be OL .Oin 39s too fast, and the Rate since last Observation, taken in a similar manner, 2 sec. 5-lOth gaining. We have thence the Sea rror and Rate of it obtained. (See the Rules and Examples given at page 155.) To shape a Course in this case, we lay the ruler over the place of th Ship and Cape St. John, N. F, and find the true Course to be N. W. J N., the Variation allowed to tho right gives the Compass Course required to steer N. by W. J W. TJie distance off at present is immaterial, but both Bearing and Distance may be found by a case in Middle Latitude or Mercator's Sailing. In Ships of great speed, when working up the day's work, it will be found more corrrct to turn the Coarse steered into degrees, and apply the Variation, (also in degrees,) to it, and thenca find the Difference •( Latitude and Departure. KKEPING THE LOG-BOOK. 195 KEEPING THE LOG-BOOK IN CIVIL TIME. The tipper Ship Dauntless, W. Griffen, Commander, from Santa Crm towards St. Johns a. 1 K. \3 H. K. '7 COURSES. WINDS. L. w. EKMARKS, FEIDAY, MARCH 17tH, 1854. N N. W E. by N. t4 A. M. Fresh W-eeze and clear weather. 2 14 tt " " At 2h, squared the ya' Is and set the lower studding-sail. Set up and secured the boom braces, and preventer breast and back 3 15 t( East. i( 4 14 1 (t " t( stays. 6 I a it it 1* 6 14 15 14 1 9 4 4t it At 6h, The Magnetic Variation at Sunrise was 20' Westerly. 8 1 (4 At 8h, Longitude in by Chronometer was 27° 57' 30" W. 9 15 M U u Watch employed about the rigging fixing chafing gear. 10 15 ti (( " Carpenler I'epairin^ the longboat. 11 15 W ti (1 Pumps carefully attended. 12 15 itioD u a (4 Noon. Strong steady Trade wind , Varii Course Dist D. LaL Dep. Lat. DR. 20° 52'N. Lon. D.R.28° 34'W.|Lon.Chr. 28°40'W.|Bar. 80 00 19° W. N.40°W. 287 220 N. 185 W. LatObs. 20 60 N. Dif. Lon. 3 15 W. D. R. since yester- Ther. 79° Iday 28 34 I 15 N N. W. East. W P. M. do. weather. All possible sail set. 2 15 u t< U Signalized the Ship Shannon from Havre, bound to New Orleans, 3 15 (C M 4* out 30 days. 4 15 (t U 44 At 4h, Long, in by Chronometer 29° 26' "W. 6 15 i< t« 4i At 5h, Carried away the top-gallant studding-sail booms. Made 6 14 w M 44 up the sails and sent the booms down on deck. 7 15 a U (4 At Sunset the Magnetic Var. was Obs. to be 20° Westerly. 8 15 t4 u 44 At 8h, squally-like clouds in the N. W. and the Barometer falling. 9 15 u u (( Ship approaching the Northern hmit of the N. E. Trade wind. 10 15 (4 n 41 Hautled all the small sails. 11 15 M M 44 At Mid. The wind heading the Ship off, in all studding-sails, and 12 H. 15 u U braced forward the yards. K. H. K. cotrasK. WINDS. L. W. REMARKS, SATUaOAY, MARCH 1 8tH, 1854. 1 10 N. W. N. K by N. 41 A. M. Very squally weather, with heavy rain ; handed the stay- 2 10 it K 11 sails ami flying-jib. 3 10 M i( 44 4 6 6 7 10 10 10 10 10 Ct ti It Heavy ground swell from the N. W. « (1 <4 At Sunrise the Magnetic Varia. was Oba. to be 19' 30' W. 8 W. by N. North. At 8h, lu first reef of the top-sails and set top-gallant-sails over 9 10 1 t4 t( l( them. 10 10 1 u U i( No observations, Sun obscure. 11 10 1 l( n l< Noon. Strong gale and a high topping sea. 12 10 1 ti '• ' In tdo-srallant-sails aud dduble-ieefecl tlie top-snils. | Va.i ition Course Dist. D. Lat. Dep. Lat. D.R.23° 26'N.|Lon. D.R. 32M6'W. Long. Cliro. 0° 0' Bur. 29.50 19° W. N.56'W. 280 166 N 234 W. Lat. Ob Dif. Lon. 4 12 W. D. R. since yes- Ther. 78° ' 1 tenlav S2°52'W. ( As sufficient examples of working a Day's work have been already given worked out, it is considered unnecessary to work out those in this Journal, the result only being given, that is, a summary of the whole, including the Latitude by Observation, and Lonizitude by Chronometer at Noon, the Longitude by Dead Reckoning being carried on from day to day by it-self. The Difference of Longitude made is also applied to the Longitude by Chronometer on the preceding day, and placed under the Longitude by Chronometer to-day. This affords a means of comparison. In like manner the Latitude by Dead lieckoning and that by Observation are placed under each other, which will show at any time the effect of a Current or the Error» in the reckonins. The Variation ob.served agreeing with that laid down on the Chart, we conclude there is no Local Attrac- traction on board. The Courses steered by Compas.s ni the above Days' works are turned info Degrees and Minutes, the Variation applied gives the True Course in Degrees; fo' in.stance, N. N. W. is N 23° W. nearly, and as the Variation has increased in the rirsl Day's work from 1V° 30' to 20°, we take the Mean, or 19°, as the f 'oper Variation to be allowed on the whole Day's work ; this added to N. 23° W. by Com- pass, gives the ^rue Course N. 42° W., with which and the Distance run, gives the D Latitude and Departure. 19G KKh:PING a SHIP'S log B(X)K. METHOD OF KEEPING A SHIP'S LOG-BOOK IN SEA TIME. Hanng thus given Examples of Keeping the Harbor and also the Sea Logs, in Civil Time in the com mencement of this Journal, the remainder of it will be kept in Sea Time, that is, in the usual mannei adopted on board merchant vessels. The Clipper Ship Dauntless^ W. Griffen^ Commander. H. K. a. K. COURSES. WINDS. L. W. REMARKS, SUNDAY, MARCH 19tH, 1854. • 1 2 8 4 6 « 7 8 9 9 9 9 10 10 10 10 1 1 1 West. 4i N. by W. 1 (1 P. M. Strong gale and rainy weather. Sent down the royal-yardf" and rigged iu the flying-jib-boom. W. iS. u (t (1 u t 41 1 a U • At 4h, eased the Ship by cheeking in the weather braces and keep- ing clean full-and-by, the object being to tjet well to the West- ward before a change of wind takes place, wbieb, by the falling of the Barometer to 29.40 would seem to indicate. 9 10 10 12 1 2 10 10 10 10 10 10 4i u « u tt U u u u u (t M M i( U (1 At lOh, do. weather. Midnight. Strong gale and a high sea. Pumps carefully attended Ship keeping perfectly tight. 8 4 5 6 7 8 10 10 9 9 10 10 10 10 10 10 1 1 1 K u u (( u u u M u (< u u (4 44 tt It U At 4^ A. M. Gale increasing, reefed the coursers and spanker and eased the jib-half-boom in. At 6h, the Magnetic Varia. at Sunrise, aa near as it could be ob- served, appeared to be 14° or IJ points Westerly. At 8h, observed an Alt. of the Suu. Long, in by Chron. 36° 0' W. 9 10 11 12 u (( 41 It • At lib 45m, another Alt of the Sun gave, Lat. in 21" 9' N. Noon. Stormy weather. Sun. obscure. Varif 17' ition W. Course S.57°W. Dist. 237 D. Lat. 129 S. Dep. 198 W. Lat.D.R.21''17'N. Lat Obs. 21 7 Dif. LoD. 3° 34' Lou. D.R.36 20 W. Long. Chr. 36° 36' D. R. since yester- day 36° 26' Bar. 29.36 Ther. 78° In 'he above Day's work it appears that the Magnetic Variation has changed from 19* 30' to 14°, durmg the run to the Westward since yesterday evening at Sunset, we therefore use the mean of the two, which is 17* or li points, *;n correct the Compass Course. An Altitude oi the Sun having been obtained at about 8 o'clock ft)r Chronometer, and another for the Latitude near Noon, the time by Chronometer being noted at the time of each observation, the Latitude is thence found by the method given at page 94, and the Longitude by Chronometer is found by the method given at page 140. This is the simple case ; or the Latitude may be found from the two Altitudes having the measured interval of Time between the observations by the method given at page 96. As the Ship haa plenty of sea-room it is not necessary to resort to the method given at page 144 in this case ; besides the 1st Altitude was observed at a proper distance from the Meridian, and any Error in the Latitude by Dead Reckoning would not affect the Time much, nor the Longitude by Chronometer, because the Ship is in a lo\v Latitude. One point of Leeway and li points of Variation being allowed to the left of the Course by Compass, gives the True Courses, which, with the Distance run on each, gives the Difference of Latitude and Depar- ture made good, and thence the Latitude and Longitude by Dead Reckoning. Then the Difference of Lon- gitude made by Dead Reckoning applied to the Longitude by Chronometer yesterday, gives the Longitude iji by Dead Reckoning since yesterday. This compared with the Longitude by Chronometer to-day shows the Ship to be 10' of Lon-jitude to the Westward of the Dead Reckoning. In like manner the Difference between the Latiiude by Dead Reckoning and that by observation shows the Ship to be 10' to the South- ward of the Dead Reckoning. This may be accounted for in two ways, that is, she must either have gone more distance than the Log has given her, or there may have been a Current setting in the direction of her Course. It is evident it could not have been caused by an Error in the Course, because the Error in the Latitude is to the Southward of the Dead Reckoning, and the Error in the Longitude is to the West of the Dead Reckoning, or in excess ; but had the Longitude by Chronometer been to the Eastward of the Deacf Reckoning, or less than it, it would then have been concluded that the Error was due to the Courie having been more to the Southward than that given by Log JOURNAL. 191 JOURNAL OF A VOYAGE From Santa Cruz, {Cape Verdes,) towards St. John's, Newfoundland. B. 1 2 3 4 6 6 7 b 9 10 11 12 1 2 3 4 6 6 7 8 9 10 U 12 10 8 8 8 7 7 8 8 10 10 10 10 10 10 10 10 10 10 9 9 9 9 H. K. COUE8KS. WINDS. W. S. W. N. E. by N. N. N. E. N.W. by N N. W. N.W. by W. L. W. H H aElIAEES, HONDA T, MABOH 20tH, 1864. At 1 p. M. the wind hauled more to the Westward. Wore ship to the North Eastward. At 4h, strong gale and rainy weather. At 6h SOm, the sky cleared up to the Southward. ObserTcd the Meridian Altitude of the star Siriu8,(a goodobserration,) which gave Lat in 21* 42' N. Lat by D. R. at same time 21* 86' N. At lOh, more moderate weather. Out double reefi of tha topsailr and set top-gallaut-sails over them. Midnight Fresh breeze and clear weather. At 2 A. M., weather moderating, and the head tea going down. At 4h, out reefs of the courses and spanker At 5h SOm, Lat by the Moon 23° 26' N., D A. gave 28* 17' N. At Sunrise, the Magnetic Variation observ* d was 18* 0' W. At 8h, Long, in by Chronometer 35° 26' "W. Watch on deck employed repairing chafing gear. Carpenter repairing the Longboat Noon. Cloudy weather ; Sun obscure. Varia. 13° W. Course. N. 23° E. DistlD. Lat 198 1182 N. Dep. ILatD.R. 24° 23' N. 76 KLatObs. 24 38 N. DiflLong. 1°23'E. Lon. D.R.34 57 W. Lon. Chro. 85* 8' W.j Baro. 29.80 D.R.sin.ye8t 36 13 W.I Therm. 77° To Correct the Courses Steered in Degrees. Comp. Course W. S.W. or S. 67° 30' W. N. E. by N. or N. 38° 46' K N. N. E. or N. 22' 30' R N. N E. or N. 22° 80' E 8ub.L.W.ll'15'4Va.l3°— 24 16 Add the DifiE: . . . 8 62 AddDiff..... 3 52 Sub. Diff.... 2 Course made good S. 43° 16' W. N. 37° 37' E. N. 26° 22' E. N. 20° 80' E, The Courses being corrected in the above manner, and entered into the Traverse Tab'e, with their respective distances, as usual, the nearest degree being then taken as the Course to find the Difference oi Latitude and Departure. This is a very important matter, and should be attended to in a fast-sailing vessel ; because an omis •ion of, say 2°, in the variation allowed on the Course steered, when the distance run is great, will cause a considerable error in the Dead Reckoning. When the Course is near the Meridian, or near a Parallel of Latitude, this error will amount to 4' in every 100 miles distance ; when near 45° the error will be 2' in every 100 miles. In looking over this day's work, we find that at 6h SOm the Latitude found by the Meridian Altitude of the Star Sirius. made the Ship 7' to the Northward of the Dead Reckoning, and at 5h 30' A. M., by the Meridian Altitude of the Moon, she was 9' to the Northward of the Dead Reckoning. And that the Longitude by Clironometer made her 5' of Longitude to the Eastward of the Dead Reck OKxng. She has, therefore, made less Leeway than has been allowed her, and gone more Distance than the Log gives her ; it is therefore proper to examine the Log-line ; and which, on being examined, we find to be 5 feet too long at the 5 knot mark, which would be equivalent to an error of nearly i a knot in using the 14 sec. or Short Glass, giving the Distance too small. The proper length between the knots should b« 45 feet, whereas the line was found to be 46 feet, or one foot too long on each knot. A measured space of say 22 feet 6 inches, the length of the half-knot, should be marked off on the deck, and a copper nail driven in at each end of it, as a permanent measure, whereby the line may be verified occasionally ; becaasa It is liable to shrink up as well as to stretch, when new. In fitting a new line, it should be well stretched and then thoroughly wetted, before it is measure'! and marked. IM JOURNAL. JOURNAL OF A VOYAGE. The Clipper Ship Dauntless, W. Griffen., Commander. H. K. H. K. COCESES. WINDS. L. w. REMARKS, TUESDAY, MARCH 21sT, 1854. 1 9 N.byE. iE. N.W. by W. i At 28m past Noou, Lat. Obs. 24° 43' N. 2 10 (( N.w.byw.^w At 2 P. M., out all leefs. Seiit up the royal yai-ds, rigged out the 8 10 •* " flying-jib-boom, aud set the sails. 4 10 u ii At 4h, the Long, iu bv Chronometer 35° 0' W. 6 10 u i( Steady breeze and fine weather. 6 10 li it Suiisft, Magnetic Variation Obs. 12° Westerly. At 7h 20m, Mer. Alt. # Castor. Latin 25° 66' N. D. R. 25° 64' N. 7 8 9 10 10 10 44 4t u 44 At 9h, set the stay -sails, fore and aft 10 11 M 44 11 10 U " 12 11 w « Midnight Steady breeze and fine clear weather. 1 10 u it i 2 11 tt (t A. M. Do. weather. All possible sail set. 3 10 a (( 4 11 u 4< At 4h 20m, Mer. Alt. * Antares. Lat. in 27° 25' N. D. R. 27° 27' N. 6 10 t« it 6 11 u U At 6h 3&m, Mer. Alt ( Lat in 27° 54' N. D. R. 27° 63' N. 7 10 it 4( 8 11 u tc At 8h, Long, in by Chronometer 34° 28' W. An Azimuth taken 9 10 a u same time gave the Magnetic Variation 14' Westerly. lu 11 u 4( Employed painting the boats, e N. 63' W., or N. W. by W.f W, nearly, by Compass, Distance 830 miles. JOURNAL. 203 JOURNAL OF A VOYAGE F\rom Santa Cruz, (Cape Verdes.) towards St. John's, Newfoundland. B. K. B. K. OODBSKfi. WINDS. L.W. REUAEES, SDNDAT, MABOH 26TH, 1864. 1 2 15 15 S. by W. P. M. Heavy Southerly gale and a high topping Bea running. S 4 6 6 15 15 16 16 a u « S. W. by S. At 4h, more moderate ; wind inclining to "Westerly Set the reefed S. M. sail and mizen topsail 7 8 9 10 11 12 1 2 16 16 16 16 16 16 16 16 u u u u u u At 8h, the rain ceased, and the weather made an attempt to clear up. M u « a u u a a u u At 9h 40ra Mer.Alt # Regulus. Lat in 42' 59' N. ) Mean 43° 5'N. Same time the Alt. of Pole #. Lat in 48* 1 1' N. J D. R. 42° 25'N. Midnight. Blowing bard ; vessel shipping much water on deck ; pumps carefully attended every 4 nours. 3 4 5 6 7 8 9 10 11 12 16 16 16 16 16 15 15 15 15 15 « u u u u u u u u u u u u u M u u C( u u At 4 A.M., Mer. Alt. # Antares. Lat in 43° 46' N. ) Mean 48° 53'N. Same time the Alt of Polar #, Latin 44° 0' K ) D. R. 43° 8'N. At 6h, gale moderating and the sea falling. Out close reefs of the topsails and set the jib. At 8h. obs. au Alt of the Sun. Long, in by Chron. 41° 12' W. Weather set in thick again, with mizzling rain. The temperature of the Sea-water at Noon was found to be the same as that of the air, 56°. Noon. Do. weather. Suu obscure. True bearing of St John's, N. 69° W. Distance 468 miles. Variation I Course gipta.W.lN.65°W Dist 878 D. Latj 162 N. Dep. 342W. Lat D. R. 44° I'N.IDif. Lon. 7° 46'W. Lat Ohs. 44 46 N.|Lon. D.R. 42 68W. Lon. Chr. 42° 27'W. D.R.Biaye8t 42° 68'W. Bar. 29.06 Ther. 55" The Variation allowed on this day's v/ork is 2^ points Westerly. At 9h 40m P. M., the Meridian Altitude of the Star Regulus was observed to the Southward, and at the same time an Altitude of the Polar Star was observed to the Northward. The Mean of the two Lati- tudes so found, compared with that by the Dead Reckoningj places the Ship 40' to the Northward of th« , Dead Reckoning And at 4 A. M., the Meridian Altitude of Antares was observed to the Southward, at the same time the Altitude of the Pole Star was observed to the Northward. The Mean of the two Latitudes places the Ship 45' to the Northward of the Dead Reckoning. These Observatioas may not be very accurate, on account of the obscurity of the horizon and the heavy sea running, together with the difficulty of making the Observations, but are sufficiently near to act as a warning that the Dead Reckoning is in error, and by taking Stars North and South of the Meridian the errors in the Observation are very much diminished. For instance, the Difference in the two Latitudes given by Altitudes of Antares and the Pole Star is 1 4', but the Mean of the two Latitudes is taken. The Sun's Altitude was also obtained about 8 o'clock in the morning, and by using the corrected Lati- tude in finding the Time, we get the Longitude by Chronometer as above, and which places the Ship 33' of Longitude to the Eastward of the Dead Reckoning. These errors in the Latitude and Longitude so found, shows that the Ship's Course made good is about 1 point further to the Northward than the Course by Compass makes her; she has, therefore, been run off. The Barometer having fallen to 29.5, and the weather at Noon assumed a very threatening appearance, we may look for a continuance of the gale. The Ship is now approaching the Eastern edge of the Polar Current, in which we may expect to find large masses of Ice, brought down by it from the Polar regions. On a Ship entering this current the temper- ature of the Sea water will be found to fall about 20", and may be easily ascertained by drawing a bucket of water from alongside and plunging the Thermometer into it. (See the Remarks on Currents and tho Use of the Thermometer, at page 82.) The position of the Ship by Observation being laid off on the Chart, the bearing of St. John's is found to be W. by N. } N. ; 2i points Variation allowed on that gives the bearing by Compan N. W., Distanst 468 miles. 904 JOURNAL. JOURNAL OF A VOYAGE. The Clipper Ship Dauntless, W. Grtffen, Commander. 2 8 4 6 6 1 8 9 10 11 12 1 2 S 4 6 6 7 8 9 10 11 12 16 16 17 17 17 17 10 10 10 10 9 8 8 8 8 8 12 16 16 16 16 17 17 17 H.K. COUBSKS. N.N.WiW, WINDS. South. L. W. s. s. w. Ourrent Sontb by Compass 1^ knots. REMARKS, MONDAY, MARCH 27tH, 1854. At 1 P. M., temperature of the Sea-water 50*, Air 52*. Wind backed into the Southward, and the gale mcreased. At Ih 30m, temperature of the Sea-water 40°, Air 42°. ' At 4h, it fell to 35°. Ship was then in the strength of the Polar Current. At 6h, blowing excessively hard. Close-reefed the topsails and handed the courses and jib. At 8h, the temperature fell to 33° in the water, and at the same time an Iceberg was seen ahead of the Ship. Hauled up and passed to wmdward of it. At llh, furled the mizen topsail. Midnight. Ship running under easy sail, and a bright lookout kept for ice. At 2 A. M., passed another large berg. At 4h, weather more clear. Set the reefed foresail At 6h, out close reefs and set the reefed mainsail, jib and mizen- topsail. Ship passing a great many Icebergs. Noon. Thick fog and heavy rain. Close-reefed the topsails and furled the courses. Passed several fields and detached pieces of ice. St. John's S. 89° W . , (true,) or W. N. W. by Comp., dist. 194 miles Variation 2pt8. W. Course N. 54°W Dist. 290 D.LaL 171 N. Dep. ILat. D.R.47° 87'N.|Dif Lon. 5° 36' W. 234 W. Lat. Ob Lon. D.R. 48 34 W, Long. Cliro. ' D. R. since yes- terday48°3'W. Bar. 29.10 Ther. 34° The Magnetic Variation not having been observed to-day, it is taken from the Chart, which gives 2 points Westerly. By the decrease in the temperature of the Sea-water, as noted above, the Ship evidently entered the Polar Current soon after mid-day, the Set of which is about South by the Compass, or S. S. E. (true,) and its Drift H knots an hour. It being desirable to get to the Northward of the Parallel of Latitude of St. John's jbefore the wind shifts to the Northward, a Course must be shaped for that purpose. By reference to the Ship's place on the Chart, a N. W. f W. True Course, and Distance 300 miles, would place her to- morrow at Noon near the Eastern edge of the Great Bank, in the Parallel of Latitude required. But to make this Course good, we must allow for the Set and Drift of the Current as follows : The Set of the Current being nearly in a contrary direction to the required Course, we take their Difference, 2| points, as a Course, and the Drift, H knots, as a Distance, which gives the Departure, 7-tenths. Then the average rate of sailing, say 13 knots an hour, (which the vessel is expected to make next 24 hours,) as a Distance, and "vrith 7-tenths as a Departure, find the Course, 3°, or i of a point, which subtracted from the given Course, N. W. } W., gives the required Course N.W. i W. ; the Variation, 2 points W., allowed, gives the Compass Course required to steer N. N. W. ^ W. (See the Rule in Current Sailing, page 30, Case 3d.) The Ship has passed many Icebergs to-day, and on her approach to them the Thermometer was fourJ to fall to 32°, nearly, but rose 3° after having passed them. The Mean temperature of the Sea-water in the Polar Current appeared to be 35°. The wind having backed into the Southward again, an omen of bad weather, the sail on the Ship was re- duced to the close-reefed topsails before night-fall, and a vigilant lookout kept during the night for Icebergs, as they can be seen at a considerable distance in dark weather, if a good lookout is kept for the glare oi reflection, which is a peculiar kind of phosphorus light which surrounds them. At Noon, a dense fog with heavy rain came on, and as the Barometer is rising, it indicates a shift of wind to the Northward. It was, therefore, deemed prudent to put the Ship under low canvas, in case of a sudden shift; besides, according to the Dead Reckoning, she is to the Northward of the Parallel of Latitude of the intended port. The Bearing of St. John's at Noon to-day is S. 89* W., or W. N. W. by Compass, nearly, distant 194 Biles JOURNAL. lOl^,NAL OF A VOYAGE Prom Santa Cruz, (Cape Verdes,) towards St. John's, Newfoundland. 1 2 3 4 6 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 11 11 10 10 10 10 2 2 2 2 2 2 2 5 7 14 16 16 15 15 16 15 15 S.K. OODKSES. N.W.byN. W. S. "W WINDS. Lying to. Up S. b W, OS S. by E. W. N. W. N.w.byw.^w, uvr. W. S. W. North. U M •I N. by E. 12 15 Current South Dy Compass 1^ knots. BEMABKS, TUESDAT, MABOB 28Ta, 1864. P. M. Dense fog, with mizzling rain. Wind inclining to Wft** erly. No ice visible. Bent the cables and got the anchors on the gunwale. At 4h, sounded in 60 fathoms. Temperature of the 3ea-wat«r 84" Air 36°. At 6h, blowing excessive hard and heavy sea on. Wore ship with her head to the Southward. Furled the fore and mizen topsails, and hove to under the main-topaail. At 9h, less wind and a heavy fall of rain. At lOh, the wind cbanged suddenly to the Northward, ia a tre- mendous rain squall. At Midnight, blowing hard, but the weather clearing up. At 1 A. M., set the fore and mizen topsails. At 2h, set the reefed courses and spanker. At 3h, out doable reefs and set top-gallant-sails andjiK At 4h, Mer. Alt of # An tares. Lat in 47° 29' ) Mean 47* 84' N. Same time Alt. of Polar #. Lat. in 47" 39' J D. R. 47* 86' N. At Sunrise, Mag. Varia. Obs. was 23° Westerly. Out all reefs and checked in the weather braces. At 8 A. M., Long, in by Chron. 51° 18' W. D. R. 50° 58' W. St. John's harbor bears W. N. W. by Compass, distant 60 milea. At lOh, the land was seen in that directioa At llh, made out Signal Hill, bearing W. N. W, distant 5 leaguei. Noon. Ship close in with Fort Amherst. Received on board a Pilot, and proceeded into port. Vari'n «ptW. Course S. 89° W. Dist 177 D. Lat. 3' S. Dep. 177 W. Lat Lat D.R.47' Obs. 47 34'N. 34 N. Dif. Lon. 4' Lon. D.R. 52 '25' 59 W. Long. Chron. 62" D.R. sin. yest 52 48'W.|Bar.28.90 28 W.lTher.46' At 1 P. M. came to with the small bower anchor in 8 fathoms water, abreast of the town of St John's. Furled lails and moored ship, with 45 fathoms cable on each bower anchor, and sent down top-gallant yards. Midnight. Heavy rain squalls from the N. W. This day's work ends with and contains 36 hours, in order to oommence th« Harbor Log. On referring to the above Log, it will be noticed that the Ship ran to the N. W. by N. until 4 P. M., when soundings were obtained in 60 fathoms water, on the North Eastern edge of the Great Bank of New- foundland, and at 6 P. M. she was wore round with her head to the Southward, and hove to under the elose-reefed main-topsail for the night, on account of the dense fog which prevailed, in case of meeting with ice ; and also with the view of being on the proper tack should a sudden shift of wind from the Northward take place during the night time. At 9 P. M. the gale began to moderate, and heavy showers of rain fell, the usual precursor of a violent and sudden shift of wind. The Barometer now began to rise rapidly, and at 10, a squall from the North- ward struck the Ship, and blew with great fury for about two hours, and she luffed up to the wind on the same tack, and sail was made as the wind moderated. The sky having now cleared up, the opportunity was taken of finding the Latitude by Observation ut 4 A. M., from the Meridian Altitude of Antares to the Southward, and the Altitude of the Polar Star to the Northward. The Mean of the two Latitudes so found agrees with that by Dead Reckoning, and places the Ship in the parallel of Latitude of the intended port, 47° 34' N. ; consequently, it bears W. N. W. by Compass, but we must steer i a point more to the Northward, in order to make the necessary allowanw for Leeway and Currents. At Sunrise, the Magnetic Variation was observed to be 23° W., and at 8 A. M. the Longitude by Chre- Bometer, as above, is found to be 20' to the Westward of that by Dead Reckoning since last Observation, and by a case of Parallel Sailing, or by the Chart, St. John's is found to bear true West, or W. N. W. by Ccmpass, distant 60 miles. At 10 A. M., High Land was discovered ahead, and at 11 the buildings on Signal Hill, and Fort Amherst, at the entrance of St. John's Harbor, were distinctly made out, and at Noon she closed with th« entrance of the Harbor, and took a Pilot on board. Thus making the Pass»ge from Port to Port in 18 days 6 hours, and sailed a distance of 2977 miles. In working up this day's work, the allowance for the Set and Drift cf the Current, as above, (S. S. K. irue, 36 miles in 24 hours,) must be inserted in the Traverse Tabk, aloa« irith the other Courses Distanoea, and the result of the day's work will be fou.nd as abo^e. 306 r •fa s 4 8 •as a o SS ^«, 2 ci I o I ^^ o o o ca, •- eS .3 a> -I C ID .-3 « S " S ^ S^ o « g £ *» 2 CO ^^ e m «i ■" . ^ 2 = a o b, rt «^ a •sll « 2 3 ■w '3 .3 «^ "5 _, C ^ ■2|2 .- S:s «^ s „ O^ „ 1-3 o o o to »o O oq « 1-1 ^:^^ *-^ ^ a « ^5 d ■—3 <0 CI I— I I— I cQ t* O 00 ^ CO w 05 00 t 1^ n ^^^ o o CO 05 Oi OJ «o VI 00 -f^ ^ ^'ai OJ «J cd r/l T") t-l o ,C O o fl -TD o TS TS «o CO lo to CO CO oioooot^'Oooai'OiO'^io t^ t~ t- Jt^t~t^t^to;o>ocorf tn H a Pi u o . o o « « u o E-' OTfooo CO CO CO CO CO CO ^ lO S t-000«CO.-i «0 Tf •" CO <0 CO CO •^ CO o O <-i^00CO«OOl Tf 1^ (M Cq(M-Tt »0(M»-iCq'^ COCO—1 coco o OC0-^rf00C0«i05i-i'*I>-l>- c^cqoicqcacococo'*'^-^'^ t~Ot~OOCOOCOTf: b ^ "' >fI S^ll' go a o -13 C0 »o eq 4J 13 • r-4 SO a o -a a cj 93 -a en sq o a t» — CO 13 -^ > o (D -^ L> 09 -^ cd a « - 4) a^ 1 1 ® ^ u a w '5 «^ M cd Tr o bf oq a «o (0 13 3 (V bl) 3 S Sm o \r-^ o i-( ^ a H cd *^ m' a; 0) ^ '^ "* s CO t~ t^ t- ■^ CT) eq « 13 a ^ •i3 ed h-5 -o a 01 •.H rt 13 ti tv rl o C TS cd a -4^ no 3 Q 43 I TABLES. TABLE ] .— DIFFERENCE OF LATITUDE AND DEPARTURE FOR i POINT. 1 North i East. North ; : West South J East South J "West Dist. Lut Dep. Dist Lat Dep. Dist Lat Dep. Dist. Lat Dep. Dist liat Dep. 1 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 03.2 125 124.8 06.1 185 184.8 09.1 245 244.7 12.0 6 06.0 00.3 Q6 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 09.0 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 00.6 73 72.9 03.6 133 132.8 06.5 193 192.8 09.5 253 252.7 124 14 14.0 00.7 74 73.9 03.6 134 133.8 06.6 194 1938 09.5 254 253.7 125 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 79.9 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 04.0 141 140.8 06.9 201 200.8 09.9 261 260.7 12.8 22 22.0 01.0 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 07.3 208 207.7 10.2 268 267.7 13.2 29 29.0 01.4 89 88.9 04.4 149 148.8 07.3 209 ; 208.7 10.3 269 268.7 13.2 30 31 30,0 01.5 90 89.9 04.4 150 149.8 07.4 210 209.7 1 10.3 270 269.7 13.2 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 10.5 275 274.7 13.5 36 36.0 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 10.6 277 276.7 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 10.7 279 278.7 13.7 40 41 40.0 02.0 100 99.9 04.9 160 159.8 07.9 220 219.7 10.8 280 279.7 13.7 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 07.9 222 221.7 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 08.0 224 223.7 11.0 284 283.7 13.9 45 44.9 02.2 105 104.9 05.2 165 164.8 08.1 225 224.7 11.0 285 284.7 14.0 46 45.i> 02.3 106 105.9 05.2 166 165.8 08.1 226 225.7 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 1G7.8 08.2 228 227.7 11.2 288 287.7 14.1 49 48.9 02.4 109 108.9 05.3 169 168.8 08.3 229 228.7 11.2 289 288.7 14.2 50 49.9 02.5 110 109.9 05.4 170 169.8 08.3 230 229.7 11.3 290 289.7 14.2 51 50.9 02.5 111 110.9 05.4 171 170.8 08.4 231 230.7 11.3 291 290.6 14.3 52 51.9 02.6 112 111.9 05.5 172 171.8 08.4 232 231.7 11.4 292 291.6 14.3 53 52.9 02.6 113 112.9 05.5 173 172.8 08.5 233 232.7 11.4 293 292.6 14.4 54 53.9 02.6 114 113.9 05.6 174 173.8 08.5 234 233.7 11.5 294 293.6 14.4 55 54.9 02.7 115 114.9 05.6 175 174.8 ! 08.6 235 234.7 11.5 295 294.6 14.5 56 55.9 02.7 116 115.9 05.7 176 175.8 08.6 236 235.7 11.6 296 295.6 14.5 57 56.9 02.8 117 116.9 05.7 177 176.8 08.7 237 236.7 11.6 297 296.6 14.6 58 57.9 02.8 118 117.9 05.8 17S 177.8 08.7 238 237.7 11.7 298 2;t7.6 14.6 59 58.9 02.9 119 118.9 05.8 179 178.8 08.8 239 238.7 11.7 299 29S.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 Dep. Lat. Dist Dep. Lat El«t J North. Ka .St t South. [ ForTJ-Pts.] Wpst i .North West J South. 8 TABLE I.— DIFFERENCE OF LATITUDE AND DEPARTURE FOR i POINT North i East North |We«t. South i East. South i West. Dist. Lat Dep. Dist Lat Dep. Dist Lat Dep. Dist Lat Dep. Dist Lat. Dep. 1 01.0 00.1 61 60.7 06.0 121 120.4 11.9 181 180.1 17.7 241 239.8 23.6 ') 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 00.4 64 63.7 06.3 124 123.4 12.2 184 183.1 18.0 244 242.8 23.9 5 05.0 00.5 65 64.7 06.4 125 124.4 12.3 185 184.1 18.1 245 243.8 24.0 1 6 06.0 00.6 66 65.7 06.5 126 125.4 12.4 186 185.1 18.2 246 244.8\ 24.1 \ 7 07.0 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 09.0 00.9 69 68.7 06.8 129 128.4 12.6 189 188.1 18.5 249 247.8 24.4 10 10.0 01.0 70 69.7 06.9 130 129.4 12.7 190 189.1 18.6 250 248.8 24.5 11 10.9 01.1 71 70.7 07 131 130.4 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 18.9 253 251.8 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 07.4 135 134.3 13.2 195 194.1 19.1 255 253.8 25.0 16 15.9 01.6 76 75.6 07.4 136 135.3 13.3 196 195.1 19.2 256 254.8 25.1 17 16.9 01.7 77 76.6 07.5 137 136.3 13.4 197 196.1 19.3 257 255.8 25.2 18 17.9 01.8 78 77.6 07.6 138 137.3 13.5 198 197.0 19.4 258 256.8 25.3 19 18.9 01.9 79 78.6 07.7 139 138.3 13.6 199 198.0 19.5 259 257.8 25.4 20 21 19.9 02.0 80 79.6 07.8 140 139.3 13.7 200 199.0 19.6 19.7 260 258.7 25.5 20.9 02.1 81 80.6 07.9 141 140.3 13.8 201 200.0 261 259.7 25.6 22 21.9 02.2 82 81.6 08.0 142 141.3 13.9 202 201.0 19.8 262 260.7 25.7 23 22.9 02.3 83 82.6 08.1 143 142.3 14.0 203 202.0 19.9 263 261.7 25.8 24 23.9 02.4 84 83.6 08.2 144 143.3 14.1 204 203.0 20.0 264 262.7 25.9 25 24.9 02.5 85 84.6 08.3 145 144.3 14.2 205 204.0 20.1 265 263.7 26.0 2t) 25.9 02.5 86 85.6 08.4 146 145.3 14.3 206 205.0 20.2 266 264.7 26.1 27 26.9 02.6' 87 86.6 08.5 147 146.3 14.4 207 206.0 20.3 267 265.7 26.2 28 27.9 02.7 88 87.6 08.6 148 147.3 14.5 208 207.0 20.4 268 266.7 ie, ^ 29 28.9 02.8 89 88.6 08.7 149 148.3 14.6 209 208.0 20.5 269 267.7 26.4 30 29.9 02.9 03.0 90 89.6 08.8 150 149.3 14.7 210 209.0 20.6 270 268.7 269.7 26.5 31 30.9 91 90.6 08.9 151 150.3 14.8 211 210.0 20.7 271 26.6 32 31.8 03.x 92 91.6 09.0 152 151.3] 14.9 212 211.0 20.8 272 270.7 26.7 33 32.8 03.2 93 92.6 09.1 153 152.3 15.0 213 212.0 20.9 273 271.7 26.8 34 33.8 03.3 94 93.5 09.2 154 153.3 15.1 214 213.0 21.0 274 272.7 26.9 35 34.8 03.4 95 94.5 09.3 155 154.3 15.2 215 214.0 21.1 275 273.7 27.0 36 35.8 03.5 96 95.5 09.4 156 155.2 15.3 216 215.0 21.2 276 274.7 27.1 37 36.8 03.6 97 96.5 09.5 157 156.2 15.4 217 216.0 21.3 277 275.7 27.2 38 37.8 03.7 98 97.5 09.6 158 157.2 15.5 218 217.0 21.4 278 276.7 27.2 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 41 39.8 03.9 100 99.5 09.8 160 159.2 15.7 220 218.9 21.6 280 278.7 27.4 40.8 04.0 101 100.5 09.9 161 160.2 15.8 221 219.9 21.7 281 279.6 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 44 42.8 04.2 103 102.5 10.1 163 162.2 16.0 223 221.9 21.9 283 281.6 27.7 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 04.4 105 104.5 10.3 165 164.2 16.2 225 223.9 22.1 285 283.6 27.9 46 45.8 04.5 106 105.5 10.4 166 165.2 16.3 226 224.9 22.2 286 284.6 28.0 ' 47 46.8 04.6 107 106.5 10.5 167 166.2 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 04.8 109 108.6 10.7 169 168.2 16.6 229 227.9 22.4 289 287.6 28.3 ; 50 51 49.8 04.9 110 109.5 10.8 10.9 170 169.2 16.7 230 228.9 22.5 290 288.6 28.4 50.8 05.0 HI 110.5 171 170.2 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 17.3 237 235.9 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 23.3 298 296.6 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 Lat. 240 238.8 23.5 300 298.6 29.4 Dist. Dep. Lat. Dist Dep. Lat Dist Dep. Dist Dep. Lat Dist. Dep. 1 Lat Eart i North. Emrt i Sonth. tF"'' 7* Pte-I West i North West i Sentk } TABLE I Nortli J Ef .—DIFFERENCE OF LATITUDE AND DEPARTURE FOR J POINT. 8 | ist. North i West. South i East South f West. 1 Dist. 1 Lat. Dep. Dist Lat Dep. Dist Lat Dep. Dist. Lat. Dep. Dist Lat. Dep. 01.0 00.1 61 60.3 09.0 121 119.7 17.8 181 179.0 26.6 241 23S.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 18.0 183 181.0 26.9 243 ; 240.4 35.7 4 04.0 00.6 64 DO.O 09.4 124 122.7 18.2 184 182.0 27.0 244 241.4 35.8 5 04.9 00.7 65 64.3 09.5 125 123.6 18.3 185 183.0 27.1 245 242.3 35.9 6 05.9 00.9 66 65.3 09.7 126 124.6 18.5 186 184.0 27.3 246 1 243.3 36.1 7 06.9 OI.O 67 66.3 09.8 127 125.6 18.6 187 185.0 27.4 247 1 244.3 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 08.9 01.3 69 68.3 10.1 129 127.6 18.9 189 187.0 27.7 249 246.3 36.5 10 09.9 01.5 70 69.2 10.3 130 128.6 19.1 190 187.9 27.9 250 247.3 36.7 11 10.9 01.6 71 70.2 10.4 131 129.6 19.2 191 188.9 28.0 251 248.3 36.8 1 12 11.9 01.8 72 71.2 10.6 1-32 130.6 19.4 192 189.9 28.2 252 249.3 i 37.0 1 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 13.8 02.1 74 73.2 10.9 134 132.5 19.7 194 191.9 28.5 254 251.3 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 Oi.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 20.2 198 195.9 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 29.3 260 257.2 38.1 21 20.8 03.1 81 80.1 11.9 141 139.5 20.7 201 198.8 29.5 261 258.2 38.3 22 21.8 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 12.6 146 144.4 21.4 206 203.8 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 87.0 12.9 148 146.4 21.7 208 205.7 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 31 29.7 04.4 90 89.0 13.2 150 148.4 22.0 210 207.7 30.8 270 ,267.1 39.6 30.7 04.5 91 90.0 13.4 151 149.4 22.2 211 208.7 31.0 271 ; 268. 1,39.8 | 32 31.7 04.7 92 91.0 13.5 152 150.4 22.3 212 209.7 31.1 272 269.1 39.9 33 32.0 04.8 93 92.0 13.6 153 151.3 22.4 213 210.7 31.3 273 270.0 40.1 34 33.6 05.0 94 93.0 13.8 154 152.3 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 31.5 275 272.0 40.4 36 35.6 05.3 96 95.0 14.1 156 154.3 22.9 216 213.7 31.7 276 273.0 40.5 37 36.6 05.4 97 96.0 14.2 157 155.3 23.0 217 214.7 31.8 277 274.0 40.6 38 37.6 05.6 98- 96.9 I 14.4 158 156.3 23.2 218 215.6 32.0 278 275.0 40.8 39 38.6 05.7 99 97.9 i 14.5 159 157.3 23.3 219 216.6 32.1 279 276.0,40.9 1 40 41 39.6 05.9 100 98.9 i 14.7 160 158.3 23.5 220 217.6 32.3 280 277.0 41.1 40.6 06.0 101 99.9 14.8 161 159.3 23.6 221 218.6 32.4 281 278.0 41.2 42 41.5 06.2 102 100.9,15.0 162 160.2 23.8 222 219.6 32.6 282 278.9 41.4 43 42.5 06.3 103 101.9 15.1 163 161.2 23.9 223 220.6 32.7 283 , 279.9 41.5 44 43.5 06.5 104 102.9 15.3 164 162.2 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 06.7 106 104.9 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 07.0 108 106.8 15.8 168 166.2 24.7 228 225.5 33.5 288 284.9 42.3 49 48.5 07.2 109 107.8 16.0 169 167.2 24.8 229 226.5 33.6 289 285.9 42.4 50 49.5 07.3 110 108.8 16.1 170 168.2 24.9 230 227.5 33.7 290 286.9 42.6 51 50.4 07.5 111 109.8 16.3 171 169.1 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 25.2 232 229.5 34.0 292 288.8 42.8 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 43.3 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 1 5ti 55.4 0«.2 116 1147! 17.0 176 174.1 25.8 236 233.4 34.6 296 292.8 43.4 57 56.4 08.4 117 1157 17.2 177 175.1 26.0 237 234.4 ' 34.8 297 293.8 43.6 58 57.4 08.5 118 116.7 17.3 17S 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 43.9 60 59.4 08.8 120 118.7 17.6 180 178.1 26.4 240 237.4 35.2 300 296.8 44.0 Dist Dep. Lat. Dist. Dep. Lat Dist Dep. Lat Dist Dep. Lat Dist Dep. Lat East 1 North. E ast 1 South. rForTJPts.] West J North. West J South | 4 TABLE I.— DIFFERENCE OF LATITUDE AND DEPARTURE FOR 1 POINT. | North b. Ea«t North b. West. South h. East South b. We«t. 1 Dist Lat. Dep. 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 24.4 185 181.4 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 25.4 190 191' 186.3 187.3 37.1 250 245.2 48.8 11 lO.S 02.1 71 69.6 13.9 131 128.5 25.6 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 02.5 73 71.6 14.2 J 33 130.4 25.9 193 189.3 37.7 253 24^.1 49.4 14 13.7 02.7 74 72.6 14.4 134 131.4 26.1 194 190.3 37.8 254 249.1 49.6 15 14.7 02.9 75 73.6 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 15.2 138 135.3 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 15.8 141 138.3 27.5 201 197.1 39.2 261 256 50.9 22 21.6 04.3 82 80.4 16.0 142 139.3 27.7 202 198.1 39.4 262 257 51.1 23 22.6 04.5 83 81.4 16.2 143 140.3 27.9 203 199.1 39.6 263 257 9 151.3 1 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 24.5 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 84.3 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 05.5 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 I 40.8 269 263.8 52.5 30 31 29.4 30.4 05.9 90 88.3 17.6 150 147.1 29.3 210 206.0 ! 41.0 270 264.8 52.7 06.0 91 89.3 17.8 151 148.1 29.5 211 206.9 41.2 271 265.8 52.9 32 31.4 06.2 92 90.2 17.9 152 149.1 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 29.8 213 208.9 41.6 273 267.8 53.3 34 33.3 06.6 94 92.2 18.3 154 151.0 30.0 214 209.9 41.7 274 268.7 53.5 35 34.3 Ob.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 30.4 216 211.8 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 19.3 159 155.9 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 i 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 31.8 223 218.7 43.5 283 277.6 55.2 44 43.2 08.6 104 102.0 20.3 164 160.8 32.0 224 219.7 43.7 284 :■ 278.5 55.4 45 44.1 08.8 105 103.0 20.5 165 161.8 32.2 225 220.7 43.9 285 279.5 55.6 46 45.1 09.0 106 104.0 20.7 166 162.8 32.4 226 221.7 44.1 286 280.5 55.8 47 46.1 09.2 107 104.9 20.9 167 163.8 32.6 227 222.6 44.3 287 281.5 56.0 48 47.1 09.4 108 105.9 21.1 168 164.8 32.8 228 223.6 44.5 288 282.5 56.2 49 48.1 09.6 109 106.9 21.3 169 165.8 33.0 229 224.6 44.7 289 283.4 56.4 50 49.0 09.8 110 107.9 21.5 170 166.7 33.2 230 231 225.6 44.9 290 284.4 56.6 51 50.0 09.9 111 108.9 21.7 171 167.7 33.4 226.6 '45.1 291 285.4 56.8 52 51.0 10.1 112 109.8 21.9 172 168.7 33.6 232 227.5 45.3 292 286.4 57.0 - 53 52.0 10.3 113 110.8 22 173 169.7 33.8 233 228.5 45.5 293 287.4 57.2 54 53.0 10.5 114 111.8 22.2 174 170.7 33.9 234 229.5 45.7 294 288.4 57.4 55 53.9 10.7 llf) 112.8 22.4 175 171.6 34.1 235 230.5 45.8 295 289.3 : 57.6 56 54.9 10.9 116 113.8 22.6 176 172.6 34.3 236 231.5 46.0 296 290.3 57.7 57 55.9 11.1 117 114.8 22.8 177 173.6 34.5 237 232.4 46.2 297 291.3 57.9 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 Dial. Dep. Lat Dist. Dep. Lat. Dist Dpp. Lat Dist Dep. Lat Dist Dep. t Lat 1 East ». North. East b. Sonth. Tor 7 Pts.] Wpst A. North. West b. South. | TABLE I.— DIFFERENCE OF LATITUDE AND DEPARTURE FOR IJ POINTS. 6 | North b. East i East. North b. West i Wost South b. East i East South b. West * "West. 1 Dist. Lat. Dep. Dist. 1 Lilt Dep. Dist Lilt Dep. Dist Lat Dep. Dist Lat Dep. 1 1 01.0 00.2 61 59.2 14.8 121 117.4 29.4 181 175.6 44.0 241 233.8 58.6 2 01.9 00.5 62 60.1 15.1 122 118.3 29.6 182 176.5 44.2 234.7 58.8 3 02.9 00.7 63 61.1 15.3 123 119.3 29.9 183 177.5 44.5 243 235.7 59.0 1 4 03.9 01.0 64 «2.1 15.6 124 1 20.3 30.1 184 178.5 44.7 244 236.7 59.3 5 04.9 01.2 65 d3.1 15.8 125 121.3 30.4 185 179.5 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 >=; 07.8 01.9 68 66.0 16.5 128 124.2 3>.l 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 45.9 249 241.5 60.5 10 11 09.7 02.4 70 67.9 17.0 130 126.1 31.6 190 184.3 46.2 250 242.5 60.7 10.7 02.7 71 68.9 17.3 131 127.1 31.8 191 18.5.3 46.4 251 243.5 61.0 12 11.6 02.9 72 69.8 17.5 132 128.0 32.1 192 186.2 46.7 252 244.4 61.2 13 12.6 03.2 73 70.8 17.7 133 129.0 32.3 193 187.2 46.9 253 245.4 61.5 14 13.6 03.4 74 71.8 18.0 134 130.0 32.6 194 188.2 47.1 254 246.4 61.7 15 14.6 03.6 75 72.8 18.2 135 131.0 32.8 195 189.2 47.4 255 247.4 62.0 16 15.5 03.9 76 73.7 18.5 136 131.9 33.0 196 190.1 47.6 256 248.3 62.2 17 16.5 04.1 77 74.7 18.7 137 132.9 33.3 197 191.1 47.9 257 249.3 62.4 IS 17.5 04.4 78 75.7 19.0 138 133.9 33.5 198 192.1 48.1 258 250.3 62.7 19 18.4 04.6 79 76.6 19.2 139 134.8 33.8 199 193.0 48.4 259 251.2 62.9 20 21 19.4 20.4 04.9 80 77.6 19.4 140 135.8 34.0 200 194.0 48.6 260 2.52.2 63.2 05.1 81 78.6 19.7 141 136 8 34.3 201 195.0 48.8 261 253.2 63.4 22 21.3 05.3 82 79.5 19.9 142 137.7 34.5 202 195.9 49.1 262 254.1 63.7 23 22.3 05.6 83 80.5 20.2 143 138.7 34.7 203 196.9 49.3 263 255.1 63.9 24 23.3 05.8 84 81.5 20.4 144 139.7 35.0 204 197.9 49.6 264 256.1 64.1 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 2t) 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 07.0 89 86.3 21.6 149 144.5 36.2 209 202.7 50.8 269 260.9 65.4 30 29.1 07.3 90 87.3 21.9 150 145.5 36.4 210 203.7 51.0 270 271 261.9 65.6 31 30.1 07.5 91 88.3 22.1 151 146.5 36.7 211 204.7 51.3 262.9 65.8 36 31.0 07.8 92 89.2 22.4 152 147.4 36.9 212 205.6 51.5 272 263.8 66.1 33 32.0 08.0 93 90.2 22.6 153 148.4 37.2 213 206.6 51.8 273 264.8 66.3 34 33.0 08.3 94 91.2 22.8 154 149.4 37.4 214 zv7.6 52.0 274 265.8 66.6 35 34.0 08.5 95 92.2 23.1 155 150.4 37.7 215 208.6 o'^ 2 '275 266.8 66.8 36 34.9 08.7 96 93.1 23.3 156 151.3 37.9 216 209.5 52.5 276 267.7 67.1 37 35.9 09.0 97 94.1 23.6 157 152.3 38.1 217 210.5 52.7 277 268.7 67.3 38 36.9 09.2 98 95.1 23.8 158 153.3 38.4 218 211.5 53.0 278 269.7 67.5 39 37.8 09.5 99 96.0 24.1 159 154.2 38.6 219 212.4 53.2 279 270.6 67.8 40 38.8 09.7 100 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 98.0 24.5 161 156.2 39.1 221 214.4 53.7 281 272.6 68.3 42 40.7 10.2 102 98.9 24.8 162 157.1 39.4 222 215.3 53.9 282 273.5 68.5 43 41.7 10.4 103 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 39.8 224 217.3 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 69.2 46 44.6 11.2 106 102.8 25.8 166 161.0 40.3 226 21S.2 54.9 286 277.4 69.5 47 45.6 11.4 107 103.8 26.0 167 162.0 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 41.1 229 222.1 55.6 289 280.3 70.2 50 51 48.5 12.1 110 106.7 26.7 27.0 170 164.9 41.3 41.5 230 231 223.1 55.9 290 281.3 70.5 49.5 12.4 111 107.7 171 165.9 224.1 56.1 291 282.3 70.7 52 50.4 12.6 112 108.6 27.2 172 166.8 41.8 232 225.0 56.4 292 283.2 71.0 53 51.4 12.9 113 109.6 27.5 173 167.8 42.0 233 226.0 56.6 293 284.2 71.2 54 52.4 13.1 114 110.6 •^7.7 174 168.8 42.3 •234 227.0 56.9 294 285.2 71.4 55 53.4 13.4 115 111.6 27.9 175 169.8 42.5 235 228.0 57.1 295 286.2 71.7 56 54.3 13.6 116 112.5 28.2 170 170.7 42.8 236 228.9 57.3 296 287.1 71.9 57 55.3 13.8 117 113.5 •28.4 177 171.7 43.0 237 229.9 57.6 297 288.1 72.2 58 56.3 14.1 118 114.5 28.7 178 172.7 43.3 238 230.9 57.8 298 289.1 72.4 59 57.2 14.3 119 115.4 28.9 179 173.6 43.5 239 231.8 58.1 299 290.0 72.7 60 58.2 Dep. 14.6 120 116.4 29.2 180 174.6 43.7 Lat. 240 232.8 58.8 300 291.0 72.9 Dist Lat Dist Dep. Lat Dist Dep. Dist Dep. Lat Dist Dep. Lat Eut North East f East. Ej «t South East } Eist. [For 6f Pts.] Weit North West J West. West South West f Wmi. | ^- . *■ • — '__ 1 6 TABLE I— DIFFERENCE OF LATITUDE AND DEPARTURE FOR U POINTS. | North b. East \ E ist. North h. West J- West South h. East ^ East South h. West \ West. 1 Dist Lat. Dep. 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 01.9 00.6 62 59.3 18.0 122 116.7 35.4 182 174.2 52.8 242 231.6 70.2 3 02.9 00.9 63 60.3 18.3 123 117.7 35.7 183 175.1 53.1 243 232.5 70.5 1 4 03.8 01.2 64 61.2 18.6 1-24 118.7 36.0 184 176.1 53.4 244 233.5 70.8 1 5 04.8 01.5 65 62.2 18.9 125 119.6 36.3 185 177.0 53.7 245 234.5 71.1 6 05.7 01.7 66 63.2 19.2 126 120.6 36.6 186 178.0 54.0 246 235.4 71.4 7 06.7 02.0 07 64.1 19.4 127 121.5 36.9 187 178.9 54.3 247 236.4 71.7 8 07.7 02.3 68 65.1 19.7 128 122.5 37.2 188 179.9 54.6 248 237.3 72.0 9 08.6 02.6 69 66.0 20.0 129 123.4 37.4 189 180.9 54.9 249 238.3 72.3 10 11 09.6 02.9 70 67.0 20.3 130 124.4 37.7 190 181.8 55.2 250 239.2 72.6 10.5 03.2 71 67.9 20.6 131 125.4 38.0 191 182.8 55.4 251 240.2 72.9 12 11.5 03.5 72 68.9 20.9 132 126.3 38.3 192 183.7 55.7 252 241.1 73.2 13 12.4 03.8 73 69.9 21.2 133 127.3 38.6 193 184.7 56.0 253 242.1 73.4 14 13.4 04.1 74 70.8 21.5 134 128.2 38.9 194 185.6 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 15.3 04.6 76 72.7 22.1 136 130.1 39.5 196 187.6 56.9 256 245.0 74.3 17 16.3 04.9 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 13-2.1 40.1 198 189.5 57.5 258 246.9 74.9 19 18.2 05.5 79 75.6 22.9 139 133.0 40.3 199 190.4 57.8 259 247.8 75.2 20 19.1 05.8 80 76.6 23.2 140 134.0 40.6 200 191.4 58.1 260 248.8 '75.5 1 21 •20.1 06.1 81 77.5 23.5 141 134.9 40.9 201 192.3 58.3 261 249.8 75.8 22 21.1 06.4 82 7S.5 23.8 142 135.9 41.2 202 193.3 58.6 262 250.7 76.1 23 22.0 06.7 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 07.5 86 82.3 25.0 146 139.7 42.4 206 197.1 59.8 266 254.5 ' 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 i 77.5 28 26.8 08.1 88 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 1 257.4 78.1 30 31 28.7 08.7 90 86.1,26.1 150 143.5 43.5 210 201.0 61.0 270 258.4 78.4 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 93 89.0 27.0 153 146.4 44.4 213 203.8 61.8 273 261.2 79.2 34 32.5 09.9 94 90.0 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 62.4 275 263.2 79.8 36 34.4 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 63.0 277 265.1 80.4 38 36.4 11.0 98 93.8 28.4 158 151.2 45.9 218 208.6 63.3 278 266.0 80.7 39 37.3 11.3 99 94.7 28.7 159 152.2 46.2 219 -209.6 63.6 279 267.0 81.0 40 38.3 11.6 100 95.7 29.0 160 153.1 46.4 220 210.5 63.9 280 267.9 81.3 41 39.2 11.9 101 96.7 29.3 161 154.1 46.7 221 211.5 64.2 281 268.9 81.6 42 40.2 12.2 102 97.6 29.6 162 155.0 47.0 222 212.4 64.4 282 269.9 81.9 43 41.1 12.5 103 98.6 29.9 163 156.0 47.3 223 213.4 64.7 •283 270.8 82.2 44 4-2.1 12.8 104 99.5 30.2 164 156.9 47.6 224 214.4 65.0 284 271.8 8-2.4 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 44.0 13.4 106 101.4 30.8 166 158.9 48.2 226 216.3 65.6 286 273.7 83.0 47 45.0 13.6 107 102.4 31.1 167 159.8 48.5 227 217.2 65.9 287 274.6 83.3 48 45.9 13.9 108 103.3 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 47.8 14.5 110 105.3 31.9 170 162.7 49.3 230 220.1 66.8 290 277.5 84.2 51 48.8 14.8 111 106.2 32.2 171 163.6 49.6 231 221.1 67.1 291 278.5 84.5 52 49.8 15.1 112 107.2 32.5 172 164.6 49.9 232 222.0 67.3 292 279.4 84.8 53 50.7 15.4 113 108.1 32.8 173 165.6 50.2 233 -223.0 67.6 293 280.4 85.1 54 517 15.7 14 109.1 33.1 174 166.5 50.5 234 223.9 67.9 294 281.3 85.3 55 52.6 16.0 115 1 10.0 33.4 175 167.5 50.8 235 224.9 68.2 295 282.3 85.6 56 53.6 16.3 116 111.0 33.7 176 168.4 51.1 236 2-25.8 68.5 296 283.3 85.9 57 54.5 16.5 117 112.0 34.0 177 169.4 51.4 •237 226.8 68.8 297 284.2 86.2 58 55.5 16.8 118 112.9 »34.3 178 170.3 51.7 -238 2-27.8 69.1 298 285.2] 86.5 59 56.5 17.1 119 113.9 34.5 179 171.3 52.0 239 228.7 69.4 299 286.1 1 86.8 _60 57.4 17.4 120 114.8 34.8 180 172.2 52.3 •240 ' 229.7 69.7 300 287.1 1 87.1 Dist Dep. Lat Dist Dep. Lat Dist Dep. Lat. Dist Dep. Lat Dist Dep. ; Lat | EMt North Eart i Eart. E* «t Sonth Eaat ♦ E«t. fForSif^ts] West North West J Wpst. West Sonth West i "Weit. | TABLE I.- •DIFFERENCE OF LATITUDE AND DEPARTURE FOR If POINTS. 7 i Noith b. East * Ei I8t. Nurtli b. We>\ 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 1 91.1 224 186.2 124.4 284 236.1 157.8 45 37.4 25.0 105 87.3 58.3 165 137.21 91.7 225 187.1 125.0 285 237.0 158.3 46 38.2 25.6 106 88.1 58.9 166 138.0 92.2 226 187.9 125.6 286 237.8 158.9 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 1'-^ 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 1 51 42.4 28.3 111 92.3 61.7 171 142.2 95.0 231 192.1 128.3 291 242.01 161.7 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 96.7 234 194.6 130.0 294 244.5 163.3 55 45.7 30.6 lUy 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 96.5 64.4 176 146.3 97.8 236 196.2 131.1 296 24().l 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 4S.2 32.2 118 98.1 65.6 17S 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 99.4 239 198.7 132.8 299 24S.6 166.1 60 Dist. 49.9 33.3 120 99.8 66.7 180 149.7 100.0 240 199.6 133.3 300 249.4 166.7 Dep. Lat. Dist. Dep. Lat. Dist. D(MT Lat. Dist. Dep. Lat. Dist Dep. j Lat. | N iith Satt b. Eaa1 t. S outh Ea St b. East. fPor 6 Pts ] North West h. West. South West *. Wert. | TABLE I.- -DIFFERENCE OF LATITUDE AND DEPARTURE FOR 3* POINTS. 13 1 North East * North. North West * North. South East » South. South West t South. 1 Diat. 1 Lat. Dep. Dist. Lat. 49.0 Dep. Dist Lat. Dep. Dist Lat. Dep. Dist Lat Dep. 00.8 00.6 61 36.3 121 97.2 72.1 181 145.4 107.8 241 193.6 143.6 01.6 01.2 62 49.8 36.9 122 98.0 72.7 182 146.2 108.4 242 194.4 144.2 3 024 01.8 63 50.6 37.5 123 98.8 73.3 183 147.0 109.0 243 195.2 144.8 4 03.2 02.4 64 51.4 38.1 124 99.6' 73.9 184 147.8 109.r 244 196.0 145.4 5 04.0 03.0 65 52.2 38.7 125 100.4 74.5 1 185 148.6 110.2 245 196.8 145.9 6 04.8 03.6 66 53.0 39.3 126 101.2 75.1 186 149.4 110.8 246 197.6 146.5 7 05.6 04.2 67 53.8 39.9 127 102.0 75.7 187 150.2 111.4 247 198.4 147.1 8 06.4 04.8 68 54.6 40.5 128 102.8 W.2 188 151.0 112.0 248 199.2 147.7 9\ 07.2 05.4 69 55.4 41.1 129 103.6 76.8 189 151.8 11^.6 249 200.0 148.3 iO 11 08.0 06.0 70 56.2 41.7 130 104.4 77.4 78.0 190 152.6 113.2 250 200.8 148.9 08.8 06.6 71 57.0 42.3 131 105.2 191 153.4 113.8 251 201.6 149.5 12 09.6 07.1 72 57.8 42.9 132 106.0 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 59.4 44.1 134 107.6 79.8 194 155.8 115.6 254 204.0 151.3 15 12.0 08.9 75 60.2 44.7 135 108.4 80.4 195 156.6 116.2 255 204.8 151.9 10 12.9 09.5 76 61.0 45.3 136 109.2 81.0 196 157.4 116.8 256 205.6 152.5 17 13.7 10.1 77 61.8 45.9 137 110.0 81.6 197 1,58.2 117.4 257 206.4 153.1 18 14.5 10.7 78 62.7 46.5 138 110.8 82 2 198 159.0 117.9 258 207.2 153.7 19 15.3 11.3 79 63.5 47.1 139 111.6 82.8 199 159.8 118.5 259 208.0 154.3 21 16.1 16.9 11.9 12.5 80 64.3 47.7 140 112.4 83.4 200 160.6 119.1 260 208.8 154.9 81 65.1 48.3 141 113.3 84.0 201 161.4 119.7 261 209.6 155.5 22 17.7 13.1 82 65.9 48.8 142 114.1 84.6 202 162.2 120.3 262 210.4 156.1 23 18.5 13.7 83 66.7 49.4 143 114.9 85.2 203 163.1 120.9 263 211.2 156.7 24 19.3 14.3 84 67.5 50.0 144 115.7 85.8 204 163.9 121.5 264 212.0 157.3 25 20.1 14.9 85 68.3 50.6 145 116.5 86.4 205 164.7 122.1 265 212.8 157.9 2f. 20.9 15.5 86 69.1 51.2 146 117.3 87.0 206 165.5 122.7 266 213.7 158.5 27 21.7 16.1 87 69.9 51.8 147 118.1 87.6 207 166.3 123.3 267 214.5 159.1 28 22.5 16.7 88 70.7 52.4 148 118.9 88.2 208 167.1 123.9 268 215.3 159.6 2'J 23.3 17.3 89 71.5 53.0 149 119.7 88.8 209 167.9 124.5 269 216.1 160.2 30 24.1 17.9 90 72.3 53.6 54.2 150 151 120.5 89.4 210 168.7 125.1 270 216.9 160.8 31 24.9 18.5 91 73.1 121.3 90.0 211 169.5 125.7 271 217.7 161.4 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 20.8 95 76.3 56.6 155 124.5 92.3 215 172.7 1281 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 58.4 158 156.9 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 41 32.1 23.8 100 80.3 59.6 160 128.5 95.3 220 176.7 177.5 131.1 280 224.9 166.8 32.9 24.4 101 81.1 60.2 161 129.3 95.9 221 131.6 281 225.7 167.4 42 o3.7 25.0 102 81.9 60.8 162 130.1 96.5 222 178.3 132.2 282 226.5 168.0 43 34.5 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 97.7 224 179.9 133.4 284 228.1 169.2 45 36.1 26.8 105 84.3 62.5 165 132.5 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 37.8 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 1(>9 135.7 100.7 229 183.9 136.4 289 232.1 172.2 50 51 40.2 29.8 110 111 88.4 89.2 65.5 66.1 170 136.5 101.3 230 231 184.7 137.0 290 232.9 172.8 41.0 30.4 171 137.3 101.9 185.5 137.6 291 233.7 173.3 52 41.8 31.0 112 90.0 66.7 172 138.2 102.5 232 186.3 138.2 292 234.5 173.9 53 42.6 31.6 113 90.8 67.3 173 139.0 103.1 233 187.1 138.8 293 235.3 174.5 54 43.4 32.2 114 91.6 67.9 174 139.8 103.7 234 188.0 139.4 294 236.1 175.1 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 69.7 177 142.2 105.4 237 190.4 141.2 297 238.6 176.9 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 Lat 180 144.6 107.2 240 192.8 143.0 300 241.0 178.7 Dist . Dep. Lat. Dist. Dep. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat 1 1 North Eiut f Eii t J Wesi. South V\'est J West. | 14 TABLE I.— DIFFERENCE OF LATITUDE AND DEPARTURE FOR 8^ POINTS. | North East i North. North West i North. South Eist i South. South West i South. 1 Diflt Lat Dep. Dist Lat. Dep. Dist Lat. Dep. Dist. Lat. Dep. Dist. Lat Dep. 1 00.8 00.6 61 47.2 38.7 121 93.5 76.8 181 139.9 114.8 241 186.3 152.9 2 01.5 01.3 62 47.9 39.3 122 94.3 77.4 1«2 140.7 115.5 242 187.1 153.5 3 02.3 01.9 63 48.7 40.0 123 95.1 78.0 183 141.5 116.1 243 187.8 154.2 1 4 03.1 02.5 64 49.5 40.6 124 95.9 78.7 184 142.2 116.7 244 188.6 154.81 5 03.9 03.2 65 50.2 41.2 125 96.6 79.3 185 143.0 1 17.4 245 189.4 155.4 6 04.6 0M.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 80.6 187 144.6 118.6 247 190.9 156.7 8 06.2 05.1 68 52.6 43.1 128 98.9 81.2 188 145.3 119.3 248 191.7 I57.3| 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 1 10 11 07.7 06.3 70 54.1 44.4 130 100.5 82.5 190 146.9 120.5 250 193.3 158.6 08.5 07.0 71 54.9 45.0 131 101.3 83.1 191 147.6 121.2 251 194.0 159.2 12 09.3 07.6 72 55.7 45.7 132 102.0 83.7 192 148.4 121.8 252 194.8 159,9 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 85.0 194 150.0 123.1 254 196.3 161.1 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 10.2 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 12.1 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 13.3 80 61.8 50.8 140 108.2 88.8 200 154.6 126.9 260 201.0 164.9 21 16.2 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 18.6 15.2 84 64.9 53.3 144 111.3 91.4 204 157.7 129.4 264 204.1 167.5 25 19.3 15.9 85 65.7 53.9 145 112.1 92.0 205 158.5 130.1 265 204.8 168.1 26 20.1 16.5 86 66,5 54.6 146 112.9 92.6 206 159.2 130.7 266 205.6 168.7 27 20.9 17.1 87 67.3 55.2 147 113.6 93.3 207 160.0 131.3 267 206.4 169.4 28 21,6 17.8 88 68.0 ' 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 , 207.9 170.7 30 23.2 19j0 90 69.6 70.3 57.1 150 116.0 95.2 210 162.3 133.2 270 208.7 171.3 31 24.0 19.7 91 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 97.1 213 164.7 135.1 273 211.0 173.2 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 99.0 216 167.0 137.0 276 213.4 175.1 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 75.8 62.2 158 122.1 100.2 218 168.5 138.3 278 214.9 176.1 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 64.1 161 124.5 102.1 221 170.8 140.2 281 '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 66.0 164 126.8 104.0 224 173.2 142.1 284 219.5 180.2 45 34.8 28.5 105 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 67.9 167 129.1 105.9 227 175.5 144.0 287 221.9 182.1 48 37.1 30.5 108 83.5 68.5 168 129.9 106.6 228 176.2 144.6 288 222.6 182.7 49 37.9 31.1 109 84.3 69.1 169 130.6 107.2 229 177.0 145.3 289 i 223.4 183.3 50 38.7 31.7 110 85.0 69.8 170 131.4 107.8 230 177.8 145.9 290 224.2 184.0 1 51 39.4 32.4 111 85.8 70.4 171 132.2 108.5 231 178.6 146.5 291 224.9 184.6 52 40.2 33.0 112 86.6 71.1 172 133.0 109.1 232 179.3 147.2 292 225.7 185.2 53 41.0 33.6 113 87.4 71.7 173 133.7 109.8 233 180.1 147.8 293 226.5 185.9 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 34.9 115 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 73.6 176 136.0 111.7 236 182.4 149.7 296 228.8 187,8 57 44.1 36.2 117 90.4 74.2 177 136.8 112.3 237 183.2 1.^0.4 297 229.6 188.4 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 1 189.7 1 60 DiaL 46.4 38.1 120 92.8 76.1 180 139.1 114.2 240 185.5 152.3 300 231.9 190.3 Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist Dep. Lat North Es*t i East. South East ♦ East. [For 4i Pts.] North Wpst i West. 8ou»h Wesv # Witt. | TABLE I.— DIFFERENCE OF LATITUDE AND DEPARTURE FOR 81 POINTS. 15 North East i North. North West i North. South East i South, South We» t* South. Dist 1 Lat. Dep. Dist. Lat Dep. Diat. Lat. Dep. Dist. Lat. Dep. Disi. Lat. Dep. 1 00.7 00.7 61 45.2 41.0 121 89.7 81.3 181 134.1 121.6 241 178.6 161.8 2 01.5 01.3 62 45.9 41.6 122 90.4 81.9 182 134.9 122.2 242 179.3 162.5 8 02.2 02.0 63 46.7 42.3 123 91.! 82.6 183 135.6 122.9 243 180.1 163.2 4 03.0 02.7 64 47.4 43.0 124 91.9 8:i3 184 136.3 123.6 244 180.8 163.9 5 03.7 03.4 65 48.2 43.7 L25 92.6 83.9 185 137.1 124.2 245 181.5 1 164.5 6 04.4 04.0 66 48.9 44.3 126 93.4 84.6 186 137.8 124.9 246 182.3 165.2 7 05.2 04.7 67 49.6 45.0 127 94.1 85.3 187 138.6 125.6 247 183.0 165.9 8 05.9 05.4 68 50.4 45.7 128 94.8 86.0 188 139.3 126.3 248 183.8 166.5 9 06.7 06.0 69 51.1 46.3 129 95.6 86.6 189 140.0 126.9 249 184.5 167.2 10 11 07.4 06.7 70 51.9 47.0 130 96.3 87.3 88.0 190 140.8 127.6 250 251 185.2 186.0 167.9 08.2 07.4 71 52.6 47.7 131 97.1 191 141.5 128.3 168.6 12 08.9 08.1 72 53.3 48.4 132 97.8 88.6 192 142.3 128.9 252 186.7 169.2 13 09.6 08.7 73 54.1 49.0 133 98.5 89.3 193 143.0 129.6 253 187.5 169.9 14 10.4 09.4 74 54.8 49.7 134 99.3 90.0 194 143.7 130.3 254 188.2 170.6 15 11.1 10.1 75 55.6 50.4 135 100.0 90.7 195 144.5 131.0 255 188.9 171.2 l(i 11.9 10.7 76 56.3 51.0 136 100.8 91.3 196 145.2 131.6 256 189.7 171.9 17 12.6 11.4 77 57.1 51.7 137 101.5 92.0 197 146.0 132.3 257 190.4 172.6 18 13.3 12.1 78 57.8 52.4 138 102.3 92.7 198 146.7 133.0 258 191.2 1733 19 14.1 12.8 79 58.5 53.1 139 103.0 93.3 199 147.4 133.6 259 191.9 173.9 ^0 21 14.8 15.6 13.4 14.1 80 59.3 53.7 140 103.7 94.0 200 148.2 134.3 260 192.6 174.6 81 60.0 54.4 141 104.5 94.7 201 148.9 135.0 261 193.4 175.3 22 16.3 14.8 82 60.8 55.1 142 105.2 95.4 202 149.7 135.7 262 194.1 175.9 23 17.0 15.4 83 61.5 55.7 143 106.0 96.0 203 150.4 136.3 263 194.9 176.6 24 17.8 16.1 84 62.2 56.4 144 106.7 96.7 204 151.2 137.0 264 195.6 177.3 25 18.5 16.8 85 63.0 57.1 145 107.4 97.4 205 151.9 137.7 265 196.4 178.0 2t> 19.3 17.5 86 63.7 57.8 146 108.2 98.0 206 152.6 138.3 266 197.1 178.6 27 20.0 18.1 87 64.5 58.4 147 108.9 98.7 207 153.4 139.0 267 197.8 179.3 28 20.7 18.8 88 65.2 59.1 148 109.7 99.4 208 154.1 139.7 268 198.6 180.0 29 21.5 19.5 89 65.9 59.8 149 110.4 100.1 209 154.9 140.4 269 199.3 180.6 30 31 22.2 23.0 20.1 90 66.7 60.4 150 111.1 100.7 210 155.6 141.0 270 271 200.1 181.3 20.8 91 67.4 61.1 151 111.9 101.4 211 156.3 141.7 200.8 182.0 32 23.7 21.5 92 68.2 61.8 152 112.6 102.1 212 157.1 142.4 272 201.5 182.7 33 24.5 22.2 93 68.9 62.5 153 113.4 102.7:213 157.8 143.0 273 202.3 183.3 34 25.2 22.8 94 69.6 63.1 154 114.1 103.4 214 158.6 143.7 274 203.0 184.0 35 25.9 23.5 95 70.4 63.8 155 114.8 104.1 215 159.3 144.4 275 203.8 184.7 36 26.7 24.2 96 71.1 64.5 156 115.6 104.8 216 160.0 145.1 276 204.5 185.4 37 27.4 24.8 97 71.9 65.1 157 116.3 105.4 217 160.8 145.7 277 205.2 186.0 38 28.2 25.5 98 72.6 65.8 158 117.1 106.1 218 161.5 146.4 278 206.0 186.7 39 28.9 26.2 99 73.4 66.5 159 117.8 106.8 219 162.3 147.1 279 206.7 187.4 40 29.6 26.9 100 74.1 67.2 160 118.6 107.4 220 163.0 147.7 280 207.5 188.0 41 30.4 27.5 101 74.8 67.8 161 119.3 108.1 221 163.8 148.4 281 208.2 188.7 42 31.1 28.2 102 75.6 68.5 162 120.0 108.8 222 164.5 149.1 282 208.9 189.4 43 31.9 28.9 103 76.3 69.2 163 120.8 109.5 223 165.2 149.8 283 209.7 190.1 44 32.6 29.5 104 77.1 69.8 164 121.5 110.1 224 166.0 150.4 284 210.4 190.7 45 33.3 30.2 105 77.8 70.5 165 122.3 110.8 225 166.7 151.1 285 211.2 191.4 46 34.1 30.9 '106 78.5 71.2 166 123.0 111.5 226 167.5 151.8 286 211.9 192.1 47 34.8 31.6 107 79.3 71.9 167 123.7 112.2 227 168.2 152.4 287 212.7 192.7 48 35.6 32.2 108 80.0 72.5 168 124.5 112.8 228 168.9 153.1 288 213.4 193.4 49 36.3 32.9 109 80.8 73.2 169 125.2 113.5 229 169.7 153.8 289 214.1 194.1 50 51 37.0 33.6 110 81.5 73.9 74.5 170 126.0 114.2 230 231 170.4 154.5 290 214.9 194.8 37.8 34.2 111 82.2 171 126.7 114.8 171.2 155.1 291 215.6 195.4 52 38.5 34.9 112 83.0 75.2 172 127.4 115.5 232 171.9 155.8 292 216.4 196.1 53 39.3 35.6 113 83.7 75.9 173 128.2 116.2 233 172.6 156.5 293 217.1 196.8 54 40.0 36.3 114 84.5 76.6 174 128.9 116.9 234 173.4 157.1 294 217.8 197.4 55 40.8 36.9 115 85.2 77.2 175 129.7 117.5 235 174.1 157.8 295 218.6 198.1 56 41.5 37.6 116 86.0 77.9 176 130.4 118.2 236 174.9 158.5 296 219.3 198.8 57 42.2 38.3 117 86.7 78.6 177 131.1 118.9 237 175.6 159.2 297 220.1 199.5 58 43.0 39.0 118 87.4 79.2 178 131.9 119.5 238 176.3 159.8 298 220.8 200.1 59 43.7 39.6 119 88.2 79.9 179 132.6 120.2 239 177.1 160.5 299 221.5 200.8 60 44.5 40.3 120 88.9 80.6 180 133.4 120.9 240 177.8 161.2 300 222.3 201.5 Oifit . Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. iDist Dep. Lat Dist. Dep. Lat. North East i East. South Kast i Eait. [For 4i Pts.J North West i West. South West i Wert. 1 16 TABLE I.— DIFFERENCE OF LATITUDE AND DEPARTURE FOR 4 POINTS. North East. North West. South East South West. 1 Dist Lat. Dep. Dist. Lat Dep. Dist Lat Dep. Dist Lat Dep. Dist Lat Dep. 1 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 8 02.1 02.1 63 44.5 44.5 123 87.0 87.0 183 129.4 129.4 243 171.8 171.8 4 02.8 02.8 64 453 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 88.4 185 130.8 130.8 245 173.2 173.2 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 b9.8 89.8 187 132.2 132.2 247 174.7 174.7 s 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 11 07.1 07.1 70 49.5 49.5 130 91.9 91.9 92.6 190 134.4 135.1 134.4 250 251 176.8 176.8 07.8 07.8 71 50.2 50.2 131 92.6 191 135.1 177.5 177.5 1 12 08.5 08.5 72 50.9 50.9 132 93.3 93.3 192 135.8 135.8 252 178.2 178.2 13 09.2 09.2 73 51.6 51.6 133 94.0 94.0 193 136.5 136.5 253 178.9 178.9 14 09.9 09.9 74 52.3 52.3 134 94.8 94.8 194 137.2 137.2 254 179.6 179.6 15 10.6 10.6 75 53.0 53.0 135 95.5 95.5 195 137.9 137.9 255 180.3 1<0.3 16 11.3 11.3 76 53.7 53.7 136 96.2 96.2 196 138.6 138.6 256 181.0 181.0 17 12.0 12.0 77 54.4 54.4 137 96.9 96.9 197 139.3 139.3 257 181.7 181.7 18 12.7 12.7 78 55.2 55.2 138 97.6 97.6 198 140.0 140.0 258 182.4 182.4 19 13.4 13.4 79 55.9 55.9 139 98.3 98.3 199 140.7 140.7 259 183.1 183.1 20 21 14.1 14.8 14.1 14.8 80 56.6 56.6 140 99.0 99.0 200 141.4 141.4 260 183.8 183.8 81 57.3 57.3 141 99.7 99.7 201 142.1 142.1 261 184.6 184.6 22 15.6 15.6 82 58.0 58.0 142 100.4 100.4 202 142.8 142.8 262 185.3 185.3 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 2t) 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 31 21.2 21.9 21.2 90 63.6 63.6 150 106.1 106.1 210 148.5 148.5 270 271 190.9 190.9 21.9 91 64.3 64.3 151 106.8 106.8 211 149.2 149.2 191.6 191.6 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 34 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 96 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 41 28.3 28.3 100 70.7 70.7 160 113.1 113.1 220 155.6 155.6 280 198.0 198.0 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 72.1 162 114.6 114.6 222 157.0 157.0 282 199.4 199.4 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 77.1 169 119.5 119.5 229 161.9 161.9 289 204.4 204.4 50 35.4 35.4 110 77.8 77.8 78.5 170 120.2 120.2 230 231 162.6 162.6 290 205.1 205.1 51 36.1 36.1 111 78.5 171 120.9 120.9 163.3 163.3 291 205.8 205.8 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 79.9 173 122.3 122.3 233 164.8 164.8 293 207.2 207.2 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 82.0 176 124.5 124.5 236 166.9 166.9 296 209.3 209.3 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 41.0 118 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 t)0 42.4 42.4 120 84.9 84.9 180 127.3 127.3 240 169.7 169.7 300 212.1 212.1 Dist . Dep. Lat. Dist. Dep. Lat. Dist Dep. Lat. Dist Dep. Lat. Dist Dep. 1 Lat N»rth Eajst. North West [F'or 4 Pf] .«oiith Rast. Sonth Wert. TABLE U. n 1 DIFFERENCE OF LATITUDE AND DEPARTURE FOR 1 DEGREE. Oh 4m. 1 Dist . Lat. Dep. Di^t. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. i 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 01.1 122 122.0 02.1 KS2 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 01.2 126 126.0 02.2 186,186.0 03.2 246 246 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 0'2.2 188 188.0 03.3 248 248.0 04.3 9 09.0 00.2 69 69.0 01.2 129 129.0 02.3 189 1 89.0 03.3 249 249.0 04.3 10 11 10.0 00.2 70 70.0 01.2 l.SO 130.0 02.3 190 190.0 03.3 250 250.0 04.4 11.0 00.2 71 71.0 01.2 131 131.0 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 2:.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 04.5 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 2.^7 257.0 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 01.4 141 141.0 02.5 201 201.0 03.5 261 261.0 04.6 22 22.0 00.4 82 82.0 01.4 142 142.0 02.5 202 202.0 03.5 262 262.0 04.6 23 23.0 00.4 83 83.0 01.4 143 143.0 02.5 203 203.0 03.5 263 2(i3.0 04.6 24 24.0 00.4 84 84.0 01.5 144 144.0 02.5 204 204.0 03.6 264 264.0 04.0 25 25.0 00.4 85 85.0 01.5 145 145.0 02.5 205 205.0 03.6 265 265.0 04.6 26 26.0 00.5 86 86.0 01.5 146 146.0 02.5 206 206.0 03.6 266 266.0 04.6 27 27.0 00.5 87 87.0 01.5 147 147.0 02.6 207 207.0 03.6 267 ' 267.0 04.7 28 28.0 00.5 88 88.0 01.5 148 148.0 02.6 208 208.0 03.6 268 . 268.0 04.7 29 29.0 00.5 89 89.0 01.6 149 149.0 02.6 209 209.0 03.6 269 '269.0 04.7 1 30 30.0 00.5 90 90.0 01.6 01.6 150 150.0 02.6 210 210.0 03.7 270 270.0 04.7 1 31 31.0 00.5 91 91.0 151 151.0 02.6 211 211.0 03.7 271 271.0 04.7 32 32.0 00.6 92 92.0 01.6 152 152.0 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 01.7 155 155.0 02.7 215 215.0 03.8 275 275.0 04.8 36 36.0 00.6 96 96.0 01.7 156 156.0 02.7 216 216.0 03.8 276 276.0 04.8 37 37.0 00.6 97 97.0 01.7 157 157.0 02.7 217 217.0 03.8 277 277.0 04.8 38 38.0 00.7 98 98.0 01.7 158 158.0 02.8 218 218.0 03.8 278 278.0 04.9 39 39.0 00.7 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 42.0 00.7 102 102.0 01.8 162 162.0 02.8 222 222.0 03.9 282 282.0 04.9 43 43.0 00.8 103 103.0 01.8 163 163.0 02.8 223 223.0 03.9 283 283.0 04.9 44 44.0 00.8 104 104.0 01.8 164 164.0 02.9 224 224.0 03.9 284 284.0 05.0 45 45.0 00.8 105 105.0 01.8 165 165.0 02.9 225 225.0 03.9 285 285.0 05.0 46 46.0 m.8 106 106.0 01.8 166 166.0 02.9 226 226.0 03.9 280 286.0 05.0 47 47.0 00.8 107 107.0 01.9 167 167.0 02.9 227 227.0 04.0 287 287.0 ' 05.0 48 48.0 00.8 108 108.0 01.9 1()8 168.0 02.9 2-28 228.0 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 51.0 00.9 111 111.0 01.9 171 171.0 03.0 231 231.0 04.0 291 291.0 05.1 52 52.0 00.9 112 112.0 02.0 172 172.0 03.0 232 232.0 04.0 292 292.0 05.1 53 53.0 00.9 113 113.0 02.0 173 173.0 03.0 233 233.0 04.1 293 293.0 05.1 54 54.0 00.9 114 114.0 02.0 174 174.0 03.0 234 234.0 04.1 294 294.0 05.1 55 550 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 04.1 296 296.0 05.2 r 57 57.0 01.0 117 117.0 02.0 177 177.0 03.1 237 237.0 04.1 297 297.0 05 21 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 Dist. 60.0 01.0 120 120.0 02.1 180 180.0 03.1 240 240.0 04.2 300 300.0 05.2 ] Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. | Dist. Dep. , Lat. Dist. I Dep. Lat 1 F..r 89 Dei,'ree*. 5*1 6 Em. 18 TABLE 11. DIFFERENCE OF LATITUDE AND DEPARTURE FOR 2 DEGREES. Oh 8»n. Wat. 1 Lat. Dep. Dist. Lat. Dep. Dist Lat. Dep. Dist Lat Dep. Dist Lat Dep.( 01.0 00.0 61 61.0 02.1 121 120.9 04.2 181 180.9 06.3 241 240.9 08.4 o 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 00.1 63 63.0 02.2 123 122.9 04.3 183 182.9 06.4 243 242.9 08.5 4 04.0 00.1 64 64.0 02.2 124 123.9 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 06.5 246 245.9 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 08.0 00.3 68 68.0 02.4 128 127.9 04.5 188 187.9 06.6 248 247.8 08.7 9 09.0 00.3 69 69.0 02.4 129 128.9 04.5 189 188.9 06.6 249 248.8 08.7 10 10.0 00.3 70 70.0 02.4 130 129.9 04.5 04.6 190 191 189.9 06.6 250 251 249.8 250.8 08.7 08.6 11 11.0 00.4 71 71.0 02.5 131 130.9 190.9 06.7 12 12.0 00.4 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 00.5 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 75.0 02.6 135 134.9 04.7 195 194.9 06.8 255 254.8 08.9 16 16.0 00.6 76 76.0 02.7 136 135.9 04.7 196 195.9 06.8 256 255.8 08.9 17 17.0 00.6 77 77.0 02.7 137 136.9 04.8 197 196.9 06.9 257 256.8 09.0 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 20.0 00.7 80 80.0 02.8 140 139.9 04.9 200 199.9 07.0 260 259.8 09.1 21 21.0 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 82 82.0 02.9 142 141.9 05.0 202 201.9 07.0 262 261.8 09.1 23 23.0 00.8 83 82.9 02.9 143 142.9 05.0 203 202.9 07.1 263 262.8 09.2 24 24.0 00.8 84 83.9 02.9 144 143.9 05.0 204 203.9 07.1 264 263.8 09.2 25 25.0 00.9 85 84.9 03.0 145 144.9 05.1 205 204.9 07.2 265 264.8 09.2 26 26.0 00.9 86 85.9 03.0 146 145.9 05.1 206 205.9 07.2 266 265.8 09.3 27 27.0 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 88 87.9 03.1 148 147.9 05.2 208 207.9 07.3 268 267.8 09.4 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 07.3 270 271 269.8 09.4 31 31.0 01.1 91 90.9 03.2 151 150.9 05.3 211 210.9 07.4 270.8 09.5 32 32.0 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 35.0 01.2 95 94.9 03.3 155 154.9 05.4 215 214.9 07.5 275 274.8 09.6 36 36.0 01.3 96 95.9 03.4 156 155.9 05.4 216 215.9 07.5 276 275.8 09.6 37 37.0 01.3 97 96.9 03.4 157 156.9 05.5 217 216.9 07.6 277 276.8 09.7 38 38.0 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 40.0 01.4 100 99.9 03.5 160 159.9 05.6 220 219.9 07.7 280 279.8 09.8 41 41.0 01.4 101 100.9 03.5 161 160.9 05.6 221 220.9 07.7 281 280.8 09.8 42 42.0 01.5 102 101.9 03.6 162 161.9 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 01.6 105 104.9 03.7 105 164.9 05.8 225 224.9 07.9 285 284.8 09.9 46 46.0 01.6 106 105.9 03.7 166 165.9 05.8 226 225.9 07.9 286 285.8 10.0 47 47.0 01.6 107 106.9 03.7 167 166.9 05.8 227 226.9 07.9 287 286.8 10.0 48 48.0 01.7 108 107.9 03.8 168 167.9 05.9 228 227.9 08.0 288 287.8 10.1 49 49.0 01.7 109 108.9 03.8 169 168.9 05.9 229 228.9 08.0 289 288.8 10.1 50 50.0 01.7 110 109.9 03.8 170 169.9 05.9 230 229.9 08.0 290 289.8 10.1 51 51.0 01.8 111 110.9 03.9 171 170.9 06.0 231 230.9 08.1 291 290.8 10.2 52 52.0 01.8 112 111.9 03.9 172 171.9 06.0 232 231.9 08.1 292 291.8 10.2 53 53.0 01.8 113 112.9 03.9 173 172.9 06.0 233 232.9 08.1 293 292.8 10.2 54 54.0 01.9 114 113.9 04.0 174 173.9 06.1 234 233.9 08.2 294 293.8 10.3 55 55.0 01.9 115 114.9 04.0 175 174.9 06.1 235 234.9 08.2 295 294.8 10.3 56 56.0 02.0 116 115.9 04.0 176 175.9 06.1 236 235.9 08.2 296 295.8 10.3 57 57.0 02.0 117 116.9 04.1 177 176.9 06.2 237 236.9 08.3 297 296.8 10.4 58 58.0 02.0 118 117.9 04.1 178 177.9 06.2 238 237.9 08.3 298 297.8 10.4 59 59.0 02.1 119 118.9 04.2 179 178.9 06.2 239 238.9 08.3 299 298.8 10.4 60 60.0 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. 5^ 62m. | TABLE 11. 19 DIFFERENCE OF LATITUDE AND DEPARTURE FOR 3 DEGREES. Oh 12"». Dial , Lat. Dep. Dist Lat. Dep. Dist. Lat. Dep. Dist Lat Dep. Dist Lat ! Dep. 1 01.0 00.1 61 60.9 03.2 121 120.8 06.3 181 1^0.8 09.5 241 240.7 12.6 2 02.0 00.1 62 61.9 03.2 122 121.8 06.4 1S2 181.8 09.5 242 241.7 12.7 3 03.0 00.2 63 62.9 03.3 123 122.8 06.4 183 182.7 09.6 243 242.7 12.7 4 04.0 00.2 64 63.9 03.3 124 123.8 06.5 184 183.7 09.6, 244 243.7 12.8 5 05.0 00.3 65 64.9 03.4 125 124.8 06.5 185 184.7 09.7 245 244.7 12.8 6 06.0 00.3 66 65.9 03.5 126 125.8 06.6 186 185.7 09.7 246 245.7 12.9 7 07.0 0i».4 67 66.9 03.5 127 126.8 06.6 187 186.7 09.8 247 ' 246.7 12.9 8 08.0 00.4 68 67.9 03.6 128 127.8 06.7 188 187.7 09.8 248 247.7 13.0 9 09.0 00.5 69 68.9 03.6 129 128.8 06.8 189 188.7 09.9 249 248.7 13.0 10 11 10.0 00.5 70 69.9 03.7 130 129.8 06.8 190 189.7 09.9 250 249.7 13.1 11.0 00.6 71 70.9 03.7 131 130.8 06.9 191 190.7 10.0 251 250.7 13.1 12 12.0 00.6 72 71.9 03.8 132 131.8 06.9 192 191.7 10.0 252 251.7 13.2 13 13.0 00.7 73 72.9 03.8 133 132.8 07.0 193 192.7 10.1 253 252.7 13.2 14 14.0 00.7 74 73.9 03.9 134 133.8 07.0 194 193.7 10.2 254 253.7 13.3 15 15.0 00.8 75 74.9 03.9 135 134.8 07.1 195 194.7 10.2 255 254.7 13.3 16 16.0 00.8 76 75.9 04.0 136 135.8 07.1 196 195.7 10.3 256 255.6 13.4 17 17.0 00.9 77 76.9 04.0 137 136.8 07.2 197 196.7 10.3 257 256.6 13.5 18 18.0 00.9 78 77.9 04.1 138 137.8 07.2 198 197.7 10.4 258 257.6 13.5 19 19.0 01.0 79 78.9 04.1 139 138.8 07.3 199 198.7 10.4 259 258.6 13.6 20 20.0 01.0 80 79.9 04.2 140 139.8 07.3 200 199.7 10.5 260 259.6 13.6 21 21.0 01.1 81 80.9 04.2 141 140.8 07.4 201 200.7 10.5 261 260.6 13.7 22 22.0 01.2 82 81.9 04.3 142 141.8 07.4 202 201.7 10.6 262 261,6 13.7 23 23.0 01.2 83 82.9 04.3 143 142.8 07.5 203 202.7 10.6 263 262.6 13.8 24 24.0 01.3 84 83.9 04.4 144 143.8 07.5 204 203.7 10.7 264 263.6 13.8 25 25.0 01.3 85 84.9 04.4 145 144.8 07.6 205 204.7 10.7 265 . 264.6 13.9 26 26.0 01.4 86 85.9 04.5 146 145.8 07.6 206 205.7 10.8 266 265.6 13.9 27 27.0 01.4 87 86.9 04.6 147 146.8 07.7 207 206.7 10.8 267 266.6. 14.n| 28 28.0 01.5 88 87.9 04.6 148 147.8 07.7 208 207.7 10.9 268 267.6 '14.01 29 29.0 01.5 89 88.9 04.7 149 148.8 07.8 209 208.7 10.9 269 268.6 14.1 30 30.0 01.6 90 89.9 04.7 04.8 150 149.8 07.9 210 209.7 11.0 270 269.6 14.1 31 31.0 01.6 91 90.9 151 150.8 07.9 211 210.7 11.0 271 1 270.6 14.2 : 32 32.0 01.7 92 91.9 04.8 152 151.8 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 93.9 04.9 154 153.8 08.1 214 213.7 11.2 274 273.6 14.3 35 35.0 01.8 95 94.9 05.0 155 154.8 08.1 215 214.7 11.3 275 274.6 14.4 36 36.0 01.9 96 95.9 05.0 156 155.8 08.2 216 215.7 11.3 276 275.6 14.4 37 36.9 01.9 97 96.9 05.1 157 156.8 0«.2 217 216.7 11.4 277 276.6 14.5 38 37.9 02.0 98 97.9 05.1 158 157.8 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 99.9 05.2 160 159.8 08.4 220 219.7 11.5 280 279.6 14.7 41 40.9 02.1 101 100.9 05.3 161 160.8 08.4 221 220.7 11.6 281 280.6 14.7 42 41.9 02.2 102 101.9 05.3 162 161.8 08.5 222 221.7 11.6 282 281.6 14.8 43 42.9 02.3 103 102.9 05.4 163 162.8 08.5 223 222.7 11.7 283 282.6 14.8 44 43.9 02.3 104 103.9 05.4 164 163.8 08.6 224 223.7 1 11.7 1 284 283.6 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 02.4 106 105.9 05.5 166 165.8 08.7 226 225.7 11.8 286 285.6 15.0 47 46.9 02.5 107 106.9 05.6 167 166.8 08.7 227 226.7 11.9 287 286.6 15.0 48 47.9 02.5 108 107.9 05.7 168 167.8 08.8 2-28 227.7 11.9 288 287.6 15.1 49 48.9 02.6 109 108.9 05.7 169 168.8 08.8 22!) 228.7 12.0 289 288.6 15.1 50 51 49.9 02.6 110 109.8 05.8 170 169.8 08.9 230 229.7 12.0 290 289.6 15.2 50.9 02.7 111 110.8 05.8 171 170.8 08.9 231 230.7 12.1 291 290.6 15.2 52 51.9 02.7 112 111.8 05.9 172 171.8 09.0 232 231.7 12.1 292 291.6 15.3 53 52.9 02.8 113 112.8 05.9 173 172.8 09.1 233 232.7 12.2 293 292.6 15.3 1 54 53.9 02.8 114 113.8 06.0 174 173.8 09.1 234 233.7 12.2 294 293.6 15.4 55 54.9 02.9 115 114.8 06.0 175 174.8 09.2 235 234.7 12.3 295 294.6 15.4 56 55.9 02.9 116 115.8 06.1 176 175.8 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 Ov^.3 237 236.7 12.4 297 296.6 15.5 58 57.9 03.0 118 117.8 06.2 178 177.8 09.3 238 237.7 12.5 298 297.6 15.6 59 58.9 03.1 119 118.8 06.2 179 178.8 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 1 299.6 15.7 ] 3i8t Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist Dep. 1 Lat 1 ^^^ Fiif 87 Detrrt'es. ^^> J-Sm 1 20 TABLE 11. 1 DIFFERENCE OF LATITUDE AND DEPARTURE FOR 4 DEGREES. Oh 16" t Diat. Lat. Dep. Dist. Lat. Dep. Dist. LaU Dep. Dist. LaL Dep. Dist. Lat Dep 16.8 1 01.0 00.1 61 60.9 04.3 121 120.7 08.4 181 180.6 12.6 241 240.4 2 02.0 00.1 62 61.8 04.3 122 121.7 08.5 182 181.6 12.7 242 241.4 16.9 3 03.0 00.2 63 62.8 04.4 123 122.7 08.6 183 182.6 12.8 243 242.4 17.0 4 04.0 00.3 64 63.8 04.5 124 123.7 08.6 184 183.6 12.8 244 243.4 17.0 5 05.0 00.3 65 64.8 04.5 125 124.7 08.7 185 184.5 12.9 245 244.4 17.1 6 06.0 00.4 66 65.8 04.6 126 125.7 08.8 186 185.5 13.0 246 245.4 17.2 7 07.0 00.5 67 66.8 04.7 127 126.7 08.9 187 186.5 13.0 247 246.4 17.2 8 08.0 00.6 68 67.8 04.7 128 127.7 08.9 188 187.5 13.1 248 247.4 17.3 9 09.0 00.6 69 68.8 04.8 129 128.7 09.0 189 188.5 13.2 249 248.4 17.4 10 10.0 00.7 70 69.8 04.9 130 129.7 09.1 190 191 189.5 13.3 250 249.4 17.4 17.5 11 11.0 00.8 71 70.8 05.0 131 130.7 09.1 190.5 13.3 251 250.4 12 12.0 00.8 72 71.8 05.0 132 131.7 09.2 192 191.5 13.4 252 251.4 17.6 13 13.0 00.9 73 72.8 05.1 133 132.7 09.3 193 192.5 13.5 253 252.4 17.6 14 14.0 01.0 74 73.8 05.2 134 133.7 09.3 194 193.5 13.5 254 253.4 17.7 15 15.0 01.0 75 74.8 05.2 135 134.7 09.4 195 194.5 13.6 255 254.4 17.8 16 16.0 01.1 76 75.8 05.3 136 135.7 09.5 196 195.5 13.7 256 255.4 17.9 17 17.0 01.2 77 76.8 05.4 137 136.7 09.6 197 196.5 13.7 257 256.4 17.9 18 18.0 01.3 78 77.8 05.4 138 137.7 09.6 198 197.5 13.8 258 257.4 18.0 19 19.0 01.3 79 78.8 05.5 139 138.7 09.7 199 198.5 13.9 259 258.4 18.1 20 21 20.0 01.4 80 79.8 05.6 140 139.7 09.8 200 199.5 14.0 260 259.4 18.1 18.2 20.9 01.5 81 80.8 05.7 141 140.7 09.8 201 200.5 14.0 261 260.4 22 21.9 01.5 82 81.8 05.7 142 141.7 09.9 202 201.5 14.1 262 261.4 18.3 23 22.9 01.6 83 82.8 05.8 143 142.7 10.0 203 202.5 14.2 263 262.4 18.3 24 23.9 01.7 84 83.8 05.9 144 143.6 10.0 204 203.5 14.2 264 263.4 18.4 25 24.9 01.7 85 84.8 05.9 145 144.6 10.1 205 204.5 14.3 265 264.4 18.5 26 25.9 01.8 86 85.8 06.0 146 145.6 10.2 206 205.5 14.4 266 265.4 18.6 27 26.9 01.9 87 86.8 06.1 147 146.6 10.3 207 206.5 14.4 267 266.3 18.6 28 27.9 02.0 88 87.8 06.1 148 147.6 10.3 208 207.5 14.5 268 267.3 18.7 29 28.9 02.0 89 88.8 06.2 149 148.6 10.4 209 208.5 14.6 269 268.3 18.8 30 31 29.9 02.1 90 89.8 06.3 150 151 149.6 10.5 210 209.5 14.6 270 269.3 18.8 30.9 02.2 91 90.8 06.3 150.6 10.5 211 210.5 14.7 271 270.3 18.9 32 31.9 02.2 92 91.8 06.4 152 151.6 10.6 212 211.5 14.8 272 271.3 19.0 33 32.9 02.3 93 92.8 06.5 153 152.6 10.7 213 212.5 14.9 273 272.3 19.0 34 33.9 02.4 94 93.8 06.6 154 153.6 10.7 214 213.5 14.9 274 273.3 19.1 35 34.9 02.4 95 94.8 06.6 155 154.6 10.8 215 214.5 15.0 275 274.3 19.2 36 35.9 02.5 96 95.8 06.7 156 155.6 10.9 216 215.5 15.1 276 275.3 19.3 37 36.9 02.6 97 96.8 06.8 157 156.6 11.0 217 216.5 15.1 277 276.3 19.3 38 37.9 02.7 98 97.8 06.8 158 157.6 11.0 218 217.5 15.2 278 277.3 19.4 39 38.9 02.7 99 98.8 06.9 159 158.6 11.1 219 218.5 15.3 279 278.3 19.5 40 39.9 02.8 100 99.8 07.0 160 159.6 11.2 220 219.5 15.3 280 279.3 19.5 41 40.9 02.9 101 100.8 07.0 161 160.6 11.2 221 220.5 15.4 281 280.3 19.6 42 41.9 02.9 102 101.8 07.1 162 161.6 11.3 222 221.5 15.5 282 281.3 19.7 43 42.9 03.0 103 102.7 07.2 163 162.6 11.4 223 222.5 15.6 283 282.3 19.7 44 43.9 03.1 104 103.7 07.3 164 163.6 11.4 224 223.5 15.6 284 283.3 19.8 45 449 03.1 105 104.7 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 11.6 226 225.4 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 47.9 03.3 108 107.7 07.5 168 167.6 11.7 226 227.4 15.9 288 287.3 20.1 49 48.9 03.4 109 108.7 07.6 169 168.6 11.8 229 228.4 16.0 289 288.3 20.2 50 49.9 03.5 110 109.7 07.7 170 169.6 11.9 230 229.4 16.0 290 289.3 20.2 51 50.9 03.6 111 110.7 07.7 171 170.6 11.9 231 230.4 16.1 291 290.3 20.3 52 51.9 03.6 112 111.7 07.8 172 171.6 12.0 232 231.4 16.2 292 291.3 20.4 53 52.9 03.7 113 112.7 07.9 173 172.6 12.1 233 232.4 16.3 293 292.3 20.4 54 53.9 03.8 114 113.7 08.0 174 173.6 12.1 234 233.4 16.3 294 293.3 20.5 55 54.9 03.8 115 114.7 08.0 175 174.6 12.2 235 234.4 16.4 295 294.3 20.6 56 55.9 03.9 116 115.7 08.1 176 175.6 12.3 236 235.4 16.5 296 295.3 20.6 57 56.9 04.0 117 116.7 08.2 177 176.6 12.3 237 236.4 16.5 297 296.3 20.7 58 57.9 04.0 118 117.7; 08.2 178 177.6 12.4 238 237.4 16.6 298 297.3 20.8 59 58.9 04.1 119 118.7 08.3 179 178.6 12.5 239 238.4 16.7 299 298.3 20.9 60 59.9 04.2 120 119.7 08.4 180 179.6 12.6 240 239.4 16.7 300 299.3 20.9 Hint Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. LaL Dist. Dep. Lat. For 86 Decrees. 6h 44m. 1 TABLE U. .. 1 DIFFERENCE OF LATITUDE AND DEPARTURE FOR 5 DE(}REES. Oh 20ni. Diet. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 01.0 00.1 61 60.8 05.3 121 120.5 10.5 181 INO.3 15.8 241 240.1 '21.0 2 02.0 00.2 62 61.8 05.4 122 121.5 10.6 182 181.3 15.9 242 241.1 21.1 3 03.0 00.3 ()3 62.8 05.5 123 122.5 10.7 183 182.3 15.9 243 242.1 |21.2 4 04.0 00.3 64 63.8 05.6 124 123.5 10.8 184 183.3 16.0 244 243.1 21.3 5 05.0 00.4 ()5 64.8 05.7 125 124.5 10.9 185 184.3 16.1 245 244.1 21.4 6 06.0 00.5 66 65.7 05.8 126 125.5 11.0 186 185.3 16.2 246 245.1 21.4 7 07.0 00.6 67 66.7 05.8 127 126.5 11,1 1S7 186.3 16.3 247 246. 1 21.5 8 08.0 00.7 68 67.7 05.9 128 127.5 1L2 188 187.3 16.4 248 247.1 21.6 9 09.0 00.8 69 68.7 06.0 120 128.5 11.2 189 188.3 16.5 249 248.1 21.7 10 11 10.0 00.9 70 69.7 06.1 06.2 1 :{0 129.5 11.3 190 189.3 16.6 250 249.0 21.8 11.0 01.0 71 70.7 131 130.5 11.4 191 190.3 16.6 251 ] 250.01 21.91 12 1 ; li i2.C^^l..0 72 71.7 06.3 132 131.5 11.5 192 1913 16.7 252 251.0 22.0 13.0 01.1 73 72.7 06.4 133 132.5 11.6 193 192.3 16.8 253 252.0 22.1 139 01.2 74 73.7 06.4 134 133.5 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 1963 17.2 257 256.0 22.4 18 17.9 01.6 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 n.3 259 258.0 22.6 20 19.9 01.7 80 79.7 07.0 07.1 140 139.5 12.2 200 199.2 XY.4 260 259.0 22.7 21 20.9 01.8 81 80.7 141 140.5 12.3 201 200.2 17.5 261 260.0 22.7 22 21.9 01.9 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 17.9 265 264.0 231 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 12.8 207 206.2 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= 13 209 208.2 18.2 269 268.0 , 23.4 1 30 29.9 02.6 90 89.7 07.8 07.9 150 151 149.4 13.1 210 209.2 18.3 270 ■ 269.0 , 23.5 \ 31 30.9 02.7 91 90.7 150.4 13.2 211 210.2 18.4 271 270.0 ' 23.6 32 31.9 02.8 92 91.6 08.0 152 151.4 13.2 212 211.2 18.5 272 271.0 23.7 33 32.9 02.9 93 92.6 08.1 153 152.4 13.3 213 212.2 18.6 273 272.0 23.8 34 33.9 03.0 94 93.6 08.2 154 1.53.4 13.4 214 213.2 18.7 274 273.0 23.9 35 34.9 03.1 95 94.6 08.3 155 154.4 13.5 215 214.2 18.7 275 274.0 24.0 36 35.9 03.1 96 95.6 08.4 156 155.4 13.6 216 215.2 18.8 276 274.9 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 19.0 278 278.9 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 99.6 08.7 160 159.4 13.9 220 219.2 19.2 280 278.9 24.4 41 40.8 03.6 101 100.6 08.8 161 160.4 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 42.8 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 03.8 104 103.6 09.1 164 163.4 14.3 224 223.1 19.5 284 282.9 24.8 45 44.8 03.9 105 104.6 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 1654 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 14.6 227 220.1 19.8 287 285.9 25.0 48 47.8 04,2 108 107.6 09.4 168 167.4 14.6 228 227.1 19.9 288 286.9 25.1 49 48.8 04.3 109 108.6 09.5 169 168.4 14.7 229 228.1 20.0 289 287.9 25.2 50 49.8 04.4 110 109.6 09.6 170 169.4 14.8 230 229.1 20.0 290 288.9 25.3 51 50.8 044 111 110.6 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 25.4 1 53 52. S 04.6 113 112.6 09.8 173 172.3 15.1 233 232.1 20.3 293 291.9 25.5 1 54 53.8 04.7 114 113.6 09.9 174 173.3 15.2 234 23.3.1 20.4 294 292.9 25.6 55 54.8 04.8 115 114.6 10.0 175 174.3 15.3 235 234.1 20.5 295 293.9 25.7 5t) 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 05.1 118 117.6 10.3 178 177.3 15.5 238 237.1 20.7 298 296.9 26.0 59 58. s 05.1 119 118.5 10.4 179 178.3 15.6 239 238.1 20.8 29^ 297.9 26.1 60 Dist. 59.8 05.2 120 119.5 10.5 180 179.3 15.7 240 239.1 20.9 300 298.9 26.1 Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat Dist. Dep. Lat For 85 Deijrees. 6fi 40". 1 22 ' TABLE II. DIFFERENCE OF LATITUDE AND DEPARTURE FOR 6 DEGREES. Oh 24m. DiBt Lat. Dep. Dist. Lat Dep. Dist Lat Dep. Dist Lat Dep. Diet Lat Dep.» 1 01.0 00.1 61 60.7 06.4 121 120.3 12.6 181 180.0 18.9 241 239.7 25.2 2 02.0 00.2 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 62.7 06.6 123 122.3 12.9 183 182.0 19.1 243 241.7 25.4 4 04.0 00.4 64 63.6 06.7 124 123.3 13.0 184 183.0 19.2 244 242.7 25.5 5 05.0 00.5 65 64.6 06.8 125 124.3 13.1 185 184.0 19.3 245 243.7 25.6 6 06.0 00.6 66 65.6 06.9 126 125.3 13.2 186 185.0 19.4 246 244.7 25.7 7 07.0 00.7 67 66.6 07.0 127 126.3 13.3 187 186.0 19.5 247 245.6 25.8 8 08.0 00.8 68 67.6 07.1 128 127.3 13.4 188 187.0 19.7 248 246.6 25.9 9 09.0 00.9 69 68.6 07.2 129 128.3 13.5 189 188.0 19.8 249 247.6 26.0 10 09.9 01.0 70 69.6 07.3 130 129.3 13.6 13.7 190 191 189.0 19.9 250 251 248.6 249.6 26.1 26.2 11 10.9 01.1 71 70.6 07.4 131 130.3 190.0 20.0 12 11.9 01.3 72 71.6 07.5 132 131.3 13.8 192 190.9 20.1 252 250.6 26.3 13 12.9 01.4 73 72.6 07.6 133 132.3 13.9 193 191.9 20.2 253 251.6 26.4 14 13.9 01.5 74 73.6 07.7 134 133.3 14.0 194 192.9 20.3 254 252.6 26.6 15 14.9 01.6 75 74.6 07.8 135 134.3 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 76.6 08.0 137 136.2 14.3 197 195.9 20.6 257 255.6 26.9 18 17.9 01.9 78 77.6 08.2 138 137.2 14.4 198 196.9 20.7 258 256.6 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 02.1 80 79.6 08.4 140 139.2 14.6 200 198.9 20.9 260 258.6 27.2 27.3 21 20.9 02.2 81 80.6 08.5 141 140.2 14.7 201 199.9 21.0 261 259.6 22 21.9 02.3 82 81.6 08.6 142 141.2 14.8 202 200.9 21.1 262 260.6 27.4 23 22.9 02.4 83 82.5 08.7 143 142.2 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 84.5 08.9 145 144.2 15.2 205 203.9 21.4 265 263.5 27.7 26 25.9 02.7 86 85.5 09.0 146 145.2 15.3 206 204.9 21.5 266 264.5 27.8 27 26.9 02.8 87 86.5 09.1 147 146.2 15.4 207 205.9 21.6 267 265.5 27.9 28 27.8 02.9 88 87.5 09.2 148 147.2 15.5 208 206.9 21.7 268 266.5 28.0 29 28.8 03.0 89 88.5 09.3 149 148.2 15.6 209 207.9 21.8 269 267.5 28.1 30 31 29.8 03.1 90 89.5 09.4 150 149.2 15.7 210 208.8 22.0 270 268.5 28.2 30.8 03.2 91 90.5 09.5 151 150.2 15.8 211 209.8 22.1 271 269.5 28.3 32 31.8 03.3 92 91.5 09.6 152 151.2 15.9 212 210.8 22.2 272 270.5 28.4 33 32.8 03.4 93 92.5 09.7 153 152.2 16.0 213 211.8 22.3 273 271.5 •28.5 34 33.8 03.6 94 93.5 09.8 154 153.2 16.1 214 212.8 22.4 274 272.5 28.6 35 34.8 03.7 95 94.5 09.9 155 154.2 16.2 215 213.8 22.5 275 273.5 28.7 36 35.8 03.8 96 95.5 10.0 156 155.1 16.3 216 214.8 22.6 276 274.5 28.8 37 36.8 03.9 97 96.5 10.1 157 156.1 16.4 217 215.8 22.7 277 275.5 29.0 38 37.8 04.0 98 97.5 10.2 158 157.1 16.5 218 216.8 22.8 278 276.5 29.1 39 38.8 04.1 99 98.5 10.3 159 158.1 16.6 219 217.8 22.9 279 277.5 29.2 40 39.8 04.2 100 99.5 10.5 160 159.1 16.7 220 218.8 23.0 280 278.5 29.3 41 40.8 04.3 101 100.4 10.6 161 160.1 16.8 221 219.8 23.1 281 279.5 29.4 42 41.8 04.4 102 101.4 10.7 162 161.1 16.9 222 220.8 23.2 282 280.5 29.5 43 42.8 04.5 103 102.4 10.8 163 162.1 17.0 223 221.8 23.3 283 281.4 29.6 14 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 44.8 04.7 105 104.4 11.0 165 164.1 17.2 225 223.8 23.5 285 283.4 29.8 4t3 45.7 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 04.9 107 106.4 11.2 167 166.1 17.5 227 225.8 23.7 287 285.4 30.0 46 47.7 05.0 108 107.4 11.3 168 167.1 17.t; 228 226.8 23.8 288 286.4 30.1 49 48.7 05.1 109 108.4 11.4 169 168.1 17.7 229 227.8 23.9 289 287.4 30.2 50 49.7 05.2 110 109.4 11.5 170 169.1 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 24.1 291 289,4 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 05.5 113 112.4 11.8 173 172.1 18.1 233 231.7 24.4 293 291.4 30.6 54 53.7 05.6 114 113.4 11.9 174 173.0 18.2 234 232.7 24.5 294 292.4 30.7 55 54.7 05.7 115 114.4 12.0 175 174.0 18.3 2.S5 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 06.0 117 110.4 12.2 177 176.0 18.5 237 235.7 24.8 297 295.4 31.0 58 57.7 06.1 118 117.4 12.3 178 177.0 18.6 238 236.7 24.9 298 296.4 31.1 59 58.7 06.2 119 118.3 12.4 179 178.0 18.7 239 237.7 2.').0 299 297.4 31.3 60 59,7 06.3 120 119.3 12.5 180 179.0 18.8 240 238.7 25.1 300 298.4 31.4 Lat Dist . Dep. Lat. Dist. Dep. Lat Dist. Dep. Lat Dist Dep. • Lat. Dist Dep. For 84 Df-moes, 5^^ S6m. | TABLE n. .3 DIFFERENCE OF LATITUDE AND DEPARTURE FOR 7 DEGREES. Oh 28m. 1 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 00.2 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 04.0 00.5 64 63.5 07.8 124 123.1 15.1 184 182.6 22.4 244 242.2 29.7 5 05.0 00.6 65 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 30.0 1 7 06.9 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 01.0 68 67.5 08.3 128 127.0 15.6 188 186.6 22.9 248 246.2 30.2 9 08.9 01.1 69 68.5 08.4 129 128.0 15.7 189 187.6 23.0 249 247.1 30.3 10 11 09.9 01.2 70 69.5 08.5 130 129.0 15.8 190 188.6 23.2 250 248.1 30.5 10.9 01.3 71 70.5 08.7 131 130.0 16.0 191 189.6 23.3 251 249.1 30.6 12 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 01.6 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 16 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 16.9 02.1 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 78 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 31.6 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 21 20.8 02.6 81 80.4 09.9 141 139.9 17.2 201 199.5 24.5 261 259.] 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 1 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 84 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 26 25.8 03.2 86 85.4 10.5 146 144.9 17.8 206 204.5 25.1 266 264.0 32.4 27 26.8 03.3 87 86.4 10.6 147 145.9 17.9 207 205.5 25.2 267 265.0 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 25.5 269 267.0 32.8 30 29.8 03.7 90 89.3 11.0 11.1 150 148.9 18.3 210 208.4 25.6 270 268.0 32.9 31 30.8 03.8 91 90.3 151 149.9 18.4 211 209.4 25.7 271 269.0 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 34 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 36 35.7 04.4 96 95.3 11.7 156 154.8 19.0 216 214.4 26.3 276 273.9 33.6 37 36.7 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 26.6 278 275.9 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 40.7 05.0 101 100.2 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 44 43.7 05.4 104 103.2 12.7 164 162.8 20.0 224 222.3 27.3 284 281.9 34.6 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 46 45.7 05.6 10() 105.2 12.9 166 164.8 20.2 226 224.3 27.5 286 283.9 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 48 47.6 05.8 108 107.2 13.2 168 166.7 20.5 228 226.3 27.8 288 285.9 35.1 49 48.6 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 51 50.6 06.2 111 110.2 13.5 171 159.7 20.8 231 229.3 28.2 291 288.8 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 , 85.6 1 53 52.6 06.5 113 112.9 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 36.0 5() 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 60 Dist 59.6 Dep. 07.3 120 119.1 14.6 180 178.7 21.9 240 238.2 29.2 300 297.8 36.6 Lat. Dist. Dop. Lat. Dist Dep. Lnt. Dist Dep. Lat Dist Dep. Lat F(ir S3 De".>-ii<-es. 5'' 32'". 1 24 TABLE 11. DIFFERENCE OF T-ATITUDE AND DEPARTURE FOR 8 DEGREES. ' Ob 32">. Diat Lat Pep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 33.5 1 01.0 00.1 61 60.4 08.5 121 119.8 16.8 181 179.2 25.2 241 23S.7 2 02.0 00.3 62 61.4 08.6 122 120.8 17.0 182 180.2 25.3 242 239.6 33.7 3 03.0 00.4 63 62.4 08.8 123 121.8 17.1 183 181.2 25.5 243 240.6 33.8 4 04.01 00.6 64 63.4 08.9 124 122.8 17.3 184 182.2 25.6 244 241.6 34 5 05.0 00.7 1 65 64.4 09.0 125 123.8 17.4 185 183.2 25.7 245 242.6 34 1 6 05.9 00.81 66 65.4 09.2 126 124.8 17.5 186 184.2 25.9 246 243.6 34.2 7 06.9 01.0 67 66.3 09.3 127 125.8 17.7 187 185.2 26.0 247 244.6 34.4 8 07.9 01.1 68 67.3 09.5 128 126.8 17.8 188 186.2 26.2 248 245.6 34.5 9 08.9 01.3 69 68.3 09.6 129 127.7 18.0 189 187.2 26.3 249 246.6 34 7 10 11 09.9 01.4 70 69.3 09.7 130 128.7 18.1 190 188.2 26.4 250 247.6 34.8 34.9 10.9 01.5 71 70.3 09.9 131 129.7 18.2 191 189.1 26.6 251 248.6 12 11.9 01.7 72 71.3 10.0 132 130.7 18.4 192 190.1 26.7 252 249.5 35.1 13 12.9 01.8 73 72.3 10.2 133 131.7 18.5 193 191.1 26.9 253 250.5 35.2 W 13.9 01.9 74 73.3 10.3 134 132.7 18.6 194 192.1 27.0 254 251.5 35.3 15 14.9 02.1 75 74.3 10.4 135 133.7 18.8 195 193.1 27.1 255 252.5 35.5 16 15.8 02.2 76 75.3 10.6 136 134.7 18.9 196 194.1 27.3 256 253.5 35.6 17 16.8 02.4 77 76.3 10.7 137 135.7 19.1 197 195.1 27.4 257 254.5 35.8 IS 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 18.8 02.6 79 78.2 11.0 139 137.7 19.3 199 197.1 27.7 259 256.5 36.0 20 19.8 02.8 80 79.2 11.1 140 138.6 19.5 200 198.1 27.8 260 257.5 36.2 21 20.8 02.9 81 80.2 11.3 141 139.6 19.6 201 199.0 28.0 261 258.5 36.3 22 21.8 03.1 82 81.2 11.4 i42 140.6 19.8 202 200.0 28.1 262 259.5 36.5 23 22.8 03.2 83 82.2 11.6 143 141.6 19.9 203 201.0 28.3 263 260.4 36.6 24 23.8 03.3 84 83.2 11.7 144 142.6 20.0 204 202.0 28.4 264 261.4 36.7 25 24.8 03.5 85 84.2 11.8 145 143.6 20.2 205 203.0 28.5 265 262.4 36.9 26 25.7 03.6 86 85.2 12.0 146 144.6 20.3 206 204.0 28.7 266 263.4 37.0 27 26.7 03.8 87 86.2 12.1 147 145.6 20.5 207 205.0 28.8 267 264.4 37.2 28 27.7 03.9 88 87.1 12.2 148 146.6 20.6 208 206.0 28.9 268 265.4 37.3 29 28.7 04.0 89 88.1 12.4 149 147.5 20.7 209 207.0 29.1 269 266.4 37.4 30 31 29.7 04.2 90 89.1 12.5 150 148.5 20.9 210 208.0 29.2 270 267.4 37.6 30.7 04.3 91 90.1 12.7 151 149.5 21.0 211 208.9 29.4 271 268.4 37.7 32 31.7 04.5 92 91.1 12.8 152 150.5 21.2 212 209.9 29.5 272 269.4 37.9 33 32.7 04.6 93 92.1 12.9 153 151.5 21.3 213 210.9 29.6 273 270.3 38.0 34 33.7 04.7 94 93.1 13.1 154 152.5 21.4 214 211.9 29.8 274 271.3 38.1 35 34.7 04.9 95 94.1 13.2 155 153.5 21.6 215 212.9 29.9 275 272.3 ■ 38.3 36 35.6. 05.0 96 95.1 13.4 156 154.5 21.7 216 213.9 30.1 276 273.3 38 4 37 36.6 05.1 97 96.1 13.5 157 155.5 21.9 217 214.9 30.2 277 274.3 38.6 : 38 37.6 05.3 98 97.0 13.6 158 156.5 22.0 218 215.9 30.3 278 275.3 38.7 39 38.6 05.4 99 98.0 13.8 159 157.5 22.1 219 216.9 30.5 279 276.3 3S.8 40 41 39.6 05.6 100 99.0 13.9 160 158.4 22.3 220 221 217.9 30.6 280 277.3 39.0 40.6 05.7 101 100.0 14.1 161 159.4 22.4 218.8 30.8 281 278.3 39.1 42 41.6 05.8 102 101.0 14.2 162 160.4 22.5 222 219.8 30.9 282 279.3 39.2 43 42.6 06.0 103 102.0 14.3 163 161.4 22.7 223 220.8 31.0 283 280.2 39.4 44 43.6 06.1 104 103.0 14.5 164 162.4 22.8 224 221.8 31.2 284 281.2 39.5 45 44.6 06.3 105 104.0 14.6 165 163.4 23.0 225 222.8 31.3 285 282.2 39.7 46 45.6 06.4 106 105.0 14.8 166 164.4 23.1 226 223.8 31.5 286 283.2 39.8 47 46.5 06.5 107 106.0 14.9 167 165.4 23.2 227 224.8 31.6 287 284.2 39.9 48 47.5 06.7 108 106.9 15.0 168 166.4 23.4 228 225.8 31.7 288 285.2 40.1 49 48.5 06.8 109 107.9 15.2 169 167.4 23.5 229 226.8 31.9 289 286.2 40.2 50 51 49.5 07.0 110 108.9 15.3 170 168.3 23.7 230 227.8 32.0 290 287.2 40.4 40.5 50.5 07. ^ 111 109.9 15.4 171 169.3 23.8 231 228.8 32.1 291 288.2 52 51.5 07.2 112 110.9 15.6 172 170.3 23.9 232 229.7 32.3 292 289.2 40.6 53 52.5 07.4 113 111.9 15.7 173 171.3 24.1 233 230.7 32.4 293 290.1 40.8 54 53.5 07.5 114 112.9 15.9 174 172.3 24.2 234 231.7 32.6 294 291.1 40.9 55 54.5 07.7 115 113.9 16.0 175 173.3 24.4 235 232.7 32.7 295 292.1 41.1 56 55.5 07,8 116 114.9 16.1 176 174.3 24.5 236 233.7 32.8 296 293.1 41.2 57 56.4 07.9 117 115.9 16.3 177 175.3 24.6 237 234.7 33.0 297 294.1 41.3 58 57.4 08.1 118 116.9 16.4 178 176.3 24.8 238 235.7 33.1 298 295.1 41.5 59 58.4 08.2 119 117.8 16.6 179 177.3 24.9 239 236.7 33.3 299 296.1 41.6 60 Disi 59.4 08.4 120 118.8 16.7 Lat. 180 Dist. 178.3 25.1 240 237.7 33.4 300 297.1 41.8 Lat, . Dep. Lat. Dist. Dep. Dep. Lat. Dist. Dep. Lat. Dist. Dep. For 82 Degrees. 5h 28™. | TABLE 11. 26 DIFFERENCE OF LATITUDE AND DEPARTURE FOR 9 DEGREES. Oh SBm. Dist 1 Lat Dep. Dist. Lat Dep. Dist. Lat Dep. Dist. Lat Dep. Dist Lat Dep. 01.0 00.2 61 60.2 09.5 121 119.5 18.9 181 178.8 28.3 241 238.0 37.7 •) 02.0 00.3 62 61.2 09.7 122 120.5 19.1 182 179.8 28.5 242 239.0 37.9 o 03.0 00.5 63 62.2 09.9 123 121.5 19.2 183 180.7 28.6 243 240.0 38.0 4 04.0 00.6 64 63.2 10.0 124 122.5 19.4 184 181.7 28.8 244 241.0 38.2 5 04.9 00.8 65 64.2 10.2 125 123.5 19.6 185 182.7 28.9 245 242.0 38.3 6 05.9 00.9 66 65.2 10.3 126 124.4 19.7 186 183.7 39.1 246 243.0 38.5 / 06.9 01.1 67 66.2 10.5 127 125.4 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 68.2 10.8 129 127.4 20.2 189 186.7 29.6 249 245.9 39.0 10 09.9 01.6 70 71 69.1 11.0 130 128.4 20.3 190 187.7 29.7 250 246.9 247.9 39.1 39.3 11 10.9 01.7 70.1 11.1 131 129.4 20.5 191 188.6 29.9 251 12 11.9 01.9 72 71.1 11.3 132 130.4 20.6 192 189.6 30.0 252 248.9 39.4 13 12.8 02.0 73 72.1 11.4 133 131.4 20.8 193 190.6 30.2 253 249.9 39.6 14 13.8 02.2 74 73.1 11.6 134 132.4 21.0 194 191.6 30.3 254 250.9 39.7 15 14.8 02.3 75 74.1 11.7 135 133.3 21.1 195 192.6 30.5 255 251.9 39.9 U) 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 76.1 12.0 137 135.3 21.4 197 194.6 30.8 257 253.8 40.2 18 17.8 0-2.8 78 77.0 12.2 138 136.3 21.6 198 195.6 31.0 258 254.8 40.4 19 1S.8 03.0 79 78.0 12.4 139 137.3 21.7 199 196.5 31.1 259 255.8 40.5 20 2i 19.8 03.1 80 79.0 12.5 140 138.3 21.9 200 197.5 31.3 260 256.8 257.8 40.7 40.8 20.7 03.3 81 80.0 12.7 141 139.3 22.1 201 198.5 31.4 261 22 21.7 03.4 82 81.0 12.8 142 140.3 22.2 202 199.5 31.6 262 2.58.8 41.0 23 22.7 03.6 83 82.0 13.0 143 141.2 22.4 203 200.5 31.8 263 259.8 41.1 24 23.7 03.S 84 83.0 13.1 144 142.2 22.5 204 201.5 319 264 260.7 41.3 25 24.7 03.9 85 84.0 13.3 145 143.2 22.7 205 202.5 32.1 265 261.7 41.5 26 25.7 04.1 86 84.9 13.5 146 144.2 22.8 206 203.5 32.2 266 262.7 41.6 27 26.7 04.2 87 85.9 13.6 147 145.2 23.0 207 204.5 32.4 267 263.7 41.8 28 27.7 04.4 88 86.9 13.8 .148 146.2 23.2 208 205.4 32.5 268 264.7 41.9 29 28.6 04.5 89 87.9 13.9 149 147.2 23.3 209 206.4 32.7 269 265.7 42.1 30 31 29.6 04.7 90 88.9 14.1 150 148.2 23.5 210 211 207.4 32.9 270 271 266.7 42.2 30.6 04.8 91 89.9 14.2 151 149.1 23.6 208.4 33.0 267.7 42.4 32 31.6 05.0 92 90.9 14.4 152 150.1 23.8 212 209.4 33.2 272 268.7 42.6 33 32.6 05.2 93 91.9 14.5 153 151.1 23.9 213 210.4 33.3 273 269.6 42.7 34 33.6 05.3 94 92.8 14.7 154 152.1 24.1 214 211.4 33.5 274 270.6 42.9 35 34.6 05.5 95 93.8 14.9 155 153.1 24.2 215 212.4 33.6 275 271.6 43.0 3(3 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 96.8 15.3 158 156.1 24.7 218 215.3 34.1 278 274.6 43.5 39 38.5 06.1 99 97.8 15.5 159 157.0 24.9 219 216.3 34.3 279 275.6 43.6 40 39.5 06.3 100 , 98.8 15.6 160 158.0 250 220 217.3 34.4 280 276.6 43.8 41 40.5 06.4 101 99.8 15.8 161 159.0 25.2 221 218.3 34.6 281 277.5 44.0 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 1().3 1()4 162.0 25.7 224 221.2 35.0 284 280.5 44.4 45 44.4 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 1()9 166.9 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 50.4 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 26.9 232 229.1 36.3 292 288.4 45.7 53 52.3 08.3 113 111.6 17.7 173 170.9 27.1 233 230.1 36.4 293 289.4 ' 45.8 54 53.3 08.4 114 112.6 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 37.1 297 293.3 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 0'.>.2 119 117.5 18.6 179 176.8 28.0 239 236.1 37.4 299 295.3 46.8 60 59.3 09.4 120 118.5 18.8 Lat. 180 177.8 28.2 240 237.0 37.5 300 296.3 46.9 Di8t. Dep. Lat. Dist.' Dep. Dist. Dep. Lat. Dist. Dep. Lat Dist Dep. Lat For 81 Decrees. 6^ 24m. | 26 TABLE II. DIFFERENCE OF LATITUDE AND DEPARTURE FOR 10 DEGREES. 0^ 40m. J DisL Lat. De£^ Dist, Lat. Dep. Dist Lat. Dep. Dist. Lat. Dep. Dist. Lat. 1 Dep. | 1 01.0 00.2 61 60.1 10.6 121 119.2 21.0 181 178.3 31.4 241 237 3 41.81 2 02.0 00.3 62 61.1 10.8 122 120.1 21.2 1^2 i^9.2 31.6 242 238.3 42.0 1 3 03.0 00.5 63 62.0 10.9 123 121.1 21.4 183 180.2 31.8 2431239.3 42.2 4 03.9 00.7 64 63.0 11.1 124 122.1 21.5 184 181.2 32.0 244 240.3 i2.4 5 04.9 00.9 65 64.0 11.3 125 123.1 21.7 185 182.2 32.1 245 241.3142.5 " 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 32.5 247 243.2 142.9 : 8 07.9 01.4 68 67.0 11.8 128 126.1 22.2 188 185.1 32.6 1 248 244.2; 43.1 9 08.9 01.6 69 68.0 12.0 129 127.0 22.4 189 186.1 32.8 249 245.2 43.2 10 11 09.8 01.7 70 68.9 12.2 130 128.0 22.6 190 187.1 33.0 250 246.2 43.4 10.8 01.9 71 69.9 12.3 131 129.0 22.7 191 188.1 33.2 251 247.2 43.0 12 11.8 02.1 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 23.3 194 191.1 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 34.2 257 253.1144.6 18 17.7 03.1 78 76.8 13.5 138 135.9 24.0 198 195.0 34.4 258 254.1 44.8 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 03.6 80 78.8 13.9 140 137.9 24.3 200 197.0 34.7 260 256.1 45.1 45.3 21 20.7 81 79.8 14.1 141 138.9 24.5 201 197.9 34.9 261 257.0 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 26.6 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 • 2()3.9 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 1 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 1 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 36 35.5 06.3 96 94.5 16.7 156 153.6 i 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 39.1 285 280.7 49.5 46 45.3 08.0 106 104.4 18.4 166 163.5 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 1()8 165.4 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 5] 49.2 08.7 110 108.3 19.1 170 167.4 29.5 230 226.5 39.9 290 285.6 504 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 29.9 232 228.5 40.3 292 287.6 , 50.7 1 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 40.8 295 290.5 512 56 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 58 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 41.7 300 295.4152.11 Dist Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 1 For RO Degrees. 6h 20". 1 TABLE 11. 27 GREES. Oil 44ra. DIFFERENCE OF LATITUDE AND DEPARTURE FOR 11 DE Diet Lat. Dep. Dist. Lilt. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. 241 LaL 236.6 Dep. 46.0 1 01.0 00.2 61 59.9 11.6 121 118.8 23.1 181 177.7 34.5 2 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 "^4.4 188 184.5 35.9 248 243.4 47.3 9 08.8 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 13.4 130 131 127.6 24.8 190 191 186.5 36.3 250 245.4 47.7 11 10.8 02.1 71 69.7 13.5 128.6 25.0 187.5 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 U) 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 76.0 14.9 138 135.5 26.3 198 194.4 37.8 258 253.3 49.2 19 18.7 03.6 79 77.5 15.1 139 136.4 26.5 199 19.5.3 38.0 259 254.2 49.4 21 19.6 20.6 03.8 80 78.5 15.3 140 141 137.4 138.4 26.7 200 196.3 38.2 260 255.2 256.2 49.6 49.8 04.0 81 79.5 15.5 26.9 201 197.3 38.4 261 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 31 29.4 30.4 05.7 90 88.3 17.2 150 147.2 28.6 210 206.1 40.1 270 265.0 51.5 51.7 05.9 91 89.3 17.4 151 148.2 28.8 211 207.1 40.3 271 266.0 32 31.4 06.1 92 90.3 17.6 152 149.2 29.0 212 208.1 4U.4 272 267.0 51.9 33 32.4 06.3 93 91.3 17.7 153 150.2 29.2 213 209.1 40.5 273 268.0 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 36 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 40.2 07.8 101 99.1 19.3 161 158.0 30.7 221 2i6.9 42.2 281 275.8 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 42.2 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 46 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 HI 109.0 21.2 171 167.9 32.6 231 226.8 44.1 291 285.7 55.5 52 51.0 0l>.9 1 12 109.9 21.4 172 168.8 32.8 232 227.7 44.3 292 286.6 55.7 53 52.0 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 54.0 10.5 115 112.9 21.9 175 171.8 33.4 235 230.7 44.8 295 289.6 56.3 56 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,« 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 lir,.8 22.7 179 175.7 34.2 239 284.6 45.6 299 293.5 57.1 60 58.9 11.4 120 117.8 22.9 Lat. 180 176.7 34.3 240 235.6 45.8 300 294.5 57.2 Dist Dep. Lat. Dist. Dep. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat For 79 Deajrees. 5^ 16-. 1 28 TABLE II. 1 DIFFERENCE OF LATITUDE AND DEPARTURE FOR 12 DEGREES. 0^ 48m, | Dist. 1 Lat. Dep. Dist Lat. Dep. Dist Lat. Dep. Dist. ' Lat. Dep. Dist Lat. Dep. 01.0 00.2 61 59.7 12.7 121 118.4 25.2 181 177.0 37.6 241 235.7 50.1 2 02.0 00.4 62 60.6 12.9 122 119.3 25.4 182 178.0 87.8 242 236.7 50.3 3 02.9 00.6 63 61.6 13.1 123 120.3 25.6 183 179.0 38.0 243 237.7 50.5 4 03.9 00.8 64 62.6 13.3 124 121.3' 25.8 184 180.0 38.3 244 238.7 : 50.7 5 04.9 01.0 65 63.6 13.5 125 122.3' 26.0 185 181.0 38.5 245 239.6 50.9 6 05.9 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 11 09.8 02.1 70 68.5 14.6 130 127.2 27.0 190 185.8 39.5 250 244.5 52.0 10.8 02.3 71 69.4 14.8 131 128.1 27.2 191 186.8 39.7 251 245.5 52.2 1 12 11.7 02.5 72 70.4 15.0 132 129.1 27.4 192 187.8 39.9 252 246.5 52.4 1 13 12.7 02.7 73 71.4 15.2 133 130.1 27.7 193 188.8 40.1 253 247.5 1 52.6 | 14 13.7 02.9 74 72.4 15.4 134 131.1 27.9 194 189.8 40.3 254 248.4 52.8 15 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 40.8 256 250.4 53.2 IT 16.6 03.5 77 75.3 16.0 137 134.0 28.5 197 192.7 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 16.4 139 136.0 28.9 199 194.7 41.4 259 253.3 53.8 20 19.6 04.2 80 78.3 16.6 140 136.9 29.1 200 195.6 41.6 260 254.3 54.1 21 20.5 04.4 81 79.2 16.8 141 137.9 29.3 201 196.6 41.8 261 255.3' 54.3 1 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 1 23 22.5 04.8 83 81.2 17.3 143 139.9 29.7 203 198.6 42.2 263 257.3 1 54.7 | 24 23.5 05.0 84 82.2 17.5 144 140.9 29.9 204 199.5 42.4 264 258.2 54.9 25 24,5 05.2 85 83.1 17.7 145 141.8 30.1 205 200.5 42.6 265 259.2 55.1 26 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 43.0 267 261.2:55.51 28 27.4 05.8 88 86.1 18.3 148 144.8 30.8 208 203.5 43.2 268 1262.1 155.7/ 29 28.4 06.0 89 87.1 18.5 149 145.7 31.0 209 204.4 43.5 269 263.1 i55.9' 30 29.3 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 91 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 36 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 36.2 07.7 97 94.9 20.2 157 153.6 32.6 217 212.3 45.1 277 270.9 57.6 38 37.2 07.9 98 95.9 20.4 158 154.5 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 2142 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 40.1 08.5 101 98.8 21.0 161 157.5 33.5 221 216.2 45.9 281 274.9 58.4 42 41.1 08.7 102 99.8 21.2 162 158.5 33.7 222 217.1 46.2 282 275.8 58.6 43 42.1 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 21.6 164 160.4 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 34.7 227 222.0 47.2 287 280.7 59.7 48 47.0 10.0 108 105.7 22.5 168 164.3 34.9 228 223.0 47.4 288 281.7 59.9 49 47.9 10.2 109 106.6 22.7 169 165.3 35.1 229 224.0 47.6 289 282.7 60.1 50 48.9 10.4 110 107.6 22.9 170 166.3 35.3 230 225.0 47.8 290 283.7 60.3 51 49.9 10.6 111 108.6 23.1 171 167.3 35.6 231 226.0 48.0 291 284.6 60.5 52 50 9 10.8 112 109.6 23.3 172 168.2 35.8 232 226.9 48.2 292 285.6 60.7 53 51,8 11.0 113 110.5 23.5 173 169.2 36.0 233 227.9 48.4 293 286.6 1 60.9 1 54 52,8 11.2 114 111.5 23.7 174 170.2 36.2 234 228.9 48.7 294 287.6 61.1 55 53,8 11.4 115 112.5 23.9 175 171.2 36.4 235 229.9 48.9 295 288.6 61.3 56 54.8 11.6 116 113.5 24.1 176 172.2 36.6 236 230.8 49.1 296 289.5 61.5 57 55.8 11.9 117 114.4 24.3 177 173.1 36.8 237 231.8 49.3 297 290.5 '61.7 58 56.7 12.1 118 115.4 24.5 17S 174.1 37.0 238 232.8 49.5 298 291.5 1 62.0 59 57.7 12.3 119 116.4 24.7 179 175.1 37.2 239 233.8 49.7 299 292.5 ' 62.2 60 Dist 58.7 12.5 120 117.4 24.9 180 176.1 37.4 240 234.8 49.9 300 293.4 1 62.4 ^ Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat Dist! Dep ; Lat 1 For 78 Degrees. 0" i'-J"- 1 TABLE 11. 29 1 DIFFERENCE OF LATITUDE AND DEPARTURE FOR 13 DEGREES. Oh 52>n | Dist 1 Lat. 01.0 Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat 234.8 Dep. 54.2 00.2 61 59.4 13.7 121 117.9 27.2 181 176.4 40.7 241 • > 01.9 00.4 62 60.4 13.9 122 118.9 27.4 182 177.3 40.9 242 235.8 54.4 02.9 00.7 63 61.4 14.2 123 119.8 27.7 183 178.3 41.2 243 236.8 54.7 4 03.9 00.9 64 62.4 14.4 124 120.8 27.9 184 179.3 41.4 244 237.7 54.9 5 04.9 01.1 65 63.3 14.6 125 121.8 28.1 185 180.3 41.6 245 2;;8.7 55.1 6 05.8 01.3 66 64.3 14.8 126 122.8 28.3 186 181.2 41.8 246 239.7 55.3 i 06.8 01.6 67 65.3 15.1 127 123.7 ^8.6 187 182.2 42.1 247 240.7 55.6 8 07.S 01.8 68 66.3 15.3 128 124.7 28.8 188 183.2 42.3 248 241.6 55.8 9 08.8 02.0 69 67.2 15.5 129 125.7 29.0 189 184.2 42.5 249 242.6 56.0 10 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 69.2 16.0 131 127.6 29.5 191 186.1 43.0 251 244.6 56.5 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 16.6 134 130.6 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 IG 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 17.5 04.0 78 76.0 17.5 138 134.5 31.0 198 192.9 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 21 19.5 04.5 80 77.9 18.0 140 141 136.4 31.5 200 201 194.9 195.8 45.0 260 253.3 58.5 20.5 04.7 81 78.9 18.2 137.4 31.7 45.2 261 254.3 58.7 22 21.4 04.9 82 79.9 18.4 142 138.4 31.9 202 196.8 45.4 262 255.3 58.9 23 22.4 05.2 83 80.9 18.7 143 139.3 32.2 203 197.8 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 24.4 05.6 85 82.8 19.1 145 141.3 32.6 205 199.7 46.1 265 258.2 59.6' 26 25.3 05.8 86 83.8 19.3 146 142.3 32.8 206 200.7 46.3 266 259.2 59.8 27 26.3 06.1 87 84.8 19.6 147 143.2 33.1 207 201.7 46.6 267 260.2 60.1 28 27.3 06.3 88 85.7 19.8 148 144.2 33.3 208 202.7 46.8 268 261.1 60.3 29 28.3 06.5 89 86.7 20.0 149 145.2 33.5 209 203.6 47.0 269 262.1 60.5 30 29.2 06.7 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 47.5 271 264.1 61.0 32 31.2 07.2 92 89.6 20.7 152 148.1 34.2 212 206.6 47.7 272 265.0 01.2 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 34.1 07.9 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 21.6 156 152.0 35.1 216 210.5 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 35.5 218 212.4 49.0 278 270.9 62.5 39 38.0 08.8 99 96.5 22.3 159 154.9 35.8 219 213.4 49.3 279 271.8 62.8 40 41 39.0 09.0 100 97.4 22.5 160 155.9 36.0 220 214.4 49.5 280 272.8 63.0 63.2 39.9 09.2 101 98.4 22.7 161 156.9 36.2 221 215.3 49.7 281 273.8 42 40.9 09.4 102 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 24.1 167 162.7 37.6 227 221.2 51.1 287 279.6 64.6 48 46.8 10.8 108 105.2 24.3 168 163.7 37.8 228 222.2 51.3 288 280.6 64.8 49 47.7 11.0 109 106.2 24.5 169 164.7 38.0 229 223.1 51.5 289 281.6 65.0 50 51 48.7 11.2 110 107.2 24.7 170 165.6 38.2 230 224.1 51.7 290 282.6 65.2 49.7 11.5 111 108.2 25.0 171 166.6 38.5 231 225.1 52.0 291 283.5 65.5 52 50.7 11.7 112 109.1 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 65.91 54 52.6 12.1 114 111.1 25.6 174 169.5 39.1 234 228.0 52.6 294 286.5 66.1 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 26.3 177 172.5 39.8 237 230.9 53.3 297 289.4 66.8 58 56.5 13.0 118 115.0 26.5 178 173.4 40.0 238 231.9 53.5 298 290.4 67.0 59 57.5 13.3 119 ii<;.o 26.8 179 174.4 40.3 239 232.9 53.8 299 291.3 67.3 60 58.5 13.5 120 116.9 27.0 Lat. 180 175.4 40.5 240 233.8 54.0 300 292.3 67.5 Dist. Dep. Lat. Dist. Dep. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat I "or 77 Decrees. 5h 8n>. 1 30 TABLE II. DIFFERENCE OF LATITUDE AND DFt^ARTURE FOR 14 DEGREES. 0^ SBm. Diff. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. DistI Lat 1 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 15.0 122 118.4 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 1 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 67.0 16.7 129 125.2 31.2 189 183.4 45.7 249 241.6 60.2 10 11 09.7 02.4 70 67.9 16.9 130 126.1 31.4 190 184.4' 46.0 250 242.6 60.5 10.7 02.7 71 68.9 17.2 131 127.1 31.7 191 185.3 46.2 251 243.5 60.7 12 11.6 02.9 72 69.9 17.4 132 128.1 31.9 192 186.3 46.4 252 244.5 61.0 13 12.6 03.1 73 70.8 17.7 1:^3 129.0 32.2 193 187.3 46.7 253 245.5 61.2 14 13.6 03.4 74 71.8 17.9 134 130.0 32.4 194 188.2 46.9 254 246.5 61.4 15 14.6 03.6 75 72.8 18.1 135 131.0 32.7 195 189.2 47.2 255 247.4 61.7 16 15.5 03.9 76 73.7 18.4 136 132.0 32.9 196 190.2 47.4 256 248.4 61.9 17 16.5 04.1 77 74.7 18.6 137 132.9 33.1 197 191.1 47.7 257 249.4 62.2 18 17.5 04.4 78 75.7 18.9 138 133.9 33.4 198 192.1 47.9 258 250.3 H2.4 19 18.4 04.6 79 76.7 19.1 139 134.9 33.6 199 193.1 48.1 259 251.3 «>2.7 20 19.4 04.8 80 77.6 19.4 140 135.8 33.9 200 194.1 48.4 260 252.3 ♦•,2.9 63.1 21 20.4 05.1 81 78.6 19.6 141 136.8 34.1 201 195.0 48.6 261 253.2 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 23.3 05.8 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 !»4. 11 26 25.2 06.3 86 83.4 20.8 146 141.7 35.3 206 199.9 49.8 266 258.1 1 64.4 1 27 26.2 06.5 87 84.4 21.0 147 142.6 35.6 207 200.9 50.1 267 259.1 64.6 28 27.2 06.8 88 85.4 21.3 148 143.6 35.8 208 201.8 50.3 268 260.0 64.8 29 28.1 07.0 89 86.4 21.5 149 144.6 36.0 209 202.8 50.6 269 261.0 o5.] 30 29.1 07.3 90 87.3 21.8 150 145.5 36.3 210 203.8 50.8 270 262.0 v,5.8 65.6 31 30.1 07.5 91 88.3 22.0 151 146.5 36.5 211 204.7 51.0 271; 263.0 32 31.0 07.7 92 89.3 22.3 152 147.5 36.8 212 205.7 51.3 272 ; 263.9 ■ ^5.8 \ 33 32.0 08.0 93 90.2 22.5 153 148.5 37.0 213 206.7 51.5 273 ; 264.9 66.0 34 33.0 08.2 94 91.2 22.7 154 149.4 37.3 214 207.6: 51.8 274 265.9 66.3 35 34.0 08.5 95 9*2.2 23.0 155 150.4 37.5 215 208.6 52.0 275 266.8 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 41 38.8 09.7 100 97.0 24.2 160 155.2 38.7 220 213.5 53.2 280 271.7 67.7 39.8 09.9 101 98.0 24.4 161 156.2 38.9 221 214.4 53.5 281 272.7 68.0 42 40.8 10.2 102 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 99.9 24.9 163 158.2 39.4 223 216.4 53.9 283 274.6 68.5 44 42.7 10.6 104 100.9 25.2 164 159.1 39.7 224 217.3 54.2 284 275.6 68.7 45 43.7 10.9 105 101.9 25.4 165 160.1 39.9 225 218.3 54.4 285 276.5 ; 68.9 46 44.6 11.1 106 102.9 25.6 166 161.1 40.2 226 219.3 , 5i.7 286 277.5 1 69.2 47 45.6 11.4 107 103.8 25.9 167 162.0 40.4 227 220.3 54.9 287 278.5 ' 69.4 48 46.6 11.6 108 104.8 26.1 168 163.0 40.6 228 221.2 55.2 288 279.4 ' 69.7 49 47.5 11.9 109 105.8 26.4 169 164.0 40.9 229 222.2 55.4 289 1 280.4 69.9 50 48.5 12.1 110 106.7 26.6 170 165.0 41.1 230 223.2 55.6 290 1281.4 70.2 51 49.5 12.3 111 107.7 26.9 171 165.9 41.4 231 224.1 55.9 291 '282.4 70.4 52 50.5 12.6 112 108.7 27.1 172 166.9 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 42.1 234 227.01 56.6 294 285.3 71.1 55 53.4 13.3 115 111.6 27.8 175 169.8 42.3 235 228.01 56.9 295 1 286.2 71.4 56 54.3 13.5 116 112.6 28.1 176 170.8 42.6 236 229.0 57.1 296 1 287.2 71.6 57 55.3 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 28.5 178 172.7 43.1 238 230.9 57.6 298 1289.1 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 uist 58.2 14.5 120 116.4 29.0 180 174.7 43.5 240 232.9 58.1 300 291.1 72.6 . Den. I,at. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. For 7(i Dei^rees. 5h 4'". | TABLE 11. 31 1 DIFFERENCE OF LATITUDE AND DEPARTURE FOR 15 DEGREES. Ih Qm. 1 Dist 1 Lat 01.0 Dep. Dist. Lat. Dep. Dist Lat Dep. Dist Lat. Dep. | Dist Lat 232.8 Dep. 62.4 00.3 61 58.9 15.8 121 116.9 31.3 181 174.8 46.8 241 2 01.9 00.5 62 59.9 16.0 122 117.8 31.6 182 175.8 47.1 242 233.8 62.6 3 02.9 00.8 63 60.9 16.3 123 118.8 31.8 183 176.8 47.4 243 234.7 62.9 4 03.9 01.0 64 61.8 16.6 124 119.8 32.1 184 177.7 47.6 244 235.7 63.2 5 04.8 01.3 65 62.8 16.8 125 120.7 32.4 185 178.7 47.9 245 236.7 63.4 6 05.8 01.6 66 63.8 17.1 126 121.7 32.6 186 179.7 48.1 246 237.6 63.71 7 06.8 01.8 67 64.7 17.3 127 122.7 32.9 187 180.6 48.4 247 238.6 63.91 8 07.7 02.1 68 65.7 17.6 128 123.6 3S.1 188 181.6 48.7 248 239.5 64.2 9 08.7 02.3 69 66.6 17.9 129 124.6 33.4 189 182.6 48.9 249 240.5 64.4 10 09.7 02.6 70 67.6 18.1 130 131 125.6 33.6 190 183.5 49.2 250 241.5 64.7 11 10.6 02.8 71 68.6 18.4 126.5 33.9 191 184.5 49.4 251 242.4 65.0 12 11.6 03.1 72 69.5 18.6 132 127.5 34.2 192 185.5 49.7 252 243.4 65.2 13 12.6 03.4 73 70.5 18.9 133 128.5 34.4 193 186.4 50.0 253 244.4 65.5 14 13.5 03.6 74 71.5 19.2 134 129.4 34.7 194 187.4 50.2 254 245.3 65.7 15 14.5 03.9 75 72.4 19.4 135 130.4 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 17.4 04.7 78 75.3 20.2 138 133.3 35.7 198 191.3 51.2 258 249.2 66.8 19 18.4 04.9 79 76.3 20.4 139 134.3 36.0 199 192.2 51.5 259 250.2 67.0 20 21 19.3 20.3 05.2 80 77.3 20.7 140 135.2 136.2 36.2 200 201 193.2 51.8 260 251.1 67.3 05.4 81 78.2 21.0 141 36.5 194.2 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 26 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 38.8 210 211 202.8 54.4 270 260.8 69.9 31 29.9 (>80 91 87.9 23.6 151 145.9 39.1 203.8 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 1 264.7 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 93.7 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 37.7 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 72.7 41 39.6 10.6 101 97.6 26.1 161 155.5 41.7 221 213.5 57.2 281 271.4 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 41.5 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 46 444 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 43.5 228 220.2 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 i 49.3 13.2 111 107.2 28.7 171 165.2 44.3 231 223.1 59.8 291 281.1 75.3 52 50.2 13.5 112 108.2 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 14.5 116 112.0 30.0 176 170.0 45.6 236 228.0 61.1 296 285.9 76.6 57 1 55.1 14.8 117 113.0 30.3 177 171.0 45.8 237 228.9 61.3 297 286.9 76.9 58 56.0 15.0 118 114.0 30.5 178 171.9 46.1 238 229.9 61.6 298 , 287.8 77.1 59 57.0 15.3 119 114.9 30.8 179 172.9 46.3 239 230.9 61.9 299 288.8 77.4 60 58.0 15.5 120 115.9 31.1 Lat. 180 Dist 173.9 46.6 240 231.8 62.1 300 289.8 77.6 Dist . Dep. Lat. Dist. Dep. Dep. Lat Dist. Dep. Lat. Dist. Dep. Lat For 75 Des-'-ees. 5*^ Om. | 32 TABLE II. DIFFERENCE OF LATITUDE AND DEPARTURE FOR 16 DEGREES. l^ 4ni. 1 Dist Lat Dep. Dibt Lat. Dep. Dl8t Lat. Dep. 33.4 Dist. Lat. Dep. Dist. Lat Dep. 1 01.0 00.3 61 58.6 16.8 121 116.3 181 174.0 49.9 241 231.7 66.4 2 01.9 00.6 62 59.6 17.1 122 117.3 33.6 182 174.9 50.2 242 232.6 66.7 3 02.9 00.8 63 60.6 17.4 123 118.2 33.9 183 175.9 50.4 243 233.6 67.0 4 03.8 01.1 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 ((7.5 6 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 l.sO.7 51.8 248 238.4 68.4 9 08.7 02.5 69 66.3 19.0 129 124.0 35.6 189 181.7 52.1 249 239.4 68.6 10 11 09.6 02.8 70 67.3 19.3 130 125.0 35.8 190 182.6 52.4 250 240.3 68.9 10.6 03.0 71 68.2 19.6 131 125.9 36.1 191 183.6 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 03.9 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 16 15.4 04.4 76 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 20 19.2 05.5 80 76.9 22.1 140 134.6 38.6 200 192.3 55.1 260 249.9 71.7 21 20.2 05.8 81 77.9 22.3 141 13.5.5 38.9 201 193.2 55.4 261 250.9 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 72.8 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 82.7 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 i 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 25.1 151 145.2 41.6 211 202.8 58.2 271 260.5 74.7 ;^2 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 15.5.7 44.7 222 213.4 61.2 282 271.1 ' 77.7 43 41.3 1].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 62.3 286 274.9 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 1(58 161.5 46.3 228 219.2 62.8 288 276.8 r9.4 49 47.1 13.5 109 104.8 30.0 169 162.5 46.6 229 220.1 63.1 289 277.8 ^9.7 50 48.1 13.8 110 105.7 30.3 170 163.4 46.9 230 221.1 63.4 290 278.ts /9.9 60.2 j 51 49.0 14.1 11 1 106.7 30.6 171 164.4 47.1 231 222.1 63.7 291 279.7 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 50.9 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 8..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 5(5 53.8 15.4 IK) 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 17S 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. t 82.4 60 Dist. 57.7 16.5 Lnt 120 115.4 33.1 180 173.0 49.6 240 230.7 66.2 300 288.4 82.7 Den. Dist. Dep. Lat. Dist. Dep. Lnt. Dist. Dep. Lat. Dist. Dep. Lat ] ■for 74 Deii:roe.s. 4 56™. 1 TABLE 11. 3S 1 DIFFERENCE OF LATITUDE AND DEPARTURE FOR 17 DEGREES. Ih8n>. 1 Diet 1 Lat. 01.0 Dep. Dist. Lat. Dep. Dist. Lat Dep. Dist. Lat Dep. Dist 241 Lat j Dep. 00.3 61 58.3 17.8 121 115.7 35.4 181 173.1 52.9 230.5 70.5 2 01.9 00.6 62 59.3 18.1 122 116.7 35.7 182 174.0 53.2 242 231.4 70.8 3 02.9 00.9 63 60.2 18.4 123 117.6 36.0 183 175.0 53.5 243 232.4 71.0 4 03.8 01.2 64 61.2 18.7 124 118.6 36.3 184 176.0 53.8 244 233.3 71.3 5 04.8 01.5 65 62.2 19.0 125 119.5 36.5 185 176.9 54.1 245 234.3 71.6 6 05.7 01.8 6Q 63.1 19.3 126 120.5 36.8 186 177.9 54.4 246 235.3 71.9 7 06.7 02.0 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 37.4 188 179.8 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 09.6 02.9 70 66.9 20.5 130 124.3 38.0 190 181.7 55.6 250 239.1 73.] 11 10.5 03.2 71 67.9 20.8 131 125.3 38.3 191 182.7 55.8 251 240.0 73.4 12 11.5 03.5 72 68.9 21.1 132 126.2 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 57.0 255 243.9 74.6 U) 15.3 04.7 76 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 23.4 140 133.9 40.9 200 191.3 58.5 260 248.6 76.0 21 20.1 06.1 81 77.5 23.7 141 134.8 41.2 201 192.2 58.8 261 249.6 76.3 22 21.0 06.4 82 78.4 24 142 135.8 41.5 202 193.2 59.1 262 250.6 76.6 23 22.0 06.7 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 24.9 07.6 86 82.2 25.1 146 139.6 42.7 206 197.0 60.2 266 254.4 77.8« 27 25.8 07.9 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 26.0 149 142.5 43.6 209 199.9 61.1 269 257.2 78.6 30 28.7 08.8 90 86.1 26.3 150 143.4 43.9 210 200.8 61.4 270 258.2 78.9 31 29.6 09.1 91 87.0 26.6 151 144.4 44.1 211 201.8 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 79.5 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 32.5 09.9 94 89.9 27.5 154 147.3 45.0 214 204.6 62.6 274 262.0 80.1 35 33.5 10.2 95 90.8 27.8 155 148.2 45.3 215 205.6 62.9 275 263.0 80.4 36 34.4 10.5 96 91.8 28.1 156 149.2 45.6 216 206.6 63.2 276 263.9 80.7 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 82.2 41 39.2 12.0 101 96.6 29.5 161 154.0 47.1 221 211.3 64.6 281 268.7 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 44.0 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 13.7 107 102.3 31.3 167 159.7 48.8 227 217.1 66.4 287 274.5 83.9 48 45.9 14.0 108 103.3 31.6 168 160.7 49.1 228 218.0 66.7 288 275.4 84.2 49 46.9 14.3 109 104.2 31.9 169 161.6 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 51 148.8 14.9 111 106.1 32.5 171 163.5 50.0 231 220.9 67.5 291 278.3 85.1 52 49.7 15.2 112 107.1 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 1.5.8 114 109.0 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 ef 3 297 284.0 86.8 58 55.5 17.0 118 112.8 34.5 178 170.2 52.0 238 227.6 69.0 ^98 285.0 87.1 59 56.4 17.2 119 113.8 34.8 179 171.2 52.3 239 228.6 69.9 299 285.9 87.4 60 Dist 57.4 17.5 120 114.8 35.1 Lat. 180 Dist. 172.1 52.6 240 229.5 70.2 300 286.9 87.7 Dep. 1 Lat. Dist. Dep. Dep. Lat. Dist. Dep. Lat Dist. Dep. Lat For 73 U ee:rees. 4^' 52™. | 34 TABLE 11. 1 DIFFERENCE OF LATITUDE AND DEPARTURE FOR 18 DEGREES. Ih 12.t«. 1 DisL Lat. Dep. Dist Lat. Dep. Dist. Lat. Dep. Dist. Lat Dep. Dist. ! Lat. Dep. 1 01.0 00.3 61 58.0 18.9 121 115.1 37.4 181 172.1 55.9 241 229.2 74.5 2 01.9 00.6 62 59.0 19.2 122 116.0 37.7 182 173.1 56.2 242 230.2 74.8 1 3 02.9 00.9 63 59.9 19.5 123 117.0 38.0 183 174.0 56.6 243 231.1 75.1 4 03.8 01.2 64 60.9 19.8 124 117.9 38.3 184 175.0 56.9 244 232.1 75.4 5 04.8 01.5 65 61.8 20.1 125 118.9 38.6 185 175.9 57.2 245 233.0 75.7 6 05.7 01.9 66 62.8 20.4 126 119.8 38.9 186 176.9 57.5 246 234.0 76.0 7 06.7 02.2 67 63.7 20.7 127 120.8 39.2 187 177.8 57.8 247 234.9 ! 76.3 1 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 1 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 11 09.5 03.1 70 66.6 21.6 130 123.6 40.2 190 180.7 58.7 250 237.8 77.3 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 04.0 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 04.6 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 05.8 77 73.2 23.8 137 130.3 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 20.0 06.5 81 77.0 25.0 141 134.1 43.6 201 191.2 62.1 261 248.2 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 19.3.1 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 26 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 26.6 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 29.5 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 36 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 48.5 217 206.4 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 1 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 43.7 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 70.1 287 273.0 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 15.1 109 103.7 33.7 169 160.7 52.2 229 217.8 70.8 289 274.9 89.3 50 47.6 15.5 110 104.6 34.0 170 161.7 52.5 230 218.7 71.1 290 275.8 89.6 51 48.5 15.8 111 105.6 34.3 171 162.6 52.8 231 219.7 71.4 291 276.8 89.9 52 49.5 16.1 112 106.5 34.6 172 163.6 53.2 232 220.6 71.7 292 277.7 90.2 53 50.4 16.4 113 107.5 34.9 173 164.5: 53.5 233 221.6 72.0 293 278.7 90.5 54 51.4 16.7 114 108.4 35.2 174 165,5: 53.8 234 222.5 1 72.3 | 294 279.6 90.9 55 52.3 17.0 115 109.4 .35.5 175 166.4; 54.1 235 223.5 72.6 295 280.6 91.2 56 53.3 17.3 116 110.3 35.8 176 167.4 54.4 236 224.4 72.9 296 281.5' 91.5 1 57 54.2 17.6 117 111.3 36.2 177 168.3 54.7 237 225.4 73.2 297 282.5 91.8 58 552 17.9 118 112.2 36.5 178 169.3 55.0 238 226.4 73.5 298 283.4 92.1 59 56.1 18.2 119 113.2 36.8 179 170.2 55.3 239 227.3 73.9 299 284.4 92.4 60 Diat 57.1 Dep. 18.5 120 114.1 37.1 180 171.2 55.6 240 228.3 74.2 300 285.3 92.7 Lat. Dist. 1 Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist., Dep. 1 Lat | For 72 Detrrees. 4h 48'". | TABLE 11. 86 1 DIFFERENCE OF LATITUDE AND DEPARTURE FOR 19 DEGREES. Ibi6« 1 Dist 1 Lat. 00.9 Dep. Dist. Lilt. Dep. Dist. Lilt. Dep. Dist. Lat. Dep. Dist. Lat 227.9 Dep. 78.5 00.3 61 57.7 19.9 12h 114.4 39.4 181 171.1 58.9 241 2 01.9 00.7 62 58.6 20.2 122 115.4 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 03.8 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 65 61.5 21.2 125 118.2 40.7 185 174.9 60.2 245 231.7 79.8 ;1 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 08.5 02.9 69 65.2 22.5 129 122.0 42.0 189 178.7 61.5 249 235.4 81.1 10 09.5 03.3 70 66.2 22.8 130 122.9 42.3 190 179.6 61.9 250 236.4 81.4 11 10.4 03.6 71 67.1 23.1 131 123.9 42.6 191 180.6 62.2 251 237.3 81.7 12 11.3 03.9 72 68.1 23.4 132 124.8 43.0 192 181.5 62.5 252 238.3 82.0 13 12.3 04.2 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 16 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 7^.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 18.0 06.2 79 74.7 25.7 139 131.4 45.3 199 188.2 64.8 259 244.9 84.3 20 21 18.9 06.5 80 75.6 26.0 140 132.4 45.6 200 189.1 65.1 260 245.8 84.6 85.0 19.9 06.8 81 76.6 26.4 141 133.3 45.9 201 190.0 65.4 261 246.8 22 20. S 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 23.6 08.1 85 80.4 27.7 145 137.1 47.2 205 193.8 66.7 265 250.6 86.3 26 24.6 08.5 86 81.3 28.0 146 138.0 47.5 206 194.8 67.1 266 251.5 86.6 27 25.5 08.8 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 84.2 29.0 149 140.9 48.5 209 197.6 68.0 269 254.3 87.6 30 28.4 09.8 90 85.1 29.3 150 141.8 48.8 210 198.6 68.4 270 255.3 87.9 31 29.3 10.1 91 86.0 29.6 151 142.8 49.2 211 199.5 68.7 271 256.2 88.2 32 30.3 10.4 92 87.0 30.0 152 143.7 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 30.6 154 145.6 50.1 214 202.3 69.7 274 259.1 80.2 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 36 34.0 11.7 96 90.8 31.3 156 147.5 50.8 216 204.2 70.3 276 261.0 89.9 37 35.0 12.0 97 91.7 31.6 157 148.4 51.1 217 205.2 70.6 277 261.9 90.2 38 35.9 12.4 98 92.7 31.9 158 149.4 51.4 218 206.1 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 38.8 13.3 101 95.5 32.9 161 152.2 52.4 221 209.0 72.0 281 265.7 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 44 41.6 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 46 43.5 15.0 106 100.2 34.5 166 157.0 54.0 226 213.7 73.6 286 270.4 93.1 47 44.4 1.5.3 107 101.2 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 lOi) 103.1 35.5 169 159.8 55.0 229 216.5 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 16.9 112 105.9 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 95,7 55 52.0 17.9 115 108.7 37.4 175 165.5 57.0 235 222.2 76.5 295 278.9 96.0 56 .-2.9 18.2 116 109.7 37.S 176 166.4 57.3 236 223.1 76.8 296 279.9 96.4 57 5/9 18.6 117 110.6 38.1 \17 167.4 57.6 237 224.1 77.2 297 280.8 96.7 58 54.3 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 Dist 5tV7 Dep. 19.5 120 113.5 39.1 Lat. 180 Dist. 170.2 58.6 240 226.9 78.1 300 283.7 97.7 1 Lat. Dist. Dep. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat 1 ^ i "c.r 71 DeiTiees. 4'» 44«>. | 86 TABLE 11. DIFFERENCE OF LATITUDE AND DEPARTURE FOR 20 DEGREES. Ih 20n». 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 01.9 00.7 62 58.3 21.2 122 114.6 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 84.1 7 06.6 02.4 67 63.0 22.9 127 119.3 43.4 187 175.7 64.0 247 232 1 84.5 8 07.5 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 11 09.4 03.4 70 65.8 23.9 130 122.2 44.5 190 178.5 65.0 250 234.9 85.5 10.3 03.8 71 66.7 24.3 131 123.1 44.8 191 179.5 65.3 251 235.9 85.8 12 11.3 04.1 72 67.7 24.6 132 124.0 45.1 192 180.4 65.7 2.52 236.8 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 05.1 75 70.5 25.7 135 126.9 46.2 195 183.2 66.7 255 239.6 87.2 16 15.0 05.5 76 71.4 26.0 136 127.8 46.5 196 184.2 67.0 256 240.6 87.6 17 16.0 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 06.8 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 76.1 27.7 141 132.5 48.2 201 188.9 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 19.3.6 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 19.5.5 71.1 268 251.8 91.7 29 27.3 09.9 89 83.6 30.4 149 140.0 51.0 209 196.4 71.5 269 252.8 92.0 30 28.2 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 51.6 211 198.3 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 12.0 95 89.3 32.5 155 145.7 53.0 215 202.0 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 S5.7 13.0 98 92.1 33.5 158 148.5 54.0 218 204.9 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 37.6 13.7 100 94.0 34.2 160 150.4 54.7 220 206.7 75.2 280 263.1 95.8 41 38.5 14.0 101 94.9 34.5 161 151.3 ,55.1 221 207.7 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 77.0 285 267.8 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 44.2 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 lf.8 157.9 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 51 47.9 17.4 111 104.3 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 58.8 232 218.0 79.3 292 274.4 99.9 53 49.8 18.1 113 106.2 38.6 173 162.6 59.2 233 218.9 79.7 293 275.3 100.2 54 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 17S 167.3 60.9 238 223.6 81.4 298 280.0 101.9 59 554 20.2 119 111.8 40.7 179 168.2 61.2 239 224.6 81.7 299 281.0 102.3 60 Dist 56.4 20.5 120 112.8 41.0 180 169.1 61.6 240 225..'. 82.1 300 281.9 102.6 Dep. Lat. Dist Dep. Lat Dist Dep. Lat. Dist Dep. Lat. Dist Dep. Lat 1 For 70 Degrees. 4h 40'V 1 TABLE 11. 37 1 DIFFEKENCE OF LATITUDE AND DEPARTURE FOR 21 DEGREES. Ih 24m. 1 Dist 1 Lat. 00.9 Dep. Dist. Lat. Dep. Dist. Lat Dep. Dist. Lat. Dep. Dist Lat Dep. 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 05.6 022 66 61.6 23.7 126 117.6 45.2 186 173.6 66.7 246 229.7 88.2 7 ' 0(5.5 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.& 188 175.5 67.4 248 231.5 88.9 9 , 08.4 03.2 69 64.4 24.7 129 120.4 46.2 189 176.4 67.7 249 232.5 89.2 10 09.3 03.6 70 65.4 25.1 130 131 121.4 46.6 190 1-77.4 68.1 250 233.4 89.6 11 10.3 03.9 71 66.3 25.4 122.3 46.9 191 178.3 68.4 251 234.3 90.0 1^ 11.2 04.3 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 14.9 05.7 76 71.0 27.2 136 127.0 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 49.1 197 183.9 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 21 18.7 07.2 80 74.7 28.7 140 141 130.7 131.6 50.2 200 186.7 71.7 260 242.7 93.2 19.6 07.5 81 75.6 29.0 50.5 201 187.6 72.0 261 243.7 93.5 22 20.5 07.9 82 76.6 29.4 142 132.6 50.9 202 188.6 72.4 262 244.6 93.9 23 21.5 08.2 83 77.5 29.7 143 133.5 51.2 203 189.5 72.7 263 245.5 94.3 24 22.4 08.6 84 78.4 30.1 144 134.4 51.6 204 190.5 73.1 264 246.5 94.6 25 23.3 09.0 85 79.4 30.5 145 135.4 52.0 205 191.4 73.5 265 247.4 95.0 26 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 52.7 207 193.3 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 53.4 209 195.1 74.9 269 251.1 96.4 30 28.0 lO.s 90 84.0 32.3 150 140.0 53.8 210 196.1 75.3 270 252.1 96.8 31 2S.9 11.1 91 85.0 32.6 151 141.0 54.1 211 197.0 75.6 271 253.0 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 55.9 216 201.7 77.4 276 257.7 98.9 37 34.5 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 lOO.O 40 37.3 14.3 100 93.4 35.8 160 149.4 57.3 220 205.4 78.8 280 261.4 262.3 100.3 41 38.3 14.7 101 94.3 36.2 161 150.3 57.7 221 206.3 79.2 281 100.7 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 40.1 15.4 103 96.2 36.9 163 152.2 58.4 223 208.2 79.9 283 264.2 101.4 44 41.1 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 38.0 166 155.0 59.5 226 211.0 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 48 448 17.2 108 100.8 38.7 168 156.8 i»/^ '-> ^'^O^ 212.9 81.7 288 268.9 103.2 49 45.7 17.6 lOi) 101.8 39.1 169 157.8 60.6 229 ^i«.3 ^•>l 289 269.8 103.6 50 51 46.7 17.9 110 102.7 39.4 170 158.7 60.9 230 214.7 82.4 290 270.7 103.9 47.6 18.3 HI 103.6 39.8 171 159.6 61.3 231 215.7 82.8 291 271.7 104.3 52 48.5 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 83.9 294 274.5 105.4 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 56 52.3 20.1 116 108.3 41.6 176 164.3 63.1 236 220.3 84.6 296 276.3 106.1 i) / 53.2 20.4 117 109.2 41.9 177 165.2 ()3.4 237 221.3 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 Dist. 56.0 Dep. 21.5 120 112.0 43.0 Lat. 180 168.0 64.5 240 224.1 86.0 300 280.1 107.5 Lat. Dist. Dep. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat I 'or 69 Desjrees. 4h 86m. 38 TABLE 11. 1 DIFFERENCE OF LATITUDE AND DEPARTURE FOR 22 DEGREES. In 28™. Dist Lat. Dep. Dist Lat Dep. | Dist Lat Dep. Dist Lat Dep. Dist Lat Dep. 1 00.9 00.4 61 56.6 22.9 121 112.2 45.3 181 167.8 67.8 241 223.5 90.3 2 01.9 00.7 62 57.5 23.2 122 113.1 45.7 182 168.7 68.2 242 224.4 90.7 3 02.8 01.1 63 58.4 23.6 123 114.0 46.1 183 169.7 68.6 243 225.3 91.0 4 03.7 01.5 64 59.3 24.0 124 115.0 46.5 184 170.6 68.9 244 226.2 91.4 5 04.6 01.91 65 60.3 24.3 125 115.9 46.8 185 171.5 69.3 245 227.2 91.8 6 05.6 02.2 66 61.2 24.7 126 116.8 47.2 186 172.5 69.7 246 228.1 92.2 7 06.5 02.6 67 62.1 25.1 127 117.8 47.6 187 173.4 70.1 247 229.0 92.5 8 07.4 03.0 68 63.0 25.5 128 118.7 47.9 188 174.3 70.4 248 229.9 92.9 9 08.3 03.4 69 64.0 25.8 129 119.6 48.3 189 175.2 70.8 249 230.9 93.3 10 09.3 03.7 70 64.9 26.2 130 131 120.5 48.7 190 176.2 71.2 250 231.8 93.7 11 10.2 04.1 71 65.8 26.6 121.5 49.1 191 177.1 71.5 251 232.7 94.0 12 11.1 04.5 72 66.8 27.0 132 122.4 49.4 192 178.0 71.9 252 233.7 94.4 13 12.1 04.9 73 67.7 27.3 133 123.3 49.8 193 178.9 72.3 253 234.6 94.8 14 13.0 05.2 74 6S.Q 27.7 134 124.2 50.2 194 179.9 72.7 254 235.5 95.2 15 13.9 05.6 75 69.5 28.1 135 125.2 50.6 195 180.8 73.0 255 236.4 95.5 16 14.8 06.0 76 70.5 28.5 136 126.1 50.9 196 181.7 73.4 256 237.4 95.9 17 15.8 06.4 77 71.4 28.8 137 127.0 51.3 197 182.7 73.8 257 238.3 96.3 18 16.7 06.7 78 72.3 29.2 138 128.0 51.7 198 183.6 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 97.0 20 21 18.5 07.5 80 74.2 30.0 30.3 140 141 129.8 52.4 200 185.4 74.9 260 241.1 97.4 19.5 07.9 81 75.1 130.7 52.8 201 186.4 75.3 261 242.0 97.8 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 31.1 143 132.6 53.6 203 188.2 76.0 263 243.8 98.5 24 22.3 09.0 84 77.9 31.5 144 133.5 53.9 204 189.1 76.4 264 244.8 98.9 25 23.2 09.4 85 78.8 31.8 145 134.4 54.3 205 190.1 76.8 265 245.7 99.3 26 24.1 09.7 86 79.7 32.2 146 135.4 54.7 206 191.0 77.2 266 246.6 99.6 27 25.0 10.1 87 80.7 32.6 147 136.3 55.1 207 191.9 77.5 267 247.6 100.0 28 26.0 10.5 88 81.6 33.0 148 137.2 55.4 208 192.9 77.9 268 248.5 100.4 29 26.9 10.9 89 82.5 33.3 149 138.2 55.8 209 193.8 78.3 269 249.4 100.8 30 27.8 11.2 90 83.4 33.7 150 139.1 56.2 56.6 210 194.7 78.7 270 250.3 101.1 31 28.7 11.6 91 84.4 34.1 151 140.0 211 195.6 79.0 271 251.3 101.5 32 29.7 12.0 92 85.3 34.5 152 140.9 ;">6.9 212 196.6 79.4 272 252.2 101.9 33 30.6 12.4 93 86.2 34.8 153 141.9 57.3 213 197.5 79.8 273 253.1 102.3 34 31.5 12.7 94 87.2 35.2 154 142.8 57.7 214 198.4 80.2 274 254.0 102 6 35 32.5 13.1 95 88.1 35.6 155 143.7 58.1 215 199.3 80.5 275 255.0 103.0 36 33.4 13.5 96 89.0 36.0 156 144.6 58.4 216 200.3 80.9 276 255.9 103.4 37 34.3 13.9 97 89.9 36.3 157 145.6 58.8 217 201.2 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 37.1 159 147.4 59.6 219 203.1 82.0 279 258.7 104.5 40 37.1 15.0 100 92.7 37.5 160 148.3 59.9 220 204.0 82.4 280 259.6 104.9 41 38.0 15.4 101 93.6 37.8 161 149.3 60.3 221 204.9 82.8 281 260.5 105.3 42 38.9 15.7 102 94.6 38.2 162 150.2 60.7 222 205.8 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 83.5 283 262.4 106.0 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 97.4 39.3 165 153.0 61.8 225 208.6 84.3 285 264.2 106.8 46 42.7 17.2 106 98.3 39.7 166 153.9 62.2 226 209.5 84.7 286 365.2 107.1 47 43.6 17.6 107 99.2 40.1 167 154.8 62.6 227 210.5 85.0 287 266.1 107.5 48 44.5 18.0 108 100.1 40.5 168 155.8 62.9 228 211.4 85.4 288 267.0 107.9 49 45.4 18.4 109 101.1 40.8 169 156.7 63.3 229 212.3 85.8 289 268.0 108.3 50 51 46.4 18.7 110 102.0 41.2 170 157.6 63.7 230 213.3 86.2 290 268.9 108.6 47.3 19.1 111 102.9 41.6 171 158.5 64.1 231 214.2 86.5 291 269.8 109.0 52 48.2 19.5 112 103.8 42.0 172 159.5 64.4 232 215.1 86.9 292 270.7 109.4 53 49.1 19.9 113 104.8 42.3 173 160.4 64.8 233 216.0 87.3 293 271.7 109.8 54 50.1 20.2 114 105.7 42.7 174 161.3 65.2 234 217.0 87.7 294 272.6 110.1 55 51.0 20.6 115 106.6 43.1 175 162.3 65.6 235 217.9 88.0 295 273.5 110.5 56 51.9 21.0 116 107.6 43.5 176 163.2 65.9 236 218,8 88.4 296 274.4 110.9 57 52.8 21.4 117 108.5 43.8 177 164.1 66.3 237 219.7 88.8 297 275.4 111.3 58 53.8 21.7 118 109.4 44.2 178 165.0 66.7 238 220.7 89.2 298 276.3 111.6 59 54.7 22.1 119 110.3 44.6 179 166.0 67.1 239 221.6 89.5 299 277.2 112.0 60 55.6 22.5 120 111.3 45 180 166.9 67.4 240 222.5 89.9 300 278.2 112.4 Di8< * Dep. Lat Dist. Dep. Lat. Dist Dep. Lat Dist Dop. Lat I Dist Dep. Lat For 68 Dei^rees 4h 32™. TABLE 11. 89 i DIFFERENCE OF LATITUDE AND DEPARTURE FOR 23 DEGREES, l^ 32«. 1 Diet 1 Lat Dep. Dist Lat. Dep. Dist Lilt. Dep. Dist. Lat. Dep. 70.7 Dist Lat. Dep. 00.9 00.4 61 56.2 23.8 121 111.4 47.3 181 166.6 241 221.8 94.2 2 01.8 00.8 62 57.1 24.2 122 112.3 47.7 1«2 167.5 71.1 242 222.8 94.6 3 02.8 01.2 63 58.0 24.6 123 113.2 48.1 183 168.5 71.5 243 223.7 94.9 4 03.7 01.6 64 58.9 25.0 124 114.1 48.5 184 169.4 71.9 244 1 224.6 95.3 5 04.6 02.0 65 59.8 25.4 125 115.1 ;48.8 185 170.3 72.3 245 1 225.5 95.7 6 05.5 02.3 66 60.8 25.8 126 116.0 49.2 186 171.2 72.7 246 226 4 96.1 7 06.4 02.7 67 61.7 26.2 127 116.9 49.6 187 172.1 73.1 247 1 227.4 96.5 | 8 07.4 03.1 68 62.6 26.6 128 117.8 50.0 188 173.1 73.5 248 228.3, 96.9 1 9 0S.3 03.5 69 63.5 27.0 129 118.7 50.4 189 174.0 73.8 249 229.2 97.3 10 11 09.2 03.9 70 64.4 27.4 130 119.7 50.8 190 174.9 74.2 250 230.1 97.7 10.1 04.3 71 65.4 27.7 131 120.6 51.2 191 175.8 74.6 251 231.0 98.1 12 11.0 04.7 72 66.3 28.1 132 121.5 51.6 192 176.7 75.0 252 232.0 98.5 13 12.0 05.1 73 67.2 28.5 133 122.4 52.0 193 177.7 75.4 253 232.9 98.9 14 12.9 05.5 74 68.1 28.9 134 123.3 524 194 178.6 75.8 254 233.8 99.2 15 13.8 05.9 75 69.0 29.3 135 124.3 52.7 195 179.5 76.2 255 234.7 99.6 16 14.7 06.3 76 70.0 29.7 136 125.2 53.1 196 180.4 76.6 256 235.6 100.0 17 15.6 06.6 77 70.9 30.1 137 126.1 53.5 197 181.3 77.0 257 236.6 100.4 18 16.6 07.0 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 31.3 140 128.9 54.7 200 184.1 78.1 260 239.3 101.6 21 19.3 08.2 81 74.6 31.6 141 129.8,55.1 201 185.0 78.5 261 240.3 102.0 22 20.3 08.6 82 75.5 32.0 142 130.7 55.5 202 185.9 78.9 262 241.2 102.4 23 21.2 09.0 83 76.4 32.4 143 131.6 55.9 203 186.9 79.3 263 242.1 102.8 24 22.1 09.4 84 77.3 32.8 144 132.6 56.3 204 187.8 79.7 264 243.0 103.2 25 23.0 09.8 85 78.2 332 145 133.5 56.7 205 188.7 80.1 265 243.9 103.5 26 23.9 10.2 86 79.2 33.6 146 134.4 57.0 206 189.6 80.5 266 244.9 103.9 27 24.9 10.5 87 80.1 34.0 147 135.3 57.4 207 190.5 80.9 267 245.8 104.3 28 25.8 10.9 88 81.0 34.4 148 136.2 57.8 208 '191.5 81.3 268 246.7 104.7 29 26.7 11.3 89 81.9 34.8 149 137.2 58.2 209 1 192.4 81.7 269 247.6 105.1 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 83.8 35.6 151 139.0 59.0 211 194.2 82.4 271 249.5 105.9 32 29.5 12.5 92 84.7 35.9 152 139.9 59.4 212 195.1 82.8 272 2.50.4 106.3 33 30.4 12.9 93 85.6 36.3 153 140.8 59.8 213 196.1 83.2 273 251.3 106.7 34 31.3 13.3 94 86.5 36.7 154 141.8 60.2 214 197.0 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 36 33.1 14.1 96 88.4 37.5 156 143.6 61.0 216 198.8 84.4 276 254.1 107.8 37 34.1 14.5 97 89.3 37.9 157 144.5 61.3 217 199.7 84.8 277 255.0 108.2 38 35.0 14.8 98 90.2 38.3 158 145.4 61.7 218 200.7 85.2 278 255.9 108.6 39 35.9 15.2 99 91.1 38.7 159 146.4^62.1 219 201.6 85.6 279 256.8 109.0 40 36.8 15.6 100 92.1 39.1 160 147.3 62.5 220 202.5 86.0 280 257.7 109.4 41 37.7 16.0 101 93.0 39.5 161 148.2 62.9 221 203.4 86.4 281 258.7 109.8 42 38.7 16.4 102 93.9 39.9 162 149.1 63.3 222 204.4 86.7 282 259.6 110.2 43 39.6 16.8 103 94.8 40.2 163 150.0 63.7 223 205.3 87.1 283 260.5 110.6 44 40.5 17.2 104 95.7 40.6 164 151.0 64.1 224 206.2 87.5 284 261.4 111.0 45 41.4 17.6 105 96.7 41.0 165 151.9 64.5 225 207.1 87.9 285 262.3 111.4 46 42.3 18.0 106 97.6 41.4 166 152.8 64.9 226 208.0 88.3 286 263.3 111.7 47 43.3 18.4 107 98.5 41.8 167 153.7 65.3 227 209.0 88.7 287 264.2 112.1 48 44.2 18.8 108 99.4 42.2 l«i8 154.6 65.6 228 209.9 89.1 288 265.1 112.5 49 45.1 19.1 109 100.3 42.6 169 155.6 66.0 229 210.8 89.5 289 266.0 112.9 50 46.0 19.5 110 101.3 43.0 170 156.5 66.4 230 211.7 89.9 290 266.9 113.3 51 46.9 19.9 111 102.2 43.4 171 157.4 66.8 231 212.6 90.3 291 267.9 113.7 52 47.9 20.3 112 103.1 43.8 172 158.3 67.2 232 213.6 90.6 292 268.8 114.1 53 48.8 20.7 113 104.0 44.2 173 159.2 67.6 233 214.5 91.0 293 269.7 114.5 54 49.7 21.1 114 104.9 44.5 174 160.2 68.0 234 215.4 91.4 294 270.6 114.9 55 50.6 21.5 115 105.9 44.9 175 161.1 68.4 235 216.3 91.8 295 271.5 115.3 56 51.5 21.9 116 106.8 45.3 176 162.0 68.8 236 217.2 92.2 296 272.5 115.7 57 52.5 22.3 117 107.7 45.7 177 162.9 69.2 237 218.2 92.6 297 273.4 116.0 58 53.4 22.7 118 IOS.6 46.1 17S 163.8 69.6 238 219.1 93.0 298 274.3 116.4 59 54.3 23.1 119 109.5 46.5 179 164.8 69.9 239 220.0 93.-^ 299 275.2 116.8 60 Dist 55.2 Dep. 23.4 120 110.5 46.9 180 165.7 70.3 240 220.9 93.8 300 276.2 117.2 Lat. Dist. Dep. Lat Dist Dep. Lat. Dist Dep. Lat Dist Dep. Lat For 67 Detrrees. 4t» 28m. 1 40 TABLE 11. DIFFERENCE OF LATITUDE AND DEPARTURE FOR 24 DEGREES. Ih 36m. Dist Lat. Dep. Dist. Lat. Dep. Dist. LaL Dep. Dist. Lat. Dep. Dist. Lat 220.2 Dep. 1 00.9 00.4 61 55.7 24.8 121 110.5 49.2 181 165.4 73.6 241 98.0 2 01.8 00.8 62 56.6 25.2 122 111.5 49.6 182 166.3 74.0 242 221.1 98.4 3 02.7 01.2 63 57.6 25.6 123 112.4 50.0 183 167.2 74.4 243 222.0 98.8 4 03.7 01.6 64 58.5 26.0 124 113.3 50.4 184 168.1 74.8 244 222.9 99.2 5 04.6 02.0 65 59.4 26.4 125 114.2 50.8 185 169.0 75.2 245 223.8 99.7 6 05.5 02.4 66 60.3 2().8 126 115.1 51.2 186 169.9 75.7 246 224.7 100.1 7 06.4 02.8 67 61.2 27.3 127 116.0 51.7 187 170.8 76.1 247 225.6 100.5 8 07.3 03.3 68 62.1 27.7 128 116.9 52.1 188 171.7 76.5 248 226.6 100.9 9 08.2 03.7 69 63.0 28.1 129 117.8 52.5 189 172.7 76.9 249 227.5 101.3 10 09.1 04.1 70 63.9 28.5 130 131 118.8 52.9 190 191 173.6 77.3 250 228.4 101.7 11 10.0 04.5 71 64.9 28.9 119.7 53.3 174.5 77.7 251 229.3 102.1 12 11.0 04.9 72 65.8 29.3 132 120.6 53.7 192 175.4 78.1 252 230.2 102.5 13 11.9 05.3 73 66.7 29.7 133 121.5 54.1 193 176.3 78.5 253 231.1 102.9 14 12.8 05.7 74 67.6 30.1 134 122.4 54.5 194 177.2 78.9 254 232.0 103.3 15 13.7 06.1 75 68.5 30.5 135 123.3 54.9 195 178.1 79.3 255 233.0 103.7 16 14.6 06.5 76 69.4 30.9 136 124.2 55.3 196 179.1 79.7 256 233.9 104.1 17 15.5 06.9 77 70.3 31.3 137 125.2 55.7 197 180.0 80.1 257 234.8 104.5 18 16.4 07.3 78 71.3 31.7 188 126.1 56.1 198 180.9 80.5 258 235.7 104.9 19 17.4 07.7 79 72.2 32.1 139 127.0 56.5 199 181.8 80.9 259 236.6 105.3 20 21 18.3 19.2 08.1 80 73.1 32.5 32.9 140 127.9 56.9 200 201 182.7 183.6 81.3 260 237.5 105.8 106.2 08.5 81 74.0 141 128.8 57.3 81.8 261 238.4 22 20.1 08.9 82 74.9 33.4 142 129.7 57.8 202 184.5 82.2 262 239.3 106.6 23 21.0 09.4 83 75.8 33.8 143 130.6 58.2 203 185.4 82.6 263 240.3 107.0 24 21.9 09.8 84 76.7 34.2 144 131.6 58.6 204 186.4 83.0 264 241.2 107.4 25 22.8 10.2 85 77.7 34.6 145 132.5 59.0 205 187.3 83.4 265 242.1 107.8 26 23.8 10.6 86 78.6 3').0 146 133.4 59.4 206 188.2 83.8 266 243.0 108.2 27 24.7 11.0 87 79.5 35.4 147 134.3 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 81.3 36.2 149 136.1 60.6 209 190.9 85.0 269 245.7 109.4 30 27.4 12.2 90 .82.2 36.6 150 137.0 61.0 61.4 210 191.8 85.4 270 246.7 109.8 31 28.3 12.6 91 83.1 37.0 151 137.9 211 192.8 85.8 271 247.6 110.2 32 29.2 13.0 92 84.0 37.4 152 138.9 61.8 212 193.7 86.2 272 248.5 110.6 33 30.1 13.4 93 85.0 37.8 153 139.8 62.2 213 194.6 86.6 273 249.4 111.0 34 31.1 13.8 94 85.9 38.2 154 140.7 62.6 214 195.5 87.0 274 250.3 111.4 35 32.0 14.2 95 86.8 38.6 155 141.6 63.0 215 196.4 87.4 275 251.2 111.9 36 32.9 14.6 96 87.7 39.0 156 142.5 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 89.5 39.9 158 144.3 64.3 218 199.2 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 16.3 100 91.4 40.7 160 146.2 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 94.1 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 46 42.0 18.7 106 96.8 43.1 166 151.6 67.5 226 206.5 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 51 45.7 20.3 110 100.5 44.7 170 155.3 69.1 230 210.1 93.5 290 264.9 118.0 46.6 20.7 111 101.4 45.1 171 156.2 69.6 231 211.0 94.0 291 265.8 118.4 52 47.5 21.2 112 102.3 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 58 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 60 54.8 24.4 120 109.6 48.8 Lat. 180 164.4 73.2 240 219.3 97.6 300 274.1 122.0 Diat . Dep. Lat. I Dist. Dep. Dist. Dep. Lat. Dist. Dep. Lat Dist. Dep. Lat For 66 De2:rees. 4h 24m. | TABLE 11. <> 1 DIFFERENCE OF LATITUDE AND DEPARTURE FOR 25 DEGREES. Ih 40i». 1 Dist 1 Lat Dep. Dist. Lat Dep. Dist Lat Dep. Dist. 181 Lat Dep. Dist Lat Dep, 00.9 00.4 31 55.3 25.8 121 109.7 51.1 164.0 76.5 241 218.4 101.9 2 01.8 00.8 62 56.2 26.2 122 110.6151.6 1^2 164.9 76.9 242 219.3 102.3 3 02.7 01.3 63 57.1 26.6 123 111.5 52.0 183 165.9 77.3 243 220.2 102 7 4 03.6 01.7 64 58.0 27.0 124 112.4 52.4 184 166.8 77.8 244 221.1 103.1 5 04.5 02.1 65 58.9 27.5 125 113.3 52.8 185 167.7 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 78.6 246 223.0 104.0 7 06.3 03.0 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 79.5 248 224.8 104 8 9 08.2 03.8 69 62.5 29.2 129 116.9 54.5 189 171.3 79.9 249 225.7 105.2 10 11 09.1 04.2 70 63.4 29.6 130 117.8 54.9 190 172.2 80.3 250 226.6 105.7 10.0 04.6 71 64.3 30.0 131 118.7 55.4 191 173.1 80.7 251 227.5 106.1 12 10.9 05.1 72 65.3 30.4 132 119.6 55.8 192 174.0 81.1 252 228.4 106.5 13 11.8 05.5 73 66.2 30.9 133 120.5 56.2 193 174.9 81.6 253 229.3 106.9 14 12.7 05.9 74 67.1 31.3 134 121.4 56.6 194 175.8 82.0 254 230.2 107.3 15 13.6 06.3 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 68.9 32.1 136 123.3 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 83.3 257 232.9 108.6 18 16.3 07.6 78 70.7 33.0 138 125.1 58.3 198 179.4 83.7 258 233.8 109.0 19 17.2 08.0 79 71.6 33.4 139 126.0 58.7 199 180.4 84.1 259 234.7 109.5 20 18.1 08.5 80 72.5 33.8 140 126.9 59.2 200 181.3 84.5 260 235.6 109.9 21 19.0 08.9 81 73.4 34.2 141 127.8 59.6 201 182.2 84.9 261 236.5 110.3 22 19.9 09.3 82 74.3 34.7 142 128.7 60.0 202 183.1 85.4 262 237.5 110.7 23 20.8 09.7 83 75.2 35.1 143 129.6 60.4 203 184.0 85.8 263 238.4 111.1 24 21.8 10.1 84 76.1 35.5 144 130.5 60.9 204 184.9 86.2 264 239.3 111.6 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 23.6 11.0 86 77.9 36.3 146 132.3 61.7 206 186.7 87.1 266 241.1 112.4 27 24.5 11.4 87 78.8 36.8 147 133.2 62.1 207 187.6 ^7.5 267 242.0 112.8 28 25.4 11.8 88 79.8 37.2 148 134.1 62.5 208 188.5 87.9 268 242.9 113.3 29 •26.3 12.3 89 80.7 37.6 149 135.0 63.0 209 189.4 88.3 269 243.8 113.7 30 27.2 12.7 90 81.6 38.0 150 135.9 63.4 210 190.3 88.7 270 244.711 14.1 1 31 28.1 13.1 91 82.5 38.5 151 136.9 63.8 211 191.2 89.2 271 245.6 114.5 32 29.0 13.5 92 83.4 38.9 152 137.8 64.2 212 192.1 89.6 272 246.5 115.0 33 29.9 13.9 93 84.3 39.3 153 138.7 64.7 213 193.0 90.0 273 247.4 115.4 34 30.8 14.4 94 85.2 39.7 154 139.6 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 32.6 15.2 96 87.0 40.6 156 141.4 65.9 216 195.8 91.3 276 250.1 116.6 37 33.5 15.6 97 87.9 41.0 157 142.3 66.4 217 196.7 91.7 277 251.0 117.1 38 34.4 16.1 98 88.8 41.4 158 143.2 66.8 218 197.6 92.1 278 252.0 117.5 39 35.3 16.5 99 89.7 41.8 159 144.1 67.2 219 198.5 92.6 279 252.9 117.9 40 36.3 16.9 100 90.6 42.3 160 145.0 67.6 220 199.4 93.0 280 253.8 118.3 41 37.2 17.3 101 91.5 42.7 161 145.9 68.0 221 200.3 93.4 281 254.7 118.8 42 38.1 17.7 102 92.4 43.1 162 146.8 68.5 222 201.2 93.8 282 255.6 119.2 43 39.0 18.2 103 93.3 43.5 163 147.7 68.9 223 202.1 94.2 283 256.5 119.6 44 39.9 18.6 104 94.3 44.0 164 148.6 69.3 224 203.0 94.7 284 257.4 120.0 45 40.8 19.0 105 95.2 44.4 165 149.5 69.7 225 203.9 95.1 285 258.3 120.4 46 41.7 19.4 106 96.1 44.8 166 150.4 70.2 226 204.8 95.5 286 259.2 120.9 47 42.6 19.9 107 97.0 45.2 167 151.4 70.6 227 205.7 95.9 287 260.1 121.3 1 48 43.5 20.3 108 97.9 45.6 168 152.3 71.0 228 206.6 96.4 288 261.0 121.7 49 44.4 20.7 109 98.8 46.1 169 153.2 71.4 229 207.5 96.8 289 261.9 122.1 50 51 45.3 46.2 21.1 110 99.7 46.5 170 154.1 71.8 230 208.5 97.2 290 262.8 122.6 21.6 111 100.6 46.9 171 155.0 72.3 231 209.4 97.6 291 263.7 123.0 1 52 47.1 22.0 112 101.5 47.3 172 155.9 72.7 232 210.3 98.0 292 264.6 123.4 53 48.0 22.4 113 102.4 47.8 173 156.8 73.1 233 211.2 98.5 293 1 265.5 1 123.8 54 48.9 22.8 114 103.3 48.2 174 157.7 73.5 234 212.1 98.9 294 , 266.5 ( 124.2 55 49.8 2:!.2 11.^. 104.2 48.6 175 158.6 74.0 235 213.0 99.3 295 267.4 124.7 56 50.8 23.7 116 105.1 49.0 176 1.59.5 74.4 236 213.9 99.7 296 268.3 125.1 57 51.7 24.1 117 106.0 49.4 177 160.4 74.8 237 214.8 100.2 297 269.2 125.5 58 52.6 24.5 lis 106.9 49.9 17s 161.3 75.2 238 215.7 100.6 298 270.1 125.9 59 53.5 24.9 119 107.9 50.3 179 162.2 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. Dl8t Dep. Lat Dist Dep. Lat. Dist Dep. Lat Dist Dep. Lat P 'or 65 Decrees. 4h 2011. 1 42 TABLE 11. • DIFFERENCE OF LATITUDE AND DEPARTURE FOR 26 DEGREES. Ih 44». Dist Lat. Dep. Dist. Lat, Dep. Dist. Lat. Dep. Dist. Lat Dep. Dist. Lat. Dep. 1 00.9 00.4 61 54.8 26.7 121 108.8 53.0 181 162.7 79.8 241 216.6 105.6 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 56.6 27.6 123 110.6 53.9 183 164.5 80.2 243 218.4 106.5 4 03.6 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 06.3 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 12S 115.0 56.1 188 169.0 82.4 248 222.9 108.7 9 08.1 03.9 69 62.0 30.2 129 115.9 56.5 189 169.9 82.9 249 223.8 109.2 10 11 09.0 04.4 70 62.9 30.7 130 116.8 57.0 190 170.8 83.3 250 224.7 109.6 09.9 04.8 71 63.8 31.1 131 117.7 57.4 191 171.7 83.7 251 225.6 110.0 12 10.8 05.3 72 64.7 31.6 132 118.6 57.9 192 172.6 84.2 252 226.5 110.5 13 11.7 05.7 73 65.6 32.0 133 119.5 58.3 193 173.5 84.6 253 227.4! 110.9 14 12.6 06.1 74 66.5 32.4 134 120.4 58.7 194 174.4 85.0 254 228.3 111.3 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 16 14.4 07.0 76 68.3 33.3 1-36 122.2 59.6 196 176.2 85.9 256 230.1 112.2 17 15.3 07.5 77 69.2 33.8 137 1 23. 1 60.1 197 177.1 86.4 257 231.0 112.7 18 16.2 07.9 78 70.1 34.2 138 124.0 60.5 198 178.0 86.8 258 231.9 113.1 19 17.1 08.3 79 71.0 34.6 139 124.9 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 72.8 35.5 141 126.7 61.8 201 180.7 88.1 261 234.6 114.4 22 19.8 09.6 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 21.6 10.5 84 75.5 36.8 144 129.4 63.1 204 183.4 89.4 264 237.3 115.7 25 22.5 11.0 85 76.4 37.3 145 130.3 63.6 205 184.3 89.9 265 238.2 116.2 26 23.4 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 26.1 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 1.50 134.8 65.8 210 18C.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 :J2 28.8 14.0 92 82.7 40.3 152 136.6^ 66.6 212 190.5 92.9 272 244.5 119.2 33 29.7 14.5 93 83.6 40.8 1.53 137.5 67.1 213 191.4 93.4 273 245.4 119.7 34 30.6 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 41.6 155 139.3 67.9 215 193.2 94.2 275 247.2 120.6 36 32.4 15.8 96 86.3 42.1 156 140.2 68.4 216 194.1 94.7 276 248.1 121.0 37 33.3 16.2 97 87.2 42.5 157 141.1 68.8 217 195.0 95.1 277 249.0 121.4 38 34.2 16.7 98 88.1 43.0 158 142.0 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 36.0 17.5 100 89.9 43.8 160 143.8 70.1 220 197.7 96.4 280 251.7 122.7 41 36.9 18.0 101 90.8 44.3 161 144.7 70.6 221 198.6 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 38.6 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 45.6 164 147.4 71.9 224 201.3 98.2 284 255.3 124.5 45 40.4 19.7 105 94.4 46.0 165 148.3 72.3 225 202.2 98.6 285 256.2 124.9 46 41.3 20.2 106 95.3 46.5 166 149.2 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 43.1 21.0 108 97.1 47.3 1(58 151.0 73.6 228 204.9 99.9 288 258.9 126.3 49 44.0 21.5 109 98.0 47.8 169 151.9 74.1 229 205.8 100.4 289 259.8 126.7 50 44.9 21.9 110 98.9 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 75.0 231 207.6 101.3 291 261.5 127.6 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 47.6 23.2 113 101.6 49.5 173 155.5 75.8 233 209.4 102.1 293 263.3 128.4 54 48.5 23.7 114 102.5 50.0 174 1.56.4 76.3 234 210.3 102.6 2941 264.2 128.9 55 49.4 24.1 115 103.4 50.4 175 157.3 76.7 235 211.2 103.0 295 265.1 129,3 5t) 50.3 24.5 116 104.3 50.9 176 158.2 77.2 236 212.1 103.5 296 266.0 129.8 57 51.2 25.0 117 105.2 51.3 177 159.1 77.6 237 213.0 103.9 297 266.9 1.30.2 58 52.1 25.4 118 106.1 51.7 17S 160.0 78.0 238 213.9 104.3 298 267.8 130.6 59 53.0 25.9 K9 107.0 .52.2 179 160.9 78.5 239 214.8 104.8 299 268.7 131.1 60 W8t 53.9 26.3 120 107.9 ,52.6 180 161.8 78.9 240 215.7 105.2 300 269.6 131.5 Dep. Lat. Dist. Dep, Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. 1 Lat. | i "or 64 Dei,'rfe.s. 4h 16ra. 1 TABLE 11. i 48 DIFFERENCE OF LATITUDE AND DEPARTURE FOR 27 DEGREES. la 48m. Dist 1 «2 3 4 5 6 7 8 9 10 Lat 00.9 01.8 02.7 03.6 04.5 05.3 06.2 07.1 08.0 08.9 Dep. 00.5 00.9 01.4 01.8 02.3 02.7 03.2 03.6 04.1 04.5 Dist. Lat Dep. Dist. Lilt. Dep. 54.9 55.4 55.8 56.3 56.7 57.2 57.7 58.1 58.6 59.0 Dist. Lat. Dep. Diat. 241 242 243 244 245 246 247 248 249 250 Lat Dep. 61 62 63 64 65 66 67 68 69 70 54.4 55.2 56.1 57.0 57.9 58.8 ^ 59.7 60.6 61.5 62.4 27.7 28.1 28.6 29.1 29.5 30.0 30.4 30.9 31.3 31.8 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 107.8 108.7 109.6 110.5 111.4 112.3 113.2 114.0 114.9 115.8 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 161.3 162.2 163.1 163.9 164.8 165.7 166.6 167.5 168.4 169.3 82.2 82.6 83.1 83.5 84.0 84.4 84.9 85.4 85.8 86.3 214.7 215.6 216.5 217.4 218.3 219.2 220.1 221.0 221.9 222.8 109.4 109.9 110.3 110.8 111.2 111.7 112.1 112.6 113.0 113.5 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 09.8 10.7 11.6 12.5 13.4 14.3 15.1 16.0 16.9 17.8 05.0 05.4 05.9 06.4 06.8 07.3 07.7 08.2 08.6 09.1 71 72 73 74 75 76 77 78 79 80 63.3 64.2 65.0 65.9 66.8 67.7 68.6 69.5 70.4 71.3 32.2 32.7 33.1 33.6 34.0 34.5 35.0 35.4 35.9 36.3 36.8 37.2 37.7 38.1 38.6 39.0 39.5 40.0 40.4 40.9 116.7 117.6 118.5 119.4 120.3 121.2 122.1 123.0 123.^ 124.7 59.5 59.9 60.4 60.8 61.3 61.7 62.2 62.7 63.1 63.6 64.0 64.5 64.9 65.4 65.8 66.3 66.7 67.2 67.6 6s. 1 170.2 171.1 172.0 172.9 173.7 174.6 175.5 176.4 177.3 178.2 86.7 87.2 87.6 88.1 88.5 89.0 89.4 89.9 90.3 90.8 251 252 253 254 255 256 257 258 259 260 223.6 224.5 225.4 226.3 227.2 228.1 229.0 229.9 230.8 231.7 114.0 114.4 114.9 115,3 115.8 116.2 116.7 117.1 117.6 118.0 18.7 19.6 20.5 21.4 22.3 23.2 24.1 24.9 25.8 26.7 09.5 10.0 10.4 10.9 11.3 11.8 12.3 12.7 13.2 13.6 81 82 83 84 85 86 87 88 89 90 72.2 73.1 74.0 74.8 75.7 76.6 77.5 78.4 79.3 80.2 141 142 143 144 145 146 147 148 149 150 125.6 126.5 127.4 128.3 129.2 130.1 131.0 131.9 132.8 133.7 134 5 135.4 136.3 137.2 138.1 139.0 139.9 140.8 141.7 142.6 179.1 180.0 180.9 181.8 182.7 183.5 184.4 185.3 186.2 187.1 91.3 91.7 92.2 92.6 93.1 93.5 94.0 94.4 94.9 95.3 261 262 263 264 265 266 267 268 269 270 232.6 233.4 234.3 235.2 236.1 237.0 237.9 238.8 239.7 240.6 118.5 118.9 119.4 119.9 120.3 120.8 121.2 121.7 122.1 122.6 31 32 33 34 35 36 37 38 39 40 27.6 28.5 29.4 30.3 31.2 32.1 33.0 33.9 34.7 35.6 14.1 14.5 15.0 15.4 15.9 16.3 16.8 17.3 17.7 18.2 91 92 93 94 95 96 97 98 99 100 81.1 82.0 82.9 83.8 84.6 85.5 86.4 87.3 88.2 89.1 41.3 41.8 42.2 42.7 43.1 43.6 44.0 44.5 44.9 45.4 151 152 153 154 155 156 157 158 159 160 68.6 69.0 69.5 69.9 70.4 70.8 71.3 71.7 72.2 72.6 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 188.0 188.9 189.8 190.7 191.6 192.5 193.3 194.2 195.1 196.0 95.8 96.2 96.7 97.2 97.6 98.1 98.5 99.0 99.4 99.9 271 272 273 274 275 276 277 278 279 280 241.5 242.4 243.2 244.1 245.0 245.9 246.8 247.7 248.6 249.5 123.0 123.5 123.9 124.4 124.8 125.3 125.8 126.2 126.7 127.1 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 36.5 37.4 38.3 39.2 40.1 41.0 41.9 42.8 43.7 44.6 45.4 46.3 47.2 48,1 49.0 49.9 50.8 51.7 52.6 53.5 18.6 19.1 19.5 20.0 20.4 20.9 21.3 21.8 22.2 22.7 101 102 103 104 105 106 107 108 109 110 90.0 90.9 91.8 92.7 93.6 94.4 95.3 96.2 97.1 98.0 45.9 46.3 46.8 47.2 47.7 48.1 48.6 49.0 49.5 49.9 161 162 163 164 165 166 167 168 169 170 143.5 144.3 145.2 146.1 147.0 147.9 148.8 149.7 150.6 151.5 73.1 73.5 74.0 74.5 74.9 75.4 75.8 76.3 76.7 77.2 196.9 197.8 198.7 199.6 200.5 201.4 202.3 203.1 204.0 204.9 100.3 100.8 101.2 101.7 102.1 102.6 103.1 103.5 104.0 104.4 281 282 283 284 285 286 287 288 289 290 250.4 251.3 2. 2.2 253.0 253.9 254.8 255.7 256.6 257.5 258.4 127.6 128.0 128.5 128.9 129.4 129.8 130.3 130.7 131.2 131.7 23.2 23.6 24.1 24.5 25.0 25.4 25.9 26.3 26.8 27.2 111 112 113 114 115 116 117 118 119 120 98.9 99.8 100.7 101.6 102.5 103.4 104.2 105.1 106.0 106.9 50.4 50.8 51.3 51.8 52.2 52.7 53.1 53.6 54.0 54.5 L.at. 171 172 173 174 175 176 177 178 179 180 152.4 153.3 154.1 15.5.0 155.9 156.8 157.7 158.6 159.5 160.4 77.6 78.1 78.5 79.0 79.4 79.9 80.4 80.8 81.3 81.7 231 232 233 234 235 236 237 238 239 240 205.8 206,7 207.6 208.5 209.4 210.3 211.2 212.1 213.0 213.8 104.9 105.3 105.8 106.2 106.7 107.1 107.6 108.0 108.5 109.0 291 292 293 294 295 296 297 298 299 300 Dist. 259.3 260.2 261.1 262.0 262.8 263.7 264.6 2<)5.5 2<)6.4 267.3 132.1 132.6 133.0 133.5 133.9 134.4 134.8 135.3 135.7 136.2 Dist Dep. Lat. Dist. Dep. Dist. Dep. Lat. Dist. Dep. Lat. Dep. Lat For nS Detrree* 4h 12'n. | 44 TABLE II. 1 DIFFERENCE OF LATITUDE AND DEPARTURE FOR 28 DEGREES, l^* 52n>. Dist Lat 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 54.7 29.1 122 107.7 57.3 1S2 160.7 85.4 242 213.7 113.6 3 02.6 01.4 63 55.6 29.6 123 108.6 57.7 183 161.6 85.9 243 214.6 114.1 4 03.5 01.9 64 56.5 30.0 124 109.5 58.2 184 162.5 86.4 244 215.4 114.6 5 04.4 02.3 65 57.4 30.5 125 110.4 58.7 185 163.3 86.9 245 216.3 115.0 6 05.3 02.8 66 58.3 31.0 126 111.3 59.2 186 164.2 87.3 246 217.2 115.5 7 06.2 03.3 67 59.2 31.5 127 112.1 59.6 187 165.1 87.8 247 218.1 116.0 8 07.1 03.8 68 60.0 31.9 128 113.0 60.1 188 166.0 88.3 248 219.0 116.4 9 07.9 04.2 69 60.9 32.4 129 113.9 60.6 189 166.9 88.7 249 219.9 116.9 10 11 08.8 04.7 70 61.8 32.9 i:!0 114.8 61.0 190 167.8 89.2 250 220.7 117.4 117.8 09.7 05.2 71 62.7 33.3 131 115.7 61.5 191 108.6 89.7 251 221.6 12 10.6 05.6 72 63.6 33.8 132 116.5 62.0 192 169.5 90.1 252 222.5 118.3 13 11.5 06.1 73 64.5 34.3 133 117.4 62.4 193 170.4 90.6 253 223.4 118.8 14 12.4 06.6 74 65.3 34.7 134 118.3 62.9 194 171.3 91.1 254 224.3 119.2 15 13.2 07.0 75 66.2 35.2 135 119.2 63.4 195 172.2 91.5 255 225.2 119.7 16 14.1 07.5 76 67.1 35.7 136 120.1 63.8 196 173.1 92.0 256 226.0 120.2 17 15.0 08.0 77 68.0 36.1 137 (21.0 64.3 197 173.9 92.5 257 226.9 120.7 18 15.9 08.5 78 68.9 36.6 138 121.8 64.8 198 174.8 93.0 258 227.8 121.1 19 16.8 08.9 79 69.8 37.1 139 122.7 65.3 199 175.7 93.4 259 228.7 121.6 20 17.7 09.4 80 70.6 37.6 140 123.6 65.7 200 176.6 93.9 260 229.6 122.1 21 18.5 09.9 81 71.5 38.0 141 124.5 66.2 201 177.5 94.4 261 230.4 122.5 22 19.4 10.3 82 72.4 38.5 142 125.4 66.7 202 178.4 94.8 262 231.3 123.0 23 20.3 10.8 83 73.3 39.0 143 126.3 67.1 203 179.2 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 2(^ 23.0 12.2 86 75.9 40.4 146 128.9 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 24.7 13.1 88 77.7 41.3 148 130.7 69.5 208 183.7 97.7 268 236.6 125.8 126.3 29 25.6 13.6 89 78.ft 41.8 149 131.6 70.0 209 184.5 98.1 269 237.5 30 31 26.5 14.1 90 91 79.5 42.3 150 132.4 70.4 210 185.4 98.6 270 238.4 126.8 27.4 14.6 80.3 42.7 151 133.3 70.9 211 186.3 99.1 271 239.3 127.2 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 83.9 44.6 155 136.9 72.8 215 189.8 100.9 275 242.8 129.1 36 31.8 16.9 96 84.8 45.1 156 137.7 73.2 216 190.7 101.4 276 243.7 129.6 37 327 17.4 97 85.6 45.5 157 138.6 73.7 217 191.6 101.9 277 244.6 130.0 38 33.6 17.8 98 86.5 46.0 158 139.5 74.2 218 192.5 102.3 278 245.5 130.5 39 34.4 18.3 99 87.4 46.5 159 140.4 74.6 219 193.4 102.8 279 246.3 131.0 40 41 35.3 36.2 18.8 100 88.3 46.9 160 141.3 75.1 220 194.2 103.3 280 247.2 131.5 19.2 101 89.2 47.4 161 142.2 75.6 221 195.1 103.8 281 248.1 131.9 42 .S7.1 19.7 102 90.1 47.9 162 143.0 76.1 222 196.0 104.2 282 249.0 132.4 43 38.0 20.2 103 90.9 48.4 163 143.9 76.5 223 196.9 104.7 283 249.9 132.9 44 38.8 20.7 104 91.8 48.8 164 144.8 77.0 224 197.8 105.2 284 ' 250.8 133.3 45 39.7 21.1 105 92.7 49.3 165 145.7 77.5 225 198.7 105.6 285 251.6 133.8 46 40.6 21.6 106 93.6 49.8 166 146.6 77.9 226 19:».5 106.1 286 252.5 134.3 47 41.5 22.1 107 94.5 50.2 167 147.5 78.4 227 200.4 106.6 287 253.4 134.7 48 42.4 22.5 108 95.4 50.7 i(;8 148.3 78.9 228 201.3 107.0 288 254.3 135.2 49 43,3 23.0 109 96.2 51.2 169 149.2 79.3 221> 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 j 136.1 1 51 45.0 23.9 HI 98.0 52.1 171 151.0 80.3 231 204.0 108.4 291 256.9 136.6 52 45.9 24.4 112 98.9 52.6 172 151.9 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 81.2 233 205.7 109.4 293 258.7 137.6 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 ll.i 101.5 54.0 175 154.5 82.2 235 207.5 110.3 295 260.5 138.5 5(') 49.4 26.3 116 102.4 54.5 176 155.4 82.6 236 208.4 110.8 296 261.4 139.0 57 50.3 2(5.8 117 10:].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 17S 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 60 Dist. 53.0 28.2 Lilt. 120 106.0 56.3 180 158.9 84.5 240 211.9 112.7 300 264.9 1 140.8 1 Dep. Dist. Dep. Lut. Dist, D<'p. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 1 ] For 62 Decrees. 4h 8"'. | TABLE 11. 46 DIFFERENCE OF LATITUDE AND DEPARTURE FOR 29 DEGREES. Ih 66m. • Dist 1 Lat. 00.9 Dep. Di3t. Lat. 53.4 Dep. Dist. Lat Dep. Dist. Lat Dep. Dist. 241 Lat Dep. 00.5 61 29.6 121 105.8 58.7 181 158.3 87.8 210.8 116.8 o 01.7 01.0 62 54.2 30.1 122 10t}.7 59.1 182 159.2 88.2 242 211.7 117.3 n 02.6 01.5 63 55 1 30.5 123 1U7.6 59.6 183 160.1 8S.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 04.4 02.4 65 56.9 31.;. 125 109.3 60.6 185 161.8 89.7 24.-. 214.3 118.8 6 05.2 02.9 66 57.7 32.0 126 110.2 61.1 186 1 62.7 90.2 246 215.2 119.3 7 06.1 03.4 67 58.6 32.5 127 111.1 6k6 187 163.6 90.7 247 216.0 119.7 8 07.0 03.9 68 5i>.5 33.0 128 112.0 62.1 188 1 1)4.4 91.1 248 216.9 120.2 9 07.9 04.4 69 60.3 33.5 129 112.8 <)2.5 189 16.5.3 91.6 249 217.8 120.7 10 11 08.7 04.^ 70 61.2 33.9 130 131 113.7 63 190 191 166.2 92.1 250 218.7 121.2 121.7 09.6 05.3 71 62.1 34.4 114.6 63.5 167.1 92.6 251 219.5 12 10.5 0.-).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 94.1 254 222.2 123.1 15 13.1 07.3 75 65.6 36.4 135 118.1 65.4 195 170.6 94.5 255 223.0 123.6 l() 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 OS 2 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 ■10 21 17.5 18.4 09.7 80 70.0 38.8 140 122.4 67.9 200 174.9 175.8 97.0 260 227.4 126.1 10.2 81 70.8 39.3 141 123.3 ()S.4 201 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 91>.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 73.2 210 183.7 101.8 270 236.1 130.9 31 27.1 15.0 91 79.6 44.1 151 132.1 211 184.5 102.3 271 237.0 131.4 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 l.i.O 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 1 03.7 274 239.6 132.8 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 -> / 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 IS.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 1 3!>.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 79.5 224 195.9 108.6 284 248.4 137.7 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 46 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 81.4 228 199.4 110.5 288 251.9 139.61 49 42.9 ' 23.8 10i> 95.3 52.8 169 147.8 81.9 229 200.3 111.0 289 252.8 140.11 50 51 43.7 24.2 1 10 96.2 53.3 170 148.7 82.4 230 201.2 111.5 290 253.6 140.6 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 1 12 98.0 54.3 172 150.4 83.4 232 202.9 112.5 292 255.4 141.6 53 46.4 25.7 113 98.8 54.8 173 151.3 83.9 233 203.8 113.0 293 2r.6.3 142.0 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 4fS.l 26.7 115 100.6 55.8 175 153.1 84.8 235 205.5 113.9 295 258.0 143.0 50 49.0 27.1 116 101.5 56.2 176 1.53.9 85.3 236 206.4 114.4 296 2.58.9 143.5 57 49.9 27.6 117 102.3 56.7 177 -154.8 85.8 237 207.3 114.9 297 259.8 144.0 58 50.7 28.1 118 io;;.2 57.2 178 155.7 86.3 238 208.2 115.4 298 260.6 144.5 59 51.6 2.S.6 119 104.1 57.7 179 156.6 86.8 239 209.0 115.9 299 261.5 145.0 60 Dist 52.5 Dep. 29.1 120 105.0 58.2 Lat. 180 157.4 87.3 240 209.9 116.4 300 262.4 145.4 Lat. Dist. Dep. Dist. Dep Lnt. Dist. Dep. Lat. Dist. Dep. Lat For 61 Dpp^i'Ges. 4h 4m. 1 46 TABLE II. DIFFERENCE OF LATITUDE AND DEPARTURE FOR 30 DEGREES. 2 Q 0». DisL Lat. Dep. Dist. Lat. Dep. Dl8t. Lat. Dep. Dist. Lat. ' Dep. 90.5 Dist.' Lat. Dep. 120.5 1 00.9 00.5 61 52.8 30.5 121 104.8 60.5 181 156.8 241 1 208.7 2 01.7 01.0 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 32.0 124 107.4 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 93.5 217 213.9 123 5 8 06.9 04.0 68 58.9 34.0 128 1 10.9 1 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 66.0 192 166.3 96.0 252 218.2 126.0 13 ll.o 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 68.0 196 169.7 98.0 256 221.7 128.0 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 2(54 228.6 132.0 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 75.0 210 211 181.9 105.0 270 233.8 135.0 31 26.8 15.5 91 78.8 45.5 151 130.8 75.5 182.7 105.5 271 234.7 135.5 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 16« 143.8 83.0 226 195.7 113.0 286 247.7 143.0 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 54.0 168 145.5 84.0 228 197.5 114.0 288 249.4 144.0 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 25.0 110 95.3 55.0 170 147.2 85.0 230 19i».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 8(5.5 233 201.8 116.5 293 253.7 146.5 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 59.0 17S 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 Di3t 52.0 30.0 120 103.9 60.0 180 1 55.9 90.0 240 207.8 120.0 300 1 259.8 150.0 Dep. Lat. Dist. Dep. Lat. Di8t. Dep. Lat. Dist. Dep. Lat. Dist. 1 Dep. Lat. 1 1 ''or 60 Desjrees. 4 ii 0™. 1 TABLE 11. 47 1 DIFFERENCE OF LATITUDE AND DEPARTURE FOR 31 DEGREES. 2h 4in 1 Diet Lat 1 00.9 Dep. Dist. Lat. Dep. Dist Lut Dep. Dist Lat Dep. Dist Lat Dep. 00.5 61 52.3 31.4 121 103.7 62.3 181 155.1 93.2 241 206.6 124.1 2 Ol.T 01.0 62 53.1 31.9 122 104.6 62.8 182 156.0 93.7 242 207.4 124.6 3 02.6 01.5 63 54.0 32.4 123 105.4 63.3 183 156.9 94.3 243 208.3 125.2 4 03.4 02.1 64 54.9 :;3.0 124 106.3 63.9 184 157.7 94.8 244 209.1 125.7 5 04.3 02.6 65 55.7 33.5 125 107.1 64.4 185 158.6 95.3 245 210.0 126.2 6 05.1 03.1 m 56.6 34.0 126 108.0 64.9 186 159.4 95 8 246 210.9 126.7 7 06.0 03.6 67 57.4 34.5 127 108.9 65.4 187 160.3 96 3 247 211.7 127.2 8 06.9 04.1 68 58.3 35.0 128 109.7 65'.9 188 161.1 96 8 248 212.6 127.7 9 07.7 04.6 69 59.1 35.5 129 110.6 66.4 189 162.0 97.8 249 213.4 128 2 10 08.6 05.2 70 60.0 36.1 130 131 111.4 67.0 190 162.9 97.9 250 214.3 128.8 11 09.4 05.7 71 60.9 36.6 112.3 67.5 191 163.7 98.4 251 215.1 129.3 12 10.3 06.2 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 62.6 37.6 133 114.0 68.5 193 165.4 99.4 253 216.9 130.3 14 12.0 07.2 74 63.4 38.1 134 114.9 69.0 194 166.3 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 14.6 08.8 77 66.0 39.7 137 117.4 70.6 197 168.9 101.5 257 220.3 132.4 18 15.4 09.3 78 66.9 40.2 138 118.3 71.1 198 169.7 102.0 258 221.1 132.9 19 16.3 09.8 79 67.7 40.7 139 119.1 71.6 199 170.6 102.5 259 222.0 133.4 20 21 17.1 10.3 80 68.6 41.2 41.7 140 120.0 72.1 200 201 171.4 172.3 103.0 260 222.9 133.9 :3.o 10.8 81 69.4 141 120.9 72.6 103.5 261 223.7 134.4, 22 18.9 11.3 82 70.3 42.2 142 121.7 73.1 202 173.1 104.0 262 224.6 134.9 23 19.7 11.8 83 71.1 42.7 143 122.6 73.7 203 174.0 104.6 263 225.4 135.5 24 •20.6 12.4 84 72.0 43.3 144 123.4 74.2 204 174.9 105.1 264 226.3 136.0 25 21.4 12.9 t85 72.9 43.8 145 124.3 74.7 205 175.7 105.6 265 227.1 136.5 26 22.3 13.4 86 73.7 44.3 146 125.1 75.2 206 176.6 106.1 266 228.0 137.0 27 23.1 13.9 87 74.6 44.8 147 126.0 75.7 207 1^7.4 106.6 267 228.9 137.5 28 24.0 14.4 88 75.4 45.3 148 126.9 76.2 208 178.3 107.1 268 229.7 138.0 2y 24.9 14.9 89 76.3 45.8 149 127.7 76.7 209 179.1 107.6 269 230.6 138.5 30 25.7 15.5 90 91 77.1 46.4 150 128.6 77.3 77.8 210 180.0 108.2 270 231.4 139.1 31 26.6 16.0 78.0 46.9 151 129.4 211 180.9 108.7 271 232.3 139.6 32 27.4 16.5 92 78.9 47.4 152 130.3 78.3 212 181.7 109.2 272 233.1 140.1 33 28.3 17.0 93 79.7 47.9 153 131.1 78.8 213 182.6 109.7 273 234.0 140.6 34 29.1 17.5 94 80.6 48.4 154 132.0 79.3 214 183.4 110.2 274 234.9 141.1 35 30.0 18.0 95 81.4 48.9 155 132.9 79.8 215 184.3 110.7 275 235.7 141.6 36 30.9 18.5 96 82.3 49.4 156 133.7 80.3 216 185.1 111.2 276 236.6 142.2 37 31.7 19.1 97 83.1 50.0 157 134.6 80.9 217 186.0 111.8 277 237.4 142.7 38 32.6 19.6 98 84.0 50.5 158 135.4 81.4 218 186.9 112.3 278 238.3 143.2 39 33.4 20.1 99 84.9 51.0 159 136.3 81.9 219 187.7 112.8 279 239.1 143.7 40 34.3 20.6 100 85.7 51.5 160 137.1 82.4 220 188.6 113.3 280 240.0 144.2 41 35.1 21.1 101 86.6 52.0 161 138.0 82.9 221 189.4 113.8 281 240.9 144.7 42 36.0 21.6 102 87.4 52.5 162 138.9 83.4 222 190.3 114.3 282 241.7 145.2 43 36.9 22.1 103 88.3 53.0 163 139.7 84.0 223 191.1 114.9 283 242.6 145.8 44 37.7 22.7 104 89.1 53.6 164 140.6 84.5 224 192.0 115.4 284 243.4 146.3 45 38.6 23.2 105 90.0 54.1 165 141.4 85.0 225 192.9 1 15.9 285 244.3 146.8 46 39.4 23.7 106 90.9 54.6 166 142.3 85.5 226 193.7 116.4 286 245.1 147.3 47 40.3 24.2 107 91.7 55.1 167 143.1 86.0 227 194.6 116.9 287 246.0 147.8 48 41.1 24.7 108 92.6 55.6 168 144.0 86.5 228 195.4 117.4 288 246.9 148.3 49 42.0 25.2 109 93.4 56.1 169 144.9 87.0 229 196.3 117.9 289 247.7 148.8 50 42.9 25.8 110 94.3 56.7 170 145.7 87.6 230 197.1 118.5 290 248.6 149.4 51 43.7 26.3 111 95.1 57.2 171 146.6 88.1 231 198.0 119.0 291 249.4 149.9 1 52 44.6 26.8 112 96.0 57.7 172 147.4 88.6 232 198.9 119.5 292 250.3 150.4 53 45.4 27.3 113 96.9 58.2 173 148.3 89.1 233 199.7 120.0 293 251.2 150.9 54 46.3 27.8 114 97.7 58.7 174 149.1 89.6 234 200.6 120.5 294 252.0 151.4 55 47.1 28.3 115 98.6 59.2 175 150.0 90.1 235 201.4 121.0 295 252.9 151.9 56 48.0 28.8 116 99.4 59.7 176 150.9 90.6 236 202.3 121.5 296 253.7 152.5 57 48.9 29.4 117 100.3 60.3 177 151.7 91.2 237 203.1 122.1 297 254.6 153.0 58 49.7 29.9 118 101.1 60.8 178 152.6 91.7 238 204.0 122.6 298 255.4 153.5 50 50.6 30.4 119 102.0 61.3 179 153.4 92.2 239 204.9 123.1 299 256.3 154.0 (•>0 Dist 5 1 .4 . D.?p. 30.9 120 102.9 61.8 Lat. 180 154.3 92.7 240 205.7 123.6 300 Dist 257.1 154.5 Lat. Dist. Dep. Dist Dep. Lat. Dist. Dep. Lat. Dep. Lat. ; Fit 59 Deyrrees. S^ 56iii | 48 • TABLE 11. DIFFERENCE OF LATITUDE AND DEPARTURE FOR 32 DEGREES. 2b Sm. 1 Dist. 1 Lat. Dep. Dibt Lat. Dep. Dist. Lat. Dep. Dist. 181 Lat. Dep. Dist Lat Dep. 00.8 00.5 61 51.7 32.3 121 102.6 64.1 153.5 95.9 241 204.4 127.7 2 01.7 01.1 62 52.6 32.9 122 103.5 64.7 KS2 154.3 96.4 242 205.2 128.2 3 02.5 01.6 63 53.4 33.4 123 104.3 65.2 183 155.2 97.0 243 206.1 128.8 4 03.4 02.1 64 54.3 33.9 124 105.2 65.7 184 156.0 97.5 244 206.9 129.3 5 04.2 02.6 65 55.1 34.4 125 106.0 66.2 185 15t).9 98.0 245 207.8 129.8 6 05.1 03.2 66 56.0 35.0 126 106.9 66.8 186 157.7 98.6 246 208.6 130.4 7 05.9 03.7 67 56.8 35.5 127 107.7 67.3,187 158.6 99.1 247 209.5 130.9 8 06.8 04.2 68 57.7 36.0 128 108.6 67.8 188 159.4 99.6 248 210.3 131.4 9 07.6 04.8 69 58.5 36.6 129 109.4 68.4 189 160.3 100.2 249 211.2 131.9 10 11 08.5 09.3 05.3 70 59.4 37.1 130 110.2 68.9 190 161.1 100.7 250 212.0 132.5 05.8 71 60.2 37.6 131 1 11.1 69.4 191 162.0 101.2 251 212.9 13.3.0 12 10.2 06.4 72 61.1 38.2 132 111.9 69.9 192 162.8 101.7 252 213.7 133.5 13 11.0 06.9 73 61.9 38.7 133 112.8 70.5 193 163.7 102.3 253 214.6 134.1 14 11.9 07.4 74 62.8 39.2 134 113.6 71.0 194 164.5 102.8 254 215.4 134.6 15 12.7 07.9 75 63.6 39.7 135 114.5 71.5 195 16.5.4 103.3 255 216.3 135.1 16 13.6 08.5 76 64.5 40.3 136 115.3 72.1 196 166.2 103.9 256 217.1 135.7 17 14.4 09.0 77 65.3 40.8 137 116.2 72.6 197 167.1 104.4 257 217.9 136.2 18 15.3 09.5 78 66.1 41.3 138 117.0 73.1 198 167.9 104.9 258 218.8 136.7 19 16.1 10.1 79 67.0 41.9 139 117.9 73.7 199 168.8 105.5 259 219.6 137.2 20 17.0 10.6 80 67.8 42.4 140 118.7 74.2 200 169.6 106.0 260 220.5 137.8 21 17.8 11.1 81 68.7 42.9 141 119.6 74.7 201 170.5 106.5 261 221.3 138.3 22 18.7 11.7 82 69.5 43.5 142 120.4 75.2 202 171.3 107.0 262 222.2 138.8 23 19.5 12.2 83 70.4 44.0 143 121.3 75.8 203 172.2 107.6 263 223.0 139.4 24 20.4 12.7 84 71.2 44.5 144 122.1 76.3 204 173.0 108.1 264 223.9 139.9 25 21.2 13.2 85 72.1 45.0 145 123.0 76.8 205 173.8 10S.6 265 224.7 140.4 26 22.0 13.8 86 72.9 45.6 146 123.8 77.4 206 174.7 109.2 266 225.6 141.0 27 22.9 14.3 87 73.8 46.1 147 124.7 77.9 207 175.5 109.7 267 226.4 141.5 28 23.7 14.8 88 74.6 46.6 148 125.5 78.4 208 176.4 110.2 268 227.3 142.0 29 24.6 15.4 89 75.5 47.2 149 126.4 79.0 209 177.2 110.8 269 228.1 142.5 30 31 •J 5.4 15.9 16.4 90 76.3 47.7 1.50 127.2 79.5 210 178.1 111.3 270 229.0 143.1 26.3 91 77.2 48.2 151 128.1 80.0 211 178.9 111.8 271 229.8 14.3.6 32 27.1 17.0 92 78.0 48.8 152 12^.9 80.5 212 179.8 112.3 272 230.7 144.1 33 28.0 17.5 93 78.9 49.3 153 129.8 81.1 213 180.6 112.9 273 231.5 144.7 34 28.8 18.0 94 79.7 49.8 154 130.6 81.6 214 181.5 113.4 274 232.4 145.2 35 29.7 18.5 95 80.6 50.3 155 131.4 82.1 215 182.3 113.9 275 233.2 145.7 36 30.5 19.1 96 81.4 50.9 156 132.3 82.7 216 183.2 114.5 276 234.1 146.3 37 31.4 19.6 97 82.3 51.4 157 133.1 83.2 217 184.0 115.0 277 2,34.9 146.8 38 32.2 20.1 98 83.1 51.9 158 134.0 83.7 218 184.9 115.5 278 235.8 147.3 39 33.1 20.7 99 84.0 52.5 159 134.8 84.3 219 185.7 116.1 279 236.6 147.8 40 33.9 21.2 100 84.8 53.0 160 135.7 84.8 220 186.6 116.6 280 237.5 148.4 41 34.8 21.7 101 85.7 53.5 161 136.5 85.3 221 187.4 117.1 281 238.3 148.9 42 35.6 22.3 102 86.5 54.1 162 137.4 85.8 222 188.3 117.6 282 239.1 149.4 43 36.5 22.8 103 87.3 .54.6 163 138.2 86.4 223 18!>.l 118.2 283 240.0 150.0 44 37.3 23.3 104 88.2 55.1 164 139.1 86.9 224 190.0 118.7 284 240.8 150.5 45 38.2 23.8 105 89.0 55.6 165 139.9 87.4 225 190.8 119.2 285 241.7 151.0 46 39.0 24.4 106 89.9 56.2 166 140.8 88.0 226 191.7 119.8 286 242.5 151.6 47 39.9 24.9 107 90.7 56.7 167 141.6 88.5 227 192.5 120.3 287 243.4 152.1 48 40.7 25.4 108 91.6 57.2 168 142.5 89.0 228 193.4 120.8 288 244.2 152.6 49 41.6 26.0 109 92.4 57.8 169 143.3 89.6 229 194.2 121.4 289 245.1 153.1 50 42.4 26.5 110 93.3 58.3 170 144.2 90.1 230 195.1 121.9 290 245.9 153.7 51 43.3 27.0 111 94.1 58.8 171 145.0 90.6 231 195.9 122.4 291 246.8 154.2 52 44.1 27.6 112 95.0 59.4 172 145.9 91.1 232 196.7 122.9 292 247.6 154.7 53 44 9 28.1 113 95.8 59.9 173 146.7 91.7 233 197.6 123.5 293 248.5 155.3 54 45.8 28.6 114 96.7 60.4 174 147.6 92.2 234 198.4 124.0 294f 249.3 155.8 55 46.6 29.1 115 97.5 60.9 175 148.4 92.7 235 199.3 124.5 295 250.2 156.3 56 47.5 29.7 116 98.4 61.5 176 149.3 93.3 236 200.1 125.1 296 251.0 156.9 57 48.3 30.2 117 99.2 62.0 177 150.1 93.8 237 201.0 125.6 297 251.9 157.4 5^ 49.2 30.7 118 100.1 62.5 178 151.0 94 3 238 201.8 126.1 298 252.7 157.9 59 50.0 31.3 119 100.9 63.1 179 151.8 94.9 239 202.7 126.7 299 253.6 158.4 60 Dist 50.9 31.8 120 101.8 63.6 180 152.6 95.4 240 203.5 127.2 300 254.4 159.0 Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat Dist 1 Dep. Lat For 58 Degrees. 3h 62". 1 TABLE 11. [I'age49. 1 DIFFERENCE OF LATITUDE AND DKl'ARTURE FOR 33 DEGREES. 2h 12m. 1 Dist. 1 Lat. 00.8 Dep. Dist. Lat. 51.2 Dep. Dist LaL Dep. 65.9 Dist. Lat. Dep. Dist. Lat 202.1 Dep. 00.5 61 33.2 121 101.5 181 151.8 98.6 241 131.3 01.7 01.1 62 52.0 33.8 122 102.3 66.4 182 152.6 99.1 242 203.0 131.S 3 02.5 01.6 63 52.8 34.3 123 103.2 67.0 183 153.5 99.7 243 203.8 132.3 4 03.4 02.2 64 ,53.7 34.9 124 104.0 67.5 184 154.3 100.2 244 204.6 132.9 5 04.2 02.7 65 54.5 35.4 125 104.8 68.1 185 155.2 100.8 245 205.5 133.4 6 05.0 03.3 m 55.4 35.9 126 105.7 68.6 186 156.0 101.3 246 206.3 134.0 7 05.9 03.8 67 56.2 36.5 127 106.5 69.2 187 156.8 101.8 247 207.2 134.5 8 06.7 04.4 68 57.0 37.0 128 107.3 69.V 188 157.7 102.4 248 208.0 135.1 9 07.5 04.9 69 57.9 37.6 129 108.2 70.3 189 158.5 102.9 249 208.8 135.6 10 08.4 05.4 70 58.7 38.1 130 131 109.0 70.8 190 159.3 103.5 250 209.7 136.2 136.7 11 09.2 06.0 71 59.5 38.7 109.9 71.3 191 160.2 104.0 2^1 210.5 12 10.1 06.5 72 60.4 39.2 132 110.7 71.9 192 161.0 104.6 252 211.3 1 37.2 13 10.9 07.1 73 61.2 39.8 133 111.5 72.4 193 161.9 105.1 253 212.2 137.8 14 11.7 07.6 74 62.1 40.3 134 112.4 73.0 194 162.7 105.7 254 213.0 138.3 15 12.6 08.2 75 62.9 40.8 135 113.2 73.5 195 163.5 106.2 255 213.9 138.9 16 13.4 08.7 76 63.7 41.4 136 114.1 74.1 196 164.4 106.7 256 214.7 139.4 17 14.3 09.3 77 64.6 41.9 ]37 114.9 74.6 197 165.2 107.3 257 215.5 140.0 18 15.1 09.8 78 65.4 42.5 138 115.7 75.2 198 166.1 107.8 258 216.4 140.5 19 15.9 10.3 79 66.3 43.0 139 116.6 75.7 199 166.9 108.4 259 217.2 141.1 20 21 16.8 17.6 10.9 80 81 67.1 43.6 140 141 117.4 76.2 76.8 200 201 167.7 168.6 108.9 260 218.1 141.6 11.4 67.9 44.1 118.3 109.5 261 218.9 142.2 22 18.5 12.0 82 68.8 44.7 142 119.1 77.3 202 169.4 110.0 262 219.7 142.7 23 19.3 12.5 83 69.6 45.2 143 119.9 77.9 203 170.3 110.6 263 220.6 143.2 24 20.1 13.1 84 70.4 45.7 144 120.8 78.4 204 171.1 111.1 264 221.4 143.8 25 21.0 13.6 85 71.3 46.3 145 121.6 79.0 205 171.9 111.7 265 222.2 144.3 26 21.8 14.2 86 72.1 46.8 146 122.4 79.5 206 172.8 112.2 266 223. 1 144.9 27 22.6 14.7 87 73.0 47.4 147 123.3 80.1 207 173.6 112.7 267 .223.9 145.4 28 23.5 15.2 88 73.8 47.9 148 124.1 80.6 208 174.4 113.3 268 224.8 146.0 29 24.3 15.8 89 74.6 48.5 149 125.0 81.2 209 175.3 113.8 269 22.5.6 146.5 30 25.2 16.3 90 75.5 49.0 150 125.8 81.7 210 176.1 114.4 270 226.4 147.) 31 26.0 16.9 91 76.3 49.6 151 126.6 82.2 211 177.0 114.9 271 227.3 147 6 32 26.8 17.4 92 77.2 50.1 152 127.5 82.8 212 177.8 115.5 272 228.1 148.1 33 27.7 18.0 93 78.0 50.7 1.53 128.3 83.3 213 178.6 116.0 273 229.0 148.7 34 28.5 18.5 94 78.8 51.2 154 129.2 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 52.3 156 130.8 85.0 216 181.2 117.6 276 231.5 150.3 37 31.0 20.2 97 81.4 52.8 157 131.7 85.5 217 182.0 118.2 277 232.3 150.9 38 31.9 20.7 98 82.2 53.4 158 132.5 86.1 218 182.8 118.7 278 233.2 151.4 39 32.7 21.2 99 83.0 53.9 159 133.3 86.6 219 183.7 119.3 279 234.0 152.0 40 33.5 21.8 100 83.9 54.5 160 134.2 87.1 220 221 184.5 119.8 280 234.8 235.7 152.5 41 34.4 22.3 101 84.7 55.0 161 135.0 87.7 185.3 120.4 281 153.0 42 35.2 22.9 102 85.5 55.6 162 135.9 88.2 222 186.2 120.9 282 236.5 153.6 43 36.1 23.4 103 86.4 56.1 163 136.7 88.8 223 187.0 121.5 283 237.3 154.1 44 36.9 24.0 104 87.2 56.6 164 137.5 89.3 224 187.9 122.0 284 238.2 154.7 45 37.7 24.5 105 88.1 57.2 165 138.4 89.9 225 188.7 122.5 285 239.0 155.2 46 38.6 25.1 106 88.9 57.7 166 139.2 90.4 226 189.5 123.1 286 239.9 155.8 47 39.4 25.6 107 89.7 58.3 167 140.1 91.0 227 190.4 123.6 287 240.7 156.3 48 40.3 26.1 108 90.6 58.8 168 140.9 91.5 228 191.2 124.2 288 241.5 156.9 49 41.1 26.7 109 9t.4 59.4 169 141.7 92.0 229 192.1 124.7 289 242.4 157.4 50 51 41.9 42.8 27.2 110 92.3 59.9 170 142.6 92.6 230 192.9 125.3 290 243.2 157.9 27.8 111 93.1 60.5 171 143.4 93.1 231 193.7 125.8 291 244.1 158.5 52 43.6 28.3 112 93.9 61.0 172 144.3 93.7 232 194.6 126.4 292 244.9 159.0 53 44.4 28.9 113 94.8 61.5 173 145.1 94.2 233 195.4 126.9 293 245.7 159.6 54 45.3 29.4 114 95.6 62.1 174 14.5.9 94.8 234 196.2 127.4 294 246.6 160.1 55 46.1 30.0 115 96.4 62.6 175 146.8 95.3 235 197.1 128.0 295 247.4 160.7 56 47.0 30.5 116 97.3 63.2 176 147.6 95.9 236 197.9 128.5 296 248.2 161.2 57 47.8 31.0 117 98.1 63.7 177 148.4 96.4 237 198.8 129.1 297 249.1 161.8 58 48.6 31.6 118 99.0 64.3 178 149.3 96.9 238 199.6 129.6 298 249.9 162.3 59 49.5 32.1 119 99.8 64.8 179 150.1 97.5 239 200.4 130.2 299 250.8 162.8 60 Dist 50.3 Dep. 32.7 120 100.6 65.4 Lat. 180 Dist. 151.0 98.0 240 201.3 130.7 300 251.6 163.4 Lat. Di8t. Dep. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat For 57 Deerrees. 3^ 48m. | 60 TABLE 11. 1 DIFFERENCE OF LATITUDE AND DEPARTURE FOR 34 DEGREES. 2^ 16™. | Dist Lat. Dep. DistI Lat Dep. Dist. L.at. Dep. Dist Lat. Dep. Dist Lat 1 Dep. 1 1 00.8 00.6 61 50.6 34.1 121 100.3 67.7 181 150.1 101.2 241 .199.8 134.8 1 2 01.7 01.1 62 51.4 34.7 122 101.1 68.2 182 150.9 101.8 242 200.6 135.31 3 02.5 01.7 63 52.2 35.2 123 102.0 68.8 183 151.7 102.3 243 201.5 135.91 4 03.3 02.2 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 6 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 1 71.0 187 155.0 104.6 247 204.8 '138.11 8 06.6 04.5 68 56.4 38.0 128 106.1 71.6 188 155.9 105.1 248 205.61 138.7 1 9 07.5 05.0 69 57.2 38.6 129 106.9 72.1 189 156.7 105.7 249 206.4 139.2 10 11 08.3 05.6 70 58.0 39.1 130 107.8 72.7 190 157.5 106.2 250 207.3 139.8 09.1 06.2 71 58.9 39.7 131 108.6 73.3 191 158.3 106.8 251 208.1 140.4 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 a 10.3 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 63.0 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 21.3.1 H-3 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 78.8 201 166.6 112.4 261 216.4 145.9 22 18.2 12.3 82 68.0 45.9 142 117.7 79.4 202 167.5 113.0 262 217.2 146.5 23 19.1 12.9 83 68.8 46.4 143 118.6 80.0 203 168.3 113.5 263 218.0 147.1 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 81.6 206 170.8 115.2 266 220.5 148.7 27 22.4 15.1 87 72.1 48.6 147 121.9 82.2 207 171.6 115.8 267 221.4 149.3 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 8.3.3 209 173.3 116.9 269 223.0 150.4 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 25.7 17.3 91 75.4 50.9 151 125.2 84.4 211 174.9 118.0 271 224.7 151.5 32 26.5 17.9 92 76.3 51.4 152 126.0 85.0 212 175.8 118.5 272 225.5 152.1 33 27.4 18.5 93 77.1 52.0 153 126.8 8.5.6 213 176.6 119.1 273 226.3 152.7 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 54.8 158 131.0 88.4 218 180.7 121.9 278 230.5 155.5 39 32.3 21.8 99 82.1 .")5.4 159 131.8 88.9 219 181.6 122.5 279 231.3 156.0 40 33.2 22.4 100 82.9 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 56.5 161 133.5 90.0 221 183.2 123.6 281 233.0 157.1 42 34.8 23.5 102 84.6 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 1 91.1 223 184.9 124.7 283 234.6 158.3 44 36.5 24.6 104 86.2 58.2 164 136.01 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 60.4 168 139.3 93.9 228 189.0 127.5 288 238.8 161.0 49 40.6 27.4 109 90.4 61.0 169 140.1 94.5 229 189.8 128.1 289 239.6 161.6 50 41.5 28.0 110 91.2 61.5 170 140.9 95.1 230 190.7 128.6 290 240.4 162.2 51 42.3 28.5 HI 92.0 62.1 171 141.8 95.6 231 191.5 129.2 291 241.2 162.7 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 54 44.8 30.2 114 94.5 63.7 174 144.3 97.3 234 194.0 130.9 294 243.7 164.4 55 45.6 30.8 115 95.3 64.3 175 145.1 97.9 235 194.8 131.4 295 ; 244.6 165.0 1 56 46.4 31.3 116 96.2 64.9 176 145.9 98.4 236 195.7 132.0 2961245.4 165.5 1 57 47.3 31.9 117 97.0 65.4 177 146.7 99.0 237 196.5 132.5 297 1 246.2 166.1 58 48.1 32.4 118 97.8 66.0 178 147.6 99.5 238 197.3 133.1 298 1247.1 166.6 59 48.9 33.0 119 98.7 66.5 179 148.4 100.1 239 198.1 133.6 299 247.9 167.2 60 DiaL 49.7 33.6 120 99.5 67.1 180 149.2 100.7 240 199.0 134.2 300 248.7 167.8 Bep. Lat Dist Dep. Lat Dist Dep. Lat. Dist Dep. Lat Dist Dep. Lat For 56 Degrees. 3h _44"«._ i TABLE II. tl DIFFERENCE OF LATITUDE AND DEPARTURE FOR 35 DEGREES. 2h 02m. Dl8t 1 Lat. Dep. Dist. Lilt. 50>0 Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist 241 Lat. Dep. 00.8 00.6 61 35.0 121 99.1 69.4 181 148.3 103.8 197.4 138.2 o 01.6 01.1 62 50.8 35.6 122 99.9 70.0 182 149.1 104.4 242 198.2 1M8.8 3 0-2.5 01.7 63 51.6 36.1 123 100.8 70.5 183 149.9 105.0 243 199.1 139.4 4 03.3 02.3 64 52.4 36.7 124 101.6 71.1 184 150.7 105.5 244 199.9 140.0 5 04.1 02.9 65 53.2 37.3 125 102.4 71.7 185 151.5 106.1 245 200.7 140.5 6 04.9 03.4 66 54.1 37.9 126 103.2 72.3 186 152.4 106.7 246 201.5 141.1 7 05.7 04.0 67 54.9 38.4 127 104.0 72.8 187 153.2 107.3 247 202.3 141.7 8 06.6 04.6 68 55.7 39.0 128 104.9 73.4 188 154.0 107.8 248 203.1 142.2 9 07.4 05.2 69 56.5 39.6 129 105.7 74.0 189 154.8 108.4 249 204.0 142.8 10 11 08.2 09.0 05.7 70 57.3 40.2 130 106.5 74.6 190 191 155.6 109.0 250 204.8 143.4 06.3 71 58.2 40.7 131 107.3 75.1 156.5 109.6 251 205.6 144.0 12 09.8 06.9 72 59.0 41.3 132 108.1 75.7 192 157.3 110.1 252 206.4 144.5 13 10.6 07.5 73 59.8 41.9 133 108.9 76.3 193 158.1 110.7 253 207.2 145.1 14 11.5 08 74 60.6 42.4 134 109.8 76.9 194 158.9 111.3 254 208.1 145.7 15 12.3 08.6 75 61.4 43.0 135 110.6 77.4 195 159.7 111.8 255 208.9 146.3 16 13.1 09.2 76 62.3 43.6 136 111.4 78.0 196 160.6 112.4 256 209.7 146.8 17 13.9 09.8 77 63.1 44.2 137 112.2 78.6 197 161.4 113.0 257 210.5 147.4 18 14.7 10.3 78 63.9 44.7 138 113.0 79.2 198 162.2 113.6 258 211.3 148.0 19 15.6 10.9 79 64.7 45.3 139 113.9 79.7 199 163.0 114.1 259 212.2 148.6 20 21 16.4 17.2 11.5 12.0 80 65.5 45.9 46.5 140 114.7 80.3 200 201 163.8 164.6 114.7 260 213.0 149.1 81 66.4 141 115.5 80.9 115.3 261 213.8 149.7 22 18.0 12.6 82 67.2 47.0 142 116.3 81.4 202 165.5 115.9 262 214.6 150.3 23 18.8 13.2 83 68.0 47.6 143 117.1 82.0 203 166.3 116.4 263 215.4 150.9 24 19.7 13.« 84 68.8 48.2 144 118.0 82.6 204 167.1 117.0 264 216.3 151.4 25 20.5 14.3 85 69.6 48.8 145 118.8 83.2 205 167.9 117.6 265 217.1 152.0 26 21.3 14.9 86 70.4 49.3 146 119.6 83.7 206 168.7 118.2 266 217.9 152.6 27 22.1 15.5 87 71.3 49.9 147 120.4 84.3 207 169.6 118.7 267 218.7 153.1 28 22.9 16.1 88 72.1 50.5 148 121.2 84.9 208 170.4 119.3 268 219.5 153.7 29 23.8 16.6 89 72.9 51.0 149 122.1 85.5 209 171.2 119.9 269 220.4 154.3 30 24.6 17.2 90 91 73.7 74.5 51.6 150 122.9 86.0 210 172.0 120.5 270 221.2 154.9 31 25.4 17.8 52.2 151 123.7 86.6 211 172.8 121.0 271 222.0 155.4 32 26.2 18.4 92 75.4 52.8 152 124.5 87.2 212 173.7 121.6 272 222.8 156.0 33 27.0 18.9 93 76.2 53.3 153 125.3 87.8 213 174.5 122.2 273 223.6 156.6 34 27.9 19.5 94 77.0 53.9 154 126.1 88.3 214 175.3 122.7 274 224.4 157.2 35 28.7 20.1 95 77.8 54.5 155 127.0 88.9 215 176.1 123.3 275 225.3 157.7 36 29.5 20.6 96 78.6 55.1 156 127.8 89.5 216 176.9 123.9 276 226.1 158.3 37 30.3 21.2 97 79.5 55.6 157 128.6 90.1 217 177.8 124.5 277 226.9 158.9 38 31.1 21.8 98 80.3 56.2 158 129.4 90.6 218 178.6 125.0 278 227.7 159.5 39 31.9 22.4 99 81.1 56.8 159 130.2 91.2 219 179.4 125.6 279 228.5 160.0 40 32.8 22.9 100 81.9 57.4 160 131.1 91.8 220 180.2 126.2 280 229.4 230.2 160.6 41 33.6 23.5 101 82.7 57.9 161 131.9 92.3 221 181.0 126.8 281 161.2 42 34.4 24.1 102 83.6 58.5 162 132.7 92.9 222 181.9 127.3 282 231.0 161.7 43 35.2 24.7 103 84.4 59.1 163 133.5 93.5 223 182.7 127.9 283 231.8 162.3 44 36.0 25.2 104 85.2 59.7 164 134.3 94.1 224 183.5 128.5 284 232.6 162.9 45 36.9 25.8 105 86.0 60.2 165 135.2 94.6 225 184.3 129.1 285 233.5 163.5 46 37.7 26.4 106 86.8 60.8 166 136.0 95.2 226 185.1 129.6 286 234.3 164.0 47 38.5 27.0 107 87.6 61.4 167 136.8 95.8 227 185.9 130.2 287 235.1 164.6 48 39.3 27.5 108 88.5 61.9 168 137.6 96.4 228 186.8 130.8 288 235.9 165.2 49 40.1 28.1 109 89.3 62.5 1()9 138.4 96.9 229 187.6 131.3 289 236.7 165.8 50 51 41.0 28.7 110 90.1 63.1 170 139.3 97.5 230 188.4 131.9 290 237.6 166.3 41.8 29.3 111 90.9 63.7 171 140.1 98.1 231 189.2 132.5 291 238.4 166.9 52 42.6 29.8 112 91.7 64.2 172 140.9 98.7 232 190.0 133.1 292 239.2 167.5 53 43.4 30.4 113 92.6 64.8 173 141.7 99.2 233 190.9 133.6 293 240.0 168.1 1 54 44.2 31.0 114 93.4 65.4 174 142.5 99.8 234 191.7 134.2 294 240.8 168.61 55 45.1 31.5 115 94.2 66.0 175 143.4 100.4 235 192.5 134.8 295 241.6 169.2 56 45.9 32.1 116 95.0 66.5 176 144.2 100.9 236 193.3 135.4 296 242.5 169.8 57 46.7 32.7 117 95.8 67.1 177 145.0 101.5 237 194.1 135.9 297 243.3 170.4 58 47.5 33.3 118 96.7 67.7 178 145.8 102.1 238 195.0 136.5 298 244.1 170.9 59 48.3 33.8 119 97.5 68.3 179 146.6 102.7 239 195.8 137.1 299 244.9 171.5 60 49.1 34.4 Lat. 120 98.3 68.8 180 147.4 103.2 240 196.6 137.7 300 245.7 172.1 DiBt Dep. Dist. Dep. Lat. Dist Dep. Lat. Dist. Dep. Lat Dist. Dep. Lat For 66 Dee:i'ee8. 8^ 40D1. 1 52 TABLE II. » DIFFERENCE OF LATITUDE AND DEPARTURE FOR 36 DEGREES. 2h 24ra. 1 Diat Lat. Dep. Dist. Lat. Dep. Dist Lat Dep. Dist Lat Dep. Dist Lat Dep. 1 00.8 00.6 61 49.4 35.9 121 97.9 71.1 181 146.4 106.4 241 195.0 141.7 2 01.6 01.2 62 50.2 36.4 122 98.7 71.7 182 147.2 107.0 242 195.8 142.2 3 02.4 01.8 63 51.0 37.0 123 99.5 72.3 183 148.1 107.6 243 196.6 142.8 4 03.2 02.4 64 51.8 37.6 124 100.3 72.9 184 148.9 108.2 244 '' 197.4 143.4 5 04.0 02.9 65 52.6 38.2 125 101.1 73.5 185 149.7 108.7 245 198.2 144.0 6 04.9 03.5 66 53.4 38.8 126 101.9 74.1 186 150.5 109.3 246 199.0 144.6 7 05.7 04.1 67 54.2 39.4 127 102.7 74.-6 187 151.3 109.9 247 199.8 145.2 8 06.5 04.7 68 55.0 40.0 128 103.6 75.2 188 152.1 110.5 248 200.6 145.8 9 07.3 05.3 69 .55.8 40.6 129 104.4 75.8 189 152.9 111.1 249 201.4 146.4 10 n 08.1 05.9 70 56.6 41.1 130 105.2 76.4 190 153.7 111.7 250 202.3 146.9 08.9 06.5 71 57.4 41.7 131 106.0 77.0 191 154.5 112.3 251 203.1 147.5 12 09.7 07.1 72 58.2 42.3 132 106.8 77.6 192 155.3 112.9 252 203.9 148.1 13 10.5 07.6 73 59.1 42.9 133 107.6 78.2 193 156.1 113.4 253 204.7 148.7 14 11.3 08.2 74 59.9 43.5 134 108.4 78.8 194 156.9 114.0 254 205.5 149.3 15 12.1 08.8 75 60.7 44.1 135 109.2 79.4 195 157.8 114.6 255 206.3 149.9 16 12.9 09.4 76 61.5 44.7 136 110.0 79.9 196 158.6 115.2 256 207.1 150.5 17 13.8 10.0 77 62.3 45.3 137 110.8 80.5 197 159.4 115.8 257 207.9 151.1 18 14.6 10.6 78 63.1 45.8 138 111.6 81.1 198 160.2 116.4 258 208.7 151.6 19 15.4 11.2 79 63.9 46.4 139 112.5 81.7 199 161.0 117.0 259 209.5 152.2 20 16.2 11.8 12.3 80 64.7 47.0 140 113.3 82.3 200 161.8 117.6 260 210.3 152.8 21 17.0 81 65.5 47.6 141 114.1 82.9 201 162.6 118.1 261 211.2 153.4 22 17.8 12.9 82 66.3 48.2 142 114.9 83.5 202 163.4 118.7 262 212.0 154.0 23 18.6 13.5 83 67.1 48.8 143 115.7 84.1 203 164.2 119.3 263 212.8 154.6 24 19.4 14.1 84 68.0 49.4 144 116.5 84.6 204 165.0 119.9 264 213.6 155.2 25 20.2 14.7 85 68.8 50.0 145 117.3 85.2 205 165.8 120.5 265 214.4 155.8 26 21.0 15.3 86 69.6 50.5 146 118.1 85.8 206 166.7 121.1 2661215.2 156.4 27 21.8 15.9 87 70.4 51.1 147 118.9 86.4 207 167.5 121.7 267 216.0 156.9 28 22.7 16.5 88 71.2 51.7 148 119.7 87.0 208 168.3 122.3 268 216.8,157.51 29 23.5 17.0 89 72.0 52.3 149 120.5 87.6 209 169.1 122.8 269 '217.6' 158.1 1 30 .>4.3 17.6 90 72.8 52.9 150 121.4 88.2 210 169.9 123.4 270 , 218.4 158.7 31 25.1 18.2 91 73.6 53.5 151 122.2 88.8 211 170.7 124.0 271 219.2 159.3 :^2 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 1 35 28.3 20.6 95 70.9 55.8 155 125.4 91.1 215 173.9 126.4 275 222.5 161.6 36 29.1 21.2 96 77.7 56.4 156 126.2 91.7 216 174.7 127.0 276 223.3 162.2 37 29.9 21.7 97 78.5 57.0 157 127.0 92.3 217 175.6 127.5 277 1 224.1 162.8 38 30.7 22.3 98 79.3 57.6 158 127.8 92.9 218 176.4 128.1 278 224.9 163.4 39 31.6 22.9 99 80.1 58.2 159 128.6 93.5 21'9 177.2 128.7 279 225.7 164.0 40 32.4 23.5 100 80.9 58.8 160 129.4 94.0 220 178.0 129.3 280 226.5 164.6 41 33.2 24.1 101 81.7 59.4 161 130.3 94.6 221 178.8 129.9 281 227.3 165.2 42 34.0 24.7 102 82.5 60.0 162 131.1 95.2 222 179.6 130.5 282 228.1 165.8 43 34.8 25.3 103 83.3 60.5 163 131.9 95.8 223 180.4 131.1 283 ' 229.0 166.3 44 35.6 25.9 104 84.1 61.1 164 132.7 96.4 224 181.2 131.7 284 229.8 160.9 45 36.4 26.5 105 84.9 61.7 165 133.5 97.0 225 182.0 132.3 285 230.6 167.5 46 37.2 27.0 106 85.8 62.3 166 134.3 97.6 226 182.8 132.8 286 231.4 168.1 47 38.0 27.6 107 86.6 62.9 167 135.1 98.2 227 183.6 133.4 287 , 232.2 168.7 48 38.8 28.2 108 87.4 63.5 168 135.9 98.7 228 184.5 134.0 288 233.0 169.3 49 39.6 28.8 109 88.2 64.1 169 136.7 99.3 229 185.3 134.6 289 233.8 169.9 50 51 40.5 29.4 110 89.0 64.7 170 137.5 99.9 230 186.1 135.2 290 234.6 170.5 41.3 30.0 111 89.8 65.2 171 138.3 100.5 231 186.9 135.8 291 235.4 171.0 52 42.1 30.6 112 90.6 6.5.8 172 139.2 101.1 232 187.7 136.4 292 i 236.2 171.6 53 42 9 31.2 113 91.4 66.4 173 140.0 101.7 233 188.5 137.0 293 237.0 172.2 54 43.7 31.7 114 92.2 67.0 174 140.8 102.3 234 189.3 137.5 294 237.9 172.8 55 44.5 32.3 115 93.0 67.6 175 141.6 102.9 235 190.1 138.1 295 238.7 173.4 56 45.3 32.9 116 93.8 68.2 176 142.4 103.5 236 190.9 138.7 296 239.5 174.0 57 46.1 33.5 117 94.7 68.8 177 143.2 104.0 237 191.7 139.3 297 240.3 174.6 58 46.9 34.1 118 95.5 69.4 178 144.0 104.6 238 192.5 139.9 298 241.1 175.2 59 47.7 34.7 119 96.3 69.9 179 144.8 105.2 239 193.4 140.5 299 241.9 175.7 60 48.5 35.3 120 97.1 70.5 180 145.6 105.8 240 194.2 141.1 300 242.7 176.3 Diet Dep. Lat Dist. Dep. Lat Dist Dep. Lat. Dist Dep. Lat Dist Dep. Lat » For 54 Degrees. " TABLE 11. 68 1 DIFFERENCE OF LATITUDE AND DEPARTURE FOR 37 DEGREES. 2». 28n>. 1 Dep. Diet Lat. Dep. Dist. Lat. Dep. Dist. Lilt. Dep. Dist. Lat. Dep. Dist LaL 00.8 00.0 01 48.7 36.7 121 96.0 72.8 181 144.6 108.9 241 192.5 145.0 1 2 01.0 01.2 02 49.5 37.3 122 97.4 73.4 182 145.4 109.5 242 19.3.3 145.6 3 0-2A 01.8 03 503 37.9 123 9S.2 74.0 183 146.2 110.1 243 194.1 146.2 4 03.2 02.4 04 51.1 38.5 124 99.0 74.6 184 146.9 110.7 244 194.9 146.8 5 04.0 03.0 05 51.9 39.1 125 99.8 75.2 185 147.7 111.3 245' 195.7 147.4 6 04.8 03.6 06 52.7 39.7 126 100.0 75.8 186 148.5 111.9 246 196.5 148.0 t 05.6 04.2 67 53.5 40.3 127 101.4 7(^.4 187 149.3 112.5 247,197.3 148.0 8 00.4 04.8 68 54.3 40.9 128 102.2 77.0 188 150.1 113.1 248 li»8.1 149.3 1> 07.2 05.4 69 55.1 41.5 129 103.0 77.6 189 150.9 113.7 249 198.9 149.9 10 08.0 00.0 70 55.9 42.1 130 131 103.8 78.2 190 151.7 114.3 250 199.7 150.5 11 08.8 06.6 71 56.7 42.7 104.0 78.8 191 152.5 114.9 251 200.5 151.1 12 09.0 07.2 72 57.5 43.3 132 105.4 79.4 192 153.3 115.5 252 201.3 151.7 13 10.4 07.8 73 58.3 43.9 133 100.2 80.0 193 154.1 116.2 253 202.1 152.3 14 11.2 08.4 74 59.1 44.5 134 107.0 80.6 194 154.9 116.8 254 202.9 152.9 1 15 12.0 09.0 75 59.9 45.1 135 107.8 81.2 195 155.7 117.4 255 203.7 153.5 lt> 12.8 09.6 76 ()0.7 45.7 136 108.6 81.8 196 156.5 118.0 256 204.5 154.1 17 13.0 10.2 77 61.5 46.3 137 109.4 82.4 197 157.3 118.6 257 205.2 154.7 18 14.4 10.8 78 02.3 46.9 138 110.2 83.1 198 158.1 119.2 258 206.0 155.3 19 15.2 11.4 79 63.1 47.5 139 111.0 83.7 199 158.9 119.8 259 206.8 155.9 20 21 16.0 16.8 12.0 80 63.9 64.7 48.1 48.7 140 111.8 84.3 200 159.7 120.4 260 207.6 156.5 12.6 81 141 112.6 84.9 201 160.5 121.0 261 208.4 157.1 22 17.6 13.2 82 65.5 49.3 142 113.4 85.5 202 161.3 121.6 262 209.2 157.7 23 18.4 13.8 83 66.3 50.0 143 114.2 86.1 203 162.1 122.2 203 210.0 158.3 24 19.2 14.4 84 67.1 50.6 144 115.0 86.7 204 162.9 122.8 204 210.8 158.9 25 20.0 15.0 85 67.9 51.2 145 115.8 87.3 205 163.7 123.4 205 211.6 159.5 20 20.8 15.6 86 08.7 51.8 146 116.6 87.9 206 164.5 124.0 266 212.4 160.1 27 21.6 10.2 87 09.5 52.4 147 117.4 88.5 207 165.3 124.6 267 213.2 160.7 28 22.4 16.9 88 70.3 53.0 148 118.2 89.1 208 166.1 125.2 268 214.0 161.3 29 23.2 17.5 89 71.1 53.0 149 119.0 89.7 209 166.9 125.8 269 214.8 161.9 30 31 24.0 18.1 90 91 71.9 72.7 54.2 150 119.8 90.3 210 167.7 126.4 270 215.6 162.5 24.8 18.7 54.8 151 120.6 90.9 211 168.5 127.0 271 216.4 163.1 32 25.0 19.3 92 73.5 55.4 152 121.4 91.5 212 169.3 127.6 272 217.2 163.7 33 20.4 19.9 93 74.3 50.0 153 122.2 92.1 213 170.1 128.2 273 218.0 164.3 34 27.2 20.5 94 75.1 56.0 154 123.0 92.7 214 170.9 128.8 274 218.8 164.9 35 28.0 21.1 95 75.9 57.2 155 123.8 93.3 215 171.7 129.4 275 219.6 165.5 36 28.8 21.7 96 70.7 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 94.5 217 173.3 130.6 277 221.2 106.7 38 30.3 22.9 98 78.3 59.0 158 126.2 95.1 218 174.1 131.2 278 222.0 167.3 39 31.1 2;:!.5 99 79.1 59.6 159 127.0 95.7 219 174.9 131.8 279 222.8 167.9 40 41 31.9 24.1 100 79.9 60.2 100 127.8 96.3 220 175.7 132.4 280 223.0 168.5 32.7 24.7 101 80.7 60.8 161 128.6 96.9 221 176.5 133.0 281 224.4 109.1 42 33.5 25.3 102 81.5 61.4 162 129.4 97.5 222 177.3 133.6 282 225.2 109.7 43 34.3 25.9 103 82.3 62.0 163 130.2 98.1 223 178.1 134.2 283 226.0 170.3 44 35.1 26.5 104 83.1 62.6 164 131.0 98.7 224 178.9 134.8 284 226.8 170.9 45 35.9 27.1 105 83.9 63.2 105 131.8 99.3 225 179.7 135.4 285 227.6 171.5 40 36.7 27.7 106 84.7 63.8 166 132.6 99.9 226 180.5 130.0 286 228.4 172.1 47 37.5 28.3 107 85.5 64.4 167 133.4 100.5 227 181.3 13«).0 287 229.2 172.7 48 38.3 28.9 108 86.3 65.0 168 134.2 101.1 228 182.1 137.2 288 230.0 173.3 49 39.1 29.5 109 87.1 65.6 109 135.0 101.7 229 182.9 137.8 289 230.8 173.9 50 51 39.9 30.1 110 87.8 60.2 170 135.8 102.3 230 183.7 138.4 290 231.6 174.5 40.7 30.7 HI 88.6 66.8 171 136.6 102.9 231 184.5 139.0 291 232.4 175.1 52 41.5 31.3 112 89.4 67.4 172 137.4 103.5 232 185.3 139.6 292 233.2 175.7 53 42.3 31.9 113 90.2 68.0 173 138.2 104.1 233 186.1 140.2 293 234.0 176.3 54 43.1 32.5 114 91.0 68.6 174 139.0 104.7 234 186.9 140.8 294 234.8 176.9 55 43.9 33.1 115 91.8 69.2 175 139.8 105.3 235 187.7 141.4 295 235.6 177.5 50 44.7 33.7 116 92.6 69.8 176 140.0 105.9 236 188.5 142.0 296 236.4 178.1 57 45.5 34.3 117 93.4 70.4 177 141.4 106.5 237 189.3 142.6 297 237.2 178.7 58 46.3 34.9 118 94.2 71.0 178 142.2 107.1 238 190.1 143.2 298 238.0 179.3 59 47.1 35.5 119 95.0 71.6 179 143.0 107.7 239 190.9 143.8 299 238.8 179.9 00 DiBt 47.9 . Dep. 30.1 Lat. 120 Dist. 95.8 Dep. 72.2 Lat. 180 Dist. 143.8 108.3 240 Dist. 191.7 144.4 300 239.6 180.5 Dep. Lat. Dep. Lat. Dist. Dep. Lat For 53 De2:fee8. 3^ 82n>. | 54 TABLE II. DIFFERENCE OF LATITUDE AND DEPARTURE FOR 38 DEGREES. 2^ 32m. Dist! Lat Dep. Dist Lat Dep. Dist Lat Dep. Dist. 181 Lat Dep. Dist Lat Dep. -^ 1 00.8 00.6 61 48.1 37.6 121 95.3 74.5 142.6 111.4 241 189.9 148.4 2 01.6 01.2 62 48.9 38.2 122 96.1 75.1 182 143.4 112.1 242 190.7 149.0 3 02.4 01.8 63 49.6 38.8 123 96.9 75.7 183 144.2 112.7 243 191.5 149.6 4 03.2 02.5 64 50.4 39.4 124 97.7 76.3 184 145.0 113.3 244 192.3 150.2 5 03.9 03.1 65 51.2 40.0 125 98.5 77.0 185 145.S 113.9 245 193.1 150.8 6 04.7 03.7 66 52.0 40.6 126 99.3 77.6 180 146.6 114.5 246 193.9 151,5 7 05.5 04.3 67 52.8 41.2 127 100.1 78:2 187 147.4 115.1 247 194.6 152.1 8 06.3 04.9 68 53.6 41.9 128 100.9 78.8 188 148.1 115.7 248 195.4 152.7 9 07.1 05.5 69 54.4 42.5 129 101.7 79.4 189 148.9 116.4 249 196.2 153.3 10 11 07.9 08.7 06.2 70 55.2 43.1 130 102.4 80.0 190 149.7 117.0 250 197.0 153.9 1.54.5 06.8 71 55.9 43.7 131 103.2 80.7 191 150.5 117.6 251 197.8 12 09.5 07.4 72 56.7 44.3 132 104.0 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 ll.,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 59.1 46.2 135 106.4 83.1 195 153.7 120.1 255 200.9 157.0 16 12.6 09.9 76 59.9 46.8 136 107.2 83.7 196 154.5 120.7 256 201.7 157.6 17 13.4 10.5 77 60.7 47.4 137 108.0 84.3 197 155.2 121.3 257 202.5 158.2 18 14.2 11.1 78 61.5 48.0 138 108.7 85.0 198 156.0 121.9 258 203.3 1.58.8 19 15.0 11.7 79 62.3 48.6 139 109.5 85.6 199 156.8 122.5 259 204.1 159.5 20 15.8 12.3 80 63.0 49.3 140 110.3 86.2 200 157.6 123.1 260 204.9 160.1 21 16.5 12.9 81 63.8 49.9 141 111.1 86.8 201 158.4 123.7 261 205.7 160.7 22 17.3 13.5 82 64.6 50.5 142 111.9 87.4 202 159.2 124.4 262 206.5 161.3 23 18.1 14.2 83 65.4 51.1 143 112.7 88.0 203 160.0 125.0 263 207.2 161.9 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 89.3 205 161.5 126.2 265 208.8 163.2 26 20.5 IG.O 86 67.8 52.9 146 115.0 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 69.3 54.2 148 116.6 91.1 208 163.9 128.1 268 211.2 165.0 29 22.9 17.9 89 70.1 54.8 149 117.4 91.7 209 164.7 128.7 269 212.0 165.6 30 23.6 18.5 90 70.9 55.4 150 118.2 92.3 210 165.5 129.3 270 212.8 166.2 31 24.4 19.1 91 71.7 56.0 151 119.0 93.0 211 166.3 129.9 271 213.6 166.8 32 25.2 19.7 92 72.5 56.6 152 119.8 93.6 212 167.1 130.5 272 214.3 167.5 33 26.0 20.3 93 73.3 .57.3 153 120.6 94.2 213 167.8 131.1 273 215.1 168.1 34 26.8 20.9 94 74.1 57.9 154 121.4 94.8 214 168.6 131.8 274 215.9 168.7 35 27.6 21.5 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 29.2 22.8 97 76.4 59.7 157 123.7 96.7 217 171.0 133.6 277 .218.3 170.5 38 29.9 23.4 98 77.2 60.3 158 124.5 97.3 218 171.8 134.2 278 219.1 171.2 39 30.7 24.0 99 78.0 61.0 159 125.3 97.9 219 172.6 134.8 279 219.9 171.8 40 31.5 24.6 100 78.8 61.6 160 126.1 98.5 220 173.4 135.4 280 220.6 172.4 41 32.3 25.2 101 79.6 62.2 161 126.9 99.1 221 174.2 136.1 281 221.4 173.0 42 33.1 25.9 102 80.4 62.8 162 127.7 99.7 222 174.9 136.7 282 222.2 173.6 43 33.9 26.5 103 81.2 63.4 163 128.4 100.4 223 1 175.7 137.3 283 223.0 174.2 44 34.7 27.1 104 82.0 64.0 164 129.2 101.0 224 176.5 137.9 284 223.8 174.8 45 35.5 27.7 105 82.7 64.6 165 130.0 101.6 225 177.3 138.5 285 224.6 175.5 46 36.2 28.3 106 83.5 65.3 166 130.8 102.2 226 178.1 139.1 286 225.4 176.1 47 37.0 28.9 107 84.3 65.9 167 131.6 102.8 227 178.9 139.8 287 226.2 '176.71 48 37.8 29.6 108 85.1 66.5 168 1 32.4 103.4 228 17i«.7 140.4 288 1226.9; 177.3 49 38.6 30.2 109 85.9 67.1 169 133.2 104.0 229 180.5 141.0 289 227.7 1177.9 50 39.4 30.8 110 86.7 67.7 170 134.0 104.7 230 181.2 141.6 290 1 228.5 , 178.5 51 40.2 31.4 111 87.5 68.3 171 134.7 105.3 231 182.0 142.2 291 229.3 179.2 52 41.0 32.0 112 88.3 69.0 172 135.5 105.9 232 182.8 142.8 292 230.1 179.8 53 41.8 32.6 113 89.0 69.6 173 136.3 106.5 233 183.6 143.4 293 230.9 180.4 54 42.6 33.2 114 89.8 70.2 174 137.1 107.1 234 184.4 144.1 294 231.7 181.0 55 43.3 33.9 115 90.6 70.8 175 137.9 107.7 235 185.2 144.7 295 232.5 181.6 5() 44.1 34.5 116 91.4 71.4 176 138.7 108.4 236 186.0 14.5.3 296 233.3 '■ 182.2 57 44.9 35.1 117 92.2 72.0 177 139.5 109.0 237 186.8 14,5.9 297 234.0 182.9 58 45.7 35.7 118 93.0 72.6 178 140.3 109.6 238 187.5 146.5 298 234.8 183.5 59 46.5 36.3 119 93.8 73.3 179 141.1 110.2 239 188.3 147.1 299 235.6 184 1 60 DIst 47.3 36.9 120 94.6 73.9 180 141.8 110.8 240 189.1 147.8 300 236.4 184.7 Dep. Lat. Dist. Dep. Lat Dist Dep. Lat. Dist Dep. Lat Dist Dep. Lat For 52 Degrees. 30 28". ^ TABLE 11. 6i 1 DIFFERENCE OF LATITUDE AND DEPARTURE FOR 39 DEGREES. 2b 86«". | Dist 1 Lat. 00.8 Dep. Dist Lat Dep. Dist Lat Dep. Dist Lat. Dep. Dist Lat 187.3 Dep. 151.7 00.6 61 47.4 38.4 121 94.0 76.1 181 140.7 113.9 241 2 01.6 01.3 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 03.9 03.1 65 50.5 40.9 125 97.1 78.7 185 143.8 116.4 245 190.4 154.2 6 04.7 03.8 66 51.3 41.5 126 97.9 79.3 186 144.5 117.1 246 191.2 154.8 1 05.4 04.4 (>7 52.1 42.2 127 98.7 79.9 187 145.3 117.7 247 192.0 155.4 8 06.2 0.").0 68 52.8 42. » 128 99.5 80.6 188 146.1 118.3 248 192.7 156.1 9 07.0 05.7 69 53.6 43.4 129 100.3 81.2 189 146.9 118.9 249 193.5 1567 10 07.8 06.3 06.9 70 54.4 44.1 130 131 101.0 81.8 190 191 147.7 119.6 250 194.3 157.3 158.0 11 08.5 71 5.'). 2 44.7 101.8 82.4 148.4 120.2 251 195.1 12 09.3 07.6 72 56.0 4.3.3 132 102.6 83.1 192 149.2 120.8 252 195.8 158.6 13 1(1.1 08.2 73 56.7 45.9 133 103.4 83.7 193 150.0 121.5 253 196.6 159.2 14 10.9 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 0!».4 75 58.3 47.2 135 104.9 85.0 195 151.5 122.7 255 198.2 160.5 16 12.4 10.1 7(5 59.1 47.S 136 105.7 85.6 196 152.3 123.3 256 19S.9 161.1 17 13.2 10.7 77 59.8 48.5 137 106.5 86.2 197 153.1 124.0 257 199.7 161.7 18 14.0 11.3 78 60.6 49.1 138 107.2 86.8 198 153.9 124.6 258 200.5 1 62.4 19 14.8 12.0 79 61.4 49.7 139 108.0 87.5 199 154.7 125.2 259 201.3 163.0 20 21 15.5 16.3 12.6 80 62.2 62.9 50.3 51.0 140 108.8 88.1 200 201 155.4 156.2 125.9 260 202.1 163.6 13.2 81 141 109.6 88.7 126.5 261 202.8 164.3 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 l2 125.9 101.9 222 172.5 1 39.7 282 219.2 177.5 43 33.4 27.1 103 80.0 64.8 163 126.7 102.6 223 173.3 140.3 283 219.9 178.1 44 34.2 27.7 104 80.8 65.4 1()4 127.5 103.2 224 174.1 141.0 284 220.7 178.7 45 35.0 28.3 105 81.6 66.1 l(*)5 128.2 103.8 225 174.9 141.6 285 221.5 179.4 46 35.7 28.9 106 82.4 66.7 166 129.0 104.5 226 175.6 142.2 286 222.3 180.0 47 36.5 29.r, 107 83.2 67.3 167 129.8 105.1 227 17(5.4 142.9 287 223.0 180.6 48 37.3 30.2 108 83.9 68.0 168 130.6 105.7 228 177.2 143.5 288 223.8 181.2 49 38.1 30.8 109 84.7 68.6 1()9 131.3 106.4 229 178.0 144.1 289 224.6 181.9 50 51 38.9 39.6 31.5 110 85.5 69.2 170 132.1 107.0 230 178.7 144.7 290 225.4 182. .3 32.1 111 8().3 69.9 171 132.9 107.6 231 179.5 145.4 291 226.1 1S3 1 52 40.4 32.7 1 12 87.0 70.5 172 133.7 108.2 232 180.3 146.0 292 22(5.9 ly3.s 53 41.2 33.4 113 87.8 71.1 173 134.4 108.9 233 181.1 14(5.6 293 227.7 184.4 54 42.0 34.0 114 88.6 71.7 174 13.5.2 109.5 234 181.9 1 47.3 294 228.5 185.0 55 42.7 34.6 115 89.4 72.4 175 136.0 110.1 235 182.6 147.9 295 229.3 185.6 56 43.5 35.2 116 90.1 73.0 176 1 •••.6.8 110.8 236 183.4 148.5 296 230.0 186.3 57 44.3 3.-). 9 117 90.1> 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 1 12.0 238 185.0 149.8 298 231.6 187.5 59 45.9 3r.i 119 92.5 74.9 179 139.1 112.6 239 185.7 150.4 299 232.4 188.2 60 46.6 37.8 120 Dist 93.3 Dep. 75.5 L.it 180 139.9 113.3 240 Di.*t 186.5 151.0 300 233.1 188.8 Dist Dep. Lat. Dist Dep. Lat. Dep. Lat. Diet. Dep. Lat For 51 3e!^rees. 3^ 24m. 66 \ TABLE 11. 1 DIFFERENCE OF LATITUDE AND DEPARTURE FOR 40 DEGREES. 2>> 40m 1 DisL 1 Lilt. Dep. Dist. Lat. 46.7 Dep. Dist. LaU Dep. Dist. 181 Lat. Dep. 116.3 Dist. Lat. Dep. 00.8 00.6 61 39.2 !21 92.7 77.8 138.7 241 1S4.6 154.9 2 01.5 01.3 ()2 47.5 39.9 122 93.5 78.4 Ls2 139.4 117.0 242 185.4 155.6 3 02.3 01.9 63 48.3 40.5 123 94.2 79.1 183 140.2 117.6 243 186.1 156.2 4 03.1 02.6 64 49.0 41.1 124 95.0 79.7 184 141.0 118.3 244 186.9 156.8 5 03 8 03.2 (')5 49.8 41.8 125 95.8 80.3 185 141.7 118.9 245 187.7 157.5 6 04.0 03.9 66 50.6 42.4 126 9(').5 81.0 186 142.5 119.6 246 188.4 158.1 7 1 05.4 04.5 67 51.3 43.1 127 97.3 81.6 187 143.3 120.2 247 189.2 158,8 8 06.1 05.1 68 52.1 43.7 128 98.1 82.3 188 144.0 120.8 248 190.0 1 59.4 9 06.9 05.8 69 52.9 44.4 129 98.8 82.9 189 144.8 121.5 249 1 190.7 160.1 10 11 07.7 08. -l 0().4 70 53.6 45.0 1 :!0 99.6 83.6 190 145.5 122.1 250 191.5 160.7 161.3 07.1 71 54.4 45.6 131 100.4 84.2 191 146.3 122.8 251 192.3 12 09.2 07.7 72 55.2 46.3 1 32 101.1 84.8 192 147.1 123.4 252 193.0 162.0 13 10.0 08.4 73 55.9 46.9 i;;3 101.9 85.5 193 147.8 124.1 253 193.8 162.6 14 10.7 09.0 74 56.7 47.6 134 102.6 86.1 194 14'«.6 124.7 254 194.6 163.3 15 11.5 09.6 75 57.5 48.2 135 103.4 86.8 195 149.4 125.3 255 195.3 163.9 16 12.3 10 3 76 58.2 48.9 136 104.2 87.4 196 150.1 126.0 256 196.1 164.6 17 13.0 10.9 77 59.0 49.5 137 ! 04.9 88.1 197 150.9 126.6 257 196.9 165.2 18 13.8 11.6) 78 59.8 50.1 138 105.7 88.7 198 151.7 127.3 258 197.6 165.8 19 14.6 12.2 79 60.5 50.8 139 106.5 89.3 1 99 152.4 127.9 259 198.4 166.5 20 15.3 12.9 80 61.3 51.4 140 107.2 90.0 200 153.2 128.6 260 199.2 167.1 21 16.1 13.5 81 ()2.0 52.1 141 108.0 90.6 201 J 54.0 129.2 261 ' 199.9 167.8 22 16.9 14.1 82 62.8 52.7 142 108.8 91.3 202 154.7 129.8 262 200.7 168.4 23 17.6 14.8 83 63.6 53.4 143 109.5 91.9 203 155.5 130.5 263 201.5 169.1 24 18.4 15.4 84 64.3 54.0 144 110.3 92.6 204 156.3 131.1 264 202.2 169.7 25 19.2 16.1 85 65.1 54.6 145 111.1 93.2 205 157.0 131.8 265 203.0 170.3 2*) 19.9 16.7 86 65.9 55.3 146 111.8 93.8 206 1 57.8 132.4 266 203.8 171.0 27 20.7 17.4 87 66.6 55.9 147 112.6 94.5 207 158.6 133.1 267 204.5 171.6 28 21.4 18.0 88 67.4 56.6 148 113.4 95.1 208 159.3 1337 268 205.3 172.3 29 22 2 18.6 89 68.2 57.2 149 114.1 95.8 209 160.1 134.3 269 206.1 172.9 30 23.0 19.3 90 91 68.9 69.7 57.9 150 114.9 96.4 210 160.9 135.0 270 206.8 1 173.6 31 23.7 19.9 58.5 151 115.7 97.1 211 161.6 135.6 271 207.6 174.2 32 24.5 20.6 92 70.5 59.1 152 116.4 97.7 212 162.4 136.3 272 208.4 174.8 33 25.3 21.2 93 71.2 59.8 153 117.2 98.3 213 163.2 136.9 273 209.1 175.5 34 26.0 21.9 94 72.0 60.4 154 118.0 99.0 214 163.9 137.6 274 209.9 176.1 35 2<).8 22.5 95 72.8 61.1 155 118.7 99.6 215 1<)4.7 138.2 275 210.7 176.8 3t) 27.() 23.1 !»6 73.5 61.7 156 119.5 100.3 216 165.i 138.8 276 211.4 177.4 37 2S.3 23.8 97 74.3 62.4 157 120.3 100.9 217 166.2 139.5 277 212.2 178.1 38 29.1 24.4 98 75.1 63.0 158 121.0 101.6 218 167.0 140.1 278 213.0 178.7 39 29.9 25.1 99 75.8 63.6 159 121.8 102.2 219 167.8 140.8 279 213.7 179.3 40 30.6 25.7 100 76.6 64.3 160 122.6 102.8 220 168.5 141.4 280 214.5 180.0 41 31.4 26.4 101 77.4 64.9 ir>i 123.3 103.5 221 16i).3 142.1 281 215.3 180.6 42 32.2 27.0 102 78.1 65.6 162 124.1 104.1 222 170.1 142.7 282 216.0 181.3 43 32.9 27.6 103 78.9 66.2 163 124.9 104.8 223 170.8 143.3 283 216.8 181.9 44 33.7 28.3 104 79.7 66.8 164 125.6 105.4 224 171.6 144.0 284 217.6 182.6 45 34.5 28.9 105 80.4 67.5 165 126.4 106.1 225 172.4 144.6 285 218.3 183.2 4() 35.2 29.6 lOr. 81.2 68.1 166 127.2 106.7 226 173.1 145.3 286 219.1 183.8 47 36.0 30.2 107 82.0 68.8 167 127.9 107.3 227 173.9 145.9 287 219.9 184.5 48 36.8 30.9 108 82.7 69.4 1()8 12S.7 108.0 228 174.7 146.6 288 220.6 185.1 49 37.5 .•il.5 109 83.5 70.1 169 129.5 108.6 22i) 175.4 147.2 289 221.4 185.8 50 38.3 32.1 110 84.3 70.7 170 130.2 109.3 230 1 76.2 147.8 290 222.2 1S6.4| 51 39.1 32.8 HI 85.0 71.3 171 131.0 109.9 231 177.0 148.5 291 1222.9 '187.1 52 39.8 33.4 112 85.8 72.0 172 131.8 1 10.6 232 177.7 149.1 292 223.7 1 187.7 53 40 6 34.1 113 86.6 72.6 !73 132.5 111.2 233 178.5 149.8 293 224.5 188.3 54 41.4 34.7 114 87.3 73.3 174 133.3 111.8 234 179.3 150.4 294 ' 225.2 189.0 55 42.1 35.4 ll.T 88.1 73.9 175 134.1 112.5 235 180.0 151.1 295 22().0 189.6 5(> 42.9 3().0 116 88.9 74.6 176 134.8 113.1 236 180.8 151.7 296 226.7 190.3 57 43.7 36.6 117 89.6 75.2 177 135.6 113.8 237 181.6 152.3 297 227.5 190.9 58 44.4 37.3 118 90.4 75.8 178 136.4 114.4 238 182.3 153.0 298 228.3 191.6 59 45.2 37.9 119 91.2 76.5 179 137.1 115.1 239 183.1 153.6 299 229.0 192.2 60 46.0 38.6 120 91.9 77.1 180 ! 37.9 115.7 240 183.9 154.3 300 229.8 192.8 Distl Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. F DEPARTURE FOR 41 DEGREES. 2h 44m. 1 Dist 1 Lat Dep. Dist. Lat. Dep. Dist. Lut. Dep. 79.4 Dist Lat Dep. Dist 241 Lat Dep. 00.8 00.7 61 46.0 40.0 121 91.3 181 136.6 118.7 181.9 158.1 2 01.5 01.3 62 46.8 40.7 122 92.1 80.0 182 137.4 119.4 242 182.6 158.8 3 02.3 02.0 63 47.5 41.3 123 92.8 80.7 183 138.1 120.1 243 183.4 159.4 4 03.0 02.6 64 48.3 42.0 124 93.6 81.4 184 138.9 120.7 244 184.1 160.1 5 03.8 03.3 65 49.1 42.6 125 94.3 82.0 185 139.6 121.4 245 184.9 160.7 6 04.5 03.9 66 49.8 43.3 126 95.1 82.7 186 140.4 122.0 246 185.7 161.4 7 05.3 04.() 67 50.6 44.0 127 95.8 83.3 187 141.1 122.7 247 186.4 162.0 8 06.0 05.2 68 51.3 44.6 128 96.6 84'. 188 141.9 123.3 248 187.2 162.7 9 06.8 1 05.9 69 52.1 45.3 129 97.4 84.6 189 142.6 124.0 249 187.9 163.4 10 07.5 06.6 70 52.8 45.9 130 98.1 85.3 190 191 143.4 124.7 250 188.7 164.0 11 08.3 07.2 71 53.6 46.6 131 98.9 85.9 144.1 125.3 251 189.4 164.7 12 09.1 07.9 72 54.3 47.2 132 99.6 86.6 192 144.9 126.0 252 1!»0.2 165.3 13 09.8 08.5 73 55.1 47.9 133 100.4 87.3 193 145.7 126.6 253 190.9 166.0 14 10.6 09.2 74 55.8 48.5 134 lOl.l 87.9 194 146.4 127.3 254 191.7 166.6 15 11.3 09.8 75 56.6 41>.2 135 101.9 88.6 195 147.2 127.9 255 192.5 167.3 16 12.1 10.5 76 57.4 49.9 136 102.6 89.2 196 147.9 128.6 256 193.2 168.0 17 12.8 11.2 77 58.1 50.5 137 103.4 89.9 197 148.7 129.2 257 194.0 168.6 18 13.6 11.8 78 58.9 51.2 138 104.1 90.5 198 149.4 129.9 258 194.7 169.3 !9 14.3 12.5 79 59.6 51.8 139 104.9 91.2 199 150.2 130.6 259 195.5 169.9 20 21 15.1 15.8 13.1 80 60.4 61.1 52.5 53.1 140 105.7 91.8 200 150.9 131.2 260 196.2 170.6 13.8 81 141 106.4 92.5 201 151.7 131.9 261 197.0 171.2 22 16.6 14.4 82 61.9 53.8 142 107.2 93.2 202 152.5 132.5 262 197.7 171.9 23 17.4 15.1 83 62.6 54.5 143 107.9 93.8 203 153.2 133.2 263 198.5 172.5 24 18.1 15.7 84 63.4 55.1 144 108.7 94.5 204 154.0 133.8 264' 199.2 173.2 25 18.9 16.4 85 64.2 55.8 145 109.4 95.1 205 154.7 134.5 265 200.0 173.9 20 19.6 17.1 86 64.9 56.4 146 110.2 95.8 206 155.5 135.1 266 200.8 174.5 27 20.4 17.7 87 65.7 57.1 147 110.9 96.4 207 156.2 135.8 267 201.5 175.2 28 21.1 18.4 88 66.4 57.7 148 111.7 97.1 208 157.0 136.5 288 202.3 175.8 29 21.9 19.0 89 67.2 58.4 149 112.5 97.8 209 157.7 137.1 269 203.0 176.5 30 31 22.6 .19.7 90 91 67.9 68.7 59.0 150 113.2 98.4 210 158.5 137.8 270 203.8 177.1 23.4 20.3 59.7 151 114.0 99.1 211 159.2 138.4 271 204.5 177.8 32 24.2 21.0 92 69.4 60.4 152 114.7 99.7 212 160.0 139.1 272 205.3 178.4 33 24.9 21.6 93 70.2 61.0 153 115.5 100.4 213 160.8 139.7 273 206.0 179.1 34 25.7 22.3 94 70.9 61.7 154 116.2 101.0 214 161.5 140.4 274 206.8 179.8 35 26.4 23.0 95 71.7 62.3 155 117.0 101.7 215 102.3 141.1 275 207.5 180.4 36 27.2 23.6 96 72.5 03.0 1.56 117.7 102.3 216 163.0 141.7 276 208.3 181.1 37 27.9 24.3 97 73.2 03.6 157 118.5 103.0 217 163.8 142.4 277 209.1 181.7 38 28.7 24.9 98 74.0 64.3 1.58 119.2 103.7 218 104.5 143.0 278 209.8 182.4 39 29.4 25.6 99 74.7 64.9 159 120.0 104.3 219 165.3 143.7 279 210.6 183.0 40 30.2 26.2 100 75.5 65.6 160 120.8 io.->.o 220 166.0 144.3 280 211.3 183.7 41 30.9 26.9 101 70.2 66.3 101 121.5 105.6 221 166.8 145.0 281 212.1 184.4 42 31.7 27.6 102 77.0 60.0 1 02 122.3 10(5.3 222 16T.5 145.6 282 212.8 185.0 43 32.5 28.2 103 77.7 07.0 163 123.0 106.9 223 168.3 146.3 283 21.3.6 185.7 44 33.2 28.9 104 78.5 ()8.2 104 123.8 107.6 224 169.1 147.0 284 214.3 186.3 45 34.0 29.5 105 79.2 08.9 105 124.5 108.2 225 169.8 147.6 285 215.1 187.0 46 34.7 30.2 106 80.0 09.5 106 125.3 108.9 226 170.6 148.3 286 215.8 187.6 47 35.5 30.8 107 808 70.2 107 126.0 109.6 227 171.3 148.9 287 216.6 188.3 48 36.2 31.5 108 81.5 70.9 108 126.8 110.2 228 172.1 149.0 288 217.4 188.9 49 37.0 32.1 109 82.3 71.5 109 127.5 110.9 229 172.8 150.2 289 218.1 189.6 50 51 37.7 32.8 110 83.0 72.2 170 128.3 111.5 230 173.0 150.9 290 218.9 190.3 38.5 33.5 111 83.8 72.8 171 129.1 112.2 231 174.3 151.5 291 219.6 190.9 52 39.2 34.1 112 84.5 73.5 172 129.8 112.8 232 175.1 1,52.2 292 220.4 191.6 53 40.0 34.8 113 85.3 74.1 173 130.6 113.5 233 175.8 152.9 293 221.1 192.2 54 40.8 35.4 114 86.0 74.8 174 131.3 114.2 234 170.6 153.5 294 221.9 1192.9 1 55 41.5 36.1 115 86.8 75.4 175 132.1 114.8 235 177.4 154.2 295 222.6 193.5 56 42.3 36.7 116 87.5 76.1 170 132.8 115.5 236 178.1 154.8 296 223.4 194.2 57 43.0 37.4 117 88.3 76.8 177 133.0 lir,.i 237 178.9 155.5 297 224.1 194.8 58 43.8 38.1 118 89.1 77.4 178 134.3 116.8 238 179.6 156.1 298 224.9 195.5 59 44.5 38.7 119 89.8 78.1 179 135.1 117.4 239 180.4 156.8 299 225.7 196.2 60 Dist 45.3 Dep. 39.4 Lat. 120 90.6 78.7 Lat. 180 135.8 118.1 240 181.1 157.5 300 226.4 196.8 Dist. Dep. Dist. Dep. Lat Dist Dep. Lat Dist. Dep. Lat For 49 Degrees. S^ 16" 1 68 TABLE 11. 1 DIFFERENCE OF LATITUDE AND DEPARTURE FOR 42 DEGREES. 2^ 48ni. 1 Diflt. 1 Lat. Dep. Dist. Lat. Dep 40.8 Dist. Lat. Dep. Dist. Lat. Dep. Dist Lat Dep. 00.7 00.7 61 45.3 121 89.9 81.0 181 134.0 121.1 241 179.1 161.3 2 01.5 01.3 62 46.1 41.5 122 90.7 81.6 KS2 135.3 121.8 242 179.8 161.9 3 02.2 02.0 63 46.8 42.2 123 91.4 82.3 183 136.0 122.5 243 180.6 162.6 4 03.0 02.7 64 47.6 42.8 124 92.1 83.0 184 136.7 123.1 244 181.3 163.3 5 03.7 03.3 65 48.3 43.5 125 92.9 83.6 185 137.5 123.8 245 182.1 163.9 6 04.5 04.0 66 49.0 44.2 126 93.6 84.3 186 138.2 124.5 246 182.8 164.6 7 05.2 04.7 67 49.8 44.8 127 94.4 85.0 187 139.0 125.1 247 183.6 165.3 8 05.9 05.4 68 50.5 45.5 128 95.1 85.6 188 139.7 125.8 248 184.3 165.9 9 06.7 06.0 69 51.3 46.2 129 95.9 86.3 189 140.5 126.5 249 185.0 166.6 10 11 07.4 06.7 70 52.0 46.8 130 96.6 87.0 190 141.2 127.1 250 185.8 167.3 08.2 07.4 71 52.8 47.5 131 97.4 87.7 191 141.9 127.8 251 186.5 168.0 12 08.9 08.0 72 .^3.5 48.2 132 98.1 88.3 192 142.7 128.5 252 187.3 168.6 13 09.7 08.7 73 54.2 48.8 133 98.8 89.0 193 143.4 129.1 253 188.0 169.3 14 10.4 09.4 74 55.0 49.5 134 '99.6 89.7 194 144.2 129.8 254 188.8 170.0 15 11.1 10.0 75 55.7 50.2 135 100.3 90.3 195 144.9 130.5 255 189.5 170.6 16 11.9 10.7 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 13.4 12.0 78 58.0 52.2 138 102.6 92.3 198 147.1 132.5 258 191.7 172.6 19 14.1 12.7 79 58.7 52.9 139 103.3 93.0 199 147.9 133.2 259 192.5 173.3 20 14.9 13.4 80 59.5 53.5 140 104.0 93.7 200 148.6 133.8 260 193.2 174.0 21 15.6 14.1 81 60.2 54.2 141 104.8 94.3 201 149.4 134.5 261 194.0 174.6 22 16.3 14.7 82 60.9 54.9 142 105.5 95.0 202 150.1 135.2 262 194.7 175.3 23 17.1 15.4 83 61.7 55.5 143 106.3 95.7 203 150.9 135.8 263 195.4 176.0 24 17.8 16.1 84 62.4 56.2 144 107.0 96.4 204 151.6 136.5 264 196.2 176.7 25 18.6 16.7 85 63.2 56.9 145 107.8 97.0 205 152.3 137.2 265 196.9 177.3 26 19.3 17.4 86 63.9 57.5 146 108.5 97.7 206 153.1 137.8 266 197.7 178.0 27 20.1 18.1 87 64.7 58.2 147 109.2 98.4 207 153.8 138.5 267 198.4 178.7 28 20.8 18.7 88 65.4 58.9 148 110.0 99.0 208 154.6 139.2 268 199.2 179.3 29 21.6 19.4 89 66.1 59.6 149 110.7 99.7 209 155.3 139.8 269 . 199.9 180.0 30 22.3 20.1 90 66.9 60.2 150 111.5 100.4 210 156.1 140.5 270 200.6 180.7 31 23.0 20.7 91 67.6 60.9 151 112.-8 101.0 211 156.8 141.2 271 201.4 181.3 32 23.8 21.4 92 68.4 61.6 152 113.0 iOl.7 212 157.5 141.9 272 202.1 182.0 33 24.5 22.1 93 69.1 62.2 153 113.7 102.4 213 158.3 142.5 273 202.9 182.7 34 25.3 22.8 94 69.9 62.9 154 .114.4 103.0 214 159.0 143.2 274 203.6 183.3 35 26.0 23.4 95 70.6 63.6 155 115.2 103.7 215 159.8 143.9 275 204.4 184.0 36 26.8 24.1 96 71.3 64.2 156 115.9 104.4 216 160.5 144.5 276 205.1 184.7 37 27.5 24.8 97 72.1 64.9 157 116.7 105.1 217 161.3 145.2 277 205.9 185.3 38 28.2 25.4 98 72.8 65.6 1.58 117.4 105.7 218 162.0 145.9 278 206.6 186.0 39 29.0 26.1 99 73.6 66.2 159 118.2 106.4 219 162.7 146.5 279 207.3 186.7 40 29.7 26.8 100 74.3 66.9 160 118.9 107.1 220 163.5 147.2 280 208.1 187.4 41 30.5 27.4 101 75.1 67.6 161 119.6 107.7 221 164.2 147.9 281 208.8 188.0 42 31.2 28.1 102 75.8 68.3 162 120.4 108.4 222 1*65.0 148.5 282 209.6 188.7 43 32.0 28.8 103 76.5 68.9 163 121.1 109.1 223 165.7 149.2 283 210.3 189.4 44 32.7 29.4 104 77.3 69.6 164 121.9 109.7 224 166.5 149.9 284 211.1 190.0 45 33.4 30.1 105 78.0 70.3 165 122.6 110.4 225 167.2 150.6 285 211.8 190.7 46 34.2 30.8 106 78.8 70.9 166 123.4 111.1 226 168.0 151.2 286 212.5 191.4 47 34.9 31.4 107 79.5 71.6 167 124.1 111.7 227 168.7 151.9 287 213.3 192.0 48 35.7 32.1 108 80.3 72.3 1()8 124.8 112.4 228 169.4 152.6 288 214.0 192.7 49 36.4 32.8 109 81.0 72.9 169 125.6 113.1 229 170.2 153.2 289 214.8 193.4 50 37.2 33.5 110 81.7 73.6 170 126.3 113.8 230 170.9 153.9 290 215.5 194.0 51 37.9 34.1 111 82.5 74.3 171 127.1 114.4 231 171.7 154.6 291 216.3 194.7 52 38.6 34.8 112 83.2 74.9 172 127.8 115.1 232 172.4 155.2 292 217.0 195.4 53 394 35.5 113 84.0 75.6 173 128.6 115.8 233 173.2 155.9 293 217.7 196.1 54 40.1 36.1 114 84.7 76.3 174 129.3 116.4 234 173.9 156.6 294 218.5 196.7 55 40.9 36.8 115 85.5 77.0 175 130.1 117.1 235 174.6 157.2 295 219.2 197.4 56 41.6 37.5 116 86.2 77.6 176 130.8 117.8 236 175.4 157.9 296 220.0 198.1 57 42.4 38.1 117 86.9 78.3 177 131.5 118.4 237 176.1 158.6 297 220.7 198.7 58 43.1 38.8 118 87.7 79.0 178 132.3 119.1 238 176.9 159.3 298 221.5 199.4 59 43.8 39.5 119 88.4 79.6 179 133.0 119.8 239 177.6 159.9 299 222.2 200.1 60 Dist 44.6 40.1 120 89.2 80.3 180 133.8 120.4 240 178.4 160.6 300 222.9 200.7 Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist Dep. Lat F..r 48 Degrees. 3h 12°". TABLE 11. (9 ' DIFFERENCE OF LATITUDE AND DEPARTURE FOR 43 DEGREES. 2h 62^. 1 Dist 1 Lat Dep. Di8t. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. 241 Lat. Dep. 00.7 00.7 61 44.6 41.6 121 88.5 82.5 181 132.4 123.4 176.3 164.4 2 01.5 01.4 62 45.3 42.3 122 89.2 83.2 182 133.1 124.1 242 177.0 165.0 3 02.2 02.0 63 46.1 43.0 123 90.0 83.9 183 133.8 124.8 243 177.7 165.7 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 85.2 185 135.3 126.2 245 179.2 167.1 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 49.7 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 47.7 130 131 95.1 88.7 190 139.0 129.6 250 182.8 170.5 11 08.0 07.5 71 51.9 48.4 95.8 89.3 191 139.7 130.3 251 183.6 171.2 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 90.7 193 141.2 131.6 253 185.0 172.5 14 10.2 09.5 74 54.1 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 51.1 135 98.7 92.1 195 142.6 133.0 255 186.5 173.9 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 21 14.6 15.4 13.6 80 58.5 59.2 54.6 55.2 140 102.4 95.5 200 146.3 147.0 136.4 260 190.2 177.3 14.3 81 141 103.1 96.2 201 137.1 261 190.9 178.0 22 16.1 15.0 82 60.0 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 58.0 145 106.0 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 60.7 149 109.0 101.6 209 152.9 142.5 269 196.7 183.5 30 31 21.9 20.5 90 91 65.8 66.6 61.4 150 109.7 102.3 210 153.6 143.2 270 197.5 184.1 22.7 21.1 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 66.2 157 114.8 107.1 217 158.7 148.0 277 202.6 188.9 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 41 29.3 27.3 100 73.1 68.2 160 117.0 109.1 220 160.9 150.0 280 204.8 205.5 191.0 30.0 28.0 101 73.9 68.9 161 117.7 109.8 221 161.6 150.7 281 191.6 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 71.6 165 120.7 112.5 225 164.6 153.4 285 208.4 194.4 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 73.7 168 122.9 114.6 228 166.7 155.5 288 210.6 196.4 49 35.8 33.4 lOit 79.7 74.3 169 123.6 115.3 229 167.5 156.2 289 211.4 197.1 50 51 36.6 34.1 110 S0.4 75.0 170 124.3 115.9 230 168.2 156.9 290 212.1 197.8 37.3 34.8 111 81.2 75.7 171 125.1 116.6 231 168.9 157.5 291 212.8 198.5 52 38.0 35.5 112 81.9 70.4 172 125.8 117.3 232 169.7 158.2 292 213.6 199.1 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 77.7 174 127.3 118.7 234 171.1 159.6 294 215.0 200.5 55 40.'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 39.6 118 86.3 80.5 178 130.2 121.4 238 174.1 162.3 298 217.9 203.2 59 43.1 40.2 119 87.0 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 Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat Dist. Dep. Lat For 47 Deforces. S^ 8™. | 60 TABLE II. DIFFERENCE OF LATITUDE AND DEPARTURE FOR 44 DEGREES. 2^ BSm. Diet Lat. Dep. Dist. Lat. Dep. Diet. Lat. Dep. Dist. 181 Lat. Dep. Dist Lat Dep. 1 00.7 00.7 61 43.9 42.4 121 87.0 84.1 130.2 125.7 241 173.4 167.4 2 01.4 01.4 62 44.6 43.1 122 87.8 84.7 182 130.9 126.4 242 174.1 168.1 3 02.2 02.1 63 45.3 43.8 123 88.5 85.4 183 131.6 127.1 243 174.8 168.8 4 02.9 02.8 64 46.0 44.5 124 S9.2 86.1 184 132.4 127.8 244 175.5 169.5 5 03.6 03.5 65 46.8 45.2 125 89.9 86.8 185 133.1 128.5 245 176.2 170.2 6 04.3 04.2 66 47.5 45.8 126 90.6 87.5 186 133.8 129.2 246 177.0 170.9 7 05.0 04.9 67 48.2 46.5 127 91.4 88.2 187 134.5 129.9 247 177.7 171.6 8 05.8 05.6 68 48.9 47.2 128 92.1 88.9 188 135.2 130.6 248 178.4 172.3 9 06.5 06.3 69 49.6 47.9 129 '■92.8 89.6 189 136.0 131.3 249 179.1 173.0 10 11 07.2 06.9 70 50.4 48.6 130 93.5 90.3 190 136.7 132.0 250 179.8 173.7 07.9 07.6 71 51.1 49.3 131 94.2 91.0 191 137.4 132.7 251 180.6 174.4 12 08.6 08.3 72 51.8 50.0 132 95.0 91.7 192 138.1 133.4 252 181.3 175.1 13 09.4 09.0 73 52.5 50.7 133 95.7 92.4 193 138.8 134.1 253 182.0 175.7 14 10.1 09.7 74 53.2 51.4 134 96.4 93.1 194 139.6 134.8 254 182.7 176.4 15 10.8 10.4 75 54.0 52.1 135 97.1 93.8 195 140.3 135.5 255 183.4 177.1 16 11.5 11.1 76 54.7 52.8 136 97.8 94.5 196 141.0 136.2 256 184.2 177.8 17 12.2 11.8 77 55.4 53.5 137 98.5 95.2 197 141.7 136.8 257 184.9 178.5 18 12.9 12.5 78 56.1 54.2 138 99.3 95.9 198 142.4 137.5 258 185.6 179.2 19 13.7 13.2 79 56.8 54.9 139 100.0 96.6 199 143.1 138.2 259 186.3 179.9 20 14.4 13.9 80 57.5 58.3 55.6 140 100.7 97.3 200 143.9 138.9 260 187.0 180.6 21 15.1 14.6 81 56.3 141 101.4 97.9 201 144.6 139.6 261 187.7 181.3 22 15.8 15.3 82 59.0 57.0 142 102.1 98.6 202 145.3 140.3 262 188.5 182.0 23 16.5 16.0 83 59.7 57.7 143 102.9 99.3 203 146.0 141.0 263 189.2 182.7 24 17.3 16.7 84 60.4 58.4 144 103.6 100.0 204 146.7 141.7 264 189.9 183.4 25 18.0 17.4 85 61.1 59.0 145 104.3 100.7 205 147.5 142.4 265 190.61 184.11 26 18.7 18.1 86 61.9 59.7 146 105.0 101.4 206 148.2 143.1 266 191.3; 184.8 1 27 19.4 18.8 87 62.6 60.4 147 105.7 102.1 207 148.9 143.8 267 192.1 185.5 28 20.1 19.5 88 63.3 61.1 148 106.5 102.8 208 149.6 144.5 268 192.8 186.2 29 20.9 20.1 89 64.0 61.8 149 107.2 103.5 209 150.3 145.2 269 193.5 186.9 30 21.6 20.8 90 64.7 62.5 150 107.9 104.2 210 151.1 145.9 270 194.2 187.6 31 22.3 21.5 91 65.5 63.2 151 108.6 104.9 211 151.8 146.6 271 194.9 188.3 32 23.0 22.2 92 66.2 63.9 152 109.3 105.6 212 152.5 147.3 272 195.7 188.9 33 23.7 22.9 93 66.9 64.6 153 110.1 106.3 213 153.2 148.0 273 196.4 189.6 34 24.5 23.6 94 67.6 65.3 154 110.8 107.0 214 153.9 148.7 274 197.1 190.3 35 25.2 24.3 95 68.3 66.0 155 111.5 107.7 215 154.7 149.4 275 197.8 191.0 36 25.9 25.0 96 69.1 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 98 70.5 68.1 158 113.7 109.8 218 150.8 151.4 278 200.0 193.1 39 28.1 27.1 99 71.2 68.8 159 114.4 110.5 219 157.5 152.1 279 200.7 193.8 40 28.8 27.8 100 71.9 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 29.9 103 74.1 71.5 163 117.3 113.2 223 100.4 154.9 283 203.6 196.6 44 31.7 30.6 104 74.8 72.2 164 118.0 113.9 224 161.1 155.6 284 204.3 197.3 45 32.4 31.3 105 75.5 72.9 165 118.7 114.6 225 161.9 156.3 285 205.0 198.0 46 33.1 32.0 106 76.3 73.6 166 119.4 115.3 226 162.6 157.0 286 205.7 198.7 47 33.8 32.6 107 77.0 74.3 167 120.1 116.0 227 163.3 157.7 287 206.5 199.4 48 34.5 33.3 108 77.7 75.0 168 120.8 116.7 228 164.0 158.4 288 207.2 200.1 49 35.2 34.0 109 78.4 75.7 169 121.6 117.4 229 164.7 159.1 289 207.9 200.8 50 36.0 34.7 110 79.1 76.4 170 122.3 118.1 230 165.4 159.8 290 208.6 201.5 51 36.7 35.4 111 79.8 77.1 171 12.S.0 118.8 231 166.2 160.5 291 209.3 202.1 52 37.4 36.1 112 80.6 77.8 172 123.7 119.5 232 166.9 161.2 292 210.0 202.8 53 38.1 36.8 113 81.3 78.5 173 124.4 120.2 233 167.6 161.9 293 210.8 203.5 54 38.8 37.5 114 82.0 79.2 174 125.2 120.9 234 168.3 162.6 294 211.5 204.2 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 84.9 82.0 178 128.0 123.6 238 171.2 165.3 298 214.4 207.0 59 42.4 41.0 119 85.6 82.7 179 128.8 124.3 239 171.9 166.0 299 215.1 207.7 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 JDiat Dep. Lat Dist Dep. Lat. Dist. Dep. Lilt. Dist Dep. Lat Dist Dep. Lat 1 For 46 Degrees. 8h 4m. | TABLE 11. ei 1 DIFFERENCE OF LATITUDE AND DEPARTURE FOR 45 DEGREES. 8h Qm. | Dist- 1 Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist Lat Dep. 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 44.5 123 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 1-33.2 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 90.5 188 132.9 132.9 248 175.4 175.4 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 49.5 4H.5 130 131 91.9 91.9 190 134.4 134.4 250 176.8 176.8 177.5 11 07.8 07.8 71 50.2 50.2 92.6 92.6 191 135.1 135.1 251 177.5 12 08.5 08.5 72 50.9 50.9 132 93.3 93.3 192 135.8 135.8 252 178.2 178.2 13 09.2 09.2 73 51.6 51.6 133 94.0 94.0 193 136.5 136.5 253 178.9 178.9 14 09.9 09.9 74 52.3 52.3 134 94.8 94.8 194 137.2 137.2 254 179.6 179.6 15 10.6 10.6 75 53.0 53.0 135 95.5 95.5 195 137.9 137.9 255 180.3 180.3 16 11.3 11.3 76 53.7 53.7 136 96.2 96.2 196 138.6 138.6 256 181.0 181.0 17 12.0 12.0 77 54.4 54.4 137 96.9 96.9 197 139.3 139.3 257 181.7 181.7 18 12.7 12.7 78 55.2 55.2 138 97.6 97.6 198 140.0 140.0 258 182.4 182.4 19 13.4 13.4 79 55.9 55.9 139 98.3 98.3 199 140.7 140.7 259 183.1 183.1 20 21 14.1 14J 80 56.6 57.3 56.6 140 99.0 99.0 200 141.4 141.4 142.1 260 183.8 183.8 184.6 14.8 14.8 81 57.3 141 99.7 99.7 201 142.1 261 184.6 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 34 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 96 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. J 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 72.1 162 114.6 114.6 222 157.0 157.0 282 199.4 199.4 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 7.5.0 166 117.4 117.4 226 159.8 159.8 286 2U2.2 202.2 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 77.1 169 119.5 119.5 229 161.9 161.9 289 204.4 204.4 50 51 35.4 36.1 35.4 110 77.8 77.8 170 120.2 120.2 230 162.6 162.6 290 205.1 205.1 36.1 HI 78.5 78.5 171 120.9 120.9 231 163.3 163.3 291 205.8 205.8 52 36.8 36.8 112 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 79.9 173 122.3 122.3 233 164.8 164.8 293 207.2 207.2 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 82.0 176 124.5 124.5 236 166.9 1H6.9 296 209.3 209.3 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 41.0 118 83.4 83.4 178 125.9 125.1> 238 168.3 168.3 298 210.7 210.7 59 41.7 41.^ 119 84.1 84.1 179 126.6 126.6 239 169.0 169.0 299 211.4 211.4 60 Dist 42.4 Dep. 42.4 120 84.9 84.9 Lat. 180 Dist 127.3 127.3 240 169.7 169.7 300 21'>..1 212.1 Lat. Dist. Dep. Dep. Lat. Dist. Dep. Lat. Dist Dep. Lat For 45 Deg:i-ees, 3^ Om. | 62 TABLE III. MERIDIONAL PARTS. M. 03 1° 2o 3^ 40 50 6° 70 go 90 10° no 12° 13° M. 60 120 180 240 300 361 421 482 542 603 664 725 787 1 1 61 121 181 241 301 362 422 483 543 604 665 726 788 1 2 2 62 122 182 242 302 363 423 484 544 605 666 727 789 2 3 3 63 123 183 243 303 364 424 485 545 606 667 728 790 3 4 4 64 124 184 244 304 365 425 486 546 607 668 729 791 4 5 5 65 125 185 245 305 366 426 487 547 608 669 730 792 5 6 6 66 126 186 246 306 367 427 488 548 609 670 731 793 6 7 7 67 127 187 247 307 368 428 489 549 610 671 732 794 7 8 8 68 128 188 248 308 369 429 490 550 611 672 734 795 8 9 9 69 129 189 249 309 370 430 491 551 612 673 735 796 9 10 10 70 130 190 250 310 371 431 492 552 613 674 736 797 10 11 11 71 131 191 251 311 372 432 493 553 614 675 737 798 11 12 12 72 132 192 252 312 373 433 494 554 615 676 738 799 12 13 13 73 133 193 253 313 374 434 495 555 616 677 739 800 13 14 14 74 134 194 254 314 375 435 496 556 617 678 740 801 14 15 15 75 135 195 255 315 376 436 497 557 618 679 ^741 802 15 16 16 76 136 196 256 316 377 437 498 558 619 680 742 803 16 17 17 77 137 197 257 317 378 438 499 559 620 681 743 804 17 18 18 78 138 198 258 318 379 439 500 560 621 682 744 805 18 19 19 79 139 199 259 319 380 440 501 561 622 683 745 806 19 20 20 80 140 200 260 320 381 441 502 562 623 684 746 807 20 . 21 21 81 141 201 261 321 382 442 503 564 624 685 747 808 21 22 22 82 142 202 262 322 383 443 504 565 625 687 748 809 22 23 23 83 143 203 263 323 384 444 505 566 626 688 749 810 23 24 24 84 144 204 264 324 385 445 506 567 627 689 750 811 24 25 25 85 145 205 265 325 386 446 507 568 628 690 751 812 25 26 26 86 146 206 266 326 387 447 508 569 629 691 752 813 26 27 27 87 147 207 267 327 388 448 509 570 631 692 753 815 27 28 28 88 148 208 268 328 389 449 510 571 632 693 754 816 28 29 29 89 149 209 269 330 390 450 511 572 633 694 755 817 29 30 30 90 150 210 270 331 391 451 512 573 634 695 756 818 30 31 31 91 151 211 271 332 392 452 513 574 635 696 7.57 819 31 32 32 92 152 212 272 333 393 453 514 575 636 697 758 820 32 33 33 93 153 213 273 334 394 454 515 576 637 698 759 821 33 34 34 94 154 214 274 335 395 455 516 577 638 699 760 822 34 35 35 95 155 215 275 336 396 456 517 578 639 700 761 823 35 36 36 96 156 216 276 337 397 457 51« 579 640 701 762 824 36 37 37 97 157 217 277 338 398 458 519 580 641 702 763 825 37 38 38 98 1.58 218 278 339 399 459 520 581 642 703 764 826 38 39 39 99 159 219 279 340 400 460 521 582 643 704 765 827 39 40 40 100 160 220 280 341 401 461 522 583 644 705 766 828 40 41 41 101 161 221 281 342 402 462 523 584 645 706 767 829 41 42 42 102 162 222 282 343 403 463 524 585 646 707 768 830 42 43 43 103 163 223 283 344 404 464 525 586 647 708 769 831 43 44 44 104 164 224 284 345 405 465 526 587 648 709 770 832 44 45 45 105 165 225 285 346 406 466 527 588 649 710 771 833 45 46 46 106 166 226 286 347 407 467 528 589 650 711 772 834 46 47 47 107 167 227 287 348 408 468 529 590 651 712 773 835 47 48 48 108 168 228 288 349 409 469 530 591 652 713 774 836 48 49 49 109 169 229 289 350 410 470 531 592 653 714 775 837 49 50 50 110 170 230 290 351 411 471 532 593 654 715 777 838 50 51 51 111 171 231 291 352 412 472 533 594 655 710 778 839 51 52 52 112 172 232 292 353 413 473 534 595 656 717 779 840 52 53 53 113 173 233 293 354 414 1 474 535 596 657 718 780 841 53 54 54 114 174 234 294 355 415 1 476 536 597 658 719 781 842 54 55 55 115 175 235 295 356 416:477 537 598 659 720 782 843 55 56 56 116 176 236 296 357 417 478 538 599 660 721 783 844 56 57 57 117 177 237 297 358 418 479 539 '600 661 722 784 845 57 58 58 lis 178 238 298 359 419 480 540 601 662 723 785 846 58 59 59 119 179 239 299 360 420 481 541 602 663 724 786 847 59 M. 0° 1° 2° 3° 40 50 60 70 8° 90 10° 11° 12° 130 M. TABLE III. MERIDIONAL PARTS. .. 1 M. 140 150 16° 17° 18° 190 20° 21° 22° 230 24° 250 26° 27° M. 1 2 3 4 848 850 851 852 853 910 911 913 914 915 973 974 975 976 977 1035 1036 1037 1038 1039 109!s 1099 1100 1101 1102 1161 1163 1164 1165 1166 1225 1226 1227 1228 1229 1289 1290 1291 1292 1293 1354 1355 1356 1357 1358 1419 1420 1421 1422 1423 1484 1485 1486 1487 1488 1550 1551 1552 1553 1554 1(516 1618 1()19 1620 1621 1684 1685 168() 1687 1688 1 2 3 4 5 6 7 8 9 854 855 856 857 858 916 917 918 919 920 978 979 980 981 982 1041 1042 1043 1044 1045 1103 1105 1106 1107 llOts 1167 116^^ 1169 1170 1171 1230 1232 1233 1234 1235 1295 1296 12*97 1298 1299 1359 1360 1361 1362 1363 1424 1425 1426 1427 1428 1490 1491 1492 1493 1494 1556 1557 1558 1559 1560 1622 1623 1624 1625 1626 1689 1690 1691 1693 1694 5 6 7 8 9 10 11 12 13 14 859 860 861 862 8H3 921 922 923 924 925 983 984 985 996 987 1046 1047 1048 1049 1050 1109 1110 1111 1112 1113 1172 1173 1174 1175 1176 1236 1237 1238 1239 1240 1300 1301 1302 1303 1304 1364 1366 1367 1368 1369 1430 1431 1432 1433 1434 1495 1496 1497 1498 1499 1561 1562 1563 1564 1565 1628 1629 1630 1631 1632 1695 1696 1697 1698 1699 10 11 12 13 14 15 16 17 18 19 864 865 866 867 868 926 927 928 929 930 988 989 990 991 993 1051 1052 1053 1054 1055 1114 1115 1116 1117 1118 1177 1178 1179 1181 1182 1241 1242 1243 1244 1245 1305 1306 1307 1308 1310 1370 1371 1372 1373 1374 1435 1436 1437 1438 1439 1500 1502 1503 1504 1505 1567 1568 1569 1570 1571 1633 1634 1635 1637 1638 1700 1701 1703 1704 1705 15 16 17 18 19 20 21 22 23 24 869 870 871 872 873 931 932 933 934 935 994 995 996 997 99y 1056 1057 1058 1059 1060 1119 1120 1121 1122 1123 1183 1184 1185 1186 1187 1246 1248 1249 1250 1251 1311 1312 1313 1314 1315 1375 1376 1377 1379 1380 1440 1441 1443 1444 1445 1506 1507 1508 1509 1510 1572 1573 1574 1575 1577 1639 1640 1641 1642 1643 1706 1707 1708 1709 1711 20 21 22 23 24 25 26 27 28 29 874 875 876 877 878 93t) 9D7 938 939 941 999 1000 1001 1002 1003 1061 1063 1064 1065 1066 1125 1126 1127 1128 1129 1188 1189 1190 1191 1192 1252 1253 1254 1255 1256 1316 1317 1318 1319 1320 1381 1382 1383 1384 1385 1446 1447 1448 1449 1450 1511 1513 1514 1515 1516 1578 1579 1580 1581 1582 1644 1645 1647 1648 1649 1712 1713 1714 1715 1716 25 26 27 28 29 30 31 32 33 34 879 880 882 883 884 942 943 944 945 946 1004 1005 1006 1007 1008 1067 1068 1069 1070 1071 1130 1131 U3-2 1133 1134 1193 1194 1195 1196 1198 1257 1258 1259 1260 1261 1321 1322 1324 1325 1326 1386 1387 1388 1389 1390 1451 1452 1453 1455 1456 1517 1518 1519 1520 1521 1583 1584 1585 1586 1588 1650 1651 1652 1653 1654 1717 1718 1720 1721 1722 30 31 32 33 34 35 36 37 38 39 885 886 887 888 889 947 948 949 950 951 1009 1010 1011 1012 1013 1072 1073 1074 1075 1076 1135 1136 1137 1138 1139 1199 1200 1201 1202 1203 1262 1264 1265 1266 1267 1327 1328 1329 1330 1331 1392 1393 1394 1395 1396 1457 1458 1459 1460 1461 1522 1524 1525 1526 1527 1589 1590 1591 1592 1593 1656 1657 1658 1659 1660 1723 1724 1725 1726 1727 35 36 37 38 39 40 41 42 43 44 890 891 892 893 894 952 953 954 955 956 1014 1015 1016 J018 1019 1077 1078 1079 1080 1081 1140 1141 1142 1144 1145 1204 1205 1206 1207 1208 1268 1269 1270 1271 1272 1332 1333 1334 1335 1336 1397 1398 1399 1400 1401 1462 1463 1464 1465 1467 1528 1529 1530 1531 1532 1594 1595 1596 1598 1599 1661 1662 1663 1664 1666 1729 1730 1731 1732 1733 40 41 42 43 44 45 46 47 48 49 895 896 897 898 899 957 958 959 960 '.♦61 1020 1021 1022 1023 1024 1082 1084 1085 1086 1087 1146 1147 1148 1148 1150 1209 1210 1211 1212 1213 1273 1274 1275 1276 1277 1338 1339 1340 1341 1342 1402 1403 1405 1406 1407 1468 1469 1470 1471 1472 1533 1535 1536 1537 1538 1600 1601 1602 1603 1604 1667 1668 1669 1670 1671 1734 1735 1736 1738 1739 45 46 47 48 49 50 51 52 53 54 900 901 902 903 904 962 963 964 965 966 1025 1026 1027 1028 1(^29 1088 1089 1090 1091 1092 1151 1152 1153 1154 1155 1215 1216 1217 1218 1219 1278 1280 1281 1282 1283 1343 1344 1345 1346 1347 1408 1409 1410 1411 1412 1473 1474 1475 1476 1477 1539 1540 1541 1542 1543 1605 1606 160s 1609 1610 1672 1673 1675 1676 1677 1740 1741 1742 1743 1744 50 51 52 53 54 55 56 57 58 59 905 906 907 908 909 968 969 970 971 972 1030 1031 1032 1033 1034 1093 1094 1095 1096 1097 1156 1157 1158 115!) 1160 1220 1221 1222 1223 1224 1284 1285 1286 1287 1288 1348 1349 1350 1352 1353 1413 1414 1415 1416 1418 1479 1480 1481 1482 1483 1544 1546 1547 1548 1549 1611 1612 1613 1614 1615 1678 1679 1680 1681 1682 1746 1747 1748 1749 1750 55 56 57 58 59 M. 14° 150 16° 170 18° 190 203 21° 22=' 230 24° 25° 26° 27° M. 64 TABLE III. MERIDIONAL PARTS. M. 28^ 29^ 30° 31° 32° 33° 34° 35° 36° 37° 38° 39° 40° 41° M. 1 2 3 4 1751 1752 1753 1755 1756 1819 1821 1822 1823 1824 1888 1890 1891 1892 1893 1958 1959 1960 1962 1963 2028 2030 2031 2032 2033 2100 2101 2102 2103 2104 2171 2173 2174 2175 2176 2244 2246 2247 2248 2249 2318 2319 2320 2322 2323 2393 2394 2395 2396 2398 2468 2470 2471 2472 2473 2545 2546 2548 2549 2550 2623 2624 2625 2627 2628 2702 2703 2704 2706 2707 1 2 3 4 5 6 7 8 9 1757 1758 1759 1760 1761 1825 1826 1827 1829 1830 1894 1895 1896 1898 1899 1964 1965 1966 1967 1969 2034 2035 2037 2038 2039 2105 2107 2108 2109 2110 2178 2179 2180 2181 2182 2250 2252 2253 2254 2255 2324 2325 2327 2328 2329 2399 2400 2401 2403 2404 2475 2476 2477 2478 2480 25512629 25532631 25542632 25552633 2557 2634 2708 2710 2711 2712 2714 5 6 7 8 9 10 11 12 13 14 1762 1764 1765 1766 1767 1831 1832 1833 1834 1835 1900 1901 1902 1903 1905 1970 1971 1972 1973 1974 2040 2041 2043 2044 2045 2111 2113 2114 2115 2116 2184 2185 2186 2187 2188 2257 2258 2259 2260 2261 2330 2332 2333 2334 2335 2405 2406 2408 2409 2410 2481 2482 2484 2485 2486 2558 2559 2560 2562 2563 2636 26:!7 2638 2640 2641 2715 2716 2718 2719 2720 10 11 - 12 13 14 15 16 17 18 19 1768 1769 1770 1772 1773 1837 1838 1839 1840 1841 1906 1907 1908 1909 1910 1976 1977 1978 1979 1980 2046 2047 2048 2050 2051 2117 2119 2120 2121 2122 2190 2191 2192 2193 2194 2263 2264 2265 2266 2268 2337 2338 2339 2340 2342 2411 2413 2414 2415 2416 2487 2489 2490 2491 2492 2564 2566 2567 2568 2569 2642 2644 2645 2646 2648 2722 2723 2724 2726 2727 15 16 17 18 19 20 21 22 23 24 1774 1775 1776 1777 1778 1842 1843 1845 1846 1847 1912 1913 1914 1915 1916 1981 1983 1984 1985 1986 2052 2053 2054 2056 2057 2123 2125 2126 2127 2128 2196 2197 2198 2199 2200 2269 2270 2271 2272 2274 2343 2344 2345 2346 2348 2418 2419 2420 2422 2423 2494 2495 2496 2498 2499 2571 2572 2573 2575 2576 2649 2650 2651 2653 2654 2728 2729 2731 2732 2733 20 21 22 23 24 : 25 26 27 28 29 1780 1781 1782 1783 1784 1848 1849 1850 1852 1853 1917 1918 19-^0 1921 1922 1987 1988 1990 1991 1992 2058 2059 2060 2061 2063 2129 2131 2132 2133 2134 2202 2203 2204 2205 2207 2275 2276 2277 2279 2280 2349 2350 2351 2353 2354 2424 2425 2427 2428 2429 2500 2501 250:; 2504 2505 2577 2578 2580 2581 2582 2655 2657 2658 2659 2661 2735 2736 2737 2739 2740 25 26 27 28 29 30 31 32 33 34 1785 1786 1787 1789 1790 1854 1855 1856 1857 1858 1923 1924 1925 1927 192« 1993 1994 1995 1997 1998 2064 2065 2066 2067 2069 2135 2137 2138 2139 2140 2208 2209 2210 2211 2213 2281 2282 2283 2285 2286 2355 2356 2358 2359 2360 2430 2432 2433 2334 2335 2506 2508 2509 2510 2512 2584 2585 2586 2588 2589 2662 2663 2665 2666 2667 2742 2743 2744 2746 2747 30 31 32 33 34 i 35 36 37 38 39 1791 1792 1793 1794 1795 1860 1861 1862 1863 1864 1929 1930 1931 1932 1934 1999 2000 2001 2002 2004 2070 2071 2072 2073 2075 2141 2143 2144 2145 2146 2214 2215 2216 2217 2219 2287 2288 2290 2291 2292 2361 2363 2364 2365 2366 2437 2438 2439 2440 2442 2513 2514 2515 2517 2518 2590 2591 2593 2594 2595 2669 2670 2671 2673 2674 2748 2750 2751 2752 2754 35 36 37 38 39 40 41 42 43 44 1797 1798 1799 1800 1801 1865 1866 1868 1869 1870 1935 1936 1937 1938 1939 2005 2006 2007 2008 2010 2076 2077 2078 2079 2080 2147 2149 2150 2151 2152 2220 2221 2222 2224 2225 2293 2295 2296 2297 2298 2368 2369 2370 2371 2373 2443 2444 2445 2447 2448 2519 2521 2522 2523 2524 2597 2598 2599 2601 2602 2675 2676 2678 2679 2680 2755 2756 2758 2759 2760 40 41 42 43 44 45 46 47 48 49 1802 1803 1805 1806 1807 1871 1872 1873 1875 1876 1941 1942 1943 1944 1945 2011 2012 2013 2014 2015 2082 2083 2084 2085 2086 2153 2155 2156 2157 2158 2226 2227 2228 2230 2231 2299 2301 2302 2303 2304 2374 2375 2376 2378 2379 2449 2451 2452 2453 2454 2526 2527 2528 2530 2531 2603 2604 2606 2607 2608 2682 2683 2684 2686 2687 2762 2763 2764 2766 2767 45 46 47 48 49 1 50 51 52 53 54 180S 1809 1810 1811 1813 1«77 1878 1879 1880 1881 1946 1948 1949 1950 1951 2017 2018 2019 2020 2021 2088 2089 2090 2091 2092 2159 2161 2162 2163 2164 2232 2233 2235 2236 2237 230() 2307 2308 2309 2311 2380 2381 2383 2384 3385 2456 2457 2458 2459 2461 2532 2533 2535 2536 2537 2610 2611 2612 2614 2615 2688 2690 2691 2692 2694 2768 2770 2771 2772 2774 50 51 52 53 54 55 56 57 58 59 1814 1815 1816 1817 1818 1883 1884 1885 1886 1887 1952 1953 1955 1956 1957 2022 2024 2025 2026 2027 2094 2095 2096 2097 2098 2165 2167 2168 2169 2170 2238 2239 2241 2242 2243 2312 2313 3314 1316 2317 2386 2388 2389 2390 2391 2462 2463 2464 2466 2467 2538 2540 2541 2542 2544 2616 2617 2619 2620 2621 2695 2696 2698 2699 2700 2775 2776 2778 2779 2780 55 56 57 58 59 M. 28° 29° 30° 31° 32° 33° 34° 35° 36° 37° 38° 39° 40O 410 M. TABLE 111. Gti MERIDIONAL PARTS. M. 42° 43^ 440 45" 46" 470 48" 49" 50" 51" 52" 53" 54" 55" i M. 2782 2863 ,!946 3030 3116 3203 3292 3382 3474 3569 3665 3764 3865 3968 1 783 804 947 031 117 204 293 384 476 570 667 765 866 970 1 2 784 866 949 033 118 206 295 385 478 572 668 767 868 971 2 3 786 867 950 034 120 207 296 387 479 574 670 769 870 973 3 4 787 869 951 036 121 209 298 388 481 575 672 770 871 975 4 5 2788 2870 2953 3037 3123 3210 3299 3390 3482 3577 3673 3772 3873 3977 5 6 790 871 954 038 124 212 301 391 484 578 675 774 875 978 6 7 791 873 956 040 126 213 302 393 485 580 677 775 877 980 7 8 792 874 957 041 127 214 303 394 487 582 678 777 878 982 8 9 794 875 958 043 129 216 305 396 488 583 680 779 880 984 9 10 2795 2877 2960 3044 3130 3217 3306 3397 3490 3585 3681 3780 3882 3985 10 11 797 878 961 046 131 219 308 399 492 586 683 782 883 987 11 12 . 798 880 963 047 133 220 309 400 493 588 685 784 885 989 12 13 799 881 964 048 134 222 311 402 495 590 686 785 887 991 13 14 801 882 965 050 136 223 312 403 496 591 688 787 889 992 14 15 2802 2884 2967 3051 3137 3225 3314 3405 3498 3593 3690 3789 3890 3994 15 16 803 885 968 053 139 226 316 407 499 594 691 790 892 996 16 17 805 886 970 054 140 228 317 408 501 596 693 792 894 998 17 18 806 888 971 055 142 229 319 410 503 598 695 794 895 999 18 19 807 889 972 057 143 231 320 411 504 599 696 795 897 4001 19 20 2809 2891 2974 3058 3144 3232 3322 3413 3506 3601 3698 3797 3899 4003 20 21 810 892 975 060 146 334 323 414 507 602 699 799 901 005 21 22 811 893 976 061 147 235 325 416 509 604 701 800 902 006 22 23 813 895 978 063 149 237 326 417 510 606 703 802 904 008 23 24 814 896 1*79 064 150 238 328 419 512 607 704 804 906 010 24 25 2815 2897 2981 3065 3152 3240 3329 3420 3514 3609 3706 3806 3907 4012 25 26 817 899 982 067 153 241 331 422 515 610 708 807 909 014 26 27 818 900 983 068 155 242 332 423 517 612 709 809 911 015 27 28 820 902 985 070 156 244 334 425 518 614 711 811 913 017 28 29 821 903 986 071 157 245 335 427 520 615 713 812 914 019 29 30 2822 2904 2988 3073 3159 3247 3337 3428 3521 3617 3714 3814 3916 4021 30 31 824 906 989 074 160 248 338 430 523 618 716 816 918 022 31 32 825 907 991 075 162 250 340 431 525 620 717 817 919 024 32 33 826 908 992 077 163 251 341 433 526 622 719 819 921 026 33 34 828 910 993 078 165 253 343 434 528 623 721 821 923 028 34 35 2829 2911 2995 3080 3166 3254 3344 3436 3529 3625 3722 3822 3925 4029 35 36 830 913 996 081 168 256 346 437 531 626 724 824 926 031 36 37 832 914 998 083 169 257 347 439 532 628 726 826 928 033 37 38 833 915 999 084 171 259 349 440 534 630 727 827 930 035 38 39 834 917 3000 085 172 260 350 442 536 631 729 829 932 037 39 40 2836 2918 3002 3087 3173 3262 3352 3443 3537 3633 3731 3831 3933 4038 40 41 837 919 003 088 175 263 353 445 539 634 732 832 935 040 41 42 839 921 005 090 176 265 355 447 540 636 734 834 937 042 42 43 840 922 006 091 178 266 356 448 542 638 736 836 938 044 43 44 841 924 007 093 179 268 358 450 543 639 737 838 940 045 44 45 2843 2925 3009 3094 3181 3269 3359 3451 3545 3641 3739 3839 3942 4047 45 46 844 926 010 095 182 271 361 453 547 643 741 841 944 049 46 47 845 928 012 097 184 272 362 454 548 644 742 843 945 051 47 48 847 929 013 098 185 274 364 456 550 646 744 844 947 052 48 49 848 931 014 100 187 275 365 457 551 647 746 846 949 054 49 50 2849 2932 3016 3101 3188 3277 3367 3459 3553 3649 3747 3848 3951 4056 50 51 851 933 017 103 190 278 368 460 555 651 749 849 952 058 51 52 832 935 019 104 191 280 370 462 556 652 750 851 954 060 52 53 854 936 020 105 192 281 371 464 558 654 752 853 956 061 53 54 855 937 021 107 194 283 373 465 559 655 754 854 958 063 54 55 2856 2939 3023 3108 31953284 3374 3467 3561 3657 3755 3856 3959 4065 55 56 858 940 024 110 197 286 376 468 562 659 757 858 961 067 56 57 859 942 026 111 198 287 378 470 564 660 759 860 963 069 57 58 860 943 027 113 200; 289 379 471 566 662 760 861 964 070 58 59 862 944 029 114 201 290 381 473 567 664 762 863 966 072 59 M. 42° 430 440 450 46° 470 48" 49" 50" 51" 52" 53" 54" 55" M. 66 TABLE III. . MERIDIONAL PARTS. M. 56° 157° 58° 1 590 60° i 61° 62°|63° 64° 65° 66° 67° 68° 69° M. '- 4074 4183 429444091 4527 4649 4775'|4905 5039 5179 5324 54745631 5795 1 076 184 296 411 529 651 777 907 042 181 326 477 633 797 1 2 077 186 298 413 531 653 779 909 044 184 328 479 636 800 2 3 079 188 300 415 533 655 781 912 046 186 331 482 639 803 3 4 081 190 302 417 535 657 784 914 049 188 333 484 742 806 4 5 4083 4192 4304 4419 4537 4660 4786 4916 5051 5191 5336 5487 5644 5809 5 6 085 194 306 421 539 662 788 918 053 193 338 489 647 811 6 7 086 195 308 423 541 664 790 920 055 195 341 492 650 814 7 8 088 197 309 425 543 666 792 923 058 198 343 495 652 817 8 9 090 199 311 427 545 668 794 925 060 200 346 497 655 820 9 10 4092 4201 4313 4429 4547 4670 4796 4927 5062 5203 5348 5500 5658 5823 10 11 094 203 315 431 549 672 798 929 065 205 351 502 660 825 11 12 095 205 317 433 551 674 801 931 067 207 353 505 663 828 12 13 097 207 319 434 553 676 803 934 069 210 356 507 666 831 13 14 099 208 321 436 555 678 805 936 071 212 358 510 668 834 14 15 4101 4210 4323 4438 4557 4680 4807 4938 5074 5214 5361 5513 5671 5837 15 16 103 212 325 440 559 682 809 940 076 217 363 515 674 839 16 17 104 214 327 442 562 684 811 943 078 219 366 518 676 842 17 18 106 216 328 444 564 687 814 945 081 222 368 520 679 845 18 19 108 218 331) 446 566 689 816 947 08S 224 371 523 682 848 19 20 4110 4220 4332 4448 4568 4691 4818 4949 5085 5226 5373 5526 5685 5851 20 21 112 221 334 450 570 693 820 951 088 229 376 528 687 854 21 22 113 223 336 452 572 695 822 954 090 231 378 531 690 856 22 23 115 225 338 454 574 697 824 956 092 234 380 533 693 859 23 24 117 227 340 456 576 699 826 958 095 236 383 536 695 862 24 25 kiio 4229 4342 4458 4578 4701 4829 4960 5097 5238 5385 5539 5698 5865 25 26 121 231 344 460 580 703 831 963 099 241 388 541 701 868 26 27 122 232 346 462 582 705 833 965 102 243 390 544 704 871 27 28 124 234 347 464 584 707 835 967 104 246 393 546 706 874 28 29 126 236 349 466 586 710 837 969 106 248 395 549 709 876 29 30 4128 4238 4351 4468 4588 4712 4839 4972 5108 5250 5398 5552 5712 5879 30 31 130 240 353 470 590 714 842 974 111 253 401 554 715 882 31 32 132 242 355 472 592 716 844 976 113 255 403 557 717 885 32 33 133 244 357 474 594 718 846 978 115 258 406 559 720 888 33 34 135 246 359 476 596 720 848 981 118 260 408 562 723 891 34 35 4137 4247 4361 4478 4598 4722 4850 4983 5120 5263 5411 5565 5725 5894 35 36 139 249 363 480 600 724 852 985 122 265 413 567 728 896 36 37 141 251 365 482 602 726 855 987 125 267 416 570 731 899 37 38 142 253 367 484 604 728 857 990 127 270 418 573 734 902 38 39 144 255 369 486 606 731 859 992 129 272 421 575 736 905 39 40 4146 4257 4370 4488 4608 4733 4861 4994 5132 5275 5423 5578 5739 5908 40 41 148 259 372 490 610 735 863 996 134 277 426 580 742 911 41 42 150 260 374 492 612 737 865 999 136 280 428 5S3 745 914 42 43 152 262 376 494 614 739 868 5001 139 282 431 586 747 917 43 44 153 264 378 495 616 741 870 503 141 284 433 588 750 919 44 45 4155 4266 4380 4497 4618 4743 4872 5005 5143 5287 5436 5591 5753 5922 45 46 157 268 382 499 620 745 874 008 146 289 438 594 756 925 46 47 159 270 384 501 623 747 876 000 148 292 441 596 758 928 47 48 161 272 386 503 625 750 879 012 151 294 443 599 761 931 48 49 162 274 388 505 627 752 881 014 153 297 446 602 764 934 49 50 4164 4275 4390 4507 4629 4754 4883 5017 5155 5299 5448 5604 5767 5937 50 51 166 277 392 509 631 756 885 019 158 301 451 607 770 940 51 52 168 279 394 511 633 758 887 021 160 304 454 610 772 943 52 53 170 281 396 513 635 760 890 023 162 306 456 612 775 946 53 54 172 283 398 515 637 762 892 026 165 309 459 615 778 948 54 55 4173 4285 4399 4517 4639 4764 4894 5028 5167 5311 5461 5617 5781 5951 55 56 175 287 401 519 641 766 896 030 169 314 464 620 783 954 56 57 177 289 403 521 643 769 898 033 172 316 466 623 786 957 57 58 179 291 405 523 645 771 901 035 174 319 469 625 789 960 58 59 181 292 407 525 647 773 903 037 176 321 471 628 792 963 59 M. 5()0 570 58° 590 60° 61° 62° 63° 64° 65° 66° 67° 68° 69° M. TABLE 111. 67 MERIDIONAL PARTS. M. 70° 71° 72° 1 73° 740 750 76° 770 780 17.JO 80° 81° 82^ 830 M. 5966 6146 6335 6534 6746 6970 7210 7467 7745 8046 8375 8739 9145> 9606 1 969 149 338 538 749 974 214 472 749 051 381 745 153 614 1 2 972 152 341 541 753 978 218 476 754 056 387 752 160 622 2 3 975 155 345 545 757 982 222 481 759 061 393 758 167 631 3 4 978 158 348 548 760 986 227 485 764 067 398 765 174 639 4 5 o981 6161 6351 6552 6764 6990 7231 7490 7769 8072 8404 8771 9182 9647 5 6 984 164 354 555 768 994 235 494 774 077 410 788 189 655 6 7 986 167 358 558 771 997 239 498 778 083 416 784 196 664 7 8 989 170 361 562 775 7001 243 503 783 088 422 791 203 672 8 9 992 173 364 565 779 005 247 507 788 093 427 797 211 680 9 10 5995 6177 6367 6569 6782 7009 7252 7512 7793 8099 8433 8804 9218 9689 10 11 998 180 371 572 786 013 256 516 798 104 439 810 225 697 11 12 6001 183 374 576 790 017 260 521 803 109 445 817 233 706 12 13 004 186 377 579 793 021 264 525 808 115 451 823 240 714 13 14 007 189 380 583 797 025 268 530 813 120 457 830 248 723 14 15 6010 6192 (>384 6586 6801 7029 7273 7535 7817 8125 8463 8836 9255 9731 15 16 013 195 387 590 804 033 277 539 822 131 469 843 262 740 16 17 016 198 390 593 808 037 281 544 827 136 474 849 270 748 17 18 019 201 394 597 812 041 285 548 832 141 480 856 277 757 18 19 022 205 397 600 815 045 289 553 837 147 486 863 285 765 19 20 6025 6208 6400 6603 6819 7048 7294 7557 7842 8152 8492 8869 9292 9774 20 21 028 211 403 607 823 052 298 562 847 158 498 876 300 783 21 22 031 214 407 610 826 056 302 566 852 163 504 883 307 791 22 23 034 217 410 614 830 060 306 571 857 168 510 889 315 800 23 24 25 037 220 413 617 834 064 311 576 862 174 516 896 322 809 24 6040 6223 6417 6621 6838 7068 7315 7580 7867 8179 8522 8903 9330 9817 25 26 043 226 420 624 841 072 319 585 872 185 528 909 337 .826 26 27 046 230 423 628 845 076 323 589 877 190 534 916 345 835 27 28 049 233 427 631 849 080 328 594 882 196 540 923 353 844 28 29 052 236 430 635 853 084 832 599 887 201 546 930 360 852 29 30 6055 6239 6433 6639 6856 7088 7336 7603 7892 8207 8552 8936 9368 9861 30 . 31 058 242 437 642 860 092 341 608 897 212 558 943 376 870 31 32 061 245 440 646 864 096 345 612 902 218 565 950 383 879 32 33 064 249 443 649 868 100 349 617 907 223 571 957 391 888 33 34 067 252 447 653 671 104 353 622 912 229 577 963 399 897 34 35 6070 6255 6450 6656 6875 7108 7358 7626 7917 8234 8583 8970 9407 9906 35 36 073 258 453 660 879 112 362 631 922 240 589 977 414 915 36 37 076 ,261 457 663 883 116 366 636 927 245 595 984 432 924 37 38 079 264 460 667 886 120 371 640 932 251 601 991 430 933 38 39 082 268 463 670 890 124 375 645 937 256 607 998 438 942 39 40 6085 6271 6467 6674 6894 7128 7379 7650 7942 8262 8614 9005 9445 9951 40 41 088 274 470 677 898 132 384 654 948 267 620 012 453 960 41 42 091 277 473 681 901 136 388 659 953 273 626 018 461 969 42 43 094 280 477 685 905 140 392 664 958 279 632 025 469 978 43 44 097 283 480 (i88 909 145 397 668 963 284 638 032 477 987 44 45 6100 6287 6483 6692 6913 7149 7401 7673 79()8 8290 8644 9039 9485 9996 45 46 103 290 487 695 917 153 406 678 973 295 651 046 493 10005 46 47 106 293 490 69i» 920 157 410 683 978 301 657 053 501 015 47 48 101* 296 494 702 924 161 414 687 983 307 663 060 509 024 48 49 112 299 497 706 928 165 419 692 989 312 669 067 517 033 49 50 6115 6303 6500 6710 0932 7169 7423 7697 7994 8318 8676 9074 9525 10043 50 51 118 306 004 713 936 173 427 702 999 324 682 081 533 052 51 52 121 309 007 717 940 177 432 706 8004 329 688 08y 541 061 52 53 124 312 Oil 720 943 181 436 711 009 335 695 096 549 071 53 54 127 315 014 724 947 185 441 716 014 341 701 103 557 080 54 55 6130 6319 6517 6728 6951 7189 7445 7721 8020 8347 8707 9110 9565 10089 55 56 133 322 521 731 955 194 449 725 025 352 714 117 573 099 56 57 136 3-25 524 735 959 198 454 730 030 358 720 124 581 108 57 58 140 328 528 738 963 202 458 735 035 364 726 131 589 118 58 59 143 332 531 742 966 206 463 740 040 369 733 138 598 127 59 M. 70° 71° 72° 73° 740 750 76° 770 78° 790 80° 81° 82° 830 M. 68 TABLE IV. MEAN REFRACTION. App. Alt. Refrao. App. Alt Refrac. App. Alt Refrac. App. Alt Refraa App. Alt Refrac. o ' / // o ' / ti o ' t ti o ' / n o / / // 34 17 10 5 20 20 2 39 30 1 41 50 49 10 32 15 10 5 15 10 2 37 20 1 39 30 48 20 30 23 20 5 10 20 2 36 40 1 38 51 47 30 28 40 30' 5 6 30 2 35 ,31 1 37 30 46 40 27 27 40 5 1 40 2 33 20 1 35 52 45 50 25 41 50 4 56 50 2 32 40 1 34 30 44 1 24 22 11 4 52 21 2 31 32 1 33 53 44 10 23 9 10 4 48 10 2 29 20 1 32 30 43 20 22 2 20 4 44 20 2 28 40 1 31 54 42 30 21 30 4 40 30 2 27 33 1 30 30 41 40 20 2 40 4 36 40 2 26 20 1 28 55 40 50 19 9 50 4 82 50 2 25 40 1 27 30 40 2 18 20 12 4 28 22 2 24 34 1 26 56 39 10 17 34 10 4 25 10 2 22 20 1 25 30 39 20 16 51 20 4 21 20 2 21 40 1 24 57 38 30 16 11 30 * 4 18 30 2 20 35 1 23 30 38 40 15 34 40 4 14 40 2 19 20 1 22 58 37 50 14 59 50 4 11 50 2 18 40 1 21 30 36 3 14 26 13 4 8 23 2 17 36 1 20 59 35 10 13 55 10 4 5 10 2 15 20 1 19 30 34 20 13 27 20 4 2 20 2 14 40 1 18 60 33 30 13 30 3 59 30 2 13 37 1 17 30 33 40 12 34 42 3 56 40 2 12 20 1 16 61 32 50 12 10 50 3 53 50 2 11 40 1 15 30 32 4 11 47 14 3 50 24 2 10 38 1 14 62 31 10 11 26 10 3 47 10 2 9 20 1 14 30 31 20 11 5 20 3 45 20 2 8 40 1 13 63 30 30 10 46 30 3 42 30 2 7 39 1 12 30 29 40 10 28 40 3 40 40 2 6 20 1 11 64 28 50 10 10 50 3 37 50 2 5 40 1 10 30 28 5 9 54 15 3 35 25 2 5 40 1 9 65 27 10 9 38 10 3 32 10 2 4 20 1 9 30 27 20 9 23 20 3 30 20 2 3 40 1 8 66 26 30 9 9 30 3 28 30 2 2 41 1 T 30 25 40 8 55 40 3 25 40 2 1 20 1 7 67 24 50 8 42 50 3 23 50 2 40 1 6 30 24 6 8 30 16 3 21 26 1 59 42 1 5 68 23 10 8 18 10 3 19 10 1 58 20 1 4 30 22 20 8 6 20 3 17 20 1 57 40 1 3 69 21 30 7 56 30 3 15 30 1 56 43 1 2 70 20 40 7 45 40 3 13 40 1 56 20 1 2 71 19 50 7 35 50 3 11 50 I 55 40 1 1 72 18 7 7 25 17 3 9 27 1 54 44 1 73 17 10 7 16 10 3 7 10 1 53 20 1 74 16 20 7 7 20 3 5 20 1 52 40 59 75 15 30 6 59 30 3 3 30 1 51 45 58 76 14 40 6 50 40 3 1 40 1 51 20 58 77 13 50 6 42 50 2 59 50 1 50 40 57 78 12 8 6 35 18 2 58 28 1 49 46 56 79 11 10 6 27 10 2 56 10 1 49 20 56 80 10 20 6 20 20 2 54 20 1 48 40 55 81 9 30 6 13 30 2 53 30 1 47 47 54 82 8 40 6 6 40 2 51 40 1 47 20 54 83 7 50 6 50 2 50 50 1 46 40 53 84 6 9 5 54 19 2 48 29 1 45 48 52 85 5 10 5 48 10 2 47 10 1 45 20 52 86 4 20 5 42 20 2 45 20 1 44 40 51 87 3 30 5 36 30 2 44 30 1 43 49 50 88 2 40 5 31 40 2 42 40 1 43 20 50 89 1 50 5 25 50 2 40 50 1 42 40 49 90 ~ TABLES V, VI, Vll, Vlll. - 69 TABLE V. TABLE Vn. niP Off THK HORIZON. MOO.l'S AUGMENTATION. ])'8 ] )'8 Skmidiametkr by the Nautical Alk lANAC. Height Height Height App. "1 ' "1 ' "1 f It ' "1 ' "1 / II In Feet. Dip. in Feet. Dip. in Feet. Dip. Alt 14.40 15.0015.20 15.40 16.00 16.20 16.40 1 II 1 II 1 n o it II ti II II II It 1 0.58 28 5.10 125 10.56 ? 1 2 1.22 30 5.21 \m 11. 9 3 1 1 1 1 1 1 1 3 1.40 32 5.31 135 11.22 6 2 2 2 2 2 2 2 4 1.55 34 5.40 140 11.35 9 2 2 3 3 3 3 3 5 2. 9 36 5.50 145 11.47 1^ 3 3 3 3 4 4 4 6 2.22 38 6.00 150 11.59 15 4 4 4 4 4 5 5 7 2.33 40 6.10 155 12.11 18 4 5 5 5 5 5 6 8 2.44 42 6.19 160 12.23 21 5 5 6 6 6 6 7 9 2.54 44 6.28 165 12.34 24 6 6 6 7 7 7 7 10 3.03 46 6.37 170 12.45 27 6 7 7 7 8 8 8 11 14 15 16 17 18 19 20 3.12 3.21 3.29 3.37 3.45 3.53 4. 1 4. 8 4.15 4.22 48 50 55 60 65 70 75 80 85 90 6.45 6.53 7.11 7.29 7.47 8. 5 8.23 8.40 8.57 9.14 175 180 185 190 195 200 210 220 230 240 12.56 13. 7 13.18 13.29 13.40 13.50 14.10 14.30 14.50 15. 9 30 33 36 39 42 45 48 51 54 57 7 8 8 9 9 10 10 11 11 12 7 8 8 9 10 10 11 12 12 13 8 8 9 10 10 11 11 12 12 13 8 8 9 10 11 11 12 12 13 13 8 9 10 11 11 12 12 13 13 14 9 9 10 11 12 12 13 13 14 14 9 10 11 11 12 13 13 14 14 15 21 4.28 95 9.30 250 15.27 60 65 12 13 13 14 13 14 14 15 14 15 15 16 lb 16 22 4.34 100 9.46 260 15.44 70 13 14 14 15 16 16 17 23 4.40 105 10. 1 270 16. 75 14 14 15 15 16 16 17 24 4.46 110 10.16 280 16.16 80 14 14 15 16 16 17 18 25 26 4.52 4.58 115 120 10.30 10.43 290 300 16.31 16.46 90 14 15 15 16 17 17 18 ' 1 TABLE VIIL DIP OF THE HOai7C >N — AT DIFFEAENT DISTANOXS FROM THE \ \ OBSERVER. Dista of Lf in M nee HEIO HT or THE «YK IN FBET. 1 ind f. les. 5 10 15 20 25 3( ) 35 40 45 50 !80 M. 0.1 25 1 1 \ 56 84 112] 1 14016 1 1 9197 225 252 S TABLE VL 0.2 l'^ L 28 42 56 70 8 5 99 113 1261 40 0.3 i ) 19 28 37 as: 5 6 65 75 84 93 70 sun's FARAT.I.AX IH ALTTnTDK. 0.4 ' r 14 21 28 35 4 2 49 56 63 0.5 ( 0.6 i 0.7 ^ 0.8 ^ 0.9 ; 5 11 17 99, 28 3 4 39 45 50 56 Altitade. Parallax. ) 9 1 8 t 7 I (5 14 12 10 9 19 16 14 12 23 2 20 2 17 2 15 1 8 33 4 28 ,1 25 9 1-1 37 32 28 25 42 36 31 28 47 40 35 31 o 10 20 It 9 9 8 1.0 . 3 6 8 11 14 1 7 2C 23 25 27 1.2 , 3 5 7 . 9 12 1 4 K ^ 19 21 23 30 8 1.4 3 4 6 8 10 1 2 \A t 16 18 20 40 7 1.6 3 4 5 7 9 1 1 15 . 14 16 18 50 6 1.8 2 3 5 6 8 1 IS \ 13 14 16 60 5 2.0 2 3 5 6 7 9 11 12 13 15 70 4 2.2 2 3 5 6 7 8 K ) 11 12 14 80 2 2.4 2 3 5 6 7 8 £ ) 11 12 13 11 90 2.6 2.8 2 3 2 3 4 4 5 5 6 6 8 i 7 6 ) 10 \ .9 11 10 **■ "*" •. 3.0 2 3 4 5 6 7 J \ 8 9 10 3.5 2 3 4 5 6 6 '■ r 8 9 9 4.0 2 3 4 4 5 6 '■ r 7 8 8 4.5 2 3 4 4 5 5 ( J 6 7 8 5.0 2 3 4 4 5 5 ( 5 6 7 7 6.0 2 3 4 4 5 5 ( } 6 7 7 7.0 2 3 4 4 5 5 ( 5 6 7 71 70 TABLE IX. FOB CORRECTING THE OBSERVED ALTITUDE OF THI : SUN'S LOWER LIMB, WHEN 1 TAKEN BY A FORE OBSERVATION. Obs. Alt HEIGHT OF THE EYE ABOVE FHE SEA IN FEET. 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 o ' 5 3.8 1 3.5 3.1 2.8 2.5 2. 3 2.1 1 1.8 1.6 1.4 t 1.2 1 1.0 0.8 1 0.6 0.5 0.3 5 20 4.3 4.0 3.6 3.3 3.1 2. 8 2.6 2.3 2.1 1.9 1.7 1.5 1.3 1.1 1.0 0.8 5 40 4.8 4.5 4.1 3.8 3.5 3. 3 3.1 2.8 2.6 2.4 2.2 2.0 1.8 1.6 1.5 1.3 6 5.3 4.9 4.6 4.3 4.0 3. 7 3.5 3.3 3.0 2.8 2.6 2.4 2.2 2.1 1.9 1.7 6 20 5.7 5.4 5.0 4.7 4.4 4. 1 3.9 3.7 3.3 3.2 3.0 2.8 2.6 2.5 2.3 2.0 6 40 6.0 5.7 5.3 5.0 4.7 4. 5 4.3 4.0 3.8 3.6 3.4 3.2 3.0 2.8 2.7 2.3 7 6.4 6.0 5.7 5.4 5.1 4. 8 4.6 4.4 4.1 3.9 3.7 3.5 3.3 3.2 3.0 2.7 7 20 6.7 6.3 6.0 5.7 5.4 5. 1 4.9 4.7 4.4 4.2 4.0 3.8 3.6 3.5 3.3 3.1 7 40 6.9 6.6 6.2 5.9 5.7 5. 4 5.2 4.9 4.7 4.5 4.3 4.1 3.9 3.8 3.6 3.4 8 7.2 6.8 6.5 6.2 5.9 5. 7 5.4 5.3 5.0 4.8 4.6 4.4 4.2 4.0 3.9 3.7 8 20 7.5 7.1 6.7 6.5 6.2 5. 9 5.7 5.5 5.2 5.0 4.8 4.6 4.4 4.3 4.1 3.9 8 40 7.7 7.3 7.0 6.7 6.4 6. 1 5.9 5.7 5.5 5.2 5.0 4.8 4.7 4.5 4.3 4.1 9 7.9 7.5 7.2 6.9 6.6 6. 4 6.1 5.9 5.7 5.5 5.3 5.1 4.9 4.7 4.5 4.4 9 20 8.1 7.7 7.4 7.1 6.8 6. 6 6.3 6.1 5.9 5.7 5.5 5.3 5.1 4.9 4.7 4.6 9 40 8.3 7.9 7.6 7.3 7.0 6. 7 6.5 6.3 6.1 5.8 5.6 5.4 5.3 5.1 4.9 4.7 10 8.5 8.1 7.8 7.5 7.2 6. 9 6.7 6.5 6.2 6.0 5.8 5.6 5.4 5.3 5.1 4.9 10 30 8.7 8.3 8.0 7.7 7.4 7. 2 6.9 6.7 6.5 6.3 6.1 5.9 5.7 5.5 5.4 5.2 11 8.9 8.6 8.2 7.9 7.6 7. 4 7.2 6.9 6.7 6.5 6.3 6.1 5.9 5.7 5.6 5.4 11 30 9.1 8.8 8.4 8.1 7.8 7. 6 7.4 7.1 6.9 6.7 6.5 6.3 6.1 5.9 5.8 5.6 12 9.3 9.0 8.7 8.3 8.0 7. 8 7.6 7.3 7.1 6.9 6.7 6.5 6.3 6.2 6.0 5.8 13 9.6 9.3 9.0 8.7 8.4 8. 1 7.9 7.7 7.4 7.2 7.0 6.8 6.6 6.5 6.3 6.1 14 9.9 9.6 9.2 8.9 8.7 8. 4 8.2 7.9 7.7 7.5 7.3 7.1 6.9 6.8 6.6 6.4 15 10.2 9.8 9.5 9.2 8.9 8. 7 8.4 8.2 8.0 7.8 7.6 7.4 7.2 7.0 6.9 6.7 16 10.4 10.1 9.7 9.4 9.1 8. 9 8.7 8.4 8.2 8.0 7.8 7.6 7.4 7.2 7.1 6.9 17 10.6 10.3 9.9 9.6 9.3 9. 1 8.9 8.6 8.3 8.2 8.0 7.8 7.6 7.4 7.3 7.1 18 10.8 10.4 10.1 9.8 9.5 9. 3 9.0 8.8 8.6 8.4 8.2 8.0 7.8 7.6 7.5 7.3 19 11.0 10.6 10.3 10.0 9.7 9. 4 9.2 9.0 8.8 8.5 8.3 8.1 8.0 7.8 7.6 7.4 20 11.1 10.7 10.4 10.1 9.8 9. 6 9.3 9.1 8.9 8.7 8.5 8.2 8.1 7.9 7.7 7.6 21 11.2 10.9 10.5 10.2 10.0 9. 7 9.5 9.2 9.0 8.8 8.6 8.4 8.2 8.1 7.9 7.7 22 11.4 11.0 10.7 10.4 10.1 9. 8 9.6 9.4 9.1 8.9 8.7 8.5 8.3 8.2 8.0 7.8 23 11.5 11.1 10.8 10.5 10.2 9. 9 9.7 9.5 9.2 9.0 8.8 8.6 8.4 8.3 8.1 7.9 24 11.6 11.2 10.9 10.6 10.3 10. 9.8 9.6 9.3 9.1 8.9 8.7 8.5 8.4 8.2 8.0 25 11.7 11.3 11.0 10.7 10.4 10. 1 9.9 9.7 9.4 9.2 9.0 8.8 8.6 8.5 8.3 8.1 26 11.7 11.4 11.0 10.7 10.5 10. 2 10.0 9.7 9.5 9.3 9.1 8.9 8.7 8.6 8.4 8.2 27 11.8 11.5 11.1 10.8 10.5 10. 3 10.1 9.8 9.6 9.4 9.2 9.0 8.8 8.6 8.5 8.3 28 11.9 11.6 11.2 10.9 10.6 10. 4 10.2 9.9 9.7 9.5 9.3 9.1 8.9 8.7 8.5 8.4 30 12.0 11.7 11.3 11.0 10.8 10. 5 10.3 10.0 9.8 9.6 9.4 9.2 9.0 8.9 8.7 8.5 32 12.2 11.8 11.5 11.2 10.9 10. 6 10.4 10.2 9.9 9.7 9.5 9.3 9.1 9.0 8.8 8.6 34 12.3 11.9 11.6 11.3 11.0 10. 7 10.5 10.3 10.1 9.9 9.6 9.4 9.2 9.1 8.9 8.7 36 12.4 12.0 11.7 11.4 11.1 10. 8 10.6 10.4 10.2 9.9 9.7 9.5 9.3 9.2 9.0 8.8 38 12.5 12.1 11.8 11.5 11.2 10. 9 10.7 10.5 10.2 10.0 9.8 9.6 9.4 9.3 9.1 8.9 40 12.5 12.2 11.8 11.5 11.3 11. 10.8 10.5 10.3 10.1 9.9 9.7 9.5 9.4 9.2 9.0 42 12.6 12.2 11.9 11.6 11.3 11. 1 10.8 10.6 10.4 10.2 10.0 9.8 9.6 9.4 9.3 9.1 44 12.7 12.H 12.0 11.7 11.4 11. 1 10.9 10.7 10.5 10.2 10.1 9.8 9.7 9.5 9.3 9.1 46 12.7 12.4 12.0 11.7 11.5 11. 2 11.0 10.7 10.5 10.3 10.2 9.9 9.7 9.6 9.4 9.2 48 12.8 124 12.1 11.8 11.5 11. 3 11.0 10.8 10.6 10.4 10.2 10.0 9.8 9.6 9.5 9.3 50 12.8 12.5 12.2 11.9 11.6 11. 3 11.1 10.9 10.6 10.4 10.3 10.0 9.8 9.7 9.5 9.3 52 12.9 12.5 12.2 11.9 11.6 11. 4 11.1 10.9 10.7 10.5 10.3 10.1 9.9 9.7 9.6 9.4 54 13.0 12.6 12.3 12.0 11.7 11. 4 11.2 11.0 10.7 10.5 10.3 10.1 9.9 9.8 9.6 9.4 56 13.0 12.6 12.3 12.0 11.7 11. 5 11.2 ■11.0 10.8 10.6 10.4 10.2 10.0 9.8 9.7 9.5 58 13.0 12.7 12.3 12.0 11.7 TT 5 11.3 ll.O 10.8 10.6 10.4 10.2 10.0 '9.9 ' 9.7 9.5 60 13.1 12.7 12.4 12.1 11.8 11. 6 11.3 11.1 10.9 10.6 10.4 10.2 10.1 9.9 9.7 9.5 62 13.1 12.8 12.4 12.1 11.8 11. 6 11.4 11. J 10.9 10.7 10.5 10.3 10.1 9.9 9.8 9.6 64 13.2 12.8 12.5 12.2 11.9 11. 6 11.4 11.2 10.9 10.7 10.5 10.3 10.1 10.0 9.8 9.6 66 13.2 12.8 12.5 12.2 11.9 11. 7 11.4 11.2 11.0 10.8 10.6 10.4 10.2 10.0 9.8 9.7 70 13.3 12.9 12.0 12.3 12.0 11. 8 11.5 11.3 11.0 10.8 10.6 10.4 10.2 10.1 9.9 9.7 80 13.4 13.1 12.7 12.4 12.1 11. 9 11.7 11.4 11.2 11.0 10.8 10.6 10.4 10.2 10.1 9.9 90 13.6 13.2 12.9 12.6 12.3 12. 11.8 11.6 11.3 11.1 10.9 10.7 10.5 10.4 10.2 10.0 Month. Jan. Fkb. Mab. April, Mat, June, Jdlt, Auo. 1 Sept. Oct. Nov. Deo. Correction, -f0'.3 4-0'. 2 4-0 U jO — -0'.2 — 0'.2 — C !!£ — -0'.2 -0'.] [ +0'.l + 0'.2 - f0'.2 TABLE X. nl SUN'S DECLINATION FOR THE YEAR 1854 FOR APPARENT NOON AT GREENWICH. 1 DATS. JAN. PBB. MARCH. APRIL. MAY. JUNE. JULY. AUGUST. SEPT. OCT. 1 NOV. 1 DEC 1 o ' o ' O ' O ' O ' O ' O ' O / C ' O ■ O / O ; 1 23 IS 17 as 7 35S 4 32N 15 4N 22 3N 23 8N 18 4N 8 19N 3 lOS 14 26S 21 49S 2 22 56 16 49 7 12 4 55 15 22 22 11 23 4 17 48 7 57 3 33 14 45 21 58 3 22 50 16 31 6 49 5 18 15 40 22 19 22 59 17 33 7 35 3 56 15 4 22 7 4 22 44 16 13 6 26 5 41 15 57 22 26 22 54 17 17 7 13 4 20 15 23 22 15 5 22 38 15 55 6 3 6 4 16 14 22 33 22 49 17 1 6 51 4 43 15 41 22 23 6 22 30 15 37 5 40 6 26 16 31 22 40 22 43 16 45 6 29 5 6 15 59 22 31 7 22 23 15 18 5 17 6 49 16 48 22 46 22 37 16 28 6 6 5 29 16 17 22 38 8 22 15 14 59 4 53 7 11 17 5 22 51 22 30 16 11 5 44 5 52 16 35 22 44 9 22 7 14 40 4 30 7 34 17 21 22 56 22 24 15 54 5 21 6 15 16 52 22 50 10 21 58 14 21 4 7 7 56 17 37 23 1 22 16 15 37 4 59 6 38 17 9 22 56 11 21 49 14 1 3 43 8 18 17 52 23 6 22 8 15 19 4 36 7 17 26 23 1 12 21 39 13 41 3 19 8 40 18 7 23 10 22 15 1 4 13 7 23 17 42 23 6 13 21 29 13 21 2 56 9 2 18 22 23 13 21 52 14 43 3 50 7 45 17 58 23 10 14 21 19 13 1 2 32 9 24 18 37 23 17 21 43 14 25 3 27 8 8 18 14 23 14 15 21 8 12 41 2 9 9 45 18 51 23 19 21 34 14 6 3 4 8 30 18 30 23 17 16 20 57 12 20 1 45 10 6 19 5 23 22 21 24 13 47 2 41 8 52 18 45 23 20 17 20 45 11 59 1 21 10 28 19 19 23 24 21 14 13 28 2 17 8 14 19 23 23 18 20 33 11 38 57 10 49 19 33 23 25 21 4 13 9 1 54 8 36 19 14 23 24 19 20 20 11 17 34 11 9 19 46 23 26 20 53 12 49 1 31 9 58 19 28 23 26 20 20 8 10 55 lOS 11 30 19 58 23 27 20 42 12 30 1 8 10 20 19 42 23 27 21 19 54 10 34 14N 11 51 20 11 23 28 20 31 12 10 44 10 41 19 56 23 28 22 19 41 10 12 37 12 11 20 23 23 27 20 19 11 50 2lN 11 3 20 9 23 28 23 19 27 9 50 1 1 12 31 20 34 23 27 20 7 11 29 3S 11 24 21 22 23 27 24 19 13 9 28 1 25 12 51 20 46 23 26 19 55 11 9 26 11 45 20 34 23 26 25 18 58 9 5 1 48 13 11 20 57 23 25 19 42 10 48 49 12 6 20 46 23 25 26 18 43 8 43 2 12 13 30 21 7 23 23 19 29 10 27 1 13 12 26 20 57 23 23 27 18 28 8 21 2 35 13 49 21 18 23 21 19 15 10 6 1 36 12 47 21 9 29 21 28 18 12 7 58 2 59 14 8 21 28 23 18 19 2 9 45 2 13 7 21 19 23 18 29 17 56 3 22 14 27 21 37 23 15 18 48 9 24 2 23 13 27 21 30 23 15 30 17 40 3 45 14 46 21 46 23 12 18 33 9 3 2 46 13 47 21 40 23 11 31 17 23 4 9 21 55 18 19 8 41 14 6 23 7 SUN'S DECI .INATI ON FOR THE YI :ar 1855. DAYS. JAN. FEB. MARCH. APRIL. MAY. JUNE. JULY. AUG. SEPT. OCT. NOV. DEC. 1 O ' O ' O ' O ' O ' O ' O ' O / O ' O 1 o / O 1 1 23 28 17 US 7 41S 4 25N 14 59N 22 IN 23 9N 18 8N 8 25N 3 3S 14 21S 21 47S 2 22 57 16 53 7 19 4 49 15 17 22 9 23 5 17 53 8 3 3 27 14 40 21 56 3 22 52 16 36 6 56 5 12 15 35 22 17 22 1 17 37 7 42 3 50 14 59 22 5 4 22 46 16 18 6 33 5 35 15 52 22 24 22 56 17 21 7 19 4 13 15 17 22 13 5 22 39 16 6 10 5 57 16 10 22 31 22 50 17 5 6 57 4 36 15 36 22 21 6 22 32 15 42 5 46 6 20 16 27 22 38 22 45 16 49 6 35 4 59 15 54 22 29 7 22 25 15 23 5 23 6 43 16 44 22 44 22 39 16 33 6 13 5 23 16 12 22 36 8 22 17 15 5 5 7 5 17 22 50* 22 32 16 16 5 50 5 46 16 30 22 42 9 22 9 14 46 4 36 7 28 17 16 22 55 22 25 15 59 5 27 6 8 16 46 22 49 10 22 14 26 4 13 7 50 17 32 23 22 18 15 41 5 5 6 31 17 4 22 54 11 21 51 14 7 3 49 8 12 17 48 23 4 22 10 15 24 4 42 6 54 17 21 23 12 21 42 13 47 3 26 8 34 18 3 23 9 22 2 15 6 4 19 7 17 17 38 23 4 13 21 32 13 27 3 2 8 56 18 18 23 12 21 54 14 48 3 56 7 39 17 54 23 9 14 21 22 13 7 2 39 9 18 18 33 23 16 21 45 14 30 3 33 8 2 18 10 23 13 15 21 11 12 46 2 15 9 39 18 47 23 19 21 36 14 11 3 10 8 24 18 25 23 16 16 21 12 25 1 51 10 1 19 2 23 21 21 27 13 52 2 47 8 46 18 41 23 19 17 20 48 12 5 1 28 10 22 19 15 23 23 21 17 13 33 2 24 9 8 18 56 23 22 18 20 36 11 44 1 4 10 43 19 29 23 25 21 7 13 14 2 1 9 30 19 10 23 24 19 20 24 11 22 40 11 4 19 42 23 26 20 56 12 55 1 37 9 52 19 24 23 25 20 20 11 11 1 ITS >11 24 19 55 23 27 20 45 12 35 1 14 10 14 19 38 23 27 21 19 58 10 39 71N 11 45 20 7 23 27 20 34 12 15 51 10 35 19 52 23 28 22 19 44 10 18 31 12 5 20 19 23 27 20 22 11 55 27 11 57 20 5 23 27 23 19 31 9 56 54 12 25 20 31 23 27 20 10 11 35 4N 11 18 20 18 23 27 24 19 16 9 34 1 18 12 45 20 43 23 26 19 58 11 14 20S 11 39 20 30 23 26 25 19 2 9 12 1 42 13 5 20 54 23 25 19 45 10 54 43 12 20 42 23 25 26 18 47 8 49 2 5 13 25 21 4 23 23 19 32 10 33 1 6 12 21 20 54 23 23 27 18 32 8 27 2 29 13 44 21 15 23 21 19 19 10 12 1 30 12 41 21 5 23 21 28 18 16 8 4 2 52 14 3 21 25 23 19 19 5 9 51 1 53 13 1 21 16 23 19 29 18 3 16 14 22 21 34 23 16 18 51 9 30 2 17 13 22 21 27 23 16 30 17 44 3 39 14 40 21 44 23 13 18 37 9 9 2 40 13 41 21 37 2? 12 31 17 27 4 2, 21 52 18 23 8 47 14 1 23 8 ThiiTal >U will a iiwer rery nearly for erery f< )ni yea™ take iftarwards. but if g n from Table XII. reater ace uracy ii reqtii r«d, < b oor rectio a miut b« 1 72 TABLE X. "n SUN'S DECLINATION FOR THE YEAR 1856 FOR APPARENT NOON AT GREENWICH. 1 DAYS. JAN. FEB. MARCH. APRIL. MAY. JUNE. JULY. AUGUST. SEPT. OCT. NOV. DEC. 1 O ' O / O ' O ' O ' O ' O / O ' ' O / o 1 O / 1 23 3S 17 15S 7 25S 4 42N 15 12N 22 7N 23 6N 17 57N 8 9N 3 208 14 358 21 53S 2 22 59 16 58 7 2 5 5 15 30 22 15 23 2 17 41 7 47 3 44 14 54 22 2 3 22 53 16 41 6 39 5 28 15 48 22 22 «2 67 17 26 7 25 t 7 15 12 22 11 4 22 47 16 23 6 16 5 51 16 5 22 29 22 52 17 10 7 3 4 30 15 31 22 19 5 22 41 16 5 5 53 6 14 16 22 22 36 22 46 16 54 6 41 4 53 15 49 22 27 6 22 34 15 47 5 29 6 37 16 39 22 42 22 40 16 37 6 19 5 16 16 7 22 34 7 22 27 15 28 5 6 6 59 16 56 22 28 22 34 16 20 6 56 5 39 16 25 22 41 8 22 19 15 10 4 43 7 22 17 12 22 53 22 27 16 3 5 34 6 2 16 42 22 47 9 22 11 14 51 4 19 7 44 17 28 22 59 22 20 15 46 5 11 6 25 17 22 53 10 22 3 14 31 3 56 8 6 17 44 23 3 22 13 15 28 4 48 6 48 17 17 22 58 11 21 54 14 12 3 32 8 28 17 59 23 7 22 05 15 11 4 25 7 11 17 33 23 3 12 21 44 13 52 3 9 8 50 18 14 23 11 21 56 14 53 4 2 7 33 17 49 23 8 13 21 35 13 32 2 45 9 12 18 29 23 15 21 48 14 34 3 39 7 56 18 5 23 12 14 21 24 13 12 2 21 9 33 18 44 23 18 21 39 14 16 3 16 8 18 18 21 23 15 15 21 14 12 52 1 58 9 55 18 58 23 20 21 29 13 57 2 53 8 40 18 37 23 18 16 21 3 12 31 1 34 10 16 19 12 23 23 21 20 13 38 2 30 9 02 18 52 23 21 17 20 51 12 10 1 10 10 37 19 25 23 24 21 9 13 19 2 7 9 24 19 6 23 23 18 20 39 11 49 47 10 58 19 38 23 26 20 59 13 1 44 9 46 19 21 23 25 19 20 27 11 28 23S 11 19 19 51 23^27 20 48 12 40 1 20 10 08 19 35 23 26 20 20 14 11 7 IN 11 39 20 4 23 27 20 37 12 20 57 10 30 19 48 23 27 21 20 1 10 45 24 12 20 16 23 27 20 25 12 34 10 51 20 2 23 27 22 19 48 10 23 48 12 20 20 28 23 27 20 13 11 40 IOn 11 12 20 14 23 27 23 19 34 10 2 1 12 12 40 20 40 23 26 20 1 11 20 13S 11 33 20 27 23 27 24 19 20 9 40 1 35 13 20 51 23 25 19 49 10 59 37 11 54 20 39 23 25 25 19 6 9 17 1 59 13 19 21 1 23 24 19 36 10 39 1 12 15 20 51 23 24 26 18 51 8 55 2 22 13 39 21 12 23 22 19 23 10 18 1 23 12 36 21 2 23 22 27 18 36 8 33 2 46 13 58 21 22 23 20 19 9 9 57 1 47 12 56 21 13 29 19 28 18 20 8 10 3 9 14 17 21 32 27 17 18 55 9 36 2 10 13 16 21 24 23 16 29 18 5 7 48 3 33 14 35 21 41 23 14 18 41 9 14 2 34 13 36 21 34 23 13 30 17 48 3 56 14 54 21 50 23 10 18 27 8 53 2 57 13 56 21 44 23 9 31 17 32 4 19 21 59 18 12 8 31 14 15 23 5 SUN'S DECI .INATI ON FO] 9. 1 'HE YEAR 1857. DAYS. JAN. FEB. MARCH. APRIL. MAY. JUNE. JULY. AUG. SEPT. OCT. NOV. DEC. 1 O ' r O ' O ' O ' O ' / o / O ' o / o / O t 1 23 OS 17 2S 7 30S 4 37N 15 8N 22 5N 23 7N 18 ON 8 15N 3 158 14 308 21 51S 2 22 54 16 45 7 7 5 15 26 22 13 23 3 17 45 7 53 3 38 14 49 22 3 22 49 16 27 6 44 5 23 15 43 22 20 22 58 17 30 7 31 4 1 15 8 22 9 4 22 43 16 10 6 21 5 46 16 1 22 28 22 53 17 14 7 9 4 24 15 26 22 17 5 22 36 15 51 5 58 6 8 16 18 22 34 22 48 16 58 6 46 4 48 15 45 22 25 6 22 29 15 33 5 35 6 31 16 35 22 41 22 42 16 41 6 24 5 11 16 3 22 32 7 22 21 15 14 5 12 6 54 16 51 22 47 22 36 16 24 6 2 5 34 16 21 22 39 8 22 13 14 55 4 48 7 16 17 8 22 52 22 29 16 8 5 39 5 57 16 38 22 45 9 22 5 14 36 4 25 7 38 17 24 22 57 22 22 15 50 5 16 6 20 16 56 22 51 10 21 56 14 17 4 1 8 1 17 40 23 2 22 14 15 33 4 54 6 42 17 13 22 57 11 21 47 13 57 3 38 8 23 17 56 23 6 22 7 15 15 4 31 7 5 17 29 23 2 12 21 37 13 37 3 14 8 45 18 10 23 10 21 58 14 57 4 8 7 28 17 46 23 7 13 21 27 13 17 2 51 9 6 18 25 23 14 21 50 14 39 3 45 7 60 18 2 23 11 14 21 16 12 57 2 27 9 28 18 40 23 17 21 41 14 21 3 22 8 13 18 17 23 14 15 21 5 12 36 2 4 9 50 18 54 23 20 21 32 14 2 2 59 8 35 18 33 23 18 16 20 54 12 15 1 40 10 11 19 8 23 22 21 22 13 43 2 36 8 57 18 48 23 21 17 20 42 11 54 1 16 10 32 19 22 23 24 21 12 13 24 2 12 9 19 19 3 23 23 18 20 30 11 33 52 10 53 19 35 23 25 21 2 13 5 1 49 9 41 19 17 23 25 19 20 18 11 12 29 11 14 19 48 23 26 20 51 12 45 1 26 10 3 19 31 23 26 20 20 5 10 50 5S .11 34 20 1 23 27 20 40 12 23 1 3 10 24 19 45 23 27 21 19 51 10 29 19N 11 55 20 13 23 27 20 28 12 5 39 10 46 19 58 23 27 22 19 38 10 7 42 12 15 20 25 23 27 20 16 11 45 16N 11 7 20 11 23 27 23 19 24 9 45 1 6 12 35 20 37 23 27 20 4 11 25 088 11 28 20 24 23 27 24 19 9 9 23 1 30 12 55 20 48 23 26 19 52 11 4 31 11 49 20 36 23 26 25 18 55 9 1 1 53 13 15 20 59 26 24 19 39 10 44 54 12 10 20 48 23 24 26 18 40 8 38 2 17 13 34 21 9 23 22 19 26 10 23 1 18 12 31 21 23 22 27 18 24 8 16 2 40 13 53 21 20 23 20 19 12 10 2 1 41 12 51 21 11 23 20 28 18 8 7 £3 3 4 14 12 21 29 23 18 18 59 9 41 2 5 13 11 21 21 23 17 29 17 52 3 27 14 31 21 39 23 14 18 45 9 19 2 28 13 31 21 32 23 14 3U 17 36 1 3 50 14 49 21 48 23 11 18 30 8 58 2 51 13 51 21 42 23 10 31 17 19 ( 4 14 21 57 18 15 8 36 14 11 23 lUt b* TUiTal >1« will Al itrwn T«rj r nearly for vrarj fo nr years a ifterwardi , but if gi reatar aeo araoy ia raqnired, a o«n raotio ■ m ^^^ takei 1 from Ta ble Xll. ,^^^^ ^^ ^^ l,^.. n TABLE XI. CORRECTION OF THE SUN'S DECLINATION AT SEA FOR LONGITUDE AND FOR TIME. DECLINATION. O o 2 o 4 e 6 o 10 o 12 o 14 o 16 o 17 o 18 o 19 o 20 o 21 o 21i o 22 22i o 23 o 23i TIMS FROM NOON. 10 20 30 40 50 2-0 2-6 3-3 0' 0-6 1-2 1-8 2-5 3-1 0- 2 0- 3 4 5 6|0 M. 4C 20 40 20 60 70 80 90 100 3-9 4-6 5'2 5-9 6-5 3-9 4-6 5-2 5-9 6-5 40 20 40 20 40 20 _0 40 2) 10 120 130 140 150 7-2 7-8 8-5 9-1 9-8 7-2 7-8 8-5 9-1 9-8 160 170 180 10-5 10-4 10 11-1 11-1 11 11-8 11-7 11 10- 10' 11- 9' 10' 11' IN WEST LONOITUDB. When the Declina. is { Oe^'elTng.llibtract TIME BEFORE NOON. xm. ^^. T\ V • i Increasinff, Subtract When the Declina. is j decreasing, Add. IN EAST LONOITUDE ^Tn_ .iL T-» !• • < Increasing, Subtract. When the Declina. is j D^^easing, Add. TIME AFTERNOON. When the Declina. is \ o^J^elTn^g, Subtract. TABLE XIL CORRECTION OF THE SUN'S DECLINATION IN TABLE X., AFTER THE YEARS FOLLOWING 1854. 1855 1856, AND 1857. 1854 1858 1862 1866 1870 1874 1878 1855 1859 1863 1867 1871 1875 1879 1856 1860 1864 1868 1872 1876 1880 1857 1861 1865 1869 1873 1877 1881 SUB. SUB. SUB. SUB. SUB. SUB. 1 / 1 t / / January i 0.1 0-3 0-4 0-6 0-7 0-9 10 0.2 0.5 0-8 1-0 1-3 1-6 20 0.4 0-7 1-1 1-4 1-8 2-2 30 0.5 1-0 1-5 2-0 2-5 3-0 Feb'rt 10 0-6 1-1 1-6 2-2 2-8 3-4 20 0-6 1-2 1-9 2-5 3-1 3-7 28 0-7 1-3 2-0 2-6 3-3 4-0 March 10 0-7 1-4 2-1 2-8 3-5 4-2 20 0-7 1-4 2-1 2-8 3-6 4-3 ADD. ADD. ADD. ADD. ADD. ADD. 30 0-7 1-4 2-1 2-8 3-5 4-2 April 10 0-7 1-4 2-1 2-7 3-4 4-1 20 0-6 1-3 1-9 2-5 3-2 3-9 30 0-6 1-1 1-7 2-3 2-8 3-4 Mat 10 0-5 0-9 1-5 2-0 2-5 3-0 20 0-4 0-8 1-2 1-6 1-9 2-3 30 0-3 0-5 0-8 1-0 1-4 1-7 June: 10 0-2 0-3 0-4 0-5 0-7 0-9 20 0-0 0-0 0-1 0-1 0-1 0-1 SUB. SUB. SUB. SUB. SUB. SUB. 30 0-1 0-3 0-4 0-6 0-7 0-8 1854 1855 1856 1857 June July 30 10 20 30 August 10 20 30 Skpt. 10 20 30 Oct. 10 0-7 20 0-6 30 0-5 Nov. 10 0-5 20 0-4 30 0-2 1 Dec. 10 20 30 1858 1859 1860 1861 SUB. 0-1 0-2 0-4 0-5 0-5 0-6 0-7 0-7 0-7 ADD. 0-7 0-2 0-0 SUb. 0-1 1862 1863 1864 1865 SUB. I 0-3 0-5 0-7 1-0 1-1 1-3 1-4 1-4 1-4 ADD. 1-4 1-4 1-3 1-1 1-0 0-8 0-5 0-3 0-0 SUB, 0-3 1866 1867 1868 1869 SUB. / 0-4 0-8 1-1 1-5 1870 1871 1872 1873 1-7 1-9 2-0 2-1 2-1 ADD. 2-1 2-0 1-9 1-6 1-4 1-2 0-7 0-4 0-1 SUB. 0-4 SUB. / 0-6 1-0 1-4 2-0 2-3 2-5 2-7 2-8 2-9 ADD. 2-8 2-7 2-5 2-2 1-9 1-5 I'C 0-6 0-1 SUB. 0-6 1874 1875 1876 1877 SUB. / 0-7 1-3 1-8 2-5 2-8 3-2 3-4 1878 1879 1880 1881 SUB. 0-8 1-6 2-2 3-0 3-4 3-9 4-1 3-5 4-2 3-6 4-3 ADD. > ADD. 3-5 I 4-2 3-4 3-2 2-8 4-1 3-9 3-4 2-4 2-0 1-3 2-8 2-5 1-6 7 2 SUB. 1 7 1 0-8 0-3 SUB. 0-9 To apply the Correction in Table XII Rednca the proposed year by Subtracting any number of Fouri until it corresponds to one of the years for -which the Beclination is given in Table X., and take out the Declination for that year against the day of the month, and take out the Correction from Table XII., found opposite the «ame day of the month, and under the pro poaed year, vrhich is expressed In minutes Hnd tenths ; if the tenths are more than 5 increase the minutes by 1, but if less, throw them away. This applied as directed in the above Table, (add or subtract) to or from the Declination taken from Table X., will give tne correct Decimation for the proposed year until the year ISfll. 74 TABLE XIII.— SUN'S RIGHT ASCENSION. | BAYS. JAN. FEB. MARCH. APRIL. MAY. JUNE. JULY. AUGUST. SEPT. OCT. NOV. DEC. H. M H. M. H. M. H. M. H. M. H. M. H. M. H. M. U. H. H. M H. M. B. M. 1 18.47 20.59 22.49 0.42 2.33 4.36 6.40 8.45 10.41 12. 2£ 1 14.25 16.29 2 18.52 21 3 22.52 0.46 2.37 4.40 6.44 8.49 10.45 12.33| 14.29 16.34 3 18.56 21. « 22.56 0.49 2.41 4.44 6.49 8.53 10.48 12.3^ 1 14.33 16.38 4 19. C 1 21.12 23. 0.53 2.45 4.48 6.53 8.57 10.52 12.40 14.37 16.42 5 19. £ 21.16 23. 3 0.57 2.49 4.52 6.57 9. 1 10.56 12.44 14.41 16.47 6 19. fl 21.20 23. 7 1. 2.53 4.57 7. 1 9. 4 10.59 12.47 14.45 16,51 7 19. la 21.24 23.11 1. 4 2.56 5. I 7. 5 9. 8 11. 3 12.5] 14.49 16.55 8 19.16 21.28 23.15 1. 8 3. 5. 5 7. 9 9.12 11. 7 12.55 14.53 17. 9 19.22 21.32 23.18 1.11 3. 4 5. 9 7.13 9.16 11.10 12.58 14.57 17. 4 10 19.27 21.36 23.22 1.15 3. 8 5.13 7.17 9.20 11.14 13. 2 15. 1 17. 9 11 19.3] 21.39 23.26 1.19 3.12 5.17 7.21 9.23 11.17 13. 6 15. 5 17.13 12 19.35 21.43 23.29 1.22 3.16 5.21 7.25 9.27 11.21 13. 9 15. 9 17.17 13 19.40 21.47 23.33 1.26 3.20 5.26 7.30 9.31 11.24 13.13 15.13 17.22 14 19.44 21.51 23.37 1.30 3.24 5.30 7.34 9.35 11.28 13.17 15.18 17.26 15 19.48 21.55 23.40 1.33 3.28 5.34 7.38 9.39 11.32 13.2] I 15.22 17.31 16 19.52 21.59 23.44 1.37 3.32 5.38 7.42 9.42 11.35 13.24 15.26 17.35 17 19.57 22. 3 23.48 1.41 3.36 5.42 7.46 9.46 11.39 13.28 15.30 17.39 18 20. 1 22. 7 23.51 1.44 3.40 5.46 7.50 9.50 11.42 13.32 15.34 17.44 19 20. 5 22.11 23.55 1.48 3.43 5.50 7.54 9.53 11.46 13.36 15.38 17.48 20 20.10 22.14 23.58 1.52 3.47 5.55 7.58 9.57 11.50 13.39 15.42 17.53 21 20.14 22.18 0. 2 1.56 8.51 5.59 8. 2 10. 1 11.53 13.43 15.47 17.57 22 20.18 22.22 0. 6 1.59 3.55 6. 3 8. 6 10. 5 11.57 13.47 15.51 18. 2 23 20.22 22.26 0. 9 2. 3 4. 6. 7 8.10 10. 8 12. 13.51 15.55 18. 6 24 20.26 22.30 0.13 2. 7 4. 4 6.11 8.14 10.12 12. 4 13.55 15.59 18.11 25 20.31 22.33 0.17 2.11 4. 8 6.15 8.18 10.16 12. 8 13.58 16. 4 18.15 26 20.35 22.37 0.20 2.14 4.12 6.20 8.22 10.19 12.11 14. 2 16. 8 18.19 27 20.39 22.41 0.24 2.18 4.16 6.24 8.26 10.23 12.15 14. ( 3 16.12 18.24 28 20.43 22.45 0.28 2.22 4.20 6.28 8.30 10.27 12.18 14.10 16.16 18.28 29 20.47 0.31 2.26 4.24 6.32 8.33 10.30 12.22 14.14 16.21 18.33 30 20.51 0.35 2.30 4.28 6.36 8.37 10.34 12.26 14.18 16.25 18.37 31 20. 5i 0.38 4.32 8.41 10.38 14.22 18.42 The Rigl It Ascension given in this Table Is for lere accuracy is rec he year 18.54, and will answer approximately for several years afterwards, but uired. it must be biken from the Nautical Almanac. , EaUATTC )N OF TIME FOI I APPARENT NC NEA TA >0N AT RLY FC BLE XIV. GREENWICH, FOR THE )R 1858, 1862, AND 1866. YEAR 1854, AND WILL ANSWER V DAYS. JAN. FEB. MAR. APRIL. MAY. JUNE. JULY. AUO. SEPT. OCT. NOV. DECEMBER. ADD ADD i ItD SUB. ADD ADD SUB. SUB. SUB. K S. I «. S. M. s. M. S. H. M. M. S. M. S. M. S M. S. M. S. 1 I. 3. H. 8. 1 3.51 13.55 12 .37 ADD. 4. 3. 1 SUB. 2.32 3.26 6. 3 0. 5 10.171 6.16 SUB. 10.47 2 4.20 14. 2 12 .25 3.42 3. 9 2.23 3.38 6. 0.24 10.361 6.18 10.25 ■ 3 4.48 14. 9 12 .12 3.24 3.16 2.13 3.49 5.55 0.43 10.541 6.18 10. 1 4 5.15 14.15 11 .59 3. 6 3.22 2. 4 4.00 5.50 1. 2 11.131 6.17 9.37 5 5.42 14.20 11 .46 2.48 3.28 1.53 4.11 5.45 1.22 11.31 1 6.16 9.12 6 6. 9 14.24 11 .32 2.31 3.33 1.43 4.21 5.38 1.42 11.491 6.14 8.47 7 6.35 14.27 11 .17 2.13 3.37 1.32 4.31 5.32 2. 2 12. 61 6.11 8.22 8 7. 1 14.30 11 . 2 1.56 3.42 ?.21 4.40 5.24 2.23 12.231 6. 7 7.55 9 7.26 14.31 IC .47 1.39 3.45 1.10 4.50 5.16 2.43 12.391 6. 2 7.29 10 7.50 14.32 IC ► .32 1.22 3.48 t> .o» 4.58 5. 8 3. 4 12.551 5.57 7. 2 11 8.14 14.33 IC (.16 1. 6 3.51 0.46 5. 7 4.59 3.25 13.11 1 5.50 6.34 12 8.38 14.32 c 1.59 0.50 3.52 0.34 5.14 4.49 3.45 13.261 5.43 6. 6 13 9. 14.31 c 1.43 0.34 3.54 0.22 5.22 4.39 4. 6 13.401 5.35 5.38 14 9.22 14.29 c (.26 0.18 3.54 0.10 5.29 4.28 4.27 13.541 5.25 5. 9 15 9.44 14.26 c >. 9 0. 3 3.54 ADD. 0. 3 5.35 4.17 4.50 14. 81 5.16 4.40 16 10. 5 14.22 i 5.51 SOB. 0.12 3.53 0.16 5.41 4. 5 5.10 14.211 5. 5 4.11 17 10.25 14.18 i 5.34 0.26 3.51 0.28 ».5.47 3.53 5.31 14.331 4.53 3.41 18 10.44 14.13 { }.16 0.40 3.49 0.41 5.52 3. 40 5.52 14.441 4.41 3.11 19 11. 2 14. 7 ^58 0.54 3.46 0.54 5.56 3.27 6.13 14.551 4.27 2.42 20 11.20 14. 1 ^4o 1. 7 3.43 1. 7 6. 3.13 6.34 15 61 4.13 2.12 21 11.38 13.54 r.22 1.20 3 39 1.20 6. 4 2.59 6.55 15.151 3.58 1.42 22 11.54 13.46 r. 4 1.32 3.34 1.34 6. 7 2.44 7.16 15.251 3.42 1.12 23 12.10 13.38 ( 5.45 1.44 3.29 1.47 6. 9 2.29 7 36 15.331 3.26 0.41 24 12.24 13.29 t ).27 1.56 3.24 2. 6.11 2.14 7 57 15.411 3. 9 0.11 25 12.39 13.20 ( 5. 8 2. 7 3.18 2.12 6.12 1.58 8.18 15.481 2.51 ADD. 0.19 26 12.52 13.10 ( I 5.50 2.17 3.11 2.25 6.12 1.41 8.38 15.541 2.32 0.49 27 13. 4 13. ; t. 5.32 2.27 3. 4 2.38 6.12 1.25 8.58 16. 01 2.12 1.18 28 13.16 12.49 ». 5.13 2.36 2.57 2.50 6.12 1. 8 9.18 16. 41 1.52 1.4S 29 13.27 / 1.55 2.45 2.49 3. 3 6.11 0.50 9.38 16. 91 1.31 2.17 30 13.37 ^ 1.36 2.54 2.41 3.15 6. 9 0.32 9.57 16.121 1.10 2.46 31 13.46 4.18 6. 6 0.14 16.15 3.15 r TABLE XIV. 78 • |k(1UATI0N of time for AlPARENT NOON A.T GREENWICH, FOR THE YEAR 1855, AND WILL ANSWER NEARLY FOR 1859, laGi, AND 1867. DATS. JAN. FEB. HAS. APRIL. 1 MAY. JUNK. JULY. AUO. SEPT. OCT. NOV. DECBMBRB. | ADD ADD ADD BUB. ADD ADD SUB. SUB. SUB. SI. 8. M. S. M. 8. M. 8. M. 8. H. 8. U. S. M. 8. M. 8. M. S. M. S. M. 8. 1 3.44 13.52 12.40 ADD. 4. 4 2.59 SUB. 2.34 3.23 6. 3 0. 10.12 16.15 SUB. 10.52 2 4.12 14. 12.28 3.46 3. 7 2.25 3.34 6. 0.19 10.31 16.17 10.30 3 4.40 14. 7 12.15 3.28 3.14 2.16 3.46 5.56 0.38 10.49 16.17 10. 6 4 5. 8 14.13 12. 2 3.11 3.20 2. 6 3.57 5.51 0.57 11. 8 16.17 9.42 5 5.35 14.18 11.49 2.53 3.26 1.56 4. 8 5.46 1.17 11.26 16.16 9.18 6 6. 2 14.23 11.35 2.35 3.31 1.46 4.18 5.40 1.37 11.44 16.14 8.53 7 6.28 14.26 11.21 2.18 3.36 1.3S 4.28 5.33 1.57 12. 1 16.11 8.27 8 6.54 14.29 11. 6 2. 1 3.40 1.24 4.38 5.26 2.17 12.18 16. 7 8. 1 9 7.20 14.31 10.51 1.44 3.44 1.13 4.47 5.18 2.38 12.35 16. 3 7.35 10 7.44 14.32 10.36 1.27 3.47 1. 1 4.56 5.10 2.58 12.51 15.57 7. 8 11 8. 8 14.33 10.20 1.10 3.49 0.49 5. 4 5. 1 3.19 13. 6 15.51 6.40 12 8.32 14.32 10. 4 0.54 3.51 0.37 5.12 4.51 3.40 13.21 15.44 6.12 13 8.55 14.31 9.47 0.38 3.53 0.25 5.20 4.41 4. 1 13.36 15.36 5.44 14 9.17 14.29 9.30 0.23 3.54 0.13 5.27 4.30 4.22 13.50 15.27 5.16 15 9.38 14.26 9.13 0. 7 3.54 0. 5.33 4.19 4.43 14. 4 15.18 4.47 16 9.59 14.23 8.56 SOB. 0. 8 3.54 ADD. 0.12 5.39 4. 8 5. 4 14.17 15. 7 4.18 17 10.20 14.19 8.39 0.22 3.53 0.25 5.45 3.55 5.26 14.29 14.56 3.48 18 10.39 14.14 8.21 0.36 3.51 0.38 5.50 3.43 5.47 14.41 14.44 3.19 19 10.58 14. 9 8. 3 0.50 3.49 0.51 5.54 3.30 6. 8 14.52 14.30 2.49 20 11.16 14. 2 7.45 1. 4 8.47 1. 4 5.59 3.16 6.29 15. 3 14.17 2.19 21 11.33 13.56 7.27 1.16 3 44 1.17 6. 2 3. 2 6.50 15.13 14. 2 1.49 22 11.50 13.48 7. 8 1.29 3.40 1.30 6. 5 2.47 7.11 15.22 13.46 1.19 23 12. 5 13.40 6.50 1.41 3.36 1.43 6. 7 2.32 7.31 15.31 13.30 0.49 24 12.20 13.31 6.32 1.53 3.31 1.56 6. 9 2.17 7.52 15.39 13.13 0.19 25 12.35 13.22 6.13 2. 4 3.25 2. 8 6.11 2. 1 8.12 15.46 12.55 XDD. 0.11 26 12.48 13. 12 5.55 2.14 3.20 2.21 6.11 1.45 8.33 15.52 12.36 0.41 27 13. 1 13. 2 5.36 2.24 3.13 2.34 6.12 1.28 8.53 15.58 12.17 1.11 28 13.13 12.51 5.18 2.34 3. 6 2.46 6.11 1.11 9.13 16. 3 11.57 1.41 29 13.24 4.59 2.43 2.59 2.59 6.10 0.54 9.33 16. 7 11.36 2.10 30 13.34 4.41 2.51 2.51 3.11 6. 8 0.36 9.52 16.11 11.14 2.40 31 13.43 4.23 2.43 6. 6 0.18 16.13 3. 9 EQUATI 3N OF TIME FOR THE YEAR 18^ •6, AND WHICH WILL AN£ 5WER NEARLY FOR 1860, 1864, AND 1868. | DAV8. JAN. FEB. MAR. APRIL MAY. JUNE. JULY. Aua. SEPT. OCT. NOV. DECEMBER. | ADD. ADD ADD SUB. ADD. ADD. SUB. SUB» SUB. M. 8. M. S. M. S. M. 8. M. S. M. 8. H. 6. M. S. M. S. M. S. H. 6. H. 8. 1 3-36 13-50 12-31 ADD. 3-51 3- 5 SUB. 2-28 3 31 6- 0-14 10-25 16-16 SUB. 10-36 2 4- 4 13-58 12-19 3-33 3-12 2-19 3 42 5-56 0-33 10-44 16-17 30-13 3 4-33 14- 5 12- 6 3-16 3-19 2- 9 3 53 5-52 0-52 11- 3 16-17 9-49 4 5- 14-11 11-53 2-58 3-25 1-59 4 4 5-47 1-12 11-21 16-16 9-24 5 5-28 14-17 11-39 2-40 3-30 1-49 4 15 5-41 1-31 11-28 16-14 8-59 6 5-55 14-22 11-25 2-23 3-35 1-38 4 25 5-35 1-51 11-56 16-11 8-34 7 6-21 14-26 11-11 2- 6 3-39 1-27 4 •35 5-28 2-11 12-13 16- 8 8- 8 8 6-47 14-29 10-56 1-49 3-43 1-16 4 44 5-20 2-32 12-30 16- 4 7-42 9 7-13 14-31 10-40 1-32 3-46 1- 4 4 53 5-12 2-52 12-46 15-58 7-15 10 7-38 14-33 10-25 1-15 3-49 0-53 5 2 5- 3 3-13 13- 2 15-52 6-47 11 8- 2 14-33 10- 9 0-59 3-51 0-41 5 10 4-54 3-34 13-17 15-46 6-20 12 8-26 14-33 9-52 0-43 3-52 0-29 5 17 4-44 3-55 13-32 15-38 5-52 13 8-49 14-32 9-36 0-27 3-53 0-16 5 25 4-34 4-16 13-46 15-30 5-23 14 9-11 14-31 9-19 0-12 3-54 0- 4 5 31 4-23 4-37 14- 15-20 4-55 15 9-33 14-28 9- 2 SUB. 0- 3 3-54 ADD. 0- 9 5 38 4-11 4-58 14-13 15-10 4-26 16 9-54 14-25 8-44 0-18 3-53 0-21 5 43 3-59 5-19 14-26 14-59 3-56 17 10-15 14-21 8-26 0-32 3-52 0-34 5 48 3-46 5-41 14-38 14-47 3-27 18 10-34 14-16 8- 9 0-46 3-50 0-47 5 53 3-33 6- 2 14-49 14-34 2-57 19 10-53 14-11 7-51 0-59 3-47 1- 5 57 3-20 6-23 15- 14-21 2-517 20 11-12 14- 5 7-32 1-13 3-45 113 6 1 3- 6 6-44 15-10 14- 6 1-67 21 11-29 13-58 7-14 1-25 3-41 1-26 6 4 2-51 7- 5 15-20 13-51 1-27 22 11-46 13-51 6-56 1-38 3-37 1-39 6 6 2-36 7-26 15-29 13-35 0-57 23 12- 2 13-43 6-37 1-49 3-32 1-52 6 8 2-21 7-46 15-37 13-18 0-27 24 12-17 13-35 6-19 2- 1 3-27 2- 4 6 10 2- 5 8- 7 15-44 13- ADD. 0. 3 25 12-31 13-25 6- 2-11 3-22 2-17 6 11 1-49 8-27 15-51 12-42 0-33 26 12-45 13-16 5-42 2-22 3-15 2-30 6 It 1-33 8-48 15-57 12-22 1- 3 27 12-58 13- 5 5-23 2-31 3- 9 2-42 6 11 1-16 9- 8 16- 2 12- 2 1-33 28 13-10 12-55 5- 5 2-41 3- 2 2-55 6 10 0-58 9-27 16 6 11 -42 2- 2 29 13-21 14-43 4-46 2-49 2-54 3- 7 6 8 0-41 9-47 16 10 11-20 2-32 30 13-31 4-28 2-67 2-46 3-19 6 6 0-23 10- 6 16-13 10-68 3- 1 31 13-41 4-10 1 2-37 1 6 4 0. 5 16-15 3-29 74 • TABLE XIV. B 5-0 5- 5 6'C 6 5 7 7 •4 6- 100 0-6 1-1 1-7 2 •2 2- 8 3 3 3 9 4 4 5 ' U| J • 6 6- I 6-7 7 2 7 8 8 -3 6-40 110 0-6 1-2 1-8 2 •4 3- 1 3 7 4 3 4 9 5-5 6-1 6- 7 7-3 7 9 8 6 9 •2 7-20 120 0-7 1-3 2-0 O -J •7 3- 3 4 4 7 5 3 6-0 6-7 7 • 3 8-C 8 7 9 3 10 -0 8- 130 0-7 1-4 2-2 2 •9 3- 6 4 3 5 1 5 8 6-5 7-2 7- 9 8-7 9 4 10 1 lu •8 8-40 140 0-8 1-6 2-3 3 •1 3- 9 4 7 5 4 6 2 7-0 7-8 8- 6 9-3 10 1 10 9 11 •7 9-20 150 0-8 1-7 2-5 3 •3 4- 2 5 5 8 8 >7 7-5 8-2 9- 210-C 10 8 11 7 12 -5 10- 160 0-9 1-8 2-7 3 •6 4- 4 5 3 6 2 7 1 8-0 8-9 9- 810-7 11 6 12 4 13 -3 10-40 170 0-9 1-9 2-8 3 •8 4- 7 5 7 6 6 7 6 8-5 9-4 10. 411-3 12 3 13 2 14 -2 11-20 180 1-0 2-0 3-0 4-0 5- 6-0 7-0 8-0| 9-0 10-0 11- 012-C 13-01 14 15-0 12- IN WEST LONGITUDE. IN EAST LONGITUDE 1 Wh .. t' • S Increasing Add. en the Equa. is { decreasing, Subtract. m.„ .he Equ.. i. { ",3™^- ^;,t-'- 1 TIME BEFORE NOON. TIME AFTERNOON. "Wl ., r, . < Increasinsf, Subtract. en the Equa. is j j)^„^^i^^^ Add. WhentheEqua.i8 5 Increasing, Add 1 ^ ( Decreasing, bublract. 1 76 TABLE XV.- -Part First. LOGARITHM OF THE SUN'S HOUR ANCfLE, OR THE TIME FROM NOOW EXTENDING TO 64' 30". a 8 13 4) Log. cc ad 1 s Log. CD 03 1 § a u Log. O} QO 1 § Log. 00 m 1 i S 03 Log. s 4 1 § .9 " 3 02 Log. 1. 4.677 7.40 6.446 14.20 6.990 21. 7.322 30.20 7.641 45. 7.982 10 811 50 465 30 7.000 10 328 40 650 30 992 20 927 8. 483 40 010 20 335 31. 660 46. 8.001 30 5.030 10 501 50 019 30 342 20 669 30 010 40 121 20 519 15. 029 40 349 40 678 47. 020 50 2(»4 30 536 10 039 50 355 32. 687 30 029 2. 279 40 553 20 048 22. 362 20 696 48. 038 10 349 50 569 30 058 10 368 40 705 30 047 20 414 9. 586 40 067 20 375 33. 714 49. 056 30 473 10 602 50 076 30 382 20 723 30 065 40 530 20 617 16. 085 40 388 40 731 50. 074 50 582 30 633 10 094 50 394 34. 740 30 082 3. 632 40 648 20 103 23. 400 20 748 51. 090 10 678 50 663 30 112 10 407 40 757 30 099 20 723 10. 677 40 121 20 413 35. 765 52. 107 30 766 10 692 50 130 30 419 20 773 30 116 40 806 20 706 17. 138 40 425 40 781 53. 124 50 845 30 720 10 147 50 431 36. 789 30 132 4. 881 40 734 20 155 24. 438 20 797 54. 140 10 917 50 747 30 163 10 444 40 805 30 148 20 951 11. 760 40 172 20 449 37. 813 55. 156 30 984 10 773 50 180 30 455 20 821 30 164 40 6.015 20 786 18. 188 40 461 40 829 56. 172 50 046 30 798 10 190 50 467 38.. 836 30 179 5. 075 40 811 20 204 25. 473 20 844 57. 187 10 103 50 .824 30 212 20 484 40 851 30 194 20 132 12. 836 40 219 40 496 39. 859 58. 202 30 158 10 848 50 227 26. 507 20 866 30 209 40 182 20 860 19. 235 20 518 40 873 59. 217 50 209 30 871 10 242 40 529 40. 881 30 224 6. 234 40 883 20 250 27. 540 20 888 60. 231 10 258 50 894 30 257 20 550 40 895 30 238 20 281 13. 905 40 264 40 561 41. 902 61. 246 30 303 10 916 50 272 28. 571 30 912 30 253 40 325 20 927 20. 279 20 582 42. 923 62. 259 50 347 30 938 10 286 40 592 30 933 30 267 7. 367 40 949 20 294 29. 602 43. 943 63. 274 10 388 50 959 30 301 20 612 30 953 30 280 20 408 14. 969 40 308 40 622 44. 963 64. 287 30 427 10 980 50 315 30. 631 30 973 30 294 • 76 TABLE XV.— Pak. Second. 1 LOGARITHMS^ OF THE LATITUDE AND DECLINATION WHEN THEY ARE OF THE | SAME NAMK | DECLINATION. Lat. o 0° 1° 2° 3° 40 50 6° 70 8° 90 10° 11° 12° Lat. 1.359 1.279 1.212 1.153 1.101 1.055 1.012 0.974 1 1 358 278 211 152 100 053 1.011 1 2 ! 1 357 277 209 151 098 051 2 3 356 276 208 149 097 3 4 354 274 206 147 4 5 1,359 352 272 204 5 6 279 1.358 350 270 6 7 212 278 1.357 1 348 7 8 153 211 277 1.356 1 8 9 101 152 209 276 1.354 9 10 055 100 151 208 272 1.352 10 11 1,012 1.053 1.0!>8 1.149 1.206 1.272 1.350 11 12 0.974 Oil 051 097 147 204 270 1.348 12 13 938 0.972 009 051 094 145 201 267 1.345 13 14 904 936 0.970 007 047 092 142 199 264 1.342 14 15 873 902 934 0.967 004 045 089 139 196 261 1.339 15 16 844 871 900 931 0.965 00.2 042 086 136 193 258 1.336 16 17 816 841 868 897 928 0.962 0.999 039 083 133 189 254 1.332 17 18 789 813 839 866 895 925 959 0.995 035 080 129 185 250 18 19 764 787 811 836 863 891 922 956 0.992 032 076 125 181 19 20 740 761 784 807 833 859 888 919 952 0.988 028 072 121 20 21 0.717 0.737 0.758 0.781 0.804 0.829 0.856 0.884 0.915 0.948 0.984 1.023 1.067 21 22 695 714 734 755 777 801 825 852 880 911 944 0.980 019 22 23 673 691 710 730 752 773 807 821 848 876 906 939 0.975 23 24 652 670 688 707 727 747 769 793 817 844 871 902 934 24 25 632 649 666 684 703 723 743 765 788 813 839 867 897 25 26 613 629 645 662 680 699 718 739 760 783 808 834 861 26 27 594 609 625 641 658 676 694 714 734 756 778 803 828 27 28 575 590 605 620 637 653 671 689 709 729 750 i 773 797 28 29 557 571 586 600 616 632 649 666 684 703 724 745 767 29 30 540 553 567 581 596 611 627 643 661 679 698 718 739 30 31 0.522 0.535 0.548 0.562 0.576 0.591 0.606 0.622 0.638 0.655 0.673 0.692 0.712 31 32 505 518 530 543 557 571 585 600 616 632 649 667 686 32 33 489 500 513 525 538 551 565 580 594 610 626 643 661 33 34 472 483 495 507 519 532 546 559 574 588 604 620 636 34 35 456 467 478 489 501 514 526 540 553 567 582 597 612 35 36 440 450 461 472 484 495 508 520 533 548 560 575 590 36 37 424 434 445 455 466 478 489 501 514 526 540 553 568 37 38 408 418 428 438 449 460 471 482 494 507 519 532 546 38 39 393 402 412 422 432 442 453 464 475 487 499 512 525 39 40 377 386 396 405 415 425 435 447 457 468 480 492 504 40 41 0.362 0.371 0.3H0 0.389 0.398 0.408 0.418 0.428 0.438 0.449 0.460 0.472 0.484 41 42 347 355 364 373 382 391 400 410 420 431 441 452 464 42 43 331 340 348 358 365 374 383 393 402 412 422 433 444 43 44 316 324 332 340 349 357 366 375 384 394 404 414 424 44 45 301 309 316 324 333 341 349 358 367 376 385 395 405 45 46 286 293 301 308 316 324 332 341 349 358 367 376 386 46 47 271 278 285 292 300 308 315 323 331 340 349 358 367 47 48 255 262 269 276 284 291 299 306 314 322 331 339 348 48 49 240 247 254 260 267 275 282 289 297 305 312 321 329 49 50 225 231 238 244 251 258 265 272 2^9 287 294 302 310 50 51 209 0.216 0.222 0.228 0.235 0.241 0.248 0.255 0.262 0.269 0.276 0.284 0.291 51 52 194 200 206 212 218 225 231 238 244 251 258 265 273 52 53 178 184 190 196 202 208 214 220 227 233 240 247 254 53 54 162 168 173 179 185 191 197 203 209 215 222 228 235 54 55 146 152 157 162 168 174 179 185 191 197 204 210 216 55 56 130 135 140 146 151 156 162 168 173 179 185 191 197 56 57 •114 118 124 129 134 139 144 150 155 160 166 172 178 57 58 097 100 106 111 116 121 126 131 137 142 148 153 159 58 59 080 084 089 094 098 103 108 113 118 123 128 134 139 59 60 062 067 071 076 080 085 090 094 099 104 109 114 119 60 77 TABLE XV.— Part Second. LOGARITHMS OF THE LATITUDE AND DECLINATION WHEN THEY ARE OF THE SAME NAMK DKCLINATION. Lat. 13° 14° 15° 16° 170 18° 190 20° 21° 22° 230 24° 250 Lat. 0.938 0.904 0.873 0.844 0.816 0.789 0.764 0.740 0.717 0.695 0.673 0.652 0.632 I 1 972 936 902 871 841 813 787 761 737 714 691 660 649 ll 666 ' 2 1 ' 2 1.009 970 934 900 868 839 811 784 758 734 710 687 3 049 1.007 967 931 897 866 836 807 781 755 730 707 683 3 ! 4 094 047 1.004 965 928 895 863 832 804 777 751 726 703 4 5 145 092 045 1.002 962 925 891 ' 859 829 801 773 747 722 5 6 201 142 089 042 999 959 922 888 856 825 797 770 743 6 ^ 7 267 199 139 086 1.039 995 956 919 884 852 821 7'93 765 7 8 345 264 196 136 083 1.035 992 952 915 880 848 818 788 8 9 342 261 191 133 080 1.032 988 948 911 876 844 813 9 . 10 339 258 189 129 076 1.028 984 944 906 871 y38 10 11 1.336 1.254 1.185 1.125 1.072 1.023 0.980 0.939 0.902 0.866 11 12 332 250 181 121 067 1.019 975 934 896 12 13 328 246 177 116 063 1.014 970 929 13 14 323 242 172 112 058 1.009 964 14 15 319 237 167 106 053 1.003 15 16 314 232 162 101 047 16 17 308 226 157 095 17 18 1.S28 303 221 150 18 19 246 1.323 298 215 19 20 177 242 1.319 ' 291 20 21 1.116 1.172 1.237 1.314 21 22 063 112 167 232 1.308 1 1 22 23 014 058 106 162 226 1.303 23 24 0.970 009 052 101 156 221 1.297 24 25 929 0.965 004 047 095 151 215 1.291 25 26 890 924 0.959 0.998 041 090 144 208 1.285 26 ^ 27 856 886 918 953 0.992 035 083 138 202 1.278 27 28 823 850 880 912 947 0.986 028 076 131 195 1.271 28 29 791 817 844 874 906 940 0.979 021 069 124 188 1.264 29 30 761 785 811 838 867 899 934 0.972 014 062 117 181 1.256 30 31 0.733 0.755 0.779 0.804 0.831 0.860 0.892 0.926 0.965 1.007 1.055 1.109 171 31 32 706 726 748 772 797 824 853 885 919 0.957 0.999 046 100 32 ' 33 679 699 720 742 765 790 817 846 877 911 949 0.992 038 33 34 654 672 692 712 734 757 782 809 838 869 903 941 0.983 34 35 630 647 665 685 705 727 750 774 801 829 861 894 931 35 36 606 622 640 658 677 697 719 742 766 792 821 852 885 36 37 583 598 615 632 650 669 689 710 733 758 784 812 842 37 38 560 575 591 607 624 642 661 681 702 724 749 775 803 38 39 538 552 507 582 599 615 633 652 672 693 715 740 765 39 40 517 530 544 559 574 590 607 624 643 662 683 706 729 40 41 0.496 0.509 0.522 0.536 0.550 0.565 0.581 0.597 0.615 0.633 0.653 0.674 696 41 42 475 487 500 513 527 541 556 572 588 605 623 643 663 42 43 455 466 478 491 504 517 532 546 562 578 595 613 632 43 44 435 446 457 469 482 494 508 522 536 552 568 585 602 44 45 415 426 436 448 460 472 484 498 511 526 541 557 573 45 46 395 405 416 427 438 449 461 474 487 501 515 530 545 46 47 376 386 396 406 416 427 439 451 463 476 490 504 518 47 48 357 366 375 385 395 406 417 428 440 452 465 479 492 48 49 337 346 355 365 374 384 395 405 417 428 440 453 407 49 50 51 318 327 335 344 354 362 373 383 394 405 416 428 440 50 0.299 0.307 0.316 0.324 0.333 0.342 )0.351 0.361 0.371 0.381 0.392 0.404 0.415 51 52 280 288 296 304 312 321 330 339 349 359 369 379 390 52 53 261 269 276 284 292 300 309 317 326 336 346 355 365 53 54 242 249 257 264 271 279 287 296 304 313 322 332 341 54 55 223 230 236 244 251 258 266 274 282 291 299 309 318 55 56 204 210 217 223 230 237 245 252 260 268 277 286 294 56 57 184 190 197 203 210 216 223 231 238 246 254 262 270 57 58 164 170 176 183 189 195 202 209 216 223 231 238 246 58 59 145 150 156 162 168 174 180 187 194 201 208 215 222 59 60 125 130 135 141 147 153 159 165 171 178 185 192 198 60 1 78 TABLE XV.— Part Third. LOGARITHMS OF THE LATITUDE AND DECLINATION WHEN THEY ARE OP CONTRARY NAMES. DECLINATION. ; Lat. 0° 1° 2° 3° 40 50 6° 70 8° 90 10° 11° 12° Lat. o 1.359 1.279 1.212 1.153 1.101 1.055 1.012 0.979 1 1.360 280 213 154 102 056 014 0.975 931 1 2 1.360 281 213 155 103 057 015 0.976 941 907 2 3 1.360 281 213 155 104 058 016 0.977 942 909 878 3 4 1.360 280 213 155 104 058 016 0.978 943 910 879 850 4 5 1.359 j 280 213 155 104 058 016 0.978 943 910 880 851 824 5 6 2791 213 155 104 058 016 0.979 943 911 880 852 825 799 6 ' 7 219 154 103 058 016 0.978 943 911 881 851 825 800 776 7I 8 153 102 057 016 0.978 943 911 881 852 825 800 776 753 8 9 101 056 015 0.977 943 910 880 852 825 800 776 754 732 9 10 055 014 0.976 942 910 880 852 825 800 776 754 732 711 10 ll 11 1.012 0.975 0.941 0.9U9 0.879 0.851 0.825 0.800 0.776 0.754 0.732 0.711 0.692 12 0.974 939 907 878 850 824 799 775 753 732 711 692 673 12 13 938 906 876 849 823 798 775 752 731 711 691 672 654 13 14 904 875 847 822 797 774 751 730 710 691 672 654 636 14 15 873 846 820 795 772 750 729 709 690 671 653 636 619 15 16 844 818 794 772 749 728 708 689 670 653 635 619 603 16 17 816 792 769 747 726 706 687 669 651 634 617 ~602 586 17 18 789 767 745 724 705 686 668 650 633 617 601 586 571 18 19 764 743 722 703 684 666 648 632 615 600 584 570 555 19 20 740 720 700 682 664 646 630 614 598 583 568 554 540 20 21 21 0.717 0.698 0.679 0.661 0.644 0.628 0.612 0.596 0.581 0.567 0.553 0.539 0.525 22 695 676 659 642 625 609 594 579 565 551 537 524 511 22 23 673 656 639 623 607 592 577 563 549 535 522 509 497 23 24 652 636 621 604 589 575 560 547 533 520 508 495 483 24 25 632 616 601 586 572 558 544 531 518 505 493 481 469 25 26 613 598 583 569 555 541 528 515 503 491 479 467 456 26 27 594 579 565 551 538 525 512 500 488 476 465 454 442 27 28 575 561 548 535 522 509 497 485 473 462 451 440 429 28 29 557 544 531 518 506 494 482 470 459 448 437 427 416 29 30 540 527 514 502 490 478 467 456 445 434 425 414 403 30 31 31 0.522 0.510 0.498 0.486 0.474 0.463 0.452 0.442 0.431 0.421 0.411 0.401 0.391 32 505 493 482 470 459 448 438 427 417 407 397 388 378 32 33 489 477 466 455 444 434 423 413 403 394 384 375 366 33 34 472 461 450 440 429 419 409 399 390 380 371 362 353 34 35 456 445 435 424 414 405 395 386 376 367 358 349 341 35 36 440 429 419 410 400 390 381 372 363 354 345 337 328 36 37 424 414 404 395 385 376 367 358 350 341 333 324 316 37 38 408 399 389 380 371 362 353 345 336 328 320 312 304 38 39 393 384 374 365 357 348 340 331 323 315 307 299 291 39 40 377 368 360 351 342 334 326 318 310 302 294 287 279 40 41 0.362 0.353 0.345 U.336 0.328 0.320 0.312 0.304 0.297 0.289 0.282 0.274 0.267 41 42 347 338 330 322 314 306 299 291 284 276 269 262 255 42 43 331 323 315 308 300 292 285 278 270 263 256 249 242 43 44 316 308 301 2!»3 286 279 271 264 257 250 243 237 230 44 45 301 294 286 279 272 265 258 251 244 237 231 224 217 45 46 286 279 271 264 257 251 244 237 231 224 218 211 205 46 47 271 264 257 250 243 237 230 224 217 211 205 198 192 47 48 255 249 242 235 229 223 216 210 204 198 191 185 179 48 49 240 234 227 221 215 208 202 196 190 184 178 172 167 49 50 51 225 219 212 206 200 194 188 182 176 171 165 159 154 50 0.209 0.203 0.197 0.191 0.185 0.180 0.174 0.168 0.163 0.157 0.151 0.145 0.140 51 52 194 188 182 175 171 165 160 154 149 143 138 132 127 52 53 178 172 167 161 156 150 145 140 134 129 124 119 114 53 54 162 157 151 ^ 146 141 136 130 125 120 115 110 105 100 54 55 146 141 136 131 125 120 115 110 105 101 096 091 086 55 56 130 125 120 115 no: 105 100 095 091 086 081 077 072 56 57 114 109 104 099 094 090 085 080 076 071 066 062 057 57 58 097 092 087 083 078 074 069 065 060 056 051 047 043 58 59 080 075 071 066 062 058 053 049 045 040 036 032 028 59 60 062 058 054 0501 045 041 037 033 029! 024 020 016 012 60 TAliLK XV.— Part Third. 19 1 LOaARlTHMS OF THE LATITUDE AND DECLINATION WHEN THEY ARE OF | CONTRARY NAMES. I DECLINATION. | Lat, 13° 14° 15° 16° 17° 18° 19° 20° 21° 22° 23° 24° 25° Lat o 0.938 0.904 0.873 0.844 0.816 0.789 0.764 0.740 0.717 0.695 0.673 0.653 0.632 '1 1 906 875 846 818 792 767 743 720 698 676 656 636 616 1 2 876 847 820 794 769 745 722 700 679 659 639 620 604 2 3 849 821 795 771 747 724 703 682 661 642 623 604 586 3 4 823 797 772 749 726 705 684 ,664 644 625 607 589 571 4 5 798 774 750 728 706 686 666 646 628 609 592 574 557 5 6 775 751 721> 70S 687 668 648 630 612 594 577 561 544 6 7 752 730 709 689 669 650 632 614 596 579 563 547 531 7 8 731 710 690 670 651 633 615 598 581 565 549 534 518 8 9 711 691 671 653 634 617 600 583 567 551 535 521 505 9 10 691 672 653 635 618 601 584 568 553 537 522 508 493 10 11 0.672 0.654 0.636 0.619 0.602 0.5S6 0.570 0.554 0.539 0.524 0.509 0.495 0.481 ll 12 654 636 619 603 586 571 555 540 525 511 497 483 469 12 13 637 620 603 587 571 556 541 527 512 498 485 471 457 13 14 620 603 587 572 557 542 527 513 499 486 473 460 446 14 15 602 587 572 557 542 528 514 500 487 474 461 449 435 15 16 587 572 557 542 528 515 501 488 475 462 449 438 424 16 17 571 557 542 528 515 501 488 475 463 450 438 427 413 17 18 556 542 I 528 515 501 488 475 463 451 438 426 416 402 18 19 541 527! 514 501 488 475 463 451 439 427 415 405 392 19 20 527 513: 500 488 475 463 451 439 427 416 404 394 382 20 21 21 0.512 0.499 0.487 0.475 0.462 0.451 0.439 0.427 0.416 0.405 0.393 0.383 0.372 22 498 486 474 462 450 438 427 416 405 394 383 372 362 22 23 485 472 461 449 438 426 415 404 393 383 372 361 352 23 24 471 459 448 437 425 414 404 393 382 372 362 351 342 24 25 458 446 435 424 413 403 392 382 372 361 351 341 332 25 26 445 434 423 412 402 391 381 371 361 351 341 331 322 26 27 432 421 410 400 390 380 370 360 350 340 331 321 312 27 28 419 408 398 388 378 368 358 349 339 330 320 311 302 28 29 406 396 386 376 367 357 347 338 329 320 310 302 292 29 30 394 384 374 364 355 346 336 327 318 309 300 293 283 30 31 0.381 0.372 0.362 0.353 0.344 0.335 0.326 0.317 0.308 0.299 0.290 0.282 0.273 31 32 369 359 350 341 332 323 315 306 297 289 280 272 263 32 33 356 347 338 330 321 312 304 295 287 278 270 262 253 33 34 344 335 327 318 310 301 293 285 276 268 260 252 243 34 35 332 324 315 307 298 290 282 275 , 266 258 250 242 233 35 36 320 312 303 295 287 279 271 263 256 248 240 232 224 36 37 308 300 292 284 276 268 260 253 245 237 230 222 214 37 38 296 288 280 272 265 257 250 242 235 227 220 212 204 38 39 2s4 276 269 261 ,254 246 239 231 224 217 210 202 194 39 40 272 264 257 250 242 235 228 221 214 207 199 192 185 40 41 0.260 0.252 0.245 0.238 0.231 0.224 0.217 0210 0.203 0.196 0.188 0.182 0.175 41 42 247 240 233 227 220 213 206 199 192 186 178 172 165 42 43 235 228 222 215 208 202 195 188 182 175 168 162 155 43 44 223 216 210 203 197 190 184 177 171 164 158 152 145 44 45 211 204 198 192 185 179 173 166 160 154 147 142 135 45 46 198 192 186 180 174 167 161 155 149 143 136 132 125 46 47 48 186 180 174 168 162 156 150 144 138 132 126 121 114 47 173 168 162 156 150 144 138 132 127 121 115 110 103 48 49 161 155 149 144 138 132 126 121 115 109 104 099 092 49 50 148 142 137 131 126 120 115 109 104 098 093 087 081 50 51 0.135 0.130 0.121 0.119 0.113 0.108 0.103 0.097 0.092 0.086 0.081. 0.076 0.070 51 52 122 117 111 106 101 096 090 085 080 075 069 064 058 52 53 108 103 098 093 088 083 078 073 068 063 058 052 047 53 54 095 090 085 080 075 070 065 060 055 051 046 041 035 54 55 081 076 072 067 062 057 052 048 043 038 033 029 024 55 56 067 063 058 053 049 044 039 035 030 025 021 017 Oil 56 57 053 048 044 039 035 030 026 021 017 012 008 004 9.998 57 58 038 034 030 025 021 017 013 008 003 9.999 9.995 9.990 985 58 59 023 019 015 Oil 007 002 9.998 9.994 9.990 985 981 977 972 59 60 008 004 000 9.996 9.992 9.988 984 980 976 971 967 963 959 60j so TABLE XV. PART FOURTa PART FIFTH. OONTAININO THE 8DM OK THE TWO LOGS AND THE | CONTAINING THE LIMITS OF THE TIME FUOM OOBJIEOTION FOE ALTITUDE. NOON AT WHICH THE OB3EBVATION SHOULD BE MADE. 1 , , , .2 s 1 a .11 II 2 !> DEO. OF THE SAME NAME AS THE LATITUDE. | 1 H •S -:i 12 •o -J 12 "3 3 1 & o a g % -^ i 1 1 < a 2 3i 3 P ^ J ^M 3 ^ 03 ^ Lat 0° 5° 10° 15° 20^ 24° o ' 0. 1 6.464 O ' 0.51 8.171 O 1 1.41 8.468 o h m b m h m h m h m b m 2 765 52 180 1.42 472 0.0 0.4 0.6 0.9 0.12 0.15 3 941 53 189 1.43 476 5 3 1 4 6 9 12 4 7.066 54 196 1.44 481 10 6 4 1 5 7 10 5 163 55 204 1.45 485 15 9 7 4 2 4 8 6 242 56 212 1.46 489 20 12 10 7 5 2 5 7 309 57 220 1.47 493 25 16 13 10 8 5 2 8 367 58 227 1.48 497 30 19 16 13 12 9 6 9 418 59 235 1.49 501 35 24 21 18 15 13 10 10 464 1. 242 1.50 505 40 28 25 22 20 17 15 11 505 1. 1 249 1.51 509 44 32 29 26 24 21 20 12 543 1. 2 256 1.52 513 48 36 33 30 30 27 25 13 578 1. 3 263 1.53 516 52 44 41 36 36 34 32 14 610 1. 4 270 1.54 521 56 55 47 44 42 38 36 15 16 640 668 1. 5 1. 6 277 283 1.55 1.56 524 528 60 58 54 52 50 ^ 44 17 694 1. 7 290 1.57 532 DEOUNATIO N OF THE CONTKAET NAME TO THE 18 719 1. 8 296 1.58 536 LATITUDE. 19 20 742 765 1. 9 1.10 303 309 1.59 2. 539 543 h m b m h m b m b m b m 21 786 1.11 315 2. 1 546 0.0 0.4 0. 7 0.10 0.13 0.16 22 806 1.12 321 2. 2 549 5 3 7 9 13 16 18 23 825 1.13 327 2. 3 553 10 7 10 13 17 19 21 24 844 1.14 333 2. 4 557 15 10 13 17 20 21 24 25 862 1.15 339 2. 5 560 20 13 16 19 23 25 28 26 879 1.16 345 2. 6 564 25 18 20 23 26 28 31 27 895 1.17 350 2. 7 567 30 21 23 26 30 32 35 28 911 1.18 356 2. 8 571 35 25 27 30 34 36 39 29 926 1.19 361 2. 9 574 40 30 32 33 38 40 43 30 941 1.20 367 2.10 578 44 34 37 38 43 46 48 31 955 1.21 372 2.11 581 48 38 42 45 48 51 53 32 969 1.22 377 2.12 584 52 44 48 52 55 58 1. 33 982 1.23 383 2.13 587 56 50 54 57 1. 1. 3 1. 5 34 35 995 8.008 1.24 1.25 389 393 2.14 2.15 591 594 60 58 57 1. 4 1. 6 1. 9 1.12 36 020 1.26 398 2.1-6 597 . 37 032 1.27 403 2.17 600 38 044 1.28 408 2.18 603 39 054 1.29 413 2.19 606 40 066 1.30 419 2.20 610 41 077 1.31 423 2.21 613 42 087 1.32 427 2.22 616 43 097 1.33 432 2.23 619 44 107 1.34 437 2.24 622 45 117 1.35 441 2.25 625 46 126 1.36 446 2.26 628 47 136 1.37 450 2.27 631 48 145 1.38 455 2.28 634 . 49 154 1.39 459 2.29 637 60 163 1.40 464 2.30 640 J TABLE XVI. " APPARENT TIME 0? THE SUTS RISING AND SETTING. | 1 DECLINATION OP THE SAME NAME AS fHE LATITUDE. 1 0° 2° 40 6° 8° 1 90 10° Ris. SetL Ris. Sett Ris. Sett Ris. Sett Ris. Sett. Ris. Sett Ris. Sett H. M. H. M. H. M. H. M. ■J. M. H. M. H. M. H. M. H. M. H. M H. M. H. M. a. M. H. M. 6.0 6.0 6. 6. 6. 6. 6. 6. 6. 6. 6. 6. 6. 6. 2 6.0 6.0 6. 6. 6. 6. 6. 6. 5.59 6. 1 5.59 6. 1 5.59 6. 1 4 tJ.O 6.0 6. 6. Q 5.59 6. 1 5.59 6. 1 5.58 6. 2 5.58 6. 2 5.57 6. 3 6 6.0 6.0 6. 6. 5.58 6. 2 5.58 6. 2 5.57 6. 3 5.57 6. 3 5.56 6. 4 8 6.0 6.0 5.59 6. I 5.58 6. 2 5.57 6. 3 5.56 6. 4 5.55 6. 5 5.55 6. 5 10 6.0 6.0 5.59 6. 1 5.57 6. 3 5.56 6. 4 5.54 6. 6 5.54 6. 6 5.53 6. 7 12 6.0 6.0 5.58 6. 2 5.57 6. 3 5.55 6. 5 5.53 6. 7 5.53 6. 7 5.52 6. 8 14 6.0 6.0 5.58 6. 2 5.56 6. 4 5.54 6. 6 5.52 6. 8 5.51 6. 9 5.51 6. 9 16 6.0 6.0 5.58 6. 2 5.55 6. 5 5.53 6. 7 5.51 6. 9 5.50 6.10 5.48 6.12 18 6.0 6.0 5.58 6. 2 5.55 6. 5 5.52 6. 8 5.50 6.10 5.48 6.12 5.47 6.13 20 6.0 6.0 5.57 6. 3 5.54 6. 6 5.51 6. 9 5.48 6.12 5.47 6.13 5.45 6.13 21 6.0 6 5.57 6. 3 5.54 6. 6 5.51 6. 9 5.48 6.12 5.46 6.14 5.44 6.16 22 6.0 6.0 5.57 6. 3 5.54 6. 6 5.50 6.10 5.47 6.13 5.45 6.15 5.44 6.16 23 6.0 6.0 5.57 6. 3 5.53 6. 7 5.50 6.10 5.46 6.14 5.44 6.16 5.43 6.17 24 6.0 6.0 5.57 6. 3 5.53 6. 7 5.49 6.11 5.46 6.14 5.43 6.17 5.42 6.18 25 6.0 6.0 5.56 6. 4 .5.53 6. 7 5.49 6.11 5.45 6.15 5.42 6.18 5.41 6.19 26 6.0 6.0 5.56 6. 4 5.52 6. 8 5.48 6.12 5.44 6.16 5.41 6.19 5.40 6.20 27 6.0 6.0 5.56 6. 4 5.52 6. 8 5.48 6.12 5.44 6.16 5.41 6.19 5.39 6.21 28 6.0 6.0 5.56 6. 4 5.51 6. 9 5.47 6.13 5.43 6.17 5.40 6.20 5.38 6.22 29 6.0 6.0 5.56 6. 4 5.51 6. 9 5.47 6.13 5.42 6.18 5.39 6.21 5.38 6.22 30 6.0 6.0 5.55 S. 5 5.51 6. 9 5.46 6.14 5.41 6.19 5.38 6.22 5.37 6.23 31 6.0 6.0 5.55 6. 5 5.50 6.10 5.46 6.14 5.41 6.19 5.37 6.23 5.36 6.24 32 6.0 6.0 5.55 6. 5 5.50 6.10 5.45 6.15 5.40 6.20 5.36 6.24 5.35 6.25 33 6.0 6.0 .^.55 6. 5 5.50 6.10 5.44 6.16 5.39 6.21 5.35 6.25 5.34 6.26 34 6.0 6.0 5..55 6. 5 5.49 6.11 5.44 6.16 5.38 6.22 5.35 6.25 5.33 6.27 35 6.0 6.0 .^.55 6. 5 5.49 6.11 5.43 6.17 5.37 6.23 5.34 6.26 5.32 6.28 36 6.0 6.0 5.55 6. 5 5.48 6.12 5.42 6.18 5.37 6.23 5.33 6.27 5.31 6.29 37 6.0 6.0 .5.55 6. 5 5.48 6.12 5.42 6.18 5.36 6.24 5.32 6.28 5.29 6.31 38 6.0 6.0 5.55 6. 5 5.47 6.13 5.41 6.19 5.35 6.25 5.31 6.29 5.28 6.32 39 6.0 6.0 5.55 6. 5 5.47 6.13 5.40 6.20 5.34 6.26 5.29' 6.31 5.27 6.33 40 0.0 6.0 5.54 6. 6 5.47 6.13 5.40 6.20 5.33 6.27 5.28 6.32 5.26 6.34 41 6.0 6.0 5.54 6. 6 5.46 6.14 5.39 6.21 5.32 6.28 5.27 6.33 5.25 6.35 42 6.0 6.0 5.54 6. 6 5.46 6.14 5.38 6.22 5.31 6.29 5.26 6.34 5.23 6.37 43 6.0 6.0 5.53 6. 7 5.45 6.15 5.38 6.22 5.30 6.30 5.25 6.35 5.22 6.38 44 6.0 6.0 5.53 6. 7 5.45 6.15 5.37 6.23 5.29 6.31 5.24 6.36 5.21 6.39 45 6.0 6.0 5.52 6. 8 5.44 6.16 5.36 6.24 5.28 6.32 5.22 6.38 5.19 6.41 46 6.0 6.0 5.52 6. 8 5.43 6.17 5.35 6.25 5.27 6.33 5.21 6.39 5.18 6.42 47 6.0 6.0 5.51 6. 9 5.43 6.17 5.34 6.26 5.25 6.35 5.19 6.41 5.16 6.44 48 6.0 6.0 5.51 6. 9 5.42 6.18 5.33 6.27 5.24 6.36 5.18 6.42 5.15 6.45 49 6.0 6.0 5.51 6. 9 5.42 6.18 5.32 6.28 5.23 6.37 5.16 6.44 5.13 6.47 50 6.0 6.0 5.50 6.10 5.41 6.19 5.31 6.29 5.21 6.39 5.15 6.45 5.11 6.49 51 6.0 6.0 5.50 6.10 5.40 6.20 5.30 6.30 5.20 6.40 5.13 6.47 5.10 6.50 52 6.0 6.0 5.50 6.10 5.39 6.21 5.29 6.31 5.19 6.41 5.11 6.49 5. 8 6.52 53 6.0 6.0 5.49 6.11 5.39 6.21 5.28 6.32 5.17 6.43 5.10 6.50 5. 6 6.54 54 6.0 6.0 5.49 6.11 5.38 6.22 5.27 6.33 5.15 6.45 5. 8 6.52 5. 4 6.56 55 6.0 6.0 5.49 6.11 5.37 6.23 5.25 6.35 5.14 6.46 5. 6 6.54 5. 2 6.58 56 6.0 6.0 5.48 6.12 5.36 6.24 5.24 6.36 5.12 6.48 5. 5 6.55 4.59 7. 1 57 6.0 6.0 5.48 6.12 5.35 6.25 5.23 6.37 5.10 6.50 5. 4 6.56 4.57 7. 3 58 6.0 6.0 5.47 6.13 5.34 6.26 5.21 6.39 5. 8 6.52 5. 6.58 4.54 7. 6 59 6.0 6.0 5.47 6.13 5.33 6.27 5.20 6.40 5. 6 6.54 4.59 7. 1 4.52 7. 8 60 6.0 6.0 5.46 6.14 5.32 6.28 5.18 6.40 5. 4 6.56 4.56 7. 4 4.49 7.11 61 6.0 6.0 5.46 6.14 5.31 6.29 5.16 6.44 5. 1 6.59 4.54 7. 6 4.46 7.14 62 6.0 6.0 5.45 6.15 5.30 6.30 5.14 6.46 4.59 7. 1 4.51 7. 9 4.43 7.17 63 6.0 6.0 5.44 6.16 5.28 6.32 5.12 6.48 4.56 7. 4 4.48 7.12 4.39 7.21 64 6.0 6,0 5.44 6.16 5.27 6.33 5.10 6.50 4.53 7. 7 4.44 7.16 4.35 7.25 65 6.0 6.0 5.43 6.17 5.26 6.34 5. 8 6.52 4.50 7.10 4.41 7.19 4.31 7.29 66 6.0 6.0 5.42 6.18 5.24 6.35 5. 5 6.54 4.47 7.13 4.37 7.23 4.27 7.33 661 6.0 6.0 5.42 6.18 5.23 6.36 5. 4 6.56 4.44 7.16 4.34 7.26 4.24 7.36 Lat Sett Ris. Sett Ris. Sett. Ris. Sett Ris. Sett Ris. Sett Ria. Sett. Rio. LATITUDE A] ND DECI JNATION OF COI JTBABT NAMES. . 1 82 TABLE XVI. 1 APPARENl' TIME Oi" THE SUN'S RISING AND SETTING. | 1 DECLINATION OF THE SAME NAME A3 THE LATITUDE. 1 no 1 12° 1 13° 14° 1 15° 16° 170 1 Ris. Sett Ris. Sett Ris. Sett Ris. Sett Ris. Sett. Ris. Sett Ria. Sett o H. M. H. M. H. M. H. U. H. M. H. M. H. M. H. M. H M. H. M. H. M. B. H. H. M. H. K. 6. 6. 6. 6. 6. 6. 6. 6. 6. 6. 6. 6. 6. 6. 2 5.59 6. 1 5.58 6. 2 5.58 6. 2 5.58 6. 2 5.58 6. 2 5.58 6. 2 5.58 6. 2 4 5.57 6. 3 5.57 6. 3 5.56 6. 4 5.56 6. 4 5.56 6. 4 5.56 6. 4 5.55 6. 5 6 5.56 6. 4 5.55 6. 5 5.55 6. 5 5.54 6. 6 5.54 6. 6 5.53 6. 7 5.53 6. 7 8 5.54 6. 6 5.53 6. 7 5.53 6. 7 5.52 6. 8 5.51 6. 9 5.51 6. 9 5.50 6.10 10 5.52 6. 8 5.52 •6. 8 5.51 6. 9 5.50 6.10 5.49 6.11 5.49 6.12 5.48 6.12 12 5.51 6. 9 5.50 6.10 5.49 6.11 5.48 6.12 5.47 6.13 5.46 6.14 5.45 6.15 14 5.50 6.10 5.48 6.12 5.48 6.12 5.46 6.14 5.45 6.15 5.44 6.16 5.43 6.17 16 5.47 6.13 5.46 6.14 5.45 6.15 5.44 6.16 5.42 6.18 5.41 6.19 5.40 6.20 18 5.46 6.14 5.44 6.16 5.43 6.17 5.41 6.19 5.40 6.20 5.39 6.21 5.37 6.23 20 5.44 6.16 5.42 6.18 5.41 6.19 5.39 6.21 5.38 6.22 5.36 6.24 5.34 6.26 21 5.43 6.17 5.41 6.19 5.40 6.20 5.38 6.22 5.36 6.24 5.35 6.25 5.33 6.27 22 5.42 6.18 5.40 6.20 5.39 6.21 5.37 6.23 5.35 6.25 5.33 6.27 5.32 6.28 23 5.41 6.19 5.39 6.21 5.38 6.22 5.36 6.24 5.34 6.26 5.32 6.28 5..30 6.30 24 5.40 6.20 5.38 6.22 5.36 6.24 5.34 6.26 5.33 6.27 5.31 6.29 5.29 6.31 25 5.39 6.21 5.37 6.23 5.35 6.25 5.33 6.27 5.31 6.29 5.29 6.31 5.27 6.33 26 5.38 6.22 5.36 6.24 5.34 6.26 5.32 6.28 5.30 6.30 5.28 6.32 5.26 6.34 27 5.37 6.23 5.35 6.25 5.33 6.27 5.31 6.29 5.29 6.31 5.26 6.34 5.24 6.36 28 5.36 6.24 5.34 6.26 5.32 6.28 5.30 6.30 5.27 6.33 5.25 6.35 5.23 6.37 29 5.35 6.25 5.33 6.27 5.31 6.29 5.28 6.32 5.26 6.34 5.23 6.37 5.21 6.39 30 5.34 6.26 5.32 6.28 5.29 6.31 5.27 6.33 5.24 6.36 5.22 6.38 5.19 6.41 31 5.33 6.27 5.31 6.29 5.28 6.32 5.26 6.34 5.23 6.37 5.20 6.40 5.18 6.42 32 5.32 6.28 5.29 6.31 5.27 6.34 5.24 6.36 5.21 6.39 5.19 6.41 5.16 6.44 33 5.31 6.29 5.28 6.32 5.24 6.36 5.23 6.37 5.20 6.40 5.17 6.43 5.14 6.46 34 5.30 6.30 5.27 6.33 5.23 6.37 5.21 6.39 5.18 6.42 5.15 6.45 5.12 6.48 35 5.29 6.31 5.26 6.34 5.21 6.39 5.20 6.40 5.17 6.43 5.14 6.46 5.11 6.49 36 5.28 6.32 5.24 6.36 5.20 6.40 5.18 6.42 5.15 6.45 5.12 6.48 5. 9 6.51 37 5.26 ().34 5.25 6.37 5.18 6.42 5.17 6.43 5.13 6.47 5.10 6.50 5. 7 6.53 38 5.25 6.35 5.22 6.38 5.17 6.43 5.15 6.45 5.12 6.48 5. 8 6.52 5 5 6.55 39 5.24 6.36 5.20 6.40 5.15 6.45 5.13 6.47 5.10 6.50 5. 6 6.54 5. 3 6.57 40 5.22 6.38 5.19 6.41 5.14 6.46 5.12 6.48 5. 8 6.52 5. 4 6.56 5. 1 6.59 41 5.21 6.39 5.17 6.43 5.12 6.48 5.10 6.50 5. 6 6.54 5. 2 6.58 4.48 7. 2 42 5.20 6.40 5.16 6.44 5.10 6.50 5. 8 6.52 5. 4 6.56 5. 7. 4.56 7. 4 43 5.18 6.42 5.14 6.46 5. 8 6.52 5. 6 6.54 5. 2 6.58 4.48 7. 2 4.54 7. 6 44 5.17 6.43 5.13 6.47 5. 7 6.53 5. 4 6.56 5. 7. 4.56 7. 4 4.51 7. 9 45 5.15 6.45 5.11 6.49 5. 5 6.55 5. 2 6.58 4.58 7. 2 4.53 7. 7 4.49 7.11 46 5.14 6.46 5. 9 6.51 5. 4 6.56 5. 7. 4.56 7. 4 4.51 7. 9 4.46 7.14 47 5.12 6.48 5. 7 6.53 5. 3 6.57 4.58 7. 2 4.53 7. 7 4.48 7.12 4.43 7.17 48 5.10 6.50 5. 5 6.55 5. 1 6.59 4.56 7. 4 4.51 7. 9 4.46 7.14 4.41 7.19 49 5. 8 6.52 5. 3 6.57 4.58 7. 2 4.53 7. 7 4.48 7.12 4.43 7.17 4.38 7.22 50 5. 6 6.54 5. 1 6.59 4.56 7. 4 4.51 7. 9 4.46 7.14 4.40 7.20 4.35 7.25 51 5. 4 6.56 4.59 7. 1 4.54 7. 6 4.58 7.12 4.43 7.17 4.37 7.23 4.31 7.29 52 5. 2 6.58 4.57 7. 3 4.51 7. 9 4.46 7.14 4.40 7.20 4.34 7.26 4.28 7.32 53 5. 7. 4.54 7. 6 4.49 7.11 4.43 7.17 4.37 7.23 4.31 7.29 4.24 7.36 54 4.58 7. 2 4.52 7. 8 4.46 7.14 4.40 7.20 4.33 7.27 4.27 7.33 4.20 7.40 55 4.56 7. 4 4.49 7.11 4.43 7.17 4.37 7.23 4.30 7.30 4.23 7.37 4.16 7.44 56 4.53 7. 7 4.47 7.13 4.40 7.20 4.33 7.27 4.26 7.34 4.19 7.41 4.12 7.48 57 4.50 7.10 4.44 7.16 4.37 7.23 4.30 7.30 4.23 7.37 4.15 7.45 4. 8 7.52 58 4.47 7.13 4.40 7.20 4.33 7.27 4.26 7.34 4.18 7.42 4.11 7.49 4. 3 7.57 59 4.44 7.16 4.37 7.23 4.30 7.30 4.22 7.38 4.14 7.46 4. 6 7.54 3.58 8. 2 8. 8 60 4.41 7.19 4.34 7.26 4.26 7.34 4.18 7.42 4. 9 7.51 4. 1 7.59 3.52 61 4.38 7.22 4.30 7.30 4.22 7.38 4.13 7.47 4. 4 7.56 3.55 8. 5 3.46 8.14 62 4.34 7.26 4.26 7.34 4.17 7.43 4. 8 7.52 3.59 8. 1 3.49 8.11 3.40 8.20 63 4.30 7.30 4.21 7.39 4.12 7.48 4. 3 7.57 3.53 8. 7 3.43 8.17 3.33 8.27 64 4.26 7.34 4.17 7.43 4. 7 7.53 3.57 8. 3 3.47 8.13 3.36 8.24 3.25 8.35 65 4.21 7.39 4.12 7.48 4. 1 7.59 3.51 8. 9 3.40 8.20 3.28 8.32 3.16 8.44 66 4.18 7.42 4. 6 7.54 3.55 8. 5 3.44 8.16 3.32 8.28 3.20 8.40 3. 7 8.53 m\ 4.14 7.46 4. 3 7.57 3.52 8. 8 3.40 8.20 3.28 8.32 3.15 8.45 3. 1 8.59 Lat Sett Ris. Sett Ris. Sett Ris. Sett Ris. Sett Ris. Sett Ris. Sett. Ria. LATITUDE A] so DECLINATION OF CONTRARY NAMES. 1 TABLE XVI. 83 APPARENT TIME OF THE SUN'S RISING AND SETTING. 3 at DECLINATION OF THE SAME NAME AS THE LATITUDE. 1 18° 1 19° 20° 21° 22° 23° 2310 1 Ris. SetL Ris. Sett Ris. Sett Ris. Sett Ris. Sett Ris. Sett Ris. Sett o H. M. H. M. B. M. H. M. H. M. H. M. H. M. H. M. H. M. H. M. H. M. H. M H M. H. U. 6. 6. 6. 6. 6. 6. 6. 6. 6. 6. 6. 6. 6. 6. 2 5.58 6. 2 5.58 6. 2 5.58 6. 2 5.57 6. 3 5.57 6. 3 5.57 6. 3 5.57 6. 3 4 5.55 6. 5 5.55 6. 5 5.55 6. 5 5.54 6. 6 5.54 6. 6 5.53 6. 7 5.53 6. 7 6 5.52 6. 8 5.52 6. 8 5.52 6. 8 5.51 6. 9 5.51 6. 9 5.50 6.10 5.50 6.10 8 5.50 6.10 5.49 6.11 5.49 6.12 5.48 6.12 5.47 6.12 5.47 6.13 5.46 6.14 10 5.47 6.13 5.46 6.14 5.46 6.15 5.45 6.16 5.44 6.16 5.43 6.17 5.43 6.17 12 5.44 6.16 5.44 6.17 5.43 6.18 5.42 6.19 5.41 6.20 5.40 6.20 5.39 6.21 14 5.41 6.19 5.40 6.20 5.39 6.21 5.38 6.22 5.37 6.23 5.36 6.24 5.35 6.25 16 5.39 6.21 5.37 6.23 5.36 6.24 5.35 6.25 5.33 6.27 5.32 6.28 5.31 6.29 18 5.36 6.24 5.34 6.26 5.33 6.27 5.31 6.29 5.30 6.30 5.28 6.32 5.28 6.32 20 5.33 6.27 5.31 6.29 5.30 6.30 5.28 6.32 5.26 6.34 5.24 6.36 5.24 6.36 21 5.31 6.29 5.30 6.30 5.28 6.32 5.26 6.34 5.24 6.36 5.22 6.38 5.22 6.38 22 5.30 6.30 5.28 6.32 5.26 6.34 5.24 6.36 5.22 6.38 5.21 6.39 5.20 6.40 23 5.28 6.32 5.26 6.34 5.24 6.36 5.22 6.38 5.21 6.39 5.19 6.41 5.18 6.42 24 5.27 6.33 5.25 6.35 5.23 6.37 5.21 6.39 5.19 6.41 5.16 6.44 5.15 6.45 25 5.25 6.35 5.23 6.37 5.21 6.39 5.19 6.41 5.17 6.43 5.14 6.46 5.13 6.47 26 5.24 6.36 5.21 6.39 5.19 6.41 5.17 6.43 5.15 6.45 5.12 6.48 5.11 6.49 27 5.22 6.38 5.20 6.40 5.17 6.43 5.15 6.45 5.12 6.48 5.10 6.50 5. 9 6.51 28 5.20 6.40 5.18 6.42 5.15 6.45 5.13 6.47 5.10 6.50 5. 8 6.52 5. 7 6.53 29 5.18 6.42 5.16 6.44 5.13 6.47 5.11 6.49 5. 8 6.52 5. 6 6.54 5. 4 6.56 30 5.17 6.43 5.14 6.46 5.11 6.49 5. 9 6.51 5. 6 6.54 5. 3 6.57 5. 2 6.58 31 5.15 6.45 5.12 6.48 5. 9 6.51 5. 7 6.53 5. 4 6.56 5. 1 6.59 5. 7. 32 5.13 6.47 5.10 6.50 5. 7 6.53 5. 4 6.56 5. 2 6.58 4.59 7. 1 4.57 7. 3 33 5.11 6.49 5. 8 6.52 5. 5 6.55 5. 2 6.58 4.59 7. 1 4.56 7. 4 4.55 7. 5 34 5. 9 6.51 5. 6 6.. 54 5. 3 6.57 5. 7. 4.57 7. 3 4.53 7. 7 4.52 7. 8 35 5. 7 6.53 5. 4 6.56 5. 1 6.59 4.58 7. 2 4.54 7. 6 4.51 7. 9 4.49 7.11 36 5. 5 6.55 5. 2 6.58 4.59 7. 1 4.55 7. 5 4.52 7. 8 4.48 7.12 4.46 7.14 37 5. 3 6.5» 5. 7. 4.56 7. 4 4.53 7. 7 4.49 7.11 4.45 7.15 4.44 7.16 38 5. 1 6.59 4.58 7. 2 4.53 7. 7 4.50 7.10 4.46 7.14 4.43 7.17 4.41 7.19 39 4.59 7. 1 4.55 7. 5 4.51 7. 9 4.48 7.12 4.44 7.16 4.40 7.20 4.38 7.22 40 4.57 7. 3 4.53 7. 7 4.49 7.11 4.45 7.15 4.41 7.19 4.37 7.23 4.35 7.25 41 4.54 7. 6 4.50 7.10 4.46 7.14 4.42 7.18 4.38 7.22 4.33 7.27 4.31 7.29 42 4.52 7. 8 4.48 7.12 4.43 7.17 4.39 7.21 4.35 7.25 4.30 7.30 4.28 7.32 43 4.49 7.11 4.45 7.15 4.41 7.19 4.36 7.24 4.31 7.29 4.27 7.33 4.24 7.36 44 4.47 7.13 4.42 7.18 4.38 7.22 4.33 7.27 4.28 7.32 4.23 7.37 4.21 7.39 45 4.44 7.16 4.39 7.21 4.35 7.25 4.30 7.30 4.25 7.35 4.20 7.40 4.17 7.43 46 4.41 7.19 4.36 7.24 4.31 7.29 4.26 7.34 4.21 7.39 4.16 7.44 4.13 7.47 47 4.3S 7.22 4.33 7.27 4.28 7.32 4.23 7.37 4.17 7.43 4.12 7.48 4. 9 7.51 48 4.35 7.25 4.30 7.30 4.25 7.35 4.19 7.41 4.13 7.47 4. 7 7.53 4. 5 7.55 49 4.32 7.28 4.27 7.33 4.21 7.39 4.15 7.45 4. 9 7.51 4. 3 7.57 4. 8. 50 4.29 7.31 4.23 7.37 4.17 7.43 4.11 7.49 4. 5 7.55 3.58 8. 2 3.55 8. 5 51 4.25 7.35 4.19 7.41 4.13 7.47 4. 7 7.53 4. 8. 3.54 8. 6 3.50 8.10 52 4.22 7.38 4.15 7.45 4. 9 7.51 4. 2 7.58 3.55 8. 5 3.48 8.12 3.45 8.15 53 4.18 7.42 4.11 7.49 4. 4 7.56 3.58 8. 2 3.50 8.10 3.43 8.17 3.39 8.21 54 4.14 7.46 4. 7 7.53 4. 8. 3.52 8. 8 3.45 8.15 3.37 8.23 3.33 8.27 55 4. 9 7.51 4. 2 7.5S 3.55 8. 5 3.47 8.13 3.39 8.21 3.31 8.29 3.27 8.33 56 4. 5 7.55 3.57 8. 3 3.49 8.11 3.41 8.19 3.33 8.27 3.24 8.36 3.20' 8.40 57 '4. 8. 3.52 8. 8 3.44 8.16 3.35 8.25 3.26 8.34 3.17 8.43 3.12 8.18 58 3.55 8. 5 3.46 8.14 3.38 8.22 3.28 8.32 3.19 8.41 3. 9 8.51 3. 4 8.56 59 3.49 8.11 3.40 8.20 3.31 8.29 3.21 8.39 3.11 8.49 2. 9. 2.55 9. 5 60 3.43 8.17 3.34 8.26 3.24 8.36 3.13 8.47 3. 2 8.58 2.51 9. 9 2.45 9.15 61 3.36 8.24 3.26 8.34 3.16 8.44 3. 5 8.55 2.53 9. 7 2.40 9.20 2.34 9.26 62 3.29 8.31 3.18 8.42 3. 7 8.53 2.55 9. 5 2.42 9.18 2.28 9.32 2.21 9.39 63 3.22 8.38 3.10 8.50 2.58 9. 2 2.44 9.16 2.30 9.30 2.14 9.46 2. 6 9.54 64 3.13 8.47 3. 9. 2.47 9.13 2.32 9.28 2.16 9.44 1.58 10. 2 1.48 10.12 65 3. 3 8.57 2.50 9.10 2.35 9.25 2.18 9.42 2. 10. 1.38 10.22 1.26 10.34 66 2.53 9. 7 2.37 9.23 2.21 9.39 2. 2 9.58 1.39 10.21 1.10 10.50 0.51 ill. 9 66 ^2.46 9.14 2.30 9.30 2.12 9.48 1.51 10. 9 1.26 10.34 0.48 11.12 0. 12. Lat. Sett Ris. Sett. Ris. Sett Ris. Sett Ris. Sett Ris. Sett Ris. Sett Ris. LATITUDE AND DECLINATION OF OOKTBAKY NAMES. 84 TABLE XVII. ALTITUDES BY WHICH THE APPARENT TIME MAY BE FOUND WITH THE GREATEST ACCURACY. Lat DBCLINXTTON OF THE OBJECT, OF THE SAME NJIME AS THE LA.TITUDE. 1 Lat 2° 40 6° 8° ] 10°] 12°] [40 [6° 1 8° 20°; 12° 240 ', 260 28°; 30°; 32° 34° ; 36°. 38° 10° o o 1 30 14 10 7 6 5 4 4 3 3 3 2 2 2 2 2 2 2 2 2 1 2 90 30 19 15 12 10 8 7 6 6 5 5 5 4 4 4 4 3 3 3 2 3 42 49 30 22 18 15 12 11 10 9 8 7 7 6 6 6 5 5 5 5 3 4 30 90 42 30 24 20 17 15 13 12 11 10 9 9 8 8 7 7 7 6 4 5 24 53 56 39 30 25 21 18 16 15 13 12 11 11 10 9 9 9 8 8 5 6 20 42 90 49 37 30 26 22 20 18 16 15 14 13 12 11 11 10 10 9 6 7 17 35 59 61 45 36 30 26 23 21 19 17 16 15 14 13 13 12 11 11 7 8 15 30 49 90 53 42 35 30 27 24 22 20 19 17 16 15 14 14 13 13 8 9 12 26 42 63 64 49 40 34 30 27 25 23 21 20 18 17 16 15 15 14 9 10 11 24 37 53 90 57 46 39 34 30 28 25 23 22 20 19 18 17 16 16 10 11 10 22 33 47 66 67 52 44 38 34 31 28 26 24 22 21 20 19 18 17 11 12 10 20 30 42 59 90 59 49 42 37 34 31 28 26 25 23 22 21 20 19 12 13 9 18 28 38 51 68 68 55 47 41 37 34 31 29 27 25 24 23 21 20 13 14 8 17 20 35 46 59 90 61 52 45 40 37 33 31 29 27 26 24 23 22 14 15 8 16 24 33 42 53 69 70 57 49 44 40 36 34 31 29 28 26 25 24 15 16 7 15 22 30 39 49 61 90 63 54 47 43 39 36 33 31 30 28 27 25 16 17 7 14 21 28 36 45 56 71 71 59 51 46 42 39 36 34 32 30 28 27 17 18 6 13 20 27 34 42 52 63 90 65 56 49 45 41 38 36 34 32 30 29 18 19 6 12 19 25 32 40 48 58 72 72 60 53 48 44 41 38 36 34 32 30 19 20 6 12 18 24 31 37 45 54 65 90 66 57 51 47 43 40 38 36 34 32 20 21 6 11 17 23 29 35 42 50 60 73 73 62 55 50 46 43 40 38 36 34 21 22 5 11 16 22 28 34 40 47 56 66 90 67 59 53 49 45 42 40 38 36 22 23 5 10 16 21 26 32 38 45 52 61 73 74 63 57 51 48 44 42 39 37 23 24 5 10 15 20 25 31 36 43 49 57 67 90 68 60 54 50 47 44 41 39 24 25 5 9 14 19 24 29 35 41 47 54 62 74 75 64 58 53 49 46 43 41 25 26 5 9 14 19 23 28 33 39 45 51 59 68 90 69 61 56 52 48 45 43 26 27 4 9 13 18 22 27 32 37 43 49 56 64 75 76 65 59 54 51 48 45 27 28 4 9 13 17 22 26 31 36 41 47 53 60 69 90 70 62 57 53 50 47 28 29 4 8 12 17 21 25 30 35 40 45 51 57 65 76 76 66 60 56 52 49 29 30 4 8 12 16 20 25 29 34 38 43 49 54 61 70 90 71 64 58 54 51 30 31 4 8 12 16 20 24 28 33 37 42 47 52 58 66 76 77 67 61 57 53 31 32 4 8 11 15 19 23 27 32 36 40 45 50 56 62 71 90 71 64 60 56 32 33 4 7 11 15 19 22 26 31 35 39 43 48 54 60 67 77 77 68 62 58 33 34 4 7 11 14 18 22 26 30 34 38 42 47 52 57 63 72 90 72 65 61 34 35 3 7 10 14 18 21 25 29 33 37 41 45 50 55 61 68 77 78 69 63 35 36 3 7 10 14 17 21 24 28 32 36 40 44 48 53 58 65 72 90 73 66 36 37 3 7 10 13 17 20 24 27 31 35 39 43 47 51 56 62 68 78 78 70 37 38 3 7 10 13 16 20 23 27 30 34 38 41 45 50 54 59 65 73 90 74 38 39 3 6 10 13 16 19 23 26 29 33 37 40 44 48 53 57 62 69 78 78 39 40 3 6 9 12 16 19 22 25 29 32 36 39 43 47 51 55 60 66 73 90 40 42 3 6 9 12 15 18 21 24 28 31 34 37 41 45 48 52 57 62 67 74 42 44 3 6 9 12 15 17 20 23 26 29 33 36 39 43 46 50 54 58 62 68 44 46 3 6 8 11 14 17 20 23 25 28 31 34 38 41 44 48 51 55 59 63 46 48 3 5 8 11 14 16 19 22 24 27 30 33 36 39 42 46 49 52 56 60 48 50 3 5 8 10 13 16 18 21 24 27 29 32 35 38 41 44 47 50 54 57 50 52 3 5 8 10 13 15 18 20 23 26 28 31 34 37 39 42 45 48 51 55 52 54 2 5 7 10 12 15 17 20 22 25 28 30 33 36 38 41 43 46 49 53 54 56 2 5 7 10 12 15 17 19 22 24 27 29 32 35 37 40 42 45 48 51 56 68 2 5 7 9 12 14 17 19 21 24 26 29 31 34 36 39 41 44 47 49 58 60 2 5 7 9 12 14 16 19 21 23 26 28 30 33 35 38 40 43 45 48 60 62 2 5 7 9 11 14 16 18 20 23 25 27 80 32 35 37 39 42 44 47 62 64 2 4 7 9 11 13 16 18 20 22 25 27 29 31 34 36 39 41 43 46 64 6Q 2 4 7 9 11 13 15 18 20 22 24 26 29 31 33 35 38 40 42 45 66 68 2 4 4 6 6 9 11 13 15 17 19 22 24 26 28 30 33 35 37 39 42 44 68 70 2 9 11 13 15 17 19 21 23 26 28 30 32 34 36 39 41 43 70 72 2 4 6 8 11 13 15 17 19 21 23 25 28 30 32 34 35 38 40 42 72 74 2 4 6 8 10 12 15 17 19 21 23 25 27 29 31 33 35 38 40 42 74 76 2 4 6 8 10 12 14 16 19 21 23 25 27 29 31 33 35 37 39 42 76 80 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 35 37 39 41 80 ^ 2° 40 6° 8° 10° 12° 14° 16° 18° •20° 22° 24° 26° 28° 30° 32° 34° 36° 38° 40° TABLE XVIII. 86 1 FOR FINDING THE APPARENT TIME OF 24 OF THE PRINCIPAL STARS PASSING | THE MERIDIAN THROUGHOUT THE YEAR. JANUARY. DAT. DAT. DAT. DAY. DAT. DAT. DAT. DAT. DAT. DAT. DAT. NAMES. 1 3 6 9 12 15 18 21 24 27 30 H. M. H. M. H. M. H. M. H. ;u. H. M. H. M. H. M. B. M. H. M. H. M. Polar Stab, . . . 6.2D 6.12 5.58 5.45 5.32 5.19 5. 6 4.54 4.41 4.29 4.16 ACHERNAR, .... 6.46 6.38 6.24 6.11 5.58 5.45 5.32 5.20 5. 7 4.55 4.42 Aldebaran, . . . 9.42 9.34 9.20 9. 7 8.54 8.41 8.28 8.16 8. 3 7.51 7.38 Capella, 10.20 10.12 9.58 9.45 9.32 9.19 9. 6 8.54 8.41 8.29 8.16 RiGEL, 10.22 10.14 10. 9.47 9.34 9.21 9. 8 8.56 8.43 8.31 8.18 Betelguese, . . . 11. 1 10.53 10.39 10.26 10.13 10. 9.47 9.35 9.22 9.10 8.57 Canopus, 11.35 11.27 11.13 11. 10.47 10.34 10.21 10. 9 9.56 9.44 9.31 SiRIUS, 11.53 11.45 11.31 11.18 11. 5 10.52 10.39 10.27 10.14 10. 2 9.49 Castor, 12.39 12.31 12.17 12. 4 11.51 11.38 11.25 11.13 11. 10.48 10.35 Pollux, 12.50 12.42 12.28 12.15 1202 11.49 11.36 11.24 11.11 10.59 10.46 ■' Argus, 14.25 14.10 14. 3 13.50 13.37 13.24 13.11 12.59 12.46 12.34 13.21 Regulus, 15.15 15. 6 14.53 14.40 14.27 14.14 14. 1 13.49 13.36 13.24 13.11 Dubhe, 16. 9 16. 15.47 1.5.34 15.21 15. 8 14.55 14.43 14.30 14.18 14. 5 Cross, foot Star. 17.33 17.25 17.11 16.58 16.45 16.32 16.19 16. 7 15.54 15.42 15.29 Spica, 18.31 18.23 18. 9 17.56 17.43 17.30 17.17 17. 5 16.52 16.40 16.27 Arcturus, .... 19.23 19.14 19. 1 18.48 18.35 18.22 18. 9 17.57 17.44 17.32 17.19 Antares, 21.34 21.25 21.12 20.59 20.46 20.33 20.20 20. 8 19.55 19.43 19.30 Vega, 23.46 23.37 23.24 23.11 22.58 22.45 22.32 22.20 22. 7 21.55 21.42 Altair, 0.58 0.49 0.36 0.23 0.10 23.57 23.44 23.32 23.19 23. 7 22.54 Pavonis, 1.28 1.19 1. 6 0.53 0.40 0.27 0.14 0. 2 23.49 23.37 23.24 Ctgni, 1.50 1.41 1.28 1.15 1. 2 0.49 0.36 0.24 0.11 23.59 23.46 Gruis, 3.14 3. 5 2.52 2.39 2.26 2.13 2. 1.48 1.35 1.23 1.10 Fomalhaut, . . . 4. 4 3.55 3.42 3.29 3.16 3. 3 2.50 2.38 2.25 2.13 2. Pegasi, 4.12 4. 3 3.50 3.37 3.24 3.11 2.58 2.46 2.33 2.21 2. 8 FEBRUARY. I names. 1 3 6 9 12 15 18 21 24 27 30 H. M. H. M. B. M. H. M. H. U. H. M. H. M. H. M. H. M. B. H. H. M. Polar Star, . . . 4. 8 4. 3.48 3.36 3.24 3.12 3. 1 2.49 2.38 2.26 0. Achernar, . . . . 4.34 4.26 4.14 4. 2 3.50 3.38 3.27 3.15 3. 4 2.52 0. Aldebaran, . . . 7.30 7.22 7.10 6.58 6.46 6.34 6.23 6.11 6. 5.48 0. Capella, 8. 8 8. 7.48 7.36 7.24 7.12 7. 1 6.49 6.38 6.26 RiGEL, 8.10 8. 2 7.50 7.38 7.26 7.14 7. 3 6.51 6.40 6.28 Betelguesk, . . . 8.49 8.41 8.29 8.17 8. 5 7.53 7.42 7.30 7.19 7. 7 Canopus, 9.23 9.15 9. 3 8.51 8.39 8.27 8.16 8. 4 7.53 7.41 SiRIUS, 9.41 9.33 9.21 9. 9 8.57 8.45 8.34 8.22 8.11 7.59 Castor, 10.27 10.19 10. 7 9.55 9.43 9.31 9.20 9. 8 8.57 8.45 Pollux, 10.38 10.30 10.18 10. 6 9.54 9.42 9.31 9.19 9. 8 8.56 Argus, 12.14 12. 6 11.54 11.42 11.30 11.18 11. 7 10.55 10.44 10.32 Regulus, 13. 3 12.55 12.43 12.31 12.19 12. 7 11.56 11.44 1133 11.21 Dubhe, 13.57 13.49 13.37 13.25 13.13 13. 1 12.50 12.38 12.27 12.15 Cross, foot Star, 15.21 15.13 15. 1 14.49 14.37 14.25 14.14 14. 2 13.51 13 39 Spica, 16.19 16.11 15.51) 1 5.47 15.35 15.23 lo.l2 15. 14.49 14.37 Arcturus, .... 17.11 17. 3 16.51 16.39 16.27 16.15 16. 4 15.52 15.41 15.29 Antares, 19.22 19.14 19. 2 18.50 ls.38 18.26 18.15 18. 3 17.52 17.40 Vega, 21.34 21.26 21.14 21. 2 20.50 20.38 20.27 20.15 20. 4 19.52 Altair, 22.46 22.38 22.26 22.14 22. 2 21.50 21.39 21.27 21.16 21. 4 Pavonis, 23.16 23. 8 22.56 22.44 22.32 22.20 22. 9 21.57 21.46 21.34 Ctgni, 23.38 23.30 23.18 23. 6 22.54 22.42 22.31 22.19 22. 8 21.56 Gruis, 1. 1 0.53 0.41 0.29 0.17 0. 5 23.54 23.42 23.31 23.19 Fomalhaut, . . . 1.52 1.44 1.32 1.20 1. 8 0.56 0.45 0.33 0.22 0.10 Pegasi, 2. 1..52 1.40 1.28 l.ic, 1. 4 0..53 0.41 0.30 0.18 86 TABLE XVIII. FOR FINDING THE APPARENT TIME OF 24 OF THE PRINCIPAL 3TARS PASSING THE MERIDIAN THROUGHOUT THE YEAR. MARCH. NAMSS. Polar Star, achernar, . Aldebaran, Capella, . RiGEL, . . Betelguese Canopus, . SiRIUS, . . Castor, , Pollux, . Argus, . . Regulus, Dubhe, , Cross, foot Spica, . , Arcturus, Antares, . Veoa, . . Altair, . Pavonis, , Cygni, . Gruis, . Fomalhaut, Peoasi, . . . Star DAT. 1 H. M. 2.18 2.44 5.39 6.17 6.19 6.56 7.30 7.48 8.34 8.45 10.21 11.13 12. 7 13.31 14.29 15.21 17.33 19.45 20.57 20.27 21.4!> 23.12 0. 3 0.11 DAT. 3 H. M 2.10 2.36 5.31 6. 9 6.11 6.48 7.22 7.40 8.26 8.37 10.13 11. 5 11.59 13.23 14.21 15.13 17.25 19.37 20.49 21.19 21.41 23. 4 23.55 0. 3 DAY. 6 H. M. 1..59 2.25 5.20 5.58 6. 6.37 7.11 7.29 8.15 8.26 10. 2 10.54 11. 4S 13.12 14.10 15. 2 17.14 19.26 20.38 21. 8 21.30 22.53 23.44 23.52 DAr. 9 DAY. 12 H. M. 1.48 2.14 5. 9 5.47 5.49 6.27 7. 1 7.19 8. 4 8.15 9.51 10.43 11.37 13. 1 13.59 14.51 17. 3 19.15 20.27 20.57 21.19 22.42 23.33 23.41 H. 1.37 2. 3 4.58 5.36 5.38 6.15 6.49 7. 7 7.53 8. 4 9.40 10.32 11.26 12.50 13.48 14.40 16.52 19. 4 20.16 20.46 21. 8 22.31 23.22 23.30 DAY. 15 H. M. 1.26 1.52 4.47 5.25 5.27 6. 4 6.38 6.56 7.42 7.53 9.29 10.21 11.15 12.39 13.37 14.29 16.41 18.53 20. 5 20.35 20.57 22.20 23.11 23.19 DAY. 18 H. M. 1.15 1.41 4.36 5.14 5.16 5.53 6.27 6.45 7.31 7.42 9.18 10.10 11. 4 12.28 13.26 14.18 16.30 18.42 19.54 20.24 20.46 22. 9 23. 23. 8 DAY. 21 H. M 1. 4 1.30 4.25 5. 3 5. 5 5.42 6.16 6.34 7.20 7.31 9. 7 9.59 10.53 12.17 13.15 14. 7 16.19 18.31 19.43 20.13 20.35 21.58 22.49 22.57 DAY. 24 H. M. 0.53 1.19 4.14 4.52 4.54 5.31 6. 5 6.23 7. 9 7.20 8.56 9.49 10.42 12. 6 13. 4 13.56 16. 8 18.20 19.32 20. 2 20.24 21.47 22.38 22.46 DAY. DAY. 27 30 B. M 0.43 1. 9 4. 4 4.42 4.44 5.21 5.55 6.13 6.. 59 7.10 8.46 9.38 10.32 11.56 12.54 13.46 15.58 18.10 19.22 19.52 20.14 21.37 22.28 22.36 H. I 0.32 0.58 3.53 4.31 4.33 5.10 5.44 6. 2 6.48 6.59 8.35 9.27 10.21 11.45 12.43 l;^.35 15.47 17.59 19.11 19.41 20. 3 21.26 22.17 22.25 APRIL, NAMES. Polar Star, . AcHERNAR, . . Aldebaram, . Capella, . . . RiGEL, .... Betelguese, . Canopus, . SiRIUS, . . Castor, . Pollux, . Argus, . . Regulus, , 1 Dubhe, Cross, foot Star, Spica, Arcturus, . . . . Antares, . . . . Vega, Altair, . . Pavonis, . . Cygni, . . . Gruis, . . . Fomalhaut, Pegasi, . . B. M 0.24 0.50 3.46 4.24 4.26 5. 5 5.39 5.57 6.43 6.54 8.30 9.19 10.13 11.37 12.35 13.27 15.38 17.50 19. 2 19.32 19.54 21.17 22. 7 22.15 B. M. 0.17 0.43 3.39 4.17 4.19 4.58 5.32 5.50 6.36 6.47 8.23 9.12 10. 6 11.30 12.28 13.20 15.31 17.43 18.55 19.25 19.47 21.10 22. 22. 8 B. M 0. 6 0.32 3.28 4. 6 4. 8 4.47 5.21 5.39 6.25 6.36 8.12 9. 1 9.55 11.19 12.17 13. 9 15.20 17.32 18.44 19.14 19.36 20.59 21.49 21.57 B. M. 23.55 0.21 3.17 3.55 3.57 4.36 5.10 5.28 .6.14 6.25 8. 8.50 9.44 11. 8 12. 6 12.58 1.5. 9 17.21 18.32 19. 3 19.25 20.48 21.38 21.46 12 B. M 23.44 0.10 3. 6 3.44 3.46 4.25 4.59 5.17 6. 3 6.14 7.50 8.39 9.33 10.57 11.55 12.47 14.58 17.10 18.22 18.52 19.14 20.37 21.27 21.35 15 B. 23.33 23.59 2.55 3.33 3.35 4.14 4.48 5. 6 5.52 6. 3 7.39 8.28 9.22 10.46 11.44 12.36 14.47 16.59 18.11 18.41 19. 3 20.26 21.16 21.24 18 B. M. 23.22 23.48 2.44 3.22 3.24 4. 3 4.37 4.55 5.41 5.52 7.28 8.17 21 B. M. 23.11 23.37 2.33 3.11 3.13 3.52 9.11 10.35 11.33 12.25 14.36 16.48 18. 18.30 18.52 20.15 21. 5 21.13 4.26 4.44 5.30 5.41 7.17 8. 6 9. 10.24 11.22 12.14 14.25 16.37 17.49 18.19 18.41 20. 4 20.54 21. 2 24 B. M 23. 23.26 2.22 3. 3. 2 3.41 4.15 4.33 5.19 5.30 7. 6 7.55 8.49 10.13 11.11 12. 3 14.14 16.26 17.38 18. 8 18,30 19.53 20.43 20.52 27 a. M. 22.48 23.14 2.10 2.48 2.50 3.29 4. 3 4.21 5. 7 5.18 6.54 7.43 30 a. M. 22.37 23. 3 1.59 2.37 2.39 3.18 8.37 10. 1 10.59 11.51 14. 2 16.14 17.26 17.56 18.18 19.41 20.31 20.39 3.52 4.10 5.56 5. 7 6.43 7.32 8.26 9.50 10.48 11.40 13.51 16. 17.15 17.45 18. 7 19.30 20.20 20.28 TABLE XVIII. 87 FOR FINDING THE APPARENT TIME OF 24 OF THE PRINCIPAL STARS PASSING THE MERIDIAN THROUGHOUT THE YEAR. MAY. NAMES. Polar Star, . achernar, . . Aldebaran, . Capella, . . . RiOEL, .... Betelotjese, . Canopus, , Sirius, . , Castor, , Pollux, , Argus, . , Reoulus, DAT. H. M. 22.33 22.59 1.55 2.33 2.35 3.14 DAY. 3 H. M. 22.26 22.52 1.48 2.26 2.28 3. 7 DUBHE, Cross, foot Star. Spica, Arcturus, . . . . Antares, Vega, Altair, Pavonis, Cygni, Gruis, fomalhaut, . . . Pegasi, 3.48 4. 6 4.52 5. 3 6.39 7.28 8.22 9.46 10.44 11.36 13.47 15.59 17.11 17.41 18. 3 19.26 20.17 20.25 DAY. 6 H. M. 22.14 22.40 1.36 2.14 2.16 2.55 3.41 3.59 4.45 4.56 6.32 7.21 8.15 9.39 10.37 11.29 13.40 15.52 17. 4 17.34 17.56 19.19 20.10 20.18 3.29 3.47 4.33 4.44 6.20 7. 9 8. o 9.27 10.25 11.17 13.28 15.40 DAY. 9 DAY. 12 H. M. 22. 2 22.28 1.24 2. 2 2. 4 2.43 3.17 3.35 4.21 4.30 6. 8 6.57 7.51 9.15 10.13 11. 5 13.16 15.28 H. M. 21.51 22.17 1.13 1.5 1.53 2.32 3. 6 3.24 4.10 4.21 5.57 6.46 DAY. 15 H. M. 21.39 22.06 1.01 1.39 1.41 2.20 DAY. 18 H. I 21.27 21.53 0.49 1.27 1.29 2. 8 DAY. 21 16.52 17.22 17.34 19. 7 19.58 20. 6 16.40 17.10 17.22 18.55 19.46 19.54 7.40 9. 4 10. 2 10.54 13. 5 15.17 10.29 16.59 17.11 18.44 19.35 19.43 2.54 3.12 3.58 4. 9 5.45 6.34 7.28 8.52 9.50 10.42 12.53 1.5. 5 16.17 16.47 16.59 18.32 19.23 19.31 2.42 3. 3.46 3.57 5.33 6.22 7.16 8.40 9.38 10.30 12.41 14.53 H. M 21.15 21.41 0.37 1.15 1.17 1.56 DAT. 24 H. M 21. 3 21.29 0.25 1. 3 1. 5 1.44 DAY. 27 2.30 2.58 2.34 3.45 5.21 6.10 7. 4 8.28 9.26 10.18 12.29 14.41 16. 5 16.35 16.47 18.20 19.11 19.19 2.18 2.46 2.22 3.33 5. 9 5.58 6.52 8.16 9.14 10. 6 12.17 14.29 H. M. 20.51 21.17 0.13 0.51 0.53 1.32 DAT. 30 H. M. 20.39 21.05 0.01 0.39 0.41 1.20 2. 6 2.34 2.10 3.21 4.57 5.46 6.40 8. 4 9. 2 9.54 12. 5 14.17 15.53 16.23 16.35 18. 8 18.59 19. 7 15.41 16.11 16.23 17.56 18.47 18.55 1.54 2.22 1.58 3. 9 4.45 5.34 6.28 7.52 8.50 9.42 11.53 14. 5 15.29 15.59 16.11 17.44 18.35 18.43 15.17 15.47 15.59 17.32 18.23 18.31 JUNE. NAMES. Polar Star, . Aohernar, . . Aldebaran, . Capella, . . . RiGEL, .... Betelguese, . Canopus, Sirius, . Castor, Pollux, Argus, . Regulus, 1 H. M. 20.31 20.57 23.53 0.31 0.33 1.12 H. M. 20.22 20.48 23.44 0.22 0.24 1. DuBHE, Cross, foot Star, Spica, Arcturus, . . . . Antares, Vega, Altair, . . Pavonis, . . Cygni, . . . Gruis, . . . Fomalhaut, Pkgasi,. . . 1 .46 2. 4 2.50 3. 1 4.37 5.26 6.20 7.44 8.42 9.34 11.45 13.57 15. 9 15.39 16. 1 17.24 18.15 18.23 1.39 1.55 2.41 2.52 4.28 5.17 6.11 7.35 8.:- 9.25 11.36 13.48 15. 15.30 15.52 17.15 18. 6 18.14 H. M. 20.10 20.36 23.32 0.10 0.12 0.51 1.25 1.43 2.29 2.40 4.16 5. 5 5.59 7.23 8.21 9.13 11.24 13.36 14.48 15.18 15.40 17. 3 17.54 18. 2 H. M. 19.58 20.24 23.22 23.58 0. 0.39 12 H. M. 19.45 20. 1 1 23. 9 23.45 23.49 0.26 1.13 1.31 2.17 2.28 4. 4 4.53 5.47 7.11 8. 9 9. 1 11.12 13 24 14.36 15. 6 15.28 16.51 17.42 17.50 1. 1.18 2. 4 2.15 3.51 4.40 5.34 6.58 7.56 8.58 10.59 13.11 14.23 14.53 15.15 16.38 17.29 17.37 15 H. M. 19.33 1 9.59 22.57 23.33 23.37 0.14 0.48 1. 6 1.52 2. 3 3.39 4.28 5.22 6.46 7.44 8.46 10.47 12.59 14.11 14.41 15. 3 16.26 17.17 17.25 18 H. M. 19.20 19.46 22.44 23.20 23.24 0. 1 0.35 0.53 1.39 1.50 3.26 4.15 5. 9 6.33 7.31 8.33 10. S4 12.46 13.58 14.28 14.50 16.13 17. 4 17.12 21 H. M. 19. 8 19.34 22.32 23. 8 23.12 23.59 0.23 0.41 1.27 1.38 3.14 4. 3 4.57 6.21 7.19 8.21 10.22 12.34 13.46 14.16 14.38 16. 1 16.52 17. 24 H. M. 18.55 19.21 22.19 22.55 22.59 23.46 0.10 0.28 1.14 1.25 3. 1 3.50 4.44 6. 8 7. 6 8. 8 10.10 12.21 13.33 14. 3 14.25 15.48 16.39 16.47 27 H. M. 18.43 19. 9 22. 7 22.43 22.47 23.34 23.48 0.16 1. 2 1.13 2.49 3.38 4.32 5.56 6.54 7.56 9.57 12. 9 13.21 13.51 14.13 15.36 16.27 16.35 30 H. M. 18.30 18.56 21.54 22.30 22.34 23.21 23.35 0. 3 0.49 1. 2.36 3.25 4.19 5.43 6.41 7.43 9.44 11.56 13. 8 13.38 14. 15.23 16.14 16.22 88 TABLE XVIII. FOR FINDING THE APPARKNT TIME OF 24 OF THE PRINCIPAL STARS PASSING THE MERIDIAN THROUGHOUT THE YEAR JULY. NAMES. Polar Star, achkrnar, . Aldebaran, Capella, , RlOEL, . , Betelguese Canopus, . SiRIUS, . . Castor, , Pollux, , Argus, . . Regulus, DUBHK, Cross, foot Spica, . . Arcturus, Antares, . Vega, . . Altair, . . Pavonis, . Ctgni, . . Gruis, . . fomalhaut, Pegasi, . . . Star, DAT. 1 H. H. 18.26 18.52 21.48 22.26 22.28 23. 7 23.41 23.59 0.45 0.56 2.32 3.21 4.17 5.39 6.37 7.29 9.40 11.52 13. 4 13.34 13.56 15.19 16.10 16.18 DAT. 3 H. M. 18.18 18.44 21.40 22.18 22.20 22.59 23.33 23.51 0.37 0.48 2.24 3.13 4. 9 5.31 6.29 7.21 9.32 11.44 12.56 13.26 13.48 15.11 16. 2 16. 8 DAT. 6 B. M. 18. 6 18.32 21.28 22. 6 22. 8 22.47 23.21 23.39 0.25 0.36 2.12 3. 1 3.57 5.19 6.17 7. 9 9.20 11.32 12.44 13.14 13.36 14.59 15.50 15.56 DAT. 9 DAT. 12 H. U. 17.53 18.19 21.15 21.53 2155 22.34 23. 8 23.26 0.12 0.23 1.59 2.48 3.44 5. 6 6. 4 6.56 9. 7 11.19 12.31 13. 1 13.23 14.46 15.37 15.43 H. M. 17.41 18. 7 21. 3 21.41 21.43 22.22 22.56 23.14 0. 0.11 1.47 2.36 3.32 4.54 5.52 6.44 8.55 11. 7 12.19 12.49 13.11 14.34 15.25 15.31 DAT. 15 H. M 17.29 17.55 20.51 21.29 21.31 22.10 22.44 23. 2 23.48 23.59 1.35 2.24 3.20 4.42 5.40 6.32 8.43 10.55 12. 7 12.37 12.59 14.22 15.13 15.19 DAT. 18 H. U. 17.17 17.43 20.39 21.17 21.19 21.58 22.32 22.50 23.36 23.47 1.23 2.12 3. 8 4.30 5.28 6.20 8.31 10.43 11.55 12.25 12.47 14.10 15. 1 15. 7 DAT. 21 H. M 17. 5 17.31 20.27 21.05 21. 7 21.46 22.20 22.38 23.24 23.35 1.11 2. 2.56 4.18 5.16 6. 8 8.19 10.31 11.43 12.13 12.35 13.58 14.49 14.55 DAT. 24 16.53 17.19 20.15 20.53 20.55 21.34 22. 8 22.26 23.12 23.23 0.59 1.48 2.44 4. 6 5. 4 5.56 8. 7 10.19 11.31 12. 1 12.28 13.46 14.37 14.43 DAT. DAT. 27 30 H. H. 16.41 17. 7 20. 3 20.41 20.43 21.22 21.56 22.14 23. 23.11 0.47 1.36 2.32 3.54 4.52 5.44 7.55 10. 7 11.19 11.49 12.11 13.34 14.25 14.31 H. M. 16.29 16.55 19.51 20.29 20.31 21.10 21.44 22. 2 22.48 22.59 0.35 1.24 2.20 3.42 4.40 5.32 7.43 9.55 11. 7 11.37 11.59 13.22 14.13 14.19 AUGUST. NAMES. Polar Star, . . . achernar, . . . . Aldebaran, . . . Capella, RiGEL, Betelguese, . . . Canopus, SiRIUS, Castor, Pollux, Argus, Regulus, DUBHB, Cross, foot Star, Spica, Arcturus, . . . . Antares, . . . . Vega, Altair, Pavonis, Cyoni, Gruis, Fomalhaut, . . . Pegasi, H. M. 16.21 16.47 19.43 20.21 20.23 21. 2 21.36 21.54 22.40 22.51 0.27 1.16 2.10 3.34 4.32 5.24 7.35 9.47 10.59 11.29 11.51 13.14 14. 5 14.13 H. M. 16.14 16.40 19.36 20.14 20.16 20.55 21.29 21.47 22.33 22.44 0.20 1. 9 2. 3 3.27 4.25 5.17 7.28 9.40 10.52 11.22 11.44 13. 7 13.58 14. 6 H. 16. 16.28 19.24 20. 2 20. 4 20.43 21.17 21.35 22.21 22.32 0. 8 0.57 1.51 3.15 4.13 5. 5 7.16 9.28 10.40 11.10 11.32 12.55 13.46 13.54 H. M. 15.51 16.17 19.13 19.51 19.53 20.32 21. 6 21.24 22.10 22.21 23.57 0.46 1.40 3. 4 4. 2 4.54 7. 5 9.17 10.29 10.. 59 11.21 12.44 13.35 13.43 12 H. M 15.39 16. 5 19.01 19.39 19.41 20.20 20.54 21.12 21.58 22. 9 2:^45 0.34 1.28 2.52 3.50 4.42 6.53 9. 5 10.17 10.47 11. 9 12.32 13.23 13.31 15 H. M, 15.28 15.54 18.50 19.28 19.30 20. 9 20.43 21. 1 21.47 21.58 23.34 0.23 1.17 2.41 3.39 4.31 6.42 8.54 10. 6 10.36 10.58 12.21 13.12 i:{.20 18 H. M. 15.17 15.43 18.39 19.17 19.19 19.58 21 20.32 20.50 21.36 21.47 23.23 0.12 1. 6 2.30 3.28 4.20 6.31 8.43 9.55 10.25 10.47 12.10 13, 1 13. 9 H. M. 15. 6 15.32 18.28 19. 6 19. 8 19.47 24 20.21 20.39 21.25 21.36 23.12 0. 1 0.55 2.19 2.17 4. 9 6.20 8.32 9.44 10.14 10.36 11.59 12.50 12.58 H. U. 14.54 15.20 18.16 18.54 18.56 19.35 27 20. 9 20.27 21.13 21.24 23. 23.49 0.43 2. 7 2. 5 3.57 6. 8 8.20 9.32 10. 2 10.24 11.47 11.38 12.46 H. M. 14.44 15. 9 18.05 18.44 18.45 19.24 19.58 20.16 21. 2 21.13 22.49 23.38 0.32 1.56 1..54 3.46 557 8. 9 9.21 9.51 10.13 11.36 11.27 12.35 30 H. M. 14.34 14.59 17.54 18.34 18.85 19.14 19.48 20. 6 20.52 21. 3 22.39 23.28 0.22 1.46 1.44 3.36 5.47 7.59 9.11 9.41 10. 3 11.26 11.17 12.25 TABLE XVIII. 89 FOE FINDING THE APPARENT TIME OF 24 OF THE PRINCIPAL STARS PASSING THE MERIDIAN THROUGHOUT THE YEAR. SEPTEMBER. NAMES. Polar Star, achernar, . Aldebaran, Capella, , RiGKL, . , Betelgxtese Canopus, . Smius, . . Castor, . Pollux, . Argus, . . Regulus, . DUBHE, . Cross, foot Spica, . . Arcturits, Antares,. Vega, . . Altair, . Pavonis, , Cyoni, . . Gruis, . , f jmalhaut, Peoasi, . . . Star DAT. 1 H. M. 14.25 14.51 17.47 18.25 18.27 19. 6 19.40 19.58 20.44 20.55 22.32 23.20 0.14 1.38 2.36 3.28 5.39 7.51 9. 3 9.33 9.55 11.18 12. 9 12.17 DAT. 3 H. M 14.18 14.44 17.40 18.18 18.20 18.59 19.33 19.51 20.37 20.48 22.24 23.13 0. 7 1.31 2.29 3.21 5.32 7.44 8.56 9.26 9.48 11.11 12. 2 12.10 DAT. 6 H. M. 14. 7 14.33 17.29 18. 7 18. 9 18.48 19.22 19.40 20.26 20.37 22.13 23. 2 23.56 1.20 2.18 3.10 5.21 7.33 8.45 9.15 9.37 11. 11.51 11.59 DAT. 9 a. M 13.56 14.22 17.18 17.56 17.58 18.37 19.11 19.29 20.15 20.26 22. 2 22.51 23.45 1. 9 2. 7 2.59 5.10 7.22 8.34 9. 4 9.26 10.49 11.40 11.48 DAT. 12 ,H. M. 13.46 14.12 17. 8 17.46 17.48 18.27 19. I 19.19 20. 5 20.16 21.52 22.41 23.35 0.59 1.57 2.49 5. 7.12 8.24 8.54 9.16 10.39 11.30 11.38 DAT. 15 H. M. 13.35 14. 1 16.57 17.35 17.37 18.16 18.50 19. 8 19.54 20. 5 21.41 22.30 23.24 0.48 1.46 2.38 4.49 7. 1 8.13 8.43 9. 5 10.28 11.19 11.27 DAT. 18 H. M. 13.24 13.50 16.46 17.24 17.26 18. 5 18.39 18.57 19.43 19.54 21.30 22.19 23.13 0.37 1.35 2.27 4.38 6.50 8. 2 8.32 8.54 10.17 11. 8 11.16 DAT. 21 a. M. 13.13 13.39 16.35 17.13 17.15 17.54 P\T. 24 a. 1 13. 2 13.28 16.24 17. 2 17. 4 17.43 18.28 18.46 19.32 19.43 21.19 22. 8 23. 2 0.26 1.24 2.16 4.27 6.39 7.51 8.21 8.43 10. 6 10.57 11. 5 18.17 18.35 19.21 19.32 21. 8 21.57 DAT. 27 H. M 12.52 13.18 16.14 16.52 16.54 17.33 18. 7 18.25 19.11 19.22 20.58 21.47 22.51 22.41 0.15 1.13 2. 5 4.16 6.28 7.40 8.10 8.32 9.55 10.46 10.54 DAT. 30 H. M. 12.41 13. 7 16. 3 16.41 16,43 17.22 17.56 18.14 19. 19.11 20.47 21.36 0. 1. 1.55 4. 6.18 7.30 8. 8.22 9.45 10.36 10.44 22.30 23.54 0.52 1.44 3.55 6. 7 7.19 \49 8.11 9.34 10.25 10.33 OCTOBER. NAMES. Polar Star, AcHERNAR, . Aldebaran, Capella, . RiGEL, . . Betbloitssk. Canopus, . SiRIUS, . , Castor, , Pollux, . Argus, . , Regulus, , DuBHE, . . Cross, foot Spioa, . . Arcturus, Antares, . Vega, . . Altair, . Pavonis, . Cygni, . . Gruis, . , Fomalhaut, Pegasi,. . . Star 1 a. M. 12.37 13. 3 15.59 16.37 16.39 17.18 17.52 18.10 18.56 19. 7 20.43 21.32 22.26 23.50 0.48 1.40 3.51 6. 3 7.15 7.45 8. 7 9.30 10.21 10.29 H. M. 12.30 12.56 15.52 16.30 16.32 17.11 17.45 18. 3 18.49 19. 20.36 21.25 22.19 23.43 0.41 1.33 3.44 5.56 7. 8 7.38 8. 7 9.23 10.14 10.22 a. M 12.19 12.45 15.41 16.19 16.21 17. 17.34 17.52 18.38 18.49 20.25 21.14 22. 8 23.32 0.30 1.22 3.33 5.45 6.57 7.27 7.56 9.12 10. 3 10.11 9 a. u. 12. 8 12.34 15.30 16. 8 16.10 16.49 17.23 17.41 18.27 18.38 20.14 21. 3 21.57 23.21 0.19 1.11 3.22 5.34 6.46 7.16 7.45 9. 1 9.52 10. 12 a. M 11.57 12.23 15.19 15.57 15.59 16.38 17.12 17.30 18.16 18.27 20. 3 20.52 21.46 23.10 0. 8 1. 3.11 5.23 6.35 7. 5 7.34 8.50 9.41 9.49 15 a. M 11.46 12.12 15. 8 15.46 15.48 16.27 17. 1 17.19 18. 5 18.16 19.52 20.41 21.35 22.59 23.57 0.49 3. 5.12 6.24 6.54 7.23 8.39 9.30 9.38 18 a. M. 11.35 12. 1 14.57 15.35 15.37 16.16 16.50 17. 8 17.54 18. 5 19.41 20.30 21.24 22.48 23.46 0.38 2.49 5. 1 6.13 6.43 7.12 8.28 9.19 9.27 21 , 24 a. M. 11.23 11.49 14.45 15.23 15.25 16. 4 16.38 16.56 17.42 17.53 19.29 20.18 H. M 11.12 11.38 14.34 15.12 15.14 15.53 21.12 22.36 23.34 0.26 2.37 4.49 6. 1 6.31 7. 8.16 9. 7 9.15 16.27 16.45 17.31 17.42 19.18 20. 7 21. 1 22.25 23.23 0.15 2.26 4.38 5.50 6.20 6.49 8. 5 8.56 9. 4 27 u. a. 11. 11.26 14.22 15. 15. 2 15.41 16.15 16.33 17.19 17.30 19. 6 19.55 20.49 22.13 23.11 0. 3 2.14 4.26 5.38 6. 8 6.37 7.53 8.44 8.52 30 a. M. 10.49 11.15 14.11 14.49 14.51 15.30 16. 4 16.22 17. 8 17.19 18.55 19.44 20.38 22. 2 23. 23.52 2. 3 4.15 5.27 5.57 6.26 7.42 8.33 8.41 »3 TABLE XVIII. FOR FINDING THE APPARENT TIME OF 24 OF THE PRINCIPAL STARS PASSING THE MERIDIAN THROUGHOUT THE YEAR. NOVEMBER. NAMES. Polar Star, achernab, . Aldebaran, Capblla, , RiGEL, . , Betelguese Canopus, . Sirius, . . Castor, . Pollux, . Argus, . . Regulus, DUBHE, . Cross, foot Spica, . . Arctubus, Antares, . Vega, . . Alt air, . . Pavonis, . Ctgni, . . Gbuis, . . fomalhaut, Pegasi, . . . Stab DAT. 1 H. M. 10.41 11. 7 14. 3 14.41 14.43 15.22 15.56 16.14 17. 17.11 18.47 19.36 20.30 21.54 22.52 23.44 1.55 4. 7 5.19 5.49 6.11 7.34 8.25 8.33 DAY. 3 H. M. 10.33 10.59 13.55 14.33 14.35 15.14 15.48 16. 6 16.52 17. 3 18.39 19.28 20.22 21.46 22.44 23.36 1.47 3.59 5.11 5.41 6. 3 7.26 8.17 8.25 DAT. 6 DAf. 9 H. M. 10.21 10.47 13.43 14.21 14.23 15. 2 4.59 5.29 5.51 7.14 8. 5 8.13 H. M 10. 9 10.35 13.31 14. 9 14.11 14.50 15.24 15.42 16.28 16.39 18.15 19. 4 DAY. 12 H. M 9.57 10.23 13.19 13.57 13.59 14.38 15.12 15.30 16.16 16.27 18. 3 18.52 19.58 21.22 22.20 23.12 1.23 3.35 4.47 5.17 5.39 7. 2 7.53 8. 1 19.46 21.10 22. 8 23. 1.11 3.23 4.35 5. 5 5.27 6.50 7.41 7.49 DAY. 15 H. M. 9.45 10.11 13. 7 13.45 13.47 14.26 15. 15.18 16. 4 16.15 17.51 18.40 19.34 20.58 21.56 22.48 0.59 3.11 4.23 4.53 5.15 6.38 7.29 7.37 DAY. 18 H. M. 9.32 9.58 12.54 13.32 13.34 14.13 14.47 15. 5 15.51 16. 2 17.38 18.27 19.21 20.45 21.43 22.35 0.46 2.58 4.10 4.40 5. 2 6.25 7.16 7.24 DAY, 21 H. M. 9.20 9.46 12.42 13.20 13.22 14. 1 14.35 14.53 15.39 15.50 17.26 18.15 19. 9 20.33 21.31 22.23 0.34 2.46 3.58 4.28 4.50 6.13 7. 4 7.12 DAY. 24 H. M 9. 7 9.33 12.29 13. 7 13. 9 13.48 14.22 14.40 15.26 15.37 17.1 18. 2 18.56 20.20 21.18 22.10 0.21 2.33 3.45 4.15 4.37 6. 6.51 6.59 DAY. 27 H. M. 8.54 9.20 12.16 12.54 12.56 13.35 14. 9 14.27 15.13 15.24 17. 17.49 18.43 20.07 21. 5 21.57 0. 8 2.20 3.32 4. 2 4,24 5.47 6.38 6.46 DAY, 30 H. H. 8,41 9. 7 12. 3 12.41 12.43 13.22 13.56 14.14 15. 15.11 16.47 17.86 18.30 19.54 20.52 21.44 23.55 2. 7 3.19 3.49 4,1J 5.34 6.25 6.33 DECEMBER. names. Polar Stab, achebnab, . Aldebaban, Capella, , Rigel, . , Betelgxtese, Canopus, . SiBIUS, . . Castob, . Pollux, . Argus, . . Regulus, . Dubhe, . Cross, foot Spica, . . Arcturus, Antabes, Vega, . . Altaib, . Pavonis, , Ctgni, . . Gbuis, . . FoMALHAUT, Pegasi, . . Star 1 H. M. 8.37 9. 3 11.59 12.37 12.39 13.18 13.52 14,10 14,56 15. 7 16.43 17.32 18.26 19.50 20,48 21.40 23.51 2. 3 3.15 3.45 4. 7 5.30 6.21 6.29 H. U 8.29 8.55 11,51 12.29 12.31 13.10 13.44 14. 2 14.48 14.59 16.35 17.24 18.18 19.42 20,40 21,32 23.43 1.55 3, 7 3,37 3.59 5.22 6.13 6.21 6 H. M 8.15 8.41 11.37 12.15 12.17 12.56 13.30 13.48 14.34 14.45 16.21 17.10 18. 4 19.28 20.26 21.18 23.29 1.41 2.53 3.23 3.45 5. 8 5.59 6. 7 H. 8. 8.28 11.24 12, 2 12, 4 12,43 13.17 13.35 14.21 14.32 16. 8 16.57 17.51 19.15 20.13 21. 5 23,16 1.28 2.40 3.10 3.32 4.55 5.46 5,54 12 H. M. 7.49 8.15 11.11 11.49 11.51 12,30 13. 4 13.22 14. 8 14.19 15.55 16.44 17.38 19. 2 20. 20.52 23. 3 1.15 2.27 2.57 3.19 4.42 5,33 5,41 15 H. M. 7.36 8. 2 10.58 11.36 11.38 12.17 12.51 13. 9 13.55 14. 6 15.42 16,31 17,25 18.49 19.47 20.39 22.50 1. 2 2.14 2.44 3. 6 4.29 5.20 5,28 18 H. M. 7,23 7.49 10.45 11.23 11.25 12. 4 12.38 12.56 13.42 13.53 15.29 16.18 17.12 18.36 19.34 20.26 22.37 0.49 2. 1 2.31 2.53 4.16 5. 7 5.15 21 H. M. 7. 9 7.35 10.3 11. 9 11.11 11.50 12.24 12.42 13.28 13.39 15.15 16. 4 17.00 18.22 19.20 20.12 22.23 0.35 1.47 2.17 2.39 4. 2 4.53 5, 1 24 H. M. 6,56 7.22 10.18 10.56 10.58 11,37 12.11 12.29 13.15 13.26 15. 2 15.51 16.46 18. 9 19. 7 19.59 22.10 0.2 2 1.34 2. 4 2.26 3.49 4,40 4,48 27 H. U 6.43 7. 9 10. 5 10.43 10.45 11.24 30 11.58 12.16 13. 2 13.13 14,49 15,38 16,33 17.56 18.54 19.46 21.57 0. 9 1.21 1.51 2.13 3.36 4.27 4.35 H. M. 6.29 6.55 9.51 10.29 10.31 11.10 11.44 12. 2 12.48 12.59 14.35 15.24 16.20 17.42 18.40 19.32 21.43 23,5 5 1. 7 1.37 1.59 3.22 4.13 4,2jj TABLES XIX— X: s:. 91 TABLE XIX. PLACES OF 24 OF THE PRINCIPAL FLKED STARS, FOR THE YEAR 1864. | UAO. NAME. 1 EIGHT ASCENSION. ANNUAL VAS. DECLINATION, ANNUAL VAE. 2 Polar Star, H. M. 8. 1 6 3 +17.83 O ' 88 32 N. It + 19-3 ACHERNAR, . 1 32 15 2-23 57 59 S. -18-5 Aldebaran, 4 27 32 3-43 16 13 N. + 7-9 Capella, . . 5 6 55 4-41 45 51 N. + 4-8 RiGEL, . . . 5 7 31 2-b» 8 23 S. - 4-6 Betelguesh, 5 47 17 3-24 7 22 N. + 1-2 Canopus, , . 6 20 44 1-33 52 37 S. + 1-8 SiRIUS, . . . 6 38 43 2-65 16 31 S. + 4-5 Castor, . . . 7 25 17 3-86 32 12 N. - 7-2 Pollux, . . 7 36 21 3-68 28 22 N. - 8-1 2 Argus, . . . 9 11 37 0-73 69 4S. — 14-8 Regulus, . . 10 35 3-22 12 41 N. — 17-4 DUBHE, Cross, 10 54 50 12 18 31 3-81 3-27 62 32 N. 62 17 S. -19-2 +20-0 foot Star, . . Spica,. . . . 13 17 29 3-15 10 24 S. + 18-9 Arcturus, . 14 8 59 2-73 19 57 N. -19-9 Antares, . . 16 20 24 3-66 26 6S. + 8-5 Vega,. . . . 18 31 57 201 38 39 N. + 2-8 Altair, . . 19 43 37 2-93 8 29 N. + 8-4 Pavonis, . . 20 14 4-81 57 12 S. -11-0 2 Cygni, . . . 20 36 27 204 44 46 N. + 12-6 Gruis, . . . 21 59 3 3-82 47 40 S. -17-3 Fomalhaut, 22 49 32 3-31 30 25 S, -191 2 Pegasi, . . . • • • • • 22 57 30 2-98 1 14 25 N. + 19-3 Sign -f" means add. Sign — me ans subtract. TABLE XX. 1 CORRECTION TO BE SUBTRACTED FROM THE OBSERVED ALTITUDE OF A FIXED | STAR, OR A PLANET, TO FIND THE TRUE ALTITUDE. | Obs Alt HEIGHT OF THE EYE ABOVE THE SEA KJ FEET. #'s Obs. AIL . 4 6 8 10 12 14 16 18 20 22 24 26 28 30 o 5 1 11.8 12.2 12.6 12.9 1 13.2 1 13.5 13.7 1 14.0 14.2 14.4 14.6 14.8 15.0 / 15.1 o 5 6 10.4 10.8 11.2 11.5 11.8 12.1 12.3 12.6 12.8 13.0 13.2 13.4 13.6 13.7 6 7 9.3 9.7 10.1 10.4 10.7 11.0 11.2 11.5 11.7 11.9 12.1 12.3 12.5 12.6 7 8 8.4 8.8 9.2 9.5 9.8 10.1 10.3 10.6 10.8 11.0 11.2 11.4 11.6 11.7 8 9 7.7 8.1 8.5 8.8 9.1 9.4 9.6 9.9 10.1 10.3 10.5 10.7 10.9 11.0 9 10 7.2 7.6 8.0 8.3 8.6 8.9 9.1 9.4 9.6 9.8 10.0 10.2 10.4 10.5 10 11 6.7 7.1 7.5 7.8 8.1 8.4 8.6 8.9 9.1 9.3 9.5 9.7 9.9 10.0 11 12 6.3 6.7 7.1 7.4 7.7 8.0 8.2 8.5 8.7 8.9 9.1 9.3 9.5 9.6 12 14 5.7 6.1 6.5 6.8 7.1 7.4 7.6 7.9 8.1 8.3 8.5 8.7 8.9 9.0 14 16 5.2 5.6 6.0 6.3 6.6 6.9 7.1 7.4 7.6 7.8 8.0 8.2 8.4 8.5 16 18 4.8 5.2 5.6 5.9 6.2 6.5 6.7 7.0 7.2 7.4 7.6 7.8 8.0 8.1 18 20 4.5 4.9 5.3 5.6 5.9 6.2 6.4 6.7 6.9 7.1 7.3 7.5 7.7 7.8 20 22 4.3 4.7 5.1 5.4 5.7 6.0 6.2 6.5 6.7 6.9 7.1 7.3 7.5 7.6 22 26 3.9 4.3 4.7 5.0 5.3 5.6 5.8 6.1 6.3 6.5 6.7 6.9 7.1 7.2 26 30 3.6 4.0 4.4 4.7 5.0 5.3 5.5 • 5.8 6.0 6.2 6.4 6.6 6.8 6.9 30 35 3.3 3.7 4.1 4.4 4.7 5.0 5.2 5.5 5.7 5.9 6.1 6.3 6.5 6.6 35 40 3.1 3.5 3.9 4.2 4.5 4.8 5.0 5.3 5.5 5.7 5.9 6.1 6.3 6.4 40 45 2.9 3.3 3.7 4.0 4.3 4.6 4.8 5.1 5.3 5.5 5.7 5.9 6.1 6.3 45 50 2.7 3.1 3.5 3.8 4.1 4.4 4.6 4.9 5.1 5.3 5.5 5.7 5.9 6.1 50 55 2.6 3.0 3.4 3.7 4.0 4.3 4.5 4.8 5.0 5.2 5.4 5.6 5.8 6.0 55 60 2.5 2.9 3.3 3.6 3.9 .4.2 4.4 4.7 4.0 5.1 .5.3 5.5 5.7 5.9 60 65 2.4 2.8 3.2 3.5 3.8 4.1 4.3 4.6 4.8 5.0 5.2 5.4 5.6 5.8 65 70 2.3 2.7 3.1 3.4 3.7 4.0 4.2 4.5 4.7 4.9 5.1 5.3 5.5 5.7 70 80 2.1 2.5 2.9 3.2 3.6 3.8 4.0 4.3 4.5 4.7 4.9 5.1 5.3 5.5 80 90 1.9 2.3 2.7 3.0 3.3 3.6 3.8 4.1 4.3 4.5 4.7 4.9 5.1 5.3 90 TABLE XXI. TO FIND THE LATITUDE BY AN ALTITUDE OF THE POLAR STAR. When the Right Ab censioD of the Meri- dian is found in thin column, the correction is Subtractive. EXPLANATION OF THE TABLE, WHICH 18 CALCULATED FOE THE TEAE 1854. Enter the side column, with the Right Ascension of the Meridian and the Altitude of the Star at the top, and at the angle of meeting will be the required correction. When the Right A»- cension of the Meri- dian is found in this column, the correction is Additive. <4 3s R. A- M. APPABENT ALTITUDE OF THE POLAR STAE. R. A. M. 8 H. If. H. U. 10° 20° 30° 40° 50° 60° H. M. H. M. SUB. O ' o ' O ' O ' O ' O ' f 1 1 1 28 1 28 1 28 1 28 1 28 1 28 13 13 3 1 30 30 1 27 1 27 1 27 1 27 1 27 1 27 12 30 13 30 3 2 24 1 25 1 25 1 24 1 24 1 24 1 24 12 14 3 2 20 23 40 1 23 1 23 1 23 1 22 1 22 1 22 11 40 14 20 3 2 40 23 20 1 20 1 20 1 20 1 20 1 19 1 19 11 20 14 40 3 3 23 1 16 1 16 1 16 1 16 1 15 1 15 11 10 15 3 3 10 22 50 1 14 1 14 1 14 1 14 1 13 1 13 10 50 15 10 3 3 20 22 40 1 12 1 12 1 12 1 12 1 11 1 10 10 40 15 20 3 3 30 22 30 1 10 1 9 1 9 1 9 1 8 1 7 10 30 15 30 3 3 40 22 20 1 8 1 8 1 8 1 8 1 7 1 5 10 20 15 40 2 3 50 22 10 1 6 1 5 1 5 1 4 1 3 1 1 10 10 15 50 2 4 22 1 3 1 2 1 2 1 2 1 1 1 1 10 16 2 4 10 21 50 1 1 1 1 1 59 9 50 16 10 2 4 20 21 40 57 57 57 57 56 55 9 40 16 20 2 4 30 21 30 54 54 54 54 53 52 9 30 16 30 2 4 40 21 20 51 51 51 51 50 49 9 20 16 40 2 4 50 21 10 48 48 48 48 47 46 9 10 16 50 2 5 21 45 44 44 44 44 42 9 17 2 5 10 20 50 41 41 40 40 40 39 8 50 17 10 2 5 20 20 40 38 37 37 37 37 35 ^ 8 40 17 20 1 5 30 20 30 35 34 34 33 33 31 8 30 17 30 5 40 20 20 31 30 30 29 29 27 8 20 17 40 5 50 20 10 27 26 26 25 25 24 8 10 17 50 6 20 23 22 22 21 21 20 8 18 6 10 19 50 19 18 18 17 17 16 7 50 18 10 6 20 19 40 15 14 14 13 13 12 7 40 18 20 1 6 30 19 30 12 11 11 10 10 9 7 30 18 30 6 40 19 20 8 7 7 6 6 5 7 20 18 40 6 50 19 10 4 3 3 2 2 1 7 10 18 50 6 55 19 5 1 2 2 2 3 4 7 19 «t 1 TABLE XXII. ■ OOBBEOTION OF THE TIME OF THE MOON'S MERIDIAN PASSAGE, OVER THE | MERIDIAN ( OF GREENWICH, TO THE TIME OF HER PASSAGE OVER ANY OTHER MERIDIAN. DAILY VABIATION OF THE MOON's PASSING THK MERIDIAN. x. X. u. M. u. M. u. M. M. u. M. M. K. H. s 40 42 44 46 48 50 52 54 56 58 60 62 64 66 M. M. II. M. II. M. M. M. M. M. H. u. IL H. 10 1 1 1 1 1 1 1 1 1 2 2 2 2 2 20 2 2 2 2 3 3 3 3 3 3 3 3 3 4 30 3 3 4 4 4 4 4 4 4 5 5 5 5 5 40 4 4 5 5 5 5 6 6 6 6 6 7 7 7 50 5 6 6 6 6 7 7 7 7 8 8 8 9 9 60 6 7 7 7 8 8 8 9 9 9 10 10 10 11 70 7 8 8 9 9 9 10 10 10 11 11 12 12 12 80 9 9 10 10 10 11 11 12 12 12 13 13 14 14 90 10 10 11 11 12 12 13 13 13 14 14 15 15 16 100 11 12 12 12 13 13 14 14 15 15 16 17 17 18 110 12 13 13 14 14 15 15 16 16 17 18 18 19 19 120 13 14 14 15 15 16 17 17 18 19 19 20 20 21 130 14 15 15 16 17 17 18 19 19 20 21 21 22 23 140 15 16 17 17 18 19 20 20 21 22 22 23 24 25 150 16 17 18 19 19 20 21 22 22 23 24 25 26 26 160 17 18 19 20 21 21 22 23 24 25 26 26 27 28 170 18 19 20 21 22 23 24 25 25 26 27 28 29 30 180 19 20 21 22 23 24 25 26 27 28 29 30 31 32 Th e Sums taken from th is Table mnet be added to the time of the Moon's Meridian F assage i n the Naut ical Aln lanac, ii a West Longitude, and subtracted in East, will give the Mean Time of her Mei ■idian Passj ige at t le Ship TABLE XXIII. FOR REDUCING THE MOON'S DECLINATION TO THE GREENWICH TIME OF THE OBSERVATION. D Diff of FOR OD Moon's HOURS FKOM NOON OB MIDNIGHT. MINUTES. Declina- tion in 12 M. M. M. M hours. 1 2 3 4 5 6 7 8 9 10 11 12 24 36 48 r o ' O ' O ' o ' O ' O ' o ' O ' o ' o ' o ' o ' t / / 5 1 1 2 2 2 3 3 4 4 5 10 1 2 2 3 4 5 6 7 7 8 9 1 15 1 2 4 5 6 7 9 10 11 12 14 1 1 20 2 3 5 7 8 10 12 13 15 17 18 1 1 25 2 4 6 8 10 12 15 17 19 21 23 1 2 30 2 5 7 10 12 15 17 20 22 25 27 1 2 35 3 6 9 12 15 17 20 23 26 29 32 2 2 40 3 7 10 13 17 20 23 27 30 33 37 2 3 45 4 7 11 15 19 22 26 30 34 37 41 2 3 50 4 8 12 17 21 25 29 33 37 42 46 2 2 3 55 5 9 14 18 23 27 32 37 41 46 51 2 3 4 1 5 10 15 20 25 30 35 40 45 50 55 2 3 4 1 5 5 11 16 22 27 32 38 43 49 54 1 2 3 4 1 10 6 12 17 23 29 35 41 47 52 58 1 4 2 3 5 1 15 6 12 19 25 31 37 44 50 56 1 2 1 9 2 4 5 1 20 7 13 20 27 33 40 47 53 1 1 7 1 13 3 4 5 1 25 7 14 21 28 35 42 50 57 1 4 1 11 1 18 3 4 6 1 30 7 15 22 30 37 45 52 1 1 7 1 15 1 22 3 4 6 1 35 8 16 24 32 40 47 55 1 3 1 11 1 19 1 27 2 3 5 6 1 40 8 17 25 33 42 50 58 1 7 1 15 1 23 1 32 2 3 5 7 1 45 9 17 26 35 44 52 1 1 1 10 1 19 1 27 1 36 2 3 5 7 1 50 9 18 27 37 46 55 1 4 1 13 1 22 1 32 1 42 2 4 5 7 1 55 10 19 29 38 48 57 1 7 1 17 1 26 1 36 1 45 2 4 6 8 2 10 20 30 40 50 1 1 10 1 20 1 30 1 40 1 50 2 4 6 8 2 5 10 21 31 42 52 1 2 1 13 1 23 1 34 1 44 1 55 2 4 6 8 2 10 11 22 32 43 54 1 5 1 16 1 27 1 37 1 48 1 59 2 4 6 9 2 15 11 22 34 45 56 1 7 1 19 1 30 1 41 1 52 2 4 2 4 7 9 2 20 12 23 35 47 58 1 10 1 22 1 33 1 45 1 57 2 8 2 5 7 9 2 25 12 24 36 48 1 1 12 1 25 1 37 1 49 2 1 2 13 2 5 7 10 2 30 12 25 37 50 1 2 1 15 1 27 1 40 1 52 2 5 2 17 2 5 7 10 2 35 13 26 39 52 1 5 1 17 1 30 1 43 1 56 2 9 2 22 3 5 8 10 2 40 13 27 40 53 1 7 1 20 1 33 1 47 2 2 13 2 27 3 5 8 11 2 45 14 27 41 55 1 9 1 22 1 36 1 50 2 4 2 17 2 31 3 5 8 11 2 50 14 28 42 57 1 11 1 25 1 39 1 53 2 7 2 22 2 36 3 6 8 11 2 55 15 29 44 58 1 13 1 27 1 42 1 57 2 11 2 26 2 40 3 6 9 12 3 15 15 30 45 1 1 15 1 30 1 45 2 2 15 2 30 2 45 3 6 9 12 12 3 5 31 46 1 2 1 17 1 32 1 48 2 3 2 19 2 34 2 50 3 6 9 3 10 16 32 47 1 3 1 19 1 35 1 51 2 7 2 22 2 38 2 54 3 6 9 13 3 15 16 32 49 1 5 1 21 1 37 1 54 2 10 2 26 2 42 2 59 3 6 10 13 3 20 17 33 50 1 7 1 23 1 40 1 57 2 13 2 30 2 47 3 3 3 7 10 13 3 25 17 34 51 1 8 1 25 1 42 2 2 17 2 34 2 51 3 8 3 7 10 14 3 30 17 35 52 1 10 1 27 1 45 2 2 2 20 2 37 2 55 3 12 3 7 10 14 3 35 18 36 54 1 12 1 30 1 47 2 5 2 23 2 41 2 59 3 17 4 7 11 14 3 40 IS 37 55 1 13 1 32 1 50 2 8 2 27 2 45 3 3 3 22 4 7 11 15 3 45 19 37 56 1 15 1 34 1 52 2 11 2 39 2 49 3 7 3 26 4 7 11 15 Note. — This Table is constructed upon the following principle: — Rule. Say as 12 hours is to the diflFerence or change in the Moon's Declination in 12 hours, so is the time past Greenwich N oon or Midnight to the Correction, which must be applied to the Declination at the preceding Noon or Mi doig'bt. aooording as it is increasing or decreasing. 06 TABLE XTIV. CORRECTION OF THE M00N*3 SEMIDIAMETER, OR HORIZONTAL PARALLAX, FOR ANT GIVEN TIME BETWEEN NOON AND MIDNIGHT, OR OF THE SUN OR A PLANET'S DECLINATION FOR A GIVEN TIME FROM THE PRECEDING NOON. I 2 2 a=-a VARIATION OF THE Jf 'S SEMIDIAMETER, OR HORIZONTAL PARALLAX, IN 12 HOOR8. ** o a * 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 fr 20 21 22 n 23 /r 24 25 26 27 rf 28 H. M. 30 1 1 30 2 2 30 3 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 2 2 1 1 1 2 2 1 1 2 2 2 1 1 2 2 3 1 1 2 2 3 1 1 2 2 3 3 1 1 2 2 3 3 1 1 2 2 3 4 1 1 2 3 3 4 1 1 2 3 4 4 1 1 2 3 4 4 1 2 2 3 4 5 1 2 2 3 4 5 1 2 ■3 3 4 5 1 2 3 4 5 5 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 7 1 2 3 5 6 7 B. 1 2 3 4 5 6 3 30 4 4 30 5 5 30 6 2 2 2 1 2 2 2 2 2 2 2 2 2 3 3 2 2 3 3 3 3 2 3 3 3 4 4 3 3 3 4 4 4 3 3 4 4 5 5 3 4 4 5 5 5 3 4 4 5 5 6 4 4 5 5 6 6 4 5 5 6 6 7 4 5 6 6 7 7 5 5 6 7 7 8 5 6 6 7 8 8 5 6 7 7 8 9 6 6 7 8 9 9 6 7 7 8 9 10 6 7 8 9 10 10 6 7 8 9 10 11 7 8 9 10 11 11 7 8 9 10 11 12 7 8 9 10 11 12 8 9 10 11 12 13 8 9 10 11 12 13 8 9 10 12 18 14 7 8 9 10 11 12 6 30 7 7 30 8 8 30 9 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 4 4 3 3 4 4 4 4 4 4 4 5 5 5 4 5 5 5 6 6 5 5 6 6 6 7 5 6 6 7 7 7 6 6 7 7 8 8 6 7 7 8 8 9 7 8 8 9 9 10 8 8 9 9 10 10 8 9 9 10 11 11 9 9 10 11 11 12 9 10 11 11 12 13 10 11 12 13 13 10 n 12 13 13 14 11 12 12 13 14 15 11 12 13 14 15 10 17 17 18 19 20 21 12 13 14 15 16 16 17 18 19 20 21 22 12 13 14 15 16 17 18 19 20 21 22 23 13 14 15 16 17 18 14 15 16 17 18 19 14 15 16 17 18 19 15 16 17 18 19 20 15 16 17 19 20 21 13 14 15 16 17 18 9 30 10 10 30 11 11 30 12 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 4 4 4 4 4 4 5 5 5 5 5 5 5 6 6 6 6 6 6 7 7 6 7 7 7 8 8 7 7 8 8 9 9 8 8 9 9 10 10 9 9 10 10 11 11 9 10 10 11 11 12 10 11 11 12 12 13 11 12 12 13 13 14 12 12 13 14 14 15 13 13 14 15 15 16 13 14 15 16 16 17 14 15 16 16 17 18 15 16 17 17 18 19 16 17 17 18 19 20 19 20 21 5i2 %'^ 24 20 21 22 23 24 ''25 21 22 23 24 25 26 21 22 24 25 26 27 22 23 24 26 27 28 19 20 21 22 23 24 TIME AFTER NOON OR MIDNIGHT. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 ^ 26 27 28 VARIATION OF THE OR PLANETS* DECLINATION IN 24 HOURS. Not and the the ang Green-w the ang E.— dii le ich let -Ec fere f n N )f E ter ;nc< lee oon nee th ! or .ing an ting 8 '] ch d t rab ing ill be ill leT e ii] be difif bel vitt th the erei the tb eS CO ice cor el emi rre or rec Mm dia ctio cha bion sfr me n; nge ,to om ter or, of be Gr anc ent th< ap een 1 E er J Si plie wic ori the in ( d t h J ZOD ri^ )r ] icec fooi td rht Plat >rdii 1 or Par rd lat't M alls . P idn IX th «cli igh D 1 eT rit ar I in 2h abl ion, i in tl our e w at ere s ai ith tht asii itb tb< ) bo igo tid b T :to rd e o< *P. tift ' eff- jlumn, and at > from xud at 9««iiig. M TABLE XXV. CONTAINING THE CORRECTION FOR THE MOON'S PARALLAX IN ALTITUDE, GIVEN IN MINUTES AND TENTHS, WHICH IS ALWAYS ADDITIVE TO THE APPARENT ALTITUDK J) '8 Ap. Alt. o 5 6 7 8 9 10 HORIZONTAL PARALLAX. 54' 43-9 45-2 46-2 4G-9 47-6 47-9 55' 44-9 46-2 47-2 47-9 48-6 48-9 56' 45-9 47-2 48-2 48-9 49-6 49-8 57' 46-9 48-2 49-2 49-9 50-6 508 58' 47-9 49-2 50-2 50-9 51-6 51-8 59' 48-9 50-2 51-2 51-9 52-6 52-8 60' 49-9 51-2 52.2 52-9 53-6 53-8 J) '8 Ap. 61 y^it. 50-9 52-2 53-2 53-9 54-6 54.8 48 49 50 51 52 53 HORIZONTAL PARALLAX. 54' 35-3 34-6 33-9 33-2 32-5 31-8 55' 35-9 35-3 34-6 33-8 33-1 32-4 56' 36-6 35-9 35-2 34-5 33-7 33-0 57' 37-3 36-6 35-8 351 34-4 33-6 58' 38-0 37-2 36-5 35-7 350 34-2 59' 38-6 37-9 371 36-4 35-6 34-8 60' 39-3 38-5 36-8 37-0 36-2 35-4 40-0 39-2 38-4 37-6 36-8 36-0 61' 11 12 13 14 15 16 48-2 48-4 48-5 48-6 48-6 48-6 49-2 49 4 49-5 49-6 49-6 49-5 50-1 50-4 50-5 50.5 50-5 50-5 51-1 51-3 51-4 51-5 51-5 51-5 521 52-3 52-4 52-5 52-5 52-4 531 53-3 53-4 53-4 53-4 53-4 541 54-2 54-4 54-4 54-4 54-4 550 55-2 55-3 55-4 55-4 55-3 54 55 56 57 58 59 311 30-3 29-6 28-8 28-0 27-2 31-6 30-9 301 29-3 28-6 27-8 32-2 31-5 30-7 29-9 291 28-3 32-8 320 31-2 30-4 29-6 28-6 33-4 32-6 31-8 310 30 29-3 34-0 33-2 34-6 33-8 32-4 32-9 31-5|32-1 30-7 31-2 29-6 30-3 35-2 34-3 33-5 32-6 31-7 30-9 17 18 19 20 21 22 48-5 48-4 48-3 48-1 47-9 47-7 49-5 49-4 49-2 49-1 4S-9 48-6 50-4 50-3 50-2 50-0 49-8 49-5 51-4 51-3 511 50-9 50-7 50-5 52-3 52-2 521 51-9 51-7 51-4 53-3 53-2 530 52-8 52-6 52-3 54-3 541 53-9 53-8 53-5 53-3 55-2 55-1 54-9 54-7 54-6 54-2 60 61 62 63 64 65 26-5 25-7 24-9 24-0 232 22-4 27-0 26-1 25-3 24-5 23-7 22-8 27-5 26-6 25-6 24-9 24-1 23-2 28-0 27-1 26-3 25-4 24-5 23-7 28-5 27-6 26-7 25 9 25-0 24-1 29-01 281 27-2 26-3 25-4 24-5 29-0 28-6 27-7 26-8 25-8 24-9 30-0 29-1 28-1 27 2 26-3 25-3 23 24 25 26 27 28 29 30 31 32 33 34 47-4 47-2 46-9 46-6 46-2 45-9 48-4 48-1 47-8 47-5 471 46-8 49-3 49 48-7 48-4 48-0 47-6 50-2 49-9 49-6 49-3 48-9 48-5 511 50-9 50-5 50-2 49-8 49-4 52-1 51-8 51-4 51-] 50-7 50-3 53-0 52 52-3 52 51-6 51-2 53-9 53-6 52-2 52-9 52-5 52-1 66 67 68 69 70 71 21-5 20-7 19-9 19-0 18-1 17-3 22-0 21 20 19-4 18-5 17-6 22-4 21-5 20-6 19-7 18-8 17-9 2-2 -8 21-9 21-0 20-1 19-2 18-^ 23 2 22-3 21-4 20-4 19-5 18-6 23-6 22-7 21-7 20-8 19-8 18'9 24-0 23-0 22-1 21-1 20-2 19-2 24-4 23-4 22-5 20-5 20-5 19-5 45-5 45-1 44-7 44-3 43-8 43-4 46-4 46-0 45-6 451 44-7 44-2 47-3 46-8 46-4 45-9 45-5 45-0 481 47-7 47-3 46-8 46-3 45-8 49-0 48-6 481 47-7 47-2 46-7 49-9 49-4 49-0 48-5 48-0 47-5 50-8 50-3 49-9 49-4 48-9 48-3 51-6 51-2 50-7 50-2 49-7 49-2 72 73 74 75 76 77 16-4 15-5 14-6 13-7 12-8 11-9 16-7 158 14-9 140 13-1 12-2 17-0 16-1 15-2 14-2 13-3 12-4 17o 16-4 15-4 14-5 13-5 12-6 17-6 16-7 15-7 14-8 13-8 12-8 17-9 17-0 16-0 15-0 14-0 13-1 18-2 17 16-3 15-3 14-3 13-3 18-5 17-6 16-5 15-5 14-5 13-5 35 36 37 38 39 40 41 42 43 44 45 46 47 430 42-3 41-9 41-3 40-8 40-2 43-7 43-2 42-7 421 41-6 41-0 44-5 43-9 43-5 42-9 42-3 41-8 45-d 44-8 44-3 43-7 431 42-5 46-1 45-6 451 44-5 43-9 43-3 46-9 46-4 45-9 45-3 44-7 441 47-8 47-2 46-8 461 45-4 44-8 48-6 48-0 47-5 46-9 46-2 45-6 78 79 80 81 82 83 11-0 10-1 9-2 8-3 7-4 6-5 11-2 lO-o 9-4 8-5 7-5 6-6 11-4 10-5 9-6 8-6 7-7 6-7 11-7 10-7 9-7 8-8 7-8 6-8 11-9 10-9 9-9 8-9 7-9 6-9 12-1 11-1 10-1 9-1 8-1 7-1 12-3 11-3 10-3 9-2 8-2 7-2 3if7 39-1 38-5 37-9 37-2 36-6 35-9 40-4 39-8 39-2 38-6 37-9 o/' 0^.3 36-6 41-2 40-6 39-9 39-3 38-6 38-0 37-3 41-9 41-3 40-7 401 39-4 38-7 38-0 42-7 42-0 41-4 40-7 40-1 39-4 38-7 43-4 42-8 421 41-5 40-8 40-1 39-4 44-2 43-5 42-9 42-2 41-5 40-8 40-0 44-9 44-3 43-6 42-9 42-2 41-5 40-7 84 85 86 87 88 89 90 5-6 4-6 3-7 2-8 1-9 0-9 00 5-7 4-7 3-8 2-8 1-9 0-9 0-0 5-8 4-8 3-8 2-9 1-9 1-0 00 5-9 4-9 3-9 2-9 2-0 1-0 0-0 6-0 5-0 4-0 3-0 2-0 1-0 00 6-1 5-1 4-0 3-0 2-0 1-0 0-0 6-2 5-2 4-1 3-1 2-1 1-0 0-0 12-5 11-5 10-4 9-4 8-4 7-3 6-3 5-3 4-2 3-1 2-1 1-0 0-0 Enter this Table with the Apparent Altitude at the side, and the Horizontal Parallax at the top, and at the angle of meeting will be the required correction ; and if Seconds be required, multiply the Tenths by 6 will gire Seconds. TABLE XXVI. [Pag6«7. TO TURN DEGREES INTO TIME, OR, TIME INTO DEGREES. OAfirrA^B. Time. degrees. Time. Degrees. Time. Miuutcs of Oegrees. Time. Seconds of Degrees. Tim«. A^^ie^B. H. M. B. If. H. M. M. 8. & T. 1 0. 4 61 4. 4 121 8. 4 1 0. 4 1 0.4 2 0. 8 62 4. 8 122 8. 8 2 0. 8 2 0. 8 3 0.12 63 4.12 123 8.12 3 0.12 3 0.12 4 0.16 64 4.16 124 8.16 4 0.16 4 0.16 5 0.20 65 4.20 125 8.20 5 0.20 5 0.20 6 0.24 66 4.24 126 8.24 6 0.24 6 0.24 7 0.28 67 4.28 127 8.28 7 0.28 7 0.28 8 0.32 68 4.32 128 8.32 8 0.32 8 0.32 9 0.36 69 4.36 129 8.36 9 0.36 9 0.36 10 0.40 70 4.40 130 8.40 10 0.40 10 0.40 11 0.44 71 4.44 131 8.44 11 0.44 11 0.44 12 0.48 72 4.48 132 8.48 12 0.48 12 0.48 13 0.52 73 4.52 133 8.52 13 0.52 13 0.52 14 0.56 74 4.56 134 8.56 14 0.56 14 0.56 15 1. 75 5. 135 9. 15 1. 15 1. It) 1. 4 76 5. 4 136 9. 4 16 1. 4 16 1. 4 17 1. 8 77 5. 8 137 9. 8 17 1. 8 17 1. 8 18 1.12 78 5.12 138 9.12 18 1.12 18 1.12 19 1.16 79 5.16 139 9.16 19 1.16 19 1.16 20 1.20 80 5.20 140 9.20 20 1.20 20 1.20 21 1.24 81 5.24 141 9.24 21 1.24 21 1.24 22 1.28 82 5.28 142 9.28 22 1.28 22 1.28 23 1.32 83 5.32 143 9.32 23 1.32 23 1.32 24 1.36 84 5.36 144 9.36 24 1.36 24 1.36 25 1.40 85 5.40 145 9.40 25 1.40 25 1.40 26 1.44 86 5.44 146 9.44 26 1.44 26 1.44 27 1.48 87 5.48 147 9.48 27 1.48 27 1.48 28 1.52 88 5.52 148 9.52 28 1.52 28 1.52 29 1.56 89 5.56 149 9.56 29 1.56 29 1.56 30 2. 90 6. 150 10. 30 2. 30 2. 31 2. 4 91 6. 4 151 10. 4 31 2. 4 31 2. 4 32 2. 8 92 6. 8 152 10. 8 32 2. 8 32 2. 8 33 2.12 93 6.12 153 10.12 33 2.12 33 2.12 34 2.16 94 6.16 154 10.16 34 2.16 34 2.16 35 2.20 95 6.20 155 10.20 35 2.20 35 2.20 36 2.24 96 6.24 156 10.24 36 2.24 36 2.24 37 2.28 97 6.28 157 10.28 37 2.28 37 2.28 38 2.32 98 6.32 158 10.32 38 2.32 38 2.32 39 2.36 99 6.36 159 10.36 39 2.36 39 2.36 40 2.40 100 6.40 160 10.40 40 2.40 40 2.40 41 2.44 101 6.44 161 10.44 41 2.44 41 2.44 42 2.48 102 6.48 162 10.48 42 2.48 42 2.48 43 2.52 103 6.52 163 10.52 43 2.52 43 2.52 44 2.56 104 6.56 164 10.56 44 2.56 44 2.56 45 3. 105 7. 165 11. 45 3. 45 3. 46 3. 4 106 7. 4 166 11. 4 46 3. 4 46 3. 4 47 3. 8 107 7. 8 167 11. 8 47 3. 8 47 3. 8 48 3.12 108 7.12 168 11.12 48 3.12 48 3.12 49 3.16 109 7.16 169 11.16 49 3.16 49 3.16 50 .3.20 110 7.20 170 11.20 50 3.20 50 3.20 51 3.24 111 7.24 171 11.24 51 3.24 51 3.24 52 3.28 112 7.28 172 11.28 52 3.28 52 3.28 53 3.32 113 7.32 173 11.32 53 3.32 53 3.32 54 3.36 114 7.36 174 11.36 54 3.36 54 3.36 55 3.40 115 7.40 175 11.40 55 3.40 55 3.40 56 3.44 116 7.44 176 11.44 56 3.44 56 3.44 57 3.48 117 7.48 177 11.48 57 3.48 57 3.48 58 3.52 118 7.52 178 11.52 58 3.52 58 3.52 59 3 56 119 7.56 179 11.56 59 3.56 59 3.56 60 4. 120 8. 180 12. 60 4. 60 4. 38 TABLE XXVII. LOGARITHMS OF THE LATITUDE AND POLAR DISTANCE. ' LATITUDE, OB POLAR DISTANCE. SECANT. o Ic o c o c Ic o 3 O C o ( M. or 90 1 I . 91 2 . 92 ; J . 93 4 . 94 5 . 95 6 . 96 ' r . 97 ! ? . 98 9 . 99 00000 00007 00026 00060 00106 00166 00239 00325 00425 00538 60 1 00000 00007 00027 00060 00107 00167 00240 00326 00426 00540 39 2 00000 00007 00027 00061 00108 00168 00241 00328 00428 00542 58 3 00000 00007 00028 00062 00108 00169 00243 00330 00430 00544 57 4 00000 00008 00028 00062 00109 00170 00244 00331 00432 00546 56 5 0.00000 00008 00029 00063 00110 00171 00245 00333 00434 00548 55 6 00000 00008 00029 00064 00111 00172 00247 00334 00435 00550 54 7 00000 00008 00030 00064 00112 00173 00248 00336 00437 00552 53 8 00000 00008 00030 00065 00113 00175 00249 00337 00439 00554 52 9 00000 00009 00031 00066 00114 00176 00251 00339 00441 00556 51 10 0.00000 00009 00031 00066 00115 00177 00252 00341 00443 00558 50 11 00000 00009 00032 00067 00116 00178 00253 00342 00444 00560 49 12 00000 00010 00032 00068 00117 00179 00255 00344 00446 00562 48 13 00000 00010 00033 00068 00118 00180 00256 00345 00448 00564 47 14 00000 00010 00033 00069 00119 00181 00258 00347 00450 00566 46 15 0.00000 00010 00033 00070 00120 00183 00259 00349 00452 00568 45 16 00000 00011 00034 00071 00121 00184 00260 00350 00454 00571 44 17 00001 00011 00034 00071 00121 00185 00262 00352 00455 00573 43 18 00001 00011 00035 00072 00122 00186 00263 00353 00457 00575 42 19 00001 00011 00036 00073 00123 00187 00264 00355 00459 00577 41 20 0.00001 00012 00036 00074 0-)124 00188 00266 00357 00461 00579 40 21 00001 00012 00037 00074 0.»125 00190 00267 00358 00463 00581 39 22 00001 00012 00037 00075 00126 00191 00269 00360 00465 00583 38 ' 23 00001 00013 00038 00076 00127 00192 00270 00362 00467 00585 37 24 00001 00013 00038 00077 00128 00193 00272 00363 00468 00587 36 25 0.00001 00013 00039 00077 00129 00194 00273 00365 00470 00589 35 26 00001 00014 00039 00078 00130 00196 00274 00367 00472 00591 34 27 00001 00014 00040 00079 00131 00197 00276 00368 00474 00593 33 28 00001 00014 00040 00080 00132 00198 00277 00370 00476 00596 32 29 00002 00015 00041 00080 00133 00199 00279 00371 00478 00598 31 30 0.00002 00015 00041 00081 00134 00200 00280 00373 00480 00600 30 31 00002 0C015 00042 00082 00135 00202 00282 00375 00482 OOfiOa 29 32 00002 00016 00042 00083 00136 00203 00283 00376 00483 00604 28 31 00002 00016 00043 00083 00137 00204 00284 00378 00485 00606 27 34 00002 00016 00044 00084 00138 00205 00286 00380 00487 00608 26 35 0.00002 00017 00044 00085 00139 00207 00287 00382 00489 00610 25 36 00002 00017 00045 00086 00140 00208 00289 00383 00491 00612 24 37 00003 00017 00045 00087 00141 00209 00290 00385 00493 00615 23 38 00003 00018 00046 00087 00142 00210 00292 00387 00495 00617 22 39 00003 00018 00046 00088 00143 00212 00293 00388 00497 00619 21 40 0.00003 00018 00047 00089 00144 00213 00295 00390 00499 00621 20 41 00003 00019 00048 00090 00145 00214 00296 00392 00501 00623 19 ■ 42 00003 00019 00048 00091 00146 00215 00298 00393 00503 00625 18 43 00003 00019 00049 00091 00147 00217 00299 00395 00505 00628 17 44 00004 00020 00049 00092 00148 00218 00301 00397 00506 00630 16 45 0.00004 00020 00050 00093 00149 00219 00302 00399 00508 00632 15 46 00004 00021 00051 00094 00150 00220 00304 00400 00510 00634 14 47 00004 00021 00051 00095 00152 00222 00305 00402 00512 00636 13 48 00004 00021 00052 00096 00153 00223 00307 00404 00514 00638 12 49 00004 00022 00052 00096 00154 00224 00308 00405 00516 00641 11 50 0.00005 00022 00053 00097 00155 00225 00310 00407 00518 00643 10 51 00005 00023 00054 00098 00156 00227 00311 00409 00520 00645 9 52 00005 00023 00054 00099 00157 00228 00313 00411 00522 00647 8 53 00005 00023 00055 00100 00158 00229 00314 00412 00524 00649 7 54 00005 00024 00056 00101 00159 00231 00316 00414 00526 0O652 6 55 00006 00024 00056 00102 00160 00232 00317 00416 00528 00654 5 56 00006 00025 00057 00102 00161 00233 00319 00418 00530 00656 4 57 00006 00025 ( J058 00103 00162 00235 00320 00419 00532 00658 3 58 00006 00026 00056 00104 00163 00236 00322 00421 00534 00660 2 59 00006 00026 00059 00105 00164 00237 00323 00423 00536 00663 I 60 00006 00026 00060 00106 00165 00239 00325 00425 00538 0066" M 89° 88° 87° 86° 85^ 84° 83° 82° 81° 80° POLAR DISTANCE. CO-SECAI sTT. ^^" TABLE XXVll. »9 1 LOGARITHMS OF THE LATITUDE AND POLAR DISTANCE. LATITUDE, OR POLAR DISTANCE. SECANT. c o o o o o o o o o o o 1 o o o o o o o o M. 10 or 100 11.101 00805 12 102 13.103 14.104 15.105 16.106 ] 17.107 18.108 1 19.109 0.00665 00960 01128 01310 01506 01716 01940 02179 02433 60 1 00667 00808 00962 01131 01313 01509 01719 01944 02183 02437 59 2 00669 00810 00965 01133 01316 01512 01723 01948 02188 02442 58 3 00672 00813 00968 01136 01319 01516 01727 01952 02192 02446 57 4 00674 00815 00970 01139 01322 01519 01730 01956 02196 02450 56 55 5 0.00676 00818 00973 01142 01325 01523 01734 01960 02200 02455 6 00678 00820 00976 01145 01329 01526 01738 01964 02204 02459 54 7 00681 00823 00978 01148 01332 01529 01741 01968 02208 02464 53 8 00683 00825 00981 01151 01335 01533 01745 01971 02212 02468 52 9 00685 00828 00984 01154 01338 01536 01748 01975 02216 02472 51 10 0.00687 00830 00987 01157 01341 01540 01752 01979 02221 02477 50 11 00690 00833 00989 01160 01344 01543 01756 01983 02225 02481 49 12 00692 00835 00992 01163 01348 01547 01760 01987 02229 02485 48 13 00694 00838 00995 01166 01351 01550 01763 01991 02233 02490 47 14 00696 00840 00998 01169 01354 01553 01767 01995 02237 02494 46 15 0.00699 00843 01000 01172 01357 01557 01771 01999 02241 02499 45 16 00701 00845 01003 01175 01360 01560 01774 02003 02246 02503 44 17 00703 00848 01006 01178 01364 01564 01778 02007 02250 02508 43 18 00706 00850 01009 01181 01367 01567 01782 02011 02254 02512 42 19 00708 00853 00855 01011 01014 01184 01370 01571 01785 02014 02258 02516 41 20 0.00710 01187 01373 01574 01789 02018 02262 02521 40 21 00712 00858 01017 01190 01377 01578 01793 02022 02266 02525 39 22 00715 00860 01020 01193 01380 01581 01796 02026 02271 02530 38 23 00717 00863 01022 01196 01383 01585 01800 02030 02275 02534 37 24 00719 00865 00868 01025 01199 01386 01588 01591 01804 02034 02279 02539 36 25 0.00722 01028 01202 01390 01808 02038 02283 02543 35 26 00724 00870 01031 01205 01393 01595 01811 02042 02287 02547 34 27 00726 00873 01033 01208 01396 01598 01815 02046 02292 02552 33 28 00729 00876 01036 01211 01399 01602 01819 02050 02296 02556 32 29 00731 00878 01039 01214 01403 01605 01823 02054 02300 02561 31 30 00733 00881 01042 01217 .01406 01609 01826 02058 02304 02565 30 31 00736 00883 01045 01220 01409 01612 01830 02062 02309 02570 29 32 00738 00886 01047 01223 01412 01616 01834 02066 02313 02574 28 33 00740 00888 01050 01226 01416 01619 01838 02070 02317 02579 27 34 00743 00891 01053 01229 01419 01623 01841 02074 02321 02583 26 35 0.00745 00894 01056 01232 01422 01627 01845 02078 02326 02588 25 36 00748 00896 01059 01235 01426 01630 01849 02082 02330 02592 24 37 00750 00899 01062 01238 01429 01634 01853 02086 02334 02597 23 38 00752 00901 01064 01241 01432 01637 01856 02090 02338 02601 22 39 00755 00904 01067 01244 01435 01641 01860 02094 02343 02S06 21 40 0.00757 00907 01070 01247 01439 01644 01864 02098 02347 02610 20 41 00759 00909 01073 01250 01442 01648 01868 02102 02351 02615 19 42 00762 00912 01076 01254 01445 01651 01871 02106 02355 M2619 18 43 00764 00914 01079 01257 01449 01655 01875 02110 02360 02624 17 44 00767 00917 01081 01260 01452 01658 01879 02114 02364 02628 IG 45 0.00769 00920 01084 01263 01455 01662 01883 02118 02368 02633 15 46 00771 00922 01087 01266 01459 01666 01887 02122 02372 02637 14 47 00774 00925 01090 01269 01462 01669 01890 02126 02377 02642 13 48 00776 00928 01093 01272 01465 01673 01894 02130 02381 02647 12 49 00779 00930 01096 01275 01469 01676 01898 02134 02385 02651 11 50 0.00781 00933 01099 01278 01472 01680 01902 02139 02390 02656 10 51 00783 00936 01102 01281 01475 01683 01906 02143 02394 02660 9 52 00786 00938 01104 01285 01479 01687 01910 02147 02398 02665 8 53 00788 00941 0111)7 01288 01482 01691 01913 02151 02403 02669 7 54 00791 00944 OHIO 01291 01485 01694 01917 02155 02407 02674 6 55 1) 00793 00946 01113 01294 01489 01698 01921 02159 02411 02678 5 56 00796 00949 01116 01297 01492 01701 01925 02163 02416 02683 4 57 00798 00952 01119 01300 01495 01705 01929 02167 02420 02688 3 58 00800 00954 01122 01303 01499 01709 01933 02171 02424 02692 2 59 00803 00957 01125 01306 01502 01712 01937 02175 02429 02697 1 60 00805 00960 01128 01310 01506 01716 01940 02179 02433 02701 5 79° 78° 77° 76° 75 74° 73° 72° 71' TO- M. L_ POLAR DISTANCE. CO-SECANT. 1 100 TABLE XXVII. i LOGARITHMS OF THE LATITUDE AND POLAR DISTANCE. LATITUDE, OR POLAR DISTANCE. SECANT. 1 o o o o o o o o o o o o o o o o o o o . M. 20 or 110 21.111 02985 22.112 23.113 24.114 25.115 26.116 27 117 28.1«8 05407 29.119 60 0.02701 03283 03597 03927 04272 04634 05012 05818 1 02706 02990 03289 03603 03933 04278 04640 05018 05413 05825 59 2 02711 02995 03294 03608 03938 04284 04646 05025 05420 05832 58 3 02715 02999 03299 03613 03944 04290 04652 05031 05427 05839 57 4 02720 03004 03304 03619 03950 04296 04659 05038 05433 05846 56 55 5 0.02724 03009 03309 03624 03955 04302 04665 05044 05440 05853 6 02729 03014 03314 03630 03961 04308 04671 05051 05447 05860 54 7 02734 03019 03319 03635 03966 04314 04677 05057 05454 05867 53 8 02738 03024 03324 03640 03972 04320 04683 05064 05460 05874 52 9 02743 03029 03330 03646 03978 04326 04690 05070 05467 05881 51 10 0.02748 03034 03335 03651 03983 04332 04696 05077 05474 05888 50 11 02752 03038 03340 03657 03989 04337 04702 05083 05481 05895 49 12 02757 03043 03345 03662 03995 04343 04708 05089 05487 05902 48 13 02762 03048 03350 03667 04000 04349 04714 05096 05494 05910 47 14 02766 03053 03355 03673 04006 04355 04721 05102 05501 05917 46 15 0.02771 03058 03360 03678 04012 04361 04727 05109 05508 05924 45 16 02776 03063 03366 03684 04018 04367 04733 05115 05515 05931 44 17 02780 03068 03371 03689 04023 04373 04739 05122 05521 05938 43 18 02785 03073 03376 03695 04029 04379 04746 05129 05528 05945 42 19 20 02790 03078 03083 03381 03386 03700 04035 04385 04752 05135 05535 05952 41 0.02794 03706 04040 04391 04758 05142 05542 05959 40 21 02799 03088 03392 03711 04046 04397 04764 05148 05549 05966 39 22 02804 03093 03397 03716 04052 04403 04771 05155 05555 05973 38 23 02808 03097 03402 03722 04058 04409 04777 05161 05562 05980 37 24 02813 03102 03407 03727 03733 04063 04415 04783 05168 05569 05988 36 25 0.02818 03107 03412 04069 04421 04789 05174 05576 05995 35 26 02822 03112 03418 03738 04075 04427 04796 05181 05583 06002 34 27 02827 03117 03423 03744 04080 04439 04802 05187 05590 06009 33 28 02832 03122 03428 03749 04086 04439 04808 05194 05596 06016 32 29 02837 03127 03433 03755 03760 04092 04445 04815 05201 05603 06023 31 30 30 0.02841 03132 03438 04098 04451 04821 05207 05610 06030 31 02846 03137 03444 03766 04103 04457 04827 05214 05617 06037 29 32 02851 03142 03449 03771 04109 04463 04833 05220 05624 06045 28 33 02855 03147 03454 03777 04115 04469 04840 05227 05631 06052 27 34 02860 03152 03459 03782 04121 04127 04475 04846 05233 05240 05638 06059 26 35 0.02865 03157 03465 03788 04481 04852 05645 06066 25 36 02870 03162 03470 03793 04132 04487 04859 05247 05651 06073 24 37 02874 03167 03475 03799 04138 04493 04865 05253 05658 06080 23 38 02879 03172 03480 03804 04144 04500 04871 05260 05665 06088 22 39 02884 0.02889 03177 03486 03810 04150 04506 04512 04878 05266 05672 06095 21 40 03182 03491 03815 04156 04884 05273 05679 06102 20 41 02893 03187 03496 03821 04161 04518 04890 05280 05686 06109 19 42 02898 03192 03502 03826 04167 04524 04897 052S6 05693 06116 18 43 02903 03197 03507 03832 04173 04530 04903 05293 05700 06124 17 44 02908 0.02913 03202 03512 03838 04179 04536 04910 05300 05707 06131 16 45 03207 03517 03843 04185 04542 04916 05306 05714 06138 15 46 02917 03212 03523 03849 04190 04548 04922 05315 05721 06145 14 47 02922 03217 03528 03854 04196 04554 04929 05320 05727 06153 13 48 02927 03222 03533 03860 04202 04560 04935 05326 05734 06160 12 49 02932 03228 03539 03865 04208 04214 04566 04941 05333 05741 06167 11 50 0.02937 03233 03544 03871 04573 04948 05340 05748 06174 10 51 02941 03238 0354,» 03877 04220 04579 04954 05346 05755 06181 9 52 02946 03243 03555 03882 04225 04585 04961 05353 05762 06189 8 53 02951 03248 03560 03888 04231 04591 04967 05360 05769 06196 7 54 02956 03253 03565 03571 03893 04237 04597 04603 04973 05366 05776 06203 6 55 0.02961 03258 03899 04243 04980 05373 05783 06211 5 56 02965 03263 03576 03905 04249 04609 04986 05380 05796 06218 4 57 02970 03268 03581 03910 04255 04616 04993 05386 05797 06225 3 58 02975 03273 03587 03916 04261 04^622 04999 05393 05804 06232 2 'iii 02980 03278 03592 03921 04267 04628 05005 05400 05811 06240 1 6b j 02985 03283 03597 03927 04272 04634 05012 05407 05818 06247 69° 68° 67° 66' 65 64 63* 62" 61* 60' M. P OLAR DISTANCE. < 30-8KCAh fT. TABLE XXVII. 101 LOGARITHMS OF THE LATITUDE AND POLAR DISTANCK ■ LATITUDE OR POLAR DISTANCE. SECAN T o o o o o o o o o o o o o o o o o o o o M. 30 or 120 31.121 32.122 33.123 34.124 08143 35.125 36.126 37.127 38.128 39.129 60 0.06247 06693 07158 07641 08664 09204 09765 10347 10950 1 06254 06701 07166 07649 08151 08672 09213 09775 10357 10960 59 2 06262 06709 07174 07657 08160 08681 09223 09784 10367 10970 58 3 06269 06716 07182 07665 08168 08690 09232 09794 10376 10980 57 4 5 06276 06724 07190 07674 08177 08699 09241 09803 10386 10991 56 55 0.062S3 06731 07197 07682 08185 087b8 09250 09813 10396 11001 6 06291 06739 07205 07690 08194 08717 09259 09822 10406 11011 54 7 06298 06747 07213 07698 08202 08726 09269 09832 10416 11022 53 8 06305 06754 07221 07707 08211 08734 09278 09841 10426 11032 52 9 10 06313 06762 07229 07715 08219 08743 09287 09851 10436 11042 51 0.063 20 06770 07237 07723 08228 08752 09296 09861 10446 11052 50 11 06327 06777 07245 07734 08237 08761 09306 09870 10456 11063 49 12 06335 06785 07253 07740 08245 08770 09315 09880 10466 11073 48 13 06342 06793 07261 07748 08254 08779 09324 09889 10476 11083 47 14 06350 06800 07269 07756 08262 08788 09333 09899 10486 11094 46 45 15 0.06357 06808 07277 07765 08271 08797 09343 09909 10496 11104 16 06364 06816 07285 07773 08280 08806 09352 09918 10505 11114 44 17 06372 06823 07293 07781 08288 08815 09361 09928 10515 11125 43 18 06379 06831 07301 07789 08297 08824 09370 09937 10525 11135 42 19 06386 06839 07309 07317 07798 08305 08833 09380 09389 09947 09957 10535 11145 41 40 20 0.06394 06846 07806 08314 08842 10545 11156 21 06401 06854 07325 07814 08323 08851 09398 09966 10555 11166 39 22 06409 06862 07333 07823 08331 08859 09408 09976 10565 11176 38 23 06416 06869 07341 07831 08340 08868 09417 09986 10575 11187 37 24 06423 06877 07349 07839 08349 08877 09426 09995 10585 11197 36 25 0.06431 06885 07357 07848 08357 08886 09435 10005 10595 11207 35 26 06438 06892 07365 07856 08366 08895 09445 10015 10605 11218 34 27 06446 06900 07373 07864 08375 08904 09454 10024 10615 11228 33 28 06453 06908 07381 07873 08383 08913 09463 10034 10625 11239 32 29 06461 06916 07389 07881 07889 08392 08922 09473 10044 10636 11249 31 30 30 0.06468 06923 07397 08401 08931 09482 10053 10646 11259 31 06475 06931 07405 07898 08409 08940 09491 10063 10656 11270 29 32 06483 06939 07413 07906 08418 08949 09501 10073 10666 11280 28 33 06490 06947 07421 07914 08427 08958 09510 10084 10676 11291 27 34 06498 06954 07429 07923 08435 08967 09520 10092 10686 11301 26 25 35 0.06505 06962 07437 07931 08444 08977 09529 10102 10696 11312 36 06513 06970 07445 07940 08453 08986 09538 10112 10706 11322 24 37 06520 06978 07454 07948 08462 08995 09548 10121 10716 11332 23 38 06528 06986 07462 07956 08470 09004 09557 10131 10726 11343 22 39 06535 06993 07470 07965 08479 09013 09566 10141 10736 11353 21 40 0.06543 07001 07478 07973 08488 09022 09576 10151 10746 11364 20 41 06550 07009 07486 07982 08496 09031 09585 10160 10756 11374 19 42 06558 07017 07494 07990 08505 09040 09595 10170 10767 11385 18 43 06565 07024 07502 07998 08514 09049 09604 10180 10777 11395 17 44 06573 07032 07510 08007 08523 09058 09614 10190 10787 11406 16 45 0.06580 07040 07518 08015 08531 09067 09623 10199 10797 11416 15 46 06588 07048 07527 08024 08540 09076 09632 10209 10807 11427 14 47 06595 07056 07535 0S032 08549 09085 09642 10219 10817 11437 13 48 06603 07064 07543 08041 08558 09094 09651 10229 10827 11448 12 49 06610 07071 07551 08049 08567 08575 09104 09661 10239 10838 11458 11 50 0.06618 07079 07559 08058 09113 09670 10248 10848 11469 10 51 06625 07087 07567 08066 08584 09122 09680 10258 10858 11479 9 52 06633 07095 07575 08075 08593 09131 09689 10268 10868 11490 8 53 06640 07103 07584 08084 08602 09140 09699 10278 10878 11501 7 54 06648 07111 07592 08092 08611 09149 09708 10288 10888 11511 6 5 55 0.06656 07119 07600 08100 08619 09158 09718 10298 10899 11522 56 06663 07126 07608 08109 08628 09168 09727 10307 10909 11532 4 57 06671 07134 07616 08117 08637 09177 09737 10317 10919 11543 3 58 06678 07142 07624 08126 08646 09186 09746 10327 10929 11553 2 69 06686 07150 07633 08134 08655 09195 09756 10337 10940 11564 1 60 06693 07158 07641 08143 08664 09204 09765 10347 52° 10950 11575 59' 58° 57° 56' 55° 54° 53° 51° 50° M. p OLAR DISTANCK. CO-SECAI fT. 102 TABLE XXVII. LOGARITHMS OF THE LATITUDE AND POLAR DISTANCE. LATITUDE, OR POLAR DISTANCE. 8KCAST. M. o o 40 or 130 o o 41.131 12222 12233 12244 12255 12266 o 42.132 o o 43.133 o 44.134 o o 45.135 o o 46.136 o o 47.137 o o 48.138 17449 17463 17177 17491 17505 C 49.139 1 2 3 4 0.11575 11585 11596 11606 11617 12893 12904 12915 12927 12938 13587 13599 13611 13623 13634 14307 14319 14331 14343 14355 15051 15064 15077 15089 15102 15823 15836 15849 15862 15875 16622 16635 16649 16662 .16676 18306 18320 18335 18349 18364 60 59 58 57 56 5 6 7 8 9 0.11628 11638 11649 11660 11670 12277 12288 12299 12310 12321 12950 12961 12972 12984 12995 13646 13658 13670 13682 13694 14368 14380 14392 14404 14417 15115 15127 15140 15153 15165 15888 15901 15915 15928 15941 16689 16703 16717 16730 16744 17519 17533 17547 17561 17576 18378 18393 18408 18422 18437 55 54 53 52 51 10 11 12 13 14 0.11681 11692 11702 11713 11724 12332 12343 12354 12365 12376 13007 13018 13030 13041 13053 13705 13717 13729 13741 13753 14429 14441 14453 14466 14478 15178 15191 15204 15216 15229 15954 15967 15980 15994 16007 16758 16771 16785 16798 16812 17590 17604 17618 17632 17646 18451 18466 18481 18495 18510 50 49 48 47 46 15 16 17 18 19 0.11734 11745 11756 11766 11777 12387 12399 12410 12421 12432 12443 12454 12465 12476 12487 13064 13076 13087 13098 13110 13121 13133 13145 13156 13168 13765 13777 13789 13800 13812 14490 14503 14515 14527 14540 15242 15255 15267 15280 15293 16020 16033 16046 16060 16073 16826 16839 16853 16867 16880 17660 17674 17689 17703 17717 18525 18539 18554 18569 18583 45 44 43 42 41 20 21 22 23 24 0.11788 11799 11809 11820 11831 13824 13836 13848 13860 13872 14552 14564 14577 14589 14601 15306 15318 15331 15344 15357 16086 16099 16113 16126 16139 16894 16908 16922 16935 16949 17731 17745 17760 17774 17788 18598 18613 18628 18642 18657 40 39 38 37 36 25 26 1 27 28 29 0.11842 11852 11863 11874 11885 12499 12510 12521 12532 12543 13179 13191 13202 13214 13225 13884 13896 13908 13920 13932 14614 14626 14639 14651 14663 15370 15382 15395 15408 15421 16152 16166 16179 16192 16205 16963 16977 16990 17004 17018 17802 17816 17831 17845 17859 18672 18686 18701 18716 18731 35 34 33 32 31 30 31 32 33 34 0.11895 11906 11917 11928 11939 12554 12566 12577 12588 12599 13237 13248 13260 13272 13283 13944 13956 13968 13980 13992 14676 14688 14701 14713 14726 15434 15447 15460 15472 15485 16219 16232 16245 16259 16272 17032 17045 17059 17073 17087 17874 17888 17902 17916 17931 18746 18760 18775 18790 18805 30 29 28 27 26 35 36 37 38 39 0.11949 11960 11971 11982 11993 0.12004 12015 12025 12036 12047 12610 12622 12633 1264*4 12655 13295 13306 13318 13330 13341 14004 14016 14028 14040 14052 14738 14750 14763 14775 14788 15498 15511 15524 15537 15550 16285 16299 16312 16326 16339 17101 17115 17128 17142 17156 17945 17959 17974 17988 18002 18820 18834 18849 18864 18879 25 24 23 22 21 20 19 18 17 16 40 41 42 43 44 12666 12678 12689 12700 12712 13353 13365 13376 13388 13400 14064 14076 14088 14100 14112 14800 14813 14825 14838 14850 15563 15576 15589 15602 15615 16352 16366 16379 16392 16406 17170 17184 17198 17212 17225 18017 18031 18045 18060 18074 18894 18909 18924 18939 18954 45 46 47 48 49 0.12058 12069 12080 12091 12102 12723 12734 12745 12757 12768 13411 13423 13435 13446 13458 14124 14136 14149 14161 14173 14863 14875 14888 14900 14913 15627 15640 15653 15666 15679 16419 16433 16446 16460 16473 17239 17253 17267 17281 17295 18089 18103 18118 18132 18146 18968 18983 18998 19013 19028 15 14 13 12 11 50 51 52 53 54 0.12113 12123 12134 12145 12156 12779 12791 12802 12813 12825 13470 13482 13493 13505 13517 14185 14197 14209 14221 14234 14926 14938 14951 14963 14976 15692 15705 15718 15731 15745 16487 16500 16514 16527 16541 17309 17323 17337 17351 17365 18161 18175 18190 18204 18219 19043 19058 19073 19088 19103 10 9 8 7 6 55 56 57 58 59 60 0.12167 12178 12189 12200 12211 12222 12836 12847 12859 12870 12881 12893 13528 13540 13552 13564 13575 13587 14246 14258 14270 14282 14294 14307 14988 15001 15014 15026 15039 15051 15758 15771 15784 15797 15810 15823 16554 16568 16581 16595 16608 16622 17379 17393 17407 17421 17435 17449 18233 18248 18262 18277 18291 18306 19118 19133 19148 19163 19178 19193 5 4 3 2 1 49° 48° 47" 46° 45° 44° 43° 42' 41° 40° M. POLAR DISTANCE. CO-SECANT. | TABLE XXVII. 108 LOGARITHMS OF THE LATITUDE AND POLAR DISTANCK • LATITUDE. SECANT. ■ 1 o o o o o o o o o o 1 M. 50 51 52 53 54 55 56 57 58 59 60 0.19193 20113 21066 22054 23078 24141 25244 26389 27579 28816 1 19208 20128 21082 22070 23096 24159 25263 26409 27599 28837 59 2 19223 20144 21098 22087 23113 24177 25281 26428 27619 28858 58 3 19238 20160 21114 22104 23130 24195 25300 26448 27640 28879 57 4 19254 20175 21131 22121 23148 24213 2 fT. 106 TABLE XXVII. LOGARITHMS OF THE LATITUDE AND POLAR DISTANCE. | LATITDDE. SECANT. 1 o o o o o o o ■ o n o o M. 80 81 82 83 84 85 86 87 88 89 60 0.76033 80567 85644 91411 0.98077 1.05970 1.15642 1.28120 1.45716/1.75814 1 76105 80647 85734 91514 98197 06115 15823 28362 46081 76544 59 2 76177 80727 85825 91617 98318 06260 16004 28605 46448 77287 58 3 76248 80807 85915 91720 98439 06406 16187 28849 46817 78042 57 4 76321 80887 86006 86096 91824 98560 06552 16370 29095 47190 78811 56 55 5 0.76393 80967 91928 0.98682 1.06699 1.16554 1.29342 1.47566 1.79593 6 76465 81048 86187 92032 98804 06846 16739 29591 47945 80390 54 7 76538 81129 86278 92137 98926 06993 16925 29841 48327 81202 53 8 76610 81210 86370 92242 99049 07141 17112 30093 48713 82029 52 9 76683 81291 86461 92347 99172 07290 17299 30346 49103 82872 51 10 0.76756 81372 86553 92452 0.99296 1.07439 1.17487 1.30600 1.49495 1.83732 50 11 76829 81453 86645 92558 99419 07589 17676 30856 49892 84609 49 12 76902 81535 86737 92663 99544 07739 17866 31114 50292 85505 48 13 76975 81617 86829 92769 99668 07890 18056 31373 50696 86419 47 14 15 77048 81698 86922 92876 99793 08041 1 08193 18248 31633 51104 87353 1.88307 46 45 0.77122 81780 87015 92982 0.99918 1.18440 1.31896 1.51515 16 77195 81863 87108 93089 1.00044 08345 18633 32159 51931 89283 44 17 77269 81945 87201 93196 00170 08498 18827 32425 52350 90282 43 18 77343 82027 87294 93304 00296 08651 19022 32692 52774 91304 42 19 77417 82110 87388 87481 93411 00423 08805 19218 32901 53201 92350 41 20 0.77491 82193 93519 1.00550 1.08960 1.19415 1 .33231 1.53633 1.93422 40 21 77565 82276 87576 93628 00678 09115 19612 33503 54070 94522 39 22 77639 82359 87669 93736 00806 09270 19811 33777 54511 95650 38 23 77714 82442 87764 93845 00934 09426 20010 34053 54956 96808 37 24 77789 82526 87858 93954 01063 09583 20211 34330 55406 97998 36 35 25 0.77863 82609 87953 94063 1.01192 1.09740 1.20412 1.34609 1.55861 1.99222 26 77938 82693 88048 94173 01321 09898 20614 34890 56320 2.00480 34 27 78013 82777 88143 94283 01451 10057 20817 35173 56784 01777 33 28 78088 82861 88239 94393 01581 L0216 21021 35457 57254 03113 32 29 30 78164 82945 88334 94503 94614 01712 10375 21226 35744 57728 04492 31 30 0.78239 83030 88430 J. 01843 1.10536 1.21432 1.36032 1.58208 2.05916 31 78315 83114 88526 94725 01974 10696 21639 36322 58693 07388 29 32 78390 83199 88623 94836 02106 10858 21848 36615 59184 08912 28 33 78466 83284 88719 94948 02238 11020 22057 36909 59680 10491 27 34 78542 83369 88816 95060 02371 11183 22267 37205 60182 12130 2.13834 26 25 35 0.78618 83455 88913 95172 1.02504 1.11346 1.22478 1.37503 1.60690 36 78694 83540 89010 95285 02637 11510 22690 37804 61204 15607 24 37 78771 83626 89107 95397 02771 11674 22903 38106 61724 17455 23 38 78847 83711 89205 95510 02905 11839 23117 38411 62250 19385 22 39 78924 83797 89303 95624 03040 12005 23332 38718 62783 21406 21 20 40 0.79001 83884 89401 95738 1.03175 1.12171 1.23549 1.39027 1.63322 2.23525 41 79078 83970 89499 95851 03311 12339 23766 39338 63868 25752 19 42 79155 84056 89598 95966 03447 12506 23985 39651 64422 28100 18 43 79232 84143 89696 96080 03583 12675 24204 39967 64982 30583 17 44 79309 84230 89795 96195 03720 12844 24425 40285 65550 33216 16 45 0.79387 84317 89894 96310 1.03857 1.13013 1.24647 1.40605 1.66125 2.36018 15 46 79465 84404 89994 96426 03995 13184 24870 40928 66708 39015 14 47 79542 84492 90093 96542 04133 13355 25094 41253 67298 42233 13 48 79620 84579 90193 96658 04272 13526 25320 41581 67897 45709 12 49 79698 84667 90293 96774 04411 13699 25546 41911 68505 49488 11 10 50 0.79777 84755 90394 96891 1 04550 1.13872 1.25774 1.42243 1.69121 2.53627 51 79855 84843 90494 97008 04690 14045 26003 42579 69746 58203 9 52 79933 84931 90595 97126 04830 14220 26233 42916 70379 63318 8 53 80012 85020 90696 97243 04971 14395 26465 43257 71023 69118 7 54 80091 85109 90798 90899 973(il 05113 14571 26697 43600 71676 75812 6 5 55 0.80170 85197 97480 1.05254 1.14748 1.26931 1.43946 1.72339 2.83730 56 80249 85286 91001 97598 05397 14925 27166 44295 73012 93121 4 57 80328 85376 91103 97717 05539 15103 27403 44646 73696 3.05915 3 58 80408 85465 91205 97837 05683 15282 27640 45001 74391 23524 2 59 80487 85555 91308 97957 05826 15461 27880 45358 75097 53627 1 60 80567 85644 91411 98077 05970 15642 28120 45718 2" 75814 9° 8° 7° 6" 5° 4° 3' 1° 0° M. POLAK DISTANCE. CO-SECaNT. I TABLE XXVllL LOGARITHMS OF THE HALF SUM AND DIFFERENCE. HALF 8UM. 107 CO-SINK. M. o 89 1 2 3 4 10 11 12 13 14 15 16 17 18 19 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 24186 23456 22713 21958 21189 . 20407 19610 18799 17971 17128 88 5 J 282 53919 53552 53183 5 2810 3.52434 52055 51673 51287 50897 3.1 (i268 15391 14495 13581 12647 3.11693 10717 09718 08696 07650 3 87 .71880 71638 71395 71151 70905 .70658 70409 70159 69907 69654 86 20 3 06578 21 05478 22 04350 23 03192 24 02002 25 3 .00779 26 2 .99520 27 98223 28 96887 29 95508 2.94084 92612 91088 89509 87870 505(15 50108 49708 49304 48896 48485 48069 47650 47226 46799 85 3.84358 84177 83996 83813 83630 3.83446 83261 83075 82888 82701 ,46367 45930 45489 45044 44594 .69400 69144 68886 68627 _68367 .68104 67841 67575 67308 67039 .66769 66497 66223 65947 65670 3.82513 82324 82134 81944 81752 3.441393 43680 43216 42746 42272 3.41792 41307 40816 40320 39818 2.86166 84393 82545 80615 78594 3.39310 38796 38276 37750 37217 2.76475 74248 71900 69417 66784 2.63982 60985 57767 54291 50512 .94030 93885 93740 93594 93448 3.93301 93154 93007 92859 _92710 .92561 92411 92261 92110 91959 o 84 4. 01923 01803 01682 01561 0J440 .01318 01196 01074 00951 00828 o 83 4.0S589 084S6 08383 08280 08176 o 82 .08072 07968 07863 07758 07653 3.81560 81367 81173 80978 80782 3.91807 91655 91502 91349 91195 .00704 00581 00456 00332 00207 14356 14266 14175 14085 13994 13904 13813 13722 13630 13539 81 19433 19353 19273 19193 19113 3. 80585 80388 80189 79990 79789 3.91040 90885 90730 90574 90417 .65391 65110 64827 64543 64256 .63968 63678 63385 63091 62795 3.79588 79386 79183 78979 78774 3.78568 78361 78152 77943 77733 3. 3.90260 90102 89943 89784 89625 00082 .99956 99830 99704 99577 99450 99322 99194 99066 98937 .07548 07442 07337 07231 07124 3.98808 98679 98549 98419 98288 4.05937 05827 05717 05607 05497 .62497 62196 61894 61589 61282 3.36678 36132 35578 35018 34450 3.60973 60662 60349 60033 59715 2.46373 41797 36682 30882 24188 2.16270 06579 1.94085 76476 46373 ('0000 0^ ,33875 33292 32702 32103 31495 .30879 30255 29621 28927 28324 3.27661 26988 26304 25609 24903 24186 V 3.89464 89304 89142 88980 88817 3.77522 77310 77097 76883 76667 3.76451 76234 76015 75796 75575 .59395 59072 58747 58419 58089 3. 3.98157 98026 97894 97762 97629 3.88654 88490 88326 88161 87995 3.87829 87661 87494 87325 87156 75353 75130 74906 74680 74454 .57757 3 57421 57084 56743 56400 .56054 55705 55354 54999 54642 54282 ,74226 73997 73767 73535 7330 .73069 72834 72597 72360 72120 71880 .86987 86816 86645 86474 86301 .86128 85955 85780 85605 85429 3.97496 97363 97229 97095 96960 .07018 06911 06804 06696 06589 .06481 06372 06264 06155 06046 13447 13355 13263 13171 13078 12985 12892 12799 12706 12612 12519 12425 12331 12236 12142 19033 18952 18871 18790 18709 o 80 23967 23895 23823 23752 2367f) 23607 23535 23462 23390 23317 18628 18547 18465 18383 18302 18220 18137 18055 17973 17890 4.05386 05275 05164 05052 04940 3.96825 96689 96553 96417 96280 .96143 96005 95867 95728 90589 .85252 85075 84897 84718 84539 84358 .95450 95310 95170 95029 94887 3.94746 94603 94461 94317 94174 94030 .04828 04715 04603 04490 04376 .04262 04149 04034 03920 03805 12047 11952 11857 11761 11666 17807 17724 17641 17558 17474 11570 11474 11377 11281 11184 17391 17307 17223 17139 17055 11087 10990 10893 10795 10697 4.03690 03574 03458 Co342 03226 4.03109 02992 02874 02757 02639 4.02520 02402 02283 02163 02043 01923 10599 10501 10402 10304 10205 10106 10006 09907 09807 09707 09606 09506 09405 09304 09202 16970 16886 16801 16716 16631 16545 16460 16374 16289 16203 16116 16030 15944 15857 15770 15683 15596 15508 1C421 15233 09101 08999 08897 08795 08692 08589 15245 15157 15069 14980 14891 14803 14714 14624 14535 14445 14356 8° 23244 23171 23098 23025 22952 22878 22805 22731 22657 22583 60 59 58 57 56 55 54 53 52 51 22509 22435 22361 22286 22211 50 49 48 47 46 22137 22062 21987 21912 21836 21761 21685 21610 21534 21458 21382 21306 21229 21153 21076 45 44 43 42 _41 40 39 38 37 _36 35 34 33 32 31 30 29 28 27 26 20999 20922 20845 20768 20691 20613 20535 20458 20380 20302 20223 20145 20067 19988 19909 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 19830 19751 19672 19592 19513 19433 10 9 8 7 6 5 4 3 2 1 M. DIFFERENCE. SINE. 108 TABLE XXVIII. -] LOGARITHMS OF THE HALF SUM AND DIFFERENCK 1 HALF SUM. CO-BINK. o o o o o o o o o M. 79 78 77 76 75 74 73 46594 72 71 70 4.28060 31788 35209 38368 41300 44034 48998 51264 53405 60 1 27995 31728 35154 38317 41252 43990 46552 48959 51227 53370 59 2 27930 31669 35099 38266 41205 43946 46511 48920 51191 53336 58 3 27864 31609 35044 38215 41158 43901 46469 48881 51154 53301 57 4 5 27799 31549 34989 38164 41110 43857 46428 48842 51117 53266 56 55 4.27734 31490 34934 38113 41063 43813 46386 48803 51080 53231 6 27668 31430 34879 38062 41016 43769 46345 48764 51043 53196 54 7 27602 31370 34824 38011 40968 43724 46303 48725 51007 53161 53 8 27537 31310 34769 37960 40921 43680 46262 48686 50970 53126 52 9 27471 31250 34713 37909 40873 43635 46220 48647 50933 53092 51 10 4.27405 31189 34658 37858 40825 43591 46178 48607 50896 53056 50 11 27339 31129 34602 37806 40778 43546 46136 48568 50858 53021 49 12 27273 31068 34547 37755 40730 43502 46095 48529 50821 52986 48 13 27206 31008 34491 37703 40682 43457 46053 48490 50784 52951 47 14 27140 30947 34436 37652 37600 40634 43412 46011 48450 50747 52916 46 15 4.27073 30887 34380 40586 43367 45969 48411 50710 52881 45 16 27007 30826 34324 37549 40538 43323 45927 48371 50673 52846 44 17 26940 30765 34268 37497 40490 43278 45885 48332 50635 52811 43 18 26873 30704 34212 37445 40442 43233 45843 48292 50598 52775 42 19 20 26806 30643 34156 37393 40394 43188 45801 48252 50561 52740 41 4.26739 30582 34100 37341 40346 43143 45758 48213 50523 52705 40 21 26672 30521 34043 37289 40297 43098 45716 48173 50486 52669 39 22 26605 30459 33987 37237 40249 43053 45674 48133 50449 52634 38 23 26538 30398 33931 37185 40200 43008 45632 48094 50411 52598 37 24 26470 30336 33874 37133 40152 42962 45589 48054 50374 52563 36 25 4.26403 30275 33818 37081 40103 42917 45547 48014 50336 52527 35 26 26335 30213 33761 37028 40055 42872 45504 47974 50298 52492 34 27 26267 30151 33704 36976 40006 42826 45462 47934 50261 52456 33 28 26199 30090 33647 36924 39958 42781 45419 47894 50223 52421 32 29 26131 30028 33591 36871 39909 42735 45377 47854 50185 52385 52350 31 30 30 4.26063 29966 33534 36819 39860 42690 45334 47814 50148 31 25995 29903 33477 36766 39811 42644 45292 47774 50110 52314 29 32 25927 29841 33420 36713 39762 42599 45249 47734 50072 52278 28 33 25858 29779 33362 36660 39713 42553 45206 47694 50034 52242 27 34 25790 29716 33305 33248 36608 39664 42507 45163 47654 49996 52207 26 35 4.25721 29654 36555 39615 42461 45120 47613 49958 52171 25 36 25652 29591 33190 36502 39566 42416 45077 47573 49920 52135 24 37 25583 29529 33133 36449 39517 42370 45035 47533 49882 52099 23 38 25514 29466 33075 36395 39467 42324 44992 47492 49844 52063 22 39 40 25445 4.25376 2940.3 33018 36342 39418 42278 44948 47452 49806 52027 21 20 29340 32960 36289 39369 42232 44905 47411 49768 51991 41 25307 29277 32902 36236 39319 42186 44862 47371 49730 51955 19 42 25237 29214 32844 36182 39270 42140 44819 47330 49692 51919 18 43 •^5168 29150 32786 36129 39220 42093 44776 47290 49654 51883 17 44 25098 29087 32728 36075 39170 42047 44733 47249 49615 51847 16 45 4.25028 29024 32670 36022 39121 42001 44689 47209 49577 51811 15 46 24958 28960 32612 35968 39071 41954 44646 47168 49539 51774 14 47 24888 28896 32553 35914 39021 41908 44602 47127 49500 51738 13 48 24818 28833 32495 35860 38971 41861 44559 47086 49462 51702 12 49 24748 28769 32437 35806 38921 41815 44516 47045 49424 51666 11 50 4.24677 28705 32378 35752 38871 41768 44472 47005 49385 51629 10 51 24607 28641 32319 35698 38821 41722 44428 46964 49347 51593 9 52 24536 28577 32261 35644 38771 41675 44385 46923 49308 51557 8 53 24466 28511 32202 35590 38721 41628 44341 46882 49269 51520 7 54 24395 28448 32143 35536 38670 41582 41535 44297 44253 46841 49231 51484 6 55 4.24324 28384 32084 35481 38620 46800 49192 51447 5 56 24253 28319 32025 35427 38570 41488 44210 46758 49153 51411 4 57 24181 28254 31966 35373 38519 41441 44166 46717 49115 51374 3 58 24110 28190 31907 35318 38469 41394 44122 46676 49076 51338 2 59 24039 28125 31847 35263 38418 41347 44078 46635 49037 51301 1 60 23967 28060 3178S 35209 38368 41300 44034 46594 48998 51264 10° 11' 12° 13° 14° 15° 16° 17° 18* 19° M. DIFFER ENCE. SIN E. TABLE XXVIII. 109 1 LOGARITHMS 1 OF THE HALF SUM AND DIFFERENCE. HALF SUM. CO-SINE. 1 o o o o o o o o o M. 69 68 57358 67 66 65 64 63 62 61 60 4 55433 59188 60931 62595 64184 65705 67161 68557 69897 60 1 55400 57326 59158 60903 62568 64158 65680 67137 68534 69875 59 2 55367 57295 59128 60875 62541 64132 65655 67113 68512 69853 58 3 55334 57264 59098 60846 62513 64106 65630 67090 68489 69831 57 4 5 55301 57232 59069 60818 62486 64080 65605 67066 68466 69809 56 55 4.55268 57201 59039 60789 62459 &4054 65580 67042 68443 69787 6 55235 57169 59009 60761 62432 64028 65556 67018 68420 69765 54 7 55202 57138 58979 60732 62405 64002 65531 66994 68397 69743 53 8 55169 57107 58949 60704 62377 63976 65506 66970 68374 69721 52 9 55136 57075 58919 60675 62350 63950 65481 66946 68351 69699 51 10 4.55102 57044 58889 60646 62323 63924 65456 66922 68328 69677 50 11 55069 57012 58859 60618 62296 63898 65431 66899 68305 69655 49 12 55036 56980 58829 60589 62268 63872 65406 66875 68282 69633 48 13 55003 56949 58799 60561 62241 63846 65381 66851 68260 69611 47 14 54969 56917 58769 60532 62214 63820 65356 66827 68237 69589 46 15 4.54936 56886 58739 60503 62186 63794 65331 66803 68213 69567 45 16 54903 56854 58709 60474 62159 63767 65306 66779 68190 69545 44 17 54869 56822 58678 60446 62131 63741 65281 66755 68167 69523 43 18 54836 56790 58648 60417 62104 63715 65255 66731 68144 69501 42 19 54802 56759 58618 60388 62076 63689 65230 66706 68121 69479 41 20 4.54769 56727 58588 60359 62049 63662 65205 66682 68098 69456 40 21 54735 56695 58557 60331 62021 63636 65180 66658 68075 69434 39 22 54702 56663 58527 60302 61994 63610 65155 66634 68052 69412 38 23 54668 56631 58497 60273 61966 63583 65130 66610 68029 69390 37 24 54635 56599 58467 60244 61939 63557 65104 66586 68006 69368 36 25 4.54601 56568 58436 60215 61911 63531 65079 66562 679«2 69345 35 26 54567 56536 58406 60186 61883 63504 65054 66537 67959 69323 34 27 54^34 56504 58375 60157 61856 63478 65029 66513 67936 69301 33 28 54500 56472 58345 60128 61828 63451 65003 66489 67913 69279 32 29 54466 56440 58314 60099 61800 63425 64978 66465 67890 69256 31 30 4.54433 56408 58284 60070 61773 63398 64953 66441 67866 69234 30 31 54399 56375 58253 60041 61745 63372 64927 66416 67843 69212 29 32 54365 56343 58223 60012 61717 63345 64902 66392 67820 69189 28 33 54331 56311 58192 59983 61689 63319 64877 66368 67796 69167 27 34 35 54297 4.54263 56279 58162 59954 61662 63292 64851 66343 67773 69144 26 56247 58131 59924 61634 63266 64826 66319 67750 69122 25 36 54229 56215 58101 59895 61606 63239 64800 66295 67726 69100 24 37 54195 56182 58070 59866 61578 63213 64775 66270 67703 69077 23 38 54161 56150 58039 59837 61550 63186 64749 66246 67680 69055 22 39 40 54127 4.54093 56118 58008 59808 61522 63159 64724 66221 67656 69032 21 20 56085 57978 59778 61494 63133 64698 66197 67633 69010 41 54059 56053 57947 59749 61466 63106 64673 66173 67609 68987 19 42 54025 56n21 57916 59720 61438 63079 64647 66148 67586 68965 18 43 53991 55988 57885 59690 61410 63052 64622 66124 67562 68542 17 44 53957 55956 57855 59661 61382 63026 64596 66099 67539 68920 68897 16 15 45 4.53922 55923 57824 59632 61354 62999 64571 66075 67515 46 53888 55891 57793 59602 61326 62972 64545 66050 67492 68875 14 47 53854 55858 57762 59573 61298 62945 64519 66025 67468 68852 13 48 53819 55826 57731 59543 61270 62918 64494 66001 67445 68829 12 49 50 53785 55793 57700 59514 61242 62892 62865 64468 65976 67421 68807 11 4.53751 55761 57669 59484 61214 64442 65952 67398 68784 10 51 53716 55728 57638 59455 61186 62838 64417 65927 67374 68762 9 52 53682 55695 57607 59425 61158 62811 64391 65902 67350 68739 8 53 53647 55663 57576 59396 61129 62784 64365 65878 67327 68716 7 54 53613 55630 57545 59366 61101 62757 64339 64313 65853 67303 68694 6 55 4.53578 55597 57514 59336 61073 62730 65828 67280 68671 5 56 53544 55564 57482 59307 61045 62703 64288 65804 67256 68648 4 57 53.509 55532 57451 59277 61016 62676 64262 65779 67232 68625 3 58 53475 55499 57420 59247 60988 62649 64236 65754 67208 68603 2 59 53440 55466 57389 59218 60960 62622 64210 65729 67185 68580 1 60 5340.5 55433 57358 59188 60931 62595 64184 65705 67161 68557 20' 2/ 22° 23° 24° 25° 26° 27° 28° 29° M. DIFFER] ENCE. SIN E. HO LOGi TABLE XXVIII. LRITHMS OF THE HALF SUM AND DIFFERENCE. HALF SUM. C0-8INE. 1 o o o o o o o o o « M. 59' 58 57 56 55 54 53 52 51 50 60 4.71184 72421 73611 74756 75859 76922 77946 78934 79887 80807 1 71163 72401 73591 74737 75841 76904 77930 78918 79872 80792 59 2 71142 72381 73572 74719 75823 76887 77913 78902 79856 807^7 58 3 71121 72360 73552 74700 75805 76870 77896 78886 79840 80762 57 4 71100 72340 73533 74681 75787 76852 77879 78869 79825 80746 56 65 5 4.71079 72320 73513 74662 75769 76835 77862 78853 79809 80731 6 71058 72299 73494 74644 75751 76817 77846 78837 79793 80716 54 7 71036 72279 73474 74625 75733 76800 77829 78821 79778 80701 53 8 71015 72259 73455 74606 75714 76782 77812 78805 79762 80686 52 9 10 70994 72238 73435 74587 75696 76765 77795 78788 79746 80671 51 50 4.70973 72218 73416 74568 75678 76747 77778 78772 79731 80656 11 70952 72198 73396 74549 75660 76730 77761 78756 79715 80641 49 12 70931 72177 73377 74531 75642 76712 77744 78739 79699 80625 48 13 70909 72157 73357 74512 75624 76695 77727 78723 79684 80610 47 14 70888 72137 73337 74493 75605 76677 77711 78707 79668 80595 46 15 4.70867 72116 73318 74474 75587 76660 77694 78691 79652 80580 45 16 70846 72096 73298 74455 75569 76642 77677 78674 79636 80565 44 17 70824 72075 73278 74436 75551 76625 77660 78658 79621 80550 43 18 70803 72055 73259 74417 75533 76607 77643 78642 79605 80534 42 19 70782 72034 73239 73219 74398 75514 76590 77626 78625 79589 80519 41 20 4.70761 72014 74379 75496 76572 77609 78609 79573 80504 40 21 70739 71994 7320 ) 74360 75478 76554 77592 78592 79558 80489 39 22 70718 71973 73180 74341 75459 76537 77575 78576 79542 80473 38 23 70697 71952 73160 74322 75441 76519 77558 78560 79526 80458 37 24 70675 71932 73140 74303 74284 75423 76501 77541 78543 78527 79510 80443 36 25 4.70654 71911 73121 75405 76484 77524 79494 80428 35 26 70633 71891 73101 74265 75386 76466 77507 78510 79478 ^0412 34 27 70611 71870 73081 74246 75368 76448 77490 78494 79463 80397 33 28 70590 71850 73061 74227 75350 76431 77473 78478 79447 80382 32 29 30 70568 71829 73041 74208 74189 75331 76413 77456 78461 79431 80366 31 30 4.70547 71809 73022 75313 76395 77439 78445 79415 80351 31 70525 71788 73002 74170 75294 76378 77422 78428 79399 80336 29 32 70504 71767 72982 74151 75276 76360 77405 78412 79383 80320 28 33 70482 71747 72962 74132 75258 76342 77387 78395 79367 80305 27 34 70461 71726 72'»42 74113 75239 76324 77370 78379 79351 80290 26 25 35 4.70439 71705 72922 74093 75221 76307 77353 78362 79335 80274 36 70418 71685 72902 74074 75202 76289 77336 78346 79319 80259 24 37 70396 71664 72883 74055 75184 76271 77319 78329 79304 80244 23 38 70375 71643 72863 74036 75165 76253 77302 78313 79288 80228 22 39 70353 71622 72843 74017 75147 76236 77285 78296 79272 80213 21 20 40 4.70332 71602 72823 73997 75128 76218 77268 78280 79256 80197 41 70210 71581 72803 73978 75110 76200 77250 78263 79240 80182 19 42 70288 71560 72783 73959 75091 76182 77233 78246 79224 80166 18 43 70267 71539 72763 73940 75073 76164 77216 78230 79208 80151 17 44 70245 71519 71498 72743 73921 75054 76146 77199 78213 79192 80136 16 45 4.70224 72723 73901 75036 76129 77181 78197 79176 80120 15 46 7^202 71477 72703 73882 75017 76111 77164 78180 79160 80105 14 47 7'^180 71456 72683 73863 74999 76093 77147 78163 79144 80089 13 48 •^1159 71435 72663 73843 74980 76075 77130 78147 79128 80074 12 49 73137 71414 72643 73824 74961 74943 76057 77112 78130 7P111 80058 11 10 50 4.70115 71393 72622 73805 76039 77095 78113 79095 80043 51 70093 71373 72602 73785 74924 76021 77078 78097 79079 80027 9 52 70072 71352 72582 73766 74906 76003 77061 78080 79063 80012 8 53 70050 71331 72562 73747 74887 75985 77043 78063 79047 79996 7 54 55 70028 71310 72542 72522 73727 74868 75967 77026 78047 79031 79981 6 5 4.70006 71289 73708 74850 75949 77009 78030 79015 79965 56 69984 71268 72502 73689 74831 75931 76991 78013 78999 79950 4 57 69963 71247 72482 73669 74812 75913 76974 77997 78983 79934 3 58 69941 71226 72461 73650 74794 75895 76957 77980 78967 79918 2 59 69919 71205 72441 73630 74775 75877 76939 77963 78950 79903 1 60 69897 71184 72421 73611 74756 75859 76922 77946 37° 78934 79887 30° 31° 32° 33° 34° 35° 36° 38° 39° M. 1^^ DIFFER! -NCE. 8IN E. TABLE XXVIII. u, 1 LOGARITHMS OF THE HALF SUM AND DIFFERENCK HALF f 3UM. C0-8INE. o o o o o o o o " o M 49 48 82551 47 46 45 44 43 42 41 40 4 81fi94 83378 84177 84949 85693 86413 87107 87778 88425 60 1 SKjSO 82537 83365 84164 84936 85681 86401 87096 87767 88415 59 2 81665 82523 83351 84151 84923 85669 86389 87085 87756 88404 58 3 81651 82509 83338 84138 84911 85657 86377 87073 87745 88394 57 4 5 81636 82495 83324 84125 84898 85645 86366 87062 87734 88383 56 4.81622 82481 83311 84112 84885 856S2 86354 87050 87723 88372 55 6 81607 82467 83297 84099 84873 85620 86342 87039 87712 88362 54 7 SI 592 82453 83283 84085 84860 85608 86330 87028 87701 88351 53 8 81578 82439 83270 84072 84847 85596 86318 87016 87690 88340 52 9 81563 82424 83256 84059 84835 85583 86306 87005 87679 88330 51 10 4.81549 82410 83242 84046 84822 85571 86295 86993 87668 88319 50 11 81534 82396 83229 84033 84809 85559 86283 86982 87657 88308 49 12 81519 82382 83215 84020 84796 85547 86271 86970 87646 88298 48 13 81505 82368 83202 84006 84784 85534 86259 86959 87635 88287 47 14 15 81490 82354 83188 83993 84771 85522 86247 86947 87624 88276 46 4.81475 82340 83174 83980 84758 85510 86235 86936 87613 88266 45 16 81461 82326 83161 83967 84745 85497 86223 86924 87601 88255 44 17 81446 82311 83147 83954 84733 85485 86211 86913 87590 88244 43 18 81431 82297 83133 83940 84720 85473 86200 86902 87579 88234 42 19 20 81417 82283 83120 83927 84707 85460 85448 86188 86890 87568 88223 41 4.81402 82269 83106 83914 84694 86176 86879 87557 88212 40 21 81387 82255 83092 83901 84682 85436 86164 86867 87546 88201 39 22 81372 82240 83078 83887 84669 85423 86152 86855 87535 88191 38 23 SISS'^ 82226 83065 83874 84656 85411 86140 86844 87524 88180 37 24 81343 82212 83051 83861 84643 85399 86128 86832 87513 88169 36 25 4.81328 82198 83037 83848 84630 85386 86116 86821 87501 88158 35 26 81314 82184 83023 83834 84618 85374 86104 86809 87490 88148 34 27 81299 82169 83010 83821 84605 85361 86092 86798 87479 88137 33 28 81284 82155 82996 83808 84592 85349 86080 86786 87468 88126 32 29 81269 82141 82982 83795 84579 85337 86068 86775 87457 88115 31 30 4 81254 82126 82968 83781 84566 85324 86056 86763 87446 88105 30 31 81240 82112 82955 83768 84553 85312 86044 86752 87434 88094 29 32 81225 82098 82941 83755 84540 85299 86032 86740 87423 88083 28 33 81210 82084 82927 83741 84528 85287 86020 86728 87412 88072 27 34 81195 82069 82913 82899 83728 84515 85274 86008 86717 87401 88061 26 35 4.81180 82055 83715 84502 85262 85996 86705 87390 88051 25 36 81166 82041 82885 83701 84489 85250 85984 86694 87378 88040 24 37 81151 82026 82872 83688 84476 85237 85972 86682 87367 88029 23 38 81136 82012 82858 83674 84463 85225 85960 86670 87356 88018 22 39 81121 81998 82844 83661 84450 85212 85948 86659 87345 88007 21 20 40 4.81106 81983 82830 83648 84437 85200 85936 86647 87334 87996 41 81091 81969 82816 83634 84424 85187 85924 86635 87322 87985 19 42 81076 81955 82802 83621 84411 85175 85912 86624 87311 87975 18 43 81061 81940 82788 83608 84398 85162 85900 86612 87300 87964 17 44 81047 81926 82775 83594 84385 85150 85888 86600 87288 87953 16 45 4.81032 81911 82761 83581 84373 85137 85876 86589 87277 87942 15 46 81017 81897 82747 83567 84360 85125 85864 86577 87266 87931 14 47 81002 81882 82733 83554 84347 85112 85851 86565 87255 87920 13 48 80987 81868 82719 83540 84334 85100 85839 86554 87243 87909 12 49 80972 81854 82705 83527 84321 85087 85827 86542 87232 87898 87887 11 10 50 4.80957 81839 82691 83513 84308 85074 85815 86530 87221 51 80942 81825 82677 83500 84295 85062 85803 86518 87209 87877 9 52 80927 81810 82663 83486 84282 85049 85791 86507 87198 87866 8 53 80912 81796 82649 83473 84269 85037 85779 86495 87187 87855 7 54 80897 81781 82635 83459 84255 85024 85766 86483 87175 87844 6 5 55 4.80882 81767 82621 83446 84242 85012 85754 86472 87164 87833 56 80867 81752 82607 83432 84229 84999 85742 86460 87153 87822 4 57 80852 81738 82593 83419 84216 84986 85730 86448 87141 87811 3 58 80837 81723 82579 83405 84203 84974 85718 86436 87130 87800 2 59 80822 81709 82565 83392 84190 84961 85706 86425 87119 87789 1 60 80807 81694 82551 83378 84177 84949 85693 86413 87107 87778 40° 41° 42° 43° 44° 45° 46° 47° 48- 49° M. _^ DIFFER ENCE. SIN E. 8 112 TABLE XXVIII. LOGARITHMS OF THE HALF SUM AND DIFFERENCE. HALF SUM. . JO-SINE. 1 o o o o o o o o o M. 39 38 37 36 35 34 33 32 31 30 4.89050 89653 90235 90796 91336 91857 92359 92842 93307 93753 60 1 89040 89643 90225 90787 91328 91849 92351 92834 93299 93746 59 2 89030 89633 90216 90777 91319 91840 92343 92826 93291 93738 58 3 89020 89624 90206 90768 91310 91832 92334 92818 93284 93731 57 4 5 89009 89614 90197 90759 91301 91823 92326 92810 93276 93724 56 4.88999 89604 90187 90750 91292 91815 92318 92803 93269 93717 55 6 88989 89594 90178 90741 91283 91806 92310 92795 93261 93709 54 7 88978 89584 90168 90731 91274 91798 92302 92787 93253 93702 53 8 88968 89574 90159 90722 91266 91789 92293 92779 93246 93695 52 9 88958 89564 90149 90713 91257 91781 92285 92771 93238 93687 51 10 4.88948 89554 90139 90704 91248 91772 92277 92763 93230 93680 50 11 88937 89544 90130 90694 91239 91763 92269 92755 93223 93673 49 12 88927 89534 90120 90685 91230 91755 92260 92747 93215 93665 48 13 88917 89524 90111 90676 91221 91746 92252 92739 93207 93658 47 14 88906 89514 90101 90667 91212 91738 92244 92731 93200 93650 46 15 4.88896 89504 90091 90657 91203 91729 92235 92723 93192 93643 45 16 88886 89495 90082 90648 91194 91720 92227 92715 93184 93636 44 17 88875 89485 90072 90639 91185 91712 92219 92707 93177 93628 43 18 88865 89475 90063 90630 91176 91703 92211 92699 93169 93621 42 19 20 88855 89465 90053 90620 91167 91695 92202 92691 93161 93614 41 4.88844 89455 90043 90611 91158 91686 92194 92683 93154 93606 40 21 88834 89445 90034 90602 91149 91677 92186 92675 93146 93599 39 22 88824 89435 90024 90592 91141 91669 92177 92667 93138 93591 38 23 88813 89425 90014 90583 91132 91660 92169 92659 93131 93584 37 24 88803 89415 90005 90574 91123 91651 92161 92651 93123 93577 36 25 4.88793 89405 89995 90565 91114 91643 92152 92643 93115 93560 35 26 88782 89395 89985 90555 91105 91634 92144 92635 93108 93.562 34 27 88772 89385 89976 90546 91096 91625 92136 92627 93100 93554 id 28 88761 89375 89966 90537 91087 91617 92127 92619 93092 93547 32 29 88751 89364 89956 90527 91078 91608 92119 92611 93084 93539 31 30 4.88741 89354 89947 90518 91069 91599 92111 92603 93077 93532 30 31 88730 89344 89937 90509 91060 91591 92102 92595 93069 93525 29 32 88720 89334 89927 90499 91051 91582 92094 92587 93061 93517 28 33 88709 89324 89918 90490 91042 91573 92086 92579 93053 93510 27 34 88699 89314 89908 89898 90480 91033 91565 92077 92571 93046 93502 26 35 4.88688 89304 90471 91023 91556 92069 92563 93038 93495 25 36 88678 89294 89888 90462 91014 91547 92060 92555 93030 93487 24 37 88668 89284 89879 90452 91005 91538 92052 92546 93022 93480 23 38 88657 89274 89869 90443 90996 91530 92044 92538 93014 93472 22 39 88647 89264 89859 90434 90987 91521 92035 92530 93007 93465 21 40 4.88636 89254 89849 90424 90978 91512 92027 92522 92999 93457 20 41 88626 89244 89840 90415 90969 91504 92018 92514 92991 93450 19 42 88615 89233 89830 90405 90960 91495 92010 92506 92983 93442 18 43 88605 89223 89820 90396 90951 91486 92002 92498 92976 93435 17 44 88594 89213 89810 90386 90942 91477 91993 92490 92968 93427 16 45 4.88584 89203 89801 90377 90933 91469 91985 92482 92960 93420 15 ^ 46 88573 89193 89791 90368 90924 91460 91976 92473 92952 93412 14 47 88563 89183 89781 90358 90915 91451 91968 92465 92944 93405 13 48 88552 89173 89771 90349 90906 91442 91959 92457 92936 93397 12 49 50 88542 89162 «9761 90339 90896 91433 91951 92449 92929 93390 11 4.88531 89152 89752 90330 90887 91425 91942 92441 92921" 93382 10 51 88521 89142 89742 90320 90878 91416 91934 92433 92913 93375 9 52 88510 89132 89732 90311 90869 91407 91925 92425 92905 93367 8 53 88499 89122 89722 90301 90860 91398 91917 92416 92897 93360 7 54 88489 89112 89712 90292 90851 91389 91908 92408 92889 93362 6 5 55 4.88478 89101 89702 90282 90842 91381 91900 92400 92881 93344 56 88468 89091 89693 90273 90832 91372 91891 92392 92874 93337 4 57 88457 89081 89683 90263 90823 91363 91883 92384 92866 93329 3 58 88447 89071 89673 90254 90814 91354 91874 92376 92858 93322 2 59 88436 89060 89663 90244 90S05 91345 91866 92367 92850 93314 1 60 88425 89050 89653 90235 90796 91336 91857 92359 92842 93307 50° sr 52° 53° 54° 55° 56° 57° 58° 59° M. DIFFER ENCE. SIN rs. c TABLE XXVIII. 118 LOGARITHMS OF THE HALF SUM AND DIFFERENCE. HALF SUM. CO-SINE. M. o 29 e 28 o 27 o 26 95366' o 25 95728 o 24 o 23 o 22 o 21 o 20 4.94182 94593 94988 96073 96403 96717 97015 97299 60 1 I 94175 94587 94982 95360 95722 96067 96397 96711 97010 97294 59 | 2 9^4168 94580 94975 95354 95716 96062 96392 96706 97005 97289 58 3 94161 94573 94969 95348 95710 96056 96387 96701 97001 97285 57 4 5 94154 94567 94962 95341 95704 96050 96381 96696 96996 97280 56 55 4.94147 94560 94956 95335 95698 96045 96376 96691 96991 97276 6 94140 94553 94949 95329 95692 96039 96370 96686 96986 97271 54 7 94133 94546 94943 95323 95686 96034 96365 96681 96981 97266 53 8 94126 94540 94936 95317 95680 96028 96360 96676 96976 97262 52 9 10 94119 94533 94930 95310 95674 96022 96354 96670 96971 97257 51 4.94112 94526 94923 95304 9566S! 96017 96349 96665 96966 97252 50 11 94105 94519 94917 95298 95663 96011 96343 96660 96962 97248 49 12 94098 94513 94911 95292 95657 96005 96338 96655 96957 97243 48 13 94090 94506 94904 95286 95651 96000 96333 96650 96952 97238 47 14 94083 94499 94898 95279 95645 95994 96327 96645 96947 97234 46 45 15 4.94076 94492 94891 95273 95639 95988 96322 96640 96942 97229 1^ 94069 944*5 94884 95267 95633 95982 96316 96634 96937 97224 44 17 94062 94479 94878 95261 95627 95977 96311 96629 96932 97220 43 18 94055 94472 94871 95254 95621 95971 96305 96624 96927 97215 42 19 94048 94465 94865 94858 95248 95615 95965 96300 96294 96619 96614 96922 97210 41 20 4.94041 94458 95242 95609 95960 96917 97206 40 21 94034 94451 94852 95236 95603 95954 96289 96608 96912 97201 39 22 94027 94445 94845 95229 95597 95948 96284 96603 96907 97196 38 23 94020 94438 94839 95223 95591 95942 96278 96598 96903 97192 37 24 94012 94431 94832 95217 95585 95937 96273 96593 96898 97187 36 25 4.94005 94424 94826 95211 95579 95931 96267 96588 96893 97182 35 26 93998 94417 94S19 95204 95573 95925 96262 96582 96888 97178 34 27 93991 94410 94813 95198 95567 95920 96256 96577 96883 97173 33 28 93984 94404 94806 95192 95561 95914 96251 96572 96878 97168 32 29 30 93977 94397 94799 95185 95179 95555 95908 96245 96567 96873 97163 31 30 4.93970 94390 94793 95549 95902 96240 96562 96868 97159 31 93963 94383 94786 95173 95543 95897 96234 96556 96863 97154 29 32 93955 94376 94780 95167 95537 95891 96229 96551 96858 97149 28 33 93948 94369 94773 95160 95531 95885 96223 96546 96853 97145 27 34 93941 94362 94767 94760 95154 95525 95879 96218 96541 96848 97140 26 25 35 4.93934 94355 95148 95519 95873 96212 96535 96843 97135 36 93927 94349 94753 95141 95513 95868 96207 96530 96838 97130 24 37 93920 94342 94747 95135 95507 95862 96201 96525 96833 97126 23 38 93912 94335 94740 95129 95500 95856 96196 96520 96828 97121 22 39 93905 94328 94734 95122 95494 95850 96190 96514 96823 97116 21 20 40 4.93898 94321 94727 95116 95488 95844 96185 96509 96818 97111 41 93891 94314 94720 95110 95482 95839 96179 96504 96813 97107 19 42 93884 94307 94714 95103 95476 95833 96174 96498 96808 97102 18 43 93876 94300 94707 95097 95470 95827 96168 96493 96803 97097 17 44 93869 94293 94286 94700 95090 95464 95821 96162 96488 96798 97092 16 45 4.93862 94694 95084 95458 95815 96157 96483 96793 97087 15 46 93855 94279 94687 95078 95452 95810 96151 96477 96788 97083 14 47 93847 94273 94680 95071 95446 95804 96146 96472 96783 97078 13 48 93840 94266 94674 95065 95440 95798 96140 96467 96778 97073 12 49 93833 94259 94667 95059 95434 95792 96135 96461 96772 97068 11 50 4.93826 94252 94660 95052 95427 95786 96129 96456 96767 97063 10 51 93819 94245 94654 95046 95421 95780 96123 96451 96762 97059 9 52 93811 94238 94647 95039 95415 95775 96118 96445 96757 97054 8 53 93804 94231 94640 95033 95409 95769 96112 96440 96752 97049 7 54 93797 94224 94634 94627 95027 95403 95763 96107 96435 96747 97044 6 5 55 4.93789 94217 95020 95397 95757 96101 96429 96742 97039 56 93782 94210 94620 95014 95391 95751 96095 96424 96737 97035 4 57 93775 94203 94614 95007 95384 95745 96090 96419 96732 97030 3 58 93768 94196 94607 95001 95378 95739 96084 96413 96727 97025 2 59 93760 94189 946)0 94995 95372 95733 96079 96408 96722 97020 1 60 93753 94182 94593 94988 95366 95728 96073 96403 67° 96717 97015 60° 61° 62° 63° 64° 65° 66° 68° 69° M. DIFFERENCE. SINK. 114 TABLE XXVIIl. n LOGARITHMS OF THE HALF SUM AND DIFFERENCE. 1 HALF SUM. co-anrx. o o o o o o O o o o M. 19 18 97821 17 16 15 14 13 12 11 10 4.97567 98060 98284 98494 98690 98872 99040 99195 99335 60 1 97563 97817 98056 98281 98491 98687 98869 99038 99192 99333 59 2 97558 97812 98052 98277 98488 98684 98867 99035 99190 99331 5S 3 97554 97808 98048 98273 98484 98681 98864 99032 99187 99328 .^7 4 5 97550 97804 98044 98270 98481 98678 98861 99030 99185 99326 56 4.97545 97800 98040 98266 98477 98675 98858 99027 99182 99324 55 6 97541 97796 98036 98262 98474 98671 98855 99024 99180 99322 54 7 97536 97792 98032 98259 98471 98668 98852 99022 99177 99319 53 8 97532 97788 98029 98255 98467 98665 98849 99019 99175 99317 52 9 97528 97784 98025 98251 98464 98662 98846 99016 99172 99315 51 10 4.97523 97779 98021 98248 98460 98659 98843 99013 99170 99313 50 11 97519 97775 98017 98244 98457 98656 98840 99011 99167 99310 49 12 97515 97771 98013 98240 98453 98652 98837 99008 99165 99308 48 13 97510 97767 98009 98237 98450 98649 98834 99005 99162 99306 47 14 97506 97763 98005 98233 98229 98447 98646 98831 99002 99160 99304 46 15 4.97501 97759 98001 98443 98643 98828 99000 99157 99301 45 16 97497 97754 97997 98226 98440 98640 98825 98997 99155 99299 44 17 97492 97750 97993 98222 98436 98636 98822 98994 99152 99297 43 18 97488 97746 97989 98218 98433 98633 98819 98991 99150 99294 42 19 97484 97742 97986 98215 98429 98630 98816 98989 99147 99292 41 20 4.97479 97738 97982 98211 98426 98627 98813 98986 99145 99290 40 21 97475 97734 97978 98207 98422 98623 98810 98983 99142 99288 39 22 97470 97729 97974 98204 98419 98620 98807 98980 99140 99285 38 23 97466 97725 97970 98200 98415 98617 98804 98978 99137 99283 37 24 97461 97721 97966 98196 98412 98614 98801 98975 99135 99281 36 25 4.97457 97717 97962 98192 98409 98610 98798 98972 99132 99278 35 26 97453 97713 97958 98189 98405 98607 98795 98969 99130 99276 34 27 97448 97708 97954 98185 98402 98604 98792 98967 99127 99274 33 28 97444 97704 97950 98181 98398 98601 98789 98964 99124 99271 32 29 30 97439 97700 97946 98177 98395 98597 98786 98961 99122 99269 31 4.97435 97696 97942 98174 98391 98594 98783 98958 99119 99267 30 31 97430 97691 97938 98170 98388 98591 98780 98955 99117 99264 29 32 97426 97687 97934 98166 98384 98588 98777 98953 99114 99262 28 33 97421 97683 97930 98162 98381 98584 98774 98950 99112 99260 27 34 97417 97679 97926 98159 98377 98581 98771 98947 99109 99257 26 35 4.97412 97674 97922 98155 98373 98578 98768 98944 99106 99255 25 36 97408 97670 97918 98151 98370 98574 98765 98941 99104 99252 24 37 97403 97666 97914 98147 98366 98571 98762 98938 99101 99250 23 38 97399 9766-2 97910 98144 98363 98568 98759 98936 99099 99248 22 39 97394 4.97390 97657 97906 98140 98359 98565 98756 98933 99096 99245 21 40 97663 97902 98136 98356 98561 98753 98930 99093 99243 20 41 97385 97649 97898 98132 98352 98558 98750 98927 99091 99241 19 42 97381 97645 97894 98129 98349 98555 98746 98924 99088 99238 18 43 9r376 97(540 97890 98125 98345 98551 98743 98921 99086 99236 17 44 97372 97636 97886 9S121 98342 98548 98740 98919 99083 99233 16 45 4.97367 97632 97882 98117 98338 98545 98737 98916 99080 99231 15 46 97363 97627 97878 98113 98334 98541 98734 98913 99078 99229 14 47 97358 97623 97874 98110 98331 98538 98731 98910 99075 99226 13 48 97353 97619 97870 98106 98327 98535 98728 98907 99072 99224 12 49 97349 97615 97866 98102 98324 98531 98725 98904 99070 99221 11 50 4.97344 97610 97861 98098 98320 98528 98722 98901 99067 99219 10 51 97340 97606 97857 9S094 98317 98525 98719 98898 99064 99217 9 52 97335 97602 97853 98090 98313 98521 98715 98896 99062 99214 8 53 97331 97597 97849 98087 98309 98518 98712 98893 99059 99212 7 54 97326 97593 97845 98083 98306 98515 98709 98890 99056 99209 6 55 4.97322 97589 97841 98079 98302 98511 98706 98887 99054 99207 5 56 97317 97584 97837 98075 98299 9S508 98703 98884 99051 99204 4 57 97312 97580 97833 98071 98295 98505 98700 98881 99048 99202 3 58 97308 97576 97829 98067 98291 98501 98697 98878 99046 99200 2 59 97303 97571 97825 98063 98288 98498 98694 98875 99043 99197 1 60 97299 97567 97821 98060 98284 98494 98690 98872 99040 99195 70° 71* 72' 73° 74° 75° 76° 77° 78° 79° M. l_ DIFFER ENCE. 8I^ rE. TABLE XXVIII. 116 LOGARITHMS OF THE HALF SUM AND DIFFERENCE. HALF SUM, CO-BINK. o o o o o o o o o o M. 9 8 7 6 5 4 3 2 1 4.99462 99575 99675 99761 99834 99894 99940 99974 99993 00000 60 1 99460 99573 99674 99760 99833 99893 99940 99973 99993 00000 59 2 99458 99572 99672 99759 99832 99892 99939 99973 99993 00000 58 3 99456 99570 99670 99757 99831 99891 99938 99972 99993 00000 57 4 99454 99568 99669 99667 99756 99830 99^91 99938 99972 99992 00000 56 55 5 4.99452 99566 99755 99829 99890 99937 99971 99992 00000 6 99450 99565 99666 99753 99828 99889 99936 99971 99992 00000 54 7 99448 99563 99664 99752 99827 99888 99936 99970 99992 00000 53 8 99446 99561 99663 99751 99825 99887 99935 99970 99992 00000 52 9 99444 99559 99661 99749 99824 99886 99934 99969 99991 00000 51 10 4.99442 99557 99659 99748 99823 99885 99934 99969 99991 00000 50 11 99440 99556 99658 99747 99822 99884 99933 99968 99991 00000 49 12 99438 99554 99656 99745 99821 99883 99932 99968 99990 00000 48 13 99436 99552 99655 99744 99820 99882 99932 99967 99990 00000 47 14 99434 99550 99653 99742 99819 99881 99931 99967 99990 00000 46 45 15 4.99432 99548 99651 99741 99817 99880 99930 99967 99990 00000 16 99429 99546 99650 99740 99816 99879 99929 99966 99989 00000 44 17 99427 99545 99648 99738 99815 99879 99929 99966 99989 99999 43 18 99425 99543 99647 99737 99814 99878 99928 99965 99989 99999 42 19 99423 99541 99645 99643 99736 99813 99877 99927 99926 99964 99964 99989 99999 41 40 20 4.99421 99539 99734 99812 99876 99988 99999 21 99419 99537 99642 99733 99810 99875 99926 99963 99988 99999 39 22 99417 99535 99640 99731 99809 99874 99925 99963 99988 99999 38 23 99415 99533 99638 99730 99808 99873 99924 99962 99987 99999 37 24 99413 99532 99637 99728 99727 99807 99872 99923 99962 99987 99999 36 35 25 4.99411 99530 99635 99806 99871 99923 99961 99987 99999 26 99409 99528 99633 99726 99804 99870 99922 99961 99986 99999 34 27 99407 99526 99632 99724 99803 99869 99921 99960 99986 99999 33 28 99404 99524 99630 99723 99802 99868 99920 99960 99986 99999 32 29 30 99402 99522 99629 99721 99720 99801 99867 99920 99959 99985 99985 99998 31 4.99400 99520 99627 99800 99866 99919 99959 99998 30 31 99398 99518 99625 99718 99798 99865 99918 99958 99985 99998 29 32 99396 99517 99624 99717 99797 99864 99917 99958 99984 99998 28 33 99394 99515 99622 99716 99796 99863 99917 99957 99984 99998 27 34 99392 99513 99620 99714 99795 99862 99916 99956 99984 99998 26 25 35 4.99390 99511 99618 99713 99793 99861 99915 99956 99983 99998 36 99388 99509 99617 99711 99792 99860 99914 99955 99983 99998 24 37 99385 99507 99615 99710 99791 99859 99913 99955 99983 99997 23 38 99383 99505 99613 99708 ,99790 99858 99913 99954 99982 99997 22 39 99381 99503 99612 99707 99788 99857 99912 99954 99982 99997 21 20 40 4.99379 99501 99610 99705 99787 99856 99911 99953 99982 99997 41 99377 99499 99608 99704 99786 99855 99910 99952 99981 99997 19 42 99375 99497 99607 99702 99785 99854 99909 99952 99981 99997 18 43 99372 99495 99605 99701 99783 99853 99909 99951 99981 99997 17 44 99370 99494 99603 99699 99782 99852 99908 99951 99980 99996 16 45 4.99368 99492 99601 99698 99781 99851 99907 99950 99980 99996 15 46 99366 99490 99600 99696 99780 99850 99906 99949 99979 99996 14 47 99364 99488 99598 99695 99778 99848 99905 99949 99979 99996 13 48 99362 99486 99596 99693 99777 99847 99904 99948 99979 99996 12 49 99359 99484 99595 99692 99776 99846 99904 99903 99948 99978 99996 11 50 4.99357 99482 99593 99690 99775 99845 99947 99978 99995 10 51 99355 99480 99591 99689 99773 99844 99902 99946 99977 99995 9 52 99353 99478 99589 99687 99772 99843 99901 99946 99977 99995 8 53 99351 99476 99588 99686 99771 99842 99900 99945 99977 99995 7 54 55 99348 99474 99586 99584 99684 99769 99841 99899 99944 99976 99995 6 6 4.99346 99472 99683 99768 99840 99898 99944 99976 99994 56 99344 99470 99582 99681 99767 99839 99898 99943 99975 99994 4 57 99342 99468 99581 99680 99765 99838 99897 99942 99975 99994 3 58 99340 99466 99579 99678 99764 99837 99896 99942 99974 99994 2 59 99337 99464 99577 99677 99763 99836 99895 99941 99974 99994 1 60 99335 99462 99575 99675 99761 99834 99894 99940 99974 99993 80" 81° 82° 83° 84° 85° 86° 87° 88° 89° M. DIFFERENCE. 81 116 TABLE XXIX. HOUR AN LOGARITHMS OF THE APPARENT TIME, OR HOUR ANGLE. OLE, HOURS, OB APP. TIME P. M. j PROPORTIONAL PARTS FOR SECONDS. 1 B. 8. s. 8. 8. a s. S. 8. s. s. s. s. s. s. « M. 10 20 30 40 50 60 1 2 3 4 5 6 7 8 9 1 3 4 • 12127 72333 07551 32539 51921 67757 59 1 i. 67757 81147 92745 02976 12127 20406 27963 58 1 2 5.27963 34916 41352 46345 52951 58216 63181 57 3 63181 67877 72332 76570 80611 84472 88168 56 4 1 88168 91714 95121 98399 01557 04605 07550 55 5 6.07550 10398 13155 15828 18421 20938 23385 54 6 23385 25765 28081 30337 32536 34681 36774 53 7 36774 38817 40814 42766 44675 46543 48372 52 8 48372 50162 51916 53636 55323 56977 58600 51 9 58600 60194 61759 63296 64806 66291 67751 50 10 6-67751 69186 70598 71988 73355 74702 76028 49 11 76028 77334 78620 79888 81137 82369 83584 48 12 83584 84782 85963 87129 88279 89414 90535 47 13 90535 91641 92733 93812 94877 95930 96970 46 14 |. 96970 97997 99013 00017 01009 01990 02960 45 15 7 02960 03920 04869 05807 06736 07655 08564 44 93 187 280 373 467 560 653 746 840 16 08564 09464 10354 11236 12108 12972 13827 43 87 175 263 350 438 526 614 702 789 17 13827 14674 15513 16344 17167 17982 18790 42 82 165 248 331 413 496 579 662 744 18 18790 19590 20383 21168 21947 22719 23483 41 78 156 234 313 391 469 547 625 704 19 20 23483 24241 24993 25738 26477 27210 27936 40 74 148 222 296 370 444 518 592 666 7.27936 28656 29371 30079 30782 31479 32171 39 70 140 211 281 352 422 492 563 633 21 32171 32857 33538 34213 34884 35549 36209 38 67 134 201 268 335 403 470 537 604 22 36209 36864 37514 38159 38800 39435 40067 37 64 128 192 256 320 385 449 513 577 23 40067 40693 41315 41933 42546 43155 43760 36 61 123 184 245 306 368 430 491 552 24 43760 44361 44957 45549 46138 46722 47302 35 59 118 171 235 295 353 412 471 531 25 7.47302 47879 48452 49021 49586 50148 50706 34 56 113 169 226 282 339 396 452 509 26 50706 51260 51811 52358 52902 53443 53980 33 54 109 163 218 272 327 381 436 490 27 53980 54514 55045 55572 56096 56017 57135 32 52 105 157 209 262 314 367 420 472 28 57135 57650 58162 58670 59176 59679 60179 31 51 101 152 202 253 303 354 405 455 29 60179 60676 61170 61662 62151 62636 63120 30 49 98 147 195 244 293 342 392 441 30 7.63120 63600 64078 64553 65026 65496 65964 29 47 95 142 189 236 284 331 378 426 31 65964 66429 66891 67351 67809 68264 68717 28 46 92 137 183 229 275 321 366 412 32 68717 69167 69616 70061 70505 70946 71385 27 44 89 133 178 222 267 311 355 400 33 71385 71822 72257 72689 73119 73548 73974 26 43 86 129 172 215 258 301 344 388 34 73974 74398 74819 75239 75657 76073 76487 25 42 83 125 167 209 251 293 334 377 35 7.76487 76898 77308 77716 78122 78526 78929 24 41 81 122 162 203 243 284 325 366 36 78929 79329 79728 80124 80519 80912 81303 23 40 79 118 158 197 237 277 316 356 37 81303 81693 82081 82467 82851 83234 83615 22 39 77 115 154 192 231 270 308 347 38 83615 83994 84372 84747 85122 85494 85866 21 38 75 112 150 187 225 263 300 338 39 85866 86235 86603 86969 87334 87697 88059 20 37 73 109 146 182 219 256 292 329 40 7.88059 88419 88778 89135 89491 89846 90198 19 36 71 106 142 178 213 249 284 321 41 90198 90550 90900 91248 91596 91941 92286 18 35 70 1-04 139 174 208 243 278 313 42 92286 92629 92970 93311 93650 93987 94324 17 34 68 102 136 170 204 238 272 306 43 94324 94659 94992 95325 95656 95986 96315 16 33 66 100 133 166 199 232 265 299 44 45 .96315 96642 96968 97293 97617 97939 98260 15 32 65 97 130 162 194 227 259 292 ^.98260 98580 98899 99217 99534 99849 00163 14 32 63 95 127 158 190 222 253 286 46 8.00163 00476 00788 01099 01409 01717 02025 13 31 62 93 124 155 186 218 248 270 47 02025 02331 02636 02941 03244 03546 03847 12 30 61 91 121 152 182 212 243 273 48 03847 04147 04446 04744 05041 05336 05631 11 30 60 89 119 148 178 208 238 268 49 05631 05925 06218 06510 06800 07090 07379 10 29 58 87 116 145 175 204 233 262 50 8.07379 07667 07954 08240 08525 08809 09092 9 28 57 85 114 142 171 200 228 257 51 09092 09374 09656 09936 10216 10494 10772 8 28 56 84 112 140 .168 196 224 252 62 10772 11048 11324 11599 11873 12147 12419 7 27 55 82 110 138 165 193 220 248 53 12419 12691 12961 13231 13500 13768 14035 6 27 54 81 108 135 162 189 216 243 54 14035 14302 14567 14832 15096 15359 05621 5 26 53 79 106 133 159 185 212 239 55 8.15621 15883 16144 16404 16663 16921 17179 4 26 52 78 104 130 156 182 208 234 56 17179 17436 17692 17947 18202 18455 18708 3 25 51 77 102 127 153 179 204 229 57 18708 18961 19212 19463 19713 19963 20211 2 25 50 75 100 125 150 175 200 224 58 20211 20459 20706 20953 21198 21444 21688 1 24 49 73 98 123 147 172 196 220 69 21688 21932 22175 22417 22658 22899 23140 24 48 72 96 120 145 169 193 217 60s. 50s. 40s. 30s. 20s. 10s. Os. M. 1 Is. 28. 3s. 4s. 5s. 6s. 7s. 8s. 9s. 11 OR 23 HOURS, OR APP. TIME A. M. | PROPORTIONAL PARTS yOR SRCONDS. | TABLE XXIX. m 1 LOGABITHMS OF THE APPARENT TIME OR HOUR ANGLE. | ] aOUR ANGLE, 1 HOUR, OR APP. TIME P. M. PROPORTIONAL PARTS FOR SECONDS. 1 S. 8. s. 8. 8. s. 8. 8. 8. 8. 8. e. 8. 8. s. 8. M. 10 20 30 40 50 60 1 2 3 4 5 6 7 8 9 8.23140 23379 23618 23856 24094 24331 24567 59 24 47 71 95 118 142 166 190 213 1 24567 24802 25037 25272 25505 25738 25971 58 23 47 70 93 116 140 163 187 210 2 25971 26203 26434 26664 26894 27123 27352 57 23 46 69 92 115 138 161 184 207 3 27352 27580 27807 28034 28260 28486 28711 56 23 45 68 91 113 136 159 181 204 4 28711 28935 29159 29383 29605 29827 30049 5i 22 44 67 89 111 133 156 178 201 5 8.30049 30270 30490 30710 30929 31148 31366 54 22 44 66 87 109 131 153 175 198 6 31366 31583 31800 32016 32233 32448 32663 53 22 43 65 86 108 130 151 173 195 7 32663 32877 33091 33304 33517 33729 33940 52 21 43 64 85 106 128 149 170 192 8 33940 34151 34362 34572 34782 34991 35199 51 21 42 63 84 105 126 147 168 189 9 35199 35407 35614 35821 36028 36234 36439 50 21 41 62 83 103 124 145 165 186 10 8.36439 36644 36849 37053 37256 37459 37662 49 20 41 61 82 102 122 143 163 184 11 37662 37864 38065 38266 38467 38667 38866 48 20 40 60 81 100 120 141 161 181 12 38866 39066 39264 39463 39660 39858 40055 47 20 40 60 80 99 119 139 159 179 13 40055 40251 40447 40642 40837 41032 41226 46 20 39 59 78 98 118 137 157 177 14 15 41226 41420 41613 41806 41998 42191 42382 45 19 39 58 77 96 116 135 154 174 8.42382 42573 42764 42954 43144 43333 43522 44 19 38 57 76 95 114 133 152 171 16 43522 43710 43898 44086 44273 44460 44647 43 19 37 56 75 93 112 131 150 169 17 44647 44833 45018 45204 45388 45573 45757 42 19 37 55 74 92 111 130 148 167 18 45757 45940 46124 46306 46489 46671 46852 41 18 37 55 73 91 110 128 146 165 19 46852 47034 47215 47395 47575 47755 47934 40 18 36 54 72 90 108 126 144 162 20 8.47934 48113 48292 48470 48647 48825 49002 39 18 35 53 71 89 107 125 142 160 21 49002 49179 49355 49531 49706 49882 50056 38 18 35 53 70 88 106 123 141 158 22 50056 50231 50405 50579 50752 50925 51098 37 17 35 52 70 87 104 122 139 157 23 51098 51270 51442 51614 51785 51956 52127 36 17 34 52 69 86 103 120 138 155 24 52127 52297 52467 52636 52805 52974 53143 35 17 34 51 68 85 102 119 136 153 25 8.53143 53311 53479 53646 53814 53980 54147 34 17 33 50 67 83 100 117 134 151 26 54147 54313 54479 54645 54810 54975 55139 33 17 33 50 66 82 99 116 132 149 27 55139 55303 55467 55631 55794 55957 56120 32 16 33 49 65 81 98 114 130 147 28 56120 56282 56444 56606 56767 56928 57089 31 16 32 48 64 80 97 113 129 145 29 57089 57249 57410 57569 57729 57888 58047 30 16 32 48 63 80 96 111 127 143 30 8.58047 58206 58364 58522 58680 58837 58994 29 16 32 47 63 79 95 110 126 142 31 58994 59151 59308 59464 59620 59776 59931 28 16 31 47 62 78 94 109 125 141 32 59931 60086 60241 60395 60550 60704 60857 27 15 31 46 62 77 93 108 123 139 33 60857 61011 61164 61317 61469 61621 61773 26 15 30 46 61 77 92 107 122 138 34 61773 61925 62076 62228 62379 62529 62679 25 15 30 45 60 76 91 106 121 136 35 8.62679 62830 62979 63129 63278 63427 63576 24 15 30 45 60 75 90 105 119 134 36 63576 63724 63872 64020 64168 64315 64463 23 •15 30 45 59 74 89 104 118 133 37 64463 64609 64756 64902 65048 65194 65340 22 15 29 44 58 73 88 102 117 132 38 65340 65485 65630 65775 65920 66664 66208 21 15 29 43 58 72 87 101 116 130 39 66208 66352 66496 66639 66782 66926 67067 20 14 29 43 57 72 86 100 115 129 40 8.67067 67209 «7352 67494 67635 67777 67918 19 14 28 43 57 71 85 99 113 128 41 67918 68059 68199 68340 68480 68620 68759 18 14 28 42 56 70 84 98 112 126 42 68759 68899 £9038 69177 69316 69454 69593 17 14 28 42 55 69 83 97 111 125 43 69593 69731 69869 70006 70144 70281 70418 16 14 27 41 55 69 82 96 110 124 44 45 70418 70554 70691 70827 70963 71099 71234 15 14 27 41 54 68 82 95 109 123 8.71234 71370 71505 71640 71774 71909 72043 14 14 27 40 54 67 81 95 108 122 46 72043 72177 72311 72444 72578 72711 72844 13 13 27 40 53 67 80 94 107 121 47 72844 72977 73109 73241 73374 73505 73637 12 13 26 40 53 66 79 93 106 119 48 73637 73768 73900 74031 74162 74292 74423 11 13 26 39 52 65 78 92 105 118 49 74423 74553 74683 74813 74942 75072 75201 10 13 26 39 52 65 78 91 104 117 50 8.75201 75330 75458 75587 75715 75843 75971 9 13 26 38 51 64 77 90 103 116 51 75971 76099 76227 76354 76481 76608 76735 8 13 25 38 51 63 76 89 102 115 52 76735 76862 76988 77114 77240 77366 77492 7 13 25 38 50 63 76 88 101 114 53 77492 77617 77742 77867 77992 78117 78241 6 13 25 37 50 62 75 87 100 113 54 78241 78365 78489 78613 78737 78861 78984 5 12 25 37 50 62 75 87 99 112 55 8.78984 79107 79230 79353 79475 79598 79720 4 12 25 37 49 61 74 86 98 111 56 79720 79842 79964 80085 80207 80328 80449 3 12 25 37 49 61 73 85 98 110 57 80449 80570 80691 80812 80932 81052 81172 2 12 24 36 48 60 73 85 97 109 58 81172 81292 81412 81531 81651 81770 81889 1 12 24 36 48 60 72 84 96 108 59 81889 82008 82126 82245 82363 82481 82599 12 24 36 48 60 72 83 95 107 60s. 508. 408. 308. 20s. 10s. Os. M. Is. 2s. 3s. 4s. 58. 68. 78. 8s. 9s. _^_ 10 OR 22 HOURS, OR APP. TIME A. M. | PROPOR' noN AL PART 8 FOR SECONDS. | 118 TABLE XXIX. 1 B OFB 'KGLE, " A.RITHMS OF THE APPARENT TIME, OR HOUR ANGLE. 1 HOURS, OR APP. TIME P. M. PROPORTIONAL PARTS FOR SECONDS. e. S. B. s. s. 8. s. s. S. S. s. S. g Is. s. B. M. 10 20 30 40 50 60 1 2 3 4 5 6 7 <3 9 105 8.82599 82717 82835 82952 83069 83187 83303 59 12 23 35 47 59 70 82 93 1 83303 83420 83537 83653 83769 83885 84001 58 12 23 35 46 58 70 81 93 105 2 84001 84117 84233 84348 84464 84579 84694 57 11 23 35 46 57 69 80 92 104 3 84694 84808 84923 85037 85152 85266 85380 56 11 23 34 45 57 68 80 91 103 4 85380 85494 85607 85721 85834 85947 86060 55 11 23 34 45 57 68 79 90 102 5 8.86060 86173 86286 86398 86511 86623 86735 54 11 22 34 45 56 67 78 90 101 6 86735 86847 86959 87070 87182 87293 87404 53 11 22 33 45 56 67 78 89 100 7 87404 87515 87626 87736 87847 87957 88068 52 11 22 33 44 55 66 78 89 100 8 88068 88178 88288 88397 88507 88616 88726 51 11 22 33 44 55 66 77 88 99 9 10 88726 88835 88944 89053 89162 89270 89379 50 11 22 33 44 55 65 76 87 98 8.89379 89487 89595 89703 89811 89918 90026 49 11 22 32 43 54 65 76 86 97 11 90026 90133 90241 90348 90455 90562 90668 48 11 21 32 43 54 64 75 86 96 12 90668 90775 90881 90988 91094 91200 91306 47 11 21 32 42 53 64 74 85 95 13 91306 91411 91517 91622 91728 91833 91938 46 11 21 32 42 53 63 73 84 95 14 91938 92043 92147 92252 92356 92461 92565 45 10 21 32 42 53 63 73 84 94 15 8.92565 92669 92773 92877 92980 93084 93187 44 10 21 31 42 52 62 73 83 93 16 93187 93290 93393 93496 93599 93702 93804 43 10 20 31 41 52 62 72 82 93 17 93804 93907 94009 94111 94213 94315 94417 42 10 20 31 41 51 61 71 82 93 18 94417 94519 94620 94722 94823 94924 95025 41 10 20 30 40 51 61 71 81 91 19 95025 95126 95227 95327 95428 95528 95628 40 10 20 30 40 50 60 70 80 90 90 20 8.95628 95728 95828 95928 96028 96128 96227 39 10 20 30 40 50 60 70 80 21 96227 96326 96426 96525 96624 96723 96821 38 10 20 30 40 50 60 69 79 89 22 96821 96920 97018 97117 97215 97313 97411 37 10 20 30 39 49 59 69 79 88 23 97411 97509 97607 97704 97802 97899 97996 36 10 19 29 39 49 59 68 78 87 24 97996 98094 98191 98288 98384 98481 98578 35 10 19 29 39 49 58 68 77 87 86 25 8.98578 98674 98770 98866 98963 99058 99154 34 10 19 29 38 48 58 67 77 26 99154 99250 99346 99441 99536 99632 99727 33 10 19 29 38 48 57 67 76 86 27 1-99727 99822 99917 00012 00106 00201 00295 32 9 19 28 38 47 57 66 76 85 28 9.00295 00390 00484 00578 00672 00766 00860 31 9 19 28 38 47 56 66 75 85 29 00860 00953 01047 01140 01234 01327 01420 30 29 9 19 28 37 47 56 65 75 84 83 30 9.01420 01513 01606 01698 01791 01884 01976 9 18 28 37 46 55 65 74 31 01976 02068 02161 02253 02345 02437 02528 28 9 18 28 37 46 55 64 74 83 32 02528 02620 02712 02803 02894 02986 03077 27 9 18 27 37 46 55 64 73 82 33 03077 03168 03259 03350 03440 03531 03621 26 9 18 27 36 45 54 64 73 82 34 03621 03712 03802 03892 03982 04072 04162 25 24 9 18 27 36 45 54 63 72 81 81 35 9.04162 04252 04341 04431 04520 04610 04699 9 18 27 36 45 54 63 72 36 04699 04788 04877 04966 05055 05144 05232 23 9 18 27 36 45 53 62 71 80 37 05232 05321 05409 05498 05586 05674 05762 22 9 18 26 35 44 53 62 71 79 38 05762 05850 05938 06025 06113 06200 06288 21 9 17 26 35 44 53 61 70 79 39 06288 06375 06462 06550 06637 06724 06810 20 9 17 26 35 43 52 61 70 78 40 9.06810 06897 06984 07070 07157 07243 07329 19 9 17 26 35 43 52 61 69 78 41 07329 07415 07501 07587 07673 07759 07845 18 9 17 26 34 43 52 60 69 77 42 07845 07930 08016 08101 08186 08271 08357 17 9 17 26 34 43 51 60 68 77 43 08357 08442 08526 08611 08696 08781 08865 16 8 17 25 34 42 51 59 67 76 44 45 08865 08949 09034 09118 09202 09286 09370 15 8 17 25 34 42 51 59 67 76 9.09370 09454 09538 09622 09705 09789 09872 14 8 17 25 34 42 50 59 67 76 46 09872 09955 10039 10122 10205 10288 10371 13 8 17 25 33 42 50 58 66 75 47 10371 10453 10536 10619 10701 10784 10866 12 8 16 25 33 41 50 58 66 74 48 10866 10948 11030 11112 11194 11276 11358 11 8 16 25 33 41 49 57 66 74 49 1135^ 11440 11521 11603 11684 11765 11847 10 8 16 24 33 41 49 57 65 73 50 9.11847 1192!^ 12009 12090 12171 12252 12332 9 8 16 24 32 40 49 57 65 73 51 12332 12413 12494 12574 12655 12735 12815 8 8 16 24 32 40 48 56 64 73 52 12815 12895 12975 13055 13135 13215 13295 7 8 16 24 32 40 48 56 64 72 53 13295 13374 13454 13533 13613 13692 13771 6 • 8 16 24 32 40 48 56 64 72 54 55 13771 13850 13929 14008 14087 14166 14245 5 8 16 24 32 40 47 55 63 71 9.14245 14323 14402 14480 14559 14637 14715 4 8 16 24 31 39 47 55 63 71 56 14715 14793 14871 14949 15027 15105 15183 3 8 16 23 31 39 47 55 62 70 57 15183 15260 15338 15415 15493 15570 15647 2 8 15 23 31 39 47 54 62 70 58 15647 15724i 15802 15879 15955 16032 16109 1 8 15 23 31 38 46 54 62 69 59 16109 16186 16262 16339 16415 16492 16568 8 15 2s. 23 3s. 31 38 46 54 61 69 60s. 50s. 40s. 30s. 20s. 10s. Os. M. Is., 4s. 5s. 6s. 7s. 8s. 9s 9 OR 21 HOURS, OR APP. TIME A. M. [ PRO POR noN AL I 'ART S FC )R S ECONDS. 1 ■ TABLE XXIX. 119 1 LOGARITHMS OF THE APPARENT TIME, OR HOUR ANGLE. HOUR ANGLE, 3 HOURS, OR APP. TIME P. M. | PROPORTIONAL PARTS FOR SECONDS. 1 «. B. 8. B. s. B. 8. 8. B. 8. 8. s. s. 8. S. 8. 1 M. 10 20 30 40 50 60 1 2 3 4 5 6 7 8 9 M6568 16644 16720 16796 16872 16948 17024 59 8 15 23 30 38 46 53 61 68 1 17024 17100 17175 17251 17326 17402 17477 58 8 15 23 30 38 45 53 60 68 2 17477 17553 17628 17703 17778 17853 17928 57 7 15 22 30 37 45 52 60 67 3 17928 18003 18077 18152 18227 18301 18376 56 7 14 22 30 37 45 52 60 67 4 18376 18450 18524 18598 18673 18747 18821 ^5 7 14 22 30 37 44 52 59 67 5 9.18821 18895 18968 19042 19116 19190 19263 54 7 14 22 30 37 44 52 59 67 6 19263 19337 19410 19483 19557 19630 19703 53 7 14 22 29 37 44 51 59 66 7 19703 19776 19849 19922 19995 20067 20140 52 7 14 22 29 37 44 51 58 66 8 20140 20213 20285 20358 20430 20502 20574 51 7 14 22 29 36 44 51 58 65 9 20574 20647 20719 20791 20863 20935 21006 50 7 14 22 29 36 43 50 58 65 10 9.21006 21078 21150 21221 21293 21364 21436 49 7 14 21 29 36 43 50 57 64 11 21431S 21507 21578 21650 21721 21792 21863 48 7 14 21 28 36 43 50 57 64 12 2186:^ 21934 22004 22075 22146 22216 22287 47 7 14 21 28 35 42 49 56 63 13 22287 22358 22428 22498 22569 22639 22709 46 7 14 21 28 35 42 49 56 63 14 15 22709 22779 22849 22919 22989 23059 23128 45 7 14 21 28 35 42 49 56 63 9.23128 23198 23268 23337 23407 23476 23545 44 7 14 21 28 35 42 49 56 63 16 23545 23615 23684 23753 23822 23891 23960 43 7 14 21 28 35 41 48 55 62 17 23960 24029 24098 24166 24235 24304 24372 42 7 14 21 28 35 41 48 55 62 18 24372 24441 24509 24577 24646 24714 24782 41 7 14 21 27 34 41 48 55 62 19 24782 24850 24918 24986 25054 25122 25190 40 7 14 20 27 34 41 48 54 61 20 9.25190 25257 25325 25393 25460 25527 25595 39 7 14 20 27 34 41 47 54 61 21 25595 25662 25729 25796 25864 25931 25998 38 7 13 20 27 34 40 47 54 60 22 25998 26065 26132 2tJ198 26265 26332 26398 37 7 13 20 27 34 40 47 54 60 23 2639S 26465 26532 26598 26664 26731 26797 36 ^7 4 13 20 27 33 40 47 53 60 24 25 26797 26863 26929 26995 27061 27127 27193 35 7 13 20 26 33 40 46 53 59 9.27193 27259 27325 27390 27456 27521 27587 34 7 13 20 26 33 40 46 53 59 26 27587 27652 27718 27783 27848 27914 27979 33 7 13 20 26 33 39 46 52 59 27 27979 28044 28109 28174 28239 28304 28368 32 6 13 20 26 32 39 46 52 59 28 28368 28433 28498 28562 28627 28691 28756 31 6 13 20 26 32 39 46 52 59 29 28756 28820 28885 28949 29013 29077 29141 30 6 13 19 26 32 39 45 52 58 30 9.29141 29205 29269 29333 29397 29461 29524 29 6 13 19 26 32 38 45 51 58 31 29524 29588 29652 29715 29779 29842 29905 28 6 13 19 25 32 38 45 51 57 32 29905 29969 30032 30095 30158 30221 30285 27 6 13 19 25 32i 38 44 51 57 33 30285 30347 30410 30473 30536 30599 30661 26 6 13 19 25 32 38 44 50 57 34 30661 30724 30787 30849 30912 30974 31036 25 6 12 19 25 31 38 44 50 56 35 9.31036 31099 31161 31223 31285 31347 31409 24 6 12 19 25 31 37 43 50 56 36 31409 31471 31533 31595 31657 31719 31780 23 6 12 19 25 31 37 43 50 56 37 31780 31842 31903 31965 32026 32088 32149 22 6 12 18 25 31 37 43 49 55 38 32149 32210 32272 32333 32394 32455 32516 21 6 12 18 24 31 37 43 49 55 39 32516 32577 32638 32699 32760 32820 32881 20 6 12 18 24 31 37 43 49 55 40 9.32881 32942 33002 33063 33123 33184 33244 19 6 12 18 24 30 »6 42 48 55 41 33244 33304 33365 33425 33485 33545 33605 18 6 12 18 24 30 36 42 48 54 42 33605 336tij 33725 33785 33845 33905 33965 17 6 12 18 24 30 36 42 48 54 43 33965 34024 34084 34143 34203 34262 34322 16 6 12 18 24 30 36 42 48 54 44 45 34322 34381 34441 34500 34559 34618 34677 15 6 12 18 24 30 36 41 47 53 9.34677 34736 34795 34854 34913 34972 35031 14 6 12 18 24 30 35 41 47 53 46 35031 35O90 35148 35207 35266 35324 35383 13 6 12 18 24 30 35 41 47. 53 47 35383 35441 35499 35558 35616 35674 35733 12 6 12 18 23 29 35 41 47 53 48 35733 35791 35849 35907 35965 36023 36081 11 6 12 17 23 29 35 41 46 52 49 36081 36139 36196 36254 36312 36369 36427 10 6 12 17 23 29 35 41 46 52 50 9.36427 36485 36542 36599 36657 36714 36771 9 6 11 17 23 29 35 40 46 52 51 36771 3682y 36886 36943 37OO0 37057 37114 8 6 11 17 23 29 34 40 46 51 52 37114 37171 37228 37285 37342 37399 37455 7 6 11 17 23 29 34 40 46 51 53 3745£ i 3751S 3756S 37625 37682 37738 37794 6 6 11 17 23 28 34 40 45 51 54 37794 [ 37851 37907 37963 38020 38076 38412 38132 5 6 11 17 22 28 34 39 45 51 55 9.^8131 ! 38186 S 38244 38300 38356 38468 4 6 11 17 22 28 34 39 45 50 56 38466 i 38524 [ 38579 38635 38691 38746 38802 3 6 11 17 22 28 33 39 44 50 57 3880S ! 38857 3891S 38968 39024 39079 39134 2 6 11 17 22 28 33 39 44 50 58 39134 [ 39189 1 39245 . 39300 39355 39410 39465 1 6 11 16 . 22 28 i 33 39 1 44 60 59 3946£ > 3952C 1 39575 i 39630 39684 39739 39794 6 11 le ; 22 28 ! 33 39 » 44 [ 50 60s. 50s. 40s. ' 'Os. 1 20s. 10s. Os. M. Is. 2s. 3s. 4s. 5s. 6s. .7s. 8s. 9s. ; 8 OR 20 HOURS, OR APP. TIME A. M. ( PRC •PORTIONAL PARTS FOR SECONDS. 1 "? 120 TABLE XXIX. J LOGARITHMS OP THE APPARENT TIME, OR HOUR ANGLE. HOCB ANGLE, 4 H0UK8, OR APP. TIME P. M. PROPORTIONAL 1 PARTS FOR SECONDS. 8. 8. s. s. s. 8. 8. 8. 8. 8. & 8. a 8. 8. 8. M. 10 20 30 40 50 60 1 2 3 4 5 6 7 8 9 9.39794 39849 39903 39958 40012 40067 40121 59 6 11 16 22 28 33 39 44 50 1 40121 40176 40230 40284 40339 40393 40447 58 5 11 16 22 27 33 38 44 49 2 40447 40501 40555 40609 40663 40717 40771 57 5 11 16 22 27 32 38 43 49 3 40771 40825 40879 40933 40986 41040 41094 56 5 11 16 22 27 32 38 43 49 4 41094 41147 41201 41254 41308 41361 41415 55 5 11 16 21 27 27 32 37 43 48 5 9.41415 41468 41521 41575 41628 41681 41734 54 5 11 16 21 32 37 43 48 6 41734 41787 41840 41893 41946 41999 42052 53 5 11 16 21 27 32 37 43 48 7 42052 42105 42157 42210 42263 42315 42368 52 5 10 16 21 26 31 37 42 47 8 42368 42420 42473 42525 42578 42630 42682 51 5 10 16 21 26 31 37 42 47 9 42682 42735 42787 42839 42891 42943 42996 50 5 10 16 21 26 31 36 42 47 10 9.42996 43048 43100 43151 43203 43255 43307 49 5 10 16 21 26 31 36 42 47 11 43307 43359 43411 43462 43514 43565 43617 48 5 10 15 21 26 31 36 41 46 12 43617 43669 43720 43771 43823 43874 43925 47 5 10 15 20 25 31 36 41 46 13 43925 43977 44028 44079 44130 44181 44232 46 5 10 15 20 25 31 36 41 46 14 44222 44283 44334 44385 44436 44487 44538 45 5 10 15 20 25 31 36 41 46 15 9.44538 44589 44639 44690 44741 44791 44842 44 5 10 15 20 25 30 35 40 45 16 44842 44892 44943 44993 45044 45094 45144 43 5 10 15 20 25 30 35 40 45 17 45144 45195 45245 4.'-295 45345 45395 45446 42 5 10 15 20 25 30 35 40 45 18 45446 45496 45546 45595 45645 45695 45745 41 5 10 15 20 25 30 35 40 45 19 45745 45795 45845 45894 45944 45994 46043 40 5 10 15 20 25 30 35 3.^ 40 45 20 9.46043 46093 46142 46192 46241 46291 46340 39 5 10 15 20 25 30 40 45 21 46340 46389 46439 46488 46537 46586 46635 38 5 10 15 20 25 29 34 39 44 22 46635 46684 46733 46782 46831 46880 46929 37 5 10 15 20 24 29 34 39 44 23 46929 46978 47027 47076 47124 47173 47222 36 5 10 15 20 24 29 34 39 44 24 47222 47270 47319 47367 47416 47464 47513 35 5 10 15 19 24 29 34 39 44 25 9.47513 47561 47610 47658 47706 47754 47803 34 5 10 14 19 24 29 34 38 43 26 47803 47851 47899 47947 47995 48043 48091 33 5 10 14 19 24 29 34 38 43 27 48091 48139 48187 48235 48282 48330 48378 32 5 10 14 19 24 29 34 38 43 28 48378 48425 48473 48521 48568 48616 48664 31 5 9 14 19 24 29 33 38 43 29 48664 48711 48758 48806 48853 48900 48948 30 5 9 14 19 24 28 33 38 42 30 9.48948 48995 49042 49089 49137 49184 49231 29 5 9 14 19 23 28 33 38 42 31 49231 19512 49278 49325 49372 49419 49465 49512 28 5 9 14 19 23 28 33 38 42 32 49559 49606 49653 49699 49746 49793 27 5 9 14 19 23 28 33 37 42 33 49793 49839 49886 49932 49979 50025 50071 26 5 9 14 19 23 28 33 37 42 34 50071 50118 50395 50164 50211 50257 50303 50349 25 5 9 14 19 23 28 33 37 42 41 35 9.50349 50441 50488 50534 50580 50626 24 '^ 9 14 18 23 28 32 37 36 50626 50672 50717 50763 50809 50855 50901 23 9 14 18 23 28 32 37 41 37 50901 50946 50992 51038 51083 51129 51174 22 5 9 14 18 23 27 32 36 41 38 51174 51220 51265 51311 51356 51402 51447 21 5 9 14 18 23 27 32 36 41 39 51447 51492 51538 51583 51628 51673 51718 20 4 9 13 18 22 27 31 36 40 40 9.51718 51763 51808 51853 51898 51943 51988 19 4 9 13 18 22 27 31 36 40 41 51988 52033 32078 52123 52168 52212 52257 18 4 9 13 18 22 27 31 36 40 42 52257 52302 52346 52391 52435 52480 52525 17 4 9 13 18 22 27 31 36 40 43 52525 52569 52613 52658 52702 52747 52791 16 4 9 13 18 22 27 31 36 40 40 44 02791 52835 52879 52923 52968 53012 53056 15 4 9 13 18 22 27 31 35 45 9.53056 53100 53144 53188 53232 53276 53320 14 4 9 13 18 22 26 31 35 40 46 ,53320 53364 53407 53451 53495 53539 53582 13 4 9 13 18 22 26 31 35 40 47 53582 53626 53670 53713 53757 53800 53844 12 4 9 13 17 22 26 30 35 39 48 53844 53887 53931 53974 54017 54061 54104 11 4 9 13 17 22 26 30 35 39 49 54104 54147 54190 54234 54277 54320 54363 10 4 9 13 17 22 26 30 35 39 50 9 54363 54406 54449 54492 54535 54578 54621 9 4 9 13 17 22 26 30 34 39 51 54621 54664 54707 54749 54792 54835 54878 8 4 9 13 17 22 26 30 34 39 52 54878 54920 54963 55005 55048 55091 55133 7 4 8 13 17 21 26 30 34 38 53 55133 55175 55218 55260 55303 55345 55387 6 4 8 13 17 21 26 30 34 38 54 55387 55430 55472 55514 55556 55598 55641 5 4 8 13 17 21 25 29 34 38 55 9.55641 55683 55725 55767 55809 55851 55893 4 4 8 13 17 21 25 29 34 38 56 65893 55934 55976 56018 56060 56102 56144 3 4 8 13 17 21 25 29 34 38 57 56144 56185 56227 56269 56310 56352 56393 2 4 8 12 17 21 25 29 33 37 58 56393 56435 56476 56518 56559 56601 56642 1 4 8 12 17 21 25 29 33 37 59 56642 56683 56725 56766 56807 56848 56889 4 8 12 16 20 25 29 33 37 60s. 50s. 40s. 303. 20s. 10s. Os. M. 1 Is. 2s. 3s. 4s. 5s. 6s. 7s. Ss. 9s. 7 OR 19 HOURS, OR APP, TIME A. M. PRO P0R1 PION AL r •ARTS FC R b ECONDS. ( TABLE XXIX. LOGARITHMS OF THE APPARENT TIME, OR HOUR ANGLE. 121 HOITB ANGLE, 5 HOURS, OR APP. TIME P. M. | PROPORTIONAL PARTS FOR SECONDS. 1 8. & 8. a. 8. 8. 8. 8. 8. 8. 1 8. 1 8. 8. B. S M. 10 20 30 40 50 60 1 2 3 4 6 7 8 9 i ). 56889 56931 56972 57013 57054 57095 57136 59 4 8 12 16 20 25 29 33 37 1 57136 57177 57218 57259 57299 57340 57381 58 4 8 12 16 20 25 29 33 37 2 57381 57422 57463 57503 57544 57585 57625 57 4 8 12 16 20 25 29 33 37 3 57625 57666 57706 57747 57787 57828 57868 56 4 8 12 16 20 24 28 32 36 4 57868 57909 57949 57990 58030 58070 58110 ,.55 4 8 12 16 20 24 28 32 36 o J. 58110 58151 58191 58231 58271 58311 58351 54 4 8 12 16 20 24 28 32 36 6 58351 58391 58431 58471 58511 58551 58591 53 4 8 12 16 20 24 28 32 36 7 58591 58631 58671 58711 58750 58790 58830 ( 0:d 4 8 12 16 20 24 28 32 36 8 58830 58870 58909 58949 58988 59028 59068 51 4 8 12 16 20 24 28 32 36 9 10 59068 59107 59147 59186 59225 59265 59304 50 4 8 12 16 20 24 28 32 36 9.59304 59344 59383 59422 59461 59501 591540 49 4 8 12 16 20 24 28 32 36 11 59540 59579 59618 59657 59696 59735 59774 48 4 8 12 16 20 23 27 31 35 12 59774 59813 59852 59891 59930 59969 60008 47 4 8 12 16 20 23 27 31 35 13 60008 60047 60085 60124 60163 60202 60240 46 4 8 12 16 20 23 27 31 35 14 60240 60279 60318 60356 60395 60433 60472 45 4 8 12 16 20 23 27 31 35 15 9.60472 60510 60549 60587 60625 60664 60702 44 4 8 12 15 19 23 27 31 35 16 60702 60740 60779 60817 60855 60893 60931 43 4 8 12 15 19 23 27 31 35 17 60931 60970 61008 61046 61084 61122 61160 42 4 8 11 15 19 23 27 30 34 18 61160 61198 61236 61274 61311 61349 61387 41 4 8 11 15 19 23 27 30 34 19 20 61387 61425 61463 61500 61538 61576 61613 40 4 8 11 15 19 23 27 30 34 9.61613 61651 61689 61726 61764 61801 61839 39 4 8 11 15 19 23 27 30 34 21 61839 61876 61914 61951 61988 62026 62063 38 4 7 11 15 19 22 26 30 34 22 62063 62100 62138 62175 62212 62249 62287 37 4 7 11 15 19 22 26 30 34 23 62287 62324 62361 62398 62435 62472 62509 36 4 7 11 15 18 22 26 30 33 24 62509 62546 62583 62620 62657 62693 62730 35 4 7 11 15 18 22 26 26 30 33 25 9.62730 62767 62804 62841 62877 62914 62951 34 4 7 11 15 18 22 30 33 26 62951 62987 63024 63061 63097 63134 63170 33 4 7 11 15 18 22 26 29 33 27 63170 63207 63243 63279 63316 63352 63389 32 4 7 11 15 18 22 26 29 33 28 63389 63425 63461 63497 63534 63570 63606 31 4 7 11 14 18 22 25 29 32 29 30 63606 63642 63678 63715 63751 63787 63823 30 4 7 11 14 18 22 25 29 32 9.63823 63S59 63895 63931 63966 64002 64038 29 4 7 11 14 18 22 25 29 32 31 64038 64074 64110 64146 64181 64217 64253 28 4 7 11 14 18 22 25 29 32 32 64253 64289 64324 64360 64395 64431 64467 27 4 7 11 14 18 21 25 28 32 33 64467 64502 64538 64573 64609 64644 64679 26 4 7 11 14 18 21 25 28 32 34 64679 64715 64750 64785 64821 64856 64891 25 4 7 11 14 18 21 25 28 32 35 9.64891 64926 64962 64997 65032 65067 65102 24 4 7 10 14 18 21 25 28 31 36 65102 65137 65172 65207 65242 65277 65312 23 3 7 10 14 18 21 25 28 31 37 65312 65347 65382 65417 65452 65486 65521 22 3 7 10 14 18 21 25 28 31 38 65521 65556 65591 65625 65660 65695 65729 21 3 7 10 14 18 21 25 28 31 39 65729 65764 65799 65834 65868 65902 65937 20 3 7 10 14 17 21 24 28 31 40 9.65937 6597-1 66006 66040 66074 66109 66143 19 3 7 10 14 17 21 24 28 31 41 66143 66177 66212 66246 66280 66314 66348 18 3 7 IC 14 17 21 24 28 31 42 66348 66383 66417 66451 66485 66519 66553 17 3 7 10 14 17 20 24 27 31 43 66553 66587 66621 66655 '66689 66723 66757 16 3 7 10 14 17 20 24 27 30 44 66757 66791 66824 66858 66892 66926 66959 15 3 7 10 14 17 20 24 27 30 45 9.66959 66993 67027 67060 67094 67128 67161 14 a 7 10 14 17 20 24 27 30 46 67161 67195 67228 67262 67295 67329 67362 13 J 7 10 13 17 20 23 27 30 47 67362 67396 67429 67462 67496 67529 67562 12 3 7 10 13 17 20 23 27 30 48 67562 67596 67628 67662 67695 67729 67762 11 3 7 10 13 17 20 23 27 30 49 67762 67795 67825 67861 67894 67927 6796C 10 3 7 10 13 16 20 23 26 30 50 9.6796C 67993 68026 6805S 68092 68125 68158 9 3 7 10 13 16 20 23 26 30 ' 51 68158 681 9C 68223 68256 6828L 68322 68354 8 ? 7 10 13 16 20 23 26 30 52 68354 68387 6842C ) 68452 68485 ) 68517 6855C 7 J 7 10 13 16 19 23 26 29 53 6855C 68583 6861.' ) 68648 6868C ) 68713 68745 6 t 7 10 13 16 19 23 26 29 54 55 6874.^ 68777 6881C ) 6884[ [ ii9036 68874 68907 68939 5 3 7 10 13 16 19 23 26 29 9.6893i 68971 69004 69068 6910C 69132 4 6 10 13 16 19 22 26 29 56 69132 • 69164 [ 69197 ' 69229 69261 6929."] 69325 3 3 6 10 13 16 19 22 26 29 57 6932c ) 6935^ i 6938C 1 69421 69453 69484 69516 2 3 6 10 13 16 19 22 26 29 58 69516 ; 6954? 6958C ) 69612 69644 [ 69675 69707 1 3 6 10 13 16 19 22 26 29 59 69707 69739 6977( ) 69^^02 69834 69866 69897 3 6 10 13 16 19 22 26 29 60s. 50s. 40s. 308. 20s. 10s. Os. M. Is. 2s. 38. 4s. 5s. 6s. 7s. 8s. 9s. _ 6 OR 18 HOURS, OR APP. TIME A. M. PROPORTIONAL PARTS FOR 8ECO ND8. V 122 TABLE XXIX. LOGi >LE, 6 i^RITHMS OF THE APPARENT TIME, OR HOUR ANGLE. 1 HOUR AN( HOURS, OR APP. TIME P. M. PROPORTIONAL PARTS FOR SECONDS. 1 8. 8. S. 8. s. s. s. S. 8. S. 6. 8. s. S. S. d. 1 M. 10 20 30 40 50 60 1 2 3 4 5 6 7 8 9 J. 69897 69929 69960 69992 70023 70055 70086 59 3 6 9 13 16 19 22 25 28 1 70086 70118 70149 70180 7021V70243 70274 58 3 6 9 13 16 19 22 25 28 ( 2 70274 70306 70337 70368 7039? ■'^431 70462 57 3 6 9 13 16 19 22 25 28 • 3 70462 70493 70524 70555 70586 7v.617 70648 56 3 6 9 12 15 19 22 25 28 4 70648 70680 70710 70741 70772 70803 70834 55 3 6 9 12 15 19 22 25 28 5 9.70834 70865 70896 70927 70958 70988 71019 54 3 6 9 12 15 19 22 25 28 6 71019 71050 71081 71111 71142 71173 71203 53 3 6 9 12 15 19 22 25 28 7 71203 71234 71265 71295 71326 71356 71387 52 3 6 9 12 15 18 21 24 27 8 71387 71417 71448 71478 71509 71539 71569 51 3 6 9 12 15 18 21 24 27 9 10 71569 71600 71630 71660 71691 71721 71751 50 3 6 9 12 15 18 21 24 27 9.71751 71781 71812 71842 71872 71902 71932 49 3 6 9 12 15 18 21 24 27 11 71932 71962 71992 72022 72052 72082 72112 48 3 6 9 12 15 18 21 24 27 12 72112 72142 72172 72202 72232 72262 72292 47 3 6 9 12 15 18 21 24 27 13 72292 72322 72352 72381 72411 72441 72471 46 3 6 9 12 15 18 21 24 27 14 72471 72500 72530 72560 72589 72619 72648 45 3 6 9 12 15 18 21 24 27 15 9.72648 72678 72708 72737 72767 72796 72825 44 3 6 9 12 15 18 21 24 27 16 72825 72855 72884 72914 72943 72972 73002 43 3 6 9 12 15 18 21 24 27 17 73002 73031 73060 73090 73119 73148 73177 42 3 6 9 12 14 17 20 23 26 18 73177 73207 73236 73265 73294 73323 73352 41 3 6 9 12 14 17 20 23 26 19 73352 73381 73410 73439 73468 73497 73526 40 3 6 9 12 14 17 20 23 26 20 9.73526 73555 73584 73613 73642 73671 73699 39 3 6 9 12 14 17 20 23 26 21 73699 73728 73757 73786 73815 73843 73872 38 3 6 9 11 14 17 20 23 26 22 73872 73901 73929 73958 73987 74015 74044 37 3 6 9 11 14 17 20 23 26 23 74044 74072 74101 74129 74158 74186 74215 36 3 6 9 11 14 17 20 23 26 24 74215 74243 74272 74300 74328 74357 74385 35 3 6 9 11 14 17 20 23 26 25 9.74385 74413 74442 74470 74498 74526 74554 34 3 6 8 11 14 17 20 22 25 26 74554 74583 74611 74639 74667 74695 74723 33 3 6 8 11 14 17 20 22 25 27 74723 74751 74779 74807 74835 74863 74891 32 3 6 8 11 14 17 20 22 25 28 74891 74919 74947 74975 75003 75031 75059 31 3 6 8 11 14 17 20 22 25 29 75059 75086 75114 75142 75170 75197 75225 30 3 6 8 11 14 17 20 22 25 30 9.75225 75253 75280 75308 75336 75363 75391 29 3 5 8 11 14 16 19 22 25 31 75391 75418 75446 75474 75501 75528 75556 28 3 5 8 11 14 16 19 22 25 32 75556 75583 75611 75638 75666 75693 75720 27 3 5 8 11 14 16 19 22 25 33 75720 75748 75775 75802 75830 75857 75884 26 3 5 8 11 14 16 19 22 25 34 75884 75911 75938 75966 75993 76020 76047 25 24 3 5 8 11 14 16 19 22 22 24 24 35 9.76047 76074 76101 76128 76155 76182 76209 3 5 8 11 14 16 19 36 76209 76236 76263 76290 76317 76344 76371 23 3 5 8 11 14 16 19 22 24 37 76371 76397 76424 76451 76478 76505 76531 22 3 5 8 11 14 16 19 21 24 38 76531 76558 76585 76611 76638 76665 76691, 21 3 5 8 11 14 16 19 21 24 39 76691 76718 76745 76771 76798 76824 76851 20 3 5 8 11 13 16 19 21 24 40 9.76851 76877 76904 76930 76957 76983 77009 19 3 5 8 11 13 16 18 21 24 41 77009 77036 77062 77089 77115 77141 77167 18 3 5 8 11 13 16 18 21 24 42 77167 77194 77220 77246 77272 77298 77325 17 3 5 8 10 13 16 18 21 24 43 77325 77351 77377 77«)3 77429 77455 77481 16 3 5 8 10 13 16 18 21 24 44 77481 77507 77533 77 59 77585 77611 77637 15 3 t. 8 10 13 16 18 21 23 45 9.77637 77663 77689 77715 77741 77766 77792 14 3 8 10 13 15 18 21 23 46 77792 77818 77844 77870 77895 77921 77947 13 3 8 10 13 15 18 21 23 47 77947 77972 77998 78024 78049 78075 78101 12 3 t 8 10 13 1^ 18 21| 23 48 78101 78126 78152 78177 78203 78228 78254 11 3 «. • 8 Id 13! 1.^ 18 20 23 49 78254 78279 78305 78330 7835S 78381 78406 10 3 «. 8 10 13 15 18 20 23 50 9.78406 78431 78457 78482 78507 78533 78558 9 3 8 IC 13 15 17 20 23 51 78558 78583 78608 78633 78659 78684 78709 8 3 tJ IC 13 15 17 20 23 52 78709 78734 78759 78784 78809 78834 78859 7 3 IC 13 15 17 20 23 53 78859 78884 78909 78934 78959 78984 79009 6 3 A 10 13 15 17 20 23 54 79009 79034 79059 79084 79108 79133 79158 ! 5 2 *- IC 18 15 17 20 23 55 9.7915? 79183 7920S 79232 79257 79282 79306 . 4 2 IC 13 15 17 20 23 56 79306 79331 79356 79380 79405 79430 79454 [ 3 2 IC 13 15 17 2(1 22 57 79454 [ 79479 79503 79528 79552 79577 79601 2 2 f IC 1 12 15 17 20 22 58 79601 79626 7965C 79674 79699 79723 79747 1 2 ft IC 12 15 11 2C 22 59 79747 79772 79796 79821 79845 79869 79893 2 ( IC 12 15 11 2C 22 60.'5. 50s. 40s. 30s. 20s. 10s. Os. M. Is. 2s. 3s. 4s. 5s. 6s. 7s. 8s. 9s. 5 OR 17 HOURS, OR APP. TIME A. M. _ PRC )POK TIONAL PARTS FOR SECONDS TABLE XXIX. 123 1 LOGARITHMS OF THE APPARENT TIME, OR HOUR ANGLE. HOUR ANGLE, 7 HOURS, OR APP. TIME P. M. PROPORTIONAL PARTS FOR SECONDS. 1 0. S. 8. 8. 8. 8. 8. 8. 8. 8. 8. 8. 8. 8. 8. 8. M. 10 20 30 40 50 60 1 2 3 4 5 6 7 8 9 i ). 79893 79918 79942 79966 79990 80014 80038 59 2 5 7 10 12 14 17 19 22 1 80038 80063 80087 80111 80135 80159 80183 58 2 5 7 10 12 14 17 19 22 2 80183 80207 80231 80255 80279 80303 80327 57 2 5 7 10 12 14 17 19 22 3 80327 80350 80374 80398 80422 80446 80470 56 2 5 7 10 12 14 17 19 22 4 80470 80494 80517 80541 80565 80588 80612 55 2 5 7 9 12 14 16 19 21 5 3.80612 80636 80660 80683 80707 80730 80754 54 2 5 7 9 12 14 16 19 21 6 80754 80778 80801 80825 80848 80872 80895 53 2 5 7 9 12 14 16 19 21 7 80895 80919 80942 80966 80989 81012 81036 ,52 2 5 7 9 12 14 16 19 21 8 81036 81059 81082 81106 81129 81152 81176 51 2 5 7 9 11 14 16 18 21 9 81176 81199 81222 81245 81269 81292 81315 50 2 5 7 9 11 14 16 18 21 10 9.81315 81338 81361 81384 81407 81430 81454 49 2 5 7 9 11 14 16 18 21 11 81454 81477 81500 81523 81546 81569 81592 48 2 5 7 9 11 14 16 18 21 12 81592 81614 81637 81660 81683 81706 81729 47 2 5 7 9 11 14 16 18 21 13 81729 81752 81775 81797 81820 81843 81866 46 2 5 7 9 11 14 16 18 21 1 14 81866 81888 81911 81934 81956 81979 82002 45 2 5 7 9 11 14 16 18 20 15 9.82002 82024 82047 82070 82092 82115 82137 44 2 5 7 9 11 14 16 18 20 , 16 82137 82160 82182 82205 82227 82250 82272 43 2 5 7 9 11 14 16 18 20 17 82272 82294 82317 82339 82362 82384 82406 42 2 5 7 9 11 14 16 18 20 18 82406 82429 82451 82473 82495 82518 82540 41 2 5 7 9 11 14 16 18 20 19 82540 82562 82584 82606 82629 82651 82673 40 2 4 7 9 11 13 15 18 20 20 9.82673 82695 82717 82739 82761 82783 82805 39 2 4 7 9 11 13 15 18 20 21 82805 82827 82849 82871 82893 82915 82937 38 2 4 7 9 11 13 15 18 20 22 82937 82959 82981 83003 83025 83046 83068 37 2 4 7 9 11 13 15 18 20 23 83068 83090 83112 83134 83155 83177 83199 36 2 4 7 9 11 13 15 18 20 24 83199 83220 83242 83264 83285 83307 83329 35 2 4 6 9 11 13 15 17 19 25 9.83329 83350 83372 83393 83415 83436 83458 34 2 4 6 9 11 13 15 17 19 26 83468 83479 83501 83522 83544 83565 83587 33 2 4 6 9 11 13 15 17 19 27 83587 83608 83629 83651 83672 83694 83715 32 2 4 6 9 11 13 15 17 19 28 83715 83736 83757 83779 83800 83821 83842 31 2 4 6 9 11 13 15 17 19 29 83842 83864 83885 83906 83927 83948 83969 30 2 4 6 8 11 13 15 17 19 30 9.83969 83990 84011 84033 84054 84075 84096 29 2 4 6 8 11 13 15 17 19 31 84096 84117 84138 84159 84179 84200 84221 28 2 4 6 8 11 13 15 17 19 32 84221 84242 84263 84284 84305 84326 84346 27 2 4 6 8 11 13 15 17 19 33 84346 84367 84388 84409 84430 84450 84471 26 2 4 6 8 11 13 15 17 19 34 84471 84492 84512 84533 84554 84574 84595 25 2 4 6 8 10 12 14 16 18 18 35 9.84595 84616 84636 84657 84677 84698 84718 24 2 4 6 8 10 12 14 16 36 84718 84739 84759 84780 84800 84821 84841 23 2 4 6 8 10 12 14 16 18 37 84841 84861 84882 84902 84923 84943 84963 22 2 4 6 8 10 12 14 16 18 38 84963 84984 85004 85024 85044 85065 85085 21 2 4 6 8 10 12 14 16 18 39 85085 85105 85226 85125 85145 85166 85186 85206 20 2 4 6 8 10 12 14 16 18 40 9.85206 85246 85266 85286 85306 85326 19 2 4 6 8 10 12 14 16 18 41 85326 85346 85366 85386 85406 85426 85446 18 2 4 6 8 10 1§ 14 16 18 42 85446 85466 85486 85506 85526 85546 85565 17 2 4 6 8 10 12 14 16 18 43 85565 85585 85605 85625 85645 85664 85684 16 2 4 6 8 10 12 14 16 18 44 85684 85704 85724 85743 85763 85783 85802 15 2 4 6 8 10 12 14 16 18 45 9.85802 85822 85841 85861 85881 85900 85920 14 2 A 6 8 10 12 14 16 18 46 85920 85939 85959 85978 85998 86017 86037 13 2 4 [ 6 fl 10 12 14 16 18 47 86037 8605fc 86076 86095 86114 86134 86153 12 2 4 [ 6 S IC 12 14 16 18 48 86153 86172 86192 86211 8623C 8625C 86269 11 2 4 [ 6 8 10 12 14 16 18 49 86269 8628S 86307 86327 86346 86365 86384 [ 10 2 4 [ 6 ? IC 12 14 16 18 50 9.86384 86403, 8642.'^ 86442 86461 8648C 1 86499 9 2 ' 4 i 9 11 13 15 i7 51 86499 8651S 86537 86556 8657t i 86594 [ 8661S 8 2 4 . S 9 11 13 15 17 52 86613 86632 86651 86670 8668C 1 8670J ! 86727 7 2 ! 4 ; 8 9 11 13 15 17 53 86727 8674f 86764 [ 86783 86802 ! 86821 8684C ) 6 2 ! 4 ) ? S 11 13 15 17 54 55 8684C 8685S ! 86877 86896 8691^ ) 8693c 86952 ! 5 2 ! 4 1 8 ! 9 11 13 15 17 9.8695S ! 86971 8699C ) 87008 87027 8704f i 87064 I 4 2 ! 4 ; 8 ! 9 11 13 15 17 56 87064 [ 8708r 87101 87120 8713E ! 87157 87175 i 3 2 ' 4 ; 7 9 11 Ic 15 17 57 8717f ) 87194 [ 87212 ! 87231 8724£ 1 8726J ! 87286 ) 2 2 4 . 7 9 11 IS 15 17 58 8728( ) 8730^ ) 8732c I 87341 8736C I 8737S 87396 ; 1 2 4 . 7 9 11 Vc ! 15 . 17 59 8739f i 8741^ ) 8743c I 87451 8747C I 8748? ! 87506 2 4 ; 1 c 1 11 U ! 15 i 17 605. 50s. 40s. 308. 208. 10s. Os. M. Is. 2s. 3s. 4&. 5s. 6s. 7s. 8s. 9s. 4 OR 16 HOURS, OR APP. TIME A. M. PROPORTIONAL PARTS F OR i 3ECOND8. 1 124 TABLE XXIX. n LOGARITHMS OF THE APPARENT TIME, OR HOUR ANGLE. 1 HOUR AN&I.B, 8 HOURS, OR APP. TIME P. M. PROPORTIONAL PARTS FOR SECONDS. | 8. ■' ■ s. 8. 8. 6. 8. s. S. 8. 8. 8. 8. s. a a 1 M. IJ 20 30 40 50 60 1 2 3 4 5 6 7 8 ' 9.87506 87524 87543 87561 87579 87597 87615 o9 2 4 5 7 9 11 13 14 16 1 1 87615 87633 87652 87670 87688 87706 87724 58 2 4 5 7 9 11 13 14 16 2 87724 87742 87760 87778 87796 87814 87832 57 2 4 5 7 9 11 13 14 16 3 87832 87850 87868 87886 87904 87921 87939 56 2 4 5 7 9 11 13 14 16 4 87939 87957 87975 87993 88011 88028 88046 55 2 4 5 7 9 11 13 14 16 5 9.88046 88064 88082 88100 88117 88135 88153 54 2 4 5 7 9 11 13 14 16 6 88153 88170 88188 88206 88223 88241 88259 53 2 3 5 7 9 11 12 14 16 7 88259 88276 88294 88311 88329 88346 88364 52 2 3 5 7 9 11 12 14 16 8 88364 88381 88399 88416 88434 88451 88469 51 2 3 5 7 9 11 12 14 16 9 88469 88486 88503 88521 88538 88556 88573 50 2 3 5 7 9 11 12 14 16 10 9.88573 88590 88607 88625 88642 88659 88677 49 2 3 5 7 8 10 12 14 15 11 88677 88694 88711 88728 88745 88763 88780 48 2 3 5 ■ 7 8 10 12 14 15 12 88780 88797 88814 88831 88848 88865 88882 47 2 3 5 7 8 10 12 14 15 13 88882 88899 88916 88933 88950 88967 88984 46 2 3 5 7 8 10 12 14 15 14 88984 89001 89018 89035 89052 89069 89086 45 44 2 3 5 7 8 10 12 14 15 15 9.89086 89103 89120 89137 89153 89170 89187 2 3 5 7 8 10 12 14 15 16 89187 89204 89221 89237 89254 89271 89287 43 2 3 5 7 8 10 12 14 15 17 89287 89304 89321 89338 89354 89371 89387 42 2 3 5 7 8 10 12 14 15 18 89387 89404 89421 89438 89454 89470 89487 41 2 3 5 7 8 10 12 13 15 19 89487 89503 89520 89536 89553 89569 89586 40 2 3 5 7 8 10 12 13 15 20 9.89586 89602 89619 89635 89651 89668 89684 39 2 3 5 7 8 16 12 13 15 21 89684 89701 89717 89733 89749 89766 89782 38 2 3 5 7 8 10 12 13 15 22 89782 89798 89815 89831 89847 89863 89879 37 2 3 5 7 8 10 12 13 15 23 89879 89896 89912 89928 89944 89960 89976 36 2 3 5 6 8 10 11 13 14 24 89976 89992 90008 90024 90040 90056 90072 35 2 3 5 6 8 10 11 13 14 25 9.90072 90088 90104 90120 90136 90152 90168 34 2 3 5 6 8 10 11 13 14 26 90168 90184 90200 90216 90232 90248 90263 33 2 3 5 6 8 10 11 13 14 27 90263 90279 90295 90311 90327 90342 90358 32 2 3 5 6 8 10 11 13 14 28 90358 90374 90390 90405 90421 90437 90452 31 2 3 5 6 8 10 11 13 14 29 90452 90468 90484 90499 90515 90531 90546 30 2 3 5 6 8 10 11 13 14 30 (.90546 90562 90577 90593 90608 90624 90639 29 2 3 5 6 8 9 11 12 14 31 90639 90655 90670 90686 90701 90717 90732 28 2 3 5 6 8 9 11 12 14 32 90732 90747 90763 90778 90794 90809 90824 27 2 3 5 6 8 9 11 12 14 33 90824 90840 90855 90870 90885 90901 90916 26 2 3 5 6 8 9 11 12 14 34 90916 9093) 90946 90961 90977 90992 91007 25 2 3 5 6 8 9 11 12 14 35 9.91007 91022 91037 91052 91067 91083 91098 24 2 3 4 6 7 9 10 12 14 36 91098 91113 91128 91143 91158 91173 91188 23 2 3 4 6 7 9 10 12 14 37 91188 91203 91218 91233 91248 91262 91277 22 2 3 4 6 7 9 10 12 14 38 91277 91292 91307 91322 91337 91352 91367 21 2 3 4 6 7 9 10 12 14 39 91367 91381 91396 91411 91426 91440 91455 20 2 3 4 6 7 9 10 12 14 40 9.91455 91470 91485 91499 91514 91529 91543 19 3 4 6 7 9 10 12 13 41 91543 91558 91573 91587 91602 91616 91631 18 3 4 6 7 9 10 12 13 42 91631 91645 91660 91674 91689 91703 91718 17 3 4 6 7 9 10 12 13 43 91718 91732 91747 91761 91776 91790 91805 16 3 4 6 7 9 10 12 13 44 91805 91819 91833 91848 91862 91876 91891 15 — V, 3 4 6 7 9 10 12 13 45 9 9i?91 91905 91919 91934 91948 91962 91976 14 1 3 4 6 7 8 10 11 13 46 91976 91991 92005 92019 92033 92047 92061 13 3 4 6 7 8 10 11 13 47 92061 92076 92090 92104 92118 92132 92146 12 3 4 6 7 8 10 11 13 48 92146 92160 92174 92188 92202 92216 92230 11 3 4 6 7 8 10 11 13 49 92230 92244 92258 92272 92286 92300 92314 10 3 4 6 7 8 10 11 13 50 9.92314 92328 92342 92355 92369 92383 92397 9 3 4 6 7 8 10 11 13 51 92397 92411 92425 92438 92452 92466 92480 8 3 4 6 7 8 10 11 13 52 92480 92493 92507 92521 92534 92548 92562 7 3 4 5 7 8 9 11 12 53 92562 92575 92589 92603 92616 92630 92643 6 3 4 5 7 8 9 11 12 54 55 92643 92657 92670 92684 92698 92711 92725 5 4 3 4 5 7 8 9 11 12 9.92725 92738 92751 92765 92778 92792 92805 3 4 5 7 8 9 11 12 56 92805 92819 92832 92845 92859 92872 92885 3 3 4 5 7 8 9 11 12 57 92885 92899 92912 92925 92939 92952 92965 2 3 4 5 7 8 9 11 12 58 92965 92978 92992 93005 93018 93031 93044 1 3 4 5 7 8 9 10 12 59 93044 93057 93071 )30S!4 93097 93110 93123 3 4 2s. 3s. 5 7 8 9 10 12 - 60s. 508. 40s. 30s. 20s. 10s. Os. M. Is. 4s. 5s. 6s. 78. 8s. 9s. 3 OR 15 HOURS, OR APP. TIME A. M. | PRC ► PORTION AL PARTS FOR S ECONDS. 1 126 TABLE XXX. FOR CORRECTING THE LONGITUDE BY CHRONOMETER FR JM THE EFFECT OF AN ERROR IN THE LATITUDE USED IN FINDING THE TIME. TABLE A. EitUr this Table %nth the Latitude worked with at the Side, and the Hour Angle at the Tap. (See explanation of this Table at page 144.) 1 Lat. HOUR ANOLK. HOUR ANOLE. HOUR ANGLE. HOUR. AN. B. A H. U. H. U H. H H. H H. M H. M. H. H H. M H. M H. U H. M. H. H H. H H. M H. M. H. H H. M. H. 11. D.R. 1 1 10 1 20 1 30 1 40 1 50 2 2 10 2 20 2 30 2 45 3 3 15 3 30 3 45 4 4 30 5 o ' // / n ' n / // / // ^ // 1 n / n t n 1 n * n t tl / // r tl 1 tl / II 1 tl t tl 2 0. 8 0. 7 0. 6 0. 5 0. 4 0. 4 0. 4 0. 3 0. 3 0. 2 0. 2 0. 2 0. 2 0. 1 0. 1 0. 1 0. 0. 4 0.15 0.13 0.12 0.10 0. 9 0. 8 0. 7 0. 7 0. b 0. 5 0. 5 0. 4 0. 4 0. 3 0. 2 0. 2 0. 2 0. 1 6 0.23 0.20 0.17 0.15 0.13 0.12 0.10 0.10 0. 9 0. 8 0. 7 0. 7 0. 6 0. 5 0. 4 0. 3 0. 2 0. 2 8 0.31 0.27 0.23 0.20 0.18 0.16 0.14 0.13 0.12 0.11 0.10 0. 9 0. 8 0. 7 0. 6 0. 5 0. 4 0. 3 10 0.40 0.34 0.29 0.25 0.22 0.20 0.25 0.18 0.16 0.15 0.14 0.12 0.11 0. 9 0. 8 0. 7 0. 6 0. 5 0. 3 12 0.47 0.40 0.35 0.31 0.28 0.22 0.20 0.18 0.16 0.14 0.13 0.11 0.10 0. 8 0. 7 0. 5 0, 4 14 0.56 0.47 0.41 0.36 0.32 0.29 0.26 0.23 0.21 0.19 0.17 0.15 0.13 0.11 0.10 0. 8 0. 6 0. 4 16 1. 4 0.54 0.47 0.41 0.37 0.33 0.29 0.27 0.25 0.22 0.19 0.16 0.15 0.13 0.11 0.10 0. 7 0. 5 18 1.12 1. 2 0,53 0.47 0.41 037 0.34 0.31 0.28 0.25 0.22 0.19 0.17 0.15 0.13 0.11 0. 8 0. 6 20 1.22 1. 9 1. 0.53 0.47 0.43 0.47 0.38 0.34 0.31 0.28 0.25 0.22 0.19 0.17 0.15 0.13 0. 9 0. 6 22 1.31 1.17 1. 7 0.58 0.52 0.42 0.38 0.35 0.32 0.28 0.24 0.21 0.19 0.16 0.14 0.10 0. 7 24 1.40 1.25 1.13 1. 4 0.57 0.52 0.46 0.42 0.38 0.35 0.31 0.26 0.23 0.20 0.18 0.15 0.11 0. 7 26 1.49 1.33 1.20 1.11 1. 3 0.56 0.50 0.46 0.42 0.38 0.34 0.29 0.26 0.22 0.20 0.17 0.12 0. 8 28 1.59 1.41 1.28 1.17 1. 8 1. 1 0.55 0.50 0.46 0.41 0.37 0.32 0.28 0.25 0.22 0.19 0.13 0. 8 30 2. 9 1.50 1.35 1.23 1.14 1. 7 1. 0.54 0.49 0.45 0.39 0.34 0.31 0.26 0.23 0.20 0.14 0. 9 32 2.19 1.59 1.43 1.31 1.20 1.12 1. 5 0.59 0.53 0.49 0.43 0.37 0.33 0.27 0.25 0.22 0.16 0.10 34 2.31 2. 8 1.51 1.30 1.27 1.18 1.10 1. 4 0.58 0.53 0.46 0.40 0.35 0.31 0.27 0.23 0.17 0.11 36 2.43 2.18 2. 1.45 1.34 1.24 1.16 1. 8 1. 2 0.57 0.59 0.43 0.38 0.34 0.29 0.25 0.18 0.11 38 2.55 2.29 2. 9 1.53 1.41 1.30 1.21 1.14 1. 7 1. 1 0.53 0.47 0.41 0.36 0.31 0.27 0.19 0.13 40 3. 8 2 40 2.19 2. 2 1.48 1.37 1.27 1.19 1.12 1. 5 0.57 O.50 0.44 0.39 0.34 0.29 0.21 0.13 42 3.22 2.52 2.28 2.10 1.56 1.44 1.34 1.25 1.17 1.10 1. 1 0.54 0.47 0.41 0.36 0.31 0.22 0.14 44 3.36 3. 4 2.39 2.20 2 .4 1.52 1.40 1.31 1.23 1.16 1. 6 0.58 0.51 0.44 0.39 0.34 0.24 0.16 46 3.51 3.16 2.5a 2.30 2.13 1.59 1.47 1.38 1.29 1.21 1.11 1. 2 0.55 0.47 0.41 0.36 0.25 0.17 48 3.31 3. 3 2.41 2.23 2. 8 1.55 1.44 1.35 1.27 1.16 1. 7 0.58 0.51 0.44 0.38 0.28 0.18 50 3.16 2.53 2.34 2.17 2. 4 1.52 1.43 1.34 1.21 1.11 1. 3 0.56 0.47 0.41 0.29 0.19 52 3. 5 2.44 2.281 2.13 2. 1.50 1.40 1.28 1.17 1. 7 0.59 0.51 0.44 0.32 0.20 54 3.19 2.57 2.38, 2.23 2.10 2.58 1.48 1.34 1.23 1.13 1. 3 0.65 0.47 0.34 0.22 56 3.35 3.11 2.50 2.34 2.20 2. 7 1.56 1.41 1.29 1.18 1. 8 0.59 0.51 0.37 0.24 58 3.52 3.26 3. 4 2.44 2.31 2.17 2. 5 1.49 1.36 1.24 1.14 1. 4 0.55 0.40 0.26 60 4.10 3.43 3.20 3. 2.43 2.29 2.16 1.58 1.44 1.31 1.20 1.10 1. 0.43 0.28 62 / 4. 2 3.37 3.14 2.57 2.39 2.27 2. 8 1.63 1.39 1.26 1.16 1. 5 0.47 0.30 64 3.56 3.33 3.13 2.56 2.40 2.20 2. 3 1.58 1.34 1.22 1.11 0.51 0.33 66 3.53 3.32 3.13 2.56 2.34 2.15 1.58 1.43 1.30 1.18 0.56 0.36 68 1 1 3.53 3.32 3.14 2.49 2.28 2.10 1.54 1.39 1.26 1. 1 0.40 TABLE B. ErUer this Table with the Declination at the Side, and the Hour Angle at the Top. Dbo. HOOK ANOLB. HOUR ANOLE. HOUR ANOLE. HOUR AN. H. A. H. M. H. M. H. H. H. H. H. M. H. M. H. M. H. M. H. M. H. M. H. M. H. M H. M. H. M. H. M. H. H. H. M. H. M 1 1 10 1 20 1 30 1 40 1 50 2 2 10 2 20 2 30 2 45 3 3 15 3 30 3 45 4 4 30 5 / n f M / // t n t n t tt f ft t n r n / tt / tt / tt t tt t It 1 tt / tl / // 1 n 2 0. 8 0. 7 0. 6 0. 5 0. 5 0. 5 0. 4 0. 4 0. 4 0.04 0. 3 0. 3 0. 3 0. 2 0. 2 0. 2 0. 2 0. 2 4 0.16 0.14 0.12 0.11 0.10 0. 9 0. 8 0. 8 0. 7 0.07 0. 7 0. 6 0. 5 0. 5 0. 5 0. 5 0. 5 0. 4 6 0.25 0.21 0.19 0.16 0.15 0.14 0.13 0.12 0.11 0.10 0.10 0. 9 0. 8 0. 8 0. 8 0. 7 0. 7 0. 7 8 0.32 0.28 0.25 0.22 0.20 0.18 0.17 0.16 0.14 0.14 0.13 0.12 0.11 0.11 0.10 0.10 0. 9 0. 9 10 0.41 0.35 0.31 0.28 0.25 0.23 0.21 0.20 0.19 0.17 3.16 3.19 0.15 0.14 0.13 0.12 0.12 o.n 0.11 12 0.49 0.43 0.37 0.33 0.30 0.28 0.25 0.24 0.22 0.21 0.18 0.17 0.16 0.16 0.15 0.14 0.13 14 0.58 0.50 0.44 0.39 0.35 0.32 0.30 0.28 0.26 0.25 0.23 0.21 0.20 0.19 0.18 0.17 0.16 0.15 16 1. 7 0.57 0.50 0.45 0.41 0.37 0.34 0.32 0.30 0.28 3.26 0.25 0.23 0.22 0.21 0.20 0.19 0.18 18 1.16 1. 5 0.57 0.51 0.46 0.42 0.39 D.36 0.34 3.32 3.29 0.28 0.26 0.25 0.23 0.22 0.21 0.20 20 1.25 1.13 1. 4 0.57 0.52 0.47 0.44 [).41 D.38 1.36( 3.33 0.31 0.29 0.28 0.26 0.25 0.23 0.22 f 22 1.34 1.20 1.11 1. 4 0.58 0.52 0.49 [).45 ').42( T.40( 3.37 0.34 0.32 0.31 0.29 0.28 0.26 0.25 j 24 1.43 1.27 1.18 1.11 1. 4 O.b; 0.54] T.49 1.46 1.44( 3.41 0.37| 0.35 0.34 0.32 0.31 0.29 0.28 126 TABLE XXXI. LOGARITHMS OF THE APPARENT DISTANCE APPARENT DISTANCE, M. 18» 19° 20° 21° 22° 23° M. Log. S. Log. T. Log. S. Log. T. Loy-. S. Log. T. Log. S. Log. T. Log. S. Log. T. Log. S. iLog. T. 0.4900 0.5118 0.5126 0.5370 0.5341 0.5611 0.5543 0.5842 0.5736 0.6064 0.59190.6279 1 4904 5122 5130 5374 5344 5615 5547 5846 5739 6068 5922 6282 1 2 4908 5126 5134 5378 5347 5619 5550 5849 5742 6071 5925 6286 2 3 4911 5131 5137 538i- 5351 5622 5553 5853 5745 6075 5928 6289 3 4 4915 5135 5141 5386 5354 5626 5556 5857 5748 6079 5931 6293 4 5 0.4919 0.5139 0.5145 0.5390 0.5358 0.5630 0.5560 0.5861 0.5751 0.6082 0.5934 0.6296 5 6 4923 5143 5148 5394 5361 5634 5563 5864 5754 6086 5937 6300 6 7 4927 5148 5152 5398 5365 5638 5566 5868 5758 6090 5940 6303 7 8 4931 5152 5156 5402 5368 5642 5570 5872 5761 6093 5943 6307 8 9 4935 5156 5159 5407 5372 5646 5573 5876 5764 6097 5945 6310 9 10 0.4939 0.5161 0.5163 0.5411 0.5375 0.5650 0.5576 0.5879 0.5767 0.6100 0.5948 0.6314 10 11 4942 5165 5167 5415 5379 5654 5579 5883 5770 6104 5951 6317 11 12 4946 5169 5170 5419 5382 5658 5583 5887 5773 6108 5954 6321 12 13 4950 5173 5174 5423 5385 5662 5586 5891 5776 6111 5957 6324 13 14 4954 5178 5177 5427 5389 5665 5589 5894 5779 6115 5960 6328 14 15 0.4958 0.5182 0.5181 0.5431 0.5392 0.5669 0.5592 0.5898 0.5782 0.6118 0.5963 0.6331 15 16 4962 5186 5185 5435 5396 5673 5596 5902 5785 6122 5966 6334 16 17 4965 5190 5188 5439 5399 5677 5599 5906 5789 6126 5969 6338 17 18 4969 5195 5192 5443 5402 5681 5602 5909 5792 6129 5972 6341 18 19 4973 5199 5196 5447 5406 5685 5605 5913 5795 6133 5975 6345 19 20 0.4977 0.5203 0.5199 0.5451 0.5409 0.5689 0.5609 0.5917 0.5798 0.6136 0.5978 0.6348 20 21 4981 5207 5203 5455 5413 5693 5612 5921 5801 6140 5981 6352 21 22 4984 5212 5206 5459 5416 5696 5615 5924 5804 6144 5984 6355 22 23 4988 5216 5210 5463 5420 5700 5618 5928 5807 6147 5987 6359 23 24 4992 5220 5213 5467 5423 5704 5621 5932 5810 6151 5990 6362 24 25 0.4996 0.5224 0.5217 0.5471 0.5426 0.5708 0.5625 0.5935 0.5813 0.6154 0.5992 0.6366 25 26 5000 5228 5221 5475 5430 5712 5628 5939 5816 6158 5995 6369 26 27 5003 5233 5224 5479 5433 5716 5631 5943 5819 6162 5998 6373 27 28 5007 5237 5228 5483 5436 5720 5634 5947 5822 6165 6001 6376 28 29 5011 5241 5231 5487 5440 5724 5638 5950 5825 6169 6004 6380 29 * 30 0.5015 0.5245 0.5235 0.5491 0.5443 0.5727 0.5641 0.5954 0.5828 0.6172 0.6^7 0.6383 30 31 5019 5249 5239 5496 5447 5731 5644 5958 5831 6176 6010 6386 31 32 5022 5254 5242 5500 5450 5735 5647 5961 5834 6179 6013 6190 32 33 5026 5258 5246 5504 5453 5739 5650 5965 5838 6183 6016 6393 33 34 5030 5262 5249 5508 5457 5743 5654 5969 5841 6187 6019 6397 34 35 0.5034 0.5266 0.5253 0.5512 0.5460 0.5747 0.5657 0.5972 0.5844 0.6190 0.6022 0.6400 35 36 5037 5270 5256 5516 5463 5750 5660 5976 5847 6194 6024 6404 36 37 5041 5275 5260 5520 5467 5754 5663 5980 5850 6197 6027 6407 37 38 5045 5279 5263 5524 5470 5758 5666 5984 5853 6201 6030 6411 38 39 5049 5283 5267 5528 5474 5762 5670 5987 5856 6204 603S 6414 39 40 0.5052 5287 0.5270 0.5531 0.5477 0.5766 0.5673 0.5991 0.5859 0.6208 0.6036 0.6417 40 ' 41 5056 5292 5274 5535 5480 5770 5676 5995 5862 6211 6039 6421 41 42 5060 5295 5278 5539 5484 5773 5679 5998 5865 6215 6042 6424 42 43 5064 5299 5281 5543 5487 5777 5682 6002 5868 6219 6045 6428 43 44 5067 5304 5285 5547 5490 5781 5685 6006 5871 6222 6047 6431 44 45 0.5071 0.5308 0.5288 0.5551 0.5494 0.5785 0.5689 0.6009 0.5874 0.6226 0.6050 0.6435 45 46 5075 5312 5292 5555 5497 5789 5692 6013 5877 6229 6053 6438 46 47 5078 5316 5295 5559 5500 5792 5695 6017 5880 6233 6056 6441 47 48 5082 5320 5299 5563 5504 5796 5698 6020 5883 6236 6059 6445 48 49 5086 5324 5302 5567 5507 5800 5701 6024 5886 6240 6062 6448 49 50 0.5090 0.5329 0.5306 0.5571 0.5510 0.5804 0.5704 0.6028 0.5889 0.6243 0.6065 0.6452 50 51 5093 5333 5309 5575 5514 5808 5708 6031 5892 6247 6068 6455 51 52 5097 5337 5313 5579 5517 5811 5711 6035 5895 6250 6070 6459 52 53 5101 5341 5316 5583 5520 5815 5714 6039 5898 6254 6073 6462 53 54 5104 5345 5320 5587 5523 5819 5717 6042 5901 6257 6076 6465 54 55 0.5108 0.5349 0.5323 0.5591 0.5527 0.5823 0.5720 0,6046 0.5904 0.6261 0.6079 0.6469 55 56 5112 5353 5327 5595 5530 5827 5723 6050 5907 6264 6082 6472 56 57 5115 5357 5330 5599 5533 5830 5726 6053 5910 6268 6085 6476 57 58 5119 5362 5334 5603 5537 5834 5730 6057 5913 6271 6087 6479 58 59 5123 5366 5337 5607 5540 5838 5733 6060 5916 6275 6090 6482 59 60 5126 5370 5341 5611 5543 5842 5736 6064 5919 6279 6093 6486 60 M. Log. S. Log. T. Log. S. Log. T. Log. S. Log. T. Log. S. Log. T. Log. 8. Log. T. Log. 8. Log. T. M. 18° 19° 20° 2 I* 22° 23° APPARENT DISTANCE. 1 TABLE XXXI. '87 LOGARITHMS OF THE APPARENT DISTANCE. i' APPARENT DISTANCE. M. 2 25° 26° 27° 28° 29* M Log. S. Log. T. Log. S. Log. T. Log. 8. Log. T. Log. S. Log. T. Log. S. Log. T. Log. 8. Log. T 0.6093 0.6486 0.6259 0.6687 0.6418 0.6882 0.6570 0.7072 0.6716 0.7257 0.6856 0.7438 1 6096 6489 6262 6690 6421 6885 6573 7075 6718 7260 6858 7441 1 2 6099 6493 6265 6693 6424 6888 6575 7078 6721 7263 6860 7443 2 3 6102 6496 6268 6697 6426 6891 6578 7081 6723 7266 6863 7446 3 4 6104 6499 6270 6700 6429 6895 6580 7084 6726 7269 6865 7449 4 5 0.6107 0.6503 0.6273 0.6703 0.6431 0.6898 0.6583 0.7087 0.6728 0.7272 0.6867 0.7452 5 6 6110 6506 6276 6706 6434 6901 6585 7090 6730 7275 6869 7455 6 7 6113 6510 6278 6710 6437 6904 6588 7093 6733 7278 6872 7458 7 8 6116 6513 6281 6713 6439 6907 6590 7097 6735 7281 6874 7461 8 9 6119 6516 6284 6716 6442 6911 6593 7100 6737 7284 6876 7464 9 10 0.6121 0.6520 0.6286 0.6720 0.6444 0.6914 0.6595 0.7103 0.6740 0.7287 0.6878 0.7467 11 6124 6523 6289 6723 6447 6917 6598 7106 6742 7290 6881 7470 11 12 bl27 6527 6292 6726 6449 6920 6600 7109 6744 7293 6883 7473 12 13 6130 6530 6295 6729 6452 6923 6603 7112 6747 7296 6885 7476 13 14 6133 6533 6297 6733 6455 6927 6605 7115 6749 7299 6887 7479 14 15 15 0.6135 0.6537 0.6300 0.6736 0.6457 0.6930 0.6607 0.7118 0.6752 0.7302 0.6890 0.7482 16 6138 6540 6303 6739 6460 6933 6610 7121 6754 7305 6892 7485 16 17 6141 6543 6305 6743 6462 6936 6612 7125 6756 7308 6894 7488 17 18 6144 6547 6308 6746 6465 6939 6615 7128 6759 7311 6896 7491 18 19 6147 6550 6311 6749 6467 6942 6617 7131 6761 7314 6899 7494 19 20 0.6149 0.6553 0.6313 0.6752 0.6470 0.6946 0.6620 0.7134 0.6763 0.7317 0.6901 0.7497 20 21 6152 6557 6316 6756 6472 6949 6622 7137 6766 7320 6903 7600 21 22 6155 6560 6319 6759 6475 6952 6625 7140 6768 7324 6905 7503 22 23 6158 6564 6321 6762 6477 6955 6627 7143 6770 7327 6908 7506 23 24 6161 (1.567 6324 6765 6480 6958 6629 7146 6773 7330 6910 7509 24 25 0.6163 0.6570 0.6327 0.6769 0.6483 0.6962 0.6632 0.7149 0.6775 0.7333 0.6912 0.7512 25 26 6166 6574 6329 6772 6485 6965 6634 7152 6777 7336 6914 7515 26 27 6169 6577 6332 6775 6488 6968 6637 7156 6780 7339 6917 7518 27 28 6172 6580 6335 6778 6490 6971 6639 7159 6782 7342 6919 7521 28 29 6175 6584 6337 6782 6493 6974 6642 7162 6784 7345 6921 7523 29 30 0.6177 0.6587 0.6340 0.6785 0.6495 0.6977 0.6644 0.7165 0.6787 0.7348 0.6923 0.7526 30 31 6180 6590 6342 6788 6498 6981 6646 7168 6789 7351 6926 7529 31 32 6183 6594 6345 6791 6500 6984 6649 7171 6791 7354 6928 7632 32 33 6186 6597 6348 6795 6503 6987 6651 7174 6794 7357 6930 7535 33 34 35 6188 6600 6350 6798 6505 6990 6654 7177 6796 7360 6932 7538 34 0.6191 0.6604 0.6353 0.6801 0.6508 0.6993 0.6656 0.7180 0.6798 0.7363 0.6935 0.7541 35 36 6194 6607 6356 6804 6510 6996 6659 7183 6801 7366 6937 7544 36 37 6197 6610 _6358 6808 6513 6999 6661 7186 6803 7369 6939 7647 37 38 6199 6614 6361 6811 6515 7003 6663 7189 6805 7372 6941 7550 38 39 6202 6617 6364 6814 6518 7006 6666 7192 6808 7375 6943 7553 39 40 0.6205 0.6620 0.6366 0.6817 6521 0.7009 0.6668 0.7196 0.6810 0.7378 0.6946 9.7556 40 41 6208 6624 6369 6821 6523 7012 6671 7199 6812 7381 6948 7559 41 42 6210 6627 6371 6824 6526 7015 6673 7202 6814 7384 6950 7562 42 43 6213 6630 6374 6827 6528 7018 6675 7205 6817 7387 6952 7566 43 44 6216 6634 6377 6830 6531 7022 6678 7208 6819 7390 6954 7568 44 45 0.6219 0.6637 0.6379 0.6834 0.6533 0.7025 0.6680 0.7211 0.6821 0.7393 0.6957 0.7571 45 46 6221 6640 6382 6837 6536 7028 6683 7214 6824 7396 6959 7573 46 47 6224 6644 6385 6840 6538 7031 6685 7217 6826 7399 6961 7576 47 48 6227 6647 6387 6843 6541 7034 6687 7220 6828 7402 6963 7679 48 49 6230 6650 6390 6846 6543 7037 6690 7223 6831 7405 6966 7582 49 50 0.6232 0.6654 0.6392 0.6850 0.6546 0.7040 0.6692 0.7226 0.6833 0.7408 0.6968 0.7685 60 51 6235 6657 6395 6853 6548 7043 6695 7229 6835 7411 6970 7688 51 52 6238 6660 6398 6856 6551 7047 6697 7232 6837 7414 6972 7691 52 53 6240 6664 6400 6859 6553 7050 6699 7235 6840 7417 6974 7594 53 54 6243 6667 6403 6863 6556 7053 6702 7238 6842 7420 6977 7597 54 55 0.6246 0.6670 0.6405 0.6866 0.6558 0.7056 0.6704 0.7241 0.6844 0.7423 0.6979 0.7600 55 56 6249 6674 6408 6869 6561 7059 6707 7245 6847 7426 6981 7603 56 57 6251 6677 6411 6872 6563 7062 6709 7248 6849 7429 6983 7606 57 58 6254 6680 6413 6875 6566 7065 6711 7251 6851 7432 6985 7609 58 59 6257 6683 6416 6879 6568 7069 6714 7254 6853 7435 6988 7611 59 60 6259 6687 6418 6882 6570 7072 6716 7257 6856 7438 6990 7614 60 M. Log. 8. Log. T. Log. S. Log. T. Log. 8. Loff. T. Log. S. L"g. T. Log. S. Log. T. Log. 8. Log. T. M. 24° 25* 26° 27° 28° 29° APPARENT DISTANCE. 1 1S8 TABLE XXXI. LOGARITHMS OF THE APPARENT DISTANCE APPARENT DISTANCE. M. 30° 31" 32° 33° 34° , 35° Log. S. Log. T. Log. S. Log. T. Log. S. Log. T. Log. S. Log. T. Log. 8. Log. T. Log. «. Log. T. M 0.6990 0.7614 0.71180.7788 0.7242 0.7958 0.7361 0.8125 0.7476 0.8290 0.7586 0.8452 1 6992 7617 7121 7791 7244 7961 7363 8128 7477 8293 7588 8455 1 2 6994 7620 7123, 7793 7246 7964 7365 8131 7479 8295 7590 8458 2 3 6996 7623 7125 7796 7248 7966 7367 8133 7481 8298 7591 8460 3 4 5 6998 7626 " 27 7799 7250 7969 7369 8136 7483 8301 7593 8463 4 0.7001 0.7629 0.7129 0.7802 0.7252 0.7972 0.7371 0.8139 0.7485 0.8303 0.7595 0.8466 5 6 7003 7632 7131 7805 7254 7975 7373 8142 7487 8306 7597 8468 6 7 7005 7635 7133 7808 7256 7978 7375 8145 7489 8309 7599 8471 7 8 7007 7638 7135 7811 7258 7980 7377 8147 7491 8312 7600 8474 8 9 7009 7641 7137 7813 7260 7983 7379 8150 7492 8314 7602 8476 9 10 0.7012 0.7644 0.7139 0.7816 0.7262 0.7986 0.7380 0.8153 0.7494 0.8317 0.7604 0.8479 10 11 7014 7646 7141 7819 7264 7989 7382 8156 7496 8320 7606 8482 11 12 7016 7649 7144 7822 7266 7992 7384 8158 7498 8323 7607 8484 12 13 7018 7652 7146 7825 7268 7994 7386 8161 7500 8325 7609 8487 13 14 7020 7655 7148 7828 7270 7997 7388 8164 7502 8328 7611 8490 14 15 0.7022 0.7658 0.7150 0.7831 0.7272 0.8000 0.7390 0.8167 0.7504 0.8331 0.7613 0.8493 15 16 7025 7661 7152 7833 7274 8003 7392 8169 7505 8333 7615 8495 16 17 7C27 7664 7154 7836 7276 8006 7394 8172 7507 8336 7616 8498 17 18 7029 7667 7156 7839 7278 8008 7396 8175 7509 8339 7618 8501 18 19 7031 7670 7158 7842 7280 8011 7398 8178 7511 8342 7620 8503 19 20 0.7033 0.7673 0.7160 0.7845 0.7282 0.8014 0.7400 0.8180 0.7513 0.8345 0.7622 0.8506 20 21 7035 7675 7162 7848 7284 8017 7402 8183 7515 8347 7624 8509 21 22 7037 7678 7164 7850 7286 8020 7404 8186 7517 8350 7625 8511 22 23 7040 7681 7166 7853 7288 8022 7406 8189 7518 8352 7627 8514 23 24 7042 7684 7168 7856 7290 8025 7407 8191 7520 8355 7629 8517 24 25 0.7044 0.7687 0.7171 0.7859 0.7292 0.8028 0.7409 0.8194 0.7522 0.8358 0.7631 0.8519 25 26 7046 7690 7173 7862 7294 8031 7411 8197 7524 8361 7632 8522 26 27 7048 7693 7175 7865 7296 8034 7413 8200 7526 8363 7634 8525 27 28 7050 7696 7177 7868 7298 8036 7415 8202 7528 8366 7636 8527 28 29 7053 7699 7179 7870 7300 8039 7417 8205 7529 8369 7638 8530 29 30 0.7055 0.7701 0.7181 0.7873 0.7302 0.8042 0.7419 0.8208 0.7531 0.8371 0.7640 0.8532 30 31 7057 7704 7183 7876 7304 8045 7421 8211 7533 8374 7641 8535 31 32 7059 7707 7185 7879 7306 8047 7423 8213 7535 8377 7643 8538 32 33 7061 7710 7187 7882 7308 8050 7425 8216 7537 8379 7645 8541 33 34 7063 7713 7189 7885 7310 8053 7427 8219 7539 8382 7647 8543 34 35 0.7065 0.7716 0.7191 0.7887 0.7312 0.8056 0.7428 0.8222 0.7540 0.8385 0.7648 0.8546 35 36 7068 7719 7193 7890 7314 8059 7430 8224 7542 8388 7650 8549 36 37 7070 7722 7195 7893 7316 8061 7432 8227 7544 8390 7652 8551 37 38 7072 7725 7197 7896 7318 8064 7434 8230 7546 8393 7654 8554 38 39 7074 7727 7199 7899 7320 8067 7436 8233 7548 8396 7655 8557 39 40 0.7076 0.7730 0.7201 0.7902 0.7322 0.8070 0.7438 0.8235 0.7550 0.8398 0.7657 0.8559 40 41 7078 7733 7203 7904 7324 8072 7440 8238 7551 8401 7659 8562 41 42 7080 7736 7205 7907 7326 8075 7442 8241 7553 8404 7661 8565 42 43 7082 7739 7208 7910 7328 8078 7444 8243 7555 8406 7662 8567 43 44 7085 7742 7210 7913 7330 8081 7446 8246 7557 8409 7664 8570 44 45 0.7087 0.7745 0.7212 0.7916 0.7332 0.8084 0.7447 0.8249 0.7559 0.8412 0.7666 0.8573 45 46 7089 7748 7214 7918 7334 8086 7449 8252 7561 8415 7668 8575 46 47 7091 7750 7216 7921 7336 8089 7451 8254 7562 8417 7669 8578 47 48 7093 7753 7218 7924 7338 8092 7453 8257 7564 8420 7671 8581 48 49 7095 7756 7220 7927 7340 8095 7455 8260 7566 8423 7673 8583 49 50 0.7097 0.7759 0.7222 0.7930 0.7342 0.8097 0.7457 0.8263 0.7568 0.8425 0.7675 0.8586 50 51 7099 7762 7224 7933 7344 8100 7459 8265 7570 8428 7676 8589 51 52 7102 7765 7226 7935 7345 8103 7461 8268 7571 8431 7678 8591 52 53 7104 7768 7228 7938 7347 8106 7462 8271 7573 8433 7680 8594 53 54 7106 7771 7230 7941 7349 8109 7464 8274 7575 8436 7682 8597 54 55 0.7108 0.7773 0.7232 0.7944 0.7351 0.8111 0.7466 0.8276 0.7577 0.8439 0.7683 0.8599 55 56 7110 7776 7234 7947 7353 8114 7468 8279 7579 8442 7685 8602 56 57 7112 7779 7236 7949 7355 8117 7470 8282 7581 8444 7687 8605 67 58 7114 7782 7238 7952 7357 8120 7472 8284 7582 8447 7689 8607 58 59 7116 7785 7240 7955 7359 8122 7474 8287 7584 8450 7690 8610 59 60 7118 7788 7242 7958 7361 8125 7476 8290 7586 8452 7692 8613 60 M. Loe. S. Lop. T. Log. S. Log. T. Log. S. Log. T. Log. S. L..g. T. Log. 9. Log. T. Log. S. Log. T. M 30° 31" 32° 33° 34° 1 35° APPARENT DISTANCE TABLE XXXI. 129 LOGARITHMS OF THE APPARENT DISTANCE. APPARENT DISTANCE. M. 36* 37' J 38° 39° 1 40° 41- 1 M. Log. S. Log. T. Log. S. Log. T. Log. S . Log. T. Log. S. Log. TJ Log. S. Log. T. Log. S. Log. T. 1 0.7692 0.8613 0.7795 0.8771 0.7893 0.8928 D. 79890.90841 0.8081 0.9238 C. 81690. 9392 1 7694 8615 7796 8774 7895 8931 7990 9086 8082 9241 8171 9394 1 2 7696 8618 7798 8776 7897 8933 7992 9089 8084 9243 8172 9397 2 3 7697 8621 7800 8779 7898 8936 7993 9091 8085 9246 8174 9399 3 4 7699 8623 7801 8782 7900 8939 79195 9094 8087 9248 8175 9402 4 5 0.7701 0.8626 0.7803 0.8784 0.7901 0.8941 0.7997 0.9097 0.8088 0.9251 0.8177 0.9404 5 6 7703 8629 7805 8787 7903 8944 7998 9099 8090 9254 8178 9407 6 7 7704 8631 7806 8790 7905 8946 8000 9102 8091 9256 8180 9409 7 8 7706 8634 7808 8792 7906 8949 8001 9104 8093 9259 8181 9412 8 9 770S 8637 7810 8795 7908 8952 8003 9107 8094 9261 8182 9415 9 10 0.7710 0.8639 0.7811 0.8797 0.7910 0.8954 0.8004 0.9110 0.8096 0.9264 0.8184 0.9417 10 11 7711 8642 7813 8800 7911 8957 8006 9112 8097 9266 8185 9420 11 12 12 7713 8644 7815 8803 7913 8959 8007 9115 8099 9269 8187 9422 13 7715 8647 7816 8805 7914 8962 8009 9117 8100 9271 8188 9425 13 14 15 7716 8650 7818 8808 7916 8965 8010 9120 8102 9274 8190 9427 14 0.7718 0.8652 0.7820 0.8811 0.7918 0.8967 0.8012 0.9122 0.8103 0.9277 0.8191 0.9430 15 16 7720 8655 7821 8813 7919 8970 8014 9125 8105 9279 8193 9432 16 17 7722 8658 7823 8816 7921 8972 8015 9128 8106 9282 8194 9435 17 18 7223 8660 7825 8818 7922 8975 8017 9130 8108 9284 8195 9438 18 19 7725 8663 7826 8821 7924 8978 8018 9133 8109 9287 8197 9440 19 20 0.7727 0.8666 0.7828 0.8824 0.7926 0.8980 0.8020 0.9135 0.8111 0.9289 0.8198 0.9443 20 21- 7728 8668 7830 8826 7927 8983 8021 9138 8112 9292 8200 9445 21 22 7730 8671 7831 8829 7929 8985 8023 9140 8114 9295 8201 9448 22 23 7732 8674 7833 8831 7930 8988 8024 9143 8115 9297 8203 9450 23 24 7734 8676 7835 8834 7932 8990 8026 9146 8117 9300 8204 9453 24 25 0.7735 0.8679 0.7836 1) . 8837 0.7934 0.8993 0.8027 0.9148 0.8118 0.9302 0.8206 0.9455 25 26 7737 8682 7838 8839 7935 8996 8029 9151 8120 9305 8207 9458 26 27 7739 8(i84 7840 8842 7937 8998 8031 9153 8121 9307 8208 9460 27 28 7740 8687 7841 8845 7938 9001 8032 9156 8122 9310 8210 9463 28 29 30 774-2 8689 7843 8847 7940 9003 8034 9158 8124 9312 8211 9466 29 0.7744 0.8692 0.7844 0.8850 0.7942 0.9006 0.8035 0.9161 0.8125 0.9315 0.8213 0.9468 30 31 7746 8695 7846 8852 7943 9009 8037 9164 8127 9318 8214 9471 31 32 7747 8697 7848 8855 7945 9011 8038 9166 8128 9320 8216 9473 32 33 7749 8700 7849 8858 7946 9014 8040 9169 8130 9323 8217 9476 33 34 35 7751 8703 7851 8860 7948 9016 8041 9171 8131 9325 8218 9478 34 0.7752 0.8705 0.7853 0.8863 0.7949 0.9019 0.8043 0.9174 0.8133 0.9328 0.8220 0.9481 ''S 36 7754 8708 - 7854 8865 7951 9022 8044 9176 8134 9330 8221 9483 ii 37 7756 8711 7856 8868 7953 9024 8046 9179 8136 9333 8223 9486 % 38 7758 8713 7858 8871 7954 9026 8047 9182 8137 9335 8224 9488 38 39 7759 87 If 7859 8873 7956 9029 8049 9184 8139 9338 8225 9491 39 40 0.7761 0.8718 0.7861 0.8876 0.7957 0.9032 0.8050 0.9187 0.8140 0.9341 0.8227 0.9494 40 41 7763 87-21 7863 8879 7959 9035 8052 9189 8142 9343 8228 9496 41 42 7764 8724 7864 8881 7960 9037 8053 9192 8143 9346 8230 9499 42 43 7766 8726 7866 8884 7962 9040 8055 9194 8145 9348 8231 -9501 43 44 7768 8729 7867 8886 7964 9042 8056 9197 8146 9351 8233 9504 44 45 0.7769 0.8732 0.7869 0.8889 0.7965 0.9045 0.8058 0.9200 0.8148 0.9353 0.8234 0.9506 45 46 7771 8734 7871 8892 7967 9048 8060 9202 8149 9356 8235 9509 46 47 7773 8737 7872 8894 7968 9050 8061 9205 8150 9358 8237 9511 47 48 7774 8740 7874 8897 7970 9053 8063 9207 8152 9361 8238 9514 48 49 7776 8742 7876 8899 7972 9055 8064 9210 8153 9364 8240 9516 49 50 50 0.7778 0.8745 0.7877 0.8902 0.7973 0.9057 0.8066 0.9212 0.8155 0.9366 0.8241 0.9519 51 7780 8747 7879 8905 7975 9060 8067 9215 8156 9369 8242 9522 51 52 7781 8750 7880 8907 7976 9063 8069 9218 8158 9371 8244 9524 5 53 7783 8753 7882 8910 7978 9066 8070 9220 8159 9374 8245 9527 53 54 7785 875 f 7884 8912 7979 9068 8072 9223 8161 9376 8247 9529 5; 55 0.7786 0.8758 0.7885 0.8915 0.7981 0.9071 0.8073 0.9225 0.8162 0.9379 0.8248 0.9532 55 56 7788 8761 7887 8918 7982 9073 8075 9228 8164 9381 8249 9534 56 57 779f 8763 7889 8920 7984 9076 8076 9230 8165 9384 8251 9537 57 58 7791 8766 7890 8923 7986 9079 8078 9233 8167 9387 8252 9539 58 59 7793 8769 7892 8925 7987 9081 8079 9236 8168 9389 8254 9542 59 60 7795 8771 -7893 8928 7989 9084 8081 9238 8169 9392 8255 9544 60 M. Log. S. Log. T. Log. S. Log. T. Log. S. Log. T. Log. S. Log. T. Log. S. Log. T. Log. S. Log. T. M a 6* 37' 38° 39° 40* 1 4 I* APPARENT DISTANCE. 1 130 TABLK XXXT. LOGARITHMS OF THE APPARENT DISTANCE. APPARENT DISTANCE. 1 M. 42° 1 43- 44" 45° 46' 470 M. Log. S. Log. T. Log. S Log. T. Log. S. Log. T. Log. S. Log. T. Log. S. Log. T. Log. S. Log.T. 0.8255 0.9544 0.8338 0.9697 0.8418 0.9848 0.8495 1.0000 0.8569 1.0152 0.8641 1.0303 1 8257 9547 8339 9699 8419 9851 8496 0003 8571 0154 8642 0306 1 2 8258 9549 8341 9702 8420 9853 8497 0005 8572 0157 8644 0309 2 3 8259 9552 8342 9704 8422 9856 8499 0008 8573 0159 8645 0311 3 4 8261 9555 8343 9707 8423 9858 8500 0010 8574 0162 8646 0314 4 5 0,8262 0.9557 0.8345 0.9709 0.8424 0.9861 0.8501 1.0013 0.8575 1.0164 0.8647 1.0316 5 6 8264 9560 8346 9712 8426 9864 8502 0015 8577 0167 8648 0319 6 7 8265 9562 8347 9714 8427 9866 8504 0018 8578 0169 8650 0321 7 8 8266 9565 8349 9717 8428 9869 8505 0020 8579 0172 8651 0324 8 9 8268 9567 8350 9719 8429 9871 8506 0023 8580 0174 8652 0326 9 10 0.8269 0.9570 8351 0.9722 0.8431 0.9874 0.8507 1.0025 0.8582 1.0177 0.8653 1.0329 10 11 8270 9572 8353 9724 8432 9876 8509 0028 8583 0179 8654 0331 11 12 8272 9575 8354 9727 8433 9879 8510 0030 8584 0182 8655 0334 12 13 8273 9577 8355 9729 8435 9881 8511 0033 8585 0185 8657 0336 13 14 8275 9580 8357 9732 8436 9884 8512 0035 8586 0187 8658 0339 14 15 0.8276 0.9582 0.8358 0.9735 0.8437 0.9886 0.8514 1.0038 0.8588 1.0190 0.8659 1.0341 15 16 8277 9585 8359 9737 8439 9889 8515 0040 8589 0192 8660 0344 16 17 8279 9588 8361 9740 8440 9891 8516 0043 8590 0195 8661 0347 17 18 8280 9590 8362 9742 8441 9894 8517 0045 8591 0197 8662 0349 18 19 8282 9593 8363 9745 8442 9896 8519 0048 8592 0200 8663 0352 19 20 0.8283 0.9595 0.8365 9747 0.8444 0.9899 0.8520 1.0051 0.8594 1.0202 0.8665 1.0354 20 21 8284 9598 8366 9750 8445 990] 8521 0053 8595 0205 8666 0357 21 22 8286 9600 8367 9752 8446 9904 8522 0056 8596 0207 8667 0359 22 23 8287 9603 8369 9755 8448 9907 8524 0058 8597 0210 8668 0362 23 24 8289 9605 8370 9757 8449 9909 8525 0061 8598 0212 8669 0364 24 25 0.8290 0.9608 0.8371 0.9760 0.8450 0.9912 0.8526 1.0063 0.8600 1.0215 0.8671 1.0367 25 26 8291 9610 8373 9762 8451 9914 8527 0066 8601 0217 8672 0369 26 27 8293 9613 8374 9765 8453 9917 8529 0068 8602 0220 8673 0372 27 28 8294 9615 8375 9767 8454 9919 8530 0071 8603 0222 8674 0374 28 29 8295 9618 8377 9770 8455 9922 8531 0073 8604 0225 8675 0377 29 30 30 0.8297 0.9621 0.8378 0.9773 0.8457 0.9924 0.8532 1.0076 0.8606 1.0228 0.8676 1.0379 31 8298 9623 8379 9775 8458 9927 8534 0078 8607 0230 8677 0382 31 32 8300 9626 8381 9778 8459 9929 8535 0081 8608 0233 8679 0385 32 33 8301 9628 8382 9780 8460 9932 8536 0083 8609 0235 8680 0387 33 34 35 8302 9631 8383 9783 8462 9934 8537 0086 8610 0238 8681 0390 34 0.8304 0.9633 0.8385 0.9785 0.8463 0.9937 0.8539 1.0088 0.8612 1.0240 0.8682 1.0392 35 36 8305 9636 8386 9788 8464 9939 8540 0091 8613 0243 8683 0395 36 37 8306 9638 8387 9790 8466 9942 8541 0093 8614 0245 8684 0397 37 38 8308 9641 8389 9793 8467 9944 8542 0096 8615 0248 8686 0400 38 39 8309 9643 8390 9795 8468 9947 8544 0099 8616 0250 8687 0402 39 40 40 0.8311 0.9646 0.8391 0.9798 0.8469 0.9949 0.8545 1.0101 0.8618 1.0253 0.8688 1.0405 41 8312 9648 8393 9800 8471 9952 8546 0104 8619 0255 8689 0407 41 42 8313 9651 8394 9803 8472 9955 8547 0106 8620 0258 8690 0410 42 43 8315 9653 8395 9805 8473 9957 8549 0109 8621 0260 8691 0412 43 44 8316 9656 8397 9808 8475 9960 8550 0111 8622 0263 8692 0415 44 45 0.8317 0.9659 0.8398 0.9810 0.8476 0.9962 0.8551 1.0114 0.8624 1.0265 0.8694 1.0418 45 46 8319 9661 8399 9813 8477 9965 8552 0116 8625 0268 8695 0420 46 47 8320 9664 8401 9816 8478 9967 8553 0119 8626 0271 8696 0423 47 48 8322 9666 8402 9818 8480 9970 8555 0121 8627 0273 8697 0425 48 49 8323 9669 8403 9821 8481 9972 8556 0124 8628 0276 8698 0428 49 50 0.8324 0.9671 0.8405 0.9823 0.8482 0.9975 0.8557 1.0126 0.8629 1.0278 0.8699 1.0430 50 51 8326 9674 8406 9826 8483 9977 8558 0129 8631 0281 8700 0433 51 52 8327 9676 8407 9828 8485 9980 8560 0131 8632 0283 8702 0435 52 53 8328 9679 8409 9831 8486 9982 8561 0134 8633 0286 8703 0438 53 54 55 8330 9681 8410 9833 8487 9985 8562 0136 8634 0288 8704 0440 54 0.8331 0.9684 0.8411 0.9836 0.8489 0.9987 0.8563 1.0139 0.8635 1.0291 0.8705 1.0443 55 56 8332 9686 8412 9838 8490 9990 8564 0142 8637 0293 8706 0445 56 57 8334 9689 8414 9841 8491 9992 8566 0144 8638 0296 8707 0448 57 58 8335 9691 8415 9843 8492 9995 8567 0147 8639 0298 8708 0451 58 59 8336 9694 8416 9846 8494 9997 8568 0149 8640 0301 8710 0453 59 60 8338 9697 8418 9848 8495 1.0000 8569 0152 8641 0303 8711 0456 60 M. '. '". s. Log. T. Log. S. Loe. T. Log. S. Log. T. Log. S. Log. T. Log. S. Log. T. Log. S. Log. T. M. 42' 43- 44° 45° 46" 47° APPARENT DISTANCE. i TABLE XXXI. 131 LOGARITHMS OF THE APPARENT DISTANCE. APPARENT DISTANCE, M. 48' 49' _\ 60' 51' 52" 53" M. Log. S. Log. T. Log. S. Log. T. Log. S. Log. T. Log. S. L..g. T. Log. S. Log. T. Log. S. Log.T. 0.8711 1.0456 0.8778 1.0608 0.8843 1.0762 0.8905 1 0916 0.8965 1.1072 0.9023 1.1229 1 8712 0458 8779 0611 8844 0764 8906 0919 8966 1075 9024 1231 1 2 8713 0461 8780 0613 8845 0767 8907 0921 8967 1077 9025 1234 2 3 8714 0463 8781 0616 8846 0770 8908 0924 8968 1080 9026 1237 3 4 8715 0466 8782 0619 8847 0772 89q9 0927 8969 1082 9027 1239 4 5 0.8716 1.0468 0.8783 1.0621 0.8848 1.0775 0.8910 1.0929 0.8970 1.1085 0.9028 1.1242 5 6 8718 0471 8784 0624 8849 0777 8911 0932 8971 1088 9029 1245 6 7 8719 0473 87S5 062ti 8850 0780 8912 0934 8972 1090 9030 1247 7 8 8720 0476 8787 0629 8851 0782 8913 0937 8973 1093 9031 1250 8 9 8721 0479 8788 8789 0631 8852 0785 8914 0940 8974 1095 9032 1253 9 10 0.8722 10481 1 .0634 0.8853 1.0788 0.8915 1.0942 0.8975 1.1098 0.9033 1.1255 10 11 8723 0484 8790 0636 8854 0790 8916 0945 8976 1101 9034 1258 11 12 8724 0486 8791 0639 8855 0793 8917 0947 8977 1103 9035 1260 12 13 8725 0489 8792 0642 8856 0795 8918 0950 8978 1106 9036 1263 13 14 8727 0491 8793 0644 8857 0798 8619 0953 8979 1108 9037 1266 14 15 0.8728 1.0494 0.8794 1.0647 0.8858 1.0800 0.S920 1.0955 0.8980 1.1111 0.9038 1.1268 15 16 8729 0496 8795 0649 8859 0803 8921 0958 8981 1114 9039 1271 16 17 8730 0499 8796 0652 8860 0806 8922 0960 8982 1116 9040 1274 17 18 8731 0501 8797 0654 8862 0808 8923 0963 8983 1119 9041 1276 18 19 8732 0504 8799 0657 8863 0811 8924 0965 8984 1121 9041 1279 19 20 0.8733 1.0506 0.8800 1.0659 0.8864 1.0813 0.8925 1.0968 0.8985 1.1124 0,9042 1.1282 20 21 8734 0509 8801 0662 8865 0816 8926 0971 8986 1127 9043 1284 21 22 8736 0512 8802 0665 8866 0818 8927 0973 8987 1129 9044 1287 22 23 8737 0514 8803 0667 8867 0821 8928 0976 8988 1132 9045 1289 23 24 8738 0517 8804 0670 8868 0824 8929 0978 8989 1135 9046 1292 24 25 0.8739 1.0519 0.8805 1.0672 0.8869 1.0826 0.8930 1.0981 0.8990 1.1137 0.9047 1.1295 25 26 8740 0522 8806 0675 8870 0829 8931 0984 8991 1140 9048 1297 26 27 8741 0524 8807 0677 8871 0831 8932 0986 8992 1142 9049 1300 27 28 8742 0527 8808 0680 8872 0834 8933 0989 8993 1145 9050 1303 28 29 30~ 874:^ 0529 8809 0682 8873 0836 8934 0991 8994 1148 9051 1305 29 0.8745 1.0532 0.8810 1.0685 0.8874 1.0839 0.8935 1.0994 0.8995 1.1150 0.9052 1.1308 30 31 8746 0534 8812 0688 8875 0842 8936 0997 8996 1153 9053 1311 31 32 8747 0537 8813 0690 8876 0844 8937 0999 8997 1155 9054 1313 32 33 8748 0540 8814 0693 8877 0847 8938 1002 8998 1158 9055 1316 33 34 8749 0542 8815 0695 8878 0849 8939 1004 8999 1161 9056 1318 34 35 0.8750 1.0545 0.8816 1.0698 0.8879 1.0852 0.8940 1.1007 0.9000 1.1163 0.9056 1.1321 35 36 8751 0547 '^817 0700 8880 0854 8941 1010 9000 1166 9057 1324 36 37 8752 0550 8818 0703 8881 0857 8942 1012 9001 1169 9058 1326 37 38 8753 0552 8819 0705 8882 0860 8943 1015 9002 1171 9059 1329 38 39 8755 0555 8820 0708 8883 0862 8944 1017 9003 1174 9060 1332 39 40 0.8756 1.0557 0.8821 1.0711 0.8884 1.0865 0.8945 1.1020 0.9004 1.1176 0.9061 1.1334 40 41 8757 0560 8822 0713 8885 0867 8946 1022 9005 1179 9062 1337 41 42 8758 0562 8823 0716 8887 0870 8947 1025 9006 1182 9063 1340 42 43 8759 0565 8824 0718 8888 0872 8948 1028 9007 1184 9064 1342 43 44 45 8760 0568 8825 0721 8889 0875 8949 1030 9008 1187 9065 1345 44 0.8761 1.0570 0.8827 1.0723 0.8890 0.0878 0.8950 1.1033 0.9009 1.1189 0.9066 1.1348 45 46 8762 0573 8828 0726 8891 0880 8951 1035 9010 1192 9067 1350 46 47 8763 0575 8829 0729 8892 0883 8952 1038 9011 1195 9068 1353 47 48 8765 0578 8830 0731 8893 0885 8953 1041 9012 1197 9069 1356 48 49 50 8766 0580 8831 0734 8894 0888 8954 1043 9013 1200 9069 1358 49 0.8767 1.0583 0.8832 1.0736 0.8895 1.0890 0.8955 1.1046 0.9014 1.1203 0.9070 1.1361 50 51 8768 0585 8833 0739 8896 0893 8956 1048 9015 1205 9071 1364 51 52 8769 0588 8834 0741 8897 0896 8957 1051 9016 1208 9072 1366 52 53 S770 0591 8835 0744 8898 0898 8958 1054 9017 1210 907» 1369 53 54 8771 0593 8836 0746 8899 0901 8959 1056 9018 1213 9074 1371 54 55 0.8772 1.0596 0.8837 1.0749 0.8900 1.0903 0.8960 1.1059 0.9019 1.1216 0.9075 1.1374 55 56 8773 0598 8838 0752 8901 0906 8961 1061 9020 1218 9076 1377 56 57 8775 0601 8839 0754 8902 0909 8962 1064 9021 1221 9077 1379 57 58 8776 0603 8840 0757 8903 0911 8963 1067 9022 1224 9078 1382 58 59 8777 0606 8841 0759 8904 0914 8964 1069 9023 1226 9079 1385 59 60 8778 0608 8843 0762 8905 0916 8965 1072 9023 1229 9080 1387 60 M. Log. S. Log T. Log. 8. Log. T. Log. S. Log. T. Log. S. Log. T. Log. 8. Log. T. Log. S. Log.T. M. 48- 49' 60° 51* 52* 5 J' APPARENT DISTANCE. 1 132 TABLE XXXI. 1 LOGARITHMS OF THE APPARENT DISTANCE. J APPARENT DISTANCE. i M. 54- 55' 56° 1 57° . 58° 59° M. Log. S. Log-T. Log. S. Log. T. Log. S. Log. T. Log. S. Log. T. Log. S. Log. T. Log. S. Log. T. 0.9080 1.1387 0.9134 1.1548 0.9186 1.1710 0.9236 1.1875 0.9284 1.2042 0.9331 1.2212 60 1 9080 1390 9135 1550 9187 1713 9237 1878 9285 2045 9331 2215 69 2 9081 1393 9135 1553 9187 1716| 9238 1880 9286 2048 9332 2218 58 3 9082 1395 9136 1556 91881 1718 9238 1883 9287 2051 9333 2221 67 4 9083 1398 9137 1558 9189 1721 9239 1886 9287 2053 9334 2224 56 5 0.9084 1.1401 0.9138 1.1561 0.9190 1.1724 0.9240 1.1889 0.9288 1.2056 0.9334 1 2227 55 6 9085 1403 9139 1564 9191 1726 9241 1891 9289 2059 9335 2229 54 7 9086 1406 9140 1567 9192 1729 9242 1894 9290 2062 9336 2232 53 8 9087 1409 9141 1569 9193 1732 9242 1897 9291 2065 9337 2235 52 9 9088 1411 9142 1572 9193 1735 9243 1900 9291 2067 9337 2238 61 10 0.9089 1.1414 0.9142 1.1575 0.9194 1.1737 0.9244 1.1903 0.9292 1.2070 0.9338 1.2241 50 11 9090 1417 914b 1577 9195 1740 9245 1905 9293 2073 9339 2244 49 12 9091 1419 9144 1580 9196 1743 9246 1908 9294 2076 9340 2247 48 13 9091 1422 9145 1583 9197 1746 9247 1911 9294 2079 9340 2250 47 14 9092 1425 9146 1585 9198 1748 9247 1914 9295 2082 9341 2252 46 15 0.9093 1.1427 0.9147 1.1588 0.9198 1.1751 0.9248 1.1916 0.9296 1.2084 0.9342 1.2255 45 16 9094 1430 9148 1591 9199 1754 9249 1919 9297 2087 9343 2258 44 17 9095 1433 9149 1594 9200 1757 9250 1922 9298 2090 9343 2261 43 18 9096 1435 9149 1596 9201 1759 9251 1925 9298 2093 9344 2264 42 19 9097 1438 9150 1599 9202 1762 9251 1928 9299 2096 9345 2267 41 20 0.9098 1.1441 0.9151 1.1602 0.9203 1.1765 0.9252 1.1930 0.9300 1.2098 0.9346 1.2270 40 21 9099 1443 9152 1604 9204 1767 9253 1933 9301 2101 9346 3273 3» 22 9100 1446 9153 1607 9204 1770 9254 1936 9301 2104 9347 2275 38 23 9101 1449 9154 1610 9205 1773 9255 1939 9302 2107 9348 2278 37 24 9101 1451 9155 1612 9206 1776 9255 1941 9303 2110 9349 2281 36 25 0.9102 1.1454 0.9156 1.1615 0.9207 1.1778 0.9256 1.1944 0.9304 1.2113 0.9349 1.2284 35 26 9103 1457 9156 1618 9208 1781 9257 1947 9305 2115 9350 2287 34 27 9104 1459 9157 1621 9209 1784 9258 1950 9305 2118 9351 2290 33 28 9105 1462 9158 1623 9209 1787 9259 1953 9306 2121 9352 2293 32 29 9106 1465 9159 1626 9210 1789 9259 1955 9307 2124 9352 2296 31 30 0.9107 1.1467 0.9160 1.1629 0.9211 1.1792 0.9260 1.1958 0.9308 1.2127 0.9353 1.2299 30 31 9108 1470 9161 1631 9212 1795 9261 1961 9308 2130 9354 2301 29 32 9109 1473 9162 1634 9213 1798 9262 1964 9309 2132 9355 2304 28 33 9110 1475 9163 1637 9214 1800 9263 1966 9310 2135 9355 2307 27 34 35 9110 1478 9163 1639 9214 1803 9264 1969 9311 2138 9356 2310 26 0.9111 1.1481 0.9164 1.1642 0.9215 1.1806 0.9264 1.1972 0.9312 1.2141 0.9357 1.2313 25 36 9112 1483 9165 1645 9216 1809 9265 1975 9312 2144 9358 2316 24 37 9113 1486 9166 1648 9217 1811 9266 1978 9313 2147 9358 2319 23 38 9114 1489 9167 1650 :)218 1814 9267 1980 9314 2150 9359 2322 22 39 9115 1491 9168 1653 9219 1817 9268 1983 9315 2152 9360 2325 21 40 0.9116 1.1494 0.9169 1.1656 0.9219 1.1820 0.9268 1.1986 0.9315 1.2155 0.9361 1.2327 20 41 9117 1497 9169 1658 9220 1822 9269 1989 9316 2158 9361 2330 19 42 9118 1499 9170 1661 9221 1825 9270 1992 9317 2161 9362 2333 18 43 9119 1502 9171 1664 9222 1828 9271 1994 9318 2164 9363 2336 17 44 9119 1505 9172 1667 9223 1831 9272 1997 9318 2167 9364 2339 16 45 0.9120 1.1507 0.9173 1.1669 0.9224 1.1833 0.9272 1.2000 0.9319 1.2169 0.9364 1.2342 15 46 9121 1510 9174 1672 9224 1836 9273 2003 9320 . 2172 9365 2345 14 47 9122 1513 9175 1675 9225 1839 9274 2006 9321 2175 9366 2348 13 48 9123 1516 9175 1677 9226 1842 9275 2008 9322 2178 9367 2351 12 49 9124 1518 9176 1680 9227 1844 9275 2011 9322 2181 9367 2354 11 50 0.9125 1.1521 0.9177 1.1683 0.9228 1.1847 0.9276 1.2014 0.9323 1.2184 0.9368 1.2356 10 51 9126 1524 9178 1686 9229 1850 9277 2017 9324 2187 9369 2359 9 52 9127 1526 9179 1688 9229 1853 9278 2020 9325 2189 9369 2362 8 53 9127 1529 9180 1691 9230 1855 9279 2022 9325 2192 9370 2365 7 54 9128 1532 9181 1694 9231 1858 9279 2025 9326 2195 9371 2368 6 55 0.9129 1.1534 0.9181 1.1697 0.9232 1.1861 0.9280 1.2028 0.9327 1.2i98 0.9372 1.2371 5 56 9130 1537 9182 1699 92.33 1864 9281 2031 9328 2201 9372 2374 4 57 9131 1540 9183 1702 9233 1867 9282 2034 9328 2204 9373 2377 3 58 9132 1542 9184 1705 9-234 1869 9283 2036 9329 2207 9374 2380 2 59 9133 1545 9185 1707 9235 1872 9283 2039 9330 2209 937» 2383 1 60 9134 1548 9186 1710 9236 1875 9284 2042 9331 2212 9375 2386 M. Log. 8. Log. T. Log. S. Log. T. Log. S. 'og T. Log. 3. Log. T. Log. S. Log. T. Log. 8. ' Log. T. M. 125* 124° 123° 122° 121° 120° APPARENT DISTANCE. | TABLE XXXI. 133 LOGARITHMS OF THE APPARENT DISTANCE APPARENT DISTANCE. M. 60° 1 61* 62° 63° 1 64° 1 65° M. Log. S. Log. T. Log. S. Log. T. Log. 8. Log. T. Log. S. 1 Log. T. Log. S. 1 Log. T. Log. S. Log. T. 3.93751 L.2386( ).9418] .2562 ( ). 9459 1 .27430.9499 J 1.29280.9537 1.3118 3.9573 1.3313 (id 1 9376 2389 9419 2565 9460 2746 9499 2931 9537 3121 9573 3317 59 2 9377 2391 9420 2568 9461 2749 9500 3935 9538 3125 9574 3320 58 3 9377 2394 9420 2571 9461 2752 9501 2938 9538 3128 9575 3323 57 4 9378 2397 9421 2574 9462 2755 950a 2941 9539 3131 9575 3326 56 5 3.9379 1.2400 ).9422 1.2577 ( 3.9463 1.2759 3.9502 1 . 2944 3.9540 1.3134 30'=:6 1.3330 55 6 9380 2403 9422 2580 9463 2762 9503 2947 9540 3137 9576 3333 54 7 9380 2406 9423 2583 9464 2765 9503 2950 9541 3141 9577 3336 53 8 9381 2409 9424 2586 9465 2768 9504 2953 9542 3144 9577 3340 52 9 9382 2412 9424 2589 9465 2771 9505 2957 9542 3147 9578 3343 61 10 0.9383 1.2415 0.9425 1.2592 0.9466 1.2774 0.9505 1.296U 0.9543 1.3150 0.9579 1.3346 50 11 9383 2418 9426 2595 9467 2777 9506 2963 9543 3154 9579 3350 49 12 9384 2421 9427 2598 9467 2780 9506 2966 9544 3157 9580 3353 48 13 9385 2424 9427 2601 9468 2783 9507 2969 9545 3160 9580 3356 47 14 9385 2427 9428 2604 9469 2786 9508 2972 9545 3163 9581 3360 46 15 0.9386 1.2429 0.9429 1.2607 0.9469 1.2789 0.9508 1.2975 0.9546 1.31660.9582 1.3363 45 16 9387 2432 9429 2610 9470 2792 9509 2978 9546 3170 9582 3366 44 17 9388 2435 9430 2613 9471 2795 9510 2982 9547 3173 9583 3370 43 18 9388 2438 9431 2616 9471 2798 9510 2985 9548 3176 9583 3373 42 19 20 9389 2441 9431 2619 9472 2801 9511 2988 9548 3179 9584 3376 41 0.9390 1.2444 0.9432 1.2622 0.9473 1.2804 0.9512 1.2991 0.9549 1.3183 0.9584 1.3380 40 21 9391 2447 9433 2625 9473 2808 9512 2994 9549 3186 9585 3383 39 22 9391 2450 9433 2628 9474 2811 9513 2997 9550 3189 9586 3386 38 23 9392 2453 9434 2631 9475 2814 9513 3001 9551 3192 9586 3390 37 24 9393 2456 9435 2634 9475 2817 9514 3004 9551 3196 9587 3393 36 25 0.9393 1.2459 0.9436 1.2637 0.9476 1.2820 0,9515 1.3007 0.9552 1.3199 0.9587 1.3396 35 26 9394 2462 9436 2640 9477 2823 9515 3010 9552 3202 9588 3400 34 27 9395 2465 9437 2643 9477 2826 9516 3013 9553 3205 9588 3403 33 28 9396 2468 9438 2646 9478 2829 9517 3016 9554 3209 9589 3406 32 29 9396 2471 9438 2649 9479 2832 9517 3019 9554 3212 9590 3410 31 30 0.9397 1.2474 0.9439 1.2652 0.9479 1.2835 0.9518 1.3023 0.9555 1.3215 0.9590 1.3413 30 31 9398 2477 9440 2655 9480 2838 9519 3026 9555 3218 9591 3416 29 32 9398 2479 9440 2658 9481 2841 9519 3029 9556 3222 9591 3420 28 33 9399 2482 9441 2661 9481 2844 9520 3032 9557 3225 9592 3423 27 34 35 9400 2485 9442 2664 9482 2848 9520 3035 9557 3228 9593 3426 26 0.9401 1.2488 0.9442 1.2667 0.9483 1.2851 0.9521 1.3038 0.9558 1.3231 0.9593 1.3430 25 36 9401 2491 9443 2670 9483 2854 9522 3042 9558 3235 9594 3433 24 37 9402 2494 9444 2673 9484 2857 9522 3045 9559 3238 9594 3436 23 38 9403 2497 9444 2676 9485 2860 9523 3048 9560 3241 9595 3440 22 39 9403 2500 9445 2680 9485 2863 9524 3051 9560 3244 9595 3443 21 40 0.9404 1 2503 0.9446 1.2683 0.9486 1.2866 0.9524 1.3054 0.9561 1.3248 0.9596 1.3447 20 41 9405 2506 9447 2686 9486 2869 9525 3058 9561 3251 9597 3450 19 42 9406 2509 9447 2689 9487 2872 9525 3061 9562 3254 9597 3453 18 43 9406 2512 9448 2692 9488 2875 9526 3064 9563 3257 9598 3457 17 44 9407 2515 9448 2695 9488 2879 9527 3067 9563 3261 9598 3460 16 45 0.9408 1.2518 0.9449 1.2698 0.9489 1.2882 0.9527 1.3070 0.956-4 3.3264 0.9599 1.3463 15 46 940? 2521 9450 2701 949C 2885 9528 3073 9564 3267 9599 3467 14 47 9409 252-^ 9451 270-4 9490 2888 9529 3077 9565 3271 9600 3470 13 48 941C 2527 9451 2707 9491 2891 9529 308C 956fc 3274 9601 3473 12 49 941C ) 253C 9452 - 271C ) 9492 2894 953C 3083 956€ 3277 9601 3477 11 50 0.9411 1.253c !0.945c 1.271c 0.9492 1.2897 0.953C 11.3086 0.9567 1.3280 0.9602 1.3480 10 51 9415 ! 2536 i 945c ! 27H ) 949S 290C 9531 3089 9567 3284 9602 3484 9 52 941c \ 253c ) 945^ I 271C 1 949-5 [ 2903 9532 . 3093 9568 3287 9603 3487 8 53 941c s 2545 ! 945^ ) 2725 ! 9494 [ 2907 9532 ' 3096 9569 3290 9603 3490 7 54 941^ I 254; ) 945f > 272^ ) 949^ ) 291C 953c 309S 9569 3294 9604 3494 6 55 0.941^ J1.254J 50.945f 51.272^ ?0.949f )1.291c 0.953-4 H.3105 0.957C »1.3297 0.9604 1.3497 5 56 941^ j 255] 945^ ' 2731 949f ) 291C 953-4 [ 310t 957C 1 330C 9605 3501 4 57 941( ) 255- \ 945^ ' 273^ I 9497 ' 29U 953t ) 3109 9571 3303 9606 3504 3 58 941' r 255' • 945J 5 273'; ' 949J ! 2925 ! 953^ ) 3115 9572 ! 3307 9606 3507 2 59 941' I 256( ) 945t > 274C ) 949J ! 292.! ) 953f 5 311; 9575 ! 331C 9607 3511 1 60 941J i 2565 I 945i ) 274: } 949c > 2925 i 9537 ' 31U 957c ! 331c 9607 3514 M. Log. S. Log. T. Log. S. Log. T Log. S. Log. T. Log. S. Log. T. Log. 3. Log. T. Log. 3. Log. T. M. 119° 118° 117° 116° 115° 114° APPARENT DISTANCE. 134 TABLE XXXI. LOGARITHMS OF THE APPARENT DISTANCE. APPARENT DISTANCE. M. 66" 67* 68° 69° 70° 71° M. 60 Log. S. Log. T. Log. S. Log. T. Log. S. Log. T. Log. S. Log. T. Log. S. Log. T. Log. S. 1 Log. T. 0.9607 1.3514 0.9640 1.3721 0.9672 1.3936 0.9702 1.4158 0.9730 1.4389 9757 1 4630 1 9608 3518 9641 3725 9672 3940 9702 4162 9730 4393 9757 1634 59 2 9608 3521 9641 3729 9673 3943 9702 4166 9731 4397 9758 1638 58 3 9609 3524 9642 3732 9673 3947 9703 4170 9731 4401 9758 4643 57 4 9610 3528 9642 3736 9674 3950 9703 4173 9732 4405 9758 4647 56 55 5 0.9610 1.3531 0.9643 1.3739 0.9674 1.3954 0.9704 1.4177 0.9732 1.4409 0.9759 1.4651 6 9611 3535 9643 3743 9675 3958 9704 4181 9733 4413 9759 4655 54 7 9611 3538 9644 3746 9675 3961 9705 4185 9733 4417 9760 4659 53 8 9612 3541 9645 3750 9676 3965 9705 4189 9734 4421 9760 4663 52 9 9612 3545 9645 3753 9676 3969 9706 4192 9734 4125 9761 4667 51 10 0.9613 1.3548 0.9646 1-3757 0.9677 1.3972 0.9706 1.4196 0.9734 1.4429 0.9761 1.4671 50 11 9613 3552 9646 3760 9677 3976 9707 4200 9735 4433 9761 4676 49 12 9614 3555 9647 3764 9678 3980 9707 4204 9735 4437 9762 4680 48 13 9615 3559 9647 3767 9678 3983 9708 4208 9736 4441 9762 4684 47 14 9615 3562 9648 3771 9679 3987 9708 4211 9736 4445 9763 4688 46 45 15 0.9616 1.3565 0.9648 1.3774 0.9679 1.3991 0.9709 1.4215 0.9737 1.4449 0.9763 1.4692 16 9616 3569 9649 3778 9680 3994 9709 4219 9737 4453 9764 4696 44 17 9617 3572 9649 3781 9680 3998 9710 4223 9738 4457 9764 4700 43 18 9617 3576 9650 3785 9681 4002 9710 4227 9738 4461 9764 4705 42 19 9618 3579 9650 3789 9681 4005 9711 4230 9739 4465 9765 4709 41 40 20 0.9618 1.3583 0.9651 1-3792 0.9682 1.4009 0.9711 1.4234 0.9739 1.4469 0.9765 1.4713 21 9619 3586 9651 3796 9682 4013 9712 4238 9739 4473 9766 4717 39 22 9620 3589 9652 3799 9683 4016 9712 4242 9740 4476 9766 4721 38 23 9620 3593 9652 3803 9683 4020 9713 4246 9740 4480 9767 4725 37 24 9621 3596 9653 3806 9684 4024 9713 4250 9741 4484 9767 4730 36 25 0.9621 1.3600 0.9654 1.3810 0.9684 1.4028 0.9714 1.4253 0.9741 1.4488 0.9767 1.4734 35 26 9622 3603 9654 3813 9685 4031 9714 4257 9742 4492 9768 4738 34 27 9622 3607 9655 3817 9685 4035 9714 4261 9742 4496 9768 4742 33 28 9623 3610 9655 3821 9686 4039 9715 4265 9743 4500 9769 4746 32 29 9623 3614 9656 3824 9686 4042 9715 4269 9743 4504 9769 4751 31 ;^o 30 0.9624 1.3617 0.9656 1.3828 0.9687 1.4046 0.9716 1.4273 0.9743 1.4509 0.9770 1.4755 31 962'5 3620 9657 3831 9687 4050 9716 4276 9744 4513 9770 4759 29 32 9625 3624 9657 3835 9688 4053 9717 4280 9744 4517 9770 4763 28 33 9626 3627 9658 3838 9688 4057 9717 4284 9745 4521 9771 4767 27 34 9626 3631 9658 3842 9689 4061 9718 4288 9745 4525 9771 4772 26 25 35 0.9627 1.3634 0.9659 1.3846 0.9689 1.4065 0.9718 1.4292 0.9746 1.4529 0.9772 1.4776 36 9627 3638 9659 3849 9690 4068 9719 4296 9746 4533 9772 4780 24 37 9628 3641 9660 3853 9690 4072 9719 4300 9747 4537 9773 4784 23 38 9628 3645 9660 3856 9691 4076 9720 4304 9747 1541 9773 4788 22 39 9629 3648 9661 3860 9691 4079 9720 4307 9747 4545 9773 4793 21 20 40 0.9629 1.3652 0.9661 1.3864 0.9692 1.4083 0.9721 1.4311 0.9748 1.4549 0.9774 1.4797 41 9630 3655 9662 3867 9692 4087 9721 4315 9748 4553 9774 4801 19 42 9631 3659 9662 3871 9693 4091 9722 4319 9749 4557 9775 4805 18 43 9631 3662 9663 3874 9693 4094 9722 4323 9749 4561 9775 4810 17 44 45 9632 3666 96631 3878 9694 4098 9722 4327 9750 4565 9775 4814 16 15 0.9632 1.3669 0.9664 1.3882 0.9694 1.4102 0.9723 1.4331 0.9750 1.4569 0.9776 1.4818 46 9633 3673 9664 3885 9695 4106 9723 4335 9751 4573 9776 4822 14 47 9633 3676 9665 3889 9695 4109 9724 4338 9751 4577 9777 4827 13 48 9634 3679 9665 3892 9696 4113 9724 4342 9751 4581 9777 4831 12 49 9634 3683 9666 3896 9696 4117 9725 4346 9762 4.585 9778 4835 11 10 50 0.9635 1.3686 0.9667 1.3900 0.9697 1.4121 0.9725 1.4350 0.9752 1.4589 0.9778 1.4839 51 9635 3690 9667 3903 9697 4124 9726 4354 9753 4593 9778 4844 9 52 9636 3693 9668 3907 9698 4128 9726 4358 9753 4598 9779 4848 8 53 9636 3697 9668 3910 9698 4132 9727 4362 9754 4602 9779 4852 7 54 9637 3700 9669 3914 9699 4136 9727 4366 9754 4606 9780 4857 6 5 55 0.9638 1.3704 ..9669 1.3918 0.9699 1.4139 0.9728 1.4370 0.9755 1.4610 0.9780 1.4861 56 9638 3707 9670 3921 9700 4143 9728 4374 9755 4614 9780 4865 4 57 9639 3711 9670 3925 9700 4147 9728 4378 9755 4618 9781 4869 3 58 9639 3714 9671 3929 9701 4151 9729 4381 9756 4622 9781 4874 2 59 9640 3718 9671 3939 9701 4154 9729 4385 9756 4626 9782 4878 1 60 9640 3721 9672 3936 9702 4158 9730 4389 9757 4630 9782 4882 M. Log. S. Log. T. Log. 8. Log. T. Log. 8. Log. T. Log. 8. Log. T. Log. 8. Log. T. Lop. S. Log. T. M. US' 112° 1 iir 1 110° 109° 1 108° APPAKENT DISTANCE. 1 TABLE XXXI. 135 LOGARITHMS OF THE APPARENT DISTANCE. APPARENT DISTANCE, 7 M. 72" 1 73° 74' 75° 76° 7' Log. T. M. Log. S. Log. T. Log. S. Log. T. Log. S. Log. T. Log. S. Log. T. Log. S. Log. T. tog. S. C.9782 1.4882 0.9806 1.5147 0.9828 1.5425 0.9849 1.5719 0.9869 1.6032 0.9887 1.6366 60 1 9782 4887 9806 5151 9829 5430 9850 5725 9869 6038 9888 6372 59 2 9783 4891 9807 5156 9829 5435 9850 5730 9870 6043 9888 6378 58 3 .9783 4895 9807 5160 9829 5439 9850 5735 9870 6048 9888 6384 57 4 9784 4899 9807 5165 9830 5444 9851 , 5740 9870 6054 9888 6389 .'16 5 0.9784 1.4904 0.9808 1.5169 0.9830 1.5449 0.9851 1.5745 0.9871 1.6059 0.9889 1.6395 55 t) 9785 4908 9808 5174 9831 5454 9851 5750 9871 6065 9889 6401 .••)4 7 9785 4912 9809 5178 9831 5459 9852 5755 9871 6070 9889 6407 53 8 9785 4917 9809 5183 9831 546 > 9852 ■5760 9872 6076 9890 6413 52 9 9786 4921 9809 5187 9832 546t; 9852 5765 9872 6081 9890 6419 51 50 10 0.9786 1.4925 0.9810 1.519-2 0.9832 1.5473 0.9853 1.5770 0.9872 1.6086 0.9890 1.6424 11 9787 4930 9810 5197 9832 5478 9853 5775 9872 6092 9890 6430 49 12 9787 4934 9811 5201 9833 5483 9853 5780 9873 6097 9891 6436 -18 13 9787 4938 9811 5206 9833 5487 9854 5786 9873 6103 9891 6442 47 14 9788 4943 9811 5210 9833 5492 9854 5791 9873 6108 9891 6448 46 45 15 0.9788 1.4947 0.9812 1.5215 0.9834 1.5497 0.9854 1.5796 0.9874 1.6114 0.9892 1.6454 16 9789 4951 9812 5219 9834 5502 9855 5801 9874 6119 9892 6459 44 17 9789 4H56 9812 5224 9835 5507 9855 5806 9874 6125 9892 6465 43 18 9789 4960 9813 5229 9835 5512 9855 5811 9875 6130 9892 6471 42 19 9790 4965 9813 5233 9835 5516 9856 5816 9875 6136 9893 6477 41 40 20 0.9790 1.4969 0.9814 1.5238 0.9836 1.5521 0.9856 1.5822 0.9875 1.6141 0.9893 1.6483 21 9791 4973 9814 5242 9836 5526 9856 5827 9876 6147 9893 6489 39 22 9791 4978 9814 5247 9836 5531 9857 5832 9876 6152 9894 6495 38 23 9791 4982 9815 5252 9837 5536 9857 5837 9876 6158 9894 6501 37 24 9792 4986 9815 5256 9837 5541 9857 5842 9876 6163 9894 6507 36 25 0.9792 1.4991 0.9815 1.5261 0.9837 1.5546 0.9858 1.5847 0.9877 1.6169 0.9894 1.6513 35 26 9793 4995 9816 5265 9838 5551 9858 5853 9877 6174 9895 6519 34 27 9793 5000 9816 5270 9838 5555 9858 5858 9877 6180 9895 6525 33 28 9793 5004 9817 5275 9838 5560 9859 5863 9878 6185 9895 6531 32 29 9794 5008 9817 5279 9839 5565 9859 5868 9878 6191 9896 6536 31 30 30 0.9794 1.5013 0.9817 1.5284 0.9839 1.5570 0.9859 1.5873 0.9878 1.6196 0.9896 1.6542 31 9795 5017 9818 5289 9839 5575 9860 5879 9879 6202 9896 6548 29 32 9795 5022 9818 5293 9840 5580 9860 5884 9879 6208 9896 6554 28 33 9795 5026 9818 5298 9840 5585 9860 5889 9879 6213 9897 6560 27 34 979- 5030 9^19 5303 9840 5590 9861 5894 9880 6219 9897 6566 26 25 35 0.9796 1.5035 0.9819 1.5307 0.9841 1.5595 0.9861 1.5900 0.9880 1.6224 0.9897 1.6572 36 9797 5039 9820 5312 9841 5600 9861 5905 9880 6230 9897 6578 24 37 9797 5044 9820 5317 9842 5605 9862 5910 9880 6236 9898 6584 23 38 9797 5048 9820 5321 9842 5610 9862 5915 9881 6241 9898 6591 22 39 40 9798 5053 9821 5326 9842 5614 9862 5921 9881 6247 9898 6597 21 20 0.9798 1 .5057 0.9821 1.5331 0.9843 1.5619 0.9863 1.5926 0.9881 1.6252 0.9899 1.6603 41 9799 5061 9821 5335 9843 5624 9863 5931 9882 6258 9899 6609 19 42 9799 5066 9822 5340 9843 5629 9863 5936 9882 6264 9899 6615 18 43 9799 5070 9822 5345 9844 5634 9864 5942 9882 6269 9899 6621 17 44 9800 5075 9823 5350 9844 5639 9864 5947 9883 6275 9900 6627 16 15 45 0.9800 1.5079 0.9823 1.5354 0.9844 1.5644 0.9864 1.5952 0.9883 1.6281 0.9900 1.6633 46 9801 5084 9823 5359 9845 5649 9865 5958 9883 6286 9900 6639 14 47 9801 5088 9824 5363 9845 5654 9865 5963 9883 6292 9901 6645 13 48 9801 5092 9824 5368 9845 5659 9865 5968 9884 6298 9901 6651 12 49 9802 5097 9824 5373 9846 5664 9866 5973 9884 6303 9901 6657 11 10 50 0.9802 1.5102 9825 1.5378 0.9846 1.5669 0.9866 1.5979 0.9884 1.6309 0.9901 1.6664 51 9802 5106 9825 5382 9846 5674 9866 5984 9885 6315 9902 6670 9 52 9803 5111 9826 5387 9847 5679 9867 5989 9885 6320 9902 6676 R 53 9803 5115 9826 5392 9847 5684 9867 5995 9885 6326 9902 6682 7 54 9804 5120 9826 5397 9847 5689 9867 6000 9885 6332 9902 6688 6 5 55 0.9804 1.5124 0.9827 1.5401 0.9848 1.5694 0.9868 1.6005 0.9886 1.6338 0.9903 1.6694 56 9804 5129 9827 5406 9848 5699 9868 6011 9886 6343 9903 6700 4 57 9805 5133 9827 5411 9848 5704 9868 6016 9886 6349 9903 6707 3 5» 9805 5138 9828 5416 9849 5709 9868 6022 9887 6355 9904 6713 2 59 9806 5142 9828 5420 9849 5714 9869 6027 9887 6361 9904 6^19 1 60 9806 5147 9828 5425 9849 5719 9869 6032 9887 6366 9904 c;25 M Log. S. Log. T. Log. S. Log. T. Log. S. Log. T. Log. S. Log. T. Log. S. Log. T. Log. s. Log. T M. 107' 106' 1 105° 104° 103* 1 H )2* APPARENT DISTANCE 1 126 TABLE XXXi. LOGARITHMS OF THE APPARENT DISTANCE. APPARENT DISTANCE. M. 78° 79" 80° 81° 82° 83° M. Log. S. Log. T. Log. S. Log. T. Log. S. Log. T. Log. S. Log. T. Log. S. Log. T. Log. S. Log. T. 0.9904 1.6725 0.9919 1.7113 0.9934 1.7537 0.9946 1.8003 0.9958 1.8522 0.9968 1.9109 6C 1 9904 6731 9920 7120 9934 7544 9946 8011 9958 8531 9968 9119 59 2 9905 6738 9920 7127 9934 7552 9947 8019 9958 8540 9968 9129 58 3 9905 6744 9920 7134 9934 7559 9947 8027 9958 8550 9968 9140 57 4 9905 6750 9920 7141 9934 7566 9947 8036 9958 8559 9968 9151 56 55 5 0.9905 1.6756 0.9921 1.7147 0,9935 1.7574 0.9947 1.8044 0.9958 1.8568 0.9968 1.9161 6 9906 6763 9921 7154 9935 7581 9947 8052 9959 8577 9968 9172 54 7 9906 6769 9921 7161 9935 7589 9948 8060 9959 8587 9969 9182 53 8 9906 6775 9921 7168 9935 7596 9948 8069 9959 8596 9969 9-193 52 9 9906 6781 9922 7175 9936 7604 9948 8077 9959 8605 1.9969 9204 51 50 10 0.9907 1.6788 0.9922 1.7181 0.9936 1.7611 0.9948 1.8085 0.9959 1.8615 1 . 9-969 1.9214 11 9907 6794 9922 7188 9936 7619 9948 8094 9959 8624 9969 9225 49 12 9907 6800 9922 7195 9936 7626 9949 8102 9960 8633 9969 9236 48 13 9907 6807 9923 7202 9936 7634 9949 8110 9960 8643 9969 9246 47 14 9908 6813 9923 7209 9937 7641 9949 8119 9960 8652 9970 9257 46 15 0.9908 1.6819 0.9923 1.7216 0.9937 1.7649 0.9949 1.8127 0.9960 1.8662 1.9970 1.9268 45 16 9908 6826 9923 7223 9937 7657 9949 8136 9960 8671 9970 9279 44 17 9908 6832 9924 7230 9937 7664 9950 8144 9960 8681 9970 9290 43 18 9909 6838 9924 7236 9937 7672 9950 8152 9961 8690 9970 9301 42 19 9909 6845 9924 7243 9938 7679 9950 8161 9961 8700 9970 9312 41 20 0.9909 1.6851 0.9924 1.7250 0.9938 1.7687 0.9950 1.8170 0.9961 1.8709 1.9971 1.9322 40 21 9910 6858 9925 7257 9938 7695 9950 8178 9961 8719 9971 9333 39 22 9910 6864 9925 7264 9938 7702 9951 8186 9961 8728 9971 9344 38 23 9910 687(1 9925 7271 9939 7710 9951 8195 9962 8738 9971 9355 37 24 9910 6877 9925 7278 9939 7718 9951 8203 9962 8748 9971 9367 36 25 0.9911 1.6883 0.9925 1.7285 0.9939 1.7725 0.9951 1.8212 0.9962 1.8757 1.9971 1.9378 35 26 9911 6890 9926 7292 9939 7733 9951 8221 9962 8767 9971 9389 34 27 9911 6896 9926 7299 9939 7741 9951 8229 9962 8777 9972 9400 33 28 9911 6902 9926 7306 9940 7748 9952 8238 9962 8786 9972 9411 32 29 9912 690"\) 9926 7313 9940 7756 9952 8246 9963 8796 9972 9422 31 ^- 30 0.9912 1.6915 0.9927 1.7320 0.9940 1.7764 0.9952 1.8255 0.9963 1.8806 1.9972 1.9433 30 31 9912 6922 9927 7327 9940 7772 9952 8264 9963 8815 9972 9445 29 32 9912 6928 9927 7334 9940 7779 9952 8272 996^3 S825 9972 9456 2S 33 9913 6935 9927 7342 9941 7787 9953 8281 9963 8835 9972 9467 27 34 9913 6941 9928 7349 9941 7795 9953 8290 9963 8845 9973 9479 26 35 0.9913 1 6948 0.9928 1.7356 0.9941 1.7803 0.9953 1.8298 0.9964 1.8855 1.9973 1.9490 25 \ 36 9913 6954 9928 7363 9941 7811 9953 8307 9964 8865 9973 9501 24 37 9914 6961 9928 7370 9942 7819 9953 8316 9964 8875 9973 9513 23 38 9914 6967 9929 7377 9942 7826 9954 8325 9964 8884 9973 9524 22 39 9914 fi974 9929 7384 9942 7834 9954 8333 9964 8894 9973 9536 21 40 0.9914 1.6980 0.9929 1.7391 0.9942 1.7842 0.9954 1.8342 0.9964 1.8904 1.9973 1.9547 20 41 9915 6987 9929 7399 9942 7850 9954 8351 9964 8914 9974 9559 19 42 9915 6994 9929 7406 9943 7858 9954 8360 9965 8924 9974 9570 18 43 9915 7oon 9930 7413 9943 7866 9954 8369 9965 8934 9974 9582 17 44 9915 7007 9930 7420 9943 7874 9955 8378 9965 8944 9974 9593 16 45 0.9916 1.7013 0.9930 1.7427 0.9943 1.7882 0.9955 1.8387 0.9965 1.8955 1.9974 1.9605 15 46 9916 7020 9930 7435 9943 7890 9955 8395 9965 8965 9974 9617 14 47 9916 7027 9931 7442 9944 7898 9955 8404 9965 8975 9974 9629 13 48 991 fi 7033 9931 7449 9944 7906 9955 8413 9966 8985 9975 9640 12 49 9917 7040 9931 7456 9944 7914 9956 8422 9966 8995 9975 9652 11 50 0.9917 1.7047 0.9931 1.7464 0.9944 1.7922 0.9956 1.8431 0.9966 1.9005 1.9975 1.9664 10 51 9917 7053 9931 7471 9944 7930 9956 8440 9966 9016 9975 9676 9 52 9917 7060 9932 7478 9945 7938 9956 8449 9966 9026 9975 9688 8 53 9918 7066 9932 7485 9945 7946 9956 8458 9966 9036 9975 9700 7 54 9918 7073 9932 7493 9945 7954 9956 8467 9967 9046 9975 9711 6 5 55 0.9918 1.7080 0.9932 1.7500 0.9945 1.7962 0.9957 1.8476 0.9967 1.9057 1.9975 1.9723 56 9918 7087 9933 7507 9945 7970 9957 8485 9967 9067 9976 9735 4 57 9919 7093 9933 7515 9946 7978 9957 8495 9967 9077 9976 9747 3 58 9919 7100 9933 7522 9946 7987 9957 8504 9967 9088 9976 9760 2 59 9919 7107 9933 7529 9946 7995 9957 8513 9967 9098 9976 9772 1 60 9919 7113 9934 7537 9946 8003 9958 8522 9968 9109 9976 9784 M. Log. S. Log. T. Log. S. Log. T. Log. S. Log.'T. Log. .S. Log. T. Log. s. Log. T. log. 8. Log. T. M. lor 100° 99° 98° 97° 96° APPARENT DISTANCE. j .... TABLE XXAi. 137 LOGARITHMS OF THE APPARENl DlSTAi^ClS. APPARENT DISTANCE. M. 84° 85° 86° 87° 1 88° 89° M. Log. S. Log. T. Log. s. Log. T. Log. S. Log. T. Log. b. 1 Log. T. Log. S. Log. T. Log. S. Log. T. 0.9976 1.9784 J. 9983; 2.0580( ).9989S 2.15540.9994 2.2806 3.9997 2.4569 0.9999 2.7581 60 1 9976 9796 9984 0595 9989 1572 9994 2830 9997 4606 9999 7654 59 2 9976 980S 9984 0610 9990 1590 9994 2855 9997 4642 9999 7728 58 3 9977 9820 9984 0624 9990 1608 9994 2879 9997 4679 9999 7804 57 4 9977 9833 9984 0639 9990 1627 9994 2904 9998 4717 9999 7880 56 5 0.9977 1.9845 3.9984 2.0654 D.9990 2.1645 3.9994 2.2929 0.9998 2.4754 0.9999 2.7959 55 6 9977 9857 9984 0669 9990 1664 9994 2954 9998 4792 9999 8038 54 7 9977 9870 9984 0684 9990 1683 9995 2979 9998 t830 9999 8120 53 8 9977 9882 9984 0698 9990 1701 9995 3004 9998 4869 9999 8202 52 9 10 9977 9895 9984 0713 9990 1720 9995 3029 9998 4908 1.0000 8287 51 0.9977 1.9907 0.9985 2.0728 0.9990 2.1739 0.9995 2.3055 0.9998 2.4947 1.0000 2.8373 50 11 9978 9920 9985 0744 9990 1758 9995 3081 9998 4987 0000 8460 49 12 9978 9932 9985 0759 9990 1777 9995 3106 9998 5027 0000 8550 48 13 9978 9945 9985 0774 9991 1796 9995 3132 9998 5067 0000 8641 47 14 9978 9957 9985 0789 9991 1815 9995 3158 9998 5108 0000 8735 46 15 0.9978 1.9970 0.9985 2.0804 0.9991 2.1835 0.9995 2.3185 0.9998 2.5149 1.0000 2.8830 45 16 9978 9983 9985 0820 9991 1854 9995 3211 9998 5191 0000 8928 44 17 9978 9995 9985 0835 9991 1874 9995 3238 9998 5233 0000 9028 43 18 9978 2.0008 9985 0850 9991 1893 9995 3264 9998 5275 0000 9130 42 19 9979 0021 9985 0866 9991 1913 9995 3291 9998 5318 0000 9235 41 20 0.9979 2.0034 0.9986 2.0882 0.9991 2.1933 0.9995 2.3318 0.9998 2.5362 1.0000 2.9342 40 21 9979 0047 9986 0897 9991 1952 9995 3346 9998 5405 0000 9452 39 22 9979 0060 9986 0913 9991 1972 9995 3373 9998 5449 0000 9565 38 23 9979 0073 9986 0929 9991 1992 9995 3401 9998 5494 0000 9681 37 24 9979 0086 9986 0944 9991 2012 9996 3429 9998 5539 0000 9799 .36 25 0.9979 2.0099 0.9986 2.0960 0.9991 2.2033 0.9996 2.3456 0.9998 2.5584 1.0000 2.9922 35 26 9979 0112 9986 0976 9992 2053 9996 3485 9998 5630 0000 3.0048 34 27 9980 0125 9986 0992 9992 2073 9996 3513 9998 5677 0000 0177 33 28 9980 0138 9986 1008 9992 2094 9996 3541 9998 5724 0000 0311 32 29 9980 0151 9986 024 9992 2114 9996 3570 9998 5771 0000 0449 31 30 0.9980 2.0164 0.9987 2.1040 0.9992 2.2135 0.9996 2.3599 0.9999 2.5819 1.0000 3.0591 30 31 9980 0178 9987 1056 9992 2156 9996 3628 9999 5868 0000 0739 29 32 9980 0191 9987 1073 9992 2177 9996 3657 9999 5917 0000 0891 28 33 9980 0204 9987 1089 9992 2198 9996 3687 9999 5967 0000 1049 27 34 35 9980 0218 9987 1105 9992 2219 9996 3717 9999 6017 0000 1213 26 25 0.9981 2.0231 0.9987 2.1122 0.9992 2.2240 0.9996 2.3746 0.9999 2.6068 1.0000 3.1383 36 9981 0244 9987 1138 9992 2261 9996 3777 9999 6119 0000 1561 24 37 9981 0258 9987 1155 9992 2283 9996 3807 9999 6171 0000 1745 23 38 9981 0271 9987 1171 9992 2304 9996 3837 9999 6224 0000 1938 22 39 9981 0285 9987 1188 9993 2326 9996 3868 9999 6277 0000 2140 21 40 0.9981 2.0299 0.9988 2.1205 0.9993 2.2348 0.9996 2.3899 0.9999 2.6331 1.0000 3.2352 20 41 9981 0312 9988 1222 9993 2369 9996 3930 9999 6386 0000 2575 19 42 9981 0326 9988 1238 9993 2391 9996 3962 9999 6441 0000 2810 18 43 9982 0340 9988 1255 9993 2413 9997 3993 9999 6497 0000 3058 17 44 9982 0354 9988 1272 9993 2435 9997 4025 9999 6554 0000 3322 16 45 0.9982 2.0367 0.9988 2.1289 0.9993 2.2458 0.9997 2.4057 0.9999 2.6611 1.0000 3.3602 15 46 9982 0381 9988 1306 9993 2480 9997 4089 9999 6670 0000 3901 14 47 9982 0395 9988 1324 9993 2502 9997 4122 9999 6729 0000 4223 13 48 9982 0409 998^ 1341 9993 2525 9997 4155 9999 6789 0000 4571 12 49 9982 0423 9988 1358 9993 2548 9997 4188 9999 6850 0000 4949 11 50 0.9982 2.0437 0.9989 2.1376 0.9993 2.2571 0.9997 2.4221 0.9999 2.6911 1.0000 3.5363 10 51 9982 0451 9989 1393 9993 2594 9997 4255 9999 6974 0000 5820 9 52 9983 0466 9989 1411 9993 2617 9997 4289 9999 7037 0000 6332 8 53 9983 048C 9989 1425 9994 2640 9997 4323 9999 7101 0000 6912 7 54 9983 0494 9989 1446 9994 2663 9997 4357 9999 7167 0000 7581 6 5 55 0.9983 2.0508 0.998S 2.146-^ 0.9994 2.2687 0.9997 2.4392 0.9999 2.7233 1.0000 3.8373 56 9983 0523 998£ 148[ 9994 27lf 9997 4427 9999 7300 0000 9342 4 57 9983 053'/ 998£ 1 149£ 9994 2734 9997 4462 9999 7369 oooo 4.0592 3 58 9983 0555 998£ 1 1517 9994 275? 9997 4497 9999 7438 0000 2352 2 59 9983 056( ; 998C > 153^ 9994 2782 9997 4533 9999 7509 0000 5363 1 60 M. 9983 058( ) 998C > 155^ 9994 2806 9997 456S 9999 7581 ooon Leg. S. Log. T. Log. S. Log. T Log. S. Loe. T. Loj. S. Log. T. Log. S. Log. T. Log. S. 1 Log. T. M 95" 94' 93° 92° ' 91° 90° APPARENT DISTANCE. 1 138 TARLE XXXII. LOGARITH MS OF THE FIRST i a taken from the Top, and al VND SECOND CORRECTIONS. The First Correction it always to b so the Second, when the Apparent Distance ii greater than 9fV.I 2 DEGREES. 11' , s. 0' r 2' 3' 4' 5' 6' 7' 8 9' 10' 1.0000 1.0024 1.0049 1.0073 1.0098 1.0122 1.0147 1.0172 1.0197 1.0223 1.0248 1.0274 60 1 1 0000 0025 0049 0073 0098 0123 0148 0173 0198 0223 0249 027,4 59 2 0001 0025 0049 0074 0098 0123 0148 0173 0198 0224 0249 0275' 58 1 3 0001 0025 0050 0074 0099 0124 0148 0174 0199 0224 0250 0275 57 1 4 0002 0026 0050 0075 0099 0124 0149 0174 0199 0224 0250 0276 56 5 1.0002 1.0026 1.0051 1.0075 1.0100 1.0124 1.0149 1.0174 1.0200 1.0225 1.0250 1.0276 55 6 0002 0027 0051 0075 0100 0125 0150 0175 0200 0225 0251 0276 64 7 0003 0027 0051 0076 0100 0125 0150 0175 0200 0226 0251 0277 53 8 0003 0027 0052 0076 0101 0126 0151 0176 0201 0226 0252 0277 52 9 0004 0028 0052 0077 0101 0126 0151 0176 0201 0227 0252 0278 51 50 10 1.0004 1.0028 1.0053 1.0077 1.0102 1.0126 1.0151 1.0176 1.0202 1.0227 1.0252 1.0278 11 0004 0029 0053 0077 0102 0127 0152 0177 0202 0227 0253 0279 49 12 0005 0029 0053 0078 0103 0127 0152 0177 0202 0228 0253 0279 48 13 0005 0029 0054 0078 0103 0128 0153 0178 0203 0228 0253 0279 47 14 0006 0030 0054 0079 0103 0128 0153 0178 0203 0229 0254 0280 46 15 1.0006 1.0030 1.0C55 1.0079 1.0104 1.0129 1 0153 1.0179 1.0204 1.0229 1.0255 1.0280 45 16 0006 0031 0055 0080 0104 0129 0154 0179 0204 0230 0255 0281 44 17 0007 0031 0055 0080 0105 0129 0154 0179 0205 0230 0255 0281 43 18 0007 0031 0056 0080 0105 0130 0155 0180 0205 0230 0256 0282 42 19 20 0008 0032 0056 0081 0105 0130 0155 0180 0205 0231 0256 0282 41 1.0008 1.0032 1.0057 1.0081 1.0106 '.0131 1.0156 1.0181 1.0206 1.0231 1.0257 1.0282 40 21 0008 0033 0057 0082 0106 0131 0156 0181 0207 0232 0257 0283 39 22 0009 0033 0057 0082 0107 0131 0156 0181 0207 0232 0258 0283 38 23 0009 0034 0058 0082 0107 0132 0157 0182 0207 0233 0258 0284 37 24 0010 0034 0058 0083 0107 0132 0157 0182 0208 0233 0258 0284 36 25 1.0010 1.0034 1.0059 1.0083 1 .0108 1.0133 1.0158 1.0183 1.0208 1.0233 1.0259 1.0285 35 26 0010 0035 0059 0084 0108 0133 0158 0183 0208 0234 0259 0285 34 27 0011 0035 0060 0084 0109 0134 0158 0184 0209 0234 0259 0285 33 28 0011 0036 0060 0084 0109 0134 0159 0184 0209 0235 0260 0286 32 29 0012 0036 0060 0085 0110 0134 0159 0184 0210 0235 0260 0286 31 30 1.0012 1.0036 1.0061 1.0085 1.0110 1.0135 1.0160 1.0185 1.0210 1.0235 1.0261 1.0287 30 31 0012 0037 0061 0086 0110 0135 0160 0185 0211 0236 0261 0287 29 32 0013 0037 0062 0086 0111 0136 0161 0186 0211 0236 0261 0288 28 33 0013 0038 0062 0087 0111 0136 0161 0186 o".n 0237 0262 0288 27 34 0014 0038 0062 0087 0112 0136 0161 0187 0212 0237 0262 0288 26 35 1.0014 1.0038 1.0063 1.0087 1.0112 1.0137 1.0162 1.0187 1.0212 1.0238 1.0263 1.0289 25 36 0015 0039 0063 0088 0112 0137 0162 0187 0213 0238 0263 0289 24 37 0015 0039 0064 0088 0113 0138 0163 0188 0213 0238 0264 0290 23 38 0015 0040 0064 0089 0113 0138 0163 0188 0213 0239 0264 0290 22 39 0016 0040 0064 0089 0114 0139 0163 0189 0214 0239 0264 0291 21 40 1.0016 1.0040 1.0065 1.0089 1.0114 1.0139 1.0164 1.0189 1.0214 1.0240 1.0265 1.0291 20 41 0017 0041 0065 0090 0114 0139 0164 0189 0215 0240 0266 0291 19 42 0017 0041 0066 0090 0115 0140 0165 0190 0215 0241 0266 0292 18 43 0017 0042 0066 0091 0115 0140 0165 0190 0216 0241 0267 0292 17 44 0018 0042 0066 0091 0116 0141 0166 0191 0216 0241 0267 029 16 45 1.0018 1.0042 1.0067 1.0091 1.0116 1.0141 1.0166 1.0191 1.0216 1.0242 1.0267 1.0293 15 46 0019 0043 0067 0092 0117 0141 0166 0192 0217 0242 0268 0294 14 47 0019 0043 0068 0092 0117 0142 0167 0192 0217 0243 0268 0294 13 48 0019 0044 0068 0093 0117 0142 0167 0192 0218 0243 0269 0294 12 49 0020 0044 0068 0093 0113 0143 0168 0193 0218 0244 0269 0295 11 50 1.0020 1.0044 1.0069 1.0093 1.0118 1.0143 1.0168 1.0193 1.0219 1.0244 1.0270 1.0295 10 51 0021 0045 0069 0094 0119 0143 0169 0194 0219 0244 0270 0296 9 52 0021 0045 0070 0094 0119 0144 0169 0194 0219 0245 0270 0296 8 53 0021 0046 0070 0095 0119 0144 0169 0194 0220 0245 0271 0297 7 54 55 0022 0046 0071 0095 0120 0145 0170 0195 0220 0246 0271 0297 6 1.0022 1.0046 1.0071 1.0096 1.0120 1.0145 1.0170 1.0195 1.0221 1.0246 1.C272 1.0297 5 56 0023 0047 0071 0096 0121 0146 0171 0196 0221 0247 0272 0298 4 57 0023 0047 0072 0096 0121 0146 0171 0196 0221 0247 0273 0298 3 58 i 59' 0023 0048 0072 0097 0122 0146 0171 0197 0222 0247 0273 0299 2 0024 0048 0073 0097 0122 0147 0172 0197 0222 0248 0273 0299 1 60 0024 0049 0073 0098 0122 0147 0172 0197 0223 0248 0274 0300 ' 59' 58' 57' 56' 55' 54' 53' 1 52' 51' 50' 49' 48' s. 7 DEGREES. the Botto 1 vn, en the Apparent Distance is less than 9tP, the Second Oorrection is to be tak»n from " 1 TABLE XXXII. 139 1 LOGARITHMS OF THE FIRST AND SECOND CORRECTIONS. The First Correction is alvaya to be taken from the Top, and also the Second, when tie Apparent Distance is^ reaUr than »0O 1 2 DEGREES. 1 s. 12' 13' 14' 15' 16' 17' 18' 19' 20' 21' 22' 23' 1 1.0300 1.0326 1.0352 1.0378 1.0405 1.0431 1.0458 1.04841.0512 1.0539 1.0566 1.0594 60 1 0300 0326 0352 -0378 0405 0432 0458 0485 0512 0539 0567 0594 59 2 0300 0326 0353 0379 0406 0432 0459 0485 0512 0540 0567 0595 58 3 0301 0327 0353 0379 0406 0433 0459 0486 0513 0540 0568 0595 57 4 0301 0327 0353 0380 0406 0433 0460 0486 0513 0541 0568 0596 56 55 5 1.0302 1.0328 1.0354 1.0380 1.0407 1.0434 1.0460 1.0487 1.0514 1.0541 1.0568 1.0596 6 0302 0328 0354 0381 0407 0434 0461 0487 0514 0541 0569 0596 54 7 03C3 0329 0355 0381 0408 0434 0461 0488 0515 0542 0569 0597 53 8 0303 0329 0355 0381 0408 0435 0462 0488 0515 0542 0570 0597 52 9 0304 0329 0356 0382 0409 0435 0462 0489 0516 0543 0570 0598 51 50 10 1.0304 1.0330 1.0356 1.0382 1.0409 1.0436 1.0462 1.0489 1.0516 1.0543 1.0571 1.0598 11 0304 0330 0356 0383 0409 0436 0463 0489 0517 0544 0571 0599 49 12 0305 0331 0357 0383 0410 0437 0463 0490 0517 0544 0572 0599 48 13 0305 0331 0358 0384 .0410 0437 0464 0490 0517 0545 0572 0600 47 14 0306 0332 0358 0384 0410 0438 0464 0491 0518 0545 0573 0600 46 15 1.0306 1.0332 1.0359 1.0384 1.0411 1.0438 1.0465 1.0491 1.0518 1.0546 1.0573 1.0601 45 16 0307 0333 0359 0385 0411 0438 0465 0492 0519 0546 0573 0601 44 17 0307 0333 0360 0385 0412 0439 0466 0492 0519 0546 0574 0602 43 18 0307 0333 0360 0386 0412 0439 0466 0493 0520 0547 0574 0602 42 19 0308 0334 0361 0386 0413 0440 0466 0493 0520 0547 0575 0602 41 40 20 1.0308 1.0334 1.0361 1.0387 1.0413 1.0440 1.0467 1.0493 1.0521 1.0548 1.0575 1.0603 21 0309 0335 0361 0387 0414 0440 0467 0494 0521 0548 0576 0603 39 22 0309 0335 0362 0388 0414 0441 0468 0494 0521 0549 0576 0604 38 23 0310 0336 0362 0388 0414 0441 0468 0495 0522 0549 0577 0604 37 24 0310 0336 0362 0388 0415 0442 0469 0495 0522 0550 0577 0605 36 25 1.0310 1.0336 1.0363 1.0389 1.0415 1.0442 1.0469 1.0496 1.0523 1.0550 1.0578 1.0605 35 26 0311 0337 0363 0389 0416 0442 0470 0496 0523 0551 0578 0606 34 27 0311 0337 0.^63 0390 0416 0443 0470 0497 0524 0551 0579 0606 33 28 0312 0338 0364 0390 0417 0443 0470 0497 0524 0552 0579 0607 32 29 0312 0338 0364 0391 0417 0444 0471 0498 0525 0552 0579 0607 31 30 1.0313 1.0339 1.0365 1.0391 1.0418 1.0444 1.0471 1.0498 1.0525 1.0552 1.0580 1.0608 30 31 0313 0339 0365 0392 0418 0445 0471 0498 0526 0553 0580 0608 29 32 0313 0339 0366 0392 0418 0445 ' 0472 0499 0526 0553 0581 0609 28 33 0314 0340 0366 0392 0419 0446 0472 0499 0526 0554 0581 0609 27 34 35 0314 0340 0366 0393 0419 0446 0472 0500 0527 0554 0582 0609 26 1.0315 1.0341 1.0367 1.0393 1.0420 1.0446 1.0473 1.0500 1.0527 1.0555 1.0582 1.0610 25 36 0315 0341 0367 0394 0420 0447 0474 0501 0528 0555 0583 0610 24 37 0316 0342 0368 0394 0421 0447 0474 0501 0528 0556 0583 0611 23 38 0316 0342 0368 0395 0421 0448 0475 0502 0529 0556 0584 0611 22 39 40 0317 0342 0369 0395 0422 0448 0475 0502 0529 0557 0584 0612 21 1.0317 1.0343 1.0369 1.0395 1.0422 1.0449 1.0475 1.0502 1.0530 1.0557 1.0585 1.0612 20 41 0318 0343 0370 0396 0422 0449 0476 0503 0531 0557 0585 0613 19 42 0318 0344 0370 0396 0423 0450 0476 0503 0531 05 58 0585 0613 18 43 0318 0344 0370 0397 0423 0450 0477 0504 0531 0558 0586 0614 17 44 0319 0345 0371 0397 0424 0450 0477 0504 0532 0559 0586 0614 16 45 1.0319 1.0345 1.0371 1.0398 1.0424 1.0451 1.0478 1.0505 1.0532 1.0559 1.0587 1.0615 15 46 0319 0346 0372 0398 0425 0451 0478 0505 0532 0560 0587 0615 14 47 0320 0346 0372 0399 0425 0452 0479 0506 0533 0560 0588 0615 13 48 0320 0346 0373 0399 0426 0452 0479 0506 0533 0561 0588 0616 12 49 0321 0347 0373 0399 0426 0453 0480 0507 0534 0561 0589 0616 11 50 1.0321 1.0347 1.0374 1.0400 1.0426 1.0453 1.0480 1.0507 1.0534 1.0562 1.0589 1.0617 10 51 0322 0348 0374 0400 0427 0454 0480 0507 0535 0562 0590 0617 9 52 0322 0348 0374 0401 0427 0454 0481 0508 0535 0562 0590 061S 8 53 0323 0349 0375 0401 0428 0454 0481 0508 0536 0563 0591 0618 7 54 0323 0349 0375 0402 0428 0455 0482 0509 0536 0563 0591 0619 6 55 1.0323 1.0349 1.0376 1.0402 1.0429 1.0455 1.0482 1.0509 1.0536 1.0564 1.0591 1.0619 5 56 0324 03.50 0376 0403 0429 0456 0483 0510 0537 0/64 0592 0620 4 57 0324 0350 0377 0403 0430 0456 0483 0510 0537 Of 65 0592 0620 3 58 0325 0351 0377 0403 0430 0457 0484 0511 0538 0565 0593 0621 2 59 0325 0351 0377 0404 0430 0457 0484 0511 0538 0566 0593 0621 1 60 0326 0352 0378 0404 0431 0458 0484 0512 0539 OiS6 0594 0621 47' 46' 45' 44' 43' 42' 1 41' 1 40' 39' 38 37' 36' s. 7 DEGREES. ■WTi en the Apparent I istance is less than 90O, the Second Correction s to be taken from the Botto 1 140 TABLE XXXII. LOGARITHMS OF THE FIRST AND SECOND CORRECTIONS. The First Correction is alwayg to b 9 taken from the Top, and al 2 DEG] so the Second, -vrhen the Apparent Distance is greater than 909. lEES. s. 24' 25' 26' 27' 28' 29' 30' 31' 32' 33' 34' 35' 1 2 3 4 1.0621 0622 0622 0623 0623 1.0649 0650 0650 0651 0651 1.0678 0678 0678 0679 0679 1.0706 0706 0707 0707 0708 1.0734 0735 0735 0736 0736 1.0763 0763 0764 0764 0765 1.0792 0792 0793 0793 0794 1.0821 0821 0822 0822 0823 1.0850 0851 0851 0852 0852 1.0880 0880 0881 0881 0882 1.0909 0910 0910 0911 0911 1.0939 0940 0940 0941 0941 60 1 59 5>J 57 56 5 6 7 8 9 1.0624 0624 0625 0625 0626 1.0652 0652 0653 0653 0654 1.0680 0680 0681 0681 0682 1.0708 0709 0709 0710 0710 1,0737 0737 0738 0738 0739 1.0765 0766 0766 0767 0767 1.0794 0795 0795 0796 0796 1.0823 0824 0824 0825 0825 1.0853 0853 0854 0854 0855 1.0882 0883 0883 0883 0884 1.0912 0912 0913 0913 0914 1.0942 0942 0943 0943 0944 55 54 53 ,52 51 10 11 12 13 14 1.0626 0627 0627 0628 0628 1.0654 0655 0655 0655 0656 1.0682 0683 0683 0684 0684 1.0711 0711 0711 0712 0712 1.0739 0740 0740 0740 0741 1.0768 0768 0769 0769 •0770 1.0797 0797 0798 0798 0799 1.0826 0826 0827 0827 0828 1.0855 0855 0856 0856 0857 1.0884 0885 0885 0886 0886 1.0914 0915 0915 0916 0916 1.0944 0945 0945 0946 0946 50 49 48 47 46 15 16 17 18 19 1.0628 0629 0629 0630 0630 1.0656 0657 0657 0658 0658 1.0685 0685 0686 0686 0686 1.0713 0713 0714 0714 0715 1.0741 0742 0742 0743 0743 1.0770 0771 0771 0772 0772 1.0799 0800 0800 0801 0801 1.0828 0829 0829 0830 0830 1.0857 0858 0858 0859 0859 1.0887 0887 0888 0888 0889 1.0917 0917 0918 0918 0919 1.0947 0947 0948 0948 0949 45 44 43 42 41 20 21 22 23 24 1.0631 0631 0632 0632 0633 1.0659 0659 0660 0660 0661 1.0687 0687 0688 0688 0689 1.0715 0716 0716 0717 0717 1.0744 0744 0745 0745 0746 1.0773 0773 0774 0774 0774 1.0801 0802 0802 0803 0803 1.0831 0831 0832 0832 0833 1.0860 0860 0861 0861 0862 1.0889 0890 0890 0891 0891 1.0919 0920 0920 0921 0921 1.0949 0950 0950 0951 0951 40 39 38 37 36 25 26 27 28 29 1.0633 0634 0634 0634 0635 1.0661 0662 0662 0663 0663 1.0689 0690 0690 0691 0691 1.0718 0718 0719 0719 0720 1.0746 .0747 0747 0748 0748 1.0775 0775 0776 0776 0777 1.0804 0804 0805 0805 0806 1.0833 0834 0834 0834 0835 1.0862 0863 0863 0864 0864 1.0892 0893 0893 0894 0894 1.0922 0922 0923 0923 0924 1.0952 0952 0953 0953 0954 35 34 33 32 31 30 31 32 33 34 1.0635 0636 0636 0637 0637 1.0663 0664 0664 0665 0665 1.0692 0692 0693 0693 0694 1.0720 0721 0721 0721 0722 1.0749 0749 0750 0750 0751 1.0777 0778 0778 0779 0779 1.0806 0807 0807 0808 0808 1.0835 0836 0836 0837 0837 1.0865 0865 0866 0866 0867 1.0895 0895 0896 0896 0897 1.0924 0925 0925 0926 0926 1.0954 0955 0955 0956 0956 30 29 28 27 26 35 36 37 38 39 1.0738 0638 0639 0639 0640 1.0666 0666 0667 0667 0668 1.0694 0694 0695 0695 0696 1.0722 0723 0723 0724 0724 1.0751 0751 0752 0752 0753 1.0780 0780 0781 0781 0782 1.0809 0809 0810 0810 0811 1.0838 0838 0839 0839 0840 1.0867 0868 0868 0869 0869 1.0897 0898 0898 0899 0899 1.0927 0927 0928 0928 0929 1.0957 0957 0958 0958 0959 25 24 23 22 21 40 41 42 43 44 1.0640 0641 0641 0641 0642 1.0668 0669 0669 0670 0670 1.0696 0697 0697 0698 0698 1.0725 0725 0726 0726 0727 1.0753 0754 0754 0755 0755 1.0782 0783 0783 0784 0784 1.0811 0812 0812 0813 0813 1.0840 0841 0841 0842 0842 1.0870 0870 0871 0871 0872 1.0899 0900 0900 0901 0901 1.0929 0930 0930 0931 0931 1.0959 0960 0960 0961 0961 20 19 18 17 16 45 46 47 48 49 1.0642 0643 0643 0644 0644 1.0670 0671 0671 0672 0672 1.0699 0699 0700 0700 0701 1.0727 0728 0728 0729 0729 1.0756 0756 0757 0757 0758 1.0785 0785 0786 0786 0787 1.0814 0814 0815 0815 0816 1.0843 0843 0844 0844 0845 1.0872 0873 0873 0874 0874 1.0902 0902 0903 0903 0904 1.0932 0932 0933 0933 0934 1.0962 0962 0963 0963 0964 15 14 13 12 11 50 51 52 53 54 1.0645 0645 0646 0646 0647 1.0673 0673 0674 0674 0675 1.0701 0702 0702 0703 0703 1.0730 0730 0730 0731 0731 1.0758 0759 0759 0760 0760 1.0787 0787 0788 0788 0789 1.0816 0816 0817 0817 0818 1.0845 0846 0846 0847 0847 1.0875 0875 0876 0876 0877 1.0904 0905 0905 0906 0906 1.0934 0935 0935 0936 0936 1.0964 0965 0965 0966 0966 10 9 8 7 6 5 4 3 2 1 55 56 57 58 59 60 1.0647 0648 0648 0648 0649 0649 1.0675 0676 0676 0677 0677 0678 1.0703 0704 0704 0705 0705 0706 1.0732 0732 0733 0733 0734 0734 1.0761 0761 0762 0762 0762 0763 1.0789 0790 0790 0791 0791 0792 1.0818 0819 0819 0820 0820 0821 1.0848 0848 0849 0849 0850 0850 1.0877 0878 0878 0879 0879 0880 1.0907 0907 0908 0908 0«»09 0909 1.0937 0937 0938 0938 0939 0939 1.0967 0967 0968 0968 0969 (1969 35' 1 34' 33' 32' 1 31' 30' 29' 28' 1 27' 26' 25' 1 24' S. 7 DBGREES. When the Apparent Distance is less than 90O, the Second Correction is to be taken from the Bottom. 1 TABl-K XXXII. 141 LOGARITHMS OF THE FIRST AND SECOND CORRECTIONS. The First Corruction is always to be taken from the Top, and also the Socond, when the Apparent Distance is griper than SO".! 2 DEGKEES. | s. 36' 37' 38' 39' 40' 41' 42' 43' 44' 45' 46' 47' 60 1.0969 1.0999 1.1030 1.1061 1.1091 1.1123 1.1154 1.1186 1.1217 1.1249 1.1282 1.1314 1 0970 lOOi) 1030 1061 1092 1123 1154 1186 1218 1250 1282 1315 59 2 0970 1000 1031 1062 1092 1124 1155 1187 1218 1250 1283 1315 58 3 0971 1001 1031 1062 1093 1124 1156 1187 1219 1251 1283 1316 57 4 0971 1001 1032 1063 1094 1125 1156 • 1188 1219 1252 1284 1316 56 5 1.0972 1.1002 1.1032 1.1063 1.1094 1.1125 1.1157 1.1188 1.1220 1.1252 1.1284 1.1317 55 6 0972 1002 1032 1064 1095 1126 1157 1189 1221 1253 1285 1317 54 7 0973 1003 1033 1064 1095 1126 1158 1189 1221 1253 1285 1318 53 8 0973 1003 1034 1065 1096 1127 1158 1190 1222 1254 1286 1319 52 9 0974 1004 1034 1065 1096 1127 1159 1190 1222 1254 1287 1319 51 10 1.0974 1.1004 1.1035 1.1066 1.1097 1.1128 1.1159 1.1191 1.1223 1,1255 1.1287 1.1320 50 11 0975 1005 1035 1066 1097 1128 1160 1191 1223 1255 1288 1320 49 12 0975 1005 1036 1067 1098 1129 1160 1192 1224 1256 1288 1321 48 13 0976 1006 1036 1067 1098 1129 1161 1192 1224 1256 1289 1321 47 14 0976 1006 1037 1068 1099 1130 1161 1193 1225 1257 1289 1322 46 15 1.0977 1.1007 1,1037 1.1068 1.1099 1.1130 1.1162 1.1193 1.1225 1.1257 1.1290 1.1322 45 16 0977 1007 1038 1069 1100 1131 1162 1194 1226 1258 1290 1323 44 17 0978 1008 1039 1069 1100 1131 1163 1195 1226 1259 1291 1323 43 18 0978 1008 1039 1070 1101 1132 1163 1195 1227 1259 1291 1324 42 19 0979 1009 1040 1070 1101 1132 1164 1196 1227 1260 1292 1325 41 20 1.0979 1.1009 1.1040 1.1071 1.1102 1.1133 1.1164 1.1196 1.1228 1.1260 1.1292 1.1325 40 21 0980 1010 1041 1071 1102 1134 1165 1197 1229 1261 1293 1326 39 22 0980 1011 1041 1072 1103 1134 1165 1197 1229 1261 1294 1326 38 23 0981 1011 1042 1072 1103 1135 1166 1198 1230 1262 1294 1327 37 24 0981 1012 1042 1073 1104 1135 1167 1198 1230 1262 1295 1327 36 25 1.0982 1.1012 1.1043 1.1073 1.1104 1.1136 1.1167 1.1199 1.1231 1.1263 1.1295 1.1328 35 26 0982 1013 1043 1074 1105 1136 1168 1199 1231 1264 1296 1328 34 27 0983 1013 1044 1074 1105 1137 1168 1200 1232 1264 1296 1329 33 28 0983 1014 1044 1075 1106 1137 1169 1200 1232 1265 1297 1329 32 29 0984 1014 1045 1075 1106 1138 1169 1201 1233 1265 1297 1330 31 30 30 1.0984 1.1015 1.1045 1.1076 1.1107 1.1138 1.1170 1.1201 1.1233 1.1266 1.1298 1.1331 31 3985 1016 1046 1076 1108 1139 1170 1202 1234 1266 1298 1331 29 32 0985 1016 1046 1077 1108 1139 1171 1202 1234 1267 1299 1332 28 33 0986 1017 1047 1078 1109 1140 1171 1203 1235 1267 1300 1332 27 34 35 0986 1017 1047 1078 1110 1140 1172 1204 1235 1.1236 1268 1300 1333 26 25 1.0987 1.1018 1.1048 1.1079 1.1110 1.1141 1.1172 1.1204 1.1268 1.1301 1.1333 36 0987 1018 1.048 1079 nil 1141 1173 1205 1237 1269 1301 1334 24 37 0988 1019 1049 1080 1111 1142 1173 1205 1237 1269 1302 1334 23 38 0988 1019 1049 1080 1112 1142 1174 1206 1238 1270 1302 1335 22 39 0989 1020 1050 1081 1112 1143 1174 1206 1238 1270 1303 1335 21 40 1.0989 1.1020 1.1050 1.1081 1.1112 1.1143 1.1175 1.1207 >.1239 1.1271 1.1303 1.1336 20 41 0990 1021 1051 1082 1113 1144 1175 1207 1239 1271 1304 1337 19 42 0990 1021 1051 1082 1113 1145 1176 1208 1240 1272 1304 1337 18 43 0991 1022 1052 1083 1114 1145 1177 1208 1240 1273 1305 1338 17 44 0991 1022 1052 1083 1114 1146 1177 1209 1241 1273 1306 1338 16 45 1.0992 1.1023 1.1053 1.1084 1.1115 1.1146 1.1178 1.1209 1.1241 1.1274 1.1306 1.1339 15 46 0992 1023 1053 1084 1115 1147 1178 1210 1242 1274 1307 1339 14 47 0993 1024 1054 1085 1116 1147 1179 1210 1242 1275 1307 1340 13 48 0993 1024 1054 1085 1116 1148 1179 1211 1243 1275 1308 1340 12 49 0994 1025 1055 1086 1117 1148 1180 1211 1243 1276 1308 1341 11 10 50 1.0994 1.1025 1.1055 1.1086 1.1117 1.1149 1.1180 1.1212 1.1244 ).1276 1.1309 1 1342 51 0995 1026 1056 1087 1118 1149 1181 1213 1245 1277 1309 1342 9 52 0995 1026 1056 1087 1118 1150 1181 1213 1245 1277 1310 1343 8 53 0996 1027 1057 1088 1119 1150 1182 1214 1246 1278 1310 1343 7 54 0996 1027 1057 1088 1119 1151 1182 1214 1246 1278 1311 1344 6 55 1.0997 1.1028 1.105^ 1.1089 1.1120 1.1151 1.1183 1.1215 1.1247 1.1279 > 1311 1.1344 5 56 0997 1028 1058 1089 1120 1152 1183 1215 1247 1280 1312 1345 4 57 0998 1028 1059 1090 1121 1152 1184 1216 1248 1280 1313 1345 3 58 0998 1029 1060 1090 1122 1153 1184 1216 1248 1281 1313 1346 2 59 0999 1029 1060 1091 1122 1153 1185 1217 1249 1281 1314 1346 1 fiO 0999 1030 1061 1091 1123 1154 1186 1217 1249 1282 1314 1347 23' 1 22' 21' 25: 19' 18' 17' 1 16' 15' 14' 1 13' 1 12' s. 7 DEGREES. "vr hen the Appajent Distance ialeas than 90". the Second Correction IS to be taken from the Botb i>-n. 142 TABLE XXXIl. The^ LOGARITHMS OF THE FIRST AND SECOND CORRECTIONS. J rst Correction is always to be taken from the Top. and also the Second, when the Apparent Distance is greater thaa 90° ■1 2 DEGREES. S. 48' 49' 50' 51' 52 53' 54' 55' 56' 57' 68' 59' 60 1.1347 1.1380 1.1413 1.1447 1.1481 1.1515 1.1549 1.1584 1.1619 1.1654 1.1689 1.1725 1 1348 1381 1414 1447 1481 1515 155» 1584 1619 1654 1690 1725 59 2 1348 1381 1414 1448 1482 1516 1550 1585 1620 1655 1690 1726 58 3 1349 1382 1415 1449 1482 1516 1551 1585 1620 1655 1691 1727 57 4 1349 1382 1416 1449 1483 1517 1551 1586 1621 1656 1692 1727 56 55 5 1.1350 1.1383 1.1416 1.1450 1.1483 1.1518 1.1552 1.1587 1.1621 1.1657 1.1692 1.1728 6 1350 1383 1417 1450 1484 1518 1552 1587 1622 1657 1693 1728 54 7 1351 1384 1417 1451 1485 1519 1553 1588 1623 1658 1693 1729 53 8 1351 1384 1418 1451 1485 1519 1554 1588 1623 1658 1694 1730 52 9 1352 1385 1418 1452 1486 1520 1554 1589 1624 1659 1694 1730 51 50 10 1.1352 1.1386 1.1419 1.1452 1.1486 1.1520 1.1555 1.1589 1.1624 1.1660 1.1695 1.1731 11 1353 1386 1419 1453 1487 1521 1555 1590 1625 1660 1696 1731 49 12 1354 1387 1420 1454 1487 1522 1556 1591 1625 1661 1696 1732 48 13 1354 1387 1421 1454 1488 1522 1556 1591 1626 1661 1697 1733 47 14 1355 1388 1421 1455 1489 1523 1557 1592 1627 1662 1697 1733 46 15 1.1355 1.1388 1.1422 1.1455 1.1489 1.1523 1.1558 1.1592 1.1627 1.1663 1.1698 1.1734 45 16 1356 1389 1422 1456 1490 1524 1558 1593 1628 1663 1699 1734 44 17 1356 1389 1423 1456 1490 1524 1559 1593 1628 1664 1699 1735 43 18 1357 1390 1423 1457 1491 1525 1559 1594 1629 1664 1700 1736 42 19 1357 1391 1424 1458 1491 1526 1560 1595 1630 1665 1700 1736 41 20 1.1358 1.1391 1.1424 1.1458 1.1492 1.1526 1.1561 1.1595 1.1630 1.1665 1.1701 1.1737 40 21 1359 1392 1425 1459 1493 1527 1561 1596 1631 1666 1702 1737 39 22 1359 1392 1426 1459 1493 1527 1562 1596 1631 1667 1702 1738 38 23 1360 1393 1426 1460 1494 1528 1562 1597 1632 1667 1703 1739 37 24 1360 1393 1427 1460 1494 1528 1563 1598 1633 1668 1706 1739 36 25 1.1361 1.1394 1.1427 1.1461 1.1495 1.1529 1.1563 1.1598 1.1633 1.1668 1.1704 1.1740 35 26 1361 1394 1428 1461 1495 1530 1564 1599 1634 1669 1705 1740 34 27 1362 1395 1428 1462 1496 1530 1565 1599 1634 1670 1705 1741 33 28 1362 1396 1429 1463 1496 1531 1565 1600 1635 1670 170b 1742 32 29 1363 1396 1429 1463 1497 1531 1566 1600 1635 1671 1706 1742 31 30 1.1363 1.1397 1.1430 1.1464 1.1498 1.1532 1.1566 1.1601 1.1636 1.1671 1.1707 1.1743 30 31 1364 1397 1431 1464 1498 1532 1567 1602 1637 1672 1708 1743 29 32 1365 1398 1431 1465 1499 1533 1567 1602 1637 1673 1708 1744 28 33 1365 1398 1432 1465 1499 1534 1568 1603 1638 1673 1709 1745 27 34 35 1366 1399 1432 1466 1500 1534 1569 1603 1638 1674 1709 1745 26 25 1.1366 1.1399 1.1433 1.1467 1.1500 1.1535 1.1569 1.1604 1.1639 1.1675 1.1710 1.1746 36 1367 1400 1433 1467 1501 1535 1570 1605 1640 1675 1711 1746 24 37 1367 1401 1434 1468 1502 1536 1570 1605 1640 1676 1711 1747 23 38 1368 1401 1435 1468 1502 1536 1571 1606 1641 1676 1712 1748 22 39 1368 1402 1435 1469 1503 1537 1571 1606 1641 1677 1712 1748 21 40 1.1369 1.1402 1.1436 1.1469 1.1503 1.1538 1.1572 1.1607 1.1642 1.1677 1.1713 1.1749 20 41 1370 1403 1436 1470 1504 1538 1573 1607 1643 1678 1714 1749 19 42 1370 1403 1437 1470 1504 1539 1573 1608 1643 1678 1714 1750 18 43 1371 1404 1437 1471 1505 1539 1574 1609 1644 1679 1715 1751 17 44 1371 1404 1438 1472 1506 1540 1574 1609 1644 1680 1715 1751 16 45 1.1372 1.1405 1.1438 1.1472 1.1506 1.1540 1.1575 1.1610 1.1645 1.1680 1.1716 1.1752 15 46 1372 1405 1439 1473 1507 1541 1576 1610 1645 1681 1717 1752 14 47 1373 1406 1440 1473 1507 1542 1576 1611 1646 1681 1717 1753 13 48 1373 1406 1440 1474 1508 1542 1577 1612 1647 1682 1718 1754 12 49 1374 1407 1441 1474 1508 1543 1577 1612 1647 1683 1718 1754 11 50 1.1374 1.1407 1.1441 1.1475 1.1509 1.1543 1.1578 1.1613 1.1648 1.1683 1.1719 1.1755 10 51 1375 1408 1442 1476 1510 1544 1578 1613 1648 1684 1719 1755 9 52 1376 1408 1442 1476 1510 1544 1579 1614 1649 1684 1720 1756 8 53 1376 1409 1443 1477 1511 1545 1580 1614 1650 1685 1721 1757 7 54 1377 1409 1443 1477 1511 1546 1580 1615 1650 1686 1721 1757 6 55 I 1377 1.1410 1.1444 1.1478 1.1512 1.1546 1.1581 1.1616 1.1651 1.1686 .17221 1.1758 5 56 1378 1411 1445 1478 1512 1547 1581 1616 1651 1687 1722 1759 4 57 1378 1411 1445 1479 1513 1547 1582 1617 1652 1687 1723 1759 3 58 1379 1412 1446 1479 1514 1548 1582 1617 1652 1688 1724 1760 2 59 1379 1412 1446 1480 1514 1548 1583 1618 1653 1689 1724 1760 1 60 1380 1413 1447 1481 1515 1549 1584 1619 1654 1689 1725 1761 11' 10' 9' 1 8' 1 7' 6' 1 5' 1 4' 1 3' 2' 1 1' 0' s. 7 DEGREES. ^ , •w tien the Apparent Distance inle»$ than 90", the Second C orrection is to be t! iken from the Bottc )m. 1 TABLE XXXll. 143 1 LOGARITHMS OF THE FIRST AND SECONE CORRECTIONS. idO« Che Fiist Corxeotion is always to be taken from the Top. and also the Second, whet I the Apparent Distance ih greater thai 3 DEGKEES. 1 S. 0' 1' 2' 3' 4' 5' 6' 7' 8' 9' 10' 11' 60 i.i;6i 1.1797 1.1834 1.1871 1.1908 1.1946 1.1984 1.2022 1.2061 1.2099 1.2139 1.2178 1 1762 1798 1835 1871 1909 1946 1984 2023 2061 2100 2139 2179 59 2 1762 1798 1835 1872 1909 1947 1985 2023 2062 2101 2140 2180 58 3 1763 1799 1836 1873 1910 1948 1986 2024 2062 2101 2141 2180 57 4 1763 1800 1836 1873 1911 1948 1986 • 2025 2063 2102 2141 2181 56 5 1.1764 1.1800 1.1837 1.1874 1.1911 1.1949 1.1987 1.2025 1.2064 1.2103 1.2142 1.2182 55 6 1765 1801 1838 1875 1912 1950 1987 2026 2064 2103 2143 2182 54 7 1765 1802 1838 1875 1913 1950 1988 2026 2065 2104 2143 2i83 53 8 1766 1802 1839 1876 1913 1951 1989 2027 2066 2106 2144 2184 52 9 1766 1803 1839 1876 1914 1951 1989 2028 2066 2105 2145 2184 51 10 1.1767 1.1803 1.1840 1.1877 1.1914 1.1952 1.1990 1.2028 1.2067 1.2106 1.2145 1.2185 50 11 1768 1804 1841 1878 1915 1953 1991 2029 2068 2107 , 2146 2186 49 12 1768 1805 1841 1878 1916 1953 1991 2030 2068 2107 2147 2186 48 13 1769 1805 1842 1879 1916 1954 1992 2030 2069 2108 2147 2187 47 14 1769 1806 1843 1880 1917 1955 1993 2031 2070 2109 2148 2188 46 15 1.1770 1.1806 1.1843 1.1880 1.1918 1.1955 1.1994 1.2032 1.2070 1.2109 1.2149 1.2188 45 16 1771 1807 1844 1881 1918 1956 1994 2032 2071 2110 2149 2189 44 17 1771 1808 1844 1881 1919 1956 1995 2033 2072 2111 2150 2190 43 18 1772 1808 1845 1882 1919 1957 1996 2033 2072 2111 2151 2190 42 19 1772 1809 1846 1883 1920 1958 1996 2034 2073 2112 2151 2191 41 20 1.1773 1.1809 1.1846 1.1883 1.1921 1.1959 1.1997 1.2035 1.2073 1.2113 1.2152 1.2192 40 21 1774 1810 1847 1884 1921 1960 1997 2035 2074 2113 2153 2192 ?9 22 1774 1811 1847 1884 1922 1960 1998 2036 2075 2114 2153 2193 38 23 1775 1811 1848 1885 1923 1961 1998 2037 2075 2115 2154 2194 37 24 1775 1812 1849 1886 1923 1962 1999 2037 2076 2115 2155 2194 36 25 1.1776 1.1812 1.1849 1.1886 1.1924 1.1962 1.2000 1.2038 1.2077 1.2116 1.2155 1.2195 35 26 1777 1813 1850 1887 1924 1963 2000 2039 2078 2116 2156 2196 34 27 1777 1814 1850 1888 1925 1963 2001 2039 2079 2117 2157 2196 33 28 1778 1814 1851 1888 1926 1964 2001 2040 2079 2118 2157 2197 32 29 1778 1815 1852 1889 1926 1964 2002 2041 2080 2118 2158 2198 31 30 30 1.1779 1.1816 1.1852 1.1889 1.1927 1.1965 1.2003 1.2041 1.2080 1.2119 1.2158 1.2198 31 1780 1816 1853 1890 1928 1965 2003 2042 2081 2120 2159 2199 29 32 1780 1817 1854 1891 1928 1966 2004 2042 2081 2120 2160 2200 28 33 1781 1817 1854 1891 1929 1967 2005 2043 2082 2121 2161 2200 27 1 34 35 1781 1818 1855 1892 1929 1967 2005 2044 2083 2122 2161 2201 26 1.1782 1 .1819 1.1856 1.1893 1.1930 1.1968 1.2006 1.2044 1.2083 1.2122 1.2162 1.2202 25 36 1783 1819 1.857 1893 1931 1968 2007 2045 2084 2123 2163 2202 24 37 1783 1820 1857 1894 1931 1969 2007 2046 2085 2124 2163 2203 23 38 1784 1820 1858 1894 1932 1970 2008 2046 2085 2124 2164 2204 22 39 1785 1821 1858 1895 1933 1970 2009 2047 2086 2125 2165 2204 21 40 1.1785 1.1822 1.1859 1.1896 1.1933 1.1971 1.2009 1.2048 1.2086 1.2126 1.2165 1.2205 20 41 1786 1822 1859 1896 1934 1972 2010 2048 2087 2126 2166 2206 19 42 1786 1823 1860 1897 1934 1972 2010 2049 2088 2127 2167 2206 18 43 1787 1823 1860 1898 1935 1973 2011 2050 2088 2128 2167 2207 17 44 1788 1824 1861 1898 1936 1974 2012 2050 2089 2128 2168 2208 16 45 1.1788 1.1825 1.1862 1.1899 1.1936 1.1974 1.2012 1.2051 1.2090 1.2129 1.2169 1.2208 15 46 1789 1825 1862 1899 1937 1975 2013 2052 2090 2130 2169 2209 14 47 1789 1826 1863 1900 1938 1975 2014 2052 2091 2130 2170 22J0 13 48 1790 1827 1863 1901 1938 1976 2014 2053 2092 2131 2170 2210 12 49 1791 1827 1864 1901 1939 1977 2015 2053 2092 2132 2171 2211 11 50 1.1791 1.1828 1.1865 1.1902 1.1939 1.1977 1.2016 1.2054 1.2093 1.2132 1.2172 1.2212 10 51 1792 1828 1865 1903 1940 1978 2016 2055 2094 2133 2172 2212 9 52 53 ' 64 1792 1829 1866 1903 1941 1979 2017 2055 2094 2134 2173 2213 8 1793 1830 1867 1904 1941 1979 2017 2056 2095 2134 2174 2214 7 1794 1830 1867 1904 1942 1980 2018 2057 2096 2135 2174 2214 6 55 1.1794 1.1831 1.1868 1.1905 1.1942 1.1981 1.2019 1.2057 1.2096 1.2136 1.2175 1.2215 5 56 1795 1831 1868 1906 1943 1981 2019 2058 2097 2136 2176 2216 4 57 1795 1832 1869 1906 1944 1982 2020 2059 2098 2137 2176 2216 3 58 1796 1833 1870 1907 1944 1982 2021 2059 2098 2137 2177 2217 2 59 1797 1833 1870 1908 1945 1983 2021 2060 2099 2138 2178 2218 1 60 1797 1834 1871 1908 1946 1984 2022| 2061 2099 2139 2178 2218 69' 58' 57' 56' 55' 54' 53' 52- 51' 50- 1 49- 48' s. 6 DEGREES. W Tien the Apparent Distance 8 less than 90", the Second Correction is to be taken from the Bottom. 10 14^1 TABLE XXXIi. LOGARITHMS OF THE FIRST AND SECOND CORRECTIONS. Th« First Correction is always to be ta.ken frorr the Top, and also the Second, when the Apparent Distance ia greater than 90°. S. 10 11 12 13 14 15 16 17 18 19 20 '21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 3 DEGREES. 1: .2218 2219 2220 2220 2221 .2222 2223 2223 2224 2225 .2225 2226 2227 2227 2228 .2229 2229 2230 2231 2231 .2232 2233 2233 2234 2235 13' .2259 2260 2260 2261 2262 1, 2262 2263 2264 2264 2265 .2266 2266 2267 2268 2268 2269 2270 2270 2271 2272 .2235 2236 2237 223 2238 .2239 2239 2240 2241 2241 .2242 2243 2243 2244 2245 .2245 2246 2247 2247 2248 .2249 2249 2250 2251 2251 .2252 2253 2253 2254 2255 .2256 2256 2257 2258 2258 2259 .2272 2273 2274 2274 2275 .2276 2277 2277 2278 2279 .2279 2280 2281 2281 2282 14' .2300 2300 2301 2302 2302 1 2303 2304 2304 2305 2306 1. 2307 2307 2308 2309 2309 2310 2311 2312 2313 2313 .2314 2315 2315 2316 2317 1.2317 2318 2319 2320 2320 2283 2283 2284 2285 2285 1, 2286 2287 2287 2288 2289 .2289 2290 2291 2291 2292 2293 2294 2294 2295 2296 .2296 2297 2298 2298 2299 2300 ir 46 .2321 2321 2322 2322 2323 15' .2341 2342 2342 2343 2344 2344 2345 2346 2346 2347 2348 2348 2349 2350 2350 .2351 2352 2353 2353 2354 .2355 2355 2356 2357 2357 1.2358 2359 2359 2360 2361 2324 2324 2325 2326 2326 1 2327 2328 2328 2329 2330 2331 2331 2332 2333 2333 .2334 2335 2335 2336 2337 .2337 2338 2339 2339 2340 2341 2362 2363 2364 2364 16' .2382 2383 2384 2384 2385 1. 2386 2387 2387 2388 2389 1 2389 2390 2391 2391 2392 2393 2394 2394 2395 2396 .2396 2397 2398 2398 2399 1.2400 2401 2401 2402 2403 1.23621.2403 1.2365 2366 2366 2367 2368 .2368 2369 2370 2371 2371 .2372 2373 2373 2374 2375 .2375 2376 2377 2378 2378 .2379 2380 2380 2381 2382 2382 2404 2405 2405 17 .2424 2425 2426 2426 2427 1, 2428 2429 2429 2430 2431 .2431 2432 2433 2433 2434 1, 2435 2436 2436 2437 2438 .2438 2439 2440 2441 2441 .2442 2443 2443 2444 2445 1.2445 2446 2447 2448 2406 2448 1.2407 2408 2408 2409 2410 1 2410 2411 2412 2412 2413 .2414 2415 2415 2416 2417 2417 2418 2419 2419 2420 1.2421 2422 2422 2423 2424 2424 1.2449 2450 2450 2451 2452 .2453 2453 2454 2455 2455 .2456 2457 2458 2458 2459 18' 2467 2467 2468 2469 2470 1 2470 2471 2472 2472 2473 .2474 2475 2475 2476 2477 .2477 2478 2479 2480 2480 1, 2481 2482 2482 2483 2484 1 2485 2485 2486 2487 2487 1.2488 2489 2489 2490 2491 2492 2492 2493 2494 2494 19' I. 2510 2510 2511 2512 2512 .2513 2514 2515 2515 2516 1 2517 2517 2518 2519 2520 .2520 2521 2522 2522 2523 ,2524 2525 2525 2526 2527 .2527 2528 2529 2530 2530 1.2531 2532 2533 2533 2534 1.2535 2535 2536 2537 2538 1.24951.2538 2496 2497 2497 2498 1, 2460 2460 2461 2462 2462 45' 44' 43' 1.2463 2464 2465 2465 2466 2467 42' I 2499 2499 2500 2501 2502 2502 2503 2504 2504 2505 1.2506 2507 2507 2508 2509 2610 2539 2540 2540 2541 20' 1, 2553 2553 2554 2555 2556 2556 2557 2558 2559 2559 .2560 2561 2561 2562 2563 .2564 2564 2565 2566 2566 .2567 2568 2569 2569 2570 1 2571 2572 2572 2573 2574 1.2574 2575 2576 2577 2577 1.2578 2579: 2580 2580 2581 21' .2596 2597 2598 2599 2599 2600 2601 2601 2602 2603 2604 2604 2605 2606 2607 .2607 2608 2609 2610 2610 .2611 2612 2612 2613 2614 .2615 2615 2616 2617 2618 1.2618 2619 2620 2621 2621 .2542 2543 2543 2544 2545 2545 2546 2547 2548 2548 1.2549 2550 2551 2551 2552 2553 1.2582 2583 2583 2584 2585 2585 2586 2587 2588 2588 1 2589 2590 2591 2591 2592 1.2593 2593 2594 2595 2596 2596 1.2622 2623 2624 2624 2625 1.2626 2626 2627 2628 2629 22' 2640 2641 2642 2643 2643 .2644 2645 2646 2646 2647 .2648 2649 2649 2650 2651 1, 2652 2652 2653 2654 2655 1, 2655 2656 2657 2657 2658 1. 2659 2660 2660 2661 2662 .2663 2663 2664 2665 2666 1.2666 2667 2668 2669 2669 .2629 2630 2631 2632 2632 .2633 2634 2635 2635 2636 1.2637 2638 2638 2639 2640 2640 1.2670 2671 2672 2672 2673 23' .2685 2686 2687 2688 2688 1, 2689 2689 2690 2691 2692 2692 2693 2694 2695 2695 2696 2697 2698 2698 2699 .2700 2701 2701 2702 2703 .2704 2704 2705 2706 2707 1.2707 2708 2709 2710 2710 1.2711 2712 2713 2713 2714 .2674 2675 2675 2676 2677 .2678 2678 2679 2680 2681 41' I 40' 39' 1 38' 1.2681 2682 2683 2684 2684 2685 1.2715 2716 2716 2717 2718 .2719 2719 2720 2721 2722 2722 2723 2724 2725 2725 37' .2726 2727 2728 2729 2729 2730 36' 6 DEGREES. 60 59 58 67 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 S3 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 _0^ s. When the Apparent Distance is lets than 90°, the Second Correction is to be taken from the Bottom. TABLE XXXII. 145 LOGARITHMS OF THE FIRST AND SECOND CORRECTIONS. Tha Fint Correction is always to be taken from the Top, and also the Second, when the Apparent Distance it greater thaa 90°. 3 DEGREES. S. 24' 25' 26' 27' 28' 29' 30' 31' 32' 33' 34' 35' 60 1.2730 1.2775 1.2821 1.2868 1.2915 1.2962 1.3010 1.3059 1.3108 1.3158 1.3208 1.3259 1 2731 2776 2822 2869 2916 2963 3011 3060 3109 3158 3209 3259 59 2 7232 2777 2823 2869 2916 2964 3012 3060 3110 3159 3209 3260 58 3 2732 2778 2824 2870 2917 2965 3013 3061 3110 3160 3210 3261 57 4 5 ^33 2779 2825 2871 2918 2965 3014 3062 3111 3161 3211 3262 56 1.2734 1.2779 1.2825 1.2872 1.2919 1.2966 1.3014 1.3063 1.3112 1.3162 1.3212 1.3263 55 6 2735 2780 2826 2873 2920 2967 3015 3064 3113 3163 3213 3264 54 7 2735 2781 2827 2873 2920 2968 3016 3065 3114 3163 3214 3265 53 8 2736 2782 2828 2874 2921 2969 3017 3065 3114 3164 3214 3265 52 9 2737 2782 2828 2875 2922 2969 3018 3066 3115 3165 3215 3266 51 10 1.2738 1.2783 1.2829 1.2876 1.2923 1.2970 1.3018 1.3067 1.3116 1.3166 1.3216 1.3267 50 11 2738 2784 2830 2876 2924 2971 3019 3068 3117 3167 3217 3268 49 12 2739 2785 2831 2877 2924 2972 3020 3069 3118 3168 3218 3269 48 13 2740 2785 2831 2878 2925 2973 3021 3069 3119 3168 3219 3270 47 14 15 2741 2786 2832 2879 2926 2973 3022 3070 3119 3169 3220 3270 46 1.2741 1.2787 1.2833 1.2880 1.2927 1.2974 1.3022 1.3071 1.3120 1.3170 1.3220 1.3271 45 16 2742 2788 2834 2880 2927 2975 3023 3072 3121 3171 3221 3272 44 17 2743 2788 2835 2881 2928 2976 3024 3073 3122 3172 3222 3273 43 18 2744 2789 2835 2882 2929 2977 3025 3073 3123 3173 3223 3274 42 19 2744 2790 2836 2883 2930 2977 3026 3074 3124 3173 3224 3275 41 40 20 1.2745 1.2791 1.2837 1.2883 1.2931 1.2978 1.3026 1.3075 1.3124 2.3174 1.3225 1.3276 21 2746 2792 2838 2884 2931 2979 3027 3076 3125 3175 3225 3276 39 22 2747 2792 2838 2885 2932 29S0 3028 3077 3126 3176 3226 3277 38 23 2747 2793 2839 2886 »933 2981 3029 3078 3127 3177 3227 3278 37 24 2748 2794 2840 2887 2934 2981 3030 3078 3128 3178 3228 3279 36 25 1.2749 1.2795 1.2841 1.2887 1.2935 1.2982 1.3030 1.3079 1.3129 1.3178 1.3229 1.3280 35 26 2750 2795 2841 2888 2935 2983 3031 3080 3129 3179 3230 3281 34 27 2750 2796 2842 2889 2936 2984 3032 3081 3130 3180 3231 3282 33 28 2751 2797 2843 2890 2937 2985 3033 3082 3131 3181 3231 3282 32 29 2752 2798 2844 2891 2938 2985 3034 3082 3132 3182 3232 3283 31 30 1.2753 1.2798 1.2845 1.2891 1.2939 1.2986 1.3034 1.3083 1.3132 1.3183 1.3233 1.3284 30 31 2753 2799 2845 2892 2939 2987 3035 3084 3133 3183 3234 3285 29 32 2754 2800 2846 2893 2940 2988 3036 3085 3134 3184 3235 3286 28 33 2755 2801 2847 2894 2941 2989 3037 3086 3135 3185 3236 3287 27 34 2756 2801 2848 2894 2942 2989 3038 3087 3136 3186 3236 3288 26 35 1.2756 1.2802 1.2848 1.2895 1.2942 1.2990 1.3039 1.3087 1.3137 1.3187 1.3237 1.3288 25 36 2757 2803 2849 2896 2943 2991 3039 3088 3138 3188 3238 3289 S4 37 2758 2804 2850 2897 2944 2992 3040 3089 3138 3188 3239 3290 23 38 2759 2805 2851 2898 2945 2993 3041 3090 3139 3189 3240 3291 22 39 40 2760 2805 2852 2898 2946 2993 3042 3091 3140 3190 3241 3292 21 1.27fi0 1,2806 1.2852 1.2899 1.2946 1.2994 1.3043 1.3091 1.3141 1.3191 1.3242 1.3293 20 41 2761 2807 2853 2900 2947 2995 3043 3092 3142 3192 3242 3294 19 42 2762 2808 2854 2901 2948 2996 3044 3093 3143 3193 3243 3294 18 43 2763 2808 2855 2901 2949' 2997 3045' 3094' 3143 3193 3244 3295 17 44 2763 2809 2855 2902 2950, 2;|Q7 3046 3095 3144, 3194 3245 3296 16 l.-) 1.2764 1.2810 1.2856 1.2903 1.2950 1.2998 1.3047 1.3096 1.3145 1.3195 1.3246 1.3297 15 46 2765 2811 2857 2904 2951 2999 3047 3096 3146 3196 3247 3298 14 47 2766 2811 2858 2905 2952 3000 3048 3097 3147 3197 3247 3299 13 48 2766 2812 2859 2905 2953 3001 3049 3098 3148 3198 3248 3200 12 49 2767 2813 2859 2906 2954 3001 3050 3099 3148 3198 3249 3200 11 50 1.2768 1.2814 1.2860 1.2907 1.2954 1.3002 1.3051 1.3100 1.3149 1.3199 1.3250 1.3301 10 51 2769 2815 2861 2908 2955 3003 3052 3101 3150 3200 3251 3302 9 52 2769 2815 2862 2909 2956 3004 3052 3101 3151 3201 3252 3303 8 53 2770 2816 2862 2909 2957 3005 3053 3102 3152 3202 3253 3304 7 54 2771 2817 2863 2910 2958 3005 3054 3103 .1153 3203 3253 3305 6 55 1.2772 1.2818 1.2864 1.2911 1.2958 1.3006 1.3055 1.3104 1.3153 1.3204 1.3254 1.3306 5 56 2772 2818 2865 2912 2959 3007 3056 ;no5 3154 3204 3255 3306 4 57 2773 2819 2866 2912 2960 3008 3056 3105 3155 3205 3256 3307 3 58 2774 2820 2866 2913 2961 3009 3057 3106 3156 , 3206 3257 33f8 2 59 2775 2821 2867 2914 2962 3009 3058 3107 3157 3207 3258 3309 1 60 2775 2821 2868 2915 2962 3010 3059 3108 3158 3208 3259 3310 35" 34' 33' 32' 1 31' 30' 29' 1 28' 27' 26' 25 1 24' S. 6 DfiG REES. Wl len the Apparent Distance is lets than 90°, the Second Correction U to be taken from the Bottom. 1 146 TABLE XXXII. LOGARITHMS OF THE FIRST AND SECOND CORRECTIONS. The Fin' Correction is always to b e taken from the Top, and also the Second, -when the Apparent Distance is greater than 90° 3 DEGREES. ' S. 36' 37' 38' 39' 40' 41' 42' 43' 44' 45' 46' 47' 60 1 3310 1.3362 1.3415 1.3468 1.3522 1.3576 1.3632 1.3688 1.3745 1.3802 1.3860 1.3919 1 3311 3363 3415 3469 3523 3577 3633 3689 3746 3803 3861 3920 59 • 2 3312 3364 3416 3470 3524 3578 3634 3690 3746 3804 3862 3921 58 3 3313 3365 3417 3471 3525 3579 3635 3691 3747 3805 3863 3922 57 4 3313 3365 3418 3471 3525 3580 3635 3692 3748 3806 3864 3023 56 5 1.3314 1.3366 1.3419 1.3472 1.3526 1.3581 1.3636 1.3693 1.3749 1.3807 1.3865 1.3924 55 6 3315 3367 3420 3473 3527 3582 3637 3694 3750 3808 3866 3925 54 7 3316 3368 3421 3474 3528 3583 3638 3695 3751 3809 3867 3926 53 8 3317 3369 3422 3475 3529 3584 3639 3695 3752 3810 3868 3927 52 9 3318 3370 3423 3476 3530 3585 3640 3696 3753 3811 3869 3928 51 10 1.3319 1.3371 1.3423 1.3477 1.3531 1.3586 1.3641 1.3697 1.3754 1.3812 1.3870 1.3929 50 11 3319 3372 3424 3478 3532 3587 3642 3698 3755 3813 3871 3930 49 12 3320 3372 3425 3479 3533 3587 3643 3699 3756 3814 3872 3931 48 13 3321 3373 3426 3480 3534 3588 3644 3700 3757 3815 3873 3932 47 14 15 3322 3374 3427 3480 3535 3589 3645 3701 3758 3816 3874 3933 46 1.3323 1.3375 1.3428 1.3481 1.3535 1.3590 1.3646 1.3702 1.3759 1.3817 1.3875 1.3934 45 16 3324 3376 3429 3482 3536 3591 3647 3703 3760 3818 3876 3935 44 17 3325 3377 3430 3483 3537 3592 3648 3704 3761 3819 3877 3936 43 18 3325 3378 3431 3484 3538 3593 3649 3705 3762 3819 3878 3937 42 19 3326 3379 3431 3485 3539 3594 3649 3706 3763 3820 3879 3938 41 40 20 1.3327 1.3379 1.3432 1.3486 1.3540 1.3595 1.3650 1.3707 1.3764 2.3821 1.3880 1.3939 21 3328 3380 3433 3487 3541 3596 3651 3708 3765 3822 3881 3940 39 22 3329 3381 3434 3488 3542 3597 3652 3709 3766 3823 3882 3941 38 23 3330 3382 3435 3488 3543 3598 3653 3709 3767 3824 3883 3942 37 24 3331 3383 3436 3489 3544 3598 3654 3710 3768 3825 3884 3943 36 25 1.3332 1.3384 1.3437 1.3490 1.3545 1.3599 1.3655 1.3711 1.3768 1.3826 1.3885 1.3944 35 26 3332 3385 3438 3491 3545 3600 3656 3712 3769 3827 3886 3945 34 27 3333 3386 3438 3492 3546 3601 3657 3713 3770 3828 3887 3946 33 28 3334 3386 3439 3493 3547 3602 3658 3714 3771 3829 3888 3947 32 29 30 3335 3387 3440 3494 3548 3603 3659 3715 3772 3830 3889 3948 31 1.3336 1.3388 1.3441 1.3495 1.3549 1.3604 1.3660 1.3716 1.3773 1.3831 1.3890 1.3949 30 31 3337 3389 3442 3496 3550 3605 3661 3717 3774 3832 3891 3950 29 32 3338 3390 3443 3497 3551 3606 3662 3718 3775 3833 3892 3951 28 33 3338 3391 3444 3498 3552 3607 3663 3719 3776 3834 3893 3952 27 34 333S 3392 3445 3499 3553 3608 3663 3720 3777 3835 3894 3953 26 35 1.3340 1.339a 1.3446 1.3500 1.3554 1.3609 1.3664 1.3721 1.3778 1.3836 1.3895 1.3954 25 36 3341 3393 3446 3501 3555 3610 3665 3722 3779 3837 3896 3955 24 37 3342 3394 3447 3502 3555 3610 3666 3723 3780 3838 3897 3956 23 38 3343 3395 3448 3503 3556 3611 3667 3724 3781 3839 3898 3957 22 39 3344 3396 3449 3504 3557 3612 3668 3725 3782 3840 3899 3958 21 40 1.3345 1.3397 1.3450 1.3505 1.3558 1.3613 1.3669 1.3726 1.3783 1.3841 1.3900 1.3959 20 41 3345 3398 3451 3506 3559 3614 3670 3727 3784 3842 3901 3960 19 ■ 42 3346 3399 3452 3506 3560 3615 3671 3727 3785 3843 3902 3961 18 43 3347 3400 3453 3507 3561 3616 3672 3728 3786 3844 3903 3962 17 44 3348 3400 3454 3508 3562 3617 3673 3729 3787 3845 3904 3963 16 15 45 1.3349 1.3401 1.3454 1.3509 1.3563 1.3618 1.3674 1.3730 1.3788 1.3846 1.3905 1.3964 46 3350 3402 3455 3510 3564 3619 3675 3731 3789 3847 3906 3965 14 47 3361 3M? 34.fi(i 35J 1 2.W^ 3620 3676 3732 3790 3848 3907 3966 13 48 3351 3404 3457 3512 3565 3621 3677 3733 3791 3849 3908 3967 12 49 3352 3405 3458 3513 3566 3622 3677 3734 3792 3850 3909 3968 11 50 1.3353 1.3406 1.3459 1.3513 1.3567 1.3623 1.3678 1.3735 1.3793 1.3851 1.3910 1.3969 10 51 3354 3407 3460 3514 3568 3623 3679 3736 3793 3852 3911 3970 9 52 3355 3408 3461 3515 3569 3624 3680 3737 3794 3853 3912 3971 8 53 3356 3408 3462 3516 3570 3625 3681 3738 3795 3854 3913 3972 7 54 55 3357 3409 3463 3516 3571 3626 3682 3739 3796 3855 3914 3973 6 1,3358 1.3410 1.3463 1.3517 1.3572 1.3627 1.3683 2,3740 1.3797 1.3856 1.3915 1.3974 5 56 3358 3411 3464 3518 3573 3628 3684 3741 3798 3856 3916 3975 4 57 3359 3412 3465 3519 3574 3629 3685 3742 3799 3857 3917 3976 3 58 3360 3413 3466 3520 3575 3630 3686 3743 3800 3858 3918 3977 2 59 3361 3414 3467 3521 3576 3631 3687 3744 3801 3859 3919 39V8 1 60 3362 3415 3468 3522 3576 3632 3688 3745 3802 3860 3919 3979 23' 22' 21' 20' 19' IS' 17' I 16' 1 15' 1 41' i 13' 12' s. 6 DEGREES. ■m an the Apparent I istance ie less than 90°, the Second Correction is to be taken from the Botto 1 TABLE XXXII. 147 1 LOGARITHMS OF THE FIRST AND SECOND CORRECTIONS. 1 90°. rhe First Correction ia attoays to be taken from the Top, and also the Second, when the Apparent Distance la greater thai 3 DEGREES. 1 S. 48' 49' 50' 51' 52' 53' 54' 55- 56' 57' 58' 59' 1.3979 1.4040 1.4102 1.4164 1.4228 1.4292 1.4357 1.4424 1.4491 1.4559 1.4629 1.4699 60 1 3980 4041 4103 4165 4229 4293 4358 4425 4492 4560 4630 4701 59 2 3981 4042 4104 4166 4230 4294 4359 4426 4493 4562 4631 4702 68 3 3982 4043 4105 4167 4231 4295 4361 4427 4494 4563 4632 4703 57 4 3983 4044 4106 4168 4232 4296 4362 4428 4495 4564 4633 4704 56 5 1.3984 1.4045 1.4107 1 4169 1.4233 1.4297 1.4363 1.4429 1.4497 1.4565 1.4635 1.4705 55 6 3985 4046 4108 4171 4234 4298 4364 4430 4498 4566 4636 4707 54 3986 4047 4109 4172 4235 4300 4365 4431 4499 4567 4637 4708 53 8 3987 4048 4110 4173 4236 4301 4366 4433 4500 4569 4638 4709 52 9 3988 4049 4111 4174 4237 4302 4367 4434 4501 4570 4639 4710 51 10 1.3989 1.4050 1.4112 1.4175 1.4238 1.4303 1.4368 1.4435 1.4502 1.4571 1.4640 1.4711 50 11 3990 4051 4113 4176 4239 4304 4369 4436 4503 4572 4642 4712 49 12 3991 4052 4114 4177 4240 4305 4370 4437 4504 4573 4643 4714 48 13 3992 4053 4115 4178 4241 4306 4372 4438 4506 4574 4644 4715 47 14 3993 4054 4116 4179 4243 4307 4373 4439 4507 4575 4645 4716 46 15 1.3995 1.4055 1.4117 1.4180 1.4244 1.4308 1.4374 1.4440 1.4508 1.4577 1.4646 1.4717 45 16 3996 4056 4118 4181 4245 4309 4375 4441 4509 4578 4648 4718 44 17 3997 4058 4119 4182 4246 4310 4376 4443 4510 4579 4649 4720 43 18 3998 4059 4120 4183 4247 4311 4377 4444 4511 4580 4650 4721 42 19 3999 4060 4121 4184 4248 4313 4378 4445 4512 4581 4651 4722 41 20 1.4000 1.4061 1.4122 1.4185 1.4249 1.4314 1.4379 1.4446 1.4514 2.4582 1.4652 1.4723 40 21 4001 4062 4124 4186 4250 4315 4380 4447 4515 4584 4653 4724 39 22 4002 4063 4125 4187 4251 4316 4381 4448 4516 4585 4655 4726 !}8 23 4003 4064 4126 4188 4252 4317 4383 4449 4517 4586 4656 4727 37 24 4004 4065 4127 4189 4253 4318 4384 4450 4518 4587 4657 4728 36 25 1.4005 1.4066 1.4128 1.4191 1.4254 1.4319 1.4385 1.4452 1.4519 1.4588 1.4658 1.4729 35 26 4006 4067 4129 4192 4255 4320 4386 4453 4520 4589 4659 "4730 34 27 4007 4068 4130 4193 4256 4321 4387 4454 4522 4590 4660 4732 33 28 4008 4069 4131 4194 4258 4322 4388 4455 4523 4592 4662 47R3 32 29 4009 4070 4132 4195 4259 4323 4389 4456 4524 4593 4663 4734 31 30 1 .4010 1.4071 1.4133 1.4196 1.4260 1.4325 1.4390 1.4457 1.4525 1.4594 1.4664 1.4735 30 31 4011 4072 4134 4197 4261 4326 4391 4458 4526 4595 4665 4736 29 32 4012 4073 4135 4198 4262 4327 4393 4459 4527 4596 4666 4737 28 33 4013 4074 4136 4199 4263 4328 4394 4460 4528 4597 4668 4739 27 34 4014 4075 4137 4200 4264 4329 4395 4462 4530 4599 4669 4740 26 35 1.4015 1.4076 1.4138 1.4201 1.4265 1.4330 1.4396 1.4463 1.4531 1.4600 1.4670 1.47A1. 25 36 4016 4077 4139 4202 4266 4331 4397 4464 4532 4601 4671 4742 24 37 4017 4078 4140 4203 4267 4332 4398 4465 4533 4602 4672 4744 23 38 4018 4079 4141 4204 4268 4333 4399 4466 4534 4603 4673 4745 22 39 4019 4080 4142 4205 4269 4334 4400 4467 4535 4604 4675 4746 21 40 1.4020 1.4081 1.4143 1.4206 1.4270 1.4335 1.4401 1.4468 1.4536 1.4606 1.4676 1.4747 20 41 4021 4082 4144 4207 4271 4336 4402 4469 4538 4607 4677 4748 19 42 4022 4083 4145 4209 4273 4338 4404 4471 4539 4608 4678 4750 18 43 4023 4084 4146 4210 4274 4339 4405 4472 4540 4609 4679 4751 17 44 4024 4085 4147 4211 4275 4340 4406 4473 4541 4610 4680 4752 16 15 45 1.4025 1.408b 1.4149 1.4212 1.4276 1.4341 1.4407 1.4474 1.4542 1.4611 1.4682 1.4753 46 4026 4087 4150 4213 4277 4342 4408 4475 4543 4612 4683 4754 14 47 4027 4088 4151 4214 4278 4343 4409 4476 4544 4614 4684 4756 13 48 4028 4089 4152 4215 4279 4344 4410 4477 4546 4615 4685 4757 12 49 4U29 4090 4153 4216 4280 4345 4411 4479 4547 4616 4686 4758 11 50 1.403(. 1 .4'J91 1.4154 1.4217 1.4281 1.4346 1.4412 1.4480 1.4548 1,4617 1.4688 1.4759 10 51 4031 4092 4155 4218 4282 4347 4414 4481 4549 4618 4689 4760 9 52 403ii 4093 4156 4219 4283 4349 4415 4482 4550 4619 4690 4762 8 53 4033 4095 4157 4220 4284 4350 4416 4483 4551 4621 4691 4763 7 54 55 403^ 409h 4158 4221 4285 4351 4417 4484 4552 4622 4692 4764 6 1.403c 1.4097 1.4159 1.4222 1.4287 1.4352 1.4418 1.4485 1.4554 1.4623 1.4693 1.4765 5 n6 403(. 4098 4160 4223 4288 4353 4419 4486 4555 4624 4695 4766 4 57 4037 4099 4161 4224 4289 4354 442C 4488 ! 4556 4625 4696 4768 3 58 403i^ i 410C 416-2 4226 4290 4355 4421 448S 4557 4626 4697 4769 2 59 403ir 4101 4163 4227 4291 4356 4422 449C 4558 4628 4698 4770 1 60 404C ) 4102 4164 4228 4292 4357 4424 4491 4559 4629 4699 4771 u' 10' 9' 8' 1 7' 6' 5' 1 4' 3' 2 1' 0' S. 6 DEGREES. "Whea the Apparent Distance Is less than 90°, the Second Correction is to be taken from the Bottom. 148 TABLE XXXII. LOGARITHMS OF THE FIRST AND SECOND CORRECTIONS. ) The Pint Correction is always to be taken from the Top, and also the Second, when the Apparent Distance is greater than 90" . 4 DEGREES. s. 0' 1' 2' 3' 4' 5' 6' 7' 8' 9' 10' 11' 60 1.4771 1.4844 1.4918 1.4994 1.5071 1.5149 1.5229 1.5310 1.5393 1.5477 1.5563 1.5651 1 4772 4845 4920 4995 5072 5150 5230 5311 5394 5478 5564 5652 59 2 4774 4847 4921 4997 5073 5152 5231 5313 5395 5480 5566 5654 58 3 4775 4848 4922 4998 5075 5153 5233 5314 5397 5481 5567 5655 57 4 4776 4849 4923 4999 5076 5154 5234 5315 5398 5483 5569 5657 56 55 5 1.4777 1.4850 1.4925 1.5000 1.5077 1.5156 1.5235 1.5317 1.5400 1.5484 1.5570 1.5658 ' 6 4778 4852 4926 5002 5079 5157 5237 5318 5401 5486 5572 5660 54 7 4780 4853 4927 5003 5080 5158 5238 5320 5402 5487 5573 5661 63 8 4781 4854 4928 5004 5081 5160 5240 5321 5404 5488 5575 5663 52 9 4782 4855 4930 5005 5082 5161 5241 5322 5405 5490 5576 5664 51 10 1.4783 1.4856 1.4931 1.5007 1.5084 1.5162 1.5242 1.5324 1.5407 1.5491 1.5578 1.5666 50 11 4785 4858 4932 5008 5085 5164 5244 5325 5408 5493 5579 5667 49 12 4786 4859 4933 5009 5086 5165 5245 5326 5409 5494 5580 5669 48 13 4787 4860 4935 5011 5088 5166 5246 5328 5411 5496 5582 5670 47 14 4788 4861 4936 5012 5089 5168 5248 5329 5412 5497 5583 5671 46 15 1.4789 1.4863 1.4937 1.5013 1.5090 1.5169 1.5249 1.5331 1.5414 1.5498 1.5585 1.5673 45 1 16 4791 4864 4938 5014 5092 5170 5250 5332 5415 5500 5586 5674 44 17 4792 4865 4940 5016 5093 5172 5252 5333 5416 5501 5588 5676 43 18 4793 4866 4941 5017 5094 5173 5253 5335 5418 5503 5589 5677 42 19 4794 4868 4942 5018 5095 5174 5254 5336 5419 5504 5591 5679 41 20 1.4795 1.4869 1.4943 1.5019 1.5097 1.5175 1.5256 1.5337 1.5421 1.5506 1.5592 1.5680 40 21 4797 4870 4945 5021 5098 5177 5257 5339 5422 5507 5594 5682 39 22 4798 4871 4946 5022 5099 5178 5258 5340 5423 5508 5595 5683 38 23 4799 4873 4947 5023 5101 5179 5260 5341 5425 5510 5596 5685 37 24 4800 4874 4949 5025 5102 5181 5261 5343 5426 5511 5598 5686 36 25 1.4801 1.4875 1.4950 1.5026 1.5103 1.5182 1.5262 1.5344 1.5428 1.5513 1.5599 1.5688 35 26 4803 4876 4951 5027 5105 5183 5264 5346 5429 5514 5601 5689 34 27 4804 4877 4952 5028 5106 5185 5265 5347 5430 5516 5602 5691 33 28 4805 4879 4954 5030 5107 5186 5266 5348 5432 5517 5604 5692 32 29 4806 4880 4955 5031 5108 5187 5268 5350 5433 5518 5605 5694 31 30 1.4808 1.4881 1.4956 1.5032 1.5110 1.5189 1.5269 1.5351 1.5435 1.5520 1.5607 1.5695 30 31 4809 4882 4957 5034 5111 5190 5271 5353 5436 5521 5608 5697 29 32 4810 4884 4959 5035 5112 5191 5272 5354 5437 5522 5610 5698 28 33 4811 4885 4960 5036 5114 5193 5273 5355 5439 5524 5611 5700 27 34 4812 4886 4961 5037 5115 5194 5275 5357 5440 5526 5613 5701 26 35 1.4814 1.4887 1.4962 1.5039 1.5116 1.5195 1.5276 1.5358 1.5442 1.5527 1.5614 1.5703 25 36 4815 4889 4964 5040 5118 5197 5277 5359 5443 5528 5615 5704 24 37 4816 4890 4965 5041 5119 5198 5279 5361 5445 5530 5617 5706 23 38 4817 4891 4966 5043 5120 5199 5280 5362 5446 5531 5618 5707 22 39 4819 4892 4967 5044 5122 5200 5281 5364 5447 5533 5620 5709 21 40 1.4820 1.4894 1.4969 1.5045 1.5123 1.5202 1.5283 1.5365 1.5449 1.5534 1.5621 1.5710 20 41 4821 4895 4970 5046 5124 5203 5284 5366 5450 5536 5623 5712 19 42 4822 4896 4971 5048 5125 5205 5285 5368 5452 5537 5624 5713 18 43 4823 4897 4972 5049 5127 5206 5287 5369 5453 5538 5626 5715 17 44 4825 4899 4974 5050 5128 5207 5288 5370 5454 5540 5627 5716 16 45 1.4826 1.4900 1.4975 1.5051 1.5129 1.5209 1.5290 1.5372 1.5456 1.5541 1.5629 1.5718 15 46 4827 4901 4976 5053 5131 5210 5291 5373 5457 5543 5630 5719 14 47 4828 4902 4977 5054 5132 5211 5292 5375 5459 5544 5632 5721 13 48 4830 4903 4979 5055 5133 5213 5294 5376 5460 5546 5633 5722 12 49 4831 4905 4980 5057 5135 5214 5295 5377 5461 5547 5635 5724 11 50 1.4832 1.4906 1.4981 1.5058 1.5136 1.5215 1.5296 1.5379 1.5463 1.5549 1.5636 1.5725 10 51 4833 4907 4983 5059 5137 5217 5298 5380 5464 5550 5637 5727 9 52 4834 4908 4984 5061 5139 5218 5299 5382 5466 5551 5639 5728 8 53 4836 4910 4985 5062 5140 5219 5300 5383 5467 5553 5640 5730 7 54 4837 4911 4986 5063 5141 5221 5302 5384 5469 5554 5642 5731 6 55 1.4838 1.4912 1.4988 1.5064 1.5143 1.5222 1.5303 1.5386 1.5470 1.5556 1.5643 1.5733 5 56 4339 4913 4989 5066 5144 5223 5305 5387 5471 5557 5645 5734 4 57 4841 4915 4990 5067 5145 5225 5306 5389 5473 5559 5646 5736 3 58 4842 4916 4991 5068 5146 5226 5307 5390 5474 5560 5648 5737 2 59 4843 4917 4992 5070 5148 5227 5309 5391 5476 5562 5649 5739 1 60 4844 4918 4994 5071 5149 5229 5310/ 5393 5477 5563 5651 5740 59' 58' 1 57' 56' 55' 54' 53' 52' 51' | 50' 49' 48' s. S DEGREES. Wl len the Apparent Distance \»leti than 90", the Second Correction is to be taken from the Botto - 1 TABLE XXXll. 149 LOGARITHMS OF THE FIRST AND SECOND CORRECTIONS. 1 k^ First Correotion is always to be taken from the Top, and also the Second, when the Apparent Distance is greater than 90° 1 4 DE0KEE3. 1 12' 13' 14' 15' 16' 17' 18' 19' 20' 21' 22' 23' 60 1.5740 1.58321.5925 1.6021 1.6118,1.6218 1.6320 1.6425 1.6532 1.6642 1.6755 1.6871 1 5742 5833 5927 6022 6120^ 6220' 6322 6427 6534 6644 6757 6873 59 .> 5743 5835 5928 6024 6121 6221 6324| 6428 6536 6646 6759 6875 58 3 5745 5836 5930 6025 0123 6223 6325 6430 6538 6648 6761 6877 57 4 5746 5838 5931 6027 6125 6225 6827 6432 6539 6650 6763 6879 56 5 1.5748 1.5839 1.5933 1.6029 1.6126 1.6226 1.6329 1.6434 1.6541 1.6651 1.6764 1.6881 55 t) 5749 5841 5935 6030 6128 6228 6331 6435 6543 6653 6766 6882 54 1 5751 5843 5936 6032 6130 6230 6332 6437 6545 6655 6768 6884 53 8 5752 5844 5938 6033 6131 6232 6334 6439 6547 6657 6770 6886 52 9 5754 5846 5939 6035 6133 6233 6336 6441 6548 6659 6772 6888 51 10 1.5755 1.5847 1.5941 1.6037 1.6135 1.6235 1.6338 1.6443 1.6550 1.6661 1.6774 1.6890 50 11 5757 5849 5942 6038 6136 6237 6339 6444 6552 6663 6776 6892 49 12 5758 5850 5944 6040 6138 6238 6341 6446 6554 6664 6778 6894 48 13 5760 5852 5946 6042 6140 6240 6343 6448 6556 6666 6780 6896 47 14 5761 5853 5947 6043 6141 6242 6344 6450 6558 6668 6782 6898 46 15 1.5763 1.5855 1.5949 1.6045 1.6143 1.6243 1.6346 1.6451 1.6559 1.6670 1.6784 1.6900 45 16 5765 5856 5950 6046 6145 6245 6348 6453 6561 6672 6785 6902 44 17 5766 5858 5952 6048 6146 6247 6350 6455 6563 6674 6787 6904 43 18 5768 5860 5954 6050 6148 6248 6351 6457 6565 6676 6789 6906 42 19 5769 5861 5955 6051 6150 6250 6353 6459 6567 6677 6791 6908 41 20 1.5771 1.5863 1.5957 1.6053 1.6151 1.6252 1.6355 1.6460 1.6568 1.6679 1.6793 1.6910 40 ■n 5772 5864 5958 6055 6153 6254 6357 6462 6570 6681 6795 6912 39 i-Z 5774 5866 5960 6056 6155 6255 6358 6464 6572 6683 6797 6914 38 23 5775 5867 596r 6058 6156 6257 6360 6466 6574 6685 6799 6916 37 U 25 5777 5869 5963 6059 6158 6259 6362 6467 6576 6687 6801 6918 36 1.5778 1.5870 1.5965 1.6061 1.6160 1.6260 1.6364 1.6469 1.6578 1.6689 1.6803 1.6920 35 26 5780 5872 5966 6063 6161 6262 6365 647V 8579 6691 6805 6922 34 27 5781 5874 5968 6064 6163 6264 6367 6472il 6581 6692 6807 6924 33 28 5783 5875 5969 6066 6165 6265 6369 6475 6583 6694 6809 6926 32 29 5784 5877 5971 6067 6166 6267 6371, 6476 6585 6696 6810 6928 31 30 1.5786 1.5878 1.5973 1.6069 1.6168 1.6269 1.6372 1.6478 1.6587 1.6698 1.6812 1.6930 30 31 5787 5880 5974 6071 6169 6271 6374 6480 6589 6700 6814 6932 29 32 5789 5881 5976 6072 6171 6272 6376 6482 6590 6702 6816 6934 28 33 5790 5883 5977 6074 6173 6274 6377 6484 6592 6704 6818 6936 27 34 5792 5884 5979 6076 6174 6276 6379 6485 6594 6706 6820 6938 26 35 1.5793 1.5886 1.5981 1.6077 1.6176 1.6277 1.6381 1.6487 1.6596 1.6708 1.6822 1.6940 25 36 5795 5888 5982 6079 6178 6279 6383 6489 6598 6709 6824 6942 24 37 5796 5889 5984 6081 6179 6281 6384 6491 6600 6711 6826 6944 23 38 5798 5891 5985 6082 6181 6282 6386 6492 6601 6713 6828 6946 22 39 5800 5892 5987 6084 6183 6284 6388 6494 6603 6715 6830 6948 21 10 1.5801 1.5894 1.5989 1.6085 1.6185 1.6286 1.6390 1.6496 1.6605 1.6717 1.6832 1.6950 20 11 5803 5895 5990 6087 6186 6288 6391 6498 6607 6719 6834 6952 19 42 5804 5897 5992 6089 6188 6289 6393 6500 6609 6721 6836 6954 18 13 5806 5898 5993 6090 6190 6291 6395 6501 6611 6723 6838 6956 17 14 5807 5900 5995 6092 6191 6293 6397 6503 6612 6725 6840 6958 16 .45 1.5809 1.6902 1.5997 1.6094 1.6193 1.6294 1.6398 1.6505 1.6614 1.6726 1.6841 1.696*0 15 46 5810 5903 5998 6095 6195 6296 6400 6507 6616 6728 6843 6962 14 47 5812 5905 6000 6097 6196 6298 6402 6509 6618 6730 6845 6964 13 48 5813 5906 6001 6099 6198 6300 6404 6510 6620 6732 6847 6966 12 49 5815 5908 6003 6100 6200 6301 6406 6512 6622 6734 6849 6968 11 50 1.5? 16 1.5909 1.6005 1.6102 1.6201 1.6303 1.6407 1.6514 1.6624 1.6736 1.6851 1.6970 10 51 5818 5911 6006 6103 6203 6305 6409 6516 6625 6738 6853' 6972 9 52 5819 5913 6008 6105 6205 6306 6411 6518 6627 6740 6855 6974 8 53 5821 5914 6009 6107 6206 6308 6413 6519 6629 6742 HH.'iT 6976 7 54 5823 5916 6011 6108 6208 6310 6414 6521 6631 6743 6859 6978 6 55 1.5824 1.5917 1.6013 1.6110 1.6210 1.6312 1.6416 1.6523 1.6633 1.6745 1.68611 6980 5 56 5826 5919 6014 6112 6211 6313 6418 6525 6635 6747 6863 6982 4 57 5827 5920 6016 6113 6213 6315 6420 6527 6637 6749 6865 6984 3 58 5829 5922 6017 6115 6215 6317 6421 6529 6638 6751 6867, 6986 2 59 5830 5924 6019 6117 6216 6319 6423 6530 6640 6753 6869 6988 1 60 5832 5925 6021 6118 6218 6320 6425 6532 6642 6755 6871 6990 47' 46' 1 45' 44' 1 43' 42' 41' 1 40' 1 39' 38' 37' 36' S. - 6 DEGREES. When the Apparent Distance ialess than 90°, the Second Correction is to be taken from the Bottom. 150 TABLE XXXII. LOGARITHMS OF THE FIRST AND SECOND CORRECTIONS. Tt» First Correction i» aitoays to be taken from the Top, and also the Second, when the Apparent Distance itgrcattr than 90O.| 4 DEGREES. 1 S. 24' 25' 26' 27' 28' 29' 30' 31' 32' 33' 34' 35' 1.6990 1.7112 1.7238 1.7368 1.7501 1.7639 1.7782 1.7929 1.8081 1.8239 1.8403 1.8573 60 1 6992 7114 7240 7370 7503 7641 7784 7931 8084 8242 8406 8576 59 2 6994 7116 7242 7372 7506 7644 7786 7934 8O186 8244 8409 8579 58 3 6996 7118 7244 7374 7508 7646 r789 7936 8089 8247 8411 8582 57 4 6998 7120 7246 7376 7510 7648 7791 7939 8091 8250 8414 8583 56 5 1.7000 1.7122 1.7249 1.7379 1.7513 1.7651 1.7794 1.7941 1.8094 1.8253 1.8417 1.8588 55 6 7002 7124 7251 7381 7515 7653 7796 7944 8097 8255 8420 8591 64 7 7004 7127 2253 7383 7517 7655 7798 7946 8099 8258 8423 8594 53 8 7006 7129 7255 7385 7519 7658 7801 7949 8102 8261 8425 8597 52 9 7008 7131 7257 7387 7522 7660 7803 7951 8104 8263 8428 8599 51 10 1.7010 1.7133 1.7259 1.7390 1.7524 1.7663 1.7806 1.7954 1 .8107 1.8266 1.8431 1.8602 50 11 7012 7135 7261 7392 7526 7665 7808 7956 8110 8269 8434 8605 49 12 7014 7137 7264 7394 7528 7667 7811 7959 8112 8271 8437 8608 48 13 7016 7139 7266 7396 7531 7670 7813 7961 8115 8274 8439 8611 47 14 15 7018 7141 7268 7398 7533 7672 7815 7964 8117 8277 8442 8614 46 1.7020 1.7143 1.7270 1.7401 1.7535 1.7674 1.7818 1.7966 1.8120 1.8279 1.8445 1.8617 45 16 7022 7145 7272 7403 7538 7677 7820 7969 8123 8282 8448 8620 44 17 7024 7147 7274 7405 7540 7679 7823 7971 8125 8285 8451 8623 43 18 7026 7149 7276 7407 7542 7681 7825 7974 8128 8288 8453 8626 42 19 7028 7152 7279 7409 7544 7684 7828 7976 8131 8290 8456 8629 41 40 20 1.7030 1.7154 1.7281 1.7412 1.7547 1.7686 1.7830 1.7979 1.8133 1.8293 1.8459 1.8632 21 7032 7156 7283 7414 7549 7688 7832 7981 8136 8296 8462 8635 39 22 7034 7158 7285 7416 7551 7691 7835 7984 8138 8298 8465 8637 38 23 7036 7160 7287 7418 7554 7693 7837 7987 8141 8301 8467 8640 37 24 7038 7162 7289 7421 7556 7696 7840 7989 8144 8304 8470 8643 36 25 1.7040 1.7164 1.7291 1.7423 1.7558 1.7698 1.7842 1.7992 1.8146 1.8307 1.8473 1.8646 35 26 7042 7166 7294 7425 7560 7700 7845 7994 8149 8309 8476 8649 34 27 7044 7168 7296 7427 7563 7703 7847 7997 8152 8312 8479 8652 33 28 7046 7170 7298 7429 7565 7705 7850 7999 8154 8315 8482 8655 32 29 30 7048 7172 7300 7432 7567 7707 7852 8002 8157 8318 8484 8658 31 1.7050 1.7175 1.7302 1.7434 1.7570 1.7710 1.7855 1.8004 1.8159 1.8320 1 8487 1.8661 30 31 7052 7177 7304 7436 7572 7712 7857 8007 8162 8323 8490 8664 29 32 7055 7179 7307 7438 7574 7714 7859 8009 8165 8326 8493 8667 28 33 7057 7181 7309 7441 7576 7717 7862 8012 8167 8328 8496 8670 27 34 35 7059 7183 7311 7443 7579 7719 7864 8014 8170 8331 8499 8673 26 1.7061 1.7185 1.7313 1.7445 1.7581 1.7722 1.7867 1.8017 1.8173 1.8334 1.8502 1.8676 25 36 7063 7187 7315 7447 7583 7724 7869 8020 8175 8337 8504 8679 24 37 7065 7189 7317 7450 7586 7726 7872 8022 8178 8339 8507 8682 23 38 7067 7191 7320 7452 7588 7729 7874 8025 8181 8342 8510 8685 22 39 7069 7193 7322 7454 7590 7731 7877 8027 8183 8345 8513 8688 21 40 1.7071 1.7196 1.7324 1.7456 1.7593 1.7734 1.7879 1.8030 1.8186 1.8348 1.8516 1.8691 20 41 7073 7198 7326 7458 7595 7736 7882 8032 8188 8350 8519 8694 19 42 7075 7200 7328 7461 7597 7738 7884 8035 8191 8353 8522 8697 18 43 7077 7202 7330 7463 7600 7741 7887 8037 8194 8356 8524 8700 17 44 7079 7204 7333 7465 7602 7743 7889 8040 8196 8359 8527 8703 16 15 45 1.7081 1.7206 1.7335 1.7467 1.7604 1.7745 1.7891 1.8043 1.8199 1.8361 1.8530 1.8706 46 7083 7208 7337 7470 7607 7748 7894 8045 8202 8364 8533 8709 14 47 7085 7210 7339 7472 7609 7750 7896 8048 8204 8367 8536 8712 13 48 7087 7212 7341 4774 7611 7753 7899 8050 8207 8370 8539 8715 12 49 7089 7215 7344 7476 7613 7755 7901 8053 8210 8372 8542 8718 11 50 1.7091 1.7217 1.7346 1.7479 1.7616 1.7758 1.7904 1.8055 1.8212 1.8375 1.8544 1.8721 10 51 7093 7219 7348 7481 7618 7760 7906 8058 8215 8378 8547 8724 9 52 7096 7221 7350 7483 7620 7762 7909 8061 8218 8381 8550 8727 8 53 7098 7223 7352 7485 7623 7765 7911 8063 8220 8384 8553 8730 7 54 7100 7225 7354 7488 7625 7767 7914 8066 8223 8386 8556 8733 6 5 55 1.7102 1.7227 1.7357 1.7490 1.7627 1.7769 1.7916 1.8068 1.8226 1.8389 1.8559 1.8736 56 7104 7229 7359 7492 7630 7772 7919 8071 8228 8392 8562 8739 4 57 7106 7232 7361 7494 7632 7774 7921 8073 8231 8395 8565 8742 3 58 7108 7234 6363 7497 7634 7777 7924 8076 8234 8397 8568 8745 2 59 7110 7236 7365 7499 7637 7779 7926 8079 8236 8400 8570 8748 1 60 1 7112 7238 7368 7501 7639 7782 7929 8081 8239 8403 8573 8751 35 1 34' 33' 32' 1 31' 30' 29' 28' 27' 26' 25' 24' S. 5 DEGREES. 1 ^^ Wl hen the Apparent Distance is less thai 1 9llO, the Second C orrection ii to be taken from the Bottom. 1 TABLE XXXll. 151 LOGARITHMS OF THE FIRST AND SECOND CORRECTIONS. Th« Firit OoRMtion is always to be taken from ihe Top, and also the Second, when the Apparent Distance ii greater than 90" -1 4 DEGKEES. 1 S. 36' 37' 38' 39' 40' 41' 42' 43' 44' 45' 46' 47' 60 1.8751 1.8935 1.9128 1.9331 1.9542 1.9765 2.0000 2.0248 2.0512 2.0792 2.1091 2.1413 1 8754 8939 9132 9334 9546 9769 0004 0252 0516 0797 1097 1419 59 2 8757 8942 9135 9337 9550 9773 0008 0257 0521 0801 1102 1424 58 3 8760 8945 9138 9341 9553 9777 0012 0261 0525 0806 1107 1430 57 4 8763 8948 9142 9344 9557 9780 0016 0265 0530 0811 1112 1436 56 5 1.8766 1.8951 1.9145 1.9348 1.9561 1.9784 2.00^0 2.0270 2.0534 2.0816 2.1117 2.1441 55 6 8769 8954 9148 9351 9564 9788 0024 0274 0539 0821 1123 1447 54 7 8772 8958 9152 9355 9568 9792 0028 0278 0543 0826 1128 1452 53 8 8775 8961 9155 9358 9571 9796 0032 0282 0548 0831 1133 1458 52 9 10 8778 8964 9158 9362 9575 9800 0036 0287 0552 0835 1138 1464 51 1.8781 1.8967 1.9162 1.9365 1.9579 1.9803 2.0040 2.0291 2.0557 2.0840 2.1143 2.1469 50 11 8784 8970 9165 9369 9582 9807 0044 0295 0562 0845 1149 1475 49 12 8787 8973 9168 9372 9586 9811 0049 0300 0566 0850 1154 1481 48 13 8790 8977 9172 9376 9590 9815 0053 0304 0571 0855 1159 1486 47 14 8793 8980 9175 9379 9593 9819 0057 0308 0575 0860 1164 1492 46 15 1.8796 1.8983 1.9178 1.9383 1.9597 1.9823 2.0061 2.0313 2.0580 2.0865 2.1170 2.1498 45 16 8799 8986 9181 9386 9601 9827 0065 0317 0585 0870 1175 1503 44 17 8802 8989 9185 939.0 9604 9830 0069 0321 0589 0875 1180 1509 43 18 8805 8992 9188 9393 9608 9834 0073 0326 0594 0880 1186 1515 42 19 8808 8996 9191 9397 9612 9838 0077 0330 0598 0884 1191 1520 41 20 1.8811 1.8999 1.9195 1.9400 1.9615 1.9842 2.0081 2.0334 2.0603 2.0889 2.1196 Sf.l526 40 21 8814 9002 9198 9404 9619 9846 0085 0339 0608 0894 1201 1532 39 22 8817 9005 9201 9407 9623 9850 0089 0343 0612 0899 1207 1538 38 23 8821 9008 9205 9411 9626 9854 0093 0347 0617 0904 1212 1543 37 24 8824 9012 9208 9414 9630 9858 0098 0352 0621 0909 1217 1549 36 35 25 1.8827 1.9015 1.9212 1.9418 1.9634 1.9861 2.0102 2.0356 2.0626 2.0914 2.1223 2.1555 26 8830 9018 9215 9421 9638 9865 0106 0360 0631 0919 1228 1561 34 27 8833 9021 9218 9425 9641 9869; 0110 0365 0635 0924 1233 1566 33 28 8836 9024 9222 9428 9645 9873 01141 0369 0640 0929 1239 1572 32 29 8839 9028 9225 9432 9649 9877 0118 0374 0645 0934 1244 1578 31 30 1.8842 1.9031 1.9228 1.9435 1.9652 1.9881 2.0122 2.0378 2.0649 2.0939 2.1249 2.1584 30 31 8845 9034 9232 9439 9656 9885 0126 0382 0654 0944 1255 1589 29 32 8848 9037 9235 9442 9660 9889 0131 0387 0659 0949 1260 1595 28 33 8851 9041 9238 9446 9664 9893 0135 0391 0663 0954 1266 1601 27 34 35 8854 9044 9242 9449 9667 9897 0139 0395 0668 0959 1271 1607 26 25 1.8857 1.9047 1.9245 1.9453 1.9671 1.9901 2.0143 2.0400 2.0673 2.0964 2.1276 2.1613 36 8861 9050 9249 9456 9675 9905 0147 0404 0678 0969 1282 1619 24 37 8864 9053 9252 9460 9678 9908 0151 0409 0682 0974 1287 1624 23 38 8867 9057 9255 9464 9682 9912 0156 0413 0687 0979 1292 1630 22 39 8870 9060 9259 9467 9686 9916 0160 0418 0692 0984 1298 1636 21 40 1.8873 1.9063 1.9262 1.9471 1.9690 1.9920 2.0164 2.0422 2.0696 2.0989 2.1303 2.1642 20 41 8876 9066 9266 9474 9693 9924 0168 0426 0701 0994 1309 1648 19 42 8879 9070 9269 9478 9697 9928 0172 0431 0706 0999 1314 1654 18 43 8882 9073 9272 9481 9701 9932 0176 0435 0711 1004 1320 1660 17 44 8885 9076 9276 9485 9705 9936 0181 0440 0715 1009 1325 1665 16 15 45 1.8888 1.9079 1.9279 1.9488 1.9708 1.9940 2.0185 2.0444 2.0720 2.1015 2.1331 2.1671 46 8892 9083 9283 9492 9712 9944 0189 0449 0725 1020 1336 1677 14 47 8895 9086 9286 9496 9716 9948 0193 0453 0730 1025 1342 1683 13 48 8898 9089 9289 9499 9720 9952 0197 0458 0734 1030 1347 1689 12 49 8901 9092 9293 9503 9723 9956 0202 0462 0739 1035 1352 1695 11 50 1.8904 1.9096 1.9296 1.9506 1.9727 1.9960 2.0206 2.0467 2.0744 2.1040 2.1358 2.1701 10 51 8907 9099 9300 9510 9731 9964 0210 0471 0749 1045 1363 1707 9 52 8910 9102 9303 9514 9735 9968 0214 0475 0753 1050 1369 1713 8 53 8913 9106 9306 9517 9739 9972 0219 0480 0758 1055 1374 1719 7 54 8917 9109 9310 9521 9742 9976 0223 0484 0763 1061 13«0 1725 6 5 55 1.8920 1.9112 1.9313 1.9524 1.9746 1.9980 2.0227 2.0489 2.0768 2.1066 2.13vti 2.1731 56 8923 9115 9317 9528 9750 9984 0231 0493 0773 1071 13 ill 1737 4 57 8926 9119 9320 9532 9754 9988 0235 0498 0777 1076 1397 1743 3 58 8929 9122 9324 9535 9758 9992 0240 0502 0782 1081 1402 1749 2 59 8932 9125 9327 9539 9761 9996 0244 0507 0787 1086 1408 1755 1 60 8935 9128 9331 9542 9765 2.0000 0248 0512 0792 1091 1413 1761 23' 22' 1 21' 20' 19' 18' 17' 16' 15' 14' 13' 12' S. 5 DEGREES. Wl lien the Apparent Distance is lets than 90", the Second Correction is to be taken from the Botto » 1 J 52 TABLE XXXII. \ LOGARITHMS OF THE FIRST AND SI XOND ond, whe CORRECTIONS. | Ih* Fint Correction it alieays to be taken from the Top, and also the Sec a the Apparent Distance is greater than OOO.f 4 DEGREES. \ S. 48' 49' 50' 51' 52' 53' 54' 55' 56' 57' 58' 69' 2.1761 2.2139 2.2553 2.3010 2.3522 2.4102 2.4771 2.5563 2.6532 2.7782 2.9542 3.2553 60 1 1767 2145 2560 3018 3531 4112 4783 5578 6550 7806 9579 2626 59 2 1773 2152 2567 3026 3540 4122 4795 5592 6568 7830 9615 2700 58 3 1779 2159 2574 3034 3549 4133 4808 5607 6587 7855 9652 2775 57 4 1785 2165 2582 3043 3558 4143 4820 5621 6605 7879 9690 2852 56 5 2.1791 2.2172 2.2589 2.3051 2.3567 2.4154 2.4832 2.5636 2.6624 2.7904 2.9727 3.2931 55 6 1797 2178 2596 3059 3576 4164 4844 5651 6642 7929 9765 3010 54 7 1803 2185 2604 3067 3586 4175 4856 5666 6661 7954 9803 3091 53 8 1809 2192 2611 3075 3595 4185 4869 5680 6679 7979 9842 3174 52 9 181ti 2198 2618 3083 3604 4196 4881 5695 6698 8004 9881 3259 51 50 10 2.1822 2.2205 2.2626 2.3091 2.3613 2.4206 2.4894 2.5710 2.6717 2.8030 2.9920 3.3345 11 1828 2212 2633 3100 3623 4217 4906 5725 6736 8055 9960 3432 49 12 1834 22.18 2640 3108 3632 4228 4918 5740 6755 8081 3.0000 3522 48 13 1840 2225 2648 3116 3641 4238 4931 5755 6774 8107 0040 3613 47 14 1846 2232 2655 8124 3650 4249 4943 5771 6793 8133 0081 3707 46 15 2.1852 2.2239 2.2663 2.3133 2.3660 2.4260 2.4956 2.5786 2.6812 2.8159 3.0122 3.3802 45 16 1859 2245 2670 3141 3669 ^3678 4270 4969 5801 6832 8186 0164 3900 44 17 1865 2252 2678 3149 4281 4981 5816 6851 8212 0206 4000 43 18 1871 2259 2685 3158 3688 4292 4994 5832 6871 8239 0248 4102 42 19 1877 2266 2692 3166 3697 4303 5007 5847 6890 8266 0291 4206 41 40 20 2.1883 2.2272 2.2700 2.3174 2.3707 2.4314 2.5019 2.5863 2.6910 2.8293 3.0334 3.4314 21 1889 2279 2707 3183 3716 4325 5032 5878 6930 8320 0378 4424 39 22 1896 2286 2715 3191 3726 4335 5045 5894 6950 8348 0422 4536 38 23 1902 2293 2722 3199 3735 4346 5058 5909 6970 8375 0467 4652 37 24 1908 2300 2730 3208 3745 4357 5071 5925 6990 8403 0512 4771 36 35 25 2.1914 2.2307 2.2738 2.3216 2.3754 2.4368 2.5084 2.5941 2.7010 2.8431 3.0557 3.4894 26 1921 2313 2745 3225 3764 4379 5097 5957 7030 8459 0603 5019 34 27 1927 2320 2753 3233 3773 4390 5110 5973 7050 8487 0649 5149 33 28 1933 2327 2760 3242 378o 4401 5123 5989 7071 8516 0696 5283 32 29 1939 2334 2768 3250 3792 4412 5136 6005 7091 8544 0744 5421 31 30 2.1946 2. 2341 2.2775 2.3259 2.3802 2.4424 2.5149 2.6021 2.7112 2.8573 3.0792 3.5563 30 31 1952 2348 2783 3267 3812 4435 5162 6037 7133 8602 0840 5710 29 32 1958 2355 2791 3276 3821 4446 5175 6053 7154 8632 C889 5863 28 33 1965 2362 2798 3284 3831 4457 5189 6069 7175 8661 0939 6021 27 34 1971 2368 2806 3293 3841 4468 5202 6085 7196 8691 0989 6185 26 25 35 2.1977 2.2375 2.2814 2.3301 2.3851 2.4480 2.5215 2.6102 2.7217 2.8721 3.1040 3.6355 36 1984 2382 2821 3310 3860 4491 5229 6118 7238 8751 1091 6532 24 37 1990 2389 2829 3319 3870 4502 5242 6135 7259 8781 1143 6717 23 38 1996 2396 2837 3327 3880 4514 5256 6151 7281 8811 1196 6910 22 39 2003 2403 2845 3336 3890 4525 5269 6168 7302 8842 1249 7112 21 40 2.2009 2.2410 2.2852 2.3345 2.3900 2.4536 2.5283 2.6185 2.7324 2.8873 3.1303 3.7324 20 41 2016 2417 2860 3353 3910 4548 5296 6201 7346 8904 1358 7547 19 42 2022 2424 2868 3362 3919 4559 5310 6218 7368 8935 1413 7782 18 43 2028 2431 2876 3371 3929 4571 5324 6235 7390 8967 1469 8030 17 44 2035 2438 2883 3379 3939 4582 5337 6252 7412 8999 1526 8293 16 15 45 2.2041 2.2445 2.2891 2.3388 2.3949 2.4594 2.5351 2.6269 2.7434 2.9031 3.1584 3.8573 46 2048 2453 2899 3397 3959 4606 5365 6286 7456 9063 1642 8873 14 47 2054 2460 2907 3406 3969 4617 5379 6303 7479 9096 1701 9195 13 48 2061 2467 2915 3415 3979 4629 5393 6320 7501 9128 1761 9542 12 49 2067 2474 2923 3423 3989 4640 5407 6338 7524 9162 1822 9920 11 50 2.2073 2.2481 2.2931 2.3432 2 . 4000 2.4652 2.5421 2.6355 2.7547 2.9195 3.1883 4.0334 10 51 2080 2488 2939 3441 4010 4664 5435 6372 7570 9228 1946 0792 9 52 3086 2495 2946 3450 4020 4676 5449 6390 7593 9262 2009 1303 8 53 2093 2502 2954 3459 4030 4688 5463 6407 7616 9296 2073 1883 7 54 2099 2510 2962 3468 4040 4699 5477 6425 7639 9331 2139 2553 6 55 2.2106 2.2517 2.2970 2.3477 2 . 4050 2.4711 2.5491 2.6443 2.7663 2.9365 3.2205 4.3345 5 56 2113 2524 2978 3486 4061 4723 5506 6460 7686 9400 2272 4314 4 ; 57 2119 2531 2986 3495 4071 4735 5520 6478 7710 9435 2341 5563 3 58 2126 2538 2994 3504 4081 4747 5534 6496 7734 9471 2410 7324 2 59 2132 2545 3002 3513 4091 4759 5549 6514 7757 9506 2481 5.0334 1 60 2139 2553 3010 3522 4102 4771 5563 6532 7782 9542 2553 11' 1^ 9' 8" 7' 1 6' 5' 4' 3' 1 2' 1' 0' s. 5 DEGREES. 1 1 . When the Apparent Distance is leas than 90°, the Second Correction is to be taken from the Bottom. 1 TABLE. 153 1 ANGLE OF AZIMUTH AND CORRESPONDING CHANGE OF ALTITUDE IN ONE MINCJTE OF TIME. Enter this Table with the Latitude in, at the side, and opposite to which, in the body of the Table, find the approximate Azimuth or Sun's Angle from the Meridian in Degrees at the time of the observation. Then *l the Top will be found the Sun's change of altitude in 1 minute of time. This Table is useful to verify a set of Altitudes for Chronometer, taken when the Sun is not on the Prime Vertical, and for other purposes when precision is required. Lai. CHANQK OP ALTITUDE IN 1 MUfUTB. / / / / t / r / t 1 / / / 1 1 .> 4 5 6 7 ? 9 10 11 12 13 14 15 ,1 O 4 8 12 o 15 o 19 o 24 o 28 o 32 o 37 o 42 o 47 o 53 o 60 o 69 o 87 i 4 8 12 15 19 24 28 32 37 42 47 53 60 69 87 4 4 8 12 15 20 24 28 32 37 42 47 53 60 69 6 4 8 12 16 20 24 28 32 37 42 48 54 61 70 8 4 8 12 16 20 24 28 33 37 42 48 54 61 71 10 4 8 12 16 20 24 28 33 38 43 48 54 62 71 11 4 8 12 16 20 24 28 33 38 43 48 55 62 72 12 4 8 12 16 20 24 . 28 33 38 43 49 55 62 73 13 4 8 12 16 20 24 29 33 38 43 49 55 63 73 14 4 8 12 16 20 24 29 33 38 43 49 56 63 74 15 4 8 12 16 20 24 29 34 38 44 49 56 64 75 16 4 8 12 16 20 25 29 34 39 44 50 56 64 76 17 4 8 12 16 20 25 29 34 39 44 50 57 65 77 "18 4 8 12 16 21 25 29 34 39 44 50 57 66 79 19 4 8 12 16 21 25 30 34 39 45 51 58 66 81 20 4 8 12 16 21 25 30 35 40 45 51 58 67 83 21 4 8 12 17 21 25 30 35 40 46 52 59 68 89 22 4 8 12 17 21 26 30 35 40 46 52 60 69 23 4 8 13 17 21 26 30 35 41 46 53 60 70 24 4 8 13 17 21 26 31 36 41 47 53 61 72 25 4 8 13 17 22 26 31 36 41 47 54 62 73 26 4 9 13 17 22 26 31 36 42 48 55 63 75 27 4 9 13 17 22 27 32 37 42 48 55 64 77 28 4 9 13 18 22 27 32 37 43 49 56 65 79 29 4 9 13 18 22 27 32 37 43 50 57 66 82 30 4 9 13 18 23 27 33 38 44 50 58 67 31 4 9 13 18 23 28 33 38 44 51 f59 69 32 5 9 14 18 23 28 33 39 45 52 60 71 33 5 9 14 19 23 28 34 39 46 53 61 73 34 5 9 14 19 24 29 34 40 46 54 62 75 35 3 9 14 19 24 29 35 41 47 54 64 78 36 5 9 14 19 24 30 35 41 48 55 65 81 37 5 10 14 19 25 30 36 42 49 57 67 38 5 10 15 20 25 30 36 43 49 58 69 39 5 10 15 20 25 31 37 43 51 59 71 40 5 10 15 20 26 31 38 44 52 60 73 41 5 10 15 21 26 32 38 45 53 62 76 42 5 10 16 21 27 33 39 46 54 64 81 43 5 10 16 21 27 33 40 47 55 66 44 5 11 16 22 28 34 40 48 57 68 45 5 11 16 22 28 34 41 49 58 71 46 5 11 17 23 29 35 42 50 60 74 47 6 11 17 23 29 36 43 51 62 78 48 6 11 17 23 30 37 44 53 64 85 49 6 12 18 24 31 38 45 54 66 50 6 12 18 25 31 32 38 47 56 69 51 6 12 19 25 39 48 58 72 52 6 12 19 26 33 41 49 60 77 53 6 13 19 26 34 42 51 62 85 54 7 13 20 27 35 43 53 65 55 7 13 20 28 36 44 54 68 56 7 14 21 28 37 46 57 73 57 7 14 22 29 38 47 59 78 58 7 15 22 30 40 49 62 59 ■7 15 23 31 40 51 65 60 61 8 8 15 24 32 42 53 69 16 24 33 43 56 74 62 8 16 25 35 45 58 84 63 8 17 26 36 47 62 64 9 18 27 37 49 66 65 9 18 28 39 52 70 66 9 19 29 41 55 80 1 X) 154 TABLE XXXIII. THIRD CORRECTION, TO APPARENT DISTANCE 20o. . Alt. APPARENT ALTITUDE OF THE SUN, OR A STAB. 3>'s App Alt. 6» 70 S* 90 10«> 11° 12» 14° 16° 1 II 18° 20° 22° 24° 26° 28° 30° o 1 It t n / // / II 1 II / n / II 1 II / // / // / II 1 II / II / II / // 6 1 38 1 42 1 46 I 55 2 7 2 19 2 34 3 9 3 43 4 17 4 51 5 25 5 59 6 32 H 7 1 46 1 37 1 40 1 46 1 53 2 3 2 12 2 36 3 1 3 29 3 57 4 24 4 50 5 16 7 8 1 55 1 43 1 36 1 40 1 44 1 49 1 56 2 14 2 35 2 56 3 17 3 39 4 4 21 4 42 8 9 2 8 1 51 1 40 1 36 1 39 1 42 1 45 1 57 2 12 2 29 2 47 3 5 3 23 3 41 3 58 9 10 2 23 2 1 46 1 40 1 36 1 37 1 39 1 46 1 56 2 10 2 24 2 38 2 53 3 8 2 44 3 23 2 56 3 37 10 11 2 38 2 11 1 54 1 45 1 38 1 37 1 37 1 40 1 46 1 56 2 8 2 20 2 32 3 7 11 12 2 53 2 23 2 3 1 51 1 41 1 37 1 35 1 37 1 41 1 47 1 56 2 6 2 16 2 26 2 35 2 44 12 13 3 9 2 35 2 13 1 57 1 46 1 40 1 37 1 35 1 37 1 41 1 48 1 56 2 4 2 12 2 19 2 26 13 14 3 25 2 47 2 23 2 3 1 52 1 44 1 39 1 33 1 34 1 37 1 42 1 48 1 54 2 2 5 2 11 14 15 3 41 3 2 34 2 11 1 58 1 49 1 42 1 35 1 33 1 35 1 38 1 41 1 45 1 50 1 54 1 59 15 16 3 58 3 13 2 45 2 20 2 4 1 54 1 46 1 36 1 32 1 33 1 34 1 36 1 38 1 42 1 46 1 50 16 17 4 15 3 26 2 56 2 29 2 10 1 59 1 50 1 38 1 33 1 31 1 32 1 33 1 34 1 36 1 39 1 42 17 18 4 32 3 40 3 7 2 38 2 17 2 4 1 54 1 40 1 34 1 30 1 30 1 30 1 31 1 32 1 34 1 36 18 19 4 49 3 53 3 18 2 47 2 24 2 9 1 58 1 43 1 35 1 31 1 29 1 29 1 29 1 30 1 32 1 33 19 20 5 5 4 6 3 28 2 56 2 31 2 15 2 2 1 46 1 37 1 31 1 32 1 28 1 28 1 28 1 29 1 30 1 30 1 27 20 21 21 5 21 4 19 3 39 3 4 2 38 2 20 2 6 1 49 1 39 1 29 1 27 1 27 1 27 1 27 22 5 36 4 32 3 49 3 12 2 46 2 26 2 11 1 53 1 40 1 33 1 29 1 26 1 25 1 25 1 25 1 25 22 23 5 51 4 44 3 59 3 20 2 53 2 32 2 16 1 57 1 42 1 34 1 29 1 26 1 25 1 24 1 24 1 23 23 24 6 5 4 56 4 9 3 28 3 2 38 2 22 2 1 43 1 35 1 30 1 26 1 24 1 24 1 23 1 22 24 25 6 19 5 7 4 18 3 36 3 7 2 44 2 26 2 3 1 45 1 36 1 30 1 26 1 24 1 23 1 21 1 20 2b 26 6 32 5 18 4 27 3 44 3 14 2 49 2 31 2 6 1 47 1 37 1 31 1 27 1 25 1 23 1 21 1 19 26 27 6 45 5 29 4 35 3 52 3 20 2 54 2 35 2 8 1 49 1 38 1 32 1 28 1 25 1 23 1 21 1 19 27 1 28 5 39 4 42 3 59 3 26 2 59 2 38 2 11 1 50 1 39 1 33 1 28 1 25 1 23 1 21 1 19 28 29 4 49 4 6 3 32 3 4 2 41 2 13 1 52 1 40 1 33 1 28 1 25 1 23 1 21 1 19 29 30 4 12 3 37 3 8 2 45 2 15 1 54 1 41 1 34 1 28 1 25 1 23 1 21 1 19 30 31 3 42 3 12 2 49 2 16 1 56 1 42 1 34 1 28 1 25 1 22 1 20 1 18 31 32 3 16 2 52 2 18 1 58 1 43 1 34 1 28 1 24 1 21 1 19 1 18 32 33 2 55 2 20 1 59 1 43 1 33 1 27 1 24 1 21 1 19 1 17 33 34 2 21 1 59 1 43 1 33 1 26 1 23 1 20 1 18 1 16 34 35 2 22 1 59 1 43 1 32 1 25 1 22 1 19 1 17 1 15 35 36 1 59 1 42 1 31 1 24 1 20 1 17 1 15 1 14 36 37 1 59 1 42 1 30 1 23 1 19 1 16 1 14 1 13 37 38 1 41 1 29 1 22 1 18 1 15 1 13 1 12 38 39 1 41 1 28 1 21 1 17 1 13 1 11 1 11 39 40 1 27 1 20 1 15 1 12 1 10 1 10 40 41 1 26 1 18 1 13 1 10 1 9 1 8 41 42 1 17 1 11 1 8 1 7 1 7 42 43 1 16 1 10 1 6 1 5 1 5 43 44 / 1 9 1 4 1 3 1 3 44 46 48 1 7 1 2 1 1 46 48 59 56 56 50 ) 52 50 50 5^ 45 52 54 54 56 66 58 • 58 60 60 62 62 64 64 66 66 68 68 70 72 70 72 74 74 76 ' 76 78 78 80 80 82 82 84 84 86 1 86 6° 70 8«» 90 1 10<» 11° 12° 140 16°^ 18° 20° 22° 24° 26° 28° 1 30° ^H. 5-8 App, Alt, 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 32 33 34 35 36 37 38 39 40 41 42 43 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 TABLE XXXIII. THIRD CORRECTION, TO APPARENT DISTANCE 20°. APPARENT ALTITUDE OF TUB SUN, OR STAR. 12= 34^' 360 380 42© 450 5Q0 16 52 32 16 3 53 44 37 33 30 27 24 22 21 19 17 17 17 17 18 2 38 2 21 2 7 1 56 1 46 1 39 1 34 1 30 1 26 1 23 1 -21 1 20 13 12 11 10 9 56 52 48 44 32' 2 13 59 48 40 34 29 1 25 1 22 1 20 1 18 1 18 1 16 1 16 1 15 1 15 1 16 1 17 17 1 16 17 1 16 1^1 15 l?'l 14 14 1 13 1 12 1 11 1 10 1 10 1 9 58 54 49 43 38 14 13 13 14 15 1 51 1 41 1 34 1 28 1 23 1 20 1 18 1 16 1 14 1 15 1 14 1 13 1 13 1 12 1 11 1 10 1 9 1 9 1 8 59 55 50 45 40 35 34^ 12 11 10 11 12 1 26 1 12 1 12 1 12 1 11 1 11 1 10 1 9 1 8 1 1 6 59 56 51 46 42 38 34 36° I 38*= 21 18 15 12 9 58 55 51 47 44 40 36 33 30 1 8 1 4 1 1 1 57 58 59 59 59 1 1 1 50 50 50 1 59 59 59 58 56 54 51 48 45 42= 42 39 36 33 30 27 46° 51 51 52 53 53 54 54 55 55 55 55 55 55 55 54 51 49 47 45 54= 58® 62" 66° 70° 74° 78° 82° i,6° 42 43 43 44 45 46 47 47 48 48 48 48 48 48 53 43 41 38 35 32 29 27 25 50° 49 48 47 45 44 r ff It 36 37 38 39 39 39 40 40 40 41 42 41 39 37 35 32 30 27 25 23 54° 43 43 43 43 42 32 32 33 33 34 35 29 30 40 39 38 37 36 34 32 29 27 25 23 21 58° 37 38 39 40 40 38 36 35 35 34 32 31 29 27 26 24 23 22 21 31 33 35 36 35 33 32 32 31 25 27 29 30 31 24 25 27 34 31 30 29 28 27 26 62° 25 24 23 22 21 66° 29 29 29 29 28 27 27 26 25 24 23 22 21 C 20 27 26 26 27 27 26 26 25 24 24 23 22 21 21 20 70= 74° 22 23 23 24 25 25 25 24 23 22 22 21 22 22 23 21 21 21 78° 23 22 21 21 10 20 20 82° 155 3) App A.t. o 6 7 8 9 10 21 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 44 45 46 48 50 52 54 56 21 20 20 20 19 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 86° 156 TABLE XXXIII. THIRD CORRECTION, TO APPARENT DISTANCE 24''. App.. Alt. APPARENT ALTITUDE OF THE SUN, OR A STAR. D's App. Alt. 6° 70 8» 9° 10* 11° 120 140 16° 1 II 18° 20° 22° 24° 26° 28° 30° o r It f II / // / n 1 n t II 1 II 1 n 1 II / II / // / II / II 1 II / II 6 1 28 1 31 1 35 1 42 1 52 2 3 2 16 2 46 3 16 3 47 4 19 4 50 5 20 5 50 6 20 6 50 6 7 1 35 1 27 1 30 1 34 1 39 1 46 1 54 2 15 2 38 3 3 3 29 3 55 4 20 4 46 5 10 5 34 7 8 1 45 1 32 1 26 1 28 1 30 1 35 1 41 1 58 2 17 2 37 2 58 3 18 3 39 4 1 4 20 4 39 8 9 1 56 1 39 1 30 1 25 1 26 1 29 1 34 1 44 1 59 2 15 2 31 2 48 3 6 3 24 3 40 3 56 9 10 2 8 1 48 1 36 1 29 1 25 1 26 1 28 1 35 1 45 1 57 2 13 2 27 2 43 2 58 3 12 2 49 3 26 10 11 2 21 1 58 1 43 1 34 1 28 1 24 1 26 1 30 1 36 1 46 1 58 2 11 2 24 2 37 3 H 12 2 36 2 9 1 52 1 41 1 33 1 27 1 24 1 26 1 30 1 37 1 47 1 58 2 9 2 20 2 29 2 38 12 13 2 51 2 20 2 1 1 48 1 38 1 31 1 27 1 24 1 27 1 32 1 40 1 48 1 57 2 6 2 14 2 22 13 14 3 6 2 31 2 10 1 55 1 43 1 35 1 30 1 23 1 25 1 28 1 33 1 40 1 48 1 55 2 2 2 10 14 15 3 21 2 42 2 20 2 2 1 50 1 39 1 33 1 24 1 23 1 22 1 25 1 24 1 34 1 40 1 46 1 52 1 59 15 16 3 36 2 54 2 30 2 9 1 56 1 44 1 36 1 26 1 23 1 25 1 29 1 33 1 38 1 44 1 50 16 17 3 51 3 6 2 40 2 17 2 S 1 49 1 39 1 28 1 23 1 21 1 23 1 26 1 29 1 34 1 39 1 43 17 18 4 6 3 18 2 49 2 25 2 8 1 54 1 43 1 31 1 24 1 20 1 21 1 23 1 26 1 30 1 34 1 37 18 19 4 21 3 30 2 59 2 33 2 14 1 59 1 47 1 33 1 25 1 21 1 20 1 22 1 24 1 27 1 30 1 32 19 20 4 35 3 42 3 9 2 41 2 21 2 6 1 52 1 36 1 27 1 22 1 23 1 19 1 20 1 22 1 24 1 26 1 28 1 25 20 21 4 50 3 54 3 19 2 50 2 28 2 11 1 56 1 39 1 29 1 20 1 19 1 20 1 21 1 23 21 22 5 4 4 6 3 28 2 58 2 35 2 17 2 1 1 42 1 31 1 24 1 20 1 18 1 19 1 19 1 20 1 22 2£ 23 5 19 4 18 3 38 3 6 2 43 2 23 2 6 1 46 ) 33 1 25 1 21 1 18 1 18 1 18 1 18 1 19 23 24 5 33 4 29 3 48 3 14 2 51 2 29 2" 12 1 50 1 36 1 27 1 22 1 19 1 17 1 17 1 17 1 17 24 25 5 47 4 41 3 57 3 22 2 58 2 35 2 17 1 53 1 38 1 28 1 30 1 23 1 20 1 18 1 16 1 16 1 16 25 26 6 1 4 52 4 6 3 30 3 4 2 41 2 22 1 57 "l 41 1 24 1 20 1 18 1 16 1 15 1 15 26 27 6 14 5 4 4 15 3 38 3 10 2 47 2 27 2 1 43 1 32 1 25 1 21 1 18 1 15 1 14 1 13 27 28 6 27 5 15 4 23 3 45 3 16 2 53 2 32 2 4 1 46 1 34 1 27 1 21 1 18 1 15 1 13 1 12 28 29 6 38 5 26 4 32 3 53 3 22 2 58 2 38 2 8 1 49 1 36 1 28 1 22 1 18 1 15 1 13 1 11 29 30 6 50 5 36 4 41 4 3 28 3 3 2 44 2 12 1 52 1 38 1 29 1 23 1 19 1 15 1 13 1 11 30 31 31 7 5 45 4 50 4 7 3 34 3 8 2 49 2 16 1 55 1 40 1 30 1 24 1 19 1 15 1 13 1 11 32 5 53 4 58 4 14 3 40 3 13 2 54 2 19 1 57 1 41 1 31 1 24 1 19 1 15 1 13 1 11 32 33 5 5 4 20 3 46 3 18 2 58 2 22 1 59 1 42 1 31 1 24 1 19 1 15 1 13 1 11 33 34 4 25 3 51 3 22 3 1 2 24 2 1 1 43 1 32 1 25 1 20 1 15 1 13 1 11 34 35 3 56,3 26 3 3 2 26 2 2 1 45 1 33 1 25 1 20 1 15 1 13 1 11 35 36 3 30 3 5 2 28 2 4 1 46 1 34 1 25 1 20 1 15 1 12 1 10 36 37 3 7 2 30 2 6 1 47 1 35 1 25 1 20 1 15 1 12 1 10 37 38 2 32 2 7 1 48 1 35 1 25 1 20 1 15 1 12 1 10 38 39 2 34 2 8 1 49 1 35 1 25 1 19 1 15 1 12 1 10 39 40 2 9 1 50 1 35 1 25 1 19 1 15 1 11 1 9 40 41 2 10 1 60 1 35 1 25 1 19 1 15 1 11 1 8 41 42 1 51 1 36 1 25 1 19 1 14 1 10 1 7 42 43 1 52 1 36 1 25 1 18 1 13 1 9 1 6 43 44 1 36 1 25 1 18 1 13 1 8 1 5 44 46 48 1 36 1 25 1 17 1 12 1 7 1 3 46 * 1 25 1 17 1 10 1 5 1 1 48 50 1 17 1 8 1 4 59 50 52 1 7 1 3 58 52 54 1 2 57 54 56 56 56 58 58 60 60 62 62 64 64 66 66 68 68 70 1 70 72 I 72 74 , 74 76 76 78 78 80 80 82 82 84 84 86 86 6<» 70 8» 90 in» 110 12° 140 16« 18° 20° 22" 24° 26° 28° 30° 1 TABLE XXXlll. 157 1 1 THIRD CORREOTION. TO APPARENT DISTANCE 24° App. \ APPARENT ALTITUDK OF THK SUN, OR STAR. App Alt. '32« 34° 360 38«» 420 46° 50° 54° 58° 62° 66" 70" 74° 78" 82° *6° Alt. o 6 / tf 1 // t n t // / n 1 It 1 1' 1 n / >> t II 1 II 1 II t n / // / // / // o 6 7 8 4 58 7 8 9 4 12 9 10 3 39 3 51 10 11 3 11 3 21 3 30 11 12 2 48 2 56 3 5 3 12 12 13 2 30 2 37 2 44 2 49 13 14 2 16 2 22 2 27 2 32 14 15 2 4 2 9 2 14 2 18 15 16 16 54 59 2 3 2 6 2 11 17 46 50 53 56 2 17 18 40 43 45 47 1 51 18 19 35 37 39 41 1 43 19 20 30 32 33 34 1 36 1 38 20 21 26 27 28 29 1 30 1 31 21 22 22 23 24 24 1 25 1 25 22 23 20 20 21 21 1 21 1 21 23 24 18 18 19 19 1 18 1 17 1 15 24 25 26 16 16 17 17 1 16 1 14 1 11 25 14 14 14 14 1 13 1 11 1 8 26 27 13 13 12 12 1 1 1 9 1 6 27 28 12 12 11 10 1 9 1 7 1 4 1 1 28 29 11 U 10 9 1 8 1 5 1 2 59 29 30 11 10 9 8 1 7 1 4 1 57 30 31 10 9 8 8 1 6 1 2 58 55 31 32 9 9 8 7 1 5 1 1 57 54 51 82 33 9 8 7 6 1 4 1 1 57 53 50 33 34 9 7 6 5 1 3 1 57 53 49 34 35 9 7 6 5 1 2 1 56 52 48 \ 35 36 36 8 7 6 4 1 2 1 56 51 47 44 37 8 6 5 3 1 1 58 55 51 46 43 37 38 8 6 5 3 1 57 54 50 46 43 38 39 8 6 4 2 59 56 52 48 45 42 39 40 7 5 4 2 59 55 51 47 44 41 39 40 41 41 6 4 3 1 58 54 50 47 44 41 38 42 5 4 3 1 57 54 50 47 44 41 38 42 43 4 3 2 56 53 50 47 43 40 37 34 43 44 3 2 1 59 56 53 50 47 43 40 37 34 44 46 1 59 58 55 52 49 46 43 40 37 34 32 46 48 48 59 59 58 57 54 51 49 46 43 40 37 34 32 50 57 57 56 55 53 50 48 45 43 40 37 34 32 30 50 52 55 54 53 52 51 49 47 45 43 40 37 34 32 30 52 54 54 52 51 50 49 47 46 44 42 39 37 34 32 29 27 54 56 53 51 49 48 47 45 44 43 41 38 36 34 31 29 27 56 58 52 49 47 46 45 44 43 42 40 37 35 33 31 29 27 26 58 60 47 45 44 43 42 41 40 38 36 34 32 30 28 27 26 60 62 43 43 41 40 39 38 37 35 33 31 29 28 27 26 62 64 42 39 38 38 37 36 34 32 30 29 28 27 26 64 66 68 38 37 37 36 35 33 31 29 28 27 26 25 66 37 35 35 34 34 33 31 29 28 27 26 25 68 70 34 34 33 33 32 30 28 27 26 25 25 70 72 33 33 32 32 31 29 28 26 25 24 25 72 74 32 31 31 30 29 28 26 25 24 74 76 31 30 30 29 28 27 25 24 24 76 78 29 29 29 28 27 25 24 78 80 28 28 28 27 26 25 24 80 82 27 27 26 25 24 82 84 26 26 25 25 24 84 86 26 25 25 86 32" 34« 1 36*» 38" 42" 46" 50« 54" 58" 62" 66" 70" 1 74" 78" 82° 86° _J 158 TABLE XXXIII. THIRD CORRECTION, TO APPARENT DISTANCE 28«». App. APPARENT ALTITUDE OF THE SUN, OR A STAR. App. Alt. Alt. 6° 7° S" 1 9° 10° 11° 1 12° 14° 16° 1 It 18° 20° 22° 24° 26° 28° 30° o r // r n / II / // / II / II 1 II / n / // / // 1 II t II 1 II 1 II 1 II 6 1 20 1 23 1 27 1 33 40 49 2 00 2 28 2 56 3 24 3 53 4 21 4 48 5 15 5 42 6 9 6 7 1 25 1 20 1 23 1 27 32 38 1 45 2 5 2 26 2 49 3 13 3 36 3 58 4 20 4 43 5 6 7 8 1 32 1 24 1 20 1 22 25 29 1 35 1 50 2 7 2 26 2 46 3 4 3 23 3 42 4 1 4 20 8 9 1 41 1 29 1 23 1 20 22 24 1 28 1 39 1 52 2 7 2 22 2 37 2 53 3 9 3 25 3 41 9 10 1 53 1 37 1 28 1 23 20 — 21 20 1 23 1 30 1 39 1 52 1 41 2 5 2 18 2 31 2 44 2 58 3 11 10 11 2 6 1 46 1 34 1 27 23 1 21 1 24 I 31 1 52 2 4 2 15 2 26 2 37 2 48 11 12 2 19 1 56 1 41 1 32 1 26 22 1 19 1 21 1 26 1 33 1 42 1 52 2 1 2 10 2 20 2 30 ■ 12 13 2 32 2 6 1 49 1 38 30 25 1 21 1 20 1 23 1 28 1 34 1 42 49 1 57 2 6 2 15 13 14 2 46 2 17 1 58 1 44 34 28 1 23 1 19 1 21 1 24 1 28 1 34 40 1 47 55 2 3 14 15 3 00 2 28 2 7 1 51 39 32 1 25 1 20 1 19 1 21 1 24 1 28 33 1 39 45 1 52 15 16 16 3 14 2 39 2 16 1 58 45 36 1 28 1 21 1 18 1 19 1 21 1 24 28 1 33 38 44 17 3 28 2 51 2 25 2 5 51 41 1 32 1 23 1 19 1 18 1 19 1 21 24 1 28 33 38 17 18 3 41 3 2 2 35 2 13 58 46 1 36 1 25 1 20 1 17 1 18 1 19 21 1 24 28 33 18 19 3 55 3 13 2 45 2 21 2 5 52 1 41 1 27 1 21 1 18 1 16 1 17 18 1 21 24 28 19 20 4 9 3 24 2 55 2 29 2 11 57 1 46 1 30 1 23 1 18 1 19 1 16 1 15 — 16 15 1 18 21 24 20 21 4 23 3 35 3 4 2 37 2 17 2 3 1 51 1 33 1 25 1 16 1 14 1 16 18 20 21 22 4 36 3 46 3 13 2 45 2 24 2 9 1 56 1 36 1 27 1 20 1 16 1 13 14 1 15 16 17 22 23 4 49 3 57 3 22 2 53 2 31 2 14 2 1 1 40 1 29 1 22 1 17 1 13 13 1 13 14 15 23 24 5 2 4 8 3 31 3 2 37 2 20 2 6 1 43 1 31 1 24 1 18 1 14 12 1 12 12 13 24 25 5 16 4 19 3 40 3 8 2 43 2 26 2 11 1 47 1 34 1 26 1 28 1 19 1 15 13 1 11 11 12 25 26 26 5 29 4 30 3 49 3 15 2 50 2 32 2 16 1 51 1 36 1 20 1 15 13 1 11 11 11 27 5 42 4 41 3 58 3 23 2 57 2 38 2 21 1 55 1 39 1 30 1 21 1 16 13 1 11 10 10 27 28 5 55 4 52 4 7 3 30 3 4 2 44 2 26 1 59 1 42 1 32 1 22 1 17 14 1 11 10 10 28 29 6 7 5 3 4 16 3 38 3 11 2 50 2 31 2 3 1 45 1 34 1 24 1 18 14 1 12 10 10 29 30 6 19 5 13 4 25 3 45 3 18 2 bb 2 36 2 7 1 47 1 36 1 26 1 19 15 1 12 10 9 30 31 31 6 31 5 23 4 34 3 52 3 25 3 1 2 41 2 10 1 50 1 38 1 27 1 20 15 1 12 10 9 32 6 4^ 5 32 4 43 3 59 3 31 3 7 2 46 2 13 1 53 1 40 1 29 1 21 16 1 12 10 9 32 33 6 53 5 41 4 51 4 6 3 37 3 12 2 51 2 17 1 56 1 42 1 31 1 22 16 1 12 10 9 33 34 7 4 5 50 4 58 4 13 3 43 3 17 2 55 2 20 1 58 1 44 1 32 1 23 17 1 12 10 9 34 35 7 15 5 59 5 5 4 20 3 48 3 21 2 59 2 23 2 00 1 46 1 33 1 23 1 24 17 1 13 10 8 35 36 6 8 5 11 4 26 3 53 3 25 3 3 2 26 2 3 1 47 1 34 18 1 13 10 8 36 37 5 17 4 32 3 58 3 29 3 7 2 29 2 5 1 49 1 35 1 25 18 1 13 10 8 37 38 4 38 4 2 3 33 3 10 2 32 2 7 1 51 1 36 1 26 19 1 14 10 8 38 39 4 6 3 37 3 12 2 34 2 9 1 52 1 37 1 27 19 1 14 11 8 39 40 3 41 3 15 2 37 2 11 1 53 1 38 1 27 20 1 15 11 8 40 41 3 17 2 40 2 13 1 54 1 39 1 28 20 1 15 11 8 41 42 i 2 42 2 )5 1 55 1 40 1 29 21 1 15 10 7 44 43 2 44 2 17 1 06 1 40 1 29 21 1 15 10 7 43 44 2 18 1 57 1 41 1 30 21 1 15 10 7 44 46 48 2 19 1 59 1 42 1 30 1 31 22 1 15 10 7 46 2 1 43 22 1 15 10 6 48 50 1 44 1 32 23 1 15 10 6 50 52 1 33 24 1 15 9 5 52 54 25 1 15 9 5 54 56 1 15 9 4 56 58 1 9 3 58 60 3 60 62 62 64 64 66 — — — 66 68 68 70 70 72 72 74 74 1 76 1 76 78 78 80 80 82 82 84 84 1 86 26° 86 L_ 6" 70 go ■ go 100 1|0 12° 140 16" 18° 20° 22° 24° 28°) 30° 1 TABLE XXXlll. 159 J)'s App. Alt. THIRD CORRECTION, TO APPARENT DISTANCE 28°. APPARENT ALTITUDE OF THE SUN, OR STAR. App Alt. o 32° 34^ 36° 38° 42° 46° 50° 54° 58° 62° 66° 70° 74° 78° 82° 86° o f // 1 tt / // / It / n 1 II 1 n / // / n / // / // t II 1 II 1 It 1 II 6 6 37 7 4 6 7 8 5 28 5 49 6 8 7 4 40 4 57 5 11 8 9 3 58 4 13 4 26 4 38 9 10 3 25 3 38 3 50 4 2 \ 10 11 3 3 12 3 23 3 33 11 12 2 40 2 50 2 59 3 7 3 22 12 13 2 24 2 33 2 41 2 48 3 ; 13 1 14 2 11 2 18 2 25 2 31 2 42 14 15 1 59 2 6 2 12 2 17 2 27 15 16 16 1 50 56 2 1 2 6 2 14 2 21 17 1 43 48 52 1 56 2 3 2 9 17 18 1 37 41 45 1 48 1 54 1 59 18 19 1 31 35 38 1 41 1 46 1 50 19 20 1 26 29 32 1 34 1 38 1 42 1 45 20 21 1 22 25 27 1 29 1 32 1 36 1 38 21 22 1 19 21 23 1 25 1 28 1 30 1 32 22 23 1 17 18 20 1 22 1 24 1 26 1 27 23 24 1 15 16 17 1 18 1 20 1 22 1 23 1 24 24 25 1 13 14 14 1 15 1 16 1 18 1 19 1 19 25 26 1 11 12 12 1 13 1 13 1 14 1 15 1 15 26 27 1 10 11 11 1 11 1 11 1 11 1 12 1 12 27 28 1 10 10 10 1 10 1 10 1 9 1 9 1 9 1 9 28 29 1 10 10 10 1 9 1 9 1 8 1 7 1 6 1 6 29 30 1 9 9 9 1 8 1 8 1 7 1 6 1 4 1 3 30 31 31 1 8 8 7 1 7 1 6 1 5 1 4 1 2 1 1 32 1 8 7 6 1 6 1 5 1 4 1 3 1 1 1 59 32 33 1 7 6 5 1 5 1 4 1 3 1 2 1 58 56 33 34 1 7 5 4 1 4 1 3 1 2 1 1 59 57 54 34 35 1 7 5 4 1 3 1 2 1 1 1 58 55 53 35 36 36 1 6 5 1 4 1 3 1 1 1 58 56 54 52 51 37 1 6 4 3 1 2 1 59 57 55 53 51 50 37 38 1 6 4 3 1 1 59 58 56 54 52 50 49 38 39 1 6 4 2 1 59 57 55 53 51 49 47 39 40 1 6 4 2 1 58 57 55 52 50 48 46 44 40 41 41 1 6 4 2 1 58 56 54 51 49 47 45 43 42 1 5 4 2 59 57 55 53 50 48 46 44 42 42 43 1 5 3 1 59 57 55 53 50 48 46 44 42 41 43 44 1 5 3 1 59 56 54 52 50 47 45 43 41 40 44 46 48 1 4 2 58 55 53 51 49 47 44 42 40 39 46 48 1 3 1 59 57 54 52 50 48 46 43 41 39 38 37 50 1 3 1 58 56 53 51 49 47 45 42 40 38 37 36 50 52 1 2 57 55 52 50 48 46 44 42 40 38 36 35 34 52 54 1 2 59 56 54 51 49 47 45 43 41 39 37 35 34 33 54 56 1 1 58 55 53 50 48 46 44 42 40 38 36 35 34 33 32 56 58 1 57 54 52 49 47 45 43 41 39 37 36 35 34 32 31 58 60 58 55 53 51 48 46 44 42 40 38 37 36 35 34 32 31 60 2 56 54 52 50 47 45 43 41 39 3S 37 36 35 34 32 31 62 r,4 52 50 49 46 44 42 40 38 37 36 35 34 33 32 30 64 66 68 48 48 45 43 41 39 38 37 36 35 34 33 31 29 66 68 46 43 41 40 38 37 36 35 34 33 32 30 28 70 42 40 39 38 37 36 35 34 33 31 29 70 72 41 39 38 37 36 35 34 33 32 30 28 72 74 39 37 36 35 34 33 32 30 28 74 76 38 36 35 34 34 33 31 29 27 76 78 36 34 34 33 32 30 28 78 80 35 34 33 32 31 30 28 80 82 33 32 31 30 29 82 84 32 32 31 30 29 84 86 31 30 29 86 32° 34" 36® 38° 42° 46° 50° 54° 58° 62° 66° 70° 74° 78° 82° 86° .. 11 160 . TABLE XXXIII. THIRD CORRECTION, TO APPARENT DISTANCE 82<». APPARENT ALTITUDE OF THE SUN, OR A STAR. App. Alt. Alt. 6« 70 8° 90 10° 11° 12° 14° 16° 18° 20° 1 22° 1 24° 26° 28° 30° f II o 1 tr t ti t n / // f n / // / // / // / 11 / n / II / II / II / II / // 6 1 18 1 21 1 25 1 30 I 37 1 47 1 59 2 23 2 48 3 13 3 39 4 5 4 30 4 55 5 20 5 45 6 7 1 23 1 18 1 21 1 24 1 28 1 33 1 42 2 2 18 2 37 2 58 3 20 3 42 4 4 4 25 4 46 7 8 1 30 1 22 1 18 1 20 1 22 1 25 1 29 1 42 1 57 2 14 2 32 2 50 3 8 3 26 3 44 4 2 8 9 1 38 1 27 1 20 1 18 1 19 1 21 1 23 1 31 1 44 1 58 2 12 2 26 2 41 2 56 3 11 3 26 9 10 1 47 1 33 1 23 1 20 1 18 1 19 1 20 1 25 1 34 1 45 1 57 2 9 2 21 2 34 2 46 2 59 10 11 1 57 1 41 1 28 1 23 1 19 1 17 1 18 1 21 1 27 1 36 1 46 1 56 2 6 2 17 2 28 2 39 11 12 2 9 1 50 1 34 1 27 1 22 1 19 1 17 1 19 1 23 1 29 1 37 1 46 1 55 2 4 2 13 2 23 12 13 2 21 1 59 1 41 1 32 1 26 1 21 1 18 1 17 1 20 1 24 1 30 1 37 1 45 1 53 2 1 2 9 13 14 2 34 2 8 1 50 1 38 1 30 1 24 1 20 1 16 1 18 1 21 1 25 1 30 1 36 1 43 1 51 58 14 15 2 47 2 18 1 59 1 45 1 35 1 28 1 22 1 17 1 16 1 18 1 21 1 25 1 30 1 35 1 42 49 15 16 2 59 2 28 2 7 1 52 1 41 1 32 1 25 1 19 1 15 1 16 1 18 1 21 1 25 1 29 1 35 41 16 17 3 12 2 38 2 16 1 59 1 47 1 36 1 28 1 21 1 16 1 15 1 16 1 18 1 21 1 25 1 30 35 17 18 3 25 2 48 2 25 2 7 1 52 1 41 1 32 1 23 1 17 1 14 1 15 1 17 1 19 1 22 1 25 29 18 19 3 38 2 58 2 34 2 14 1 58 1 46 1 36 1 25 1 18 1 15 1 14 1 15 1 17 1 19 1 22 25 19 20 3 50 3 9 2 43 2 21 2 4 1 51 1 40 1 27 1 20 1 16 1 13 1 14 1 15 1 17 1 19 21 20 21 4 3 3 19 2 52 2 28 2 10 1 56 1 45 1 30 1 22 1 17 1 14 1 13 1 14 1 15 1 16 18 21 22 4 15 3 30 3 2 35 2 17 2 2 1 50 1 33 1 24 1 18 1 14 1 11 1 12 1 13 1 14 16 22 23 4 28 3 40 3 9 2 42 2 24 2 7 1 55 1 36 1 26 1 19 1 15 1 12 1 11 1 12 1 13 14 23 24 4 40 3 51 3 17 2 50 2 30 2 13 I 59 1 39 1 28 1 21 1 16 1 12 1 10 1 11 1 11 12 24 25 4 52 4 1 3 26 2 57 2 36 2 18 2 4 1 42 1 30 1 22 1 17 1 13 1 11 1 10 1 10 10 25 26 5 4 4 12 3 34 3 5 2 43 2 24 2 8 1 46 1 32 1 24 1 18 1 13 1 11 1 9 1 9 9 26 27 5 16 4 22 3 43 3 12 2 50 2 30 2 13 1 50 1 34 1 26 1 19 1 14 1 11 1 9 1 8 8 27 28 5 28 4 33 3 52 3 20 2 57 2 35 2 17 1 53 1 37 1 27 1 20 1 15 1 11 1 9 1 7 8 28 29 5 41 4 44 4 1 3 28 3 3 2 41 2 21 1 57 1 40 1 29 1 21 1 16 1 12 1 10 1 8 7 29 30 5 53 4 54 4 10 3 35 3 9 3 15 2 46 2 26 2 1 43 1 31 1 23 1 17 1 13 1 10 1 8 6 30 31 6 5 5 4 4 19 3 42 2 52 2 31 2 4 1 46 1 33 1 24 1 18 1 13 1 10 1 8 6 31 32 6 17 5 14 4 27 3 49 3 21 2 57 2 36 2 8 1 49 1 36 1 26 1 19 1 14 1 11 1 9 7 32' 33 6 29 5 23 4 35 3 56 3 27 3 2 2 41 2 12 1 52 1 38 1 27 1 20 1 15 1 11 1 9 7 33 34 6 40 5 32 4 43 4 3 3 32 3 7 2 46 2 15 1 55 1 40 1 29 1 21 1 16 1 12 1 9 7 34 35 6 50 5 40 4 50 4 9 3 38 3 12 2 50 2 19 1 58 1 43 1 31 1 22 1 17 1 13 1 9 7 35 36 6 59 5 48 4 57 4 15 3 43 3 16 2 54 2 22 2 1 1 45 1 32 1 23 1 18 1 13 1 10 7 36 37 7 7 5 56 5 4 4 21 3 49 3 21 2 59 2 25 2 4 1 47 1 34 1 24 1 19 1 14 1 10 7 37 38 7 15 6 3 5 10 4 29 3 54 3 25 3 3 2 28 2 6 1 49 1 35 1 25 1 19 1 14 1 10 7 38 39 7 22 6 10 5 16 4 33 3 59 3 30 3 7 2 31 2 8 1 51 1 36 1 26 1 20 1 15 1 10 7 39 40 6 17 5 21 4 38 4 4 3 34 3 11 2 34 2 10 1 52 1 38 1 27 1 20 1 15 1 11 1 12 8 40 ; 41 5 26 4 43 4 8 3 38 3 15 2 36 2 13 1 54 1 39 1 28 1 21 1 16 8 41 42 4 47 4 12 3 42 3 18 2 39 2 16 1 56 1 41 1 29 1 22 1 16 1 12 8 42 43 4 16 3 46 3 21 2 42 2 18 1 58 1 42 1 30 1 22 1 16 1 12 8 43 44 3 50 3 24 2 45 2 20 2 1 43 1 31 1 23 1 17 1 12 8 44 46 48 3 27 2 50 2 23 2 2 1 45 1 32 1 24 1 17 1 12 8 46 2 54 2 26 2 4 1 47 1 34 1 25 1 18 1 12 8 48 50 2 29 2 6 1 49 1 36 1 26 1 19 1 13 8 50 52 2 8 1 51 1 38 1 28 1 19 1 13 8 52 54 1 53 1 39 1 29 1 20 1 14 8 54 56 1 40 1 30 1 21 1 14 8 56 58 1 30 1 21 1 14 8 58 60 1 21 1 14 8 60 S2 1 14 8 62 64 8 64 66 66 68 68 70 70 72 72 74 74 76 76 78 78 80 80 82 82 84 84 86 21 86 «<» 70 8«» 90 10« 11° 12° I 14° 16" 18° 20° 22° 24° 26° _28° 3 TABLE XXXIll. 161 1 THIRD CORRECTION, TO APPARENT DISTANCE 32°. D's App. Alt. APPARENT ALTITUDE OF THE SUN, DR STAR. App 32° 34° 36° 38° 42° 46° 50° 54° 58° 62° 66° 70° 74° ' 78° 82° 1 8b' Alt. o 1 ti / n 1 tt 1 tt 1 tt f tt / // / tt t It / // / // / ft 1 // / It 1 II 1 II 1 6 6 10 6 33 6 55 7 15 el 7 5 7 5 26 5 44 6 2 71 8 4 20 4 37 4 52 5 7 5 35 8 9 3 41 3 56 4 10 4 24 4 50 9 10 3 12 3 25 3 38 3 50 4 12 10 11 2 51 3 2 3 13 3 23 3 42 11 12 2 33 2 43 2 51 3 00 3 17 3 33 12 13 2 18 2 26 2 34 2 42 2 56 3 9 13 14 2 5 2 12 2 19 2 27 2 39 2 50 14 15 1 55 2 2 2 8 2 14 2 25 2 35 15 16 1 47 53 58 2 3 2 13 2 22 2 30 16 17 1 40 45 50 1 54 2 2 2 11 2 18 17 18 1 34 38 42 1 46 1 53 2 2 7 18 19 1 "29 33 36 1 39 1 45 1 51 1 57 19 20 1 25 28 31 1 33 1 38 1 43 1 49 1 54 20 21 1 21 24 26 1 28 1 32 1 37 1 42 1 46 21 22 1 18 20 22 1 24 1 27 1 31 1 35 1 39 22 23 1 15 17 19 1 20 1 23 1 27 1 30 1 34 23 24 1 13 14 16 1 17 1 20 1 23 1 26 1 29 1 32 24 25 1 11 12 13 1 15 1 17 1 19 1 21 1 24 1 26 25 26 1 9 10 11 1 12 1 14 1 16 1 17 1 19 1 21 26 27 1 8 9 9 1 10 1 12 1 13 1 14 1 16 1 17 27 28 1 8 8 8 1 9 1 10 1 11 1 12 1 13 1 14 1 15 28 29 1 7 7 7 1 7 1 8 1 9 ] 9 1 10 1 11 1 11 29 30 1 6 6 6 1 6 1 6 1 7 1 7 1 7 1 8 1 8 30 31 1 6 6 6 1 5 1 5 1 5 1 5 1 5 1 5 1 5 31 32 1 6 A 5 5 1 4 1 4 1 4 1 4 1 4 1 3 1 3 1 3 32 33 1 5 4 4 1 3 1 3 1 2 1 2 1 2 1 1 1 1 1 1 33 34 1 5 4 3 1 2 1 2 1 1 1 1 59 59 59 34 35 1 5 3 3 1 2 1 1 1 59 58 57 57 57 35 36 36 1 5 3 2 1 1 1 1 1 58 57 56 56 55 54 37 1 5 3 1 1 1 59 57 56 55 55 54 53 37 38 1 5 3 1 1 59 58 56 55 54 54 53 52 38 39 1 5 3 1 59 58 57 56 54 53 52 51 50 39 40 1 5 2 59 58 56 55 53 52 51 50 49 48 40 41 1 5 2 59 58 56 54 52 51 50 49 48 47 41 42 1 5 2 59 57 55 53 51 50 49 48 47 47 42 43 1 5 2 58 56 54 52 51 49 48 47 47 46 45 43 44 1 5 2 58 55 53 51 50 49 48 47 46 45 44 44 46 1 5 2 58 55 52 51 50 48 47 46 45 44 43 46 48 48 1 5 2 59 57 55 52 50 49 47 46 45 44 43 42 41 50 1 2 59 57 54 51 49 48 47 46 44 43 42 41 40 50 52 1 4 1 58 56 53 51 49 47 46 45 43 42 41 40 39 38 52 54 1 4 1 58 56 53 50 48 46 45 44 42 41 40 39 38 37 54 56 1 4 1 58 56 52 49 47 45 44 42 41 40 39 38 37 36 56 58 58 1 4 1 b% 56 52 49 47 45 43 41 40 39 38 37 36 35 60 1 4 57 55 51 48 46 44 42 40 39 38 37 36 35 35 60 62 1 3 59 56 54 51 48 45 43 41 39 38 37 36 35 34 34 62 64 1 3 59 56 54 50 47 45 43 41 38 38 37 36 35 34 33 64 66 68 1 3 59 56 54 50 47 44 42 40 38 37 36 35 34 33 66 59 55 53 48 46 44 42 40 38 37 36 35 34 33 68 70 55 52 48 45 43 41 39 37 36 35 34 33 70 72 52 47 44 42 40 38 37 36 35 33 32 72 74 47 44 42 40 38 36 35 34 32 74 1 76 47 43 41 39 38 36 35 34 32 M 78 43 41 39 37 35 34 33 78 80 43 41 39 37 35 34 33 80 82 40 38 36 34 33 82 84 39 38 36 34 33 84 86 37 35 34 86 32* 34° 36° 38° 42° 46° 50° 54° 58° 62° 66° 70° 74° i 78° 82° 86° 1C2 TART 90 10° 11° 12° 14° 16° / ti 18° 20° 22° 24° 1 26° 28° 30° o / tt / // / fr t n / // / M / tt r n / // / It 1 II 1 II 1 II / // / // 6 1 17 1 19 1 22 1 27 1 33 1 42 1 52 2 13 2 34 2 56 3 19 3 43 4 7 4 31 4 55 5 18 6 7 1 20 1 17 1 19 1 22 1 26 1 31 1 37 1 52 2 10 2 28 2 48 3 8 3 27 3 46 4 6 4 25 7 8 1 25 1 20 1 17 1 19 1 21 1 23 1 27 1 39 1 53 2 8 2 24 2 40 2 57 3 14 3 30 3 46 8 9 1 32 1 24 1 19 1 17 1 18 1 19 1 21 1 29 1 40 1 52 2 5 2 19 2 33 2 47 3 2 3 16 9 10 1 42 1 30 1 23 1 19 1 16 1 17 1 18 1 23 1 31 1 40 1 51. 1 42 fe 2 2 14 2 27 2 40 2 52 10 11 1 52 1 37 1 28 1 22 1 18 I 16 1 17 1 19 1 25 1 33 1 51 2 1 2 12 2 23 2 33 11 12 2 3 1 45 1 34 1 26 1 20 1 17 1 15 1 17 1 21 1 27 1 34 1 41 50 1 59 2 8 2 17 12 13 2 14 1 53 1 40 1 30 1 23 1 19 1 16 1 15 1 18 1 23 1 28 1 34 41 1 49 57 2 5 13 1 14 2 25 2 1 1 47 1 35 1 26 1 21 1 18 1 14 1 16 1 19 1 24 1 29 35 1 41 49 55 14 15 2 36 2 10 1 54 1 41 1 30 1 25 1 21 1 16 1 15 1 17 1 21 1 18 1 25 30 1 35 41 46 15 16 16 2 48 2 20 2 2 1 47 1 35 1 29 1 24 1 18 1 13 1 15 1 21 25 1 29 34 39 17 3 2 30 2 10 1 53 1 40 1 33 1 28 1 20 1 15 1 14 1 16 1 18 21 1 24 28 33 17 18 3 12 2 40 2 18 2 1 46 1 38 1 32 1 22 1 16 1 13 1 15 1 16 18 1 20 23 27 18 19 3 24 2 49 2 27 2 7 I 51 1 43 1 36 1 25 1 18 1 15 1 14 1 15 16 1 18 20 23 19 t 20 3 35 2 59 2 35 2 14 1 57 1 48 1 40 1 28 1 21 1 16 1 17 1 12 1 13 14 13 1 16 18 — 20 18 20 21 ! 1 21 3 46 3 9 2 43 2 21 2 3 1 53 1 44 1 31 1 23 1 13 1 12 1 14 16 22 3 57 3 18 2 61 2 28 2 9 1 58 1 48 1 34 1 25 1 18 1 14 1 11 12 1 13 14 15 22 23 4 9 3 28 2 59 2 35 2 16 2 3 1 52 1 36 1 26 1 19 1 14 1 11 10 1 11 12 13 23 24 4 20 3 37 3 7 2 42 2 22 2 8 1 56 1 39 1 28 1 20 1 15 1 11 9 1 9 10 11 24 25 4 32 3 47 3 15 2 49 2 28 2 13 2 1 42 1 30 1 22 1 15 1 11 9 1 8 8 9 25 26 4 43 3 56 3 23 2 56 2 34 2 18 2 4 1 45 1 32 1 23 1 16 1 12 9 1 7 7 7 26 27 4 55 4 6 3 31 3 3 2 40 2 23 2 9 1 48 1 35 1 25 1 17 1 12 9 1 7 6 6 27 28 5 6 4 15 3 39 3 10 2 46 2 28 2 13 1 52 1 38 1 27 1 19 1 13 9 1 7 6 6 28 29 5 17 4 25 3 47 3 17 2 52 2 34 2 18 1 56 1 40 1 29 1 20 1 13 9 1 7 6 5 29 30 5 28 4 34 3 54 3 24 2 58 2 39 2 23 2 1 43 1 31 1 21 1 14 10 1 8 6 5 30 31 31 5 39 4 43 4 2 3 31 3 4 2 44 2 28 2 4 1 46 1 33 1 23 1 16 11 1 8 6 5 32 5 49 4 52 4 10 3 37 3 10 2 49 2 33 2 7 1 49 1 35 1 25 1 17 12 1 9 7 5 32 33 5 59 5 4 18 3 44 3 16 2 54 2 37 2 10 1 51 1 37 1 27 1 19 14 1 10 7 5 33 34 6 9 5 8 4 25 3 50 3 22 2 59 2 41 2 13 1 53 1 39 1 29 1 21 15 1 11 8 6 34 35 6 19 5 16 4 32 3 56 3 28 3 4 2 46 2 16 1 56 1 41 1 30 1 22 16 1 11 8 6 35 36 6 28 5 24 4 38 4 2 3 33 3 9 2 50 2 19 1 59 1 43 1 32 1 23 17 1 12 9 6 36 37 6 38 5 32 4 45 4 8 3 39 3 14 2 54 2 22 2 1 1 45 1 33 1 24 18 1 13 9 6 37 38 6 47 5 40 4 52 4 14 3 44 3 18 2 58 2 25 2 4 1 47 1 35 1 26 19 1 14 10 6 38 39 6 57 5 48 4 59 4 20 3 49 3 23 3 2 2 28 2 G 1 49 1 36 1 27 20 1 14 10 7 39 40 7 6 5 56 5 5 4 25 3 54 3 27 3 6 2 31 2 8 1 51 1 38 1 28 21 1 15 11 7 40 41 7 16 6 4 5 12 4 31 3 59 3 31 3 10 2 33 2 11 1 53 1 40 1 30 22 1 15 11 8 41 42 7 25 6 12 5 18 4 36 4 3 3 35 3 13 2 36 2 14 1 55 1 42 1 31 22 1 16 11 8 42 ' 43 7 33 6 19 5 24 4 41 4 8 3 39 3 17 2 39 2 16 1 57 1 43 1 32 23 1 16 11 8 43 44 6 26 5 30 4 46 4 12 3 43 3 20 2 42 2 18 1 59 1 45 1 33 24 1 17 12 9 44 ' 46 48 5 41 4 55 4 20 3 50 3 26 2 47 2 22 2 2 1 47 1 35 1 37 25 1 18 13 9 46 i 4 27 3 57 3 32 2 52 2 26 2 5 1 49 27 1 20 14 10 48 50 3 38 2 57 2 30 2 8 1 51 1 39 29 1 21 15 10 50 52 3 1 2 33 2 11 1 53 1 41 31 1 22 16 11 52 54 2 36 2 13 1 55 1 43 32 1 23 16 11 54 56 2 15 1 57 1 44 33 1 24 17 11 56 1 1 59 1 45 1 46 34 35 36 1 25 1 26 1 26 1 26 18 18 18 19 '9 12 12 12 12 13 58 60 62 64 66 TABLE P. EFFECT OF SUN'S VA E e •. 90 Add the Numbers above th Knet to 2rd Correction, sub tract the others. )'« S App - Alt. 5 un's Apparent Altitu( 1 13 i 68 70 72 '10 20 3 1 J 40 506 U7080 n 1 f It « 5 0^ 1 3 5 7 74 10 1 20 4 30 6 40 9 60 60 70 80 2^ 4 5 76 3 1 1 5 3 I 8 5 3 7 5 7 .a 'o_ 2 4 5 6 4 2 : 2 4 : 6 < 1 2 1 J 2 1 I 3 2 I 28° 78 80 82 84 86 ; 110 12° 14° I60 18° 20° 22° 24° 26° 30° TABLE XXXIII. 163 THIRD CORRECTION, TO APPARENT DISTANCE 360. App. Alt. APPARENT ALTITUDE OF THE SUN, OR STAR. App 32«» 34° 360 38° 42° 46° 50° 54° 58° 62° 66° 70° 74° 78° 1 82° 86° Alt. 1 // f tf f // > ff / n ' n f rr r It 1 n / // 1 II / n t II 1 II r II 1 II o 6 5 40 6 1 6 22 6 43 7 24 ' 6| 7 4 43 5 1 5 19 5 36 6 11 A 8 4 1 4 16 4 31 4 46 5 16 5 45 8 9 3 29 3 42 3 55 4 8 4 33 4 58 9 10 11 3 2 4 43 3 16 3 27 3 38 3 59 4 20 % 10 2 54 3 4 3 13 3 32 3 50 11 12 2 27 2 36 2 45 2 53 3 10 3 25 3 40 12 13 2 13 2 21 2 29 2 37 2 51 3 4 3 16 13 14 2 2 2 9 2 16 2 23 2 36 2 47 2 57 14 15 1 53 1 59 2 5 2 11 2 23 2 33 2 42 15 16 16 45 1 50 56 2 1 2 12 2 21 2 29 2 36 17 38 1 42 47 1 53 2 2 2 10 2 17 2 24 17 18 32 1 36 40 1 45 1 53 2 1 2 7 2 13 18 19 27 1 30 34 1 38 1 45 1 52 1 58 2 3 19 20 23 1 26 29 1 33 1 38 1 44 1 49 1 54 1 58 20 21 20 1 22 25 1 28 1 33 1 38 1 43 1 47 1 51 21 22 17 1 18 20 1 23 1 28 1 33 1 37 1 41 1 45 22 23 14 1 15 17 1 19 1 24 1 28 1 32 1 36 1 39 23 24 11 1 12 14 1 16 1 20 1 23 1 27 1 31 1 34 1 37 24 25 26 9 1 10 11 1 13 1 16 1 19 1 22 1 26 1 29 I 31 25 26 8 1 8 9 1 11 1 13 1 16 1 18 1 21 1 24 1 26 27 7 1 7 8 1 9 1 11 1 13 1 15 1 17 1 20 1 22 27 28 6 1 6 7 1 8 1 9 1 11 1 12 1 14 1 16 1 18 20 28 29 6 1 6 6 1 7 1 8 1 9 1 10 1 11 1 13 1 14 16 29 30 5 1 5 5 1 6 1 7 1 7 1 8 1 9 1 10 1 11 13 30 31 31 5 1 5 5 1 5 1 6 1 6 1 6 1 7 1 8 1 9 10 32 4 1 4 5 1 5 1 5 1 5 1 5 1 5 1 6 1 7 8 1 9 32 33 4 1 4 4 1 4 1 4 1 4 1 4 1 4 1 4 1 5 5 1 6 33 34 4 1 3 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 3 1 3 34 35 4 1 3 3 1 3 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 35 36 36 4 1 3 2 1 2 1 1 1 1 I 1 1 1 1 1 37 4 I 3 2 1 1 59 59 59 59 59 59 59 59 58 37 38 4 1 3 1 58 58 58 58 58 58 58 58 57 38 39 5 1 3 1 58 58 58 58 57 57 57 56 56 39 40 5 1 3 1 58 57 57 57 57 56 56 55 54 53 40 41 6 1 3 59 57 56 56 56 56 55 54 53 52 52 41 42 6 1 3 59 57 56 55 55 55 54 53 52 51 51 42 43 6 1 3 59 56 55 54 54 54 53 52 51 50 50 49 43 44 6 1 3 59 56 54 53 5S 53 52 51 50 49 49 48 44 46 6 1 3 59 56 54 53 52 51 50 49 48 48 47 47 46 48 48 7 1 3 59 56 54 52 51 49 48 47 46 46 45 45 45 oO 7 1 3 59 56 53 51 50 48 47 46 45 45 44 44 44 50 52 7 1 3 59 55 52 50 49 48 47 46 45 44 43 42 42 52 54 7 1 3 59 55 52 50 48 47 46 45 44 43 42 41 41 54 56 7 1 3 58 55 52 49 48 47 46 45 44 43 42 041 40 56 58 7 1 3 58 55 52 49 47 46 45 44 43 42 41 40 39 58 60 7 1 3 58 55 51 48 46 45 44 43 42 41 40 39 38 60 62 7 1 3 58 54 51 48 46 44 43 42 41 40 39 38 62 64 7 1 3 58 54 51 48 46 44 43 42 40 39 38 37 64 66 8 1 3 57 54 50 47 45 43 42 ^ 41 39 38 37 66 68 68 8 1 3 57 54 50 47 45 43 42 40 39 38 37 70 8 1 3 57 53 50 47 44 42 41 40 39 38 70 72 1 3 57 53 50 46 43 41 40 39 38 72 74 57 52 49 46 43 41 40 39 38 74 1 76 57 52 48 45 43 41 39 38 37 76 78 78 51 48 45 42 40 39 37 80 51 47 44 42 40 39 37 80 82 47 44 41 40 38 1 82 84 47 44 41 39 38 84 86 44 41 39 86 32'' 34° 36° 38° 42° 46° 50° 54° 58° 62° 66° 70° 1 74° 1 78° 1 82° 86° t — . 164 TABLE XXXUI. THIRD CORRECTION, TO APPARENT DISTANCE 40° App. Alt. APPARENT ALTITUDE OF THE SUN, OB A STAR. App. Alt. fe« 70 8» 90 10° 11° 12° 14° 16° / II 18° 20° 22° 24° I 26° 28° 30° 1 o / n t tf t n t n / It / // 1 II 1 II 1 II 1 II 1 II / // 1 II 1 II / n 6 1 16 1 18 1 21 1 25 1 31 1 39 1 47 2 5 2 26 2 48 3 10 3 32 3 54 4 16 4 38 4 59 6 7 1 19 1 16 1 18 1 21 1 24 1 28 1 34 1 48 2 4 2 22 2 40 2 58 3 16 3 34 3 62 4 10 7 8 1 24 1 19 1 16 1 18 1 20 1 22 1 26 1 36 1 50 2 4 2 18 2 33 2 48 3 4 3 20 3 36 8 9 1 31 1 23 1 19 1 16 1 18 1 19 1 21 1 27 1 38 1 49 2 1 2 13 2 25 2 38 2 52 3 5 9 10 1 40 1 29 1 23 1 19 1 16 1 17 1 18 1 21 1 29 1 38 1 48 1 58 2 9 2 20 2 32 2 44 10 11 1 50 1 36 1 28 1 22 1 18 1 15 1 16 1 18 1 23 1 31 1 39 1 48 1 57 2 7 2 17 2 27 11 12 2 1 1 44 1 34 1 26 1 20 1 17| 1 15 1 17 1 20 1 26 1 33 1 40 1 48 1 57 2 5 2 13 12 13 2 11 1 52 1 40 1 30 1 23 1 19 1 16 1 16 1 18 1 22 1 28 1 34 1 41 1 48 55 2 2 13 14 2 21 2 1 46 1 34 1 26 1 21 1 17 1 15 1 17 1 19 1 23 1 28 1 34 1 40 46 53 14 15 2 31 2 8 1 52 1 39 1 30 1 23 1 19 1 16 1 15 1 17 1 20 1 23 1 27 1 32 38 44 15 16 2 41 2 16 1 58 1 44 1 34 1 26 1 21 1 17 1 14 1 15 1 17 1 19 1 22 1 26 31 37 16 17 2 52 2 24 2 4 1 49 1 38 1 30 1 24 1 19 1 15 1 14 1 15 1 17 1 19 1 22 26 31 17 18 3 3 2 32 2 11 1 54 1 43 1 34 1 28 1 21 1 16 1 13 1 14 1 15 1 17 1 19 22 26 18 19 3 14 2 41 2 18 2 1 48 1 39 1 32 1 23 1 17 1 14 1 13 1 14 1 15 1 17 19 22 19 20 3 25 2 50 2 25 2 6 1 53 1 43 1 36 1 25 1 19 1 15 1 12 1 12 1 13 1 15 16 19 20 21 3 36 2 59 2 32 2 12 1 58 1 47 1 39 1 27 1 20 1 16 1 13 1 11 1 12 1 13 14 16 21 22 3 47 3 8 2 40 2 18 2 4 1 52 1 43 1 30 1 22 1 17 1 13 1 11 1 11 1 12 13 14 22 23 3 58 3 17 2 48 2 25 2 10 1 57 1 47 1 33 1 24 1 18 1 14 1 12 1 10 1 10 11 12 23 24 4 9 3 26 2 56 2 32 2 15 2 2 1 51 1 37 1 26 1 19 1 15 1 12 1 9 1 9 9 10 24 25 4 20 3 35 3 4 2 39 2 21 2 7 1 56 1 40 1 28 1 21 1 16 1 13 1 10 1 8 8 9 25 26 4 30 3 44 3 12 2 45 2 27 2 12 2 1 43 1 30 1 22 1 17 1 13 1 10 1 8 8 9 26 27 4 41 3 53 3 20 2 52 2 33 2 17 2 4 1 47 1 33 1 24 1 18 1 14 1 11 1 8 7 8 27 28 4 51 4 2 3 28 2 59 2 39 2 23 2 8 1 50 1 35 1 25 1 19 1 14 1 11 1 8 7 28 29 5 1 4 11 3 36 3 6 2 45 2 28 2 12 1 53 1 38 1 27 1 20 1 15 1 12 1 9 7 7 29 30 5 12 4 20 3 44 3 13 2 50 2 56 2 33 2 17 1 56 1 40 1 29 1 21 1 15 1 12 1 9 7 e 30 31 5 23 4 29 3 52 3 2C 2 38 2 21 2 1 43 1 30 1 22 1 16 1 12 1 9 7 6 31 32 5 33 4 3? 3 59 3 27 3 1 2 43 2 26 2 3 1 45 1 32 1 23 1 17 1 13 1 10 7 6 32 33 5 43 4 46 4 6 3 33 3 7 2 48 2 30 2 6 1 47 1 34 1 24 1 18 1 14 1 10 8 6 33 34 5 52 4 54 t4 13 3 39 3 13 2 53 2 34 2 9 1 49 1 36 1 26 1 19 1 15 1 11 8 6 34 35 6 1 5 2 4 20 3 4£ . 3 19 2 58 2 38 2 12 1 51 1 38 1 27 1 20 1 15 1 11 8 6 35 36 6 10 5 IC 4 26 3 51 3 24 3 2 2 42 2 15 1 54 1 40 1 29 1 22 1 16 1 12 8 6 36 37 6 18 5 17 4 32 3 57 3 29 3 7 2 46 2 18 1 57 1 42 1 31 1 23 1 17 1 12 9 7 37 38 6 26 5 24 4 38 4 3 3 33 3 11 2 50 2 21 2 n 1 44 1 33 1 25 1 18 1 13 9 7 38 , 39 6 34 5 31 4 44 4 g 1 3 38 3 15 2 54 2 24 2 2 1 46 1 35 1 26 1 19 1 14 10 7 39 40 6 42 5 38 4 50 4 13 3 42 t 3 47 3 19 2 58 2 27 2 5 1 48 1 37 1 28 1 20 1 14 10 7 40 41 6 50 5 4S 4 56 4 18 3 24 3 2 2 30 2 8 1 51 1 39 1 29 1 21 1 15 11 8 41 42 6 58 5 52 5 2 4 24 \ 3 51 3 28 3 6 2 33 2 10 1 53 1 41 1 30 1 22 1 16 11 8 42 43 7 7 5 5S 5 8 4 29 3 56 3 32 3 10 2 36 2 13 1 55 1 43 1 32 1 23 1 17 12 9 43 44 7 16 6 6 5 14 4 34 \ 4 3 36 3 13 2 39 2 15 1 57 1 44 1 33 1 24 1 18 13 9 44 46 7 33 6 21 5 26 4 44 i 4 9 3 44 3 20 2 44 2 19 2 1 1 47 1 35 1 37 1 27 1 20 14 10 46 48 7 50 6 Zt > 5 38 4 54 \ 4 18 3 51 3 27 2 49 2 23 2 5 1 50 1 29 1 22 15 11 48 50 5 50 5 l \ 4 27 3 58 3 33 2 54 2 27 2 8 1 52 1 39 1 31 1 23 17 12 50 52 4 36 4 5 3 39 2 59 2 31 2 11 1 54 1 42 1 32 1 24 18 13 52 54 3 45 3 4 2 35 2 14 1 56 1 44 1 34 1 26 19 14 54 56 3 9 2 39 2 17 1 58 1 46 1 36 1 28 20 14 56 2 43 2 19 2 21 2 2 2 2 4 1 48 1 49 1 50 1 51 1 37 1 38 1 39 1 40 1 40 1 29 1 30 1 30 1 31 1 31 — 21 22 22 23 24 24 24 15 15 16 16 17 68 60 62 64 66 TABLE P EFFECT OF STJN'B Pi e le. Add tht Numbers above th lines to 3rd Correr.tion, sub tract the others. >'8s App _ Alt. 6 Bn'» Apparent Altitnc 10 20 3 J 40 50 6 0170 80 90 1 31 17 17 17 68 70 72 74 5 10 I 1 2 4 i 3 If 6 4 6 / tt ft n 20 4 30 6 40 8 50 60 70 80 90 3 1 1 532 7 5 4 9 7 5 9 7 8 2 ' 2 4 5 6 7 3 1 1 2 " 4 ; 5 ' 6 ' 6 \ i 3 r J 2 2 » 3 76 78 80 82 84 86 11» 12° 14° 16° 18° 20° 22° 24° 26° r>0 30° 2o TABLE XXXlll. 165 THIRD CORRECTION. TO APPARENT DISTANCE 40°. A pp. All. APPARENT ALTITUDE OF THE SUN, OR STAR. 3>'s App Alt. 32° 34° 36° 38° 42° 46° 50° 54° 58° 62° 66° 70° 74° 78° 82» , 86° o / n / ft > II 1 n 1 II / ir 1 II / n 1 II / II / // / II 1 II / It 1 n / II 6 5 19 5 39 5 59 6 19 6 57 7 33 1 6 7 4 27 4 44 5 1 5 18 5 51 6 20 7 8 3 51 4 6 4 20 4 34 5 1 6 26 5 50 8 9 3 20 3 34 3 46 3 58 4 22 4 44 5 5 9 10 2 56 3 8 3 19 3 30 3 50 4 9 4 27 * 10 11 2 37 2 47 2 57 2 6 3 25 3 42 3 58 11 12 2 22 2 30 2 39 2 48 3 5 3 20 3 33 3 46 12 13 2 10 2 17 2 25 2 32 2 47 3 1 3 13 3 25 13 14 2 2 6 2 12 2 18 2 32 2 44 2 55 3 4 14 15 16 1 50 1 56 2 1 2 7 2 19 2 30 2 40 2 48 15 16 1 42 1 47 1 52 58 2 8 2 18 2 27 2 35 2 42 17 1 36 1 40 1 45 50 1 59 2 8 2 16 2 23 2 30 17 18 1 31 1 34 1 38 43 1 51 1 59 2 6 2 12 2 19 18 19 1 26 1 29 1 33 36 1 44 1 51 1 58 2 3 2 9 19 20 1 22 1 24 1 27 30 1 37 1 44 1 50 1 55 2 2 5 20 21 1 18 1 20 1 23 26 1 32 1 38 1 44 1 49 1 53 1 57 21 22 1 15 1 17 1 19 22 1 28 1 33 1 38 1 43 1 47 1 50 22 23 1 13 1 14 1 16 19 1 24 1 29 1 33 1 38 1 42 1 45 23 24 1 11 1 12 1 14 16 1 21 1 25 1 29 1 33 1 37 1 40 43 24 25 26 1 lU 1 11 1 12 14 1 18 1 21 1 25 1 29 1 32 1 35 37 25 1 9 1 10 1 11 12 1 15 1 18 1 21 1 25 1 28 1 30 32 26 27 1 8 1 9 1 9 10 1 13 1 15 1 18 1 21 1 24 1 26 27 27 28 1 7 1 8 1 8 9 1 11 1 13 1 16 1 18 1 20 1 22 23 24 28 29 1 7 1 7 1 7 8 1 9 1 11 1 13 1 15 1 16 1 18 19 20 29 30 1 6 1 6 1 6 7 1 8 1 9 1 11 1 12 1 13 1 15 16 17 30 31 31 1 6 1 6 1 6 7 1 7 1 8 1 9 1 10 1 11 1 13 14 15 32 1 6 1 6 1 6 6 1 6 1 6 1 7 1 8 1 9 1 10 11 12 13 32 33 1 5 1 5 1 5 5 1 5 1 5 1 6 1 6 1 7 1 8 9 10 10 33 34 1 5 1 4 1 4 4 1 4 1 4 1 5 1 5 1 6 1 7 7 8 8 34 35 1 5 1 4 1 4 -- 4 1 4 1 4 1 4 1 4 1 4 1 5 5 6 6 35 36 36 1 5 1 4 1 3 3 1 3 1 3 1 3 1 3 1 3 1 4 4 4 4 1 4 37 1 5 1 4 1 3 2 1 2 1 2 1 2 1 1 1 1 1 2 2 2 2 1 2 37 38 1 5 1 4 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 38 39 1 5 1 4 1 2 1 1 1 1 59 Q 59 59 59 59 59 59 39 40 1 5 1 4 1 2 1 1 59 59 58 58 57 57 57 57 57 57 40 41 41 1 6 1 4 1 2 1 59 58 58 57 57 56 56 56 56 56 56 42 1 6 1 4 1 2 58 57 57 56 56 55 55 55 55 55 55 42 43 1 6 1 4 1 2 58 57 56 55 55 54 54 54 54 54 54 54 43 44 1 6 1 4 1 2 58 56 55 54 54 53 53 53 53 53 53 53 44 46 1 7 1 4 1 2 58 56 54 53 53 52 52 51 51 51 51 51 4:' 46 48 48 1 8 1 5 1 2 58 55 53 52 52 51 51 50 49 49 4y 50 1 8 1 5 1 2 57 54 52 51 51 50 49 48 48 48 48 C 48 50 52 1 9 1 5 1 2 57 54 52 50 50 49 48 47 47 46 46 46 52 54 1 9 1 5 1 2 57 54 51 49 49 48 47 46 46 45 45 45 54 56 1 10 1 6 1 3 56 53 51 49 48 47 46 45 45 44 44 44 56 58 1 10 1 6 1 3 56 53 50 48 47 46 45 45 44 43 43 58 60 1 10 1 7 1 4 56 52 50 48 47 45 44 44 43 42 42 60 62 1 11 1 7 1 4 56 52 50 48 46 45 44 43 42 U 42 1 62 64 1 11 1 7 1 4 56 52 49 47 45 44 43 42 41 41 64 66 68 1 12 1 7 1 4 56 52 49 47 45 3 43 42 42 41 66 68 1 12 I '8 1 4 56 52 49 47 45 43 42 42 41 70 1 12 1 8 1 4 55 51 48 46 44 43 42 42 70 72 1 13 1 8 1 4 55 51 48 46 44 43 42 41 72 1 74 1 13 1 8 1 4 55 51 48 46 44 43 42 74 76 1 8 1 4 55 51 48 46 44 42 41 76 78 78 1 4 55 51 48 46 43 42 80 55 51 48 46 43 41 80 82 55 51 48 46 43 82 84 55 51 48 46 43 84 86 51 48 45 1 86 32° 34° 36° 38° 42° 46° 50° 54° 58° 62° 1 66° 1 70° 1 74° 1 78° 1 82° 86° 166 TABLE XXXllI. THIRD CORRECTION, TO APPARENT DISTANCE U° • App. Alt. APPARENT ALTITUDE OF THE SUN, OR A STAR. 1>'B App. Alt. 6° 70 8« 9° 10° 11° 12° 14° 16° 18° 20° 22° 24° 26° 28° 30° o t ft t tf / // 1 tl / ft 1 tl / II / II / // / // / II 1 If / tl / // 1 // 6 1 16 1 18 1 21 1 25 1 31 1 37 1 45 2 3 2 23 2 44 3 5 3 25 3 45 4 5 4 25 4 44 6 7 1 20 1 16 1 18 1 20 1 24 1 28 1 33 1 46 2 1 2 17 2 34 2 51 3 8 3 25 3 42 3 59 7 8 1 25 1 19 1 16 1 17 1 19 1 22 1 25 1 35 1 47 2 2 14 2 29 2 43 2 58 3 12 3 27 8 9 1 31 1 23 1 18 1 15 1 16 1 18 1 21 1 27 1 36 1 47 1 59 2 12 2 24 2 36 2 48 3 9 10 1 39 1 28 1 21 1 17 1 15 1 16 1 18 1 22 1 29 1 38 1 31 1 48 1 58 2 8 2 18 2 29 2 39 10 11 1 48 1 34 1 25 1 20 1 17 1 15 1 16 1 19 1 24 1 39 1 47 1 56 2 5 2 14 2 24 11 12 1 58 1 41 1 30 1 23 1 19 1 16 1 15 1 17 1 20 1 25 1 32 1 38 1 46 1 54 2 2 2 11 12 13 2 8 1 48 1 35 1 27 1 22 1 18 1 16 1 15 1 17 1 21 1 26 1 32 1 38 1 45 52 59 13 14 2 18 1 56 1 41 1 31 1 25 1 20 1 17 1 14 1 15 1 18 1 22 1 27 1 32 1 38 44 49 14 15 16 2 28 2 4 1 47 1 36 1 29 1 23 1 19 1 15 1 14 1 16 1 19 1 23 1 27 1 32 37 42 15 16 2 38 2 12 1 53 1 41 1 33 1 26 1 21 1 17 1 14 1 15 1 17 1 20 1 23 1 27 32 36 17 2 48 2 20 ii 1 47 1 37 1 30 1 24 1 19 1 15 1 15 1 16 1 18 1 20 1 23 26 30 17 18 2 58 2 28 2 8 1 53 1 42 1 34 1 27 1 20 1 16 1 14 1 15 1 16 1 18 1 20 22 25 18 19 3 8 2 37 2 15 1 59 1 47 1 38 1 30 1 22 1 17 1 14 1 14 1 15 1 16 1 17 19 22 19 20 3 18 2 45 2 22 2 5 1 52 1 42 1 34 1 25 1 19 1 15 1 17 1 13 1 14 1 14 1 15 17 19 20 21 3 29 2 54 2 30 2 12 1 57 1 46 1 37 1 27 1 21 1 14 1 12 1 13 1 14 15 17 21 22 3 39 3 2 2 37 2 18 2 3 1 51 1 41 1 30 1 23 1 18 1 14 1 11 1 12 1 13 14 16 22 23 3 49 3 11 2 45 2 24 2 8 1 55 1 45 1 33 1 25 1 19 1 15 1 12 1 11 1 12 13 14 23 24 4 3 19 2 52 2 31 2 14 2 I 49 1 36 1 27 1 20 1 16 1 12 1 10 1 10 11 13 24 25 4 10 3 28 2 59 2 37 2 20 2 5 1 53 1 39 1 29 1 21 1 22 1 17 1 13 1 10 1 9 10 11 25 26 4 20 3 36 3 6 2 43 2 25 2 10 1 57 1 42 1 31 1 17 1 13 1 10 1 8 9 9 26 27 4 30 3 45 3 13 2 49 2 31 2 15 2 1 1 45 1 32 1 23 1 18 1 14 1 11 1 9 8 8 27 28 4 39 3 53 3 20 2 55 2 36 2 20 2 5 1 47 1 34 1 25 1 19 1 15 1 12 1 9 7 7 28 29 4 48 4 1 3 27 3 1 2 41 2 24 2 9 1 49 1 36 1 27 1 20 1 15 1 12 1 9 7 6 29 30 4 57 4 9 3 34 3 7 2 46 2 29 2 14 1 52 1 38 1 28 1 21 1 16 1 13 1 9 7 6 30 31 5 7 4 17 3 41 3 13 2 51 2 34 2 19 1 55 1 40 1 30 1 22 1 17 1 13 1 10 8 6 31 32 5 16 4 25 3 48 3 19 2 56 2 38 2 23 1 58 1 42 1 31 1 23 1 18 1 14 1 10 8 6 32 33 5 25 4 33 3 54 3 25 3 1 2 43 2 27 2 1 1 44 1 33 1 24 1 19 1 15 1 11 9 7 33 34 5 34 4 40 4 1 3 30' 3 6 2 47 2 31 2 4 1 47 1 35 1 26 1 20 1 15 1 11 9 7 34 35 5 43 4 48 4 8 3 3«i 3 11 2 52 2 35 2 7 1 50 1 37 1 27 1 21 1 16 1 12 9 7 35 36 5 51 4 55 4 14 3 42 3 15 2 56 2 39 2 11 1 53 1 39 1 28 1 22 1 17 1 13 10 7 36 37 6 15 3 4 21 3 47 3 20 3 2 43 2 15 1 56 1 41 1 30 1 23 1 17 1 13 10 8 37 38 6 g 5 10 4 27 3 52 3 24 3 4 2 47 2 18 1 58 1 43 1 32 1 24 1 18 1 14 11 8 38 39 6 18 5 18 4 33 3 58 3 29 3 8 2 51 2 21 2 1 1 45 1 33 1 25 1 19 1 14 11 8 39 40 6 27 5 25 4 39 4 3 3 33 3 12 2 54 2 24 2 3 1 46 1 35 1 26 1 20 1 15 11 8 40 41 6 36 .5 32 4 45 4 8 3 38 3 16 2 58 2 27 2 6 1 48 1 37 1 27 1 21 1 16 12 9 41 42 6 U . 5 39 4 51 4 13 3 42 3 20 3 1 2 30 2 8 1 50 1 39 1 29 1 22 1 16 12 9 42 43 6 5c t 5 46 4 57 4 18 3 47 3 24 3 4 2 33 2 10 1 52 1 40 1 30 1 23 1 17 13 9 43 44 7 ( ) 5 53 5 5 4 23 3 51 3 28 3 7 2 35 2 12 1 54 1 42 1 32 1 24 1 18 13 10 44 46 7 U I 6 6 5 14 4 33 4 3 35 3 14 2 40 2 17 1 58 1 45 1 35 1 37 1 26 1 20 14 10 46 18 7 21 ' 6 IS 5 25 4 43 4 9 3 43 3 21 2 45 2 21 2 2 1 48 1 28 1 21 15 11 48 50 7 4( ) 6 29 5 35 4 52 ! 4 18 3 50 3 27 2 50 2 25 2 6 1 52 1 40 1 31 1 23 16 11 50 52 7 55 5 6 4C 1 5 45 5 1 4 26 3 57 3 33 2 55 2 29 2 10 1 56 1 43 1 33 1 25 18 12 52 54 5 55 5 £ ) 4 34 4 4 3 39 3 2 33 2 14 1 59 1 46 1 35 1 26 19 13 64 56 1 • 4 42 4 10 3 45 3 5 2 37 2 17 2 2 1 49 1 37 1 39 1 40 1 42 1 43 1 44 1 27 20 14 56 58 60 62 64 66 1 ' 3 50 3 10 2 41 2 44 2 47 2 20 2 22 2 24 2 26 2 4 2 5 2 6 2 7 2 8 1 51 1 52 1 53 1 54 1 55 1 29 1 30 1 31 1 32 1 33 1* 21 22 23 24 25 26 27 15 16 17 18 19 TABLB P. EFFECT OF SUN'b TA lH « «. 3 14 Add the Numbers above th lines to 3rd Correction, sul tract the others. J 8 S App- Alt 5 u n's Appare nt Altitnd 1 56 1 45 1 45 1 34 1 35 20 21 68 70 lU •20 3 3 40 50 6 0|70|80 90 5 10 1 on •! 1 3 5 2 4 1 a 1 3 a 5 4 2 ' 6 5 3 ^ 1 i II It I i 2 1 1 36 29 30 22 22 23 72 74 76 78 30 5 40 7 60 g 60 70 ,80 7 8 5 4 7 5 8 7 8 2 4 5 6 7 1 ( 3 1 4 ; 6 ■) 6 ) 1 > 1 1 > 2 a 1 3 1 28'' 80 82 84 86 11° 12° 14° 16° 18° 20° 22® 24° 26° 30° TABLE XXXIII. 167 THIRD CORRECTION, TO APPARENT DISTANCE 44o. App. Alt. APPARENT ALTITUDE OF THE SUN, OR STAR. >'8 App Alt. 32« 34° 36«> 38° 42° 46° 1 50° 54° 58° 62° 66° 70° 74° 78° 82° 86" o > It / // / // r rr / f> / ') / // 1 ft f n / // 1 // / n / II 1 ff 1 II / // o 6 5 3 5 22 5 41 5 59 6 36 7 10 7 40 6 7 4 15 4 31 4 47 5 2 5 33 6 1 6 29 7 8 3 40 3 53 4 6 4 20 4 46 5 11 5 35 5 58 R 9 3 12 3 24 3 35 3 47 4 10 4 31 4 51 5 10 9 10 2 50 3 3 10 3 20 3 39 3 58 4 17 4 34 » 10 11 2 33 2 42 2 52 3 3 17 3 33 3 48 4 3 11 12 2 19 2 27 2 36 2 44 2 59 3 13 3 26 3 39 3 51 12 13 2 6 2 13 2 21 2 29 2 43 2 56 3 9 3 20 3 29 13 14 1 55 2 2 2 9 2 16 2 29 2 41 2 53 3 2 3 10 14 15 I 47 1 53 1 59 2 5 2 17 2 28 2 38 2 47 2 54 15 16 16 1 40 1 45 1 50 56 2 7 2 17 2 26 2 34 2 41 2 47 17 1 34 1 38 1 43 48 1 58 2 7 2 15 2 22 2 29 2 35 17 18 1 29 1 33 1 37 42 1 51 1 59 2 6 2 12 2 18 2 24 18 19 1 25 1 28 1 32 36 1 44 1 52 1 59 2 4 2 9 2 14 19 20 1 22 1 25 1 28 31 1 38 1 46 1 52 1 57 2 1 2 6 2 11 20 21 21 1 19 1 22 1 25 27 1 33 1 40 1 46 1 51 1 55 1 59 2 2 22 1 17 1 19 1 22 24 1 29 1 35 1 40 1 45 1 49 1 53 55 22 23 1 15 1 17 1 19 21 1 25 1 30 1 35 1 40 1 44 1 47 49 23 24 1 14 1 15 1 16 18 1 22 1 26 1 30 1 35 1 39 1 42 44 46 24 25 26 1 12 1 13 1 14 16 1 19 1 22 1 26 1 30 1 34 1 37 39 40 25 1 10 1 11 1 12J 14 1 16 1 19 1 22 1 26 1 30 1 32 34 38 26 27 1 9 1 10 1 11 12 1 14 1 16 1 19 1 23 1 26 1 28 30 31 27 28 1 8 1 9 1 10 11 1 12 1 14 1 17 1 20 1 22 1 24 26 27 28 28 29 1 7 1 8 1 8 9 1 10 1 12 1 15 1 17 1 19 1 21 22 23 25 29 30 1 6 1 7 1 7 8 1 9 1 10 1 12 1 14 1 16 1 18 19 20 22 30 31 31 1 6 1 6 1 6 7 1 8 1 8 1 10 1 12 1 14 1 15 17 18 19 32 1 5 1 6 1 6 6 1 7 1 7 1 8 1 10 1 12 1 13 14 15 16 17 32 33 1 5 1 5 1 5 5 1 6 1 6 1 7 1 8 1 9 1 10 11 12 13 14 33 34 1 5 1 4 1 4 4 1 5 1 5 1 6 1 6 1 7 1 8 9 10 11 12 34 35 1 5 1 4 1 4 4 1 4 1 4 1 5 1 5 1 5 1 6 7 8 9 10 35 36 36 1 5 1 4 1 3 3 1 3 1 ? 1 4 1 4 1 4 1 5 5 6 7 8 1 9 37 1 6 1 4 1 3 2 1 2 1 2 1 3 1 3 1 3 1 4 4 5 5 6 1 7 37 38 1 6 1 4 1 2 1 1 1 1 1 1 2 1 2 1 2 1 3 3 4 4 4 1 5 38 39 1 6 1 4 1 2 1 1 1 1 1 1 1 1 1 1 2 2 3 3 3 1 4 39 40 1 6 1 4 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 3 40 41 1 7 1 5 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 41 42 1 7 1 5 1 3 1 59 59 59 59 59 59 59 59 59 59 59 59 42 43 1 7 1 5 1 3 1 59 59 58 58 58 58 58 58 58 58 58 58 43 44 1 7 1 5 1 3 1 59 58 57 57 57 57 57 57 57 57 57 57 44 46 1 7 1 5 1 3 1 59 57 56 56 56 56 55 55 55 55 55 55 46 48 48 1 8 1 6 1 4 2 59 57 55 55 55 54 54 54 53 53 53 53 50 1 8 1 6 1 4 2 59 57 55 54 54 53 53 53 52 52 52 52 50 52 1 9 1 6 1 4 2 59 56 54 53 53 52 52 51 51 51 50 61 52 54 1 10 1 7 1 4 2 59 56 54 53 52 51 51 50 50 49 49 54 56 1 10 1 7 1 5 2 59 56 54 52 51 50 50 49 49 48 47 56 58 1 11 1 8 1 5 3 59 56 53 51 50 49 49 48 48 47 58 60 1 11 1 8 1 5 3 59 56 53 51 50 49 48 47 47 46 60 62 1 12 1 9 1 6 3 59 56 53 51 49 48 47 47 46 62 64 1 13 1 9 1 6 3 59 56 53 51 49 48 47 46 45 64 6fi 1 14 1 10 1 7 4 59 56 53 51 49 48 47 46 66 68 68 1 15 1 11 1 7 4 59 56 53 51 49 47 46 45 70 1 16 1 11 1 7 4 59 55 53 51 49 47 46 70 72 1 16 1 12 1 8 4 59 55 52 50 48 46 45 72 74 1 16 1 12 1 8 4 59 55 52 50 48 46 74 76 1 17 1 12 1 8 5 59 55 52 49 47 46 76 78 78 1 17 1 12 1 8 5 59 55 52 49 47 80 1 12 1 8 5 59 55 52 49 47 80 82 1 8 5 59 55 52 49 82 84 5 59 55 52 49 84 86 59 55 52 86 32" 34" 36" 3>" 42° 46° 50° 54° 58° 62° 66° 70° 1 74° 1 78° 1 82" 86° 1 \ 168 TARI.K XXXIH. THIRD CORRECTION, TO APPARENT DISTANCE 48*». •'" APPARENT ALTITUDE OF THE StTN, OK A STAR. App. A.pp. Alt. Alt. 6" 70 8» 9° 10° 11° 12° 14° 16° 18° 20° 22° 24° 26° 28° 30° o 1 n t n / tf t If / If r ff / ff f It 1 If / ft / If f II / If / // f If f ft % 1 16 1 17 1 19 1 23 1 29 1 36 1 43 2 1 2 20 2 39 2 58 3 16 3 35 3 54 4 13 4 32 6 7 1 19 1 16 1 17 1 19 1 23 1 28 1 33 1. 46 2 2 16 2 32 2 47 3 2 3 18 3 34 3 50 7 8 1 24 ] 19 1 16 1 17 1 19 1 22 1 26 1 35 1 47 1 59 2 12 2 25 2 39 2 53 3 7 3 21 8 9 1 30 1 23 1 18 1 16 1 17 1 19 1 21 1 28 1 37 1 47 1 58 2 9 2 20 2 32 2 44 2 55 9 10 1 37 1 27 1 21 1 18 1 16 1 17 1 18 1 23 1 30 1 38 1 47 1 56 2 6 2 16 2 26 2 36 10 11 1 45 1 33 1 25 1 21 1 18 1 16 1 17 1 20 1 25 1 32 1 39 1 47 1 55 2 4 2 13 2 22 11 12 1 53 1 39 1 30 1 24 1 21 1 18 1 16 1 19 1 22 1 27 1 33 1 40 1 47 1 54 2 2 2 10 12 13 13 2 2 1 46 1 36 1 28 1 24 1 20 1 18 1 17 1 19 1 23 1 28 1 34 1 40 1 46 1 53 2 14 2 11 1 54 1 42 1 33 1 27 1 23 1 20 1 16 1 17 1 20 1 24 1 29 1 34 1 39 1 45 1 51 14 15 2 20 2 1 1 48 1 37 1 42 1 30 1 26 1 22 1 17 1 16 1 18 1 21 1 24 1 29 1 33 1 38 1 43 15 16 2 30 2 9 1 54 1 34 1 29 1 24 1 18 1 16 1 17 1 18 1 20 1 24 1 28 1 32 1 37 16 17 2 40 2 17 2 1 47 1 38 1 32 1 27 1 20 1 17 1 16 1 17 1 18 1 21 1 25 1 28 1 32 17 18 2 50 2 25 2 7 1 52 1 42 1 35 1 30 1 22 1 18 1 15 1 16 1 17 1 19 1 22 1 25 1 28 18 19 3 2 32 2 14 1 58 1 46 1 39 1 33 1 24 1 19 1 16 1 15 1 16 1 17 1 19 1 22 1 24 19 20 3 9 2 40 2 20 2 26 2 3 1 51 1 43 1 36 1 27 1 30 1 21 1 17 1 14 1 15 1 16 1 17 1 16 1 19 1 21 20 21 3 18 2 48 2 9 1 56 1 47 1 40 1 23 1 18 1 15 1 14 1 15 1 17 1 19 21 22 3 27 2 56 2 33 2 15 2 2 1 52 1 43 1 32 1 24 1 19 1 16 1 13 1 14 1 15 1 16 1 18 22 23 3 37 3 3 2 40 2 21 2 7 1 56 1 46 1 35 1 26 1 20 1 16 1 14 1 13 1 14 1 15 1 16 23 24 3 46 3 11 2 47 2 26 2 12 2 1 50 1 37 1 27 1 21 1 17 1 14 1 12 1 13 1 13 1 14 24 25 3 56 3 19 2 54 2 32 2 17 2 5 1 54 1 40 1 29 1 22 1 24 1 18 1 15 1 13 1 12 1 12 1 13 25 26 26 4 5 3 27 3 1 2 38 2 22 2 9 1 58 1 42 1 31 1 19 1 16 1 13 1 11 1 11 1 12 27 4 15 3 34 3 8 2 44 2 27 2 14 2 2 1 44 1 33 1 25 1 20 1 16 1 13 1 11 1 10 1 11 27 28 4 24 3 42 3 15 2 50 2 32 2 18 2 6 1 47 1 35 1 27 1 21 1 17 1 14 1 12 1 10 1 10 28 29 4 33 3 50 3 21 2 56 2 37 2 23 2 10 1 50 1 37 1 28 1 22 1 18 1 15 1 12 1 10 1 9 29 30 4 42 3 58 3 28 3 2 2 42 2 27 2 13 1 53 1 40 1 30 1 23 1 19 1 15 1 12 1 '0 1 9 30 31 31 4 51 4 6 3 35 3 8 2 47 2 31 2 17 1 57 1 42 1 32 1 25 1 20 1 16 1 13 1 11 1 9 32 5 4 13 3 42 3 14 2 52 2 35 2 20 2 1 44 1 33 1 26 1 21 1 16 1 .3 1 n 1 9 32 33 5 9 4 21 3 49 3 20 2 57 2 39 2 23 2 3 1 46 1 35 1 27 1 22 1 17 1 14 1 12 1 10 33 34 5 18 4 28 3 55 3 25 3 2 2 44 2 27 2 6 1 49 1 37 1 28 1 23 1 18 1 14 1 12 1 10 34 35 5 27 4 36 4 1 3 31 3 7 2 48 2 31 2 35 2 9 1 52 1 39 1 30 1 24 1 25 1 19 1 15 1 12 1 10 35 36 5 35 4 43 4 8 3 37 3 12 2 52 2 12 1 54 1 41 1 31 1 19 1 15 1 12 1 10 36 37 5 44 4 5(1 4 14 3 42 3 17 2 57 2 39 2 16 1 56 1 43 1 33 1 26 1 20 1 16 1 13 1 11 37 38 5 52 4 57 4 20 3 47 3 22 3 1 2 43 2 19 1 59 1 45 1 34 1 27 1 21 1 17 1 14 1 11 38 39 6 5 4 4 26 3 53 3 26 3 5 2 47 2 22 2 2 1 47 1 35 1 28 1 22 1 17 1 14 1 11 39 40 6 8 5 11 4 32 3 58 3 30 3 10 2 51 2 25 2 5 1 49 1 37 1 29 1 23 1 18 1 15 1 12 40 41 6 16 5 18 4 38 4 3 3 35 3 14 2 55 2 28 2 7 1 51 1 39 1 31 1 24 1 19 1 16 1 13 41 42 6 24 5 24 4 44 4 8 3 40 3 18 2 58 2 31 2 10 1 53 1 41 1 33 1 26 1 20 1 16 1 13 42 43 6 32 5 31 4 50 4 13 3 44 3 22 3 2 2 33 2 12 1 55 1 43 1 34 1 27 1 21 1 17 1 14 43 44 6 39 5 37 4 55 4 1? 3 48 3 26 3 5 2 36 2 14 1 57 1 45 1 36 1 28 1 22 1 18 1 15 44 46 6 53 5 49 5 5 4 2? 3 56 3 34 3 12 2 41 2 18 2 1 1 48 1 38 1 30 1 23 1 18 1 15 46 48 48 7 7 6 1 5 15 4 37 4 4 3 41 3 18 2 46 2 22 2 5 1 51 1 40 1 31 1 24 1 19 1 16 50 7 21 6 13 5 25 4 M ) 4 12 3 47 3 2A 2 51 2 26 2 8 1 53 1 42 1 33 1 25 1 20 1 16 50 52 7 34 6 2'1 \ 5 34 4 5^ I 4 20 3 53 3 3n 2 56 2 30 2 12 1 56 1 44 1 35 1 27 1 22 1 17 52 54 7 47 6 3£ > 5 43 5 ] 4 27 3 59 3 36 3 1 2 34 2 15 1 59 1 46 1 37 1 29 1 23 1 19 54 56 8 C » 6 M ) 5 51 5 I I 4 34 4 5 3 41 3 6 2 38 2 18 2 2 1 49 1 39 1 31 1 25 1 20 56 58 5 59 5 11 5 4 40 4 46 4 11 4 16 3 U 3 5C 3 54 ) 3 10 I 3 13 I 3 15 3 17 2 42 2 45 2 47 2 49 2 51 2 21 2 23 2 25 2 27 2 29 2 4 2 6 2 8 2 10 2 11 1 51 1 53 1 54 1 56 1 57 1 41 1 42 1 43 1 45 1 46 1 32 1 33 1 34 1 35 1 36 1 26 1 27 1 28 1 28 1 29 1 30 1 30 1 21 1 21 1 22 1 22 1 23 58 60 62 64 66 TABLE P. EFFECT OF SUN's PAE Add the Numbers above the lines to^rd Corrertion, sub- tract the others. f " Sun's Apparent Altitude. App .. 2 31 2 12 2 13 1 58 1 59 ! 47 1 48 1 37 1 38 1 24 1 24 68 70 Alt. 5 10 •20 3(l4f 50 60 7 O80 [90 tl 1 It f »t ff ff 2 1 49 1 39 1 31 1 24 72 5 1 2 3 4 5 1 50 1 40 1 32 1 25 74 10 1 1 20 3 3 30 5 5 40 7 6 50 9 8 60 9 1 2 3 1 1 3 2 1 543 6 5 4 8 6 5 4 2 2 3 4 5 3 J 1 V 1 i 2 \ 3 : r 1 1 41 1 33 1 25 76 78 80 82 84 1 33 1 26 1 26 70 80 9(1 9 7 fi 8 7 7 5 6 4 . 86 11° 12° 14° 16° 18° 20° 22° 24° 26° 28° 30° TABLE XXXIII. THIRD CORRECTION, TO APPARENT DISTANCE 48°. App. Alt. APPARENT ALTITUDE OF THE SUN, OB STAR. 32* 34° 36° 38° 42° 46° 50° 64° 58° 62° 66° 70° 74° 78° 82° 86° t n / // / n r >r / n / It t n ; ti / // / ti / // / // t // / // / ti / // 6 4 51 5 10 5 28 5 46 6 18 6 49 7 19 7 47 7 4 6 4 21 4 36 4 51 5 19 5 45 6 11 6 35 7 8 3 34 3 iS 4 1 4 14 4 38 5 1 5 22 5 42 6 1 8 9 3 7 3 19 3 30 3 41 4 3 4 24 4 43 5 5 17 9 10 2 47 2 57 2 40 3 7 3 17 3 36 3 54 4 11 4 26 4 40 10 11 2 31 2 49 2 57 3 14 3 30 3 44 3 57 4 10 11 •12 2 17 2 25 2 33 2 40 2 55 3 9 3 22 3 34 3 45 3 55 12 13 2 6 2 13 2 20 2 27 2 40 2 52 3 4 3 15 3 25 3 32 13 14 1 57 2 4 2 10 2 16 2 27 2 38 2 49 2 59 3 8 3 15 14 15 1 49 1 55 2 1 2 6 2 16 2 26 2 35 2 44 2 53 3 15 16 16 1 42 1 47 1 52 57 2 7 2 15 2 23 2 32 2 40 2 46 2 52 17 1 36 1 41 1 45 50 1 59 2 6 2 14 2 22 2 29 2 34 2 40 17 18 1 31 1 35 1 39 43 1 51 1 59 2 6 2 13 2 19 2 24 2 29 18 19 1 27 1 31 1 34 38 1 45 1 52 1 58 2 4 2 10 2 15 2 19 19 20 1 24 1 27 1 30 33 1 39 1 45 1 51 1 57 2 2 2 7 2 11 2 15 __ 20 21 1 22 1 24 1 27 29 1 34 1 40 1 45 1 51 1 56 2 2 4 2 7 21 22 1 20 1 22 1 24 26 1 30 1 35 1 40 1 45 1 50 1 54 57 59 22 23 1 18 1 19 1 21 23 1 27 1 31 1 36 1 40 1 45 1 49 51 53 23 24 1 16 1 17 1 19 21 1 25 1 28 1 32 1 36 1 40 1 44 46 48 50 ^ 24 25 26 1 14 1 15 1 16 18 1 22 1 25 1 29 1 32 1 36 1 39 1 34 41 43 45 25 1 12 1 13 1 14 16 1 19 1 23 1 26 1 29 1 32 1 36 38 40 26 27 1 11 1 12 1 13 14 1 17 1 20 1 23 1 26 1 28 1 30 32 34 36 27 28 1 10 1 11 1 12 13 1 15 1 18 1 20 1 23 1 25 1 27 28 30 32 34 28 29 1 9 1 10 1 11 12 1 14 1 16 1 18 1 20 1 22 1 24 25 27 28 30 29 1 30 1 9 1 10 1 10 11 1 12 1 14 1 16 1 18 1 19 1 21 22 24 25 26 30 31 1 9 1 9 1 9 10 1 11 1 12 1 14 1 16 1 17 1 19 20 21 22 23 31 32 1 8 1 8 1 8 9 1 10 1 11 1 13 1 14 1 15 1 17 18 19 19 20 21 32 33 1 8 1 7 1 7 8 1 9 1 10 1 11 1 12 1 13 1 15 16 17 17 17 18 33 34 1 8 1 6 1 6 7 1 8 1 9 1 10 1 11 1 12 1 13 14 14 15 15 J 16 34 35 1 8 1 6 1 5 G 1 7 1 8 1 9 1 9 1 10 1 11 12 12 13 13 14 13 35 36 36 1 8 1 6 1 5 5 1 5 1 6 1 7 1 7 1 8 1 9 10 10 11 11 12 37 1 9 1 7 1 5 4 1 4 1 5 1 6 1 6 1 7 1 7 8 8 9 9 10 • 11 37 38 1 9 1 7 1 5 3 1 3 1 4 1 5 1 5 1 6 1 6 7 7 8 8 8 ! 9 38 39 1 9 1 7 1 5 3 1 3 1 3 1 4 1 4 1 5 1 5 6 6 6 7 7 J 7 39 40 1 9 1 7 1 5 3 1 2 1 2 1 3 1 3 1 4 1 4 5 5 5 6 6 1 6 1 t 40 41 41 1 10 1 8 1 5 3 1 1 1 1 1 2 1 2 1 3 1 3 4 4 4 5 5 42 1 1-0 1 8 1 5 3 1 1 1 1 1 1 1 2 1 2 1 2 3 3 3 4 4 1 4 42 43 1 11 1 8 1 6 4 1 1 1 1 1 1 1 1 1 1 2 2 2 3 3 1 3 43 44 1 12 1 9 1 6 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 44 46 1 12 1 9 1 6 4 1 1 59 59 59 59 59 59 59 59 59 59 59 46_ 48 48 1 13 1 10 1 7 4 1 1 59 58 58 58 58 57 57 57 57 57 67 50 1 13 1 10 1 7 5 1 1 59 57 57 57 57 56 56 56 56 56 50 52 1 14 1 11 1 8 5 1 1 59 57 56 56 56 55 55 54 54 54 52 54 1 15 1 11 1 8 6 1 2 59 57 56 55 55 54 54 53 53 54 56 1 15 1 11 1 8 6 1 2 59 57 55 54 54 53 53 52 52 56 58 1 16 1 12 1 9 6 1 2 59 57 55 54 53 52 52 51 . 68 1 60 1 16 1 12 1 9 6 1 2 59 57 55 53 52 52 51 50 60 62 1 17 1 13 1 10 7 1 2 59 57 55 53 52 51 51 62 64 1 17 1 13 1 10 7 1 2 59 57 55 53 52 51 50 64 66 68 1 18 1 14 1 10 7 1 3 59 57 54 52 51 50 66 1 18 1 14 1 10 7 1 3 59 56 54 52 51 50 68 70 1 19 1 15 1 11 8 1 3 59 56 54 52 51 70 72 1 19 1 15 1 11 8 1 3 59 56 54 52 50 72 74 1 20 1 15 1 11 8 1 3 59 56 53 51 74 76 1 20 1 16 1 12 8 1 3 59 56 53 51 76 78 1 21 1 16 1 12 9 1 4 59 56 53 78 80 1 21 1 16 1 12 9 1 4 59 56 53 80 82 1 21 1 16 1 12 9 1 4 59 56 82 84 1 16 1 12 9 1 -1 59 56 84 86 1 12 9 1 -1 59 86 32^ 34° 36° 38° 42° 46° 50° 54° 58° 62° 66° 70° 74° 78° 82° 86° 170 TABLE XXXIII. 1 THIRD CORRECTION, TO APPARENT DISTANCE 62='. 9 Fs" APPARENT ALTITUDE OF THE SUN, OR STAR. D's App Alt. App. Alt. 6» 70 30 90 lO* 11» 12° 140 16° 18° 20° 22° 24° 26° 1 2B° 1 30° o t It / // / // t n / fi 1 II / // / n / II / // 1 II 1 II 1 // 1 // 1 If / // 6 1 18 1 19 1 21 1 24 1 30 1 37 1 44 2 2 17 2 34 2 51 3 10 3 28 3 47 4 6 4 24 6 7 1 21 1 18 1 19 1 21 1 24 1 29 1 34 1 46 2 2 14 2 28 2 42 2 57 3 12 3 27 3 43 7 8 1 25 1 21 1 18 1 19 1 21 1 24 1 27 1 36 1 47 1 58 2 11 2 23 2 36 2 50 3 3 3 16 8 9 1 30 1 24 1 20 1 18 1 19 1 21 1 23 1 29 1 37 1 47 1 57 2 8 2 19 2 31 2 42 2 53 9 10 1 37 1 28 1 23 1 20 1 18 1 19 1 21 1 25 1 30 1 38 1 46 1 56 2 6 2 16 2 26 2 36 10 11 1 45 1 34 1 28 1 23 1 20 1 18 1 19 1 22 1 26 1 32 1 39 1 47 5Q 2 4 2 13 2 22 11 12 1 54 1 41 1 33 1 27 1 22 1 20 1 18 1 20 1 23 1 27 1 33 1 40 47 54 2 2 2 10 12 1 13 2 2 1 48 1 38 1 31 1 25 1 22 1 19 1 19 1 21 1 24 1 29 1 35 41 47 54 2 1 13 1 14 2 11 1 55 1 44 1 35 1 28 1 24 1 21 1 18 1 19 1 22 1 26 1 30 35 41 47 52 14 " 15 2 19 2 2 1 50 1 39 1 32 1 27 1 23 1 19 1 18 1 20 1 23 1 26 30 35 40 44 15 16 16 2 28 2 9 1 55 1 44 1 35 1 30 1 25 1 20 1 17 1 18 1 20 1 23 26 30 1 34 38 17 2 37 2 16 2 1 48 1 39 1 33 1 27 1 21 1 18 1 17 1 18 1 20 23 26 30 33 17 18 2 46 2 23 2 6 1 53 1 43 1 36 1 30 1 23 1 19 1 16 1 17 1 18 20 23 ■1 26 29 18 19 2 56 2 30 2 12 1 59 1 48 1 40 1 33 1 25 1 20 1 17 1 16 1 17 18 20 ^ 23 26 19 20 3 5 2 37 2 18 2 4 1 52 1 44 1 37 1 27 1 22 1 18 1 15 1 16 17 18 20 23 20 21 3 14 2 44 2 24 2 9 1 57 1 48 1 40 1 29 1 23 1 19 1 16 1 16 16 17 18 20 21 22 3 23 2 52 2 31 2 15 2 1 1 52 1 44 ,1 32 1 25 1 20 1 16 1 15 15 16 17 18 22 23 3 32 2 59 2 38 2 20 2 6 1 56 1 47 1 34 1 26 1 21 1 17 1 15 14 15 16 17 23 24 3 41 3 7 '2 44 2 26 2 11 2 1 51 1 37 1 28 1 22 1 18 1 15 14 14 16 16 24 25 26 3 50 3 14 2 51 2 31 2 16 2 4 1 54 1 40 1 30 1 23 1 19 1 16 14 13 14 15 25 3 59 3 22 2 58 2 37 2 21 2 8 1 58 1 42 1 32 1 25 1 20 1 16 14 . 13 13 14 26 27 4 8 3 30 3 5 2 42 2 26 2 12 2 2 1 45 1 33 1 26 1 21 1 17 15 14 13 13 27 28 4 17 3 38 3 12 2 48 2 31 2 16 2 6 1 48 1 35 1 28 1 22 1 18 15 14 13 13 28 29 4 26 3 45 3 19 2 53 2 36 2 21 2 10 1 51 1 37 1 29 1 23 1 19 16 14 13 12 29 1 30 31 4 34 3 53 3 25 2 59 2 41 2 25 2 13 1 54 1 39 1 31 1 24 1 19 16 14 13 12 30 1 4 43 4 3 32 3 5 2 45 2 29 2 17 1 57 1 41 1 32 1 25 1 20 17 15 13 12 31 32 4 52 4 3 3 38 3 10 2 50 2 34 2 20 1 59 1 43 1 34 1 27 1 21 17 15 13 12 32 33 5 4 15 3 44 3 16 2 55 2 38 2 24 2 2 1 45 1 36 1 29 1 23 18 15 13 12 33 34 5 9 4 22 3 50 3 21 2 59 2 42 2 27 2 5 1 48 1 38 1 30 1 24 19 16 14 12 34 35 5 17 4 29 3 56 3 27 3 4 2 46 2 31 2 7 1 51 1 40 1 32 1 25 20 17 14 12 35 36 36 5 26 4 36 4 2 3 32 3 9 2 50 2 34 2 10 1 53 1 42 1 33 1 26 21 17 14 12 37 5 34 4 42 4 8 3 37 3 14 2 54 2 38 2 13 1 56 1 44 1 34 1 27 22 18 15 13 37 38 5 42 4 49 4 13 3 42 3 18 2 58 2 42 2 16 1 58 1 46 1 36 1 28 22 18 15 13 38 39 5 50 4 56 4 19 3 47 3 23 3 2 2 46 2 19 2 1 1 48 1 38 1 30 23 18 15 13 39 40 5 58 5 3 4 24 3 52 3 27 3 6 2 49 2 22 2 3 1 50 1 39 1 31 25 19 16 14 40 41 41 6 6 5 9 4 30 3 57 3 32 3 10 2 53 2 25 2 6 1 52 1 41 1 32 26 20 16 14 42 6 14 5 15 * 35 4 2 3 36 3 14 2 56 2 28 2 8 1 54 1 42 1 34 27 21 17 15 42 43 6 21 5 21 4 41 4 7 3 40 3 18 3 C 2 31 2 11 1 56 1 44 1 35 28 22 18 15 43 44 6 28 5 27 4 46 4 12 3 44 3 22 3 3 2 34 2 13 1 58 1 45 1 37 29 23 19 16 44 46 6 42 5 39 4 56 4 21 3 52 3 29 3 IC 2 39 2 18 2 1 1 48 1 39 31 24 20 17 46 48 48 6 55 5 51 5 6 4 30 3 59 3 36 3 16 2 44 2 22 2 5 1 51 1 41 33 26 21 18 50 7 8 6 2 5 16 4 38 4 7 3 43 3 23 2 49 2 26 2 8 1 54 1 43 35 27 22 19 50 52 7 21 6 13 5 25 4 46 4 15 3 50 3 2S 2 54 2 30 2 11 1 57 1 45 36 29 24 20 52 54 7 33 6 23 5 34 4 53 ■4 22 3 56 3 3S 2 59 2 34 2 14 2 1 48 38 31 25 21 54 56 7 44 6 33 5 43 4 59 4 29 4 2 3 4C 3 4 2 38 2 17 2 2 1 50 40 32 26 22 56 58 58 7 53 6 42 5 50 5 6 4 35 4 7 3 45 3 8 2 42 2 20 2 5 1 53 42 33 27 23 60 8 2 6 49 5 56 5 12 4 40 4 12 3 5C 3 12 2 46 2 23 2 7 1 55 44 35 29 24 60 62 6 2 5 14 4 45 4 16 3 54 3 15 2 49 2 26 2 9 1 57 46 36 30 25 62 64 4 50 4 20 3 58 3 18 2 51 2 28 2 11 1 59 48 37 31 26 64 66 4 1 3 20 2 53 2 30 2 13 2 49 39 32 26 66 68 3 22 2 54 2 32 2 15 2 1 50 40 33 27 68 70 2 55 2 33 2 16 2 2 51 41 34 28 70 72 2 34 2 17 2 3 52 42 34 28 72 74 2 18 2 4 53 43 35 29 74 76 2 5 54 44 36 29 76 78 1 55 44 36 30 78 80 45 37 30 80 82 38 30 82 84 31 84 86 86 6" 70 8° 9" 10° 11° 12° 14° 16° 18° 20° 22° 24° 26° 28° 30° TABLE XXXllI. 171 THIRD CORRECTION. TO APPARENT DISTANCE 52°. D's APPARENT ALTITUDE OF THE SUN. OR STAR. • V App. Alt. App Alt. 32° 340 36° 38° 1 42° 46° 50° 54^ 58° 62° 66° 70° 74° 78° 82° 86° o r n / n t II / /' / // / II / II / // / n r II 1 // / // f // / // / // 1 ft ■> 6 4 43 5 1 5 18 5 34 6 6 6 36 7 4 7 29 7 53 6 7 3 59 4 14 4 29 4 43 5 9 5 34 5 58 6 20 6 42 7 8 3 30 3 43 3 55 4 8 4 30 4 52 5 13 5 32 5 50 6 6 8 9 3 4 3 15 3 26 3 37 3 58 4 17 4 36 4 51 5 5 5 18 9 10 2 45 2 54 2 38 3 4 3 14 3 32 3 48 4 4 4 20 4 33 4 6 '4 45 10 11 11 2 30 2 47 2 55 3 11 3 26 3 40 3 54 4 10 12 2 17 2 25 2 32 2 40 2 54 3 7 3 20 3 32 3 43 3 52 4 1 12 13 2 7 2 13 2 20 2 26 2 39 2 51 3 3 3 14 3 24 3 32 3 38 13 14 1 58 2 3 2 9 2 14 2 26 2 37 2 48 2 58 3 7 3 14 3 20 14 15 1 49 1 54 1 59 2 4 56 2 15 2 26 2 35 2 44 2 52 2 59 3 5 15 16 1 42 1 47 1 51 2 7 2 16 2 24 2 32 2 40 2 46 2 52 2 57 16 17 1 37 1 41 1 45 50 2 2 8 2 15 2 22 2 29 2 35 2 40 2 44 17 18 1 32 1 36 1 40 45 53 2 2 7 2 13 2 19 2 25 2 30 2 33 18 19 1 29 1 32 1 36 40 47 1 53 2 2 6 2 11 2 10 2 21 2 24 19 20 1 26 1 29 1 32 35 — 41 37 1 47 1 53 1 47 1 59 2 4 2 9 2 13 2 16 2 19 20 21 1 23 1 26 1 28 31 1 42 1 53 1 58 2 2 2 6 2 9 2 11 21 22 1 21 1 23 1 25 28 33 1 37 1 42 1 47 1 52 1 56 59 2 2 2 4 22 23 1 19 1 21 1 23 25 29 1 33 1 38 1 42 1 47 1 51 54 56 1 58 23 24 1 17 I 19 1 21 23 26 1 30 1 34 1 38 1 42 1 46 49 51 1 53 1 55 24 25 1 16 1 17 1 19 20 23 21 1 27 1 30 1 34 1 37 1 41 44 46 1 48 1 49 25 26 1 15 1 16 1 17 18 1 24 1 27 1 30 1 33 1 36 39 41 1 43 1 44 26 27 1 14 1 15 1 16 17 19 1 22 1 24 1 27 1 30 1 32 35 37 1 39 1 40 27 28 1 13 1 14 1 15 16 17 1 20 1 22 1 24 1 27 1 29 31 33 1 35 1 36 1 37 28 29 1 12 1 13 1 14 15 16 1 18 1 20 1 22 1 24 1 26 28 30 1 31 1 32 1 33 29 30 1 12 1 12 1 13 13 14 1 16 1 18 1 20 1 22 1 24 25 27 24 1 28 1 29 1 30 30 31 1 11 1 11 1 12 12 13 1 15 1 16 1 18 1 20 1 22 23 1 25 1 2« 1 27 31 32 1 11 1 11 1 11 11 12 1 14 1 15 1 16 1 18 1 20 21 22 1 23 1 23 1 24 1 25 32 33 1 11 1 10 1 10 10 11 1 13 1 14 1 15 1 17 1 18 19 20 1 21 1 21 1 22 1 22 33 34 1 11 1 10 1 10 10 11 1 12 1 13 1 14 1 16 1 17 17 18 1 19 1 19 1 20 1 20 34 35 1 11 1 10 1 10 10 10 1 11 1 12 1 13 1 14 1 15 15 16 1 17 1 17 1 18 1 18 35 36 1 11 1 10 1 9 9 9 1 10 1 11 1 11 1 12 1 13 13 14 1 15 1 15 1 16 1 16 3^ 37 1 11 1 10 1 9 9 9 1 9 1 10 1 10 1 11 1 11 12 12 1 13 1 13 1 14 1 14 37 38 1 11 1 10 1 9 8 8 1 9 1 9 1 9 1 10 1 10 11 11 1 11 1 11 1 12 1 12 38 39 1 11 1 10 1 9 8 8 1 8 1 8 1 8 1 9 1 9 10 10 1 10 1 10 1 10 1 10 39 40 1 12 1 10 1 9 8 7 1 7 1 7 1 7 1 8 1 8 9 9 1 9 1 9 1 9 1 9 40 41 41 1 12 1 11 1 9 8 7 1 7 1 7 1 7 1 7 1 7 8 8 1 8 1 8 1 8 1 8 42 1 13 1 11 1 » 8 6 1 6 1 6 1 6 1 6 1 6 7 7 1 7 1 7 1 7 1 7 42 43 1 13 1 11 1 9 8 6 1 6 1 6 1 6 1 6 1 6 6 6 1 6 1 6 1 6 1 6 43 44 1 14 1 11 1 9 8 6 1 5 1 5 1 5 1 5 1 5 5 5 1 5 1 5 1 5 1 5 44 46 1 14 1 12 1 10 9 6 1 4 1 4 1 3 1 4 1 4 1 4 4 3 1 3 1 3 1 3 46 48 1 15 1 13 1 11 9 6 1 4 1 3 1 3 1 2 1 2 1 1 1 1 1 1 1 48 50 1 16 1 14 1 11 9 6 1 4 1 2 1 2 1 2 1 1 1 1 1 1 50 52 1 17 1 15 1 12 9 6 1 4 1 2 1 1 1 1 1 1 59 58 52 54 1 18 1 15 1 12 9 6 1 4 1 2 1 1 1 59 59 58 57 54 56 1 18 1 15 1 12 10 6 1 4 1 2 1 59 58 58 57 56 56 58 60 62 1 19 1 20 1 21 1 16 1 16 1 17 1 13 1 13 1 13 10 10 10 6 7 7 1 4 1 4 1 4 1 2 1 2 1 1 1 1 59 59 58 58 58 57 56 57 56 55 56 55 TABLK P. EFFECT OF SHN's PAS AtU the Numiers above the 64 1 22 1 18 1 14 11 7 1 4 1 1 59 57 56 u 54 lines to 3rd Ccrrection, sub- 66 1 22 1 18 1 14 11 7 1 4 I 1 59 57 55 54 tract the others. )8 App Alt. Sun's Apparent Altitude | 68 1 22 1 18 1 14 1 14 1 1 7 1 3 1 3 1 1 58 58 56 56 70 1 23 1 18 11 7 5 10-2 3 30 40 5 60 70 5 3090 72 1 23 1 19 1 15 11 7 1 3 1 57 55 tr n II /' it / n // " 74 1 24 1 19 1 15 11 7 1 3 1 57 5 1 2 3 4 4 76 1 24 1 19 1 15 12 7 1 3 1 56 10 20 r 1 \_ 331 2 3 -i 1 4 3 1 78 1 24 1 19 1 15 12 7 1 3 1 30 5 4 3 "a r 80 1 24 1 19 1 15 12 7 1 3 1 40 7 6 5 4 3 2 1 1 B 82 1 25 1 20 1 16 12 7 1 3 50 B 8 6 5 4 3 3 2 84 1 25 1 20 1 16 12 7 1 3 60 70 80 90 9 7 6 5 4 4 3 86 1 25 1 21 1 16 12 7 ei V 8 6 ti 7 6 7 5 32° 34° 36° oqo 42° 46° 50° 54° 58° 62° aao 70° 1 HM^ '-' 172 TABLE XXXIII. 1 THIRD CORRECTION, TO APPARENT DISTANCE 56°. 1 J's APPARENT ALTITUDE OF THE SUN, OR STAR. :D's| App. Alt. App 6° 70 8° Q*' 100 11° 12° 14° 16° 18° 1 20° 22° 24° 26° 28° 30° Alt. o / // r // f ff. / ff / // / ff r ff r rr 1 ft / // t n / // / // / // / ff / // 6 1 20 1 22 1 25 1 29 1 35 1 41 1 48 2 2 2 18 2 35 2 52 3 10 3 27 3 45 4 3 4 20 6 7 1 23 1 20 1 22 1 24 1 27 1 32 1 37 1 48 2 1 2 15 2 29 2 43 2 58 3 12 3 27 3 42 7 8 1 28 1 23 1 20 1 21 1 23 1 26 1 29 1 38 1 48 2 2 12 2 23 2 35 2 48 3 1 3 14 8 9 1 34 1 27 1 22 1 20 1 21 1 23 1 25 1 31 1 39 48 58 2 8 2 18 2 29 2 40 2 50 9 10 1 40 1 31 1 25 1 22 1 20 1 21 1 22 1 26 1 32 39 48 1 56 2 5 2 15 2 24 2 33 10 11 1 47 1 30 1 29 1 25 1 22 1 20 1 21 1 23 1 27 33 4!^ 1 47 55 2 4 2 12 2 20 11 12 1 54 1 42 1 33 1 28 1 24 1 21 1 20 1 21 1 24 28 34 1 40 47 1 55 2 2 2 9 12 13 2 2 1 48 1 38 1 31 1 26 1 23 1 21 1 20 1 22 25 30 1 35 41 1 47 1 54 2 13 14 2 10 1 54 1 43 1 35 1 29 1 25 1 22 1 19 1 20 23 27 1 31 36 1 41 1 47 1 52 14 15 2 18 2 1 1 48 1 39 1 33 1 28 1 24 1 21 1 19 21 24 1 27 32 1 36 1 41 1 46 15 16 16 2 27 2 8 1 53 1 43 1 36 1 31 1 26 1 22 1 19 19 21 1 24 28 1 32 1 36 1 40 17 2 35 2 15 1 59 1 47 1 40 1 34 1 29 1 23 1 20 18 19 1 22 25 1 28 1 32 1 35 17 18 2 44 2 22 2 4 1 52 1 43 1 37 1 31 1 25 1 20 17 18 1 20 22 1 25 1 28 1 31 18 19 2 53 2 29 2 10 1 57 1 47 1 40 1 34 1 26 1 21 18 17 1 19 20 1 23 1 25 1 28 19 20 3 2 2 36 2 16 2 2 1 51 1 44 1 37 1 28 1 22 19 17 1 18 19 1 21 1 23 1 25 20 21 3 11 2 44 2 22 2 8 1 55 1 47 1 40 1 30 1 24 20 18 1 17 18 1 19 1 21 1 23 21 22 3 20 2 51 2 29 2 13 2 1 51 1 43 1 32 1 25 21 18 1 16 17 1 18 1 19 1 21 22 23 3 29 2 58 2 35 2 18 2 5 1 55 1 46 1 35 1 27 22 19 1 17 16 1 17 1 18 1 19 23 24 3 38 3 5 2 42 2 23 2 9 1 59 1 50 1 37 1 29 24 20 1 17 16 1 16 1 17 1 18 24 25 26 3 47 3 13 2 49 2 29 2 14 2 3 1 53 1 39 1 31 25 27 21 1 18 16 1 16 1 16 1 17 25 26 3 55 3 20 2 55 2 34 2 19 2 7 1 57 1 42 1 33 22 1 19 17 1 16 1 16 1 16 27 4 4 3 27 3 1 2 39 2 24 2 12 2 1 1 45 1 35] 28 23 1 19 17 1 16 1 16 1 16 27 28 4 12 3 34 3 8 2 45 2 29 2 16 2 5 1 48 1 37 30 24 1 20 18 1 16 1 15 1 16 28 29 4 21 3 41 3 14 2 50 2 33 2 20 2 8 1 51 1 39 31 25 1 21 18 1 16 1 15 1 15 29 30 4 29 3 48 3 20 2 55 2 38 2 24 2 12 1 54 1 41 33 26 1 21 18 1 16 1 15 1 15 30 31 31 4 38 3 55 3 26 3 2 43 2 28 2 16 1 57 1 44 34 28 1 22 18 1 16 1 16 1 15 32 4 46 4 2 3 32 3 6 2 48 2 32 2 19 2 1 46 36 29 1 23 19 1 17 1 16 1 15 32 33 4 54 4 9 3 39 3 11 2 53 2 36 2 23 2 3 1 49 38 31 1 25 20 1 17 1 16 1 15 33 34 5 2 4 16 3 46 3 16 2 57 2 40 2 26 2 6 1 51 40 32 1 26 21 1 18 1 16 1 15 34 35 5 10 4 23 3 51 3 22 3 2 2 44 2 30 2 9 1 53 42 34 1 27 22 1 18 1 16 1 15 35 36 36 5 18 4 30 3 57 3 27 3 6 2 48 2 33 2 12 1 55 44 35 1 28 23 1 19 1 17 1 16 37 5 26 4 37 4 3 3 32 3 10 2 52 2 37 2 15 1 58 46 37 1 29 24 1 20 1 18 1 16 37 38 5 33 4 43 4 8 3 37 3 14 2 56 2 41 2 17 2 48 38 1 30 25 1 21 1 18 1 16 38 39 5 41 4 50 4 14 3 42 3 19 3 2 45 2 20 2 2 50 39 1 31 25 1 21 1 18 1 16 39 40 41 5 48 4 56 4 19 3 47 3 23 3 4 2 48 2 23 2 4 51 40 1 32 26 1 22 1 19 ! 16 40 5 55 5 2 4 25 3 52 3 28 3 8 2 51 2 25 2 6 53 42 1 33 27 1 23 1 20 1 17 41 42 6 2 5 8 4 30 3 57 3 32 3 11 2 54 2 28 2 9 55 43 1 34 28 1 24 1 20 1 17 42 43 6 9 5 14 4 35 4 2 3 36 3 15 2 58 2 31 2 12 57 44 1 35 29 1 25 1 21 1 17 43 44 6 16 5 20 4 40 4 7 3 40 3 19 3 1 2 34 2 14 59 46 1 37 31 1 26 1 22 1 18 44 46 6 29 5 32 4 50 4 16 3 48 3 26 3 8 2 40 2 18 2 2 49 1 40 33 1 28 1 23 1 19 46 48 48 6 42 5 43 4 59 4 24 3 56 3 33 3 14 2 45 2 22 2 6 52 1 43 36 1 30 1 25 1 20 50 6 54 5 54 5 8 4 32 4 3 3 40 3 19 2 50 2 26 2 9 55 1 45 38 1 32 1 26 1 21 50 52 7 6 6 4 5 17 4 39 4 10 3 46 3 24 2 55 2 30 2 12 58 1 48 40 1 33 1 27 1 22 52 54 7 18 6 14 5 25 4 46 4 16 3 52 3 29 2 59 2 34 2 15 2 1 50 42 1 35 1 29 1 24 54 56 7 29 6 24 5 33 4 53 4 22 3 57 3 34 3 3 2 37 2 19 2 3 1 52 43 1 36 1 30 1 25 56 58 7 40 6 33 5 41 5 4 28 4 2 3 39 3 7 2 41 2 22 2 6 1 54 45 1 37 1 31 1 26 58 60 7 50 6 41 5 48 5 7 4 34 4 7 3 43 3 11 2 44 2 25 2 8 1 56 47 1 39 1 32 1 27 60 62 7 58 6 48 5 55 5 13 4 40 4 12 3 48 3 15 2 47 2 28 2 11 1 58 48 1 40 1 33 1 28 62 64 8 6 6 55 6 1 5 19 4 45 4 17 3 52 3 18 2 50 2 30 2 13 8 50 1 41 1 34 1 29 64 66 68 6 7 5 24 4 50 4 21 3 56 3 20 2 53 2 32 2 15 2 2 51 1 42 1 35 1 29 66 4 55 4 25 4 3 22 2 55 2 34 2 17 2 4 52 1 43 1 36 1 30 68 70 4 4 3 24 2 57 2 36 2 18 2 5 53 1 44 1 37 1 31 70 72 3 26 2 59 2 37 2 19 2 6 54 1 45 1 38 1 32 72 74 3 1 2 38 2 20 2 7 55 1 46 1 39 1 32 74 76 2 39 2 21 2 8 56 1 47 1 39 1 33 76 78 2 22 2 8 57 1 48 1 40 1 33 78 80 2 9 58 1 48 1 40 1 34 80 82 58 1 48 1 40 1 34 82 84 1 49 1 41 1 34 84 86 22° 1 41 1 34 86 6" 7» 8° 9** 10" 11° 12° 14° 16° 18° 20° 24° 26° 28° 30° TABLE XXXIII. I7S 1 THIRD CORRECTION, TO APPARENT DISTANCE 66<». D'B A pp. Alt. APPARENT AhTlTVDK OF THE SUN, OR STAR. ' App. 32° 340 36° 38° 42° 46° 1 50° 54° 58° 62° 66° 70° 74° 78° 82° 86° Alt. o / ff / ff / /r f tr 1 II 1 II 1 II / /' / II / // / II 1 // / n / // / // / // 6 4 37 4 54 5 10 5 26 5 56 6 25 6 52 7 15 7 37 7 58 6| 7 3 57 4 11 4 25 4 38 5 3 5 29 5 52 6 12 6 31 6 48 7 8 3 26 3 38 3 51 4 3 4 26 4 47 5 5 5 23 5 40 5 55 6 8 8 9 3 1 3 12 3 23 3 33 3 53 4 12 4 30 4 46 5 5 13 5 25 9 10 11 2 43 2 53 3 2 3 11 3 3 28 9 3 45 4 1 4 15 4 27 4 39 4 50 10 11 2 29 2 37 2 45 2 53 3 24 3 38 3 50 4 1 4 12 4 21 12 2 16 2 23 2 30 2 38 2 52 3 6 3 18 3 28 3 38 3 47 3 56 4 4 12 13 2 6 2 12 2 18 2 25 2 37 2 50 3 1 3 10 3 19 3 28 3 36 3 42 13 14 1 57 2 3 2 8 2 14 2 25 2 36 2 47 2 56 3 4 3 12 3 19 3 24 14 15 1 50 1 55 1 59 2 5 2 15 2 25 2 35 2 44 2 51 2 58 3 4 3 10 15 16 1 44 1 48 1 53 1 58 2 7 2 16 2 25 2 33 2 39 2 45 2 51 2 57 3 2 16 17 1 39 1 43 1 48 1 52 2 2 8 2 16 2 24 2 30 2 35 2 40 2 45 2 49 17 18 1 35 1 39 1 43 1 47 54 2 1 2 8 2 15 2 21 2 26 2 31 2 35 2 38 18 19 1 31 1 35 1 38 1 42 48 55 2 1 2 7 2 13 2 18 2 23 2 27 2 30 19 20 1 28 1 31 1 34 1 37 43 49 1 55 1 49 2 2 6 2 10 2 13 2 19 2 22 2 24 20 21 1 25 1 27 1 30 1 33 38 44 1 54 59 2 3 2 7 2 11 2 14 2 16 21 22 1 22 1 24 1 27 1 30 34 39 1 44 1 48 52 1 56 2 2 4 2 6 2 8 22 23 1 20 1 22 1 24 1 27 31 35 1 40 1 44 47 1 51 54 57 2 2 2 23 24 1 19 1 20 1 22 1 25 28 32 1 36 1 40 43 1 46 49 52 1 54 1 56 1 58 24 25 1 18 1 19 1 21 1 23 26 29 1 33 1 36 39 1 42 44 47 1 49 1 51 1 53 25 26 1 17 1 18 1 19 1 21 24 27 1 30 1 33 35 1 38 40 42 1 44 1 46 1 48 26 27 1 16 1 17 1 18 1 19 22 25 1 27 1 30 32 1 35 37 39 1 40 1 42 1 44 27 28 1 16 1 16 1 17 1 18 20 23 1 25 1 27 29 1 32 34 36 1 37 1 39 1 40 1 41 28 29 1 15 1 15 1 16 1 17 19 21 1 23 1 25 27 1 29 31 33 1 34 1 35 1 36 1 37 29 30 1 15 1 15 1 16 1 16 17 19 1 21 1 23 25 1 27 29 30 28 1 31 1 32 1 33 1 34 30 31 1 14 1 14 1 15 1 15 16 18 1 19 1 21 23 1 25 27 1 29 1 29 1 30 1 31 31 32 1 14 1 14 1 14 1 14 15 17 1 18 1 19 21 1 23 25 26 1 27 1 27 1 27 1 28 32 33 1 14 1 13 1 13 1 13 14 16 1 17 1 18 20 1 21 23 24 1 25 1 25 1 25 1 26 33 34 1 14 1 13 1 13 1 13 14 15 1 16 1 17 19 1 20 21 22 1 23 1 23 1 23 1 24 34 35 1 14 1 13 1 13 1 13 — 13 12 14 1 15 1 14 1 16 17 1 18 19 20 1 21 1 21 1 21 1 22 35 36 1 14 1 13 1 12 1 12 13 1 15 16 1 16 17 18 1 19 1 19 1 19 1 20 36 37 1 14 1 13 1 12 1 12 12 12 1 13 1 14 15 1 15 16 16 1 17 1 17 1 17 1 18 37 33 1 14 1 13 1 12 1 11 11 12 1 13 1 13 14 1 14 15 15 1 16 1 16 1 16 1 17 38 39 1 14 1 13 1 12 1 11 11 11 1 12 1 12 13 1 13 13 13 1 14 1 14 1 15 1 15 39 40 1 14 1 13 1 12 1 11 10 10 1 11 1 11 12 1 12 12 12 1 12 1 13 1 13 1 13 40 41 41 1 15 I 14 1 12 1 11 10 10 1 10 1 10 11 1 11 11 11 1 11 1 12 1 12 42 1 15 1 14 1 12 1 11 9 9 1 9 1 9 10 1 10 10 10 1 10 1 11 1 11 42 43 1 15 1 14 1 12 1 11 9 9 1 9 1 9 9 1 9 9 9 1 9 1 10 1 10 43 44 1 16 1 14 1 12 1 11 9 8 1 8 1 8 8 1 8 8 8 1 8 1 9 1 9 1 44 46 1 17 1 15 1 13 1 12 9 7 1 7 1 7 6 1 6 6 7 1 7 1 7 46 48 1 17 1 15 1 13,1 12 9 7 1 6 1 6 5 1 5 5 5 1 5 1 6 48 50 1 18 1 16 1 14 1 12 9 6 1 5 1 5 4 1 4 4 4 1 4 50 52 1 19 1 17 1 15 1 13 9 6 1 4 1 4 3 1 3 3 3 1 3 52 54 1 20 1 17 1 15 1 13 9 6 1 4 1 3 3 1 2 2 2 54 56 1 21 1 18 1 16 1 14 10 6 1 4 1 2 2 1 1 1 1 1 i 56 58 60 62 1 22 1 23 1 24 1 19 1 19 1 20 1 16 1 16 1 17 1 14 1 14 1 14 10 10 10 6 6 6 1 4 1 4 1 4 1 2 1 2 1 2 1 1 1 1 1 1 1 TABLE P. EFFECT OF BUN's PAR Add the Numbers above the 64 1 24 1 20 1 17 1 14 7 1 4 1 2 1 lines to 3rd Correction, sub- 66 1 25 1 21 1 18 1 15 7 1 4 1 2 tract the others. )'8 App A t. Sun's Apparent Altitude. 1 | 68 70 1 25 1 26 1 21 1 22 1 18 1 19 1 15 1 16 7 7 1 4 1 4 1 2 1 2 1 5 10 a 3 30 40 5 60 70^ iopo 72 1 27 1 23 1 19 1 16 Hi 7 1 4 1 2 ft ft f // t t ' " " n n 74 1 27 1 23 1 19 1 16 1 7 1 4 5 1 a 3 4 I 4 76 1 28 1 23 1 19 1 16 11 1 1 7 7 1 4 10 20 30 1 1 3 3 2 5 4 3 1 1 2 2 ; 1 1 1 1 i 2 2 I 78 1 28 1 23 1 20 1 17 80 1 29 1 24 1 201 1 17 1 7 40 6 6 5 4 3 5 ! 2 1 1 82 1 29 1 24 1 20 1 17 50 8 7 6 5 4 < 3 3 84 86 1 29 1 29 1 24 1 24 1 20 1 20 1 17 1 17 70 j 80 90 9 8 7 9 S 8 6 7 8 8 5 t 6 f 7 4 • 1 32° Q40 36° 38'' 4 70 46° 50° 54° 58° 1 62° fiR° 70» 1 174 TABLE XXXIII. THIRD CORRECTION, TO APPARENT DISTANCE 60° [ A.pp. Alt. APPARENT ALTITUDE OF THE SUN, OR STAR. 3>'6 App 6« 70 8° 9° 10° 1 11° 1 12° 14° 1 16° 1 18° 20° 22° 1 24° 26° 28° 30° Alt. o f tt / // t It / n 1 If / // 1 n / n 1 // / // 1 // / II 1 II / II / // 6 1 22 1 23 1 25 1 28 33 40 1 47 2 1 2 16 2 33 2 50 3 8 3 25 3 41 3 58 4 15 6 7 24 1 22 1 26 1 25 28 33 1 37 47 59 2 13 2 27 2 41 2 55 3 9 3 23 3 37 7 8 28 1 24 1 22 1 23 25 28 1 31 39 48 59 2 11 2 23 2 35 2 48 3 3 12 8 9 33 1 28 1 24 1 22 24 25 1 27 33 40 49 58 2 8 2 18 2 29 2 39 2 50 9 10 40 1 33 1 27 1 24 23 24 1 25 29 34 41 49 1 57 2 6 2 15 2 25 2 34 iO 11 47 1 38 1 31 1 27 24 23 1 24 26 30 36 42 49 1 57 2 5 2 13 2 21 11 12 55 1 43 1 36 1 30 26 24 1 23 25 28 32 37 43 1 49 1 56 2 3 2 11 12 13 2 3 1 49 1 40 1 34 29 26 1 24 24 26 29 33 38 1 43 1 49 1 55 2 2 13 14 2 10 1 55 1 45 1 38 32 28 1 25 23 25 27 30 34 1 38 1 43 1 49 1 54 14 15 2 18 2 1 1 50 1 42 36 31 1 27 24 23 25 27 30 1 34 1 38 1 43 1 48 15 16 16 2 26 2 7 1 55 1 46 39 34 1 29 25 22 23 25 27 1 30 1 34 1 38 1 43 17 2 34 2 13 2 1 50 43 37 1 31 26 22 22 23 25 1 28 1 31 1 34 1 38 17 18 2 42 2 20 2 5 1 54 46 40 1 34 27 23 21 22 23 1 25 1 28 1 31 1 34 18 19 2 50 2 27 2 11 1 59 50 43 1 36 29 24 22 21 22 1 23 1 26 1 28 ] 31 19 20 2 59 2 34 2 17 2 4 54 46 1 39 31 25 22 20 21 1 22 1 24 1 26 1 28 20 21 21 3 7 2 41 2 23 2 9 1 58 50 1 42 33 26 23 21 20 1 21 1 22 1 24 1 25 22 3 15 2 48 2 29 2 14 2 2 53 1 45 35 28 24 21 20 1 20 1 21 1 22 1 23 22 23 3 24 2 55 2 35 2 19 2 7 57 1 48 37 30 25 22 20 1 20 1 20 1 21 1 22 23 24 3 32 3 2 2 41 2 24 2 10 2 1 1 52 40 31 26 23 21 1 20 1 20 1 20 1 21 24 25 26 3 41 3 9 2 47 2 29 2 2 15 20 2 4 1 55 42 33 27 29 24 22 1 20 1 19 1 19 1 20 25 3 49 3 16 2 53 2 34 2 8 1 59 45 35 25 22 1 20 1 19 1 19 1 19 26 27 3 58 3 23 2 59 2 39 2 25 2 12 2 3 48 38 31 26 23 1 21 1 19 1 19 1 19 27 28 4 6 3 30 3 5 2 44 2 29 2 16 2 7 51 40 32 27 23 1 21 1 19 1 18 1 18 28 29 4 15 3 37 3 11 2 49 2 33 2 20 2 11 53 42 34 28 24 1 21 1 19 1 18 1 18 29 30 4 23 3 44 3 17 2 54 2 38 2 24 2 14 56 44 35 29 24 1 21 1 19 1 18 1 18 30 31 31 4 31 3 51 3 23 2 59 2 42 2 28 2 18 1 59 46 37 30 25 1 22 1 20 1 18 1 18 32 4 39 3 58 3 29 3 4 2 47 2 32 2 21 2 2 48 38 31 26 1 22 1 20 1 19 1 18 32 33 4 47 4 5 3 34 3 9 2 52 2 36 2 25 2 5 51 40 33 27 1 23 1 20 1 19 1 18 33 34 4 55 4 12 3 40 3 14 2 56 2 40 2 28 2 8 53 41 34 28 1 24 1 21 1 19 1 18 34 35 5 3 4 18 3 46 3 19 3 2 44 2 32 2 11 55 43 35 29 1 25 1 22 1 20 1 18 35 36 36 5 10 4 24 3 52 3 24 3 4 2 48 2 35 2 14 57 45 37 31 1 26 1 22 1 20 1 18 37 <) 18 4 31 3 58 3 29 3 8 2 52 2 39 2 17 59 47 38 32 1 27 1 23 1 21 1 19 37 38 25 4 38 4 4 3 34 3 12 2 55 2 42 2 20 2 2 49 40 33 1 28 1 24 1 21 1 19 38 39 5 32 4 45 4 10 3 39 3 17 2 59 2 46 2 22 2 4 51 42 35 1 29 1 25 1 22 1 20 39 40 41 5 39 4 51 4 15 3 44 3 21 3 3 2 49 2 25 2 6 53 43 36 1 30 1 26 1 22 1 20 40 5 46 4 57 4 21 3 49 3 26 3 7 2 52 2 27 2 8 55 45 37 1 31 1 27 1 23 1 20 41 42 5 53 5 3 4 26 3 53 3 30 3 11 2 55 2 30 2 10 56 46 38 1 32 1 28 1 24 1 21 42 43 6 5 9 4 31 3 58 3 35 3 15 2 58 2 32 2 13 58 48 40 1 34 1 29 1 25 1 22 43 44 6 7 5 15 4 36 4 3 3 39 3 19 3 1 2 35 2 15 2 49 41 1 35 1 30 1 26 1 22 44 46 48 6 21 5 26 4 46 4 12 3 47 3 26 3 7 2 40 2 19 2 4 52 43 1 37 1 31 1 27 1 23 46 48 6 34 5 37 4 55 4 20 3 54 3 32 3 13 2 45 2 23 2 8 56 46 1 39 1 33 1 28 1 24 50 6 47 5 48 5 4 4 28 4 1 3 37 3 19 2 50 2 27 2 11 59 48 1 41 1 35 1 29 1 25 50 52 6 59 5 58 5 13 4 36 4 8 3 43 3 25 2 55 2 31 2 14 2 2 51 1 43 1 36 1 31 1 27 52 54 7 11 6 8 5 22 4 44 4 15 3 49 3 30 2 59 2 35 2 18 2 4 53 1 45 1 38 1 33 1 28 54 56 58 7 7 22 31 6 17 5 30 4 51 4 21 3 55 3 35 3 4 2 38 2 21 2 7 56 1 47 1 40 1 34 1 29 56 6 25 5 37 4 58 4 27 4 1 3 40 3 8 2 41 2 24 2 10 1 58 1 49 1 41 1 35 1 30 58 60 7 40 6 32 5 45 5 4 4 32 4 6 3 45 3 12 2 44 2 27 2 12 2 1 50 1 42 1 36 1 31 60 62 7 48 6 39 5 52 5 10 4 38 4 11 3 50 3 16 2 48 2 29 2 14 2 2 1 52 1 44 1 37 1 32 62 64 7 56 6 46 5 58 5 16 4 43 4 15 3 55 3 19 2 51 2 31 2 16 2 4 1 53 1 45 1 38 1 33 64 66 68 8 3 6 53 6 2 5 20 4 47 4 19 3 59 3 22 2 54 2 33 2 18 2 5 1 55 1 46 1 39 1 34 66 8 10 6 59 6 6 5 24 4 51 4 23 4 2 3 25 2 56 2 35 2 19 2 6 1 56 1 47 1 40 1 34 68 70 6 10 5 27 4 54 4 26 4 4 3 27 2 58 2 36 2 20 2 7 1 57 1 48 1 41 1 35 70 72 4 57 4 29 4 6 3 28 3 2 38 2 21 2 8 1 58 1 49 1 41 1 35 72 74 4 8 3 29 3 2 2 39 2 22 2 9 1 59 1 50 1 42 1 36 74 76 3 30 3 3 2 41 2 23 2 1 59 1 50 1 42 1 36 76 78 3 4 2 42 2 24 2 11 2 1 51 1 43 1 37 78 80 2 43 2 25 2 12 2 1 1 51 1 43 1 37 80 82 2 26 2 12 2 1 1 52 1 44 1 38 82 84 2 12 2 2 1 52 1 44 1 38 84 86 2 2 1 52 1 44 1 38 86 6° 7° 8" 9" 10° 11° 12° 14° 16° 18° 20° 22° 24° 26° 28° 30° TABLE XXXIII. r 17. A THIRD CORRECTION, TO APPARENT DISTANCE eo**. A.pp. Alt. o APPARENT ALTITUDE OF THE SUN, OR STAR. >'8 App. Alt. 32° 340 36° 38° 42° 46° 1 50° 54° 58° 1 62° 66° 1 70° 74° 78° 82° 86° t n 1 n 1 n t II / // / // / II / II 1 II / // / II / II 1 II 1 II / // / II 6 4 32 4 48 5 3 5 19 5 49 6 17 6 44 7 7 7 28 7 47 8 3 6 7 3 51 4 5 4 19 4 32 4 58 5 22 5 44 6, 4 6 22 6 38 6 53 7 8 3 23 3 35 3 47 3 59 4 22 4 42 5 1 5 19 5 35 5 50 6 2 6 13 8 9 3 3 10 3 20 3 30 3 49 4 8 4 25 4 41 4 55 5 8 5 19 5 30 9 10 2 43 2 51 3 3 9 3 26 3 42 3 58 4 12 4 24 '4 35 4 45 4 54 10 11 11 2 29 2 37 2 44 2 52 3 7 3 21 3 35 3 48 3 59 4 9 4 18 4 26 12 2 18 2 25 2 32 2 39 2 52 3 5 3 17 3 29 3 39 3 48 3 56 4 3 4 8 12 13 2 8 2 15 2 21 2 28 2 39 2 51 3 2 3 12 3 21 3 30 3 38 3 44 3 48 13 14 2 2 6 2 12 2 18 2 28 2 38 2 48 2 57 3 6 3 14 3 21 3 26 3 29 14 15 1 53 1 58 2 3 2 8 2 18 2 27 2 36 2 45 2 34 2 53 3 3 6 3 11 3 15 15 16 1 47 1 51 1 55 2 2 9 2 18 2 26 2 41 2 48 2 53 2 58 3 2 3 6 16 17 1 42 1 45 1 49 1 53 2 M 2 9 2 17 2 24 2 31 2 37 2 42 2 46 2 50 2 53 17 18 1 37 1 40 1 44 1 47 1 54 2 1 2 9 2 16 2 22 2 27 2 32 2 36 2 40 2 42 18 •19 1 33 1 36 1 39 1 42 1 48 55 2 2 2 9 2 15 2 19 2 24 2 28 2 31 2 33 19 20 1 30 1 32 1 35 1 38 1 44 50 1 56 2 2 1 56 2 8 2 12 2 16 2 20 2 23 2 25 2 27 20 21 1 27 1 29 1 32 1 35 1 40 46 1 51 2 1 2 6 2 10 2 13 2 15 2 17 2 19 21 22 1 25 1 27 1 29 1 32 1 37 42 1 47 1 51 56 2 2 4 2 6 2 8 2 10 2 12 22 23 1 23 1 25 1 27 1 30 1 34 38 1 43 1 47 51 55 59 2 1 2 3 2 4 2 6 23 24 1 22 1 23 1 25 1 27 1 31 35 1 40 1 44 47 *■ 51 54 I 56 1 58 1 59 2 1 2 3 24 25 1 21 1 22 1 23 1 25 1 29 1 26 32 1 36 1 40 43 47 49 1 51 1 53 1 54 1 56 1 57 25 26 1 20 1 21 1 22 1 23 29 1 33 1 37 40 43 45 1 47 1 49 1 60 1 51 1 52 26 27 1 19 1 20 1 21 1 22 1 24 27 1 30 1 34 37 40 42 1 43 1 45 1 46 1 47 1 48 27 28 1 19 1 19 1 20 1 21 1 23 25 1 28 1 31 34 37 39 1 40 1 41 1 42 1 43 1 44 28 29 1 18 1 18 1 19 1 20 1 22 23 1 26 1 29 31 34 36 1 37 1 38 1 39 1 40 1 41 29 30 1 18 1 18 1 18 1 19 1 20 22 1 24 1 27 29 31 33 1 34 1 31 1 35 1 36 1 37 1 38 30 31 1 18 1 18 1 18 1 18 1 19 20 1 22 1 25 27 29 30 1 32 1 33 1 34 1 35 31 32 1 17 1 17 1 17 1 17 1 18 19 1 21 1 23 25 27 28 1 29 1 30 1 31 1 31 1 32 32 33 1 17 1 16 1 16 1 16 1 17 18 1 19 1 21 23 25 26 1 27 1 28 1 29 1 29 1 30 33 34 1 17 1 16 1 16 1 16 1 16 17 1 18 1 20 22 23 24 1 25 1 26 1 27 1 27 1 28 34 35 1 17 1 16 1 16 1 16 1 16 16 1 17 1 18 20 21 22 1 23 1 24 1 25 1 25 1 26 35 36 1 17 1 16 1 15 1 16 1 16 16 1 16 1 17 18 19 20 1 21 1 22 1 23 1 23 1 24 36 37 1 17 1 16 1 15 1 15 1 15 15 1 15 1 16 17 18 19 1 20 1 21 1 21 1 22 37 38 1 17 1 16 1 15 1 14 1 14 14 1 14 1 15 16 17 18 1 19 1 20 1 20 1 21 38 39 1 18 1 16 1 15 1 14 1 13 13 1 13 1 14 15 16 17 1 17 1 18 1 18 1 19 39 40 1 18 1 16 1 15 1 14 1 13 13 1 13 1 14 14 15 16 1 16 1 17 1 17 1 17 40 41 41 1 18 1 16 1 15 1 14 1 12 12 1 12 1 13 13 14 15 1 15 1 16 1 16 42 1 18 1 16 1 15 1 14 1 12 12 1 12 1 12 12 13 14 1 14 1 15 1 15 42 43 1 19 1 17 1 16 1 14 1 12 11 1 11 1 11 11 12 13 1 13 1 14 1 14 43 44 1 19 1 17 1 16 1 14 1 12 11 1 11 1 11 11 11 12 1 12 1 13 1 13 44 4H 1 20 1 18 1 16 1 14 1 12 11 1 10 1 10 10 10 11 1 11 1 11 46 48 1 21 1 19 1 17 1 15 1 12 10 1 9 1 9 9 9 10 1 10 1 10 48 50 1 22 1 19 1 17 1 15 1 12 10 1 9 1 8 8 8 8 1 8 50 52 1 23 1 20 1 17 1 15 1 12 10 1 8 1 8 8 7 7 1 7 52 54 1 24 1 21 1 18 1 16 1 13 10 1 8 1 7 7 6 6 54 56 1 25 1 22 1 19 1 16 1 13 10 1 8 1 7 7 6 6 1 56 58 60 62 64 1 26 1 27 1 28 1 29 1 23 1 24 1 24 1 25 11? 1 21 1 21 1 17 1 18 1 18 1 18 1 13 1 14 1 14 1 14 10 10 10 10 1 8 1 8 1 8 1 8 1 7 1 7 1 6 1 6 6 6 5 5 5 5 ' ' 1 TABLK P. KFFKCT OF SITn's PAR 1 1 Add the Numbers above th lines to 3rd Correction, sub tract th« others. e 66 1 29 1 25 1 21 1 18 1 14 11 1 8 1 6 App Alt. Sun's Apparent Altituc 68 70 72 1 2g 1 3f 1 3f 1 25 . 26 1 26 1 22 1 VI 1 23 1 19 1 19 1 2C 1 15 1 15 1 15 11 11 11 1 8 1 8 1 8 1 6 5 IUp2( II 1 DOG II 40; m 60 r tt 3 4 2 3 _1_ 2 1 70 80 90 * II 74 76 1 31 1 31 1 27 1 27 1 2.'3 1 23 1 2r 1 2(j 1 15 1 15 11 11 6 10 20 30 1 3 6 1 1 3 2 4 3 1 1 3 3 2 '2 " 3 1 I 2 78 1 as ! 1 28 1 24 1 2C 1 15 80 82 84 1 3i 1 3^ 1 3S ! 1 28 ! 1 28 ! 1 28 1 24 ! 1 24 1 24 1 21 1 21 1 21 1 15 40 50 60 70 8 6 .1 7 6 8 7 !) 6 8 4 5 6 7 3 5 6 (i 3 2 4 3 5 4 2 .3 2 86 1 3c t 1 28 ! 1 24 80 90 8 8 7 32° 34° 36° 38° 42° 46° 50° 54° 58° 62° 66° 70° 12 176 TABLE XXXIII. THIRD CORRECTION, TO APPARENT DISTANCE W>. 1 App. Alt. APPAKENT ALTITUDE OF THE SUN, OR STAR. 1 1>*8 App 6° 70 8° 90 10° 11° 12° 14° 16° 1 18° 20« 22° 1 24° 1 26° 1 28° 30° Alt. o r /f r ff r tt 1 It 1 II / // / II 1 II 1 II / II 1 // / // f II 1 // / II / II 6 1 26 1 27 1 29 1 32 1 36 1 42 1 49 2 3 2 19 2 35 2 51 3 8 3 24 3 40 3 56 4 12 6 7 1 28 1 26 1 27 1 29 1 32 1 35 1 40 1 51 2 3 2 15 2 28 2 42 2 56 3 9 3 22 3 36 7 8 1 32 1 28 1 26 1 27 1 29 1 31 1 34 1 42 1 51 2 2 2 13 2 24 2 36 2 48 3 3 11 8 9 1 37 1 31 1 28 1 26 1 27 1 28 1 30 1 36 1 43 1 52 2 1 2 10 2 20 2 31 2 41 2 51 9 10 1 43 1 35 1 30 1 27 1 26 1 27 1 28 1 32 1 37 1 44 1 51 59 2 8 2 17 2 26 2 36 10 11 1 50 1 40 1 33 1 29 1 27 1 26 1 27 1 29 1 33 1 38 44 51 59 2 7 2 14 2 22 11 12 1 57 1 45 1 37 1 32 1 29 1 27 1 26 1 28 1 30 1 34 38 44 51 58 2 5 2 12 12 13 2 4 1 50 1 41 1 35 1 31 1 29 1 27 1 27 28 1 31 34 38 44 50 57 2 3 13 14 2 12 1 56 1 46 1 39 1 34 1 31 1 29 1 26 27 1 29 31 34 39 44 50 65 14 15 2 20 2 2 1 51 1 43 1 37 1 33 1 30 1 27 26 1 27 29 31 35 40 1 44 49 15 16 2 27 2 8 1 56 1 47 1 41 1 36 1 32 1 28 25 1 26 27 29 32 36 40 44 16 17 2 35 2 14 2 1 1 51 1 45 1 39 1 34 1 29 26 1 25 26 ..* 28 30 33 36 40 17 18 2 43 2 21 2 6 1 56 1 48 1 42 1 37 1 31 27 1 2.5 25 26 28 30 33 36 18 19 2 51 2 27 2 12 2 1 52 1 45 1 39 1 32 28 1 25 25 25 27 28 ^ 30 33 19 20 2 59 2 34 2 17 2 5 1 56 1 49 1 42 1 34 29 1 26 24 24 1 25 26 ^ 28 30 20 21 21 3 7 2 41 2 23 2 10 2 1 52 1 45 1 36 30 1 26 24 23 24 25 26 28 22 3 15 2 48 2 29 2 15 2 4 1 55 1 48 1 38 31 1 27 25 23 23 24 25 26 22 23 3 23 2 55 2 35 2 20 2 8 1 59 1 51 1 40 33 1 28 25 23 23 * 24 24 25 23 24 3 31 3 2 2 41 2 25 2 12 2 2 1 54 1 42 34 1 29 26 24 23 23 « 24 25 24 25 26 3 39 3 8 2 47 2 30 2 17 2 6 1 57 1 44 36 1 30 26 24 23 23 23 ^ 24 25 3 47 3 15 2 53 2 35 2 21 2 10 2 1 47 38 1 32 27 25 23 23 23 23 26 27 3 56 3 22 2 59 2 40 2 26 2 14 2 4 1 50 40 1 33 28 25 23 23 22 23 27 28 4 4 3 29 3 5 2 45 2 30 2 18 2 7 1 53 42 1 35 29 26 24 23 22 22 28 29 4 12 3 36 3 11 2 50 2 35 2 22 2 11 1 55 44 1 36 30 27 25 23 22 22 29 30 31 4 20 3 42 3 17 2 55 2 39 2 26 2 15 1 58 46 1 38 32 28 25 24 23 22 30 4 28 3 49 3 23 3 2 43 2 30 2 18 2 48 1 40 33 29 26 24 23 22 31 32 4 36 3 55 3 28 3 5 2 48 2 34 2 22 2 3 50 1 41 34 30 26 24 23 22 32 33 4 44 4 2 3 34 3 10 2 52 2 38 2 26 2 6 53 1 43 36 30 27 24 23 22 33 34 4 52 4 8 3 39 3 15 2 56 2 41 2 29 2 8 55 1 44 37 31 28 25 23 22 34 35 5 4 15 3 45 3 20 3 1 2 45 2 33 2 11 57 1 46 38 32 28 25 23 22 35 36 5 7 4 21 3 51 3 25 3 5 2 49 2 36 2 14 1 59 1 47 39 33 29 26 24 23 36 37 5 14 4 28 3 57 3 30 3 9 2 53 2 40 2 17 2 2 1 49 41 34 30 27 25 23 37 38 5 21 4 34 4 2 3 35 3 14 2 57 2 43 2 20 2 4 1 52 43 36 31 27 25 23 38 39 5 28 4 41 4 7 3 39 3 18 3 1 2 46 2 23 2 6 1 54 45 37 32 28 25 23 39 40 5 35 4 47 4 12 3 44 3 22 3 4 2 49 2 26 2 9 1 56 46 38 33 29 26 24 40 41 5 42 4 53 4 17 3 49 3 26 3 8 2 52 2 29 2 11 1 58 48 40 34 29 26 24 41 42 5 49 4 59 4 22 3 53 3 30 3 11 2 55 2 31 2 13 2 49 41 35 30 27 24 42 43 5 56 5 5 4 27 3 58 3 34 3 15 2 59 2 34 2 15 2 2 51 42 36 31 28 25 43 44 6 2 5 11 4 32 4 3 3 38 3 19 3 2 2 36 2 16 2 3 52 44 38 32 29 26 44 46 6 15 5 21 4 42 4 11 3 45 3 26 3 8 2 41 2 22 2 6 55 47 40 34 30 27 46 48 6 28 5 32 4 52 4 19 3 53 3 32 3 14 2 45 2 26 2 10 1 58 49 42 36 32 28 48 50 6 40 5 42 5 1 4 27 4 3 38 3 20 2 50 2 29 2 14 2 1 51 44 37 33 29 50 52 6 52 5 52 5 10 4 35 4 7 3 44 3 25 2 55 2 33 2 17 2 4 54 46 39 34 30 52 54 7 3 6 1 5 18 4 42 4 14 3 50 3 30 2 59 2 37 2 20 2 7 56 48 41 35 31 54 56 7 14 6 10 5 26 4 49 4 20 3 55 3 35 3 3 2 41 2 23 2 9 58 49 43 37 32 56 58 7 24 6 18 5 34 4 56 4 25 4 C 3 39 3 7 2 44 2 26 2 11 2 52 45 38 33 58 60 7 32 6 26 5 41 5 2 4 30 4 5 3 44 3 11 2 47 2 29 2 14 2 2 64 47 40 35 60 62 7 40 6 33 5 47 5 7 4 35 4 10 3 49 3 15 2 50 2 31 2 16 2 4 55 48 41 36 62 64 7 48 6 40 5 53 5 12 4 40 4 15 3 53 3 19 2 52 2 34 2 19 2 6 56 49 42 37 64 66 7 65 6 47 5 59 5 17 4 45 4 19 3 57 3 22 2 54 2 36 2 21 2 8 67 50 43 38 66 68 8 1 6 53 6 4 5 22 4 49 4 23 4 1 3 24 2 56 2 38 2 22 2 9 1 59 51 44 38 68 70 8 7 6 59 6 8 5 26 4 53 4 26 4 4 3 26 2 58 2 40 2 23 2 10 2 62 45 39 70 72 8 12 7 4 6 11 5 30 4 56 4 29 4 6 3 28 3 2 41 2 24 2 11 2 1 63 46 39 72 74 6 14 5 33 4 59 4 31 4 8 3 30 3 2 2 42 2 25 2 12 2 2 54 47 40 74 76 5 1 4 33 4 9 3 32 3 4 2 43 2 26 2 13 2 3 54 47 40 76 78 4 10 3 33 3 6 2 44 2 27 2 14 2 3 54 47 41 78 80 3 34 3 7 2 45 2 28 2 15 2 4 65 47 41 80 82 3 8 2 46 2 29 2 16 2 4 65 48 42 82 84 2 47 2 29 2 16 2 5 56 49 42 84 86 2 29 2 16 2 6 56 49 42 86 6<» 70 8" 9° 10° 11° 12° 14° 16° 18° 20° 22° 24° 1 2 r,° 28° 30° „_ TABLE XXXIIL 177 THIRD COR Rl ACTION. TO APPARE T ALTITUDE OF THE Ml DISTANCE 64°. D's A.pp. Alt. APPAR] f, OR BTAB ■• App. Alt. 32° 34° 1 36» 1 38° 1 42° 46° 1 50° 54= 1 58° 62° 66° 70° 74° 78° 82° 86° o / n / It / // / II 1 11 1 // / II / II / II / // / // r II / II / n 1 II / // o 6 4 29 4 45 5 5 15 5 43 6 10 6 36 6 59 7 20 7 39 7 54 8 7 6 7 3 49 4 2 4 15 4 28 4 53 5 16 5 37 5 57 6 15 6 32 6 46 6 59 7 8 3 22 3 34 3 45 3 56 4 18 4 38 4 57 5 15 5 31 5 46 5 58 6 7 6 16 8 9 3 6 3 10 3 20 3 30 3 49 4 7 4 23 4 38 4 52 ? 5 5 16 5 26 5 34 9 10 2 43 2 52 3 1 3 10 3 27 3 42 3 56 4 9 4 21 \ 32 4 42 4 51 4 59 10 11 2 30 2 37 2 45 2 54 3 9 3 22 3 35 3 47 3 57 4 7 4 16 4 24 4 31 11 12 2 19 2 25 2 33 2 40 2 53 3 5 3 17 3 27 3 37 3 47 3 56 4 3 4 8 4 13 12 13 2 9 2 15 2 22 2 28 2 40 2 51 3 1 3 11 3 20 3 29 3 37 3 43 3 47 3 51 13 14 2 1 2 7 2 13 2 18 2 29 2 39 2 48 2 57 3 6 3 14 3 20 3 25 3 29 3 33 14 15 1 54 2 2 5 2 10 2 19 2 29 2 37 2 45 2 53 3 3 5 3 10 3 14 3 18 15 16 1 48 53 58 2 3 2 11 2 20 2 28 2 35 2 42 2 48 2 53 2 57 3 1 3 5 3 8 16 17 1 43 47 52 56 2 4 2 12 2 20 2 26 2 32 2 38 2 43 2 47 2 51 2 54 2 56 17 18 1 39 43 47 50 58 2 5 2 12 2 18 2 24 2 30 2 35 2 39 2 42 2 44 2 46 18 19 1 36 39 42 46 52 59 2 5 2 11 2 17 2 22 2 27 2 31 2 34 2 36 2 38 19 20 1 33 36 38 42 — 48 44 54 1 59 1 54 2 5 2 11 2 15 2 20 2 23 2 26 2 28 2 30 2 32 20 21 1 30 33 35 38 49 2 2 5 2 9 2 13 2 16 2 18 2 20 2 22 2 23 21 22 1 28 30 33 35 40 45 1 50 55 1 59 2 3 2 6 2 9 2 11 2 13 2 15 2 16 22 23 1 27 28 30 32 37 41 1 46 51 1 54 58 2 1 2 3 2 5 2 7 2 9 2 10 23 24 1 26 27 28 30 34 38 1 42 47 1 50 54 1 57 59 2 2 2 2 4 2 5 24 25 1 25 26 27 28 32 35 1 39 43 1 47 50 1 53 55 1 56 1 58 1 59 2 25 26 1 24 25 1 26 27 30 33 1 36 40 1 44 47 1 49 51 1 52 1 54 1 55 1 56 26 27 1 23 24 25 26 28 31 1 34 37 1 41 44 1 46 47 1 49 1 50 1 51 1 52 27 28 1 23 1 23 24 25 26 29 1 32 35 1 38 41 1 43 44 1 45 1 46 1 47 1 48 28 29 1 22 22 23 24 25 27 1 30 32 1 35 38 1 40 41 1 42 1 43 1 44 1 45 29 30 1 22 22 23 23 24 26 1 28 30 1 33 1 31 35 1 37 38 35 1 39 1 40 1 41 1 42 30 31 31 1 22 22 22 22 23 24 1 26 28 33 1 34 1 36 1 37 1 38 1 40 32 1 21 21 21 21 22 23 1 25 27 1 29 31 1 32 33 1 34 1 35 1 36' 1 38 32 33 1 21 21 21 21 21 22 1 24 26 1 27 29 1 30 31 1 32 1 33 1 34 33 34 1 21 20 20 20 20 21 1 23 25 1 26 27 1 28 29 1 30 1 31 1 32 34 35 1 21 20 20 20 20 21 1 22 23 1 24 25 1 26 27 1 28 1 29 1 30 35 36 1 21 20 19 19 19 20 1 21 22 1 23 24 1 25 26 1 26 1 27 1 28 36 37 1 21 20 19 19 19 19 1 20 21 1 22 23 1 24 25 1 25 1 26 37 38 1 21 20 19 18 18 18 1 19 20 1 21 22 1 23 24 1 24 1 25 38 39 1 21 20 19 18 18 18 1 18 19 1 20 21 1 21 22 1 22 1 23 39 40 1 22 20 19 18 17 17 1 18 18 1 19 20 1 20 21 1 21 1 22 40 41 41 1 22 20 19 18 17 17 1 17 17 1 18 19 1 19 20 1 20 42 1 22 20 19 18 16 16 1 16 17 1 17 18 1 18 19 1 19 42 43 1 23 21 19 18 16 16 1 16 16 1 16 17 1 17 18 1 18 43 44 1 23 21 19 18 16 16 1 16 16 1 16 16 1 16 17 1 17 44 46 1 24 22 20 18 16 15 1 15 1 15 — 15 14 1 15 15 1 15 16 46 48 1 25 22 20 19 16 15 1 14 14 1 14 1 14 48 50 1 26 23 21 19 16 15 1 14 13 1 13 13 1 13 50 52 1 27 24 22 20 17 15 1 13 12 1 12 12 1 12 52 54 1 28 25 22 20 17 15 1 13 12 1 11 11 54 56 1 29 26 1 «3 21 17 15 1 13 12 1 11 11 56 58 60 62 1 29 1 30 1 31 26 27 28 23 24 25 21 22 22 18 18 18 15 15 15 1 13 1 13 1 13 11 11 11 1 10 1 10 TABLS P. KFFKCT OF BUN'b PAR Add the Numbers above tk* 64 1 32 28 25 22 1 18 15 1 13 11 lines to 3rd Correction, sub- 66 1 33 29 26 23 18 16 1 13 i's tract tut oiners. ■ 68 1 33 29 26 23 19 16 1 13 ^p? S an 8 10 -^ AjJJ 1,10 Dare 40 fi ni ALU 60 70 uc Ml e. on 70 1 34 3t 27 24 19 16 72 1 34 30 27 24 19 16 t* " ' " */ / ' " i> tt " 74 76 1 35 1 35 1 31 31 28 28 24 25 19 20 5 10 20 1 3 1 1 3 2 1 1 2 . 1 ' 1 ( J 3 J 2 ) 3 2 1 1 78 1 36 1 32 28 25 30 5 4 3 3 2 1 l 1 1 T 80 1 36 I 32 28 25 40 6 6 5 4 4 ; ) 3 2 2 82 1 37 32 28 50 7 7 6 5 5 ' t 4 4 84 1 37 32 60 70 8 9 8 7 9 -^ 7 6 . 7 5 6 1 86 1 37 80 8 8 8 7 32° ■3 10 QGO 38° 42° \aO 50° 54° 58° 62° 66* 70° 90 178 TABLE XXXIII. THIRD CORRECTION, TO APPARENT DISTANCE QS'^. 1 D's APPARENT ALTITUDE OF THE SUN, OR STAR. D's App. Alt. App Alt. 6» 70 80 9° 10° 11° 12° 14° 16° 18° 20° 22° 24° 26° 1 28° 1 30° / f / // / ff r It 1 ir r II / n / 1' / II 1 II 1 II / II 1 II 1 II 1 II 1 II 6 1 29 1 31 1 34 1 37 1 41 1 46 1 52 2 6 2 21 2 36 2 52 3 8 3 24 3 39 3 54 4 10 6 7 1 32 1 29 1 31 1 33 1 36 1 39 1 43 1 54 1 5 2 17 2 30 2 43 2 56 3 9 3 22 3 36 7 8 1 36 1 31 1 29 1 30 1 32 1 34 1 37 1 45 1 54 2 4 2 14 2 25 2 37 2 48 2 59 3 11 8 9 1 41 1 34 1 31 1 29 1 30 1 31 1 33 1 38 1 46 1 54 2 3 2 12 2 22 2 32 2 42 2 52 9 10 1 46 1 38 1 33 1 30 1 29 1 30 1 31 1 34 1 40 1 47 1 54 2 2 2 10 2 19 2 28 2 36 10 11 1 52 1 43 1 36 1 32 1 30 1 29 1 30 1 32 1 36 1 41 1 47 1 54 2 1 2 9 2 16 2 24 u 12 1 59 1 48 1 40 1 35 1 32 1 30 1 29 1 30 1 33 1 37 1 42 1 48 54 2 2 7 2 14 12 13 2 6 1 53 1 44 1 38 1 34 1 32 1 30 1 29 1 31 1 34 1 38 1 43 48 53 59 2 5 13 14 2 14 1 59 I 49 1 42 1 37 1 34 1 31 1 29 1 30 1 32 1 35 1 39 44 48 53 1 58 14 15 2 21 2 5 1 54 1 46 1 40 1 36 1 33 1 30 1 30 1 31 1 33 1 36 40 44 48 1 53 15 16 16 2 28 2 11 1 59 1 50 1 44 1 39 1 35 1 31 1 29 1 30 1 32 1 34 37 40 44 1 48 17 2 36 2 17 2 4 1 54 1 47 1 42 1 38 1 32 1 29 1 29 1 30 1 32 34 37 40 1 44 17 18 2 44 2 24 2 10 1 59 1 51 1 45 1 40 1 34 1 30 1 28 1 29 1 30 32 35 37 1 40 18 19 2 52 2 30 2 15 2 4 1 55 1 48 1 43 1 35 1 31 1 28 1 28 1 29 31 33 * 35 1 37 19 20 3 2 36 2 21 2 8 1 59 1 52 1 46 1 37 1 32 1 29 1 28 1 29 30 31 1 33 1 35 20 21 3 8 2 43 2 26 2 13 2 3 1 55 1 48 1 39 1 33 1 30 1 28 1 28 29 30 31 1 33 21 22 3 15 2 49 2 32 2 17 2 7 1 58 1 51 1 41 1 35 1 31 1 29 1 27 28 29 30 1 31 22 23 3 23 2 56 2 37 2 22 2 11 2 2 1 54 1 43 1 37 1 32 1 29 1 27 27 28 29 1 30 23 24 3 31 3 3 2 43 2 27 2 15 2 5 1 57 1 46 1 39 1 34 1 30 1 28 27 28 1 28 1 29 24 25 26 3 39 3 9 2 48 2 32 2 19 2 9 2 1 48 1 41 1 35 1 31 1 29 27 27 27 1 28 25 26 3 47 3 16 2 54 2 37 2 23 2 12 2 4 1 51 1 43 1 36 1 32 1 30 28 27 27 1 27 27 3 55 3 23 3 2 42 2 27 2 16 2 7 1 54 1 44 1 37 1 33 1 30 28 27 26 1 27 27 28 4 2 3 29 3 5 2 47 2 31 2 19 2 10 1 56 1 46 1 39 1 34 1 31 29 27 26 1 26 28 29 4 10 3 36 3 11 2 52 2 35 2 23 2 14 1 59 1 48 1 41 1 35 1 32 29 27 26 1 26 29 30 4 17 3 42 3 16 2 57 2 40 2 27 2 17 2 1 1 50 1 42 1 36 1 32 29 27 26 1 26 30 31 31 4 25 3 49 3 22 3 2 2 44 2 31 2 20 2 3 1 52 1 43 1 37 1 33 30 28 27 1 26 32 4 32 3 55 3 27 3 7 2 49 2 34 2 23 2 6 1 54 1 45 1 38 1 33 30 28 27 1 26 32 33 4 40 4 2 3 33 3 12 2 53 2 38 2 26 2 9 1 56 1 47 1 39 1 34 31 29 27 1 26 33 34 4 48 4 8 3 39 3 16 2 57 2 42 2 30 2 12 1 58 1 48 1 41 1 35 32 30 28 1 26 34 35 4 55 4 15 3 45 3 21 3 2 2 46 2 34 2 15 2 1 50 1 43 1 37 33)1 30 28 1 26 35 36 36 5 2 4 21 3 50 3 26 3 6 2 50 2 37 2 17 2 3 1 52 1 44 1 38 34 31 28 1 26 37 5 10 4 27 3 56 3 30 3 10 2 53 2 41 2 20 2 5 1 54 1 46 1 39 35 31 28 1 26 37 38 5 17 4 33 4 1 3 35 3 14 2 57 2 44 2 22 2 7 1 56 1 48 1 41 36 32 29 1 27 38 39 5 24 4 39 4 6 3 40 3 18 3 1 2 47 2 25 2 9 1 58 1 50 1 43 37 33 30 1 27 39 40 5 31 4 45 4 11 3 45 3 22 3 5 2 50 2 27 2 11 2 1 51 1 44 38 34 31 1 28 40 41 5 38 4 51 4 16 3 49 3 26 3 9 2 53 2 30 2 14 2 2 1 53 1 45 39 35 31 1 28 41 42 5 44 4 57 4 21 3 53 3 30 3 12 2 56 2 32 2 16 2 4 1 54 1 46 40 36 32 1 29 42 43 5 50 5 2 4 26 3 58 3 34 3 16 2 59 2 34 2 19 2 6 1 56 1 48 41 37 33 1 30 43 44 5 57 5 8 4 31 4 2 3 38 3 19 3 3 2 37 2 21 2 8 1 57 1 49 43 38 34 1 31 44 46 6 10 5 19 4 41 4 10 3 46 3 26 3 9 2 42 2 25 2 11 1 59 1 51 45 40 35 1 31 46 48 48 6 22 5 29 4 50 4 18 3 53 3 32 3 15 2 47 2 29 2 14 2 2 1 54 47 41 36 1 32 50 6 34 5 39 4 59 4 26 3 59 3 38 3 21 2 52 2 33 2 18 2 5 1 56 49 43 38 1 33 50 52 6 45 5 48 5 7 4 33 4 6 3 44 3 26 2 56 2 36 2 21 2 8 1 58 51 45 39 1 35 52 54 6 56 5 57 5 14 4 40 4 12 3 50 3 31 3 2 39 2 24 2 11 2 1 52 46 40 1 36 54 56 7 6 6 6 5 21 4 46 4 18 3 55 3 36 3 4 2 42 2 27 2 14 2 2 54 47 41 1 37 56 58 7 15 6 14 5 28 4 52 4 24 4 3 41 3 8 2 45 2 29 2 16 2 4 56 49 43 1 38 58 60 7 24 6 22 5 35 4 58 4 29 4 5 3 4S 3 12 2 48 2 32 2 18 2 6 58 51 45 1 39 60 62 7 33 6 29 5 42 5 3 4 34 4 10 3 49 3 15 2 51 2 34 2 20 2 8 59 52 46 1 40 62 64 7 41 6 35 5 48 5 8 4 39 4 14 3 53 3 18 2 54 2 36 2 22 2 10 2 1 53 47 1 41 64 66 68 7 48 6 41 5 53 5 13 4 43 4 18 3 57 3 21 2 56 2 38 2 24 2 12 2 2 54 48 1 42 66 7 55 6 47 5 58 5 17 4 47 4 22 4 3 24 2 59 2 40 2 26 2 14 2 3 55 49 1 43 68 70 8 1 6 52 6 3 5 21 4 51 4 25 4 3 3 27 3 1 2 42 2 27 2 15 2 4 56 50 1 44 70 72 8 7 6 57 6 8 5 25 4 55 4 28 4 6 3 30 3 3 2 44 2 28 2 15 2 5 57 51 1 45 72 74 8 12 7 1 6 12 5 29 4 58 4 30 4 8 3 32 3 5 2 45 2 29 2 16 2 5 57 51 1 45 74 76 8 17 7 5 6 15 5 32 5 1 4 32 4 10 3 34 3 7 2 46 2 30 2 17 2 6 58 51 1 45 76 78 6 18 5 35 5 3 4 34 4 12 3 35 3 9 2 47 2 31 2 18 2 7 58 52 1 46 78 80 5 5 4 36 4 13 3 36 3 10 2 48 2 32 2 18 2 7 59 52 1 46 80 82 4 14 3 37 3 11 2 49 2 32 2 19 2 8 59 52 1 46 82 84 3 38 3 11 2 50 2 33 2 20 2 9 2 53 1 46 84 86 3 12 2 50 2 33 2 20 2 9 2 53 86 6' 7° 8° 9° 10° 11° 12° 14° 16° 18° 20° 22° 24° 26° 28° 30° 1 TABLE XXXIII. 179 THIRD CORRECTION, TO APPARENT DISTANCE 68°. A-pp. Alt. APPARENT ALTITUDE OF THE SUN, OR STAR. >'8 App. Alt. 32° 34° 36° 1 38° 1 42° 46° 1 50° 54° 58° 1 62° 66° 70° 74° 78° 82° 1 86° 1 o 1 II / n 1 II 1 II / ri 1 II / // / /r 1 11 1 II 1 II 1 // 1 // 1 II 1 // 1 II 6 4 25 4 40 4 55 5 11 5 40 6 5 6 29 6 51 7 11 7 29 7 45 8 8 14 I 6 7 3 49 4 1 4 14 4 27 4 52 5 15 5 35 5 53 6 10 6 25 6 38 6 50 7 1 7 8 3 22 3 33 3 44 3 55 4 17 4 37 4 55 5 11 5 25 5 38 5 51 6 2 6 10 6 18 8 9 3 1 3 11 3 21 3 30 3 48 4 6 4 22 4 36 4 49 $ 5 10 5 19 5 28 5 30 9 10 2 44 2 53 3 2 3 10 3 25 3 41 3 55 4 9 3 47 4 21 4 31 4 40 4 49 4 57 5 3 10 11 11 2 31 2 39 2 47 2 54 3 8 3 22 3 35 3 58 4 8 4 16 4 23 4 29 4 34 12 2 20 2 27 2 34 2 41 2 53 3 6 3 18 3 29 3 39 3 48 3 55 4 2 4 7 4 11 4 15 12 13 2 11 2 17 2 23 2 29 2 41 2 52 3 2 3 12 3 22 3 30 3 37 3 43 3 48 3 52 3 56 13 14 2 3 2 9 2 14 2 19 2 30 2 40 2 49 2 58 3 6 3 14 3 20 3 26 3 31 3 35 3 38 14 15 1 57 2 2 2 6 2 11 2 21 2 30 2 38 2 46 2 54 3 1 3 7 3 12 3 16 3 20 3 23 15 16 1 52 1 56 2 2 4 2 13 2 21 2 29 2 37 2 44 2 50 2 55 3 3 4 3 8 3 10 3 12 16 17 1 47 1 51 55 58 2 6 2 14 2 21 2 29 2 35 2 40 2 45 2 49 2 53 2 57 2 59 3 17 18 1 43 1 47 50 54 2 1 2 8 2 14 2 21 2 27 2 32 2 36 2 40 2 44 2 47 2 49 2 50 18 19 1 40 1 43 46 50 56 2 2 2 8 2 15 2 20 2 25 2 29 2 32 2 36 2 39 2 41 2 42 19 20 1 37 1 40 43 46 — 52 48 1 57 2 3 2 9 2 14 2 18 2 22 2 25 2 28 2 31 2 33 2 34 20 21 1 35 1 37 40 43 53 1 58 2 3 2 8 2 12 2 16 2 19 2 21 2 23 2 25 2 26 21 22 1 33 1 35 37 40 44 49 1 54 1 58 2 2 2 6 2 10 2 13 2 15 2 17 2 19 2 20 22 23 1 31 1 33 35 37 41 46 1 50 1 54 1 57 2 1 2 5 2 8 2 10 2 12 2 14 2 15 23 24 1 30 1 31 33 35 39 43 1 47 1 50 53 57 2 2 3 2 5 2 7 2 9 2 10 24 25 1 29 1 30 1 29 31 33 37 40 1 44 1 47 50 53 1 56 1 59 2 1 2 2 2 4 2 5 25 26 1 28 30 32 35 38 1 41 1 44 47 50 1 53 55 57 1 58 59 2 26 27 1 27 1 28 29 30 33 36 1 38 1 41 44 47 1 50 52 53 1 54 55 1 56 27 28 1 27 1 27 28 29 31 34 1 36 1 39 41 44 1 47 49 50 1 51 52 1 52 28 29 1 26 1 26 27 28 29 32 1 34 1 37 39 41 1 44 46 47 1 48 49 29 30 1 26 1 26 26 27 28 30 1 32 1 35 37 39 1 41 — 43 40 44 1 45 46 30 31 1 25 1 25 26 26 27 29 1 31 1 33 35 37 1 39 41 1 42 43 31 32 1 25 1 25 25 25 26 28 1 29 1 31 33 35 1 37 38 39 1 40 41 32 33 1 25 1 24 25 25 26 27 1 28 1 30 31 33 1 35 36 37 1 38 33 34 1 25 1 24 24 24 25 26 1 27 1 29 30 31 1 33 34 35 1 36 34 35 1 25 1 24 24 24 24 25 1 26 1 28 29 30 1 31 32 33 1 34 35 36 1 25 1 24 23 23 23 24 1 25 1 27 28 29 1 30 30 31 1 32 36 37 1 25 1 24 23 23 23 23 1 24 1 26 27 28 1 29 29 30 37 38 1 25 1 24 23 22 22 23 1 24 1 25 26 27 1 28 28 29 38 39 1 25 1 24 23 22 22 23 1 23 1 24 25 26 1 27 27 27 39 40 1 26 1 25 24 23 22 22 1 23 1 23 24 25 1 26 26 26 40 41 41 1 26 I 25 24 23 21 21 1 22 1 22 23 24 1 25 25 42 1 27 1 25 24 23 21 21 1 21 1 22 23 23 1 24 24 42 43 1 27 1 25 24 23 21 21 1 21 1 21 22 22 1 23 23 43 44 1 28 1 26 24 23 21 20 1 20 1 20 21 21 1 22 22 44 46 1 28 1 26 25 — 24 24 21 19 1 19 1 18 1 19 20 20 1 20 46 48 1 29 1 27 25 22 19 1 18 19 19 1 19 48 50 1 30 1 28 26 25 22 20 1 18 1 18 18 18 50 52 1 31 1 29 27 25 22 20 1 18 1 17 17 17 52 54 1 32 1 29 27 26 23 20 1 18 1 17 16 54 56 1 33 1 30 28 26 23 20 1 18 1 16 15 56 58 60 62 1 34 1 35 1 36 1 31 1 32 1 33 29 29 30 27 27 28 23 23 23 20 20 20 1 18 1 18 1 18 1 16 1 16 1 1 TABLE P. EFFECT OF BUN'b PAR Add tht Numbers above the 64 66 1 37 1 38 1 33 1 34 30 31 28 28 24 24 20 20 1 17 lines to 3rd Correction, sub- tract the others. )'9 APP A t. Sun's Apparent Altitude. j 68 70 72 1 38 1 39 1 39 1 34 1 35 1 35 31 32 32 28 29 29 24 24 24 1 20 5 10 2 )30 40|5 0|60(70l n 1 " " ' t It " 74 76 1 4C 1 4f 1 3fi 1 36 32 32 29 29 S 10 20 30 1 2 3 4 u 1 3 2 4 4 1 1 3 1 ' 1 1 1 2 ' i 2 I J 2 2 J 2 1 2 1 78 1 41 1 36 1 32 80 1 41 I 3(] 40 6 fi 3 4 4 : ) 3 3 82 84 86 1 41 50 60 7 8 7 6 8 7 6 7 5 . 6 ( > 4 J 70 80 90 9 9 8 7 8 7 32° 34° QftO 38^ 42° AdO nno 54° 58° 62° 66° 7 no 1 > A 180 TABLE XXXIII. THIRD CORRECTION, TO APPARENT DISTANCE 72" App. Alt. APPARENT ALTITUDE OF THE SUN, OR STAR. 3)'s App Alt. 6» 7« 8<» 1 9* 10° 11° 12° 14° 16° 1 18° 20° 1 22° 1 240 1 26° 1 28° 30° O t 1' f n / ft t It / n / n / )) > II / II / // / // / II 1 r/ 1 // 1 II 1 II 6 1 33 1 35 1 37 1 40 1 44 1 50 1 56 2 9 2 23 2 38 2 53 3 9 3 24 3 40 3 56 4 12 6 7 1 35 1 33 1 34 1 36 1 39 1 43 1 47 1 56 2 8 2 21 2 34 2 47 3 3 12 3 25 3 38 7 8 1 39 1 35 1 33 1 34 1 36 1 38 1 41 1 48 58 2 8 2 19 2 30 2 41 2 52 3 3 3 14 8 9 1 44 1 38 1 35 1 33 1 34 1 35 1 37 1 42 50 1 58 2 7 2 17 2 26 2 35 2 44 2 54 9 10 1 50 1 42 1 37 1 34 1 33 1 34 1 35 1 38 44 1 50 1 58 2 6 2 14 2 22 2 30 2 39 10 11 11 1 56 1 46 1 40 1 36 1 34 1 33 1 34 1 36 40 1 45 51 1 58 2 5 2 12 2 20 2 27 12 2 2 1 51 1 44 1 39 1 36 1 34 1 33 1 35 37 1 41 46 1 52 58 2 4 2 11 2 17 12 13 2 9 1 56 1 48 1 42 1 39 1 36 1 34 1 34 35 1 38 42 1 47 52 58 2 4 2 9 13 14 2 16 2 2 1 53 1 46 1 42 1 39 1 36 1 33 34 1 36 39 1 43 47 52 1 57 2 2 14 15 2 23 2 8 1 58 1 50 1 45 1 41 1 38 1 34 33 1 34 36 1 39 43 47 1 51 1 56 15 16 2 30 2 14 2 3 1 54 1 48 1 43 1 40 1 35 33 1 33 34 1 36 39 43 1 47 1 52 16 17 2 37 2 20 2 8 1 58 1 51 1 46 1 42 1 36 34 1 33 34 1 35 37 40 1 44 1 48 17 18 2 45 2 27 2 13 2 2 1 54 1 48 1 44 1 37 34 1 33 33 1 34 36 38 1 41 1 44 18 19 2 53 2 33 2 18 2 7 1 58 1 51 1 46 1 39 35 1 33 33 1 34 35 37 1 39 1 41 19 20 3 1 2 40 2 24 2 11 2 2 1 54 1 49 1 41 36 1 34 33 1 33 34 35 1 37 1 39 20 21 21 3 9 2 46 2 29 2 16 2 6 1 58 1 52 1 43 37 1 34 1 33 1 33 33 34 1 35 1 37 22 3 17 2 53 2 35 2 20 2 10 2 2 1 55 1 45 39 1 35 33 1 32 33 33 1 34 1 35 22 23 3 25 2 59 2 40 2 25 2 14 2 5 1 58 1 47 40 1 36 34 1 32 32 33 1 33 1 34 23 24 3 33 3 6 2 46 2 30 2 18 2 8 2 1 1 50 42 1 37 34 1 32 32 32 1 33 1 34 24 25 26 3 41 3 12 2 51 2 35 2 23 2 12 2 4 1 52 44 1 38 35 1 33 32 32 1 32 1 33 25 26 3 48 3 18 2 57 2 40 2 27 2 16 2 8 1 55 46 1 40 36 1 33 32 31 1 31 1 32 27 3 56 3 25 3 2 2 45 2 31 2 20 2 12 1 57 48 1 41 37 1 34 32 31 1 31 1 31 27 28 4 3 3 31 3 7 2 49 2 35 2 24 2 15 2 .0 50 1 43 38 1 34 32 31 1 30 1 31 28 29 4 11 3 37 3 13 2 54 2 39 2 27 2 18 2 2 52 1 45 39 1 35 33 32 1 31 1 30 29 30 4 18 3 44 3 19 2 59 2 43 2 31 2 21 2 5 54 1 46 40 1 36 34 32 1 31 1 30 30 31 31 4 26 3 50 3 24 3 4 2 47 2 34 2 24 2 8 56 1 48 41 1 37 34 32 1 31 1 30 32 4 33 3 56 3 29 3 9 2 51 2 38 2 27 2 11 58 1 50 43 1 38 35 33 1 32 1 31 32 33 4 40 4 2 3 35 3 14 2 56 2 42 2 30 2 14 2 1 51 44 1 39 35 33 I 32 1 31 33 34 4 47 4 9 3 41 3 18 3 2 45 2 33 2 16 2 2 1 53 46 1 40 36 34 1 32 1 31 34 35 4 54 4 15 3 46 3 23 3 4 2 49 2 37 2 18 2 4 1 54 47 1 41 37 34 1 32 1 31 35 36 36 5 1 4 21 3 51 3 27 3 8 2 53 2 40 2 20 2 7 1 56 48 1 42 38 35 1 33 1 32 37 5 9 4 27 3 56 3 32 3 12 2 57 2 43 2 23 2 9 1 58 50 1 44 39 36 1 33 1 32 37 38 5 16 4 33 4 1 3 37 3 16 3 2 47 2 26 2 11 2 52 1 45 40 37 1 34 1 32 38 39 5 23 4 39 4 6 3 41 3 20 3 4 2 50 2 28 2 13 2 2 53 1 46 41 38 1 34 1 32 39 40 5 30 4 45 4 11 3 46 3 24 3 7 2 54 2 30 2 15 2 4 54 1 48 — 43 44 39 1 35 1 33 40 41 5 37 4 51 4 16 3 50 3 28 3 11 2 57 2 32 2 18 2 6 56 1 49 40 1 36 1 33 41 42 5 44 4 57 4 21 3 54 3 32 3 15 3 2 35 2 20 2 8 58 1 50 45 41 1 37 1 34 42 43 5 51 5 2 4 26 3 59 3 36 3 18 3 3 2 37 2 22 2 10 59 1 51 46 42 1 38 1 34 43 44 5 57 5 7 4 30 4 3 3 40 3 22 3 6 2 41 2 24 2 12 2 1 1 53 47 43 1 39 1 35 44 46 6 9 5 17 4 39 4 11 3 47 3 29 3 12 2 45 2 28 2 15 2 4 1 55 49 44 1 40 1 36 46 48 48 6 21 5 27 4 48 4 19 3 54 3 35 3 18 2 50 2 32 2 18 2 7 1 58 51 45 1 41 ] 38 50 6 32 5 37 4 57 4 26 4 1 3 41 3 23 2 55 2 35 2 21 2 10 2 53 47 1 43 1 39 50 52 6 43 5 46 5 6 4 33 4 7 3 46 3 28 2 59 2 39 2 24 2 12 2 2 55 49 1 44 1 40 52 54 6 54 5 55 5 14 4 40 4 13 3 52 3 33 3 3 2 43 2 27 2 15 2 5 57 50 1 45 1 41 54 56 7 4 6 4 5 22 4 47 4 19 3 57 3 38 3 7 2 47 2 31 2 18 2 7 59 52 1 46 1 42 56 58 7 13 6 12 5 29 4 53 4 25 4 2 3 43 3 11 2 50 2 34 2 21 2 9 2 53 1 47 1 43 58 60 7 22 6 20 5 35 4 58 4 30 4 7 3 47 3 15 2 53 2 37 2 23 2 11 2 2 54 1 49 1 44 60 62 7 31 6 27 5 41 5 3 4 35 4 11 3 51 3 19 2 56 2 39 2 25 2 13 2 4 56 1 50 1 45 62 64 7 39 6 33 5 47 5 8 4 40 4 15 3 55 3 22 2 59 2 41 2 27 2 15 2 5 57 1 51 1 46 64 66 7 46 6 39 5 53 5 13 4 44 4 19 3 59 3 25 3 1 2 43 2 29 2 16 2 6 58 1 52 1 47 66 68 7 52 6 45 5 58 5 18 4 48 4 23 4 2 3 28 3 3 2 45 2 30 2 18 2 7 1 59 1 52 1 47 68 70 7 58 6 50 6 3 5 22 4 52 4 26 4 4 3 30 3 5 2 47 2 31 2 19 2 8 2 1 53 1 48 70 72 8 4 6 55 6 7 5 26 4 55 4 29 4 7 3 32 3 7 2 48 2 33 2 20 2 9 2 1 1 54 1 48 72 74 8 9 7 ( 6 10 5 30 4 58 4 31 4 9 3 34 3 9 2 49 2 34 2 21 2 10 2 2 1 55 1 49 74 76 8 13 7 4 6 14 6 33 5 1 4 33 4 11 3 35 3 11 2 50 2 35 2 22 2 11 2 2 1 56 1 49 76 78 8 16 7 7 6 17 5 36 5 3 4 35 4 12 3 37 3 12 2 51 2 36 2 23 2 12 2 3 1 56 1 50 78 80 8 19 7 10 6 19 5 38 5 5 4 37 4 14 3 38 3 13 2 52 2 37 2 24 2 13 2 4 1 57 1 51 80 82 6 21 5 40 5 7 4 39 4 16 3 39 3 13 2 53 2 38 2 24 2 13 2 4 1 57 82 84 5 9 4 41 4 17 3 40 3 14 2 54 2 38 2 24 2 14 2 5 84 86 4 18 3 41 3 15 2 54 2 38 2 24 2 14 86 6° 7» 8« g' 10° 11° 12° 14° 16° 18° 20° 22° 24° 26° 28° 30° TABLE XXXIil. 181 THIRD CORRECTION, TO APPARENT DISTANCE 72°. J>'8 App. Alt. APPARENT ALTITUDE OF THE SUN, OR STAR. >'8 App. Alt. 32° 34° 36° 38° 42° 46° 50° 54° 58° 62* 66° 1 70° 74° 78° 1 82° 86° / // r n / rr / n / It t // f rr / // / II 1 // r // 1 II 1 II 1 // 1 II ' "I o 6 4 27 4 41 4 56 5 11 5 38 6 3 6 27 6 48 7 8 7 27 7 42 7 55 8 6 8 16 e 7 3 51 4 3 4 16 4 28 4 51 5 12 5 32 5 51 6 8 6 23 6 36 6 48 6 58 7 7 7 8 3 25 3 36 3 47 3 58 4 18 4 36 4 54 5 11 5 26 5 39 5 51 6 1 6 9 6 16 6 22 8 9 3 4 3 14 3 24 3 33 3 51 4 8 4 23 4 37 4 50 5 1 5 11 5 20 5 28 5 35 5 41 9 10 2 48 •2 57 3 6 3 14 3 29 3 44 3 58 4 10 4 22 4 33 4 42 4 50 4 57 5 3 5 7 10 11 11 2 35 2 43 2 51 2 58 3 11 3 25 3 37 3 48 3 59 4 9 4 17 4 24 4 30 4 35 4 39 12 2 24 2 31 2 38 2 45 2 57 3 9 3 20 3 31 3 41 3 49 3 57 4 3 4 8 4 12 4 16 4 20 12 13 2 15 2 21 2 27 2 33 2 45 2 56 3 6 3 16 3 24 3 32 3 39 3 45 3 49 3 53 3 56 3 59 13 14 2 7 2 13 2 18 2 24 2 34 2 44 2 54 3 2 3 10 3 18 3 24 3 29 3 33 3 36 3 39 3 41 14 15 2 1 2 6 2 11 2 16 2 25 2 34 2 43 2 51 2 58 3 5 3 11 3 16 3 20 3 23 3 25 3 27 15 16 1 56 2 1 2 5 2 9 2 18 2 26 2 33 2 41 2 48 2 54 2 59 3 4 3 8 3 11 3 13 3 15 16 17 1 52 1 56 1 59 2 3 2 11 2 19 2 25 2 32 2 39 2 45 2 50 2 54 2 57 3 3 2 3 4 17 18 1 48 1 51 1 54 1 58 2 6 2 13 2 19 2 25 2 31 2 37 2 42 2 46 2 48 2 50 2 52 2 54 18 19 1 44 1 47 1 50 1 54 2 1 2 7 2 13 2 19 2 25 2 30 2 35 2 38 2 40 2 42 2 44 2 45 19 20 1 41 1 44 1 47 1 50 1 56 2 2 2 7 2 13 2 19 2 23 2 28 2 31 2 33 2 35 2 36 2 37 20 21 1 39 1 41 1 44 1 46 1 52 1 57 2 2 2 8 2 13 2 17 2 21 2 24 2 26 2 28 2 29 2 30 21 22 1 37 1 39 1 41 1 43 1 48 1 53 1 58 2 3 2 7 2 11 2 15 2 18 2 20 2 22 2 23 2 24 22 23 1 36 1 37 1 39 1 41 1 45 1 50 1 54 1 59 2 2 2 6 2 10 2 13 2 15 2 16 2 17 2 18 23 24 1 35 1 36 1 37 1 39 1 43 1 47 1 51 1 55 1 58 2 2 2 5 2 8 2" 10 2 11 2 12 2 13 24 25 1 34 1 35 1 36 1 38 1 41 1 44 1 48 1 51 1 54 1 58 2 1 2 3 2 5 2 6 2 8 25 26 1 33 1 34 1 35 1 36 1 39 1 42 1 45 1 48 1 51 54 57 1 59 2 1 2 2 2 4 26 27 1 32 1 33 1 34 1 35 1 37 1 40 1 43 1 45 1 48 51 54 1 56 1 57 58 2 27 28 1 32 1 32 1 33 1 34 1 35 1 38 1 41 1 43 1 46 48 51 1 53 1 54 55 1 56 28 29 1 31 1 32 1 i2 1 33 1 34 1 36 1 39 1 41 1 44 46 48 1 50 1 52 53 29 30 1 31 1 31 1 .■?! i 32 1 31 1 32 1 31 1 33 1 35 1 37 1 39 1 42 44 46 1 47 1 49 50 30 31 31 1 30 1 32 1 34 1 36 1 38 1 40 42 44 1 45 1 46 47 32 I 29 1 30 1 30 1 30 1 31 1 33 1 35 1 36 1 38 40 42 1 43 1 44 45 32 33 1 29 1 29 1 29 1 30 1 31 1 32 1 33 1 34 1 36 38 40 1 41 1 42 33 34 1 30 1 29 ] 29 1 29 1 30 1 31 1 32 1 33 1 34 36 38 1 39 1 40 34 35 1 30 1 29 1 29 1 29 1 30 1 30 1 31 1 32 1 33 35 36 1 37 1 38 35 36 36 1 31 I 29 1 28 1 28 1 29 1 30 1 31 1 32 1 33 34 35 1 36 1 36 37 1 31 1 30 1 28 1 28 1 29 1 29 1 30 1 31 1 32 33 34 1 35 37 38 1 31 1 30 1 28 1 27 1 29 1 28 1 30 1 31 1 32 33 33 1 34 38 39 1 31 1 30 1 29 1 28 1 28 1 28 1 29 1 30 1 31 32 32 1 32 39 40 1 31 1 30 1 29 1 28 1 27 1 28 1 28 1 29 1 30 30 30 1 30 40 41 41 1 31 1 30 1 29 1 28 1 27 1 27 1 27 1 28 1 28 29 29 42 1 32 1 31 1 29 1 28 1 26 1 26 1 26 1 27 1 27 28 28 42 43 1 32 1 31 1 29 1 28 1 26 1 26 1 26 1 26 1 26 27 27 43 44 1 33 1 31 1 30 1 28 1 26 1 26 1 25 1 25 1 25 26 26 44 46 1 34 1 32 1 30 1 29 1 27 1 25 1 25 1 24 1 25 1 25 25 46 48 1 35 1 32 1 30 1 29 1 27 1 25 1 24 1 24 1 24 48 50 1 36 1 33 1 31 1 30 1 27 1 25 1 24 1 23 1 23 60 52 1 37 1 34 1 31 1 30 1 27 1 25 1 23 1 22 1 23 62 54 1 37 1 34 1 32 1 31 1 28 1 25 1 23 1 22 64 56 1 38 1 35 1 33 1 31 1 28 1 25 1 23 1 22 6b 58 60 62 64 66 1 39 1 39 1 40 1 41 1 42 1 36 1 36 1 37 1 38 1 38 1 34 1 34 1 35 1 36 1 36 1 32 1 32 1 32 1 33 1 33 1 28 1 28 1 28 1 28 1 28 1 25 1 25 1 25 1 25 1 23 1 23 TABLK P. BrFBCT o» sun's pa r I Add the Numbers above th lines to Srd Correction, sub tract the others. e App Alt. s 5 , 68 70 1 43 1 4S 1 39 1 39 1 36 1 1 36 1 34 1 34 1 29 10 2 130 40.^ ()()() 70 80 00 72 74 76 1 i4 1 44 1 At \ 1 4C [ 1 4C ) 1 4C ) 1 36 > 1 36 » 1 34 10 20 30 40 n 1 2 3 4 6 // # 1 1 3 2 4 4 6 S 1 ' 2 3 5 1 1 ' 3 4 2 2 1 1 1 1 2 2 4 4 2 j_ 1 2 3 1 2 78 80 1 4t > sc 50 7 7 6 6 5 5 5 60 8 8 7 7 6 S 84 86 1 70 9 80 90 8 e 9 8 7 8 7 32° 34° 36° 38° A oo A cO 1 ftnO 54° 58° coO 6fi° 70° 1 1 lU f tjyj 182 TABLE XXXIII. THIRD CORRECTION, TO APPARENT DISTANCE 76". D's App. Alt. APPARENT ALTITUDE OF THE SON, OR STAR. App. Alt. 6° 7° 8° 90 10° 11° 12° 14° 16° 18° 20° 1 22° 1 24° 1 26° 1 28° 1 30° 1 o t II / // / // 1 n / n / // / II / n / n / It / // 1 // 1 /r 1 // 1 ,/' , II 6 1 37 1 39 1 41 1 44 1 48 1 54 2 2 13 2 27 2 42 2 57 3 13 3 28 3 43 3 58 4 13 6 7 1 40 1 37 1 38 1 40 1 43 1 47 1 51 2 1 2 12 2 24 2 37 2 50 3 3 3 15 3 28 3 40 7 8 1 44 1 40 1 37 1 38 1 40 1 42 1 45 1 52 2 2 2 12 2 22 2 33 2 44 2 54 3 5 3 16 8 9 1 49 1 43 1 39 1 37 1 38 1 39 1 41 1 46 1 54 2 2 2 11 2 20 2 30 2 39 2 48 2 58 9 10 1 54 1 46 1 41 1 39 1 37 1 38 1 39 1 42 1 48 1 55 2 2 2 10 2 18 2 26 2 34 2 43 10 11 2 1 50 1 44 1 41 1 39 1 37 1 38 1 40 1 44 1 49 55 2 2 2 9 2 16 2 23 2 31 11 12 2 6 1 55 1 48 1 44 1 41 1 38 1 37 1 38 1 41 1 45 50 56 2 2 2 8 2 15 2 21 12 13 2 12 2 1 52 1 47 1 43 1 40 1 38 1 37 1 39 1 42 46 51 56 2 2 2 8 2 13 13 14 2 19 2 6 1 56 1 50 1 45 1 42 1 40 1 37 1 38 1 40 43 47 52 57 2 2 2 7 14 15 2 26 2 12 2 1 1 54 1 48 1 44 1 42 1 38 1 37 1 39 41 45 49 53 1 57 2 1 15 16 2 34 2 18 2 6 1 58 1 51 1 47 1 44 1 39 1 37 1 38 40 43 46 49 53 56 16 17 2 41 2 24 2 11 2 4 1 54 1 49 1 46 1 40 1 38 1 37 39 41 43 46 49 52 17 18 2 49 2 30 2 17 2 6 1 58 1 52 1 48 1 42 1 39 1 36 38 39 41 43 46 49 18 19 2 57 2 36 2 22 2 10 2 2 1 55 1 50 1 43 1 40 1 37 37 38 39 41 43 46 19 20 3 5 2 43 2 27 2 15 2 6 1 58 1 52 1 49 1 41 1 38 36 37 38 39 41 43 20 21 3 12 2 49 2 33 2 20 2 10 2 2 1 55 1 47 1 42 1 39 37 36 37 38 39 41 21 22 3 20 2 50 2 38 2 24 2 14 2 5 1 58 1 49 1 44 1 40 38 36 36 37 38 39 22 23 3 28 3 3 2 44 2 39 2 18 2 9 2 1 1 51 1 45 1 41 38 36 35 36 37 38 23 24 3 36 3 9 2 49 2 34 2 22 2 12 2 4 1 54 1 47 1 42 39 37 1 35 36 1 36 37 24 25 26 3 44 3 15 2 54 2 39 2 26 2 16 2 7 2 11 1 56 1 45 I 44 40 37 36 36 36 37 25 26 3 51 3 21 3 2 44 2 30 2 20 1 59 1 51 1 45 41 38 36 35 35 36 27 3 59 3 28 3 5 2 49 2 34 2 23 2 14 2 2 1 53 1 47 42 39 37 36 35 35 27 28 4 6 3 34 3 10 2 54 2 38 2 27 2 17 2 4 1 54 1 48 43 39 37 36 35 35 28 29 4 13 3 40 3 15 2 58 2 42 2 31 2 21 2 7 1 56 1 49 44 40 38 36 35 34 29 30 4 20 3 46 3 52 3 21 3 3 2 47 2 34 2 24 2 9 1 58 1 51 45 41 — 39 39 37 35 34 30 31 4 27 3 26 3 7 2 51 2 38 2 28 2 12 2 1 52 46 42 37 35 34 31 32 4 34 3 58 3 31 3 12 2 55 2 42 2 31 2 14 2 2 1 54 48 43 40 38 36 35 32 33 4 41 4 4 3 37 3 16 2 59 2 45 2 34 2 17 2 4 1 55 49 44 41 38 36 35 33 34 4 48 4 10 3 42 3 20 3 3 2 49 2 37 2 19 2 6 1 57 50 45 42 39 37 35 34 35 36 4 55 4 16 4 22 3 47 3 25 3 7 3 11 2 52 2 41 2 22 2 8 1 59 52 46 42 39 37 35 35 36 5 2 3 53 3 29 2 56 2 44 2 24 2 11 2 1 53 47 43 40 38 36 37 5 9 4 27 3 58 3 34 3 15 3 2 47 2 27 2 13 2 3 55 48 44 41 38 36 37 38 5 16 4 33 4 3 3 38 3 19 3 3 2 50 2 29 2 15 2 4 56 49 45 42 39 37 38 39 5 23 4 38 4 8 3 43 3 23 3 7 2 53 2 31 2 17 2 6 58 51 46 42 39 37 39 40 5 30 4 44 4 13 3 47 3 27 3 10 2 56 2 34 2 19 2 8 59 52 47 43 40 38 40 41 5 37 4 50 4 18 3 51 3 31 3 14 2 59 2 36 2 22 2 10 2 53 48 44 41 38 41 42 5 43 4 55 4 23 3 55 3 34 3 17 3 2 2 39 2 24 2 12 2 1 54 49 45 42 39 42 43 5 49 5 1 4 28 3 59 3 38 3 20 3 5 2 41 2 26 2 14 2 3 56 50 46 43 40 43 44 5 55 5 6 4 33 4 3 3 41 3 24 3 8 2 44 2 28 2 15 2 4 57 51 47 43 40 44 46 6 7 5 16 4 42 4 11 3 49 3 31 3 14 2 49 2 32 2 18 2 7 59 53 48 44 41 46 48 6 19 5 26 4 51 4 19 3 56 3 37 3 20 2 54 2 35 2 21 2 10 2 2 55 50 46 43 48 50 6 30 5 36 4 59 4 27 4 3 3 43 3 25 2 58 2 39 2 25 2 13 2 4 57 51 47 44 50 52 6 41 5 46 5 7 4 34 4 10 3 49 3 30 3 3 2 43 2 28 2 16 2 6 59 53 49 45 52 54 6 51 5 55 5 15 4 41 4 17 3 55 3 35 3 7 2 47 2 31 2 19 2 9 2 1 55 50 46 54 56 58 7 1 6 4 5 22 4 48 4 23 4 3 40 3 11 2 50 2 34 2 22 2 12 2 3 56 51 47 56 7 11 6 12 5 29 4 54 4 28 4 5 3 45 3 15 2 53 2 37 2 25 2 14 2 5 57 52 48 58 60 7 20 6 20 5 36 5 4 33 4 9 3 49 3 19 2 56 2 40 2 27 2 16 2 6 59 53 49 60 62 7 28 6 27 5 42 5 5 4 37 4 14 3 53 3 22 2 59 2 43 2 29 2 18 2 8 2 54 50 62 64 7 3fc 6 34 5 48 5 10 4 41 4 18 3 57 3 25 3 2 2 45 2 31 2 20 2 10 2 2 56 51 64 66 68 7 43 6 40 5 54 5 15 4 45 4 22 4 1 3 28 3 5 2 47 2 33 2 21 2 11 2 3 57 52 66 7 49 6 45 5 59 5 19 4 49 4 26 4 5 3 31 2 8 2 49 2 35 2 23 2 13 2 4 58 53 68 70 7 5.'} 6 50 6 3 5 23 4 53 4 29 4 8 3 34 2 10 2 51 2 36 2 24 2 14 2 5 58 ill 70 1 72 8 1 6 54 6 7 5 27 4 57 4 32 4 11 3 37 3 12 2 52 2 37 2 25 2 15 2 6 59 54 72 74 8 e 6 58 6 10 5 30 5 4 34 4 13 3 39 3 13 2 53 2 38 2 26 2 16 2 7 2 54 74 76 78 8 11 7 2 6 13 5 33 5 3 4 36 4 15 3 41 3 14 2 54 2 39 2 26 2 16 2 7 2 1 55 76 8 1£ . 7 € 6 16 5 36 5 5 4 38 4 17 3 42 3 15 2 55 2 40 2 27 2 17 2 8 2 1 78 80 8 1? ! 7 9 6 19 5 38 5 7 4 40 4 19 3 43 3 16 2 56 2 40 2 28 2 18 2 9 80 82 8 2C 17 11 6 21 5 40 5 9 4 42 4 2( 3 44 3 17 2 57 2 41 2 28 2 18 82 84 8 2£ ! 7 13 6 23 5 42 5 10 4 43 4 21 3 45 3 18 2 58 2 41 2 28 84 86 6 25 5 44 5 11 4 44 4 22 3 45 3 18 2 58 2 42 86 6° 70 g' 9° 10° 11° 12° 14° 16° 18° 20° 22° 24° 26° 28° 30° ^_^ TABLE XXXllI. 183 1 THIRD CORRECTION, TO APPARENT DISTANCE 76" D's App. Alt. APPARENT ALTITUDE OF THE SUN, OR STAR. App. Alt. 32" 340 36° 38° 42° 46° 50° 54° 58° 1 62° 66° 1 70° 74° 78° 82° 86° 1 n » II 1 II / // / // / II / II / // 1 II / // 1 // ' II / II 1 II 1 II / II 6 4 28 4 42 4 57 5 11 5 37 6 2 6 26 6 47 7 6 7 24 7 40 7 54 8 6 8 13 8 20 6 7 3 53 4 5 4 17 4 29 4 52 5 13 5 33 5 52 6 9 6 24 6 37 6 48 6 57 7 5 7 12 7 8 3 27 3 38 3 49 3 59 4 19 4 38 4 56 5 12 5 26 5 39 5 51 6 1 6 9 6 16 6 21 6 26 8 9 3 8 3 17 3 26 3 35 3 52 4 8 4 24 4 38 4 51 5 3 5 13 5 22 5 29 5 35 5 40 5 44 9 10 11 2 52 3 3 8 3 16 3 31 3 46 4 1 4 14 4 25 4 35 4 44 4 52 4 59 5 4 5 8 5 11 10 11 2 39 2 46 2 53 3 3 14 3 27 3 40 3 51 4 2 4 12 4 20 4 27 4 33 4 38 4 42 4 45 12 2 28 2 34 2 41 2 47 3 3 12 3 23 3 34 3 43 3 52 4 4 6 4 11 4 15 4 19 4 22 12 13 2 19 2 25 2 30 2 36 2 48 2 59 3 9 3 19 3 28 3 36 3 43 3 48 3 53 3 57 4 4 2 13 14 2 12 2 17 2 22 2 27 2 38 2 48 2 58 3 6 3 14 3 22 3 28 3 33 3 37 3 41 3 43 3 45 14 15 16 2 5 2 10 2 15 2 19 2 29 2 38 2 47 2 55 3 3 3 9 3 16 3 20 3 24 3 27 3 29 3 31 15 2 2 4 2 9 2 13 2 21 2 29 2 37 2 45 2 52 2 58 3 4 3 8 3 12 3 15 3 17 3 19 16 17 1 56 1 59 2 3 2 7 2 14 2 22 2 29 2 36 2 43 2 49 2 54 2 58 3 2 3 4 3 6 3 8 17 18 1 52 1 55 1 58 2 2 2 9 2 16 2 23 2 30 2 36 2 42 2 46 2 50 2 53 2 55 2 57 2 58 18 19 1 49 1 51 1 54 1 58 2 4 2 11 2 17 2 24 2 30 2 35 2 39 2' 42 2 45 2 47 2 49 2 5C 19 20 21 1 46 1 48 1 51 1 54 2 1 56 2 6 2 12 2 18 2 24 2 28 2 32 2 35 2 37 2 39 2 41 2 42 20 1 43 1 45 1 48 1 51 2 2 2 7 2 13 2 18 2 22 2 26 2 29 2 31 2 33 2 34 21 22 1 41 1 43 1 46 1 48 1 53 1 58 2 3 2 8 2 13 2 17 2 20 2 23 2 25 2 27 2 28 22 23 1 40 1 42 1 44 1 46 1 50 1 55 1 59 2 3 2 8 2 12 2 15 2 17 2 19 2 21 2 23 23 24 1 39 1 40 1 42 1 44 1 48 1 52 1 56 1 59 2 4 2 7 2 10 2 12 2 14 2 16 2 18 24 25 1 38 1 39 1 40 1 42 1 46 1 49 1 53 1 56 2 2 3 2 6 2 8 2 10 2 12 25 26 1 37 1 38 1 39 1 41 1 44 1 47 1 50 1 53 56 69 2 2 2 4 2 6 2 8 26 27 1 36 1 37 1 38 1 40 1 42 1 45 1 48 1 50 53 66 59 2 1 2 3 2 5 27 28 1 36 1 37 1 38 1 39 1 41 1 43 1 46 1 48 50 53 56 1 58 2 2 2 28 29 1 35 1 36 1 37 1 38 1 40 1 42 1 44 1 46 48 50 53 1 55 1 57 29 30 1 35 1 35 1 36 1 37 1 38 1 40 1 42 1 44 1 42 46 48 50 1 52 1 50 1 54 30 31 1 34 1 34 1 35 1 36 1 37 1 39 1 40 44 46 48 1 52 31 32 1 34 1 34 1 34 1 35 1 36 1 38 1 39 1 41 43 44 46 1 48 1 60 32 33 1 34 1 33 1 34 1 35 1 35 1 37 1 38 1 40 42 43 45 1 46 33 34 1 34 1 33 1 33 1 34 1 35 1 36 1 37 1 39 41 42 44 1 46 34 35 1 34 1 33 1 33 1 33 1 34 1 35 1 36 1 38 39 40 42 I 43 35 36 1 35 1 34 1 33 1 33 1 33 1 34 1 35 1 37 38 39 40 1 41 36 37 1 35 1 34 1 33 1 32 1 33 1 33 1 34 1 36 37 38 39 37 38 I 35 1 34 1 33 1 32 1 32 1 33 1 34 1 35 36 37 38 38 39 1 36 1 34 1 33 1 32 1 32 1 33 1 33 1 34 35 36 36 39 40 1 36 1 35 1 34 1 33 1 32 1 32 1 33 1 34 34 35 35 40 41 41 1 37 I 35 1 34 1 33 1 32 1 32 1 32 1 33 33 34 42 1 37 1 35 1 34 1 33 1 31 1 31 1 32 1 32 33 33 42 43 1 37 1 35 1 34 1 33 1 31 1 30 1 31 1 31 32 32 43 44 1 38 1 36 1 34 1 33 1 31 1 30 1 30 1 31 31 31 44 46 1 39 1 37 1 35 1 34 1 31 1 29 1 29 1 29 1 30 30 - 46 48 1 40 1 38 1 36 1 34 1 31 1 29 1 29 1 29 48 50 52 54 56 1 41 1 42 1 43 1 44 1 38 1 39 1 40 1 41 1 ;i7 1 37 1 38 1 38 1 35 1 35 1 36 1 36 1 32 1 32 1 33 1 33 1 30 1 30 1 30 1 30 1 29 1 29 1 29 1 29 1 29 1 28 1 1 1 50 52 54 56 58 60 62 TABLE P. EFFECT OF SUn's Pi LR t e. Add the Numbers above th lines to 3rd Correction, sub tract the others. 58 60 62 1 45 1 46 1 46 1 42 1 43 1 43 1 39 1 40 1 40 1 37 1 37 1 37 1 33 1 33 1 33 1 30 1 30 )'8 App Alt. Sun's Apparent Altitud 5 lU-i 3 30 40 .'5 60 7C 80 90 64 1 47 1 44 1 41 1 38 1 33 ft fl * 1" ^^ ~ » It n — 64 66 68 70 72 74 76 1 48 1 44 1 41 1 38 5 10 15 20 25 .30 35 40 45 50 55 60 65 70 75 80 90 1 1 2 3 4 4 5 6 6 7 7 8 8 8 9 9 1 CI 1 1 2 2 3 2 4 :) 4 4 5 4 6 .1 6 e 7 (i 7 1 8 ; 8 ? 8 6 9 i. 9 i Q F ' 1 2 3 3 4 6 5 6 6 7 7 8 ) 8 ) 1 1 2 2 3 4 4 5 6 6 7 7 I ] _1_ J "o 1) 1 1 1 2 2 2 3 3 3 4 3 3 4 4 5 5 5 6 1 1 1 2 66 68 70 72 74 76 1 49 1 4£ 1 4S 1 5C 1 45 1 4S 1 1 45 > 1 41 1 41 1 38 78 80 82 ' 84 > 86 78 80 82 84 86 32° 34° 36° 38° 42° 46° 50° 54° 58° 62° 66° 1 184 TABLE XXXIII. THIRD CORRECTION, TO APPARENT DISTANCE 80«. App. Alt. APPARENT ALTITUDE OF THE SUN, OR STAR. D's App. 6° 70 8° 9^ 10° 11° 12° 14° 16° 18° 20° 1 22° 1 24° 1 26° 1 28* 30° Alt. o r II / // / II 1 II / // 1 II / // 1 n / // / II 1 // / // t f/ / // / // / II * 6 1 41 1 43 1 46 1 50 1 54 1 59 2 4 2 17 2 32 2 47 3 2 3 17 3 32 3 47 4 2 4 16 6 7 1 44 1 41 1 43 1 45 1 48 1 51 1 55 2 5 2 17 2 29 2 41 2 54 3 6 3 19 3 31 3 441 7 8 1 48 1 43 1 41 1 42 1 44 1 46 1 49 1 56 2 6 2 16 2 26 2 37 2 48 2 59 3 10 3 20 8 9 1 52 1 46 1 43 1 41 1 42 1 44 1 46 1 51 1 58 2 6 2 15 2 25 2 34 2 43 2 62 3 1 9 10 1 57 1 50 1 46 1 43 1 41 1 42 1 44 1 47 1 54 1 59 2 6 2 14 2 22 2 30 2 38 2 46 10 11 2 3 1 54 1 49 1 45 1 43 1 41 ] 42 1 45 1 49 1 54 59 2 6 2 13 2 20 2 27 2 34 11 12 2 9 1 59 1 52 1 48 1 45 1 43 1 41 1 43 1 46 1 50 54 2 2 6 2 12 2 19 2 25 12 13 2 16 2 4 1 56 1 51 1 48 1 45 1 42 1 42 1 44 1 47 51 56 2 1 2 6 2 12 2 18 13 14 2 23 2 10 2 1 54 1 50 1 47 1 44 1 41 1 43 1 45 48 52 57 2 2 2 7 2 12 14 15 2 30 2 16 2 5 1 58 1 53 1 49 1 46 1 42 1 42 1 44 46 49 53 1 58 2 2 2 7 15 16 2 37 2 22 2 10 2 2 1 56 1 52 1 48 1 43 1 41 1 43 45 47 50 54 58 2 2 16 17 2 45 2 2» 2 15 2 6 1 59 1 54 1 50 1 45 1 42 1 42 43 45 48 51 54 58 17 18 2 53 2 34 2 21 2 11 2 3 1 57 1 52 1 47 1 43 1 41 42 44 46 48 51 54 18 19 3 2 41 2 26 2 15 2 7 2 1 54 1 48 1 44 1 42 41 43 44 46 49 61 19 20 3 8 2 47 2 31 2 20 2 10 2 3 1 57 1 50 1 46 1 43 41 42 43 45 47 49 20 21 21 3 16 2 54 2 37 2 24 2 14 2 6 1 59 1 52 1 47 1 44 42 41 42 1 43 45 47 22 3 23 3 2 43 2 29 2 18 2 9 2 2 1 54 1 49 1 45 42 40 41 42 43 45 22 23 3 31 3 6 2 47 2 33 2 22 2 13 2 5 1 57 1 51 1 47 43 41 40 41 42 44 23 24 3 38 3 12 2 53 2 38 2 25 2 16 2 8 1 59 1 52 1 48 44 41 40 41 42 43 24 25 26 3 46 3 18 2 58 2 42 2 29 2 19 2 12 2 1 1 54 1 49 45 42 40 .. 40 41 42 25 26 3 53 3 24 3 4 2 47 2 33 2 23 2 15 2 3 1 55 1 50 46 43 41 40 41 ^ 42 27 4 1 3 31 3 10 2 52 2 37 2 26 2 19 2 6 1 57 1 51 47 43 41 40 40 41 27 28 4 8 3 37 3 15 2 56 2 41 2 30 2 22 2 8 1 59 1 53 48 44 42 41 40 40 28 29 4 15 3 43 3 20 3 1 2 46 2 34 2 26 2 11 2 1 1 55 49 45 43 41 40 39 29 30 31 4 22 3 49 3 25 3 5 2 50 2 38 2 29 2 14 2 3 1 56 50 46 44 42 40 39 30 31 4 29 3 55 3 30 3 10 2 54 2 41 2 32 2 17 2 5 1 58 52 47 44 42 40 39 32 4 36 4 1 3 35 3 14 2 58 2 45 2 35 2 19 2 7 1 59 53 48 45 43 41 39 32 33 4 43 4 7 3 40 3 19 3 2 2 49 2 38 2 22 2 9 2 1 54 49 46 44 42 40 33 34 4 50 4 12 3 45 3 23 3 6 2 52 2 41 2 24 2 11 2 2 56 50 47 44 42 40 34 35 4 57 4 18 3 50 3 28 3 10 2 56 2 44 2 27 2 14 2 4 57 51 47 44 42 40 35 36 36 5 4 4 24 3 55 3 32 3 14 3 2 47 2 29 2 16 2 6 58 52 48 45 43 41 37 5 11 4 29 4 3 37 3 19 3 3 2 50 2 32 2 18 2 8 2 53 49 46 44 42 37 38 5 18 4 35 4 5 3 42 3 23 3 7 2 54 2 34 2 20 2 9 2 1 54 49 46 44 42 38 39 5 25 4 41 4 10 3 46 3 27 3 11 2 58 2 36 2 22 2 10 2 2 55 50 47 45 43 39 40 41 5 31 4 47 4 15 3 50 3 31 3 14 3 1 2 38 2 24 2 12 2 4 57 51 47 45 43 40 5 38 4 52 4 20 3 54 3 35 3 18 3 4 2 41 2 26 2 14 2 5 58 52 48 46 44 41 42 5 44 4 57 4 25 3 58 3 3S 3 21 3 7 2 44 2 28 2 16 2 7 59 53 49 46 44 42 43 5 51 5 3 4 30 4 2 3 42 3 25 3 10 2 46 2 30 2 17 2 8 2 1 55 50 47 45 43 44 5 57 5 8 4 35 4 6 3 46 3 28 3 13 2 48 2 32 2 19 2 10 2 2 56 51 48 45 44 46 6 9 5 18 4 44 4 14 3 53 3 35 3 19 2 53 2 36 2 23 2 13 2 4 58 53 49 46 46 48 6 20 5 28 4 53 4 22 4 3 41 3 25 2 58 2 39 2 26 2 15 2 7 2 55 51 48 48 50 6 31 5 38 5 1 4 30 4 6 3 47 3 30 3 3 2 43 2 29 2 18 2 9 2 2 56 52 49 60 52 6 41 5 47 5 9 4 37 4 12 3 53 3 35 3 7 2 47 2 32 2 21 2 12 2 4 58 54 50 52 54 6 51 5 56 5 17 4 44 4 18 3 58 3 39 3 11 2 51 2 35 2 24 2 14 2 6 59 55 52 54 56 7 1 6 5 5 24 4 50 4 24 4 3 3 44 3 15 2 54 2 38 2 26 2 17 2 8 2 1 57 53 56 58 7 11 6 14 5 31 4 56 4 30 4 8 3 49 3 19 2 57 2 41 2 29 2 19 2 10 2 3 58 54 68 60 7 20 6 22 5 38 5 2 4 35 4 13 3 54 3 23 3 2 44 2 31 2 21 2 12 2 5 59 55 60 62 7 28 6 29 5 44 5 7 4 40 4 18 3 58 3 27 3 3 2 47 2 3o 2 22 2 13 2 6 2 56 62 64 7 36 6 35 5 50 5 12 4 44 4 22 4 2 3 31 3 6 2 49 2 3.5 2 24 2 15 2 7 2 1 56 64 66 68 7 43 6 41 5 55 5 17 4 49 4 26 4 6 3 34 3 9 2 51 2 37 2 26 2 16 2 8 2 2 57 66 7 49 6 46 6 5 21 4 53 4 30 4 9 3 37 3 12 2 53 2 39 2 27 2 17 2 9 2 3 68 68 70 7 55 6 51 6 5 5 25 4 57 4 33 4 12 3 39 3 14 2 55 2 41 2 29 2 19 2 10 2 4 59 70 72 8 6 55 6 9 5 29 5 4 36 4 14 3 41 3 16 2 57 2 42 2 30 2 20 2 11 2 5 2 72 74 8 5 6 59 6 13 5 32 5 3 4 38 4 16 3 43 3 18 2 58 2 43 2 31 2 21 2 12 2 5 74 76 8 9 7 3 6 16 5 35 5 6 4 40 4 18 4 19 3 44 3 19 2 59 2 44 2 32 2 22 2 13 76 78 8 13 7 6 6 19 5 37 5 8 4 42 3 45 3 20 3 2 45 2 32 2 22 78 80 8 16 7 9 6 21 5 40 5 10 4 44 4 21 3 46 3 21 3 1 2 45 2 33 80 82 8 19 7 12 6 23 5 42 5 12 4 45 4 22 3 47 3 22 3 2 2 46 82 84 8 22 7 14 6 25 5 44 5 13 4 46 4 23 3 48 3 23 3 3 84 86 8 24 7 16 6 27 5 46 5 14 4 47 4 24 3 49 3 24 86 6=* 70 %" 9° 10° 11° 12° 14° 16° 18° 20° 22° 24° 26° 28° 30° ^^^_ TABLE XXXUI. 185 1 THIRD CORRECTION, TO APPARENT DISTANCE 80<». | App. Alt. APPARENT ALTITUDE OF THE SUN, OR STAR. App. Alt. 32" 340 1 3 50 38° 1 42° 46° 50° 54° 58° 62° 66° 70° 74° 78° 82<» 86° o / // f f f / 1 r / // / ff / n / // / // 1 II 1 II / // ' II 1 II 1 II 1 II / /; 6 4 30 4 44 4 58 5 12 5 39 6 4 6 28 6 49 7 8 7 26 7 41 7 54 8 5 8 13 8 19 8 1A \ 6 p t 3 56 4 8 4 19 4 30 4 52 5 14 5 35 5 54 6 11 6 26 6 39 6 50 6 59 7 6 7 12 7 H ) 7 8 3 31 3 41 3 52 4 2 4 23 4 42 4 59 5 15 5 29 5 42 5 54 6 4 6 12 6 18 6 23 6 27 8 9 3 11 3 21 3 30 3 39 3 56 4 12 4 28 4 42 4 54 5 5 5 15 5 24 5 32 5 38 5 43 5 46 ; 9 10 2 54 3 3 3 12 3 20 3 35 3 50 4 4 4 16 4 28 4 39 4 48 4 56 5 2 5 7 5 11 5 \A \ 10 11 11 2 42 2 49 2 57 3 5 3 19 3 32 3 44 3 56 4 7 4 16 4 24 4 31 4 36 4 41 4 45 4 47 12 2 32 2 38 2 45 2 52 3 5 3 17 3 28 3 38 3 48 3 57 4 5 4 11 4 15 4 19 4 22 4 11 ) 12 13 2 24 2 30 2 36 2 42 2 53 3 4 3 14 3 23 3 32 3 40 3 47 3 53 3 57 4 1 4 4 4 i ) 13 14 2 18 2 23 2 28 2 33 2 43 2 53 3 2 3 11 3 19 3 26 3 32 3 38 3 42 3 46 3 48 3 4c ) 14 15 16 2 12 2 16 2 21 2 25 2 34 2 43 2 34 2 52 3 3 7 3 13 3 19 3 25 3 29 3 32 3 34 3 3( ) 15 2 6 2 10 2 14 2 18 2 26 2 42 2 50 2 56 3 2 3 8 3 13 3 17 3 20 3 22 3 2- 1 16 17 2 1 2 4 2 8 2 12 2 20 2 27 2 34 2 41 2 47 2 53 2 58 3 3 3 6 3 9 3 11 17 18 1 57 2 2 3 2 7 2 14 2 21 2 28 2 34 2 40 2 46 2 50 2 54 2 57 3 3 2 18 19 1 54 56 1 59 2 2 2 9 2 16 2 22 2 28 2 34 2 39 2 43 2 47i ^ 50 2 52 2 53 19 20 1 51 53 1 56 1 58 2 5 2 11 2 17 2 22 2 28 2 33 2 37 2 40 2 43 2 45 2 46 20 21 1 49 51 1 53 55 2 1 2 7 2 12 2 17 2 22 2 27 2 31 2 34 2 37 2 38 21 22 1 47 49 1 51 53 58 2 3 2 8 2 13 2 17 2 21 2 25 2 28 2 31 2 32 22 23 1 46 47 1 49 51 55 2 2 4 2 9 2 13 2 17 2 20 2 23 2 26 2 27 23 24 1 45 46 1 47 49 53 1 57 2 1 2 5 2 9 2 13 2 16 2 19 2 21 2 22 24 25 1 44 45 1 46 48 51 1 54 1 58 2 1 2 5 2 9 2 12 2 14 2 16 25 26 1 43 44 1 45 46 49 1 52 1 55 1 58 2 2 2 5 2 8 2 10 2 12 26 27 1 42 43 1 44 45 47 1 50 1 53 1 56 59 2 2 2 5 2 7 2 8 27 28 1 41 42 1 43 ■'■ 44 46 1 48 1 51 1 54 57 59 2 2 2 4 2 5 28 29 1 40 41 1 41 42 44 1 46 1 49 1 52 55 57 59 2 1 29 30 1 39 40 1 40 41 43 1 45 1 48 1 51 53 55 57 1 59 30 31 1 39 4Q 1 40 41 42 1 44 1 46 1 49 51 53 55 1 57 31 32 1 39 39 1 39 40 41 1 43 1 45 1 47 49 51 53 1 5^ 32 33 1 39 39 1 39 40 41 1 42 1 44 1 46 48 49 51 33 34 1 39 39 1 39 40 41 1 42 1 43 1 45 47 48 49 34 35 1 39 39 1 39 39 40 1 41 1 42 1 44 45 46 47 35 36 1 40 39 1 39 39 40 1 41 1 42 1 43 44 45 1 46 36 37 1 41 40 1 39 38 39 1 40 1 41 1 42 43 44 37 38 1 41 40 1 39 38 39 1 40 1 41 1 42 42 43 38 39 1 41 40 1 39 38 39 1 39 1 40 1 41 41 42 39 40 1 41 40 1 39 38 38 1 38 1 39 1 40 40 41 40 41 1 42 41 1 40 39 38 1 38 1 38 1 39 39 41 42 1 42 41 1 40 39 37 1 37 1 37 1 38 38 42 43 1 43 41 1 40 39 37 1 37 1 37 1 37 38 43 44 1 43 42 1 40 39 37 1 37 1 36 1 37 37 44 46 1 44 42 1 41 40 38 1 37 1 36 1 36 46 48 1 45 43 1 41 40 38 1 37 1 36 1 36 48 50 52 54 56 1 46 1 47 1 48 1 49 44 45 46 47 1 42 1 43 1 44 1 44 41 38 1 36 1 36 ' 1 1 50 41 42 42 38 38 38 1 36 1 36 1 36 1 35 TABLB P. EFFECT OF SUN't PAK 52 54 56 Add the Numbers above the lines to 3rd Correction, sub- tract the others. 58 1 50 A7 1 45 42 43 43 38 58 60 62 64 66' 60 62 1 51 1 52 48 49 1 45 1 46 38 App Alt. Snn's Apparent Altitude. 1 5 10 2( 3 30 40 5 60 70 f !U90 64 1 52 49 1 46 43 „ tl 1 1* " t » n It ft n 66 1 53 49 1 46 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 90 1 1 2 3 4 4 5 6 6 7 7 8 8 8 9 9 1 I 1 1 2 2 3 3 4 :t 4 4 6 5 6 5 6 6 7 6 7 7 8 7 8 8 8 8 9 8 9 8 1 2 2 3 4 4 5 6 6 7 7 e 8 1 ( 1 3 ' 3 ; 4 : 4 . 5 , « < 7 1 ) I I 2 3 3 } 3 t 4 5 4 5 3 \ ' 2 2 3 1 1 2 68 70 72 74 76 1 54 1 55 1 50 68 70 72 74 76 78 80 82 84 86 78 80 82 84 86 ^^^ 32° 38" 42° 58° 62° 66° » 1 1 i54" 36° 46° 50° 54° 186 TABLE XXXIII. THIRD CORRECTION, TO APPARENT DISTANCE 84°. J '8 APPARENT ALTITUDE OF THE SUN, OR STAR. D's App Alt. App. Alt. 6° 70 8<» 9«» 100 II* 12° 14° 16° 1 18° 1 20° 22° 1 24° 26° 28° 30° 1 o 1 II 1 If 1 II 1 II / II / // 1 It / II / // 1 11 / // 1 r/ f // / ^/ 1 // / // l 6 1 47 1 49 1 51 1 54 1 59 2 4 2 10 2 22 2 36 2 50 3 5 3 20 3 35 3 50 4 5 4 20 6 1 7 1 50 1 47 1 48 1 50 1 53 1 56 2 2 10 2 21 2 33 2 45 2 57 3 10 3 23 3 35 3 48 7 8 1 53 1 49 1 47 1 48 1 50 1 52 1 55 2 2 2 11 2 21 2 31 2 42 2 53 3 3 3 14 3 25 8 9 1 57 1 52 1 49 1 47 1 48 1 50 1 52 1 57 2 4 2 12 2 21 2 30 2 39 2 48 2 58 3 7 9 10 2 2 1 55 1 51 1 49 1 47 1 48 1 50 1 53 1 59 2 5 2 12 2 20 2 27 2 35 2 44 2 52 10 11 2 8 1 59 1 54 1 51 1 49 1 47 1 48 1 51 55 59 2 5 2 12 2 18 2 36 2 33 2 41 11 12 2 14 2 4 1 57 1 53 1 51 1 48 1 47 1 49 52 55 59 2 5 2 11 2 18 2 25 2 31 12 13 2 20 2 9 2 1 1 56 1 53 1 50 1 48 1 48 1 50 52 55 2 2 6 2 11 2 17 2 23 13 14 2 27 2 14 2 5 1 59 1 55 1 52 1 50 1 47 48 50 53 57 2 2 2 6 2 11 2 16 14 15 2 34 2 20 2 10 2 3 1 58 1 54 1 51 1 48 47 49 51 54 1 58 2 2 2 7 2 11 15 16 2 42 2 26 2 15 2 7 2 1 1 56 1 53 1 49 47 48 50 52 55 59 2 3 2 7 16 17 2 49 2 32 2 20 2 11 2 4 1 59 1 55 1 50 48 47 48 50 53 56 2 2 3 17 18 2 57 2 38 2 25 2 16 2 8 2 2 1 57 1 52 49 46 47 49 51 54 57 2 18 19 3 4 2 44 2 31 2 20 2 12 2 5 1 59 1 53 50 47 46 48 49 52 54 67 19 20 3 12 2 50 2 36 2 25 2 15 2 8 2 2 1 55 51 48 46 47 48 50 52 55 20 21 3 20 2 57 2 42 2 29 2 19 2 11 2 5 1 57 52 49 47 46 47 48 50 52 21 22 3 27 3 3 2 47 2 34 2 23 2 14 2 8 1 59 54 50 47 46 46 47 49 50 22 23 3 35 3 9 2 52 2 38 2 27 2 18 2 11 2 1 56 52 48 46 46 47 48 49 23 24 3 42 3 15 2 57 2 42 2 30 2 21 2 14 2 3 57 53 49 46 46 46 47 48 24 25 26 3 49 3 21 3 3 2 47 2 34 2 25 2 17 2 6 59 54 ~55 50 47 46 46 46 47 25 26 3 56 3 27 3 8 2 52 2 38 2 28 2 20 2 8 2 51 48 47 46 46 46 27 4 4 3 34 3 13 2 56 2 42 2 32 2 24 2 11 2 2 56 52 49 47 46 45 46 27 28 4 11 3 40 3 18 3 1 2 46 2 35 2 27 2 13 2 4 58 53 49 47 46 45 45 28 29 4 19 3 47 3 24 3 5 2 51 2 39 2 30 2 16 2 6 59 54 50 48 46 45 45 29 30 31 4 26 3 53 3 29 3 10 2 55 2 43 2 33 2 18 2 8 2 1 55 51 49 47 46 45 30 31 4 33 3 59 3 35 2 14 2 59 2 46 2 36 2 21 2 10 2 3 57 52 49 47 46 45 32 4 40 4 5 3 40 3 19 3 3 2 50 2 39 2 24 2 12 2 4 58 53 50 48 46 45 32 33 4 47 4 11 3 45 3 24 3 7 2 54 2 42 2 27 2 14 2 5 59 54 50 48 46 45 33 34 4 54 4 16 3 50 3 28 3 11 2 57 2 45 2 29 2 16 2 7 2 55 51 48 47 46 34 35 5 1 4 22 3 55 3 33 3 15 3 1 2 49 2 32 2 19 2 9 2 2 56 52 49 47 46 35 36 36 5 8 4 28 4 3 37 3 19 3 5 2 52 2 34 2 21 2 10 2 3 58 53 49 47 46 37 5 15 4 34 4 5 3 42 3 23 3 8 2 56 2 37 2 23 2 12 2 4 59 54 50 48 47 37 38 5 21 4 40 4 10 3 46 3 27 3 12 2 59 2 39 2 25 2 14 2 6 2 55 51 49 47 38 39 5 28 4 45 4 15 3 51 3 31 3 15 3 2 2 42 2 27 2 16 2 7 2 1 56 52 49 47 39 40 5 34 4 51 4 20 3 55 3 35 3 19 3 5 2 44 2 29 2 18 2 9 2 3 57 52 49 47 40 41 5 41 4 56 4 25 3 59 3 39 3 23 3 8 2 47 2 31 2 20 2 11 2 4 58 53 50 48 41 42 5 47 5 1 4 30 4 3 3 43 3 26 3 11 2 49 2 33 2 21 2 12 2 5 59 54 51 49 42 43 6 53 5 7 4 35 4 7 3 47 3 30 3 14 2 52 2 35 2 23 2 13 2 7 2 55 52 50 43 44 6 5 12 4 40 4 11 3 50 3 34 3 17 2 54 2 37 2 25 2 15 2 8 2 1 56 53 51 44 46 48 6 12 5 22 4 49 4 19 3 57 3 40 3 23 2 59 2 41 2 29 2 18 2 10 2 3 58 55 52 46 6 24 5 32 4 58 4 27 4 4 3 46 3 29 3 4 2 45 2 32 2 21 2 12 2 5 2 56 53 48 50 6 35 5 42 5 6 4 35 4 11 3 52 3 35 3 9 2 49 2 35 2 24 2 15 2 8 2 2 58 55 50 52 6 45 5 51 5 14 4 42 4 17 3 58 3 40 3 13 2 53 2 38 2 27 2 18 2 10 2 4 2 57 52 54 6 55 6 5 22 4 49 4 23 4 4 3 45 3 17 2 57 2 41 2 30 2 20 2 12 2 6 2 2 58 54 56 58 7 5 6 9 5 29 4 55 4 29 4 9 3 50 3 21 3 1 2 44 2 32 2 22 2 14 2 8 2 3 59 56 7 14 6 17 5 36 5 1 4 34 4 14 3 55 3 25 3 4 2 47 2 35 2 24 2 16 2 9 2 4 2 58 60 7 22 6 25 5 42 5 6 4 39 4 19 3 59 3 29 3 7 2 50 2 37 2 26 2 17 2 10 2 5 2 1 60 62 7 30 6 32 5 48 5 11 4 44 4 23 4 3 3 33 3 10 2 53 2 39 2 28 2 19 2 12 2 7 2 2 62 64 7 38 6 39 5 54 5 16 4 49 4 27 4 7 3 36 3 13 2 56 2 41 2 29 2 20 2 13 2 8 2 3 64 66 7 45 6 45 6 5 21 4 54 4 31 4 11 3 39 3 16 2 58 2 43 2 31 2 22 2 15 2 9 2 3 66 68 7 51 6 60 6 5 5 25 4 58 4 35 4 15 3 41 3 19 3 2 45 2 33 2 24 2 16 2 10 2 4 68 70 7 57 6 54 6 9 5 29 5 2 4 39 4 18 3 44 3 21 3 2 2 46 2 34 2 25 2 17 2 10 70 72 8 2 6 58 6 13 5 33 5 6 4 42 4 21 3 46 3 23 3 3 2 47 2 35 2 26 2 18 72 74 8 fi 7 2 6 17 5 36 5 9 4 44 4 23 3 48 3 24 3 4 2 48 2 36 2 27 74 76 8 10 7 5 6 20 5 39 5 11 4 46 4 25 3 50 3 25 3 5 2 49 2 37 76 78 78 8 14 7 8 6 23 5 42 5 13 4 48 4 26 3 51 3 26 3 6 2 50 80 8 18 7 11 6 26 5 45 5 15 4 50 4 27 3 52 3 27 3 7 80 82 8 21 7 14 6 28 5 47 5 17 4 51 4 28 3 53 3 28 82 84 8 24 T 17 6 30 5 49 5 18 4 52 4 29 3 54 84 86 8 26 7 19 6 31 5 50 5 19 4 53 4 30 86 6° 7" 8° 1 9° i 10° 11" 12° 14° 16° 18° 20° 22° 24° 26° 28° 30° TABLE XXXUI. 18, 1' THIRD CORRECTION, TO APPARENT DISTANCE 84". - App. Alt. APPARENT ALTITUDE OF THE SUN, OR STAR. • '8 App Alt. 32° 34* ( 36° 38° 42° 46° 50° 54° 58° 62° 66° 70° 74° 78° 82° 86° 1 It 1 II 1 II / n / // / II / II 1 II / // / /' 1 // / // / II ; II / II 1 II o 6 4 34 4 48^ 5 2 5 15 5 41 6 6 6 29 6 51 7 10 7 27 7 42 7 55 8 6 8 14 8 21 8 27 6 7 4 4 12 4 24 4 36 4 58 5 19 5 39 5 58 6 15 6 30 6 42 6 53 7 2 7 9 7 15 7 19 7 8 3 36 3 47 3 57 4 7 4 27 4 46 5 4 5 20 5 34 5 46 5 58 6 9 6 17 6 23 6 28 6 31 8 9 3 16 3 25 3 34 3 43 4 4 17 4 33 4 47 4 59 5 10 5 20 5 29 5 36 5 42 5 47 5 50 9 10 3 1 3 9 3 17 3 25 3 41 3 55 4 9 4 21 4 as 4 43 4 53 5 1 5 7 5 13 5 17 5 19 4 54 10 11 11 2 48 2 55 3 3 3 10 3 24 3 37 3 50 4 2 4 12 4 21 4 30 4 37 4 43 4 48 4 51 12 2 38 2 44 2 51 2 58 3 10 3 22 3 34 3 45 3 54 4 2 4 10 4 16 4 22 4 26 4 28 4 30 12 13 2 29 2 35 2 41 2 47 2 58 3 9 3 20 3 29 3 38 3 45 3 52 3 58 4 3 4 7 4 9 13 14 2 22 2 27 2 33 2 38 2 48 2 58 3 8 3 16 3 24 3 31 3 37 3 43 3 47 3 51 3 53 14 15 2 16 2 21 2 26 2 30 2 39 2 48 2 40 2 57 3 5 3 12 3 19 3 25 3 30 3 34 3 37 3 40 15 16 2 11 2 15 2 20 2 24 2 32 2 48 2 56 3 2 3 9 3 15 3 19 3 23 3 26 3 29 16 17 2 7 2 10 2 14 2 18 2 26 2 34 2 41 2 48 2 54 3 3 5 3 9 3 13 3 15 17 18 2 3 2 6 2 10 2 13 2 21 2 28 2 34 2 40 2 46 2 52 2 57 3 1 3 4 3 6 18 19 2 2 3 2 6 2 9 2 16 2 23 2 29 2 34 2 40 2 45 2 49 2 53 2 56 2 58 19 20 1 57 2 2 2 2 5 2 12 2 18 2 24 2 29 2 34 2 38 2 42 2 45 2 48 2 50 20 21 1 54 1 57 1 59 2 2 2 8 2 13 2 19 2 24 2 29 2 33 2 36 2 39 2 41 21 22 1 52 1 54 1 56 1 59 2 4 2 9 2 14 2 19 2 24 2 28 2 31 2 34 2 36 22 23 1 50 1 52 1 54 1 56 2 1 2 5 2 10 2 15 2 19 2 23 2 26 2 29 2 32 23 24 1 49 1 50 1 52 1 54 1 58 2 2 2 7 2 11 2 15 2 19 2 22 2 25 2 28 24 25 1 48 1 49 1 50 1 52 1 56 1 54 2 2 4 2 8 2 12 2 15 2 18 2 21 25 26 1 47 1 48 1 49 1 51 1 58 2 2 2 5 2 9 2 12 2 15 2 17 26 27 1 47 1 48 1 49 1 50 1 53 1 56 2 2 3 2 6 2 9 2 12 2 14 27 28 1 46 1 47 1 48 1 49 1 51 1 64 1 58 2 1 2 3 2 6 2 9 2 11 28 29 1 46 1 47 1 47 1 48 1 50 1 53 1 56 1 59 2 1 2 4 2 6 29 30 1 45 1 46 1 46 1 47 1 49 1 52 1 55 1 57 1 56 2 2 2 2 3 30 31 1 45 1 45 1 46 1 47 1 49 1 51 1 54 1 58 2 2 1 31 32 1 45 1 45 1 45 1 46 1 48 1 50 1 52 1 54 1 56 1 58 1 59 32 33 1 45 1 45 1 45 1 46 1 47 1 49 1 51 1 53 1 54 1 56 33 34 1 45 1 44 1 44 1 45 1 46 1 48 1 50 1 52 1 53 1 54 34 35 1 45 1 44 1 44 1 45 1 46 1 47 1 49 1 50 1 51 1 52 35 36 1 46 1 45 1 44 1 44 1 45 1 46 1 48 1 49 1 50 1 50 «6 37 1 46 1 45 1 44 1 44 1 45 1 45 1 47 1 48 1 49 37 38 1 46 1 45 1 44 1 44 1 44 1 45 1 46 1 47 1 48 38 39 1 46 1 45 1 44 1 44 1 44 1 44 1 45 1 46 1 47 39 40 1 46 1 45 1 45 1 45 1 44 1 44 1 45 1 45 1 46 40 41 1 47 1 46 1 45 1 45 1 44 1 44 1 44 1 44 41 42 1 48 1 47 1 46 1 45 1 43 1 43 1 44 1 44 42 43 1 49 1 48 1 46 1 45 1 43 1 43 1 44 1 44 43 44 1 49 1 48 1 47 1 45 1 43 1 43 1 43 44 46 1 50 1 49 1 47 1 45 1 43 1 43 1 43 46 48 1 51 1 50 1 48 1 46 1 44 1 43 1 42 48 50 52 54 56 1 53 1 54 1 55 1 56 1 51 1 51 1 52 1 53 1 49 1 49 1 49 1 50 1 47 1 47 1 47 1 48 1 44 1 44 1 44 1 44 1 43 1 42 ' 1 50 52 54 TABLE P. EFFECT OF SON's PAR . To be. subtracted from the Third Correction. 56 58 60 62 58 60 62 1 56 1 57 1 58 1 53 1 54 1 54 1 50 1 51 1 51 1 48 1 48 )8 App Alt. Sun's Apparent Altitude. 1 5 10 2 30 40 5 60 70 80 90 64 1 59 1 55 n /* # ~ "^ If f n It ~~ 64 66 1 59 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 90 1 1 o 3 4 4 5 6 6 7 7 8 8 8 9 9 9 1 1 1 2 '. 3 C 4 r 4 4 5 t 6 ; 6 e 7 ' 7 ' 8 ' 8 i 8 t 9 i 9 1 ! 2 t 3 I 3 4 » 5 > 5 > 6 J 6 r 7 r 7 i 8 ) 1 I 3 4 5 5 6 6 7 B 1 1 2 2 2 2 3 3 1 4 4 4 5 5 8 1 2 2 3 4 1 1 66 68 70 72 74 76 78 80 82 84 86 1 68 70 72 74 76 78 80 82 84 86 1 32° 34° 36° 38° 42° 46° 50° 54° 58° 62° 66° ■ , , 188 TABLE XXXIII. THIRD CORRECTION, TO APPARENT DISTANCE 88° • i J '8 APPARENT ALTITUDE OF THE SUN, OR STAR. J "6 App. Alt. App. Alt. 0^ 6° 70 8° 9° 10" 11° 12° 14° 16° 18° 20° 22° 24° 26° 1 28° 3 o / n 1 It 1 n / n / II 1 II / II 1 II / // 1 II 1 II / // 1 II 1 // / // 1 /r 6 1 53 1 54 1 56 1 59 2 4 2 10 2 16 2 28 2 42 2 56 2 11 3 26 3 41 3 56 4 11 4 25 6 7 1 55 1 53 1 54 1 56 1 59 2 3 2 7 2 16 2 27 2 39 2 51 3 4 3 16 3 28 3 40 3 52 7 8 1 58 1 55 1 53 1 54 1 56 1 59 2 2 2 8 2 17 2 27 2 37 2 48 2 59 3 9 3 19 3 30 8 9 2 2 1 58 1 55 1 53 1 54 1 56 1 58 2 3 2 10 2 18 2 26 2 35 2 45 2 54 3 3 3 12 9 10 2 7 2 I 1 57 1 55 1 53 1 54 1 56 2 2 5 2 11 2 18 2 25 2 34 2 43 2 50 2 58 10 11 2 13 2 5 2 1 57 1 55 1 53 1 54 1 57 2 1 2 6 2 12 2 18 2 25 2 32 2 39 2 47 11 12 2 19 2 10 2 4 2 1 57 1 54 1 53 1 55 1 58 2 2 2 7 2 12 2 18 2 24 2 30 2 37 12 13 2 26 2 15 2 8 2 3 1 59 1 56 1 54 1 54 1 56 1 59 2 3 2 7 2 12 2 18 2 23 2 29 13 14 2 33 2 21 2 12 2 6 2 1 1 58 1 56 1 53 1 55 1 57 2 2 3 2 7 2 12 2 17 2 22 14 15 2 40 2 26 2 16 2 9 2 4 2 1 57 1 54 1 54 1 55 1 58 2 2 4 2 8 2 13 2 17 15 16 2 47 2 32 2 20 2 13 2 7 2 2 1 59 1 55 1 53 1 54 1 56 1 58 2 1 2 5 2 9 2 13 16 17 2 54 2 37 2 25 2 17 2 10 2 5 2 1 1 56 1 53 1 53 1 55 1 57 1 59 2 2 2 5 2 9 17 18 3 2 2 43 2 30 2 21 2 13 2 7 2 3 1 58 1 54 1 52 1 54 1 56 1 58 2 2 2 2 5 18 19 3 10 2 49 2 35 2 25 2 16 2 10 2 5 1 59 1 55 1 53 1 53 1 54 1 56 58 2 2 3 19 20 3 17 2 55 2 41 2 29 2 20 2 13 2 8 2 1 1 56 1 54 1 52 1 53 1 54 56 1 58 2 1 20 21 21 3 25 3 2 2 46 2 34 2 24 2 17 2 11 2 3 1 58 1 55 1 53 1 52 I 53 55 1 57 59 22 3 32 3 8 2 52 2 39 2 28 2 20 2 14 2 5 1 59 1 56 1 53 1 52 1 53 54 1 55 57 22 23 3 40 3 15 2 57 2 43 2 32 2 24 2 17 2 7 2 1 1 57 1 54 1 52 1 52 53 1 54 55 23 24 3 47 3 21 3 2 2 48 2 36 2 27 2 20 2 9 2 2 1 58 1 55 1 53 1 52 52 1 53 54 24 25 26 3 55 3 27 3 8 2 52 2 40 2 31 2 23 2 27 2 11 2 4 2 1 56 1 53 1 52 52 1 53 54 25 26 4 2 3 33 2 13 2 57 2 44 2 35 2 14 2 6 2 1 1 57 1 54 1 53 52 1 52 53 27 4 10 3 39 3 18 3 2 2 48 2 38 2 30 2 17 2 8 2 2 1 58 1 55 1 53 52 1 52 52 27 28 4 17 3 45 3 23 3 6 2 52 2 42 2 33 2 19 2 10 2 4 1 59 1 55 1 53 52 1 52 52 28 29 4 24 3 51 3 28 3 11 2 56 2 46 2 37 2 22 2 12 2 5 2 1 56 1 53 52 1 52 52 29 30 4 31 3 57 3 34 3 15 3 2 49 2 40 2 24 2 14 2 6 2 1 1 57 1 54 53 1 52 52 30 31 4 39 4 3 3 40 3 20 3 4 2 53 2 43 2 27 2 16 2 8 2 2 1 58 1 55 53 1 52 52 31 32 4 46 4 9 3 45 3 25 3 8 2 56 2 46 2 29 2 18 2 9 2 3 1 59 1 56 54 1 53 52 32 33 4 53 4 15 3 51 3 29 3 12 3 2 50 2 31 2 20 2 11 2 5 2 1 56 54 1 53 53 33 .14 5 4 21 3 56 3 34 3 17 3 4 2 53 2 34 2 22 2 13 2 7 2 1 1 57 55 1 54 53 34 35 5 7 4 27 4 1 3 38 3 21 3 7 2 56 2 37 2 24 2 15 2 8 2 2 1 58 56 1 54 53 35 36 3ff 5 13 4 33 4 6 3 43 3 25 3 11 2 59 2 40 2 26 2 17 2 10 2 4 1 59 56 1 54 53 37 5 20 4 39 4 11 3 48 3 29 3 15 3 2 2 43 2 28 2 19 2 11 2 5 2 57 1 55 54 37 38 5 27 4 45 4 16 3 52 3 33 3 18 3 5 2 46 2 31 2 21 2 13 2 6 2 1 58 1 56 54 38 39 5 34 4 51 4 21 3 57 3 37 3 22 3 8 2 49 2 33 2 22 2 14 2 7 2 2 58 1 56 55 39 40 41 5 40 4 56 4 26 4 1 3 41 3 25 3 11 2 51 2 35 2 24 2 16 2 17 2 9 2 3 59 1 57 55 40 5 47 5 2 4 31 4 5 3 45 3 29 3 14 2 54 2 38 2 26 2 10 2 4 2 1 57 65 41 42 5 53 5 7 4 36 4 9 3 49 3 32 3 17 2 56 2 40 2 28 2 19 2 11 2 5 2 1 1 58 56 42 43 6 5 13 4 41 4 14 3 53 3 36 3 20 2 59 2 42 2 30 2 20 2 12 2 6 2 2 ) 59 57 43 44 6 6 5 19 4 46 4 18 3 57 3 39 3 23 3 1 2 44 2 32 2 22 2 13 2 7 2 3 2 58 44 46 48 6 18 5 29 4 55 4 26 4 4 3 46 3 29 3 6 2 48 2 35 2 25 2 16 2 9 2 5 2 2 59 46 6 29 5 39 5 4 4 34 4 11 3 52 3 35 3 11 2 52 2 39 2 28 2 18 2 11 2 7 2 3 2 48 50 6 40 5 48 5 12 4 41 4 17 3 58 3 41 3 15 2 56 2 42 2 31 2 21 2 13 2 9 2 5 2 2 50 52 6 51 5 57 5 20 4 48 4 23 4 2 3 47 3 19 2 59 2 45 2 34 2 24 2 16 2 10 2 6 2 3 52 54 7 1 6 6 5 28 4 55 4 29 4 8 3 52 3 23 3 3 2 48 2 36 2 27 2 18 2 12 2 8 2 4 54 56 7 10 6 15 5 35 5 1 4 35 4 14 3 57 3 27 3 7 2 51 2 39 2 29 2 20 2 14 2 9 2 5 56 58 7 19 6 23 5 42 5 7 4 40 4 19 4 2 3 31 3 10 2 54 2 42 2 31 2 22 1 16 2 11 2 6 58 60 7 28 6 31 5 48 5 12 4 45 4 24 4 6 3 35 3 13 2 57 2 44 2 33 2 24 1 17 2 12 2 7 60 62 7 36 6 38 5 54 5 17 4 50 4 29 4 10 3 38 3 16 2 59 2 46 2 35 2 26 2 19 2 13 2 8 62 64 7 44 6 45 6 5 22 4 55 4 33 4 14 3 42 3 19 3 2 2 48 % 37 2 28 2 20 2 14 2 9 64 66 68 7 51 6 51 6 5 5 27 5 4 37 4 18 3 45 3 22 3 4 2 50 2 39 2 30 2 22 2 15 66 7 58 6 56 6 10 5 32 5 4 4 41 4 21 3 48 3 25 3 6 2 51 2 40 2 31 2 23 68 70 S 4 7 1 6 15 5 36 5 8 4 44 4 23 3 50 3 27 3 8 2 53 2 41 2 32 70 72 •' IC 7 S 6 19 5 40 5 11 4 47 4 25 3 52 3 29 3 9 2 53 2 42 72 74 > If > 7 9 6 23 5 43 5 14 4 49 4 27 3 54 3 30 3 10 2 54 74 76 78 8 ^<3 7 13 6 26 5 46 5 17 4 51 4 29 3 56 3 31 3 11 76 8 2S ! 7 16 6 29 5 49 5 19 4 53 4 31 3 57 3 32 78 80 8 21 i 7 19 6 31 5 52 5 21 4 55 4 33 3 58 80 82 8 26 ! 7 22 6 33 5 54 5 23 4 57 4 35 82 84 8 3( ) 7 24 6 35 5 56 5 15 84 86 8 35 5 7 26 6 37 86 &'' 70 8° 9<» 10° 11" 12° 14° 16° 18° 20° 22° 24° 26° 28° 30° _ TABLE XXXIII. 189 1 THIRD CORRECTION, TO APPARENT DISTANCE 899 A.pp. Alt. APPARENT ALTITUDE OP THE SUN, OR STAR. >'8 App Alt. o 32° 34" 36° 1 38° 42° 46° 50° 54° 58° 62° 66° 1 70° 74° 78° 82° 86° o 1 ti / // 1 // r II / II 1 II / II / II / II / II / II / II / // / // 1 II / II 6 4 40 4 54 5 8 5 22 5 48 6 13 6 36 6 57 7 16 7 34 7 49 8 2 8 13 8 21 8 27 8 32 6 7 4 4 4 16 4 28 4 40 5 3 5 25 5 45 6 4 6 21 6 36 6 49 7 7 9 7 16 7 22 7 27 7 8 3 41 3 52 4 3 4 13 4 33 4 52 5 10 5 26 5 40 5 53 6 5 6 15 6 23 6 29 6 34 6 37 8 9 3 22 3 31 3 41 3 50 4 8 4 24 4 39 4 53 5 5 5 16 5 26 5 35 5 43 5 49 5 54 9 10 3 6 3 14 3 22 3 30 3 46 4 1 4 15 4 27 4 38 4 49 4 58 5 7 5 14 5 19 5 23 10 11 11 2 54 3 2 3 9 3 16 3 30 3 43 3 56 4 7 4 17 4 27 4 36 4 43 4 49 4 53 4 57 12 2 44 2 51 2 58 3 4 3 16 3 28 3 40 3 50 4 4 8 4 16 4 23 4 28 4 32 4 36 12 13 2 35 2 41 2 47 2 53 3 4 3 15 3 26 3 35 3 44 3 52 3 59 4 5 4 10 4 13 13 14 2 27 2 33 2 38 2 44 2 54 3 4 3 14 3 22 3 30 3 37 3 44 3 50 3 54 3 57 14 15 16 2 22 2 27 2 32 2 36 2 46 2 55 3 4 3 11 3 18 3 25 3 31 3 37 3 41 3 44 15 2 17 2 21 2 26 2 30 2 39 2 47 2 55 3 2 3 9 3 15 3 21 3 26 3 30 3 33 16 17 2 12 2 16 2 21 2 25 2 33 2 40 2 47 2 54 3 3 6 3 12 3 16 3 19 17 18 2 8 2 12 2 16 2 20 2 27 2 34 2 41 2 47 2 53 2 58 2 3 3 7 3 10 18 19 2 5 2 8 2 12 2 16 2 22 2 29 2 35 2 41 2 47 2 52 2 56 2 59 3 2 19 20 2 3 2 6 2 9 2 12 2 18 2 24 2 30 2 35 2 41 2 46 2 49 2 52 2 54 20 21 2 1 2 3 2 6 2 8 2 14 2 19 2 25 2 30 2 35 2 40 2 43 2 46 21 22 1 59 2 1 2 3 2 5 2 10 2 15 2 20 2 25 2 30 2 35 2 38 2 41 22 23 1 57 1 59 2 1 2 3 2 7 2 12 2 16 2 21 2 26 2 30 2 33 2 36 23 24 1 56 1 57 59 2 1 2 5 2 9 2 13 2 17 2 22 2 26 2 29 2 31 24 25 1 55 1 56 57 1 59 2 3 2 6 2 10 2 14 2 18 2 22 2 25 25 26 1 54 1 55 56 1 58 2 1 2 4 2 8 2 12 2 15 2 18 2 21 26 27 1 53 1 54 1 55 1 57 2 2 3 2 6 2 10 2 13 2 15 2 17 27 28 1 53 1 54 55 1 56 1 58 2 1 2 4 2 8 2 11 2 13 2 14 28 29 1 52 1 53 54 1 55 1 57 2 2 3 2 6 2 8 2 10 29 30 1 52 1 53 53 1 54 1 56 1 59 2 2 2 4 2 6 2 8 30 31 1 52 1 52 52 1 53 1 55 1 58 2 2 2 2 4 2 5 31 32 1 51 1 52 52 1 53 1 55 1 57 1 59 2 1 2 2 2 3 32 33 1 52 1 51 51 1 52 1 54 1 56 1 58 1 59 2 33 34 1 52 1 51 51 1 52 1 53 1 55 1 57 1 58 1 69 34 35 1 52 1 51 51 1 51 1 52 1 54 1 56 1 57 1 57 35 36 1 53 1 52 51 1 51 1 52 1 53 1 55 1 56 1 56 36 37 1 53 1 52 51 1 51 1 51 1 52 1 54 1 56 37 38 1 53 1 52 51 1 50 1 51 1 52 1 53 1 54 38 39 1 54 1 52 51 'l 50 1 51 1 52 1 52 1 53 39 40 1 54 1 53 52 1 51 1 50 1 51 1 52 1 52 40 41 41 1 54 1 53 52 1 51 1 50 1 51 1 51 42 1 54 1 53 52 1 51 1 50 1 51 1 51 42 43 1 55 1 54 53 1 52 1 51 1 51 1 51 43 44 1 56 1 54 53 1 52 1 51 1 50 1 50 44 46 1 57 1 55 53 1 52 1 51 1 50 46 48 1 58 1 56 54 1 53 1 51 1 50 48 *50 52 54 1 59 2 2 1 1 57 I 58 1 58 55 55 56 56 1 53 1 53 1 54 1 54 1 51 1 52 ' 1 50 52 54 TABLE P. BF FBCT OF IDN's PAK . 56 58 60 62 2 2 1 59 To be subtracted from th« Third Correction. 56 58 60 62 2 3 2 3 2 4 1 59 1 59 1 56 APP A t. Sun's Apparent Altitude. 1 5 10 2 30 40 5 60 7( )8C 90 64 ft ' t* ft — — 64 66 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 90 1 2 2 3 4 4 5 6 6 7 7 8 8 8 9 9 9 1 1 1 2 S 3 C 4 4 4 4 5 i 6 C 6 i 7 • 7 ' 8 i 8 i 8 i 9 9 1 1 ! 2 3 4 4 5 6 ! r 7 r 7 ) 8 i i 1 1 2 3 4 4 5 6 6 7 7 I 1 1 1 1 2 2 2 3 3 3 4 4 4 4 4 5 5 1 2 66 68 70 72 74 7ti 78 80 82 84 86 68 70 72 74 76 ! 78 80 82 84 86 36° 38° 50° 54° 58° 62° 66° 32° 34° 42° 46° 190 TABLE XXXIIl. THIRD CORRECTION, TO APPARENT DISTANCE 92". 2>'8 App. Alt. APPARENT ALTITUDE OF THE SUN, OR STAR. App. Alt. 6» 70 8° 9 10° 11 I" 12° 14° 16° 18° 20° 22° 24° 26° 28° 30° / // t ti 1 tt t n 1 // / n 1 It I II ; II t II / II / // ' ." r // t rf 1 II 6 1 id 2 1 2 3 2 6 2 10 2 15 2 21 2 34 2 48 3 3 3 18 3 33 3 48 4 3 4 18 4 33 6 7 2 1 1 59 2 1 2 3 2 5 2 9 2 13 2 22 2 33 2 45 2 58 3 11 3 24 3 36 3 48 4 7 8 2 4 2 1 1 59 2 2 2 2 4 2 7 2 14 2 23 2 33 2 44 2 55 3 5 3 16 3 26 3 37 8 9 2 8 2 4 2 1 1 59 2 2 2 2 4 2 9 2 16 2 24 2 33 2 42 2 51 3 1 3 10 3 19 9 10 2 13 2 7 2 3 2 1 1 59 2 2 2 2 6 2 11 2 17 2 24 2 32 2 40 2 48 2 57 3 5 10 11 2 19 2 11 2 6 2 3 2 1 1 59 2 2 3 2 7 2 12 2 18 2 24 2 31 2 39 2 46 2 54 11 12 2 25 2 16 2 10 2 6 2 3 2 1 1 59 2 1 2 4 2 8 2 13 2 18 2 24 2 31 2 37 2 44 12 13 2 32 2 21 2 14 2 9 2 5 2 2 2 2 2 2 2 5 2 9 2 14 2 19 2 24 2 30 2 36 13 14 2 39 2 27 2 18 2 12 2 7 2 4 2 2 1 59 2 1 2 3 2 6 2 10 2 14 2 19 2 24 2 29 14 15 2 46 2 32 2 22 2 15 2 10 2 6 2 3 2 2 2 1 2 4 2 7 2 10 2 15 2 19 2 24 15 16 2 53 2 38 2 27 2 19 2 13 2 8 2 5 2 1 1 59 2 2 2 2 4 2 7 2 11 2 15 2 19 16 17 3 2 44 2 32 2 23 2 16 2 11 2 7 2 3 2 1 59 2 1 2 3 2 5 2 8 2 12 2 15 17 18 3 8 2 50 2 37 2 27 2 19 2 14 2 9 2 4 2 1 1 59 2 2 2 2 4 2 6 2 9 2 12 18 19 3 16 2 56 2 42 2 31 2 22 2 16 2 11 2 6 2 2 2 2 2 1 2 2 2 4 2 7 2 10 19 20 3 23 3 2 2 48 2 36 2 26 2 19 2 14 2 8 2 3 2 1 59 2 2 1 2 3 2 5 2 8 20 21 3 31 8 9 2 54 2 41 2 30 2 23 2 17 2 10 2 5 2 1 1 59 1 59 2 2 2 2 4 2 6 21 22 3 38 3 15 2 59 2 45 2 34 2 26 2 20 2 12 2 6 2 2 2 1 59 2 2 1 2 2 2 4 22 23 3 46 3 22 3 4 2 50 2 38 2 30 2 23 2 14 2 8 2 3 2 1 59 1 59 2 2 1 2 2 23 24 3 53 3 28 3 9 2 54 2 42 2 34 2 27 2 16 2 9 2 4 2 1 2 1 59 59 2 2 1 24 25 26 4 1 3 34 3 15 2 59 2 46 2 37 2 30 2 19 2 11 2 5 ~1 2 2 2 1 59 59 2 2 25 26 4 9 3 40 3 20 3 3 2 50 2 41 2 33 2 22 2 13 2 2 4 2 1 1 59 59 59 2 27 4 17 3 46 3 26 3 8 2 55 2 45 2 36 2 24 2 15 2 9 2 5 2 2 2 59 59 2 27 28 4 24 3 52 3 31 3 13 2 59 2 48 2 39 2 27 2 17 2 11 2 6 2 2 2 59 59 59 28 29 4 31 3 58 3 36 3 18 3 3 2 52 2 43 2 29 2 19 2 12 2 7 2 3 2 1 2 59 59 29 30 4 38 4 4 3 41 3 22 3 7 2 56 2 46 2 32 2 21 2 13 2 8 2 4 2 1 2 59 59 30 31 31 4 46 4 10 3 47 3 27 3 12 3 2 50 2 35 2 23 2 15 2 9 2 5 2 2 2 1 59 59 32 4 53 4 16 3 52 3 32 3 16 3 4 2 53 2 37 2 25 2 16 2 11 2 7 2 3 2 1 2 59 32 33 5 4 22 3 58 3 37 3 20 3 8 2 57 2 40 2 27 2 18 2 12 2 8 2 4 2 1 2 59 33 34 5 7 4 28 4 3 3 41 3 24 3 11 3 2 42 2 29 2 20 2 14 2 9 2 5 2 2 2 1 2 34 35 5 14 4 34 4 8 3 46 3 28 3 15 3 3 2 45 2 31 2 22 2 15 2 10 2 6 2 3 2 1 2 2 1 35 36 36 5 21 4 40 4 13 3 50 3 32 3 18 3 6 2 47 2 33 2 24 2 17 2 11 2 7 2 4 2 2 37 5 28 4 46 4 18 3 55 3 36 3 22 3 9 2 50 2 36 2 25 2 18 2 12 2 8 2 5 2 3 2 1 37 38 5 34 4 52 4 23 4 3 40 3 25 3 12 2 53 2 38 2 27 2 20 2 14 2 9 2 6 2 4 2 2 38 39 5 41 4 58 4 28 4 4 3 44 3 29 3 15 2 55 2 40 2 29 2 21 2 15 2 10 2 7 2 4 2 2 39 40 41 5 47 5 J 4 33 4 8 3 48 3 32 3 18 2 58 2 42 2 31 2 22 2 16 2 11 2 • 2 5 2 3 40 5 54 5 9 4 38 4 12 3 52 3 35 3 21 3 2 45 2 33 2 24 2 17 2 12 2 8 2 5 2 3 41 42 6 5 14 4 43 4 16 3 55 3 39 3 24 3 2 2 47 2 34 2 25 2 18 2 13 2 9 2 6 2 4 42 43 6 7 5 20 4 48 4 21 3 59 3 42 3 27 3 5 2 49 2 36 2 27 2 20 2 14 2 10 2 7 2 4 43 44 6 13 5 25 4 53 4 25 4 3 3 46 3 30 3 8 2 51 2 38 2 28 2 21 2 15 2 11 2 8 2 5 44 45 46 6 19 5 31 4 58 4 29 4 7 3 49 3 33 3 11 53 2 40 2 30 2 22 2 16 2 12 2 8 2 5 45 6 25 5 36 5 2 4 33 4 10 3 52 3 36 3 13 2 55 2 42 2 31 2 24 2 18 2 13 2 9 2 6 46 47 6 31 5 41 5 7 4 37 4 13 3 55 3 39 3 16 2 57 2 44 2 33 2 25 2 19 2 14 2 10 2 7 4f 48 6 37 5 46 5 11 4 41 4 17 3 59 3 42 3 18 2 59 2 46 2 35 2 27 2 20 2 15 2 11 2 8 48 50 6 47 5 56 5 19 4 48 4 24 4 5 3 48 3 22 3 4 2 49 2 37 2 29 2 22 2 16 2 12 2 9 50 52 54 6 57 7 7 6 5 5 27 4 55 4 30 4 11 3 53 3 26 3 8 2 53 2 41 2 32 2 24 2 18 2 13 2 10 52 6 14 5 35 5 2 4 36 4 16 3 58 3 30 3 11 2 56 2 44 2 34 2 26 2 20 2 15 2 11 54 56 7 17 6 23 5 42 5 9 4 42 4 21 4 3 3 34 3 14 2 59 2 47 2 37 2 29 2 22 2 16 2 12 56 58 7 27 6 31 5 49 5 15 4 47 4 26 4 8 3 38 3 17 3 2 2 49 2 39 2 31 2 24 2 18 2 13 58 lO 7 36 6 39 5 56 5 21 4 53 4 31 4 13 3 42 3 20 3 5 2 52 2 41 2 32 2 25 2 20 2 14 60 (i2 64 7 45 6 46 6 2 5 26 4 58 4 36 4 17 3 46 3 23 3 8 2 54 2 43 2 34 2 26 2 21 62 7 53 6 53 6 8 5 31 5 3 4 41 4 21 3 50 3 26 3 10 2 56 2 44 2 35 2 27 64 66 8 1 6 59 6 13 5 36 5 8 4 45 4 25 3 53 3 29 3 12 2 57 2 45 2 37 66 68 8 8 7 5 6 18 5 41 5 12 4 49 4 28 3 56 3 32 3 14 2 58 2 46 68 70 8 14 7 10 6 23 5 45 5 16 4 52 4 31 3 58 3 34 3 15 2 59 70 72 8 20 7 15 6 28 5 49 5 19 4 55 4 33 4 3 35 3 16 72 74 74 8 25 7 19 6 31 5 53 5 22 4 57 4 35 4 1 3 36 76 8 29 7 23 6 34 5 56 5 25 4 59 4 37 4 2 76 78 8 32 7 26 6 37 5 58 5 27 5 1 4 39 78 80 8 34 7 28 6 39 6 5 1^9 80 82 8 36 7 30^6 41 82 6' 7° ^' 9° 10° 11" 12" 14" 16" 18" 20" 22° 24" 26° 28° 30° TABLE XXXlll. 191 1 THIRD CORRECTION, TO APPARENT DISTANCE 92°. 1 App. Alt. APPARENT ALTITUDE OF THE SUN, OR STAR. ^'8 App Alt 32^ 34° 36° 38° 40° 42° 46° 50° 54° 58° 62° 66° 70° 74° 78° 82° / II / II > // 1 II / // / // / II t II 1 II 1 II / II / II ' II 1 II 1 II t II 6 4 47 5 2 5 16 5 30 5 44 5 57 6 21 6 44 7 5 7 24 7 42 7 59 8 12 8 22 8 30 8 36 6 7 4 12 4 24 4 36 4 48 5 5 11 5 33 5 53 6 12 6 29 6 44 6 58 7 10 7 18 7 25 7 30 7 8 3 48 3 59 4 10 4 20 4 30 4 40 4 59 5 17 5 33 5 48 6 1 6 13 6 23 6 31 6 37 6 41 8 9 3 29 3 38 3 48 3 57 4 6 4 14 4 30 4 45 5 5 13 5 25 5 35 5 44 5 52 5 58 9 10 11 3 13 3 1 3 21 3 30 3 38 3 45 3 52 4 8 4 22 4 34 "4 46 4 57 5 7 5 15 5 22 5 27 10 11 3 8 3 16 3 22 3 29 3 36 3 50 4 3 4 14 4 24 4 34 4 43 4 51 4 57 5 2 12 2 51 2 57 3 4 3 10 3 17 3 23 3 35 3 47 3 57 4 6 4 15 4 23 4 30 4 36 4 41 12 13 2 42 2 47 2 53 2 59 3 6 3 12 3 23 3 33 3 42 3 51 4 4 7 4 13 4 17 13 14 2 34 2 39 2 44 2 50 2 56 3 2 3 12 3 21 3 30 3 38 3 46 3 52 3 57 4 1 14 15 16 2 28 2 33 2 38 2 43 2 37 2 48 2 53 3 2 3 11 3 19 3 26 3 33 3 39 3 44 3 49 15 16 2 23 2 28 2 32 2 42 2 46 2 54 3 2 3 9 3 16 3 22 3 28 3 33 3 38 17 2 19 2 23 2 27 2 32 2 36 2 40 2 47 2 54 3 1 3 7 3 13 3 19 3 24 17 18 2 16 2 19 2 23 2 27 2 31 2 34 2 41 2 48 2 54 3 3 6 3 11 3 15 18 19 2 13 2 16 2 19 2 23 2 26 2 29 2 36 2 42 2 48 2 54 2 59 3 4 3 7 19 20 2 10 2 13 2 16 2 19 2 22 2 18 2 25 2 31 2 37 2 43 2 48 2 53 2 57 3 20 21 2 8 2 10 2 13 2 16 2 21 2 26 2 32 2 38 2 43 2 47 2 51 21 22 2 6 2 8 2 10 2 13 2 15 2 17 2 22 2 28 2 33 2 38 2 42 2 45 22 23 2 4 2 6 2 8 2 10 2 12 2 14 2 19 2 24 2 29 2 34 2 38 2 41 23 24 2 2 2 4 2 6 2 8 2 10 2 12 2 16 2 21 2 26 2 30 2 34 2 38 24 25 2 1 2 3 2 4 2 6 2 8 2 10 2 14 2 18 2 22 2 26 2 30 25 26 2 1 2 2 2 3 2 5 2 6 2 8 2 12 2 15 2 19 2 23 2 26 26 27 2 2 1 2 2 2 4 2 5 2 7 2 10 2 13 2 16 2 20 2 23 27 28 1 59 2 2 1 2 3 2 4 2 6 2 8 2 11 2 14 2 17 2 20 28 29 1 59 1 59 2 2 2 2 3 2 5 2 7 2 10 2 12 2 15 29 30 1 59 1 59 2 2 1 2 2 2 4 2 6 2 9 2 11 2 13 — ^ 30 31 31 1 59 1 59 1 59 2 2 1 2 3 2 5 2 7 2 9 2 11 32 1 59 1 59 1 59 2 2 1 2 2 2 4 2 6 2 7 2 9 32 33 1 59 1 59 1 59 1 59 2 2 1 2 3 2 5 2 6 33 34 1 59 1 58 1 59 1 59 2 2 1 2 2 2 4 2 5 34 35 1 59 1 58 1 59 1 59 2 2 2 1 2 3 2 4 - 35 36 36 2 1 59 1 59 1 59 2 2 2 1 2 2 2 3 37 2 1 59 1 59 1 58 1 59 1 59 2 2 1 37 38 2 1 59 1 59 1 58 1 59 1 59 2 2 1 38 39 2 1 2 1 59 1 58 1 58 1 59 1 59 2 39 40 2 1 2 1 59 1 58 1 58 1 58 1 59 2 40 41 41 2 1 2 1 59 1 59 1 58 1 58 1 58 42 2 2 2 1 59 1 59 1 58 1 58 1 58 42 43 2 2 2 1 2 1 59 1 58 1 58 1 58 43 44 2 3 2 1 2 1 59 1 58 1 58 1 57 44 45 2 3 2 2 2 1 2 1 59 1 58 45 46 2 4 2 2 2 1 2 1 59 1 58 46 47 48 50 2 4 2 5 2 fi 2 7 2 2 2 3 2 4 2 5 2 1 2 2 2 2 2 3 2 2 1 2 1 2 1 1 59 1 59 2 1 58 1 59 1 ' 1 47 48 50 TABLS P. EFFECT OF BITN's PAR 52 To be subtracted from the 52 54 56 5P 60 54 56 2 8 2 9 2 5 2 5 2 3 e. )'e App Aft. Sun's Apparent Altituc 6S 2 lO' 5 IU2 30 tt 40 5 tt 60 70 80 90 tl 60 „ 62 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 90 I 2 o 3 4 4 5 6 6 7 7 8 8 9 9 9 1 1 2 S 2 '. 3 C 4 4 4 £ 5 fi 6 f. 6 t 7 ' 7 ' 8 i 8 i 8 i 9 9 1 2 . 2 3 4 5 5 6 ) 7 r 7 r 8 i 8 \ 1 2 3 3 4 S 5 fi 7 7 1 1 1 2 2 2 3 3 3 13 3 1 4 5 5 5 6 't i 62 64 66 68 70 72 64 66 68 70 72 74 76 78 80 82 74 76 78 80 82 32« 34° 36° 38° 40° 42° 46° 50° 54° 58° 62° 13 192 TABLE XXXIII. THIRD CORRECTION, TO APPARENT DISTANCE 96° D's App. Alt. APPARENT ALTITUDE OF THE 3UN, OR STAR. ])'s _ App., 6" 70 8° 9° 10° 11° 12° 14° 16° 18° 1 20° 22° 24 1° 26° 1 28° 1 30° 1 Alt. o t II 1- II / // 1 II 1 II f 1, t II / II 1 II 1 // 1 II 1 II / II > II 1 ^r / // 6 2 6 2 8 2 10 2 13 2 17 2 22 2 28 2 41 2 55 3 10 3 26 3 41 3 56 4 11 4 26 4 41 6 7 2 9 2 6 2 8 2 10 2 12 2 16 2 20 2 29 2 40 2 52 3 5 3 18 3 31 3 43 3 56 4 8 7 8 2 12 2 8 2 6 2 7 2 9 2 12 2 15 2 22 2 31 2 40 2 51 2 2 3 13 3 24 3 35 3 45 8 9 2 16 2 11 2 8 2 6 2 7 2 9 2 12 2 17 2 24 2 31 2 40 2 49 2 59 3 8 3 18 3 27 9 10 11 2 20 2 14 2 10 2 8 2 6 2 7 2 9 2 13 2 18 2 24 2 32 2 40 2 48 2 56 3 4 3 12 10 2 26 2 18 2 13 2 10 2 7 2 6 2 7 2 10 2 14 2 19 2 25 2 32 2 39 2 46 2 53 3 1 11 12 2 32 2 23 2 17 2 13 2 9 2 7 2 6 2 8 2 11 2 15 2 20 2 26 2 32 2 38 2 45 2 52 12 13 2 39 2 28 2 21 2 16 2 12 2 9 2 7 2 7 2 9 2 12 2 16 2 21 2 26 2 32 2 38 2 44 13 14 2.46 2 33 2 25 2 19 2 14 2 11 2 9 2 6 2 8 2 10 2 13 2 18 2 22 2 27 2 32 2 37 14 15 2 53 2 39 2 29 2 22 2 17 2 14 2 11 2 7 2 7 2 9 2 11 2 15 2 19 2 23 2 28 2 2 32 28 15 16 16 3 1 2 45 2 34 2 26 2 20 2 16 2 13 2 8 2 5 2 8 2 10 2 13 2 16 2 20 2 24 17 3 8 2 51 2 39 2 30 2 23 2 19 2 15 2 9 2 7 2 7 2 9 2 11 2 14 2 17 2 21 2 24 17 18 3 15 2 57 2 44 2 34 2 26 2 21 2 17 2 11 2 8 2 6 2 8 2 10 2 12 2 15 2 18 2 21 18 19 3 23 3 3 2 49 2 38 2 30 2 24 2 19 2 13 2 9 2 7 2 7 2 8 2 10 2 13 2 15 2 18 19 20 3 30 3 9 2 54 2 43 2 34 2 27 2 22 2 15 2 11 2 8 2 6 2 7 2 9 2 11 2 13 2 15 20 21 3 38 3 16 3 2 48 2 37 2 30 2 25 2 17 2 12 2 9 2 7 2 7 2 8 2 9 2 11 2 13 21 22 3 46 3 22 3 5 2 52 2 41 2 33 2 28 2 19 2 14 2 10 2 8 2 6 2 7 2 8 2 10 2 12 22 23 3 54 3 28 3 11 2 57 2 45 2 37 2 31 2 21 2 15 2 11 2 8 2 6 2 6 2 7 2 q 2 11 23 24 4 1 3 34 3 16 3 I 2 49 2 41 2 35 2 23 2 17 2 12 2 9 2 7 2 6 2 7 2 8 2 10 24 25 26 4 9 3 41 3 22 3 6 2 53 2 45 2 38 2 26 2 19 2 14 16 2 11 2 8 2 6 2 7 2 8 2 9 25 26 4 16 3 47 3 27 3 11 2 57 2 48 2 41 2 29 2 21 2 2 12 2 9 2 7 2 6 2 7 2 8 27 4 24 3 53 3 33 3 15 3 1 2 52 2 44 2 31 2 23 2 17 2 13 2 10 2 8 2 6 2 6 2 7 27 28 4 31 4 3 38 3 20 3 fi 2 55 2 47 2 34 2 24 2 18 2 14 2 11 2 9 2 7 2 6 2 7 28 29 4 39 4 6 3 44 3 25 3 10 2 59 2 50 2 36 2 26 2 20 2 15 2 12 2 10 2 8 2 7 2 6 29 30 4 46 4 12 3 49 3 29 3 14 3 3 2 53 2 38 2 28 2 21 2 16 2 13 2 10 2 8 2 7 2 6 30 31 4 53 4 18 3 55 2 34 3 18 3 7 2 57 2 41 2 30 2 23 2 18 2 14 2 11 2 9 2 8 2 7 31 32 5 4 24 4 3 39 3 23 3 11 3 1 2 44 2 32 2 25 2 19 2 15 2 12 2 9 2 8 2 7 32 33 5 7 4 30 4 5 3 44 3 27 3 15 3 4 2 46 2 34 2 26 2 20 2 16 2 13 2 10 2 8 2 7 33 34 5 14 4 36 4 11 3 49 3 32 3 19 3 7 2 48 2 36 2 28 2 21 2 17 2 14 2 11 2 9 2 8 34 35 36 5 21 4 42 4 16 3 54 3 36 3 23 3 11 2 51 2 38 2 30 2 23 2 18 2 15 2 12 2 10 2 8 35 36 5 28 4 48 4 21 3 59 3 40 3 26 3 14 2 54 2 40 2 32 2 25 2 20 2 16 2 13 2 11 2 9 37 5 35 4 54 4 26 4 3 3 44 3 29 3 17 2 57 2 43 2 33 2 26 2 21 2 17 2 14 2 11 2 9 37 38 5 42 5 4 31 4 8 3 48 3 33 3 20 2 59 2 45 2 35 2 27 2 22 2 18 2 15 2 12 2 10 38 39 5 49 5 6 4 36 4 12 3 52 3 36 3 23 3 2 2 47 2 37 2 29 2 23 2 19 2 16 2 13 2 11 39 40 41 5 55 5 12 4 41 4 16 3 56 3 40 3 26 3 5 2 50 2 39 2 30 2 24 2 20 2 16 2 13 2 11 40 6 2 5 18 4 46 4 20 4 3 44 3 30 3 7 2 52 2 41 2 32 2 25 2 21 2 17 2 14 2 12 41 42 6 8 5 23 4 51 4 24 4 4 3 47 3 33 3 10 2 54 2 43 2 34 2 27 2 22 2 18 2 15 2 13 42 43 6 14 5 29 4 56 4 29 4 8 3 51 3 36 3 13 2 55 2 45 2 35 2 28 2 23 2 19 2 16 2 13 43 44 6 20 5 34 5 1 4 33 4 11 3 54 3 39 3 16 2 59 2 47 2 37 2 29 2 24 2 20 2 17 2 14 44 45 46 6 26 5 39 5 6 4 37 4 14 3 57 3 42 3 19 3 1 2 48 2 38 2 30 2 25 2 21 2 17 2 14 45 6 32 5 44 5 10 4 41 4 18 4 3 45 3 21 3 3 2 50 2 39 2 31 2 26 2 22 2 18 2 15 46 47 6 38 5 49 5 15 4 45 4 22 4 3 3 48 3 24 3 5 2 52 2 41 2 33 2 27 2 23 2 19 2 16 47 48 6 44 5 54 5 19 4 49 4 25 4 7 3 51 3 26 3 7 2 53 2 42 2 34 2 28 2 24 2 20 2 16 48 49 6 50 5 59 5 23 4 53 4 29 4 10 3 54 3 28 3 9 2 55 2 44 2 36 2 29 2 25 2 21 2 17 49 50 51 6 55 7 C 6 4 5 27 4 57 4 32 4 13 3 57 3 30 3 11 2 56 2 45 2 37 2 31 2 26 2 21 2 17 50 6 9 5 31 5 1 4 36 4 16 4 3 32 3 13 2 58 2 47 2 38 2 32 2 27 2 22 2 18 51 52 7 £ 6 14 5 35 5 4 4 39 4 19 4 3 3 34 3 15 3 2 48 2 39 2 33 2 28 2 23 2 18 52 54 7 \t . 6 23 5 43 5 11 4 45 4 25 4 8 3 38 3 19 3 2 2 51 2 42 2 35 2 29 2 24 2 19 54 56 7 11 . 6 31 5 51 5 18 4 51 4 30 4 13 3 42 3 22 3 6 2 54 2 45 2 37 2 30 2 25 2 19 56 58 60 7 3f i 6 39 5 58 5 24 4 56 4 35 4 17 3 46 3 26 3 9 2 57 2 47 2 39 2 31 2 25 58 7 M ) 6 46 6 4 5 3C 5 1 4 39 4 21 3 50 3 29 3 12 2 59 2 49 2 41 2 32 60 62 7 5t\ I 6 53 6 IC 5 35 5 6 4 44 4 25 3 54 3 32 3 15 3 1 2 50 2 42 62 64 8 S ! 7 6 16 5 40 5 11 4 48 4 29 3 58 3 35 3 17 3 3 2 51 64 66 8 1( ) 7 7 6 21 5 45 5 16 4 52 4 33 4 1 3 38 3 19 3 4 66 68 70 8 Vi ' 7 13 6 26 5 5C 5 21 4 56 4 36 4 3 3 40 3 21 68 8 2-: 1 7 18 6 31 5 54 5 25 5 4 39 4 5 3 42 70 72 8 2t ) 7 23 6 36 ! 5 5S ! 5 28 5 3 4 41 4 7 72 74 8 3: 5 7 27 6 4C ) 6 1 5 31 5 6 4 43 74 7* 8 3' r 7 21 6 4c ! 6 4 5 34 76 7. 8 41 ) 7 34 6 46 ' 78 1 «' -0 8° 9" 10° 11° 12° 14° 16° 18° 20° 22° 124° 26° 28° 30° _^ TABLE XXXUI. 193 1 THIRD CORRECTION, TO APPARENT DISTANCE 96". 1 S's App. Alt. APPARENT ALTITUDE OF THE SUN, OR STAR. >'8 App. Alt. 32» 34» 36° 38° 40° 42° 44° 46° 50° 54° 58° 1 62° 66° 70° 74° 78° o r tt / n ^ ti / // ^ // ^ It / // / II r /> / // / II / II / II 1 II 1 II / // o 6 4 56 5 10 5 24 5 38 5 51 6 4 6 17 6 29 6 52 7 14 7 34 7 52 8 9 8 23 8 33 8 40 6 7 4 20 4 32 4 44 4 56 5 8 5 20 5 31 5 42 6 2 6 20 6 37 6 52 7 6 7 18 7 28 7 35 7 8 3 56 4 7 4 18 4 29 4 39 4 49 4 59 5 8 5 26 5 42 5 56 6 9 6 21 6 31 6 40 6 47 8 9 3 37 3 46 3 55 4 4 4 13 4 23 4 32 4 40 4 56 5 10 5 23 5 34 5 44 5 53 6 1 9 10 11 3 22 3 30 3 37 3 45 3 53 3 38 4 2 4 10 4 17 4 31 4 43 4 55 5 6 5 16 5 24 5 31 10 11 3 9 3 17 3 24 3 31 3 45 3 52 3 59 4 11 4 22 4 33 4 43 4 52 5 5 7 12 2 59 3 6 3 12 3 19 3 25 3 32 3 38 3 45 3 55 4 5 4 15 4 24 4 32 4 39 4 46 12 13 2 50 2 56 3 2 3 8 3 14 3 20 3 26 3 32 3 42 3 51 4 4 8 4 15 4 21 13 14 2 42 2 48 2 53 2 58 3 4 3 9 3 15 3 20 3 30 3 39 3 48 3 55 4 1 4 6 14 15 16 2 36 2 41 2 46 2 50 2 55 3 3 5 3 10 3 19 3 28 3 36 3 43 3 49 3 54 15 2 32 2 36 2 40 2 44 2 48 2 53 2 57 3 2 3 10 3 18 3 25 3 32 3 38 3 44 16 17 2 28 2 31 2 35 2 39 2 43 2 47 2 51 2 55 3 3 3 10 3 16 3 22 3 28 17 18 2 24 2 27 2 31 2 35 2 38 2 42 2 45 2 49 2 56 3 2 3 8 3 14 3 19 18 19 2 21 2 24 2 27 2 31 2 34 2 37 2 40 2 44 2 50 2 56 3 2 3 7 3 11 19 : 20 2 18 2 21 2 24 2 27 2 30 2 26 2 33 2 36 2 39 2 45 2 51 2 56 3 1 3 4 20 21 2 16 2 19 2 21 2 24 2 29 2 32 2 35 2 41 2 46 2 51 2 55 21 22 2 14 2 17 2 19 2 21 2 23 2 26 2 28 2 31 2 37 2 42 2 46 2 50 22 23 2 13 2 15 2 17 2 19 2 21 2 23 2 25 2 28 2 33 2 38 2 42 2 45 23 24 2 11 2 13 2 15 2 17 2 19 2 21 2 23 2 25 2 30 2 35 2 38 2 41 24 25 2 10 2 11 2 13 2 15 2 17 2 19 2 21 2 23 2 27 2 31 2 35 25 26 2 9 2 10 2 12 2 13 2 15 2 17 2 19 2 21 2 25 2 28 2 31 26 27 2 8 2 9 2 11 2 12 2 14 2 16 2 18 2 20 2 23 2 25 2 27 27 28 2 8 2 9 2 10 2 11 2 13 2 15 2 17 2 18 2 21 2 23 2 24 28 29 2 7 2 8 2 9 2 10 2 12 2 13 2 15 2 17 2 19 2 21 29 30 2 7 2 8 2 9 2 10 2 11 2 12 2 14 2 15 2 17 2 19 30 31 31 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 14 2 16 2 17 32 2 6 2 7 2 7 2 8 2 9 2 10 2 11 2 12 2 14 2 16 32 33 2 6 2 6 2 7 2 7 2 8 2 9 2 10 2 11 2 13 33 34 2 7 2 6 2 7 2 7 2 8 2 9 2 10 2 11 2 12 34 35 2 7 2 6 2 6 2 7 2 7 2 8 2 9 2 10 2 11 35 36 2 8 2 7 2 6 2 6 2 7 2 8 2 9 2 9 2 10 36 37 2 8 2 7 2 6 2 6 2 7 2 7 2 8 2 8 37 38 2 9 2 8 2 7 2 6 2 6 2 7 2 8 2 8 38 39 2 9 2 8 2 7 2 6 2 6 2 7 2 7 2 8 39 40 2 10 2 8 2 7 2 6 2 6 2 6 2 7 2 7 40 41 41 2 10 2 9 2 8 2 7 2 7 2 6 2 6 42 2 11 2 9 2 8 2 7 2 7 2 6 2 6 42 43 2 11 2 10 2 8 2 7 2 7 2 (i 43 44 2 12 2 10 2 8 2 7 2 7 2 6 44 45 2 12 2 10 2 9 2 8 2 7 45 46 2 13 2 11 2 9 2 8 2 7 46 47 48 49 2 13 2 13 2 14 2 11 2 11 2 12 2 9 2 9 2 10 2 10 2 8 2 8 ' 47 48 49 TABLK P. EFFECT OF BUN'b r AB . 50 2 14 2 12 To be subtracted from the Third Correction. 50 51 52 54 51 52 54 2 14 2 15 2 15 2 12 2 12 > )'8 App Alt. Sun's Apparent Altitude. 1 5ll0 2( )30 40 5 60 70 J ?0 90 56 7, // f * ■"■ tt f ' »/ // // // 56 58 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 90 1 2 o 3 4 5 5 6 6 7 7 8 8 9 9 9 1 t 2 2 2 3 3 3 4 4 5 5 5 5 6 6 7 7 7 ^ 8 8 8 8 8 8 9 9 1 2 3 4 4 5 6 6 7 7 8 1 2 i 3 . 4 ' 4 5 . 6 ( 6 7 1 1 2 2 } 3 1 4 5 5 5 S 2 3 3 8 68 60 62 64 66 68 70 72 74 76 78 60 62 64 66 68 70 72 74 76 7g 44° 46° 50° 54° 58° ' 32** 34° 36° 38" 40° 42° 194 TABLE XXXIII. THIRD OORREOTION, TO APPARENT DISTANCE 100°. J's App. Alt. APPARENT ALTITUDE OF THE SUN, OR STAR. App- 6° 70 80 9° \0° 11* 12<» 140 16° 18° 20° 1 22° 24° 1 26° 28° 1 30° 1 Alt. o t II / // / n 1 II 1 II 1 II / n 1 II 1 II / II / II / // f // / n 1 // / // fi 2 13 2 15 2 18 2 21 2 25 2 31 2 37 2 49 3 3 3 18 3 33 3 48 4 4 4 19 4 34 4 49 6 7 2 16 2 13 2 15 2 17 2 20 2 24 2 29 2 38 2 49 3 1 3 13 3 25 3 38 3 50 4 3 4 16 7 8 2 19 2 15 2 13 2 14 2 16 2 19 2 23 2 31 2 39 2 49 2 59 3 10 3 21 3 32 3 43 3 54 8 9 2 23 2 18 2 15 2 13 2 14 2 16 2 19 2 25 2 32 2 40 2 48 2 58 3 7 3 16 3 26 3 35 9 10 2 28 2 22 2 18 2 15 2 13 2 14 2 16 2 21 2 26 2 33 2 40 2 48 2 56 3 4 3 13 3 21 10 11 2 33 2 26 2 21 2 17 2 15 2 13 2 14 2 18 2 22 2 27 2 33 2 40 2 47 2 54 3 2 3 10 11 12 2 40 2 30 2 24 2 20 2 17 2 14 2 13 2 16 2 19 2 23 2 28 2 34 2 40 2 46 2 53 3 12 13 2 47 2 35 2 28 2 23 2 19 2 16 2 14 2 14 2 17 2 20 2 24 2 29 2 34 2 40 2 45 2 51 13 14 2 54 2 40 2 32 2 26 2 21 2 18 2 16 2 13 2 15 2 18 2 21 2 25 2 30 2 35 2 39 2 44 14 15 3 1 2 46 2 36 2 29 2 24 2 '/I 2 18 2 14 2 14 2 16 2 19 2 22 2 26 2 30 2 34 2 39 15 16 3 8 2 52 2 41 2 33 2 27 2 23 2 20 2 16 2 13 2 15 2 17 2 20 2 23 2 26 2 30 2 35 16 17 3 15 2 58 2 46 2 37 2 30 2 25 2 22 2 17 2 14 2 14 2 16 2 18 2 21 2 24 2 27 2 31 17 18 3 23 3 4 2 51 2 41 2 33 2 28 2 24 2 19 2 15 2 13 2 15 2 17 2 19 2 22 2 25 2 28 18 19 3 30 3 11 2 56 2 45 2 37 2 31 2 26 2 20 2 16 2 14 2 14 2 16 2 17 2 20 2 22 2 25 19 20 3 38 3 17 3 2 2 50 2 41 2 34 2 29 2 22 2 18 2 15 2 13 2 15 2 16 2 18 2 20 2 23 20 21 3 45 3 24 3 8 2 54 2 45 2 38 2 32 2 24 2 19 2 16 2 14 1 14 2 15 2 17 2 19 2 21 21 22 3 53 3 30 3 13 2 59 2 49 2 41 2 35 2 26 2 21 2 18 2 15 1 13 2 14 2 1© 2 18 2 20 22 23 4 1 3 36 3 19 3 4 2 53 2 45 2 38 2 28 2 23 2 19 2 16 1 13 2 13 2 15 2 17 2 19 23 24 4 9 3 42 3 24 3 9 2 58 2 49 2 42 2 31 2 24 2 20 2 17 2 14 2 13 2 14 2 16 2 18 24 25 26 4 16 3 49 3 30 3 14 3 2 2 53 2 45 2 33 2 26 2 21 23 2 18 2 15 2 14 2 14 2 15 2 17 25 26 4 24 3 55 3 35 3 19 3 6 2 56 2 48 2 36 2 28 2 2 19 2 16 2 14 2 14 2 15 2 16 27 4 31 4 2 3 41 3 24 3 11 3 2 51 2 38 2 30 2 24 2 20 2 17 2 15 2 14 2 14 2 15 27 28 4 39 4 8 3 46 3 28 3 15 3 4 2 54 2 40 2 32 2 25 2 21 2 18 2 16 2 15 2 14 2 15 28 29 4 46 4 14 3 52 3 33 3 19 3 7 2 58 2 43 2 34 2 26 2 22 2 19 2 17 2 15 2 14 2 14 29 30 4 54 4 20 3 57 3 38 3 23 3 11 3 1 2 45 2 36 2 28 2 24 2 21 2 18 2 16 2 15 2 14 30 31 31 5 1 4 26 4 3 3 42 3 27 3 15 3 5 2 48 2 38 2 30 2 25 2 22 2 19 2 17 2 15 2 14 32 5 8 4 33 4 8 3 47 3 31 3 18 3 8 2 51 2 40 2 32 2 27 2 23 2 20 2 17 2 16 2 15 32 33 5 16 4 39 4 14 3 52 3 36 3 22 3 11 2 54 2 42 2 33 2 28 2 24 2 21 2 18 2 16 2 15 33 34 5 23 4 45 4 19 3 57 3 40 3 26 3 15 2 56 2 44 2 35 2 29 2 25 2 22 2 19 2 17 2 16 34 35 5 30 4 51 4 24 4 29 4 2 4 7 3 44 3 30 3 18 2 59 2 46 2 37 2 31 2 26 2 23 2 20 2 18 2 16 35 36 36 5 37 4 57 3 48 3 34 3 22 3 2 2 49 2 39 2 32 2 28 2 24 2 20 2 18 2 17 37 5 44 5 3 4 35 4 12 3 52 3 38 3 25 3 5 2 51 2 41 2 34 2 29 2 25 2 21 2 19 2 18 37 38 5 51 5 9 4 40 4 16 3 56 3 41 3 28 3 8 2 54 2 43 2 36 2 30 2 26 2 22 2 20 2 18 38 39 5 58 5 15 4 45 4 21 4 3 45 3 31 3 11 2 56 2 45 2 37 2 31 2 27 2 23 2 21 2 19 39 40 6 4 5 21 4 50 4 25 4 4 3 48 3 34 3 14 2 58 2 47 2 38 2 32 2 28 2 24 2 22 2 20 40 41 6 11 5 27 4 55 4 29 4 8 3 52 3 38 3 17 3 1 2 49 2 40 2 34 2 29 2 25 2 22 2 20 41 42 6 18 5 33 5 4 33 4 12 3 55 3 41 3 19 3 3 2 51 2 41 2 35 2 30 2 26 2 23 2 21 42 43 6 24 5 38 5 5 4 38 4 16 3 59 3 44 3 22 3 6 2 53 2 43 2 36 2 31 2 27 2 24 2 22 43 44 6 30 5 44 5 9 4 42 4 20 4 2 3 47 3 24 3 8 2 55 2 45 2 38 2 32 2 28 2 25 2 22 44 45 46 6 36 5 49 5 14 4 46 4 24 4 6 3 50 3 27 3 10 2 57 2 47 2 39 2 33 2 29 2 26 2 23 45 6 42 5 54 5 18 4 50 4 27 4 9 3 53 3 29 3 12 2 59 2 48 2 41 2 35 2 30 2 27 2 24 46 47 6 48 5 59 5 23 4 54 4 31 4 12 3 56 3 32 3 14 3 2 50 2 42 2 36 2 31 2 28 2 25 47 48 6 54 6 4 5 27 4 58 4 34 4 15 3 59 3 34 3 16 3 2 2 51 2 43 2 37 2 32 2 28 2 25 48 49 7 -0 6 9 5 32 5 2 4 38 4 18 4 2 3 37 3 18 3 4 2 53 2 45 2 38 2 33 2 29 2 26 49 50 51 7 5 6 14 5 36 5 6 4 41 4 31 4 5 3 39 3 20 3 5 2 54 2 46 2 39 2 34 2 30 2 26 50 7 11 6 19 5 41 5 10 4 45 4 24 4 8 3 42 3 22 3 7 2 55 2 47 2 40 2 35 2 31 2 27 51 52 7 16 6 24 5 45 5 14 4 48 4 27 4 11 3 44 3 24 3 9 2 57 2 49 2 42 2 36 2 31 2 27 52 53 7 21 6 29 5 49 5 17 4 52 4 30 4 14 3 46 3 26 3 11 2 59 2 50 2 43 2 37 2 32 53 54 7 26 6 34 5 53 5 21 4 55 4 33 4 16 3 48 3 28 3 12 3 2 51 2 44 2 37 2 32 54 55 56 7 31 6 39 5 57 5 24 4 58 4 36 4 19 3 50 3 30 3 14 3 1 2 52 2 45 2 38 55 7 3€ 6 43 6 5 27 5 1 4 39 4 22 3 52 3 32 3 16 3 2 2 53 2 46 2 39 56 58 7 4f 6 51 6 7 5 33 5 7 4 44 4 26 3 56 3 36 3 19 3 5 2 55 2 47 58 60 7 56 ; 6 58 6 14 5 39 5 12 4 49 4 31 4 3 39 3 22 3 8 2 57 60 62 8 t > 7 6 10 5 45 5 17 4 54 4 36 4 4 3 42 3 24 3 10 62 64 8 12 7 12 6 26 5 51 5 22 4 59 4 40 4 7 3 45 3 26 64 66 8 21 7 IS 6 32 5 57 5 27 5 3 4 43 4 10 3 47 66 68 8 26 \ 7 2£ 6 38 6 2 5 32 5 7 4 45 4 13 68 70 8 3f ) 7 3C 1 6 43 6 7 5 36 5 11 4 4S 70 72 8 4( ) 7 21 ► 6 47 6 11 5 40 72 74 8 4^ I 7 4C ) 6 51 74 6° 70 8° 9° 10° 11° 120 14° 16° 18° 20° 22° 24" 26° 28° 30° TABLE XXXIll. 195 1 THIRD CORRECTION, TO APPARENT DISTANCE lOO^. D's A.pp. Alt. APPARENT ALTITUDE OF THE 8CN, OR STAR. Api^ Alt. e 32° 34° 36° 38° 40° 42° 44° 46° 48° 60° 54°, 58° 62° 66° 70° [ 74° o / II f // / // 1 It / // / // / II / // 1 II / f/ 1 II 1 II 1 II 1 II 1 II / II 6 5 4 5 19 6 34 5 48 6 2 6 15 6 28 6 41 6 63 7 4 7 26 7 46 8 5 8 20 8 33 8 44 ti 7 4 29 4 41 4 54 5 6 5 18 5 30 5 41 5 52 6 3 6 13 6 32 6 60 7 6 7 19 7 30 7 40 7 8 4 5 4 16 4 27 4 38 4 48 4 58 5 8 5 17 5 26 6 35 5 62 6 7 6 20 6 32 6 43 7 52 |i: 9 3 45 3 55 4 5 4 15 4 24 4 32 4 41 4 49 4 57 « 4 5 19 6 33 5 45 5 56 6 7 (1 10 11 3 30 3 39 3 47 3 55 4 3 4 11 4 la 4 26 4 33 4 40 4 54 5 6 5 16 5 26 6 36 lO 11 3 18 3 26 3 33 3 40 3 47 3 54 4 1 4 8 4 15 4 21 4 33 4 44 4 54 5 3 6 12 12 3 7 3 14 3 21 3 27 3 34 3 40 3 47 3 53 3 59 4 4 4 15 4 25 4 34 4 43 4 52 12 13 2 58 3 4 3 10 3 16 3 22 3 28 3 34 3 40 3 46 3 51 4 4 9 4 17 4 25 13 14 2 50 2 56 2 1 3 7 3 12 3 18 3 23 3 29 3 34 3 39 3 48 3 56 4 4 4 10 14 15 16 2 44 2 49 2 54 2 59 2 52 3 4 3 9 3 14 3 19 3 24 3 28 3 37 3 45 3 52 3 69 15 2 39 2 44 2 48 2 57 3 2 3 7 3 11 3 16 3 19 3 27 3 35 3 42 3 49 16 17 2 35 2 39 2 43 2 47 2 51 2 56 3 3 4 3 8 3 12 3 19 3 26 3 33 17 18 2 31 2 35 2 38 2 42 2 46 2 50 2 54 2 68 3 1 3 6 3 12 3 18 3 24 18 19 2 28 2 31 2 34 2 38 2 42 2 45 2 49 2 52 2 55 2 59 3 5 3 11 3 16 19 20 2 25 2 28 2 31 2 35 2 38 2 35 2 41 2 44 2 47 2 50 2 54 3 3 5 3 10 20 21 2 23 2 26 2 29 2 32 2 38 2 40 2 43 2 46 2 49 2 66 3 21 22 2 22 2 24 2 27 2 29 2 32 2 35 2 37 2 40 2 43 2 45 2 50 2 55 22 23 2 21 2 23 2 25 2 27 2 29 2 32 2 34 2 37 2 40 2 42 2 46 2 60j 23 24 2 20 2 22 2 23 2 25 2 27 2 29 2 32 2 35 2 37 2 39 2 43 2 46 24 25 2 19 2 20 2 21 2 23 2 25 2 23 2 27 2 30 2 32 2 34 2 36 2 40 25 26 2 18 2 19 2 20 2 21 2 25 2 28 2 30 2 32 2 34 2 37 26 27 2 17 2 18 2 19 2 20 2 22 2 24 2 26 2 28 2 30 2 32 2 34 27 28 2 16 2 17 2 18 2 19 2 21 2 23 2 24 2 26 2 28 2 30 2 31 28 29 2 15 2 16 2 17 2 18 2 20 2 22 2 23 2 25 2 26 2 28 29 30 2 15 2 16 2 17 2 18 2 19 2 21 2 22 2 24 2 25 2 26 30 31 2 14 2 15 2 16 2 17 2 18 2 20 2 21 2 22 2 23 2 24 31 32 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 21 2 22 2 23 32 33 2 15 2 15 2 15 2 16 2 17 2 18 2 19 2 20 2 21 33 34 2 15 2 15 2 15 2 16 2 17 2 18 2 19 2 19 2 20 34 35 2 15 2 15 2 15 2 15 2 16 2 17 2 18 2 18 35 36 36 2 16 2 15 2 15 2 15 2 16 2 17 2 17 2 18 37 2 17 2 16 2 15 2 15 2 16 2 16 2 17 37 38 2 17 2 16 2 16 2 15 2 16 2 16 2 17 38 39 2 18 2 17 2 16 2 16 2 16 2 16 39 40 2 18 2 17 2 16 2 16 2 16 2 16 I 1 40 41 41 2 19 2 18 2 17 2 16 2 16 42 2 19 2 18 2 17 2 16 2 16 42 43 2 20 2 18 2 17 2 16 43 44 2 20 2 19 2 17 2 16 44 45 2 21 2 19 2 17 45 46 2 21 2 19 2 17 46 47 2 22 2 19 47 48 49 60 2 22 2 23 2 23 2 19 48 49 50 TABLK P. XrFZCTOF IVN'b PAR. To be subtracted from the Third Correction. 51 62 53 54 51 52 53 54 APP A t. Sun's Appuant Altitnde. 1 5 10 2( 3 30 40 5 O60 7C 76 80 55 5 10 15 20 25 30 35 10 45 50 55 60 65 70 75 1 2 2 3 4 5 5 6 7 7 8 8 8 9 9 *f * 1 t 2 2 S 4 4 4 5 5 5 6 6 C 7 : 7 '' 8 6 8 i 9 9 H 2 2 3 4 . 5 5 6 7 r 7 r 6 ) } 2 3 3 4 5 « 6 7 2 S 2 3 3 3 4 4 4 1 4 5 5 3 9 8 65 56 58 60 62 64 66 68 60 62 64 66 68 70 72 74 66 68 70 72 74 320 34° 36° 38° 40° 42° 44° 46° 48° 60° 54° 196 TABLE XXXIII. THIRD CORRECTION, TO APPARENT DISTANCE 104" J) '8 APPARENT ALTITUDE OF THE SUN, OR STAR. D'8 App. Alt. App. Alt. 6<» 70 8° 9° 10° 11° 12° 14° 1 16° 18° 20° 22° 1 24° 1 26° 28° 30° o r II / n 1 n 1 II / II 1 II 1 II 1 II 1 II 1 II 1 II / II 1 // 1 II / II 1 II 6 2 20 2 22 2 25 2 29 2 33 2 39 2 45 2 58 3 13 3 28 3 43 3 59 4 15 4 30 4 46 5 1 6 7 2 23 2 20 2 22 2 25 2 28 2 32 2 36 2 46 2 57 3 10 3 23 3 36 3 48 4 1 4 14 4 27 7 8 2 26 2 22 2 20 2 22 2 24 2 27 2 30 2 38 2 47 2 57 3 8 3 20 3 31 3 42 3 53 4 4 8 9 2 30 2 25 2 22 2 21 2 22 2 24 2 26 2 32 2 39 2 48 2 57 3 7 3 17 3 26 3 36 3 46 9 10 2 36 2 29 2 25 2 22 2 21 2 22 2 24 2 28 2 34 2 41 2 48 2 56 3 5 3 14 3 23 3 31 10 11 2 42 2 34 2 28 2 24 2 22 2 21 2 22 2 25 2 30 2 35 2 41 2 48 2 55 3 4 3 11 3 19 11 12 2 48 2 39 2 32 2 27 2 24 2 22 2 21 2 23 2 27 2 31 2 36 2 42 2 48 2 56 3 2 3 9 12 13 2 56 2 44 2 36 2 30 2 26 2 24 2 22 2 22 2 25 2 28 2 32 2 38 2 43 2 49 2 55 3 1 13 14 3 2 2 49 2 40 2 33 2 29 2 26 2 24 2 22 2 23 2 26 2 30 2 34 2 39 2 43 2 48 2 54 14 15 3 9 2 54 2 45 2 37 2 32 2 28 2 26 2 23 2 22 2 25 2 28 2 31 2 35 2 39 2 43 2 48 15 16 3 16 3 2 50 2 41 2 35 2 31 2 28 2 24 2 22 2 24 2 26 2 29 2 32 2 35 2 39 2 44 16 17 3 23 3 6 2 55 2 45 2 38 2 33 2 30 2 26 2 23 2 23 2 25 2 27 2 30 2 33 2 36 2 40 17 18 3 31 3 13 3 2 49 2 41 2 36 2 33 2 27 2 24 2 22 2 24 2 26 2 28 2 31 2 34 2 37 18 19 3 38 3 19 3 5 2 53 2 45 2 39 2 35 2 29 2 25 2 23 2 23 2 24 2 26 2 29 2 31 2 34 19 20 3 46 3 25 3 11 2 58 2 49 2 43 2 38 2 31 2 27 2 24 2 22 2 23 2 25 2 27 2 29 2 32 20 21 3 54 3 32 3 16 3 3 2 53 2 46 2 41 2 33 2 28 2 25 2 23 1 22 2 24 2 26 2 28 2 30 21 22 4 2 3 38 3 22 3 8 2 57 2 50 2 44 2 35 2 30 2 26 2 24 1 22 2 23 2 25 2 27 2 29 22 23 4 10 3 45 3 27 3 13 3 2 2 54 2 47 2 38 2 32 2 28 2 25 1 23 2 22 2 24 2 26 2 28 23 24 4 18 3 51 3 33 3 18 3 6 2 57 2 50 2 40 2 33 2 29 2 26 2 24 2 22 2 23 2 25 2 27 24 25 26 4 26 3 58 3 39 3 22 3 10 3 1 2 54 2 42 2 35 2 30 31 2 27 2 24 2 23 2 23 2 24 2 26 25 26 4 33 4 4 3 44 3 27 3 15 3 5 2 57 2 44 2 36 2 2 28 2 25 2 24 2 23 2 24 2 26 27 4 41 4 11 3 50 3 32 3 19 3 9 3 2 47 2 38 2 32 2 29 2 26 2 24 2 23 2 24 2 25 27 28 4 49 4 18 3 56 3 37 3 23 3 12 3 3 2 49 2 40 2 34 2 30 2 27 2 25 2 24 2 24 2 25 28 29 4 57 4 24 4 1 3 42 3 28 3 16 3 7 2 52 2 42 2 35 2 31 2 28 2 26 2 25 2 24 2 25 29 30 5 4 4 30 4 7 3 47 3 32 3 20 3 10 2 55 2 44 2 37 2 33 2 30 2 27 2 25 2 24 2 24 30 31 5 12 4 37 4 13 3 52 3 3b 3 24 3 14 2 58 2 46 2 39 2 34 2 31 2 28 2 26 2 25 2 24 31 32 5 19 4 44 4 19 3 57 3 41 3 28 3 17 3 2 49 2 41 2 36 2 32 2 29 2 27 2 26 2 25 32 33 5 27 4 51 4 25 4 2 3 46 3 32 3 21 3 3 2 51 2 43 2 37 2 33 2 30 2 28 2 26 2 25 33 34 5 34 4 58 4 30 4 7 3 50 3 36 3 24 3 5 2 54 2 45 2 39 2 34 2 31 2 29 2 27 2 26 34 35 5 42 5 4 4 36 4 12 3 55 3 40 3 27 3 8 2 56 2 47 2 40 2 35 2 32 2 30 2 28 2 2 27 27 35 36 36 5 49 5 10 4 41 4 17 3 59 3 44 3 31 3 11 2 58 2 49 2 42 2 37 2 33 2 30 2 28 37 5 56 5 16 4 46 4 21 4 3 3 47 3 35 3 14 3 1 2 51 2 43 2 38 2 34 2 31 2 29 2 27 37 38 6 3 5 22 4 51 4 26 4 7 3 51 3 38 3 17 3 4 2 53 2 45 2 39 2 35 2 32 2 30 2 28 38 39 6 10 5 28 4 56 4 31 4 11 3 55 3 41 3 20 3 6 2 55 2 47 2 41 2 36 2 33 2 31 2 29 39 40 6 16 5 33 5 1 4 36 4 15 3 59 3 45 3 23 3 9 2 57 2 49 2 42 2 37 2 34 2 32 2 30 40 41 6 23 5 39 5 6 4 40 4 19 4 3 3 49 3 26 3 11 2 59 2 51 2 44 2 39 2 35 2 32 2 30 41 42 6 30 5 44 5 11 4 44 4 23 4 6 3 53 3 29 3 13 3 1 2 52 2 45 2 40 2 36 2 33 2 31 42 43 6 37 5 50 5 16 4 49 4 27 4 10 3 56 3 32 3 15 3 3 2 54 2 47 2 41 2 37 2 34 2 31 43 44 6 43 5 55 5 21 4 53 4 31 4 13 3 59 3 35 3 18 3 5 2 55 2 48 2 42 2 38 2 35 2 32 44 45 46 6 50 6 1 5 26 4 58 4 35 4 17 ,4 2 3 38 3 20 3 6 2 57 2 50 2 44 2 39 2 35 2 32 45 6 56 6 6 5 31 5 2 4 39 4 20 4 5 3 40 3 22 3 8 2 58 2 51 2 45 2 40 2 36 2 33 46 47 7 2 6 12 5 36 5 6 4 43 4 24 4 8 3 43 3 24 3 10 3 2 52 2 46 2 41 2 37 2 34 47 48 7 8 6 17 5 40 5 10 4 46 4 27 4 11 3 45 3 26 3 12 3 1 2 53 2 48 2 42 2 38 2 34 48 49 7 14 6 23 5 45 5 14 4 50 4 30 4 14 3 47 3 28 3 14 3 3 2 55 2 49 2 43 2 38 49 50 7 20 6 28 5 49 5 18 4 53 4 33 4 17 3 50 3 30 3 16 3 4 2 56 2 50 2 44 2 39 50 51 7 26 6 33 5 53 5 22 4 57 4 36 4 20 3 52 3 32 3 18 3 6 2 58 2 51 2 45 51 52 7 32 6 38 5 57 5 26 5 4 39 4 23 3 54 3 34 3 20 3 8 2 59 2 52 2 45 52 53 7 37 6 43 6 2 5 29 5 4 4 42 4 26 3 56 3 36 3 22 3 9 3 2 52 53 54 7 42 6 48 6 6 5 33 5 7 4 45 4 29 3 58 3 38 3 23 3 10 3 1 2 53 54 t 55 56 7 47 6 53 6 10 5 36 5 10 4 48 4 32 4 3 40 3 25 3 12 3 1 55 1 7 52 6 57 6 14 5 40 5 13 4 51 4 34 4 3 42 3 26 3 13 3 2 56 57 7 57 7 1 6 18 5 44 5 16 4 54 4 37 4 5 3 44 3 28 3 14 57 58 8 2 7 5 6 22 5 47 5 19 4 57 4 39 4 7 3 46 3 29 3 15 58 59 8 6 7 9 6 26 5 50 5 22 5 4 41 4 9 3 48 3 31 59 60 8 10 7 13 6 30 5 53 5 25 5 2 4 43 4 11 3 50 3 3? 60 62 8 19 7 19 6 36 5 59 5 30 5 6 4 47 4 15 3 52 62 64 8 27 7 26 6 42 6 4 5 35 5 10 4 51 4 19 64 66 8 35 7 33 6 47 6 9 5 40 5 14 4 54 1 66 68 8 43 7 39 6 52 6 14 5 45 68 70 8 49 7 45 6 57 , 1 70 6° 70 8° 9° 10° 11° 12° 14° 16° 18° 20° 1 22° 1 24^ 1 26° 28^ 30° TABLE XXXIII. 197 1 THIRD CORREOTION, TO APPARENT DISTA^''CE 104". - 1 D'K APPARENT ALTITUDE OF THE SUN, OR STAR. >'s App. All. o App Alt. 32° 34<» 36° 38° 40° 42° 440 46° 48° 50° 52° 1 54° 58° 62° 66° 70° / // / 11 / // r 11 1 II 1 II / II 1 II / II / II 1 II / /' 1 II 1 II / // / II 6 5 16 5 31 5 45 6 6 14 6 28 6 41 6 54 7 6 7 18 7 29 7 40 8 8 19 8 35 8 4S 6 ; 4 42 4 56 5 8 5 20 5 31 5 42 5 53 6 4 6 15 6 26 6 37 6 47 7 4 7 19 7 33 7 4t i 7 s 4 Iti 4 28 4 39 4 49 4 59 5 9 5 19 5 28 5 38 5 47 5 57 6 6 6 21 6 34 6 46 6 57 8 9 3 55 4 5 4 15 4 25 4 34 4 43 4 52 5 5 8 5 16 5 24 5 32 5 46 5 58 6 9 9 10 11 3 40 3 49 3 58 4 7 4 15 4 23 4 31 4 38 4 45 4 52 4 59 5 6 5 18 5 30 5 40 10 11 3 27 3 35 3 43 3 51 3 58 4 5 4 12 4 19 4 26 4 32 4 38 4 44 4 55 5 6 5 16 12 3 16 3 23 3 30 3 37 3 44 3 51 3 58 4 4 4 10 4 17 4 23 4 28 4 38 4 47 4 56 12 13 3 7 3 13 3 20 3 26 3 33 3 39 3 45 3 51 3 56 4 2 4 7 4 12 4 22 4 30 13 14 2 59 2 5 3 11 3 17 3 23 3 29 3 34 3 39 3 44 3 49 3 54 3 59 4 8 4 15 14 15 2 53 2 58 3 4 3 9 3 15 3 20 3 25 3 29 3 34 3 38 3 43 3 47 3 56 3 3 15 16 16 2 48 2 53 2 58 3 3 3 8 3 12 3 17 3 21 3 25 3 29 3 33 3 37 3 45 3 52 17 i 44 2 49 2 53 2 58 3 2 3 6 3 10 3 14 3 17 3 21 3 25 3 29 3 3b 17 18 i 41 2 45 2 49 2 53 2 57 3 1 3 4 3 8 3 11 3 15 3 18 3 22 3 29 18 19 Z 3% 2 41 2 45 2 49 2 53 2 56 2 59 3 3 3 6 3 9 3 12 3 16 3 22 19 20 21 i 35 2 33 2 38 2 42 2 45 2 49 2 52 2 55 2 58 3 1 3 4 3 7 3 10 3 lb 20 2 36 2 39 2 42 2 45 2 48 2 51 2 54 2 57 3 3 3 3 5 21 22 2 31 2 34 2 36 2 39 2 42 2 45 2 47 2 50 2 53 2 56 2 59 2 1 22 23 2 30 2 32 2 34 2 37 2 39 2 42 2 44 2 47 2 50 2 53 2 55 2 57 23 24 2 29 2 31 2 33 2 35 2 37 2 40 2 42 2 44 2 47 2 50 2 52 2 54 24 26 2 28 2 29 2 31 2 33 2 35 2 38 2 40 2 42 2 44 2 47 2 49 25 26 2 27 2 28 2 30 2 32 2 34 2 36 2 38 2 40 2 42 2 44 2 46 26 27 2 26 2 27 2 29 2 31 2 32 2 34 2 36 2 38 2 40 2 41 27 28 2 26 2 27 2 28 2 30 2 31 2 33 2 35 2 36 2 38 2 39 28 29 2 25 2 26 2 27 2 29 2 30 2 32 2 33 2 34 2 36 29 30 2 25 2 26 2 27 2 28 2 29 2 31 2 32 2 33 2 34 30 31 31 2 24 2 25 2 20 2 27 2 28 2 30 2 31 2 32 32 2 24 2 25 2 26 2 27 2 28 2 29 2 30 2 31 32 33 2 24 2 24 2 25 2 26 2 27 2 28 2 29 33 34 2 25 2 24 2 25 2 26 2 27 2 27 2 28 34 35 2 26 2 25 2 25 2 26 2 26 2 27 35 36 2 26 2 25 2 25 2 26 2 26 2 27 36 37 2 26 2 25 2 25 2 26 2 26 37 38 2 27 2 26 2 26 2 26 2 26 38 39 2 27 2 26 2 26 2 26 39 40 2 28 2 27 2 26 2 26 40 41 41 2 28 2 27 2 26 42 2 29 2 27 2 26 42 43 2 29 2 27 43 44 2 30 2 28 44 45 2 30 45 46 2 31 46 47 47 48 49 50 48 49 50 51 TABLE P. KFFSCTOFIUN'BPAR- 51 ro be subtracted from tA« 52 53 54 TMrd Correction. 52 53 54 Afp- Alt. 8n n'» Apparent Altitude . 1 55 5 10 -if )30 40 5 60 70S 90 65 56 5 1 1 2 2 2 S ! 3 3 rf n 56 57 10 2 2 2 3 3 ; 1 4 4 57 58 IS 20 2 3 3 3 4 4 3 4 4 i 5 .' 1 4 t 5 4 58 59 25 4 4 5 5 5 ( 5 69 60 30 35 40 5 5 5 6 6 e 6 6 1 6 6 7 6 ( 7 7 i 60 62 62 45 7 7 • H 64 . 50 7 8 6 64 66 55 8 8 e ! 66 68 80 65 8 8 9 9 68 70 50° 70 9 70 3 2° 340 36° 38"» 40° 42° 44° 46° 48° 52° 198 TABLE XXXIII. THIRD pORRECTION, TO APPARENT DISTANCE 108» J '8 App. Alt. APPARENT ALTITUDE OF THE SUN, OR STAR. J>'8 App Alt. 6° 7" 80 9° lO* 11° 1 12° 14° 1 16° 18° 20° 22° 1 24° 1 26° 28° 30° o t II 1 fi / // r II / ;/ 1 // 1 n / n 1 II 1 II / II 1 II / // / // 1 'f 1 /' 6 2 30 •2 32 2 35 2 39 2 44 2 50 2 56 3 9 3 24 3 39 3 55 4 11 4 27 4 43 4 59 5 15 6 7 2 33 2 30 2 32 2 35 2 39 2 43 2 48 2 58 3 10 3 22 3 35 3 48 4 2 4 15 4 28 4 41 7 8 2 36 2 32 2 30 2 32 2 35 2 38 2 42 2 49 2 58 3 9 3 20 3 31 3 42 3 54 4 6 4 17 8 9 2 40 2 35 2 32 2 31 2 33 2 35 2 38 2 43 2 50 2 58 3 8 3 18 3 28 3 38 3 48 3 58 9 10 2 46 2 39 2 35 2 33 2 31 2 33 2 35 2 39 2 44 2 51 2 59 3 7 3 16 3 25 3 34 3 43 10 11 2 52 2 44 2 38 2 35 2 33 2 32 2 33 2 37 2 41 2 46 2 53 3 3 7 3 15 3 23 3 30 11 12 2 59 2 49 2 42 2 38 2 35 2 33 2 32 2 35 2 39 2 43 2 48 2 54 3 3 7 3 14 3 20 12 13 3 6 2 54 2 46 2 41 2 37 2 35 2 33 2 34 2 37 2 40 2 44 2 49 2 54 3 3 6 3 L2 13 14 3 13 2 59 2 54 2 44 2 40 2 37 2 35 2 33 2 35 2 38 2 41 2 45 2 49 2 54 2 59 3 5 14 15 3 20 3 5 2 56 2 48 2 43 2 39 2 37 2 34 2 34 2 36 2 39 2 42 2 46 2 50 2 54 2 59 15 16 3 28 3 11 3 1 2 52 2 46 2 42 2 39 2 35 2 33 2 35 2 37 2 40 2 43 2 46 2 50 2 54 16 17 3 35 3 17 3 6 2 56 2 49 2 45 2 42 2 37 2 34 2 34 2 35 2 38 2 40 2 43 2 47 2 50 17 x8 3 43 3 24 3 11 3 2 53 2 48 2 44 2 39 2 35 2 33 2 34 2 36 2 38 2 41 2 44 2 47 18 19 3 50 3 31 3 17 3 5 2 57 2 51 2 46 2 40 2 36 2 34 2 33 2 35 2 37 2 39 2 42 2 45 19 20 3 58 3 37 3 22 3 10 3 1 2 54 2 49 2 42 2 38 2 35 2 33 2 34 2 36 2 38 2 40 2 43 20 21 4 6 3 44 3 28 3 14 3 4 2 57 2 52 2 44 2 39 2 36 2 34 2 34 2 35 2 37 2 39 2 41 21 22 4 14 3 51 3 31 3 19 3 8 3 2 55 2 46 2 41 2 37 2 35 2 34 2 35 2 36 2 38 2 40 22 23 4 22 3 58 3 40 3 24 3 12 3 4 2 58 2 48 2 42 2 38 2 36 2 34 2 34 2 35 2 37 2 39 23 24 4 30 4 4 3 46 3 29 3 17 3 8 3 1 2 50 2 44 2 40 2 37 2 35 2 34 2 35 2 36 2 38 24 25 26 4 38 4 11 3 51 3 34 3 22 3 12 3 4 2 53 2 46 2 41 '43 2 38 2 36 2 34 2 34 2 35 2 37 25 26 4 46 4 18 3 57 3 39 3 26 3 16 3 8 2 55 2 48 2 2 39 2 37 2 35 2 34 2 35 2 36 27 4 54 4 25 4 3 3 44 3 31 3 20 3 11 2 58 2 50 2 44 2 40 2 38 2 36 2 35 2 34 2 35 27 28 5 2 4 31 4 9 3 49 3 35 3 24 3 15 3 2 52 2 46 2 42 2 39 2 37 2 35 2 34 2 35 28 29 5 10 4 37 4 15 3 54 3 40 3 28 3 18 3 3 2 54 2 47 2 43 2 40 2 38 2 36 2 35 2 35 29 30 5 18 4 44 4 21 3 59 3 44 3 32 3 22 3 6 2 56 2 49 2 45 2 41 2 38 2 36 2 35 2 35 30 31 31 5 26 4 51 4 27 4 4 3 48 3 36 3 25 3 9 2 58 2 50 2 46 2 42 2 39 2 37 2 36 2 35 32 5 33 4 58 4 33 4 9 3 52 3 40 3 28 3 11 3 2 52 2 47 2 43 2 40 2 38 2 37 2 36 32 33 5 41 5 5 4 38 4 14 3 57 3 44 3 32 3 14 3 2 2 54 2 48 2 44 2 41 2 39 2 37 2 36 33 34 f 48 5 11 4 43 4 19 4 1 3 47 3 36 3 17 3 5 2 56 2 50 2 45 2 42 2 40 2 38 2 37 34 35 5 56 5 18 4 49 4 24 4 5 3 51 3 39 3 20 3 7 2 58 2 51 2 46 2 43 2 41 2 39 2 2 37 38 35 36 36 6 3 5 24 4 55 4 29 4 10 3 55 3 42 3 23 2 9 3 2 53 2 48 2 44 2 42 2 40 37 6 10 5 30 5 4 34 4 14 3 59 3 46 3 26 3 12 3 2 2 55 2 49 2 45 2 42 2 40 2 38 37 38 6 17 5 36 5 5 4 39 4 19 4 3 3 50 3 29 3 15 3 4 2 57 2 51 2 46 2 43 2 41 2 39 38 39 6 24 5 42 5 10 4 44 4 24 4 7 3 54 3 32 3 17 3 6 2 58 2 52 2 47 2 44 2 42 2 40 39 40 6 31 5 48 5 15 4 49 4 28 4 11 3 57 3 35 3 20 3 8 3 2 54 2 49 2 45 2 43 2 40 40 41 6 38 5 54 5 20 4 54 4 33 4 15 4 1 3 38 3 22 3 10 3 1 2 55 2 50 2 46 2 43 2 41 41 42 6 45 5 59 5 25 4 58 4 37 4 18 4 5 3 41 3 24 3 12 3 3 2 56 2 51 2 47 2 44 2 41 42 43 6 52 6 5 5 30 5 3 4 41 4 22 4 9 3 44 3 27 3 14 3 5 2 58 2 52 2 48 2 45 2 42 43 44 6 59 6 11 5 36 5 7 4 45 4 26 4 12 3 47 3 29 3 16 3 6 2 59 2 53 2 49 2 46 2 43 44 45 46 7 6 6 17 5 41 5 12 4 49 4 30 4 16 3 50 3 31 3 18 3 8 3 1 2 55 2 50 2 47 45 7 12 6 22 5 46 5 16 4 53 4 34 4 19 3 52 3 33 3 20 2 10 3 2 2 56 2 51 2 47 46 47 7 18 6 27 5 51 5 20 4 57 4 37 4 22 3 55 3 36 3 22 3 12 3 4 2 58 2 52 47 48 7 24 6 32 5 56 5 24 5 4 41 4 25 3 57 3 38 3 24 3 13 3 5 2 59 2 53 48 49 7 30 6 37 6 1 5 28 5 4 4 44 4 28 4 3 41 3 26 3 15 3 7 3 49 50 7 36 6 42 6 5 5 32 5 7 4 47 4 31 4 2 3 43 3 28 3 17 3 8 3 1 50 51 7 42 6 47 6 10 5 36 4 11 4 50 4 34 4 5 3 45 3 30 3 18 3 9 51 62 7 47 6 52 6 14 5 40 5 14 4 53 4 37 4 7 3 47 3 32 3 19 3 10 52 63 7 53 6 57 6 18 5 43 5 18 4 56 4 39 4 1© 3 49 3 34 3 20 53 54 7 68 7 2 6 22 5 47 5 21 4 59 4 42 4 12 3 51 3 35 3 21 54 65 56 8 4 7 7 6 26 5 51 5 24 5 2 4 45 4 14 3 53 3 36 5f 8 9 7 11 6 30 5 54 5 27 5 5 4 47 4 16 3 55 3 38 56 57 8 14 7 16 6 34 5 58 5 30 5 8 4 50 4 18 3 57 67 58 8 19 7 20 6 38 6 1 5 33 5 11 4 52 4 20 3 58 58 59 8 24 7 25 6 42 6 4 5 36 5 14 4 54 4 22 69 60 8 28 7 29 6 45 6 8 5 39 5 16 4 56 4 24 60 fil 8 33 7 33 6 48 6 11 5 42 5 19 4 58 61 62 8 37 7 37 6 51 6 14 5 45 5 21 5 62 63 8 41 7 40 6 54 6 17 5 48 5 23 63 64 8 45 7 43 6 57 6 20 64 66 8 53 7 46 7 66 6» 7° 8» 9° 10« 11" 120 14° 16° 18° 20° 22° 24° 26° 28° 30° TABLE XXXUl. , 199 THIRD CORRECTION, TO APPARENT DISTANCE 108". J) '8 App. Alt. APPARENT ALTITUDE OF THB SUN, OR STAR. D'B App Alt. o 6 7 8 9 10 11 12 13 14 15 32<» 34<» 36" 38° 40° 42° 44° 46° 48° 50° 52° 54° 56° 58° 62° 66° 6 7 8 9 10 / n 5 30 4 55 4 29 4 8 3 52 1 n 5 45 5 8 4 41 4 18 4 6 5 21 4 52 4 28 4 9 t n 6 15 5 34 5 3 4 38 4 18 6 29 5 46 5 13 4 48 4 27 / II 6 44 5 58 5 23 4 57 4 36 1 II 6 58 6 10 5 34 5 6 4 44 1 n 7 11 6 22 5 44 5 15 4 52 7 23 6 33 5 54 5 23 4 59 / II 7 34 6 43 6 4 5 31 5 6 / II 7 45 6 53 6 13 5 38 5 I 1 II 7 56 7 2 6 22 5 45 5 20 1 II 8 6 7 11 6 30 5 53 5 27 1 II 8 16 7 20 6 38 6 1 5 33 1 n 8 35 7 35 6 51 6 14 5 45 8 63 7 47 7 1 11 12 13 14 15 3 38 3 27 3 18 3 10 3 4 3 46 3 34 3 24 3 16 3 9 3 54 3 41 3 30 3 22 3 14 4 2 3 48 3 37 3 28 3 20 4 10 3 56 3 44 3 34 3 25 4 18 4 4 3 51 3 40 3 31 4 25 4 11 3 58 3 46 3 36 4 33 4 18 4 4 3 52 3 42 4 40 4 21 4 10 3 58 3 47 4 47 4 30 4 15 4 3 3 52 4 53 4 36 4 21 4 8 3 56 4 59 4 42 4 26 4 12 4 1 5 5 4 47 4 30 4 16 4 5 5 11 4 52 4 34 4 20 4 8 5 20 5 16 17 18 19 20 2 59 2 54 2 51 2 48 2 46 3 3 2 58 2 54 2 51 2 49 2 47 2 45 2 43 2 42 2 40 3 8 3 3 2 59 2 55 2 52 2 50 2 48 2 46 2 44 2 42 2 41 2 40 2 39 2 38 2 37 3 13 3 7 3 3 2 59 2 56 3 18 3 12 3 7 3 3 2 59 3 23 3 17 3 11 3 6 3 2 3 28 3 21 3 15 3 10 3 6 3 33 3 26 3 20 3 14 3 9 3 38 3 30 3 24 3 18 3 13 3 43 3 35 3 28 3 22 3 16 3 47 3 39 3 32 3 25 3 19 3 51 3 43 3 35 3 28 3 22 3 55 3 46 3 38 3 58 16 17 18 19 20 21 22 23 24 25 2 44 2 42 2 41 2 40 2 39 2 53 2 50 2 48 2 46 2 44 2 56 2 53 2 50 2 48 2 46 2 45 2 44 2 42 2 41 2 40 2 59 2 56 2 53 2 51 2 49 3 2 2 59 2 56 2 53 2 51 3 5 3 2 2 59 2 56 2 53 3 9 3 5 3 2 2 59 2 56 3 12 3 8 3 4 3 1 3 14 3 10 21 22 23 24 25 26 27 28 29 30 2 38 2 37 2 36 2 36 2 35 2 39 2 38 2 38 2 37 2 36 2 43 2 42 2 41 2 40 2 39 2 47 2 45 2 44 2 42 2 41 2 49 2 47 2 46 2 44 2 43 2 51 2 49 2 47 2 54 26 27 28 29 30 31 32 33 34 35 2 35 2 35 2 36 2 36 2 36 2 36 2 36 2 36 2 36 2 36 2 37 2 37 2 36 2 36 2 36 2 38 2 38 2 37 2 37 2 37 2 39 2 39 2 38 2 38 2 40 2 40 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 36 37 38 39 40 2 37 2 38 2 38 2 39 2 39 2 36 2 37 2 37 2 38 2 38 2 36 2 36 2 36 2 36 41 42 43 44 45 2 40 2 40 46 47 48 49 50 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 66 r ABLB P. KFFICT 01 SUN'b FAR 51 52 53 54 55 To be subu*tttd from the Third Correction. >'8 App - A t. 5 10 15 20 25 30 35 40 45 50 55 60 65 70 Snn's Apparent Altitude . j 5 tOpO 1 1 2 2 2 3 13 3 4 4 4 4 4 5 5 5 6 6 6 6 6 7 7 7 7 8 8 8 8 8 8 9 8 9 9 30 ** 2 3 4 5 6 6 7 8 8 40 5 #/ t 3 : 4 ^ 4 ; 5 ; a ( 7 • 7 60 > II i 3 1 4 5 5 ) 5 65 8 It 3 90 56 57 58 59 60 ' 61 62 63 64 66 1 . 32° 34<» 36» 38" 40° 42° 44° 46° 48° 50° 52° 200 • TABLE XXXllI. THIRD CORRECTION, TO APPARENT DISTANCE 112* A-PP. Alt. APPARENT ALTITUDE OF THE SUN, OR STAR. D's App. Alt. 6° 70 8° 9° 10° 11° 12° 14° 16° 18° 20° 22° 24° 28° 28° 30° o 6 7 8 9 10 2 40 2 42 2 46 2 51 2 57 2 42 2 40 2 42 2 45 2 49 / // 2 43 2 42 2 41 2 43 2 45 1 II 2 45 2 42 2 43 2 41 2 43 / II 2 51 2 49 2 45 2 43 2 42 / II 3 2 53 2 48 2 45 2 43 / II 3 7 2 08 2 52 2 48 2 45 1 II 3 21 3 8 3 2 54 2 49 1 II 3 36 3 20 3 9 3 1 2 55 / II 3 52 3 33 3 19 3 9 3 2 / II 4 8 3 46 3 31 3 19 3 10 1 II 4 24 3 59 3 42 3 29 3 19 1 II 4 40 4 13 3 54 3 40 3 28 1 II 4 56 4 26 4 6 3 50 3 37 1 II 5 12 4 40 4 18 4 3 46 ' " 5 28 4 54 4 30 4 11 3 56 6 7 8 9 10 11 12 13 14 15 3 3 3 9 3 16 3 23 3 31 2 54 2 59 3 4 3 10 3 16 2 48 2 52 2 56 3 3 5 2 45 2 48 2 51 2 54 2 58 2 43 2 45 2 47 2 50 2 53 2 42 2 43 2 45 2 47 2 49 2 43 2 42 2 43 2 45 2 47 2 46 2 44 2 43 2 43 2 44 2 50 2 47 2 45 2 44 2 44 2 56 2 52 2 49 2 47 2 46 3 3 2 58 2 54 2 51 2 49 3 11 3 5 3 2 56 2 53 3 19 3 12 3 6 3 1 2 57 3 27 3 19 3 12 3 6 3 1 3 55 3 26 3 18 3 12 3 6 3 44 3 34 3 25 3 17 3 11 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 3 39 3 47 3 55 4 3 4 11 3 22 3 29 3 35 3 41 4 48 3 10 3 15 3 20 3 26 3 32 3 2 3 6 3 10 3 15 3 20 2 56 2 59 3 2 3 6 3 10 2 51 2 54 2 57 3 3 3 2 48 2 50 2 53 2 56 2 58 2 45 2 46 2 48 2 50 2 52 2 43 2 44 2 45 2 46 2 48 2 45 2 44 2 44 2 45 2 45 2 47 2 46 2 45 2 44 2 44 2 50 2 48 2 47 2 46 2 45 2 54 2 51 2 49 2 48 2 47 2 57 2 54 2 52 2 50 2 49 3 2 2 58 2 55 2 53 2 51 3 6 3 2 2 59 2 56 2 54 2 52 2 51 2 50 2 49 2 48 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 4 19 4 27 4 35 4 43 4 52 3 54 4 1 4 8 4 15 4 22 3 38 3 44 3 50 3 56 4 3 3 25 3 30 3 35 3 40 3 46 3 15 3 20 3 24 3 28 3 33 3 7 3 11 3 15 3 19 3 23 3 1 3 5 3 8 3 11 3 15 2 54 2 56 2 58 3 1 3 3 2 49 2 51 2 52 2 54 2 55 2 46 2 47 2 48 2 49 2 51 2 44 2 45 2 46 2 47 2 48 2 44 2 44 2 45 2 45 2 46 2 46 2 45 2 44 2 44 2 45 2 48 2 47 2 46 2 45 2 44 2 50 2 49 2 48 2 47 2 46 5 5 8 5 16 5 24 5 32 4 29 4 37 4 44 4 51 4 57 4 9 4 15 4 21 4 27 4 33 3 51 3 56 4 2 4 7 4 12 3 38 3 42 3 47 3 52 3 57 3 27 3 31 3 36 3 40 3 45 3 18 3 22 3 26 3 31 3 35 3 5 3 8 3 11 3 14 3 17 2 57 2 59 3 2 3 5 3 7 2 52 2 54 2 56 2 58 3 2 49 2 51 2 52 2 53 2 55 2 47 2 48 2 49 2 50 2 52 2 45 2 45 2 46 2 46 2 47 2 44 2 45 2 46 2 46 2 47 2 45 2 45 2 45 2 45 2 46 2 47 2 46 2 46 3 46 3 46 31 32 33 34 35 5 40 5 48 5 56 6 4 6 11 5 4 5 10 5 17 5 24 5 31 4 39 4 45 5 51 5 56 5 2 4 17 4 22 4 28 4 33 4 38 4 2 4 7 4 12 4 16 4 21 3 49 3 54 3 58 4 2 4 6 3 39 3 43 3 46 3 50 3 53 3 20 3 23 3 26 3 29 3 32 3 9 3 12 3 14 3 17 3 19 3 2 3 4 3 6 3 8 3 10 2 57 2 58 3 3 2 3 4 2 53 2 54 2 55 2 57 2 59 2 49 2 51 2 52 2 53 2 55 2 48 2 49 2 50 2 51 2 52 2 47 2 47 2 48 2 49 2 50 2 46 2 46 2 47 2 48 2 49 36 37 38 39 40 6 19 6 26 6 33 6 41 6 48 5 37 5 44 5 50 5 56 6 2 5 7 5 13 5 18 5 24 5 29 4 43 4 48 4 53 4 58 5 3 4 25 4 29 4 33 4 37 4 41 4 10 4 14 4 17 4 21 4 25 3 57 4 1 4 4 4 8 4 11 3 35 3 38 3 41 3 44 3 47 3 21 3 24 3 26 3 29 3 32 3 12 3 14 3 16 3 18 3 20 3 5 3 7 3 9 3 10 3 12 3 3 1 3 3 3 4 3 B 2 56 2 57 2 cy 2 59 3 1 2 53 2 54 2 55 2 56 2 57 2 51 2 52 2 53 2 54 2 55 2 49 2 50 2 51 2 52 2 53 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 n 58 59 60 6 55 7 2 7 8 7 15 7 22 6 8 6 14 6 20 6 26 6 32 5 35 5 40 5 46 5 51 5 56 5 8 5 13 5 18 5 23 5 28 4 45 4 49 4 53 4 58 5 3 4 28 4 32 4 36 4 40 4 44 4 15 4 18 4 22 4 25 4 28 3 50 3 53 3 56 3 59 4 2 3 35 3 38 3 40 3 42 3 45 3 22 3 25 3 27 3 29 3 31 3 13 3 15 3 17 3 19 3 21 3 7 3 8 3 10 3 12 3 14 3 2 3 3 3 5 3 6 3 8 2 58 2 59 3 3 1 2 55 2 56 41 42 43 44 45 7 28 7 35 7 42 7 48 7 55 6 38 6 44 6 49 6 54 6 59 6 2 6 7 6 12 6 16 6 21 5 33 5 37 5 41 5 45 5 49 5 8 5 12 5 16 5 20 5 23 4 47 4 51 4 55 4 58 5 2 4 31 4 34 4 38 4 41 4 44 4 5 4 8 4 11 4 14 4 17 3 47 3 50 3 52 3 55 3 57 3 33 3 36 3 38 3 40 3 42 3 23 3 25 3 26 3 28 3 29 3 15 3 16 3 17 3 9 46 47 48 49 50 8 1 8 7 8 13 8 19 8 25 7 4 7 9 7 14 7 19 7 23 6 25 6 29 6 34 6 38 6 42 5 53 5 57 6 1 6 5 6 8 5 27 5 30 5 34 5 37 5 41 5 5 5 8 5 12 5 15 5 18 4 47 4 50 4 53 4 56 4 59 4 19 4 22 4 24 4 26 4 28 3 59 4 1 4 3 4 4 3 44 3 46 51 52 53 54 55 8 30 8 35 8 40 8 45 8 5C 7 28 7 33 7 38 7 43 7 48 6 47 6 51 6 55 6 59 7 2 6 12 6 15 6 19 6 22 6 25 5 44 5 47 5 50 5 53 5 56 5 21 5 24 5 27 5 29 5 1 5 4 5 6 4 30 56 57 58 59 60 61 62 63 64 65 8 54 8 58 9 2 9 5 7 52 7 56 7 5S 7 5 7 8 6 28 61 62 63 64 66 1 6° 7° 8° 9° 10° 11° 12° 140 16° 18° 20° 22° 24° 26° 28° 30° 1 TABLE XXXIII. THIRD CORRECTION, TO APPARENT DISTANCE 112°. 201 App. Alt. APPARENT ALTITUDE OF THE SUN, OR STAR. >'8 App Alt. 32° 34° 36° 38° 40° 42° 44° 46° 48° 50° 52° 54° 56° 58° 60° 62° o 6 7 8 9 10 / It 5 44 5 7 4 42 4 21 4 5 t It 6 5 21 4 54 4 32 4 14 t n 6 16 5 34 5 5 4 42 4 23 / If 6 31 5 47 5 16 4 52 4 32 1 II 6 46 6 5 27 5 1 4 40 / II 7 6 13 5 38 5 11 4 49 / II 7 14 6 25 5 49 5 21 4 58 1 II 7 27 6 37 6 5 31 5 7 1 II 7 40 6 49 6 10 5 140 5 15 1 II 7 53 7 6 20 5 48 5 23 / n 8 5 7 10 6 29 5 56 5 31 1 II 8 18 7 20 6 38 6 4 5 38 1 II 8 30 7 30 6 47 6 11 5 44 1 II 8 41 7 39 6 55 6 18 5 50 / // 8 50 7 47 7 2 6 24 5 55 / // 8 58 7 55 7 8 o 6 7 8 9 10 11 12 13 14 15. 11 12 13 14 15 3 52 3 41 3 31 3 23 3 16 4 3 48 3 38 3 29 3 21 4 8 3 55 3 44 3 35 3 27 4 16 4 2 3 50 3 41 3 33 4 23 4 9 3 57 3 47 3 38 4 31 4 16 4 4 3 53 3 44 4 39 4 24 4 10 3 59 3 50 4 47 4 31 4 17 4 6 3 56 4 55 4 38 4 23 4 12 4 1 5 2 4 44 4 29 4 17 4 6 5 8 4 50 4 35 4 22 4 10 5 14 4 56 4 40 4 26 4 14 5 19 5 1 4 45 4 30 5 24 5 5 16 17 18 19 20 3 10 3 6 3 3 3 2 57 3 15 3 11 3 7 3 4 3 1 3 21 3 16 3 12 3 8 3 5 3 26 3 20 3 16 3 12 3 8 3 31 3 25 3 20 3 16 3 12 3 9 3 6 3 3 3 1 2 59 2 57 2 56 2 55 2 54 2 53 3 37 3 30 3 25 3 20 3 16 3 42 3 35 3 29 3 24 3 20 3 47 3 40 3 34 3 28 3 23 3 19 3 15 3 12 3 9 3 52 3 45 3 38 3 32 3 26 3 22 3 18 3 57 3 49 3 42 3 35 3 29 4 1 3 53 3 46 4 4 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 2 55 2 53 2 52 2 51 2 50 2 58 2 56 2 55 2 53 2 52 3 2 3 2 5S 2 56 2 54 3 5 3 3 3 1 2 59 2 57 3 12 3 9 3 6 3 4 3 1 3 16 3 12 3 9 3 7 3 4 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 2 49 2 48 2 47 2 47 2 47 2 51 2 50 2 49 2 48 2 48 2 53 2 52 2 51 2 50 2 49 2 55 2 54 2 53 2 52 2 51 2 59 2 57 2 56 3 1 31 32 33 34 35 2 47 2 47 2 47 2 48 2 48 2 48 2 48 2 48 2 48 2 48 2 49 2 49 2 49 2 49 2 50 2 50 36 37 38 39 40 2 49 2 49 2 50 2 48 36 37 38 39 40 41 42 43 44 45 41 42 43 44 45 46 47 48 49 50 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 TABLE P. EFFECT OF iOW'i PAR . 51 52 53 54 55 To bt subtraettd from tht Third Correction. )'8 App Ah. 5 10 15 20 25 30 35 40 45 50 55 60 05 Sun's Apparent Altitnde.l 5 1 2 3 4 4 5 7 7 8 8 9 9 10 2( 2 S 2 3 3 4 4 4 5 £ 5 ( 6 1 7 - 7 f e i 9 9 )30 It 3 4 4 5 > C ) 7 r 7 r 8 ) 405 tf 1 3 ' 4 5 . 6 8 7 60 1 4 5 5 5 S 65 4 80 n 90 56 57 58 59 fiO 61 62 63 64 65 32° 34° 36° 38° 40° 42° 44° 46° 48° 50° 52° 1 202 TABLE XXXIII. THIRD CORRECTION, TO APPARENT DISTANCE 116» App. APPARENT ALTITUDE OF THE 8UK, OR STAR. App. Alt. 6° 70 8» 90 lOO \V* 12° 13° 140 15° 160 18° 20° 22° 240 26° Alt. o 6 7 8 9 10 2 50 2 62 2 56 3 1 3 7 2 62 2 50 2 62 2 55 2 59 t // 2 55 2 62 2 50 2 62 2 55 / // 2 59 2 55 2 62 2 60 2 52 t n 3 4 2 58 2 54 2 62 2 51 1 n 3 10 3 2 2 67 2 54 2 52 1 n 3 17 3 8 3 1 2 57 2 54 t n 3 25 3 13 3 5 3 2 57 / // 3 33 3 19 3 10 3 4 3 / // 3 41 3 25 3 15 3 8 3 3 3 49 3 32 3 21 3 13 3 7 / It 4 6 3 46 3 32 3 21 3 14 1 II 4 22 4 3 44 3 31 3 22 1 It 4 39 4 14 3 56 3 42 3 31 1 It 4 56 4 28 4 8 3 53 3 41 t II 5 13 4 42 4 20 4 4 3 50 6 7 8 9 10 11 12 13 14 15 3 13 3 20 3 27 3 35 3 43 3 4 3 9 3 15 3 21 3 27 2 68 3 2 3 6 3 11 3 16 2 54 2 67 3 1 3 5 3 9 2 62 2 64 2 57 3 3 4 2 51 2 53 2 55 2 57 3 2 53 2 52 2 53 2 55 2 57 2 55 2 53 2 52 2 53 2 55 2 67 2 55 2 53 2 52 2 53 3 2 57 2 55 2 54 2 53 3 3 3 2 58 2 56 2 54 3 9 3 5 3 2 2 59 2 57 3 16 3 10 3 6 3 3 3 3 23 3 16 3 11 3 7 3 4 3 31 3 23 3 17 3 12 3 8 3 39 3 30 3 23 3 18 3 14 11 12 13 14 15 16 17 18 19 20 3 51 3 59 4 7 4 16 4 24 3 33 3 40 3 47 3 64 4 1 3 21 3 27 3 33 3 39 3 45 3 13 3 17 3 22 3 27 3 32 3 7 3 11 3 14 3 18 3 22 3 3 3 6 3 9 3 12 3 16 3 3 2 3 5 3 8 3 11 2 57 2 59 3 1 3 4 3 7 2 55 2 57 2 59 3 1 3 3 2 54 2 55 2 56 2 58 3 2 53 2 54 2 55 2 56 2 58 2 55 2 55 2 54 2 55 2 56 2 58 2 57 2 56 2 55 2 55 3 1 2 59 2 58 2 57 2 57 3 5 3 3 3 1 3 2 59 3 10 3 7 3 5 3 3 3 2 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 4 33 4 41 4 49 4 58 5 6 4 8 4 15 4 22 4 29 4 36 3 51 3 57 4 4 4 10 4 16 3 37 3 43 3 49 3 54 4 3 27 3 32 3 37 3 42 3 47 3 20 3 24 3 28 3 32 3 37 3 14 3 17 3 21 3 24 3 28 3 32 3 35 3 39 3 43 3 47 3 9 3 12 3 15 3 18 3 21 3 5 3 7 3 10 3 13 3 16 3 2 3 4 3 7 3 10 3 12 3 3 2 3 4 3 7 3 9 2 57 2 59 3 3 2 3 4 2 56 2 57 2 58 2 59 3 1 2 57 2 56 2 57 2 58 2 59 2 59 2 58 2 58 2 57 2 68 3 1 3 3 2 59 2 59 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 5 15 5 23 5 31 5 39 5 47 4 43 4 50 4 57 5 4 6 11 4 22 4 28 4 34 4 40 4 46 4 5 4 11 4 16 4 21 4 26 3 52 3 57 4 1 4 6 4 10 3 41 3 45 3 49 3 54 3 58 3 24 3 27 3 31 3 34 3 38 3 18 3 21 3 24 3 27 3 30 3 14 3 16 3 19 3 21 3 24 3 11 3 13 3 15 3 17 3 19 3 6 3 8 3 9 3 11 3 13 3 2 3 4 3 5 3 7 3 8 3 3 2 3 3 3 4 3 5 2 69 3 3 1 3 2 3 3 2 58 2 59 2 59 3 3 1 3 2 3 3 3 4 3 5 3 6 5 55 6 3 6 12 6 20 6 29 5 18 6 26 6 33 5 40 5 47 4 52 4 58 5 5 6 11 5 17 4 32 4 37 4 42 4 47 4 53 4 15 4 20 4 25 4 30 4 35 4 2 4 6 4 11 4 15 4 20 3 51 3 55 3 59 4 2 4 6 4 10 4 14 4 18 4 22 4 26 3 42 3 46 3 48 3 52 3 55 2 34 3 37 3 40 3 43 3 47 3 27 3 30 3 33 3 36 3 40 3 22 3 25 3 27 3 30 3 33 3 15 3 17 3 19 3 21 3 24 3 10 3 12 3 13 3 15 3 17 3 6 3 8 3 9 3 10 3 12 3 4 3 5 3 6 3 7 3 9 36 37 38 39 40 6 37 6 45 6 63 7 1 7 8 5 55 6 2 6 9 6 16 6 23 5 23 5 29 5 35 6 41 5 47 4 58 5 4 6 9 5 15 5 20 4 40 4 45 4 50 4 54 4 58 4 24 4 29 4 33 4 37 4 41 3 59 4 2 4 6 4 10 4 13 3 50 3 53 3 57 4 4 3 3 43 3 46 3 49 3 52 3 54 3 36 3 39 3 42 3 45 3 47 3 26 3 29 3 31 3 33 3 36 3 19 3 21 3 23 3 25 3 27 3 14 3 15 3 17 3 19 3 20 3 10 3 11 3 13 3 15 3 16 3 7 3 8 3 9 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 7 15 7 22 7 30 7 37 7 45 6 29 6 35 6 41 6 47 6 63 6 53 5 58 6 4 6 9 6 15 5 25 5 30 5 35 5 40 5 45 5 3 5 7 5 12 5 16 6 21 4 45 4 49 4 53 4 57 5 ] 4 30 4 33 4 37 4 41 4 44 4 17 4 20 4 23 4 27 4 30 4 6 4 9 4 12 4 15 4 18 3 57 4 4 3 4 6 4 9 3 50 3 53 3 55 3 68 4 1 3 39 3 41 3 43 3 45 3 47 3 29 3 31 3 33 3 34 3 21 3 23 41 42 43 44 45 7 52 7 69 8 6 8 12 8 18 6 69 7 5 7 10 7 15 7 20 6 20 6 25 6 30 6 35 6 40 6 49 5 54 6 69 6 4 6 8 6 25 6 29 6 33 5 37 5 41 5 6 6 9 5 13 6 16 5 20 4 48 4 52 4 55 4 58 6 1 4 33 4 37 4 40 4 43 4 46 4 21 4 24 4 27 4 30 4 33 4 11 4 14 4 17 4 19 4 3 4 6 4 8 3 49 46 47 48 49 50 51 52 53 54 65 56 57 58 69 60 8 24 8 30 8 36 8 42 8 48 7 26 7 31 7 37 7 42 7 47 6 45 6 60 6 55 6 59 7 3 6 12 6 16 6 20 6 24 6 28 5 45 5 49 6 53 6 50 5 23 5 27 5 30 5 4 6 7 4 49 51 52 53 54 55 8 54 8 5S 9 2 7 62 7 57 7 7 56 57 68 69 60 61 62 63 64 65 61 62 63 64 65 6« 70 8° 9° 10° 11° 12° 13° 14° 15° 16° 18°^ 20° 22° 24° 26° _^,^ TABLE XXXllI. 203 THIRD CORRECTION, TO APPARENT DISTANCE 116° ])'8 App. Alt. APPARENT ALTITUDE OP THE SUN, OR STAR. App Alt o 6 7 8 9 10 11 12 13 14 15 28° 30° 1 32° 34° 36° 38° 40° 42° 44° 46° 48° 50° 52° 54° 56° 58° 1 II 9 3 6 7 8 9 10 5 30 4 56 4 33 4 15 4 5 46 5 10 4 45 4 26 4 10 / II 6 3 5 25 4 58 4 37 4 20 / II 6 19 5 40 5 11 4 47 4 29 / II 6 36 5 55 5 24 4 58 4 39 1 II 6 52 6 9 5 36 5 8 4 48 / II 7 7 6 22 5 47 5 19 4 58 1 II 7 22 6 34 5 58 5 29 5 7 / // 7 36 6 46 6 8 5 39 5 16 1 II 7 51 6 58 6 18 5 49 5 25 1 >i 8 5 7 9 6 28 5 59 5 33 /• II 8 18 7 20 6 38 6 8 5 41 1 II 8 30 7 31 6 48 6 16 5 49 8 42 7 42 6 58 6 24 5 56 1 II 8 53 7 52 7 8 11 12 13 14 15 3 48 3 38 3 30 3 24 3 19 3 57 3 46 3 37 3 30 3 25 4 6 3 54 3 44 3 37 3 31 4 15 4 2 3 52 3 44 3 37 4 23 4 10 4 3 51 3 43 4 32 4 18 4 7 3 57 3 49 4 41 4 26 4 14 4 4 3 55 4 49 4 34 4 21 4 10 4 1 4 57 4 41 4 27 4 16 4 6 5 5 4 48 4 33 4 21 4 1] 5 12 4 54 4 39 4 27 4 17 5 19 5 1 4 45 4 33 5 25 5 7 16 17 18 19 20 3 15 3 12 3 9 3 7 3 5 3 20 3 16 3 13 3 10 3 8 3 26 3 21 3 17 3 14 3 11 3 31 3 26 3 22 3 18 3 15 3 37 3 31 3 26 3 22 3 19 3 16 3 14 3 12 3 10 3 9 3 42 3 36 3 31 3 27 3 23 3 47 3 41 3 36 3 31 3 27 3 53 3 46 3 40 3 35 3 31 3 58 3 51 3 45 3 39 3 34 4 2 3 55 3 49 4 8 ^ 16 17 18 19 20 21 22 23 24 25 3 4 3 3 3 2 3 1 3 3 6 3 5 3 4 3 3 3 2 3 9 3 7 3 6 3 5 3 4 3 12 3 10 3 9 3 8 3 7 3 20 3 17 3 15 3 13 3 11 3 23 3 20 3 18 3 16 3 27 3 23 21 22 23 24 25 26 27 28 29 30 3 3 2 59 2 59 3 3 2 3 1 3 3 3 3 4 3 3 3 2 3 1 3 1 3 6 3 5 3 4 3 3 3 3 3 7 3 6 3 5 3 9 26 27 28 29 30 31 32 33 34 35 31 32 33 34 35 3 1 3 2 3 2 3 3 3 4 3 3 1 3 1 3 2 3 1 3 2 36 37 38 39 40 3 5 36 37 38 39 40 41 42 43 44 45 41 42 43 44 45 46 47 48 49 50 • 46 47 48 49 50 51 52 53 54 '.ih 56 57 58 59 60 61 62 63 64 65 I TABLB P. xrracT or aini'i fab. 51 52 53 54 55 To be subtracted from th* Third Correction. )'8 App A t. 5 10 15 20 2.5 .30 35 40 45 50 55 60 Snn't Apparent Altitade. i 5 '* 2 2 3 '4 5 5 6 7 7 8 9 9 10 2( a 2 2 3 3 i 4 5 5 6 6 6 8 7 7 8 8 8 8 9 )30 3 4 5 6 6 7 8 40 5 If » 4 4 5 S 5 t 6 7 D60 tt 5 1 70 80 It BO 56 57 58 59 60 61 62 63 64 65 34° 38° 44° 28" 30° 32« 36° 40° 42° 46° 48° J '8 App. Alt 204 TABLE XXXIII. THIRD CORRECTION, TO APPARENT DISTANCE 120°. APPARENT ALTITUDE OF THE SUN, OR STAR. 6° 6 3 1 7 3 3 8 3 7 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 3 12 3 18 3 25 3 33 3 41 3 49 3 57 3 3 3 3 3 12 8» t It 3 17 3 23 3 28 3 34 3 41 14 23 32 40 4 49 4 58 5 7 5 16 5 25 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 5 34 5 42 5 51 6 6 8 48 55 3 10 17 4 24 4 31 4 39 4 46 4 53 12 16 20 25 30 3 11 3 7 3 5 3 4 3 6 8 11 15 19 23 3 36 3 42 3 48 3 54 4 1 10" ll" 12° 13 / It 3 17 3 11 3 8 3 6 3 5 3 3 3 11 3 14 3 18 24 16 11 8 6 5 5 5 16 5 24 5 31 6 17 6 25 6 34 6 43 6 51 59 8 16 24 32 46 47 48 49 50 51 52 53 54 55 40 47 55 3 11 5 39 5 46 5 54 6 2 6 9 4 7 4 14 4 21 4 27 4 33 3 28 3 32 3 37 3 42 3 48 4 40 4 47 4 53 5 5 6 5 12 5 18 5 25 5 31 5 38 16 23 30 37 44 50 56 2 9 15 18 25 32 39 45 ffi 57 58 59 60 8 51 8 57 9 3 9 9 61 62 63 64 65 21 27 33 39 45 44 50 56 3 53 3 58 4 4 4 10 4 15 4 20 4 25 4 31 4 37 4 43 3 22 3 25 3 29 3 33 3 38 3 42 3 47 3 52 3 57 4 2 3 5 3 6 3 8 3 11 3 14 3 32 3 22 3 15 3 11 3 8 3 6 3 5 3 6 3 8 3 11 3 17 3 20 3 23 3 26 3 30 3 34 3 39 3 43 3 47 3 51 4 48 4 54 5 5 6 5 l2 5 5 5 5 85 6 14 6 19 6 25 6 31 6 36 6 41 6 46 6 52 6 57 7 2 7 51 7 57 8 3 18 23 28 34 39 44 50 55 5 10 15 20 25 30 4 4 12 4 17 4 22 4 27 4 32 4 37 4 42 4 47 4 52 57 2 7 12 17 22 27 32 37 42 8 6 34 13 56 1 5 10 13 15 18 21 3 39 3 28 3 20 3 14 3 10 14= 47 34 25 18 14 3 11 3 9 3 8 3 7 3 8 3 24 3 20 28 32 36 39 43 3 11 3 12 3 14 3 17 3 47 3 51 3 55 3 59 15 4 3 4 19 4 23 4 27 4 32 4 37 4 42 4 46 4 50 4 55 4 59 5 5 5 13 5 17 5 22 46 51 55 59 3 26 30 34 37 23 26 30 33 36 9 10 15= 55 40 29 22 17 3 13 3 11 3 9 3 8 3 7 3 12 3 15 3 17 3 19 3 22 3 25 3 28 3 31 3 39 3 43 3 47 3 50 3 54 4 7 4 11 4 15 4 19 4 24 4 28 4 32 4 36 4 40 4 44 4 48 4 52 4 56 5 5 4 70 go 8 11 14 3 57 4 1 4 5 4 9 4 12 4 15 4 34 37 40 43 46 3 3 3 11 3 13 16° 17° 18° 19 4 47 35 26 20 16 13 11 9 8 3 15 3 13 3 17 3 19 3 21 3 23 3 26 3 49 3 52 3 56 3 59 4 2 4 19 4 23 4 27 4 31 4 35 4 39 4 42 4 46 4 49 53 56 4 4 13 4 16 4 20 4 24 4 28 4 31 4 34 4 37 4 40 29 32 35 37 40 3 43 3 46 3 49 3 52 3 55 3 3 9 3 10 3 11 12 54 40 31 24 3 19 3 15 3 13 3 11 3 9 3 15 3 16 3 18 3 20 3 23 3 25 3 28 3 30 3 33 3 36 3 38 3 41 3 44 3 47 3 50 3 58 4 2 15 18 21 24 27 10° 11° 12° 13° 14° 15° 16° 3 3 3 9 3 10 3 12 21 1 46 36 28 3 22 3 1 3 15 3 12 3 11 30 8 52 41 33 20« 22= >'8 App Alt. 39 15 59 47 38 3 26 3 21 3 17 3 14 3 12 3 10 3 9 3 9 3 10 3 11 13 14 16 18 20 3 22 3 25 3 27 3 29 3 32 3 34 3 36 3 39 3 42 3 46 53 56 59 1 4 4 7 4 10 4 13 4 16 47 50 53 55 58 12 13 14 16 18 11 10 10 9 10 3 30 3 24 3 20 3 17 3 14 47 30 12 58 47 3 38 3 31 3 26 3 22 3 1 3 20 3 22 3 24 3 26 3 28 11 12 13 15 17 12 11 11 10 10 3 30 3 32 3 35 3 37 3 40 4 1 4 3 4 6 42 45 47 50 52 3 18 3 20 3 22 3 23 3 25 3 27 3 29 3 32 3 34 3 36 38 41 43 45 47 10 11 12 14 3 16 16 6 7 8 9 10 11 12 13 14 15 3 ]4 3 13 3 12 3 12 17 18 19 20 3 15 16 18 20 21 23 3 25 3 27 3 29 3 31 3 33 55 57 3 49 35 37 39 41 43 11 11 12 13 14 21 22 23 24 25 3 15 3 16 3 17 3 18 3 19 3 20 3 22 3 24 3 26 3 28 30 31 33 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 TABLK P. EFFECT OF SHN's PAR. To be subtracted from the Third Correction. At)P Sun's Apparent Altitnd*. | A t. 5 10 20 30 40 50 55 If 70 80 90 5 2 2 3 3 4 5 5 10 2 3 3 4 5 6 15 3 4 4 5 ti 7 20 4 4 5 6 7 25 5 5 6 7 7 30 6 6 7 8 35 6 7 8 40 7 8 8 45 8 8 1 50 8 9 1 55 9 46 47 48 49 50 51 52 53 54 65 56 57 58 59 60 61 62 63 64 66 TABLE XXXIII. 205 THIRD CORRECTION. TO APPARENT DISTANCE 120». D'8 App. Alt. APPARENT ALTITUDE OF THE SUN, OR STAR. App. Alt. 24« 26° 280 30° 32° 34° 36° 38° 40° 42° 44° 46° 48° 50° 62° 54° o 6 7 8 9 10 11 12 13 14 15 / n 5 15 4 45 4 25 4 9 3 57 5 32 5 4 38 4 20 4 7 1 II 5 49 5 15 4 51 4 31 4 17 t n 6 6 5 30 5 4 4 43 4 27 1 n 6 23 5 45 5 17 4 55 4 37 1 II 6 41 6 5 30 5 7 4 47 / II 6 58 6 15 5 43 5 18 4 57 4 42 4 28 4 16 4 6 3 58 / II 7 14 6 29 5 56 5 28 5 7 / II 7 30 6 43 6 8 5 38i 5 17 7 46 6 56 6 20 5 49 5 27 1 II 8 2 7 8 6 31 6 5 37 8 17 7 21 6 42 6 10 5 46 1 II 8 31 7 33 6 53 6 20 5 55 1 II 8 44 7 45 7 3 6 29 6 3 / n 8 57 7 57 7 13 1 II 9 9 6 7 8 9 10 3 47 3 39 3 32 3 27 3 23 3 56 3 47 3 39 3 33 3 29 4 5 3 55 3 46 3 39 3 34 4 14 4 3 3 53 3 46 3 40 4 23 4 11 4 3 52 3 46 4 32 4 19 4 8 3 59 3 52 4 51 4 36 4 24 4 13 4 4 4 59 4 44 4 31 4 20 4 11 5 8 4 52 4 38 4 27 4 18 5 17 5 4 46 4 34 4 24 5 25 5 7 4 53 4 40 5 33 5 14 11 12 13 14 15 16 17 18 19 20 3 20 3 18 3 16 3 15 3 14 3 25 3 22 3 20 3 18 3 16 3 30 3 27 3 24 3 21 3 19 3 36 3 32 3 28 3 25 3 23 3 41 3 36 3 32 3 29 3 27 3 46 3 41 3 37 3 33 3 31 3 52 3 47 3 42 3 38 3 35 3 58 3 52 3 47 3 43 3 39 4 4 3 58 3 52 3 47 3 43 4 10 4 3 3 57 4 16 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 3 13 3 12 3 12 3 12 3 12 3 15 3 14 3 13 3 13 3 13 3 17 3 16 3 15 3 15 3 15 3 21 3 19 3 18 3 17 3 17 3 24 3 22 3 21 3 20 3 19 3 28 3 26 3 24 3 23 3 21 3 32 3 29 3 27 3 26 3 36 3 33 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 3 13 3 14 3 15 3 16 3 17 3 14 3 14 3 14 3 15 3 16 3 15 3 15 3 15 3 15 3 16 3 16 3 16 3 16 3 16 3 16 3 18 3 18 3 18 3 20 3 18 3 19 3 21 3 22 3 24 3 17 3 18 3 19 3 20 3 17 3 18 36 37 38 39 40 3 26 36 37 38 39 40 41 42 43 44 45 41 42 43 44 45 46 47 48 49 50 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 51 52 53 54 55 56 57 58 59 60 fil 62 63 64 65 61 62 63 64 65 24° 26o 28" 30° 32° 34° 380 40° 42° 440 46° 48° 50° 52° 54° 206 TABLE XXXIV • PROPORTIONAL LOGARITHMS. 1. I I. m. h. m. b. m. 1. in. D 1 h. m. a , 1. m. o ' ix. m. o > h. m. h. m h. m. a. ( ) o|< ) 1 2 3 4 50 6 7 8 9| i i J. 2553 1.9542 1.7782 1.6532 1.5563 1.4771 1.4102 1.3522 1.3010 1 < 1.0334 2481 9506 7757 6514 5549 4759 4091 3513 3002 1 2 : J.7324 2410 9471 7734 6496 5534 4747 4081 3504 2994 2 3 5563 2341 9435 7710 6478 5520 4735 4071 3495 2986 3 4 4314 2272 9400 7686 6460 5506 4723 4061 3486 2978 4 5 . J. 3345 2.2205 1.9365 1.7663 1.6443 1.5491 1.4711 1.4050 1.3477 1.2970 5 6 2553 2139 9331 7639 6425 5477 4699 4040 3468 2962 6 7 1883 2073 9296 7616 6407 5463 4688 4030 3459 2954 7 8 1303 2009 9262 7593 6390 5449 4676 4020 3450 2946 8 9 0792 1946 9228 7570 6372 5435 4664 4010 3441 2939 9 10 3.0334 2.1883 1.9195 1.7547 1.6355 1.5421 1.4652 1.4000 1.3432 1.2931 10 11 2.9920 1822 9162 7524 6338 5407 4640 3989 3423 2923 11 12 9542 1761 9128 7501 6320 5393 4629 3979 3415 2915 12 13 9195 1701 9096 7479 6303 5379 4617 3969 3406 2907 13 14 8873 1642 9063 7456 6286 5365 4606 3959 3397 2899 14 15 2.8573 2.1584 1.9031 1.7434 1.6269 1.5351 1.4594 1.3949 1.3388 1.2891 15 16 8293 1526 8999 7412 6252 5337 4582 3939 3379 ■ 2883 16 17 8030 1460 8967 7390 6235 5324 4571 3929 3371 2876 17 18 7782 1413 8935 7368 6218 5310 4559 3919 3362 2868 18 19 7547 1358 8904 7346 6201 5296 4548 3910 3353 2860 19 20 2.7324 2.1303 1.8873 1.7324 1.6185 1.5283 1.4536 1.3900 1.3345 1.2852 20 21 7112 1249 8842 7302 6168 5269 4525 3890 3336 2845 21 22 6910 1196 8811 7281 6151 5256 4514 3880 3327 2837 22 23 6717 1143 8781 7259 6135 5242 4502 3870 3319 2829 23 24 6532 1091 8751 7238 6118 5229 4491 3860 3310 2821 24 25 2.6355 2.1040 1.8721 1.7217 1.6102 1.5215 1.4480 1.3851 1 3301 1.2814 25 26 6185 0989 8691 7196 6085 5202 4468 3841 3293 2806 26 27 6021 0939 8661 7175 6069 5189 4457 3831 3284 2798 27 28 5863 0889 8632 7154 6053 5175 4446 3821 3276 2791 28 29 5710 0840 8602 7133 6037 5162 4435 3812 3267 2783 29 30 30 2.5563 2.0792 1.8573 1.7112 1.6021 1.5149 1.4424 1.3802 1 3259 1.2775 31 5421 0744 8544 7091 6005 5136 4412 3792 3250 2768 31 32 5283 0696 8516 7071 5989 5123 4401 3783 3242 2760 32 33 5149 0649 8487 7050 5973 5110 4390 3773 3233 2753 33 34 5019 0603 8459 7030 5957 5097 4379 3764 3225 2745 34 35 35 2.4894 2.0557 1.8431 1.7010 1.5941 1.5084 1.4368 1.3754 1.3216 1.2738 36 4771 0512 8403 6990 5925 5071 4357 3745 3208 2730 36 37 4652 0467 8375 6970 5909 5058 4346 3735 3199 2722 37 38 4536 0422 8348 6950 5894 5045 4335 3726 3191 2715 38 39 4424 0378 8320 6930 5878 5032 4325 3716 3183 2707 39 40 2.4314 2.0334 1.8293 1.6910 1.5863 1.5019 1.4314 1.3707 1.3174 1.2700 40 41 4206 0291 8266 6890 5847 5007 4303 3697 3166 2692 41 42 4102 0248 8239 6871 5832 4994 4292 3688 3158 2685 42 43 4000 0206 8212 6851 5816 4981 4281 3678 3149 2678 43 44 3900 0164 8186 6832 5801 4969 4270 3669 3141 2670 44 45 2.3802 2.0122 1.8159 1.6812 1.5786 1.4956 1.4260 1.3660 1.3133 1.2663 45 46 3707 0081 8133 6793 5771 4943 4249 3650 3124 2655 46 47 3613 0040 8107 6774 5755 4931 4238 3641 3116 2648 47 48 3522 0000 8081 6755 5740 4918 4228 3632 3108 2640 48 49 3432 1.9960 8055 6736 5725 4906 4217 3623 3100 2633 49 50 2.3345 1.9920 1.8030 1.6717 1.5710 1.4894 1.4206 1.3613 1 3091 1.2626 50 51 3259 9881 8004 6698 5695 4881 4196 3604 3083 2618 51 52 3174 9842 7979 6679 5680 4869 4185 3595 3075 2611 52 53 3091 9803 7954 6661 5666 4856 4175 3586 3067 2604 53 54 55 3010 9765 7929 6642 5651 4844 4164 3576 3059 2596 54 2.2931 1.9727 1.7904 1.6624 1.5636 1.4832 1.4154 1.3567 1.3051 1.2589 55 56 2852 9690 7879 6605 5621 4820 4143 3558 3043 2582 56 57 2775 9652 7855 6587 5607 4808 4133 3549 3034 2574 57 58 2700 9615 7830 6568 5592 4795 4122 3540 3026 2567 58 59 2626 9579 7806 6550 5578 4783 4112 3531 3018 2560 59 ] 2 3 4 5 6 7 8 9 207 TABLE XXXIV • • PROPORTIONAL LOGARITHMS — tl 1 / ' » 1 o ' 1 o . 6 I o ' o , Q 1 ■. 1 L. m.l 1. m. b. m. b. m. 1. m. h. m. b. m. h. m. h. m. h. m. • ( 3 100 11 12 13 14 15 16 17 18 19 1.2553 1.2139 1.1761 1.1413 1.1091 1.0792 1.0512 1.0248 1.0000 0.9765 1 2545 2132 1755 1408 1086 07»7 0507 0244 0.9996 9761 1 2 2538 2126 1749 1402 1081 0782 0502 0240 9992 9758 2 3 2531 2119 1743 1397 1076 0777 0498 0235 9988 9754 3 4 2524 2113 1737 1391 1071 0773 0493 0231 9984 9750 4 5 5 1.2517 1.2106 1.1731 1.1386 1.1066 1.0768 1.0489 1.0227 0.9980 0.9746 6 2510 2099 1725 1380 1061 0763 0484 0223 9976 9742 6 7 2502 2093 1719 1374 1055 0758 0480 0219 9972 9739 7 8 2495 2086 1713 1369 1050 0753 0475 0214 9968 9735 8 9 2488 2080 1707 1363 1045 0749 0471 0210 9964 9731 9 10 1.2481 1.2073 1.1701 1.1358 1.1040 1.0744 1.0467 1.0206 0.9960 0.9727 10 11 2474 2067 1695 1352 1035 0739 0462 0202 9956 9723 11 12 2467 2061 1689 1347 1030 0734 0458 0197 9952 9720 12 13 2460 2054 1683 1342 1025 0730 0453 0193 9948 9716 13 14 2453 2048 1677 1336 1020 0725 0449 0189 9944 9712 14 15 1.2445 1.2041 1.1671 1.1331 1.1015 1.0720 1.0444 1.0185 0.9940 0.9708 15 16 2438 2035 1665 1325 1009 0715 0440 0181 9936 9705 16 17 2431 2028 1660 1320 1004 0711 0435 0176 9932 9701 17 18 2424 2022 1654 1314 0999 0706 0431 0172 9928 9697 18 19 2417 2016 1648 1309 0994 0701 0426 0168 9924 9693 19 20 1.2410 1.2009 1.1642 1.1303 1.0989 1.0696 1.0422 1.0164 0.9920 0.9690 20 21 2403 2003 1636 1298 0984 0692 0418 0160 9916 9686 21 22 2396 1996 1630 1292 0979 0687 0413 0156 9912 9682 22 23 2389 1990 1624 1287 0974 0682 0409 0151 9908 9678 23 24 2382 1984 1619 1282 0969 0678 0404 0147 9905 9675 24 25 25 1.2375 1.1977 1.1613 1.1276 1.0964 1.0673 1.0400 1.0143 0.9901 0.9671 26 2368 1971 1607 1271 0959 0668 0395 0139 9897 9667 26 27 2362 1965 1601 1266 0954 0663 0391 0135 9893 9664 27 28 2355 1958 1595 1260 0949 0659 0387 0131 9889 9660 28 29 2348 1952 1589 1255 0944 . 0654 0382 0126 9885 9656 29 30 1.2341 1.1946 1.1584 1.1249 1.0939 1.0649 1.0378 1.0122 0.9881 0.9652 30 31 2334 1939 1578 1244 0934 0645 0374 0118 9877 9649 31 32 2327 1933 1572 1239 0929 0640 0369 0114 9873 9645 32 33 2320 1927 1566 1233 ,0924 0635 0365 0110 9869 9641 33 34 35 2313 1921 1561 1228 0919 0631 0360 0106 9865 9638 34 1.2307 1.1914 1.1555 1.1223 1.0914 1.0626 1.0356 1.0102 0.9861 0.9634 35 36 2300 1908 1549 1217 0909 0621 0352 0098 9858 9630 36 37 2293 1902 1543 1212 0904 0617 0347 0093 9854 9626 37 38 2286 1896 1538 1207 0899 0612 0343 0089 9850 9623 38 39 2279 1889 1532 1201 0894 0608 0339 0085 9846 9619 39 40 1.2272 1.1883 1.1526 1.1196 1.0889 1.0603 1.0334 1.0081 0.9842 0.9615 40 41 2266 1877 1520 1191 0884 0598 0330 0077 9838 9612 41 42 2259 1871 1515 1186 0880 0594 0326 0073 9834 9608 42 43 2252 1865 1509 1180 0875 0589 0321 0069 9830 9604 43 44 2245 1859 1503 1175 0870 0585 0317 0065 9827 9601 44 45 1.2239 1.1852 1.1498 1.1170 1.0865 1.0580 1.0313 1.0061 0.9823 0.9597 45 46 2232 1846 1492 1164 0860 0575 0308 0057 9819 9593 46 47 '2-225 1840 1486 1159 0855 0571 0304 0053 9815 9590 47 48 2218 1834 1481 1154 0850 0566 0300 0049 9811 9586 48 49 2212 1.1828 1475 1149 0845 0562 0295 0044 9807 9582 49 50 50 1.2205 1.1822 1.1469 1.1143 1.0840 1.0557 1.0291 1.0040 0,9803 0.9579 51 2198 1816 1464 1138 0835 0552 0287 0036 9800 9575 51 52 2192 1809 1458 1133 0831 0548 0282 0032 9796 9571 52 53 2185 1803 1452 1128 0826 0543 0278 0028 9792 9568 53 54 2178 1797 1447 1123 0821 0539 0274 0024 9788 9564 54 55 1.2172 1.1791 1.1441 1.1117 1.0816 1.0534 1.0270 1.0020 0.9784 0.9561 55 56 2165 1785 1436 1112 0811 0530 0265 0016 9780 9557 56 57 2159 1779 1430 1107 0806 0525 0261 0012 9777 9553 57 58 2152 1773 1424 1102 0801 0521 0257 0008 9773 9550 58 59 2145 1767 1419 1097 0797 0516 0252 0004 9769 9546 59 10 11 12 13 14 15 16 17 18 19 14 208 TABLE XXXIV. PROPORTIONAL LOGARITHMS. • 1 • I. m. ii 1 < >. m. i • • > < 1. m. b. m. 1 1 I c 1. m. 1 * ' 1. m. h. m. a. m. o « h. m. O t h. m. o / h. m. O 1 h. m. C > 20( ) 21 ( ) 22 ( ) 23 24 ( ) 25 26 27 28l0 29|0 30| 31 ( ).9542 9331 9128 8935 8751 8573 8403 8239 8081 7929 7782 7639 1 9539 9327 9125 8932 8748 8570 8400 8236 8079 7926 7779 7637 1 2 9535 9324 9122 8929 8745 8568 8397 8234 8076 7924 7777 7634 2 3 9532 9320 9119 8926 8742 8565 8395 8231 8073 7921 7774 7632 3 4 " 5 ( 9528 9317 9115 8923 8739 8562 8392 8228 8071 7919 7772 7630 4 6 3.9524 9313 9112 8920 8736 8559 8389 8226 8068 7916 7769 7627 6 9521 9310 9109 8917 8733 8556 8386 8223 8066 7914 7767 7625 6 7 9517 9306 9106 8913 8730 8253 8384 8220 8063 7911 7765 7623 7 8 9514 9303 9102 8910 8727 8550 8381 8218 8061 7909 7762 7620 8 9 10 9510 9300 9099 8907 8724 8547 8378 8215 8058 7906 7760 7618 9 0.9506 9296 9096 8904 8721 8544 8375 8212 8055 7904 7757 7616 10 11 9503 9293 9092 8901 8718 8542 8372 8210 8053 7901 7755 7613 11 12 9499 9289 9089 8898 8715 8539 8370 8207 8050 7899 7753 7611 12 13 9496 9286 9086 8895 8712 8536 8367 8204 8048 7896 7750 7609 13 14 16 9492 9283 9083 8892 8709 8533 8364 8202 8045 7894 7748 7607 14 15 0.9488 9279 9079 8888 8706 8530 8361 8199 8043 7891 7745 7604 16 9485 9276 9076 8885 8703 8527 8359 8196 8040 7889 7743 7602 16 17 9481 9272 9073 8882 8700 8524 8356 8194 8037 7887 7741 7600 17 18 9478 9269 9070 8879 8697 8522 8353 8191 8035 7884 7738 7597 18 19 20 9474 9266 9066 8876 8694 8519 8350 8188 8032 7882 7736 7595 19 20 0.9471 9262 9063 8873 8691 8516 8348 8186 8030 7879 7734 7593 21 9467 9259 9060 8870 8688 8513 8345 8183 8027 7877 7731 7590 21 22 9464 9255 9057 8867 8685 8510 8342 8181 8025 7874 7729 7588 22 23 9460 9252 9053 8864 8682 8507 8339 8178 8022 7872 7726 7586 23 24 9456 9249 9050 8861 8679 8504 8337 8175 8020 7869 7724 7583 24 25 25 0.9453 9245 9047 8857 8676 8502 8334 8173 8017 7867 7722 7581 26 9449 9242 9044 8854 8673 8499 8331 8170 8014 7864 7719 7579 26 27 9446 9238 9041 8851 8670 8496 8328 8167 8012 7862 7717 7577 27 28 9442 9235 9037 8848 8667 8493 8326 8165 8009 7859 7714 7574 28 29 30 9439 9232 9034 8845 8664 8490 8323 8162 8007 7857 7712 7572 29 30 0.9435 9228 9031 8842 8661 8487 8320 8159 8004 7855 7710 7570 31 9432 9225 9028 8839 8658 8484 8318 8157 8002 7852 7707 7567 31 32 9428 9222 9024 8836 8655 8482 8315 8154 7999 7850 7705 7565 32 33 9425 9218 9021 8833 8652 8479 8312 8152 7997 7847 7703 7563 33 34 35 9421 9215 9018 8830 8649 8476 8309 8149 7994 7845 7700 7560 34 0.9418 9212 9015 8827 8646 8473 8307 8146 7992 7842 7698 7558 35 36 9414 9208 9012 8824 8643 8470 8304 8144 7989 7840 7696 7556 36 37 9411 9205 9008 8821 8640 8467 8301 8141 7987 7837 7693 7554 37 38 9407 9201 9005 8817 8637 8465 8298 8138 7984 7835 7691 7551 38 39 40 9404 9198 9002 8814 8635 8462 8296 8136 7981 7832 7688 7549 39 40 0.9400 9195 8999 8811 8632 8459 8293 8133 7979 7830 7686 7547 41 9397 9191 8996 8808 8629 8456 8290 8131 7976 7828 7684 7544 41 42 9393 9188 8992 8805 8626 8453 8288 8128 7974 7825 7681 7542 42 43 9390 9185 8989 8802 8623 8451 8285 8125 7971 7823 7679 7540 43 44 45 9386 9181 8986 8799 8620 8448 8282 8123 7969 7820 7677 7538 44 0.9383 9178 8983 8796 8617 8445 8279 8120 7966 7818 7674 7535 45 46 9379 9175 8980 8793 8614 8442 8277 8117 7964 7815 7672 7533 46 47 9376 9172 8977 8790 8611 8439 8274 8115 7961 7813 7670 7531 47 48 9372 9168 8973 8787 8608 8437 8271 8112 7959 7811 7667 7528 48 49 50 9369 9165 8970 8784 8605 8434 8269 8110 7956 7808 7665 7526 49 0.9365 9162 8967 8781 8602 8431 8266 8107 7954 7806 7663 7524 50 51 9362 9158 8964 8778 8599 8428 8263 8104 7951 7803 7660 7522 61 52 9358 9155 8961 8775 8597 8425 8261 8102 7949 7801 7658 7519 52 53 3955 9152 8958 8772 8594 8423 8258 8099 7946 7798 7655 7517 53 54 55 9351 9148 8954 8769 8591 8420 8255 8097 7944 7796 7653 7515 54 55 0.9348 9145 8951 8766 8588 8417 8253 8094 7941 7794 7651 7513 56 9344 9142 8948 8763 8585 8414 8250 8091 7939 7791 7648 7510 56 57 9341 9138 8945 8760 8582 8411 8247 8089 7936 7789 7646 7508 57 58 9337 9135 8942 8757 8579 8409 8244 8086 7934 7786 7644 7506 58 59 9334 9132 8939 8754 8576 8406 8242 8084 7931 7784 7641 7503 59 2G 21 22 23 24 25 26 27 28 29 30 31 - TABLE XXXIV. ' 209 PROPORTIONAL LOGARITHMS " 1 > 1 O ' » ' > 1 < > 1 < '1 b / < > / i / ' 1 « 1 " .. 1 n. m. h. m. li. m. 1. m. : 1. m. h. m.| 1. m. 1 1. m. h. m. 1 1. nL. h. m. 1. m. a ( ) 32 3 33 3 34 3 35 ( 3 36 ) 37 ( ) -38 3 39 3 40 4110 42| 43 ( 3.7501 7368 7238 7112 6990 6871 6755 6642 6532 6425 6320 6218 1 7499 7365 7236 7110 6988 6869 6753 6640 6530 6423 6319 6216 1 2 7497 7363 7234 7108 6986 6867 6751 6638 6529 6421 6317 6215 2 3 7494 7361 7232 7106 6984 6865 6749 6637 6527 6420 6315 6213 3 4 5 7492 7359 7229 7104 6982 6863 6747 6635 6525 6418 6313 6211 4 J. 7490 7357 7227 7102 6980 6861 6745 6633 6523 6416 6312 6210 5 6 7488 7354 7225 7100 6978 6859 6743 6631 6521 6414 6310 6208 6 7 7485 7352 7223 7098 6976 6857 6742 6629 6519 6413 6308 6206 7 8 7483 7350 7221 7096 6974 6855 6740 6627 6518 6411 6306 6205 8 9 10 7481 7348 7219 7093 6972 6853 6738 6625 6516 6409 6305 6203 9 3.7479 7346 7217 7091 6970 6851 6736 6624 6514 6407 6303 6201 10 11 7476 7344 7215 7089 6968 6849 6734 6622 6612 6406 6301 6200 11 12 7474 7341 7212 7087 6966 6847 6732 6620 6510 6404 6300 6198 12 13 7472 7339 7210 7085 6964 6845 6730 6618 6509 6402 6298 6196 13 14 15 7470 7337 7208 7083 6962 6843 6728 6616 6507 6400 6296 6195 14 0.7467 7335 7206 7081 6960 6841 6726 6614 6505 6398 6294 6193 15 16 7465 7333 7204 7079 6958 6840 6725 6612 6503 6397 6293 6191 16 17 7463 7330 7202 7077 6956 6838 6723 6611 6501 6395 6291 6190 17 18 7461 7328 7200 7075 6954 6836 6721 6609 6500 6393 6289 6188 18 19 20 7458 7326 7198 7073 6952 6834 6719 6607 6498 6391 6288 6186 19 20 0.7456 7324 7196 7071 6950 6832 6717 6605 7496 6390 6286 6185 21 7454 7322 7193 7069 6948 6830 6715 6603 6494 6388 6284 6183 21 22 7452 7320 7191 7067 6946 6828 6713 6601 6492 6386 6282 6181 22 23 7450 7317 7189 7065 6944 6826 6711 6600 6491 6384 6281 6179 23 24 25 .7447 7315 7187 7063 6942 6824 6709 6598 6489 6383 6279 6178 24 0.7445 7313 7185 7061 6940 6822 6708 6596 6487 6381 6277 6176 25 26 7443 7311 7183 7059 6938 6820 6706 6594 6485 6379 6276 6174 26 27 7441 7309 7181 7057 6936 6818 6704 6592 6484 6377 6274 6173 27 28 7438 7307 7179 7055 6934 6816 6702 6590 6482 6376 6272 6171 28 29 30 7436 7304 7177 7052 6932 6814 6700 6589 6480 6374 6271 6169 29 0.7434 7302 7175 7050 6930 6812 6698 6587 6478 6372 6269 6168 30 31 7432 7300 7172 7048 6928 6810 6696 6585 6476 6371 6267 6166 31 32 7429 7298 7170 7046 6926 6809 6694 6583 6475 6369 6265 6165 32 33 7427 7296 7168 7044 6924 6807 6692 6581 6473 6367 6264 6163 33 34 35 7425 7294 7166 7042 6922 6805 6691 6579 6471 6365 6262 6161 34 35 0.7423 7291 7164 7040 6920 6803 6689 6578 6469 6364 6260 6160 36 7421 7289 7162 7038 6918 6801 6687 6576 6467 6362 6259 6158 36 37 7418 7287 7160 7036 6916 6799 6685 6574 6466 6360 6257 6156 37 38 7416 7285 7158 7034 6914 6797 6683 6572 6464 6358 6255 6155 38 39 ~40 7414 7283 7156 7032 6912 6795 6681 6570 6462 6357 6354 6153 39 0.7412 7281 7154 7030 6910 6793 6679 6568 6460 6355 6252 6151 40 41 7409 7279 7152 7028 6908 6791 6677 6567 6459 6353 6250 6150 41 42 7407 7276 7149 7026 6906 6789 6676 6565 6457 6351 6248 6148 42 43 7405 7274 7147 7024 6904 6787 6674 6563 6455 6350 6247 6146 43 44 45 7403 7272 7145 7022 6902 6785 6672 6561 6453 6348 6245 6145 44 0.7401 7270 7143 7020 6900 6784 6670 6559 6451 6346 6243 6143 45 46 7398 7268 7141 7018 6898 6782 6668 6558 6450 6344 6242 6141 46 47 7396 7266 7139 7016 6896 6780 6666 6556 6448 6343 6240 6140 47 48 7394 7264 7137 7014 6894 6778 6664 6554 6446 6341 6238 6138 48 49 50 7392 7261 7135 7012 6892 6776 6663 6552 6444 6339 6237 6136 49 0.7390 7259 7133 7010 6890 6774 6661 6550 6443 6338 6235 6135 50 51 7387 7257 7131 7008 6888 6772 6659 6548 6441 6336 6233 6133 51 52 7385 7255 7129 7006 6886 6770 6657 6547 6439 6334 6232 6131 52 53 7383 7253 7127 7004 6884 6768 6655 6545 6437 6332 6230 6130 53 54 55 7381 7251 7124 7002 6882 6766 6653 6543 6435 6331 6228 6128 54 0.7379 7249 7122 7000 6881 6764 6651 6541 6434 6329 6226 6126 55 56 7376 7246 7120 6998 6879 6763 6650 6539 6432 6327 6225 6125 '56 57 7374 7244 7118 6996 6877 6761 6648 6538 6430 6325 6223 6123 57 58 7372 7242 7116 6994 6875 6759 6646 6536 6428 6324 6221 6121 58 59 7370 7240 7114 6992 6873 6757 6644 6534 6427 6322 6220 6120 59 - as 33 34 3£ 36 37 38 39 40 41 42 43 210 TABLE XXXIV. PROPORTIONAL LOGARITHMS 11 9 1 ' ' ° 1 1 / 6 , 1 » y • / '1 « "' 1 i} •. 1 k. m. li. m. h. m. 1. m. li. m.h. m. tt. m. 1. m. li. m. ti. m.i b. m.| h. m- t. ( ) 44 45 460 47 480* 49 50 51 520 53 54 55 J. 6118 6021 5925 5832 5740 5651 5563 5477 5393 5310 5229 5149 1 6117 6019 5924 5830 5739 5649 5562 5476 5391 5309 5227 5148 1 2 6115 6017 5922 5829 5737 5648 5560 5474 5390 5307 5226 5146 2 3 6113 6016 5920 5827 5736 5646 5559 5473 5389 5306 5225 5145 3 4 5 6112 6014 5919 5826 5734 5645 5557 5471 5387 5305 5223 5144 4 [)-6110 6013 5917 5824 5733 5643 5556 5470 5386 5303 5222 5143 5 6 6108 6011 5916 5823 5731 5642 5554 5469 5384 5302 5221 5141 6 7 6107 6009 5914 5821 5730 5640 5553 5467 5383 5300 5219 5140 7 8 6105 6008 5913 5819 5728 5639 5551 5466 5382 5299 5218 5139 8 9 10 6103 6006 5911 5818 5727 5637 5550 5464 5380 5298 5217 5137 9 0.6102 6005 5909 5816 5725 5636 5549 5463 5379 5296 5215 5136 10 11 6100 6003 5908 5815 5724 5635 5547 5461 5377 5295 5214 5135 11 12 6099 6001 5906 5813 5722 6633 5546 5460 5376 5294 5213 5133 12 13 6097 6000 5905 5812 5721 5632 5544 5459 5375 5292 5211 5132 13 14 15 6U95 5998 5903 5810 5719 5630 5543 5457 5373 5291 5210 5131 14 0.6094 5997 5902 5809 5718 5629 5541 5456 5372 5290 5209 5129 15 16 6092 5995 5900 5807 5716 5627 5540 5454 5370 5288 5207 5128 16 17 6090 5993 5898 5806 5715 5626 5538 5453 5369 5287 5206 5127 17 18 6089 5992 5897 5804 5713 5624 5537 5452 5368 5285 5205 5125 18 19 20 6087 5990 5895 5803 5712 5623 5536 5450 5366 5284 5203 5124 19 20 0.6085 5989 5894 5801 5710 5621 5534 5449 5365 5283 5202 5123 21 6084 5987 5892 5800 5709 5620 5533 5447 5364 5281 5201 5122 21 22 6082 5985 5891 5798 5707 5618 5531 5446 5362 5280 5199 5120 22 23 6081 5984 5889 5796 5706 5617 5530 5445 5361 5279 5198 5119 23 24 6079 5982 5888 5795 5704 5615 5528 5443 5359 5277 5197 5118 24 25 0.6077 5981 0886 5793 5703 5614 5527 5442 5358 5276 5195 5116 25 26 6076 5979 5884 5792 5701 5613 5526 5440 5357 5275 5194 5115 26 27 6074 5977 5883 5790 5700 5611 5524 5439 5355 5273 5193 5114 27 28 6072 5976 5881 5789 5698 5610 5522 5437 5354 5272 5191 5112 28 29 30 6071 5974 5880 5787 5697 5608 5521 5436 5353 5271 5190 5111 29 30 0.6069 5973 5878 5786 5695 5607 5520 5435 5351 5269 5189 5110 31 6067 5971 5877 5784 5694 5605 5518 5433 5350 5268 5187 5108 31 32 6066 5969 5875 5783 5692 5604 5517 5432 5348 5266 5186 5107 32 33 6064 5968 5874 5781 5691 5602 5516 5430 5347 5265 5185 5106 33 34 35 6063 5966 5872 5780 5689 5601 5514 5429 5346 5264 5183 5105 34 0.6061 5965 5870 5778 5688 5599 5513 5428 5344 5262 5182 5103 35 36 6059 5963 5869 5777 5686 5598 5511 5426 5343 5261 5181 5102 36 37 6058 5961 5867 5775 5685 5596 5510 5425 5341 5260 5179 5101 37 38 6056 5960 5866 5774 5683 5595 5508 5423 5340 5258 5178 5099 38 39 40 6055 5958 5864 5772 5682 5594 5507 5422 5339 5257 5177 5098 39 0.6053 5957 5863 5771 5680 5592 5506 5421 5337 5256 5175 5097 40 41 6051 5955 5861 5769 5679 5591 5504 5419 5336 5254 5174 5095 41 42 6050 5954 5860 5768 5677 5589 5503 5418 5335 5253 5173 5094 42 43 6048 5952 5858 5766 5676 5588 5501 5416 5333 5252 5172 5093 43 44 45 6046 5950 5856 5765 5674 5586 5500 5415 5332 5250 5170 6092 44 0.6045 5949 5855 5763 5673 5585 5498 5414 5331 5249 5169 5090 45 46 6043 5947 5853 5761 5671 5583 5497 5412 5329 5248 5168 5089 46 47 6042 5946 5852 5760 5670 5582 5496 5411 5328 5246 5166 5088 47 48 6040 5944 5850 5758 5669 5580 5494 5409 5326 5245 5165 5086 48 49 50 6038 5942 5849 5757 5667 5579 5493 5408 5325 5244 5164 5085 49 0.6037 5941 5847 5755 5666 5578 5491 5407 5324 5242 5162 5084 50 51 6035 5939 5846 5754 5664 5578 5490 5405 5322 5241 5161 5082 51 52 6033 5938 5844 5752 5663 5575 5488 5404 5321 5240 6160 5081 52 53 6032 5936 5843 5751 5661 5573 5487 5402 5320 5238 5158 5080 53 54 55 6030 5935 5841 5749 5660 5572 5486 5401 5318 5237 5157 5079 54 0.6029 5933 5839 5748 5658 5570 5484 5400 5317 5235 5156 5077 55 56 6027 5931 5838 5746 5657 5569 5483 5398 5315 5234 5154 5076 56 57 6025 5930 5836 5745 5655 5567 5481 5397 5314 5233 5153 5075 57 58 6024 5928 5835 5743 5654 5566 5480 5395 5313 5231 5152 5073 58 59 6022 5927 5833 5742 5652 5564 5478 5394 5311 5230 5150 5072 59 A4 [0 At »0 46 47 48 49 50 51 52 53 54 65 211 TABLE XXXIV. • PROPORTIONAL LOGARITHMS. " a 1. I 1. m. 1 / < 1. m. ; > 1. m. 1. m. 1. m. 1. m. ' n. m. O f \\. ID. o h. m. • 1 \k. m. 1 h. m. #1 1. ( ) 56 ) 57 ( ) 58 59| I 01 1| 1 2 1 3 1 4 1 5 I 6 1 7 ( J. 5071 4994 4918 4844 4771 4699 4629 4559 4491 4424 4357 4292 1 1 5070 4993 4917 4843 4770 4698 4628 4558 4490 4422 4356 4291 1 1 2 5068 4991 4916 4842 4769 4697 4626 '4557 4489 4421 4355 4290 2 3 5067 4990 4915 4841 4768 4696 4625 4556 4488 4420 4354 4289 3 4 5 5066 4989 4913 4839 4766 4695 4624 4555 4486 4419 4353 4288 4 5 0.5064 4988 4912 4838 4765 4693 4623 4554 4485 4418 4352 4287 6 5063 4986 4911 4837 4764 4692 4622 4552 4484 4417 4351 4285 6 7 5062 4985 4910 4836 4763 4691 4621 4551 4483 4416 4350 4284 7 8 5061 4984 4908 4834 4762 4690 4619 4550 4482 4415 4349 4283 8 9 10 5059 4983 4907 4833 4760 4689 4618 4549 4481 4414 4347 4282 9 0.5058 4981 4906 4832 4759 4688 4617 4548 4480 4412 4346 4281 10 11 6057 4980 4905 4831 4758 4686 4616 4547 4479 4411 4345 4280 11 12 5055 4979 4903 4830 4757 4685 4615 4546 4477 4410 4344 4279 12 13 5054 4977 4902 4828 4756 4684 4614 4544 4476 4409 4343 4278 13 14 15 5053 4976 4901 4827 4754 4683 4612 4543 4475 4408 4342 4277 14 15 0.5051 4975 4900 4826 4753 4682 4611 4542 4474 4407 4341 4276 16 5050 4974 4899 4825 4752 4680 4610 4541 4473 4406 4340 4275 16 17 5049 4972 4897 4823 4751 4679 4609 4540 4472 4405 4339 4274 17 18 5048 4971 4896 4822 4750 4678 4608 4539 4471 4404 4338 4273 18 19 20 5046 4970 4895 4821 4748 4677 4607 4538 4469 4402 4336 4271 19 20 0.5045 4969 4894 4820 4747 4676 4606 4536 4468 4401 4335 4270 21 5044 4967 4892 4819 4746 4675 4604 4535 4467 4400 4334 4269 21 22 5043 4966 4891 4817 4745 4673 4603 4534 4466 4399 4333 4268 22 23 5041 4965 4890 4816 4744 4672 4602 4533 4465 4398 4332 4267 23 24 5040 4964 4889 4815 4742 4671 4601 4532 4464 4397 4331 4266 24 25 25 0.5039 4962 4887 4814 4741 4670 4600 4531 4463 4396 4330 4266 26 5037 4961 4886 4812 4740 4669 4599 4530 4462 4395 4329 4264 26 27 5036 4960 4885 4811 4739 4668 4597 4528 4460 4394 4328 4263 27 28 5035 4959 4884 4810 4738 4666 4596 4527 4459 4393 4327 4262 28 29 30 5034 4957 4882 4809 4736 4665 4595 4526 4458 4391 4326 4261 29 30 0.5032 4956 4881 4808 4735 4664 4594 4525 4457 4390 4325 4260 31 5031 4955 4880 4806 4734 4663 4593 4524 4456 4389 4323 4269 31 32 5030 4954 4879 4805 4733 4662 4592 4523 4455 4388 4322 4268 32 33 5028 4952 4877 4804 4732 4660 4590 4522 4454 4387 4321 4256 33 34 35 5027 4951 4876 4803 4730 4659 4589 4520 4453 4386 4320 4255 34 35 0.5026 4950 4875 4801 4729 4658 4588 4519 4452 4385 4319 4254 36 5025 4949 4874 4800 4728 4657 4587 4518 4450 4384 4318 4253 36 37 5023 4947 4873 4799 4727 4656 4586 4517 4449 4383 4317 4252 37 38 5022 4946 4871 4798 4726 4655 4585 4516 4448 4381 4316 4261 38 39 40 5021 4945 4870 4797 4724 4653 4584 4515 4447 4380 4315 4250 39 40" 0.5019 4943 4869 4795 4723 4652 4582 4514 4446 4379 4314 4249 41 5018 4942 4868 4794 4722 4651 4581 4512 4445 4378 4313 4248 41 42 5017 4941 4866 4793 4721 4650 4580 4511 4444 4377 4311 4247 42 43 5016 4940 4865 4792 4720 4649 4579 4510 4443 4376 4310 4246 43 44 45 5014 4938 4864 4791 4718 4648 4578 4509 4441 4375 4309 4246 44 45 0.5013 4937 4863 4789 4717 4646 4577 , 4508 4440 4374 4308 4244 46 5012 4936 4861 4788 4716 4645 iJ7.5 4507 4439 4373 4307 4243 46 47 5011 4935 4860 4787 4715 4644 4574 4506 4438 4372 4306 4241 47 48 5009 4933 4859 4786 4714 4643 4573 4505 4437 4370 4305 4240 48 49 50 5008 4932 4858 4785 4712 4642 4572 4503 4436 4369 4304 4239 49 0.5007 4931 4856 4783 4711 4640 4571 4502 4435 4368 4303 4238 50 51 5005 4930 4855 4782 4710 4639 4570 4501 4434 4367 4302 4237 61 52 5004 4928 4854 4781 4709 4638 4569 4500 4433 4366 4301 4236 52 53 5003 4927 4853 4780 4708 4637 4567 4499 4431 4365 4300 4235 53 54 55 5002 4926 4852 4778 4707 4636 4566 4498 4430 4364 4298 4234 54 55 0.5000 4925 4850 ■4777 4705 4635 4565 4497 4429 4363 4297 4233 56 4999 4923 4849 4776 4704 4633 4564 4495 4428 4362 4296 4232 56 57 4998 4922 4848 4775 4703 4632 4563 4494 4427 4361 4295 4231 57 58 4997 4921 4847 4774 4702 4631 4562 4493 4426 4359 4294 4230 58 59 4995 4920 4845 4772 4701 4630 4560 4492 4425 4358 4293 4229 59 56 67 58 59 1 1 1 1 2 1 3 1 4 1 5 1 6 1 7 212 TABLE XXXIV. PROPORTIONAL LOGARITHMS. " ' c > ' c > ' O ' |0 ' |0 ' |0 ' (O ' |0 ' (O ' 1 r,o '1 rr a. k m. b k. la. h L. m. fa m. h m. h m. h m. fa m. h m. fa m. h. in.|ti k. m. 1. 1 8] 91 101 11 1 121 131 141 15 1 161 17 ] 1811 19 .4228 4164 4102 4040 3979 3919 3860 3802 3745 ■ 3688 | 3632 3576 1 4227 4163 4101 4039 3978 3919 3859 3801 3744 3687 3631 3576 1 2 4226 4162 4100 4038 3977 3918 3858 3800 3743 3686 3630 3575 2 3 4224 4161 4099 4037 3976 3917 3857 3799 3742 3685 3629 3574 3 4 5 C 4223 4160 4098 4036 3975 3916 3856 3798 3741 3684 3628 3573 4 (.4222 4159 4097 4035 3974 3915 3856 3797 3740 3683 3627 3572 5 6 4221 4158 4096 4034 3973 3914 3855 3796 3739 3682 3626 3571 6 7 4220 4157 4095 4033 3972 3913 3854 3795 3738 3681 3625 3570 7 8 4219 4156 4093 4032 3971 3912 3853 3794 3737 3680 3624 3569 8 9 10 ( 4218 4155 4092 4031 3970 3911 3852 3793 3736 3679 3623 3568 9 10 ).4217 4154 4091 4030 3969 3910 3851 3792 3735 3678 3623 3567 11 4216 4153 4090 4029 3968 3909 3850 3792 3734 3677 3622 3566 11 12 4215 4152 4089 4028 3967 3908 3849 3791 3733 3677 3621 3565 12 13 4214 4151 4088 4027 3966 3907 3848 3790 3732 3676 3620 3565 13 14 15 ( 4213 4150 4087 4026 3965 3906 3847 3789 3731 3675 3619 3564 14 ).4212 4149 4086 4025 3964 3905 3846 3788 3730 3674 3618 3563 15 16 4211 4147 4085 4024 3963 3904 3845 3787 3729 3673 3617 3562 16 17 4210 4146 4084 4023 3962 3903 3844 3786 3728 3672 3616 3561 17 18 4209 4145 4083 4022 3961 3902 3843 3785 3727 3671 3615 3560 18 ; 19 20 4207 4144 4082 4021 3960 3901 3842 3784 3727 3670 3614 3559 19 20 ! 0.4206 4143 4081 4020 3959 3900 3841 3783 3726 3669 3613 3558 21 4205 4142 4080 4019 3958 3899 3840 3782 3725 3668 3612 3557 21 22 4204 4141 4079 4018 3957 3898 3839 3781 3724 3667 3611 3556 22 23 4203 4140 4078 4017 3956 3897 3838 3780 3723 3666 3610 3555 23 24 25 4202 4139 4077 4016 3955 3896 3837 3779 3722 3665 3610 3555 24 0.4201 4138 4076 4015 3954 3895 3836 3778 3721 3664 3609 3554 25 26 4200 4137 4075 4014 3953 3894 3835 3777 3720 3663 3608 3553 26 27 4199 4136 4074 4013 3952 3893 3834 3776 3719 3663 3607 3552 27 28 4198 4135 4073 4012 3951 3892 3833 3775 3718 3662 3606 3551 28 29 30 4197 4134 4072 4011 3950 3891 3832 3774 3717 3661 3605 3550 29 0.4196 4133 4071 4010 3949 3890 3831 3773 3716 3660 3604 3549 30 31 4195 4132 4070 4009 3948 3889 3830 3772 3715 3659 3603 3548 31 32 4194 4131 4069 4008 3947 3888 3829 3771 3714 3658 3602 3547 32 33 4193 4130 4068 4007 3946 3887 3828 3770 3713 3657 3601 3546 33 34 35 4192 4129 4067 4006 3945 3886 3827 3769 3712 3656 3600 3545 34 0.4191 4128 4066 4005 3944 3885 3826 3768 3711 3655 3599 3545 35 [ 36 4189 4127 4065 4004 3943 3884 3825 3768 3710 3654 3598 3544 36 37 4188 4126 4064 4003 3942 3883 3824 3767 3709 3653 3598 3543 37 38 4187 4125 4063 4002 3941 3882 3823 3766 3709 3652 3597 3542 38 39 40 4186 4124 4062 4001 3940 3881 3822 3765 3708 3651 3596 3541 39 0.4185 4122 4061 4000 3939 3880 3821 3764 3707 3650 3595 3540 40 ; 41 4184 4121 4060 3999 3938 3879 3820 3763 3706 3649 3594 3539 41 42 4183 4120 4059 3998 3937 3878 3820 3762 3705 3649 3593 3538 42 43 4182 4119 4058 3997 3936 3877 3819 3761 3704 3648 3592 3537 43 44 45 4181 4118 4056 3996 3935 3876 3818 3760 3703 3647 3591 3536 44 0.4180 4117 4055 3995 3934 3875 3817 3759 3702 3646 3590 3535 45 46 4179 4116 4054 3993 3933 3874 3816 3758 3701 3645 3589 3535 46 47 4178 4115 4053 3992 3932 3873 3815 3757 3700 3644 3588 3534 47 48 4177 4114 4052 3991 3931 3872 3814 3756 3699 3643 3587 3533 48 49 50 4176 4113 4051 3990 3930 3871 3813 3755 3698 3642 3587 3532 49 0.4175 4112 4050 3989 3929 3870 3812 3754 3697 3641 3586 3531 50 51 4174 4111 4049 3988 3928 3869 3811 3753 3696 3640 3585 3530 51 52 4173 4110 4048 3987 3927 3868 3810 3752 3695 3639 3584 3529 52 53 4172 4109 4047 3986 3926 3867 3809 3751 3694 3638 3583 3528 53 54 4171 4108 4046 3985 3925 3866 3808 3750 3693 3637 3582 3527 54 55 0.4169 4107 4045 3984 3924 3865 3807 3749 3693 3636 3581 3526 55 56 4168 4106 4044 3983 3923 3864 3806 3748 3692 3635 3580 3525 56 57 4167 4105 4043 3982 3922 3863 3805 3747 3691 3635 3579 3525 57 58 4166 4104 4U42 3981 3921 3862 3804 3746 3690 3634 3678 3524 58 59 4165 4103 4041 3980 3920 3861 3803 3746 3689 3633 3577 3523 59 J Bl < U K )1 11 [1 n il U tl 14 U If il 16 1 n 1 18 1 19 i TABLE XXXIV • 213 PROPORTIONAL . LOGARITHMS -rr-i 1 / .|< ,,. / o 1 o f " t o / = >l' '1 1 1 1 '1 '/ *. 1 1. m. h. m.lli. m.|l] I. m. b m. h k. m. b I. m. b L. m. h. m.|h. m.|> 1. m. h. m.| 1. ] 1 20 I 21] I 22 1 23 1 24 1 25 1 26 1 27 1 28{] 1 29 1 30 1 31| ( ).3522 .3468 3415 3362 3310 3259 3208 3158 3108 3059 3010 2962 1 3521 3467 3414 3361 3309 3258 32Q7 3157 3107 3058 3009 2062 1 2 3520 3466 3413 3360 3308 3257 3206 3156 3106 3057 3009 2961 •2 3 3519 3465 3412 3359 3307 3256 3205 3155 3105 3056 3008 2960 3 4 5 3518 3464 3411 3358 3306 3255 3204 3154 3105 3056 3007 2959 4 3.3517 3463 3410 3358 3306 3254 3204 3153 3104 3055 3006 2958 5 6 3516 3463 3409 3357 3305 3253 3203 3153 3103 3054 3005 2958 6 7 3515 3462 3408 3356 3304 3253 3202 3152 3102 3053 3005 2957 7 8 3514 3461 3408 3355 3303 3252 3201 3151 3101 3052 3004 2956 8 9 10 3514 3460 3407 3354 3302 3251 3200 3150 3101 3052 3003 2955 9 10 5.3513 3459 3406 3353 3301 3250 3199 3149 3100 3051 3002 2954 11 3512 3458 3405 3352 3300 3249 3198 3148 3099 3050 3001 2954 11 12 3511 3457 3404 3351 3300 3248 3198 3148 3098 3049 3001 2953 12 13 3510 3456 3403 3351 3299 3247 3197 3147 3097 3048 3000 2952 13 14 15 3509 3455 3402 335) 3298 3247 3196 3146 3096 3047 2999 2961 14 0.3508 3454 3401 3349 3297 3246 3195 3145 3096 3047 2998 2950 15 16 3507 3454 3400 3348 3296 3245 3194 3144 3095 3046 2997 2950 16 17 3506 3453 3400 3347 3295 3244 3193 3143 3094 3045 2997 2949 17 18 3506 3452 3399 3346 3294 3243 3193 3143 3093 3044 2996 2948 18 19 20 3505 3451 3398 3345 3294 3242 3192 3142 3092 3043 2995 2947 19 20 0.3504 3450 3397 3345 3293 3242 3191 3141 3091 3043 2994 2946 21 3503 3449 3396 3344 3292 3241 3190 3140 3091 3042 2993 2946 21 22 .3502 3448 3395 3343 3291 3240 3189 3139 3090 3041 2993 2945 22 23 3501 3447 3394 3342 3290 3239 3188 3138 3089 3040 2992 2944 23 24 25 3500 3446 3393 3341 3289 3238 3188 3138 3088 3039 2991 2943 24' 0.3499 3446 3393 3340 3288 3237 3187 3137 3087 3039 2990 2942 25 26 3498 3445 3392 3339 3288 3236 3186 3136 3087 3038 2989 2942 26 27 3497 3444 3391 3338 3287 3236 3185 3135 3086 3037 2989 2941 27 28 3497 3443 3390 3338 3286 3235 3184 3134 3085 3036 2988 2940 28 29 30 3496 3442 3389 3337 3285 3234 3183 3133 3084 3035 2987 2939 29 0.3495 3441 3388 3336 3284 3233 3183 3133 3083 3034 2986 2939 30 31 3494 3440 3387 3335 3283 3232 3182 3132 3082 3034 2985 2938 31 32 3493 3439 3386 3334 3282 3231 3181 3131 3082 3033 2985 2937 32 33 3492 3438 3386 3333 3282 3231 3180 3130 3081 3032 2984 2936 33 34 35 3491 3438 3385 3332 3281 3230 3179 3129 3080 3031 2983 2935 34 0.3490 3437 3384 3332 3280 3229 3178 3129 3079 3030 2982 2935 35 36 3489 3436 3383 3331 3279 3228 3178 3128 3078 3030 2981 2934 36 37 3488 3435 3382 3330 3278 3227 3177 3127 3078 3029 2981 2933 37 38 3488 3434 3381 3329 3277 3226 3176 3126 3077 3028 2980 2932 38 39 40 3487 3433 3380 3328 3276 3225 3175 3125 3076 3027 2979 2931 39 0.3486 3432 3379 3327 3276 3225 3174 3124 3075 3026 2978 2931 40 41 3485 3431 3379 3326 3275 3224 3173 3124 3074 3026 2977 2930 41 42 3484 3431 3378 3325 3274 3223 3173 3123 3073 3025 2977 2929 42 43 3483 3430 3377 3325 3273 3222 3172 3122 3073 3024 2976 2928 43 44 45 3482 3429 3376 3324 3272 3221 3171 3121 3072 3023 2975 2927 44 0.3481 3428 3375 3323 3271 3220 3170 3120 3071 3022 2974 2927 45 46 3480 3427 3374 3322 3270 3220 3169 3119 3070 3022 2973 2926 46 47 3480 3426 3373 3321 3270 3219 3168 3119 3069 3021 2973 2925 47 48 3479 3425 3372 3320 3269 3218 3168 3118 3069 3020 2972 2924 48 49 50 3478 3424 3372 3319 3268 3217 3167 3117 3068 3019 2971 2924 40 50 0.3477 3423 3371 3319 3267 3216 3166 3116 3067 3018 2970 2923 51 3476 3423 3370 3318 3266 3215 3165 3115 3066 3018 2969 2922 51 52 3475 3422 3369 3317 3265 3214 3164 3114 3065 3017 2969 2921 52 53 3474 3421 3368 3316 3265 3214 3163 3114 3065 3016 2968 2920 53 54 55 3473 3420 3367 3315 3264 3213 3163 3113 3064 3015 2967 2920 54 0.3472 3419 3366 3314 3263 3212 3162 3112 3063 3014 2966 2919 55 56 3471 3418 3365 3313 3262 3211 3161 3111 3062 3014 2965 2918 56 57 3471 3417 3365 3313 3261 3210 3160 3110 3061 3013 2965 2917 57 58 3470 3416 3364 3312 3260 3209 3159 3110 3060 3012 2964 2916 58 59 3469 3415 3363 3311 3259 3209 3158 3109 3060 3011 2963 2916 59 1 2( )1 2] 1 2S 1 23 1 2< H 25 1 26 1 27 1 28 1 29 1 30 1 31 214 TABLE XXXIV. PROPORTIONAL LOGARITHMS. - tf e 1 ' c ) ' o ' ( 3 ' O ' |( D ' o ' 1 o ' o ' o ' o ' o ' n 1. b I. m. h m. h. m. 1 1. m. '. 1. m. 1. m. h. m.l h. m. h. m. h. m. h. m. h. m. 1. 1 32|] 33 1 34 1 35 1 36 1 37 1 38j 1 39 1 40 1 41 1 42 1 43 ( ).2915 2868 2821 2775 2730 2685 2640 2596 2553 2510 2467 2424 1 2914 2867 2821 2775 2729 2684 2640 2596 2552 2509 2466 2424 1 2 2913 2866 2821) 2774 2729 2684 2639 2595 2551 2508 2465 2423 2 3 2912 2866 2819 2773 2728 2683 2638 2594 2551 2507 2465 2422 3 4 5 2912 2865 2818 2772 2727 2682 2638 2593 2550 2507 2464 2422 4 5 3.2911 2864 2818 2772 2726 2681 2637 2593 2549 2506 2463 2421 6 2910 2863 2817 2771 2725 2681 2636 2592 2548 2505 2462 2420 6 7 2909 2862 2816 2770 2725 2680 2635 2591 2548 2504 2462 2419 7 8 2909 2862 2815 2769 2724 2679 2635 2591 2547 2504 2461 2419 ■ 8 9 10 2908 2861 2815 2769 2723 2678 2634 2590 2546 2503 2460 2418 9 0.2907 2860 2814 2768 2722 2678 2633 2589 2545 2502 2460 2417 10 11 2906 2859 2813 2767 2722 2677 2632 2588 2545 2502 2459 2417 11 12 2905 2859 2812 2766 2721 2676 2632 2588 2544 2501 2458 2416 12 13 2905 2858 2811 2766 2720 2675 2631 2587 2543 2500 2458 2415 13 14 15 2904 2857 2811 2765 2719 2675 2630 2586 2543 2499 2457 2415 14 15 0.2903 2856 2810 2764 2719 2674 2629 2585 2542 2499 2456 2414 16 2902 2855 2809 2763 2718 2673 2629 2585 2541 2498 2455 2413 16 17 2901 2855 2808 2763 2717 2672 2628 2584 2540 2497 2455 2412 17 18 2901 2854 2808 2762 2716 2672 2627 2583 2540 2497 2454 2412 18 19 20 2900 2853 2807 2761 2716 2671 2626 2583 2539 2496 2453 2411 19 20 0.2899 2852 2806 2760 2715 2670 2626 2582 2538 2495 2453 2410 21 2898 2852 2805 2760 2714 2669 2625 2581 2538 2494 2452 2410 21 22 2898 2851 2805 2759 2713 2669 2624 2580 2537 2494 2451 2409 22 23 2897 2850 2804 2758 2713 2668 2624 2580 2536 2493 2450 2408 23 24 25 2896 2849 2803 2757 2712 2667 2623 2579 2535 2492 2450 2408 24 25 0.2895 2848 2802 2756 2711 2666 2622 2578 2535 2492 2449 2407 26 2894 2848 2801 2756 2710 2666 2621 2577 2534 2491 2448 2406 26 27 2894 2847 2801 2755 2710 2665 2621 2577 2533 2490 2448 2405 27 28 2893 2846 2800 2754 2709 2664 2620 2576 2533 2489 2447 2405 28 29 30 2892 2845 2799 2753 2708 2663 2619 2575 2532 2489 2446 2404 29 30 0.2891 2845 2798 2753 2707 2663 2618 2574 2531 2488 2445 2403 31 2891 2844 2798 2752 2707 2662 2618 2574 2530 2487 2445 2403 31 32 2890 2843 2797 2751 2706 2661 2617 2573 2530 2487 2444 2402 32 33 2889 2842 2796 2750 2705 2660 2616 2572 2529 2486 2443 2401 33 34 35 2888 2842 2795 2750 2704 2660 2615 2572 2528 2485 2443 2401 34 35 0.2888 2841 2795 2749 2704 2659 2615 2571 2527 2485 2442 2400 36 2887 2840 2794 2748 2703 2658 2614 2570 2527 2484 2441 2399 36 37 2886 2839 2793 2747 2702 2657 2613 2569 2526 2483 2441 2398 37 38 2885 2838 2792 2747 270] 2657 2612 2569 2525 2482 2440 2398 38 39 40 2884 2838 2792 2746 2701 2656 2612 2568 2525 2482 2439 2397 39 40 0.2883 2837 2791 2745 2700 2655 2611 2567 2524 2481 2438 2396 41 2883 2836 2790 2744 2699 2655 2610 2566 2523 2480 2438 2396 41 42 2882 2835 2789 2744 2698 2654 2610 2566 2522 2480 2437 2395 42 43 2881 2835 2788 2743 2698 2653 2609 2565 2522 2479 2436 2394 43 44 45 2880 2834 2788 2742 2697 2652 2608 2564 2521 2478 2436 2394 44 0.2880 2833 2787 2741 2696 2652 2607 2564 2520 2477 2435 2393 45 46 2879 2832 2786 2741 2695 2651 2607 2563 2520 2477 2434 2392 46 ' 47 2878 2831 2785 2740 2695 2650 2606 2562 2519 2476 2433 2391 47 48 2877 2831 2785 2739 2694 2649 2605 2561 2518 2475 2433 2391 48 49 50 2876 2830 2784 2738 2693 2649 2604 2561 2517 2475 2432 2390 49 0.2876 2829 2783 2738 2692 2648 2604 2560 2517 2474 2431 2389 50 51 2875 2828 2782 2737 2692 2647 2603 25.59 2516 2473 2431 2389 51 52 2874 2828 2782 2736 2691 2646 2602 2559 2515 2472 2430 2388 52 53 2873 2827 2781 2735 2690 2646 2601 2558 2515 2472 2429 2387 53 54 55 2873 2826 2780 2735 2689 2645 2601 2557 2514 2471 2429 2387 54 55 lo.2872 2825 2779 2734 2689 2644 2600 2556 2513 2470 2428 2386 56 2871 2825 2779 2733 2688 2643 2599 2556 2512 2470 2427 2385 56 57 2870 2824 2778 2732 2687 2643 2599 2555 2512 2469 2426 2384 57 58 2869 2823 2777 2732 2687 2642 2598 2554 2511 2468 2426 2384 58 59 2869 2822 2776 2731 2686 2641 2597 2553 2510 2467 2425 2383 59 1 32 1 33 1 34 1 35 1 36 1 37 1 38 1 39 1 40 1 41 1 42 1 43 215 TABLE XXXIV. PROPORTIONAL LOGARITHMS. 1. 1 > 1 * \. m. I m. 3 f [I. ni. ' ti. m. 3 ' ti. ra. 1. m. 1. m. O f h. ra. O ( h. in. • r h. m. h. m. ti. m. ■. I 44 I 45 1 46 1 47 1 48 1 49 1 50 1 51 1 52 1 53 I 54 1 55 J. 2382 2341 2300 2259 2218 2178 2139 2099 2061 2022 1984 1946 1 23SJ 2340 2299 2258 2218 2178 2138 2099 2060 2021 1983 1945 1 2. 2381 2339 2298 2258 2217 2177 2137' 2098 2059 2021 1982 1944 2 3 2380 2339 2298 2257 2216 2176 2137 2098 2059 2020 1982 1944 3 4 5 2380 2338 2297 2256 2216 2176 2136 2097 2058 2019 1981 1943 4 5 0.2379 2337 22J6 2256 2215 2175 2136 2U96 2057 2019 1981 1943 b 2378 2337 2296 2255 2214 2174 2135 2096 2057 2018 1980 1942 6 7 2378 2336 2295 2254 2214 2174 2134 2095 2056 2017 1979 1941 7 8 2377 2335 2294 2253 2213 2173 2134 2094 2055 2017 1979 1941 8 9 10 2376 2335 2294 2253 2212 2172 2133 2094 2055 2016 1978 1940 9 10 0.2375 2334 2293 2252 2212 2172 2132 2093 2054 2016 1977 1939 11 2375 2333 2292 2251 2211 2171 2132 2092 2053 2015 1977 1939 11 12 2374 2333 2291 2251 2210 2170 2131 2092 2053 2014 1966 1938 12 13 2373 2332 2291 2250 2210 2170 2130 2091 2052 2014 1975 1938 13 14 15 2373 2331 2290 2249 2209 2169 2130 2090 2052 2013 1975 1937 14 15 0.2372 2331 2289 2249 2208 2169 2129 2090 2051 2012 1974 1936 16 2371 2330 2289 2248 2208 2168 2128 2089 2050 2012 1974 1936 16 17 2371 2329 2288 2247 2207 2167 2128 2088 2050 2011 1973 1935 17 18 2370 2328 2287 2247 2206 2167 2127 2088 2049 2010 1972 1934 18 19 20 2369 2328 2287 2246 2206 2166 2126 2087 2048 2010 1972 1934 19 20 0.2368 2327 2286 2245 2205 2165 2126 2086 2048 2009 1971 1933 21 2368 2326 2285 2245 2204 2165 2125 2086 2047 2009 1970 1933 21 22 2367 2326 2285 2244 2204 2164 2124 2085 2046 2008 1970 1932 22 23 2366 2325 2284 2243 2203 2163 2124 2085 2046 2007 1969 1931 23 24 25 2366 2324 2283 2243 2202 2163 2123 2084 2045 2007 1968 1931 24 25 0.2365 2324 2283 2242 2202 2162 2122 2083 2044 2006 1968 1930 26 2364 2323 2282 2241 2201 2161 2122 2083 2044 2005 1967 1929 26 27 2364 2322 2281 2241 2200 2161 2121 2082 2043 2005 1967 1929 27 28 2363 2322 2281 2240 2200 2160 2120 20C1 2042 2004 1966 1928 28 29 30 2362 2321 2280 2239 2199 2159 2140 2081 \ 2042 2003 1965 1928 29 30 0.2362 2320 2279 2239 2198 2159 2119 2080 2041 2003 1965 1927 31 2361 2320 2279 2238 2198 2158 2] 18 2179 2041 2002 1964 1926 31 32 2360 2319 2278 2237 2197 2157 2118 2079 2040 2001 19j63 1926 32 33 2359 2318 2277 2237 2196 2157 2117 2078 2039 2001 1963 1925 33 34 35 2359 2317 2277 2236 2196 2156 2116 2077 2039 2000 1962 1924 34 0.2358 2317 2276 2235 2195 2155 2116 2077 2038 2000 1962 1924 35 36 2357 2316 2275 2235 2194 2155 2115 2076 2037 1999 1961 1923 36 37 2357 2315 2274 2234 2194 2154 2115 2075 2037 1998 1960 1923 37 38 2356 2315 2274 2233 2193 2153 2114 2073 2036 1998 1960 1922 38 39 40 2355 2314 2273 2233 2192 2153 2113 2074 2035 1997 1959 1921 39 40 0.2355 2313 2272 2232 2192 2152 2113 2073 2035 1996 1958 1921 41 2354 2313 2272 2231 2191 2151 2112 2073 2034 1996 1958 1920 41 42 2353 2312 2271 2231 2190 2151 2111 2074 2033 1995 1957 1919 42 43 2353 2311 2270 2230 2190 2150 2111 2072 2033 1994 1956 1919 43 44 45 2352 2311 2270 2229 2189 2149 2110 2071 2032 1994 1956 1918 44 45 0.2351 2310 2269 2229 2188 2149 2109 2070 2032 1993 1955 1918 46 2350 2309 2268 2228 2188 2148 2109 2070 2031 1993 1955 1917 46 47 2350 2309 2268 2227 2187 2147 2108 2069 2030 1992 1954 1916 47 48 2349 2308 2267 2227 2186 2147 2107 2068 2030 1991 1953 1916 48 49 ^ 50 2348 2307 2266 2226 2186 2146 2107 2068 2029 1991 1953 1915 49 50 0.2348 2307 2266 2225 2185 2145 2106 2067 2028 1990 1952 1914 51 2347 2306 2265 2225 2184 2145 2105 2066 2028 1989 1951 1914 51 , 52 2346 6305 2264 2224 2184 2144 2105 2066 2027 1989 1951 1913 52 53 2346 2304 2264 2223 2183 2143 2104 2065 2026 1988 1950 1913 53 54 55 2345 2304 2263 2223 2182 2143 2103 2064 2026 1987 1950 1912 54 55 0.2344 2303 226-2 2222 2182 2142 2103 2064 2025 1987 1949 1911 56 2344 2302 2262 2221 2181 2141 2102 2063 2025 1986 1948 1911 56 57 2343 2302 2261 2220 2180 2141 2101 2062 2024 1986 1948 1910 57 58 2342 2301 2260 2220 2180 2140 2101 2062 2023 1985 1947 1909 58 i 59 2342 2300 2260 2219 2179 2139 2100 2061 2023 1984 1946 1909 59 1 44 1 45 1 46 1 47 1 48 1 49 1 50 1 51 1 52 1 53 1 54 1 55 TABLE XXXTV. PROPORTIONAL LOGARITHMS I '/ c } ( D ' 3 ' r. O ' O ' 1 o ' o ' o ' o ' o ' J) ' n •. 1 I. m. . 1. m. ti. m. b. m.l 1. m. h. m. h. m. 1. xa. 1. m. h. m. h. m. h. m. %. ] I 56 I 57 1 581 59| 2 2 1 2 2 2 3|2 4|2 5|2 6| 2 7 ( ).1908 1871 1834 1797 1761 1725 1689 1654 1619 1584 1549 1515 1 1908 1870 1833 1797 1760 1724 1689 1653 1618 1583 1548 1514 1 2 1907 1870 1833 1796 1760 1724 1688 1652 1617 1582 1548 1514 2 3 1906 186^» 1832 1795 1759 1723 1687 1652 1617 1582 1547 1513 3 4 5 ( 1906 1868 1831 1795 1759 1722 1687 1651 1616 1581 1547 1512 4 3.1905 1868 1831 1794 1758 1722 1686 1651 1616 1581 1546 1512 6 6 1904 1867 1830 1794 1757 1721 1686 1650 1615 1580 1546 1511 6 7 1904 1867 1830 1793 1757 1721 1685 1650 1614 1580 1545 1511 7 8 1903 1866 1829 1792 1756 1720 1684 1649 1614 1579 1544 1510 8 9 10 1903 1865 1828 1792 1755 1719 1684 1648 1613 1578 1544 1510 9 3.1902 1865 1828 1791 1755 1719 1683 1648 1613 1578 1543 1509 10 11 1901 1864 1827 1791 1754 1718 1683 1647 1612 1577 1543 1508 11 12 1901 1863 1827 1790 1754 1718 1682 1647 1612 1577 1542 1508 12 13 1900 1863 1826 1789 1753 1717 1681 1646 1611 1576 1542 1507 13 14 15 1899 1862 1825 1789 1752 1717 1681 1645 1610 1576 1541 1507 14 0.1899 1862 1825 1788 1752 1716 1680 1645 1610 1575 1540 1506 15 16 1898 1861 1824 1788 1751 1715 1680 1644 1609 i574 1540 1506 16 17 1898 1860 1823 1787 1751 1715 1679 1644 1609 1574 1539 1505 17 18 1897 1860 1823 1786 1750 1714 1678 1643 1608 1573 1539 1504 18 19 20 1896 1859 1822 1786 1749 1714 1678 1643 1607 1573 1538 1504 19 20 0.1896 1859 1822 1785 1749 1713 1677 1642 1607 1572 1538 1503 21 1895 1858 1821 1785 1748 1712 1677 1641 1606 1571 1537 1503 21 22 1894 1857 1820 1784 1748 1712 1676 1641 1606 1571 1536 1502 22 23 1894 1857 1820 1783 1747 1711 1676 1640 1605 1570 1536 1502 23 24 25 1893 1856 1819 1783 1746 1711 1675 1640 1605 1570 1535 1501 24 0.1893 1855 1819 1782 1746 1710 1675 1639 1604 1569 1535 1500 25 26 1892 1855 1818 1781 1745 1709 1674 1638 1603 1569 1534 1500 26 27 1891 1854 1818 1781 1745 1709 1673 1638 1603 1568 1534 1499 27 28 1891 1854 1817 1780 1744 1708 1673 1637 1602 1567 1533 1499 28 29 30 1890 1853 1816 1780 1743 1708 1672 1637 1602 1567 1532 1498 29 0.1889 18.52 1816 1779 1743 1707 1671 1636 1601 1566 1532 1498 30 31 1889 1852 1815 1778 1742 1706 1671 1635 1600 1566 1531 1497 31 32 1888 1851 1814 1778 1742 1706 1670 1635 1600 1565 1531 1496 32 33 1888 1850 1814 1777 1741 1705 1670 1634 1599 1565 1530 1496 33 34 35 1887 1850 1813 1777 1740 1705 1669 1634 1599 1564 1530 1495 34 0.1886 1849 1812 1776 1740 1704 1668 1633 1598 1563 1529 1495 35 36 1886 1849 1812 1775 1739 1703 1668 1633 1598 1563 1528 1494 36 37 1885 1848 1811 1775 1739 1703 1667 1632 1597 1562 1528 1494 37 38 1884 1847 1811 1774 1738 1702 1667 1631 1596 1562 1527 1493 38 39 40 1884 1847 1810 1774 1737 1702 1666 1631 1596 1561 1527 1493 39 40 0.1883 1846 1809 1773 1737 1701 1665 1630 1595 1561 1526 1492 41 1883 1846 1809 1772 1736 1700 1665 1630 1595 1560 1526 1491 41 42 1882 1845 1808 1772 1736 1700 1664 1629 1594 1559 1525 1491 42 43 1881 1844 1808 1771 1735 1699 1664 1628 1593 1559 1524 1490 43 44 45 1881 1844 1807 1771 5734 1699 1663 1628 1593 1558 1524 1490 44 45 0.1 88C 1843 1806 1770 1734 1698 1663 1627 1592 1558 1523 1489 46 1880 1843 1806 1769 1733 1697 1662 1627 1592 1557 1523 1489 46 47 1879 1842 1805 1769 1733 1697 1661 1626 1591 1556 1522 1488 47 48 1878 1841 1805 1768 1732 1696 1661 1626 1591 1556 1522 1487 48 49 50 1878 1841 1804 1768 1731 1696 1660 1625 1590 1555 1521 1487 49 50 0.1877 1840 1803 1767 1731 1695 1660 1624 1589 1555 1520 1486 51 1876 1839 1803 1766 1730 1694 1659 1624 1589 1554 1520 1486 51 52 1876 1839 1802 1766 1730 1694 1658 1623 1588 1554 1519 1485 52 53 1875 1838 1802 1765 1729 1693 1658 1623 1588 1553 1519 1h85 53 54 55 1875 1838 1801 1765 1728 1693 1657 1622 1587 1552 1518 1484 64 0.1874 1837 1800 1764 1728 1692 1657 1621 1587 1552 1518 1483 55 56 1873 1836 1800 1763 1727 1692 1656 1621 1586 1551 1517 1483 56 57 1873 1836 1799 1763 1727 1691 1655 1620 1585 1551 1516 1482 57 58 1872 1835 1798 1762 1726 1690 1655 1620 1585 1550 1516 1482 58 59 1871 1835 1798 1762 1725 1690 1654 1619 1584 1550 1515 1481 59 1 5( 31 5' n 5J Bl 5[ )2 ( )2 1 2 i 2 3 2 4 2 5 2 6 2 7 1 __ TABLE XXXIV. ..17 PROPORTIONAL LOGARITHMS • If ( > / o ' o ' 3 ' 3 ' o ' o t o ' o ' o ' o ' o ' o n 1 i< m. h. m. h. m. 1. m. 1. ra. h. ra. h. m. h. ra h. m. h. ra. h. m. h. m. h. ni. s. I 82 92 10 2 11 2 12 2 13 2 14|2 i5 2 162 17 2 18 2 19 2 20 0.1481 1447 1413 138U 1347 1314 1282 1249 1217 1186 1154 1123 1091 1 1480 1446 1413 1379 1346 1314 1281 1249 1217 1185 1153 1122 1091 1 2 1479 1446 1412 1379 1346 1313 1281 1248 1216 1184 1153 1 1 22 1090 2 3 1479 1445 1412 1378 1345 1313 1280 1248 1216 1184 1152 1121 1090 3 4 1478 1445 1411 1378 1345 1312 1280 .1247 1215 1183 1152 1120 1089 4 5 0.1478 1444 1411 1377 1344 1311 1279 1247 1215 1183 1151 1120 1089 5 6 1477 1443 1410 1377 1344 1311 1278 1246 1214 1182 1151 1119 1088 6 7 1477 1443 1409 1376 1343 1310 1278 1246 1214 1182 1150 1119 1088 7 8 1476 1442 1409 1376 1343 1310 1277 1245 1213 1181 1150 .1118 1087 8 9 1476 1442 1408 1375 1342 1309 1277 1245 1213 1181 1149 1118 1087 9 10 0.1475 1441 1408 1374 1342 1309 1276 1244 1212 1180 1149 1117 1086 10 11 1474 1441 1407 1374 1341 1308 1276 1243 1211 1180 1148 1117 1086 11 12 1474 1440 1407 1373 1340 1308 1275 1243 1211 1179 1148 1116 1085 12 13 1473 1440 1406 1373 1340 1307 1275 1242 1210 1179 1147 1116 1085 13 14 1473 1439 1406 1372 1339 1307 1274 1242 1210 1178 1147 1115 1084 14 15 0.1472 1438 1405 1372 1339 1306 1274 1241 1209 1178 1146 1115 1084 15 16 1472 1438 1404 1371 1338 1306 1273 1241 1209 1177 1146 1114 1083 16 17 1471 1437 1404 1371 1338 1305 1273 1240 1208 1177 1145 1114 1083 17 18 1470 1437 1403 1370 1337 1304 1272 1240 1208 1176 1145 1113 1082 18 19 1470 1436 1403 1370 1337 1304 1271 1239 1207 1175 1144 1113 1082 19 20 0.1469 1436 1402 1369 1336 1303 1271 1239 1207 1175 1143 1112 1081 20 21 1469 1435 1402 1368 1335 1303 1270 1238 1206 1174 1143 1112 1081 21 22 1468 1435 1401 1368 1335 1302 1270 1238 1206 1174 1142 1111 1080 22 23 1468 1434 1401 1367 1334 1302 1269 1237 1205 1173 1142 nil 1080 23 24 1467 1433 1400 1367 1334 1301 1269 1237 1205 1173 1141 1110 1079 24 25 0.1467 1433 1399 1366 1333 1301 1268 1236 1204 1172 1141 1110 1079 25 26 1466 1432 1399 1366 1333 1300 1268 1235 1204 1172 1140 1109 1078 26 27 1465 1432 1398 1365 1332 1300 1267 1235 1203 1171 1140 1109 1078 27 28 1465 1431 1398 1365 1332 1299 1267 1234 1202 1171 1139 1108 1077 28 29 1464 1431 1397 1364 1331 1298 1266 1234 1202 1170 1139 1108 1076 29 30 0.1464 1430 1397 1363 1331 1298 1266 1233 1201 1170 1138 1107 1076 30 31 1463 1429 1396 1363 1330 1297 1265 1233 1201 1169 1138 1106 1075 31 32 1463 1429 1396 1362 1329 1297 1264 1232 1200 1169 1137 1106 1075 32 33 1463 1428 1395 1362 1329 1296 1264 1232 1200 1168 1137 1105 1074 33 34 1461 1428 1394 1361 1328 1296 1263 1231 1199 1168 1136 1105 1074 34 35 0.1461 1427 1394 1361 1328 1295 1263 1231 1199 1167 1136 1104 1073 35 36 1460 1427 1393 1360 1327 1295 1262 1230 1198 1167 1135 1104 1073 36 37 1460 1426 1393 1360 1327 1294 1262 1230 1198 1166 1135 1103 1072 37 38 1459 1426 1392 1369 1326 1294 1261 1229 1197 1165 1134 1103 1072 38 39 1459 1425 1392 1359 1326 1293 1261 1229 1197 1165 1134 1102 1071 39 40 0.1458 1424 1391 1358 1325 1292 1260 1228 1196 1164 1133 1102 1071 40 41 1458 1424 1391 1357 1325 1292 1260 1227 1196 1164 1132 1101 1070 41 42 1457 1423 1390 1357 1324 1291 1259 1227 1195 1163 1132 1101 1070 42 43 1456 1423 1389 1356 1323 1291 1259 1226 1195 1163 1131 1100 1069 43 44 1456 1422 1389 1356 1323 1290 1258 1226 1194 1162 1131 1100 1069 44 45 0.1455 1422 1388 1355 1322 1290 1257 1225 1193 1162 1130 1099 1068 45 46 1455 1421 1388 1355 1322 1289 1257 1225 1193 1161 1130 1099 1068 46 47 1454 1421 1387 1354 1321 1289 1256 1224 1192 1161 1129 1098 1067 47 48 1454 1420 1387 1354 1321 1288 1256 1124 1192 1160 1129 1098 1067 48 49 1453 1419 1386 1353 1320 1288 1255 1223 1191 1160 1128 1097 1066 49 50 0.1452 1419 1386 1352 1320 1287 1255 1223 1191 1159 1128 1097 1066 50 51 1452 1418 1385 1352 1319 1287 1254 1222 1190 1159 1127 1096 1065 51 52 1451 1418 1384 1351 1319 1286 1254 1222 1190 1158 1127 1096 1065 52 53 1451 1417 1384 1351 1318 1285 1253 1221 1189 1158 1126 1095 1064 53 54 1450 1417 1383 1350 1317 1285 1253 1221 1189 1157 1126 1095 1064 54 55 0.1450 1416 1383 1350 1317 1284 1252 1220 1188 1157 1125 1094 1063 55 56 1449 1416 1382 1349 1316 1284 1252 1219 1188 1156 1125 1094 1063 56 57 1449 1415 1382 1349 1316 1283 1251 1219 1187 1156 1124 1093 1062 57 58 1448 1414 1381 1348 1315 1283 1250 1218 1187 1155 1124 1092 1062 58 59 1447 1414 1381 1348 1315 1282 1250 1218 1186 1154 1123 1092 1061 59 2 8 2 9 2 10 1 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 182 19 2 20 218 TABLE XXXIV PROPORTIONAL LOGARITHMS. // c » ' ,0 ' |0 ' \0 ' lO 'I ' o ' o / o ' o ' o ' o ' o ' ff a. h. m. h. m. h. m. 1. m. h. m. \. m. h. m. h. m. h. m. h. m. h. m. h. m. h. m. a. 2 212 22 2 23 i 24 2 25 2 26 2 27 2 28 2 29 2 30 2 312 32 2 33 ( 3.1061 1030 0999 0969 0939 0909 0880 0850 0821 0792 0763 0734 0706 1 1060 1029 0999 0969 0939 0909 0879 0850 0820 0791 0762 0734 0705 1 2 1060 1029 0998 0968 0938 0908 0879 0849 0820 0791 0762 0733 0705 8 3 1059 1028 0998 0968 0938 0908 0878 0849 0819 0790 0762 0733 0704 1 4 1058 1028 0997 0967 0937 0907 0878 0848 0819 0790 0761 0761 0732 0704 4 5 9.1058 1027 0997 0967 0937 0907 0877 0848 0818 0789 0732 0703 5 6 1057 1027 0996 0966 0936 0906 0877 0847 0818 0789 0760 0731 0703 6 7 1057 1026 0996 0966 0936 0906 0876 0847 0817 0788 0760 0731 0703 7 8 1056 1026 0995 0965 0935 0905 0876 0846 0817 0788 0759 0730 0702 8 9 1056 1025 0995 0965 0935 0905 0875 0846 0816 0787 0759 0730 0702 9 10 0.1055 1025 0994 0964 0934 0904 0875 0845 0816 0787 0758 0730 0701 10 11 1055 1024 0994 0964 0934 0904 0874 0845 0816 0787 0758 0729 0701 11 12 1054 1024 0993 0963 0933 0903 0874 0844 0815 0786 0757 0729 0700 12 13 1054 1023 0993 0963 0933 0903 0873 0844 0815 0786 0757 0728 0700 13 14 1053 1023 0992 0962 0932 0902 0873 0843 0814 0785 0756 0728 0699 14 15 0.1053 1022 0992 0962 0932 0902 0872 0843 0814 0785 0756 0727 0699 15 16 1052 1022 0991 0961 0931 0901 0872 0842 0813 0784 0755 0727 0698 16 17 1052 1021 0991 0961 0931 0901 0871 0842 0813 0784 0755 0726 0698 17 18 1051 1021 0990 0960 0930 0900 1871 0841 0812 0783 0754 0726 0697 18 19 1051 1020 0990 0960 0930 0900 0870 0841 0812 0783 0754 0725 0697 19 20 0.1050 1020 0989 0959 0929 0899 0870 0840 0811 0782 0753 0725 0696 20 21 1050 1019 0989 0959 0929 0899 0869 0840 0811 0782 0753 0724 0696 21 22 1049 1019 0988 0958 0928 0898 0869 0839 0810 0781 0752 0724 0695 22 23 1049 1018 0988 0958 0928 0898 0868 0839 0810 0781 0752 0723 0695 23 24 1048 1018 0987 0957 0927 0897 0868 0838 0809 0780 0751 0723 0694 24 25 0.1048 1017 0987 0957 0927 0897 0867 0838 0809 0780 0751 0722 0694 25 26 1047 1017 0986 0956 0926 0896 0867 0837 0808 0779 0751 0722 0694 26 27 1047 1016 0986 0956 0926 0896 0866 0837 0808 0779 0750 0721 0693 27 28 1046 1016 0985 0955 0925 0895 0866 0836 0807 0778 0750 0721 0693 28 29 1046 1015 0985 0955 0925 0895 0865 0836 0807 0778 0749 0721 0692 29 30 0.1045 1015 0984 0954 0924 0894 0865 0835 0806 0777 0749 0720 0692 30 31 1045 1014 0984 0954 0924 0894 0864 0835 0806 0777 0748 0720 0691 31 32 1044 1014 0983 0953 0923 0893 0864 0834 0805 0776 0748 0719 0691 32 33 1044 1013 0983 0953 0923 0893 0863 0834 0805 0776 0747 0719 0690 33 34 1043 1013 0982 0952 0922 0892 0863 0834 0804 0775 0747 0718 0690 34 35 0.1043 1012 0982 0952 0922 0892 0862 0833 0804 0775 0746 0718 0689 35 36 1042 1012 0981 0951 0921 0891 0862 0833 0803 0774 0746 0717 0689 36 37 1042 1011 0981 0951 0921 0891 0861 0832 0803 0774 0745 0717 0688 37 38 104l| 1011 0980 0950 0920 0890 0861 0832 0802 0774 0745 0716 0688 38 39 1041 1010 0980 0950 0920 0890 0860 0831 0802 0773 0744 0716 0687 39 40 0.1040 1009 0979 0949 0919 0889 0860 0831 0801 0773 0744 0715 0687 40 41 1040 1009 0979 0949 0919 0889 0859 0830 0801 0772 0743 0715 0686 41 42 1039 1008 0978 0948 0918 0888 0859 0830 0801 0772 0743 0714 0686 42 43 1039 1008 0978 0948 0918 0888 0858 0829 0800 0771 0742 0714 0686 43 44 1038 1007 0977 0947 0917 0887 0858 0829 0800 0771 0742 0713 0685 44 45 0.1037 1007 0977 0947 0917 0887 0857 0828 0799 0770 0741 0713 0685 45 46 1037 1006 0976 0946 0916 0886 0857 0828 0799 0770 0741 0712 0684 46 47 1036 1006 0976 0946 0916 0886 0856 0827 0798 0769 0740 0712 0684 47 48 1036 1005 0975 0945 0915 0885 0856 0827 0798 0769 0740 0711 0683 48 49 1036 1005 0975 0945 0915 0885 0855 0826 0797 0768 0740 0711 0683 49 50 0.103£ 1004 0974 0944 0914 0884 0855 0826 0797 0768 0739 0711 0682 50 51 1034 1004 0974 0944 0914 0884 0855 0825 0796 0767 0739 0710 0682 51 52 1034 [ 1003 0973 0943 0913 0883 0854 0825 0796 0767 0738 0710 0681 52 53 1033 1003 0973 0943 0913 0883 0854 0824 0795 0766 0738 0709 0681 53 54 1033 1002 0972 0942 0912 0883 0853 0824 0795 0766 0737 0709 0680 54 55 0.1032 1002 0972 0942 0912 0882 0853 0823i 0794 0765 0737 0708 0680 55 56 1032 1001 0971 0941 0911 0882 0852 0823 0794 0765 0736 0708 0679 56 57 1031 1001 0971 0941 0911 0881 0852 0822 0793 0764 0736 0707 0679 57 58 1031 1000 0970 0940 0910 0881 0851 0822 0793 0764 0735 0707 0678 58 59 103C 1000 0970 0940 0910 0880 0851 0821 0792 0763 0735 0706 0678 59 2 21 2 22 2 23 2 24 2 25 2 26 2 27 2 28 2 29 2 30 2 31 2 32 2 33 J 219 TABLE XXXIV. PROPORTIONAL LOGARITHMS. It ' O ' O ' O ' |0 ' |0 ' |o '1 D ' 3 ' O ' ' ' ' ti s. h in, h. m. h> m. li I. m.hi I. m.lh. m. t 1. m. li. m. 1 ti. m. h. m. d. m. K. m. h. ni. 1. 2 \ 342 35 2 36 2 37|2 38(2 39|2 40|2 4l{ 2 42 2 43 2 44 2 45 2 46 ( ).0678 0649 0621 0594 0566 0539 0512 0484 0458 0431 0404 0378 0352 1 0677 0649 0621 0593 0566 0538 05L1 0484 0457 0430 0404 0377 0351 1 2 0677 0648 0621 0593 0565 0538 0511 0484 0457 0430 0403 0377 0351 2 3 0676 0648 0620 0592 0565 0537 0510 0483 0456 0430 0403 0377 0350 3 4 0676 0648 0620 0592 0564 0537 0510 0483 0456 0429 0403 0376 0350 4 5 ( ).0675 0647 0619 0591 0564 0536 0509 0482 0455 0429 0402 0376 0349 5 6 0675 0647 0619 0591 0563 0536 0509 0482 0455 0428 0402 0375 0349 6 7 0674 0646 0618 0591 0563 0536 0508 0481 0454 0428 0401 0375 0349 7 8 0674 0646 0618 0590 0562 0535 0508 0481 0454 0427 0401 0374 0348 8 9 0673 0645 0617 0590 0562 0535 0507 0480 0454 0427 0400 0374 0348 9 10 1 5.0673 0645 0617 0589 0562 0534 0507 0480 0453 0426 0400 0374 0347 10 11 0672 0644 0616 0589 0561 0534 0507 0480 0453 0426 0399 0373 0347 11 12 0672 0644 0616 0588 0561 0533 0506 0479 0452 0426 0399 0373 0346 12 13 0671 0643 0615 0588 0560 0533 0506 0479 0452 0425 0399 0372 0346 13 14 0671 0643 0615 0587 0560 0532 0505 0478 0351 0425 0398 0372 0346 14 15 0.0670 0642 0615 0587 0559 0532 0505 0478 0451 0424 0398 0371 0345 15 16 0670 0642 0614 0586 0559 0531 0504 0477 0450 0424 0397 0371 0345 16 17 0670 0641 0614 0586 0558 0531 0504 0477 0450 0423 0397 0370 0344 17 18 0669 0641 0613 0585 0558 0531 0503 0476 0450 0423 0396 0370 0344 18 19 0669 0641 0613 0585 0557 0530 0503 0476 0449 0422 0396 0370 0343 19 20 0.0668 0640 0612 0585 0557 0530 0502 0475 0449 0422 0395 0369 0343 20 21 0668 0640 0612 0584 0557 0529 0502 0475 0488 0422 0395 0369 0342 21 22 0667 0639 9611 0584 0556 0529 0502 0475 0448 0421 0395 0368 0342 22 23 0667 0639 0611 0583 0556 0528 0501 0474 0447 0421 0394 0368 0342 23 24 0666 0638 0610 0583 0555 0528 0501 0474 0447 0420 0394 0367 0341 24 25 0.0666 0638 0610 0582 0555 0527 0500 0473 0446 0420 0393 0367 0341 25 26 0665 0637 0609 0582 0554 0527 0500 0473 0246 0419 0393 0366 0340 26 27 0665 0637 0609 0581 0554 0526 0499 0472 0446 0419 0392 0366 0340 27 28 0664 0636 0609 0581 0553 0526 0499 0472 0445 0418 0392 0366 0339 28 29 0664 0636 0608 0580 0553 0526 0498 0471 0445 0418 0392 0365 0339 29 30 0.0663 0635 0608 0580 0552 0525 0498 0471 0444 0418 0391 0365 0339 30 31 0663 0635 0607 0579 0552 0525 0498 0471 0444 0417 0391 0364 0338 31 32 0663 0634 0607 0579 0552 0524 0497 0470 0443 0417 0390 0364 0338 32 33 0662 0634 0606 0579 0551 0524 0497 0470 0443 0416 0390 0363 0337 33 34 0662 0634 0606 0578 0551 0523 0496 0469 0442 0416 0389 0363 0337 34 35 0.0661 0633 0605 0578 0550 0523 0496 0469 0442 0415 0389 0363 0336 35 36 0661 0633 0605 0577 0550 0522 0495 0468 0442 0415 0388 0362 0336 36 37 0660 0632 0604 0577 0549 0522 0495 0468 0441 0414 0388 0362 0336 37 38 0660 0632 0604 0576 0549 0521 0494 0467 0441 0414 0388 0361 0335 38 39 0659 0631 0603 0576 0548 0521 0494 0467 0440 0414 0387 0361 0335 39 40 0.0659 0631 0603 0575 0548 0521 0493 0466 0440 0413 0387 0360 0334 40 41 0658 0630 0602 0575 0547 0520 0493 0466 0439 0413 0386 0360 0334 41 42 0658 0630 0602 0574 0547 052t) 0493 0466 0439 0412 0386 0359 0333 42 43 0657 0629 0602 0574 0546 0519 0492 0465 0438 0412 0385 0359 0333 43 44 0657 0629 0601 0573 0546 0519 0492 0465 0438 0411 0385 0359 0333 44 45 0.0656 0628 i 0601 0573 0546 0518 0491 0464 0438 0411 0384 0358 0332 45 46 0656 . 0628 ! 060C 0573 0545 0518 0491 0464 0437 0410 0384 0358 0332 46 47 065c > 0628 i 060C 0572 0545 0517 049C 0463 0437 0410 0384 0357 0331 47 48 065£ > 0627 059£ 0572 ! 0544 0517 049C 0463 0436 0410 0383 0357 0331 48 49 065£ i 0627 059E 1 0571 0544 0517 048S 0462 0436 0409 0383 0356 0330 49 50 0.0654 I 0626 5 0598 i 0571 0543 0516 0489 0462 0435 0409 0382 0356 :330 50 51 0654 \ 062f ) 0598 \ 057C ) 0543 0516 0489 0462 0435 0408 0382 0356 0329 51 52 065: \ 062; ) 0597 057C » 0542 0515 0488 0461 0434 0408 0381 0355 0329 52 53 065: 5 062; ) 0597 ' 056C 1 0542 0515 0488 ! 0461 0434 0407 0381 0355 0329 53 54 0655 J 062- I 059f 5 056£ 1 0541 0514 0387 0460 0434 0407 0381 0354 0328 54 55 0655 l 062- \ 059f 5 0568 \ 0541 0514 0487 0460 0433 0406 0380 0354 0328 55 56 065] 062: \ 059f ) 0568 \ 0541 0513 0486 • 0459 0433 0406 0380 0353 0327 56 57 0651 062: 5 059^ ) 0568 \ 054C » 0513 0486 0459 0432 0406 0379 0353 0327 57 58 065( ) 0621 \ 059; ) 0567 ' 054C » 0512 0485 0458 0432 0405 0379 0353 0326 58 59 065( ) 062S I 059^ 1 0567 ' 053£ 1 0512 - 0485 0458 0431 0405 0378 0352 0326 59 2 3^ 12 3. >2 3( 52 37 ^2 38 i2 35 »2 4C 12 41 2 42 2 43 2 44 2 45 2 46 220 TABLE XXXIV. PROPORTIONAL LOGARITHMS. // ' o ' o ' c > ' o ' |0 /jo ' 1 ' D ' O 1 o ' o ' o ' It t. fa m. h. EH* h. m. h m. i V. mm. m. h. m. i. m 1. m. h. m. h. m. h. n. h. m. t. i I 47 2 48 2 49 5 I 50 2 51|5 I 52|i I 53|2 54|2 55 2 56| 2 57 2 58 2 59 ( ).0326 0300 0274 0248 0223 0197 0172 0147 0122 0098 0073 0049 0024 1 0325 0299 0273 0248 0222 0197 0172 0147 0122 0097 0073 0048 0024 1 2 0325 0299 0273 0247 0222 0197 0171 0146 0122 0097 0072 0048 0023 2 3 0324 0298 0273 0247 0221 0196 0171 0146 0121 0096 0072 0047 0023 3 4 0324 0298 0272 0247 0221 0196 0171 0146 0121 0096 0071 0047 0023 4 5 ( 3.0323 0297 0272 0246 0221 0195 0170 0145 0120 0096 0071 0046 0022 5 6 0323 0297 0271 0246 0220 0195 0170 0145 0120 0095 0071 0046 0022 6 7 0323 0297 0271 0245 0220 0194 0169 0144 0119 0095 0070 0046 0021 7 8 0322 0296 0270 0245 0219 0194 0169 0144 0119 0094 0070 0045 0021 8 9 0322 0296 0270 0244 0€19 0194 0169 0143 0119 0094 0069 0045 0021 9 10 0.0321 0295 0270 0244 0219 0193 0168 0143 0118 0093 0069 0044 0020 10 11 0321 0295 0269 0244 0218 0193 0168 0143 0118 0093 0068 0044 0020 11 12 0320 0294 0269 0243 0218 0192 0167 0142 0117 0093 0068 0044 0019 12 13 0320 0294 0268 0243 0217 0192 0167 0142 0117 0092 0068 0043 0019 13 14 0319 0294 0268 0242 0217 0192 0166 0141 0117 0092 0067 0043 0019 14 15 0319 0293 0267 0242 •0216 0191 0166 0141 0116 0091 0067 0042 0018 15 16 0319 0293 0267 0241 0216 0191 0166 0141 0116 0091 0066 0042 0018 16 17 0318 0292 0267 0241 0316 0190 0165 0140 0115 0091 0066 0042 0017 17 18 0318 0292 0266 0241 0215 0190 0165 0140 0115 0090 0066 0041 0017 18 19 0317 0291 0266 0240 0215 0189 0164 '0139 0114 0090 0065 0041 0017 19 20 0.0317 0291 0265 0240 0214 0189 0164 0139 0114 C089 0065 0040 0016 20 21 0316 0291 0265 0239 0214 0189 0163 0139 0114 0089 0064 0040 0016 21 22 0316 0290 0264 0239 0213 0188 0163 0138 0113 0089 0064 0040 0015 22 23 0316 0290 0264 0238 0213 0188 0163 0138 0113 0088 0064 0039 0015 23 24 0315 0289 0264 0238 2013 0187 0162 0137 0112 0088 0063 0039 0015 24 25 0.0315 0289 0263 0238 0212 0187 0162 0137 0112 0087 0063 0038 0014 25 26 0314 0288 0263 0237 0212 0187 0161 0136 0112 0087 0062 0038 0014 26 27 0314 0288 0262 0237 0211 0186 0161 0136 0111 0087 0062 0038 0013 27 28 0313 0288 0262 0236 0211 0186 0161 0136 0111 0086 0062 0037 0013 28 29 0313 0287 0261 0236 0211 0185 0185 0160 0135 Olio 0086 0061 0037 0012 29 30 0.0313 0287 0261 0235 0210 0160 0135 Olio 0085 0061 0036 0012 30 31 0312 0286 0261 0235 0210 0184 0159 0134 Olio 0085 0060 0036 0012 31 32 0312 0286 0260 0235 0209 0184 0159 0134 0109 0084 0060 0036 0011 32 33 0311 0285 0260 0234 0209 0184 0158 0134 0109 0084 0060 0035 0011 33 34 0311 0285 0259 0234 0208 0208 0183 0158 0133 0108 0084 0083 0059 0035 0010 34 35 0.0310 0285 0259 0233 0183 0158 0133 0108 0059 0034 0010 35 36 0310 0284 0258 0233 0208 0182 0157 0132 0107 0083 0058 0034 0010 36 37 0310 0284 0258 0233 0207 0182 0157 0132 0107 0082 0058 0034 0009 37 38 0309 0283 0268 0232 0207 0181 0156 0131 0107 0082 0057 0033 0009 38 39 0309 0283 0257 0232 0206 0181 0156 0131 0106 0082 0057 0033 0008 39 40 0.0308 0282 0257 0231 0206 0181 0156 0131 0106 0081 0057 0032 0008 40 41 0308 0282 0256 0231 0205 0180 0153 0130 0105 0081 0056 0032 0008 41 42 0307 0282 0256 0230 0205 0180 0155 0130 0105 0080 0056 0031 0007 42 43 0307 0281 0255 0230 0205 0179 0154 0129 0105 0080 0055 0031 0007 43 44 0307 0281 0256 02^5 O230 ! 0229 0204 0179 0154 6129 0104 0080 0055 0031 0006 44 45 0.0306 O280 0204 0179 0153 0129 0104 0079 0055 0030 0006 45 46 0306 O280 0254 0229 0203 0178 0153 0128 0103 0079 0054 0030 0006 46 47 030£ 0279 0254 022S 0203 0178 0153 0128 0103 0078 0054 0029 0005 47 48 0305 0279 0253 0228 0202 0177 0152 0127 0103 0078 0053 0029 0005 48 49 030^ 0279 0253 0227 0202 0177 0152 0127 0102 0077 0053 0029 0004 49 50 0.030^ 0278 0252 0227 0202 0176 0151 0126 0102 0077 0053 0028 0004 50 51 0304 0278 0252 0227 0201 0176 0151 0126 0101 0077 0052 0028 0004 51 52 0303 0277 0252 0226 0201 0176 0151 0126 0101 0076 0052 0027 0003 52 53 0303 0277 0251 0226 0200 0175 0150 0125 0100 0076 0051 0027 0003 53 54 0302 0276 0251 0225 0225 0200 0175 0150 0125 0100 0075 0051 0027 0002 54 55 0.0302 • 0276 0250 0200 0174 0149 0124 0100 0075 0051 0026 0002 55 56 0301 0276 0250 022-1 0199 0174 0149 0124 0099 0075 0050 0026 0002 5Q 57 0301 0275 0250 0224 0199 0174 0148 0124 0099 0674 0050 0025 0001 57 58 030C 0275 0249 0224 0198 0173 0148 0123 0098 0074 0049 0025 0001 58 — --- 59 030(1 0274 0249 0223 0198 0173 0148 0123 0098 0073 0049 0025 0000 59 2 47 2 _ 48 2 49 1 2 50 2 51 2 52 2 53 2 54 2 55 2 56 2 57 2 t,>> e 59 1 FABLE XXXV. 22 i AMPLITUDES. DECLINATION. Lat. 0° 1° 20 3° 40 50 6^ 70 8° 9<^ 10° no 12° 130 140 15° . o o o o o 10 20 30 40 5-0 60 7-0 8-0 9-0 10-0 ll-O 120 13 14-0 150 10 10 2-0 30 4-1 5-1 6-1 7-0 8-1 9-1 10-1 11-2 12-2 13-2 14-.> 15-2 15 1-0 21 3-1 4-2 5-2 6.2 7-2 8-3 93 10-4 11-4 12-5 13-5 14-5 15-6 20 1-1 2-1 3-2 4-3 5-3 6-4 7-5 8-5 9-6 10-6 11-7 12-8 13-8 14-9 160 25 11 2-2 3-3 4.4 5-5 6-6 7.7 8-8 9-9 111 12-4 13-3 14-4 1 15-5 10-6 30 1-2 2-3 3-4 4-6 5-8 6-9 8.1 9-3 10-3 11-6 12-7 13-9 150 10-2 17-4 32 12 2-4 3-5 4-7 5-9 71 8-3 9-5 10-6 11-8 130 14-2 15-4 16-6 17-8 34 1-2 2-4 3-6 4-8 6-0 7-2 8-4 9-7 10-8 12-1 13-3 14-5 15? 17-0 18-2 35 1-2 2-4 3-7 4-9 6-1 7-3 8-5 9-8 110 12-2 13-5 14-7 15-9 17-2 18-4 36 1-2 2-5 3-7 4-9 6-2 7.4 8-7 9-9 11-1 12-4 13-6 149 16-1 17-4 18-7 37 1-2 2-5 3-7 5-0 6-3 7-5 8-8 10-0 11-3 12-6 138 151 16-4 17-6 18-9 38 1-3 2-5 3-8 51 6-3 7-6 8-9 10-2 11-4 12-7 14-0 15-3 16-(; 17-9 19-2 39 1-3 2-6 3-8 51 6-4 7-7 9-0 10-3 11-6 12-9 14-2 15-5 16-8 18-1 19-4 40 1-3 2-6 3-9 5-2 6-5 7-8 91 10-5 11-8 131 14-4 15-7 17-1 18-4 19-7 41 1-3 2-6 40 5-3 6-6 8-0 9-3 10-6 12-0 13-3 14-6 16 17-3 18-7 20-0 42 1-4 2-7 40 5-4 6-7 8-1 9-4 10-8 121 13-5 14-8 16-2 17-6 19-0 20-4 43 14 2-7 41 5-5 6-8 8-2 9-6 110 12-3 13-7 15-1 16-5 17-9 19-3 20-7 44 1-4 2-8 4-2 5-6 7-0 8-3 9-7 111 12-6 14-0 15-4 16-8 18-2 19-6 21-1 45 1-4 2-8 4-2 5-7 7-1 8-5 9-9 11-3 12-8 14-2 15-6 17-1 18-5 20-0 21-5 46 1-4 2-9 4-3 5-8 7-2 8-6 10-1 11-5 130 14-5 15-9 17-4 18-9 20-4 21-9 47 1-5 2-9 4-4 5-8 7-3 8-8 10-3 11-8 13-3 14-7 16-2 17-7 19-3 20-8 22-3 48 1-5 30 4-5 60 7-5 9-0 10-5 120 13-5 15-0 16-6 18-1 19-5 21-2 22-7 49 1-5 3-0 4-6 6-1 7-6 9-2 10-7 12-2 13-8 15-3 16-9 18-5 20-0 21-6 23-2 50 1-6 31 4-7 6-2 8-8 9-3 10-9 12-5 14-1 15-7 17-3 18-9 20-5 22 1 23-7 51 1-6 3-2 4-8 6-4 8-0 9-6 11-2 12-8 14-4 160 17-6 19-3 20-9 22-6 24-3 52 1-6 3-3 49 6-5 8-1 9-7 11-4 131 14-7 16-4 18-0 19-7 21-4 23 1 24-9 53 1-7 3-3 5-0 6-7 8-3 100 11-7 13-4 15-1 16-8 18-5 20-2 21-9 23-7 25-5 54 1-7 3-4 5-1 6-8 8-5 102 12-0 13-7 15-4 17-2 18-9 20-7 22-5 24-3 26-1 55 1-8 3-5 5-2 70 8-7 10-5 12-3 14-0 15-8 17-6 19-4 21-2 23-1 24-9 26-8 56 1-8 3-6 5-4 7-2 9-0 10-7 12-6 14-4 16-2 18-1 19-9 21-8 23-7 25-6 27-6 57 1-9 3-7 5-5 7-4 9-2 HI 12-9 14-8 16-7 18-3 20-5 22-4 24-4 26-4 28-4 58 1-9 3-8 5-7 7-6 9-r. 11-4 13-3 15-2 17-2 191 211 23-1 25 1 27-2 29-2 59 1-9 3-8 5-8 7-8 9-7 12-0 13-7 15-7 17-7 19-7 21-7 23-8 25-9 28-0 30-2 60 2-0 40 60 8-0 10-0 121 14-1 16-2 18-2 20-3 22-4 24-6 26-7 28-9 31-2 61 2-1 41 6 2 8-3 10-3 12-5 14-6 16-7 18-8 2 10 23-1 25-4 27-6 29-0 31 32 2 62 2-1 4-3 6-4 8-5 10-7 12-9 15-1 17-3 19-4 21-9 23-9 26-3 28-5 33-4 63 22 4-5 6-7 8-8 IM 13-4 15-6 17-9 20-1 22-5 24-8 27-3 29-6 32-3 34-7 64 2-3 4-6 6-9 91 11-5 13-9 16-2 18-5 20-9 23-3 25-7 28-3 30-9 33-5 36-2 65 2-4 4-8 71 9-5 11-9 14-4 16-8 19-3 21-7 24-2 26-8 29-5 32-5 34-9 3: -8 to Note turn -— Th( those 5 Amp teDths litudei into u in thi linatee sTabl k, W« D. e are t ultipb 'xpressed iu degrees and tenth parts of degrees and ^ tliem by six, which will jjive their value in mini tea. 222 TABLE XXXV. AMPUTUDES. DECLINATION. Lat. 16° 161° 170 17^0 18° 18^o 19° 19i° 200 201° 21° 21^° 22° 22^0 230 2310 o o o 16-0 16-6 17-0 17-5 18-0 18-5 190 19-5 20-0 20-5 21-0 21-5 22-0 22-5 23-0 23-5 10 16-2 16-7 17-3 17-8 18-3 18-8 19-3 19-9 20-3 20-8 21-3 21-8 22-3 22-9 23-4 23-9 15 16-6 171 17.-7 18-1 18-7 19-2 19.7 20-2 20-8 21 3 21-8 22-3 22-8 23-3 23-9 24-3 20 17-1 17-6 18-1 18-7 19-2 19-7 20-3 20-8 21-3 21-9 22-4 22-9 23-5 24-0 24-6 251 25 17-7 18-3 18-8 19-4 19-9 20-5 21-0 21-6 22-5 22-7 233 23-8 24-4 24-6 25-5 26-1 30 18-6 191 19-7 20-3 20-9 21-5 22-1 22.7 23-3 23-8 24-4 25 25-6 26-2 26-8 27-4 32 190 196 20-2 20-8 21-4 22-0 22-6 23-2 23-8 24-4 25-0 25-6 26-2 26-8 27-4 28-0 34 19-4 'lO-O 20-6 21-3 21-9 22-5 23-] 23-7 24-4 25-0 25-6 26-2 26-8 27-5 281 28-7 35 19-6 20-3 20-9 21-5 22-2 22-8 23-4 240 24-7 25-3 25-9 26-6 27-2 27-8 28-5 29-1 36 19-9 20-5 212 21-8 22-4 23-1 23-7 24-4 250 25-6 26-3 26-9 276 28-2 28-9 29-5 37 20-2 20-8 21-5 22-1 22-8 23-4 24-0 24-7 25-3 26-0 26-7 27-3 28-0 28-6 29-3 29-9 38 20-5 21-1 21-8 22-4 231 23-7 24-4 25-1 25-7 26-4 27-0 27-7 28-4 29-0 29-7 30-3 39 20-8 21-4 22-1 22-8 23-4 241 24-8 25-4 261 26-8 27-5 28-1 28-8 29-5 30-2 30-8 40 21-1 21-8 22-4 23-1 23-8 24-5 251 25-8 26-5 27-2 27-9 28-6 29-3 30-0 30-7 31-3 41 21-4 22-1 22-8 23-5 24-2 24-8 25-5 26-2 26-9 27-6 28-3 290 29-8 30-5 31-2 31-8 42 21-8 22-5 23-2 23-8 24-6 25-3 260 26-7 27-4 28-1 28-8 29-5 30-3 310 31-7 32-4 43 221 22-8 •23-6 24-3 25 25-7 26-4 27-1 27-8 28-6 29-3 30-1 30-8 31-5 32-3 33 44 22-5 23-2 240 24-7 25-6 26-2 26-9 27-6 28-4 291 29-8 30-6 31-4 321 32-9 33-6 45 22-9 23-7 24-4 25-2 25-9 26-7 27-4 28-2 28-9 29-7 30-4 31-2 320 32-8 33-5 34-3 46 23-4 241 24-8 25-6 26-4 27-2 27-9 28-7 29-5 30-3 31-0 31-8 32-6 33-4 34-2 35-0 47 23-8 24-6 25-4 20-2 26-9 27-7 28-5 29-3 30-1 30-9 317 32-5 33-3 341 34-9 35-7 48 24-3 251 25-9 26-7 27-5 28-3 29-1 29-9 30-7 31-6 32-4 33-2 343 34-8 35-7 36-5 49 24-8 25-6 26-5 27-3 28-1 28-9 29-7 30H 31-4 32-3 33- 1 33-9 34-8 35-7 36-5 37-4 50 25-4 26-2 27-0 27-8 28-7 29-6 30-4 31-3 32-1 33 33-9 34-8 35-6 36-5 37-4 38-3 51 26-0 26-8 27-7 28-5 29-4 30-3 311 32-0 32-9 33-8 34-7 35-6 36-5 37-5 38-4 39-3 52 26-6 27-5 28-3 29-2 301 310 31-9 32-8 33-7 34 '7 35-6 36-5 37-5 38-4 39-4 40-3 53 27-3 28-2 29-1 30-0 309 31-8 32-7 33-7 34-6 35-6 36-5 37-5 38-5 39-5 40-5 41-4 54 28-0 28-9 29-8 30-8 31-7 32-7 33-6 34-6 35-6 36-6 37-6 38-6 39-6 40-6 41-7 426 55 28-7 29-7 30-6 31-6 32-6 33-6 34-6 35-6 36-6 37-6 38-7 39-7 40-8 41-8 42-9 44-0 56 29-5 305 31-5 32-5 33-5 34-6 35-6 36-6 37-7 38-8 39-8 40-9 421 43-2 44-3 45-4 57 30-4 31-4 32-5 33-5 345 35-6 36-7 37-8 38-9 400 4M 42-3 43-4 44-6 45-8 47-0 58 31-3 32-4 33-5 34-6 35-7 36-8 37-9 39-0 40-2 41-7 42-5 43-8 45-0 46-2 47-5 48-7 59 32-3 33-5 34-6 35-7 36-8 38-0 39-2 40-4 41-6 42-8 441 45-4 46-7 48-0 49-3 50-6 60 33-4 34-6 35-8 370 38-2 39-4 40-6 41-9 43-2 44-5 45-8 471 48-5 49-9 51-4 52-8 61 346 35-8 37-1 383 39-6 40-8 42-2 43-5 44-8 46-2 47-7 49-1 50-6 52-1 53-7 55-2 62 35-9 37-2 38-5 39-8 41-2 42-5 43-9 45-3 46-8 48-2 49-8 51-3 52-9 54-6 56-3 58-0 63 • 64 37-4 38-7 401 41-5 42-9 44-3 45-8 47-3 48-8 50-5 521 53-8 55-6 57-4 59-4 61-3 390 40-4 41-8 43-3 44-8 46-4 48-0 49-6 51 3 53-0 54-8 56-7 58-7 60-8 63-0 65-3 65 40-7 42-2 43-8 45-4 47-0 48-7 50-4 52-2 54-0 560 58-0 60-1 62-4 64-9 67-6 70-4 223 TABLE XXXVI. THT? FOLLOWING TABLE CONTAINS EXTRACTS FROM THE NAUTICAL ALMANAC I FOR THE YEAR 1864, FOR THE PURPOSE OF WORKING OUT THE EXAMPLE GIVEN IN THIS WORK TO SUIT THOSE WHO MAY NOT HAVE AN ALMANAC AT HAND. THE . sun's rioht ascension, declination, (Ssc. Day of Month. Ap. RAscen. Dit 1 Hr. App. Declination. DitlHr Semid. Equa. of Time. Dif. 1 Hr. H. M. 8. 8. O ' " If • / // M. 8. • Jan. 20 20 7 38 S. 33 16 17 (( 21 19 54 26 S. 33.9 16 17 (( 25 18 57 58 S. 37.5 (( 26 18 42 58 S. 38 Feb. 7 21 23 36 10 + 14 27.32 0.106 t( 8 21 27 35 10 + 14 29.87 072 u 9 21 31 34 10 -f- 14 31.61 039 (( 10 21 35 32 10 + 14 32.55 006 (i 11 21 39 28 10 + 14 32.70 025 Maboh 5 6 3 14 S. 58 16 9 4- 11 45.76 584 (( 6 5 40 IS. 58 16 8 + 11 31.74 602 (t 10 23 21 53 9 4 6 30 S. 59 -1- 10 31.55 665 u 11 23 25 33 9 3 42 59 S. 59 + 10 15.58 679 u 23 9 22 9 1 54 N. 59 + 6 45.27 766 u 24 13 9 1 24 32 N. 59 + 6 26.88 767 u 25 1 48 7 N. 59 -f- 6 8.46 768 u 26 2 11 40 N. 58.9 + 5 50.02 768 u 27 2 35 UN. 58.6 + 5 31.56 768 <( 30 3 45 22 N. 58.2 + 4 36.36 763 t( 31 4 8 S« N. 58 + 4 18.06 759 April 1 4 31 35 N. 58 -1- 3 59.84 755 u 2 45 43 9 4 54 55 N. 58 + 3 41.71 750 « 3 49 21 9 5 17 56 N. 57 + 3 23.70 745 (( 6 1 18 9 + 2 30.50 725 u 7 1 3 57 9 + 2 13.11 716 M 16 - 11.87 603 (t 17 - 26.33 586 M 21 11 50 36 N. 51 — 1 20.06 514 M 22 12 10 53 N. 50 - 1 32.39 494 i( 30 14 45 32 N. 46 - 2 53.58 328 Mat 1 15 3 49 N. 45 ~ 3 1.44 306 M 12 3 15 50 10 18 7 27 N. 37.4 — 3 52.34 053 (( 13 3 19 45 10 18 22 25 N. 36.7 - 3 53.60 028 (i 19 19 45 36 N. 32 - 3 48.94 116 (4 20 19 58 19 N. 31 - 3 46.15 140 JlTNE 1 22 3 23 N. 20 - 2 31.92 380 (( 2 22 11 23 N. 19 - 2 22.80 395 (( 3 4 44 13 10 22 19 N. 18 15 48 — 2 13.33 410 (( 4 6 52 41 10 22 26 13 N. 17 15 48 — (( 21 23 27 32 N. July 3 6 48 34 10 + 3 49.25 455 a 4 6 52 41 10 4- 4 0.18 441 (( 12 22 19 N. 21 + 5 14.40 308 (t 19 20 53 10 N. 27 + 5 56.28 165 C( 20 20 42 8 N. 28 + 6 0.25 141 Auo. 4 17 17 7 N. 40 + 5 50.21 233 ii 5 17 1 2 N. 41 -f 5 44.64 258 (( 14 9 34 48 9 14 24 30 N. 46 + 4 28.11 469 u 15 9 38 34 9 14 5 53 N. 47 + 4 16.80 490 (t 21 10 54 9 + 2 58.97 610 (( 22 10 4 36 9 -»- 2 44.34 628 ( 31 8 41 ON. 54 15 224 TABLE XXXVI. THE sun's RIGHT ASCENSION, DECLINATION, &C. Day of Monti 1. Ap. R-Ascea Dif. 1 Hr. App. Declination. Dif. 1 Hr. Semid. Equa. of Time. Dif 1 Hr.l H. M. 8. 8. o ' " n / n 1 M. S. • Sept. 1 8 19 18 N. 54 a 6 6 28 51 N. 56 — 1 41.97 0.841 n 7 6 6 26 N. 56 — 2 2.14 849 li 24 2() S. 58 — 7 57.03 854 (i 25 49 26 S. 58 — 8 17.52 848 (( 26 12 11 12 9 1 12 52 S. 58 — 8 37.87 840 (( 27 12 14 48 9 1 36 17 S. 58 — 8 58.04 832 a 29 2 23 5 S. 58 — 9 37.78 814 u 30 2 46 27 S. 58 — 9 57.32 803 Oct. 3 12 36 31 9 ___ 10 54.34 767 (( 4 12 40 9 9 — 11 12.74 753 (( 5 12 43 47 9 — 11 30.80 738 (( 9 6 14 42 S. 57 — 12 39.01 669 (( 10 6 37 30 S. 57 — 12 55.18 647 (( 20 10 19 47 S. 53 16 6 — 15 5.77 406 «( 21 10 41 18 S. 53 16 6 — 15 15.49 378 Nov. 27 21 8 34 S. 27 12 12.25 842 (( 28 21 19 21 S. 26 — 11 52.04 871 Dec. 5 16 46 36 11 ^_ 9 12.43 1.049 Lb 6 16 50 58 11 — 8 47.26 1.071 YEAR 1851. 1 April 14 1 28 37.65 9.217 22.71 0.637 u 15 1 32 18.87 9.232 7.42 623 July 6 6 59 47.73 10.275 4 17.99 418 (( 7 7 3 54.34 10.260 4 28.3 402 1 THE moon's right ASCENSION, DECLINATION, &C. SEMID. HOR. PAR. RIGHT ASCENSION. DECLINATION. MERID 1 DATE 1 NOUN MID. NOON MID. NOON MID. NOON MID. PASS r II ' // / II 1 1 ' H, M. S. H. M. S. O ' " O ' " H. M Feb. 7 14 46 14 46 54 8 54 " ^ 4 59 57 5 25 17 23 28 49 N 24 28 15 N March 10 14 57 15 1 54 47 55 ( ) 8 12 21 8 38 20 24 13 39 N 23 3 42N (( 23 16 9 59 e \ 20 23 53 23 51 2 S a 24 16 7 59 3 20 53 47 22 19 53 S April 23 2159 ii 24 15 31 56 5( ) 51 12 S 22 43 u 25 15 26 56 35 2 2 14N June 2 15 7 15 13 55 24 55 4.- ) 18 24 3 N 16 1830N 5 21 (i 3 15 8 15 03 55 24 55 \l j 6 5 u 4 15 19 56 8 57 1^ July 3 15 31 15 38 56 49 1 (.1 4 15 45 57 41 " 11 10 36 61 n r 21 21 34 S 13 .58 a 12 16 31 61 6 19 9 21 S 14 56 Aug. 14 15 15 55 5S > 2 52 13 15 25 35 N u 15 15 9 55 30 3 16 29 17 37 37 N (( 16 14 59 14 55 54 54 54 4C 21 26 15 N 22 58 45 N IH 6 (( 17 1!>54 Sept. 26 15 53 15 56 58 11 58 23 15 26 42 15 54 24 18 52 48 S 21 1 43 S Oct. 1 {( 3 16 12 16 10 50 21 59 14 22 27 22 54 4 15 9 45 12 20 27 8 11 (( 4 16 8 16 4 59 5 58 54 23 20 24 23 46 9 9 22 4 S 6 17 29 S 1 Dec. sl 13 3 TABLE XXXVl. YEAR 1851. 226 1 THE moon's right ASCENSION, DECLINATION, &C. DATE. SEMID, HOR, PAR. R. ASCENSION. H. DECLINATION DF. 10 m. MERID. NOON MID. NOON MID. NOON MID. NOON MID. MER. PAH. April 14 15 t n 16 23 16 26 60 6 t It 60 17 » 13 14 26 21.6 S 133.33 .39 41.6 S 133.2.-:; H. 11 17.9 12 10.7 Jolt 6 7 15 59 15 55 58 39.6 58 2.1.8 11 5 31 56.5 S 122.83 6 40.5 7 .32.0 THE PLANETS 1854. DATE, NAMES. merid. passage. RIGHT ASCENSION. DECLINATION. January 1 2 28 29 Venus, Saturn H. M. 3 15.0 3 15.0 7 1.3 6 57.0 H. M. S. 21 59 15 22 2 33 3 32 8 3 32 9 O t II 13 4 40 S. 12 39 60 S. 17 2 12 N. 17 2 33 N. February 41 1 2 u 6 45.7 6 41.8. 3 32 15 3 32 18 17 3 47 N. 17 4 15 N. April 2 3 6 7 13 14 «( Venus Jupiter 18 23.7 18 20 3 47 15 3 47 41 22 27 28 22 29 44 19 51 49 19 52 36 18 9 33 N. 18 11 6 N. 6 8 43 S. 6 6 47 S. 21 6 42 S. 21 5 47 S. Junk 6 7 Mars 6 2 5 59 11 50 11 2 28 7 24 56 N. 7 13 13 N. July 3 4 Jupiter 19 44 26 19 43 55 21 39 11 S. 21 40 38 S. Septembeh . 24 25 7 4.6 7 0.9 19 17 43 19 17 52 22 44 27 S. 22 44 12 S. October u 3 4 5 6 31. 6 27.5 6 23.8 19 19 51 19 20 7 22 41 14 S. 22 40 44 S. 22 40 13 S. December 5 6 « 19 57 13 19 58 4 21 14 47 S. 21 12 27 S. LUNAR DISTANCES. date. NAMES. HOUR. DISTANCE. PRO LOO. HOUB. DISTANCE. PRO. LOG. JUNB 3 3 Sun W. Antares E. VI. MID. 86 48 23 85 29 55 .3208 .2843 IX. XV. 88 14 23 83 56 23 .3193 .2829 July 3 3 4 Jupiter E. Sun W. Sun W. III. XXI. NOON 101 46 12 100 13 12 101 46 2 .2t;i8 .2876 .2858 VI. 10 7 41 .2601 August 14 14 15 Aldebaran E. Sun E. Sun E. XVIIl. XXI. NOON 19 57 36 92 17 18 90 51 50 .3115 .3235 ..3250 XXI 18 29 45 .3175 Septembei I 26 Sun W. XI. 54 10 41 .2769 IX. 55 45 50 .2760 January 30 Aldebaran E. MID. 85 38 28 .2362 XV. 83 53 59 .2378 February 7 Sun W. NOON 117 47 51 .3488 I[I. 11 9 8 28 .3489 star's right ASCENSION AND DEC LINATION, 1851 Spica, Arcturus Right Ascension. u u H. M. S. 13 17 22 14 8 .53 Declination o 10 2; 19 5' 5 1 S. r 43 N. 226 TABLE XXXV 11. APPROXIMATE VARIATION OF THE COMPASS. N. WEST LONGITUDE. O C o o o o O o O O O o o o o o LAT. 180 170 160 150 140 130 120 110 100 o 90 80 70 60 50 40 30 20 10 O O o o o o o o o o o o o o o o o o o 60 N 17E 20E 23 k 26 B 26E 27E 27 E 4W 30W 46 W 46 W 49 W 48 w 48 w 41W 32W 28 W 58 17 20 22 25 25 26 26 24 46 46 49 48 48 39 31 28 56 17 19 21 24 25 25 25 19 40 42 47 47 45 37 30 26 54 17 19 21 23 23 24 24 30 42 43 44 41 35 29 25 52 16 18 20 22 22 23 23 25 36 38 40 38 34 28 25 50 16 18 20 21 21 22 22 22 21 20 29 36 36 35 32 27 25 48 16 18 20 21 21 18 24 33 33 33 30 27 25 46 16 17 18 20 21 20 20 ] VORTH 4 15 22 30 30 31 29 26 25 44 16 17 18 19 20 20 19 4 15 19 28 28 30 28 26 25 42 16 17 18 18 19 18 18 America. 2 12 17 24 26 28 27 25 24 ' 40 15 16 17 17 18 17 17 16 17 16 1 9 16 21 25 26 26 24 22 38 15 16 17 17 6 12 20 22 25 25 23 22 36 15 15 16 16 16 15 15 1 E 4 10 18 20 24 25 22 34 14 15 16 16 15 14 13 2 3 8 16 19 23 24 22 32 14 14 14 15 15 14 12 3 2 6 14 17 22 24 21 30 14 14 13 13 14 13 12 12 11 12 11 8 E 4 2 4 13 16 21 23 21 28 13 12 13 8 4 1 3 12 15 20 23 26 13 13 12 12 11 10 10 8 4 2 11 13 19 22 24 12 12 11 11 10 10 10 9 5 1 E 1 10 12 18 21 22 12 11 10 10 9 9 9 9 5 2 9 11 17 21 20 12 11 10 10 9 9 9 9E 9E 9 9 6 3 1 E 8 10 16 20 AFkiuA. 18 12 11 10 9 9 9 9 9 9 6 4 2 7 9 15 20 16 11 10 9 9 9 9 8 8 9 9 6 4 2 6 9 15 19 14 11 10 9 8 8 8 8 8 9 10 7 5 3 5 9 14 19 12 11 10 9 8 8 8 7 8 9 10 7 5 3 4 8 14 18 10 10 9 8 8 7 7 7 8 9 10 7 5 3 3 7 13 18 8 10 9 8 7 7 7 7 8 9 10 7 2 7 12 18 6 10 9 8 7 6 7 7 8 9 10 8 6 12 18 20 20 4 10 9 8 7 6 6 7 7 8 9 8 5 12 17 19 20 2 10 9 8 7 6 6 6 7 8 9 8 5 11 17 19 20 10 9 8 7 6 6 6 7 8 9 8 5 10 17 19 20 2S 10 9 8 6 5 6 6 7 8 9 8 1 E 4 9 16 18 20 4 10 9 8 6 5 6 6 7 8 9 8 South 1 4 8 14 18 20 6 10 9 8 6 5 6 6 7 8 9 8 America. 1 3 7 12 18 20 8 9 9 8 6 5 6 6 7 8 9 8 2 3 7 12 18 20 10 9 9 8 6 5 6 6 6 7 8 9 9 2 2 7 12 18 20 12 9 9 8 6 5 6 7 8 9 9 3 2 6 11 18 20 14 9 9 8 6 5 6 6 7 9 10 9 3 1 6 11 17 20 16 10 9 8 6 5 6 6 7 9 10 10 4 1 6 11 16 20 18 10 9 8 6 5 6 6 7 9 10 10 4 5 10 16 20 20 10 9 8 6 5 6 6 6 8 10 11 11 5 1 E 5 10 10 16 20 22 10 9 8 7 6 6 8 10 11 12 5 1 5 16 20 24 10 10 9 7 6 7 7 8 10 12 13 6 3 5 10 15 19 26 10 10 9 7 6 7 7 8 11 J2 14 10 E 6 2 4 9 15 19 28 11 10 9 7 6 7 7 8 11 13 15 10 7 3 4 9 15 19 30 11 10 9 8 7 7 7 7 7 8 9 11 12 13 15 11 7 3 3 8 14 19 32 12 11 9 8 7 14 16 12 8 4 3 8 14 19 34 12 11 9 8 7 8 8 9 13 15 17 13 8 4 2 7 14 19 36 13 11 9 9 8 8 8 9 13 15 17 13 9 5 1 6 14 19 38 13 12 10 9 8 9 8 10 13 16 17 14 9 5 1 6 14 19 40 14 13 10 9 8 9 8 11 11 14 14 17 18 15 10 6 6 14 19 42 15 14 11 10 9 9 8 17 18 16 10 6 1 E 5 13 18 44 15 14 12 11 10 10 9 12 15 18 19 17 11 7 2 5 13 18 46 15 14 12 11 10 10 9 13 16 19 20 18 12 8 2 5 13 18 48 15 12 13 12 11 9 13 16 19 21 19 13 9 3 5 13 18 50 13 14 13 12 10 11 14 15 17 18 20 22 20 14 9 4 4 12 17 62 15 14 13 21 23 21 15 10 5 4 12 17 54 14 13 12 16 19 22 24 21 16 11 6 4 12 17 56 14 12 16 19 22 25 22 ' 17 12 7 4 12 17 o o o nl o o o o o o o o o o LAT. 180 170 160 1501 140 130 120 110 100 90 80 70 60 50 40 30 20 10 S. WEST LON GITUl OE. TABLE XXXV 11. 227 APPROXIMATE VARIATION OF THE COMPASS. N. IA8T LONGITUDB. 1 O o o o o o o o o O o O O o o o o o o LAT. 10 o 20 30 40 50 o 60 70 80 90 100 110 120 130 140 1O0160 170 180 O o o o o o o o o o o o o 1 ° o o 60 N 26W 20-W 15W 3E 7E 12 E 17E 58 25 20 15 3 12 17 56 25 20 15 3 12 17 54 24 20 15 low » 3 12 17 52 24 20 15 10 2 12 16 50 23 19 18 15 10 2 12 16 48 22 14 10 2 12 16 46 22 18 12 11 3 12 16 44 21 17 13 11 Asia 1 w iw 1 E 3 12 16 42 21 17 13 11 1 1 3 12 16 40 2 • 16 13 11 2 1 3 12 16 15 38 20 16 13 11 2 1 3 7 11 36 20 16 14 12 1 3 6 10 14 34 16 14 12 1 2 3 6 10 14 32 14 13 12 2 4 6 10 14 30 12 12 2 4 7 10 13 28 IE 1 E 2 4 7 10 13 26 3w 1 2 4 7 10 13 24 Afk ICA. 3 1 3 4 7 9 12 22 3 2 1 ^ 1 E 3 5 7 9 12 20 3 2 1 E 3 5 7 9 11 18 3 2 2 3 5 7 9 11 16 3 2 2 3 5 6 8 10 14 3 2 3 4 6 7 8 10 12 12w 8w 3 2 2 2 2 3 4 6 7 8 10 10 12 8 3 2 2 2 2 3 4 6 7 8 10 8 12 8 3 2 2 2 2 3 4 6 7 8 10 6 20 12 8 3 2 2 2 2 3 4 6 7 8 10 4 20 12 8 3 2 2 2 2 3 4 6 7 8 10 2 20 12 8 3 2 2 2 2 3 4 6 7 8 10 20 13 8 4 1 1 1 2 2 3 4 6 7 8 9 2S 20 21 22 13 8 4 1 2 2 3 4 6 7 8 9 4 20 21 22 13 8 4 2W 1 1 1 1 2 4 6 7 8 9 6 20 21 22 14 9 5 2 1 2 4 6 7 8 9 8 20 21 23 15 10 6 3 1 4 6 7 8 9 10 20 21 23 15 10 6 3 1 4 6 7 8 9 12 20 21 23 16 11 7 4 2 1 W 1 4 6 7 8 9 14 20 22 24 17 12 8 4 3 1 iw 1 W 1 W 4 6 7 8 9 16 20 22 24 18 14 9 6 4 2 1 1 1 3 fl 7 9 10 18 20 22 24 19 14 10 7 5 3 2 1 1 3 6 7 9 10 20 20 22 25 20 16 12 8 6 4 5 3 2 1 3 6 7 8 9 10 22 20 22 25 21 17 13 9 7 4 3 2 1 w 4 7 10 24 20 22 25 22 18 15 10 8 6 5 4 2 1 4 7 8 9 10 26 19 22 26 23 19 16 11 9 7 5 3 2 1 4 7 8 9 10 28 19 22 26 24 20 17 12 10 8 6 4 3 1 4 7 8 9 10 30 19 22 26 29 25 22 19 14 12 10 7 5 3 1 6 8 9 10 11 32 19 23 27 30 26 24 20 16 14 11 9 7 4 2 5 8 9 10 11 34 19 23 27 30 27 24 21 18 16 13 10 7 4 2 5 8 9 10 12 36 19 24 28 31 28 26 23 20 18 15 11 7 4 2 6 9 10 11 12 38 19 24 29 32 29 26 24 21 19 16 12 9 5 3 6 9 10 12 13 40 19 24 29 32 30 28 29 26 23 21 18 14 11 5 3 7 10 10 11 12 13 42 19 25 30 33 31 28 25 23 20 16 11 6 4 7 11 13 14 44 19 25 30 33 32 30 29 27 26 24 18 12 6 4 7 10 11 14 15 46 18 24 30 33 33 30 31 29 27 26 20 14 7 5 7 10 11 14 15 48 18 24 30 33 35 34 33 31 29 28 22 16 7 5 7 10 11 14 15 50 18 24 30 33 33 36 36 35 37 33 29 30 23 17 8 6 8 11 11 14 52 17 23 30 38 37 35 34 32 23 17 8 6 8 11 12 14 54 17 23 30 33 39 38 38 36 34 33 24 17 9 7 8 11 12 56 17 23 30 33 40 40 o 39 37 34 34 26 18 9 7 8 11 o o o o o o o o o o o o LAT. 10 20 30 40 50 60 70 80 90 100 110 1 120 130 140 150 160 170 180 s. EAS1 ' LON GITITDE. _l 228 TABLE XXXV 111. CONTAINING THE TIDE HOURS, OR THE TIMES OF HIGH WATER, At the Full and Change of the Moon, (usually called the Establishment of the Port,) at the principal Porta and Harbors of the World, with the Vertical Rise of the Tide in Feet, in both Spring and Neap Range. The first two numbers, connected thus - in the Range column, denotes the Spring Range, the second the Neap Range PLAOE8. TIME. EANGE Abaco Abdl Koory.. Aberdeen .... Aberystwyth.. Abrolhos Acapulco .... Achen.. Adelaide Aden Adenara. Agoada Akaroa. Akyab Albemarle.. . . Alderney , Amboyna.. ... Amoy Amsterdam.. . — I^ LOc_.., Andamans N. Harb Andrava B.. . , Andrews, St. . Augra, Azores. — Pequenha-. Ann, Az. — St. I., Seych. Annapolis, U.S. — Nov. Scot. . Anticosta, W. Pt. Antongil B.. . . Antonio, Cuba. — Port Antwerp Aor Pulo Arbroath Apalachicola.-. Areachon . . . . Areas H. u. 8 80 12 31 48 6 44 10 30 4 9 46 7 15 6 46 83 ri2 SO 8 11 Archangel. . . A rdglass . . . . , Ardrossan. . , Arica Aroa. Arthur. Arundel Ascension.. . . Auckland Augustine B„. — U. S. Awatcha. . . . A^yi- 10 8 80 10 46 12 82 2 80 11 69 5 30 4 48 11 FT. 3 8 19-14 13-6 6 H 7 6 8 8 9- 8 9- 7 17-8 7 18-17 18 8 9 7 25 8 18 6 2i 80 PLACES. 3 80 4 9 30 10 40 4 25 1 40 87 18 Kab el mandeb — I Bahia Halfide .... Ualasore.. . Halbriggan, Ually Balta Baltimore.. Bananas . . Bancoot. . . Banda Banff. Banks . .. , Bantam. . . Ban try B_. B 10 30 11 54 8 7 52 11 15 6 30 6 16 4 30 8 4 8 80 12 10 11 6 H 30-18 14 6 14-8 4 12-7 n 2 19 10-8 6 10 4 16 2 10 13 4 8-5? ar:>ara 12 11 8 6 9 10 12 9 4 8 11 4 8 8 U 30 30 80 30 46 40 80 46 23 16 40 42 47 16 Barb* ' 6 6- e 8 lo- ll 11 6-3 12 9 12 6! 11-6 8 6 10-6 Baifleur .... Barnstable . . Barren Is.. .. Bas Is Basseen Batanes Batchian ..... Bate Buthurst Bay of Is.. . . Bayonne Beachy Hd. . Beaumaris . . Beaufort. . . . Belfast. Bell Sound.. . Belle Isle .. . . Bambatooka. Bembridge . . Bencoolen .. . Benin Berbice Bergen Bergen op Z. . Bermuda. . . Berwick on Tweed. . . Bilboa Bissao Blanco C Blewfields. . . . Blyth Bodega Bojador Bombay Bi luacca Bonny Bordeaux . . . . Boston, U. S... Botany B Bow I Boy anna B. . . . Brava BrayHd Brehat I Brest Bridgewater. . Biielle Brighton .. . . . Bristol British Sd. . . . Bruny BiienoB Ayres. Bulama L Buncrana Bushire.. . Bussora. . Button la. H. M 8 54 11 4 45 6 15 12 80 TIME. EANGE 12 8 10 16 15 10 32 6 52 10 43 8 66 11 30 4 30 11 40 4 16 4 30 1 30 8 80 7 or 8 FT. 9 12 27 17 4 6 14 7 6 16 21 21-11 7 9-6 3 7 16 6 80 11 46 1 60 2 48 11 80 12 11 10 18 68 9 6 6 55 11 31 8 0? 2 40 4 30 4 30 10 45 5 27 3 48 6 60 3 10 6 7 15 4 9? 4 80 7 54 7 30 12 6 60 7 11 16 291 14 6 2 14-10 7 PLACES. 15-11 u 9 14-11 12 7 or 4 8 15 8 12-7 37 19-9 35-18 14 16 40 n 9 var. 15 17 6 Cadiz , Ciiernarvon. . , Cajeli Calcutta . . . . . Calebar, New, Callao Cameroons R.. Camiguin . . . , Campbell I. . . Campbelton.. , Campobello . . Cambing CanBO, Gut . . , 2 9 33 1 3 6 6 47 6 6 « 12 Oi 43? 12-8 14-8 6 9 4 7 6 11 45 11 19 noon 8-4 21-16 6 8 80 8 Cantin C Canton Capricorn C. . Cargados Gar. Cardiff Carlingford. .. Carlos St Carrickfergus . Car tar et Castlereagh C. Catherine St . Catoehe, C. . . . Cayenne Cayeux. Ceuta Chaguaramus. Champion B. .. Charles, 0. . . . Charleston . . . Cliatham Chatte C Chaussey . . . , Cheduba Chepstow.. . . , Cherbourg . . , Chester , Chichester. . Chignecto. . , Chimmo B. . . , Chin-chew. . . Chin-Hae . . . Cbittagong.. . Chosari Christmas. . . Chusan Circular Hi. Clara, Sta.. . . Coast, C Cobija Cochin Cockburn . . . Cod C Colorado... Columbia R. . Comoro Condore .... Copiap6 .... Coquet Coquimbo... . Cordovan . . . Coringa Corisco Coik Coruuna .... Coupang Coy Inlet . . Cracatoa _. . . Cromer _. . . . Crooked I.. . . Crookhaven . Curieuse.. . . . Curtis, Port, Austr Cutch, G Cuxhaven.. . . Dalrymple . . . Damaun Bar . Dampier Strait Dartmouth.. . Darnley L. . , Darwin, Port H. M, 10 TIME. EANGE 2 8 2 6 11 40 3 59 11 46 10 30 2 60 2 40 8 45 11 6 1 55 3 30 9 10 7 45 7 16 54 12 6 9 11 30 7 30 7 49 10 80 11 45 11 12 25 12 25 12 10 1 30 PLACES. TIME. RANGE 7 10 11 12 4 4 9 30 46 54 4 15 11 30 8 40 12 15 30 8 80 5 45 8 37 1 30 FT. 7 4 18-12 19 8 6 4 6- 1 6 27-16 4 1 6 8 13 30 8 70? 17-8 26 14 82 16 17- 10 15-10 4 12-6 9 7- 7 4 6 12 13 11 1i 12 4 5 15-8 6 14-7 5-3 7 11-7 9 30 7 lltol 44 13 6 1 30 6 6 9 80 5 30 7 40 4 15-7 2i 12-8 7 10-6 16 10 17 11 19-11 10 24-17 Dauphin, Fort Delagoa .. Delaware R.C. Hen. c_. . . Delgado, Az.. — C _. Delhi, R Demerara Desire Devonport-. Diamond I. . Diego Gar. . — Ram. . . . — ot. C . , . Dieppe ,.. . . Discovery >. . Dislocation .. . Diu I Divy Douglas Dover Dragon's Mo... Dublin Poolb, Dunbar Duncansby .. . Dundee _. . . . Dunkirk . . . . Dunraore. . . . Durnford.. . . . Durien, Strait Easter L . . . . Edgar, Port. . Egg Harbor- . Elbe Elena ....... Embden . . . . Endeavor R.», English Rd Essington Pt. Evangelists . . Exmouth . . . . Exuma.... .. . H. M. 4 30 4 40 8 12 80 4 4 4 30 12 45 5 43 10 30 1 30 4 4 30 11 6 2 80 1 40 2 11 8 11 12 8 10 30 2 10 2 31 12 8 6 46 4 46 irr. Fairweath. C. Falmouth. . . Famine . . . Faval„ Fear, C Fernando Nor. Ferrol , Finisterre . . , Flamenco. . . Fleetwood . ., Flushing ... Folkstone . . . Foreland, N. . Fowey Francisco, St Funchal . . . ., Fundy B FT. 7 13 4-3 7 16 8 9 21 16-7 8 6 10 27-16 7 4 6 6 22-11 20 4 IS-I 9 1&-7 17-10 16 12 10 2 7 7 12 4 12 8 7 8 1 15 10 30 24 6 29 7 20 11 30 7 9 10 10 63 1 11 15 5 30 11 12 16 Gaboon, R.. . . Gallant, Port, Gal legos, R.. . Galveston . . . Gal ;vay Gambia, Bath- urst .... Gambler la. Gasp6 B. . . Gay Hd 6 9 8 601 4 82 6 4 12 17 5 18 5 14-8 28 18 9 4i 7 6-5 5 28-21 14- 17 16 8-2 9 60 8 5 48 4 15-7 60 60 87 8 6 7 TAlil.E XXXVlll. CONTAINING THE TIDE HOURS, OR THE TIMES OF HIGH WATER. 12V PLAOKS. TIME EANGE Geby I George, St ah , GeorgetowD . . (ihei'iah Gibraltar .... Glasgow Gloucester . . , Goa , Good Hope, C. Good Success . Goree Gracias, C. . . . Graud, Port . . Granville . . . . Greenock . . . . (ruasco Guatulco Guaymes Guerusey . . . . GuD Cay Guayaquil. . . . Haarlem Hague Hakluyts Hd.. Halifax. Hamburgh . . . Hammerifest. . Hardy, Port . Hartlepool . . . Harwich Hastings, St.M Hatteras, C. . • Havana Havre _ Haytien, C. .. Heligoland . . . Helena, St B.. — I Henlopen, C. . Henry, C Heraiiura,. . . , Hillsboro' Inlet Hobarton .... H North Coast of Spain. NAMES OF PLACES. St. Sebastian Light Cape Villaiio Bilbao St Nieh. Cli. Santona Mt. sumniit Saiitander mole It's Cape Blauco Island Pancba, West extremity.. . . Cape Burela. . . Cape Vares siimrait Cape Ortegal tower Ferrule Mole Coi-una, St. Autouia Castle Cape Finisterre light to be Mt. Louro, 787 fe^t. Viana Fort, St Jago Light to be Lax. N. Lo.\. W 43 43 43 19-2 27 15-8 43 27 5 43 27-9 43 36 43 34-7 43 42 43 48 43 45-2 43 29-5 43 22-5 52 54 42 44 41 42-6 2 0-5 2 58 2 54 3 26 3 48-7 6 47 6 59-2 7 21 7 41 7 66 8 12-7 8 22-7 9 15 9 44 8 43-2 Coast of Portugal. Mt. Oruellas, high. Oporto F(jrt, St. John Light Cantaros Mt. summit 6460 feet Cape Mondego light to be Figueira Light to be Burliug's Light. . Cape RocaLt. 698 ft. Mt. Ciutra summit, 1720 feet St. Juhan Fort light Lisbon, Marine Ob- servatory Cape Espichel Light 627 feet Selubal Light, 490 feet Mouchique Mouat'ns summit 3830 feet. Cape St. Vincent Lt Cape Sta. Maria Lt. Mount Figo, 2000 ft Cadiz New Obs'rt'ry C.Trafalgar Tower. Tarifa Light 40 50 41 8-8 41 9-1 40 19 40 12 40 10 39 26 38 46 38 47-2 38 40-3 38 42-4 38 24-9 38 28-9 8 21 8 37-2 8 37-5 7 38 8 64 8 51 9 80-7 9 30 9 25 9 20-5 9 8-2 9 IS 8 53 37 20 8 36 37 2-9 9 00 36 56 7 46 37 10 7 42 36 27-7 6 12 36 10 6 1 36 5 36 N. W. Coast of Africa. Cape Spartel W. Pt Mt Habile, 3000 ft. Sallee N. C. Blanco, 170 ft. Mogador C. Ghir, 1235 ft pt Mt Sum. East of C. Ghir, 4400 feet.. Fogo Pk,, 2970 ft. . . C. Bajador, W. pt. . . Down of Cintra or pk'd aiud hill.. . Senegal Lt C. V'erd, extreme.. R. Gambia Bathurst flag-statf. M. Kakulimah,2900 feet 35 48 35 28 34 2-7 33 8 31 30-5 30 88 30 39 29 11 26 7 23 6 16 0-8 14 431 13 28 9 45-8 5 55 5 43 6 46 8 38 9 46-2 9 50 9 33 10 6 14 29 16 10 16 33 17 34 16 36 13 28 Gulf of Guinea. C. Sierra Leone Lt. Freetown N. Battery Bananas Is'l Gov. ho. G.MouatPk. 1060 ft 8 30 13 18 8 29-9 13 14-5 8 8 13 11-7 6 43 111 21 Liberia. NAMES OF PLACES. C. Mesurada Lt Monrovia Gov't ho., Mai'shall Agts. ho. , Grand Bassa Amer. Agent's ho Lat. N. 19 191 8'1 5 54-1 LoN. W 10 50 10 49 10 22-7 10 4 Grain Coast. Trade Town Mt. Tobacco, 830 ft . Pt Sanguin King William Town Eurp. Factories Cape Pal mas Lt. 5 44 5 47 6 12-7 4 49 4 22-1 9 54 9 44 9 20-2 8 43 7 44-2 Ivory Coast. Oval Mt, 1315 ft.. King George Town. C. Lahou Axiin, Dutch Ft. . . C. Three Pta. S. ex- tremity 4 57 4 58 5 11 4 52 3 4 44-7 6 48 6 3 4 31 2 14-7 2 6-7 Gold Coast. Dix Cove Fort. . Elmiua. Dutch Ft C. Coast Castle Lt Camel's Hump, 1200 feet 4 47-8 5 4-8 5 5-4 5 37 1 56-7 1 22-2 1 13-7 31 Bight of Benin. R.Volta W.Ptent. Quitta. Danish Ft.. Why dab Flag-staff.. R. Quorra, or Niger E. Pt New Calebar R. entr. W. Pt Bonny R. entr. E. pt Old Calebar, Tom Shots Pt Mt Cameroons, 1376 feet C. Cameroons Rumby Mont's sum, The Mitre, 3940 ft S.Sum Gaboon R. S. pt ent King George Tower N 6 46 6 65 6 18 4 17 4 23 4 23 4 36 4 13 3 56 4 57 1 20 22 8 E. 41-2 59-7 2 6 6 4 1 1 7 8 8 19 9 12 9 30 9 18 9 57 9 23 9 44 Islands in the Bight of Biafra Fernando Po. C. Bul- len, or N. Pt 3 48 •' Peak, 10710 ft... 3 35 " S. Pt or G.Barrow 3 13 " Clarence Co. Ade- hiide Isle 3 46 Princes Isl'd Ft Sta. Anna 1 39-6 " Diamond Rks. off N. E. Pt large one. 1 407 " Brothers, 2 Isl ds. S. one 1 21*1 St. Thomas Island, Sum. 7020 ft 14-7 Ilha das Rollas off S. S. Pt 5 Anuobona,N. Pt... 1 24-3 " S. extr. rock off . . 1 286 8 43 8 47 8 43 8 47-6 7 26 5 7 27-7 7 17;6 6 33 6 30 6 88-'2 6 36-7 Islands in the N. Atlantic Ocean.— Madeira. Desertaa sm, 1610 ft 32 31-3 W. 16 30-7 NAMES OF PLACES. Madeira, E. Pt Funchal, B.Cona'late Pico Ruivo, 6100 ft. W . End or Pargo pt Great Salvage W. S. Great Piton sum.. . . Alegrauza, S. W. sum. 939 ft Graceosa, S. W. Pt. Lanzarote.N. W. Pt. S. pt Fuerteveutura, N.W Point " Port Cabras " S. PtorPtJandia Lat. N. o ( 32 43-4 32 37-7 32 45 32 48 30 7-5 30 1 29 233 29 12-7 29 2-7 28 60 28 42 28 29 28 3 LoN. W. 16 3«-6 16 54-7 16 67 17 17 15 61-;- 16 0-2 13 31-5 13 32-7 U 48 13 47 14 1 13 51-7 14 31 Canary Islands. Grand Canary, N. W. Pt " Palmas mole head " South Pt " Isleta sum. 847 ft Tenerife Isl'd., N. Pt Anaga Rk " Santa Cruz, Brit Consulate " S. PtorPtRasca " Peak 12.172 ft. " W. extremity. . . Gomera W. Pt sum. 1440 ft Ferro W. extr. (oi Merid. of Ferro) . . Palma, N. Pt " Santa Cruz, Fort Sau Miguel Corvo, N. Pt Flores, N. Extr Fayal, W. Pt " Horta, Sta. Cruz Castle 38 31.7 28 9-6 15 43-2 287 16 25 27 43-8 15 34 28 10 15 25-6 28 36-6 16 8-5 28 28-2 16 14-7 28 16 41-2 28 16-5 16 39 28 20-5 16 66 28 6-7 17 13-5 27 42-5 18 9-7 28 61-3 17 63-6 28 40-5 17 44-5 39 43-5 31 7-2 39 31-6 31 13 38 36-6 28 60-5 28 28-5 Azores Islands. Pico Peak, 8400 ft. St. George, S. E. end. Graciosa, W. Pt. . . Tercera suul 3495 ft St Michael, E. Pt. . " Delgada Lt " W. Pt. or Pt Fer- raria Lt S. Mary sum. 1660 ft 36 685 26 62 38 28 38 32-5 39 4-2 38 43-6 37 48-3 37 44-2 37 51-7 28 26 27 46-7 28 4-7 27 10-5 26 8-2 26 40-7 25 52-2 Cape Verd Islands. St Antonio, N. Pt . . " W. Pt " Summit 7400 ft.. "S. Pt «E. Pt St Vincent, S. Pt.. St Lucia, N.Pt.... Bianca, N. Pt St Nicholas, N. Pt. E. Pt. S. Pt. W. Pt. Sal, N.Pt " Martinez Peak, 1340 ft « South Pt Bonavista, N. Pt. S. Pt. W. Pt. Mayo, N. Pt 17 12 17 4 17 4 16 54-7 17 6-5 16 47 16 49 16 41 16 42 16 346 16 28 16 37-7 16 51 16 49 16 34 16 14 16 67 16 2 3 16 19 26 6-7 25 22-8 26 17 25 18-6 24 59 •24 69 24 47 24 416 24 20-6 24 24 18-6 24 26-2 22 55 22 66 22 57 22 67 22 49-5 22 69-6 23 12 236 TABLE XXXIX. NAMES or PLACES. Mayo, S. Pt " English town, flag statf bill , St Jago, E. PL. . , « Pt Piaya, Quail Is « Mt St Antonia, 7400 ft « West Pt extr... " N. or Bighude Pt FogoN. Pt " Peak, 9760 ft Biava, W. Pt S. Pt Lat. N. 15 66 16 16 8-3 1 14 54 15 2 15 17-3 16 19 15 1-5 14 66 14 49-7 14 46 LoN. W. a I 23 10 5 23 13-2 23 26 23 30-7 23 39 23 48 23 46 24 21-6 24 20 24 46-2 24 42-7 S. Coast of France. Bermuda Islands. Dock Yard Cluck.. Wreck hill Light 365 ft 32 19 32 16-3 32 14-7 64 62 64 55 64 52 NAMES OF PLACES. 0. Bearn Lt 751 ft. Fort Brescon Lt. . . Aigues Mortes Lt. Marseille, St John Fort " Observatory.. . . Plaaier Isl'd Lt. . . Mt St. Michael, Se- maphore, 1341 ft. C. Side Semaphore. Toulou Observatory, " Semaphore. Titan Isl'd. Lt. 246 ft Lat. N. o t 42 31 43 16-6 43 32 43 17-7 43 17-8 43 11-9 43 13 43 3-2 43 7-5 43 4-4 43 2-8 LoN. E. o / 3 7-6 3 30 4 8 6 21-7 5 22-2 5 14 5 22 5 61 5 56 5 66-6 6 30-7 Islands in the Med. below Cape Bon. St. Paul's Islet. Penedo de San Pe- dro, or St Paul's Mid. Rk., 60 ft. 55-5 29 23 Coasts of Med. Sea.— S. Coast of Spain. Palomos Isl'd. .... Gibraltar Mole Europa Pt Lt 150 ft 36 4 36 7-3 36 6-7 6 26 5 21-2 6 22 Gulf of Genoa. L>'.CamaratLt426ft C. Rouse sum. 1600 ft Nice, St Frances Ch Pt Mala Lt226ft. C. St Martin Mt Grande, 3100 ft Savona Citadel Genoa 3 Lights. ... Pt Chiapa sum. . . . Tino Isl'd Lt 384 ft Mouta Altissimo, 6213 ft 43 12 43 28 43 42 43 40 43 43 43 60 44 18 4 44 24-9 44 20 44 2-4 44 3 6 40-7 6 65 7 17 7 19-5 7 33 7 37 8 27-7 8 63 9 10.5 9 62 10 14 NAMES OF PLACES. Maritime Is. 2376 ft LoN. N. I Lat. E. 37 59 6 '12 4 Sardinia. Cape Figari sum... '40 69-9 LimbarraPk.4331ft 40 51 Mt Geuuargeutua, 6102 ft 40 1 Mt Seven Brothers, 3186 ft 39 18-6 C. Spartivento, S. pt 38 526 Cape Teulada sum. 725 ft 38 61-9 Toro Rock, 550 feet 38 51-6 Mount Arcueuto, or Oristauo, 2713 ft. 39 367 C. Argentera sum.. . 40 43-7 Razzolellsl'd.Lt 41 183 9 39-7 9 11 9 19 9 26-6 8 62-6 8 39-2 8 25-2 8 33-6 8 9-0 9 20-7 Minorca. Mahon Mole Lt. to be Cape Cabaleria. . . . Cape Dartuch 39 52-6 40 6 39 65 4 21 4 7 3 51 Majorca. Coast of Morocco. S. W. Coast of Italy Ceuta Lt Tangier Consul's ho, Lt 36 64 5 18 36 47-2 5 48-6 S. Coast of Spain. Estepona Sierra Berraeja Mt Fuengiro Castle . . . Malaga Mole Light, 125 feet. ..... C. Sacratif Corchuna, Castle . Alineria, Town . , Cape De Gath Cas'le Pt. Mesa Tower. . O.DeCope MtRoldan 36 26 36 29 36 32 36 43-6 36 41 36 41 36 60 36 43 36 56 37 26 37 26 5 9 5 12 4 37 4 26 3 28 3 25 2 32 2 12 E. 1 58 1 32 1 2 E. Coast of Spain. Pisa Leaning Tower Leghorn Lt Gorgona Isl'd centre. Piombino Palace. . . Mt. Argentario tele . Civita Vecchia Lt. Rome,St Peter's dm Monte Circello, St. Felix Church. . . . Gseta Lt, Orlando tr, Ischia I. Castle, E. pt Naples Observ. Capo di Monte ' Mole Lt Mt Vesuvius, 3900 ft Castelamare Lt. . . . Capr. Isl'd, S. Pt (Lt to be) Mt St Angelo, 4680 feet C. Vaticano Tower.. Scylla . Cartagena Mole Lt. C. de Pales Tower. . 0. Cervera Plana Isl'd, E. extre. Alicante Castle Lt.. Mt. Roldan Gap .... Cape St Antonio.. . ICape CuUera Tower Valencia Lt 37 36 37 36-6 38 38 10 38 20-7 38 86 38 48-6 39 12 39 28 6 C. Oropesa Pt tower Coluiiibretes Islands N. Rock Port Alfaques, San Carlos Tortosa Cath Tarragona Lt Barcelona Mole Lt . Monserrato Mt. . . . ■Cape Tosa Tower. . C. St Sebastian sum 0. de Creux, E. extr of Spain. 40 5-2 39 64 40 37-7 40 48-8 41 7 41 22-6 41 34 41 43-2 41 53 42 19-2 43 33-5 10 24 43 32-7 10 17-7 43 25-8 9 53-6 42 65-7 10 31-7 42 23.7 11 10-5 42 6-7 11 44 41 641 12 27-2 41 12-7 41 12-4 40 43-9 13 5-2 13 34-7 13 57-7 40 51-8 14 15-5 40 60-3 14 15-7 40 49 14 26 40 41-6 14 28-2 40 32 14 11-7 40 39 14 31 38 37-2 15 52- 88 14-5 16 45 E. extr. Cape Pera.. Mt Galatro Dragonera Isl'd sum S. extr. C. Salinas.. 39 42 39 38 39 36 39 14 3 27 2 28 2 18 3 4 Iviza«; Iriza Castle Pt Denserra, N. extr Port St Antonio, N. Pt Formentera Isl'd, S, E. Pt 38 54-3 39 8 39 0-4 38 38 1 26-7 1 32 1 U 1 36 Lipari Islands. Stromboli Is. 2570 ft Volcano Is., Sulphur Works Ustica Isl'd N. E. pt Fort 38 46-7 38 23-3 38 43-3 16 13-7 14 56 13 11-2 Sicily. 66 40 88 26 26 12 10 W 13 24 E. 10 44 36 33 1 16 2 11 1 55 2 58 3 13 3 20 African Coast. Ceuta Lt Tetuan Custom Ho Alboran Isl'd C. Tres Forca, N. pt. Mid Zafarine Isl'd. sum. W. end Pt Abuja, 2060 ft.. Algiers Mole Lt. . . MtAzafoun, 4360 ft Mt Babor, 6200 ft . Philippsville Lt. . . . Bona Lions Pt Lt. Galita Isl. Pk. 1240 feet Bizerta Castle Cape Cartilage Lt Zembra Island sum. 1661 ft C.Bon Tower 1176 ft 35 64 36 37 36 58 35 28 85 11 35 53 36 47-3 36 50 36 34 36 52-8 36 64-5 37 31-2 37 16-6 36 52-4 37 10 37 4-8 w. 5 18 6 18 3 1 8 2 25-7 29 E. 3 4-6 4 25 5 28 6 63 7 46'5 Faro Isl'd Lt on E. extremity Messina Lt Mt. Etna, 10.874 ft Syracuse Lt Passaro Isl'd Lt. . . Alicata Castle Light Girgenti Mole, 2 Lts, Marsala Lt Mt St Julian 2176 ft Palermo Observat'y. Light Pantellaria Is. sum. 2213 ft Liuosa Isl'd. centre. Lampion, centre. . . . Lampedusa Is. C'st 33 15-8 38 11 37 43-6 37 3 36 41-6 37 4 37 15-6 37 47-8 38 3 38 6-6 38 8-2 36 48 35 51-8 36 32-8 36 29*2 15 41-2 15 34-7 15 00 15 16-0 15 9 13 56 13 31-7 12 26-2 12 35-5 13 21-2 13 22-2 12 2 12 62 12 20 12 85'2 Malta. 8 65'5 4 49-2 10 20-2 10 48 11 35 Valetta Palace 35 53-8 Spencer's Monument' 35 63 St Elmo Lt 36 64-1 S. E. extre. Pt Delia Mare 85 49-7 14 31-2 14 30-7 14 31-6 U 84-7 Goza. N. W. Pt or Cape Demetri 86 4 14 8 TABLE XXXIX. 287 Coast of Naples. NAHES OF PLACES. 0. Spartivento C. St. Vito Lt C. Otranto, (E. Pt of Italy) , . . Islands in the Archipelago. W. Coast of the Adriatic. Aiii^elo IsTds Mid Mt. St. Tremiti Castle, CoUuiellasm.lOSOft. Aucoiia Lt San Marino, 2460 ft. Venice, St Mark.. Trieste Lii^lit Castle 41 43 42 7-3 42 52-3 43 37-7 43 57 45 25-9 45 SS-6 15 57 15 30-5 13 52 13 30-5 12 29 12 2()"2 13 46-5 NAMES OF PLACES. sum E. Coast of the Adriatic. Sausogo Isld sum. 35U feet M. Vella Sti-azza, 1070 feet St Andrea ia Pelago 1000 ft Meleda Isl'd W. Pt. Molonta Isl'd sum. . Veterguach, 39tiO ft. C. Rod.mi, 400 feet.. 44 30-9 43 59 43 1-7 42 47 42 29 9 42 19 41 37-6 14 18-2 15 2 15 45-7 17 IS 18 23-5 18 52 19 28-2 Coast of Albania. ( C. Liuguetta, 2290 ft Mt. Ciea, 6300 ft,, Parga Citadel. . . , 40 26-7 19 17-7 40 15 19 35 39 16-4 20 23-5 Ionian Islands. Hydia Island 1939 ft St. George S.E. sum 1085 ft. Zea Isl'd, Mount St Elias.. . , " Port St. Nicolau It Herniia Island sum. 900 feet Milo, MtSt. Ellas uu S. "W. Pt •24hO ft. " Port W. Pt Point Vani Paros Island, Mt St Elias, mid. 2530 ft Syra Island sum. E. side, 1415 ft. Audros Island, Mt Kovari, 3200 ft. C. Dora, islet off. . Mt Delphi, 6730 ft Skyros Isl'd, N. end sum , •' Grand Port Mt Pelion (Patras), 5310 ft Mt Ossa (Kessova), 6407 ft Mt01ympu8,9754ft Salonika C. Cassandra. Mt Athos sum. 6849 Lemnos, W. Pt S. Pt Fano Isl'd S.W.sum Corfu Citadel Lt. . M. St Giorgio, 1326 feet Paxo Isl'd N. W. Pt Light Anti paxo Isl'd. E. Pt Mt Nomali, 3750 ft Cephalonia, N. extr. Mt Elato sum. 5246 Zante, N. Pt " Mt Teri, 2274 ft. " MtSkopo.l439ft 39 50-2 39 37 39 36-5 39 13-2 39 8-7 38 41-6 38 28-5 38 8-5 37 565 37 50 37 44-6 19 20 19 55-5 19 48 20 9 20 5-7 20 37-7 20 33 20 41 20 41-5 20 44.2 20 57 W. Coast of Greece. Oxia Is. Pk. 1257 ft Lepanto en. Minaret Morea Castle, centre C. Katakolo Stamfaues Isl'd Lt. Navarino Mosque. . Mt St. Nieolo, 1627 feet _. Sapienza Isl'd sum.. Mt Makrino, 7900 ft C. Matapan C. St Angelo Cerigo Isld N. Pt . . •' « S. Pt. . Ovo Island, 550 ft.. Cerigottosm. 1230 ft Mt. Kritluna, 2600 ft Kravi Island Falconera Isl'd sum Bello Poulo sum.. . 38 18-7 38 23-4 38 ls-5 37 37-7 37 15-3 36 54-6 36 63 36 45 36 57 36 23 36 26 36 23 36 7-7 36 55 35 50-1 36 28-2 36 461 36 50-9 36 64-9 21 7 21 50 21 47 21 19 21 1-6 21 41=7 21 42 21 41-2 22 21 2 22 29-2 23 12 22 67 2 52 697 23 23 18 23 8-2 23 36-5 23 53*7 2 27-7 Lat. N. o / 37 19-6 37 28 37 37-3 37' 39-4 37 26-2 36 40-6 36 45-3 37 2-7 37 28-9 37 601 38 9-4 38 37-4 38 49-7 38 46 39 26-5 39 48 40 4-7 40 38-8 39 66-7 40 9-6 39 68-7 39 46-6 Coast of Asia Minor. LoN. E. o / 23 28 23 66 24 21-7 24 20 24 23-7 24 23-5 24 22-7 25 11-5 24 56-7 24 50-5 24 36-3 23 60-7 24 37-2 24 37 23 3 22 42 22 22 22 67-2 23 22-0 24 20 25 2 25 21-5 on NAMES OF PLACES. Tenedos Isl'd N. W. sum Mt Ida, 5750 feet Mitylene, E. Pt. . Smyrna Mill, Daragaz Pt. Sam OS, W. sum " M. Kerki,4725ft Nicaria Beacon 3390 feet Patmos, S. Pt Mt Samsouu,4130 ft Kos, Mt. Christos, 2760 ft Rhodes Lt. . . W. Pt Lat.N. o / 39 50-2 39 42 39 0-7 38 26-5 37 43-8 37 43-7 Lon. E 26 5 26 50-5 26 37-7 27 9-7 26 38-5 26 38-7 37 32-2 26 4-7 37 16 26 34-7 37 39-8 27 9 36 60 27 14-2 36 26-9 28 16-2 36 8-7 27 43-2 Candia. Turkey. Dar(ianelles, AsiaCs Gallipoli Lt Marmora Isl'd S. W. sum Constantinople, St. Sophia! Papa, or Kalolimuo Isl'd N. sum Buyuk Dereh, N Minaret Bosphorus, Europe It 40 9 40 24 40 36-5 41 0-3 40 33 41 10 1 41 14 26 24-5 26 39-7 27 36 28 69-2 28 32 29 29 3 7*2 Black Sea. Coast of Greece. Piraeus, 2 Lts . . . , Athens Parthenon , O.ColonuaTm.269ft 37 56-2 37 58 1 37 38-8 23 38-0 23 43-7 24 1-7 Varna Mosque, raid. Danube R. Soulineh Mo. Lt. Serpent Island Lt. . C. Foutane Lt Odessa Cath Tendra Isl'd N. end. 0. Khersones Lt. . . Sevastopol Ch Mt Tchatirdag S.W sum Kaffa, ov Theodosia. Cape Takli Lt Kertch Ch Yenikaleh Lt Taganrog Ch Azov Cath Anapa, E. Ch High Summit, 4 ml'a inland C. Batoum Mosque. Trebizonde, E, extr. Si nope Castle Cape Baba Asia Lt., entr. Bosp. 43 12 46 9-3 46 15-6 46 22-8 46 28'9 46 21-7 44 35 44 37-9 44 44 45 1-6 45 6-9 45 21-2 45 23-1 47 12-2 47 7 44 54'1 43 17 41 89-4 41 1 42 2-2 41 20-9 41 13 27 26-5 29 40-5 30 14-2 30 45-6 30 54-5 31 32 33 22 33 29-5 34 17-2 35 24 36 27 36 29-5 36 39-2 38 67 39 26-6 87 18-5 40 r 41 37 89 46 36 12 6 81 26 29 9-4 Candia, Minaret Lt. " E. extr. C. Salo- ra.in ' Mt Ida Gozza Isl'd W.Pt.. Boudroom Castle. . Marmorice Cape. . . Highestsum. 5980 ft 36 21 36 9-2 35 13-3 34 62 37 2 36 43-9 36 31-8 25 8-2 26 19-6 24 47 24 2-2 27 27-6 28 20-7 29 142 Coast of Karamania. MtTakhtalu7800ft C. Anamour, S. Pt. of Asia M. . . . Alexandretta Con- sul flag staff. . , C. Khynzyr, 6650 ft 36 31-7 36 0-8 36 36-3 36 16 30 28 32 49 36 9 36 62 Syria. Bairout Brit Con. . Tyre St. John d'Acre, Bas- tion, Marine gate. 33 646 33 17 32 65 36 28-2 36 12-7 36 2-5 Island of Cyprus. West extr. C. Epi- phanius N. and E. extr. C.St Andrea S. and E. extr. 0. Gatto 35 6-3 35 41-7 34 32-8 32 14-5 84 36-5 32 59-7 Egypt. Rosetta, EngL Cons . Aboukir Castle.. . . Alexandria Pt Eu- Dostos Lt Arabs Tower. C. Razat 31 24-3 31 20-5 31 11-5 30 57-7 32 57 30 28 30 5-7 29 51-6 29 83-2 21 38 Barbary. Jebel Zawan, 3917 feet Tripoli, Pasha's Cas. Jebel Thelj, N. E. sum Kuryah Isl'ds, N. E. Pt. sum 36 23 32 53-9 34 25 35 48 10 5 18 11-0 9 52 11 8 Shores of the S. Atlantic Ocean — W. Coast of Africa. Cape Lopez Loango River ent. . Congo River, S. ent s. J 36 8 43 4 89-5 11 46 6 46 12 15 K 238 TABLE XXXIX. NAMES OF PLACES. St. Paul de Loando, flag staff St. Philip de Ben- guela flag staff. . Cape Negro, 200 ft. Diaz's pillar. . . . Mt. Colquhoun, 11 or 18 L. Inland Walvisch B. Pelican point HoUam's Bird Island Angra Pequena, Pe destal point Lat. S. 8 48-1 12 33-9 15 40'7 22 33 22 52-5 24 34-7 26 38-4 Cape Voltas | 28 44 LoN. K 13 13-5 13 24 11 58 11 58 14-27 14 32 15 8 16 32 S. Coast of Africa. Koussie R., limits of Cape Colony. . Elephant's River. Cape Deseada. . . St. Helena B., Point St. Martin .... Saldanha Bay, N. Pt Dassen Island . . . Robben Island, S. pL Table B., Green Pt two Lights Deril's Peak, 3315 ft Cape Observatory . Cape of Good Hope Point, 800 feet. " Lion's Head. . . Simon's B. dockyard Cape Hangklip Pt 1800 feet Dyer Island centre. Quoin Point Cape Agulhas, S. ex- tremity of Africa Light 29 40 81 38 32 18 32 40 33 1-7 33 26-2 33 48-2 33 53-2 33 67-2 33 56 34 22 33 56 34 11-3 34 23-8 34 43-7 34 48-8 34 49-7 17 10 18 12 18 23 17 59 17 54 18 6-7 18 22-7 18 24-5 18 81-7 18 28-7 18 29 18 24 18 26 18 50-9 19 28-2 19 41-7 20 0-7 E. Coast of South America. Maranham Cath.. . Fort St. Marcas Lt Mt Melancias Peak, sand bill Point Macoripe Lt Morro Tibao, Red sand hill Cape St Roque. Pernambuco, Fort Picao C. St Augustin Ch. summit Mt Sellada, S. Peak Mo'nt Masarandupio lOm. inland. . Bahia, St. Antonio Light . . Abrolhos Isl'ds., lar- gest E. summit. Mt Pascoal summit Morrc San Juan, iso- lated , Cape Frio, S. Pt Lt Cape Negro Point Rio Janeiro, foi-t Vil- iagagnan St Sebastian Island, Sjiuth Point. . St Catherine Island, North Point. . Rio Grande de Sul, E. Point Light S. 2 31-7 2 29 3 12 3 41 4 49 5 28 * 8 3-6 8 21 8 25 12 24 13 0-7 18 6 16 54 22 32-5 23 1-3 22 57 22 54-7 23 57 27 22-5 32 7 W 44 18-7 44 18 39 18 38 29 37 18 35 16 34 51-7 34 56 35 11 38 4 38 31-7 38 42 39 20 42 41 58-2 42 39 43 9 45 15 48 25-7 52 8 NAMES OF PLACES. Great Castillos rock (like a schooner) Cape St Mary .... Maldonado Tower. Flores Islands Light Monte Video Rat Isl *' summit. . Colonia Light Buenos Ayres mole landing place. . Pt Indio Sierra Ventana,3500 feet Sierra de San An- tonio, 1700 feet. . Pt. Delgada, 200 ft S. E. cliff Lat. S. 34 24 34 39 34 53-5 34 56 34 53-3 34 53 34 28 34 35-5 35 16 38 11-7 41 41 LoN. W. » / 53 46 64 9 54 57-7 55 55 66 13-6 66 15 57 49-7 58 22 67 9 61 565 65 12 42 46 63 37 E. Coast of Patagonia. Salamanca Pk., 700 feet C. Three Pfs 2000 ft Monte "Video, 300 ft 4m. inland Wood Mt, visible 11 leagues. ...... C. Fairweather, 300 feet, S. Pt 0. Possession, mid. 300 feet Orange Peak Port Famine observ, Mt Saimento, 6800 feet, two Peaks MtBuckland4000ft Cape Tamar Staten Island C. St John Cape Horn 500 feet 45 34 47 6 48 14 49 13-7 51 321 52 17 52 28-3 53 38-3 54 27-2 54 26 53 56-5 53 43-5 55 59 67 20 65 51 66 26 67 45 68 55-5 68 56-7 69 25-5 70 58-2 70 51-5 70 22-7 73 48-5 64 44' 8 67 16 Islands in S. Atlantic Ocean. Ascension, Barrack square Green Mt'n 2820 ft Cross Hill 850 feet. St Helena, Diana's Pk. 2700 feet. . Obs'rvat'ry, showing G. M. T. Fernando Noronha, S. W. Pt " Pk. on S. E. side. Trinidad Isl'd S. Pt Martin Vas Rocks, large one Tristan d'Acunha waterfall N. side middle Inaccessible Islands, West one Nightingale Island. Gough's Isl'd 4385 55-5 57 65-7 15 57 16 65 3 52 3 60-4 20 31 20 28 37 6 37 27 16 26 ft N. Point 1 40 19 14 25-5 14 21 14 25 5 42 544 32 28 32 25-5 29 19 28 51 12 2 12 52 12 8 9 44 Falkland Islands. W. Falkland, Port Steph'ns entrance E Pt summit. . . 0. Tamer N. cliff sum Eddystone Rk 200 ft East Falkland, Port Salvador, Island entrance . 0. Carysford, N. E, cliff Shag 52 51 51 11 17 10 61 23-7 51 25-2 60 41-2 60 52 69 2-5 58 19 57 50-6 NAMES OF PLACES. Port Louis Settle ment flag staff. . C. Pembroke beacon on S. E Port William, Gov. Store House .... Beachene Isl'd, 200 feet S Point. ... Lat. S. Lon. W. 51 32 51 40-7 51 41 52 55-7 68 'J 57 42 67 61-6 59 12-7 Shores of the Indian Ocean. Cape Agulhas, S. ex- tremity of Africa C. St Blaize, S. Pt of Mossel Bay. . . Plittenburg B. S. Pt Cape St Francis. . , Cape Recif Light. , Algoa B. Command ant House " St Croix Isl'd Pk. Bird Island, E. one. Port Hood Cape Natal. Port Natal, S. Pt of ■ Bay.. Cape Vidal St Mary's Isl'd N.pt P. Melville,Elephant Isl'd, S.W. side, N.) Point Cape Corrientes. Mt. Cockburn. . . Port Mocamba, N. Pt Pk, 2000 ft Mozambique, Saint George's Island Mount Pao Loguua Peak. ... C. Paman, Hull Rk. S, 34 49-7 34 6-9 34 4-8 34 10 34 2-2 33 57 5 as 47-6 33 521 33 3-8 29 53 29 53 28 96 25 58-2 25 58 24 7-5 16 29 15 6 15 2-2 14 60 14 21 10 10 E. 20 0-7 22 11-7 23 22-6 24 52-7 25 41-2 25 39-5 25 46-5 26 18 27 58 31 2-2 81 2 32 88 33 2-6 32 57-6 35 30-6 38 66 40 36 40 48-5 40 25 40 37-6 40 10 Madagascar Island. S. extremity of Cape St Mary Leven Island, centre Murderer's Bay, N Point •. . Cape St Vincent. . N. W. extremity, or Cape St Audi'ew Cape St Sebastian, (Island om. off the Point) Woody Island. . . Amber Mountain Port Leven Lingo rk Mananhar Table Hill Tangtang flag staff Plum Island, visible 6 leagues Port Dauphin flag staff 12 26-2 12 16-7 12 34-5 12 46-5 14 39-7 16 42-5 18 2-8 25 1-3 48 45-7 48 41-2 49 11 49 54-2 50 15-7 49 46-2 49 29-2 47 2-2 Isl'ds in Mozambique Channel. Europa Island, or Bassas da India St Juan da Nova. . Mayotta, Valentine Peak Johanna Isl'd Pk. E. Point Comoro, S. E. Point Assumption island, hummock on S.E. part 22 22-5 17 35 12 64 12 16 11 64 40 24-2 42 50 45 16 44 29-6 43 83 25 38-9 25 12-5 46 7 44 18 22 12-5 21 54-4 43 18 43 20-6 16 11-4 44 31 9 46 U6 34 TABLE XX XIX. 289 Coast of Africa (Continued.) NAMES OF PLACES. MtTiiuiclaclel200ft Zanzibar Isl'd S. Pt. Waseeu Peaks, mid- dle one Mt Gibbous MurotHill K extreiu. of Africa Ras Hafoon 600 ft, East Point C. Guiirdafui, N. K extrem. of Africa. Tocotra, W. extrem ity Point " S. W. Point, Ras Kattanie, summit 1466 feet Ras Feluk 800 feet. Lat. S. o t 10 4 6 27-7 4 30 1 12-2 N. 5 41-3 10 26-8 11 60 12 .S3 12 22-5 12 LoN. E. o » 39 44 39 33 39 22 41 28' E. 46 17-2 61 22 61 16 63 18 53 32 50 51 S. Coast of Arabia. a St Antony 2772 feet C. Aden, sum. 1776 feet N. Barnlike Pk 6284 feet JebelJinjeri 1300 ft Kuria Muria Islands, W. one, Haski pk Mazeira Isl'd, S. Pt. 0. Mussendom, N. pt Great Quoin 300 ft Asses Ears 5m. inl'd Hummocks of Kenn, S. one High Clay Pk. white Conical Hill Cambay flag staff St John's Highland Terrpore Point.. . Bombay Obs'rvat'ry " Lighthouse Rajapour Harbor or Rajah Point. . . . Goa, St Ann's light Barsalore Pk. 4452 feet Mount Dilly Calicut Lt flag atafif C. Coniorin Point, S. extremity of India " Peak 12 41 12 46 14 4 17 8 17 27-2 20 7-6 26 24 26 80 28 29 28 4 25 23 20 57 22 17 20 2 19 62 18 63-7 18 51-7 18 16 15 28-3 18 50 12 2 11 15-2 8 5 8 23-2 44 10 45 3 47 32 54 58 56 35-7 58 33 56 34 56 33 51 14 61 41 62 30 71 18 72 35 5 72 43 72 40 72 48 72 47-7 73 73 51-2 74 51 76 11 76 45-5 77 80 77 30-5 Island of Ceylon. Calpeutyn Fort. . . . Colombo Liijht. . . . Pt de Galli fl. stlt Adam's Pk., 7000 ft S. extr. Doudra Hd. Elephant Rk. inland Friar's Hood Tiineomalee Light. Palmyra Point. . . . 15 561 1-8 52 55 24 29 337 49 79 46 79 49 80 11 80 29 80 84 81 32 81 40 81 14-7 80 14 Islands in the Arabian Sea.- Lacadive Islands. Aticutta, mid . Kittan, S. Pt. lU 51 11 25 72 10 73 Maldives. Containing 19 AtolU, or Oroups. Malcolm Atoll, N.E extr Powell's Is'lds N. one 6 24-6 5 29 72 40 72 54 names ok PLACEa Male Atoll, E. extr. " Kings Is'ld flag- staff, N. side LoN. N. 4 27 4 10 Lat. E. 73 42 73 29 Almirante Islands. St Joseph Island . S. 5 27 E. 53 30 Seychelle Archipelago. Frigate Isl'd, E. extr 550 feet Foquet Isl'd, S. extr. 4 35-2 5 27 56 1-2 71 46 Chagos Gro^p. Diego Garcia, S. Pt| 7 26 |72 23 Cargados Garajos. Frigate Island . Siren Island.. . 16 36 16 28 59 33 59 37 Islands in the Indian Ocean. Rodrigue Round Isl'd, 1049 ft Mauritius, Peter Botte,2600ft " Port, L. Cooper's Island Bourbon Isl'd, S. ex. Bouvet's Island. . Thompson's Isl'd. Prince Edward's Is. N. Pt Marion and Crozet's Island Kerguelen's Land, N. Pt C. St George. . . St Paul, 700 ft. . Amsterdam summit, 2760 ft Keeling Island, S. Group, S. Pt Direction Isl'd S. W. Pt Christmas Isl'd. . . . 19 41 19 60 20 11-7 20 9-7 21 24 64 20 63 66 46 46 46 9 48 41 49 54 38 43-8 37 62 12 12-6 12 6-4 10 31 63 25 57 60 67 36-7 67 31-7 65 40 6 24 5 30 87 18 60 28 69 6 70 10 77 38 77 36 96 54 96 63 105 38 NAMES OF PLACES. Rangoon city, Dagon Pagoda.. Martiiban Maulmain Pagoda. . Amherst Lt., to be. Mt sum. inland. . . . The cone, vis'ble 161 Tenasserim Island. . Juukseilon, H. Mt S Pt Pulo Pera Penang Island sum 2713 ft " Cornwallis fl. st. Pulo Dinding Salangore Hill and Fort Parcler Hill sum. C. Rachado, vis. 7 1. Malacca flag st. . . Mt Moar sum... Mount Formosa. . . Pulo Kissang, 200 ft Singapore Battery Barbukit Hill, 645 ft Pedra Branca, or Horsburgh Lt . . Bintang hill, 1200 ft Preparis Isl'd Cow t Ecrued Hili, 4S0 feet 39 4 36 16 35 6 34 33 51 2 83 51-7 33 48-7 32 55-8 32 14 28 38 26 20 24 16 23 27 22 40 22 29 21 84 20 64 20 28 20 14 20 3 19 38 LoN. E 146 SO 160 13 151 2 161 161 16 18-2 151 161 151 147 21-5 147 50-7 148 8 147 66 147 57 147 17 146 48-2 146 50 2 146 46 145 29 144 89 , one 18 22 16 66 16 4 14 62 14 41-4 14 34 12 37-5 12 16 11 19 10 37 10 41 10 41-6 9 66-6 31 48 81 87 14 1 48-7 152 35 153 40 152 56 151 66 161 7 151 150 48-6 149 20 149 e 149 7 148 31 147 48 146 69 146 17 146 146 26 146 21 145 28-6 144 41 143 27-5 143 27 142 51 142 41 142 85 142 34 144 5 169 20 169 14 '10 57 1142 18 Torres Straits. Post Booby L 80 ft Office •. Darnley I. hill 680 ft Turtle Backed Isl'd, 368 feet Mt Ernest, 807 feet Mt Augustus, 1810 f|l0 9 10 86-7 9 86-8 9 54 10 16 141 66 143 49 142 48 142 31 142 21 Gulf of Carpentaria. Wellesly Is. Sweers Island Inspection Hill, 105 feet C. Shield Mt CaledoD C. Arnheim. C. Wilberforce Pt Dale 17 8-2 189 41 18 20 136 28 12 53 136 88 12 17 187 11 53 186 84 11 86 136 7 TABLE XXXIX. 241 N. Coast of Australia. Lat. s. Lon. e. NAMES OP PLACES. or of C. Cockburn Pt EssiiigtoQ gov. h. C. Don. Cape Hothara Bathurst Is'ld S. extr C. FourciDy P.Darwiu. P. Emery on E. side of eutr. Pt. Blaze 11 18 11 22-3 11 19 12 3 11 61 12 27 12 61 132 51 132 10-7 131 48 131 20 129 57 130 51 no 11 N. W. Coast. Mt. Gasuariua C. Beinier , C. Talbot.. Port Wariauder, Chrystal Hd Port Nelson CareeO' ing beach Pr. Regent, R. ML Trafalgar summit C. Borda. C. Baskerville C. Vellaret, 150 ft.. C. Jaubert, 46 feet.. Mt. Blaze, 60 ft Depuch Island, 614 feet C.Lambert C. Preston Barrow Island, N Pt 14 23 14 13 47 14 28 15 6 16 16-6 16 36 17 9 18 19 18 68 20 20 38-4 20 36 20 30 20 40 127 40 127 28 126 46 126 58 1^ 4 125 7 122 49 122 19 122 7 121 40 119 38 117 46 117 11 116 6 115 27 New Zealand. Cape Farewell.. . Cape Foul wind. . , The Five Fingers., Bold Head Cape Patersoru. . Cape West Pt. Maequarrie.. . South Cape , Molyneux Har. N. pt. Saddle Hill , E;i8t extreme Pt. , Mt Tako, a high pk. Pt Hardy, Nelson's Monument at entr. Nelson, Aglionby pt G. Egmout, or Borul M. Egmont. 8.9000 f Entry Isl'd W. Pt 1800 ft Port Nicholson, Pen- carrow Head. , , , Black Hd C. Gable Mt IkourangL Mt Edgecumbe. ... Guvier Isl'd sm. . . . Auckland flag staff. C. Tewara Pt C. Motou-aro Wangaroa Hb. N. lid Mt Ohoura or Camp- bell C. Otou, or N. Cape Three Rings, I. one. Mt Manganui Lymoud's Hb. Bea- con Bluff. Kawia Harb. Alba tross Pt 40 31 172 47 41 46 171 29 42 4 171 25 42 67 170 40 46 24 166 30 45 56 166 8 46 20 168 10 47 17 167 32 46 25 169 55 45 56 170 31 43 46 173 14 41 42 174 25 40 44 41 14 39 20 39 15 40 64 41 27 174 53 40 14 176 55 38 31 178 26 37 55 178 16 38 177 2 36 26 176 42 36 51-5 174 45 35 51 174 35 35 26 174 27 35 173 45 84 49 84 24 34 18 36 62 ST 6 38 6 173 67 173 16 173 39 174 4 174 65 173 2 173 1 172 10 178 40 174 82 174 62 Loo-Choo Islands. Lat. N. NAMES OF PI.ACES. o / Koomisang, N.W. Pt Loo-Choo, Gr. Isl'd vis. 19 L E. extr. C. Sidmouth Herbert Isl'd entr. to Pt Melville. .. Sugar-loaf, mark for Pt Melville Montgomery Island N. Pt..." 26 24 26 12-5 26 47 26 44 26 48 27 4 Lon. E 126 47 127 41-6 128 21 127 58 127 48 128 2 Coast of China Nankin city.porcel'n Tower Uih Taou, or Staun- ton Isl'd Saddle Island.. . . Great Wall S. extr. of Coast Rock like a Junk., Lindsay I. S. W. Pt Gape Basil, Basil bay (continued.) 32 2 36 60 122 15 37 24 119 53 40 5 120 38 40 121 11 38 56 122 49 36 26 126 28 36 8 126 61 118 49 Japan Islands. Asses Ears, S. one, Nangasaki, mid. of City C. Nomo Horner Peak 0. Tschitschagoff, S. extr. of Japan I'ds C. Cochrane G. Misaki, W. Pt, Sikok Island..., Nipbon S. Pt « N. E. C. Nambu. " N. Pt C. Greig Russian Promontory W. Pt Zach Mt 32 2 32 44-8 32 86 31 9 30 67 31 51 33 18 33 26 41 23 41 32 41 9 39 52 35 26 128 36 129 62 129 42 130 28 130 36 131 27 132 17 136 47 141 30 140 60 140 8 139 38 132 20 Jesso. C. Spanberg N. extr. C.Soya.. C. Malespina. ... Pyramid Rk. off the N. EPt 44 35 45 31 43 42 46 17 145 141 51 141 18 150 30 Eamtschatka. Kronotskypk 10,610 feet Kluchevsky volcano 16,600 feet Behring Isl'd W. Pt. « ■ S. Pt. Copper Isl'd. 3. Pt. 54 45 56 "8 55 17 54 21 54 33 160 33 160 41 165 46 166 44 168 11 N. W. Coast of N. America. C. Douglas E. Pt Mt St Augustine am C. Elizabeth, E. Pt Montague Isl'd, Port Chambers, E. cove " S. Point Mt St Elias, 14.917 feet, seen 50 1. off, Mt Fairweather. C. Fairweather.. . C. Edgecumbe.. . N. 68 64 59 22 69 9 60 16 69 46 60 17 68 64 .58 61 67 2 W. 152 51 163 151 18 146 60 147 30 140 52 137 38 137 50 135 45 Russian America. names ok places. Sitka Arsenal Light C. Ommanney. . . C. Addiugton.. . . C. Muzon Lat. N. o / 67 2.9 66 9 66 27 64 43 Lon. W. o / 135 17-: 134 34 133 48 132 42 N. W. Coast (Continued.) Queen Charlotte s Is. Cape Henry " Pt North " C.St James, S.pt Port Simpson 52 52 64 20 51 56 64 33 132 25 133 11 131 2 130 18 Vancouver's Island. NootkaSo'ud friend- ly cove Esquimalt harbor. Islet entrance. .. Port Discovery W. Head Port Neah, S. W. Pt Gray's Harb. N. Hd. Fort George C. Perpetua C. Mendocino 49 35 48 25-6 48 6-6 48 22-5 47 46 11-5 44 12 40 29 126 35-6 128 37-7 122 64-5 124 S6-7 124 7 123 51 124 17 124 32 Coast of California. Mt Bolbones, 3765 feet, 10 1. inland St Francisco Fort S. side See also the Sea coast s of the United States for more particulars. Monterey Fort. . Pt. Conception. . San Juan St Diego, Pt Loma C. Goluett, S. W. Pt Pt St Bartholomew N.Head C. St. Lazaro Mount 1300 feet , C. Palmo 37 52-9 37 48-5 36 364 34 31 32 53 32 38-8 30 69 27 39-S 24 47 23 22 121 54-6 122 28 6 121 53 120 30 117 44 117 14-7 116 15 114 53-5 112 16 109 17 Gulf of California, Santa Ciuz Island. C. St Gabriel C. Haro Pt. Rosa 25 22 28 35 27 50 26 42 110 49 112 46 110 54 109 50 Mexico, West Coast. Pt Arbolado Mazatlau Custom H. San Bias Arsenal. Mt St Juan, 6220 ft 6 leagues inland. Port Navidad sum S'luth Head Colima Volcano 12- 000 feet Acapulco, Fort St Di«go 23 33 23 11-8 21 32-6 21 27 19 12 19 26 16 50-8 106 48 106 28-7 106 15-6 104 56-6 104 46 103 38 99 62 Central America. Libertad vill. fl. st. Pt Consequina Vol- cano, 3800 feet. , Volcan,Viejo5662ft Port St Juan S. bluff 13 80 12 58 12 41 11 15-2 89 17 87 37 86 58 85 63 Panama. Bahia Honda Senti Del Isl'd at eat . . . PtMala 7 436 7 26 81 SI 80 S 242 TABLE XXX IX. NAMES 07 PLACES. Panama, N. E. Baa- LlOIi ■•■•••••■ I 0. Corrientes...., lel'd Gorgona, N. pt. 1296 feet Lat. N. 8 66-9 6 33 3 LoN. W 79 31-2 77 29-5 78 9 Peru. S. W 0. Passado 21 80 32 C. St. Lorenzo 1 3 80 67 Guayaquil Arsenal. 2 12-4 79 52 7 Saddle of Payta 1300 feet 5 12 81 10 Eten Hill 640 feet a mark 6 56 79 54 Mt. Sulivan 5000 ft I7m. inland 7 17 79 21 Truxillo Ch, l^m inland 8 7-6 8 27 79 42 Guanape Hill, 700 ft 78 67 Mt. Division 3 pks. 1880 feet 9 11 78 88 Mt. Mongon summit. 3900 feet 9 88 78 22 Darwin pk., 5800 ft 10 30 77 60 Peseador Isl'ds large one 1147 12 8 77 20 Lima Bridge 77 6 Callao Arsenal 3. st. 12 4 77 13-7 San Lorenzo Island, 1284 ft., N. PL or C. St Lorenzo. .. 12 4 77 19 Ohincha Isl'ds N. pt. 13 38 76 28 Mt. Quemado 2070 ft 14 20 76 11 Mt. Camana (like a fort) 16 37 72 45 Islay, port of Are- quipa Custom H. 17 72 10-6 MorroofSama,8890 feet 17 59 18 28 70 56 70 24 Arica mole Carrasco Mt 5620 ft 4m. inland 20 58-5 70 10 Cobija Pk. 3330 feet 22 32 70 18 Mt. Mexillones 2560 feet, 3m. inland. . 23 6-5 70 35 Mt Moreno 4160 ft 23 28-6 70 88-6 Grande Pt W. sum- mit 1572 feet. ... 25 7 70 84 Port Caldera, W. hd. 27 3 70 66-2 Copiapo (landing pL) 27 19-5 71 2 Herradura Point. . . 28 6 71 16 Guasco port 28 27 71 19 Ooquimbo Signal hill Mt Edward's Ho. 29 54-2 71 19 Mt Talinay, 2300 ft 80 51 7142 Valparaiso Lt on N. "V. Pt, fort St Antonio 88 1-9 71 41-6 Aconcagua 23,200 ft 26 leagues inland S2 88-5 70 1 Bell of Quillota 6200 ft. 7 leagues inl'nd 82 67-2 71 10-5 Talcabuano, Fort Galvez 86 42 86 49-6 78 10-2 78 6-6 Coneepcion City mid Paps of Bio Bio, 800 feet S. W. summit 86 48 78 16 Mocha Isl'd summit, 1250 feet 88 28 78 59 Valdivia City mid.. 39 49 78 19 Chayapiran Volcano 8000 feet 42 48 72 84-7 Oorcobado Volcano, 7600 feet 43 11-8 72 49 Obiloe Island, W. pt 43 17 74 26 NAMES OF PLAOE& w Huafo Isl'd, N. Pt 800 feet. C. Taytao, 3000 feet W. Point. G. Tres Montes 2000 feet Pt. . . Port Otway, S. ent summit. . Dome of St Paul's, 2284 feet Port Sta. Barbara W. Head 0. Montague W. cliff 0. Three Pts. 2000 ft Diana Peak Westminster Hall. C. Deseado 0. Noir, 600 ft. S. pt 0. Desolation Pks. pt York Minster Diego Ramirez Isl'd middle. . . Ildefonsa Isl'd 100 ft middle. ,. . False C. Horn Orange Bay, Brunt Island. . . . Cape Horn 500 feet Lat. S. 43 86 45 53 46 59 46 49-5 46 36 48 2 49 7 60 2 52 8 52 37 52 55-6 84 30 64 46 65 25 56 25 55 62 65 43 55 30-8 55 69 LoN. W. 74 49 75 8 75 28 75 18-2 76 14 75 80 75 37 75 21 74 48 74 24 74 38 73 6 71 37 70 5 68 44 69 19 68 6 68 2 67 16 Islands in S. Pacific Ocean. Bishop and Clerk. . Macquarrie Isl'd, N. Point Campbell Isl'd, 1500 feet S. harbor, N, Head Auckland Islands, S. Cape " W. extreme. . . Mt Eden, 1325 feet Enderby Isl'd E. pt Peuantipode Island, small Bounty Islands . Chatham Islands, S. Isle, like a Pyra mid Juan Fernandez Isl'd N. side Cumber- land B. Fort.. S. Pt Sta. Clara Island St Ambrose, vis. 10 leagues W. Pt. Easter Island, N. E. Peak, 1323 feet Pitcairn Island 2500 feet Gambier's Isl'd, Mt Duff... Encarnacion Island St Elmo. Aurora Isl'd 250 iL N. Point Otaheite Isl'd, vis. 12 1., Pt Venus fl. St. Summit 7000 feet Papeta Harb. fl. st. Eimeo Isl'd perfora ted Pk. 4041 feet Marquesas E. extr. Ariadne Rk. 10 ft " Madalena Island 8700 feet S. Pt. . S. 56 15 64 19 52 34-4 50 56 50 60 60 35 60 30 49 82 47 44 44 20 83 87-6 88 46 26 21 27 6 25 8-6 28 8 24 46 21 20 15 60 17 29-2 17 89 17 821 17 80 10 21 10 31 E. 168 56 158 56 169 12-7 166 7 165 55 166 10 166 19 179 42 179 7 W. 176 4 78 68 79 2 80 10 109 17 180 8 NAMES OF PLACES. St Pedro Isl'd 1700 feet E. Pt Sta. Christina 3000 f. Hood Isl'd 1200 ft. Washington Island, 2000ftS.Pt.. Nukahiva,3600feet Robert's Isl'd 2000 i. Norfolk Island Mt Pitt 2000 ft. . Verraders Isl'd 2006 feet Manua Isl'd, 2600 ft summit Apolima Isl'd 472 ft Home Isl'ds, 2500 ft Pylslaart Isl'd 700 ft Eoa Isl'd 600 ft mid Kao Isl'd Pyr, 5000 f Tofona Isl'd, 2800 ft. Latte Isl'd, 1600 ft. Lakamba Isi'd, 1200 ft mid, Niau I. seen 15 Lsm. Lat. S. Lon. W. 9 57 9 66 9 25 8 56 8 65-3 8 28 58 16 54 14 15 13 49 14 18 23 34 21 24 19 42 19 45 18 49 18 14 17 59 188 45 139 10 138 67 139 33 140 6 140 48 167 46 173 48 169 26 172 3 178 18 176 4 174 57 175 175 3 174 35 178 51 179 2 Eejee Islands. Vanua Levou 1. 2070 ft. E. orUndap., Dana's Peak. . Moala Isl'd, 1800 ft S. Pt Mitre Isl'd, vis. 41.. Ticopia, vis. 10 leags 16 8 16 46 18 41 11 65 12 21 179 56 178 49 179 53 170 9 168 48 New Caledonia. New Caledonia, E. p C. Colnett " W. extr. Pt Ton nerre S. 22 16 20 29 20 24 E. 166 56 164 44 164 New Hebrides. Tanna Isi'd, Cook's Pyramid 19 809 " Volcano, 4 m. in- land 19 81 Sandwich Isl'd S.W. Pt 17 46 Pentacote Isl'd S. pt 16 69 Vanikoro Isl'd, sum. 8081 ft Ill 87 Volcano Isl'd sum. . 10 23 169 28-7 169 24 168 9 168 19 166 49 166 49 Solomon Islands. 184 56 186 40 143 60 148 11 149 29 149 80 149 34 149 47 188 29 138 48 Guadalcanar Isl'd K Pt " Mt Lammas. . Isabel Isl'd, S. Pt C. Prieto «M.Marescot,8901 feet Eddystone Rk. 1086 feet Bougainville Isl'd Mt Balbi, 10.062 ft 6 L inland N. Pt. 0. I'Averdi.. Bouka Isl'd, N. Pt. . " Summit. . . . Garret Denys, 8200 ft the highest of these Islands. . Gardner's Isl'd, 2000 ft N. Pt , 9 60 9 50 8 84 8 14 8 18 6 66 6 80 6 1 6 18 8 4 2 34 160 64 160 20 169 64 169 88 166 81 164 29 165 7 164 40 164 89 162 84 61 64 TABLE XXXIX. 248 New Ireland. MAKES OP FIACES. New Ireland, E. Pt. C. SL Mary Cape St. George Lat. S. 4 2 4 51 LoN. R 153 18 152 56 New Britain N. Pt. 0. Stephens.. 4 12 152 S. E. Pi. C. Orford. S. E. extr 5 24 152 4 Pt Roebuck 6 16 150 33 C. Gloucester, 2 p'ks 5 28 148 23 Lotteu Isl'd, above 3000 ft 5 20 147 36 Volcano, above 4000 feet 6 32 148 17 Dischamps pk. 8 m. inland 6 6 151 28 Galapagos Islands. NAMES OF PLACES. Chatham Isl'd, 1650 ft. E. Pt Mt Pitt, 800 feet " S. side watering- place Charles Isl'd 1780 fl Post-Office on N. W. side. Daylight Pt Gardner Isl'd, 760 ft Albemarle Is. 3780 ft. Iguana Cove, S. W. side Lat. S. 044 66-4 1 16-4 r2i 69 LoN. W. o t 89 20 89 88-7 90 81-7 9 28 91 32 5 NAMES OP PLACES. N. Coast of New Guinea. Cape Rodney Cape King William 13000 ft Dampier Is'l 5000 ft. Vulcan Isl'd, conical Garnot Isl'd, conical D'Urville Isl'd pk. near W. end Mt Julian, 2 1. inla'd E\ ries Mt very high sum. 8 1. inland Cyclops Mt vis. 20 L E. sum Lesson Isl'd, a high C0D3 Jobie bl'd, vis. 20 1 E. Pt Arfak Mts. S. one, 9520 ft. » N. one, 8610 feet Bee-hive Mt , Mt. Diceras, 8 m. in laud. 10 2 16 40 6 80 20-1 6 50 81 7 48 8.9 61 44 82 148 30 147 40 145 58 145 1 144 85 143 31-! 144 26 141 15 140 80 189 27 136 60 138 64 133 64 133 25 182 16 Isl'ds in the N. Pacific Ocean. Redondo Rk. 86 ft Towers Isl'd, 211 ft. E. P Abingdon Isl'd S. pt mid. 1930 ft. . . Wenman Isl'd, 830 ft Culpepper I. 550 ft Malpelo Island sum. 1200 ft Socorro Isl'd, 2000 ft S. E. Pt Benedicito Isl'd 1100 feet mid Guadalupe Isl'ds, W, one, 8400 feet .... N. 14 21 84 1 28 1 40 4 18 48 19 20 28 64 W. 91 40 90 90 49 91 64 92 4 81 82 110 52 110 86 118 20 Lat. N. Sandwich Islands. Owhyhee Isl'd, S. pt " Mowna Rou Mt 13.175 feet " East Pt " West Pt Mowee Isl'd, K Pt. " W, sum. 6126 ft. 19 6 19 28 19 84 19 42 20 44 20 48 166 49 155 88 164 56 166 6 166 68 166 14 Morotoi Isl'd, E. Pt. W. Pt. Woahoo Isl'd, E. Pt " S. or Diamond pt " Honoruru Fort. « S. W. extreme.. - W. Pt « N. Pt Atoor Isl'd, EPt.. " Hanalae, B. Brit Cons. K side.. " N. Pt Oneehow Island, K Pt " S. Pt Necker Island, 800 feet Rica de Oro Rk. or Lot's wife, 850 ft Volcanoes, 8 Sulph'r Islands " N. Isl'd San Ales- sandro « S. Isl'd, San Dio nisio, 896 feet. . . , Forfana Island Rota Isl'd, 800 ft E, Pt Assumption Island, 2026 ft Guam Isl'd, N. Pt Oalan Island, Mt Crozer about 2000 Mao Askill Islands, S. one Pouiuipet Isl'd sum, 2861 ft The highest land yet discovered is Mt Erebus, which is 12.400 ft above the sea, and is an active volcano in 21 9 21 7 21 20 21 15 21 18-2 21 17 21 86 21 43 22 8 22 14 22 16 22 21 45 28 84 29 61 24 48 25 14 24 22 26 84 14 9 19 41 18 89 6 19 6 IS 6 68 LoN. W o 156 5] 167 24 167 37 157 48 167 56 168 7 158 15 157 68 I 159 20 I 159 82 I 169 81 160 6 160 18 164 87 167 4 141 20 141 18 141 28 148 145 18 146 27 144 63 163 4-7 160 47 168 24 S. 77 88 K 166 68 f'244 COF TABLE XL. CONTAINmG THE POSITIONS OF PLACES (OMITTED IN TABLE XXXIX.) ON THE COAST OF THE UNITED STATES OF AMERICA AND WEST INDIES, TAKEN FROM THE LATEST SURVEYS. E. Coast of U. S. of America. Seal laland Lights Libby Island Liglit Baker's Island Lt, Petite Manan Is. Lt. Isle an Haute Cashes Ledge. . . . Manegan Isl'd Lt. . Penmaguid Pt. Lt. . Bantam Ledge .... Seguin Island Lt. . . Cape Small Cape Elizabeth Lt.. Wood Island Light Goat Island Light Cape Neddeck . . . Boone Island Light New Hampshire. White Island Light Portsm'th Outer Lt. Great Boar's Head. Massachusetts. Newburyport Light on Plumb. Isl'dL. Annis Squam Lt.. . Cape Ann Gloucester Hr. Lt. Baker's Island Lt. . Nahant, east pt. of Boston Harbor. Scituate Har. Light Braat Point. Gurnet Pt. Lt, ent. to Plymouth .... Beach Pt Lt, ent to Barnstable Bay . Race Point Light . . Nausette Light . . . Chatham Hr. Light Great Point Light Sankaty Hd. Light Smith's Point Cape Poge Light. . No Man's Land. . . . Gay Head Light . . Cuttyhunk IsL Lt . Sangkornet Point . Nantitcket Shoals. McBlair's Shoal . . . Old South ShoaL . . Davis' Sho. Lt Ship Georges BhoaU. S. R Point W. Point N. R Point North Shoal Third ShoaL East ShoaL Lat. N. Lon. W. u 29 44 34 44 14 44 22 43 59 42 66 43 45 43 45 43 44 43 42 43 41 43 34 43 28 43 21 43 10 43 7 42 68 43 04 42 55 42 49 42 40 42 39 42 35 42 32 42 42 42 25 12 06 42 00 Rhode Island. Brenton's Reef. . . . Beaver Tail Point . Watch Hill Pt Lt. Block IsL S. R Pt. New York and Connecticut. Montauk Pt Light Fire Island Light. . 41 42 41 41 41 41 41 41 41 41 41 41 44 04 52 40 24 17 18 25 15 21 25 27 24 04 41 41 40 67 41 88 41 42 41 48 41 68 41 61 41 47 41 26 41 27 41 18 41 09 41 04 40 38 68 68 69 69 69 69 69 70 70 70 36 51 17 28 36 44 50 11 19 25 70 36 70 28 70 88 70 41 70 47 70 49 70 41 70 35 70 89 70 47 70 54 70 43 70 88 70 86 70 16 70 15 69 57 69 57 70 03 69 57 70 17 70 27 70 49 70 50 70 67 71 11 New Jersey and Pennsylva7iia. 67 06 Barnegat Light . . 67 23 Little Egg Hr., o 68 08 Tucker's Isl. Lt 67 62 Chincoteague Lt . Carolina and Georgia. Currituck Inlet. . . , Roddy's Isl'd Light Ocracock Light . . , Doboy Bar ....«.., Amelia Isl'd Light. Florida. St. John's Light. . . CarysfortRf. LtSh, Sand Key Lt Bea. Cape Romano Carlos Bay Ent. . . Tampa Bay Ent Lt Dog Island Light. . Cape St. Bias Lt. . Islands in the West Indies. Barbadoes N. Pt . . Martinico S. R Pt. Mariegalanta S. Pt. Saintes Isl'd W. Pt Guadaloupe, Petite Terre Light t Austatia, N. Pt Saba, W. Pt Aves or Bird Island, N. Pt Berbuda, N. end . . St Bartholom's, N. St Martin's, S.RPt Anguilla Custom H. Dog & Prickly Pear Sombrero Virgin Gorda,E.Pt Santa Cruz, R ecd. Frenchman's Cap. . Sail Rock Crab IsL, R end.. . Porto Rico, Saint Juan Lt Pt Brugen, or N W. Pt Cape Roxo Monico Island Zecheo Island 69 69 69 48 51 51 67 89 67 69 67 47 67 48 67 26 67 19 71 21 71 24 71 51 71 33 71 51 73 18 Lat. N, O t 39 46 39 30 37 55 36 23 35 47 35 7 31 20 30 40 30 20 25 13 24 27 26 61 26 32 27 35 29 46 29 40 St. Domingo Island. Saona IsL, E. Pt.. Beata Island Altovela. Cape Jaqnemel. . . Isle a Vache, R end. Navassa IsL, Mid.. Jeremife C. Nichola, Mole . . Tortuga, R Pt Port Paix. Pt Picolet Grange Pt Port de Plata Old Cape Francois. Cape Samana Cape Raphael 13 19 14 80 15 52 15 52 16 10 17 32 17 89 15 41 17 43 17 54 18 5 18 13 18 17 18 36 13 30 17 45 18 14 18 16 18 7 18 29 18 32 17 56 18 9 18 24 18 12 17 87 17 28 18 13 18 6 18 25 18 40 19 49 20 1 19 56 19 47 19 66 19 46 19 42 19 18 19 3 LoN. W, 74 6 74 17 75 21 75 55 75 32 76 68 81 22 Jamaica. Morant Pt Lt Portland Pt S. Negril Morant Keys Portlan Rock Pedra Shoals, N. Pt South Rocks, above water Camanbrack, E. Pt Swan IsL, R Pt . . . Cuba. 81 36 jTrinidad. Jardines, S. E. Key. Cape Antonia Lt . . 81 33 Pt Hyecos Lt 80 13 French Cay, N. Pt. 81 52 Neuvitas Lt 81 56 Pt deMulas 82 15 Bara-o 82 47 Cape Maize 84 48 Cumberland Hr. . . 86 28 3t Jaco de Cuba Lt. 59 46 60 60 61 24 61 45 61 7 63 5 68 19 63 87 61 52 62 48 63 6 63 4 68 17 63 28 64 14 64 34 64 52 65 8 65 18 66 7 67 8 67 10 67 56 67 28 68 31 71 32 71 40 72 33 73 31 75 3 74 5 73 27 72 36 72 46 72 12 71 42 70 46 69 65 69 6 68 50 Turks and Caicos Islands. Baho de Navidad.. Silver Key Bank, — S. W. end .... — N. end. .... — N. R end . . Square Handkerc'f, S. W. end. N. R end. Grand Turk Lt . , Salt Key , Sand Key Philips' Reef N. W. Caycos . . , West Caycos... . , South Caycos . . . , Bahamas. Gt Inagua, S. W, end. Hogsties, E. end. . . Mayaguana, E. end. S. W. end French Key, R Pt Aclin'sIsL.N.Rend Bird Rock, N. W. end of Crooked Is, Miraporvos, S.E end Castle Isl Atwood's Keys, R end Watling'sIsL.N. R Pt.... Conception IsL, S. Pt Long IsL, N. Pt . . . Eluethera Isl'd, Si Pt,— Ship Chan'l Harbor IsL, N. end. Gt Abaco, N. R Pt (keys off.)... Mantanilla Reef. . . Memory Rock Gt Bahama, S. R Pt Stiriup Keys. Berry IsL, E Orange Keys N. end Lat. N, 17 56 17 44 18 16 17 26 17 7 17 40 16 60 19 45 17 25 21 43 21 40 21 61 23 11 22 50 21 40 21 10 20 21 20 15 19 55 19 57 20 13 20 18 20 55 20 35 20 52 21 9 21 31 21 19 21 14 21 43 21 52 21 37 21 3 20 65 21 40 22 23 22 21 22 35 22 45 22 51 22 00 22 7 23 6 24 7 23 47 iS 42 24 37 26 35 26 88 27 81 26 55 26 28 25 50 25 28 24 56 LoN. W, 76 77 11 10 7« 25 75 57 77 27 78 54 78 20 79 42 1 83 50 80 6 81 12 84 67 1 81 9 79 30 77 15 75 55 74 80 74 7 75 15 76 2 68 62 69 68 69 52 69 18 70 65 70 26 71 5 71 10 71 11 71 20 72 16 72 27 71 46 73 89 78 51 72 42 73 9 73 28 73 50 74 22 74 28 74 20 1 73 87 74 26 1 75 8 75 18 76 9 76 45 1 76 50 79 8 79 3 78 10 77 55 77 42 7c 9 TABLE XL. 245 Ridding Rocks, S . Mexico. Pasa de Cabello . . Brazo de Santiago St Fernando River, ent River Tampieo, ent. Cape Rojo Tamiagua Bar. .... Boca de Lima Alvarado Bar Pt Morillos. Barilla River St. Ann IsL Carmen, W. Ft IsL Real, W. Ft . . Ytteatan. Ft Piedras B0CO8 Del Rio La gartos. Los Arcos Bajo Nnevo IsL Arenas. Mogeres IsL, & Pt. Lat. N 26 12 LoN. W. O f 79 10 21 11 21 86 20 13 21 60 22 8 21 18 28 20 96 22 26 6 97 12 25 20 97 30 22 15 97 48 21 35 97 20 21 13 97 17 20 30 96 57 18 47 95 43 18 38 94 54 18 10 94 32 18 11 93 51 18 38 91 48 18 62 91 22 90 10 88 14 91 69 92 6 91 26 86 45 IsL Contoy, N. Pt . IsL Cozurael, N. Pt South Pt N. Ti'iangle South end. . . . Mauger Key Light Turneff Reef, S. Pt Half Moon KeyLt. Glover's Reef, N.Pt Cape Three Points. UtillalsL.R Ft... Rattan IsL, R Ft. . West Point... Barburet Island. . . Cape Camaron.... JVew Oranada. Fort Sabanilla, ent — Hacha Cape La Vela Ft Galinas IsLOniba.N.W.Pt — S. R Point... Cape St Roman . . . Curaco IsL, N. Pt. St Ann's Bay .... Lat. N. o f 21 82 20 85 21 15 18 46 18 23 17 36 17 JO 17 12 16 55 18 58 16 7 16 27 16 17 16 26 16 00 11 11 1 88 12 10 12 25 12 86 12 24 12 11 12 21 13 6 Lon. W o / 86 51 86 44 87 00 87 20 87 20 87 46 88 00 87 34 87 45 88 88 86 53 86 12 86 88 86 9 85 8 76 1 72 66 72 14 71 44 70 12 70 1 70 7 69 10 68 54 Little Curacoa .... Buen Ayre, N. Pt . P. Rosa Light Bird Island, E . . . . Western end . Laguira Cape Codera Orchilla IsL,W. end. Blanco Island, N . . Los Hermanos, S. Ft Tortuga Salada, R Point Margarita, R end. . W. end Testigos IsL, mid Dragon's Mouth — Point Pera .... 9erpant's Mouth,- Point YeacoB.. , Ouiana. Mouth of Essequibo — LeanwsnIsI Cape Nassau. . . . Pt Baja. Lat. N • 12 2 12 19 12 2 11 67 12 00 10 87 10 86 11 50 11 56 11 42 10 68 11 00 10 68 11 23 10 44 10 4 7 00 7 86 9 25 Lou. W. o ( ee 38 6» 31 68 17 67 82 67 46 66 56 66 8 66 14 64 37 64 29 65 15 63 60 64 28 ^^98 10 61 58 61 58 58 18 58 f« 60 48 ?46 ■AMrdiBC to Aot of OoBCTMa, in th* year one thooiand eieht hnadred and Afty-MTen, by JAMBS H. BROWKI.UW. La tk« Clark's Offio* of th« Diitriet Court of th* United State*, for th* Soathem DUtrtot of New York. NEW TIME TABLES ♦ «ICH FURNISH THE SHORTEST METHOD OF FINDING THE TIME AT SHIP (AND THENlJl THE LONGITUDE BY CHRONOMETER), AT ABOUT 8 O'CLOCK IN THE MORNING, OR 4 O'CLOCK IN THE AFTERNOON. By James H. Beowklow, Teacher of Practical Navigation amd Nautical Astronomy, 92 Madison Street, N&w York, EXPLANATION AND USE OF THE TABLES. Table A, in Two Parts. Th« first part contains the True Altitude of the Sun's centre, at the instant it is 8 hours, A. M., ot \ hours, P. M., apparent time, when the Latitude and Declination are of the same name. The second f^art contains the same, when the Latitude and Declination are of different names. These tables are entered with the degree of Declination at the top, and the degree of Latitude at the side, and the angla of meeting gives the True Altitude required. If there are miles of Latitude and Declination, two pro- portions are necessary, which may be made either meataiiy, or by the aid of Table B. Ti^BLE B, For finding the proportion of Altitude for the milet ^f Latitude and Declination, as follow* • Enter thu table with the difference of Altitude for 1° of Lat;'.;4e at the top, and the miles of Latitude at the aide, «nd the angle of meeting gives the proportion of Altitude required, in miles and tenths, which must b« added to the Altitude taken from Table A, if the Altitude was increasing with the Latitude ; or aub- tracted, if decreasing. Again, enter this table with the difference of Altitude for 1** of Declination at th« top, and the miles of Declination at the side, and take out the proportion of Altitude, to be added to the Altitude taken from Table A, if it was increasing with the Declination, or subtracted if decreasing, will ^[ive the true Altitude of the Sun's centre, from which subtract the joint correction for Semidiameter, Dip, &c., (which is usually taken at 10') to obtain the Observed Altitude of the Sun's lower limb : now •ct the Quadrant to this Altitude, and when the Sun arrives at it, note the time by Chronometer, to w&ich Apply the error, if any, and you have the Mean Time at Greenwich, and Apparent Time at Ship, whjch is either 8 hours, A. M., or 4 hours P. M. To the Apparent Time at Ship apply the Equation of Time, which will give the Mean Time at Ship, the difference between which and the Mean Time at Greenwich te the Longitude in time, turned into space at the rate of 15* to the hour, or T to 4 seconds of time. EXAMPLE. September 10th, 1857, in Latitude 30* 29' N., and Longitude by D. R. 60* W., the height of the eye being 18 feet, required the Altitude at which to set my Quadrant, so as to observe the Altitude of the Sun's lower limb at 8 o'clock in the morning, Apparent Time, and by noting the time by Chronometer, find the Longitude. The Sun's Declination on September 10th, is 4* 62' N., and Latitude 30° 29' N., being of the same name, I enter first part of Table A with 4° of Declination and 30° of Latitude, which gives the Altitude 87' 50', and under the same degree of Declination, but opposite 31° of Latitude, the Altitude is 27* 37', (rhich gives the Difference of Altitude for 1* of Latitude to be 13' decreasing. Again, entering Table A, with 5° of Declination and 30° of Latitude, gives the Altitude 28' 21', which gives the Difference of Altitude for 1° of Declination to be 31' increasing. Now enter Table B, with 13' at top, and 29' of Latitude at the side, and take out the proportion of Altitude for 29' of Latitude, which is 6' 3 tenths, tc be subtracted from Altitude 27* 50'. Again enter Table B, with 31' at top, and 52' of Declination at th« •ide, and take out the proportion of Altitude for 52' of Declination, which is 26' 9 tenths, to be added \4 Altitude 27* 50'. As the greater of these two proportions is additive, and the lesser one subtractiye, take the difference between them, which is 20' 6 tenths (or 21'), and add it to 27* 50', will give the tnw NEW TIME TABLES. S4I Altitude of the Sun's centre 28* 11', from which subtract '.O'for Semidiameter, Dip^ &c., girec the Observed Altitude of the Sun's lower limb 28* 1', to which I set my Quadrant, and when the Sun arrives at that Altitude, note the time by Chronometer; which suppose to be llhrs. 58m. lOseo., A. M^ Mean Time at Greenwich, the Longitude is found as follows . Apparent Time at Ship 8h. OOti. OOsec, A. M. Equation of Time, to subtract 3 10 Mean Time at Ship "T 56 50 A. M. Mean Time at Greenwich II 58 10 A.M. Longitude in Time 4 1 20 in degreet 60* 20' W. » Rkm&rk. — As the above method of setting the Quadrant to the Altitude, and waiting until the Sob arrives to that Altitude, may be considered somewhat inconvenient, Table C ha« been oonstnioted U> obviate that necessity. ^ Table C, in Two Parts. The first part of this table is used when the Latitude and Declination are of the same name ; the second part, when they are of different names. They are entered with the Declination at top, and Latitude at the side, and the angle of meeting gives the time (in seconds and hundredth parts of a second) corres- ponding to a change of the Sun's Altitude of one mile at 8hrs., A. M., or 4hrs., P. M. The Declination is given only for every other degree, as the change tor 1° is small, and the proportion for the intermediate degree of Declination, or for miles of Latitude and Declination, can be made either mentally or by Table B, in the same manner as the proportion of Altitude is found for miles of Lat. and Dec. By Table C, then, we obtain the time corresponding to a change of Altitude of one mile at 8hrs., A. M., or 4hr8., P. M. Now, if we observe the Sun's Altitude within a few minutes of those times, say within to minutes of them, either before or after, note the time by Chronometer ; and, after correcting th« Observed Altitude, as usual to obtain the True Altitude, take the difference in miles between it and the Altitude taken from Table A, and multiply this difference of Altitudes by the time corresponding to ou« mile, taken from Table C, and we have the time either before or after Shrs., A. M., or 4hrs., P. M., according as the Altitude observed is greater or less than the Altitude taken from Table A. In the morning, if the Altitude observed (after correcting it) is greater than the one taken from Table A, the time corres- ponding to the difference of Altitude must be added to Shrs. ; but if the Altitude observed be less, th« time must be subtracted from Shrs. In the afternoon, if the Altitude observed be greater than the one from Table A, the time must be subtracted from 4hr8. ; but if the Altitude observed be less, the time must be added to 4hr8 Suppose, in the preceding example, the Sun's Altitude had been observed a few minutes after 8 o'clock to be 30° r, and the time by Chronometer 12hr8. 7m. 39sec., A. M., the work to find the Longitude woul'' 0" as follows : Sun's UDs. Alt 30° 1' The time corresponding to a change of Alt. of one Corr. for Semid., Dip, Ac, to add.. 10 mile, at 8hrs., from Table C 4.74 True Alt. by Observation WTl Difference of Altitude 120 True Alt., from Table A 28 11 6O)568.$0(9m. 28g Diff.ofAIt8 2° or 120 miles. 540 _28 NoTB. — If the difference of Altitude does not exceed Note — Multiply the 4sec. and 74 hundredths by 60 or 60 miles, it is enough, to take out the time from 120 miles, cut off the two right hand figures, and tha Table O for the nearest degree of Declination and Lati- remaining figures are seconds. tude. Time for Diff. of Alts 9m. 28sec. App. Time from Table A 8h. 00 A. M. App Time at Ship 8 9 28 A. M Equation of Time, subt 3 10 Mean Time at Ship 8 6 Ts A. M. Mean Time at Greenwich 12 7 39 A.M. Longitude in Time 4 1 21 or 60* 20' W. Kkhark. — When the Ship is on the Equator, and the Sun is also on the Equator, that is, when hii Declination is 0, the Sun rises and sets vertically. In this case, the Sun's change of Altitude is uni- formly 1 mile in 4 seconds of time, throughout the entire day. But, under any other circumstances, the lime corresponding to a change of the Sun's Altitude of 1 mile, is more than 4 seconds. When the Lat. and Dec. are under 3°, the time from Table C may be assumed the same for 2hrB. » " u u jQ" u (( u (( u 'i J T^ 20- " » « " « « 40minut«a When the Lat. is under " 30* " " " " « "15 " " " '< « 50* " " " « « u JQ u " «< « •» gQ» « « « (i u "7 " 248 TABLE A.— Part I. Thia Table shows the True Altitude of the Sun's Centre at the instant it is 8 o'Clock in the Morning, or 4 ©'Clock in the Afternoon, Apparent Time, for more readily finding the Longitude by Chronometer.' DECLINATION AND LATITUDE OF THE SAME NAMK Lat o<> r 2° 3' 4» 6" 6" 7° 8' 9' 10' 11* 12' • o / O 1 ° 1 o f • / o / o / o / o 1 o / o / • 1 o / 30 30 29 59 29 57 29 55 29 52 29 49 29 45 29 41 29 36 29 30 29 24 29 17 1 30 30 1 30 1 30 1 30 29 58 29 56 29 53 29 50 29 46 29 42 29 37 29 31 2 29 59 30 1 30 2 30 3 30 4 30 3 30 2 30 1 29 59 29 56 29 53 29 49 29 44 3 29 57 30 1 30 3 30 5 30 7 30 8 30 8 30 8 30 7 30 5 30 3 30 1 29 57 4 29 55 30 30 4 30 7 30 10 30 12 30 13 30 14 30 14 30 14 30 13 30 12 30 10 5 29 52 29 58 30 3 30 8 30 12 30 15 30 18 30 20 30 21 30 22 30 23 30 22 30 21 6 29 49 29 56 30 2 30 8 30 13 30 18 30 22 30 25 30 28 30 30 30 31 30 32 30 32 7 29 45 29 53 30 1 30 8 30 14 30 20 30 25 30 30 30 34 30 37 30 39 30 41 30 43 8 29 41 29 50 29 59 30 7 30 14 30 21 30 28 30 34 30 39 30 43 30 47 30 50 30 53 9 '29 36 1 29 46 29 56 30 5 30 14 30 22 30 30 30 37 30 43 30 49 30 54 30 58 31 2 10 29 3U 29 42 29 53 30 3 30 13 30 23 30 31 30 39 30 47 30 54 31 31 6 31 11 11 29 24 29 37 29 49 30 1 30 12 30 22 30 32 30 41 30 50 30 58 31 6 31 13 31 19 12 29 17 29 31 29 44 29 57 30 10 30 21 30 32 30 43 30 53 31 2 31 11 31 19 31 26 13 29 9 29 25 29 39 29 53 30 7 30 20 30 32 30 44 30 55 31 5 31 15 31 25 31 33 14 15 29 1 29 18 29 33 29 49 30 3 30 17 30 31 30 44 30 66 31 8 31 19 31 30 31 39 28 53 29 10 29 27 29 43 29 59 30 15 30 29 30 43 30 57 31 10 31 22 31 34 31 45 16 28 44 29 2 29 20 29 38 29 55 30 11 30 27 30 42 30 57 31 11 31 25 31 38 31 50 17 28 34 28 54 29 13 29 31 29 50 30 7 30 24 30 41 30 57 31 12 31 27 31 41 31 54 18 28 24 28 44 29 5 29 25 29 44 30 3 30 21 30 38 30 55 31 12 31 28 31 43 31 58 19 28 13 28 35 28 56 29 17 29 37 29 57 30 17 30 35 30 54 31 11 31 28 31 45 32 1 32 3 20 28 1 28 24 28 47 29 9 29 31 29 52 30 12 30 32 30 51 21 10 31 28 31 46 21 27 50 28 14 28 37 29 29 23 29 45 30 7 30 28 30 48 21 8 31 28 31 47 Ai 5 22 27 37 28 2 28 27 28 51 29 15 29 38 30 1 30 23 30 45 31 6 31 26 31 46 32 6 23 27 24 27 50 28 16 28 41 29 6 29 31 29 54 30 18 30 40 31 3 31 24 31 46 32 6 24 27 11 27 38 28 5 28 31 28 57 29 22 29 47 30 12 30 36 30 59 81 22 31 44 32 6 25 26 57 27 25 27 53 28 20 28 47 29 14 29 40 30 5 30 30 30 55 31 19 31 42 32 5 26 26 42 27 12 27 40 28 9 28 37 29 4 29 31 29 58 30 24 30 50 31 15 31 89 32 3 27 26 27 26 58 27 27 27 57 28 26 28 54 29 22 29 50 30 17 30 44 31 10 31 36 32 1 28 26 12 26 43 27 14 27 44 28 14 28 44 29 13 29 42 30 10 30 38 31 5 31 32 31 58 29 30 25 56 25 40 26 28 27 27 31 28 2 28 33 29 3 29 33 30 2 30 31 80 59 31 27 31 54 26 13 26 45 27 18 27 50 28 21 28 53 29 23 29 54 30 23 30 53 31 22 31 50 31 25 23 25 57 26 30 27 4 27 37 28 9 28 41 29 13 29 45 30 15 30 46 Z\ 16 31 46 32 25 5 25 40 26 15 26 49 27 23 27 57 28 30 29 3 29 35 30 7 30 38 31 9 31 iO 33 24 48 25.23 25 59 26 34 27 9 27 43 28 18 28 51 29 25 29 58 30 30 31 2 31 34 34 24 29 25 6 25 42 26 19 26 54 27 30 28 5 28 39 29 14 29 48 30 21 30 54 31 27 35 24 11 24 48 25 26 26 3 26 39 27 16 27 52 28 27 29 2 29 37 30 12 30 46 31 19 36 23 52 24 30 25 9 25 46 26 24 27 1 27 38 28 14 28 50 29 26 30 2 30 37 31 11 37 23 32 24 11 24 50 25 29 26 7 26 46 27 23 28 1 28 38 29 15 29 51 30 27 31 3 38 23 12 23 52 24 32 25 12 25 51 26 30 27 9 27 47 28 25 29 3 29 40 30 17 30 53 39 22 52 23 33 24 13 24 54 25 34 26 14 26 53 27 32 28 11 28 50 29 28 30 6 30 44 40 22 31 23 13 23 54 24 35 25 16 25 57 26 37 27 17 27 57 28 37 29 16 29 55 30 33 41 22 10 22 53 23 35 24 17 24 58 25 40 26 21 27 2 27 43 28 23 29 3 29 43 30 22 42 21 49 22 32 23 15 23 58 24 40 25 22 26 4 26 46 27 27 28 9 28 49 29 30 30 10 43 21 27 22 11 22 55 23 38 24 21 25 4 25 47 26 30 27 12 27 54 28 35 29 17 29 58 44 21 5 21 49 22 34 23 18 24 2 24 46 25 29 26 13 26 56 27 38 28 21 29 3 29 45 45 20 42 21 28 22 13 22 58 23 42 24 27 25 11 25 55 26 39 27 23 28 6 28 49 29 32 46 20 19 21 5 21 51 22 37 23 22 24 7 24 52 25 37 26 22 27 6 27 50 28 34 29 18 47 19 56 20 43 21 29 22 16 23 2 23 48 24 33 25 19 26 4 26 49 27 34 28 19 29 3 48 19 33 20 20 21 7 21 54 22 41 23 27 24 14 25 25 46 26 32 27 18 28 3 28 48 49 50 19 9 19 57 20 45 21 32 22 20 23 7 23 54 24 41 25 28 26 14 27 28 47 28 32 18 45 19 33 20 22 21 10 21 58 22 46 23 34 24 21 25 9 25 56 26 43 27 30 28 16 51 18 20 19 9 19 58 20 47 21 36 22 24 23 13 24 1 24 49 25 37 26 25 27 12 28 1 52 17 56 18 45 19 35 20 24 21 14 22 3 22 52 23 41 24 29 25 18 26 d 26 54 27 42 53 17 31 18 21 19 11 20 1 20 51 21 41 22 30 23 20 24 9 24 58 25 47 26 36 27 25 54 S5 17 5 17 56 18 47 19 37 20 28 21 18 22 8 22 58 23 48 24 88 25 28 26 17 27 7 16 40 17 31 18 22 19 13 20 4 20 55 21 46 22 37 23 27 24 18 25 8 25 58 26 48 56 16 14 17 6 17 58 18 49 19 41 20 32 21 23 22 15 23 6 23 57 244 7 25 38 26 29 57 15 48 16 40 17 33 18 25 19 17 20 9 21 21 52 22 44 23 35 24 27 25 18 26 9 58 15 22 16 15 17 7 18 18 52 19 45 20 37 21 30 22 22 23 14 24 6 24 57 25 49 59 14 55 15 49 16 42 17 35 18 28 19 21 20 14 21 6 21 59 22 51 23 44 24 36 25 28 60 14 29 15 22 16 16 17 9| 18 3 18 56 19 50 20 43 21 36 22 29 23 22 24 15 25 8 TABLE . A..— Part I. 249 This Table shows the True Altitude ot the Su n's Centre at the instant it is 8 o'CIock in the Morninff. or 4 1 o'clock in the Afternoon, Apparent Time, for more readily finding the Longitude > by Chronometer. 1 DECLINATION AND LATITUDE OF THE SAME NAME. Lat. 13° 14 "15 °16 17° 18° 19' 20' 21" 22° 23* 24* 1 • 29 9 29 1 28 53 o 28 44 • 28 34 o 28 / 24 O 28 13 o 28 1 27 60 • 27 / 37 27 24 • 27 1 11 1 29 25 29 18 29 10 29 2 28 54 28 44 28 35 28 24 28 14 28 2 27 50 27 38 2 29 39 29 33 29 27 29 20 29 13 29 5 28 56 28 47 28 37 28 27 28 16 28 5 3 29 53 29 49 29 43 29 38 29 31 29 25 29 17 29 9 29 28 51 28 41 28 31 4 30 7 30 3 29 59 29 55 29 50 29 <44 29 37 29 31 29 23 29 16 29 6 28 57 5 30 20 30 17 30 15 30 11 30 7 30 3 29 57 29 52 29 45 29 38 29 31 29 22 6 30 32 30 31 30 29 30 27 30 24 30 21 30 17 30 12 30 7 30 1 29 54 29 47 7 30 44 30 44 30 43 30 42 30 41 30 38 30 35 30 32 30 28 30 23 30 18 30 12 8 30 55 30 56 30 57 30 57 30 57 30 55 30 55 30 51 30 48 30 45 30 40 30 36 9 31 5 31 8 30 10 31 11 31 12 31 12 31 11 31 10 31 8 31 6 31 3 30 59 10 31 15 31 19 31 22 31 25 31 27 31 28 31 28 31 28 31 28 31 26 31 24 31 22 11 31 25 34 30 31 34 31 38 31 41 31 43 31 45 31 46 31 47 31 46 31 46 31 44 12 31 33 31 39 31 45 31 50 31 54 31 58 32 1 32 3 32 5 32 6 32 6 32 6 13 31 41 31 49 31 55 32 2 32 7 32 12 32 16 32 20 32 22 32 26 32 26 32 27 14 31 49 31 57 32 5 32 13 32 19 32 25 32 31 32 35 32 39 32 43 32 46 32 48 15 31 55 32 5 32 14 32 23 32 31 32 38 32 45 32 61 32 56 33 33 4 33 7 16 32 2 32 13 32 23 32 33 32 42 32 50 32 58 33 5 33 12 33 17 33 23 33 27 17 32 7 32 19 32 31 32 42 32 52 33 2 33 11 33 19 33 27 33 34 33 40 33 46 18 32 12 32 25 32 38 32 50 33 2 33 13 33 23 33 32 33 41 33 50 33 57 34 4 19 32 16 32 31 32 45 32 58 33 11 33 23 33 34 33 45 33 55 34 5 34 13 34 21 20 32 20 32 35 32 51 33 5 33 19 33 32 33 45 33 67 34 8 34 19 34 29 34 38 21 32 22 32 39 32 56 33 12 33 27 33 41 33 55 34 8 34 21 34 33 34 44 34 54 22 32 25 32 43 33 33 17 33 34 33 50 34 5 34 19 34 33 34 46 34 58 35 10 23 32 26 32 46 33 4 33 23 33 40 33 57 34 13 34 29 34 44 34 58 35 12 35 24 24 32 27 32 48 33 7 33 27 33 46 34 4 34 21 34 38 34 54 35 10 35 24 35 39 25 32 27 32 49 33 10 33 31 33 51 34 10 34 29 34 47 35 4 35 21 35 37 36 52 26 32 27 32 50 33 12 33 34 33 55 34 15 34 35 34 54 35 13 35 31 35 48 36 5 27 32 26 32 50 33 13 33 36 33 58 34 20 34 41 36 1 35 21 36 40 35 59 36 16 28 32 24 32 49 33 14 33 38 34 1 34 24 34 46 35 8 35 29 36 49 36 9 36 28 29 32 21 32 48 33 13 33 39 34 3 34 27 34 51 35 13 35 36 35 57 36 18 36 38 30 32 18 32 46 33 12 33 39 34 5 34 30 34 54 35 18 35 42 36 4 36 26 36 48 31 32 14 32 43 33 11 33 38 34 5 34 32 34 57 35 22 35 47 36 11 36 34 36 57 32 32 10 32 40 33 9 33 37 34 5 34 33 34 59 36 26 35 51 36 16 36 41 37 5 33 32 5 32 35 33 6 33 35 34 4 34 33 35 1 35 28 35 55 36 21 36 47 37 12 34 31 59 32 31 33 2 33 33 34 3 34 33 35 2 35 30 35 58 36 26 36 52 37 19 35 31 53 32 25 32 58 33 29 34 1 34 32 35 2 35 31 36 1 36 29 36 57 37 24 36 31 46 32 19 32 53 33 26 33 58 34 30 35 1 35 32 36 2 36 32 37 1 37 29 37 31 38 32 13 32 47 33 21 33 54 34 27 35 35 32 36 3 36 34 37 4 37 34 38 31 29 32 5 32 41 33 16 33 50 34 24 34 58 36 30 36 3 36 35 37 6 37 37 39 31 21 31 57 32 34 33 10 33 45 34 20 34 55 35 29 36 2 36 35 37 8 37 40 40 31 11 31 49 32 26 33 3 33 39 34 15 34 51 35 26 36 1 36 35 37 8 37 41 J 41 31 1 31 40 32 18 32 56 33 33 34 10 34 47 35 23 36 68 36 34 37 8 37 42 42 30 50 31 30 32 9 32 48 33 26 34 4 34 42 35 19 35 55 36 32 37 7 37 42 43 30 39 31 19 31 59 32 39 33 18 33 57 34 36 35 14 35 51 36 29 37 6 37 42 ^^ 44 30 27 31 8 31 49 32 30 33 10 33 50 34 29 35 8 35 47 36 25 37 3 37 40 \ 45 30 14 30 56 31 38 32 20 33 1 33 42 34 22 35 2 36 41 36 21 37 37 38 46 30 1 30 44 31 27 32 9 32 51 33 33 34 14 34 65 35 36 36 16 36 66 37 36 47 29 47 30 31 31 15 31 58 32 41 33 23 34 6 34 47 35 29 36 10 36 51 37 31 48 29 33 30 18 31 2 31 46 32 30 33 13 33 56 34 39 35 21 36 3 36 45 37 27 49 29 18 30 3 30 49 31 33 32 18 33 2 33 46 34 30 35 13 35 56 36 39 37 21 60 29 3 29 49 30 35 31 20 32 6 32 51 33 36 34 20 35 4 35 48 36 31 37 15 51 28 47 29 34 30 20 31 7 31 53 32 39 33 24 34 10 34 55 35 39 36 23 37 7 52 28 30 29 18 30 5 30 52 31 39 32 26 33 12 33 58 34 44 35 30 36 15 37 53 28 13 29 1 29 50 30 37 31 25 32 12 33 33 46 34 33 35 19 36 5 36 51 54 27 56 28 45 29 33 30 22 31 10 31 58 32 46 33 34 34 21 36 8 35 65 36 4S 55 27 38 28 27 29 17 30 6 30 55 31 44 32 32 33 21 34 9 34 57 35 44 36 32 56 27 19 28 9 28 59 29 49 30 39 31 28 32 18 33 7 33 56 34 44 35 33 36 21 57 27 27 51 28 42 29 32 JO 22 31 13 32 2 32 52 33 42 34 31 35 20 36 9 58 26 41 27 32 28 23 29 14 30 5 30 56 31 47 32 37 33 27 34 17 35 7 35 67 59 26 21 27 13 28 4 28 56 29 48 30 39 31 30 32 21 33 12 34 3 34 53 35 44 60 26 26 53 27 45 28 37 29 29 30 21 31 13 32 5 32 56 33 48 34 39 36 30 250 TABLE A.— Part II. TIuB Table ahowi the True Altitude of the Sun's Centre at the instant it is 8 o'CIock in the Morninsr, or 4 1 o'clock in the Afternoon, Apparent Time, for more readily finding the Longitude by ChronometerT DECLINATION AND LATITUDE OF DIFFERENT NAMES. Lat. Qo 1' 2' Z" 4' 5* 6' 7 O 8° 9» 10* ir 12* . e t o 1 o / 1 • / o / • / / • 1 o / o / • 1 O / 30 30 29 59 29 57 29 55 29 52 29 49 29 45 29 41 29 36 29 30 29 24 29 17 1 30 29 58 29 56! 29 53 29 50 29 46 29 42 29 36 29 31 29 25 29 18 29 10 29 2 2 29 59 29 56 29 53 29 49 29 44 29 39 29 34 29 27 29 20 29 13 29 5128 56 28 47 3 29 57 29 53 29 49 29 44 29 38 29 32 29 25 29 17 29 9 29 1 28 51 28 42 28 31 4 29 55 29 50 29 44 29 38 29 31 29 24 29 16 29 7 28 58 28 48 28 38 28 27 28 15 5 29 o2 29 46 29 39 29 32 29 24 29 15 29 6 28 56 28 46 28 35 28 23 28 11 27 59 6 29 49 29 42 29 34 29 25 29 16 29 6 28 55 28 44 28 33 28 21 28 8 27 55 27 41 7 29 45 29 36 29 27 29 17 29 7 28 56 28 44 28 32 28 20 28 6 27 53 27 38 27 24 8 29 41 29 31 29 20 29 9 28 58 28 46 28 33 28 20 28 6 27 51 27 37 27 21 27 5 9 29 36 29 25 29 13 29 1 28 48 28 35 28 21 28 6 27 51 27 36 27 20 27 3 26 47 10 29 30 29 18 29 5 28 51 28 38 28 23 28 8 2? '^Z 27 37 27 20 27 3 26 45 26 27 11 29 24 29 10 28 56 28 42 28 27 28 11 27 55 27 38 27 21 27 3 26 45 26 27 26 8 12 29 17 29 2 28 47 28 31 28 15 27 59 27 41 27 24 ^7 5 26 47 26 27 26 8 25 48 13 29 9 28 54 28 37 28 21 28 3 27 45 27 27 27 8 26 49 26 29 26 9 25 48 25 27 14 29 1 28 45 28 27 28 9 27 51 27 32 27 12 26 53 26 32 26 11 25 50 25 28 25 6 15 28 53 28 35 28 16 27 57 27 38 27 18 26 57 26 36 26 15 25 53 25 31 25 8 24 45 16 28 44 28 24 28 5 27 45 27 24 27 3 26 41 26 19 25 57 25 34 25 11 24 47 24 23 17 28 34 28 14 27 53 27 32 27 10 26 48 26 25 26 2 25 39 25 15 24 51 24 26 24 1 18 28 24 28 2 27 40 27 18 26 55 26 32 26 9 25 45 25 20 24 55 24 30 24 4 23 38 19 28 13 27 50 27 28 27 4 26 40 26 16 25 51 25 26 25 1 24 35 24 9 23 42 23 15 20 28 1 27 38 27 14 26 50 26 25 26 25 34 25 8 24 41 24 14 23 47 23 19 22 52 21 27 50 27 25 27 26 35 26 9 25 42 25 16 24 49 24 21 23 53 23 25 22 57 22 28 22 27 37 27 12 26 46 26 19 25 52 25 25 24 57 24 29 24 1 23 32 23 3 22 33 22 4 23 27 24 26 58 26 31 26 3 25 35 25 7 24 38 24 9 23 40 23 10 22 40 22 10 21 39 24 27 11 26 43 26 15 25 47 25 18 24 49 24 19 23 49 23 19 22 48 82 17 21 46 21 14 25 26 57 26 28 25 59 25 30 25 24 30 23 59 23 28 22 57 22 25 21 53 21 21 20 49 26 26 42 26 13 25 43 25 12 24 41 24 10 23 39 23 7 22 35 22 3 21 30 20 57 20 24 27 26 27 25 57 25 26 24 54 24 23 23 51 23 18 22 46 22 13 21 39 21 6 20 32 19 58 1 28 26 12 25 40 25 8 24 36 24 3 23 30 22 57 22 24 21 50 21 16 20 41 20 6 19 32 1 29 30 25 56 25 23 24 51 24 17 23 44 23 10 22 36 22 1 21 27 20 52 20 16 19 41 19 5 25 40 25 6 24 32 23 58 23 24 22 49 22 14 21 39 21 3 20 27 19 51 19 :.-) 18 38 31 25 23 24 48 24 13 23 39 23 3 22 28 21 52 21 16 20 39 20 3 19 26 18 48 18 11 32 25 5 24 30 23 55 23 19 22 42 22 6 21 29 20 52 20 15 19 38 19 18 22 17 44 33 24 48 24 12 23 35 22 58 22 21 21 44 21 6 20 29 19 51 19 12 18 34 17 55 17 16 34 24 29 23 52 23 15 22 37 22 21 22 20 43 20 5 19 26 18 47 18 8 17 28 16 49 35 24 11 23 33 22 55 22 16 21 38 20 59 20 20 19 40 19 1 18 21 17 41 17 1 16 20 36 23 52 23 13 22 34 21 55 21 15 20 36 19 5Q 19 16 18 35 17 55 17 14 16 33 15 52 37 23 32 22 53 22 13 21 33 20 53 20 12 19 32 18 51 18 10 17 28 16 47 16 5 15 24 38 23 12 22 32 21 51 21 11 20 30 19 48 19 7 18 25 17 44 17 2 16 20 15 37 14 55 39 40 22 52 22 11 21 30 20 48 20 6 19 24 18 42 18 17 17 16 35 15 62 15 9 14 26 22 31 21 50 21 7 20 25 19 43 19 18 17 17 34 16 51 16 8 15 24 14 41 13 57 41 22 10 21 28 20 45 20 2 19 19 18 35 17 52 17 8 16 24 15 40 14 56 14 12 13 27 42 21 49 21 6 20 22 19 38 18 54 18 10 17 26 16 42 15 57 15 12 14 28 13 43 12 68 12 2^ 43 21 27 20 43 19 59 19 14 18 30 17 45 17 16 15 15 30 14 45 13 59 13 14 44 21 5 20 20 19 35 18 50 18 5 17 19 16 34 15 48 15 2 14 17 13 30 12 44 11 58 45 20 42 19 57 19 11 18 26 17 40 16 54 16 7 15 21 14 35 13 48 13 2 12 15 11 28 46 20 19 19 33 18 47 18 1 17 14 16 27 15 41 14 54 14 7 13 20 12 32 11 45 10 58 47 19 56 19 10 18 23 17 36 16 48 16 1 15 14 14 26 13 39 12 51 12 3 11 15 10 27 48 19 33 18 45 17 58 17 10 16 22 15 35 14 47 13 59 13 10 12 22 11 34 10 45 9 57 49 19 9 18 21 17 33 16 45 15 56 15 8 14 19 13 31 12 42 11 53 11 4 10 15 9 26 50 18 45 17 56 17 8 16 19 15 30 14 41 13 52 13 2 12 13 11 24 10 34 9 45 8 55 51 18 20 17 31 16 42 15 53 15 3 14 14 13 24 12 34 11 44 10 54 10 4 9 11 8 24 52 17 56 17 6 16 16 15 26 14 36 13 46 12 56 12 6 11 15 10 25 9 34 8 44 7 53 53 17 31 16 41 15 50 15 14 9 13 18 12 28 11 37 10 46 9 55 9 4 8 13 7 22 54 17 5 16 15 15 24 14 33 13 42 12 51 11 59 11 8 10 17 9 25 8 34 7 42 6 61 55 16 40 15 49 14 57 14 6 13 14 12 22 11 31 10 39 9 47 8 55 8 4 7 12 6 20 66 16 14 15 22 14 30 13 38 12 46 11 54 11 2 10 10 9 18 8 25 7 33 6 41 5 48 57 15 48 14 56 14 3 13 11 12 18 11 26 10 33 9 41 8 48 7 55 7 2 6 9 5 17 58 15 22 14 29 13 36 12 43 11 50 10 57 10 4 9 11 8 18 7 25 6 32 5 38 4 45 59 14 55 14 2 13 9 12 15 11 22 10 29 9 35 8 42 7 48 6 54 6 1 5 7 4 14 60 14 29 13 35 12 41 11 47 10 54 10 9 6 8 12 7 18 6 24 5 30 4 36 3 42 1 TABLE A.— Part II 251 Thi« T*bie •hows the Trae Altitude of the Sun's Centre at the instant it is 8 o'Clock in the Mornine or 4 o'Clocit; in the Aaernoon, Apparent Time, for more readily finding the Longitude by Chronometer.' DECLINATION AND LATITUDE OF DIFFERENT NAMEa Lat. 130 14° 15^ 16' 17° 18' 19" 20° 21° 22° 23* 24' • e / > o t • f • / o / o f o / o / o / O f • / 29 9 29 1 28 53 28 44 28 34 28 24 28 13 28 1 27 50 27 37 27 24 27 11 1 28 54 28 45 28 35 28 24 28 14 28 i 27 50 27 38 27 25 27 12 26 58 26 43 2 28 37 28 27 28 16 28 5 27 53 27 40 27 28 27 14 27 26 46 26 31 26 16 3 28 21 28 9 27 57 27 45 27 32 27 18 27 4 26 50 26 35 26 19 26 3 25 47 4 28 3 27 51 27 38 27 24 27 10 26 55 26 40 26 25 26 9 25 52 25 35 25 18 6 27 45 27 32 27 18 27 3 26 48 26 32 26 16 26 25 42 25 25 25 7 24 49 6 27 27 27 12 26 57 26 41 26 25 26 9 25 51 25 34 25 16 24 57 24 38 24 19 7 27 8 26 53 26 36 26 19 26 2 25 45 25 26 25 8 24 49 24 29 24 9 23 49 8 26 49 26 32 26 15 25 57 25 39 25 20 25 1 24 41 24 21 24 1 23 40 23 19 9 26 29 26 11 25 53 25 34 25 15 24 55 24 35 24 14 23 53 23 32 23 10 22 48 10 26 9 25 50 25 31 25 11 24 51 24 30 24 9 23 47 23 25 23 3 22 40 22 17 11 25 48 25 28 25 8 24 47 24 26 24 4 23 42 23 19 22 57 22 33 22 10 21 46 la 25 27 25 6 24 45 24 23 24 1 23 38 23 15 22 52 22 28 22 4 21 39 21 14 13 25 6 24 44 24 21 23 58 23 35 23 12 22 48 22 23 21 59 21 33 21 8 20 42 14 24 44 24 21 23 57 23 33 23 9 22 45 22 20 21 55 21 29 21 3 20 37 20 10 15 24 21 23 57 23 33 23 8 22 43 22 17 21 52 21 26 20 59 20 32 20 6 19 38 16 23 58 23 33 23 8 22 42 22 16 21 50 21 23 20 56 20 29 20 1 19 33 19 5 17 23 35 23 9 22 43 22 16 21 50 21 22 20 55 20 27 19 59 19 30 19 1 18 32 18 23 12 22 45 22 17 21 50 21 22 20 54 20 26 19 57 19 28 18 58 18 29 17 69 19 22 48 22 20 21 52 21 23 20 55 20 26 19 56 19 27 18 57 18 27 17 56 17 26 20 22 23 21 55 21 26 20 56 20 27 19 57 19 27 18 56 18 26 17 55 17 23 16 62 21 21 59 21 29 20 59 20 29 19 59 19 28 18 57 18 26 17 54 17 22 16 50 16 18 22 21 33 21 3 20 32 20 1 19 80 18 58 18 27 17 55 17 22 16 50 16 17 16 44 23 21 8 20 37 20 5 19 33 19 1 18 29 17 56 17 23 16 50 16 17 15 43 15 10 84 20 42 20 10 19 38 19 5 18 32 17 59 17 2€' 16 52 16 18 16 44 15 10 14 35 25 20 16 19 43 19 10 18 37 18 3 17 29 16 55 16 20 15 46 15 11 14 36 14 1 26 19 50 19 16 18 42 18 8 17 33 16 58 16 23 15 48 15 13 14 37 14 2 13 26 27 19 23 18 49 18 14 17 39 17 3 16 28 15 52 15 16 14 40 14 4 13 27 12 61 28 18 56 18 21 17 45 17 9 16 33 15 57 15 21 14 44 14 7 13 30 12 53 12 16 29 18 29 17 53 17 16 16 40 16 3 15 26 14 49 14 11 13 34 12 56 12 18 11 40 30 18 2 17 25 16 47 16 10 15 32 14 55 14 17 13 39 13 12 22 11 44 11 6 31 17 34 16 56 16 18 15 40 15 2 14 23 13 45 13 6 12 27 11 48 11 8 10 29 32 17 6 16 27 15 49 15 10 14 31 13 51 13 12 12 33 11 53 11 13 10 34 9 64 33 16 37 15 58 15 19 14 39 13 59 13 20 12 40 12 11 19 10 39 9 58 9 18 34 16 9 15 29 14 49 14 9 13 28 12 48 12 7 11 26 10 45 10 4 9 23 8 42 35 15 40 14 59 14 19 13 38 12 57 12 15 11 34 10 53 10 11 9 29 8 48 8 6 36 15 11 14 30 13 48 13 7 12 25 11 43 11 1 10 19 9 37 8 55 8 12 7 30 37 14 42 14 13 18 12 35 11 53 11 10 10 28 9 45 9 2 8 20 7 37 6 54 38 14 12 13 30 12 47 12 4 11 21 10 38 9 55 9 11 8 28 7 44 7 1 6 17 39 13 43 12 59 12 16 11 32 10 49 10 5 9 21 8 37 7 53 7 9 6 25 5 41 40 13 13 12 29 11 '45 11 1 10 16 9 32 8 48 8 3 7 19 6 34 5 49 5 5 41 12 43 11 58 11 14 10 29 9 44 8 59 8 14 7 29 6 44 5 59 6 13 4 28 42 12 13 11 28 10 42 9 57 9 11 8 26 7 40 6 55 6 9 5 23 4 37 3 52 43 11 42 10 57 10 11 9 25 8 39 7 53 7 6 6 20 5 34 4 48 4 1 3 15 44 11 12 10 25 9 39 8 52 8 6 7 19 6 32 5 46 4 59 4 12 3 25 2 38 45 10 41 9 54 9 7 8 20 7 33 6 46 5 58 5 11 4 24 3 36 2 49 2 2 46 19 10 9 23 8 35 7 48 7 6 12 5 24 4 37 3 49 3 1 2 13 1 25 47 9 39 8 51 8 3 7 15 6 27 5 39 4 50 4 2 3 14 2 25 1 37 48 48 9 8 8 20 7 31 6 42 5 54 5 5 4 16 3 27 2 38 1 49 1 1 12 49 8 37 7 48 6 59 6 10 5 20 4 31 3 42 2 52 2 3 1 14 24 50 8 6 7 16 6 26 5 37 4 47 3 57 3 7 2 18 1 28 38 51 7 34 6 44 5 54 5 4 4 14 3 23 2 33 1 43 52 2 52 7 3 6 12 5 22 4 31 3 40 2 49 1 59 1 8 17 53 6 31 5 40 4 49 3 58 3 7 2 15 1 24 33 54 55 5 59 5 8 4 16 3 25 2 33 1 41 50 5 28 4 36 3 44 2 52 2 1 7 15 56 4 56 4 3 3 11 2 18 1 26 33 57 4 24 3 31 2 38 1 45 52 58 3 52 2 59 2 5 1 12 19 59 3 20 2 26 1 32 39 60 2 AH 1 54 1 6 1 252 TABLE B. — Sexagesimal Proportional Table For finding the proportion of Altitude for Miles oi Latitude and Declination, to be applied to the Altitude taken from Table A. Mile* of Lat. or Decli. DIFFERENCE OF ALTITUDE FOB . r OF LATITUDE OR DEOLUfATION. r 3' 5' 7' 9' 11' 13' 15' 17' 19' 21' 23' 25' 27' r 1 0.0 0.1 0.1 1 0.1 0.2 / 0.2 0.2 0.3 0.3 / 0.3 > 0.4 0.4 0.4 0.6 2 0.0 O.i 0.2 0.2 0.3 0.4 0.4 0.5 0.6 0.6 0.7 0.8 0.8 0.9 3 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 4 0.1 0.2 0.3 0.5 0.6 0.7 0.9 1.0 1.1 1.3 1.4 1.6 1.7 1.8 5 0.1 0.3 0.4 0.6 0.8 0.9 1.1 1.3 1.4 1.6 1.8 1-9 B.l 2-3 6 0.1 0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 2.5 2.7 7 0.1 0.4 0.6 0.8 1.1 1.3 1.5 1.8 2.0 2.2 2.6 2.7 2.9 3.2 8 0.1 0-4 0.7 0.9 1.2 1.5 1.7 2.0 2.3 2.5 2.8 3.1 3.3 3.6 9 0.2 0.5 0.8 1.1 1.4 1.7 2.0 2.3 2.6 2.9 3.2 3.5 3.8 4.1 10 0.2 0.5 0.8 1.2 1.5 1.8 2.2 2.5 2.8 3.2 3.5 3.8 4.2 4.5 11 0.2 0.6 0.9 1.3 1.7 2.0 2.4 2.8 3.1 3.5 3.9 4.2 4.6 6.0 12 0.2 0.6 1.0 1.4 1.8 2.2 2.6 3.0 3.4 3.8 4.2 4.6 5.0 5.4 13 0.2 0.7 1.1 1.5 2.0 2.4 2.8 3.3 3.7 4.1 4.6 6.0 6.4 5.9 14 0.2 0.7 1.2 1.6 2.1 2.6 3.0 3.5 4.0 4.4 4.9 6.4 5.8 6.3 15 0.3 0.8 1.3 1.8 2.3 2.8 3.3 3.8 4.3 4.8 6.3 5.8 6.3 6.8 16 0.3 0.8 1.3 1.9 2.4 2.9 3.5 4.0 4.6 5.1 6.6 6.1 6.7 7.2 17 0.3 0.9 1.4 2.0 2.6 3.1 3.7 4.3 4.8 5.4 6.0 6.5 7.1 7.7 18 0.3 0.9 1.5 2.1 2.7 3.3 3.9 4.5 6.1 5.7 6.3 6.9 7.5 8.1 19 0.3 1.0 1.6 2.2 2.9 3.5 4.1 4.8 6.4 6.0 6.7 7.3 7.9 8.6 20 0.3 1.0 1.7 2.3 3.0 3.7 4.3 5.0 5.7 6.3 7.0 7.7 8.3 9.0 21 0.4 1.1 1.8 2.5 3.2 3.9 4.6 5.3 6.0 6.7 7.4 8.1 8.8 9.6 22 0.4 1.1 1.8 2.6 3.3 4.0 4.8 6.5 6.2 7.0 7.7 8.4 9.2 9.9 23 0.4 1.2 1.9 2.7 3.5 4.2 5.0 5.8 6.5 7.3 8.1 8.8 9.6 10.4 24 9.4 1.2 2.0 2.8 3.6 4.4 5.2 6.0 6.8 7.6 8.4 9.2 10.0 10.8 25 0.4 1.3 2.1 2.9 3.8 4.6 5.4 6.3 7.1 7.9 8.8 9.6 10.4 11.3 26 0.4 1.3 2.2 3.0 3.9 4.8 5.6 6.5 7.4 8.2 9.1 10.0 10.8 11.7 27 0.5 1.4 2.3 3.2 4.1 5.0 6.9 6.8 7.7 8.6 9.5 10.4 11.3 12.2 28 0.5 1.4 2.3 3.3 4.2 5.1 6.1 7.0 7.9 8.9 9.8 10.7 11.7 12.6 29 0.5 1.5 2.4 3.4 4.4 5.3 6.3 7.3 8.2 9.2 10.2 11.1 12.1 13.1 30 0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.6 11.5 12.6 13.5 31 0.5 1.6 2.6 3.6 4.7 5.7 6.7 7.8 8.8 9.8 10.9 11.9 12.9 14.0 32 0.5 1.6 2.7 3.7 4.8 5.9 6.9 8.0 9.1 10.1 11.2 12.3 13.3 14.4 33 0.6 1.7 2.8 3.9 5.0 6.1 7.2 8.3 9.4 10.6 11.6 12.7 13.8 14.9 34 0.6 1.7 2.8 4.0 5.1 6.2 7.4 8.6 9.6 10.8 11.9 13.0 14.2 15.3 35 0.6 1.8 2.9 3.0 4.1 5.3 6.4 7.6 8.8 9.9 11.1 12.3 13.4 14.6 15.8 36 0.6 1.8 4.2 6.4 6.6 7.8 9.0 10.2 11.4 12.6 13.8 15.0 16.2 37 0.6 1.9 3.1 4.3 5.6 6.8 8.0 9.3 10.6 11.7 13.0 14.2 16.4 16.7 38 0.6 1-.9 3.2 4.4 5.7 7.0 8.2 9.5 10.8 12.0 13.3 14.6 16.8 17.1 39 0.7 2.0 3.3 4.6 5.9 7.2 8.5 9.8 11.1 12.4 13.7 15.0 16.3 17.6 40 0.7 2.0 3.3 4.7 6.0 7.3 8.7 10.0 11.3 12.7 .14.0 15.3 16.7 18.0 41 0.7 2.1 3.4 4.6 6.2 7.5 8.9 10.3 11.6 13.0 14.4 15.7 17.1 18.5 42 0.7 2.1 3.5 4.9 6.3 7.7 9.1 10.5 11.9 13.3 14.7 16.1 17.6 18.9 43 0.7 2.2 3.6 5.0 6.5 7.9 9.3 10.8 12.2 13.6 15.1 16.5 17.9 19.4 44 0.7 2.2 3.7 5.1 6.6 8.1 9.5 11.0 12.5 13.9 16.4 16.9 18.3 19.8 45 46 0.8 2.3 3.8 5.3 6.8 8.3 9.8 11.3 12.8 14.3 15.8 17.3 18.8 20.3 0.8 2.3 3.8 5.4 6.9 8.4 10.0 11.5 13.0 14.6 16.1 17.6 19.2 20.7 47 0.8 2.4 3.9 5.5 7.1 8.6 10.2 11.8 13.3 14.9 16.5 18.0 19.6 21.2 48 0.8 2.4 4.0 5.6 7.2 8.8 10.4 12.0 13.6 15.2 16.8 18.4 20.0 21.6 49 0.8 2.5 4.1 5.7 7.4 9.0 10.6 12.3 13.9 15.5 17.2 18.8 20.4 22.1 50 51 0.8 2.5 4.2 5.8 7.5 9.2 10.8 12.5 14.2 16.8 17.5 19.2 20.8 22.5 0.9 2.6 4.3 6.0 7.7 9.4 11.1 12.8 14.5 16.2 17.9 19.6 21.3 23.0 52 0.9 2.6 4.3 6.1 7.8 9.5 11.3 13.0 14.7 16.5 18.2 19.9 21.7 23.4 53 0.9 2.7 4.4 6.2 9.0 9.7 11.5 13.3 15.0 16.8 18.6 20.3 22.1 23.9 64 0.9 2.7 4.5 6.3 9.1 9.9 11.7 13.6 15.3 17.1 18.9 20.7 22.5 24.3 55 66 0.9 2.8 4.6 6.4 9.3 10.1 11.9 13.8 16.6 17.4 19.3 21.1 22.9 24.8 0.9 2.8 4.7 6.5 9.4 10.3 12.1 14.0 16.9 17.7 19.6 21.5 23.3 26.2 57 1.0 2.9 4.8 6.7 9.6 10.5 12.4 14.3 16.2 18.1 20.0 21.9 23.8 25.7 58 1.0 2.9 4.8 6.8 9.7 10.6 12.6 14.6 16.4 18.4 20.3 22.2 24 2 26.1 59 1.0 3.0 4.9 6.9 9.9 10.8 12.8 14.8 16.7 18.7 20.7 22.6 24.6 26.6 60 1.0 3.0 5.0 7.0 9.0 11.0 13.0 15.0 17.0 19.0 21.0 23.0 25-0 27.0 TABLE B. — Sexagesimal Proportional Table 253 For finding the proportion of Altitude for Miles of Latitude and Declination, to be applied to the 1 Altitudf 3 taken from Table A. Milst of Lkt. or DwU DIFFERENCE OF AT.TITUDE FOE . r OF LATITUDE OR DECLINATION. 29' 31' 33' 35' 37' 39' 41' 43' 45' 47' 49' 51' 53' 55' 1 0.5 t 0.5 1 0.6 1 0.6 0.6 / 0.7 0.7 , 0.7 0.8 / 0.8 0.8 0.9 / 0.9 1 0.9 2 1.0 1.0 1.1 1.2 1.2 1.3 1.4 1.4 1.5 1.6 1.6 1.7 1.8 1.8 3 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 4 1.9 2.1 2.2 2.3 2.5 2.6 2.7 2.9 3.0 3.1 3.3 3.4 3.5 3.7 5 2.4 2.6 2.8 2.9 3.1 3.3 3.4 3.6 3.8 3.9 4.1 4-3 4.4 4.6 6 2.9 3.1 3.3 3.5 3.T 3.9 4.1 4.3 4.5 4.7 4.9 5.1 5.3 5.5 7 3.4 3.6 3.9 4.1 4.3 4.6 4.8 5.0 5.3 5.5 5.7 6.0 6.2 6.4 8 3.9 4.1 4.4 4.7 4.9 6.2 5.5 5.7 6.0 6.3 6.5 6.8 7.1 7.3 9 4.4 4.7 5.0 5.3 5.6 5.9 6.2 6.5 6.8 7.1 7.4 7.7 8.0 8.3 10 4.8 5.2 5.5 5.8 6.2 6.5 6.8 7.2 7.5 7.8 8.2 8.5 8.8 9.2 11 5.3 5.7 6.1 6.4 6.8 7.2 7.5 7.9 8.3 8.6 9.0 9.4 9 7 10.1 12 5.8 6.2 6.6 7.0 7.4 7.8 8.2 8.6 9.0 9.4 9.8 10.2 10 6 11.0 13 6.3 6.7 7.2 7.6 8.0 8.5 8.9 9.3 9.8 10.2 10.6 11.1 . 11.5 11.9 14 6.8 7.2 7.7 8.2 8.6 9.1 9.6 10.0 10.5 11.0 11.4 11.9 12.4 12.8 15 7.3 7.8 8.3 8.8 9.3 9.8 10.3 10.8 11.3 11.8 12.3 12.8 13.3 13.8 16 7.7 8.3 8.8 9.3 9.9 10.4 10.9 11.5 12.0 12.5 13.1 13.6 14.1 14.7 : 17 8.2 8.8 9.4 9.9 10.5 11.1 11.6 12.2 12.8 13.3 13.9 14.5 15.0 15.6 18 8.7 9.3 9.9 10.5 11.1 11.7 12.3 12.9 13.5 14.1 14.7 15.3 15.9 16.5 ' 19 9.2 9.8 10.5 11.1 11.7 12.4 13.0 13.6 14.3 14.9 15.5 16.2 16.8 17.4 20 9.7 10.3 11.0 11.7 12.3 13.0 13.7 14.3 15.0 15.7 16.3 17.0 17.7 18.3 21 10.2 10.9 11.6 12.3 13.0 13.7 14.4 15.1 15.8 16.5 17.2 17.9 18.6 19.3 22 10.6 11.4 12.1 12.8 13.6 14.3 15.0 15.8 16.5 17.2 18.0 18.7 19.4 20.2 23 11.1 11.9 12.7 13.4 14.2 15.0 15.7 16.5 17.3 18.0 18.8 19.6 20.3 21.1 > 24 11.6 12.4 13.2 14.0 14.8 15.6 16.4 17.2 18.0 18.8 19.6 20.4 21.2 22.0 25 12.1 12.9 13.8 14.6 15.4 16.3 17.1 17.9 18.8 19.6 20.4 21.3 22.1 22.9 ■ 26 12.6 13.4 U.3 15.2 16.0 16.9 17.8 18.6 19.5 20.4 21.2 22.1 23.0 23.8 27 13.1 14.0 14.9 15.8 16.7 17.6 18.5 19.4 20.3 21.2 22.1 23.0 23.9 24.8 ■ 28 13.5 14.5 11'. 4 16.3 17.3 18.2 19.1 20.1 21.0 21.9 22.9 23.8 24.7 25.7 29 14.0 15.0 16.0 16.9 17.9 18.9 19.8 20.8 21.8 22.7 23.7 24.7 25.6 26.6 30 14.5 15.5 16.5 17.5 18.5 19.5 20.5 21.5 22.5 23.5 24.5 25.5 26.5 27.5 31 15 16.0 17.1 18.1 19.1 20.2 21.2 22.2 23.3 24.3 25.3 26.4 27.4 28.4 32 15.5 16.5 17.6 18.7 19.7 20.8 21.9 22.9 24.0 25.1 26.1 27.2 28.3 29.3 33 16.0 17.1 18.2 19.3 20.4 21.5 22.6 28.7 24.8 25.9 27.0 28.1 29.2 30.3 34 16.4 17.6 18.7 19.8 21.0 22.1 23.2 24.4 25.5 26.6 27.8 28.9 30.0 31.2 35 16.9 18.1 19.3 19.8 20.4 21.6 22.8 23.9 25.1 26.3 27.4 28.6 29.8 30.9 32.1 36 17.4 18.6 21.0 22.2 23.4 24.6 25.8 27.0 28.2 29.4 30.6 31.8 33.0 37 17.9 19.1 20.4 21.6 22.8 24.1 25.3 26.5 27.8 29.0 30.2 31.5 32.7 33.9 38 18.4 19.6 20.9 22.2 23.4 24.7 26.0 27.2 28.5 29.8 31.0 32.3 33.6 34.8 39 18.9 20.2 21.5 22.8 24.1 25.4 26.7 28.0 29.3 30.6 31.9 33.2 34.5 35.8 40 19.3 20.7 22.0 23.3 24.7 26.0 27.3 28.7, 30.0 31.3 32.7 34.0 35.3 36.7 41 19.8 21.2 22.6 23.9 25.3 26.7 28.0 29.4 30.8 32.1 33.5 34.9 36.2 37.6 42 20.3 21. 7 23.1 24.5 25.9 27.3 28.7 30.1 31.5 32.9 34.3 35.7 37.1 38.5 43 20.8 22.2 23.7 25.1 26.5 28.0 29.4 30.8 32.3 33.7 35.1 36.6 38.0 39.4 44 21.3 22.7 24.2 25.7 27.1 28.6 30.1 31.5 33.0 34.5 35.9 37.4 38.9 40.3 45 46 21.8 23.3 24.8 26.3 27.8 29.3 30.8 32.3 33.8 35.3 36.8 38.3 39.8 41.3 22.2 23.8 25.3 26.8 28.4 29.9 31.4 33.0 34.5 36.0 37.6 39.1 40.6 42.2 47 22.7 24.3 25.9 27.4 29.0 30.6 32.1 33.7 35.3 36.8 38.4 40.0 41.5 43.1 48 23.2 24.8 26.4 28.0 29.6 31.2 32.8 34.4 36.0 37.6 39.2 40.8 42.4 44.0 49 23.7 25.3 27.0 28.6 30.2 31.9 33.5 35.1 36.8 38.4 40.0 41.7 43.3 44.9 50 24.2 25.8 27.5 29.2 30.8 32.5 34.2 35.8 37.5 39.2 40.8 42.5 44.2 45.8 51 24.7 26.4 28.1 29.8 31.5 33.2 34.9 36.6 38.3 40.0 41.7 43.4 45.1 46.8 52 25.1 26.9 28.6 30.3 32.1 33.8 35.5 37.3 39.0 40.7 42.5 44.2 45.9 47.7 53 25.6 27.4 29.2 30.9 32.7 34.5 36.2 38.0 39.8 41.5 43.3 45.1 46.8 48.6 54 26.1 27.9 29.7 31.5 33.5 35.1 36.9 38.7 40.5 42.3 44.1 45.9 47.7 49.5 55 26.6 28.4 30.3 32.1 33.9 35.8 37.6 39.4 41.3 43.1 44.9 46.8 48.6 50.4 66 27.1 28.9 30.8 32.7 34.5 36.4 38.3 40.1 42.0 43.9 45.7 47.6 49.5 51.3 57 27.6 29.5 31.4 33.3 35.2 37.1 39.0 40.9 42.8 44.7 46.6 48.5 50.4 52.3 58 28.0 30.0 31.9 33.8 35.8 37.7 39.6 41.6 43.5 45.4 47.4 49.3 51.2 53.1 59 88.5 30. 5| 32.5 34.4 36.4 38.4 40.3 42.3 44.3 46.2 48.2 50.2 52.1 54.1 60 29.0 31.0 33.0 35.0 37.0 39.0 41.0 43.0 45.0 47.0 49.0 51. C 53.0 55.0 254 TABLE C— First Pabt. The Time ( in seconds and hundredth parts of seconds) corresponding to a change of the Sun *s Altitude of 1 1 milC; at 8 o'clock, A. M., or 4 o'clock, P. M., and which may be assumed the same for 20 minutes; \ that is, 10 minutes either before or after 8, A. M., or 4, P. M. (See Remark at bottom of page 247 ■•) DECLINATION AND LATITUDE OF THE SAME NAME. | Lat. 0' 2'. 4' 6' 8° 10° 12° 14° 16° 18° 20° 22* 24° • s. s. s. s. s. *. s. s. 5. s. s. s. 5. 4.00 4.00 4.01 4.03 4.05 4.08 4.12 4.16 4.22 4.28 4.34 4.42 4.60 1 .00 .00 .01 .03 .05 .08 .11 .15 .21 .27 .33 .40 .48 2 .00 .00 .01 .02 .04 .07 .10 .14 .18 .25 .31 .38 .46 3 .00 .01 .01 .02 .04 .06 .10 .14 .18 .24 .30 .38 .45 4 .01 .01 .01 .02 .04 .06 .09 .13 .17 .23 .29 •35 .44 5 4.02 4.02 4.02 4.03 4.04 4.06 4 "^9 4.13 4.17 4.22 4.28 4.34 4.43 6 .03 .02 .02 .03 .04 .06 .Od .12 .16 .21 .27 .34 .42 7 .04 .03 .03 .04 .05 .06 .09 .12 .16 .21 .27 .33 .41 8 .05 .04 .04 .04 .05 .07 .09 .12 .16 .20 .26 .32 .40 9 .07 .06 .05 .05 .06 .08 .10 .12 .16 .20 .26 .32 .39 10 4.08 4.07 4.06 4.06 4.07 4.08 4.10 4.13 4.17 4.21 4.26 4.32 4,38 11 .10 .08 .07 .07 .08 .09 .11 .13 .17 .21 ,26 .32 ,38 12 .12 . .10 .09 .09 .09 .10 .12 .14 .18 .22 ,26 .32 ,38 18 .14 .12 .11 .10 .10 .11 .13 .15 .18 .22 ,26 .32 ,38 14 15 .16 ,14 .13 .12 .12 .13 .14 .16 .19 .23 .27 .32 .38 4.19 4.17 4.15 4.14 4.14 4.15 4.16 4.18 4,20 4.24 4,28 4.32 4.38 16 .22 .19 .17 .16 .16 .17 .18 .19 ,22 .25 ,29 .33 ,39 17 .25 .22 .20 .18 .18 .19 .20 .21 .24 .27 .30 .34 .40 18 .28 .25 .23 .21 .20 .21 .22 .23 .25 .28 .31 .35 ,41 19 .31 .28 1 .26 .24 .23 .23 .24 .25 .27 .30 .33 .36 ,42 20 4.34 4.31 4.29 4.27 4.26 4.26 4.26 4.27 4.29 4.31 4.34 4.38 4.43 21 .38 .34 .32 .30 .29 ,29 .29 .30 .31 .33 .36 .40 .44 22 .42 .38 .35 .34 .32 .32 .32 .32 .33 .35 .38 .42 .46 23 .46 .42 .39 .37 .36 .35 .35 .35 .36 .38 .40 .44 .48 24 .50 .46 .44 .42 .40 .38 .38 .38 .39 .41 .43 .46 .50 25 4.55 4.51 4.48 4.46 4.44 4.42 4.42 4.42 4.42 4.44 4.46 4.48 4.52 26 .60 .56 .52 .50 .48 .46 .46 .46 .46 .47 .49 .51 .65 27 .65 .61 .57 .54 .52 .50 .50 .50 .50 .50 .52 .54 .58 28 .70 .66 .62 .59 .57 .55 .54 .54 .54 .54 .55 .57 .61 29 .75 .71 .67 .64 .62 .60 .58 .58 .58 .58 .59 .61 .64 30 4.81 4.77 4.73 4.69 4.67 4.65 4.63 4.63 4.63 4.63 4.63 4.65 4.68 31 .87 .83 .79 .75 .72 .70 .68 .68 .68 .68 .68 .70 .72 32 .93 .89 .85 .81 .78 .76 .74 .73 .73 .73 .73 .74 .76 33 5.00 .95 .91 .87 .84 .82 .80 .78 .78 .78 .78 .78 .80 34 .07 5.02 .98 ,94 .90 .88 .86 .84 .83 .83 .83 .84 .85 35 5.14 5.09 5.05 5.01 4.97 .95 4 93 4.91 4.90 4.89 4.89 4.89 4.90 36 .22 .17 .13 .09 5.05 5.02 5.00 .98 .96 .95 .95 .95 .96 37 .30 .25 .21 .17 .13 .10 ,07 5.05 5.03 5.01 5.01 5.01 5.02 38 .39 .33 .29 .25 .21 .18 ,14 .12 .10 .08 .08 .08 .08 39 .48 .42 .38 .34 .30 .26 .22 .20 .18 .16 .15 .15 .15 40 5.58 5.52 5.47 5.43 5.39 5.35 5.31 5.28 5.26 5.24 5.23 5.23 6.23 41 .68 .62 .57 .52 .48 .44 .40 .37 .35 .33 .31 .30 .30 42 .78 .72 .67 .62 .58 .54 .60 .46 .44 .42 .40 .38 ,38 43 .89 .83 .77 .72 .68 .64 .60 .56 .53 .51 .49 .47 .47 44 6.00 .94 .88 .83 .78 .74 .70 .66 .63 .61 ,59 .58 ,56 45 6.12 6.06 6.00 5.94 5.89 5.85 5.81 5.77 5.74 5.71 5,69 5,67 6.66 46 .25 .18 .12 6.06 6.01 .97 .93 .89 .86 .82 ,80 ,78 ,77 47 .38 .81 .25 .19 .14 6.10 6.06 3.02 .98 .94 ,92 .90 .88 48 .52 .45 .39 .33 .27 • .23 .19 .15 6.11 6.07 6,05 6.03 6,01 49 50 .66 .60 ,54 .48 .42 .36 .32 .28 .24 .21 .18 .15 ,13 6.81 6.75 6.69 6.63 6.59 6.51 6.46 6.42 6.38 6.34 6.32 6.29 6.27 51 .97 .91 .85 .79 .73 .67 .61 .57 .53 .49 .47 .44 ,42 52 7.14 7.08 7.02 .96 .90 .84 .78 .73 .69 .65 .63 .60 ,58 53 .33 .26 .20 7.14 7.08 7.02 .96 .91 .87 .83 .80 .76 .74 54 .53 .45 ,39 .33 .27 .22 7.15 7.10 7.06 7.02 .98 .94 .91 55 7.74 7.66 7.59 7.53 7.47 7.41 7.35 7.29 7.25 7.21 7.17 7.13 7.09 56 .96 .88 .81 .74 .68 .62 .56 .50 .45 .41 .37 .33 .29 57 8.19 8.11 8.04 .98 .92 .86 .80 .74 .18 .62 .58 .64 .60 58 .44 .36 .28 8.22 8.16 8.10 8.14 .98 .92 .86 .81 .77 .73 . 69 .70 .62 .54 .47 .41 .35 .29 8.23 8.17 8.11 8.06 8.02 .98 8.25 i 60 .98 .90 .82 .75 .69 .63 .57 .51 .45 .38 .33 .29 TABLE C— Second Part. 255 The Time 'in seconds and hundredth parts of seconds) corresponding to a change of the Sun's Altitude of 1 mile, at 8 o'clock, A. M., or 4 o'clock, P. M., and which may be assumed the same for 20 minutes : ! that is, 10 mmutes either before or after 8, A. M., or 4, P. M. (See Remark at bottom of page 247). i DECLINATION AND LATITUDE OF DIFFERENT NAMESL | Lat. 1* 3° 5° 7' 9° ir 13' 15" 17° 19' 21* 23* 24' o s. s. s. s. 5. s. 5. s. s. s. 5. s. s. 1 4.00 4.01 4.03 4.05 4.08 4.11 4.16 4.20 4.26 4.32 4.39 4.47 4 62 2 .00 .02 .04 .06 .09 .12 .16 .22 .28 .34 .41 .49 .64 3 .01 .03 .05 .07 .10 .13 .18 .24 .30 .36 .43 .51 .56 4 .02 .04 .06 .08 .11 .14 .19 .26 .32 .38 .45 .54 .69 5 .03 .05 .07 .09 .12 .16 .21 ,28 .34 .40 .47 •56 61 6 4.04 4.06 4.08 4.11 4.14 4.18 4.23 4.30 4.36 4.42 4.50 4.59 4.64 7 .05 .07 .09 .13 .16 .20 .25 .32 .38 .44 .52 .61 .66 8 .06 .08 .11 .15 .18 .22 .27 .34 .40 .47 .55 .64 .69 9 .08 .10 .12 .16 .20 .24 .29 .36 .42 .50 .58 .67 .72 10 .09 .11 .14 .18 .22 .26 .32 .38 .45 .53 .61 .70 .75 11 4.11 4.13 4.16 4.20 4.24 4.29 4.35 4.41 4.48 4.56 4.64 4.74 4.79 12 .13 .15 .18 .22 .26 .32 .38 .44 .51 .59 .67 .77 .82 13 .15 .18 .21 .25 .29 .35 .41 .47 .54 .62 .70 .80 .85 14 .17 .21 .24 .28 .33 .39 .45 .51 .58 .66 .74 .84 .89 15 16 .20 .24 .28 .32 .36 .41 .47 .54 .61 .69 .78 .87 .93 4.23 4.37 4.31 4.35 4.39 4.44 4.50 4.57 4.65 4.73 4.82 4.92 4.97 17 .26 .30 .34 .38 .42 .48 .54 .61 .69 .77 .86 .96 6.01 18 .29 .33 .37 .41 .46 .52 .58 .65 .73 .81 .90 5.00 .05 19 .32 .36 .40 .44 .50 .56 .62 .69 .77 .85 .95 .05 .10 20 .35 .39 .43 .48 .54 .60 .66 .74 .82 .90 5.00 .10 .16 21 4.39 4.43 4.47 4.52 4.58 4.64 4.70 4.78 4.86 4.95 5.05 5.15 6.20 22 .43 .47 .51 .56 .62 .69 .75 83 .91 5.00 .10 .20 .26 23 .47 .51 .56, .61 .67 .74 .80 .88 .96 .05 .15 .25 .30 24 .52 .56 .61 .66 .72 .79 .85 .93 5.01 .10 .20 .30 .36 25 .57 .61 .66 .71 .77 .84 .91 4.99 .07 .16 .26 .36 .42 26 4.62 4.66 4.71 4.76 4.82 4.89 4.97 5.05 5.13 5.22 5.32 5.42 6.48 27 .67 .71 .76 .82 .88 .95 5.03 .11 .19 .28 .38 .48 .54 28 .72 .76 .81 .87 .94 5.01 .09 .17 .25 .34 .44 .54 .60 29 .77 .82 .87 .93 5.00 .07 .15 .23 .31 .41 .51 .61 .67 30 .83 .88 .93 .99 .07 .14 .22 .30 .38 .48 .58 .68 .74 31 4.89 4.95 5.00 5.06 5.14 5.21 5.29 5.37 5.45 5.55 5.65 5.75 6.81 32 .96 5.02 .07 .13 .21 .28 .36 .44 .52 .62 .72 .82 .88 33 5.03 .09 .14 .20 .28 .35 .43 .51 .59 .69 .79 .90 .96 34 .10 .16 .21 .27 .35 .42 .50 .58 .67 .77 .87 .98 6.04 35 36 .17 .24 .29 .35 .43 .50 .58 .66 .75 .85 .95 6.07 .13 5.25 5.32 5.37 5.43 5.51 5.58 5.66 5.74 5.83 5.93 6.03 6.15 6.22 37 .33 .40 .45 .52 .60 .67 .75 .83 .92 6.02 .12 .24 .31 38 .42 .48 .54 .61 .69 .76 .84 .92 6.01 .11 .21 .33 .40 39 .51 .57 .63 .70 .78 .85 .93 6.02 .11 .21 .31 .43 .49 40 .61 .67 .73 .80 .88 .95 6.03 .12 .21 .31 .41 .53 .59 41 5.71 5.77 5.83 5.90 5.98 6.05 6.13 6.23 6.32 6.42 6.52 6.63 6.69 42 .81 .87 .93 6.01 6.09 .16 .24 .34 .43 .53 .63 .74 .80 43 .92 .98 6.04 .12 .20 .27 .35 .45 .54 .64 .74 .86 .91 44 6.03 6.09 .16 .23 .31 .39 .47 .57 .66 .76 .86 .97 7.03 45 46 .15 .22 .29 .37 .45 .53 .61 .71 .88 .93 .98 7.09 .16 6.28 6.35 6.42 6.50 6.58 6.66 6.74 6.84 47 .41 .48 .55 .63 .71 .79 .87 7.97 48 .55 .62 .69 .77 .85 .93 7.01 .11 49 .69 .76 .83 .91 .99 7.07 .15 .25 50 .84 .91 .99 7.07 7.15 .23 7.00 7.07 7.15 7.23 7.31 7.39 52 .17 .24 .32 .40 .49 .57 53 .36 .43 .51 .59 .68 .76 54 .56 .63 .71 .79 .87 .95 55 66 .77 .84 .92 8.00 7.99 8.06 8.14 8.22 57 8.22 .30 .38 .46 58 .47 .55 .63 .71 59 .73 .81 .89 97 60 .01 .09 .18 .25 TO EXTRACTS FROM NAUTICAL ALMANAC, FOR 1854. WORK EXAMPLES OF LATITUDE BY THE MOON, ON PAGES 102, •103. Date. Semid. Hor. Par. Declination. Equation Of Time. Meridian. Noon. Mid. Noon. Mid. Noon. Mid. Passase. July 11 " 12 / // 16 60 o / 19 9 S. o / 21 21 S. — 6 m. h. m. 13 58 14 56 April 23 " 24 " 25 t It 16 1 / // 57 2 2 N. 51 S. + 2 m. 21 59 22 43 April 4 " 6 15 54 26 N. 26 13 N. — 3 m. 5 30 6 21 April 1 " 2 15 55 18 46 K 20 36 N. — 4 m. 3 3 3 51 April 12 « 13 16 69 7 27 S. 4 25 S. — 1 m. 11 63 12 42 FROM TO 1^ LARGE ^ORK SAW NAUTICAL ALMANAC. R EXAMPLES AS ABOVK. Date. July 11 " 12 April 23 " 24 " 25 April 4 " 5 April 1 " 2 April 12 " 13 Semld. Noon. 16 32 15 27 14 49 15 2 16 5 Mid. / // 16 37 16 31 16 Hor. Par. Noon. t n 60 32 56 85 14 49 64 16 14 58 65 3 58 64 Mid. / // 60 61 66 50 64 15 64 60 68 86 Declination. At 19 h. o / // 20 6 34 S, At 17 h. 21 16 N. At7h. 26 9 62 N. AtTh. 19 52 23 K At 18 h. 4 40 12 S. DIffi 10 m. 112 145 91 162 £q nation of Time. m. S. — 67 + 1 67 — 36 — 40 50 Meridian, Passage. | h. m. 13 58 14 56 h. m. 21 69 22 43 6 30 6 21 3 4 3 61 11 54 12 43 TO WORK EXAMPLES OF LATITTJDE BY PLANETS, ON PAGE 106. Date. January 1 2 II June 6 " 7 April 18 " 14 'teoB February 1 « 2 Names. Venus. Mars. Jupiter. (( Saturn, Meridian Passage. h. m. 3 16 6 2 18 24 6 46 Declination. 13 6 S. 12 40 S. 7 26 N. 7 13 K 21 21 7 S. 6 S. 17 17 4 N. 4 N. EqoAtion. m. — 4 + 2 — 1 - 14 TO WORK EXAMPLES OF LATITUDE BY STARS, PAGES 107, 108. Date. Names. 1 Meridian Passage. Declination. | February 27 Aldebaran h. m. 5 48 o / 16 13 N. February 28 Antares 17 36 26 6 s. Marc b 21 h26 Sirius 6 34 16 31 s. Marc Vega 'is 12 38 39 N. May 1 Vega 15 59 38 39 N. June 21 Cross-Foot Star 6 21 62 17 S. April 1 Castor 6 43 32 12 N. TO WORK LATITUDE BY POLAR STAR, PAGE 109. I>«t«. I Meridian Passage. | Right Ascension. Declination. Equation. July 1 h. ra. 18 26 h. m. 88 32 N. July 20 17 9 88 32 N. January 20 20 9 February 10 21 36 m. — 15 TO WORK EXAMPLES OF TIME BY MOON, PAGE 133. DkUL Seml-I DiuB. / 15 Hm. Par. /' 55 Right Atcatulon. DeellnaUoB. KqoatloB of Tim.. Dlt Ih. Son's Right A»cenilon. Dit I h. 6. 9l Noos. Mid. Noon. Mid. Mar. 10 b. m. 8. 8 12 21 h. m. B. 8 38 26 / 24 14 N. O / 23 4 N. m. 10 8. 31.55 .665 h. 23 5 m. 8. 21 53 TO WORK EXAMPLES OF TIME BY PLANETS, PAGE 135 Data. Eight Ascen. Declination. Equation. Dlff. 1 h. Sun's R. A. Dlff Ih. April 6 " 7 h. Ttl. s. 22 27 28 22 29 44 / 6 7S. m. 8. 2 30.50 8. .725 b. in. 8. 1 18 8. 9 December 5 « 6 19 57 13 19 58 4 21 16 S. 9 12.43 1.049 16 46 36 11 TO WORK EXAMPLES OF TIME BY STARS, ON PAGE 137. IHt«. Bight Asceiu Declination. Equation. Dlff. 1 h. Sim's E. A- Ditt Ih. February S h. m. S. 6 38 43 / 16 31 S. m. 8. 14 31.61 .39 k. m. 8. 21 81 34 8. 10 May IS ! 16 20 24 26 6 S. 3 52.34 .53 h. m. 8. 3 15 50 10 The foUovmtg wre a few from among the ncmy recommendations of the work r$- Deived by the Publishers : — New York, April 5, 1856. Mb. Shaw, — Dear Sir, — Ha nng used the new treatise on the Practice of Navigation «t Sea, by Captain William Thorns, during ten passages across the Atlantic, I am oi opinion that it is the most clear, simple, and practical work on the subject I have yet geen, containing all that is requisite to the navigator, without being encumbered with pages of useless matter. For the learner I consider it most especially desirable, for evervthing necessary for finding a ship's place on the Ocean is so simply and clearly explamed, and illustra ted by diagrams, that it must clear the mist and doubts that so often hang over him. 1 am fully of opinion that this work will, in time, be duly appreciated, and generally adopted by our sea-faring community. Very respectfully, P. E. Le Fevre, Master Steamship ArieL New Yokk, December 26, 1855. Mb. R. L. Shaw, — Dear Sir, — Captain Eldridge, of the Steamship Pacific, in con- versation with me, after having used Thorns' Practical Navigation, said : " The book recommends itself, publish it, it is sure to go." Jas. H. Brownlow, Teacher of Namgation. New York, April 5, 1856. Mb. Shaw, — Dea/r Si/r, — Having used the work on Navigation published by Captain William Tlioms, I can cheerfully recommend it to all those interested in navigation, in being the most simple and easy method of calculations. Yours, Thos. D. Ewan, Master of Steamship Southerner. Mb. R. L. Shaw, — I have used Tlioms' Navigator for several voyages, and prefer it to any other I have had before, and recommend it to all classes of navijrators, being more explicit, and best adapted to the general practice of navigation at s'ea. J. Westervelt, Master of Schooner Pea/rl. Nkw York, Ma/rch 12, 1856. New York, April V, 1856. Mb. R. L. Shaw, — Dea/r Sir, — I have used Thorns' Navigation for three voyagfti -id prefer it to any others I have seen. John Hardy, Master of Schooner D. Dc^.^d^soH. OPINION OF THE WORK, From Men of Experience, Wk, the undersigned, Captains of Ships, and others, having examined thi Manuscript of a new Treatise on the Practice of Navigation, and Nautical Astronomy, by Capt. Wm. Thoms, are of opinion that it is the most simple and practical work on the subject we have yet seen, especially for the learner, who will be greatly assisted in obtaining a knowledge of the Science by the numerous Diagrams which illustrate the subject, and is particularly adapted for Seamen, as it treats on those subjects only which have reference to the Ship's Place on the Ocean, (or Navigation proper.) Many new problems have also been introduced, which will be found of much practical value to many Captains of Ships, who may not have had an opportunity of previously becoming acquainted with them. We are therefore of opinion, that if the work is published in its present style, it will be duly appreciated by our seafaring community, and would in time be extensively used by them throughout this large maritime country. Names. Vessels Attached to. S. McKAY, Great Republic. THOMAS DIXON, Fidelia. EDWARD MURRAY, Balance. Blon. Cornelia. Telegraph. S. Austin. S. B. Strong. WM. BRAGDON, JOHN T. FRENCH, JOHN STRAKER, J. H. CASWELL, ISAAC LYNCH, WILLIAM P. JONES, Kensington. GUNDER KRABEL, Chief Mate. FRANCIS PATTERSON, " JOHN W HOLMES, R. DeWolfb. CHaS. ANDERSON, Mar. Vineyard. JAMES SAFFORD, Helene. JOHN KIRKPATRICK, Mate. AND. ARMSTRONG, Cora Linn, C. E. LUCAS, A. B. CLAUSSE, RICHARD LLOYD, A. P. FOSTER, JAMES W. TAYLOR, D. B. Warner. J. W. JEROLOMON, Alexander Law. ALF. B. LOWBER, S. S. Ericsson. JOHN R. CAVARLY, Am. Eagle. JOSEPH C. DO WD, Wm. Rathbone. RICH'D. B. MORSE, George Ratner. HENRY W. DODGE, T. & P.Wood- W. R. FOREMAN, Ohio. [ward. MARTIN ALLEN, Rapu>. PET. BORGESTONE, H. W. Mosoubk. Mate. Sword Fish. Gloucester, Mass. Adela Swift. Names. J. WILSON COMBY, WILLIAM HOWARD, VICTOR VIEROUS, CHARLES LIDBECK, WILLIAM DALY, JAMES NEWBERY, THOMAS McLEAVY, C. FERD. BROWN, G. DOUGHTY, JOS. G. WOODSIDE, FRED. WIELMANN, JOSEPH D. HUGHES, EDWARD MOORE, RUFUS BROWN, B. F. TAYLOR, LEWIS E. JACKSON, WM. L. KEMPTON, B. FRANCIS, ZACHEUS KEMPTON, J. H. ROGERS, WILLIAM LYDDON, CHAS. E. MERRY, G. RICE, J. R. McDOUGALL, JOSHUA E. SMITH, M. NICHOLAS, JOHN MOONEY, PETER WIXEN, EDWARD ABEEL, CHAS. ANDERSON, Vessels Attached t& Calhoun. Lucy Watts H. T. L. Abrasia. Gazellb. Jasper. Mary Morrm*. e. bulklet. Anstiss. Contest. Vulture. Uranus. Augusta. Mongolia. Anna Tift, Hollander. St. Joseph. Cataract. Horatio. S. B. Strong. J. N. Cooper. Skylark. B. N. Hawkins. John Stroud. Ann Elizabeth. Unattached. Governor Brow» North Wind. Isaac Wright. Qitktxax Mom. / n^TTm BOOK IS DUE ON THE LAST DATE THIS BOOK^ih^^p^^ BELOW AN INITIAL FINE OF 25 CENTS AJN iriJ.X.1^--" r^M MRP TO RETURN ■ w.UU BE ASSESSED FOR FA'UURE TO R^^^ THIS BOOK ON '^"^^^'L^f^Ts qN THE FOURTH rv^;r^TO^^J°ol°or;HE° SEVENTH O.V OVERDUE. lAfi as (935 ^PRTjBlSSr VD I5M2 V U.C. BERKELEY LIBRARIES CaQt.l5b3S3 288101 UNIVERSITY OF CALIFORNIA LIBRARY i W'\-